vxEPA
United States Municipal Environmental Research
Environmental Protection Laboratory
Agency Cincinnati OH 45268
EPA-600/2-83-102
October 1983
Research and Development
Development of
Standard
Procedures for
Evaluating Oxygen
Transfer Devices
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EPA-600/2-83-102
October 1983
DEVELOPMENT OF STANDARD PROCEDURES FOR
EVALUATING OXYGEN TRANSFER DEVICES
by
American Society of Civil Engineers
Oxygen Transfer Standards Subcommittee
William C. Boyle, Chairman
Cooperative Research Agreement No. CR805868
Project Officer
Richard C. Brenner
Wastewater Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
Although the information described in this report has been funded in
part by the U.S. Environmental Protection Agency through Cooperative Research
Agreement No. CR805868 to the American Society of Civil Engineers, it has
not been subjected to the Agency's required peer and administrative reviews
and, therefore, does not necessarily reflect the views of the Agency and
no official endorsement should be inferred. Mention of trade names or
commercial products does not constitute endorsement or recommendation for
use.
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FOREWORD
The U.S. Environmental Protection Agency was created because of in-
creasing public and government concern about the dangers of pollution to
the health and welfare of the American people. Noxious air, foul water, and
spoiled land are tragic testimonies to the deterioration of our natural
environment. The complexity of that environment and the interplay of its
components require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem solu-
tion; it involves defining the problem, measuring its impact, and searching
for solutions. The Municipal Environmental Research Laboratory develops new
and improved technology and systems to prevent, treat, and manage wastewater
and solid and hazardous waste pollutant discharges from municipal and commu-
nity sources; to preserve and treat public drinking water supplies; and to
minimize the adverse economic, social, health, and aesthetic effects of
pollution. This publication is one of the products of that research and
provides a most vital communications link between the researcher and the
user community.
This report presents a critical review of the state-of-the-art on the
testing and evaluation of oxygen transfer devices. Based on this review,
the report develops recommendations for interim standards for testing and
evaluating aeration equipment in both clean and dirty water.
Francis T. Mayo, Director
Municipal Environmental Research
Laboratory
iii
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ABSTRACT
In an effort to obtain consensus standards for the evaluation of aera-
tion devices in both clean and dirty water, the American Society of Civil
Engineers (ASCE) established a Subcommittee on Oxygen Transfer Standards in
January 1977. The objectives of the Subcommittee were to
1. review and critically evaluate the state-of-the-art of oxygen
transfer testing,
2. evaluate and critically review existing standards and identify
critical areas of disagreement and uncertainty,
3. develop documentation for recommendations for interim standards
and recommended verification methodology, and
4. prepare these standards and submit them for ASCE consensus evalua-
tion.
This report presents the outcome of this review process and provides
recommended procedures for testing of oxygen transfer devices in both clean
and dirty water. It is prepared as seven interdependent reports including
1. modelling and data interpretation,
2. unsteady state clean water tests,
3. effects of wastewater characteristics and temperature on oxygen
transfer,
4. oxygen transfer measurements in respiring systems,
5. geometry and mixing considerations,
6. gas flow measurement, and
7. power measurement.
This report was submitted in fulfillment of Cooperative Research Agree-
ment No. CR805868 by the American Society of Civil Engineers under the
partial sponsorship of the U.S. Environmental Protection Agency and covers
the period from March 1978 to December 1980.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures vii
Tables ix
Symbols and Nomenclature xi
Metric Conversions , xix
Acknowledgements . xxi
1. Introduction 1
2. Conclusions 8
3. Recommendations 9
4. Modelling and Data Interpretation .11
Recommended standard method for modelling and analyzing
unsteady state test data 11
Commentary on the recommended standard method . . 22
Example data analysis 39
References 53
5. Unsteady State Clean Water Test 56
Introduction 56
Procedural description 57
Discussion of procedural components 70
Sulfite oxidation 97
Recommendations for study 98
References 99
6. Effects of Alpha, Beta, and Theta Factors and Surfactants on
Specification, Design, and Operation of Aeration Systems 104
Introduction 104
Alpha factor 106
Alpha factor testing: an alternative approach 113
Beta factor .114
Theta factor 117
Apparent mass transfer coefficients 121
Results and conclusions 121
Future emphasis and research needs 135
References 136
7. Oxygen Transfer Measurements in Respiring Systems 140
Objectives . .140
Background 140
Theoretical development 141
Measurements in the field 150
Test procedures 155
Conclusions 193
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CONTENTS (continued)
References 194
8. Geometry, Scale-Up, and Mixing 198
Introduction 198
Definitions \ \ '.200
Geometric scale-up of factory test to field condition . ! ! [201
Mixing considerations 205
Recommended future research 208
9. Gas Flow Measurement 209
Primary flow elements 209
Secondary flow elements 215
Connections between primary and secondary flow elements . . .218
Troubleshooting the flow measurement system 219
Pulsation 221
Required measurements for gas flow determinations 223
Standard conditions 224
Conversion of standard volumetric flow rates of air to
mass flow rates of oxygen 225
Conversion of volumetric flow rates from standard
to actual flow conditions 226
Recommended standardization . ... .226
References 227
10. Power Measurement 229
General definition of terms 229
The need for standardization 230
Gas power 232
Turbine pump power 240
Total power 245
Mechanical aerator power 245
Recommended standardization 249
References 253
11. Proposed Evaluation Procedure for the Recommended Clean
Water Oxygen Transfer Test 254
Experimental research evaluation .... .254
Comparative practical evaluation 255
Appendices
A. Nonlinear Estimation Program 257
B. Basic Nonlinear Estimation Program 268
C. Alpha-Beta Test Procedure 276
D. Determination of Oxygen Uptake Rates for a Continuous System . . .283
E. Batch Desorption Testing-Peroxide Addition Details 286
F. Individual Sample Point Analysis 290
vi
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FIGURES
Number Page
1 Procedural Flowsheet-Subcommittee on Oxygen Transfer
Standards 6
2 Profile of an Oxygenation Tank 24
3 Clean Water Test Data ; . . . . 42
4 Relationship Between Estimated Values of C* and Residual
CO
Sum of Squares 52
5 Log Deficit Plot Based on C* = 11.55 mg/£ and K. a =
0.0835 min-1 °° . . . . . 53
6 Recommended Sample Point Locations ... 84
7 Error in Field Oxygen Transfer Rate as a Function of Errors
in the Measurement of the Alpha and Beta Factors when
Alpha = 0.8 and Beta = 0.9 106
8 Effect of Bubble Size on Mass Transfer 109
9 Effect of Temperature on Oxygen Transfer Rate 120
10 Diagram of Bench-Scale Diffused Aeration Alpha Apparatus . . . 126
11 Diagram of Bench-Scale Turbine Aeration Alpha Apparatus .... 127
12 Diagram of Bench-Scale Surface Aeration Alpha Apparatus .... 127
13 Gas Transfer Characteristics in a 50-gal Vessel with
Turbine Aeration in the Presence of Surfactants 128
14 Gas Transfer Characteristics in a 50-gal Vessel with
Diffused Aeration in the Presence of Surfactants 129
15 Gas Transfer Characteristics in a 50-gal Vessel with
Surface Aeration in the Presence of Surfactants 130
16 DO Versus Time for a Respiring System with Varying
Aeration Conditions 142
17 General Schematics and Nomenclature for Continuous Flow and
Batch Respiring Systems 144
18 Typical Sampling Locations for Measurement of DO for
Different Aeration Systems . 152
19 Oxygen Uptake Plot for Steady State Continuous Testing in a
Moderately Loaded Activated Sludge System 153
20 Oxygen Uptake Plot for Steady State Batch Endogenous Test ... 154
21 Steady State Test Results for Submerged Aeration Evaluation . . 162
22 Unsteady State Continuous Test DO Versus Time Plot 171
23 Unsteady State Continuous Test Semi log Plot 172
24 Unsteady State Batch Endogenous Test DO Versus Time Plot ... 174
25 Unsteady State Batch Endogenous Test Semi log Plot 175
26 Unsteady State Batch Desorption Test DO Versus Time Plot ... 178
27 Unsteady State Batch Desorption Test Semi log Plot 179
C-l Schematic of Alpha Test Apparatus 277
D-l Estimation of Oxygen Uptake Rate 284
vii
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FIGURES (continued)
Number Page
E-l Diffused Aeration-Peroxide Addition Locations 287
E-2 Surface or Turbine Aeration-Peroxide Addition Locations .... 288
E-3 Bruch Aerators in Extended Aeration Oxidation Ditches-
Peroxide Addition Locations 289
vm
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TABLES
Number Page
1 List of Members-Subcommittee on Oxygen Transfer Standards ... 3
2 Relationship Between Time and Percent Saturation for
Equation 3 18
3 Effect of Data Truncation on the Precision of Parameter
Estimation Data of Gilbert and Chen Using Equation 3 .... 38
4 Clean Water Test Data 41
5 Application of Best Fit Log Deficit Method 51
6 Excerpts from Drinking Water Standards 74
7 Additional Primary EPA Drinking Water Standards 75
8 Solubility of Oxygen in Water Exposed to Water Saturated
Air 92
9 Apparent Mass Transfer Coefficients and Alpha Factors for
the Data of Kessener and Ribbius 108
10 Variation in Oxygen Transfer Rate at the Jones Island
Treatment Plant Ill
11 Saturation Dissolved Oxygen Concentrations at Various
Chloride Levels 116
12 Temperature Correction Factors 119
13 Alpha Factors Observed by Barnhart 132
14 Alpha Factors Observed by Different Investigators for
Different Aeration Devices 133
15 Assumptions Necessary to Develop Equations for Steady and
Unsteady State Batch Tests 146
16 Assumptions Necessary to Develop Equations for Steady and
Unsteady Continuous Tests 147
17 Test Information for Continuous Testing of a Surface
Aeration System 159
18 Test Information for Batch Testing of a Surface Aeration
System 160
19 Unsteady State Continuous Test Data 170
20 Unsteady State Batch Endogenous Test Data 173
21 Nonlinear Estimation for Unsteady State Oxygen Transfer
During Endogenous Testing 176
22 Unsteady State Batch Oxygen Desorption Test Data 177
23 External Wastewater Management Process Performance Data .... 188
24 Recommended Standards for Gas Flow Measurement During
Clean Water Oxygen Transfer Tests 227
25 Recommended Equipment Efficiencies to be Used for Standard
Power Determinations 250
26 Standard Gas Delivered Power 250
27 Standard Pump Delivered Power 251
ix
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TABLES (continued)
Number Page
28 Standard Turbine Delivered Power 252
29 General Features of Proposed Experimental Research
Evaluation 256
F-l High Uptake System 291
F-2 Standard Uptake System 291
F-3 Low Uptake System 291
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SYMBOLS AND NOMENCLATURE
DIMENSIONS
m = mass
L = length
t = time
f = force
T = temperature
STANDARD CONDITIONS FOR REPORTING GAS VOLUME, FLOW RATE, AND DENSITY VALUES
1.00 atm.
20°C
0.0 percent relative humidity
STANDARD CONDITIONS FOR DISSOLVED OXYGEN SATURATION CONCENTRATION
1.00 atm. total pressure at surface
20°C
100 percent relative humidity in gas (mole function of oxygen in gas
must be specified)
SYMBOLS
A = activity of dissolved oxygen
a = area of electrode
b = membrane thickness
BMP = brake horsepower of prime mover
C = dissolved oxygen concentration in the liquid phase
Superscripts Used with C
* denotes an effective average equilibrium (saturation) value
corresponding to a given p , T, and volume
denotes a localized point value (unless identified by this
symbol, values of C are assumed to be averaged over a
region of volume)
Subscripts Used with C
°° denotes value attained at infinite time in an unsteady state
test
A denotes value in flow entering the aeration zone
AB denotes effective value in the aeration zone
xi
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SYMBOLS AND NOMENCLATURE (continued)
B denotes value in flow leaving the aeration zone
b denotes book value
f denotes dirty water field conditions
o denotes value at t = 0, estimated from the model
R denotes steady state value at a biological uptake rate of R
r denotes value in the recycle sludge flow, Q
s denotes surface saturation value at 1.00 atm. total pressure
and 100 percent relative humidity
T denotes value at a given temperature, T
TP denotes value in tap water
ww denotes value in wastewater
20 denotes value at 20°C
C1 = dissolved oxygen in the influent flow, Q1
C = specific heat at constant pressure
C = specific heat at constant volume
CV = coefficient of variation
d = actual internal pipe diameter
d = effective saturation depth at infinite time
d = Orifice bore diameter
o
E = voltage
e, = blower efficiency
e, = standard blower efficiency
e, = driver efficiency
e , = standard drive efficiency
e = gear box efficiency
e = motor efficiency
m
e = standard motor efficiency
e -, = polytropic efficiency of the blower
F = exit gas depletion factor under operating conditions
T = Faraday -- 9.649 x 104 Coulombs/mole
F = orifice area correction factor
ci
F = manometer correction factor
m
F = exit gas depletion factor at zero DO
F = super-compressibility correction factor
pc
F = pipe expansion correction factor
F = vena contract correction factor
XI1
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SYMBOLS AND NOMENCLATURE (continued)
F = relative humidity correction factor
G = dry gas specific gravity
G" = sheer modulus of elasticity
G.f = specific gravity of the manometer displacing fluid
GE = mass rate of exit gas
Gp = mass rate of feed gas
G. = mass rate of inerts in air including nitrogen, argon,and trace
elements
G = water vapor specific gravity
w
H = static head
H = Henry's Law Constant
h = differential pressure
h. = diffuser headless corrected to 68°F
i = current
K = (k - l)/k
k = ratio of specific heats C /C
K.a = true volumetric mass transfer coefficient in clean water adjusted
for gas-side oxygen depletion
K.a = apparent volumetric mass transfer coefficient in clean water (not
adjusted for gas-side oxygen depletion)
*
Superscript Used with K.a and K.a
denotes a localized point value (unless identified by this
symbol, values of K.a are to be interpreted as average
values over a given volume)
*
Subscripts Used with K.a and K.a
a denotes value applicable to aeration zone volume
f denotes value applicable to dirty water field conditions
T denotes value at a given temperature, T
TP+S denotes value applicable to tap water with a surfactant
added
ww denotes value applicable to wastewater
20 denotes value at 20°C
M = molecular weight
M = test basin water weight
M = molecular weight of air
a
M. = molecular weight of inerts
xm
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SYMBOLS AND NOMENCLATURE (continued)
oxygen in reference air to inerts
M = molecular weight of oxygen
MRo/i = mole ratio
MRog/i= mole ratl° of oxygen in off-gas air to inerts
N = shaft speed
N = concentration of ammonia nitrogen
n = number of moles
ng = number of electrons transferred in cell reaction
OTE = oxygen transfer efficiency
OTR = oxygen transfer rate
OTRf= OTR in a dirty water respiring system
P = power
*
P = measured power value
Pm = permeability coefficient
PF = power factor
PHP = prime mover horsepower
p = pressure
Subscripts Used with p
a denotes ambient pressure
b denotes base pressure
bw denotes vapor pressure of water at base conditions
f denotes flowing gas pressure
o denotes partial pressure of oxygen
oi denotes partial pressure of oxygen in the gas phase in the
inlet
or denotes partial pressure of oxygen in the gas phase in the
reactor
s denotes standard pressure of 1 atm.
T denotes value at a given temperature, T
v denotes vapor pressure of water
vpa denotes vapor pressure of water at ambient temperature
w denotes partial of water vapor in gas line
wa denotes ambient partial pressure of water vapor in the air
ws denotes partial pressure of water vapor at standard condi-
tions
1 denotes absolute inlet pressure
2 denotes absolute outlet pressure
inlet denotes absolute static heat at the gas release point
surface denotes absolute pressure at the aeration tank water surface
pm = permeability coefficient
Q = volumetric flow rate
Q1 = liquid flow entering and leaving the continuous flow reactor
xiv
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SYMBOLS AND NOMENCLATURE (continued)
Subscripts Used with Q and Q'
a denotes volumetric flow rate of air at standard conditions
das denotes dry air portion of Q
dgs denotes dry gas flow at 68°F and 14.70 psia
0 denotes volumetric flow rates of oxygen at standard condi-
tions
r denotes recycle sludge flow to the test volume
w denotes flow rate for waste activated sludge
R = rate of oxygen consumption
Subscripts Used with R
b denotes organism growth
s denotes substrate utilization
N denotes ammonia utilization
R^ = universal gas constant
R = pipe Reynolds number
r = oxygen activity coefficient
r, = inside radius of the cylinder
rQ = outside radius of the cylinder
RH = relative humidity
S = concentration in the liquid phase of substrate
S = water specific gravity
SAE = standard aeration efficiency, aeration efficiency in clean water
at standard conditions
SHP = shaft horsepower
Subscripts Used with SHP
F denotes factory unit
SOTR = standardized OTR in clean water at stated conditions of T, DO,
mixing, geometry, etc.
T = temperature
Subscripts Used with T
a denotes ambient temperature
b denotes base temperature
f denotes flowing gas temperature
1 denotes inlet temperature
p denotes pipe temperature
xv
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SYMBOLS AND NOMENCLATURE (continued)
T = torque
T = zero-load torque for reaction load device
V = volume
Subscripts Used with V
A denotes volume of aeration zone
B denotes volume of accumulation zone
g denotes reactor volume of the gas phase
VQ = temporal mean velocity gradient
W = oxygen transfer rate per unit volume in clean water
Superscript Used with W
denotes a localized point value
Subscript Used with W
f denotes value applicable to dirty water field conditions
w. = weight flow of dry air
w = weight flow of oxygen
X = concentration of biological organisms
Y = gas expansion correction factor
Y = mole fraction of oxygen in gas phase
Yd = mole fraction of oxygen in the dry feed gas
Y. = mole fraction of dry air at standard conditions
Y = mole fraction of oxygen in the exit gas
a = ratio of K.a in dirty water to K.a in clean water at equivalent
conditions of T, geometry, mixing, etc.
a* = ratio of K.a* in dirty water to K. a* in clean water at equivalent
conditions of T, geometry, mixing, etc.
3 = ratio of C* in dirty water to C in clean water at equivalent
conditions of temperature and partial pressure
Y = weight density
Subscripts Used with Y
a denotes weight density of air at standard conditions
o denotes weight density of oxygen at standard conditions
w denotes weight density of water
xvi
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SYMBOLS AND NOMENCLATURE (continued)
n = miscellaneous (bearings, etc.) efficiency of special factory
hardware
Subscript Used with n
F denotes factory unit
n = prime mover efficiency
Subscripts Used with n
F denotes factory unit
I denotes installation
nR = reducer efficiency
Subscripts Used with nR
F denotes factory unit
I denotes installation
9 = temperature adjustment factor defined so that:
KLa at Tl . (TT)
(KLa) at T2 '
for equivalent conditions of geometry, mixing, partial pressure,
and wafer quality
0* = temperature adjustment factor so that:
(KLa*) at T2 " w ' l~
Subscripts Used with 9
A denotes arithmetic temperature correction
G denotes geometric temperature
Vi = absolute viscosity
£45 = strain at 45°
p = mass density
xvn
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SYMBOLS AND NOMENCLATURE (continued)
Subscripts Used with p
a denotes mass density of air at standard conditions
0 denotes mass density of oxygen at standard conditions
w denotes mass density of water
* *
T = saturation temperature correction factor = C T/C ~r\
T = tracer
, = oxygen at ion coefficient
tt = pressure correction
xviii
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METRIC CONVERSIONS
CUSTOMARY UNIT
SI UNIT
Btu
Btu/lb
cfm
cfs
cu ft
cu ft
°F
°C
ft
ft-lb
gal
gal
gpm
gpm
hp
hp-hr
in.
Ib (force)
Ib (mass)
Ib (mass)/hp-hr
Ib/mil gal
mil gal
mgd
mgd
pcf
psf
psf
X
X
X
X
X
X
+
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1.055
2.326
4.719 x 10"4
0.02832
0.02832
28.32
0.555(°F - 32)
273
0.3048
1.356
3.785
0.003785
6.308 x 10"5
0.06308
0.7457
2.685
25.4
4.448
0.4536
0.6083
0.1198
3785
3785
0.0438
16.02
0.04788
4.882
kj
kJ/kg
m /sec
m /sec
m3
I
°C
K
= m
J
I
m3
3
= m /sec
I/sec
kW
MJ
= mm
N
kg
kg/kWh
g/m3
m3
m /day
= m /sec
kg/m3
kN/m2
kgf/m2
XIX
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METRIC CONVERSIONS (continued)
CUSTOMARY UNIT SI UNIT
x 6.895 = kN/m3
x 0.0703 = kgf/cm2
sq ft x 0.0929 = m2
sq in. x 645.2 = mm2
tons (short) x 907.2 = kg
xx
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ACKNOWLEDGEMENTS
This report represents the cooperative efforts of over 45 dedicated
engineers, the members of the ASCE Oxygen Transfer Standards Subcommittee.
It could not have been completed without their input during many long
meetings and their critical review of all draft reports. The names of these
members appear as Table 1 of this report.
The major authors of each section of this report are tabulated below.
These individuals served as subgroup leaders and were the catalyst needed to
complete the tasks.
Section 4 - Modelling and Data Interpretation
C.R. Baillod
L.C. Brown
Section 5 - Unsteady State Clean Water Test
W.L. Paulson
Section 6 - Effects of Alpha, Beta, and Theta Factors and Surfactants
on Specification, Design, and Operation of Aeration Systems
M.K. Stenstrom
R.G. Gilbert
Section 7 - Oxygen Transfer Measurements in Respiring Systems
H.J. Campbell
J.A. Mueller
J.J. McKeown
R.E. McKinney
J.R. Stukenberg
Section 8 - Geometry, Scale-Up, and Mixing
T.C. Rooney
R.N. Salzman
Section 9 - Gas Flow Measurement
F.W. Yunt
xxi
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Section 10 - Power Measurement
R.N. Salzman
P.M. Yunt
Editing of the numerous reports submitted for this final report to the
U.S. Environmental Protection Agency (EPA) has required many hours of effort.
The Subcommittee is grateful for the technical editing that was so aptly
provided by Laura Taylor, Edwin L. Barnhart and William C. Boyle.
Thanks are also in order to the ASCE administration, especially to
Robert P. Morgan, Manager of Research and Standards Services, for his assis-
tance in the many arrangements for meetings and the development of smooth
communication between the Subcommittee and ASCE Headquarters.
Finally, special thanks are in order to the EPA Project Officer,
Richard C. Brenner, who not only served as a technical Subcommittee member
but also provided the Subcommittee with administrative assistance and
editorial help on both this report and the workshop publication EPA-60Q/9-
78-021, Workshop Toward an Oxygen Transfer Standard, which was an outgrowth
of this current EPA project.
xxi i
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SECTION I
INTRODUCTION
Although considerable effort has been devoted to oxygen transfer tech-
nology over the years, it is evident that unanimity of opinion has not been
achieved in the development of standard procedures for the evaluation of
oxygen transfer devices. Presently, manufacturers rely on clean water shop
tests for describing the oxygen transfer capability of aeration equipment.
These capabilities are normally expressed as standardized oxygen transfer
rates (SOTR) in clean water at zero dissolved oxygen (DO) at 20°C. Subtle
differences in the method of data analysis- can produce differences of
10 percent in the clean water SOTR. Moreover, this uncertainty is further
magnified when translating clean water, test tank transfer rates to actual
plant conditions. Because of differences in wastewater characteristics,
tank geometry, wastewater temperature, mixing, and other system characteris-
tics, uncertainties of up to 50 percent may be introduced.
Two common complaints voiced by engineers involved in aeration equip-
ment design are the difficulties encountered in correlating manufacturers'
oxygenation claims with shop or field test data and projecting equipment
performance data to a respiring biological system in the field. The discre-
pancies between anticipated and actual performance are frequently sufficiently
large to warrant substantial field modifications to the.aeration equipment
furnished. The cost of performing such modifications and the ill will
generated offer excellent testimony to the need for a standardized method of
oxygen transfer testing and data interpretation.
There is little question that a consensus standard is needed for oxygen
transfer devices. Although several standard procedures are in existence,
these procedures are concerned primarily with the methodology of experimental
measurement and do not deal adequately with the interpretation and applica-
tion of data to engineering design. Moreover, there is no general agreement
1
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among engineers and manufacturers as to which standard procedure or set of
procedures to use. As a result, a wide variety of techniques are employed,
resulting in substantial variations in test results for the same device in
clean water tests. Even larger variations will be evident in translating
these results to full-scale design. Only when standard procedures are
developed through consensus agreement among experts in the field will a
better degree of uniformity, accuracy, and economy result. Even then, con-
tinued updating of the standard will be required.
In an effort to obtain a consensus standard procedure for the evaluation
of aeration devices, the American Society of Civil Engineers (ASCE) in January
1977 established a volunteer Subcommittee on Oxygen Transfer Standards (Table 1)
under the Committee on Environmental Standards (Technical Council on Codes
and Standards). Financial assistance was subsequently obtained from EPA to
assist the Subcommittee in the development of first-phase interim standard
procedures. The objectives of this project were to
1. review and critically evaluate the state-of-the-art of oxygen
transfer testing,
2. evaluate and critically review existing testing standards and
identify critical areas of disagreement and uncertainty,
3. develop documentation for recommendations for interim standard pro-
cedures and recommend verification methodology, and
4. prepare the proposed interim standard procedures.
Over the past 3 yr, this Subcommittee has been working towards these
project objectives. This has been accomplished through Subcommittee deliber-
ations and a sponsored workshop held in Asilomar, California, in April 1978.
The Subcommittee was divided into subgroups with responsibilities for
addressing five important areas: (1) oxygen transfer modelling and data
interpretation, (2) unsteady state clean water transfer testing, (3) respiring
systems oxygen transfer testing, (4) corrections for wastewater character-
istics and temperature (alpha, beta, and temperature corrections), and
(5) geometry and mixing considerations. Several Subcommittee members were
later assigned the tasks for also evaluating methods for power and air flow
measurements. The results of the deliberations of this Subcommittee are
included within the text of this report. They represent a group effort
based on the experience of experts in the field from industry, government,
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TABLE 1. LIST OF MEMBERS-SUBCOMMITTEE ON OXYGEN TRANSFER STANDARDS
William C. Boyle, Chairman
University of Wisconsin-Madison
3230 Engineering Building
1415 Johnson Drive
Madison, Wise. 53706
James A. Mueller. Ass't Chairman
Manhattan College
Bronx, N.Y. 10471
C. Robert Baillod
Michigan Technological University
Houghton, Mich. 49931
Edwin L. Barnhart
ELBA, Inc.
Dallas, Texas 75235
Jon H. Bender
U.S. EPA-MERL
Cincinnati, Ohio
45268
Henry H. Benjes, Jr.
Culp/Wesner/Culp
El Dorado Hills,
Cal. 95682
Arthur G. Boon
Water Research Centre
Stevenage Laboratory
Elder Way
Stevenage
Hartfordshire SGI 1TH
England
Richard C. Brenner
U.S. EPA-MERL
Cincinnati, Ohio 45268
Haskal Brociner
Clow Corporation-Chicago Pump
Melrose Park, 111. 60160
Linfield C. Brown
Tufts University
Medford, Mass. 02155
Hugh J. Campbell.Jr.
E.I. duPont de Nemours & Company
Wilmington, Del. 19898
Paul W. Cummings, Jr.
Norton Company
Worcester, Mass. 01606
Dante M. Cimadamore
ABS Pumps, Inc.
Wallingford, Conn.
06492
W. Wesley Eckenfelder, Jr.
Vanderbilt University
Nashville, Tenn. 37235
Lawrence A. Ernest
Milwaukee County Metropolitan
Sewerage Commission
Milwaukee, Wise. 53217
George R. Fisette
Mobay Chemical Corporation
Union, N.J. 07083
R. Gary Gilbert
Kenics Corporation
North Andover, Mass. 01845
Mervyn C. Goronszy
State Pollution Control Commission
Union Carbide House
Sydney, Australia 2000
Lyndell Harrington
U.S. EPA-Region VII
Kansas City, Mo. 64106
(continued on next page)
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TABLE 1. (continued)
John S. Hunter III
3M Company
St. Paul, Minn. 55133
Robert Irvine
Notre Dame University
Notre Dame, Ind. 46566
Anton A. Kalinske
Camp, Dresser & McKee, Inc.
Walnut Creek, Cal. 94596
Prof.Dr.-Ing. Rolf Kayser
Techn. Universitat of Braunschweig
3300 Braunschweig
West Germany
Paul J. Krasnoff
New York City Department of
Environmental Conservation
Wards Island, N.Y. 10035
Mikkel G. Mandt
Houdaille Industries
Pentech Division
Cedar Falls, Iowa 50613
Mark Markofsky
Institut fur Hydromechanek
Universitat of Karlsruhe
Kaiserstrasse 12
West Germany
Frederick K. Marotte
CH2M Hill
Denver, Colo. 80239
Charles Matsch
Derrick Manufacturing Corporation
Buffalo, N.Y. 14225
James J. McKeown
National Council on Air & Stream
Improvement
Tufts University
Medford, Mass. 02155
Anthony D. Nardozzi
InfiIco-Degremont, Inc.
Richmond, Va. 23288
James Y. Oldshue
Mixing Equipment Company
Rochester, N.Y. 14603
John Pai
U.S.EPA-Municipal Construction
Division
Washington, D.C. 20460
Wayne L. Paulson
University of Iowa
Iowa City, Iowa 52242
David T. Redmon
Ewing Engineering Company
Milwaukee, Wise. 53209
William S. Robertson
Simon-Hartley Ltd.
Stoke-on-Trent,
ST4 7BH England
Thomas C. Rooney
Rexnord Corporation
Milwaukee, Wise. 53214
Ronald N. Salzman
Mixing Equipment Company
Rochester, N.Y. 14603
F. Michael Saunders
Georgia Institute of Technology
Atlanta, Ga. 30332
Gerry Shell
Environmental Engineers, Inc.
Brentwood, Tenn. 37027
Vernon T. (Smokey) Stack, Jr.
Betz, Converse & Murdock, Inc.
Plymouth Meeting, Pa. 19462
(continued on next page)
-------
TABLE 1. (continued)
Michael K. Stenstrom Shang Wen (Sheldon) Yuan
University of California-Los Hazen and Sawyer
Angeles New York, N.Y. 10017
Los Angeles, Cal. 90024
Fred W. Yunt
John R. Stukenberg County Sanitation Districts of
Black & Veatch Los Angeles County
Kansas City, Mo. 64114 Whittier, Cal. 90601
Jerome D. Wren
Sanitaire-Water Pollution Control
Corporation
Milwaukee, Wise. 53201
consulting firms, and universities. This report represents the first step
in a series of steps necessary to develop an objective consensus standard for
oxygen transfer devices.
PHILOSOPHY
In examining the objectives and procedures for testing oxygen transfer
devices, the term standard as used within the context of this study refers to
a methodology for (1) the measurement of the oxygen transfer capacity of
equipment in clean water, (2) the interpretation of these test data,
(3) the application of these data to engineering design of field oxygen
transfer systems, and (4) on-site performance testing of oxygen transfer
systems.
The Subcommittee has agreed that the development of a standard must be
the outgrowth of an orderly process that includes a state-of-the-art assess-
ment, development of a procedural manual, establishment of an interim
standard or standards, and, if applicable, the final creation of a consensus
standard or standards (Figure 1). The standardized protocols must include
the details of the test procedures and methods of data analysis and uniform
methods of calculation and data reporting. This Subcommittee was selected
among experts in the field having a wide cross section of experience with
oxygen transfer devices. It was clear early in its deliberations that a
wide variety of opinions existed about the best methods for testing aeration
-------
STATE OF ART REVIEW
SUBGROUP
ANALYSES
-WORKSHOP
A B C D
PROCEDURAL MANUALS
(drafts)
PROCEDURAL MANUALS_
(adopted)
EVALUATION
PROCEDURE
DEVELOPMENT
(draft)
NEEDED _
RESEARCH
EVALUATION
PROCEDURE
(adopted)
STANDARDS
(draft)
STANDARDS
(draft)
STANDARDS
/concensus procedures'^
V ASCE/ANSI /
STANDARDS
UPGRADING
Figure 1. Procedural Flowsheet-Subcommittee on Oxygen Transfer Standards.
equipment. These opinions were based on theoretical analysis, experience
with shop testing of specific types of generic oxygen transfer equipment, and
experiences with design and operation of field equipment. Rather than dis-
mantle an existing standard, it was the decision of the Subcommittee that
each aspect of the test procedures should be carefully reviewed and a state-
of-the-art document developed that provided the pros and cons for current
practice. Based on this state-of-the-art review, it was hoped that the
Subcommittee would arrive at decisions on the best testing methods for oxygen
transfer equipment as well as data evaluation techniques.
The proposed interim standard procedures as they appear within this
report have been the outgrowth of several years of study, discussion,
-------
deliberation, and compromise. This Subcommittee is satisfied that these
interim standard procedures represent the best state-of-the-art today.
Such procedures will be of little value to the profession, however,
unless they are used and continuously critiqued. Only when standard proce-
dures are developed through consensus agreement will a better degree of
uniformity, accuracy, and economy result. Even then, continued updating of
the standard will be required. This Subcommittee will continue to function
as a standards development and review group under the ASCE Technical
Council on Codes and Standards.
FORMAT OF THIS REPORT
This report is presented as a series of interdependent topics dealing
with the testing and application of oxygen transfer devices. Three of these
sections (Sections 4, 5, and 7) present recommended procedures for testing
oxygen transfer devices and analyzing the data resulting therefrom and
document the development of these recommendations. Four other sections
(Sections 6, 8, 9, and 10) provide supplementary information required for
the interpretation and application of the standard procedures to field design.
Finally, Section 11 briefly describes proposed methods for the evaluation of
the proposed standard procedures.
-------
SECTION 2
CONCLUSIONS
The ASCE Oxygen Transfer Standards Subcommittee has made an exhaustive
review of the methods used for the testing of oxygen transfer devices. This
study included reviews of
1. modelling and data interpretation,
2. clean water unsteady state testing,
3. oxygen transfer measurements in respiring systems,
4. impacts of wastewater characteristics and temperature on oxygen
transfer,
5. effects of geometry and mixing on oxygen transfer, and
6. methods of air flow and power measurements.
Based on these reviews, recommended procedures have been presented for
the testing of oxygen transfer devices in both clean and dirty water. These
recommended procedures are delineated under the appropriate sections of this
report. To list separate, more abbreviated conclusions from this comprehen-
sive study is unwarranted since they would be out of context and may be
misinterpreted.
-------
SECTION 3
RECOMMENDATIONS
A review of state-of-the-art procedures for oxygen transfer testing and
subsequent recommendations for interim standardized procedures for that
testing represents the first step in an orderly procedure for developing a
consensus standard. It is now necessary to evaluate the proposed interim
standard procedures through field testing over a wide variety of conditions.
A proposed field testing program is described in Section 11 of this
report. Verification testing would ideally include testing for both accuracy
and precision. Precision of the proposed procedures can be obtained through
replicate testing, again under a variety of conditions with a variety of
oxygen transfer devices. Accuracy, on the other hand, requires a standard
against which the procedures can be compared. Unfortunately, no acceptable
standard for oxygen transfer exists at this time. It has been suggested
that a tracer technique using either a radioactive or nonradioactive isotope
of krypton serve as that standard.
The translation of clean water tests to field conditions still requires
a great deal of work. Currently, engineers employ corrections for waste-
water characteristics (alpha and beta), wastewater temperature (theta), and
geometry and mixing. These corrections are currently based upon experience.
Laboratory tests for alpha do not appear reliable, and rule,-of-thumb correc-
tions for scale-up of geometry, powerllevels, etc., are not entirely satis-
factory at this time. Field and laboratory research are, therefore,
essential to improve our ability to scale up clean water test data to field
conditions.
The adoption by the profession of standardized procedures for the
testing of oxygen transfer devices is the first important step in achieving
answers to many questions that still remain regarding the design, operation,
and control of aeration systems. Once standardized procedures against which
-------
comparisons can be made become recognized throughout the field, corrections
for translation of clean water performance to dirty water performance can be
more clearly studied. The net result will be more accurate designs of aera-
tion systems with savings in both capital and energy for the owner.
10
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SECTION 4
MODELLING AND DATA INTERPRETATION
RECOMMENDED STANDARD METHOD FOR MODELLING
AND ANALYZING UNSTEADY STATE TEST DATA
The Model
The basic model recommended for the analysis of both surface and sub-
surface clean water, unsteady state oxygen transfer test data is:
4£ = K.a(C*- C) (differential form) (1)
Ci U I— ^^
which, upon integration, becomes:
= - K.a t (logarithmic form) (2)
In
*
C - C
oo
or:
c = Coo " (Coo " c0)exP(-K|_a t) (exponential form) (3)
where:
C = average dissolved oxygen (DO) saturation concentration attained
°° 3
at infinite time, m/L
K, a = apparent volumetric mass transfer coefficient, t~
3
C = DO concentration at t = 0, estimated from the model, m/L
3
C = effective average DO concentration in the liquid phase, m/L
t = time, t
and the symbols m, L, t, and f are employed to denote dimensions of mass,
length, time, and force, respectively.
This model applies to a given aeration system in a given tank under
steady state hydraulic conditions. It is shown in the Commentary that this
model can be viewed either as based on a completely mixed system with uniform
11
-------
DO values in which oxygen is transferred throughout the tank volume or as
based on a compartmentalized system in which oxygen transfer is confined to a
localized aeration zone. The compartmentalized system allows for nonuniform
DO concentration values in the accumulation zone but does require that the
average DO value of the aeration zone equal the effective average of the
accumulation zone. Although this equality seems reasonable, it has not been
verified experimentally. Consequently, additional uncertainty is introduced
when the recommended model is applied to a system in which appreciable
differences exist between values of DO measured at different points in the
tank.
In both cases, the average DO concentration, C, represents a bulk
average, i.e.:
C =
where:
C = localized DO concentration, m/L
o
V - portion of the volume over which C is averaged, L
It follows that, if the results of multiple sample points are to be
analyzed by a simple average, the sample points should be chosen so that each
senses an equal portion of the tank volume.
In the application of this model to unsteady state test data, it is
recommended that:
1. The exponential form should be employed and fit to the test data by
nonlinear regression.
*
2. Values of the parameters KLa, C^, and CQ should be estimated from
the model. Individual measured values of C and C are not to be used as
CO Q
model parameters. Likewise, tabulated book values of DO surface saturation
*
concentrations are not to be used to estimate C .
oo
3. An effort should be made to gather valid DO data over as wide a
range as possible. Truncation of data at values of C less than 20 percent
of C* is allowable to avoid lingering effects of the deoxygenation technique.
However, good data at low DO values should be used in the estimation because
they are important for assessing model adequacy. A guideline that may be
applied for more precise determination of the low truncation point when
sampling intervals are small is to locate an inflection point by
12
-------
differentiating the data and truncating data at C values below 1.5 times the
C at the inflection point. However, in no case should values of C greater
than 30 percent of C* be truncated.
Truncation data at DO values approaching C^ is strongly discouraged and
is recommended only when the alternate Best Fit Log Deficit Method is
employed.
4. When lack of a computing facility prevents the application of non-
linear regression to the exponential form of the model, a linear regression
applied to the logarithmic form of the model is an acceptable alternate
technique. When this technique, termed the Best Fit Log Deficit Method is
*
used, the value of C^ is to be estimated from the model as the value giving
the minimum residual sum of squares on the log deficit plot.
5. In most cases, calculation of standard clean water and dirty water
respiring system oxygen transfer rates (SOTR and OTRf values) should be based
on the estimated values of K.a and C* along with given or separately deter-
mined values of a, 0, and 3. This approach is relatively straightforward and
simple. However, it is acceptable to base the calculations of SOTR and OTRf
on a "true" volumetric mass transfer coefficient, K.a* In this case, values
of a and 6 based on ratios of K.a values should be distinguished from values
of a* and 9* based on K.a* values.
Parameter Estimation
Inspection of the Data --
Prior to a numerical analysis, it is recommended that the data be
plotted, preferably as DO concentration versus time. The plotted data should
be examined on two accounts. First, the data should be inspected for trends
indicative of a departure from the assumed exponential form of Equation 3.
Typical examples of this phenomenon are a lag period at the beginning of
reaeration or a ramp-type trend in the data. Second, an assessment of the
noise in the data should be made. A spurious data value of especially
noisy observations may be indicative of poor experimental procedures. If
any anomalies are observed in the data record, the reasons should be noted
and a determination made whether or not to discard spurious data prior to
proceeding with the numerical analysis. The Data Trunction and Model
Adequacy subsection of this section discusses methods for handling some of
13
-------
the minor model inadequacies and noisy data.
Recommended Parameter Estimation Procedure --
The model in exponential form given by Equation 3 is best suited to the
analysis of unsteady state oxygen transfer data. The use of this equation
for parameter estimation requires that the data be in the form of DO concen-
tration versus time. It is recommended that the parameters C , K.a, and C*
o L °°
be estimated using a nonlinear least squares regression technique. The
advantages of this approach are:
1. It provides the least squares estimates and precision of these
estimates for all three parameters directly from the data.
2. It works directly with the observed DO concentration, C, rather than
with a calculated DO deficit or with an approximation to the time rate of
change of oxygen concentration.
3. It does not require the truncation of observed data as the DO
concentration approaches saturation.
4. For a given set of data, it should provide parameter estimates that
are more precise than those given by other commonly used methods.
There are two disadvantages to this procedure, but neither is felt to be
severe.
1. The method employs an iterative search for the least squares esti-
mates; thus, for practical purposes, the use of a computer (or advanced
scientific calculator) is required for parameter estimation.
2. Because of the nature of the error structure of DO concentration
versus time data, the use of Equation 3 for parameter estimation may over-
weight the observations at the beginning of the test in systems where
transfer rates are high. Weighting procedures designed to overcome this
difficulty have been suggested, but they do not offer a clear advantage over
the unweighted analysis.
Various techniques for performing nonlinear regression analysis of
unsteady state oxygen transfer test data using Equation 3 are described in
Appendix A and the Commentary. These techniques provide least squares
estimates of CQ, C^, and K^a. In addition to the least squares estimates,
the standard deviation or relative standard deviation of the parameter
estimates should be calculated and reported. This calculation is
14
-------
incorporated into many of the available computer programs for nonlinear
parameter estimation. The values of the standard deviations reflect the
degree of scatter in the test data and should be small for a good test.
Acceptable values for shop tests are 5 percent for KLa, 3 percent for C*,
and 0.3 mg/£ for C . Also, the error structure of the data should be exa-
mined by a plot of the residuals (the difference between observed and
predicted DO concentrations). Trends in the residuals may reveal possible
hydrodynamic irregularities such as surging and macroscopic mixing patterns.
More importantly, however, the residuals provide information about the
uniformity and magnitude of experimental error and about the adequacy of the
model to describe the observed data.
A Fortran computer program for performing nonlinear regression analysis
of unsteady state oxygen transfer data using Equation 3 is described in
Appendix A. The program employs an iterative linearization method to search
for the best parameter values. The program calculates the least squares
estimates and approximate standard deviations of C , C*, and KLa and computes
the residuals for a check on model adequacy.
Alternate Parameter Estimation Procedure: Best Fit Log Deficit Method --
Although the nonlinear regression method using Equation 3 is the recom-
mended standard for parameter estimation, the Best Fit Log Deficit Method
based on Equation 2 is acceptable when lack of a computing facility prevents
application of the recommended method. In this technique, the value of C*
is estimated from the model as that giving the minimum residual sum of
squares on the log deficit plot. The chief advantage of this approach is
that it can be applied by using an ordinary scientific calculator instead of
the computer required in the recommended method.
However, this approach has several disadvantages:
1. It consists of successive trial and error regression analyses, i.e.,
a separate regression analysis must be performed, and the residual sum of
squares must be calculated for each trial value of C£. Because of this, it
is time consuming and tedious.
2. The logarithmic transformation weights the data and is proper only
when the experimental error is a constant percentage of the deficit.
3. Data truncation is required as DO values approach saturation in
15
-------
order to avoid taking logs of negative numbers. It is recommended that DO
values observed at times greater than approximately 3/K. a (.95 percent satura-
tion) be truncated.
4. This method is basically a one parameter estimate, and, therefore,
standard errors of estimate comparable to those of the recommended nonlinear
method are not readily calculated.
Other Parameter Estimation Methods --
Other methods employing graphical and/or linear least squares numerical
techniques may be useful for obtaining approximate values of the parameters.
Several variations of the log deficit method have been applied to analyze
unsteady state test data. The variations here are related primarily to the
selection of C* and degree of data truncation practiced.
Possibilities for the selection of C* include
1. use of a single or average measured value,
2. use of a book surface saturation value corrected to mid or some
other depth,
3. use of a book surface saturation value corrected for depth and exit
gas depletion, and
4. estimation of C* from the model as the value giving either the
"straightest" line or the minimum residual sum of squares (.as in the
recommended alternate Best Fit Log Deficit Method).
The disadvantage of approach 1 above is that the measured value will
include error and bias the estimate of K.a. However, based on the work of
1
Ewing et al., it appears that this approach applied to good data yields
results close to those of the recommended method. This approach has been
applied by several investigators. ' ' '
Approaches 2 and 3, based on corrected surface saturation values, can
severely bias the parameter estimates. Furthermore, it must be realized
that the exit gas depletion correction will produce an estimate of KLa*
rather than K.a. These approaches are not recommended.
Approach 4 generally yields results close to those of the recommended
method and is acceptable as an alternate to the recommended nonlinear regres-
sion approach. Campbell applied this approach to analyze unsteady state
oxygen transfer data.
16
-------
All of the log deficit approaches suffer from the necessity to truncate
the data at values of C approaching C*. In addition, this method does not
enable the precision of C* to be estimated.
The direct method is based on graphical or numerical differentiation of
j P
the C versus t data in order to determine -rr. Values of both K. a and C* are
i p Qt L
then obtained directly from a plot of -rr versus C. This method has the ad-
vantage of being able to estimate two parameters. However, the differentia-
f\ C
tion inherent in the direct method produces a variable -rr- having a larger
j P ^"^
error than the error in C. The larger error in -nr causes the error in the
parameter estimates, C* and K.a, to be larger than those from the other
methods.
The recommended nonlinear regression method requires that initial
estimates of the parameter values be provided. The log deficit and/or direct
methods are useful procedures for obtaining those initial parameter values.
Experimental Design
It is recommended that unsteady state oxygen transfer tests be conducted
for as long a period of time as practicable. A minimum period of time
approximately equal to 4 divided by the anticipated value of K.a is sug-
gested. This value corresponds to a DO concentration of 98 percent of C*.
When it is practical, the test should be run to 6/K,a for the record and for
comparison with the estimated C* value. For reference, Table 2 gives the
relationship between time in multiples of reciprocal K.a and DO concentration
in terms of percent of C* for Equation 3.
It is recognized that temperature variations may affect the precision
and accuracy of the test. Therefore, as a minimum, it is suggested that the
water temperature and barometric pressure be measured at the beginning and
end of the test. The average temperature and pressure during the test along
with the beginning and ending values should be reported with the results.
It is recommended that the regression analysis be based on a minimum of
10 to 15 data values. Analysis with fewer than 10 data values will reduce
the precision of the parameter estimates and will impair the ability to
assess model inadequacy if it is present. Analysis with more than about 20
data values usually does not result in a significant improvement in the
precision of the parameter estimates and may weaken the assumption of
17
-------
TABLE 2. RELATIONSHIP BETWEEN TIME AND PERCENT SATURATION FOR EQUATION 3*
Time as DO Concentration as
Multiples of 1/K.a Percent of C*
L oo
0
0.1
0.2
0.5
0.7
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6.0
0
9.5
18
39
50
63
78
86
92
95
98
99
99+
*
C is assumed to be zero.
independence among the observations. Approximately two-thirds of these
values should be evenly distributed over the period of time between the
initial data point which is above zero and 2/K.a. The remaining one-third
of the values should be evenly distributed over the period of time covered by
2/K^a to 4/KLa. In cases of rapid transfer, the maximum time between obser-
vations should normally be 0.4 min.
In systems using multiple sampling locations, the data from each sample
point should be analyzed separately and values of the parameters should be
estimated and reported for each sampling point. The uniformity of the
separate estimates may provide useful information about the variation of
transfer characteristics within the aeration system. The average value of
each parameter will provide information about the overall transfer charac-
teristics of the aeration system.
Data Truncation and Model Adequacy
Truncation of data as the DO concentration approaches saturation is dis-
couraged because these data significantly influence the parameter estimates
of K, a and C*. This is the reason for recommending that the test be con-
L °°
ducted to at least a time approximating 4/K.a (98 percent of C*).
18
-------
Truncation of the data at low DO values presents a different problem.
Values of DO concentration less than 10 to 30 percent of saturation, C*, may
have to be truncated to avoid lingering effects of the deoxygenation tech-
nique. However, data values in this range are important in determining
whether the model given by Equation 3 is adequate. If model inadequacy is
to be manifested, it would be expected during the early portion of the
unsteady state test.
The precision of the least squares estimate of C as well as a plot of
the residuals versus time should yield meaningful information about model
adequacy. Thus, it is recommended that valid DO observations be recorded as
close to zero as possible while still avoiding the influence of deoxygena-
tion. A decision on model adequacy is subjective and normally requires a
rigorous statistical analysis. However, a general indication may be
obtained by comparing the estimate of error from the statistical fit of the
model (the square root of the residual mean square) with the experimental
error (sampling plus analytical error) in measuring DO in the test system.
If the estimate of error from the residuals is more than twice the experi-
mental error estimate, then model inadequacy may be indicated. As previously
stated, Equation 3 will adequately model the great majority of aeration
devices commonly employed in wastewater treatment systems. In the event that
the residual plot or the error analysis indicates that this model is clearly
inadequate, one of two approaches may be followed:
1. A more refined mechanistic model such as a variable gas rate model
may be investigated. However, the more sophisticated models generally
present more difficult parameter estimation problems and care must be taken
to correctly interpret and apply the resulting parameter estimates.
2. More severe data truncation may be applied in an attempt to produce
a better fit of the model to the data in the region of greatest interest.
However, this truncation tends to lower the precision of the parameter
estimates and the resulting uncertainty should be considered in interpreting
the results.
Interpretation and Rejaorting of Results
Recommended Method: Surface and Submerged Aeration --
By convention, the oxygen transfer capacity of an aeration system is
19
-------
usually expressed as the rate of oxygen transfer predicted by the model at
zero DO under standard conditions of water temperature and pressure, usually
1.0 atmosphere at a specified relative humidity and 20°C. This is termed
the standardized oxygen transfer rate (SOTR). It should be noted that the
SOTR is a hypothetical value based on zero DO in the aeration zone, which is
not usually desirable in real aeration systems operating in process water.
The SOTR value can be determined by correcting the test values of K.a and C*
to standard conditions by:
KLa20 = KLaT6
(20-T)
(5)
= r
s20
sT
PS + Ywde - Pv20
+ Ve - p
v20
(6)
where:
6 = empirical temperature correction factor ranging from 1.015 to
1.03, usually = 1.024
C* T = DO surface saturation book value at the test temperature, m/L
p = standard atmospheric pressure, usually 1.00 atm., air at 100 per-
s 2
cent relative humidity, f/L
2
p. - atmospheric pressure during test, f/L
p - saturated vapor pressure of water, f/L
d = effective saturation depth at infinite time, L, defined by
d =
Y,
w
(P, - P..T) -
sT
Y = weight density of water, m/L
W
and the subscripts T and 20 denote the quantity evaluated at the test and
20°C water temperatures, respectively.
The SOTR is then computed by:
where :
SOTR -
V == volume of water in the test tank, Lv
20
(7)
-------
"A"
It is recommended that the values of K. a?0, C^QJ e> V, and the actual
test temperature be reported along with the SOTR. If possible, the standard
deviations of the KLa, C*, and C parameter estimates should also be reported.
Frequently, the standardized aeration efficiency (SAE) or rate of oxygen
transfer per unit power input is of interest and can be computed from:
Power Input
This parameter is normally expressed in units of pounds per horsepower hour
or kilograms per kilowatt hour.
Alternate Method --
An alternate approach, applicable to subsurface gas injection systems
only, recognizes that, because of oxygen depletion in the rising gas stream,
the true value of the volumetric mass transfer coefficient, K. a*, is somewhat
larger than the apparent value of K.a, The calculation is complicated by
the fact that the temperature correction factor, 9, and the value of a are
usually given as ratios of K.a values and must be adjusted before applying
them to K.a* values. When the values of a and 6 are properly adjusted, this
approach will give standardized and field oxygen transfer rates closely
approximating those given by the recommended procedure.
As outlined in the Commentary, this approach is based on the transfer
equation, the gas side oxygen balance, and an assumed relationship between
C (see Commentary for definition) and the oxygen content of the feed and
exit gases. Different models arise when various approximations are made in
the gas side oxygen balance and various assumed relationships are employed.
o
One model, similar to that proposed by Downing and Boon and later applied by
Ewing et al . , in particular, is attractive because it reduces to the form
of Equations 1 to 3 and is amenable to the same parameter estimation methods.
An acceptable alternate method of calculating SOTR values by this model is
illustrated at the end of this section.
Application of Clean Water Test Data to Dirty Water Respiring Systems
Recommended Method --
For given values of a, $» temperature, 6 , DO concentration, and
barometric pressure, the clean water SOTR is related to an actual dirty
21
-------
water transfer rate in a respiring system by:
OT» .
" C)
(9)
where:
OTRf = oxygen transfer rate in the dirty water respiring system, m/T
pb + Ve - Pv20
= pressure correction =
T = temperature correction =
Ve - Pv20
sT
it—
s20
a =
e =
dirty water K.a
clean water K.a
*
dirty water C^
clean water C*
An acceptable alternate method based on K.a* corrected for gas side oxygen
depletion is outlined in the example problem at the end of this section.
COMMENTARY ON THE RECOMMENDED STANDARD METHOD
Models
Theoretical Development --
Fundamental relationships -- The basic model for oxygen transfer in a
dispersed gas-liquid system is given by:
Volumetric
Mass Transfer
Coefficient
x Driving Force (.10)
Rate of Mass Transfer
per Unit Volume of
Liquid
Expressed in terms of the overall liquid phase volumetric mass transfer
coefficient, this relationship becomes:
/V /\ S\ /\ /*«.
W = KLa*(C* - C)
where the A superscript is employed to indicate the local nature of the
quantities and:
(11)
22
-------
-3 -1
W = oxygen transfer rate per unit volume in clean water, ml t
K. * = true overall liquid phase mass transfer coefficient, based on the
liquid resistance, L/t
a = interfacial surface area per unit volume, L~
C* = point value of DO saturation corresponding to a given oxygen
3
partial pressure and water temperature, m/L
In applying Equation 11 to an oxygen transfer system, it must be remem-
bered that this relationship applies to a particular point. In general, the
total rate of oxygen transfer is of interest and can be evaluated by inte-
grating the local transfer rate over the volume, V:
UV = [w dV = [l
-------
Baillod' reviewed various approaches to relate C* to the inlet and exit
oxygen content of the aeration gas in terms of Henry's law constant and the
effective saturation depth.
Compartmentalized system — This system is idealized as a tank in
which oxygen transfer is confined to a localized aeration zone to which
uniform average values of K, a*, C*, and C may be applied. The remainder of
L. a
the tank serves as an accumulation zone in which DO concentration gradients
may exist.
Figure 2 shows a profile of the idealized compartmentalized system.
Fluid circulates through each zone at a volumetric flow rate, Q. Oxygen
transfer takes place primarily in the aeration zone, which would correspond
to the spray of a surface aerator or to the zone directly above the diffusers
in a spiral flow system. The fluid leaves the transfer zone and circulates
through the accumulation zone without additional oxygen transfer taking
place during circulation.
OXYGEN
AERATION
ZONE
J
CB\Q
\
ACCUMULATION
ZONE
Figure 2. Profile of an oxygenation tank.
24
-------
Oxygen balances can be written on the liquid in each zone during an
unsteady state clean water test as:
Aeration Zone:
IdC
' V
'AB
(15)
Accumulation Zone:
. r } = v
where:
(16)
Q = volumetric pumping rate of aerator, L /t
3
CR = DO concentration in flow entering the aeration zone, m/L
3
C. = DO concentration in flow leaving the aeration zone, m/L
3
V. = volume of aeration zone, L
3
Vn = volume of accumulation zone, L
K. a* = true volumetric mass transfer coefficient applicable to the
-1
aeration zone volume, t
3
CAB = effective average DO concentration in the aeration zone, m/L ,
defined by WVft = VAK,_a*(C* - CAB)
C = average DO concentration in the accumulation zone, m/L
Combining Equations 15 and 16 gives:
'B
If it is assumed that C
dC
'AB
dt
dC
dt
* - CAB>
C.g, Equation 17 reduces to:
(17)
= KLa*(C* - C)
where:
K. a* and K. a* are related by:
L La
KLa* =
VA + VB
(18)
(19)
Comparison of Equations 13 and 18 indicates that the analysis of each
system leads to the same result. The subtle difference between the equations
is that in the development of Equation 13, C and KLa* were assumed to be
uniform over the entire tank volume, whereas Equation 15 assumed uniformity
only over the aeration volume.
25
-------
The assumption of C.g = C seems reasonable but has not been experi-
mentally established for typical systems. Lack of agreement between these
concentrations would require that Equation 17 be applied to analyze unsteady
state test data. In doing this, care would be required in the definition
and measurement of CAB, the effective average DO concentration in the aera-
tion zone. It appears that this is an area in which further research is
warranted.
The recommended model (Equation 3) is based on Equations 13 and 18 and
can be applied to situations meeting the assumptions inherent in the develop-
ment of either of these equations. In many systems, aerator placement and
tank geometry produce a completely mixed system arid the recommended model may
be logically applied based on Equation 15. In other cases, however, local-
ized aeration zones may cause nonuniform DO values and the recommended model
is viewed as based on the compartmentalized system (Equation 18). Additional
uncertainty is introduced here by the unverified assumption that C = C.g.
In the case of a steady state compartmentalized respiring system,
inclusion of the biological oxygen uptake rate R (mass of oxygen per unit
volume per unit time) into the material balance equation (Equations 15 and
16) yields:
R = KLa*(C* - C) (20)
where:
R = volumetric uptake rate due to biological respiration in both the
-3 -1
aeration and accumulation zones, mL t
This development is predicated upon equal uptake rates in the aeration
and accumulation zones, an occurrence which is reasonable only if DO is
actually present (at concentrations in excess of values that limit R) in all
regions of both zones. It follows that application of the compartmentalized
model to predict transfer rates in respiring systems will be valid only when
the DO concentration is above zero in all regions of the accumulation zone.
Although the SOTR is a convenient parameter for applying clean water
data to field conditions, it should be remembered that application of the
model to a respiring system described by the compartmentalized model requires
that DO be present in all regions of the accumulation zone. Because of this,
it is incorrect to calculate oxygen transfer rates based on SOTR values for
26
-------
compartmentalized systems unless the average operating DO value in the
accumulation zone is great enough to avoid oxygen limitation on uptake rates.
Unsteady state models -- Most analyses of unsteady state aeration are
based on Equation 18.
In submerged aeration, C* varies with time during the unsteady state
test. Therefore, it is necessary to incorporate two additional relationships
into a submerged aeration model based on this equation. One of these arises
from a gas side oxygen balance and relates the oxygen content of the feed and
exit gases in terms of the gas feed rate and transfer rate:
M
o
M
_o. G V = v|£y (?n
y\ »ir rn *l ,4+! vt i;
a
where:
M , M = molecular weights of oxygen and air, respectively, m/mol
o a
Gp, GE = mass rates of feed and exit gases, respectively, m/t
GF = pad ^ad
GE = Pae Qae
Y., Y = mole fractions of oxygen in the dry feed and exit gases,
respectively
2
P,A» P=« = mass densities of feed and exit gases, respectively, m/L
au ae
Q,J» Q,« - volumetric flow rates of feed and exit gases, respectively,
au ae o
LVt-
The other equation relates C* to the oxygen content of the feed and exit
gases. Baillod' has reviewed various relationships employed for this pur-
pose. One such relationship, similar to that proposed by Downing and Boon
Ewing et
(Y, + YJ
and used subsequently by Ewing et al . is:
(.22)
where:
d = effective saturation depth, L
H = Henry's law constant, conc/mol fraction/pressure
At infinite time in the unsteady state test, C* = C* and Y = Y., so that:
C~ = Yd(Pb- PV +Ve)H (23)
27
-------
A reasonable approximation for most aeration systems is that the feed and the
exit gas rates are equal, or that Gp - GE. With this approximation,
Equations 13 or 17 and 21 to 23 can be combined to give:
dC
dt
KLa*/2d
(C* - C) (24)
where:
1 (Mn
*H = oxygenation coefficient, t , = "
C*V
KLa* Kl a*c*v
— r — = transfer number, dimensionless, =
,.. ... v^
(MQ/Ma)GF
Comparison of Equations 1 and 24 shows that the "true" and "apparent" values
of K.a are related by:
Ka
Here, the apparent transfer number, K,a/cf>,, is equal to the oxygen transfer
efficiency at zero DO concentration, OTE :
[/ a |y « p^ \t
_l_ = I °° _ oxygen transfer rate at zero DO nTI- (oc.\
*d (M0/Ma)GF Yd ~ oxygen supply rate " Ulho (-}
Typical values of the oxygenation coefficient,
-------
characteristics and water temperature on the transfer coefficient and satura-
tion value. The effect of water characteristics is accounted for by the
so-called alpha and beta factors, defined here in terms of "true" K.a, K.a*,
by:
dirty water K.a* K. a*f
a* = clean water Kj_a* = "TjT*
ft _ dirty water C* _ C*f
* " clean water C* " C*
where the subscript f denotes the dirty water field condition. It is rea-
sonable to expect that the influence of dirty water on the various saturation
values will be similar, so that:
r* r* r*
11- _±f -_!!- g (291
C* ~ C* ~ C* v '
Likewise, the influence of temperature on the transfer coefficient and satu-
ration value can be expressed in terms of the factors theta and tau, defined
by:
e*(T-20) . Vn. (30)
Taf20
C*
T = c*L (3D
L 20
where the subscript T denotes field temperature. Again, it is reasonable to
expect that the influence of temperature on the various saturation concentra-
tions will be similar, so that:
C* C* C* ,
!_ _ °°T _ sj _ _ ,~y*
r* r* ~ T* \oe-j
u 20 »20 L s20
This relationship allows the value of T to be determined from the ratio
of published surface saturation values.
The relationships given by Equations 27 and 30 are based on "true" K.a,
K.a*, values, and it has been shown that values of the "apparent" and "true"
K.a may differ by 30 percent. Because of this, it is necessary to define
29
-------
an "apparent" alpha, a, by:
dirty water K. a K.af
~ clean water K.a ~ K.a
and an "apparent" theta, 0, by:
9 " = K~i (34)
\ f20
Finally, it is necessary to correct C* for differences in atmospheric
pressure between the test, standard, and field conditions. The value of C*
is not a linear function of total atmospheric pressure, but is a linear
function of the partial pressure of dry air at the saturation depth. There-
fore, the pressure correction factor, ft, is defined as:
ft =
at ps ps * de - pv
where the various terms are as defined earlier.
Alternate approaches based on "true" or "apparent" K.a -- In an aerated,
steady state respiring system, the rate of oxygen transfer per unit volume,
Wf, will be equal to the rate of biological uptake per unit volume, R. It
has been shown earlier that, for submerged aeration, the clean water oxygen
transfer rate, W, can be adequately modelled in two ways; based on the "true"
KLa, KLa*:
W = KLa*(C* - C) (36)
and based on the "apparent" K.a:
W = KLa(C* - C) (37)
For dirty water field applications, these expressions, respectively, become:
Wf = KLa*(C*f - C) (38)
Wf = KLaf(C*f - C) (39)
The field transfer coefficients! and saturation values can be related to the
clean water values through the use of the adjustment factors, a, 8, 6, T,
30
-------
and
Wf = KLa0a*e*"(ftT(S C*2Q - C) (40)
and:
U = K a r»fl* ^Orft T* - (M fdl^
Wr- i\. Cton ^*" vi6Lp U on ^/ \"' /
T L C\J °°£U
Note that Equations 36 and 38, based on K. a*, contain a driving force based
on C*, the actual effective saturation concentration corresponding to the
actual gas side oxygen depletion. On the other hand, Equations 39 and 41,
based on K.a, incorporate a driving force based on C*, the effective satura-
tion concentration attained when the inlet and exit gas oxygen fractions are
equal. It is generally more convenient to base the driving force on C*
because it can be determined from unsteady state data. This parameter can
be incorporated into Equation 40 by defining the dimensionless exit gas deple-
tion factor, F, so that, at field conditions:
(42)
~f
giving:
V
- *
W, = K.a~n a*9* (fa$ FC - C) (43)
The exit gas depletion factor is evaluated based on the relationship
between C* and C* employed in the determination of K.a. Substitution of
R = dt" into Ec1ua't'lons 21 > 22» and 23 yields:
F - rS1- 1 - WV* (44)
Aeration design equations are frequently expressed in terms of the SOTR,
defined as the rate of oxygen transfer in clean water at zero DO and a speci-
fied temperature, usually 20°C. Based on K.a*:
SOTR = KLa*0 FQ C*2Q V (45)
31
-------
where: QTE
FQ = F evaluated at zero DO = 1 -- ^- and based on K.a:
SOTR - KLa20C;2Q V (46)
The resulting design equations for the field oxygen transfer rate, OTR-,
are developed from Equations 41 and 43:
- (T _ c) (47)
o °°20
and:
OTR = a(SQff6 - (TgC*20 - C) (48)
°°20
In applying these equations, it is essential that careful attention be
given to the definition of the various terms. Each approach will predict a
correct value for OTR,.. However, indiscriminate combinations of the two
approaches can lead to gross errors. Also, it has been shown earlier in this
report that application of the SOTR to a compartmentalized system requires
that C be greater than the value that limits the biological uptake rate, R,
in all regions.
Differences between "true" and "apparent" values of alpha and theta --
In the approach based upon the "true" K.a, K.a*, the impact of gas side
oxygen depletion must be considered both in the interpretation of unsteady
state test data and in the field application. However, this approach has the
advantage of dealing with a real volumetric mass transfer coefficient. Con-
sequently, the alpha and theta factors are defined as ratios of mass transfer
coefficients.
The "apparent" K.a approach is simpler in that the impact of gas side
oxygen depletion is automatically reflected in the estimate of KLa. A draw-
back of this approach is that the alpha and theta factors are not represented
as simple ratios of volumetric mass transfer coefficients. By combining
Equation 25 with the definitions of a* and a given in Equations 27 and 33,
it can be shown that:
a
2cf> . - K, a
Td L
32
-------
1 -1
Application of typical values of d = 0.75 min , KLa = 0.15 min , and
typically low values of a = 0.5 and 3 = 0.9 in Equation 49 indicates that the
ratio a*/a would be about 0.94, or that failure to distinguish between a* and
a could result in an error of 6 percent.
A similar development shows that the "true" and "apparent" values of
theta are related by:
e*)(20-T) 2(|)d20 " 9 T KLa20
__ _ _— - -
6 J 2
Again, application of typical values ( = 0.75 min" , KLa = 0.15 min~ ,
T = 1.1, and (f> = 1.02) indicates that (6*/6)5 = 1.0004, or that failure to
distinguish between the true and apparent values of 0 could only account for
0.04 percent error when adjusting over 5°C. The net error introduced by
failure to distinguish between "true" and apparent" values of both a and 6
would, therefore, amount to 6 percent. However, even for a given sample of
wastewater, it is difficult to measure a within an accuracy of 10 percent.
Considering wastewater variability, the accuracy of a "design" value of a
might be ±15 percent. Likewise, the uncertainty involved in values of 0 can
result in substantial errors apart from the failure to distinguish between
910
0* and 6. Values of 9 ranging from 1.020 to 1.030 are commonly employed '
and, over 5°C, would lead to differences of about 5 percent in the prediction
of field transfer rates.
Parameter Estimation
Fitting Equations to Data --
There are three immediate areas of concern when one is faced with the
problem of fitting a mathematical model to a given set of data. The first is
whether the proposed equation does in fact correctly model the system under
study. The second is how to select the "best" estimates of the parameters in
the proposed model. The third is to determine the precision of the computed
11
parameter estimates. Each of these questions has been addressed by Brown
in the context of the analysis of unsteady state oxygen transfer test data.
Excellent introductory treatments of linear least squares theory and
12
application can be found in the texts by Miller and Freund and by Wai pole
33
-------
and Myers.13 More advanced treatments of linear and nonlinear least squares
14 15
are presented in the texts by Draper and Smith, Beck and Arnold, and
Bard. A number of transformation schemes for performing weighted least
squares analysis have been suggested by Davies.
For a review of nonlinear estimation methods, including references and
program sources, refer to Chapters 7 and 8 and Appendix D of the text by Beck
ilir
15
and Arnold. The list of nonlinear programs that follows is taken from
Appendix D of Beck and Arnold.
Nonlinear Estimation Programs
BARD A nonlinear least squares program that uses the Gauss method
(Ref. D3, page 218).
BSOLVE A nonlinear least squares program that uses Marquardt's method
(Ref. D3).
NLIN IBM Share Program SD 3094 written by Marquardt and others.
Written in Fortran IV for IBM 7040. Uses Marquardt's method
with derivatives or finite difference approximations to solve
weighted least squares problems.
NLINA This is a program written at Michigan State University by
J. V. Beck and available from him. It uses the sequential and
Box-Kanemasu modifications of the Gauss method.
SSQMIN This program uses the Powell procedure and is discussed in
Ref. D3.
References (from Beck and Arnold)
Dl Himmelblau, D. M., Process Analysis by Statistical Methods,
John Wiley & Sons, Inc., New York City, 1970.
D2 Bard, Y., Nonlinear Parameter Estimation, Academic Press, Inc.
New York City, 1974.
D3 Kuester, 0. L. and Mize, J. H., Optimization Techniques with
Fortran, McGraw-Hill Book Co., New York City, 1973.
In addition, the computer science and/or statistics departments at most
major universities have general purpose nonlinear estimation programs avail-
able. One that is particularly well documented and suitable for the expo-
nential method is NREG, available from MACC at the University of Wisconsin-
Madison. Also, a nonlinear regression program at Purdue University (SPSS21)
1 g
has been applied to fitting oxygen transfer data.
34
-------
A nonlinear regression program dedicated to Equation 3 has been developed
by the Subgroup on Oxygen Transfer Modelling and Data Interpretation and is
presented in Appendix A of this report. Such a program is attractive because
it is much simpler in scope than the sophisticated general purpose routines
available on large computers. The program is based on modifications of the
19 20
method of Reed and Theriault. This strategy has been used by Marotte,
3 21
Gilbert and Libbey, and Kothandaraman in the analysis of aeration data.
Comparison of Data Analysis Techniques --
A variety of graphical and numerical procedures have been proposed for
the analysis of unsteady state oxygen transfer data. A general review of
these procedures has been given by Brown. They are conveniently grouped
into three categories: the exponential, log deficit, and direct methods.
The methods derive their name from the form of the equation used to fit the
data. The basic oxygen transfer model can be expressed in three forms; first,
the direct of differential form:
f=KLa(C*-C) (.1)
second, the log deficit form:
ln(C* - C) - ln(C* - C ) = - K. a t (2)
* co ' oo 0 L
and third, the exponential or integral form:
C = c* - (C* - Cjexp(- K.a t) (3)
ooxooOL
Exponential method -- The exponential method fits Equation 3 to the
experimental data. The values of DO concentration are used directly and
Equation 3 is fit to the data using nonlinear squares procedures. Boyle et
22 20 23 3
al. use the technique of Marotte and Marquardt and Gilbert and Libby
1 g
the technique proposed by Reed and Theriault for the analysis of first-
order kinetic data. The main advantage of this method is that the computa-
tional procedure provides least squares estimates for all three parameters
without any constraints placed on the data used (truncation) or on assumed
values of the parameters. The parameter estimates are more precise than
those obtained from the other procedures. For efficient calculations,
however, the method requires the use of a computer or advanced scientific
calculator.
35
-------
Log deficit method -- The log deficit method fits Equation 2 to the
experimental data. It has the advantage of being linear in K. a (.allowing
linear least squares to be used for parameter estimation) but requires that a
value of C* be assumed, calculated, or measured to calculate the deficits.
The estimate of K, a will be biased to the extent that C* is selected incor-
L 00
rectly. In the literature, the general concensus is that the measured value
of C when the aeration test is allowed to proceed to equilibrium is the value
2345
of choice for C*. ' ' ' Another disadvantage of the method is that the data
may have to be truncated near saturation to avoid the problem of negative
deficits, which cannot be handled logarithmically. Additional discussion of
the log deficit method is presented early in this section.
Direct method -- The direct method fits Equation 1 to the experimental
data. This method has the advantage of being linear in K.a and of not re-
quiring that a value of C* be specified to do the least squares analysis.
The main disadvantage of the direct method is that it magnifies the noise in
j P
the data. The process of approximating the rate of oxygen transfer, -rr, by
taking differences between successive concentration values results in a
variable that has substantially larger error than the error in C itself.
Even if the original test data are smooth, the scatter in the direct method
2
of analysis is noticeable. This is especially disturbing if the concentra-
24
tion data are noisy because the estimates of K.a are less precise than
with other methods and because it may be necessary to discard substantial
25
portions of the data at both high and low values of C to get a good fit.
Experimental Design
?fi
According to Berthouex and Hunter, parameter estimation is most
efficient if care is taken in selecting the times at which observations of
the dependent variable are made. For models of the type of Equation 3, it
can be shown that the important observations times are zero, 1/K.a, and
infinity. These times correspond to the maximum sensitivity of C , K.a, and
C*, respectively, to the data. Thus, an efficient experimental design should
reflect these sensitivities. The regression analysis with Equation 3,
therefore, should be based on a minimum of 10 to 15 data values. Approxi-
mately two-thirds of these values should be evenly distributed over the time
period of 0/Ki_a to 2/K|_a (or approximately 0 percent saturation to 86 percent
36
-------
saturation; see Table 1). The remaining one-third of the values should be
evenly distributed over the time period 2/KLa to 4/K^a (or 86 percent satura-
tion to 98 percent saturation). If substantial uncertainty exists concerning
the anticipated value of K.a, the test should be conducted for as long a
period of time as possible to insure a length of at least 4/K.a.
Data Truncation and Model Adequacy
Truncation in the Vicinity of Equilibrium --
22
Boyle et al. have shown that truncation increases the correlation
between K.a and C* and reduces the precision of the estimated K.a. The
lm ^^ Lm f\
information in Table 3 obtained by truncating the data of Gilbert and Chen
at various increments of 1/K.a also demonstrates this effect. The log deficit
methods require truncation to avoid negative deficits. Truncation is often
H P
necessary in the direct method because of the difficulty of estimating -rr-
as the rate of transfer approaches zero. Although truncation is generally
necessary with these methods (especially if the data are noisy), it is not
statistically desirable. The exponential method does not require truncation.
Truncation at Low Concentrations --
In the analysis of unsteady state oxygen transfer data, the emphasis is
usually placed on obtaining precise and accurate values of K.a and C*. This
is the case because these parameters are used to compute the standard oxygen
transfer rate, SOTR, which is an indicator of an aeration system's perfor-
22
mance. As has been shown by Boyle et al., data at the beginning of the test
(C < 20 percent of saturation) have negligible effect on the ability to
estimate K.a and C*. Thus, it would seem that data in this vicinity are not
important.
This is not strictly true, however. Data values in the low concentration
range are important in determining whether Equation 3 is an adequate model
to describe oxygen transfer. In the development of Equation 3, it was assumed
that the constant C* could be used in place of the time varying saturation
value C*. While this assumption is not unreasonable for many surface and
subsurface aeration systems, it may not be valid in aeration systems where
oxygen transfer is rapid and there is an appreciable gas side oxygen deple-
tion. The effect of gas side depletion, with the resultant lowering of C*,
37
-------
TABLE 3. EFFECT OF DATA TRUNCATION OF THE PRECISION OF PARAMETER
ESTIMATION DATA OF GILBERT AND CHEN2 USING EQUATION 3
CO
CO
Time of
Truncation
6/KLa
5/KLa
4/KLa
3/KLa
2/KLa
l/KLa
Least Squares
Estimate
(hr'1)
12.05
12.05
12.07
12.13
12.32
13.65
KLa
Standard
Deviation
(hr'1)
0.11
0.12
0.16
0.26
0.54
3.91
Rel. Std.
Deviation
(%)
0.9
1.0
1.4
2.1
4.3
28.7
Least Squares
Estimate
(mg/£)
10.39
10.39
10.38
10.37
10.30
9.75
C*
°00
Standard
Deviation
(mg/£)
0.01
0.02
0.03
0.06
0.15
1.39
Rel. Std.
Deviation
(%)
0.1
0.2
0.3
0.5
1.4
14.3
Correlation
Between
K, a and C*
L °°
-0.71
-0.75
-0.83
-0.90
-0.96
-0.99
-------
is most pronounced at low concentration values. Thus, observations at low DO
concentrations provide information for tests of model adequacy and should not
be truncated arbitrarily. On the other hand, DO values at the beginning of
the test may have to be discarded if a lingering effect of the deoxygenation
technique is known to exist. It should be noted that Equation 3 has been
found to adequately describe unsteady state oxygen transfer data from a great
majority of aeration devices, both surface and subsurface, commonly employed
in wastewater treatment operations.
Error Structure of Oxygen Transfer Data --
All three methods of data analysis have difficulties with the error
structure of the dependent variable. In the exponential method, the error
in the DO concentration may decrease as the concentration increases. In the
log deficit method, the error in the DO deficit increases as the deficit
decreases. In the direct method, the overall errors in the oxygen transfer
rate are high and the magnitude of the error increases as the transfer rate
increases. These observations suggest that a weighted regression analysis is
required to account for the nonconstant error distribution. The variable
transformation strategies of Davies have been applied to a limited set of
2
data. The transformations employed appear to have improved the error struc-
ture of the dependent variable. However, the results also indicated that the
least squares estimates and their precision were not markedly affected by the
transformations.
EXAMPLE DATA ANALYSIS
The following example* illustrates the recommended method for analyzing
clean water unsteady state oxygen transfer test data. Acceptable alternate
methods are also illustrated.
Test Description
A clean water field test was conducted on a coarse bubble submerged
aeration system installed in a 43-ft diameter circular tank. Test conditions
and data are given below:
*Test data supplied by Sanitaire, Water Pollution Control Corporation,
Milwaukee, Wisconsin.
39
-------
Average water temperature: 14.5°C
Local barometer: 28.88 in. Hg = 14.19 psi
Tank depth: 20.2 ft
Diffuser submergence: 18.2 ft
Air rate: 903.5 scfm (based on 1.00 atm., 20.0°C,
and 0.0 percent relative
humidity)
Tank Volume: 29,300 ft3 = 8.298 x 105£
For convenience of illustration, the data were obtained by averaging the
DO concentrations recorded from four properly located probes. (.Note: It is
recommended that, in practice, data from individual sample or probe locations
be analyzed separately and that the resulting values of K.a and C* be
averaged.) Each probe was equipped with a digital readout that recorded the
DO concentration at 15-sec intervals over the 60-min test duration. Eighteen
data values given in columns 1 and 2 of Table 4 were selected for analysis.
The value of K.a was roughly estimated to be 0.09 min" , resulting in a value
of 2/K.a of approximately 22 min. Roughly two-thirds of the data values
(11 points) were chosen at uniform intervals over the first 22 min and the
remaining seven data values were selected at uniform intervals over the period
covered by 2/K.a to 5/K,a (22 min to 55 min). A plot of these data (.Figure 3)
indicates that no anomolous values are present and that low-range truncation
is not necessary.
Recommended Parameter Estimation Method
These data were analyzed by the nonlinear least squares Fortran program
described in Appendix A, with the following initial parameter estimates:
CQ = 0.2 mg/£ C* = 11.4 mg/£ KLa = 0.1 min"1
The resulting best fit parameter estimates and standard deviations were:
Parameter" CQ C* KLa
Best fit estimate 1.12mg/£ 11.43mg/£ 0.0869 min"1
Standard deviation 0.0377 mg/£ 0.0182 mg/£ 0.00064 min"1
The DO concentrations predicted by the model are given in column 3 and
the residuals are given in column 4 of Table 4. Although some "trending" is
evident in the residuals, their values are small and the estimated error at
0.03 mg/£ is roughly equal to the experimental error involved in a single
40
-------
TABLE 4. CLEAN WATER TEST DATA*
Measured Predicted
Time DO DO
(min) (mg/£) (mg/£)
2.0 2.77 2.77
4.0 4.15 4.15
6.0 i
5.35 5.31
8.0 6.25 6.29
10.0 1
LQB 7.00
12.0 7.80 7.80
14.0 8.34 8.37
16.0 8.85 8.86
18.0 9.28 9.27
20.0 9.62 9.61
22.0 9.93 9.90
25.0 10.24 10.25
30.0 10.70 10.67
35.0 11
40.0 11
45.0 11
50.0 11
55.0 11
.00 10.93
.14 11.11
.20 11.22
.25 11.29
.30 11.34
Residual
(mg/£)
0.00
0.00
+0.04
-0.04
-0.03
0.00
-0.03
-0.01
+0.01
+0.01
+0.03
-0.01
+0.03
+0.07
+0.03
-0.02
-0.04
-0.04
*Residual sum of squares (RSS) = 0.01617 (mg/£)2
Degrees of freedom (df) = 18 - 3 = 15
F<:tirmtpH prrnr - C^ - fO'01617| * _ n no — //>
LdLiiiiaucu ciiur j
C
f - 15 - u.WJ n,a/<.
41
-------
0»
E
LJ
10
8
ro
z2 2.
0 TO 2/KLd —
11 DATA POINTS
•2/KLo TO 5/KLa
7 DATA POINTS
10 15 20 25
TIME (min)
30
35
40
45
Figure 3. Clean water test data.
-------
DO measurement. For example: If a single probe can measure DO to within
0.05 mg/£, the error in the average of four probe values would be
(0.05 mg/£)//4 = 0.025 mg/£. On this basis, it can be concluded that the
data are adequately described by the model.
The standard deviations of the parameter estimates are small and indi-
cate excellent precision. For K.a, the standard deviation is only 0.73 per-
cent of the best fit estimate. A suggested criterion for shop test
acceptability is that the standard deviation of K.a be less than 5 percent
of the best fit estimate.
Recommended Method: Calculation of SOTR Values Based on K.a
(20-T)
K . _ K .
KLa20 ~ KLaT
KLa2Q = 0.0869 min"1 (1 .
KLa2Q = 0.0990 min"1
Determine effective saturation depth. Based on Henry's Law at 14.5°C,
1.00 atm., and 100 percent relative humidity:
H =
10.26 mg/£
Yair(Ps - PvT) " 0.21(14.696 psi - 0.24 psi)
H = 3.380^
Effective saturation depth, d , at infinite time in an unsteady state test
is defined by:
C-T-»Ya1r(Pb+Ve- pvT>
d = -
e Y,
w
C*
ooj
H -
e " 0.433 psi/ft
3.380
11 •"•"/* - 14.19 psi + 0.24 PS1
psi x '
. = 4.97 ft
43
-------
Thus, the estimated C* of 11.43 mg/£ corresponds to oxygen saturation at a
depth of 24.6 percent of the tank depth.
Determine C* at 20.0°C and a barometric pressure of 1.00 atm.:
c*
s20
\20
C*20
v20
11 A* mn//f 9-17 mg/£l[14.696 psi + (0.433 ps1/ft)(4.97 ft) - 0.34 psi
y/ [10.26 mg/£J I 14.19 psi + (0.433 psi/ft R4.97 ft) - 0.34 psi
= 10.54
Finally, the SOTR is given by:
SOTR = K. a9nC* V
L 20 °o20
= 0.0990 min"1(10.54 mg/£)(8.298 x
60 min/nr
53.6 x KTmg/lbj
SOTR = 114.5 Ib/hr
Recommended Method: Application of Clean Hater Test
Data to Dirty Water Respiring Systems
The following calculations illustrate how the clean water SOTR deter-
mined above is related to an actual dirty water oxygen transfer rate, OTRf,
in a respiring system for given values of a, g, temperature, 0, DO concen-
tration, barometric pressure, and geometry.
Given: a = 0.8, 3 = 0.9, C = 2 mg/£, T = 15°C, pfa = 28.5 in. Hg
= 14.30 psi, 6 = 1.024, submergence = 18.2 ft
Approach Based on "Apparent" K.a --
where:
o -
it —
Pb"
PS '
OTRf =
cn(SOTR)6 '
c*20
^T-QO C"^
\ L pi 6 U ^or*
oo^(J
h Ve - pv20
h Ve - Pv20
0
44
-------
14.30 psi + (0.433 psi/ft)(4.97 ft) - 0.34 psi
"14.696 psi + (0.433 ps1/ft)(4.97 ft) - 0.34 psi
= 0.976
C c*
sT _ 10.15 _ , 1Q69
9-17
OTRf .
2.0 mg/
OTRf = 63.7 Ib/hr
Alternate Method: Calculation of SOTR Value Based on
K.a Corrected for Gas Side Oxygen Depletion
This approach recognizes that, because of oxygen depletion in the rising
air stream, the "true" value of the volumetric mass transfer coefficient,
K.a*, is somewhat larger than the value of K.a. The calculation is straight-
forward but is complicated by the fact that the values of a and 6 are usually
given as ratios of K.a values and must be adjusted before applying them to
K.a* values.
First, the value of the oxygenation coefficient, A., is calculated:
rM_]
A Yair
32Q7(0.0753 Ib/ft3)(903.5 ft3/min)(0.21
. y /
_
11.43 mg/£(10"3 g/mgH- lb/g)(8.298 x 105£)
<|>. = 0.7547 min"1 at 14.5°C
d
The oxygen transfer efficiency, OTE , at zero DO is given by:
K a • -1
OTE = -±- = °'0869 mln , = 0.1151 or 11.51 percent at 14.5°C
0 ^H 0.7547 min"1
45
-------
The value of the "true" KLa, KLa*, is calculated from the "apparent" K.a by:
or
1 -
OTE.
1 -
0.0869 min
-1
1 -
0.0869 min"1
2(0.7547)min"1
= 0.0922 min"1 at 14.5°C
It can be shown by combining the definition of 9* and e with the rela-
tionship between KLa* and K.a given above, that:
e
10.26 mg/l
9.17 mg/£
_
" KLaT
- 9t20~T)KLaT
2(0.7547 min"1) - 0.0869 min"1
.0245'5(0.0869 min"1)
e* 15.5
1.024
= 1.0010
0* = 1.0242
KLa* is corrected to 20°C by:
KLa*Q = KLa*9*
(20-T)
KLa*Q = 0.0922 min"1(1.0242)5'5 = 0.10516 min"1
Note that the difference between 9* and 9 is small. Greater differences will
occur at larger values of OTE .
o
46
-------
The SOTR value is given by:
SOTR
KLa20Fo C~20V
where F is the exit gas depletion factor at zero DO and:
At 20°C:
KL320
or
fr*
^14.5
Hdl4.5
C*
20
OTE,
F = 1 -
c*
L
sl4.5
f*
0
s20
' °'7547
- 0-8444
0.0990 ml
0 ^20 0.8444 min
F .
0
°-0990 "1
2(0.8444 min"1)
= 0.9414
SOTR = 0.10516 min"1(0.9414)(10.54 mg/£)(8.298 x 105£)
60 min/hr
453.6 x 10° mg/lbj
SOTR = 114.5 Ib/hr
This is identical (within rounding error) to the SOTR determined directly
from K,a (page 44).
Alternate Method: Application of Clean Water
Test Data to Dirty Water Respiring Systems
Given: a = 0.8, 3 = 0.9, C = 2 mg/£, T = 15°C, 6 = 1.024, submergence
18.2 ft
47
-------
Approach Based on "True" K.a, K.a* --
_ a*(SOTR)e*(T"20)|
F r*
^o °°20
Here again, the values of a and 6 are defined in terms of K.a ratios and must
be adjusted before applying them as a* and 9* to K.a* values. Combining the
definitions of 6* and 6 with the relationship between K.a* and K.a yields:
(20-T) ,. flll
" KLa20
0V)5 2(0.8444 min"1) - 1.024"5(1g-1^ ^f] (0.0990 min"1)
2(0.8444 min"1) - 0.0990 min"1
1.5915
K5898 min"1
6* = 1.0242
Note that the computing equation used here is equivalent to that given on
page 46 except that it is based on 20°C values for convenience.
Combining the definitions of a* and a with the relationship between f
and K, a gives:
L * 2. - K.a
a* _ Yd L
ct 2cf> . •
Evaluating this equation at 20°C:
a*. = 2(0.8444 min"1) - 0.0990 min"1
a 2(0.8444 min"1) - 0.8(0.9)(0.0990 min"1)
~ = 0.9829
48
-------
a* = 0.9829(0.8) = 0.7863
The difference between a* and a is small here. Greater differences will occur
for systems with high values of OTE and low values of a.
F = 0.9414, from page 47
The exit gas depletion factor under operating conditions, F, i,s evaluated by:
C*2Q - C)
"
0. 8(0. 8882)(0. 0990 min"1 )[1 .1069(0. 9)(0. 976)(10. 54 mg/l) - 2 mg/£]
2(0.8444 min"1)(10.54 mg/£)
F = 0.9674
Note that a trial and error procedure is avoided here by making use of the
known value of K.a. Finally, OTRf, is evaluated as:
- C)
C*
OTRf ' rtfi&fi^^
4(10.54 mg/£) J
- 2 mg/£]
OTRf = 63.7 Ib/hr
which is equivalent within rounding error, to the result given on page 45.
Alternate Parameter Estimation Procedure: Best Fit Log Deficit Method
In cases where the lack of a suitable computing facility prevents appli-
cation of the recommended nonlinear least squares method, acceptable results
may be obtained by adapting the log deficit method to estimate both K,a and
C* by trial and error. This can be performed with the aid of a hand calcula-
tor programmed to do linear regression.
49
-------
The model, expressed in linear form is:
ln5 = 11.55mg/£
KLa14 5 = °-0835 m1n"1
Following the method outlined on page 47, the SOTR is evaluated as
111.3 Ib/hr, roughly 3 percent lower than the 114.5 Ib/hr based on the non-
linear least squares procedure. This difference is caused by
1. the logarithmic transformation required for the linear regression and
2. the elimination of four data points near C* in the Best Fit Log
Deficit Method.
50
-------
TABLE 5. APPLICATION OF BEST FIT LOG DEFICIT METHOD
Time Measured DO
(min) (mg/£)
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.9
20.0
25.0
30.0
35.0
Covariance
Correlation
K.a(min~ )
2.77
4.15
5.35
6.25
7.08
7.80
8.34
8.85
9.28
9.93
10.24
10.70
11.00
coefficient
ln(li
Measured
2.167
1.995
1.816
1.658
1.486
1.308
1.151
0.975
0.798
0.451
0.231
-0.223
-0.693
o
1.50 - C)
Predicted
2.171
2.000
1.828
1.656
1.485
1.313
1.142
0.970
0.798
0.455
0.198
-0.231
-0.660
-7.683684
-0.9998587
0.085802
i
ln(11.55 - C)
Measured
2.172
2.001
1.825
1.668
1.497
1.322
1.166
0.993
0.820
0.482
0.270
-0.163
-0.598
-7.
-0.
0.
Predicted
2.165
1.998
1.831
1.664
1.497
1.330
1.163
0.996
0.829
0.495
0.245
-0.172
-0.590
474990
9999277
083472
*\
Residual sum of squares (mg/£)'
2.622 x 10
1.258 x 10
51
-------
CM
!« 18
te
'^ 16
O
OL 14
O
U_
UJ
O
12
g 10
o
UJ
CE
fe 4
I0"
ui
QL
BEST
ESTIMATE
.55 mg/t
11.4
11.5
11.6
11.7
Figure 4. Relationship between estimated values
of C* and residual sum of squares.
52
-------
e
o
I
-------
7. Baillod, C.R. , "Review of Oxygen Transfer Model Refinements and Data
Interpretation," Proceedings, Workshop Toward an Oxygen Transfer Standard
EPA 600 9/78-021, pp. 17-27, April 1979.
8. Downing, A.A. and A.G. Boon, "Oxygen Transfer in the Activated-Sludge
Process," In: Advances in Biological Waste Treatment, Ed. by W.W.
Eckenfelder, Jr. and B.J. McCabe, Pergamon Press, New York City, p. 131,
1963.
9. Eckenfelder, W.W., Jr. and D.J. O'Connor, Biological Waste Treatment,
Pergamon Press, New York City, 1961.
10. Gilbert, R.G., "Measurement of Alpha and Beta Factors," Proceedings,
Workshop Toward an Oxygen Transfer Standard, EPA-600-9/78-021, pp. 147-
162, April 1979.
11. Brown, L.C., "Oxygen Transfer Parameter Estimation, "Proceedings, Work-
shop Toward an Oxygen Transfer Standard, EPA-600-9/78-021, pp. 27-41,
April 1979.
12. Miller, I. and J.E. Freund, Probability and Statistics for Engineers,
2nd Edition, Prentice-Hall, 1977.
13. Walpole, R.E. and R.H. Meyers, Probability and Statistics for Engineers
and Scientists, 2nd Edition, MacMillan, 1978.
14. Draper, N.R. and H. Smith, Applied Regression Analysis, John Wiley and
Sons, New York City, 1966.
15. Beck J.V. and K.J. Arnold, Parameter Estimation in Engineering and
Science, John Wiley and Sons, New York City, 1977.
16. Bard, Y., Nonlinear Parameter Estimation, Academic Press, Inc., New York
City, 1974.
17. Davies O.L., Ed., Design and Analysis of Industrial Experiments, 2nd
Edition, Hafner, 1967.
18. Daigger, G.T., M.D. McGill, and C.P.L. Grady, Jr., Discussion of
"Experiences in Evaluating and Specifying Aeration Equipment," by
J.R. Stukenberg, V.N. Wabeh, and R.E. McKinney, Journal WPCF, 50:784-787,
April 1978.
19. Reed, L.J. and E.J. Theriault, "The Statistical Treatment of Reaction-
Velocity Data II. Least Squares Treatment of the Unmolecular Expression:
Y = L(l - e-kt)," Journal of Physical Chemistry, 35:950-973, 1931.
20. Marotte, F.K., "Specifications for the Purchase of Mechanical Aeration
Equipment," CH2M Hill, Inc., Consulting Engineerings, Bellevue,
Washington, September 1977.
21. Kothadaraman, V., "Effects of Contaminants of Reaeration Rates in River
Water," Proceedings of the 25th Industrial Waste Conference, Purdue
University, pp. 494-511, May 1970.
22. Boyle, W.C., P.M. Berthouex, and T.C. Rooney, "Pitfalls in. Parameter
Estimation for Oxygen Transfer Data," Journal of the Environmental
Engineering Division, ASCE, 100(EE2):391-408, April 1974.
54
-------
23. Marquardt, D.W., "An Algorithm for Least Squares Estimation of Nonlinear
Parameters," Journal of the Society for Industrial and Applied Mathe-
matics, 11(2):431-441, June 1963.
24. Stukenberg, J.R., V.N. Wahbeh, and R.E. McKinney, "Experiences in
Evaluating and Specifying Aeration Equipment," Journal WPCF, 49:66-82,
January 1977.
25. Stanton, J.L. and P.R. Bradley, "Experimental Evaluation of Sub-Surface
Aeration Systems," Proceedings of the 30th Industrial Waste Conference,
Purdue University, pp. 826-840, 1975.
26. Berthouex, P.M. and W.G. Hunter, "Problems Associated with Planning BOD
Experiments," Journal of the Sanitary Engineering Division, ASCE,
97(SAE):333-334, June 1971.
55
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SECTION 5
UNSTEADY STATE CLEAN WATER TEST
INTRODUCTION
The initial goal of the Subgroup on Unsteady State Clean Water Oxygen
Transfer Testing was to develop an unsteady state clean water test procedure.
After 2 yr of study and deliberation, it became clear that significant uncer-
tainty exists in several areas of the test procedure that cannot be readily
resolved or agreed upon. Some areas require additional study, and some
uncertainties are due to varied experiences in extensive testing programs.
This section includes a Procedural Description subsection that can serve
as a basis or guideline for preparing oxygen transfer testing specifications.
It can also be used by owners, consultants, and manufacturers in evaluating
oxygen transfer performance studies. The material presented in the Discussion
subsection and in other areas of the project report can be utilized to com-
plete the preparation of a testing and evaluation procedure. It is intended
that this procedure be applicable to shop and field testing.
The procedure focuses on obtaining oxygen supply and transfer rate data.
Detailed considerations of gas flow and power measurements, tank geometry and
mixing, and modelling and data interpretation are presented in separate
sections of the project report. Some requirements in these areas are
included to provide a more complete procedural description and indicate where
these topics are incorporated into the procedure.
To reach a reasonable degree of consensus, various options, alternative
methods, and ranges of numerical criteria were cited, e.g., alternative
dissolved oxygen (DO) analyses and cobalt levels. In some cases, e.g., water
chemistry, analytical requirements are cited without numerical limits. This
indicates an area of concern, and numerical limits may be cited for these
parameters in the future.
56
-------
An alternative or supplemental "clean water plus detergent" procedure
was included. This was done in recognition of European practice in an attempt
to possibly resolve chemical interference uncertainties and to provide a test
procedure that would demonstrate differences in performance of different
types of aeration devices (clean water versus clean water plus detergent). It
has also been noted that tests with detergent added may more closely simulate
wastewater performance. There is limited experience with this test procedure
in the United States at present. The procedure needs further development and
experience, but is included for the practical reasons noted above.
Following the Procedural Description, a multi-component Discussion
subsection is presented. Typical existing approaches of consultants and manu-
facturers and committee/organization procedures have been published by the
Water Pollution Control Federation, the American Public Health Association in
2 3
Standard Methods, and the Process Equipment Manufacturer's Association.
Outside the United States, Germany and Austria have also published testing
procedures and the Ontario Ministry of the Environment has developed a pro-
5
cedure for mechanical aerator testing.
Recommendations for additional study and procedural development are
cited. A selected reference listing of publications is also presented.
PROCEDURAL DESCRIPTION
Advance Preparations and Responsibilities
Where field testing will be conducted, the engineer-owner-manufacturer
(EOM) representatives should exchange information to assure that proper test
conditions will exist for the oxygen transfer evaluation. The engineer-owner
representatives should provide the manufacturer with detailed drawings and
specifications of the tank or tank section in which the test will be con-
ducted. Information on the water supply source and available water chemistry
data should be provided. Water samples should be made available to the manu-
facturer for laboratory experiments regarding the chemical additions that will
be made.
Once the installation of aeration equipment is completed, provision
should be made for EOM representatives to inspect the installation to verify
placement and testing conditions. Systems employing diffused air aeration
57
-------
should be tested to eliminate any leaks. Provisions for power and air flow
measurements should be verified and modifications made as needed. It may be
necessary to install equipment such as meters for power measurement, supple-
mental air piping, orifice plates, and manometers. This should be done in
advance of the oxygen transfer test.
The owner and contractor should provide the equivalent of a public water
supply, a ground water supply, or a treated surface water. Upon completion of
the installation of the aeration equipment, the test tank should be cleaned
prior to filling for testing. Once the tank is filled with the test water,
chemical and biological, e.g., algae, contamination should be avoided. It
may be necessary to dewater and re-fill the test tank during testing, and
adequate pumping and discharge arrangements should be made.
Test Tank Geometry and Aerator Placement
It is difficult to describe a required geometry or placement for testing
conducted in tanks other than the full-scale facility. Appropriate configu-
rations for a particular application should simulate the field conditions as
closely as possible. Water depths should be similar if not identical, and
interferences due to wall effects and any extraneous piping or other materials
in the tank should be minimized. The density of aerator placement, air flow
per unit volume or area, and power input per unit volume are examples of para-
meters that can be used to assist in making comparative evaluations.
Consideration should be given to utilization of shop testing or testing
of tank sections when full-scale facilities are very large, e.g., in excess
of 1 mil gal. Considerations of distribution of deoxygenation chemicals and
reasonable sampling requirements are criteria that can be considered in
making the judgement.
Some specific requirements for aerator placement and tank geometry are
described in the section on Geometry, Scale-Up, and Mixing. Minimum dimen-
sions for diffused aeration test tanks are cited. Testing of multiple
mechanical aerators is also described.
Air Flow Rate and Power Evaluations
Diffused aeration --
The air flow rate must be accurately and precisely determined using
58
-------
accepted procedures. Two recommended references for procedural assistance
are Spink, L. K., Principles and Practices of Flow Meter Engineering, and
Cusick, C. F., Flow Meter Engineering Handbook (see Section 9).
A full-scale air flow measurement system should be used with caution
when testing in portions of the plant capacity. The precision or accuracy
of the measurement device may not be adequate for test flow rates. Estimating
air flow rates to part of the plant by volumetric or area served ratios
could be used as a check but not for the primary air flow test information.
Where flow measurement equipment must be provided, calibrated orifice
plate systems, venturi tube systems, and pitot traversing methods, e.g., the
Annubar method, are recommended procedures. A precision of ± 5 percent is
recommended. It is desirable to provide a back-up or supplemental measurement
system as a check.
The air flow measurement system should be installed to avoid any poten-
tial pulsation effects from blowers. EOM representatives should establish an
allowable variation in air flow rate during a specific test run.
Data that should be obtained to relate the measured air flow to standard
conditions include in-line pressure and temperature, barometric pressure,
ambient temperature, and relative humidity. Standard conditions for air flow
are defined as 68°F (20°C), 14.70 psia U atm.j, and 36 percent relative
humidity.
When diffused aeration performance is based on power, required pressure
measurements should be made to enable the calculation of the power required.
Adiabatic and polytropic compression formulae can be used to make the calcu-
lation. Blower power measurements may be used if the total air supplied is
employed in the testing,
Mechanical aeration --
The power requirements for the oxygen transfer performance test should
be determined by procedures approved by EOM representatives. It is recom-
mended that recording polyphase watt meters be utilized to determine the total
power input of all aeration equipment. The watt meters should have a high
degree of accuracy and be capable of monitoring 10 cycles/sec peaks. Strain
gages and/or torque pickups may also be used to determine power requirements.
The equipment should be installed to minimize the measurement of power
59
-------
requirements other than those of the aeration equipment. EOM representatives
should establish appropriate efficiencies of conversion between brake and line
horsepower when needed.
EOM representatives should establish allowable liquid level variations
during a test run.
Detailed discussions of air flow measurement and power measurement are
presented in Sections 9 and 10, respectively.
Initial Water Quality
The initial test water should be equivalent to a public water supply,
either a ground water source or a treated surface water supply. (A discussion
of the relationship of Drinking Water Standards water quality to that for
oxygen transfer testing is presented in the following Discussion subsection.)
It is desirable that the water temperature be near 20°C. The temperature
should be in the 10 to 30°C range. Testing at low temperatures will result
in uncertainties of chemical reactions, especially in the deoxygenation
process. Testing outside the range may be necessary in some field conditions
and can be conducted with the approval of the EOM representatives. The
recommended temperature correction value (theta) is 1.024. (A discussion of
the variability of theta correction values is presented in Section 6.) The
test water temperature should not change more than 2°C during a reaeration
period.
Various physical and chemical constituents have been cited as interfering
with or affecting the unsteady state test and/or the analysis of DO by the
Winkler or membrane probe procedures. Prior to starting the testing program,
a representative sample of the water to be used in the test tank should be
analyzed for total dissolved solids (TDS), alkalinity, sulfate, iron, manga-
nese, residual chlorine, pH, total organic carbon or chemical oxygen demand,
cobalt, surfactant, and temperature.
EOM representatives should review these results to determine areas of
potential effect on the testing program. Procedural criteria regarding
limiting TDS or sulfate concentrations, pH effects, cobalt levels, inter-
ferences with Winkler or membrane DO testing, and interferences with the
oxygen transfer rate should be established.
The initial water chemistry may indicate a need for modifying a limiting
60
-------
TDS level, adjusting pH, using a blank in Winkler testing, stripping chlorine
initially, or other changes in the testing criteria. The analysis would also
provide a baseline for comparison with the water quality after chemical
additions during deoxygenation.
Normally, no modifications of test water quality are made for "clean
water only" testing. However, it may be that, due to a particular set of
field conditions, a surface water may have to be treated. Demonstrated oxygen
transfer rate effects due to water chemistry differences between the field
conditions and the prior test data used to predict the field performance may
be considered in agreeing upon any water quality modifications.
An alternate procedure involving the addition of anionic detergents is
described at the end of the Procedural Description subsection. Where this
testing method is used, initial surface tension measurements should also be
considered.
Deoxygenation Chemicals
Nitrogen stripping of the oxygen in the test water is one alternative
deoxygenation method. It is a widely-used laboratory and pilot plant proce-
dure, but it is not normally specified in full-scale or field testing. Some
concern exists regarding the effect of nitrogen concentration during the early
portion of the reaeration period and the practicality of nitrogen stripping
on a large scale.
Technical grade sodium sulfite (NapSO,) is the recommended chemical for
deoxygenation. The sulfite should be essentially cobalt free and contain no
impurities that would alter the oxygen transfer rate analysis. Sulfite, with
cobalt present, could be used where a range of cobalt concentrations are
permitted and the limiting cobalt concentration is not exceeded.
The sulfite should be evaluated for impurities and potential interference
in oxygen uptake evaluations. This can be done by chemical analysis of the
supplied chemical and by comparative laboratory oxygen transfer rate analysis.
Oxygen transfer rates using the supplied technical grade sulfite can be
compared against analytical grade sulfite deoxygenation and nitrogen stripping
deoxygenation methods. (A typical procedure is described in the Discussion
subsection.)
Sodium sulfite is normally added in solution or slurry form. It is
61
-------
preferred that the sulfite be essentially dissolved in a separate mixing tank
prior to its addition to the test tank. Saturated solutions contain 2.23 lb/
gal at 20°C and 3.00 Ib/gal at 30°C.
The sulfite deoxygenation reaction is catalyzed by cobalt. The cobalt
source utilized should be cobalt chloride or cobalt sulfate, reagent grade.
The cobalt should be dissolved prior to its addition to the test tank.
Caution should be observed in obtaining complete solution of the cobalt when
it is added in the sulfate form.
System Stability
The volume of water under aeration should be held constant for the test
series unless it must be changed to meet different load conditions for a
mechanical aerator. It may be necessary to set an allowable liquid level
tolerance during a run.
The aeration system should be operated to achieve steady state conditions
prior to starting the oxygen transfer evaluation. The hydraulic mixing regime
should be established in the test tank for each test condition prior to deoxy-
genation. A steady power draw has been used to determine steady state for
mechanical aerators. Some aerators require 30 to 40 min to achieve steady
state.
For diffused air systems, water must be displaced from the aeration
system prior to beginning the test. Steady manometer readings for orifice
flow measurements and consistent air flow rate measurements for other flow
measurement devices are indicative of this displacement. Lines with valves
for purging water from the aeration system may be added for testing purposes.
Initial Run
It is recommended that the initial test run conducted for each filling
of the test tank not be used as part of the compliance procedure. It should
be used to verify test procedures including sulfite dispersion, sampling
techniques, data recordings, etc. It would also provide an opportunity to
check on chemical reactions, interferences, and DO probe calibrations and
verify adequate residual cobalt, etc. It is frequently reported that chemical
and testing uncertainties have occurred during the first test run.
62
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Chemical Addition for Deoxygenation
The cobalt solution should be added prior to the beginning of oxygen
transfer testing with the aeration system operating. The solution should be
uniformly distributed into the test tank. Pumps and distribution systems may
be required for large tanks. The cobalt solution should be dispersed through-
out the tank by operating the aeration system for approximately 30 min. The
cobalt catalyst should normally be added once for each test water.
It is recommended that a concentration of from 0.10 to 0.50 mg/£ of
cobalt (as Co) be maintained in the test water. If a higher cobalt concentra-
tion is required due to low temperature (less than 10°C) testing or for other
test conditions, analytical precautions due to potential Winkler titration
interference should be observed.
Testing conditions, e.g., with detergent added, or oxygen transfer rate
results that indicate an inadequate catalyst concentration may require supple-
mental additions of cobalt. Cobalt analysis should be conducted on the test
water to assist in this evaluation.
The sodium sulfite solution is then added to deoxygenate the water. It
is recommended that sodium sulfite be dissolved in mixing tanks outside the
test tank and distributed uniformly and rapidly (in less than 3 to 4 min)
into the tank. The use of pumps and flexible piping to distribute the solu-
tion across the tank surface is recommended. Testing conditions may prevent
achieving a perfect'sulfite solution prior to the addition. Addition in a
slurry form is preferred over the direct addition in a crystal form. Extreme
care should be exercised to assure adequate dispersion and dissolution in the
test tank.
The theoretical requirement for deoxygenation is 7.88 mg/£. of sulfite
(as Na2S03) per 1.0 mg/£ DO concentration. Sulfite additions are made in
excess of stoichiometric amounts. The amount of excess is dependent on the
oxygen transfer rate of the aeration system and the size of the test tank.
The amount of excess varies from 20 to 25 percent for high transfer rate
systems. (See Discussion subsection for typical calculation.)
Sufficient sulfite solution should be added to depress the DO level
below 0.50 mg/£ at all sample points. It should be noted that consistent
repetitive testing results have been observed where the DO concentration has
63
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reached zero at all sample points and remained at zero for at least 2 min.
Results from the initial test run can be used to help establish the proper
quantity to be added.
Water Quality Monitoring During Testing
The test water quality should be reported for all testing programs. The
initial water quality analysis cited earlier will provide a base water
chemistry. The following parameters should be evaluated, but not necessarily
for each run: iron, manganese, residual chlorine, surfactant, and TOC or COD.
This analysis is related to potential interferences that may result from
multiple sulfite additions and/or contamination from adjacent operations at a
field test site.
The following parameters should be evaluated for each run: temperature,
TDS, cobalt, and pH. An analysis should also be performed for unreacted
sulfite, especially where non-uniform oxygen response data are noted during a
run. Unreacted sulfite could be present due to inadequate dispersion or
dissolution, inadequate cobalt concentration, and/or low temperature Csay
less than 10°C) reaction limitations. The sulfite ion concentration may be
determined analytically. In addition, multiple samples may be obtained and
analyzed at constant temperature to determine if there was a DO depletion
with respect to time in the samples. A significant DO depletion would indi-
cate the presence of unreacted sulfite in the test water at the time of
sampling.
The cobalt concentration normally should not change during testing.
Slight decreases have been observed in some testing. If the concentration
falls below 0.10 mg/£, additional cobalt may be needed to assure adequate
oxidation of the sodium sulfite solution.
It has been reported that high TDS levels, in the 1500 to 2000 mg/£
range, have affected oxygen transfer measurements. It is recommended that
each volume of water can be used for repetitive testing until the TDS concen-
tration reaches 1500 mg/£. Where high (say greater than 500 mg/£) TDS levels
are initially present, the limiting level may be raised. It is recommended
here that the increase in TDS level be limited to approximately 1500 mg/£.
In these cases, repetitive testing at high and low levels should be conducted
to evaluate any effects on the transfer rates.
64
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In some testing with Winkler DO titrations, pH variations have affected
the measured oxygen transfer rate. It has been recommended that the pH be
controlled at 6.9. Other studies have not observed an effect of pH on oxygen
transfer rates in the 6.5 to 9.5 range. A pH limit cannot be recommended at
this time; however, the potential for uncertainty in results especially with
Winkler titrations should be noted.
When the cobalt analysis cannot be readily made onsite in field testing,
samples should be filtered (glass fiber paper) and analyzed at a later time.
This is permissible if no water quality-related problems appear to be evident.
The cobalt addition should be carefully and accurately made.
When detergent-added testing is conducted, analysis for anionic surfact-
ant concentration and surface tension should be made for each run. Due to
reported variations in concentrations with time, multiple sampling should be
considered. Allowing a 20- to 30-min delay prior to deoxygenation may help to
stabilize the concentrations.
Sampling
The number and location of sampling points will be dictated by the size
of the test tank, aerator placement, and mixing pattern in the tank. The
sampling locations should be selected to represent regions of variable DO and
be geometrically distributed vertically and horizontally to best represent the
tank contents. If the results of multiple sample points are to be analyzed
by a simple average, the sample locations should be chosen so that each
senses an equal portion of the tank volume.
It is recommended that a minimum of four sample points be used. One
point should be at mid-depth, one at a shallow depth (.greater than 2 ft below
the surface), and one at a deep location (.greater than 2 ft above the floor).
It is suggested that sample points be at least 2 ft from walls and floors.
They should be no closer to a surface than 10 percent of the depth or the
length or width (smaller of the two dimensions) of the test tank. A greater
number of sample points is desirable and needed for large complex aeration
systems.
Two widely-used DO measurement techniques are recommended. The first
procedure is the use of DO probes located at the sample points in the test
tank. Data are obtained by directly reading DO meters and/or continuously
65
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recording the DO via a strip-chart or digital recorder. A submersible pump
and/or Kemmerer sampler should be used to obtain discrete samples for calibra-
tion checks and water chemistry analysis.
The second sampling procedure consists of continuously pumping samples
from the sampling points. All continuously-pumped sample lines should have a
uniform short residence time between the pump inlet and sample discharge or
measurement point. The pump inlet should be designed and placed to avoid air
bubble entrapment. If 300-ml DO bottles are used for sampling, the flow rate
should be adjusted to avoid air bubble entrainment and provide adequate bottle
displacement rates. A bottle displacement time of from 6 to 10 sec is
recommended.
With this system, the DO measurement may be made by a DO probe mounted in
the sample line, by a DO probe mounted with a stirrer placed into the sample
bottle, or by Winkler titration of the DO in the sample bottle. The in-line
probe system must be observed continuously to prevent line clogging or damage
to the membrane. If individual bottle samples are used, they must be care-
fully stored to prevent temperature change and degassing. They should be
analyzed for DO as soon as possible.
If the pumped sample-individual bottle technique is used, it is recom-
mended that a DO probe-meter system also be installed. This system would be
used to help set sampling times, indicate when zero DO was reached during
deoxygenation, and assist in determining the end of run by noting a stable
maximum DO concentration. With continuously recorded DO data, deoxygenation
and reaeration patterns could be studied to aid in evaluating the performance
of the aeration system.
Oxygen Transfer Measurement
To provide adequate DO data for the transfer rate evaluation, a minimum
of 10 to 15 samples or readings should be taken. Analysis of more than 20
data values usually does not result in a significant improvement in precision
and may weaken the assumption of independence among the observations. Two-
thirds of the\ values should be evenly distributed during the time period
from Q/K.a to 2/K.a. One-third of the values should be evenly distributed
from 2/K.a to 4/K.a. In cases of rapid transfer, the minimum time between
observations should be 0.5 min. The interval is dependent on the type of
66
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aeration system and conditions of operation specified.
The in-situ DO probes should be fast-response probes equipped with 1.0-
tnil membranes and agitators. The probes should be carefully calibrated using
test tank water and checked for linearity against Winkler titrated samples.
The calibration should be verified prior to each test run. The probe readings
can also be checked against discrete samples taken (Winkler titrated) during
a test run for verification of the calibration.
DO probes require considerable care and attention to provide continuous
reliable data. Back-up probes and meters should be available for replacement
2
as needed. Standard Methods reports an accuracy of ± 0.10 mg/£ and a preci-
sion of ± 0.05 mg/l for probe analysis.
If the probes are placed in sample lines to measure the DO, they would
not be equipped with agitators. The velocity of flow past the probe would
be established and maintained to provide an accurate response from the probe.
Similar care and calibration would be required for these measurements.
Probes used to measure the DO in 300-ml sample bottles should be equipped
with a stirrer. Proper calibration procedures also apply in this case.
The modified Winkler DO analytical procedure of Standard Methods
2
(Section 422) should be followed for DO titrations. Some modifications of
this procedure are under consideration by the Standard Methods Committee and
should be noted for their potential use in oxygenation testing. It appears
that phenyl arsine oxide (PAO) titrant will be approved. It is also likely
that the British method for DO measurement will be approved. In this method,
hypochlorite is added to oxidize interferences such as sulfite. Procedures
using excess iodide to prevent the loss of iodine vapor at high DO concentra-
tions should be considered if unexplained lower readings in the higher DO
ranges are experienced.
Chemical interferences in Winkler DO titrations have been observed with
some testing, especially when higher cobalt levels are used (in the 2.0 mg/£
range). An analytical procedure presented in the llth edition of Standard
Methods (1960) has been utilized to eliminate chemical effects. A sample of
the test water is taken at the end of the test run. This sample is titrated
directly without the addition of manganous sulfate solution, but with the
addition of the al kali-iodide-azide reagent. This value, called a "blank",
is subtracted from every DO measurement in the test tank to eliminate chemical
67
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interferences.
This correction procedure is not in the 14th edition of Standard
2
Methods. The "blank" has not been observed in several reports of oxygen
transfer testing, especially where cobalt concentrations have been less than
0.5 mg/£.
The Discussion subsection presents additional information regarding DO
measurement using probes and Winkler titration.
Run Duration and DO Saturation
DO data should be obtained over as wide a range as possible. Truncation
of data at DO levels less than 20 percent of C* is allowable to avoid
lingering effects of the deoxygenation technique. In no case should values
of DO greater than 30 percent of C* be truncated. Low DO values will be of
use in assessing the model adequacy.
All test runs should be continued for a period of time approximately
equal to 4 divided by the anticipated value of K.a. This normally is equiva-
lent to continuing the run until the DO concentration is 98 percent of C*.
It is desirable that each run be continued to the saturation DO level. As a
minimum, one run should be extended for each testing condition (temperature,
aerator operation, and geometry) to obtain a test saturation DO concentration.
The saturation concentration is normally reached when the run is
extended for a period equal to 6/K.a. The saturation concentration can be
considered to be that concentration that remains constant for 15 min after a
test has been continued for a time period equal to 5/KLa.
It should be noted that this report (Section 4) recommends that values
of C* be estimated from the model. Measured and tabulated values of DO satu-
00
ration concentrations should be used for comparative information and not as
model parameters. A current table of DO saturation values is presented in
the Discussion subsection for reference purposes.
Results and Interpretation
Aeration system performance should be evaluated on the basis of a mini-
mum of three repetitive tests. The performance should be stated as an oxygen
transfer rate in Ib/hr or kg/hr at zero DO and 20°C for the specified physi-
cal conditions of placement, power, and/or air flow rate for the design.
68
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The mean K, a value for the test tank, using all data, should be used to
determine the mass transfer rate. The average mass transfer rate (Ib/hr or
kg/hr) should equal or exceed the stated performance requirement with a maxi-
mum variability of ± 5 percent of the mean for shop or factory-type testing.
Variability of up to ± 10 percent may be permitted in field or full-scale
testing. Two-thirds of the runs conducted for compliance testing should equal
or exceed the required performance.
Values of K.a should be determined for each sampling point. The K.a
values should not vary more than ± 10 percent from the mean value for each
test run. It is recommended that 67 percent of the individual K.a values be
within ± 10 percent for acceptable testing. Greater variations may be consi-
dered to be indicators of poor oxygen dispersion and/or analytical errors.
Tests conducted in large tanks, e.g., in excess of 100,000 gal, may exhibit
greater variations (say ± 15 percent).
The compartmentalized model presented in Section 4 on Modelling and Data
Interpretation does not require that oxygen transfer occur throughout the tank
volume, nor does it require that DO concentrations be uniform throughout the
tank volume. For further discussion of this point, the reader is referred to
Section 4.
Additional discussion of the interpretation of results, e.g., K.a
variation and DO gradients, is presented in Sections 4 and 8.
Detergent Addition
Experience with this procedure is limited and varied. Additional infor-
mation is presented in the Discussion subsection.
A strong solution of detergent, linear alkylate sulfonate (LAS) or house-
hold detergents, is prepared using hot water (80-90°C).. The detergent
solution is added in an amount to achieve an average concentration of approxi-
mately 5 mg/£ (measured as methylene blue active substance, MBAS) during a
test run. An initial concentration of 7 mg/£ of detergent in the test water
has been used. The detergent solution is added prior to the reaeration
period and should be uniformly dispersed throughout the tank contents.
The detergent concentration (MBAS) in the test water should be analyzed
at the beginning and end of the run and at several interim points to determine
an average concentration for the run. Surface tension measurements at these
69
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times are also recommended.
The cobalt concentration should be checked to verify that adequate cata-
lyst is present. It is suggested that a cobalt addition equivalent to
0.10 mg/£ in the test water be made for each run. Provision should be made to
dispose of any foam that develops during the test. Some difficulty with
detecting end points with the Winkler DO titration procedure have been noted.
It is recommended that probes be used to monitor the DO concentration. The
remaining test procedures are as noted in earlier sections.
Detergent testing results do not necessarily yield an actual performance
alpha value for an aeration system. They may, however, provide oxygen transfer
rate information to further describe and help predict the performance of the
aeration system for municipal wastewater applications.
DISCUSSION OF PROCEDURAL COMPONENTS
The following subsection is keyed to the various Procedural Description
components. Reports in the literature and approaches used in existing
practice are cited. This is not intended to be a comprehensive literature
review.
The Procedural Description presented in the first part of this section
has been reviewed and revised by Subgroup and Subcommittee members. The in-
formation presented in this subsection will expand on some of the procedural
components to assist individuals in developing oxygen transfer test procedures.
Advance Preparations and Responsibilities
This section focuses on testing for compliance with engineering specifi-
cations. Many reports by EOM's exist citing less than satisfactory test
conditions. It is the intent of this subsection to encourage the exchange of
information with the goal being to carefully delineate and agree upon the
testing conditions that must be met and the responsibilities of each partici-
pant (engineer, owner, and contractor) in meeting the testing conditions.
Engineering firms have drafted specifications where the testing require-
ments are two paragraphs in length and others have been many pages in length.
fi 7 R
Black and Veatch, CHLM Hill, and Bovay Engineers are three examples of
firms that prepare detailed testing descriptions and performance requirement
statements.
70
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As a minimum, the performance and precision requirements and type of
testing, e.g., unsteady state with "clean water" or whatever procedure, should
be stated. The detailed testing procedure could be described in the specifi-
cations, or provisions for establishing it sufficiently in advance of the
testing date should be included in the specifications.
The responsibilities of each party should also be cited, e.g., provision
of proper air flow and power measurements, provision of water supply, con-
struction of tank sectioning or complete separation of a basin, special air
piping installation, provision for laboratory space and utilities, etc.
Test Tank Geometry and Aerator Placement
Many consultants and owners require that final acceptance tests be con-
ducted on the actual installation. In some cases, compliance testing is
permitted under shop/factory conditions. There is concern on the one hand
with obtaining proper measurements of air flow, power, and oxygen transfer
rate (chemical handling and sampling problems due to size of test tank and
field conditions) in field testing. In shop testing, the test procedures
can generally be more precisely controlled; however, the question of properly
simulating the geometry and aerator placement then becomes a major factor.
g
Stukenberg and Wahbeh have reported on problems with surface aerator testing
under shop and field conditions. They concluded that "shop testing does not
adequately predict the performance of aerators after they are installed in
the field".
Bewtra and Nicholas and Schmit et al. have reported on the effect of
tank dimensions and diffuser placement for diffused aeration systems.
12
Rooney has reported on the influence of tank geometry on aerator perfor-
mance. He concluded that "basin geometry does affect the mixing regime
established by a specific aeration device and thereby significantly influences
its oxygen transfer rate".
3
Berk et al. of the Wastewater Equipment Council, Process Equipment
Manufacturers' Association (PEMA), recommended some criteria in 1972. They
are:
Mechanical Aeration
Tank depth: 8 to 15 ft (as low as 3 ft for horizontal devices)
Power level: 0.04 to 0.30 hp/1000 gal
71
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Note: Higher power levels and/or deeper basins will be permitted where
the aeration device is tested for application in specific waste
treatment systems that would operate under similar or identical
conditions.
Diffused Aeration
Basin size: A rectangular tank with minimum length = 1.5 x depth and
minimum tank width = 3 to 6 ft
Air supply: 12 to 45 scfm/1000 ft3
Diffuser submergence: 8 to 14 ft
Note: Higher air supply and/or more diffuser submergence and/or smaller
tank length and width will be permitted under test conditions
where the aeration device is being tested for application in
specific waste treatment systems that would operate under similar
or identical conditions.
The Oxygen Transfer section of Standard Methods2 notes that the value of
KLa is affected by the type of aeration equipment and tank geometry. It is
stated that "there are no universally accepted factors that can be applied to
all aerators and test conditions to establish a reproducible K.a". It is
observed that the power applied to a unit volume ratio is widely used to
compare one system to another. An acceptable range of 0.05 to 0.20 hp/1000
gal is cited.
Section 8 of this report on Geometry, Scale-Up, and Mixing observes that
horsepower per unit volume is an unreliable measure of solids suspension
capability and further states that "the significance of relative power has
meaning only when compared to similar aeration devices under similar condi-
tions". (See Section 8 for additional discussion and guidelines regarding
geometry and mixing.)
Air Flow Rate and Power Evaluations
The discussions of these components are included in Sections 9 and 10,
respectively, of this report.
Initial Water Quality
Several investigators have reported on testing problems associated with
using water sources other than a drinking water supply, e.g., river water,
72
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lake water, or final effluent. Chemical interferences with DO analytical
procedures and oxygen transfer rates have been cited by several writers.
13
Scaccia and Lee have reported on a large number of constituents including
dissolved gases, iron salts, organic matter, and several inorganic chemicals
that interfere with DO measurement by probes and Winkler techniques.
14 15
Kalinske et al., Landberg et al., and others have reported on the effect
of high cobalt concentrations on oxygen transfer rate measurement using
Winkler DO analysis. Naimee et al. have reported on problems with high
iron and manganese concentrations and variations in test results with pH
levels. Other investigators have conducted oxygen transfer tests without
observing adverse effects due to the presence of the interfering chemicals
noted above. There is a considerable degree of uncertainty regarding the
impact of chemical constituents in the test water. Additional information
regarding water quality testing limits is presented later in this Discussion.
It would be desirable if a test or reference water quality could be
specified. Typical wordings in some organizational procedural statements
3 2
describe the test water as "clean tap water", "fresh tap water", and
4
"quality of drinking water". Other references include statements such as
"clear water", potable water", and "clear tap water".
It has been suggested that "drinking water quality" be the reference
water quality. No uniform definition of drinking water quality is recognized
throughout the industry, and many public water supplies that meet Primary
(Health) Standard water quality will vary widely in other chemical charac-
17 18
teristies. Excerpts from EPA's Drinking Water Standards ' and the World
1 9
Health Organization (WHO) .along with selected water quality goals of the
19
American Water Works Association (AWWA) are presented in Table 6. Addi-
tional Primary (Health) Standards of EPA are presented in Table 7. Many U.S.
waters do not meet the Secondary Standards.
Several modifications would be needed to adapt any of these standards as
a reference water. Several numerical limits may need changing, e.g., sulfate,
TDS, and other constituents added such as sulfite, chlorine, cobalt, etc.
If a reference water quality was established, it could be reasonably achieved
for factory, university, and research and development testing. Portable water
treatment systems would be needed in some cases to modify the water quality
73
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TABLE 6. EXCERPTS FROM DRINKING WATER STANDARDS
Constituent EPA WHO International AWWA Goals
(1975) _ (1971) _ (.1968)
Recommended Acceptable
Turbidity (TU)* 1 5 25 <0.1
Coliforms* (Very low incidence) (Very low incidence) None
pH 6.5 to 8.5
TDS (mg/£) 500
Chloride (mg/£) 250 200 600
Sulfate (mg/£) 250 200 400
Corrosivity Non-corrosive
Hardness (mg/£ as CaCOj 80 - 100
Iron (mg/£) 0.3 0.1 1.0 <0.05
Manganese (mg/£) 0.05 0.05 0.5 <0.01
Copper (mg/£) 1 0.05 1 .5 <0.2
Zinc (mg/£) 5 5 15 <1.0
Foaming agents,
MBAS (mg/£) 0.5 0.2 1.0
ABS (mg/£)
C-C1 extract (mg/£)
Odor (TON)
Color (Units)
3
15
<0.2
<0.04
None
5 50 <3
Turbidity, chlorinated hydrocarbons, and coliforms are Primary (.Health)
Standards. The remaining EPA maximum contaminant levels are Secondary
Standards. Specific pesticides are cited at low levels, and coliform
presence is specified at a very low probability of occurrence.
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TABLE 7. ADDITIONAL PRIMARY EPA DRINKING WATER STANDARDS
Constituent* Maximum Contaminant Level (mg/l)
Arsenic 0.05
Barium 1.0
Cadmium 0.010
Chromium 0.05
Lead 0.05
Mercury 0.002
Nitrate (as N) 10
Selenium 0.01
Silver 0.05
Fluoride (@ 68°F) 1.8
__
Cobalt is not included as a Primary or Secondary Standard.
for testing. Some investigators have suggested modifications such as carbon
treatment and pH adjustment in discussions of testing procedures.
As reported later in this Discussion, it has been suggested that a
"detergent-added" procedure be used. One of the purposes of this procedural
modification is to "overcome" the effects of the several interfering sub-
stances. This approach merits additional study.
Most procedural' statements recommend testing close to 20°C whenever
possible. Typical suggested acceptable temperature ranges are from 15 to
25°C. In northern climates, it may be necessary to test below 10°C. Caution
regarding dissolution of chemicals and the effect on reaction rates is
merited at low temperatures.
Stenstrom and the Alpha, Beta, and Temperature Corrections Subgroup of
20
the ASCE Subcommittee on Oxygen Transfer Standards have recommended that
temperature corrections greater than 10°C be avoided if possible. They also
have indicated that there is no consensus for a temperature correction factor.
They recommend that a theta factor is more suitable. (See Section 6 for
additional discussion.)
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De o xy g en a t i o n Ch em i c a 1 s
Nitrogen stripping is an alternate procedure. This technique has been
1 o
used in laboratory procedures by Scaccia and Lee and others and has been
21
used in shop testing by Houdaille Industries. It has not been used in full-
22
scale testing due to practical scale limitations a'nd economics. Mandt has
reported that there may be some effect on early DO readings due to the
residual nitrogen concentration from stripping. Early truncation, up to
20 percent of C*, may eliminate this effect.
There are several sources of sodium sulfite including Monsanto ("Santo-
site"), Stauffer, and Allied Chemical Companies. Nalco Chemical Company
13
also supplies sodium sulfite as Nalco 19. Scaccia and Lee and Naime et
al. have reported on "contaminants or impurities" in the sulfite that
13
affect oxygen transfer rate measurements. Scaccia and Lee report that
technical grade sodium sulfite is produced in a batch-type operation with
each batch being assigned a number. An assay of each batch is not available
but is covered by a blanket analysis stating minimum or maximum quantities
of expected chemical ingredients.
Sodium sulfite is frequently used as a boiler feed water deoxygenation
chemical. Most sulfite can be obtained "cobalt free", so the cobalt concen-
tration can be controlled by separate addition. Nalco 19, however, contains
cobalt as a catalyst for deoxygenation. The cobalt concentration in the test
water would increase with repetitive runs using this chemical.
A reagent grade sulfite could be used to avoid the impurities uncertain-
ty. Its cost is from four to seven times greater than technical grade and
its use in field or large-scale tests would be quite expensive. The price
for analytical grade sulfite in 1977-78 was in the range of $0.85 to $1.00/lb,
while the technical grade price was from $0.15 to $0.25/lb.
I O
Scaccia and Lee describe a laboratory screening test that could be
used to evaluate any effects of the sulfite on oxygen transfer rate measure-
ments. Comparative bench-scale reaeration tests could be conducted using
nitrogen stripping and/or analytical grade sulfite for deoxygenation. One
could also obtain samples of the water to be used in a field test and conduct
evaluations of possible chemical effects due to water quality differences at
the same time.
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System Stability
Various references recommend aeration periods of from 20 to 30 min to
achieve a steady state mixing condition in the test basin. Landbert et al.
observed that a 75-hp aerator requires 30 to 40 min to achieve a steady state
hydraulic regime at the Lightnin test facility. They note that power readings
and mixing velocities can be monitored to determine steady state. They
observed that steady state power readings are achieved before steady state
hydraulic conditions result. It was noted that each test condition (aerators
and basin) will have its own steady state time constant.
2
Standard Methods notes that the aeration device should be able to be
operated at a constant power output for the duration of the test. Stukenberg
g
and Wahbeh have reported on difficulties and procedures in designing shop
tests to simulate power levels of field-scale surface aerators.
Initial Run
Various investigators have reported that there have been uncertainties in
the oxygen uptake response for the initial test on a new volume of water.
It has been recommended that the initial run either be excluded from the runs
utilized in analyzing for compliance or be made optional.
23
Boon has suggested that the initial run be used to determine mixing by
adding the sulfite and cobalt solutions at one point in a short time. Scaccia
13
and Lee recommend conditioning the test liquid by adding the sulfite
solution in approximately the amount required to react with the DO in the
liquid and continue aeration until saturation DO values are achieved. They
state that this procedure allows for chemical stabilization of the test
liquid so that results from an initial compliance test will be reproducible.
Chemical Addition for Deoxygenation
Cobalt is generally added in solution. The source is normally cobalt
chloride although the sulfate or nitrate forms have also been used. Some
concern has been expressed regarding difficulties of obtaining complete
dissolution of cobalt sulfate. Cobalt is usually added once per tank of test
23
water. Boon has recommended that the cobalt concentration be analyzed prior
to each run to be certain of its presence in adequate concentration. Addi-
tional cobalt would be added as needed to maintain an adequate catalyst
77
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concentration. Rooney24 has also reported an occasional depletion in cobalt
during the test and recommends that its concentration be verified by analysis.
25
Kalinske has stated that "it has never been demonstrated that if
0.05 mg/£ of cobalt ion is added that there would be insufficient cobalt
present for catalysis irrespective of how many tests are made in the water".
14
Kalinske et al. have recommended a cobalt concentration of 0.05 mg/£. They
also noted that with cobalt ion as low as 0.05 mg/£, no unreacted sulfite was
ever detected in the presence of DO, even with the water temperature below
5°C.
?fi
Berk questions whether 0.5 mg/t of cobalt is adequate, especially for
testing in water temperatures below 10°C. He reported on testing diffi-
culties using 0.5 mg/£ of cobalt that were corrected by raising the cobalt
concentration to 2.0 mg/£. Additional discussion of cobalt levels is pre-
sented under the following subheading, Water Quality During Testing.
sulfi
J3
27 13
Boon, Scaccia and Lee, and others have recommended that the sulfite
be dissolved outside the test tank prior to its addition. Scaccia and Lee
recommend the use of mixing tanks (and heater systems where needed) to ensure
complete solubilization. They note that undissolved sulfite transferred to
the test tank may dissolve slowly causing an oxygen sink to be present during
the reaeration phase of the test and result in an apparently lower K.a. Some
284
investigators, e.g., McKinney and Kayser, have reported on successful use
of dry addition of sodium sulfite.
The sulfite must be uniformly dispersed throughout the test tank to help
27
ensure accurate reaeration results. Boon states that rapid addition at a
single point should be avoided or the concentration of DO may be variable
during reaeration, even in a tank that is fairly uniformly mixed. Scaccia
1 o
and Lee recommend transferring the sulfite solution in a time period of
approximately one-half to one basin turnover.
Sulfite additions are made in excess of the stoichiometric amount and are
dependent on DO concentrations, oxygen transfer rates, and mixing intensity.
Standard Methods2 and WPCF Manual of Practice No. 51 suggest 0.8 lb/1000 gal,
o
which represents a 22 percent excess. Berk et al. suggest 1 lb/1000 gal,
27
which represents a 50 percent excess. Boon recommends 20 percent excess.
Various references cite the necessity to go to at least twice the stoichio-
metric value to achieve a zero DO concentration. The theoretical
78
-------
stoichiometric requirement is 7.88 mg/£ of sulfite per 1.0 mg/l DO concentra-
tion. The following data represent a typical array of sulfite quantities for
different excess goals. The condition is a 100,000-gal test volume and an
initial DO of 10.0 mg/£.
Excess (%} Sulfite (Ib)
0 65.7
20 78.9
50 98.6
100 131.4
200 197.2
29
Stukenberg et al. cite the importance of achieving zero DO prior to
starting reaeration. They state that "if the basin is not deaerated com-
pletely, the results will be erratic and difficult to interpret". Kayser
reported that the West German and Austrian procedures require zero DO to be
reached and maintained for 20 to 30 min. He states that this period of
mixing at zero DO is of some importance when testing surface aerators. Boon
suggests that each in-situ probe be measuring about 0.1 to 1.0 mg/£ DO
(within ± 10 percent of the mean) at the beginning of the reaeration period.
The requirement for reaching zero DO, if 20 percent C* truncation of
low DO levels is permitted, is questioned by some investigators. Another
investigator indicated that a zero DO period of 2 min is acceptable if the
sulfite is evenly distributed. It was suggested that in tanks with mechani-
cal aerators, the DO should remain zero for the period required to establish
constant velocities, turbulence, and energy uptake.
If in-situ probes are not used, the question has been raised how one
could readily monitor the zero DO level simultaneously throughout the test
facility. Additional Winkler DO analyses or the use of a probe-BOD bottle
system would be required.
Water Quality During Testing
Testing experiences vary considerably regarding water quality limitations
and effects. It appears that the greatest number of interferences or effects
are associated with Winkler DO analytical procedures. Probe DO analysis
avoids some of the analytical problems, but there are operational trade-off's
regarding selection of the analytical procedure.
A wide range of cobalt concentrations have been used in testing. Low
79
-------
values, e.g., 0.05 mg/£, have been recommended by Kalinske et al.14 and
others to avoid interference with Winkler DO testing. Stanton and Bradley,
concerned with the potential for inadequate catalyst concentration to oxidize
the sulfite, recommend 2.0 mg/£ of cobalt. They utilize an analytical modifi-
cation ("blank") to account for Winkler DO chemical effects. Landberg et al.
reported an increase in DO versus a control sample when the Na^SC- concentra-
31 32
tion exceeded 500 mg/£ at a cobalt level of 5.0 mg/£. Naimie and Burns '
have reported that hydrogen peroxide was an interfering substance at pH's
below 6.9 and a cobalt oxide precipitate was formed at pH's greater than 6.9.
The buffering capacity and pH of the test water were determined to be the most
critical water quality parameters regarding the magnitude of the interference.
In general, water systems with higher pH values and substantial alkalinity
caused interferences of unpredictable magnitude. Naimie et al. concluded
that an accurate quantitative prediction cannot be made of the magnitude of
cobalt interference for various natural water systems with different water
quality characteristics.
13
Scaccia and Lee reported that cobalt concentrations in the range of
0.5 to 1.5 mg/£ had no effect on test results and that they normally use
27
0.5 mg/£. Boon reported that no effect on K. a was observed when testing
33
with cobalt concentrations between 0.2 and 2.0 mg/£. Paulson in tests
conducted on waters with alkalinities in the 150 to 250 mg/£ range has not
observed any cobalt interferences with cobalt concentrations from 0.10 to
0.50 mg/£.
Many investigators are recommending cobalt levels from 0.10 to 0.50 mg/£.
4
The West German and Austrian procedures as reported by Kayser recommend
0.50 mg/£. An EPA-sponsored clean water test project conducted by the Los
Angeles County Sanitation Districts used 0.10 mg/£ of cobalt as reported by
Yunt. Values closer to 0.50 mg/£ are recommended for tests conducted at
low temperatures (say less than 10°C). Multiple additions may be used with
"detergent-added" testing due to the potential decrease in cobalt concentra-
tion as a result of formation of organic complexes and stripping.
TDS or sulfate concentrations have commonly been used as a basis for
limiting the number of tests conducted on one volume of water. Landberg
et al. noted an effect on the Winkler DO determination at 1.0 mg/£ cobalt
80
-------
concentration and a Na9SO. concentration of about 1200 mg/£. Standard
2
Methods cites a decrease in solubility of oxygen of 0.009 mg/£ per 100 mg/£
of additional chloride at 20°C. For example, an increase of 1100 mg/£ of
chloride would decrease the solubility 0.10 mg/£.
3
Berk et al. recommend a limiting Na9SO. concentration of 1500 mg/£
-,- C "t
(1010 mg/£ as SO.). Scaccia and Lee recommend 1000 mg/£ as SO.. Zlokar-
35
nik reports an increase in K. a when salt concentrations exceed 1500 to
4
2000 mg/£. Kayser reports that the German/Austrian procedural limit is a
salt concentration of 2000 mg/£.
oc
Boon reported that changes in the hardness of the water and small
changes in concentrations of inorganic salts, including the sodium sulfate
content, as a result of conducting several tests in the same water had little
oc
effect on test results. Boon has also reported that up to ten tests have
been conducted in the same water with little effect on the value of K. a deter-
mined by Winkler DO analysis or probes. Boon and his co-workers recommend a
limiting IDS level of 1500 mg/£. They also report no effect of alkalinity
between 5 and 270 mg/£ on the test results. Other investigators have also
reported that they did not observe any testing uncertainties with increasing
IDS levels up to 2000 mg/£.
Some firms, Black and Veatch, Bovay, and Sanitaire, have recommended
that a repetitive testing limit for water quality be based on the number of
tests with the same volume of water. The range of allowable number of tests
38
with the same water cited is from five to ten test runs. Envirex and CH9M
7 '-
Hill permit the reuse of each volume of test water up to a limit of
1000 mg/£ of added TDS. It is suggested that repetitive runs be conducted at
high and low TDS levels to check for possible significant K. a variations in
16
testing programs. Naimie et al. have reported on chemical interferences.
They state that "data obtained from non-steady state clean water testing can
be useful in comparison of aerator efficiencies only for test waters with
very similar water quality characteristics". They observed that iron and
manganese at concentrations of 2 mq/l and probably other transitional elements
substantially enhance (up to 100 percent) oxygen mass transfer during
unsteady state clean water testing. They indicate that further work is
needed at concentrations less that 2 mg/£.
Naimie et al. also report that values of K[_a have increased as the
81
-------
hardness, pH, and sulfate content of the test water have increased. The
effects were most pronounced, for a given test water, when five or more sul-
fite additions were introduced into the test basin.
If the Winkler DO titration method is used, Naimie et al. recommend
testing at a pH of 6.9 in a 0.01-molar phosphate buffered system with 2 mg/£
of cobalt, an iron concentration less than 0.3 mg/£, and a manganese concen-
tration less than 0.05 mg/£.
13
Scaccia and Lee have reported that a large number of chemicals inter-
fere with oxygen transfer testing. No specific numerical limits other than
38
for cobalt and sulfate (cited earlier) are recommended. Envirex recommends
stripping chlorine prior to commencing testing.
Some investigators have conducted tests in the pH range of 6.5 to 8.5
without observing significant effects of pH on K.a determinations.
It has been suggested that surface tension and anionic detergent analyses
be conducted if "detergent-added" testing is conducted. Some question exists
whether to use a static or dynamic surface tension measurement. McKeown and
39 40
Okun and Gilbert have reported on surface tension measurements associated
2
with surface active agents and oxygenation. Standard Methods does not
41
present a procedure; however, American Society for Testing Materials has
published a standard test method for surface tension of water. It has been
40
reported by Gilbert that the surface tension varies during a test run, but
it appears to stabilize after approximately 20 min of aeration.
Anionic detergent concentrations can be measured by the Standard
2 42
Methods procedure as MBAS. Ewing et al. have reported on the variations
in LAS concentration with time during a test run.
The wide variation in the reported results of chemical interferences or
lack of interferences demonstrates the need for further study to clarify many
of the uncertainties. Section 6 also discusses the effects of chemical and
other factors on oxygen transfer measurement.
Sampling
Section 4 of this report recommends that each sample point location
43
sense an equal volume. Shell states that to establish the variation in
K.a at least four sampling points should be used. He indicates that the
sampling points should be placed randomly in the basin avoiding the areas
82
-------
near the aeration issue and near the walls.
Shell suggests the following criteria:
1. Do not place sample points in the plume or issue of the aeration
device.
2. Do not place sample points any closer than 3 ft from the walls,
6 ft from the corners, or 2 ft from the basin floor and liquid
surface.
3. Place one or more sampling points near the liquid inlet to the
aerator.
4. Place sampling points at the one-third and two-thirds points in the
basin both in relation to the diameter and depth. The diameter
points should be on opposite sides of the basin.
The October 1978 draft of Section 208 (Oxygen Transfer) of Standard
Methods states that "for basins greater than 50,000 gal, locate six sub-
mersible sample pumps at various depths and at least at two places that
divide the basin into approximately equal-volume sampling zones".
3
Berk et al. in the 1972 PEMA procedure recommend the following approach:
Two sampling locations shall be selected. One point
should be fairly close to the aeration device, and the
second point should be located near the tank periphery.
Submersible pumps or siphons shall be installed at two
operating depths at each sampling location. At the
first location (close to the aeration device), pumps or
siphons, shall be installed at mid-depth and three-quarters
depth from the liquid surface. At the second location
(close to the aeration tank periphery), pumps or siphons
shall be installed at one-quarter depth and three-quarters
depth from the liquid surface. This will give a total
of four sampling stations for each test.
28
Stukenberg et al. recommend a minimum of three sample points. They
note that five to seven points are normal with more than ten points utilized
29
for abnormal situations. Stukenberg et al. illustrated recommended sample
point locations for three aeration systems (Figure 6).
Section 4 of this report recommends 10 to 15 samples or DO readings
with a maximum of 20 be taken for each location. A minimum time interval of
0.5 min is suggested for sample spacing with equal time intervals recommended
in specific DO ranges as noted under the following subheading, Oxygen
Transfer Measurement.
83
-------
CD
+ 1 +2
O
+ 2
\
cS
DIFFUSED
AERATION
SURFACE
AERATION
Figure 6.
SUBMERGED
TURBINE
AERATION
Recommended sample point locations.
,43
recommends that timed samples be collected from each sample
point. At least ten samples should be collected at each point for DO con-
centration analysis. Seven or eight of these samples should have an oxygen
concentration between 10 and 90 percent of saturation. To achieve the
appropriate time interval, the following expression can be used as a first
estimate:
t = 100M/OTR (51)
where:
t = sample time interval (min), t
M" = test basin water weight (Ib x 10"6), m
OTR = estimated oxygen transfer rate (Ib 00/hr), m/t
2
Standard Methods states that as the DO increases, samples are taken at
1- to 3-min intervals or one at approximately every 1.0 mg/£ increase in DO.
The DO should be determined on six sets of samples between 10 and 80 percent
3
saturationv Berk et al. recommend a similar sampling quantity and spacing.
In-situ probes represent a widely-used sampling procedure. Boon,26
45 33 38 7 "37 A
Gilbert and Chen, Paulson, Envirex, Marotte, Sanitaire, and Kayser
have utilized this procedure and recommend it as a sampling approach in their
testing. This approach provides a continuous data source if the DO values
are recorded. It provides a large number of data points if the meters are
read directly.
Several references have been made to difficulties with reliable
84
-------
continuous operation of probes when operated in situ in test tanks. Shell43
cites several problems with the use of probes as a sampling approach including
damaged membranes, electronic malfunctions, and maintenance requirements. He
also states that probes do not indicate a finite value of oxygen concentra-
tion. He further notes that "the indicated oxygen concentration is an
average value over a period of time".
A second sampling approach is the use of either gravity flow or pumped
samples. The samples can be analyzed by either DO method, Winkler or probe.
2
Standard Methods states that the samples should be pumped at a rate
that displaces the volume of each sample bottle at least three and preferably
ten times between samples. The detention time between the pump and sample
outlet should be limited to 5 to 10 sec. Sample pumps and lines of equal
size and length should be used to minimize time differences among samples
taken at a given time.
Samples should be collected in 300-ml BOD bottles at specific time
intervals and sealed until analyzed. Sample lines should be handled care-
fully to avoid entraining air bubbles. Sampling should begin when the DO
has just begun to rise from zero as indicated by a DO electrode located near
the tank bottom and outer wall.
43
Shell has recommended the following sampling procedure:
The sampling procedure should be to place the sampling
points (pumped or siphoned) in their proper locations
in the aeration basin. Plastic tubing (about 1/4 in. diameter}
should be connected from the sample point to a central
collection point. At timed intervals, the plastic tubes
are placed into the BOD bottles such that the ends of the
tubes are within 1/2 in. of the bottle bottom.
The rate of sample flow should be such that the
bottle is filled within 5 sec. This means that the bottle
contents will be replaced a minimum of three times in 15 sec.
The length of the sample lines (for more than one
sample point) is not critical if the retention time in
the tube is less than 7.5 sec. If the retention time is
greater than 7.5 sec, then all sample lines should be of
the same length. To avoid possible data bias, the
maximum sample line retention time should be 7.5 sec or
less, if possible. Longer retention times may result in
liquid temperature changes and possible additional aeration
where air bubbles may be drawn into the sample line.
85
-------
To avoid the inclusion of air bubbles into the
sample line, the sample point should be located away
from areas of intense turbulence. The inlet to the
sample point should be in a vertical plane with the
opening at the top. The downward inlet velocity
should be such that all air bubbles larger than
500 microns are excluded.
46
Conway and Kumke continuously pumped a sample into a BOD bottle
equipped with a magnetic stirrer. A probe was used to determine the DO con-
47
centration. Mixco collects the pumped samples in BOD bottles and analyzes
them with a DO probe.
Oxygen Transfer Measurement
The Winkler DO titration method has been widely used as a DO analytical
procedure. Various oxidizing or reducing agents such as ferric and ferrous
salts, residual chlorine, oxidizable sulfur compounds, nitrate and chromate,
and readily oxidizable organics are examples of interfering substances in the
Winkler titration procedure. Naimie et al. reported on chemical inter-
ferences in oxygen transfer measurements. They have recommended pH control
and limiting iron and manganese concentrations. They also noted that the
effects of 2.0 mg/£ iron and manganese concentrations were not as pronounced
with Winkler techniques as they were with DO probes. Kalinske et al.
have reported on cobalt interference resulting in high DO readings as the
cobalt concentration increases. The limiting concentration cited for no
interference was 0.05 mg/£.
I O
Scaccia and Lee cited several substances (organic and inorganic) as
causing interference in Winkler DO titrations. They note that Standard
2
Methods modifications will correct for ferrous and nitrite ion effects.
They recommend the use of a "blank" to correct for or eliminate chemical
48
interference effects. This "blank" approach has been recommended by Lakin
30
and Stanton and Bradley to correct for chemical interferences when testing
with cobalt concentrations of 2.0 mg/£. The "blank" is obtained by titrating
a sample directly without the addition of manganous sulfate solution, but
with the addition of the alkali-iodide-azide reagent. This value is sub-
stracted from every DO measurement.
This "blank" procedure is not included in the 14th (.1975) Edition of
2
Standard Methods, nor is it proposed in the 1979 Version of Dissolved Oxygen
86
-------
in Natural and Waste Waters (DOE-London).4 There is some question as to the
45
meaning or interpretation of the "blank". Gilbert and Chen have reported
that the "blank" value was always less than 0.2 mg/£ DO when using a 0.5 mg/£
cobalt concentration. They report that the "blank" represents interference
50
caused by cobalt oxide reacting with iodide to form iodine. Stack also
reported that a cobalt precipitate that may be formed in testing causes the
liberation of iodine upon acidification in the Winkler titration procedure.
This interference results in an oxygen concentration value higher than the
actual value. Stack suggests that the basic precaution should be to either
use a low concentration of cobalt so that the interference is insignificant
or if higher concentrations of cobalt are to be utilized to use DO probes.
Montgomery and DOE-London have reported that the loss of iodine
vapor in titrations may result in lower DO values at the higher cobalt concen-
trations. This loss can be minimized by using a high iodide reagent
(Modified Pomeroy-Kirschman-Alsterberg reagent). They note that this reagent
is very viscous and may not be suitable for field use. Stack also reported
on the iodine volatility question. He recommended two actions to minimize
the problem.
2
1. If Standard Method's alkaline-iodide reagent No. 1 is to
be utilized, add the manganous sulfate and alkaline-iodide
reagents, carry the procedure through the flocculation
stage, and cool the sample to a temperature in the 10-15°C
range before adding the acid reagent. Titrate the sample
with due consideration for the volatility of iodine.
2
2. Use Standard Method's alkaline-iodine reagent No. 2 so
that iodine is present as triiodide and iodine volatility
is not a significant problem.
Samples for Winkler analysis should be analyzed for oxygen as soon as
possible after sampling. The oxygen in the sample should be chemically fixed
as soon as the sample is acquired. Mixco and Conway and Kumke recommend
that care be taken to keep the DO samples at or below the temperature of the
basin.
2 49
Standard Methods 14th Edition and the DOE-London procedures recommend
the use of sodium thiosulfate as the titrant. The current WPCF Standard
Methods Committee is recommending phenyl arsine oxide (PAD) as an equivalent
alternate titrant. PAO has been shown to have a reasonably stable normality.
DO probes are used in many testing programs. In some cases, the probes
87
-------
provide primary data and in others they are used to control Winkler sampling
o
procedures or provide supplemental information. Standard Methods reports an
accuracy of ± 0.10 mg/£ and a precision of ± 0.05 mg/£ for probe DO analysis.
Probes have been used successfully; however, many references cite con-
cerns regarding special care, extensive calibration requirements, sensitivity,
and response delays,
Naimie et al. stated that DO probe results were affected to a substan-
tial degree by concentrations of iron and manganese of 2.0 mg/£ in the test
13
water. Scaccia and Lee report that dissolved gases such as chlorine, HLS,
or S02 can interfere with DO measurements with membrane probes. Gilbert and
Chen^S reported on probe response time delay analysis. If the membrane probe
equipment has a high membrane coefficient relative to the K. a being measured,
no corrections are necessary.
52
Stack reported that documents that best describe the appropriate
procedures for use and calibration of probes are generally the literature
provided by the manufacturers. He stated that the most important criterion
is to have a good reference procedure. The three most commonly used are
1. a Winkler titration to determine the DO concentration in the cali-
bration sample,
2. an oxygen-saturated sample, or
3. a water vapor-saturated air sample.
52
With suitable care in the Winkler titration, Stack prefers the Winkler
titration. A saturated water sample is acceptable as long as an adequate
effort is made to saturate the sample and the table value for DO concentra-
tion is corrected for atmospheric pressure. In the water vapor-saturated
air approach, it is important that the probe be at the air temperature and
that the saturation value be corrected for atmospheric pressure.
50
Stack has reported that a membrane probe cannot be calibrated in clean
water and then placed in a contaminated water sample to read an oxygen con-
centration for use in the determination of a beta value. For successful
application, the probe must be calibrated in the contaminated sample utilizing
some reference technique such as Winkler titration.
Gilbert and Chen have reported on the successful use of DO probes with
the probes calibrated using saturated test water. The DO measurement was
monitored using a multi-channel recording system.
88
-------
9 7 9 f\
Boon uses DO probes in situ in his testing procedure. Boon reports
that to obtain accurate results, it is necessary to check frequently (at
least daily) the reading of each probe at zero DO concentration and at 50 and
100 percent of the air-saturation equilibrium concentrations at the same water
temperature used in the aeration tests. Calibration at 50 percent of satura-
tion is normally achieved by aerating the water with an oxygen-nitrogen gas
containing 10.5 percent 0?.
53
Conti has reported that interference due to strong electrical fields
has affected DO probe readings. Probes should be calibrated in the working
environment in which they will be used in the testing program to avoid this
interference.
54
Salzman reported that due to probe response time and gas bubble attach-
ment, in-situ use of probes is not recommended. Representative samples are
pumped to sample bottles where measurements are made at steady state condi-
tions. Probes are initially calibrated against saturated distilled water
that is analyzed for DO by Winkler titration. During the reaeration phase,
the test samples from a single point are analyzed by probe and Winkler titra-
tion to assure linearity.
13
Scaccia and Lee describe an extensive detailed procedure for probe
calibration and a linearity check using distilled water.
27
Boon states that the thinnest membrane recommended by the manufacturer
should be used to increase the sensitivity of the probe. He also reports that
any protective shields should be removed to ensure a rapid flow of water past
the membrane.
4
Kayser has reported that the West German and Austrian procedures
recommend the use of probes with agitators. Many investigators in the United
States prefer 1.0-mil thickness membranes to minimize the likelihood of
damage and utilize agitators to ensure adequate velocity past the membrane
surface.
42
Ewing et al. state that "there is some indication that more represen-
tative and reliable unsteady state test data may be obtained by multiple DO
probes than by piped samples analyzed by Winkler or probes. The assumption
of careful analysis and selection of the probe system, its application, and
its calibration schedule is inherent in the above conclusion". Conway and
89
-------
Kumke concluded in their study that reliable oxygen analyzers make possible
more rapid, accurate measurements of oxygen transfer.
It appears that the use of DO probes is a desirable procedure for
obtaining continuous data, evaluating the beginning and ending performance of
test runs, and avoiding some of the chemical interference questions associated
with Winkler titrations.
Run Duration and DO Saturation
Several references have suggested terminating a test at from 70 to 80
55
percent of DO saturation. Boyle et al. have cited the importance of
obtaining data closer to saturation to minimize errors in estimating K.a.
Recent procedural approaches are more frequently recommending that DO data be
taken to 90 or 95 percent of the saturation DO. Boyle et al.55 also noted
that truncation of DO data up to 20 percent of DO saturation will not affect
the precision of the estimate of K.a.
The truncation and run termination recommendations cited in the
Procedural Description are based on the analysis by Baillod and Brown (as
repeated in Section 4 of this report). As noted, early truncation (20 per-
cent) may avoid lingering effects of the deoxygenation technique. However,
the need for early DO values is stressed for purposes of evaluating model
adequacy.
27
Boon recommends that test runs be continued to 6/K.a to reach the air
saturation value. He uses DO values from 20 to 80 percent of the saturation
value to calculate KLa values. Kayser states that a test is finished when
the DO does not increase by more that 0.1 mg/£ within 20 minutes. This DO
reading is the saturation value.
45
Gilbert and Chen recommend that the DO saturation concentration be
determined experimentally for a given aerator type and system geometry. They
determine the value by aerating the test tank until the DO reaches saturation
and remains constant for at least 15 min. They report that truncation of an
aeration test before reaching saturation can produce substantial error in
estimates of K.a unless a precise value of C* is available.
L - 00
Standard Methods DO saturation values are corrected for test conditions
in the 1972 PEMA method by Berk et al.3 and in the Standard Methods 1978
44 25
Draft Procedure. Kalinske specifies that saturation values for DO be
90
-------
p
determined from published tables, e.g., Standard Methods, with appropriate
corrections for salinity and pressure.
Stack states that "where air-water interfaces are purposely dispersed
in an oxygen transfer system, it is recommended that oxygen saturation be
determined experimentally".
Section 4 of this report discusses truncation and DO saturation. It
recommends that C* values be estimated using the oxygen transfer model.
Measured or adjusted tabular values would be used for comparative purposes
and not as model parameters.
Hunter has recommended the use of a table of saturation DO concentra-
tions based on the 1973 International Oceanographic Tables (Table 8).
According to Hunter, this table will probably be included in the 15th Edition
of Standard Methods and is the most up-to-date and accurate information
49
currently available. These values are utilized by DOE-London in their
solubility table. Five saturation DO values are listed below for comparative
purposes.
Saturation DO Concentration (mg/£)
Water
Temperature (°C)
10
15
20
25
30
Table 8
11.27
10.07
9.07
8.24
7.54
14th Edition ?
Standard Methods
11.3
10.2
9.2
8.4
7.6
Results and Interpretation
Stukenberg recommends that three replicate tests be run per set of
aeration conditions. Rooney states that confirmation of performance should
be with at least three repeat tests with the results from all three to be
within ± 5 percent of the average. He has suggested that two additional
tests be required in order to discard one of the three original results.
4
Kayser states that after two tests if single point values of mass
transfer have a higher deviation than ± 5 percent of the average, this has to
be explained (e.g., instrument failure) or a third test is required.
46
Conway and Kumke reported that the variations of all but the extreme
91
-------
TABLE 8. SOLUBILITY OF OXYGEN IN WATER EXPOSED
TO WATER SATURATED AIR (mg/£)
Water
Temperature
(°c)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0
14.60
14.19
13.81
13.44
13.09
12.75
12.43
12.12
11.83
11.55
11.27
11.01
10.76
10.52
10.29
10.07
9.85
9.65
9.45
9.26
9.07
8.90
8.72
8.56
8.40
8.24
8.09
7.95
7.81
7.67
7.54
7.41
7.28
7.16
7.05
6.93
6.82
6.71
6.61
6.51
6.41
Chloride
57000
13.72
13.35
12.99"
12.65
12.33
12.02
11.72
11.43
11.16
10.90
10.65
10.40
10.17
9.95
9.73
9.53
9.33
9.14
8.95
8.77
8.60
8.44
8.28
8.12
7.97
7.83
7.69
7.55
7.42
7.30
7.17
7.05
6.94
6.82
6.71
6.61
6.51
6.40
6.31
6.21
6.12
(continued
Concentration
(mg/£)
10,000
12.90
12.56
12.23
11.91
11.61
11.32
11.05
10.78
10.53
10.29
10.05
9.83
9.61
9.41
9.21
9.01
8.83
8.65
8.48
8.32
8.16
8.00
7.85
7.71
7.57
7.44
7.31
7.18
7.06
6.94
6.83
6.71
6.61
6.50
6.40
6.30
6.20
6.11
6.02
5.93
5.84
on next page)
92
in Water
15,000
12.13
11.81
11.51
11.22
10.94
10.67
10.41
10.17
9.93
9.71
9.49
9.28
9.08
8.89
8.71
8.53
8.36
8.19
8.03
7.88
7.73
7.59
7.45
7.32
7.19
7.06
6.94
6.83
6.71
6.60
6.49
6.39
6.29
6.19
6.10
6.01
5.92
5.83
5.74
5.66
5.58
20,000
11.41
11.11
10.83
10.56
10.30
10.05
9.82
9.59
9.37
9.16
8.96
8.77
8.58
8.41
8.24
8.07
7.91
7.76
7.61
7.47
7.33
7.20
7.07
6.95
6.83
6.71
6.60
6.49
6.38
6.28
6.18
6.08
5.99
5.90
5.81
5.72
5.64
5.56
5.48
5.33
5.33
-------
TABLE 8. (continued)
Water
Temperature
(°c)
41
42
43
44
45
46
47
48
49
50
0
6.31
6.22
6.13
6.04
5.95
5.86
5.78
5.70
5.62
5.54
Chloride
5,000
6.03
5.94
5.85
5.77
5.69
5.61
5.53'
5.45
5.38
5.31
Concentration
(mg/-t)
10,000
5.76
5.68
5.60
5.52
5.44
5.37
5.29
5.22
5.15
5.08
in Water
15,000
5.50
5.42
5.35
5.27
5.20
5.13
5.06
5.00
4.93
4.87
20,000
5.25
5.18
5.11
5.04
4.98
4.91
4.85
4.78
4.72
4.66
Ed. note: This table now appears in the 15th Edition of Standard
Methods, APHA, Washington, D.C., 1980.
individual measurements from all clean water tests, both from series testing
and multiple sampling points in the same basin, were less than 5 percent from
the average values.
23
Boon recommends an allowable variation in the mass transfer rate of
± 10 percent.
Various references cite a requirement for complete or adequate mixing
for the unsteady state clean water test. The variations in point K.a values
and DO gradients observed have frequently been cited as indicators of mixing.
It was shown in Section 4 that the basic model recommended in this
report (Equations 1 to 3 of Modelling and Data Interpretation section) is in
accordance with the analysis of both an ideal completely mixed system and an
ideal compartmentalized system. The latter situation does not require that
DO concentrations be uniform throughout the tank nor that oxygen transfer
occur throughout the tank. However, an additional element of uncertainty
is introduced in this situation by the assumption that the mean DO concentra-
tion of the accumulation zone equals the effective average DO concentration
of the aeration zone. For further discussion of this, point, the reader is
referred to Section 4.
43
Shell states that the basic mass transfer equation requires that
93
-------
mixing be complete, where complete mixing is defined as the continuous move-
43
ment of all liquid in the basin. Shell recommends that the variation in
K.a values be used as a measure of mixing. He states that after reviewing
the results of several hundred clean water tests, it was established that
K.a values should not vary from one sample point to another more than ± 7.5
percent due to testing variations. If the K.a values vary more than ±7.5
percent and no apparent test procedure problems are found, he states that the
test results should be rejected on the basis of incomplete mixing.
07
Boon reports that unsteady state testing utilizing the basic mass
transfer equation assumes that the water being aerated is completely mixed and
that at any time the concentration of DO is uniform throughout the water. He
notes that this is usually achieved with diffused air systems but does not
strictly apply for mechanical surface aerators. Hoy!and has recommended
procedural modifications to account for DO variations in the water. He notes
that the error will be relatively small if the variation in DO at any point
in the tank, in comparison with the mean value of DO, is less than 10 percent
of the DO deficit.
9
Standard Methods notes that a single K.a value is reproducible within
±15 percent of the mean for multiple aerators and ± 8 percent for a single
2
aerator per basin. It is reported in Standard Methods that if the DO con-
centration at all points is within 0.25 mg/£ of the average DO at time t, you
may make one K.a determination. If not, then individual KLa values must be
determined for each sample point. Non-parallel slopes indicate incomplete
mixing, and the test results should be voided.
Smart, in the Ontario Ministry of the Environment procedure for
mechanical aerators, requires that the K.a values for each sample point shall
not vary more than ± 10 percent from the average value. Greater variation
shall indicate incomplete mixing and invalidate the test. Naimie et al.
report that the standard deviation of KLa data in their testing program was
equal to about 7 percent of the mean K^a values obtained during bench, pilot,
or full-scale aeration testing.
Boon23 reports that the K.a variation should not be used as an indica-
tion of poor mixing. He states that the DO variation at each sampling point
is a better indicator of poor mixing. He further states that the variation
94
-------
of K. a may be due to poor sampling procedure, inaccurate measurement of DO,
changes in the "purity" of water, sulfite presence in the water, and/or non-
uniform distribution of DO.
Shell believes that uniform DO concentration throughout the basin is
not a valid indicator of uniform or complete mixing. He states that since
all aeration devices are point sources of oxygen transfer, an oxygen concen-
tration gradient must exist across the aeration device and in the basin.
Section 8 on Geometry, Scale-Up, and Mixing presents discussion con-
cerning the evaluation of mixing. This section notes that "DO gradients are
intrinsic to the reaeration test and do not imply problems related to either
mixing or mass transfer". It is further stated that "the rate of change in
oxygen concentration with time (mg/£ hr) at various points within the test
basin is the primary indicator of mixing conditions when compared to the
mean value of all points". A coefficient of variation limitation is
suggested in Section 8 as follows:
Test Conditions Coefficient of Variation(%)
Factory 5
Field 10
The observation is made in Section 8 that satisfactory compliance with the
limits will not constitute a guarantee of adequate mixing; however, it will
define conditions of equal supply for DO throughout the basin.
Detergent Addition
As noted in the introduction to this section of the report, there are
two primary reasons for consideration of an oxygen transfer test in clean
water with detergent added. The first consideration is that of uncertainty
due to variable water chemistry effects in field testing. It is suggested by
Boon that the addition of detergents overwhelms all the small effects
caused by contaminants in the test water. He indicates that the total effect
of the 5 mg/£ of detergent will swamp the effect of the fractional concentra-
tions of other surface active agents that might be present in the water or
the trace contaminant derived from an unclean aeration basin.
The second consideration is attempting to more closely simulate or
59
predict the actual mixed liquor performance of the aeration system. Boon
has reported that the alpha values for fine bubble aeration systems (.say 0.3
95
-------
to 0.5) are significantly lower than surface air entrainment devices that
have alpha values in the 0.85 to 1.20 range. While testing with detergent
added does not yield the actual mixed liquor alpha for a given aeration device
and set of test conditions, it does provide oxygen transfer performance
results that may more closely predict actual operating performance.
Boon has reported that testing in the United Kingdom is conducted in
clean water and in clean water plus detergent. Approximately 80 percent of
the testing is conducted under clean tap water conditions. He noted that
detergent is added to tap water used for testing aerators for the reasons
noted earlier. He also indicated that its use enables reproducible results
to be obtained irrespective of the purity of the water; thus, tap water,
A
river water,or final effluent may be used. Kayser reporting on practices in
West Germany and Austria indicated that clean water testing is commonly
practiced. However, if the influence of detergents is desired, clean water
with 5 mg/£ of anionic detergents is used.
In discussing the clean water plus detergent procedure utilized in the
United Kingdom, Boon states that household detergents are used to achieve
an average concentration of anionic surfactant of 5 mg/£. An initial concen-
tration of about 7 mg/£ of anionic surfactant (expressed as Manoxol OT) is
established after the addition of the cobalt solution and the sulfite deoxy-
genation step. The detergent is prepared as a concentrated solution in hot
water and is uniformly dispersed into the test tank. The detergent concen-
tration is measured in the test water at the beginning and end of the test.
The goal is to achieve an average concentration of 5 mg/£. For subsequent
tests, cobalt is added each time, equivalent to 0.2 mg/£ of cobalt in the
test water. Additional detergent is also added to achieve an initial deter-
gent concentration of 7 mg/£.
Ewing'et al. reported on testing with pure LAS. The results indicated
that the concentration of LAS declined substantially (e.g., from 11 to 5 mg/£)
during each test and the results were quite varied, indicating poor reprodu-
cibility. The alpha values varied from 0.39 to 0.55 from the beginning to
the end of the test. They stated that "this phenomenon, which dominated the
tests using LAS, invalidates the analysis by the non-steady state method".
They also observed that significant amounts of foam billowed about the test
site. They further stated that "if such a test is to be meaningful, more
96
-------
work is required. Such work certainly seems justified because the use of the
appropriate value of alpha is of great importance and constitutes one of the
greatest areas of uncertainty and potential error in the present available
predictive methods".
40
Gilbert discussed the effect of surfactants on oxygen transfer rates
and surface tension. Gilbert cites several tests where alpha factors for
"detergent-added" testing have varied with the type of aeration system. He
notes that these results seem to support justification for use of a surface
active agent in clean water tests.
40
However, Gilbert states that "he sees no benefit in rating aerator
performance with surface active agents present. The only accomplishment
would be to introduce another variable to an already too-confused technical
area". He cited the wide variation in types and concentrations of surface
active agents in use. He also noted that the surfactant concentration
decreases during a test run and the surface tension varies during a test run.
Naimie et al. stated that "the effects of detergent on the probe and
Winkler K.a determinations for a variety of natural water systems would have
to be quantified before they could support the inclusion of the addition of
detergent to the test water in any proposed aeration testing standard".
Brenner has stated that "if the addition of detergent will give us a
handle on what might be expected in the actual field installation, we might
be better off in the long run with standard tests that use detergent".
It appears that there are several valid reasons for conducting "added-
detergent" testing despite the test uncertainties. Additional research and
testing will hopefully clarify some of the uncertainties.
SULFITE OXIDATION
It has been suggested that the sulfite oxidation (or steady flow sulfite
addition) method be discussed. Conway and Kumke and Boon have reported
on the use of sulfite oxidation and have indicated that the transfer rates
and efficiencies obtained are considerably higher (up to 40 percent) than
those determined in clean water testing and are not related to the values
27
obtained in mixed liquor. Boon has noted that a steady flow sulfite addi-
tion method as reported by Schmit et al. may be needed to evaluate oxygen
transfer in a deep shaft system. Schmit et al. suggested that the steady
97
-------
state flow method is applicable to other systems also and has several advan-
tages over the unsteady state method.
RECOMMENDATIONS FOR STUDY
1. Additional investigation is needed to consider limiting geometry
(e.g., minimum dimensions and maximum tank size).
2. Requirements regarding the required degree of mixing, if any, for
valid oxygen transfer rate analysis should be evaluated. Subgroup B
(Modelling and Data Interpretation) indicates that complete mixing
is not needed, yet such a statement is cited as a requirement in
some testing procedural descriptions.
3. Recommended procedures for air flow and power measurement should be
refined. More information is needed regarding precision of measure-
ments, best methods, type of calculation versus type of compressor,
and brake versus line horsepower.
4. The area of water quality impacts requires considerable study. Work
is needed to more clearly define which parameters have a significant
impact on transfer rates and analytical measurements and in what
concentrations. Existing information should be studied and addi-
tional experiments designed.
Results of testing at variable TDS levels should be studied further
to verify the type of testing limitation recommended.
Cobalt effects should be restudied. Consideration of catalyst
limitation and analytical interference need to be addressed.
There should be an evaluation for which tests for surface tension
should be used,and test conditions should be delineated.
5. The following questions should be addressed. What water quality
adjustments can or should be permitted? Should pH limitations be
established and test adjustments required? Can carbon be used to
remove contaminants? What other measures should be considered?
6. Can drinking water standards (EPA and/or International) be used and
modified to define "clean water" for testing?
7. Some additional development of quality control procedures for
selection of sodium sulfite deoxygenation chemicals should be
considered.
98
-------
8. Experiences with varying early (up to 30 percent of C*) oxygen
reaeration response data merit additional study to evaluate the cause
and significance of the variabilities that have been reported.
9. Some additional refinements of pumped-sample procedures may merit
study, e.g., pumpage rates, degassing, etc.
10. Oxygen transfer measurement. The Winkler DO procedure should be
updated to reflect current Standard Methods committee findings and
British experience. Topics to be addressed include cobalt inter-
ference, iodine vaporization, high TDS effects, "detergent-added"
testing end-point clarity, and the meaning and significance of the
"blank" procedure from the 1960 edition of Standard Methods.
The DO probe procedure should be evaluated for potential interfer-
ences that have been reported, e.g., iron, manganese, dissolved
gases. (Some re-evaluation is underway via the WPCF Standard
Methods Subcommittee on Dissolved Oxygen). Should agitators be used
for in-situ placement? The procedure for calibration and to ensure
stability of readings could be more clearly described.
11. Additional testing and specially designed experiments using
"detergent-added" procedures should be conducted to resolve uncer-
tainties and more clearly describe the procedure. Consideration
should be given to specifying a "standard" detergent mixture for
addition to- the test water.
12. Existing repetitive test data should be evaluated to further pre-
scribe the acceptable precision for factory and field testing.
13. The usage and interpretation of K.a point variations and DO gradients
during tests s-hould be reviewed. How do they relate to mixing
and/or test reliability?
REFERENCES
1. Water Pollution Control Federation, Aeration in Wastewater Treatment,
Manual of Practice No. 5, 1971.
2. American Public Health Association, Section 207, "Oxygen Transfer",
- Standard Methods for the Examination of Water and Wastewater, 14th
Edition, pp. 82-88, 1975.
99
-------
3. Berk, W.L., D.J. Lad, D.H. Houck, and J.A. Roeber, "Recommended Practice
in the Testing of Aeration and Oxygenation Devices," Technical Committee
Report, Wastewater Equipment Council, Process Equipment Manufacturers'
Association, May 24, 1972.
4. Kayser, R., "The German and Austrian Standards for Oxygen Transfer in
Clean Water," Report presented at workshop meeting of ASCE Subcommittee
on Oxygen Transfer Standards, San Diego, California, November 28, 1979.
5. Smart, 0., "Procedure for Evaluating Aerator Performance - Mechanical
Surface Aerators," Ontario Ministry of the Environment, Procedures
Statement, June 1977.
6. Stukenberg, J., Aeration Performance Specifications, Black and Veatch
Consultants, Kansas City, Missouri, March 1978.
7. Marotte, F.K., Specifications for the Purchase of Mechanical Aeration
Equipment, C^M Hill, Inc., Consulting Engineers, Bellvue, Washington,
September 1977.
8. Hill, R.D., Aeration Performance Specifications, Bovay Engineers, Inc.,
Houston, Texas, March 1979.
9. Stukenberg, J.R. and V.N. Wahbeh, "Surface Aeration Equipment: Field
Performance Testing Versus Shop Performance Testing," Proceedings,
Workshop Towards an Oxygen Transfer Standard, EPA-600/9-78-021,
pp. 167-179, April 1979.
10. Bewtra, J.K. and W.R. Nicholas, "Oxygenation from Diffused Air in Aera-
tion Tanks," Journal WPCF, 36:1195, October 1964.
11. Schmit, F.L., J.D. Wren, and D.T. Redmon, "The Effect of Tank Dimensions
and Diffuser Placement on Oxygen Transfer," Journal WPCF, 50:1750,
July 1978.
12. Rooney, T.C., "Influence of Tank Geometry on Aerator Performance,"
Proceedings, Workshop Towards an Oxygen Transfer Standard, EPA-600/9-
78-021, pp. 50-58, April 1979.
13. Scaccia, C. and C.K. Lee, "Large Scale Mass Transfer Evaluation Tech-
niques for Aeration Systems: A Critical Review," Paper presented at the
50th WPCF Conference, Philadelphia, October 3-6, 1977.
14. Kalinske, A.A., L.D. Lash, and G.L. Shell, "Cobalt Interference in the
Non-Steady State Clean Water Test," Water and Sewage Works, 120:54,
July 1973.
15. Landberg, C.G., B.D. Graulich, and W.H. Kipple, "Experimental Problems
Associated with the Testing of Surface Aeration Equipment," Water
Research, 3:445-455, 1969.
16. Naimie, H., S. Nelson, and D.A. McCarthy, "Influence of pH and Iron and
Manganese Concentrations on the Non-Steady State Clean Water Test for
the Evaluation of Aeration Equipment," Proceedings, Workshop Towards an
Oxygen Transfer Standard, EPA-600/9-78-021, pp. 91-104, April 1979.
17. Federal Register, National Interim Primary Drinking Water Regulations -
U.S. EPA, December 24, 1975.
100
-------
18. Federal Register, National Secondary Drinking Water Regulations - U.S.
EPA, July 19, 1979.
19. Sanks, R.L., Water Treatment Plant Design, Ann Arbor Science, pp. 37-40,
1979.
20. Stenstrom, M.K., "Alpha, Beta, and Theta Corrections," Report of Sub-
group D, ASCE Subcommittee on Oxygen Transfer Standards, May 1979.
21. Pentech Division, Houdaille Industries, Cedar Falls, Iowa, Personal
communications on testing procedures, 1977.
22. Mandt, M.G., Pentech Division, Houdaille Industries, Cedar Falls, Iowa,
Personal communications on use of nitrogen stripping, 1977.
23. Boon, A.G., Personal communication on unsteady state testing procedures,
Workshop meeting of ASCE Subcommittee on Oxygen Transfer Standards, San
Diego, California, December 1, 1979.
24. Rooney, T.C., Rexnord, Milwaukee, Wisconsin, Personal communication on
clean water test procedures, September 11, 1979.
25. Kalinske, A.A., Camp, Dresser, & McKee, Inc., Walnut Creek, California,
Personal communication on clean water test procedures, April 30, 1979.
26. Berk, W.L., Lakeside Equipment Corporation, Bartlett, Illinois, Personal
communication on cobalt concentration, June 1, 1979.
27. Boon, A.G., "Measurement of Aerator Performance," Paper presented at
symposium for British Hydromechanical Research Association, Water
Research Centre, Stevenage, England, April 25, 1980.
28. McKinney, R.D., Personal communication on sulfite addition procedures,
U.S. EPA/ASCE Workshop Toward an Oxygen Transfer Standard, Pacific
Grove, California, April 1978.
29. Stukenberg, J.R., V.N. Wahbeh, and R.E. McKinney, "Experiences in
Evaluating and Specifying Aeration Equipment," Journal WPCF, 49:66-82,
January 1977.
30. Stanton, J.L. and P.R. Bradley, "Experimental Evaluation of Subsurface
Aeration Systems," Proceedings of the 30th Industrial Waste Conference,
Purdue University, May 1975.
31. Naimie, H. and D. Burns, "Cobalt Interference in the Non-Steady State
Clean Water Test for the Evaluation of Aeration Equipment-!, Causes and
Mechanisms," Water Research, 11:659-666, 1977.
32. Naimie, H. and D. Burns, "Cobalt Interference in the Non-Steady State
Clean Water Test for the Evaluation of Aeration Equipment-11, Occurrence
and Magnitude for Various Natural Water Systems," Water Research, 11:
667-671, 1977.
33. Paulson, W.L., Unsteady State Testing Projects, Manufacturer's Reports
and University Studies, University of Iowa, Iowa City, Iowa, 1970-1979.
34. Yunt, F.W., Aeration Equipment Evaluation, Clean Water Test Procedures,
Los Angeles County Sanitation Districts' Document, September 1977.
101
-------
35. Zlokarnik, M., "Sorption Characteristics for Gas Liquid Contacting in
Mixing Vessels," 1978 Advances in Biochemical Engineering 8, Springer-
Verlog Berlin Heidelberg, Germany.
36. Boon, A.G., Water Research Centre, Stevenage, England, Personal communi-
cation on water quality interferences in unsteady state testing,
October 22, 1979.
37. Sanitaire-Water Pollution Control Corporation, Milwaukee, Wisconsin,
Aeration Equipment Performance Tests, Company Procedural Statement,
December 1976.
38. Envirex, Inc., Milwaukee, Wisconsin, Aeration Equipment Performance
Tests, Company Procedural Statement, December 1976.
39. McKeown, J.J. and D.A. Okun, "Oxygen in Waste Treatment, Effect of
Surface Active Agents on Oxygenation," Report of Department of Sanitary
Engineering, University of North Carolina, June 1960.
40. Gilbert, R.G., "Measurement of Alpha and Beta Factors", Proceedings,
Workshop Towards an Oxygen Transfer Standard, EPA-600/9-78-021, pp. 147-
162, April 1979.
41. American Society for Testing Materials, "Water", Part 31, Annual Book of
ASTM Standards, Philadelphia, 1978.
42. Ewing, L., D.T. Redmon, and J.D. Wren, "Testing and Data Analysis of
Diffused Aeration Equipment," Journal WPCF, 51:2384-2401, October 1979.
43. Shell, G. L., "Sampling Considerations," Proceedings, Workshop Towards
an Oxygen Transfer Standard, EPA-600/9-78-021, pp. 72-75, April 1979.
44. WPCF Standard Methods Joint Task Group on Oxygen Transfer, Second Draft,
Section 208, "Oxygen Transfer," October 5, 1978.
45. Gilbert, R.G. and S.J. Chen, "Testing for Oxygen Transfer Efficiency in
a Full-Scale Deep Tank," Proceedings of the 31st Industrial Waste Con-
ference, Purdue University, May 1976.
46. Conway, R.A. and G.W. Kumke, "Field Evaluation of Commercial Aeration
Equipment," Journal of the Sanitary Engineering Division, ASCE,
92(SA2):21, 1966.
47. Mixing Equipment Company, Rochester, New York, Testing Procedural Recom-
mendations, Lightnin Technical Manual, June 16, 1977.
48. Lakin, M.B., "Chemical Catalyst Interference in the Winkler Titration
Determination of Dissolved Oxygen - A Method for Correction," Water
Research, 10:961-966, 1976.
49. The Standing Committee of Analysts, The Department of the Environment,
Draft of Dissolved Oxygen in Natural and Waste Waters, 1979 Version,
Her Majesty's Stationery Office, London, England.
50. Stack, V.T., Jr., "Analytical Measurement and Saturation Values for
Dissolved Oxygen in Water," Proceedings, Workshop Towards an Oxygen
Transfer Standard, EPA-600/9-78-021, pp. 76-84, April 1979.
102
-------
51. Montgomery, H.A.C., "Discussion of Atmospheric Oxygenation in a Simulated
Stream," Journal of the Sanitary Engineering Division, ASCE, pp. 356-
358, April 1969.
52. Stack, V.T., Jr., Betz-Converse-Murdoch, Inc., Plymouth Meeting,
Pennsylvania, Personal communication on dissolved oxygen probes,
June 6, 1979.
53. Conti, J.A., Union Carbide Corporation, Personal communication on DO
probe electrical interference, January 14, 1980.
54. Salzman, R.N., Mixing Equipment Company, Rochester, New York, Personal
communication on dissolved oxygen measurement, May 16, 1979.
55. Boyle, W.C., P.M. Berthouex, and T.C. Rooney, "Pitfalls in Parameter
Estimation for Oxygen Transfer Data," Journal of the Environmental
Engineering Division, ASCE, 100(EE2):391-408, April 1974.
56. Baillod, C.R. and L.C. Brown, Report of Subgroup B, "Modelling and Data
Interpretation," ASCE Subcommittee on Oxygen Transfer Standards, March
1980.
57. Hunter, J.S., III, 3M Corporation, St. Paul, Minnesota, Personal communi-
cation on dissolved oxygen saturation, November 27, 1979.
58. Hoyland, G., "Mass-Transfer Model for Aeration," Progress in Water
Technology, 11(3}:237, 1979.
59. Boon, A.G., "Discussion of Working Group Summary Reports," Proceedings,
Workshop Towards an Oxygen Transfer Standard, EPA-600/9-78-021, pp. 260-
262, April 1979.
60. Boon, A.G., Water Research Centre, Stevenage, England, Personal communi-
cation on detergent-added testing procedure, January 18, 1980.
61. Brenner, R.C., "Discussion of Working Group Summary Reports,"
Proceedings, Workshop Towards an Oxygen Transfer Standard, EPA-600/9-78-
021, p. 261, April 1979.
103
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SECTION 6
EFFECTS OF ALPHA, BETA, AND THETA FACTORS AND SURFACTANTS ON
SPECIFICATION, DESIGN, AND OPERATION OF AERATION SYSTEMS
INTRODUCTION
Many factors influence oxygen transfer mechanisms in wastewater treat-
ment processes. Wastewater contaminants, temperature, dissolved oxygen (DO)
concentration (driving force), type of aeration device, turbulence, and basin
geometry all affect oxygen transfer rate. Since these factors make field
application of an aeration device unique, it has become standard practice to
specify aeration equipment at "standard conditions" and to develop additional
techniques for adjusting rates at standard conditions to rates at field
conditions.
Standard conditions in the United States are considered to be 20°C,
1 atm. barometric pressure, tap water, and zero DO concentration. In Europe,
standard conditions are slightly different and 10°C is the standard tempera-
ture. Additionally, in the United Kingdom, a surfactant (commercial deter-
gent) is used to change the properties of tap water to more closely approach
the properties of wastewater and to mask the effects of trace contaminants in
tap water.
Field oxygen transfer rates, OTRf, are calculated from standardized
oxygen transfer rates, SOTR, through the use of alpha, a; beta, g; and theta,
9 factors. The factors are defined as follows:
KLaww = a KLaTP (52)
C*ww = P C*TP
104
-------
(5)
where:
K,a = apparent volumetric mass transfer coefficient, t"
3
C* = average DO saturation concentration attained at infinite time, mL
ww = subscript indicating wastewater
TP = subscript indicating tap water
T = subscript indicating a given temperature, T
OTRf can be easily calculated from SOTR:
OTRf =
C*
L
(BC* - CD) (54)
where:
3
CR = desired DO concentration under normal operation, mi
Equation 54 differs slightly from Equation 48 in Section 4 in that the
saturation temperature correction factor, t, has been omitted for convenience
to illustrate the influence of a, g, and 6 on OTR,.. The importance of
properly determining the alpha, beta, and theta factors cannot be overesti-
mated. For example, the field transfer rate is only 52 percent of the
standardized transfer rate when CR = 2, a = 0.8, 3 = 0.9, and T = 18° and
assuming 6 = 1.024. Drastic over- or under-designed aeration systems can
result if inaccurate correction factors are used. A profile of errors in
field oxygen transfer rate for incorrect alpha and beta factors is shown in
Figure 7.
It is extremely difficult to accurately determine alpha, beta, and theta
parameters. It is not unusual for two individuals to measure very different
factor values for a given wastewater. In addition, manufacturers and engi-
neers have developed different methods for measurement, which result in
differences in design and specification of aeration facilities.
The purpose of this section of the report, prepared by the Alpha, Beta,
and Temperature Corrections Subgroup of the ASCE Subcommittee on Oxygen
Transfer Standards, is to present the best available techniques for measuring
and characterizing alpha, beta, and theta factors and the effect of
105
-------
o
o
a.
a.
_i
<
UJ
X
50
30
10
o: -10
o
DC.
a:
UJ
£-30
UJ
o
cr
UJ
NUMBERS ON CONTOURS CORRESPOND
TO THE PERCENT ERROR IN TRANSFER RATE
I , I I
_L
_L
Figure 7.
-20 -12 -4 4 12 20
PERCENT ERROR IN THE BETA FACTOR
Error in field oxygen transfer rate as a function of errors
in the measurement of the alpha and beta factors when
alpha = 0.8 and beta = 0.9.
surfactants on aeration systems. The best available techniques have been
selected by a consensus opinion of experts in the field of aeration --
consulting engineers, manufacturers, researchers, and academic professionals.
A review of the relevant background is presented in the initial portion
of this section, followed by a review of important and recent findings by
Subcommittee members and other researchers. The literature review and sum-
mary are to serve as partial justification for the Subgroup's conclusions.
ALPHA FACTOR
Several technical problems are associated with measuring the alpha
factor as recently discussed by Gilbert. The alpha factor varies with many
process conditions, including wastewater quality, intensity of mixing or
turbulence, suspended solids concentration, method of aeration, scale, and
other factors. The effect of aeration methods is particularly important with
106
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respect to the alpha factor. It is not unusual to observe vastly different
alpha factors using two different aeration methods for the same wastewater.
It is worthwhile to document this clatim from a historical perspective.
i
One of the first references to the dependence of the alpha factor upon
2
aeration devices was made by Kessener and Ribbius. They noted changes in
oxygen transfer rate for two different methods of aeration using tap water '
and sterilized wastewater. They reported concentration versus time data,
I
which can be used to calculate apparent mass transfer coefficients and alpha
factors (Table 9).
It is obvious from the data presented in Table 9 that the alpha factor is
2
quite different for the two aeration Systems. Kessener and Ribbius do not
attempt to explain the reasons for the large difference in alpha factors,
but indicate that such differences must be included in the design of aeration
systems. It is also interesting to note that they proposed further research
to determine if the influence of wastewater contaminants on oxygen transfer
capacity should be included in aeratojr specifications.
The effect of aeration methods on alpha was demonstrated by Holroyd and
Parker using laboratory-scale devices. They used a mixture of tap water and
several types of surfactants to show jthat diffused aeration was affected
differently than mechanical surface aeration by water contaminants. They
found that the alpha factor of a fine bubble diffuser (0.28-cm mean bubble
diameter) could be as low as 0.5 in the presence of high surfactant concen-
trations (20 to 100 mg/£). The same purfactant concentrations reduced the
alpha factor of a 30-cm diameter disc surface aerator to only 0.8. Moreover,
the different methods of aeration exhibited the greatest reductions in the
alpha factor with different types of surfactants (i.e., cationic versus
anionic).
4
Baars has reported the effects of surfactants on fine bubble Capproxi-
metely 0.25-cm mean diameter) aeration. He found that commonly-used anionic
and nonionic surfactants at 4 to 10 mg/£ concentration produced an alpha
factor ranging from 0.9 to 0.4, respectively. The addition of anti-foaming
4
agents reduced the alpha factor range from 0.8 to 0.35. Baars also tested
the Kessener brush aerator under simiflar conditions, finding that the alpha
factor increased, ranging from 1.0 to approximately 2.0 for high surfactant
concentrations. The addition of anti-foaming agents tended to reduce the
io?
-------
TABLE 9. APPARENT MASS TRANSFER COEFFICIENTS AND ALPHA
FACTORS FOR THE DATA OF KESSENER AND RIBBIUS2
Method of Aeration
Kessener brush
Kessener brush
Compressed air
Compressed air
Liquid
Tap water
Sterilized
wastewater
Tap water
Sterilized
wastewater
K.a (min" )
0.057
0.047
0.068
0.013
a
N/A
0.82
N/A
0.20
4 3
maximum alpha factors. Results similar to Baars and Holroyd and Parker's
for fine bubble diffusers have been reported by a number of investigators,
5 67
including Eckenfelder et al., Downing and Scragg, Burgess and Wood,
8 9
O'Connor, and Aiba and Toda, as well as many others.
The results of Barnhart's work (Figure 8), are particularly noteworthy
because they illustrate the importance of bubble diameter. Barnhart reports
that the addition of surfactants reduces the bubble diameter until the
critical micelle concentration is reached. Beyond the critical micelle con-
centration, very little reduction in bubble diameter occurs. Reduction in
bubble diameter produces two distinct results: an increase in surface area
per unit bubble volume and a decrease in terminal rise velocity. The
decrease in terminal rise velocity results in longer bubble retention time,
but reduces the surface renewal rate. The total of all mechanisms on alpha
(reduction of film transfer coefficient, increase in surface area and reten-
tion time, reduction in surface renewal) has been estimated by Barnhart for
fine bubble diffusers. His estimates confirm the findings of field investi-
2
gators such as Kessener and Ribbius, who observed very low alpha factors.
The oxygen transfer rate of fine bubble diffusers appears to be more reduced
by surfactants than the transfer rate of other aeration methods since the
bubble size cannot be further reduced by the surfactant.
The effects of surfactants on alpha have been investigated for various
types of surface aerators. Downing et al. investigated alpha factors for
the Searle aerator (a modified brush-type aerator) and a Simplex Cone
aerator (vertically rotating low speed surface aerator with draft tube).
108
-------
UJ
(T
UJ
o
g
or
z>
CO
QL
O
KLc BASED ON HYR VOL
OF AREA/VOL. hUO
SURFACE AREA/
VOLUME OF AIR
0
0 JO .20 .30 .40 .50 ,60 .70
BUBBLE DIAMETER, dg(cm)
Figure 8. Effect of bubble size on mass transfer. This figure
was taken from Barnhart.
The alpha factor was approximately 2.0 for the Searle aerator in the presence
of 10 mg/£ ABS. For the Simplex Cone aerator, they concluded that an increase
in oxygen transfer rate of 10 to 15 percent could be expected with surfactant
addition, which corresponds to an alpha factor of 1.1 to 1.15. They also
report that anti-foaming agents reduced the alpha factor. Similar results
12 13
have been reported by Eckenfelder and Ford and von der Emde.
The effects of surfactants on other types of aeration systems, such as
static mixers and turbine aerators, have not been widely documented. Otoski
et al. have reported on the effects of surfactants on the alpha factor for
static mixers. They found the alpha factor exceeded 1.0 at high mixing
levels and decreased at low mixing levels. One manufacturer has reported
that the alpha factor for jets ranges from 0.9 to 1.2.
The mechanism of surfactant interference has been investigated by Mancy
Ifi 17 1 ft 1 R
and Okun, McKeown and Okun, and Mancy and Barlage. Mancy and Bar! age
have shown that the effects of surfactants in aeration can be divided into
two categories: the effect of the adsorbed surfactant film, which increases
the resistance to transfer, and changes in hydrodynamic behavior of the air-
liquid interface, which results from changes in surface tension produced by
the surfactant. Included in this second category are changes in bubble
109
-------
dynamics and shape and reductions in surface renewal caused by the presence
of the adsorbed surfactants.
18
Mancy and Barlage used three experimental designs in their investiga-
tion: a 50-cm bubble column, a surface aerator, and a laminar jet orifice.
With the laminar jet aerator, they were able to observe the effects of sur-
factants on the molecular diffusion coefficient independently of changes in
hydrodynamic conditions. They demonstrated that hydrodynamic conditions,
which are in large part created by the intensity of mixing, power input, and
unique characteristics of each aeration device, will greatly affect oxygen
transfer rate. Their results, which have been supported by Mueller19 and
others, explain why different types of aeration devices are affected dif-
ferently by surfactants.
I Q
The work of Mancy and Barlage also shows that the rate of surfactant
adsorption (a function of the type of surfactant) to the gas-liquid interface
will also affect oxygen transfer. Their results provide a partial theoreti-
cal basis for the observations of many other investigators. This phenomenon
can be characterized by dynamic surface tension measurements. The commonly
accepted du Nouy ring method for measuring surface tension indicates static
surface tension and does not measure dynamic surface tension. Methods have
been proposed to measure dynamic surface tension. Among these are the
1 O
"ripple" method described by Mancy and Barlage and various rate of bubble
formation methods.
The alpha factor also changes substantially with wastewater character-
20
isties. For example, Bass and Shell report alpha factor fluctuations of
21
0.5 to 1.0 for various wastewaters and Eckenfelder has reported the alpha
factor for an industrial wastewater to vary between 0.3 and 0.8. The
variance in alpha factor can largely be attributed to the changing charac-
teristics of the raw wastewater with time of day or day of week. The results
22
of an investigation by Katz demonstrate this apparent time-varying of the
alpha factor (Table 10); the data represent the results of a 3-mo comprehen-
sive study of oxygen transfer rates. The K.a values were measured by off-gas
analysis in a two-pass aeration tank approximately 15 ft deep by 45 ft wide
by 370 ft long, equipped with fine bubble diffusers. It is not possible to
calculate alpha factors from these data since the clean or tap water transfer
rate is not known; however, a "transfer factor" has been calculated that
110
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TABLE 10. VARIATION IN OXYGEN TRANSFER RATE AT THE
JONES ISLAND TREATMENT PLANT*
Date
6/18/64
6/24/64
6/26/64
7/8/64
7/16/64
7/22/64
7/24/64
7/28/64
7/29/64
7/30/64
8/5/64
8/6/64
8/12/64
8/13/64
8/14/64
8/20/64
8/21/64
8/26/64
8/27/64
9/2/64
KLaf
(days'1)
59.6
87.8
84.0
124.7
102.4
122.5
97.1
76.3
68.9
91.0
103.2
91.0
70.1
96.4
94.8
78.6
93.2
84.7
98.6
76.3
Transfer Factor
0.66
0.97
0.93
1.39
1.13
1.36
1.08
0.85
0.76
1.01
1.13
1.01
0.78
1.07
1.05
0.87
1.03
0.94
1.09
0.85
* 99
After Katz.
fMean KLa = 90.1 days" ; variance in KLa = 273 days"2.
Transfer factor is the ratio of the observed transfer rate to the mean
transfer rate.
f
represents the ratio of the daily measured transfer rate to the mean value of
all measured rates. The transfer factor ranges from minimum of 0.66 to a
maximum of 1.39. If the maximum observed transfer rate is approximately equal
to the clean water transfer rate, then the range of observed alpha factors
can be estimated as 0.47 to 1.0. The magnitude of this range is conclusive
111
-------
evidence for the need to characterize the variance of the alpha factor due
to changing wastewater characteristics.
Kalinske and Pfeffer et al.24 report that the alpha factor also varies
with the degree of treatment and with the location of sampling points in
activated sludge aeration basins. Generally, the alpha factor is lowest for
the influent wastewater and increases to a maximum for the effluent waste-
25
water, although Marotte has observed an opposite trend.
Suspended solids concentration has also been reported to affect alpha.
26
Downing experimented with a range of suspended solids concentrations from
0 to 3,000 mg/£ and found alpha decreased with increasing solids concentra-
2
tion. Holroyd and Parker observed no change in alpha with additions of
bentonite. It is not clear whether the solids themselves affect alpha or if
the effect is produced by organics associated with the solids.
From the previous discussion, it can be concluded that:
1. The alpha factor is very strongly affected by the method of aeration,,
whether using bench-, pilot-, or full-scale equipment. It appears that
different methods of aeration have different levels of turbulence and surface
renewal, which produce a different response in the alpha factor in the
presence of surfactants.
2. The time-varying nature of many municipal and industrial wastewaters
causes large fluctuations in the alpha factor. Also, the alpha factor will
not necessarily be the same for different locations within wastewater treat-
ment plants. For municipal wastewaters and treatment systems, the alpha
factor is usually lowest for the influent wastewater and highest for the
effluent; however, this trend may not be true for industrial cases.
3. The literature contains many seemingly contradictory findings
indicating that present knowledge is inadequate to explain and quantify the
effects of process conditions on the alpha factor or that the effects on
alpha are so variable that it is not possible to develop general guidelines.
It is apparent that the effects of contaminants on the alpha factor must be
evaluated on a case-by-case basis.
4. The scale of the equipment used to determine alpha can have pro-
27 28
found effects on the results, as reported by Barnhart and Otoski among
29
others. It has been reported by Matsch that the effects of scale can be
112
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partially eliminated if proper dynamic and geometric similarity are main-
tained, but this belief is not consensus of the Subgroup. Several investiga-
tors have advanced the opinion that alpha testing in laboratory or pilot-scale
vessels should be performed at the same K. a as the proposed full-scale plant;
however, for deep-tank aeration systems, an equivalent K.a in a small pilot-
or bench-scale vessel can only be obtained at very different levels of
turbulence and air flow rates. Utilizing the "equivalent K.a" approach could
result in incorrect alpha measurement since it has been shown that the alpha
factor is related to turbulence level.
5. The ability to measure alpha independently of scale is extremely
desirable and should receive priority for development.
6. It must be emphasized that the alpha factor used for designing an
aeration system will be a range of values and not a single number.
ALPHA FACTOR TESTING: AN ALTERNATE APPROACH
The previous discussion has shown that it is extremely difficult to
determine meaningful alpha factors. An alternate approach has been suggested
that should be considered. The British have developed a different set of
conditions for specifying aeration equipment. They add 5 mg/£ of a synthetic
anionic surfactant to test waters to simulate the contaminants in wastewater
that affect oxygen transfer and to minimize the effects of trace contaminants
in tap water which affect oxygen transfer. Using this test procedure, the
British contend that more meaningful standard aeration rates are measured,
which places less importance on proper alpha factor testing. This concept
can be advanced by defining a (alpha bar) for all types of aeration equipment.
This proposal has several advantages and disadvantages. The primary
disadvantage is the length of time that would be required to develop a new
standard in the United States based on a "detergent-added" approach.
Undoubtedly, many years work would be required before all manufacturers could
change testing procedures to accommodate surfactants. Additionally, more
complex shop testing procedures place an additional burden upon manufacturers,
especially small manufacturers. Nevertheless, developing such a standard
could result in reduction of design error caused by improper alpha factor
testing. This reduction could result because the magnitude of measured alpha
factors would be much closer to unity, due to the inclusion of the effects of
113
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surface tension in the manufacturer's specifications. A new concept of
defining the alpha factor could be used, based upon British practice, as
follows:
where:
« = KLaww/KLaTP+S
KLaww = mass transfer coefficient in wastewater
KLaTP+S = mass transfer coefficient in tap water with a surfactant added
There are problems in defining a proposed standard for "alpha bar".
Ideally, the quantity of surfactant used should reduce the tap water surface
tension to less than 40 dynes/cm. However, the surface tension and surfactant
concentration can change during aeration, which has been reported by Ewing
30
et al . among others. Surface tension measuring equipment is expensive and
not easily transported. In addition, this approach does not specifically
address the problem of alpha factor dependence upon turbulence and mixing
intensity.
Many years of successful British practice represent a significant incen-
tive to develop a "detergent-added" testing practice in the United States.
"Detergent-added" testing procedures are also being evaluated in Germany and
other European countries.
BETA FACTOR
The beta factor, 3, has been defined as the ratio of the saturation DO
concentration in wastewater to the saturation DO concentration in clean tap
water:
C (56)
An accurate value of saturation DO concentration is required to accurate-
ly estimate the oxygen transfer capability of an aeration device. Unfortu-
nately, the saturation DO value is affected by a large number of variables
and process conditions, including barometric pressure, temperature, suspended
solids, dissolved organics, and dissolved solids. Many wastewaters contain
sufficiently high dissolved solids concentrations to significantly reduce the
saturation DO concentration.
The beta factor has been found to vary over a broad range, although
variations are generally less than those reported for the alpha factor.
114
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Eckenfelder et al. have reported that the beta factor for domestic waste-
water is generally about 0.95 and that it can vary over a much broader range
for industrial wastewaters. For example, they measured the beta factor for
pulp mill wastes using the Winkler test and found it varied from 0.77 to 0.97.
Significant technical problems exist in measuring beta factors. The
most common wet chemical analysis for DO, the Winkler analysis (.as specified
by Standard Methods ), is subject to interferences that make the test ineffec-
tive for some types of wastewaters. Interferences have been reported by
9 *3 9 £ 9 C\
Kalinske and Marotte among others. Marotte has found that the amount of
manganous sulfate added to the sample for DO analysis may change the measured
value of DO concentration. He has hypothesized that organic matter in some
wastewaters may chelate metal ions, such as manganese or cobalt, thereby
reducing their activity in solution and changing the measured DO.
It has been proposed that the DO probe be used to determine beta values.
This alternative is attractive since the galvanic cell in a DO probe is
isolated from the wastewater constituents that interfere with the Winkler
test. Unfortunately, the DO probe cannot be used to measure beta factors
since the probe responds to the activity of molecular oxygen and not concen-
tration. This phenomenon has been discussed extensively by Carritt and
32 33 34
Kanwisher, Mancy and Westgarth, and McKeown et al.
An alternative method for measuring beta factors, which has been pro-
20
posed by Bass and Shell and several Subcommittee members, is to use an
analytical correction factor based upon the total dissolved solids (TDS)
concentration. With this technique, a wastewater must be measured for TDS
before a beta value can be determined. Once the TDS concentration is known
and corrections are made for barometric pressure and temperature, the beta
factor can easily be calculated.
To determine the beta factor using the TDS concentration, it is necessary
to refer to a table of saturation DO values. Using an abbreviated list of
saturation DO concentrations (Table 11), it is possible to estimate the 3
factor. For example, if the TDS of a wastewater is measured as 10,000 mg/£,
the beta factor, at 25°C, can be calculated as the ratio of two saturation
values:
3 = 7.4/8.2 = 0.90 <£(cl = 10 ^/C^ , Q} (57)
115
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Table 11. SATURATION DISSOLVED OXYGEN CONCENTRATIONS
AT VARIOUS CHLORIDE LEVELS*
Wastewater
Temperature
(°C)
15
20
25
30
0
10.1
9.1
8.2
7.5
Chloride Concentration (mg/£)
5,000
9.5
8.6
7.8
7.2
10,000
9.0
8.2
7.4
6.8
15,000
8.5
7.7
7.1
6.5
*
From
Standard Methods.31
Similar results can be obtained using a DO meter with salinity calibration
capability. A number of popular DO meters have special calibration scales
to compensate for salt concentration. Usually, the calibration scales are
associated with the temperature correction potentiometer on the DO meter.
The need for temperature compensation arises from the dependence of a
membrane's permeability on temperature. It can be readily observed that a
change in membrane permeability also produces a change in cell current.
Therefore, a manufacturer can design a DO analyzer that corrects for tempera-
ture as well as activity (indicated by salt concentration) using only one
control. The mechanism of calibration can be explained from an analysis of
electro-chemical theory. The steady state current of a galvanic cell oxygen
analyzer can be computed as follows:
1 = "eFa(Pm/b)A 158)
where:
i = current (Amperes)
n = number of electrons transferred in cell reaction
ct
T = Faraday = 9.649 x 104 (Coulombs/mole)
2 2
P = permeability coefficient (cm /sec), L t
b = membrane thickness (cm), L
2 2
a = area of electrode (cm ), L
A = DO activity (g-moles/1000 cm3)
116
-------
The equation can be rewritten in terms of DO concentration:
i = ne? (Pm/b)rC (59)
where:
r = oxygen activity coefficient
3
C = DO concentration, m/L
In a dilute solution, the DO concentration is nearly equal to the DO activity
and the oxygen activity coefficient has the value of unity. In concentrated
salt solutions, the oxygen activity coefficient is greater than unity,
indicating that the DO activity is greater than the DO concentration.
Several of the Subgroup members have indicated that beta factors other
than unity have been measured using DO probes (without salinity corrections).
The existence of this phenomenon has not been well documented and can only
be explained by the presence of some contaminant in the test water that
changes the saturation DO concentration but does not change the oxygen
activity coefficient. This phenomenon, if it exists, is not known in the
experience of the majority of the Subgroup members; however, if such a
phenomenon occurs, it would be of extreme importance since considerable error
in beta factor measurements could occur. Also this phenomenon could explain
5
the low beta factors measured by Eckenfelder et al. This subject should
receive priority for further development.
THETA FACTOR
Temperature strongly affects aeration systems in a variety of ways. Per-
haps the greatest effect is on the saturation DO concentration. This subject
is well documented. The effects of saturation concentration are not included
in the theta factor since they can be handled in the field transfer equations.
The theta factor has normally been used to relate mass transfer
coefficients:
or:
KLaT = KLa20eG" (60)
KLaT = KLaO
117
-------
where:
K. ay = apparent mass transfer coefficient at temperature = T, t
-1
Kl_a20 = aPParent mass transfer coefficient at T = 20°C, t
6g = geometric temperature correction coefficient
6. = arithmetic temperature correction coefficient
K^Q = intercept value for arithmetic correction model determined by
regression of K.aT versus T data
The geometric technique, Equation 60, is more commonly used. This tech-
nique of correcting for the effects of temperature on oxygen transfer is
empirical and attempts to lump all possible factors, such as changes in
viscosity, surface tension, diffusivity of oxygen, etc. This empirical
approach has produced a great variety of correction factors. Some investi-
gators report that the geometric model yields better correction; others
report that an arithmetic model is preferred. A wide range of temperature
correction factors is reported in the literature (Table 12).
The diversity of data in Table 12 points to the inadequacy of the
simple temperature correction techniques of Equations 60 and 61. Undoubtedly,
the range of thetas could be refined if a closer evaluation of the experi-
mental conditions was made; however, a number of the investigations reported
in Table 12 were made under very precise experimental conditions and very
likely reflect a correct relation between K.a and temperature. The unavoid-
able conclusion is that presently-used temperature correction techniques are
inadequate.
Alternate methods for correcting temperature effects have been proposed
35 36 35
by Metzger and Hunter. Metzger has shown that the effect of tempera-
ture is related to the value of K.a and has recommended correction factors as
a function of K.a. This result is an implication of the temperature depen-
oc
dence of K.a upon turbulence as well as oxygen diffusivity. Hunter has
used a similar approach in relating the value of K.a to temporal mean veloc-
ity gradient: 1/2
where:
v~ = temporal mean velocity gradient, t~
2-3
P = power input, mL t
118
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TABLE 12. TEMPERATURE CORRECTION FACTORS
Temperature Correction
Coefficient
1.047
1.024
1.020
1.024
1.016
1.018
1.015
1.008
1.0192
1.020
1.02
1.024
1.028
1.02
1.047
0.0284
0.0204
0.015
Aeration Model
System
Open channel
Stirred tank
Stirred tank
Stirred tank
Stirred tank
Channel
Channel
Channel
Saran tubes
and spargers
Diffused aerators
—
—
Surface aerators
Turbine and
diffused aerators
Surface aerators
—
Stirred tank
—
Type*
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
A
A
A
Reference
Streeter et al.36
37
Elmore and West
38
Downing and Truesdale
oo
Downing and Truesdale
38
Downing and Truesdale
39
Streeter
40
Truesdale and Van Dyke
40
Truesdale and Van Dyke
Bewtra et al.41
Barnhart10
Clark et al.42
Metcalf and Eddy43
44
Eckenfelder
44
Eckenfelder
45
Lakin and Salzman
46
Ward et al .
38
Downing and Truesdale
Truesdale and Van Dyke
G = geometric; A = arithmetic
V = volume, L
U = absolute viscosity, mL~ t~
This approach accounts for the effects of temperature on liquid viscosity
and turbulence.
From a theoretical standpoint, the approach of either Metzger or
O£
Hunter is preferable; however, based upon present knowledge, it is not
possible to include such a technique in a design standard. It has been shown
119
-------
that different aeration systems can have different characteristics in the
presence of surfactants, and it is plausible that each type of aeration system
has a different correction factor based upon temperature and turbulence.
Therefore, more research and development is required before a temperature
correction technique based upon turbulence can be used.
From the previous discussion, it can be concluded that no single tempera-
ture correction technique can be applied to all methods of aeration. Also,
it is apparent that the effect of temperature on K.a results from changes in
oxygen diffusivity in addition to other factors such as turbulence.
Substantial error can result from applying incorrect theta factors to a
geometric correction technique (Figure 9). The deviation from unity increases
rapidly as the range of temperature correction increases. It is obvious that
the single most effective method for minimizing correction error is to avoid
testing during extremes of water temperature.
3.0
0.5
0 10 20 30 40 50
TEMPERATURE (°C)
Figure 9. Effect of temperature on oxygen transfer rate.
120
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APPARENT MASS TRANSFER COEFFICIENTS
Application of the experimental model to the analysis of unsteady state
reaeration test data yields an apparent value of K.a, defined as K.a. In the
case of surface aeration systems, the true and apparent values of K.a are
equal. However, in subsurface gas injection systems, differences exist
between the true and apparent values. Since a* is defined by a ratio of
true K.a values and a is defined similarly by a ratio of apparent K.a values,
differences will also exist between values of a and a*. The magnitude of
these differences depends chiefly on the oxygen transfer efficiency of the
subsurface gas injection system, with the greatest difference manifested at
high efficiencies. For further discussion of this topic, the reader is
referred to Section 4.
RESULTS AND CONCLUSIONS
From the previous discussion and literature review, it can be concluded
that alpha, beta, and theta testing is at best an inexact science. There are
many factors that are unknown or cannot be controlled in present test
procedures. Consequently, the testing technique can greatly influence results.
To reduce the discrepancies introduced by different techniques, an interim
standard is proposed for determining alpha, beta, and theta factors. The
proposed standard is based in part on the best available technology reported
in the literature and in part on the scientific and engineering judgment
of the Subgroup members. The Subgroup acknowledges that substantial updating
of this proposed standard may be necessary and desirable before it achieves
consensus status.
Alpha Factor
The alpha factor is influenced by a great number of process conditions,
including surfactants, suspended solids, other wastewater characteristics,
turbulence, geometry, scale, water temperature, and aeration method. The
alpha factor ideally should represent the ratio of the performance of a given
aeration system in wastewater to its performance in clean water. Therefore,
it is desirable to eliminate the effects of geometry, scale, and turbulence.
At present, it is not possible, or economically feasible, to specify a test
procedure that will accomplish all objectives. The following alpha test
121
-------
procedure is proposed, therefore, based on the combined technical judgement
of the Alpha, Beta, and Temperature Corrections Subgroup. It is recognized
that the procedure is preliminary and subject to change.
1. The alpha factor is not constant and a series of measurements must
be taken. Adequate aeration system design must consider the possible range
of alpha factors likely to be encountered and an assessment of the risk
associated with inadequate or excessive aeration capacity. Proper aeration
system design cannot be made without knowledge of the range of alpha's to be
encountered. It is recommended that a minimum of three tests be conducted.
2. Alpha testing must be performed using test devices similar to those
being considered for actual design. This constraint is true at all scales of
equipment. For mechanical aeration systems, the level of turbulence used in
the test devices should be the same as the proposed design. A universal
indicator of turbulence is not available, but several indicators have been
suggested, such as Reynolds number, impellar tip speed, power input per unit
volume, and power input per surface area. For diffused aeration systems, the
test diffuser must produce bubbles that are the same diameter as those
expected from the full-scale aeration device. Several tests should be made
to determine the effect of turbulence or mixing intensity on the alpha factor.
3. The alpha factor can change with the degree of treatment. Ideally,
the alpha factor should be determined using the actual fluids to be aerated.
For example, in evaluating alpha for activated sludge plants, the mixed
liquor should be used, including the suspended solids. Also for plug flow
aeration systems, the alpha factor can change throughout the aeration tank.
Proper design must account for this change. Conducting an alpha test using
untreated influent is a poor second choice to using actual mixed liquor and
often, but not always, results in lower alpha factors than are actually
observed in full-scale operation.
4. The scale and geometry of test devices should be as close as possible
to the actual design. It has been reported by one Subgroup member that the
effects of scale can be modeled, but this opinion is not the consensus of
the Subgroup.
The effect of scale on recently-developed devices such as static
aerators and jet aerators, to the knowledge of the Subgroup, has not been
122
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investigated. Ideally, the alpha factor should be independent of the size
and geometry of the device used for its determination.
5. Fresh wastewater samples should be used for alpha testing because
sample characteristics can change very rapidly with time during storage.
6. Special considerations must be made with regard to depth of sub-
mergence in diffused air systems. In diffused aeration, three distinct
phenomena occur: oxygen transfer during bubble formation, oxygen transfer
from rising bubbles, and oxygen transfer at the surface. In full-scale
systems, the first two mechanisms of transfer are significant and transfer at
the surface is usually of small importance. With small-scale devices, the
balance among the three methods can be very different, which can lead to
47
serious errors in estimating alpha factors. For example, Schmit et al.
found that a bench-scale alpha factor of 1.0 was 33 percent higher than the
alpha factor measured with full-scale equipment.
48 S
Several investigators, including Morgan and Bewtra, Aiba and Toda,
49
Ippen and Carver, and others, have demonstrated the effects of depth on
oxygen transfer in diffused aeration systems. Their work should be consulted
for further details.
7. Alpha testing can be performed for two purposes: process design or
performance testing. During a performance test, many of the restrictions on
alpha testing may be relaxed since only one value of alpha is needed at one
point in time. Also, the endogenous phase of bacterial growth can be used
for measuring alpha factors for performance testing. Endogenous-phase alpha
factor testing can lead to erroneous aeration specifications if the resulting
alpha factors are to be used for process design.
8. The likelihood of meaningful scale-up of small, lab-scale tests to
full-scale systems is remote using current, state-of-the-art procedures.
Full-scale testing should be performed whenever possible.
State-of-the-Art for Alpha Factor Determination
It is the consensus of the Subgroup that no method exists for measuring
the alpha factor that is suitable as a standard procedure. However, it is
possible to recommend standards of practice that will serve as a guide for
alpha factor measurement. Methods for evaluating the alpha factor have been
proposed by Barnhart, Mueller, Stukenberg et al., Bass and Shell,
123
-------
and Gilbert;1 the method proposed here draws heavily upon their work.
General Comments --
Alpha factor testing in small-scale vessels is at best only an educated
guess to determine transfer conditions under process conditions. It has been
stated previously by numerous investigators, most notably Kayser,51 that
alpha testing in small laboratory-scale vessels is unreliable and prone to
inconsistencies and inaccuracies. Rigorous attention to detail and experi-
mental technique can eliminate many of the inconsistencies, but even the best
testing procedures are subject to error. Consequently, the alpha factors
determined by the procedure recommended here and elsewhere are only approxi-
mate methods for obtaining process oxygen transfer rates.
General Conditions for Alpha Factor Testing --
To determine alpha factors for a wastewater to be aerated, one must
first select the source of wastewater samples. For example, if the untreated
wastewater is used, a lower alpha factor will generally be measured as com-
pared to treated wastewater. Preferably, an alpha test should utilize the
actual fluid to be aerated. For activated sludge systems, mixed liquor is
the best choice for alpha factor testing.
The oxygen consumption of the sludge can be reduced to a constant rate
by aerating the sludge until it is in the endogenous phase. In this manner,
errors in measuring oxygen uptake rate can be minimized and an alpha factor
for performance testing can be obtained. If it is desired to measure alpha
factors for normal process operation, measurements in the endogenous phase
should be avoided. Two alternatives are available: using settled mixed
liquor, which will have a very low oxygen uptake rate, or using mixed liquor
and attempting to accurately quantify the oxygen uptake rate. The reader is
directed to Section 7 of this report on Oxygen Transfer Measurements in
Respiring Systems where technique and errors associated with oxygen uptake
are discussed. It is noted, however, that the presence of biological solids
is thought to affect the alpha factor; therefore, the reader has to choose
the method that he thinks will produce the least error. The use of untreated
wastewater should be avoided, since erroneously low values of the alpha
25
factor will probably result, although Marotte has occasionally found the
124
-------
opposite to be true.
To properly measure alpha factors, it is imperative that alpha testing
be performed with devices similar to those planned for the full-scale design.
For example, fine bubble diffusers behave differently in the presence of sur-
factants than coarse bubble diffusers or mechanical aerators. To properly
test for the alpha factor in diffused aeration systems, it is necessary to
use a laboratory diffuser that produces bubbles the same diameter as the
full-scale diffuser. This may be very difficult since the hydrostatic head
at the diffuser will be different for the laboratory-scale device than for
the full-scale device. Some investigators have recommended using the
"equivalent K.a" approach for overcoming the problem, but this method is not
recommended since different levels of turbulence are often required to
achieve an "equivalent K.a".
Experimental Setup --
Bench-scale experimental setups for alpha factor testing are shown in
Figures 10, 11, and 12 for turbine, diffused, and surface aeration, respec-
tively. There are several essential features of each setup. The absorption
vessel or reactor should be as large as possible to reduce the effects of
scale. For field testing, it is often impractical to use reactors larger
than 50 gal and, in many cases, even smaller reactors must be used. If
cylindrical reactors are used, it is imperative that the vessels be baffled
with four verticle baffles running from the reactor bottom to the surface.
The baffles must extend from the wall into the reactor a distance of one-tenth
of the diameter.
Methods for deaerating and measuring DO concentrations have been recom-
mended by other Subgroups within the Oxygen Transfer Standards Subcommittee.
Also, the recommended method for data analysis should be used in alpha
factor determination. The pertinent other sections of this report should be
consulted for standard procedures.
To perform alpha determinations, it is first necessary to determine the
clean water performance of the aeration device. Clean water tests should be
conducted using tap water, which is indicative of waters used for shop
testing. Process waters that contain surfactants or waters that produce
visible foaming during aeration will yield erroneous results. It is also
125
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-RG. PIPE
~"- RG. BASE
" — PG BAFFELS
PLAN
LEGEND
P.G.- PLEXIGLASS
S.S.-STAINLESS STEEL
-PURGEMETER
-S.S. BAFFELS
-SS. TURBINE
-AIR FLOW ORIFICE
SECTION
Figure 10. Diagram of bench-scale turbine aeration alpha test
apparatus. This figure was taken from Stukenberg et al.
imperative that the reactor and internals be cleaned prior to use to insure
that all surfactants have been removed. Some investigators have found it
extremely difficult to clean surfactant-contaminated equipment. The use of an
absorbent, such as bentonite, will aid cleaning. If diffusers are used, two
sets should be purchased, one for use with clean water and the other for
process waters.
Turbulence Level --
The alpha factor has been shown to depend upon turbulence intensity.
Unfortunately, it is not possible at present to precisely translate laboratory
experimental results to full-scale applications; therefore, an attempt should
be made to perform alpha testing at the same turbulence levels that are
intended for the full-scale design. For example, Figures 13, 14, and 15
illustrate effects of power intensity on alpha factor measurements observed
52
by Hwang for turbine, diffused, and surface aeration, respectively. In
performing alpha factor testing, it is necessary to ascertain the effects of
126
-------
OIL TRAP FILLED
WITH GLASS WOOL
DO AND TEMPERATURE
METER \
WATER TRAP HALF
FILLED WITH WATER
TWO-STAGE
REGULATOR
\COMPRESSED
-> —AIR
D 0 AND TEMPERATURE
PROBE
STOPWATCH
TIMER
•TYGON TUBING —
»GAS DISPERSION TUBE
WITH DIAMETER
FRITTED
CYLINDER
PLEXIGLAS
AERATION
BASIN LIQUID
GLASS Y
CONNECTOR
I2IN.AIR STONES,
f-f-TUBING, AND CONNECTOR
FOR WASTEWATER
uj
ts>
O
tz
12 IN. AIR STONES FOR
CLEAN WATER
Figure 11. Diagram of bench-scale diffused aeration alpha test apparatus
This figure was taken from Bass and Shell.20
ELECTRONIC
TACHOMETER
VARIABLE-SPEED MOTOR
STAINLESS STEEL TANK
Figure 12. Diagram of bench-scale surface aeration alpha test apparatus,
This figure was taken from Bass and Shell.20
127
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SAA CONCENTRATION
CO
CO
o
LU
2
ID
-J
O
LU
(T
<
Q_
Q_
0.37
0.45
0.52
HORSEPOWER PER UNIT VOLUME (hp/IOOOft3)
o:
o
o
<
Q_
1.0
0.8
0.6
1
4
2
3
SAA CONCENTRATION
1 = 1 mg/r
2 = 3 mg/f
3 = 5 mg/f
4 = 15 mg/t
0.3 0.37 0.45 0.52
HORSEPOWER PER UNIT VOLUME (hp/IOOOft3)
Figure 13. Gas transfer characteristics in a 50-gal vessel with turbine
aeration in the presence of surfactants (dodecyl sodium sulfate),
128
-------
en
h- 6
O Z
•^» ^^" C.
H U 5
U i7
583
a. ir
0
SAA CONCENTRATION
O 0 mg/-P
0 1 mg/f
A 3 mg/-P
D 15 mg/P
0.52
0.60
0.68
HORSEPOWER PER UNIT VOLUME (hp/IOOOff3)
cr
o
H
<
u_
X
QL
0.8
0.6
SAA CONCENTRATION
1 = 1 mg/-e
2 = 3 mg/f
3 = 15 mg/{
0.52 0.60 0.68
HORSEPOWER PER UNIT VOLUME (hp/IOOOft3)
Figure 14. Gas transfer characteristics in a 50-gal vessel with diffused
aeration in the presence of surfactants (dodecyl sodium sulfate),
129
-------
en i
o i- 30
-I UJ
o o
> o
i- tr
Z LJ
U u.
OL (/)
< Z
Q. <
CL Q:
< h-
20
,n
I0
SAA CONCENTRATION
O 0 mg/f
D 1 mg/-P
A 5 mg /-f
0.3
0.6
0.9
1.2
1.5
HORSEPOWER PER UNIT VOLUME (hp/IOOOft3)
SAA CONCENTRATION
cr
o
1.25
O 1.0
0.75
0.50
0.25
1 = 1 mg /I
2 = 5mg/f
0.3
0.6
0.9
1.2
1.5
HORSEPOWER PER UNIT VOLUME (hp/IOOOfr)
Figure 15. Gas transfer characteristics in a 50-gal vessel with surface
aeration in the presence of surfactants (dodecyl sodium sulfate),
130
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turbulence level or power input; therefore, several experiments (at least
three) must be performed, each at a different turbulence level.
Measuring the power input level can be an extremely difficult and time-
consuming job, especially if a variable-speed mechanical mixer is used. One
must measure mixer rotational speed with a tacometer since a simple potentio-
meter setting is much too inaccurate for alpha testing. The power input to
the mixer motor must also be measured. Minor changes in mixer impeller
height can change the power the mixer is consuming and will lead to errors in
alpha factor measurement if not considered. Additionally, for turbine aera-
tors, the mixer power consumption will depend upon gas rate. Using single-
speed mixer motors does not necessarily reduce errors since power consumption
can still vary due to impeller placement and gas rate.
It is recommended that a mixer be used that is equipped with power input
measuring devices. There are several such devices on the market costing
$500 to $1000, which tends to make alpha testing very expensive. An alter-
nate approach is to modify a variable-speed DC motor controller to indicate
power. This can be achieved by adding a voltmeter in parallel with the motor
and an ammeter in series with the motor. The exact arrangement will depend
upon the type of DC motor used and will only be accurate in the upper ranges
of the motor's power/speed range.
An additional problem in determining the alpha factor is its time-
varying nature due to changes in the characteristics of the raw wastewater
with time of day. It was shown in Table 10 that the alpha factor can change
significantly over a period of time. To adequately characterize the alpha
factor, it is necessary to conduct several experiments at different times.
Preferably, at least three experiments should be performed using samples
obtained at different times during the day.
Typical Values for the Alpha Factor --
A compilation of commonly-observed alpha factors for various types of
27
wastewaters has been compiled by Barnhart (Table 13). The alpha factors
shown should only be regarded as observations and not guidelines for design.
Alpha factors have also been measured for several types of aeration
devices (Table 14). Table 14 has been included in this section to inform
the reader of previous work and not to provide guidelines for design or to
131
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TABLE 13. ALPHA FACTORS OBSERVED BY BARNHART27
*t
Wastewater Type a
Municipal wastewater 0.8 - 0.95
Synthetic wastewater 0.8 - 0.85
Synthetic fiber 0.45 - 0.65
Apple processing wastes 0.8
Soap and detergent production 0.6 (raw); 0.85 (treated)
Oils and essence production 0.5 (raw); 0.9 (.treated)
Paper (reworked) 0.65 - 0.9
Pulp and paper (Integrated mill) 0.7 - 0.8
*
Alpha factors are reported for various types of devices at various
conditions.
The summary of alpha factors reported in this table is intended to
illustrate the historical trends observed by previous investigators.
The alpha factors reported here should not be used for design purposes,
nor should they be used in lieu of testing.
serve as "standard" alpha factors.
Typical Procedures —
The following procedure serves as an example of the procedure recommended
here.
Mechanical aeration --
1. Using manufactuere's data, determine the probable power level for
the aeration system that is to be designed.
2. Using the unsteady state reaeration technique, determine K.a
(or K,a*) in tap water at power levels equal to 50 percent, 100 percent, and
150 percent of the probable power level calculated in Part 1. For turbine
aerators, measure mixer speed, power level, and gas rate.
3. Using the liquid to be aerated in the full-scale design, determine
K.a as in Part 2, using the same power levels, impeller mixer submergence
and speed should be controlled to obtain equivalent rotational speed and
power input. For activated sludge mixed liquor testing, the oxygen uptake
132
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TABLE 14. ALPHA FACTORS OBSERVED BY DIFFERENT INVESTIGATORS FOR DIFFERENT AERATION DEVICES*
Aeration Device
Comments
Reference
CO
to
Fine bubble diffuser
Brush
Surface aerators
Turbine aerators
0.4 to 0.6
0.8
Coarse bubble diffuser; 0.7 to 0.8
sparger
_, Coarse bubble diffuser 0.65 to 0.75
Static aerator 1.0 to 1.1
0.6 to 1.2
0.6 to 1.2
Lister and Boon
Kessener and Ribbius'
5- to 10-ft tank depths; 10 to 30
scfm/1000 ft3 (.tap water with
detergent)
Calculated from their data
(domestic wastewater)
10-ft tank depth; 80 to 190 scfm/
1000 ft3; 87,000-gal tank (tap
water with detergent)
22.5-ft tank depth; 25 to 92 scfm/ Schmit et al.
53
Gilbert
1
47
po
Otoski and Otoski
et al.14
1000 ft3 (tap water with detergent)
10-ft tank depth; 10 to 180 scfm/
1000 ft3; 87,000-gal tank (tap
water with detergent)
Alpha factor tends to increase with Downing et al.
increasing poser Ctap water with
detergent and small amounts of
activated sludge)
Alpha factor tends to increase with Hwanci
increasing power; 25-, 50-, and 190-
gal tanks (tap water with detergent)
11
52
The summary of alpha factors reported in this table is intended to illustrate the historical
trends observed by previous investigators. The alpha factors reported here should not be
used for design purposes, not should they be used in lieu of testing.
-------
rate stabilizes at a constant value (endogenous phase). It should be noted
that alpha factors measured during the endogenous phase may be different from
those measured during the growth phase.
4. For best approximation of the range of alpha factors, several series
(at least three) of tests should be performed at different times. Also,
alpha testing should be performed with samples from various points in plug
flow aeration tanks. Alpha factors measured on respiring samples in the
growth phase are subject to errors in measurement of oxygen uptake. The
engineer must choose between using mixed liquor or settled mixed liquor and
the errors associated with each procedure.
Diffused aeration --
1. Using manufacturer's data, select a diffuser for alpha testing that
produces bubbles the same diameter as the intended full-scale diffuser. Also,
determine the probable power level as previously.
2. Determine K.a in clean water as before, using power levels of 50
percent, 100 percent, and 150 percent of the probable power level.
3. As previously.
4. As previously.
Additional Procedures for Alpha Factor Determination
Additional procedures used for alpha factor determination are listed in
Appendix C. These procedures were included as additional guides to indivi-
duals unfamiliar with alpha factor testing. They were selected because they
represent state-of-the-art approaches to alpha testing; however, they are
not recommended as proposed consensus methods. The procedures should be used
as a "first draft" of an alpha testing procedure to be modified for each
individual use.
State of the Art for Beta Factor Determination
The beta factor can be measured using the Winkler test method if it can
be demonstrated that no interferences exist. In the event that chemical
interferences exist, the beta factor should be calculated from a TDS measure-
ment. Since the beta factor can vary with wastewater quality, a series of
tests must be performed to obtain a range of beta factors. This range must
be included in an overall system design and risk assessment, as indicated
134
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for the alpha factor.
State of the Art for Theta Factor Determination
No consensus exists for a temperature correction factor. The results
of a review of the literature indicate that geometric temperature correction
factors can range from 1.008 to 1.047 and that some aeration systems have
mass transfer coefficients that are linearly related to temperature Cas
opposed to the geometric relation). Furthermore, it has been shown that
the temperature correction factor is dependent upon turbulence.
It is recommended that a theta factor of 1.024 be used unless it is
known that a different geometric theta factor is more suitable. Consultants
and manufacturers who use theta factors other than 1.024 should be prepared
to support their position with substantive data. It is also recommended that
temperature corrections greater than 10°C be avoided, although it is recog-
nized that sometimes this may be impossible. The error that can occur if
incorrect theta factors are used and how the error is compounded if tempera-
ture corrections greater than 10°C are made were previously illustrated
(Figure 9). For example, by using a theta factor of 1.032 instead of 1.024,
the oxygen transfer rate will be overestimated by 12.5 percent.
FUTURE EMPHASIS AND RESEARCH NEEDS
Many uncertainties surround the selection of alpha, beta, and theta
factors. This review has pointed out many of those uncertainties and should
be used to define research needs. Two very high priorities are the needs for
better models to explain the effects of turbulence on both the alpha and
theta factors. Also, a fundamental analysis of the effects of scale is
needed.
It is hoped that manufacturers will assume a position of leadership in
the establishment of alpha bar factors (a) by running shop tests with deter-
gent-spiked tap water. A better understanding will undoubtedly result if
such information is developed and published.
Specific research needs have been identified that should be addressed:
1. Bench-scale alpha testing equipment should be developed that can be
scaled to accurately predict the alpha factor for full-scale equipment.
135
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2. A comprehensive evaluation of the trace contaminants in tap water
for various locations in the United States and elsewhere should be under-
taken. It is necessary to determine the magnitude of the effects of these
contaminants on clean water oxygen transfer.
3. Portable analytical equipment for measuring such parameters as
dynamic surface tension, bubble size, and mixer horsepower should be
developed. The successful development and use of such equipment will reduce
the variability of alpha testing.
4. Detergent testing should be performed to determine its suitability
as a standard procedure in the United States.
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Workshop Toward an Oxygen Transfer Standard, EPA-600/9-78-021, pp. 147-
162, April 1979.
2. Kessner, H. J. N. H. and F. J. Ribbius, "Practical Activated Sludge
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1935.
3. Holroyd, A. and H. G. Parker, "Investigations on the Dynamics of Aera-
tion," Journal of the Institute of Sewage Purification, pp. 280-297,
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4. Baars, J. K., "The Effect of Detergents on Aeration: A Photographic
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136
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12. Eckenfelder, W. W., Jr. and D. L. Ford, "New Concepts in Oxygen Transfer
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1967.
35. Metzger, I., "Effects of Temperature on Stream Aeration," Journal of the
Sanitary Engineering Division, ASCE, 94(SA6):1153-1159, December 1968.
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in Aerator Test Procedures," Proceedings, Workshop Towards an Oxygen
Transfer Standard, EPA-600/9-78-021, pp. 85-90, April 1979.
37. Elmore, H. L. and W. F. West, "Effect of Water Temperature on Stream
Reaeration," Journal of the Sanitary Engineering Division, ASCE,
87(SA6):59-71, November 1961.
38. Downing, A. L. and G. A. Truesdale, "Some Factors Affecting the Rate of
Solution of Oxygen in Water," Journal of Applied Chemistry, 5:570-581,
1955.
39. Streeter, M. W., "The Rate of Atmospheric Reaeration of Sewage Polluted
Streams," Transactions, ASCE, 39:1351, 1926.
40. Truesdale, G. A. and K. G. Van Dyke, "The Effects of Temperature on the
Aeration of Flowing Waters," Water and Waste Treatment Journal, 7:9,
1958.
41. Bewtra, J. K., W. R. Nicholas, and L. B. Polkowski, "Effect of Tempera-
ture on Oxygen Transfer in Water," Water Research, 4(1):115-123, 1970.
42. Clark, J. W., W. Viessman, and M. J. Hammer, Water Supply and Pollution
Control, Dunn Donnelley, New York City, 1977.
43. Metcalf and Eddy, Inc., Wastewater Engineering. McGraw-Hill, New York
City, 1972.
44. Eckenfelder, W. W., Jr., Industrial Water Pollution, McGraw-Hill, New
York City, 1966.
138
-------
45. Lakin, M. B. and R. N. Salzman, "Subsurface Aeration Evaluation," Paper
presented at the 50th WPCF Conference, Philadelphia, October 3-6, 1977.
46. Ward, J. C., J. S. Hunter, III, and R. B. Johansen, "The Mechanism of
Waste Treatment at Low Temperature," Partial completion report, OWRT
Project No. A-00-COLO., Colorado State University, Fort Collins,
Colorado, August 1972.
47. Schmit, F. L., J. D. Wren, and D. T. Redman, "The Effect of Tank Dimen-
sions and Diffuser Placement on Oxygen Transfer," Journal WPCF, 50:1750-
1767, July 1978.
48 Morgan, P. F. and J. K. Bewtra, "Diffused Oxygen Transfer Efficiencies,"
Journal of Air and Water Pollution," 5(2/4):181-193, 1960.
49. Ippen, A. T. and C. E. Carver, "Basic Factors of Oxygen Transfer in
Aeration Systems," Sewage Works Journal, 7:813-820, July 1954.
50. Stukenberg, J. R. > V. N. Wahbeh, and R. E. McKinney, "Experiences in
Evaluating and Specifying Aeration Equipment," Journal WPCF, 49:66-82,
January 1977.
51 Kayser, R., "Measurements of Oxygen Transfer in Clean Water and Under
Process Conditions," Paper presented at the IAWPR Specialized Conference
on Aeration, Amsterdam, September 19-22, 1978.
52. Hwang, H. J., "The Effect of Surface Active Agents on Oxygen Transfer,"
Thesis submitted to University of California-Los Angeles in partial ful-
fillment of the degree of Master of Science, June 1979.
53. Lister, A. R. and A. G. Boon, "Aeration in Deep Tanks: An Evaluation of
a Fine-Bubble Diffused-Air System," Journal of the Institute of Sewage
Purification, pp. 3-18, 1973.
139
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SECTION 7
OXYGEN TRANSFER MEASUREMENTS IN RESPIRING SYSTEMS
OBJECTIVES
Adequate test procedures must be available to permit the investigator to
assess aeration equipment performance in respiring biological systems. Sever-
al test methods have been employed in the field to determine oxygen transfer.
The twofold objectives of this section are: (1) to present a state-of-the-
art review of the most commonly-used methods for determining the rate of oxy-
gen transferred in respiring biological systems and (2) to discuss the limita-
tions of each method.
BACKGROUND
Virtually all of the methods discussed herein have been tested in either
pilot- or full-scale respiring systems. The methods span a multitude of bio-
logical treatment approaches, e.g., from high-rate activated sludge to aerated
stabilization basins. In general, the methods can be categorized according to
the rate of change of dissolved oxygen (DO) in a given reactor (or segment of
reactor). Systems in which the rate of DO change is zero at any given point
are referred to as steady state systems; the others are classified as unsteady
state systems. In some cases, influent wastewater may be diverted from a
reactor being tested. These are referred to as batch tests. The term "con-
tinuous test" is used for those cases where the influent wastewater flow is
not diverted.
Three respiring system test methods do not require a direct measure of
the oxygen uptake rate. These have been broadly categorized as the mass bal-
ance method, the off-gas method, and the tracer method. The mass balance
method requires data on the net change in oxidation level between all entering
and exiting liquid flows. The off-gas method is simply a mass balance on oxy-
gen that includes both the liquid and gas streams. The tracer method
140
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indirectly measures the rate of oxygen transfer by determining the rate of
transfer of a radioactive tracer.
The most commonly-used methods do involve the direct measurement of the
oxygen uptake rate, R, of a respiring biological system. Two of these methods
are carried out with little or no variation in DO in either batch or continu-
ous flow systems; these are referred to as "Steady State Batch Tests" and
"Steady State Continuous Tests," respectively. In the remaining two tests,
the DO level in the reactor is adjusted at the beginning of the test to be
either greater than or less than the steady state DO. These tests are refer-
red to as "Unsteady State Batch Tests" if the influent wastewater flow is dis-
continued for the test and "Unsteady State Continuous Tests" if the influent
wastewater flow is continued during testing.
The relationship between the steady state and unsteady state tests
(either batch or continuous) may be readily seen from a hypothetical example
(Figure 16). In Figure 16, the concentration of oxygen at one point in a
reactor (designated as C) is shown to decrease from CD1 to C. after the
K i mi n
aeration equipment is turned down and then is shown to increase from t .
^ f. /\ mm
through C to C^ after the aerators are turned back up (C^ may or may not
be equal to 6DO)- The concentration C simply designates the DO concentration
f\L. 0
corresponding to time t , the time at which the investigator decides to
initiate the full spectrum of data analyses. The DO concentration obviously
increases whenever the supply of oxygen exceeds the rate of biological con-
sumption, remains constant when the two rates are equal (in this case, at
Rl or ^R2^' &n^ decreases wnen the consumption rate exceeds the supply rate.
In clean water testing, sodium sulfite is used to reduce the DO level. In
clean water, however, the rate of oxygen consumption is zero after time t ,
with the test proceeding to equilibrium at the effective system saturation
concentration, C*. In a respiring system, the steady state concentration of
oxygen, CDO, is reached at time t plus tD. Note that the effective Satura-
Kd 0 K
tion concentration of oxygen that would result in the mixed liquor for a zero
respiration rate is given in Figure 16 as ct.
THEORETICAL DEVELOPMENT
In order to both properly analyze the data generated from many of the
test methods and understand those assumptions that are required for ease of
141
-------
UD
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DO CONCENTRATION AT A GIVEN
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data handling, material balances are developed for continuous flow and batch
reactors. General schematics for both continuous flow and batch systems are
presented in Figure 17 along with definitions of the selected symbols. The
remaining symbols are defined in the Symbols and Nomenclature list for the
entire report. As can be seen from the figure, the term "batch" refers to
the liquid phase only. Batch analysis allows for recycle of sludge solids
but requires that there be no net liquid flow.
Many simplifying assumptions are required to develop practical equations
that may be used to analyze the data collected in aeration testing. As a
result, this section is purposely abbreviated to relate the general sense of
the major assumptions without the more theoretical arguments. The first
simplification is at the reaction level. Reactions rates are presented as
arbitrary functions for three reactions: aerobic growth of heterotrophs ,
death and endogenous respiration, and nitrification (to nitrate nitrogen only
with the impact of nitrite nitrogen ignored). Thus, r^(S,X) is the rate of
carbonaceous substrate utilization in the growth reaction, r2(X) is the rate
of organism death in the endogeneous reaction, and r3(N,X) is the rate of
ammonia nitrogen oxidation in the nitrification reaction. The overall rates
of oxygen consumption, R; substrate utilization, RS; organism growth, R^; and
ammonia nitrogen utilization, RM, are given by:
(-R) = -y^S.X) - y2r2(X) - y3rs(N,X) (63)
(-Rs) = -r^S.X) (64)
Rb = %lrl(S'X) ' yb2r2(X) + yb3r3(N'X) (65)
" YN3r3(N'X) (66)
where:
r, , r , and r~ are positive functions with:
r^S.X) = r^X) for S >
r3(N.X) = r3(X) for N >
S and N are the concentrations of carbonaceous substrate and
143
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CONTINUOUS FLOW SYSTEM
BATCH SYSTEM
Qa . Po
Qa , PO
Qj, Cj, Q',C'0
S,, N.,
GAS P0,Vg
LIQUID
C, S, X, N,V
Q-, c,
S, N
Q • P •
ai ' 01
Qr, Cr, Xr
1°e'
r
J se>
GAS pQ,V
LIQUID
C, S, X, N, V
Qai I Poi
Qr, Cr, Xr
Qw'Cr'Xr
Figure 17. General schematics and nomenclature for continuous flow
and batch respiring systems.
SYMBOLS
•C, S, X, and N represent concentrations in the liquid phase of oxygen,
substrate, biological organisms, and ammonia nitrogen, respectively.
• CR will be used to designate the steady state concentration of oxygen
at a biological uptake rate of R.
•Q and Qa represent flow rates for liquid streams and gas streams, respec-
tively. Qw represents the flow rate for waste activated sludge.
•Po and Poi represent the partial pressures of oxygen in the gas phase in
the reactor and in the inlet, respectively.
•V and Vg represent the reactor volumes of the liquid and gas phases,
respectively.
•The subscripts i, o, r, and e in the liquid phase are used to designate
the influent wastewater, the combined streams entering the reactor, the
recycle sludge flow, and the secondary clarifier effluent, respectively.
No subscripts are used for either reactor concentrations or reactor
effluent concentrations. A bar (e.g., C) is used to represent spatially
averaged concentrations of all reactor concentrations. Note finally that
the symbol Q1 is used to designate the liquid flow entering and leaving
the continuous flow reactor (instead of Q0).
wise in a previous section.
Q0 has been defined other-
144
-------
nitrogen substrate, rexpectively, that define non-substrate limiting
conditions.
The y's represent stoichiometric coefficients (always positive) that
relate the relative mass of each component's utilization in each reac-
tion. For example, y,, y?, and y~ represent the mass of oxygen utilized
per unit mass of substrate utilized, per unit mass of organisms decayed,
and per unit mass of ammonia nitrogen utilized in the growth, endogenous,
and nitrification reactions, respectively. Furthermore, the +_ yN,
acknowledges that, in some instances, a net quantity of ammonia nitrogen
may be produced from the growth equation due to organic nitrogen (there-
fore, the plus sign) or that a net quantity may be incorporated into a
cell mass (therefore, the minus sign).
In this reaction scheme, the rate terms are constant whenever X is con-
stant and either S and N are constant or above their respective non-substrate
limiting concentrations.
The general mass balance on oxygen for the liquid phase is given in
Equation 67 for a continuous flow reactor and in Equation 68 for a batch
reactor with C at t = 0 equal to C for both equations:
V(i) = Q'(C'0 - C) - VR + VKLaf((£f - C) (67)
V[df) = Qr(Cr • C) - VR + VKLaf(C*f - C) (68)
For completely mixed reactors, C is equal to C.
The equations used to analyze results from field tests for steady state
and unsteady state conditions result directly from Equations 67 and 68. The
assumptions required to develop these equations are described in Tables 15
and 16 for both batch and continuous tests. Many of the assumptions, espe-
cially for the continuous flow systems, may not be valid. The validity of
the assumptions is discussed in the subsections dealing directly with the
test procedures.
Steady State Continuous Test
0 = Q'(C'0 - CR) - VR + VKLaf(C/;f - CR) (69)
145
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TABLE 15. ASSUMPTIONS NECESSARY TO DEVELOP EQUATIONS
FOR STEADY AND UNSTEADY STATE BATCH TESTS
Assumptions
Steady State
Test Condition
Unsteady State
Test Condtiion
(1) Aeration volume DO, CR, is
constant
(2) Recycle sludge flow, Qr is
constant or zero
(3) Recycle DO, Cp is constant
(4) Aeration volume oxygen
uptake rate, R, is constant
cr>
(5) Effective oxygen transfer
rate, K.af> is constant
Steady state conditions have
been achieved and maintained.
Recycle flow rate maintained
constant or discontinued .
Steady operation of recycle
system if in use during the
test period (e.g., sludge
blanket level constant).
Aeration volume biological
solids, X, and recycle sludge
flow, Qr, remain constant;
carbonaceous, S, and nitro-
genous, N, substrates are
near zero during the test (if
nitrification occurs in the
test system).
Carbonaceous substrate, S, is
near zero during the test;
alpha, a, value remains con-
stant during the test period.
Recycle flow rate maintained
constant or discontinued.
Steady operation of recycle
system if in use during the
test period (e.g., sludge
blanket level constant).
Aeration volume biological
solids, X, and recycle sludge
flow, Qr, remain constant;
carbonaceous, S, and nitro-
genous, N, substrates are
near zero during the test (if
nitirification occurs in the
test system).
Carbonaceous substrate, S, is
near zero during the test;
alpha, a, value remains con-
stant during the test period.
-------
TABLE 16. ASSUMPTIONS NECESSARY TO DEVELOP EQUATIONS
FOR STEADY AND UNSTEADY CONTINUOUS TESTS
Assumptions
Steady State
Test Condition
Unsteady State
Test Condition
(1) Aeration volume DO,
Cp.is constant
(2) Reactor influent flow,
Q1, is constant
(3) Influent DO, C1 ,.is
constant
(4) Aeration volume oxygen
uptake rate, R, is con-
stant
(5) Effective oxygen transfer
rate, K.a , is constant
Time of test short.
Time of test short; variation
in influent wastewater flow,
Qi, is negligible during test
period; recycle sludge flow,
Qr, is held constant.
Time of test short; variations
in influent wastewater flow,
Q-j, and DO, Ci, are negligible
during test period; recycle
sludge flow, Qr is held con-
stant.
Time of test short; aeration
volume biological solids, X,
and recycle sludge flow, Qr,
remain constant; influent
wastewater flow, Q-j, and car-
bonaceous substrate, S, vari-
ations are negligible during
test period. (Note that R may
be difficult to accurately de-
termine for systems with high
organic loadings. (Refer to test
procedure discussion for details.
Time of test short; alpha, a,
value remains constant during
the test oeriod.
Time of test short; variation
in influent wastewater flow,
Qi, is negligible during test
period; recycle sludge flow,
Qr, is held constant.
Time of test short; variations
in influent wastewater flow,
Q-j, and DO, C-;, are negligible
during test period; recycle
sludge flow, Qr, is held con-
stant.
Time of test short; aeration
volume biological solids, X,
and recycle sludge flow, Qr,
remain constant; influent waste-
water flow, Q-j, and carbonaceous
substrate, S, variations are
negligible during test period.
(Note that R may be difficult to
accurately determine for systems
with high organic loadings.
(Refer to test procedure discus-
) si on for details.)
Time of test short; alpha, a,
value remains constant during
the test period. ,
-------
Let:
Therefore:
Steady State Batch Test
0 =
Let:
Therefore:
Fl
-
Bl
= R
KL
CR>
= R
V a
_ H_(r' - C }
V l o V
F,
, _ 1
f C* - C
- VR + \IK a (c r \
VK T VN. a/j^L ,. - Up;
LT T i\
Qr
- ——(c - r }
V (Lr LR;
Bl
(70)
(71)
(72)
(73)
/7^
Unsteady State Continuous Test
Pi-Ll/^/O7* r^\ /T^\
ViT" ~ -rs ' ~\T"V^ «"^/ + ^|3r\^jr~^J (75)
U I* V 0 Li ^^T
Substitute Equation 71 into Equation 75 and rearrange to obtain Equation 76:
with C at t
Therefore:
dt
0 equal to C .
(76)
(CR - C) = (CR - Co)exp-
TT- t
(77)
Unsteady State Batch Test
§ - -R + T(Cr - C) + KLaf (C*f " C)
Substitute Equation 74 into Equation 78 and rearrange to obtain Equation 79:
dC _
dt "
(79)
with C at t
Therefore:
o equal to C .
(CR - C) = (CR
- C)exp-
148
"f Qrl
]KLaF + T]
(80)
-------
Additional mass balances can be written on the reactor systems described
in Figure 17. Specifically, the off-gas and tracer methods may be easily
shown to be governed by:
Off-Gas Method
[dp
V
o
dt
R T
M
(81)
where:
H = Henry's Law constant, ml f
R = universal gas constant, fL mol" T
T = absolute temperature of the gas, T
M = molecular weight of the gas, m/mol
dP0
For -TJT- = 0 and p = p , the governing equation results:
(Q,,Pni - QaPQ)M
K, a- = -AL-O] - a-O-— (82)
L f (3Hp0 - CR) V R I"
Oxygen transfer efficiency may be calculated using off gas measurements
based upon the following relationships:
Q ,„
OTE • \ in <83>
ore WH1)MRo/1 - WM1)HRog/1 .„,
OTE -- — ( }
- MR
OTE = -^5 SaZJ. (85)
MKo/i
where:
G. = mass rate of inerts, m/t
M = molecular weight of oxygen, m
M. = molcecular weights of inerts, m
MRo/i = mole ratio of Oxy9en to inerts in feed air
MR ,^ = mole ratio of oxygen to inerts in off gas
The mole ratios may be related to mole fractions, Y, as follow:
MRo/i °r %/i = 1 - Y - ^ - Vw C86)
149
-------
where the mole fractions for both feed air and off gas may be specified.
This test method is suitable for use as described by Mueller et al.1 for
closed-vessel systems, such as those found in many oxygen-enriched applica-
tions. It is also finding application in open tank systems as well.
Tracer Method
The tracer method is identical for clean water and respiring system con-
ditions since the tracer, T, used is a conservative, non-reactive substance.
For example, for a batch system with Qr equal to zero, the governing equation
is given by:
£ = KLaf ? (87)
with T at t = 0 known.
Because of the limited application of this method in aeration equipment
evaluations, further mathematical details are not presented in this report.
For a more detailed review of this subject, refer to detailed discussions by
Neal.2
MEASUREMENTS IN THE FIELD
The successful evaluation of aeration equipment in situ involves careful
measurements of several key parameters under full-scale operating conditions.
A discussion of these measurements and their importance in field evaluations
follows.
Dissolved Oxygen
An accurate measure of the DO concentration in an aeration volume is
essential to any evaluation of aeration equipment. For in situ testing,
direct-reading DO probes are the only practical means of measuring the DO
concentration in mixed liquor suspended solids (MLSS) samples. Following
proper calibration of the probes, considerable care and attention are
required to assure continuous reliable results under field contitions.
Aeration testing may be carried out on an entire tank or an isolated mix-
ing zone within a test volume. Typically, a minimum of three probes are used
in field testing and, depending on the type of aeration system being tested,
placement of the units in the test tank can be critical. For example, in
150
-------
aeration volumes with a relatively uniform DO concentration (e.g., well mixed
with respect to DO), probes may be located in the tank without regard to
aerator mixing pattern. However, for aeration volumes that are not well
mixed with respect to DO, probes should be strategically placed around the
specific flow pattern of the aeration device. Typical sampling locations for
DO measurement for several types of aeration equipment are illustrated in
Figure 18.
Depending on the specific application, many of the aeration devices shown
in Figure 18 will not yield a uniform DO concentration in the tank under test
conditions. In addition, the flow patterns shown in Figure 18 are typical
but are not necessarily valid for all applications. Thus, it is important to
establish a complete DO profile on the aeration system prior to testing. The
DO profile will indicate the actual mixing characteristics of the test tank
and allow proper placement of the DO probes. For further discussion on mix-
ing and the effects of basin geometry on mixing, refer to Section 8.
During field testing of aeration systems, the DO concentration should not
be the limiting factor in the biological reaction. For instance, the DO can
become limiting at approximately 0.5 mg/£ for nitrifying activated sludge
systems. Therefore, it is essential that the minimum DO be above 0.5 mg/£
and 1.5 mg/£ during testing of non-nitrifying and nitrifying activated sludge
systems, respectively.
Oxygen Uptake Rate
A significant factor for evaluating aeration equipment in respiring sys-
tems is an accurate measurement of the MLSS oxygen uptake rate, R. Experience
has shown that accurate measurement of the rapid oxygen uptakes created by
high organic loads is virtually impossible. Ideally, the oxygen uptake rate
measurements should be taken in situ or immediately at the point of sample
collection. However, as a practical matter, a finite time period elapses
prior to field measurements of this parameter. Since the oxygen uptake rate
of a sample will vary as the available soluble substrate is oxidized, signif-
icant variations in the uptake rate may be observed for samples taken from
moderately to highly loaded systems. The information presented in Figure 19
illustrates such a situation. Thus, caution is urged where oxygen uptake
151
-------
a) SURFACE AERATOR
b) SURFACE AERATOR WITH
DRAFT TUBE
a 'PREFERRED
ALTERNATE
c) TURBINE AERATOR d) DIFFUSED AERATOR
a SAMPLING LOCATIONS FOR D 0 MEASUREMENT
USING 3 IN SITU PROBES
Figure 18. Typical sampling locations for measurement of DO
for different aeration systems.
152
-------
34567
TIME (min)
8 9 10
Figure 19. Oxygen uptake plot for steady state continuous testing
in a moderately loaded activated sludge system.
rates are being measured under actual plant loading situations. One method
used for estimating the actual oxygen uptake rate under these conditions is
outlined in Appendix D.
A practical approach used to minimize the variability of the oxygen
uptake rate is testing under endogenous respiration conditions. Endogenous
respiration can be achieved by diverting the influent wastewater to other
aeration tanks and allowing the MLSS to assimilate the remaining soluble
organics. This procedure is the basis for batch testing and establishes a
low and relatively constant oxygen uptake rate that can be more accurately
measured. The data presented in Figure 20 illustrate the constant uptake
rate obtained under endogenous conditions.
153
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assumed to be the same as that occurring during operating conditions under
normal plant loading. Since the subject area involving a and 3 corrections
is rather complex, the reader should refer to Section 6 for a discussion of
the factors affecting a and 3 and procedures for their determination.
Wastewater Temperature
Wastewater temperature also affects the evaluation of field oxygen trans-
fer rates. Both oxygen transfer rate and oxygen uptake rate are significant-
ly altered by changes in temperature. Biological reactions are thought to be
governed by a doubling of rate for every 10°C increase in temperature [corre-
sponds to RT = R20 1.072^ ~*-u'] within the practical operating range of
10-30°C. Thus, if an oxygen uptake rate is measured at a wastewater tempera-
ture different from the actual operating temperature, the appropriate temper-
ature correction for reaction rate must be made during data evaluation. At
the same time, since aeration equipment is rated at 20°C, but is actually
tested at some other temperature, appropriate transfer rate adjustments must
also be applied to account for the effects of wastewater temperature. The
temperature correction for oxygen transfer is discussed in detail in Section
6. Where practical, testing at temperatures near 20°C is desirable since it
will minimize temperature corrections and allow a more accurate comparison
with transfer rates at standard conditions.
TEST PROCEDURES
Steady State Testing
Test Descriptions—
Steady state testing involves simultaneous measurement of DO and oxygen
uptake rates in full-scale aeration tanks. Testing may be conducted with or
without influent wastewater flow to the aeration tank. For convenience,
these testing methods are referred to as the continuous test (with wastewater
flow) and the batch endogenous test (without wastewater flow).
The continuous test is the classical approach of determining field oxy-
gen transfer in an aeration tank under normal operating conditions. ' ' '
A general procedure for performing this test is as follows:
1. The liquid level in the aeration tank should be adjusted to the
155
-------
desired power consumption of the aeration equipment. This liquid
level should be recorded for future reference.
2. Initially, the DO concentration should be measured at points around
the aeration tank (DO profile). The locations for measurement
should be selected to define the mixing patterns for the system and
to ensure that the entire test volume is aerobic. During the test,
a minimum of three probes should be utilized for repeated DO measure-
ments.
3. The DO concentration should be measured on both the influent and
effluent flows of the test tank.
4. The oxygen uptake rates should be measured on the mixed liquor at
the same time and at the same points that the routine DO measure-
ments are made.
5. The air and mixed liquor temperatures should be measured at the same
time as DO measurements are made.
6. The DO and oxygen uptake measurements should be repeated several
times to obtain representative and reproducible values for the spec-
ified test period.
7. Measurement of the barometric pressure and determination of an a
value (see Section 6) are required if correlation to standard con-
ditions is desired.
8. A sample of mixed liquor should be analyzed for suspended solids to
provide a MLSS concentration for reference purposes.
9. At the completion of the test, the DO probes should be recalibrated.
If the recalibration indicates a significant deviation between the
probe reading and calibration concentration (>5 percent), the
instrument should be adjusted before further testing is initiated.
The batch endogenous test is conducted by discontinuing the influent
wastewater flow to the aeration tank prior to the test period. The recycle
sludge flow to the aeration tank may be held constant or discontinued during
the test period. Operation in the endogenous phase should yield more uniform
aeration tank contents (e.g., R, DO, and a value) and should result in
156
-------
increased testing accuracy. The following steps are necessary to bring the
system to endogenous conditions:
1. The influent wastewater flow to the aeration tank must be discon-
tinued. Recycle sludge flow may be discontinued or allowed to
recycle normally to prevent septicity of the sludge in the secondary
clarifier.
2. The liquid level in the aeration tank should be adjusted to produce
the desired power consumption of the aeration equipment. This
liquid level should be recorded for future reference.
3. The mixed liquor should be allowed to stabilize for a specified time
period prior to the start of testing. Experience has shown that
typically a period of 30 min to 2 hr is sufficient to bring the
system to the endogenous respiration phase. Relatively constant
values of DO and R at a given point, as determined by frequent mea-
surements (say every 5 min) over a 30-min period, would indicate
that steady state conditions had been reached.
After these steps are completed, the oxygen transfer rate may be deter-
mined following the continuous test procedure (Steps 2 through 9} previously
outlined.
Data Evaluation--
The data obtained from the steady state tests may be evaluated using
Equation 88 as described below:
v * - System Test Constant /DD\
K. af —* =•£—^ too)
L f coof - LR
where System Test Constant is:
Continuous Test
FT = R - T(C'O ' CR) (70)
Batch Test
B = R - -y-(Cp - CR} (with recycle sludge flow) (73)
B.J - R (without recycle sludge flow) (89)
157
-------
-3-1
R = average oxygen uptake rate, ml t , of the MLSS in the test
volume, V
How,
3
3
Q' = influent flow, L /t, to the test volume, V
V = test volume, L'
3
C1 = DO level, m/L , in the test volume influent flow, Q1
3
CR = DO level, m/L , that most accurately represents the driving force,
- CR, in the transfer zone of the system. For aeration sys-
tems that have a relatively uniform DO concentration (well mixed
with resjpect to DO), CR would be the average DO of the entire test
volume, CR. For systems that are not well mixed with respect to DO
concentrations (usually associated with continuous testing), CR,
equal to^the DO level in the liquid as it flows to the aeration
device (CR— see Points a 3, Figure 18), has been shown to more
closely approximate the actual system oxygen transfer rate.St
Q = recycle sludge flow, L /t, to the test volume, V
r 3
C = DO level, m/L ,. in the recycle sludge flow, Q
*r 3
(rf = effective saturation DO level, m/L , at the test wastewater temper-
°° ature. This value will vary depending on the type of aeration
equipment tested and the aeration tank depth. For surface aera-
tion equipment, the surface saturation DO ley_el will closely approx-
imate CSf. For diffused aeration devices, Coof is unknown and must
be determined through testing.
The resulting K, af represents the field oxygen transfer rate for the specified
test temperature.
Example Calculations--
Continuous test results (hypothetical case)--Testing was conducted in a
1.0-mil gal aeration basin operating with four 40-hp floating surface aera-
tors. Recyle of sludge to the basin was 33 percent of forward flow. Probes
were positioned at four different locations in the basin that was receiving
1.5 mgd of industrial wastewater flow. Oxygen uptake rates and DO levels were
There is considerable controversy among Subcommittee members on this point.
For example, Boon et al.9 believe any value for CR other than the average
over the test volume would yield a "local value" of K[_af and not the overall
system transfer coeffient. They have reasoned that if the DO level is not
constant throughout the tank (as previously assumed in development of the
equations), then Equation 88 is not valid for evaluation of that aeration
system. Furthermore, BoonlO feels that the variation in DO concentration at
any point in the aeration test volume compared to the mean value should not
be greater than 10 percent of the deficit (C£f - CR) or the value of K|_a,
would vary by more than 10 percent of its mean value.
158
-------
measured every 20 min at each of these locations over a period of 2 hr. The
average values for these parameters and test conditions are presented in
Table 17.
The temperature of the mixed liquor during the oxygen uptake test was
19°C, necessitating correction downward to the 18°C operating temperature of
the aeration basin. Thus, the average oxygen uptake rate at 18°C was
20.7 mg/A/hr. The influent DO concentration, C0', was 4.7 mg/A. With the
values of R, CR (the oxygen content of the mixed liquor returning to the
aerator when R was determined), C*, and 6 (as determined from Section 6),
the value of K|_af may be determined from Equations 88 and 70 as follows:
Q1 = Qi + Qr = (1.5x 1.33)724 = 0.083 mil gal/hr
B = 0.97
R" = 20.7 mg/A/hr
C1 =4.7 mg/£
C* = 9.5 mg/A (book value of surface saturation at 18.0°C)
TABLE 17. TEST INFORMATION FOR CONTINUOUS TESTING
OF A SURFACE AERATION SYSTEM*
Test Conditions
Aeration temperature = 18.0°C
$ = 0.97 (determined as described in Section 6)
MLSS temperature during oxygen uptake testing = 19.0°C
Probe
Location
1
2
3
4
Average
R
(mg/A/hr)
21.6
20.8
22.2
24.1
22.2
CR
(mg/A)
4.8
4.8
4.7
4.5
4.7
The value given for each probe location represents the average of six deter-
minations over the 2-hr test period. A portion of the influent flows through
a cooling tower so that the test volume influent DO concentation, C'0, ranged
between 4.5 and 5.0 mg/A during the test period. Thus, the net change in oxy-
gen in the liquid stream flowing through the aeration tank was negligible for
the test period.
159
-------
C*f = SC* = 0.97 x 9.5 = 9.22 mg/£
C"R = 4.7 mg/£
F] = 20.7 - (0.083/1.0)(4.7 - 4.7) = 20.7 mg/H/hr
KLaf = 20.7/(9.22 - 4.7) = 4.6 hr"1
Batch endogenous test results (hypothetical case)--Wastewater flow to a
1.0-mil gal aeration basin was discontinued for 2 hr prior to data collection.
The DO and oxygen uptake rates remained essentially constant. Data were col-
lected from three locations at 20 min intervals for 80 min (Table 18). Oxygen
uptake data were collected at 19.5°C, thereby necessitating a correction in R"
down to 19°C. (R"= 13.8 mg/l/hr at 19°C). With values of R", C"R. C*. and 3
the value of K.a- may be calculated from Equations 88 and 89 as follows:
e = 0.97
R" = 13.8 mg/£/hr
G£ = 9.3 mg/£ (book value of surface saturation 19.0°C)
Cf = 3C» = 0.97 x 9.3 = 9.02 mg/£
CR = 6.1 mg/£
BI = R" = 13.8 mg/Vhr (without recycle sludge flow)
KLaf = 13.8/(9.02 - 6.1) = 4.7 hr"1
TABLE 18. TEST INFORMATION FOR BATCH TESTING
OF A SURFACE AERATION SYSTEM*
Test Conditions
Aeration temperature = 19°C
$ = 0.97 (determined as described in Section 6)
MLSS temperature during oxygen uptake testing = 19.5°C
Probe R CR
Location (mg/Vhr) (mg/&)
1 14.3 6.1
2 14.5 6.0
3 14.2 6.1
Average 14.3 6.1
*
The value given for each probe location represents the average of six deter-
minations over the 2-hr test period.
160
-------
Testing Limitations--
The limitations of a specific test method must be recognized to ensure
adequate data collection and allow an appreciation for the accuracy of the
end result. For the steady state testing approaches, the following discus-
sion outlines the specific test limitations that have been identified.
Continuous testing—An accurate determination of the value of R may be
very difficult to obtain if system influent wastewater flow and substrate con-
centration are not constant during the test period. ' In addition, if the
system being tested has a high organic loading, the value of R will be nearly
impossible to determine accurately. Appendix D outlines a method for approxi-
mating R under such continuous operating conditions, but even this approach is
only a rough estimate. Thus, the accuracy of the K.a- determination is
directly tied to the ability to determine a representative value of R for the
o
system. McKinney and Stukenberg found that for R values greater than
60 mg/£/hr errors in measurements can be significant and increase with
increasing R values.
The inability to control the a value of the test volume during the test
period may be a serious drawback to continuous testing. The a level may vary
substantially (as much as +_ 20 percent) at a given location within the tank
during the test duration due to variable influent wastewater characteristics.
In addition, the a level may even vary spatially within the tank at a given
time during the test depending on the degree of treatment and system mixing
patterns.
For many applications, specifically for surface aeration installations,
the DO concentration may vary spatially within the tank at a given time during
testing under continuous loading conditions. Therefore, the continuous test-
ing approach may not be valid for those applications where such variation
exists. Furthermore, if the variation in DO concentration at any point in
the aeration test volume compared to the mean value is greater than +_ 10 per-
cent of the deficit (C*f - CR), then the resultant KLaf should be considered
no more accurate than this measured DO variability.
The requirement of maintaining the excess DO level, CR, within a practi-
cal range during the test period may also be a limitation for some test
161
-------
applications. In order to define a reasonable range for accurate DO deter-
mination, the measured CR level should be between a minimum of 2 mg/£ and a
maximum of 75 percent of the system C*-. Limiting the test conditions to
this range will ensure the statistical validity of the DO measurement and
provide a meaningful end result.
The inability to determine a C*f value for submerged aeration systems
effectively limits the use of the continuous test. This technique may be
used for submerged aeration systems only where it is possible to perform the
test at a minimum of three different oxygen uptake rates. Different oxygen
uptake rates may be established by varying the MLSS concentration under a con-
stant organic loading rate or by varying the organic loading rate for a con-
stant MLSS concentation. Once collected, the data should be plotted as shown
* *
in Figure 21 for the graphical determination of K,a.p and 3 C^, i.e., C^,.. The
field transfer rate is the slope of the straight line plot (3.9 hr"1), and
the effective system saturation level is the X-axis intercept (9.7 mg/l).
38 mg/?/hr = MAX. 02 TRANSFER RATE
SLOPE = KLaf = 3.9 hr
3 MIXED LIQUOR ~l
OXYGEN UPTAKE
RATES
01 234 56789 10 II 12
FIELD DISSOLVED OXYGEN (mg/l)
Figure 21. Steady state test results for submerged aeration evaluation,
162
-------
Batch Testing—To achieve an endogenous respiration condition, the
influent flow to the test volume must be discontinued. For systems with
limited operational flexibility, this approach may not be practical.
When testing under endogenous respiration conditions, the a level would
not necessarily reflect the a level at normal operating conditions. There-
fore, if a field transfer rate under operating conditions is desired, the
batch test may not yield an accurate estimation of that value. Depending on
the specific application, testing under endogenous conditions would be
expected to yield higher field transfer rates due to higher a levels. On the
other hand, if the test is performed for comparison with a standard oxygen
transfer rate, this approach should provide representative information for
that comparison.
The requirement of maintaining the excess DO level, CR, witnin a practi-
cal range during the test period may prove to be a limitation for some appli-
cations of the steady state batch test as with the steady state continuous
test. In order to define a reasonable range for accurate DO determination,
the measured CD level should be between a minimum of 2 mg/H and a maximum of
K
75 percent of the system C*f. Limiting the test conditions to this range will
ensure statistical validity of the DO measurement and provide a meaningful
end result.
The inability to determine a C*f value for submerged aeration systems
effectively restricts the use of the batch test approach to a limited number
of applications (see discussion in previous subsection on continuous test
limitations).
Unsteady State Testing'
Test Descriptions—
Unsteady state testing involves reduction or discontinuation of aeration
in the test tank. This allows biological action, through the oxygen uptake of
the MLSS, to reduce the DO concentration in the test volume. (Note that the
biological organisms are analogous in this respect to the sodium sulfate used
in clean water testing.) After the DO level has been depressed sufficiently,
aeration is increased or reintroduced to the test tank. By simultaneously
monitoring the increase in DO level and the oxygen uptake rate, the field
163
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oxygen transfer rate may be determined using a classical reaeration approach
(refer to Section 5). Testing may be conducted with or without influent flow
to the aeration tank. As with steady state testing, these two methods are
referred to as the continuous test (with wastewater flow) and the batch endo-
genous test (without wastewater flow).
The continuous test attempts to determine the field oxygen transfer in
an aeration tank under normal process conditions. A general procedure for
performing this test is as follows:
1. The liquid level in the aeration tank should be adjusted to produce
the desired power consumption of the aeration equipment. This
liquid level should be recorded for future reference.
2. Initially, the DO concentration should be measured at several points
around the aeration tank (DO profile). The locations for measure-
ment should be selected to define the mixing patterns of the system
and to ensure that the entire test volume is aerobic. For the test,
a minimum of three calibrated DO probes should be installed strate-
gically within the aerator mixing zone of influence (see Figure 17)
for repeated DO measurement.
3. The DO concentration should be measured in both the influent and
effluent flows of the test tank.
4. The test should be initiated by reducing or interrupting aeration in
the test volume. (Note: The test should be conducted during oper-
ating periods when the influent flow and wastewater quality are most
uniform. This provision will minimize variations in R, a, and 3 to
allow more reproducible results.)
5. The DO concentration should be monitored continuously. When the DO
concentration approaches 0.5 mg/£ at any probe, aeration should be
increased or reintroduced to the test tank.
6. The increase in DO concentration should be recorded continuously.
Simultaneously, oxygen uptake rates should be measured at the same
locations where the DO probes are situated. As often as practical,
the oxygen uptake should be measured until the system DO concentra-
tion stabilizes at a constant value, i.e., j^O.l mg/l.
164
-------
7. The system air flow (if appropriate), energy input, mixed liquor
temperature, air temperature, and barometric pressure should be mea-
sured and recorded for each test.
8. Measurement of the barometric pressure and determination of an a
value (see Section 6) are required if correlation to standard con-
ditions is desired.
9. A sample of mixed liquor should be analyzed for suspended solids to
provide an MLSS concentration for reference purposes.
10. At the completion of the test, the DO probes should be recalibrated.
If the recalibration indicates a significant deviation between the
probe reading and calibration concentration (>5 percent), the
instrument should be adjusted before further testing is initiated.
11. Steps 4 through 10 should be repeated at least three times to
obtain representative results for data analysis.
The batch endogenous test is conducted by discontinuing the influent
wastewater flow to the aeration tank prior to the test. The recycle sludge
flow to the aeration tank may be held constant or discontinued during the test
period. Operation in the endogenous phase should yield more uniform aeration
tank contents, e.g., R, DO, and a value, and should result in increased test-
ing accuracy. The following steps are necessary to bring the system to the
endogenous condition:
1. The influent wastewater flow to the aeration tank must be discon-
tinued. Recycle sludge flow may be discontinued or allowed to
recycle normally to prevent septicity of the sludge in the second-
ary clarifier.
2. The liquid level in the aeration tank should be adjusted to produce
the desired power consumption of the aeration equipment. This
liquid level should be recorded for future reference.
3. The mixed liquor should be allowed to stabilize for a specified
time period prior to the start of testing. Experience has sh.own
that typically a period of 30 min to 2 hr is sufficient to bring
the system to the endogenous respiration phase. Relatively constant
165
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values of DO and R at a given point, as determined by frequent mea-
surements (say every 5 min) over a 30-min period, would indicate
that steady state conditions had been reached.
After these steps are completed, the oxygen transfer rate may be deter-
mined following the continuous test procedure previously outlined (Steps 2
through 11).
A batch endogenous desorption test that is very similar to the unsteady
12
state batch endogneous test has been proposed by Kayser. Instead of start-
ing the test at a very low DO concentration, the desorption test starts at a
supersaturated DO level in the test solution. The premise of the test is
that the rate of oxygen desorption is the same as the rate of oxygen transfer
to the water. The initial high DO concentration is achieved by a slug addi-
tion of hydrogen peroxide uniformly distributed over the entire test volume.
Following the initial peroxide addition, by simultaneously monitoring the
decrease in the DO level and the oxygen uptake rate at the same test tank
locations, the field oxygen transfer rate may be determined using a classical
deaeration approach. Testing is usually conducted using the following pro-
cedure:
1. The influent wastewater flow to the aeration tank must be discon-
tinued. Sludge recycle flow may be discontinued or allowed to
recycle normally to prevent septicity of the sludge in the second-
ary clarifier.
2. The liquidlevel in the aeration tank should be adusted to produce
the desired power consumption of the aeration equipment. This
liquid level should be recorded for future reference.
3. The mixed liquor should be allowed to stabilize for a specified time
period prior to the start of testing. Experience has shown that
typically a period of 30 min. to 2 hr is sufficient to bring the
system to the endogenous respiration phase. Relatively constant
values of DO and R at a given point, as determined by frequent mea-
surements (say every 5 min) over a 30-min period, would indicate
that steady state conditions had been reached.
4. Initially, the DO concentration should be measured at several points
166
-------
around the aeration tank (DO profile). The locations for measure-
ment should be selected to define the mixing patterns of the system
and to ensure that the entire test volume is aerobic. For the test,
a minimum of three calibrated DO probes should be installed stra-
tegically within the aerator mixing zone of influence (see Figure
18) for repeated DO measurement.
5. When the oxygen uptake has stabilized, the hydrogen peroxide solu-
tion should be added. Peroxide solutions of 30 to 50 percent can
be used without further dilution. While the aerators are running,
the peroxide solution should be added within a period of 5 to 6 min
or less. Even distribution of the peroxide over the whole test tank
is required (see Appendix E for details of addition for various
aeration devices). It is recommended that sufficient hydrogen
peroxide be added to increase the DO by 12 to 15 mg/£. In order to
increase the DO by 15 mg/H, a dosage of approximately 32 mg/£ as
100 percent H202 or =270 Ib/mil gal is needed.
6. The decrease in DO concentration should be recorded continuously.
Simultaneously, oxygen uptake rates should be measured at the same
tank locations. As often as practical, the oxygen uptake rates
should be measured until the system DO concentration stabilizes at
a constant value, i.e., j^O.l mg/£.
7. The system air flow (if appropriate), energy input, mixed liquor
temperature, air temperature and barometric pressure should be mea-
sured and recorded for each test.
8. Measurement of the barometric pressure and determination of an a
value (see Section 6) are required if correlation to standard con-
dition is desired.
9. A sample of mixed liquor should be analyzed for suspended solids to
provide an MLSS concentration for reference purposes.
10. At the completion of the test, the DO probes should be recalibrated.
If the recalibration indicates a significant deviation between the
probe reading and calibration concentration (>5 percent), the
instrument should be adjusted before further testing is initiated.
167
-------
11. Steps 5 through 10 should be repeated at least three times to obtain
representative results for data analysis.
Data Evaluation —
The data obtained from the unsteady state test may be evaluated using
Equation 90 as described below:
(CR - C) = CR - CQ)exp-[(KLaf + System Time Constant)!] (90)
where:
3
C = DO concentration, m/L , at any time, t
3
CR = DO level, m/L , that most accurately represents the driving force,
- CR,in the transfer zone of the system. For aeration systems
that have a relatively uniform DO concentration (well mixed with
respect to DO), CR would be the average DO of the entire test volume,
CR. For systems that are not well mixed with respect to DO concen-
trations (usually associated with continuous testing), CR, equal to
the DO level in the liquid as it flows to the aeration device
(CR — see points o3, Figure 18), has been shown to more closely
approximate the actual oxygen transfer rate. 8*
C = DO concentration at test time t = 0, m/L
System Time Constant is:
Continuous Test
01
V
Batch Test
Q
-77- (with recycle sludge flow)
0 (without recycle sludge flow)
*
There is considerable controversy among Subcommittee members on this point.
For example, Boon et al.9 believe any value for CR other than the average
over the test volume would yield a "local value" of K|_af and not the overall
system transfer coefficient. They have reasoned that if the DO level is not
constant throughout the tank (as previously assumed in development of the
equations), then Equation 88 is not valid for evaluation of that aeration sys-
tem. Furthermore, Boon^O feels that the variation in DO concentration at any
point in the aeration test volume compared to the mean value should not be
greater than 10 percent of the deficit (c£f - CR) or the value of K[_af would
vary by more than 10 percent of its mean value.
168
-------
Equation 90 is the same general form as the equation used for clean
water evaluations. Therefore, the same evaluation techniques are applicable,
except that for respiring systems the term (K,af + System Time Constant) is
obtained where K. a would be determined for clean water testing. The appro-
priate methods of analysis involve a computer program solution or graphical
solution and are described in detail in Section 4.
Once K. af has been determined, the corresponding effective field DO
saturation concentration, C*f, can be calculated. This calculation may be
performed utilizing Equation 91 as follows:
* R + (System Time Constant) (CD - C1 )
where:
C1 = DO level in the combined wastewater influent and sludge recycle
0 flow, Q1, for continuous testing and DO level in the sludge re-
cycle flow, Qr, for batch testing
Example Calculations--
The description of test procedures indicates a minimum of three in situ
probes is recommended for field test purposes. For the sake of simplicity,
the examples that follow will review only calculations based upon the data
set from one of the installed probes. The data from each probe should be
analyzed independently so that the results may be averaged to obtain the
field oxygen transfer value.
Continuous test results—The data from continuous testing of a diffused
aeration system for an industrial application are presented in Table 19. The
background information for the test is as follows:
T = 30°C
Qi = 1.2 mgd
Qr = 0.5 mgd
Q1 = 1.7 mgd
C'Q = 0 mg/X,
V = 0.75 mil gal (19-ft liquid depth)
R = 30 mg/£/hr (average of five results collected during the test
peri od )
169
-------
TABLE 19. UNSTEADY STATE CONTINUOUS TEST DATA
Time
(min)
0
1
2
3
4
5
6
7
8
9
10
11
12
DO
(mg/£)
0.2
0.4
1.0
1.3
1.7
2.0
2.2
2.5
2.6
2.9
3.1
3.2
3.4
Time
(min)
13
14
15
17
19
20
25
30
35
40
45
50
60
DO
3.5
3.6
3.6
3.9
4.0
4.1
4.2
4.4
4.4
4.5
4.5
4.5
4.5
The test data are plotted in Figures 22 and 23. From Figure 22, the
equilibrium DO concentration for the system oxygen uptake rate, CR, is
established at 4.5 mg/l. Using this value, Figure 23 was generated and K. a f
-1
was determined to be 6.9 hr . The effective field saturation DO level,
Coof> is given by Equation 91 as calculated below:
30 + fo/i/n'^cn^.S - 0.0)
C* = 4.5 + 124(0- ?5)T
f 6.9
*
cf = 4-5 + [(30 + 0.425J/6.9]
C*f = 4.5 + 4.4 = 8.9 mg/£
Batch endogenous test results — The unsteady state batch endogenous test
13
has been used by Muller et al. to analyze oxygen transfer efficiency in a
72-mgd municipal treatment plant containing diffused aerators. Twenty-four
hr prior to the test, flow was diverted around the aeration tanks being ana-
lyzed and aeration was maintained. Approximately 1 hr prior to the test, two
butterfly valves controlling air flow to the aeration tank being tested were
170
-------
05 10 15 20 25 30 35
TIME (min)
Figure 22. Unsteady state continuous test DO versus time plot.
throttled to approximately one-half the previous air flow, allowing the DO
concentration to decrease but still maintaining solids in suspension. At the
beginning of the test, air flow was increased and DO probe readings taken at
the one-third points in four aeration bays. Air flow, temperature, and pres-
sure readings for the two headers feeding the four bays were also taken along
with oxygen uptake rates. The DO data taken at one point during the test are
listed in Table 20 and plotted in Figures 24 and 25. The slope of the result-
ing line in Figure 25 is the K.af value of the aeration system, 4.2 hr~ , at
the test mixed liquor temperature. For the oxygen uptake value of 10.4
mg/£/hr and a CR value of 9.3 mg/A, C* was determined to be 12.0 mg/JL,
The above unsteady state batch endogenous data have also been analyzed
using the nonlinear least squares technique and a computer program developed
for clean water analysis. The results of this analysis are presented in
Table 21. The oxygen transfer coefficient, KLaf, was estimated at 4.05 hr
(0.0675 min ) and the CR value as 9.4 mg/fc, both close to the values esti-
mated from the semi log plot. The errors in these parameters are 2.66 percent
-1
171
-------
o»
E
o
i
-------
TABLE 20. UNSTEADY STATE BATCH ENDOGENOUS TEST DATA
Test Conditions
Mixed liquor temperature = 12°C
Mixed liquor oxygen uptake rate =10.4 mg/Ji/hr
Mixed liquor steady state DO = 9.3 mg/H
Time
(min)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
6.0
7.0
8.0
10.0
12.0
Mixed Liquor
DO
(rng/A)
0.6
0.9
1.1
1.4
1.5
1.9
2.1
2.5
3.0
3.3
3.75
4.2
5.1
5.6
Time
(min)
14.0
16.0
18.0
20.0
22.0
23.0
28.0
33.0
38.0
43.0
48.0
53.0
63.0
Mixed Liquor
DO
(mgA)
6.0
6.3
6.75
7.0
7.4
7.6
8.0
8.25
8.8
8.9
9.1
9.4
9.4
fol1ows:
T = 24°C
V = 0.43 mil gal (16.4-ft liquid depth)
R = 19.7 mg/&/hr (average of six results collected during the test
period)
The test data are plotted in Figures 26 and 27. From Figure 26, the
equilibrium DO concentration for the system oxygen uptake rate, CR, is estab-
lished at 4.9 mg/£. Using this value, Figure 27 was generated and K. af was
-1 *
determined to be 3.9 hr . The effective field saturation level, C .e, is given
OOy *•*
by Equation 91 as calculated below:
173
-------
(0
"E
=J
O
o
tu
oc
LJ
m
o
QL
OL
o
Q
l\J
9
8
7
6
5
4
3
2
1
n
_ Vii^_^
,
•
~
•'
- •
-
.
- • _
*
— * _
/
T ~
1 1 ! 1
0 10 20 30 40 50 60
TIME (min)
Figure 24. Unsteady state batch endogenous test plot of DO versus time.
C*f = 4.9 + (19.7/3.9)
C*f = 4.9 + 5.1 = 10.0 mg/£
Test Limitations--
The limitations of a specific test method must be recognized to ensure
adequate data collection and allow an appreciation for the accuracy of the end
result. For the unsteady state testing approaches, the following discussion
outlines the specific test limitations that have been identified.
Continuous testing—An accurate determination of the R value may be very
difficult to obtain if influent flow and substrate concentration vary sub-
stantially during the test period. If either of these conditions exist, the
reaeration curve may be erratic and the calculated C*f value, which is calcu-
lated using R, may be in error. As previously mentioned, a high organic load-
ing to the test system (R > 60 mg/Vhr) will also preclude an accurate measure-
174
-------
10
8
6
4
0>
1
ex
O
O
O
I
a:
O
I
0.8
0.6
0.4
0.2
O.I
I
10 20 30 40 50 60
TIME (min)
Figure 25. Unsteady state batch endogeneous test semi log plot.
o
ment of R.
Due to the flow-through testing conditions, the influence of non-uniform
influent wastewater flow and substrate concentration will cause variable sys-
tem R and a values over the test period. In addition, under flow-through con-
ditions, the maldistribution of the influent flow throughout the tank volume
can bring about spatial variation of R and a values within the test volume.
Therefore, testing should be conducted during operational periods when
fluctuations in influent flow and organic strength are minimal.
For many applications, specifically for surface aeration installations,
the DO concentration may vary spatially within the tank at a given time dur-
ing testing under continuous loading conditions. Therefore, this test
175
-------
TABLE 21. NONLINEAR ESTIMATION FOR UNSTEADY STATE OXYGEN
TRANSFER DURING ENDOGENOUS TESTING
Input data in time, DO data pairs
Input 999,999 as
Iteration
Number
0
1
2
3
last data pai
CR
(mg/A)
10
9.39391
9.39667
9.39669
r
DATA SET
Co
(mg/i)
0.1
0.488792
0.488203
0.488197
KLaf
(min-1)
0.07
0.0677646
0.0675272
0.0675274
Sum of
Squares
3.71155
0.234328
0.233152
0.233153
Standard Deviations of Parameter Estimates
Absolute Units
Percent of LSE
Estimate of Error
0.0866782
0.922437
= 0.105368
0.0554709
11.3623
1.79764E-03
2.6621
SUMMARY OF DATA
Data Point
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Time
0.5
1
1.5
2
2.5
3
4
5
6
7
8
10
12
14
16
18
20
22
23
28
33
38
43
48
Cone.
0.9
1.1
1.4
1.5
1.9
2.1
2.5
3
3.3
3.75
4.2
5.1
5.6
6
6.3
6.75
7
7.4
7.6
8
8.25
8.8
8.9
9.1
Fit Value
0.78396
1.0699
1.34635
1.61363
1.87202
2.12184
2.59688
3.04089
3.45591
3.84383
4.20642
4.86212
5.43498
5.93547
6.37273
6.75476
7.08852
7.38011
7.51179
8.0519
8.43725
8.71217
8.90832
9.04826
Residual
.11604
.0300967
.0536465
-.113625
.0279769
-.0218434
-.0968757
-.0408888
-.15591
-.0938306
-6.42061E-03
.237882
.16502
.0645294
-.0727334
-4.75597E-03
-.0885172
.0198865
.0882082
-.-5190T8
-.187245
.0878296
-8.31795E-03
.0517416
176
-------
TABLE 22. UNSTEADY STATE BATCH OXYGEN DESORPTION TEST DATA
Time
(min)
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
Mixed Liquor
DO
(mg/A)
4.8
4.8
6.2
10.5
15.0
18.5
21.5
23.5
22.6
22.2
21.0
19.5
18.1
17.2
16.2
15.6
Time
(min)
9
10
12
14
16
18
20
25
30
35
40
50
60
70
80
90
Mixed Liquor
DO
(mg/A)
15.0
15.4
13.1
12.1
11.5
10.7
10.0
8.7
7.7
7.0
6.4
5.6
5.3
5.1
4.9
4.9
approach may not be valid for those applications where such variation exists.
Furthermore, if the variation in DO concentration at any point in the aera-
tion test volume compared to the mean value is greater than +_ 10 percent of
the deficit (C*f - CR), then the resultant KLaf value should be considered no
more accurate than this measured DO variability.
For systems with a low oxygen transfer rate and a high organic loading
rate, the system equilibrium DO level, CR, may be relatively low. To obtain
sufficient test information for statistical data analysis, a reasonable range
for the test parameter (CR - C) is essential. Since the practical initial DO
level will be approximately 0.5 mg/H, a minimum CR level of 4.0 mg/H is recom-
mended for reliable evaluation of test data. This provision may prohibit con-
tinuous testing at some installations.
For surface aeration installations, the only method of reducing the DO
177
-------
O>
E
O
Q
10 20 30 40 50 60 70 80 90 100
TIME (min)
Figure 26. Unsteady state batch desorption test DO versus time plot.
concentration sufficiently may be to completely shut off the aerators or
operate them intermittently. This action would result in inadequate mixing of
the test volume, bringing about solids segregation during the deaeration phase
of the testing. As the units are turned on for the reaeration phase of the
testing, erratic results will be produced during the initial data collection
period due to the re-establishment of the uniform mixing regime. Depending
on the size and geometric configuration of the test volume, the effect of
inadequate mixing could lead to erroneous test results.
Batch testing--To achieve an endogenous respiration condition, the influ-
ent flow to the test volume must be discontinued. For systems with limited
operational flexibility, this approach may not be practical.
178
-------
0 10 20 30 40 50 60 70 80 90 100
TIME (min)
Figure 27. Unsteady state batch desorption test semilog plot.
When testing under endogenous respiration conditions, the a level would
not necessarily reflect the a level at normal operating conditions. There-
fore, if a field transfer rate under operating conditions is desired, the
batch test may not yield an accurate estimation of that value. Depending on
the specific application, testing under endogenous conditions would be
expected to yield higher field transfer rates due to higher a levels. On the
other hand, if the test is performed for comparison with a standard oxygen
transfer rate, this approach should provide representative information for
that comparison.
The requirement of maintaining the excess DO level, CR, within a practi-
cal range during the test period may prove to be a limitation for some appli-
179
-------
cations of the unsteady state batch test. In order to define a reasonable
range for accurate DO determination, the measured CD level should be between
*
a minimum of 2 mg/£ and a maximum of 75 percent of the system C.. Limiting
the test conditions to this range will ensure the statistical validity of the
DO measurement and provide a meaningful end result.
For surface aeration installations, the only method of reducing the DO
concentration sufficiently may be to completely shut off the aerators or oper-
ate them intermittently. This action would result in inadequate mixing of the
test volume and bringing about solids segregation during the deaeration phase
of the testing. As the units are turned on for the reaeration phase of the
testing, erratic results will be produced during the initial data collection
period due to the re-establishment of the uniform mixing regime. Depending
on the size and geometric configuration of the test volume, the effect of
inadequate mixing could lead to erroneous test results.
Batch desorption testing--To achieve an endogenous respiration condition,
the influent flow to the test volume must be discontinued. For systems with
limited operational flexibility, this approach may not be practical.
When testing under endogenous respiration conditions, the a level would
not necessarily reflect the a level at normal operating conditions. There-
fore, if a field transfer rate under operating conditions is desired, the
batch desorption may not yield an accurate estimation of that value. Depend-
ing on the specific application, testing under endogenous conditions would
be expected to yield higher field transfer rates due to higher a levels. On
the other hand, if the test is performed for comparison with a standard oxygen
transfer rate, this approach should provide representative information for
that comparison.
This method assumes that the hydrogen peroxide immediately and fully dis-
associates to DO and water when added to the test volume. In addition, this
approach is based on the premise that the rate of oxygen desorption from water
14
to air is the same rate as oxygen transfer from air to water. Kayser's work
seems to verify both of these assumptions. However, if the peroxide does not
fully disassociate before the start of the test, the resulting oxygen transfer
rate determination will be erroneously lower than the actual field transfer
rate.
180
-------
Other Test Approaches
In addition to the above tests, other procedures may also be employed to
evaluate aeration systems used in biological treatment. For the most part,
these procedures have not been extensively used and, therefore, cannot be
recommended as primary tests for respiring system field tests. However, these
tests may have application for specific treatment operations.
Mass Balance: Activated Sludge Systems--
The mass balance approach has been proposed to determine oxygen transfer
in operational activated sludge systems. Total oxygen balances must be made
on the influent, effluent, and waste activated sludge. The change in total
oxygen across the entire activated sludge system equals the oxygen transferred
by the aeration system. Total oxygen measurements should be based on COD,
with correction for nitrification. The major problems with the mass balance
technique lie in satisfactory measurement of waste activated sludge volumes
and in obtaining representative samples of waste activated sludge for analy-
sis. The high suspended solids concentrations in waste activated sludge make
it difficult to obtain valid data because of large errors that can result from
minor variations in the aeration volume solids inventory. While it is possi-
ble to achieve accurate mass balance measurements on small laboratory systems,
this technique has limited practical value in field-scale evaluation of aera-
tion equipment for activated sludge systems.
Mass balances have been used with some degree of success with well-mixed
activated sludge systems. Short detention time systems with sufficient
power to keep all of the solids in suspension can be evaluated by measuring
the difference between the influent and effluent COD concentrations (includ-
ing the COD of the waste sludge) over a period of time equal to at least six
times the system hydraulic retention time. With this provision, variations
in waste characteristics can be leveled out to yield more representative data.
In most cases, analysis of data over a 1-mo period should provide reasonable
correlation for evaluation of the aeration equipment.
In the mass balance evaluation, care must be taken to ensure that the
aeration system is well mixed. If suspended solids settle out in the aeration
tank, the data will indicate a higher oxygen transfer than is actually occur-
181
-------
ring. Furthermore, higher transfer rates can also be predicted for certain
industrial wastewaters where volatilization of organic compounds occur during
the aeration process. Therefore, if this technique is to be used in field
evaluations, a careful review of the potential impact of aeration tank vola-
tilization and solids deposition is recommended.
Mass Balance: Aerated Stabilization Basin Systems—
The mass balance procedure has been applied to low-rate aerated stabili-
zation basin (ASB) systems because oxygen transfer cannot be readily measured
using more direct methods. The accuracy of this method depends on the extent
to which all factors that supply and withdraw oxygen from the system are mea-
sured. A number of these factors can be minimized during the test period so
that the main factor that determines the aerator oxygen transfer is the re-
duction in BOD through the respiring system. The mass balance method is sim-
ple and straightforward, especially when the ASB system is aerator (oxygen)
limited and where signficant settleable biological solids are not produced.
Minimum DO procedure--In order to minimize or eliminate a correction
factor for the working DO in the basin, turning off or redeploying aerators
may be necessary if the system normally carries excess DO. Actually, several
tests at approximately 60, 80, and 100 percent of tuned aeration capacity may
be performed to ensure an accurate test. If the system is oxygen limited,
the aeration efficiency (Ib 02/hp-day or kg/kWh) should be equal for each test.
If the values don't agree, other limitations may exist, such as insufficient
nutrients or the presence of toxic materials.
Certain systems will lend themselves to segregation for the purpose of
testing. Basins in series or long narrow basins would be candidates for
testing of various groupings of aerators. Thus, it is possible that tests
could be made on various portions of the system at the same time and repre-
sent varying fractions of the tuned capacity. All portions of each cluster
would have to be oxygen limited. The last stages of such a system might be
omitted to improve the accuracy of the test procedure because these later
• stages are apt to produce excess DO during a portion of the test period.
The major variables in the calculation are the incoming and exiting masses
of oxygen demanding materials. COD, TOC (converted to its oxygen equivalent),
182
-------
and ultimate BOD are the appropriate parameters around which to construct the
balance. In certain cases, such as with many pulp and paper mill works, the
BODr can be used because the system removes only a small fraction of the
l calculation determines the difference between influent and ef-
fluent oxygen demand during the test period. This difference is then divided
by the operating power used by the aerators during the same period. The cal-
culation produces results in terms of Ib oxygen transferred/hp-day (or kg/kWh).
It should be recognized that under oxygen-limited conditions there is a
potential to accumulate BOD in the microbial mass that may result in an appar-
ent oxygen transfer rate, OTR, greater than the actual OTR. However, because
most ASB systems are respiring at extremely low rates, synthesis effects are
minimal and can be neglected.
There are several other adjustments that can be incorporated into the
calculation. A discussion of each follows:
DO difference-- If the system has been properly tuned, the DO concen-
tration returning to the inlet to the aeration device should be zero and the
DO concentration leaving the basin will probably be zero. Thus, the case
reduces to the situation where the incoming wastewater contains DO that would
have to be debited from the aerator transfer. For most tuned situations, this
factor represents less than 1 percent of the total transfer.
Surface area—This factor is usually disregarded. However, the
aerators could be debited with a value of 50 Ib O^/acre of surface/day. This
value represents BOD,- removal associated with treatment in unaerated stabili-
18
zation basins. Unless the ASB is very large in comparison to the power com-
bined in the aerators (i.e., greater than 10 gal/hp), the contribution of the
surface area to aeration is not a major factor.
Benthal oxygen demand--Aerated stabilization basins are not com-
pletely aerobic. However, the pumping rate of the mechanical or diffused
aerators recirculates the total basin contents through the aerobic zone to an
extent that impedes the development of highly reduced conditions. Thus,
appreciable amounts of oxygen are not required to satisfy an immediate chemi-
cal oxygen demand. However, bottom deposits, no matter how thin, constitute
a continued sink for any oxygen that reaches the bottom. Sediment oxygen
183
-------
demand studies on a variety of benthal deposits have shown uptake rates vary-
2 2
ing from 1.0-20.0 gm/m /day. A credit of 5.5 gm/m /day (50 Ib/acre/day) is
19 20 21
suggested for the benthal oxygen demand. ' ' Again, even if DO exists
near the bottom of most of the basin, the amount of oxygen removed is minimal.
Mitrification-denitrification factor—The oxygen equivalent of the
nitrogen balance will have to be considered in some systems. The aerators
should be credited with transferring the oxygen necessary to balance the
change in the oxidative state of the nitrogen species entering and exiting
the system. However, for all practical purposes, nitrification is suppressed
under oxygen-limited conditions (e.g., DO less than 1.0 mg/H) and also ceases
22
at BOD,-:N ratios of 16 or higher. Thus, nitrification and denitrification
aren't significant in the oxygen-limited equilibrium test case and the high
BOD5:N case.
Correcting for temperature—One major advantage of using the mass
balance approach is that no temperature correction is required. Biological
kinetics predict a doubling of the reaction rate with each 10°C rise in tem-
po pA pc
perature (i.e., 0 = 1.072). ' ' Thus, an oxygen-limited system operating
at 10°C would simply require less oxygen (hp) than when operated at 20°C. The
oxygen demand would be matched only to the extent that there was aeration
capacity in the system.
The oxygen transfer rate constant, K.a, is temperature dependent. The
0 value most commonly used is 1.024. This 6 value effectively offsets the
temperature coefficient for the saturation concentration of DO in water. As
an example, when DO is limited (i.e., DO = 0), the deficit equals the satura-
tion concentration. The result is that approximately the same mass rate of
oxygen is transferred into water at 10°C, at 20°C, and at 30°C under the oxy-
gen-limited condition.
Excess DO procedure—Some ASB systems can't be turned down to minimize
DO throughout the basin. Several additional factors must be considered to
compute the oxygen transferred by the aeration equipment when excess DO is
present in the basin. These factors are briefly reviewed as follows:
Driving force factor--If the basin is tested when excess DO is
present, the aeration equipment isn't operating at maximum efficiency. Thus,
184
-------
a mass balance based on BOD removal won't account for the potential transfer
that would occur had the test been performed at zero DO. In order to compute
the potential transfer, it is necessary to determine 3 and the average DO in
the basin. The average DO, £R, can be determined by testing representative
volumes of the basin during the test period. Beta will have to be measured
using the procedures prescribed elsewhere in this report. The potential BOD
removal can then be increased by the ratio of the oxygen solubility to the
oxygen deficit that exists during the test. In order to calculate the credit,
a sampling program will have to be developed based on the temperal variation
in DO at various points in the basin. Daily sampling at key locations in the
basin may be required, especially if the BOD load to the basin fluctuates
markedly. In systems where the photosynthetic addition of DO is a factor,
the mass balance may have to be determined on an hourly basis to properly pro-
portion the excess DO to the aeration system. Plug flow systems should be
segmented volumetrically and weighted using the C*f and CR values associated
with each segment.
Temperature correction—The effect of temperature on the oxygen
transfer rate will be included in the average DO concentration in the basin.
Again, this factor is offset in the calculation for the maximum oxygen trans-
fer rate at zero DO by the temperature coefficient for the saturation concen-
tration, provided 9 = 1.024. Therefore, a temperature correction is not
required.
Photosynthetic factor—Systems exhibiting photosynthesis represent
a special case in the excess DO consideration. First, the variation in DO
concentration in the basin will be a function of the availability of sunlight
and will necessitate more frequent sampling for determining DO concentrations
in the basin. Second, the contribution of DO by the algae will have to be
debited from the aerator transfer should there be periods when DO becomes
limiting in the system. During this time, BOD removal will utilize the added
oxygen.
A large population of algae in an aerated basin will probably ensure that
DO exists at most times in the basin. Thus, the only complication is debit-
ing the oxygen contributed by the algae from the driving force factor. Light
and dark bottle oxygen uptake rates could determine the mass of oxygen con-
185
-------
verted by the algae. This oxygen mass would then be equated to an equivalent
DO concentration and subtracted from CD so that the aeration potential isn't
K
overestimated. Again, this is a very special case for the mass balance pro-
cedure and hasn't been applied as a means of computing the oxygen transfer of
an aeration system.
Ni trification-denitification factor—Because excess DO is present
in the system, nitrification is expected to proceed in systems receiving sig-
nificant quantities of influent nitrogen. In activated sludge systems treat-
ing municipal wastewater, nitrogen oxidation may account for 5 to 25 percent
of the total oxygen demand. Thus, it is reasonable to expect the change in
the nitrogen oxygen demand (NOD) across the long-term system may be signfi-
cant where BOD5:N ratios are less than 16:1 in the influent.
Equations for ASB mass transfer procedures --
Minimum DO procedure—
OTRobs = T [(BODr)j + (NODr).]
J '
(92)
OTR . = OTR , - Y (8.34Q'C' ). + Accumulation Factor (93)
act ODS .L-, o j —
OTR
AE =
act
p.
(94)
Excess DO procedure--
cap
= I
(BOD ). + (NOD ).
' J ' O
B C
* - c
L
T
J
(95)
TThe nomenclature used for ASB systems is slightly different that that used
in the discussion of activated sludge testing. Therefore, the equivalent
activated sludge nomenclature has been indicated with the ASB nomenclature,
where appropriate
Accumulation factor is used to account for buildup or loss of BOD, DO, and
NOD in the basin during the test period (see example).
186
-------
where:
J=n ±
OTR = OTR - T 8.340Q'(C' - CJ. + Accumulation Factorf (96)
act cap .^-1 o e j —
OTR , = observed oxygen transfer rate accounting for the major variables
obs (Ib). m
OTR t = actual oxygen transfer rate accounting for minor variables as
acT- well (Ib), m
AE = aeration efficiency (Ib O^/hp-day), m L~ f
OTR = oxygen transfer capacity had the system been operating under
caP oxygen limiting conditions (Ib), m
BOD = the ultimate BOD removed from the system, S. - S (Ib), m
NOD = the oxygen equivalent of the nitrogen oxidation that takes
r place in the system, f(Nj - N), where f is the appropriate con-
version factor to units of oxygen (Ib), m
C = dissolve^ oxygen concentration (mg/&) (C'0 = influent, Ce = ef-
fluent, Cj = average at temperature T), m/L.3
*3
Q1 = flow into the basin (mgd), L°/t
P = operating aerator power (hp-day), Lf/t
n = total number of sampling intervals
Example calculation for minimum DO case—A 5-day completely mixed.ASB
system was operated under oxygen limiting conditions for two periods during
the month of October 1978. DO and settleable solids measurements were con-
ducted at several points in the basin each day during the test period. The
DO concentration was zero in water entering the aeration zone, and no settle-
able solids were produced. The basin was operated in a turned-down mode
during the second half of the month. The liquid level in the basin remained
constant during the test period. The performance data for the system are
summarized in Table 23,
The data for the first 16 days and the last 11 days were analyzed as
follows:
October October
Parameter 1-16 20-31
Total BOD5 reduction (Ib) 1,147,110 724,500
Total operating power (hp-day) 27,950 18,230
The mass balance considerations are computed as follows:
187
-------
TABLE 23. EXTERNAL WASTEWATER MANAGEMENT PROCESS PERFORMANCE DATA*
00
oo
Influent to Basin
Date
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Flow
(mgd)
21.6
20.5
21.2
20.0
20.7
20.2
20.2
19.8
20.5
20.7
20.7
20.0
20.9
21.4
21.0
21.4
21.2
21.3
24.1
Power
(hp)
1800
1800
1800
1700
1675
1800
1800
1800
1800
1780
1675
1700
1640
1700
1700
1780
1640
1500
1460
BOD5
(rag/A) (1000 Ib/day)
521
438
540
750
456
478
501
591
427
573
485
434
435
630
459
495
368
435
336
9,40
74.8
95.4
129.5
78.8
80.7
84.6
97.4
72.9
99.0
83.8
72.4
76.0
112.5
80.4
88.4
65.0
77.1
67.5
Effluent from Basin
Suspended Rnn Suspended
Solids Temp. u 5 Solids
(.1000 Ib/day) (°C) (1000 Ib/day) (1000 Ib/day)
24.5
47.5
21.4
36.4
22.6
29.5
26.2
23.1
27.3
20.6
30.7
19.4
15.5
20.5
16.5
14.1
24.6
33.2
29.5
30.5
30.0
30.0
30.0
30.5
31.1
28.8
28.8
28.3
29.4
29.4
20.0
30.5
28.3
28.3
28.8
27.7
26.6
26.6
11.1
14.3
16.7
15.3
18.4
18.0
23.6
13.5
14.4
10.4
9.0
13.7
9.7
28.9
29.6
26.8
21.4
13.2
17.6
19.5
25.5
15.2
14.9
15.8
9.3
17.2
18.2
18.7
14.2
19.9
23.9
13.7
16.2
18.1
20.9
15.9
22.7
22.7
(continued)
BOD5
Removal
(%)
88
81
82
88
77
78
72
86
80
90
89
81
87
74
63
70
67
83
74
-------
TABLE 23. (continued)
00
10
Influent to Basin
Date
20
21
22
23
24
25
26
27
28
29
30
21
Mean
Max
Min
Flow
(mgd)
23.1
21.9
24.1
22.6
22.1
21.2
21.4
20.9
22.6
18.6
20.0
22.1
21.3
24.1
18.6
Power
(hp)
1510
1640
1640
1530
1500
1500
1500
1500
1475
1500
1475
1460
BOD5
(mg/A)(l
433
485
600
383
464
513
268
298
393
600
471
403
473
750
268
000 Ib/day)
83.5
88.5
120.5
72.2
85.6
90.6
47.9
52.1
74.1
93.2
78.7
74.3
83.6
129.5
47.9
Suspended
Solids
(1000 Ib/day)
15.
21.
21.
16.
23.
19.
19.
27.
21.
19.
19.
86.
25.
86.
14.
6
0
9
2
4
6
1
4
1
6
4
5
6
5
1
Temp.
26.6
27.7
28.3
28.3
28.8
28.8
29.4
30.0
30.0
29.4
27.7
27.2
28.9
31.1
26.6
Effluent
BOD5
(1000 Ib/day)
23.5
33.3
16.2
10.3
36.3
24.8
18.6
14.4
13.3
15.3
15.3
15.4
18.2
36.3
9.0
from Basin
Suspended BOD5
Solids Removal
(1000 Ib/day) (%)
21.
13.
16.
4.
12.
13.
16.
15.
14.
11.
3.
19.
16.
25.
3.
5
7
0
4
0
5
1
2
3
5
5
8
3
5
5
72
62
87
86
58
73
61
72
82
84
81
81
78
90
58
For month of October 1978.
-------
DO difference—The average DO concentration in the flow entering
the basin was 1.5 mg/Jl. The DO concentration in the flow leaving the basin
was 0.0 mg/fc. The system is debited with 270 Ib 02/day [(1.5 mg/Jl) x (21.3
mgd) x (8.34)].
Surface area—The basin is 30 acres in area. This area would absorb
1500 Ib of oxygen daily at an estimated rate of 50 Ib/acre/day. This is a
debit aeration calculation.
BOD accumulation—The BOD- concentration in the basin on October 1
was 62 nigA. The BODr concentration in the basin on October 16 was 157 mg/£.
The system accumulated 83,000 Ib of BOD,- during the period of October 1-16
[(157 mg/S, - 62 mg/S,) x (8.34) x (105 mil gal)]. This is a debit in the aer-
ation calculation. The BODC concentration in the basin on October 20 was
o
122 mg/£ and by October 31 had dropped to 84 mg/£. The system lost 33,400
Ib during the period of October 20-31 [(122 mg/£ - 84 mg/Jl) x (8.34) x (105
mil gal)]. This is a credit in the aeration calculation. In this case,
which deals with paper mill waste, the BOD- difference is equivalent to the
COD difference and, thus, is also equivalent to the actual oxygen consumed.
Anaerobic factor—The sediment oxygen demand is estimated at 50 Ib/
acre/day. This calculation is the same as the surface area calculation, only
it becomes a credit in the mass balance consideration. The daily credit is
1500 Ib of oxygen.
The total mass balance in this example is:
n , October October
Parameter 1-16 20-31
BODg reduction (Ib) 1,147,110 724,500
DO difference (Ib) +4,320 +2,970
Surface area (Ib) -24,000 -16,500
Accumulation (Ib) -83,000 +33,400
Anaerobic factor (Ib) +24,000 +16,500
Total balance (Ib) 1,068,430 760,870
Aeration efficiency (Ib/hp-day) 38.2 41.6
Difference in aeration efficiency
between periods (Ib/hp-day) 3.4
Average aeration efficiency (Ib/hp-day) 39.9
190
-------
The average aeration efficiency would have been computed at 40.3 Ib/hp-
day if just the BOD5 reduction values had been used. The accumulation factors
could be further reduced by lengthening the test periods.
Limitations—The mass balance method cannot be applied in all cases. The
accuracy of test results using this method depends on the extent to which all
factors affecting the supply of oxygen to and depletion of oxygen from the
system can be identified and quantified.
The test period should be long enough to reduce effects of short-term
fluctuations in load, performance, and weather. To overcome this limitation,
it is recommended that a period equal to three theoretical detention times,
V/Q1, be used for averaging the data.
The procedure assumes that the system is at equilibrium during the test
period. Thus, the system should not be accumulating or releasing BOD that
cannot be readily accounted for. The loss of settleable solids may be a sink
for BOD in certain systems. Thus, the method is limited to systems where the
mixed liquor contains less than 0.1 ml/£ settleable solids throughout the
test period.
The mass balance method has not been employed in photosynthetically active
aerated lagoon systems for the purposes of computing aeration oxygen transfer.
This application requires further study.
Off-Gas Analysis--
Off-gas analysis has been used with full-scale, diffused aeration acti-
pc
vated sludge systems and covered tank, pure oxygen activated sludge systems.
A mass balance on oxygen in the gas phase is required; therefore, this method
is not applicable to surface aeration equipment. For systems that are not
enclosed, a collector or hood is placed in the zone of interest in the aera-
tion tank so a representative sample can be collected and analyzed for resid-
ual oxygen. As with the other methods, the validity of this technique depends
on the accuracy and precision of the various parameters that have to be mea-
sured. For low efficiency of oxygen transfer (3 to 5 percent) associated
with many diffused aeration systems, obtaining the requisite accuracy and pre-
cision of the mass balance on the input and discharge gases is difficult under
the best of conditions. However, it is recognized that significant advances
191
-------
have been made in the recent past regarding instruments and techniques for
measuring gas-phase oxygen concentration and aeration systems with oxygen
transfer efficiencies of about 10 percent are becoming more the rule than the
exception. The combined effect of these developments suggests the desirabil-
ity of additional investigation of the utility and merit of this method.
Recent efforts to develop off-gas techniques that will provide the requisite
27 28 29
accuracy and precision in field situations have been reported. ' '
Tracer Method--
A radioactive tracer technique has been proposed to measure oxygen trans-
2
fer rates in any aeration system, either in clear water or in wastewater.
The tracer method requires considerable planning, special radioactive count-
ing equipment, and a radioactive materials license to use the radioisotopes,
krypton-85 and tritium. The basic concept of the radioactive tracer tech-
nique involves direct measurement of the mass transfer of krypton-85, which
is related to the oxygen transfer rate. The tritium is used to measure the
dispersion of the tracers in the aeration tank. Both tracers are added to
the aeration tank at a single point. As the tracers are dispersed in the
aeration tank, the tritium mixes with the mixed liquor while the krypton-85
is stripped off in the gas phase. The key to this procedure lies in the fact
that the krypton-85 stripping rate from the mixed liquor is directly related
to the oxygen transfer rate from the gas into the mixed liquor. In effect,
the tracer method is an indirect method for measuring oxygen transfer. A
series of grab samples are collected and counted in a scintillation counter.
Care must be taken to ensure that gas bubbles do not form in the samples as
the krypton-85 would come to equilibrium with the gas bubbles and produce an
error in the radioactive counts. Accurate counting of the samples is essen-
tial for obtaining good results. The counting efficiency is about 30 percent
for tritium and about 90 percent for krypton-85. The tracer technique has
had limited application to date and should be used with care until additional
data are available to demonstrate its validity. It should also be recognized
that even though the quantities of radioactive materials are small, the grow-
ing concern over the use and release of any amount of radioactive materials
into the environment may restrict the use of this technique as long as other
methods are available that do not involve such materials.
192
-------
Dual Unsteady State Method--
Muller and Rysinger have recently proposed a procedure for evaluating
oxygen transfer rates under process conditions. The dual unsteady state
analysis employs unsteady state DO measurements at a high oxygen transfer rate
to raise the DO concentration to a value well above that used for process con-
ditions followed by a lower oxygen transfer rate where unsteady state DO mea-
surements are again taken. Field oxygen transfer coefficients, K^a, for each
condition may be calculated. In addition, field saturation values can be
determined for each transfer rate as well as oxygen uptake rate. The method
requires a substantial spread in K.a values from the high oxygen transfer
rate condition to the low transfer rate condition and constant uptake rates
during the test period. Test results using this method have been recently
"31 "3?
reported. l>>5
CONCLUSIONS
Aeration testing with respiring activated sludge systems is not easily
carried out and is not recommended over clean water aeration testing for
verifying aeration performance specifications. However, with careful data
collection and evaluation, it is possible to obtain reasonably valid respir-
ing system test results. After review of current testing experience and the
inherent errors of each test, the following conclusions are appropriate:
The testing techniques utilized for in situ testing are by nature very
site specific. Truly, there is clearly no "best method" based on current
technology.
Batch endogenous testing procedures are more accurate than continuous
testing techniques for estimating field transfer rates of various aeration
equipment.
The main limitation of continuous testing is the inability to accurately
measure the biological oxygen uptake rate.
For many applications, specifically for surface aeration installations,
the DO concentration may vary spatially within the tank at a given time dur-
ing testing under continuous loading conditions; therefore, conventional
testing approaches may not be valid for these applications. Further study is
required for such installations.
193
-------
For surface aeration equipment, steady state batch endogenous testing is
preferable to unsteady state batch endogenous testing.
For submerged aeration equipment, unsteady state batch endogneous testing
is preferable to steady state batch endogenous testing.
Batch endogenous desorption testing using hydrogen peroxide has been
demonstrated as an effective technique for measuring field oxygen transfer in
surface and submerged aeration systems.
The mass balance approach for determining field oxygen transfer rates
requires extensive data collection. For activated sludge systems, the
approach appears to have value in small, well-mixed systems, but is simply
not as accurate as other tests for most systems. For ASB systems, this
approach may be the only practical method available for testing. Therefore,
with reasonable care in data collection and analysis, the mass balance
approach can be useful for evaluating aeration equipment performance in re-
spiring systems.
The off-gas analysis method for field oxygen transfer measurement has had
limited application to date. One current application of this technique is
with covered tank, pure oxygen activated sludge systems. However, in view of
advancing technology in oxygen concentration measurement equipment and the
progressive increase in efficiency of aeration systems generally, this
approach deserves further evaluation.
The tracer method for field oxygen transfer determination remains essen-
tially untested. This approach requires and deserves further evaluation.
REFERENCES
1. Mueller, J.A., J. Famularo, and T.J. Mulligan, "Oxygen Transfer in
Closed Systems," Proceedings, Workshop Toward an Oxygen Transfer Stan-
dard," EPA-600/9-78-021, pp. 180-194, April 1979.
2. Neal, L.A., "Use of Tracers for Evaluation of Oxygen Transfer," Pro-
ceedings, Workshop Toward an Oxygen Transfer Standard, EPA-600-9/78-021,
pp. 210-227,April 1979).
3. McKinney, R.E., "Mathematics of Complete Mixing Activated Sludge,"
Journal of the Sanitary Engineering Division, ASCE, 88(SA3):87-113,
May 1962.
194
-------
4. Eckenfelder, Jr., W.W., "Factors Affecting the Aeration Efficiency of
Sewage and Industrial Wastes," Sewage and Industrial Wastes, 31:60-70,
January 1959.
5. Nogaj, R.J. and E. Hurwitz, "Determination of Aeration Efficiency Under
Process Conditions," Proceedings of the 18th Industrial Waste Conference,
Purdue University, pp. 674-683, April 1963.
6. Kayser, R., "Comparison of Aeration Efficiency Under Process Conditions,"
Proceedings of the 4th International Conference on Water Pollution
Research, Prague, pp. 477-496, 1969.
7. Kalinske, A.A., "Problems Encountered in Steady State Field Testing of
Aerators and Aeration Systems," Proceedings, Workshop Toward an Oxygen
Transfer Standard, EPA-600/9-78-021, pp. 205-209, April 1979.
8. McKinney, R.E. and J.R. Stukenberg, "On-Site Evaluation: Steady State
vs. Non-Steady State Testing,"Proceedings, Workshop Toward an Oxygen
Transfer Standard, EPA-600/9-78-021, pp. 195-204, April 1979.
9. Boon, A.G. (British Water Research Centre) et al., Personal communica-
tions at ASCE Subcommittee meeting, San Diego, California, November 1979.
10. Boon, A.6., British Water Research Centre, Personal communication,
January 1980.
11. Stukenberg, J.R., V.N. Wahbeh, and R.E. McKinney, "Experiences in Evalu-
ating and Specifying Aeration Equipment," Journal WPCF, 49:66-82,
January 1977.
12. Kayser, R., "Measurements of Oxygen Transfer in Clean Water and Under
Process Conditions," EIRPE Converence on Aeration, Amsterdam, 1978.
13. Mueller, J.A., S. Ghirardi, M. Nicodema, and J. Rotondo, Tallman's
Island Aeration System Evaluation, Student Field Laboratory Report,
Manhattan College Environmental Engineering and Science Program, New
York City, April 1979.
14. Kayser, R., "Testing Aeration Performance of the Treatment Plant of the
City of Nienburg," Unpublished report in German, 1970.
15. Ball, R.O. and H.J. Campbell, Jr., "Static Aeration Systems - Problems
and Performance," Proceedings of the 29th Industrial Waste Conference,
Purdue University, pp. 328-337, May 1974.
16. McKeown, J.J. and D.B. Buckley, "Mixing Characteristics of Aerated Sta-
bilization Basins," TAPPI, 54:1664-1672, October 1971.
17. Benedict, A.H. and J.J. McKeown, "Oxidation Analysis of Mill Effluents,"
Stream Improvement Bulletin No. 256, NCASI, New York City, p. 33, May
1972.
195
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18. A Manual of Practice for Biological Waste Treatment in the Pulp and Pa-
per Industry, Stream Improvement Bulletin No. 214, NCASI, New York City,
p. 115, April 1968.
19. McKeown, J.J., A.H. Benedict, and G.M. Locke, "Studies on the Behavior
of Benthal Deposits of Wood Origin," Journal WPCF, 40:R333-R353, August
1968.
20. Whittemore, R.C. and J.J. McKeown, "Interfacial Velocity Effects on the
Measurement of Sediment Oxygen Demand," Stream Improvement Bulletin No.
317, NCASI, New York City, p. 31, 1966.
21. Whittemore, R.C. and J.J. McKeown, "Further Studies of Sediment Oxygen
Demand Measurement and its Variability," Stream Improvement Bulletin No.
321, NCASI, New York City, p. 25, March 1979.
22. Klein, L., River Polution, III. Control, Butterworth, London, p. 136,
1966.
23. McKeown, J.J., D.B. Buckley, and I. Gellman, "A Statistical Documenta-
tion of the Performance of Activated Sludge and Aerated Stabilization
Basin Systems Operating in the Paper Industry," Proceedings of the 29th
Industrial Waste Conference, Purdue University, pp. 1091-1110, May 1974.
24. Alferova, L.A., I.V. Skirdov, B.M. Ponomarev, V.A. Gladkov, and I.
Rogovskaga, "Sewage Treatment in the Northern Areas of the U.S.S.R.
Report on International Symposium on Wastewater TMT in Cold Climates,
Environment Canada Report EPS 3-WP-74-3, p. 64, March 1974.
25. McKeown, J.M. and A.H. Bendict, "The Effect of Temperature on Treatment
Plant Performance and Related Temperature Studies," Stream Improvement
Bulletin No. 312, NCASI, New York City, p. 64, May 1978.
26. Downing, A.L. and A.G. Boon, "Oxygen Transfer in the Activated-Sludge
Process,"In:Advances in Biological Waste Treatment, Ed. by W.W. Ecken-
felder, Jr. and B.J. McCabe, Pergamon Press, New York City, 1963.
27. Redmon, D. and W.C. Boyle, "Preliminary Findings, Off-Gas Analysis,"
A report to ASCE Oxygen Transfer Subcommittee, Detroit, MI, October 1981.
28. Ewing, L., "New Directions," Workshop on Aeration System Design, Opera-
tions, Testing and Control, Madison, WI, August 1982.
29. Campbell, Jr., H.J., "Oxygen Transfer Testing Under Process Conditions,"
Workshop on Aeration System Design, Operation, Testing and Control,
Madison, WI, August 1982.
30. Mueller, J.A. and J.J. Rysinger, "Diffused Aerator Testing Under Pro-
cess Conditions," Proceedings of the 36th Industrial Waste Converence,
Purdue University, pp. 747-754, May 1981.
196
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31. Mueller, J.A., "Comparison of Dual Nonsteady State and Steady State
Testing of Fine Bubble Aerators at Whittier Narrows Plant, Los Angeles,"
Workshop on Aeration System Design, Operation, Testing and Control,
Madison, August 1982.
32. Mueller, J.A., R. Sullivan,and R. Donahue, "Dual Nonsteady State Evalu-
ation of Static Aerators Treating Pharmaceutical Wastes," Proceedings of
the 37th Industrial Waste Conference, Purdue University, May 1982.
197
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SECTION 8
GEOMETRY, SCALE-UP, AND MIXING
INTRODUCTION
The discussion that follows represents a synopsis of the experiences
and qualified opinions of the members of the ASCE Subcommittee for Oxygen
Transfer Standards. Little published scientific data are available in the
literature on this subject. Laboratory and field experiments designed to
quantitatively describe scale-up of oxygen transfer and mixing are highly
complex, extensive and, therefore, expensive. Currently, there is no basis
for a sound generalized theory for scale-up translations. It is the
responsibility of the design engineer and the manufacturer to define this
translation on a case-by-case basis. The Subcommittee believes that the
development of sound testing methods for oxygen transfer in both clean and
dirty water systems will ultimately lead to a better understanding of scale-
up of these systems.
The clean water reaeration test is intended to model the performance of
the installed aerator. This performance is a function of the aerator itself
and the installation geometry. Because of the interdependence of the aerator
and its environment, scale-up parameters cannot be accurately predicted with
laboratory-size aeration equipment. To meet performance specifications, many
of the aeration equipment manufacturers have secured large basins for test
purposes. In this section, recommendations are made to define the limits
between factory and field tests. In general, factory tests can be run with
greater precision and more exacting process measurements. The principal weak-
ness of the factory test is the inability to match all installation geometry
parameters. Field tests often involve compromises that result in greater
data scatter and less precision in measurements.
Because of the lack of substantive published literature, the specific
experience of the individuals representing the Subgroup on Geometry, Scale-
198
-------
up, and Mixing formed the basis for this section. The experience of Subgroup
members encompasses surface, submerged turbine, coarse bubble, and fine bub-
ble aeration devices. Among the devices not covered are oxidation ditch,
deep shaft, and jet types of aerators.
The subsection on Geometric Scale-up defines the differences between
field and factory tests that are permitted without process corrections. Dif-
ferences that exceed specified dimensions require corrections factors.
Because these correction factors are specific to each generic aeration device,
scale correction factors are not recommended. The test goal is to have a
factory test geometry that maintains the aerator parameters related to power,
pumping, and tank flow patterns. Specific recommendations on limits of vari-
ation for surface, submerged turbine, and diffused air (either rolling or
grid pattern) aeration devices are proposed. The range of test variability
for the alternative devices (deep shaft, biodiscs, oxidation ditch and jet
type aerators) is not addressed.
In the context of this report, mixing is defined as the aerator's abil-
ity to disperse DO and to provide a reasonably uniform concentation of solids
throughout the basin. These two requirements are of equal improtance, and
acceptable performance of one does not necessarily guarantee achieving both.
This mixing definition only characterizes the bulk transport phenomena.
Micromixing as related to energy dissipation and oxygen transfer in the gas
contact zone is not specifically addressed. These factors are an inherent
part of all aeration devices, and their impact is indirectly observed by the
uptake rate measurement.
DO gradients are intrinsic to the clean water reaeration test. These
gradients do not imply problems related to either mixing or mass transfer.
DO gradients are most readily observable with surface aerators and the least
observable in grid pattern diffused air systems. For a point source aerator
(i.e., surface device), oxygen transfer occurs in a small percentage of the
total volume. Remote regions of the basin are oxygenated by the bulk trans-
port of oxygen-enriched fluid. Therefore, oxygen gradients observed during
reaeration factory tests are dependent on the selection of the sample points,
basin turnover, and localized mass transfer rates.
199
-------
The individual sample point rate of change of oxygen concentration is
recommended as the primary indicator of mixing as related to the dispersion
of the oxygen-enriched fluid. The local rate of change of oxygen concentra-
tion should be relatively constant throughout the basin. There will, however,
be a time shift associated with the requirements of bulk transport to the
sample point.
In wastewater testing, an essentially uniform suspended solids concentra-
tion indicates good mixing. The uniformity or nonuniformity of the DO level
is not a good indicator of mixing in an active mixed liquor. The DO level at
each point in the basin is dependent on the distance of travel from the point
of oxygenation and the uptake rate of the liquor. Because the distribution of
DO is strongly dependent on non-mixing process parameters, it cannot be used
to indicate the degree of mixing.
DEFINITIONS
Geometry
Geometry is defined as the shape and dimensions of the aeration basin,
the location of the aeration devices, and the physical location of ancillary
equipment such as draft tubes, baffles, etc.
Mixing
Mixing is the establishment of relative movement within a basin that
influences and may be characterized by the degree of uniformity of the con-
centrations of suspended and dissolved substances.
For aeration applications, mixing is limited to DO dispersion and solids
suspension. Defined in this manner, mixing is the ability to
1. disperse DO throughout the basin and
2. provide reasonably uniform solids concentrations throughout the
liquid.
It should be noted that reference to either item 1 or 2 provides only a
partial description of mixing and does not assure the satisfaction of the
other. Both conditions must be met.
Micromixing is not evaluated in this report. Energy intensity and
200
-------
related turbulence are important factors for oxygen transfer in the gas con-
tacting zone. The reaeration test measures the impact of micromixing by
quantifying the aerator oxygenation capacity.
Factory Test
The factory test is a clean water reaeration test conducted at a facil-
ity dedicated to aerator testing. Instrumentation and laboratory facilities
associated with general research requirements are usually included.
Field Test
A field test refers to a test carried out at the site of the aeration
equipment installation.
Surface Aerator
A surface aerator is a point source aeration device that contacts the
liquid with the ambient gas blanket. Surface aerators are often identified
as high- or low-speed aerators.
Submerged Turbine Aerator
A submerged turbine aerator is defined as a point source aeration device
that delivers gas to a source of liquid pumping below the liquid surface.
.Radial and axial impellers are examples of this class of aeration device.
Diffused Aeration
Diffused aeration systems deliver gas below the liquid surface and do
not rely on supplemental liquid pumping devices for mixing. Bubble rise
creates the turbulence for mass transfer and induces liquid circulation.
Subgroups of this category are coarse and fine bubble diffusers.
Diffused aeration systems are characterized by the induced basin flow
patterns, which are dependent on the distance between diffusers and diffuser
proximity to the basin walls. The rising column of gas bubbles pumps liquid
to the surface. The gas disengages at the surface, and the liquid flows out-
ward from the bubble column until it meets a basin wall or flow from an adja-
cent diffuser.
GEOMETRIC SCALE-UP OF FACTORY TEST TO FIELD CONDITIONS
General Considerations
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All tests should be performed in a basin of dimensions close to the
application size either in the field or at the factory. In practice, the
field test versus the factory test offers a technical trade-off. The factory
test is run under carefully controlled conditions prior to field installation,
but with possible compromises in water quality differences and system geometry.
The field test in the actual basin often involves compromises in the
test procedure. Some common problems associated with field testing are inac-
curate or imprecise air measurement, excessive basin size requiring several
chemical pumping stations and excessive sample line length, and general inac-
cessibility of probes, sample pumps, etc. These are only a few of the areas
that complicate field test data interpretation and may increase data scatter.
In general, field testing of basins in excess of 1-mil gal capacity is not
recommended.
Scale-up of factory tests to field conditions requires considerable
judgment, since not all geometric variables can be precisely scaled. Expe-
rience has demonstrated that a factory test must duplicate full-scale mixing
conditions to minimize the need for scale-up factors. The test conditions
specified in the following subsections are a best judgment of conditions that
eliminate scale-up considerations for various aeration devices. For tests
beyond specified limits, aerator performance data must be corrected. Since
each generic device may differ in dependence on geometric variables, universal
corrections cannot be recommended. The manufacturer and consultant/owner
should agree on the correction procedure prior to testing.
Recommended Variation Limits for a Single Surface Aerator
1. Impeller dimensions must be maintained within +0.5 percent, speed
within +1.0 percent, and submergence within +10 percent. Changes
are limited to hub adjustments for mounting on a factory test shaft.
2. For draft tube devices, tube diameter and proximity must be main-
tained.
3. Equivalent baffling must be provided.
4. The variation between the ratios of impeller diameter to tank width
shall not exceed 6 percent.
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5. The variation between the ratios of impeller diameter to water
depth shall not exceed 10 percent.
Recommended Variation Limits for a Single Submerged Turbine Aerator
1. Impeller dimensions and speed care to be maintained as indicated
above for a surface aerator. Changes are limited to hub adjustments
for mounting on a factory test shaft.
2. Proximity of turbine to sparge, draft tube, tank bottom, etc. must
be maintained.
3. Design gas rate must be maintained within +2 percent.
4. Sparge submergence must be maintained within +4 percent.
5. Equivalent baffling must be provided.
6. The variation between the ratios of impeller diameter to tank
width shall not exceed 6 percent.
Multiple Surface or Submerged Turbine Aerators
Observations indicate that each aerator in a large basin operates as
though it were in an equivalent cell. It must be recognized that some of
the flow from a specific aerator intermixes with that of an adjacent unit,
which contributes to the overall mixing pattern of the basin. The assumption
that the equivalent cell boundaries bisect the space between adjacent aera-
tors to create defacto basin geometry is a reaonsable one for most mechanical
aerator basins and should be evaluated based on the conditions stated above.
Diffused Aeration
Rolling Pattern--
If the distance between adjacent diffusers or between diffuser and basin
wall exceeds 50 percent of the submerged depth, a roll-type pattern generally
develops. The circulatory motion established under these conditions has a
return flow near the basin bottom back to the pumped water column.
Although a roll pattern could be established by a single diffuser, this
type of mixing condition is customarily associated with multiple diffusers
mounted on a header at a spacing interval appreciably less than 50 percent
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of submergence. The result is that the major outward flow of the surface is
normal to the header. Overall mixing conditions within the basin are then
established by the number and placement of these headers along with their
proximity to basin walls and bottom. In rectangular basins, the mixing pat-
tern has been traditionally described as either spiral roll or cross roll.
A spiral flow mixing condition is established when the header is installed
parallel to the long axis of the basin. Conversely, a cross flow mixing
condition is established when the header is installed perpendicular to the
long axis of the basin.
Recommended Variation Limits for Roll-Pattern Diffused Aeration--
1. The precise diffuser must be used.
2. Diffuser spacing must be maintained within +5 percent, air flow
per diffuser within +2.0 percent, and water depth within +1.0 per-
cent.
3. Proximity to adjacent walls, floors, and diffuser lines parallel to
the axis of the roll pattern must be held within +5 percent.
4. Basin width must be maintained within +5 percent.
5. Basin length parallel to the axis of the roll pattern must be a
minimum of 4 ft and must contain a minimum of four diffuser sets.
Grid Pattern--
A grid pattern is any total floor coverage or dispersed diffusers posi-
tioning thai? does not establish a roll. In general, this pattern would
result when the maximum spacing between diffuser units in any direction does
not exceed 50 percent of submergence.
Recommended Variation Limits for Grid-Pattern Diffused Aeration—
1. The precise diffuser must be used.
2. Diffuser spacing must be maintained within +5 percent, proximity to
the floor within +5 percent, air flow per diffuser within +2.0 per-
cent, and water depth within +1.0 percent.
3. The test basin plan dimensions should exceed the water depth in at
least one direction.
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4. Each dimension should contain at least four diffuser sets.
MIXING CONSIDERATIONS
General Considerations
Only a partial evaluation of the mixing performance of a specific aera-
tion device can be made based on clean water tests. The clean water test
does establish the ability of a device to disperse the oxygen-enriched fluid
throughout the basin. Only a mixed liquor test will determine if the aera-
tor performs satisfactorily at maintaining solids in suspension.
Clean Water Test
Test Definition--
Procedures for testing, selecting sample point locations, defining the
number of samples, etc. are described in Section 5. Data analysis techniques
are presented in Section 4.
DO Gradients--
DO gradients are intrinsic to the reaeration test and do not imply prob-
lems related to either mixing or mass transfer. Gradients are readily
observed with surface and submerged turbine aerators. The magnitude of these
gradients is dependent on sample location, basin turnover, and localized mass
transfer. Gradients increase as the pumping rate decreases or the localized
oxygen transfer increases. It was shown in Section 4 that large DO gradients
imply the existence of localized transfer zones. Modelling of this phenom-
enon is based on the ideal compartmentalized system, which does not require
that DO concentrations be uniform throughout the tank nor that oxygen trans-
fer occur throughout the tank.
Individual Sample Point Analysis--
The rate of change in oxygen concentration with time (mg/£/hr) at the
various sample points within the test basin is the primary indicator of mix-
ing as related to oxygen dispersion. The local rate of change of oxygen is
the product of the mass transfer coefficient and the driving force associa-
ted with the data obtained for a single point. See Section 4 for a complete
discussion of completely mixed and compartmentalized system analyses.
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The mean and the standard deviation of the local rate of oxygen trans-
fer determined for each point may be used as a basis for estimating the
mixing process. The coefficient of variation, CV, is the recommended
analysis technique, since it is independent of the magnitude. CM, in
percent, is defined by:
CV = -j^x 100 (97)
x
where:
s = standard deviation
x = mean
Replicate tests are made using multiple sample points. Using the mass
transfer model, a local mass transfer coefficient and saturation value are
obtained for each point. These terms are corrected to standard conditions.
The product is the uptake at zero DO. The standard deviation and mean values
are calculated using no less than two-thirds of the individual uptake values
(see Appendix F). For a factory test, the coefficient of variation should be
no more than 10 percent. A similar test run in the field cannot be executed
with nearly the same degree of precision; a field coefficient of variation
could be as high as 15 to 20 percent.
The discarded uptake measurements should be reviewed. If one sample
point exhibits consistently low values for all replicate runs, either a poor
selection of representative sample points or a mixing problem in dispersing
the oxygen-enriched fluid may be indicated. Sample placement problems could
be related to
1. baffle proximity,
2. proximity to walls or basin floor, and
3. placement in a mixed flow (gas and liquid) zone in the immediate
proximity of the aerator.
Inert tracers (dissolved in the liquid phase) do not quantify mixing
conditions related to either oxygen transfer or the suspension of biological
solids.
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Velocity measurements taken during clean water tests are an indicator of
but do not guarantee solids suspension. For some aeration devices, bottom
velocities can be less in mixed liquor than in clean water. The relative mag-
nitude of this decrease has not been documented.
In general, horsepower per unit volume is not a direct indicator of mix-
ing or solids suspension capability. The significance of relative power has
meaning only when compared to similar aeration devices under similar condi-
tions. The established hydrodynamics are both aeration device and geometry
specific.
Mixed Liquor Test
A suspended solids profile taken throughout an aeration basin is the
primary quantitative measurement of adequate mixing as related to suspended
solids. The absence or presence of bottom solids must be evaluated as either
satisfactory or unsatisfactory depending on process design. The coefficient
of variation is a relative term whose acceptable limit can best be established
by process conditions. For example, low suspended solids concentrations may
vary substantially on a percentage basis because of analytical error while
high suspended sol ids concentrations are subject to variability simply because
of the combined effects of concentration, flow rate, and location of the
return sludge flow. This latter condition can be addressed by shutting off
the return sludge flow for some reasonable time (say 15 percent of the deten-
tion time) prior to withdrawing samples for a suspended solids profile. The
actual limits of CV for a standard will need to be established. Today both
10 and 20 percent are specified. It would appear that 20 percent may be
reasonable and still provide evidence of good mixing, particularly if no
biological solids are deposited on the bottom.
Procedures for conducting a satisfactory suspended solids profile are
reasonably simple and can be adapted to a particular field situation. Samples
can be either grab or pumped from remote locations. It should be recognized
that baffles, support columns, return flow piping, and stilling baffles cre-
ate localized conditions that are not representative.
While an essentially uniform suspended solids concentration in an aera-
tion basin indicates good mixing, the uniformity or nonuniformity of the DO
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concentration cannot always be used for assessing the quality of the mixing.
The DO level at each point in the basin will depend on the balance
between DO supply and consumption. The DO consumption distribution will
depend on process and basin designs. In a well-mixed reactor, DO consumption
will be nearly uniform throughout the basin. Conversely, in a reactor
designed to approach a plug flow condition, DO consumption will be relatively
high at the inlet where the feed and return sludge are introduced and then
decrease along the reactor length.
The DO supply distribution is strongly dependent on aeration system char-
acteristics. In the case where air supply is distributed uniformly about the
basin (uniform DO supply), the localized DO level will depend on the localized
rate of consumption. However, quite a different situation exists in the case
of the DO supply being essentially a point source with bulk transport serving
as the principal source of oxygen to remote locations in the basin.
DO gradients exist by definition along the liquid flow path with surface
aerators. Gradients also exist but to a lesser extent with submerged tur-
bines. With turbines, DO is introduced at a point and mass transfer occurs
throughout the bubble rise path.
From the above discussion, it is concluded that the DO concentration dis-
tribution, depending on system design and aeration system characteristics, is
in general not a good indicator of the degree of mixing of reactor contents.
RECOMMENDED FUTURE RESEARCH
1. Evaluate the ratiotracer method for potential confirmation of both
mixing and oxygen transfer. It would be necessary to demonstrate
that the results for mixed liquor are comparable to established
procedures.
2. Determine if turbulence significantly affects mixing conditions for
aeration. If it does, then the measurement(s) needed must be iden-
tified.
3. Conduct measurements of velocity distributions in relation to solids
suspension and oxygen dispersion. Compare velocity distributions in
wastewater and clean water.
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4. Evaluate the feasibility of clean water steady state testing by con-
tinuous addition of sodium sulfite. This test would produce steady
state gradients, which may simulate or be equated to a system with
biological uptake of oxygen.
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SECTION 9
GAS FLOW MEASUREMENT
Gas flow measurement is a fundamental part of oxygen transfer testing.
The objective of this section is to acquaint the reader briefly with the var-
ious types of primary and secondary flow elements available, the required mea-
surements involved, and the standard conditions at which the gas flow data are
reported. Furthermore, a complete discussion of the concentric orifice plate
is included from the initial design stage through installation and testing.
Most of the basic principles discussed herein apply to many of the various
flow measurement devices. One subsection deals solely with pulsation caused
by positive displacement blowers because of its serious effect on air flow
measurements. Also discussed are various calculations based on standard air
flow rates (scfm). Finally, recommendations as to appropriate air flow stan-
dards for clean water tests are made in the subsection entitled Recommended
Standardization.
One reference used in the writing of this section deserves special men-
tion. L.K. Spink's Principles and Practices of Flow Meter Engineering was
used extensively in the subsections dealing with the general discussion of
primary and secondary flow elements.
PRIMARY FLOW ELEMENTS
A wide variety of flow measurement devices are available. Most of these
are capable of providing very accurate results when applied in a proper manner.
It is not the intention of this subsection to recommend standard flow measur-
ing devices; rather, the different types of equipment available are discussed.
Specifying standard flow measuring equipment would place an unnecessary re-
striction on the conduct of clean water oxygen transfer tests in the field
since actual installations would not necessarily have standard equipment
available. This is not true for performance tests on blowers where codes can
and are written specifying certain standard flow measuring devices. These
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codes can be written because blowers are almost always tested in a shop where
standard equipment is available.
Flow measuring equipment for clean water testing should not be specified;
however, the overall accuracy of the system (primary and secondary flow ele-
ments) should be guaranteed to within +2 percent. If this accuracy cannot be
guaranteed, the estimated amount of the inaccuracy should always be stated
along with the flow measurements reported.
Head Meters
Most flow meters can be classified as head meters, although some meters
are available that operate on entirely different principles. Head meters con-
vert rate of flow into a differential pressure, a mechanical force, or a
change of head or level (over a weir or flume). This category of meters
includes the orifice plate, Venturi tube, flow nozzle, Lo-Loss flow tube, Dall
flow tube, pitot tube (and its variations), pipe elbow tap, target meter, weir,
flume, and others.
Head meters have a number of advantages. First, they are usually simple
and easily reproducible. Second, flow can be determined accurately without
the need for an actual fluid flow calibration of the primary measuring device.
Flow rates can be determined by merely knowing the dimensions of the primary
device and the properties of the flowing fluid. Furthermore, only well
established and easily maintained tolerances are critical in head meters. For
the special case of orifice plates, only the pipe and orifice diameters are
critical. Other parameters such as concentricity of the orifice in the pipe,
location of the differential pressure taps, and degree of smoothness of the
pipe itself are not too-critical. Any corrosive damage to the orifice bore
can be easily seen by removing the plate from the line. A further advantage
of head meters is that the differential pressures they produce are very
accurately reproducible under the same set of conditions.
Head meters operate on the principle that the rate of flow of fluid is
proportional to the square root of the pressure differential. For a given
mass flow rate, the reading of the head meter varies inversely as the square
root of the density. Head meters are also affected by viscosity, relative pipe
size, and velocity. The Reynolds number, however, serves to correlate these
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parameters with the proper meter coefficients.
Orifice Plates—
The orifice plate is probably the most common type of head meter. It is
essentially a thin plate through which a sharp, square-edged orifice has been
bored. The ratio of the orifice diameter to the inside pipe diameter is
known as the "diameter", orifice", or "beta" ratio. An orifice has a number
of variations. Generally speaking, an orifice is either concentric, eccentric,
segmental, or annular. The concentric orifice is by far the most widely used.
The other variations were derived to handle flows containing solids in suspen-
sion and water vapor. Advantages of orifice plates include accuracy, simplic-
ity, cost effectiveness, versatility, and ruggedness. A disadvantage is that
they sometimes involve a relatively high permanent pressure loss.
Venturi Tubes—
Venturi tubes are used to measure flows when a relatively low permanent
pressure loss is required. Usually they will handle about 60 percent more
flow than an orifice plate, but their permanent pressure loss is only 10 to
2
20 percent of the differential pressure. Venturi tubes are also" good for
measuring flows with solids in suspension. In addition, for the measurement
of a given air flow, they can require less upstream straight pipe than an
orifice plate. Venturi tubes consist of a converging and diverging nozzle.
The diverging section tends to make the pressure recovery efficient so that
the permanent pressure loss is low. The Venturi works on the basic principle
that the change in static pressure between two regions of different cross-
sectional area is proportional to flow. Static pressure readings are taken
in an upstream region of the Venturi and at the throat. Generally speaking,
Venturi meters are relatively expensive and somewhat large but, in many situ-
ations, these factors are more than offset by their advantages.
Flow Nozzles--
Flow nozzles are similar to Venturi tubes except they consist of a con-
verging nozzle only. While the pressure recovery is not as efficient as with
the Venturi tubes, it is still much better than with orifice plates. They
will handle about 60 percent more flow than an orifice plate with a permanent
pressure loss that varies from 30 to 80 percent of the differential pressure,
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2
depending on the diameter ratio. The principle of operation is similar to
that of Venturi tubes. Static pressure readings are taken in an upstream
region of the flow nozzle and at the trhoat. Generally speaking, flow nozzles
are less expensive than Venturi tubes, but are considerably more expensive
than orifice plates.
Lo-Loss Flow Tubes--
These devices are similar to flow nozzles except they have an added
diverging section that improves the meter's pressure recovery characteristics.
Lo-Loss tubes are not quite as efficient as Venturi meters from a pressure
recovery standpoint; however, they are somewhat shorter, which reduces the
capital cost. They are more pressure efficient than flow nozzles, however,
and are slighly more expensive as a result. A Dall flow tube is another type
of meter that is similar in principle to the Lo-Loss flow tube.
Pi tot Tubes--
The pitot tube or one of its variations, the pitot-static tube or the
Annubar (a commercially available device), provides a very low permanent pres-
sure loss. Essentially, pitot tubes are in-line pressure probes that measure
velocity head. All variations of the pitot tube measure the stagnation pres-
sure of the flow, which is equal to the static pressure plus the velocity
head. The pitot tube requires a separate measurement of static pressure,
while the pitot-static tube has a static pressure tap in the side of the
stagnation pressure probe. In both cases, the difference between the stagna-
tion pressure and the static pressure is the velocity head.
The pitot tube and the pitot-static tube are limited by the fact that
they essentially measure velocity at one point in the flow. Normally, this
velocity can be related to the average pipe velocity if the flow conditions
are steady; however, upstream pipe disturbances can alter this relationship
significantly. The Annubar, on the other hand, measures an average stagna-
tion pressure across the pipe diameter and does a better job of estimating
the average pipe velocity. Furthermore, the Annubar differs from the pitot-
static tube in that it measures a differential pressure that is somewhat
greater than the velocity head due to a slight suction condition created at
the low pressure tap. A disadvantage of the pitot tube, pitot-static tube,
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and the Annubar is that they may sometimes require a pipe size reduction to
increase the velocity head since velocity heads in normal air flow applica-
tions are usually low.
Other Types of Meters
A number of other types of meters are available for flow measurement.
Among these are magnetic meters, turbine meters, variable area meters (rota-
meters), mass flow meters, rotary lobe gas meters, and others. These meters
are good for specific applications and, with the exception of the rotameter,
are generally more complex and costly than head meters. For gas flow measure-
ment, however, it would seem that only rotameters and rotary lobe gas meters
have wide application.
Rotameters--
The rotameter is actually a variable orifice head meter. It consists of
a float in a vertical transparent tube. The inside diameter of the tube is
linearly tapered from top to bottom, with the widest portion at the top. Flow
enters the tube at the bottom, and the float rises until the weight of the
float just balances the lift generated by the buoyance of the float and the
pressure differential across it. The headless through the rotameter is essen-
tially constant and usually fairly low. The rotameter scale is nearly linear
with flow. The combination of these factors makes it exceptionally desirable
for measuring flows that vary over a wide range (i.e., 10 to 1). Furthermore,
the rotameter is not affected significantly by upstream piping disturbances;
no straight lengths of pipe are generally required. It is especially suitable
3
for pipe sizes up to 3 in.
Rotary Lobe Gas Meters--
The rotary lobe gas meter is a positive displacement device. It is
highly recommended for measuring flows from positive displacement blowers and
other pulsating equipment because it is not affected by pulsation as are head
meters. Volume flow rate is determined by measuring the rpm developed as the
air passes through the meter. Rotary lobe gas meters are usually expensive,
but, where high accuracy is required, they are exceptionally good.
In summary, there are a large number of accurate gas flow measurement
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devices. Each has its own advantages and disadvantages, and one may be bet-
4
ter suited to a particular application than another. Holman shows a compar-
ison of the operating characteristics of various flow meters. For a more
detailed analysis of the various primary flow elements, the reader is
1 2
referred to Spink and Cusick.
SECONDARY FLOW ELEMENTS
Secondary flow elements are used to measure the output of primary flow
elements. As with primary flow elements, no attempt will be made in this
section to specify certain standard secondary flow elements for oxygen trans-
fer studies. Many different types will provide acceptable results if used
properly. The only limitation is that the overall flow measurement system
accuracy encompassing both primary and secondary flow elements should be
within +2 percent.
The output from head-type primary flow elements is usually a differential
pressure. While there are a wide variety of differential pressure measuring
devices, they can be generally classified into two basic groups according to
whether or not the fluid that exerts the differential pressure is in direct
contact with an indicating fluid.
Wet Meters
According to Spink, wet meters are devices where the fluid that exerts
the differential pressure is in direct contact with the indicating fluid.
This group of meters can be further divided into liquid and liquid seal
varieties.
Liquid Meters—
With liquid meters, a difference in liquid level is developed between
the high and low pressure sides of the device. Liquid meters are the oldest,
simplest, and, generally speaking, the most accurate and reliable of all dif-
ferential pressure measuring devices. They are excellent in applications
where only visual indication is needed and where the static pressures and
the nature of the fluid are conducive to transparent tubes. Various types
of liquid manometers are available, including the U tube, well type, and
mercury float type. Of these, the U tube manometer is the simplest, the
differential pressure being the distance between the water columns in each
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leg. Well manometers are similar to U tube manometers except that the high
pressure leg of the device is actually a large reservoir. Since the volume
of the reservoir is very large relative to the volume of the manometer indi-
cator tube, it is necessary to read only one leg of the manometer; the fluid
level in the reservoir does not change appreciably. An important variation
of the well-type manometer is the inclined well-type manometer. Inclining
the manometer helps to expand the indicator scale so that the differential
pressure can be read more accurately. The mercury float-type liquid manom-
eter is similar to the other liquid meters except for a float attached to an
indicating needle following the nercury surface on the high pressure side.
This type of meter is very accurate, although relatively expensive, and for
many years it was the accepted standard meter for orifice flow measurements.
Liquid Seal Meters—
With liquid seal meters, the differential pressure is determined by the
displacement of a piston-like device across which the differential is applied
and which acts against the tension of a spring. The meter fluid acts like a
seal between the high and low pressure sides of the device. An indicating
needle senses the position of the piston. Liquid seal meters are well suited
to the measurement of low differential pressures. Generally speaking, they
are used where simple, self-powered mechanisms with considerable output power
are required. Varieties of this type of meter include the cylindrical in-
verted bell meter, the Ledoux inverted bell meter, and the ring balance meter
(similar in principle to the bell-type meters).
Dry Meters
According to Spink, dry meters are devices where the fluid that exerts
the differential pressure is not in contact with an indicating fluid. Dry
meters are becoming increasingly popular wherever indication, recording, inte-
gration, and/or transmission are required. They are relatively inexpensive
compared to the mercury float-type meter. Dry meters are of two basic types:
motion and force balance.
Motion-Type Meters--
The motion-type dry meter consists of a bellows system across which the
differential pressure is applied; the resulting force deflects a spring, and
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the motion provides the output. This type of meter is well suited to direct
indication, recording, and integration.
Force Balance-Type Meters--
The force balance-type meter employs a diaphragm against which the dif-
ferential pressure is applied. An electric current or pneumatic pressure
develops a second force, and the two forces are made to oppose each other. A
sensitive motion detector detects any imbalance in the forces and corrects the
second force until they are balanced. The magnitude of the current or pres-
sure of the second force is then directly proportional to differential pres-
sure. This type of meter is used primarily as a pressure transmitter to a
remote location.
Selection of a Secondary Flow Element
As with primary devices, the selection of a specific secondary device
for a given application depends on a number of factors. Generally speaking,
where visual indication is sufficient, liquid manometers are suitable as they
are simple, low cost, rugged, and accurate. Other needs may dictate a
requirement for other types. For a much more detailed discussion of various
secondary devices and their specific application, the reader is referred to
Spink.1
Certain basic guidelines should be followed in selecting secondary flow
elements. First of all, a secondary meter should always be sized to measure
the actual differential pressure, not the high and low pressures separately
followed by an arithmetic subtraction. The latter method usually results in
a substantial loss of accuracy.
Furthermore, it may often be appropriate to have several secondary ele-
ments with different differential pressure ranges available for use with a
given primary element, since it is often the readability of the secondary ele-
ment that limits the flow range of the overall gas flow measurement system.
Finally, it is usually appropriate with manometers to use either water
or mercury for the manometer fluid when making field differential pressure
measurements. Fluids that have a specific gravity close but not equal to that
of water should be avoided, since the possibility of contamination with water
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always exists in the field. Mercury, on the other hand, has a specific grav-
ity that is so much different from that of water that minor contamination with
water does not affect the readings significantly.
CONNECTIONS BETWEEN PRIMARY AND SECONDARY FLOW ELEMENTS
A number of factors should be considered when making differental pressure
connections between primary and secondary flow elements:
1. The manometer should be located in a shaded area as close to the pri-
mary element as possible.
2. For gas flow, the manometer should be mounted above the air line so
that the tubing slopes at least 1 in./ft. This allows any condensa-
tion in the tubing to roll back into the air lines.
3. For distances less than 50 ft, the tubing between the primary and
secondary elements should be at least 3/16 in. inside diameter. For
distances greater than 50 ft, the diameter should be increased by
approximately 1/8 in. for each additional 50 ft.
4. For greatest accuracy, the tubing on both sides of the head meter
should be of the same length and should be in the same thermal
environment.
The tubing used to connect the primary and secondary flow elements may
be made of a number of commercially available materials. Copper tubing or
pipe is recommended for permanent installations. Materials such as rubber,
polyethylene, and vinyl are fine for less permanent installations and are more
amenable to changes in the way the system is connected. Special care should
be exercised when using hard-walled tubing such as polyethylene in an outside
environment since low temperatures may cause the tubing to crack.
Valves should be placed on both primary and secondary elements. Needle
valves and other restrictive valves such as plug and globe values are not
recommended. Equalizer arrangements and check valves should be used on manom-
eters where a possibility of excessive differential pressure exists. The
equalizer is merely a cross-connection between the high and low pressure sides
of the manometer with a manual shut-off valve. Lever-operated, one-quarter
turn gas valves are very convenient for this application. Generally speaking,
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the equalizer valve is left open unless a reading is taken. This protects the
fluid in the manometer against over-pressure. Some manometers, such as those
used for measuring line pressure, may not require either equalizers or check
valves since the possibility of over-pressure may not exist.
A number of tubing connectors are available. For permanent installa-
tions, double-ferruled connectors are recommended. These can be used on any
hard-walled tubing and can also be used on soft-walled tubing with the proper
tubing insert. Fittings can be bought that will adapt to various types and
diameters of tubing and pipe. For less permanent installations, barbed tube
or hose connectors are recommended for use with flexible tubing such as rubber
or vinyl. This type of fitting, which makes connecting and disconnecting
tubing quick and easy and yet assures a positive seal, is limited to low pres-
sure installations.
TROUBLESHOOTING THE FLOW MEASUREMENT SYSTEM
After a gas flow measurement system is designed and built, it is essen-
tial that it be checked out in detail before it can be used with confidence.
First, care should be taken to ensure that the system has been built according
to specifications. This step should be followed by a thorough leak test. The
primary element, secondary element, pressure taps, tubing connections, valves,
and other related items should all be checked with a soap solution when the
line is under relatively high pressure. In the case of differential pressure
flow systems, after the leak test has been performed, the response of the
manometers should be checked. A manometer should respond rapidly to the pres-
sure differential it measures. If it does not, this is a sign of a possible
leak. An additional leak check should be performed by closing the valves on
the primary element when differential pressure is being measured. If the
manometer reading changes significantly or drifts gradually, there may be a
leak in the tubing or fittings between the manometer and the primary element
valves. An increasing differential pressure may indicate a leak to atmosphere
in the low pressure tubing; a decreasing differential pressure may indicate a
leak to atmosphere in the high pressure tubing. A decreasing differential
pressure may also indicate a leak in the equalizer valve between the high and
low pressure sides of the manometer.
219
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It is also important to make sure that the differential pressure manom-
eters zero properly. This procedure should always be performed with the sys-
tem under pressure. It is also important to make sure that the blower "sees"
the primary element during this check; in other words, no valves should be
closed between the blower and the primary element. This precaution is neces-
sary since, if pulsation is a problem, the manometer zero may be significantly
affected (see the following Pulsation subsection).
The manometer readings obtained at different flow rates and line pres-
sures should be observed and the reasonableness of the readings ascertained.
Significant oscillations can have an adverse effect on air flow measurement.
These oscillations are caused either by unsteady conditions in the line re-
sulting from inadequate lengths of straight pipe, aeration tank water level
variations, or, possibly, to blower pulsation, although it is not to be
inferred from this that blower pulsation is always accompanied by manometer
fluid oscillations. If an oscillation problem exists and if it is related to
1 9
inadequate lengths of straight pipe, then straightening vanes ' or a new
orifice plate location may help. If it is related to aeration tank water lev-
el variations, this situation can be at least partially overcome by introduc-
ing a headless in the aeration tank. If the oscillation problem is related
to pulsation, it can usually be overcome by one of the methods listed in the
following Pulsation subsection.
An additional check should be made to determine if pulsation exists in
the system. The manometer differentials should be read with two different
lengths of connecting tubing, ranging from several to 15 ft or more in length.
If the differential reading varies with tubing length, this can be a sign of
pulsation.
It is an excellent idea to check the flow measurement system against as
many known flow rates as possible. It should be kept in mind that agreement
at just one flow rate does not guarantee agreement at other flow rates and
line pressures. Positive displacement blowers can provide a very good check
on an air measurement system as long as an accurate blower air flow computa-
tion is performed (the information necessary to perform this computation is
usually available from the manufacturer). Indirect inferences as to flow rate
can also be used to check the flow measurement. These include oxygen trans-
220
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fer measurements and diffuser headlosses.
In summary, after a differential pressure flow measurement system has
been constructed, the following checks should be performed as a minimum
requirement:
1. Make sure that the system has been built according to specifications.
2. Perform a thorough leak test.
3. Check the response of the manometers to changes in differential pres-
sure.
4. Check the manometer zero under pressure.
5. Observe the manometer readings produced at different flow rates and
line pressures.
6. Check the differential pressure readings with several different
lengths of connecting tubing.
7. Check the flow measurement system against as many known flow rates
as possible.
PULSATION
Pulsation, as used here, refers to the high frequency pressure oscilla-
tions that are produced by positive displacement blowers, reciprocating com-
pressors, and other devices that create dynamic disturbances. It is a well-
known fact that pulsation can be a major source of error with head meters.
The pressure oscillations at the two pressure taps of the head meter do not
necessarily cancel out, with the result that the differential pressure pro-
duced may be considerably different than that which would have been produced
under steady flow conditions. Different types of head meters are affected
differently by pulsation, but it is probably fair to say that all are affected
to some extent. This subsection deals with the symptoms of the problem as
well as methods of correcting it.
Based on personal experience of Subcommittee members with pulsation prob-
lems, it can be stated that pulsation may be accompanied by one or more of the
following symptoms:
1. The manometer will not zero under a no-flow condition with the
221
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blower operating the line.
2. The manometer readings are affected by the length of the connecting
tubing.
3. The manometer readings may show significant fluid oscillations.
It is important to point out that the absence of the these symptoms does
not necessarily mean that the pulsation problem does not exist. If one or
more symptoms are discovered, however, pulsation may be present.
As far as corrective measures are concerned, Spink has the following to
say:
"The practical approach is to reduce or eliminate the pulsation by instal-
ling added capacity or volume together with added pressure drop in the
line between the meter and the source of pulsation."
He also goes on to say:
"Measurement may be improved by one or a combination of
1. operating at a higher differential, i.e., in a multiple meter run
installation, shutting off one or more runs,
2. installing a higher range differential guage and changing operating
conditions in order to use the increased range with the existing
orifice, as by reducing the flowing pressure, etc.,
3. reducing the pipe run diameter so as to use a higher orifice-to-pipe
diameter ratio, still operating at differentials as high as practi-
cable (increasing the dQ/d ratio will reduce the pulsation error if
the operating differential remains constant),
4. installing mufflers, headers, restrictions, or combinations of capac-
ity and pressure drop between the primary device and the source of
pulsation to reduce pulsation amplitude, and
5. locating the primary device at a point where the pulsation amplitude
is lower (as on the suction side of compressors)."
A common approach to solving a pulsation problem is the installation of
a reservoir or receiver (added capacity) between the blower and primary de-
vice. For reciprocating units, according to Ingersoll Rand's Compressed Air
222
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and Gas Data, "the combination of receiver volume and throttling will usually
dampen the pulsations sufficiently if the receiver has a minimum volume of 40
times the displacement of one stroke of the adjacent cylinder of a recipro-
cating unit."
Specific information on the design of an air flow system so that pulsa-
tion can be avoided is contained in the AGA Gas Measurement Manual. In any
system design where positive displacement compressors are being considered,
primary emphasis should be on providing substantial volume and headless be-
tween the compressor and the primary device. Once built, each system should
be checked for the symptoms mentioned earlier.
REQUIRED MEASUREMENTS FOR GAS FLOW DETERMINATIONS
A number of measurements are required for accurate gas flow determina-
tions. As a minimum, these measurements include
1. differential pressure (if applicable), h
2. flow rate (if applicable), Q
3. flowing gas temperature, Tf
4. flowing gas pressure (static pressure), pf
5. ambient temperature, T3
a
6. ambient pressure, p . and
a
7. ambient relative humidity, RH .
a
Other readings may be necessary for specific types of flow meters.
The differential and static pressure readings should be made with a
manometer of some type. Unless flow totalization or recording is required,
a simple U-tube or well-type manometer works very well. Pressure gauges can
be used for static pressure determinations, but experience has shown that,
unless these gauges are of the oil-filled variety or are at least protected
with a pulsation damper (snubber), they can be rendered useless in a short
period of time by vibration and pressure oscillations. A mercury-filled
manometer is more rugged and accurate.
Flowing gas temperature can be read with a bimetallic dial thermometer
223
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that is mounted permanently in the pipe. These thermometers can be bought
with probes of varying lengths for different pipe sizes. Where electronic
determinations are required, as in temperature compensation circuits, thermis-
tors can be employed. In any case, the probe should extend well into the cen-
ter of the pipe.
Ambient temperature can be determined with any number of commercially
available wall-mounted thermometers. Care should be taken to obtain these
readings in the shade as direct sunlight will cause erroneously high readings
due to the radiant energy of the sun.
Ambient pressure should be determined with a good quality mercurial
barometer. These readings should also be taken in a shaded area, and correc-
tions should be made for the thermal expansion of the brass indicating scale,
the change in mercury density with temperature, and the effect of the earth's
gravitational field. Tables for making these corrections are usually included
with the barometer.
Relative humidity readings should be taken with a hygrometer or a psy-
chrometer. The sling psychrometer, in particular, is portable and inexpen-
sive. Usually, wet and dry bulb thermometer readings are taken and are con-
verted to relative humidity with the use of tables that accompany the device.
Some hygrometers are available that read relative humidity directly.
STANDARD CONDITIONS
Since gases are compressible fluids, and in some instances may contain
varying amounts of water vapor, the ratio of mass flow to volumetric flow is
not a constant, but depends on the temperature, pressure, and water vapor
partial pressure. The need to relate mass flow to a volumetric flow by a
constant resulted in the term standard cubic feet per minute (scfm). This
term refers to an imaginary volumetric flow rate; it is that flow that would
exist if the same mass flow of dry gas existed at standard conditions of tem-
perature, pressure, and relative humidity. This volumetric flow rate can be
multiplied by a constant factor to obtain the mass flow of dry gas or by a
different constant factor to obtain the mass flow of gas at standard
humidity.
Standard conditions for air flow measurement are usually taken as 68°F
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(20°C, 528°R), 14.70 psia (1 atm., 760 mm Hg),and 36 percent relative humid-
ity. Standard temperature is sometimes taken as 60°F, particularly by the
natural gas industry. Blower manufacturers and others, on the other hand,
sometimes use 70°F. It is felt that 68°F is the most commonly used tempera-
ture standard in the oxygen transfer field, and this temperature has been
selected for use here. It should also be pointed out that for gases other
than air, the relative humidity standard is zero rather than 36 percent.
CONVERSION OF STANDARD VOLUMETRIC FLOW RATES OF AIR TO MASS FLOW RATES OF
OXYGEN
One method of converting a volumetric air flow rate in scfm to a mass
oxygen flow rate in Ib/hr is to first calculate the fraction of the scfm flow
that is dry air. This step can be accomplished by multiplying by the mole
fraction of dry air at standard conditions. Mole fraction is related to par-
tial pressure in the following manner:
Ydas = (14'70 ' PWs)/14-70 (98)
where:
Y. = mole fraction of dry air at standard conditions at 68°F, 14.70
psia, and 36 percent relative humdity
p = partial pressure of water vapor at standard conditions at 68PF,
14.70 psia, and 36 percent relative humdity = 0.122 psia, f/L2
Making this substitution, vdas = 0.9917. Thus, the flow rate of dry air at
standard conditions becomes:
Qdas = 0.9917 Qa (99)
where:
o
Q. = dry air porition of Q (cfm), L /t
oas a
Q = air flow at standard conditions of 68°F, 14.70 psia, and 36 per-
cent relative humidity (scfm), L3/t
where:
The density of dry air at standard temperature and pressure is 0.0752
o
. Thus, the weight flow of dry air in Ib/hr is given by:
wda = (0.0752)(60)Qdas = 4.513 Qda$ (100)
w. = weight flow of dry air (.Ib/hr), m/t
ca
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Combining Equations 99 and 100 yields:
wda = 4.475 Qa (101)
Dry air is variously taken as 23.0 to 23.2 percent by weight. Using
23.1 percent as an average, the weight flow of oxygen is related to the stan-
dard volumetric flow of air in the following manner:
* = (4.475)(0.231)Q =1.034Q (102)
Op a a
where:
w = weight flow of oxygen (Ib/hr), m/t
°2
CONVERSION OF VOLUMETRIC FLOW RATES FROM STANDARD TO ACTUAL CONDITIONS
It is often necessary to determine the actual cfm flow of air, particu-
larly when correlations are being made with headless. From ideal gas consid-
erations, the scfm and cfm air flows are related by temperature, pressure, and
relative humidity in the following manner:
Q = (14.70/pf)(Tf/528)[(pb - Pbw)/Pb3[pf/(Pf - Pw)3 (103)
where:
Q = gas flow (cfm), L3/t
For air, using standard conditions of 68°F, 14.70 psia, and 36 percent
relative humidity, the expression reduces to:
Q = 0.0276 TfQa/(pf - pj (104)
RECOMMENDED STANDARDIZATION
Recommended standards for air flow measurements taken during a clean wa-
ter test are summarized in Table 24. In summary, all data should be reported
in terms of the standard conditions of temperature, pressure, and relative
humidity shown. The guaranteed accuracy of the overall flow measurement sys-
tem (primary + secondary flow elements) should be within +2 percent. If this
cannot be guaranteed, then, it should be so stated along with any of the flow
measurements reported. Furthermore, during the conduct of any clean water
test, the air flow rate should not vary by more than +3 percent of the aver-
age value. If the air rate fluctuation is greater than this, the oxygen
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TABLE 24. RECOMMENDED STANDARDS FOR GAS FLOW MEASUREMENT
DURING CLEAN WATER OXYGEN TRANSFER TESTS
Item
Recommended Standard
Standard conditions for air
flow measurement
Standard conditions for gas
flow measurement (other
than air)
Overall flow measurement sys-
tem accuracy
Maximum allowable variation
in air flow rate during
the conduct of the clean
water test
Relationship between mass
flow rate of oxygen and
standard volumetric flow
rate of air
Standard primary element
Standard secondary element
Meter design, construction,
installation, and opera-
tion
Receiver tank for positive
displacement blowers
68°C, 14.70 psia, 36 percent
relative humidity
68°C, 14.70 psia, 0 percent
relative humidity
+2%
+3%
w = 1.034 Q,
On 3
None specified
None specified
In accordance with accepted
practice
Strongly recommended
transfer test should be considered unacceptable. Also, the weight flow of
oxygen in Ib/hr should be related to the standard volume flow of air in scfm
by a factor of 1.034.
As mentioned previously, no standardization of air flow measuring equip-
ment should be required; however, design, construction, installation,and oper-
ation should be in accordance with accepted practice. Finally, a receiver or
pulsation tank is strongly recommended in any air flow systems where a posi-
tive displacement blower is used.
REFERENCES
1. Spink, L.K., Principles and Practice of Flow Meter Engineering, 9th Edi-
tion, Foxboro Co., Foxboro, Massachusetts, 1967.
227
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2. Cusick, C.F., Flow Meter Engineering Handbook, 4th Edition, Honeywell,
Fort Washington, Pennsylvania, 1968.
3. Variable Area Flowmeter Handbook, Fischer & Porter, Warminster, Pennsyl-
vania, 1976.
4. Holman, J.P., Experimental Methods of Engineers, McGraw-Hill, New York
City, 1966.
5. Gibbs, C.W., Compressed Air and Gas Data, Ingersoll Rand Co., Woodcliff
Lake, New Jersey, 1971.
6. AGA, Gas Measurement Manual.
7. Handy Engineering Data, Hoffman, New York City, 1973.
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SECTION 10
POWER MEASUREMENT
Accurate determinations of both gas and turbine horsepower are essential
in the field of oxygen transfer. Basically, they are needed for aeration sys-
tem design, economic comparisons, and data correlations. This section dis-
cusses the meaning of various power terms used in the oxygen transfer field
and attempts to point out where confusion exists. It also discusses various
methods commonly used to make power determinations, as well as the limitations
of certain approaches. Particular emphasis is given to the need to standard-
ize the way in which clean water power data are reported for advertising or
comparison purposes.
GENERAL DEFINITION OF TERMS
Some of the basic power terms used in oxygen transfer testing are defined
in general terms below. These definitions are more fully elaborated on later
in this section.
1. Gas power - as used here, that part of the total aeration system
power that is specifically related to the gas supply.
2. Turbine pump power - that part of the total aeration system power
that is specifically related to the operation of a mechanical device,
such as a turbine or pump.
3. Water power - the work performed on the water in the form of either
gas or turbine energy.
4. Total water power - the sum of both the gas and turbine water power.
5. Delivered power - in the case of gas power, the theoretical power
required at the blower to deliver a given mass flow of gas through
a diffuser system operating under a given static head; in the case
of turbine power, the power required at the output shaft of the
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gear box to turn a shaft and impeller at a given rpm in water,
under actual conditions.
6. Total delivered power - the sum of both the gas and turbine deliv-
ered power.
7. Brake (shaft) power - the power developed or required at the shaft
of a rotating piece of equipment.
8. Total brake power - the sum of both the gas and turbine brake power.
9. Wire power - the electrical power drawn by a motor.
10. Total wire power - the sum of both the gas and turbine wire power.
THE NEED FOR STANDARDIZATION
When reviewing clean water test data, it is often unclear as to how re-
ported power determinations were actually made. Confusion may exist as to
the following:
1. Were the power determinations reported as delivered, brake, or wire
horsepower?
2. Were the power determinations measured directly or calculated?
3. If calculated, what calculation procedure was used (adiabatic, poly-
tropic, etc.)?
4. Were actual, standard, or some other ambient conditions used?
5. Was the effect of line loss as well as diffuser loss included?
6. Did the determinations include a power suction loss?
7. At what gas temperature was the diffuser headless measured?
8. At what water temperature was the turbine power draw determined?
9. What blower, motor, and drive efficiencies were used?
Questions such as the above should not exist about any reported data. In
certain cases, rather than just answering questions like the above in the con-
text of a report, it would be desirable to report standard power data. In
other words, standard conditions and procedures should be established for
power measurements such that when reference is made to standard delivered,
230
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brake, or wire horsepower, no confusion exists as to what is meant. This
standardization would apply primarily to cases where the results of shop or
field tests are to be reported for advertising or comparison purposes.
In the case of shop and field performance tests, where power determina-
tions are to be made for equipment acceptance under specified design condi-
tions, the reporting of standard power data alone would certainly not be ap-
propriate. Power results should be reported in terms of specified design con-
ditions; however, the additional reporting of standard power data would facil-
itate the comaprison of various shop and field performance tests made around
the country.
It would appear to be appropriate, therefore, to define a set of stand-
ard conditions and procedures for power determinations. It is not the pur-
pose of this section to determine the standard conditions and procedures to
be used but, rather, to demonstrate a need for standardization where it
exists. Any standard conditions or procedures should be established by
selected representatives from the oxygen transfer field. Possible standards
will be suggested, however, where appropriate.
In the case where reporting standard power data is appropriate, arguments
can be made for reporting only standard delivered power instead of standard
delivered, brake, and wire power. For one thing, it would not be necessary
to define standard motor, blower, gear box, and coupling efficiencies. It is
recommended, however, that standard brake and wire horsepower also be reported.
Comparisons made between component aeration systems would then be more realis-
tic. Due to the different efficiencies associated with a blower compared to
a turbine, reporting only standard delivered power would be very misleading
as far as the overall power requirements of the two aeration systems are con-
cerned.
Standard clean water power numbers should not be used directly when ex-
trapolating clean water test results to aeration system design. When apply-
ing clean water test data to design, it is important that power determinations
be made that use actual ambient and operating conditions and power formula-
tions that apply directly to the blower being used. The purpose of standard
power determinations is only to put the comaprison of various types of
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aeration systems on an even footing.
GAS POWER
Gas power is that part of the aeration system power requirement that is
specifically related to the gas supply. It refers to the general class of gas
power determinations, including water, delivered, brake, and wire power. In
these cases where shop and field perforamnce tests are run for equipment ac-
ceptance and the actual blower-motor combination is used, it is appropriate
to make direct power measurements. In those cases where gas power determina-
tions must be made without reference to a specific blower or motor, it is more
appropriate to calculate the power. Most often, this calculation is based on
the adiabatic compression equation.
Adiabatic Compression Equation
The adiabatic equation can be derived from basic thermodynamic principles.
Fair and Geyer have presented the derivation. It should be noted, however,
that the final form of the equation in their derivation makes some assumptions
as to ambient conditions. Basically, the equation represents the work done
along an adiabatic path between two gas states. It is based on the ideal gas
equation, pV = nRT, and the adiabatic relationship, pVc /cy = constant, where
c and c are the specific heats at constant pressure and volume, respectively.
The work performed is calculated by integrating the pressure-volume work
between the two states:
adiabatic work =
P2'T2
P1»T1
(105)
After integrating and including the efficiencies of the various components,
the following general form of the adiabatic equations can be obtained:
wire horsepower (adiabatic) = [wRiyfSBO Kebedem)][(p2/p] )K - 1] (106)
where:
w = weight flow of gas (Ib/sec), m/t
R"= universal gas constant, (ft-lbf/lt>m.0R), LfnfV1; 53.5 for air
T, = absolute inlet temeprature, °R
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2
p, = absolute inlet pressure (psia), f/L
2
P2 = absolute discharge pressure (psia), f/L
K = (k - l)/k; 0.283 for air
k = ratio of specific heats of air at constant pressure and constant
volume, c /cv; 1.395 for air
e. = blower efficiency, decimal percent
BT = drive efficiency, decimal percent
e = motor efficiency, decimal percent
The basic form of this equation can be found in Reference 2. The case
where the motor efficiency, e , is equal to 1 is equivalent to the motor
brake power. The case where the motor efficiency, e , and the drive effi-
ciency, e., are both equal to 1 is equivalent to the blower brake power.
Finally, the case where all the efficiencies are equal to 1 refers to the
perfect adiabatic case where there are no losses.
Substituting the known quantities for air into Equation 106 yields:
o
wire horsepower(adiabatic) = [(5.729 x 10 )y . Q T./(e,e .e )]
ai r a i bum
[p2/Pl)°-283 - 1] (107)
where:
Y=, = weight density of air at the temperature, pressure, and relative
33
humidity for which Q is reported (Ib/ft ), m/L
Q = air flow (cfm), L3/t
a
It is important to note the limitations of the adiabatic compression
equation. Too often it is used with the idea that it accurately describes
the operation of all blowers. While many blowers are nearly adiabatic, some
may be more adequately described by a polytropic relationship. The polytropic
power equation for air is similar to the adiabatic power equation for air
(Equation 107) except that the value of 0.283 is replaced by 0.283/e , ,
where e , is the polytropic efficiency of the blower (a purely thermodynam-
ic property). Further, the value of e. is replaced by the mechanical effi-
ciency of the blower.
Both the polytropic and adiabatic equations have been used to describe
the operation of centrifugal blowers. The operation of positive displacement
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blowers, on the other hand, has usually been described with the adiabatic
equation. With this in mind, it is probably reasonable to use the adiabatic
equation when reporting clean water data, since it has been used to describe
the operation of both types of blowers. The determination of the polytropic
and mechanical efficiencies of a blower is usually not easy. Comparisons
made between various aeration systems on the basis of adiabatic power may not
hold true when the comparison is made on the basis of polytropic power. Also,
comparisons made between the power requirements of a given aeration system at
various water depths may differ when polytropic power is used instead of
adiabatic power.
It should also be kept in mind that the adiabatic equation (Equation 106
with all efficiencies = 1) should not generally be used to calculate the rela-
tive internal energy level of the gas at a particular point in the gas dis-
tribution piping. The relative internal energy level, as used here, refers to
the increase in internal energy above that at ambient conditions. From the
First Law of Thermodynamics, the increase in internal energy of a gas is the
difference between the work performed on it and any heat loss that may occur.
For an adiabatic process, where the heat loss is zero, the increase in inter-
nal energy of gas is, thus, equal to the work performed on it.
The process of supplying air to an aeration tank, however, is not per-
fectly adiabatic in nature. The blower is not perfectly efficient, adiabeti-
cally speaking, and the pressure and thermal losses in the distribution piping
are not usually adiabatic. Thus, the adiabatic equations cannot be used to
estimate the relative internal energy level of the gas. The adiabatic equa-
tion can be used, however, at any point in the gas distribution piping to
determine the adiabatic work that would be required to compress the gas to the
line pressure at that point. This is often a very meaningful calculation.
The adiabatic equation (Equation 106 with all efficiencies = 1) cannot
be used to calculate the work that is actually performed in the water. The
actual water horsepower due to the gas is the pressure-volume work that is
done as the gas rises and expands throughout the depth of the aeration tank.
This work is probably much closer to being isothermal in nature, since the
expansion probably takes place at a temperature close to that of the water
due to the very high heat capacity of water relative to the gas. If no oxygen
234
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transfer occurred in the tank, it would be theoretically possible to calcu-
late the work performed in the water with the following integrations:
rwater surface
isothermal work =
pdV (108)
gas release point
Using the ideal gal law and assuming the temperature is constant:
i-water surface
isothermal work = nRT =
dV/V (109)
gas release point
where
n = number of moles of gas
2
p. , . = absolute static head at the gas release point, f/L
rinlet 2
p ,. = absolute pressure at the aeration tank water surface, f/L
^surface r
Since, under dynamic conditions, oxygen transfer does take place, per-
forming this integration exactly is not possible. It would seem, however,
that Equation 109 could be used to provide an approximation to the maximum
gas work performed in the water at a time of zero oxygen transfer. Knowing
the actual percent transfer, it is possible to place a lower limit on the
actual gas work performed in the water (based on mass considerations). Thus,
Equation 109 might be used to describe an approximate range for the actual
gas work performed in the water.
Water power is really only significant from a theoretical standpoint. It
may be of some value in data correlations particularly in regard to mixing.
Generally speaking, however, what is most important is the power required to
deliver a given quantity of gas through a diffuser system under specified
conditions. As mentioned previously, this can usually be approximated by the
adiabatic compression equation.
Gas Delivered Power
Gas delivered power is usually considered to be the theoretical adiabatic
power (Equation 106 with all efficiencies = 1) required at the blower to sup-
ply gas through a diffuser system operating under a given static head. For
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the special case of air:
air delivered horsepower = (5.729 x 10"3)Ya,v,QJit(P9/Pi )°'283 - ^
a 11 a I L. I
(no)
After conversations with a number of people in the oxygen transfer field,
a number of different opinions exist regarding the way this equation should be
applied. First of all, many experts consider the delivered horsepower to be
the adiabatic power required at the inlet to the diffuser, rather than at the
blower. In other words, there is some confusion as to whether line losses
should be included in the gas delivered horsepower calculation.
It should be considered at this point that the adiabatic equation (Equa-
tion 106) provides a closer approximation to the actual power required when
applied at the blower. For this reason, it would appear that the best defini-
tion of gas delivered horsepower would be the theoretical adiabatic power
required at the blower. In most cases, the horsepower so calculated would be
more realistic and practical.
The gas delivered equation (Equation 106 with all efficiencies = 1) can
be used with actual ambient and operating conditions to approximate the gas
delivered horsepower requirement on a given day at a given installation. This
is sometimes necessary from the standpoint of aeration system design and plant
operation. When reporting clean water test data for advertising or comparison
purposes, however, the use of actual ambient and operating conditions to cal-
culate gas delivered horsepower can be very misleading. It is clear from the
gas delivered horsepower equation (Equation 106 with all efficiencies = 1)
that it is possible to obtain a wide range of delivered horsepowers for a
given mass flow of gas and gauge discharge pressure because the ambient con-
ditions are also important in determining the horsepower requirement. This
fact may tend to cloud the real issue when comparisons are made between var-
ious clean water tests across the country. What is really important from a
gas standpoint is the gas flow and gauge discharge pressure at which a given
test was conducted. Different ambient conditions for the same gas flow and
gauge discharge pressure can vary the power requirements by over 30 percent.
In the case of power data to be used for advertising and comparison purposes,
calculation of a standard gas delivered power could be made from the gas flow
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and discharge pressure by assuming certain standard conditions.
The use of actual system line losses could also very well tend to confuse
diffuser horsepower comparisons made across the country. Since line losses
for any diffuser system are usually easily controlled by varying pipe size,
it would be desirable to assume a standard line loss when calculating the
standard gas delivered power. Furthermore, if possible, diffuser headloss
readings should be corrected to a standard gas temperature before using them
to calculate standard gas delivered power.
There is a need, therefore, to standardize the adiabatic power measure-
ments when reporting clean water test results for advertising or comparison
purposes. One proposed definition of standard air delivered horsepower might
be that power calculated from the adiabatic compression equation (Equations
110 or 107 with all efficiencies = 1) when compressing an scfm flow rate of
air at standard ambient conditions of 68°F, 14.70 psia, and 36 percent rela-
tive humidity to a discharge pressure set by the static head, a 1.0-psi line
loss, and a diffuser headloss corrected to 68°F. In addition, a 0.1-psi suc-
tion loss would be assumed for the blower inlet.
The standard ambient conditions mentioned are, of course, the present
standards for air flow measurement. The value of 1.0 psi is considered to be
a reasonable average system line loss, but, certainly, many other values could
be used. The tandard temperature of 68°F was selected for the diffuser head-
loss correction because it is felt that in most cases the diffuser air tem-
perature is near that of water, and the standard water temperature for oxygen
transfer measurements is 68°F. Finally, the blower suction loss of 0.1 psi is
felt to be fairly representative.
Making these substitutions into the air delivered power equation (Equa-
tion 110), the following expression for standard air delivered power is
obtained:
standard air delivered horsepower * 0.227 Q,afI05.7 t ht t H)/14.6]°"283 - 1}
am
where:
p
h, = diffuser headloss corrected to 68°F Cpsil* f/L
H = static head (psig), f/L2
237
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While it is realized that this equation i.s not an actual power determin-
ation, and is definitely not to be used for design work, it does make compar-
isons of clean water test data collected on different days in different parts
of the country more meaningful.
At this point, it is appropriate to discuss the three measurements, Q ,
H, and h. , that are required for the determination of standard air delivered
power from Equation 111 . The required accuracy of the standard air flow, Q ,
a
should be within +2 percent. The static head determination, H, can be made
most accurately with the use of a bubbler device. The bubbler is essentially
a vertical pipe with an outlet at the diffuser level. In practice, a small
air compressor can be used to bubble air down through the bubbler pipe to the
diffuser level. The bubbler piping should be large enough so that virtually
no friction losses are obtained. A connection is made between a pressure tap
in the bubbler piping and one leg of a mercury manometer so that static pres-
sure can be read directly. A bubbler is an accurate way of measuring the
static head because it compensates for the gas holdup above the diffusers.
The required accuracy on this measurement is +1 percent.
Diffuser headloss, hL, can be determined by reading diffuser inlet pres-
sure against the static head with a manometer. In order to sense diffuser
inlet pressure, a pressure tap should be installed at the inlet to a dif-
fuser(s). A connection should be made to one side of a manometer with th.e
bubbler static pressure on the other side. The resulting differential will
be the diffuser headloss. The required accuracy on this measurement should
be +5 percent. To accompany the headloss reading, measurements should also
be taken of the air flow, diffuser air temperature, and static head. As men-
tioned previously, for standard power determinations, the diffuser headloss
should be corrected to a standard diffuser air temperature at 68°F. A sum-
mary of recommended gas flow measurement standards applicable to standard gas
delivered power was shown previously in Section 9, Table 24.
Gas Brake Power
Brake or shaft power refers to the power associated with the rotating
shafts of mechanical equipment. It can refer to either input or output power,
depending on the device. With motors, for example, the brake power developed
is the motor output power. With blowers, the brake power required is the
238
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blower input power. In an actual application where the motor is connected
to the blower by means of a flexible coupling,belt drive, or gear reducer,
power losses occur between the motor and the blower. The motor brake power
developed is greater than the blower brake power required by the amount of
loss. It is important, therefore, when talking about gas brake power to dis-
tinguish between the motor and blower brake power.
In the case where actual blower-motor combinations are being tested
for equipment acceptance, it is appropriate to make direct power measurements
with the techniques discussed in the later subsection on Shaft Power Determin-
ations. The required accuracy should be +2 percent. When estimates of brake
power are required without reference to a particular blower-motor combination,
they should be calculated from the theoretical adiabatic power by using the
appropriate efficiency.
The blower brake power is related to the theoretical adiabatic power by
the blower efficiency, e,:
blower brake power = theoretical adiabatic power/e, (112)
where e, is in decimal percent.
The blower efficiency depends on a number of factors, including blower
type (centrifugal or positive displacement), number of stages, and load
(including speed, pressure differential, and ambient conditions). A sug-
gested range of blower efficiencies applicable throughout the field today is
0.5 to 0.8. Where power measurements are made directly and theoretical adia-
batic power is calculated from the adiabatic equation (Equation 106 with all
efficiencies =1), the power efficiency can be determined from Equation 112.
Motor brake power is related to the blower brake power by the drive or
coupling efficiency, e.:
gas motor brake power = blower brake power/e, (113)
where e . is in decimal percent.
This efficiency varies with the type of coupling or drive and with load.
Coupling or drive efficiencies are usually fairly high, probably between 0.9
and 1.0. If brake power measurements are made directly for the blower and
motor, then the efficiency, e,, can be determined from Equation 113.
239
-------
When reporting clean water test data for advertising or comparison pur-
poses, it is appropriate to use a standard gas brake power. It is recommended
that standard gas brake power be related to standard gas delivered power by a
standard blower efficiency, ebs, and a standard drive efficiency, e, . Rea-
sonable values for these standard efficiencies might be 0.70 and 0.95, respec-
tively, although many others could be proposed.
Gas Hire Power
Wire power is the power drawn by the motor. In the case where actual
blower-motor combinations are being tested for equipment acceptance, it is
appropriate to make these power measurements directly (see subsection on
Turbine Wire Power). The required accuracy of this measurement should be £1
percent. When estimates of wire power are required without reference to a
particular blower-motor combination, it is usually calculated from the brake
power by using the appropriate efficiency.
Gas wire power is related to gas motor brake power by the motor efficien-
cy, em:
gas wire power = gas motor brake power/e (.114)
where e is in decimal percent.
Motor efficiencies are a function of the motor and the load. Typically,
full-load motor efficiencies may range from Q.9Q to 0.95. If determinations
of the gas wire power and gas motor brake power are made directly, then e
can be calculated from Equation 114.
As with the other power terms, it is advisable to define a standard gas
wire power. It could be defined as the standard gas brake power ^standard
gas motor brake power) divided by a standard motor efficiency, e . A value
of 9.92 is suggested for e .
TURBINE PUMP POWER
Turbine (pump) power is that part of the total aeration sys.tem power
requirement that is specifically related to the operation of a mechanical
device such as a turbine or pump. It refers to the general class of turbine
(pump) power determinations, including water, delivered, brake, and wire
power. With the exception of wire power, the determinations for turbines are
240
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normally made with some type of torque measuring device. The following sub-
section discusses various methods used to measure shaft power.
Shaft Power Determinations
Shaft power can be determined with a number of torque measuring devices.
O
One of the oldest is the Prony brake, named after G.C.F.M. Richy, Baron de
Prony (1755-1839). It measures the torque required to stop the rotation of a
moving flywheel. A lever arm is attached to a braking arrangement that grips
the flywheel. The restraining force required at the end of the lever arm is
measured with a scale of some type. The torque is then calculated as follows:
Tq = Lf (115)
where
T = torque, ft-lb
L = length of the lever arm (ft)
f = force required at the end of the lever arm (Ib)
The power required is related to torque and rotational speed by the following
expression:
P = 2TTT N/33,000 (116)
where
P = power (hp), Lf/t
N = rotational speed (rpm), t~
Using this principle, actual determinations of brake power are made with
the flywheel rigidly mounted in the casing of the unit being tested, such as
a motor, blower, or gear box. The unit is mounted on a gimbal, which allows
it to rotate without appreciable power loss, and is operated under the desired
test conditions. The torque required to stop the casing of the unit from
revolving is the brake or shaft power. As might be imagined, this type of
arrangement can be difficult to set up. The Prony brake is an example of a
cradled dynamometer. There are other more modern devices of this type that
are easier to apply.
The torque cell is another method of measuring brake power and is a type
of transmission dynamometer. This method works on the principle that the
241
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strain induced in a rod or hollow cylinder is proportional to the applied
3
torque. Usually, a thin-walled metal cylinder is used as the shaft or is
connected to the shaft of the unit being tested. Strain gauges attached at
45° angles on the surface of the cylinder measure the strain developed under
load (multiple strain gauges may be installed and connected so that the axial
and transferse loads will cancel out in the final readout circuit). The
torque is related to the strain at 45° angles by:
Tq= (l/12HG(ro4- r^/ro (117)
where:
G = shear modulus of elasticity (lb/in.2), f/L2
rQ = outside radius of the cylinder (in.), L
r.j = inside radius of the cylinder (in.), L
£45 = strain at 45° angles
Power can then be calculated by Equation 116. Other types of transmission
dynamanters are also available. The required accuracy for shaft horsepower
determinations should be within +2 percent.
Turbine Delivered Power
For turbine equipment such as surface aerators and submerged turbines,
delivered horsepower is the power required at the output shaft of the gear
box to turn the shaft and impeller at the desired rotational speed in water
under actual conditions. This power is also referred to as turbine shaft or
turbine water power. The turbine delivered power is normally measured with
a brake, torque cell, or other measuring device, although it is not usually
referred to as a brake power.
As with the other power terms, it would be advisable to define a stan-
dard turbine delivered power to be used when reporting clean water data for
advertising or comparison purposes. Since water temperature would seem to be
the most important variable affecting the turbine power draw, it might be
appropriate to define standard turbine delivered power as the turbine shaft
power required at a water temperature of 68°F. While it is realized that it
would be impossible to run all power tests at 68°F, it is hoped that corre-
lations exist in the field today that might relate power draw at a given
242
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temperature to that at 68°F.
Pump Delivered Power
Pump delivered power should be calculated using the following equation:
pump delivered horsepower = QHS /3960 (118)
where:
3
Q = liquid flow rate (gpm), L /t
H = total pump head (ft of water), L
S = water specific gravity at temperature T
The flow rate, Q, should be determined from a manufacturer's H-Q curve for
the pump used. The pump head, H, should be based on actual measurement and
should be accurate to +1 percent. The standard pump delivered power should
be referenced to water at 68°F.
Turbine (Pump) Brake Power
The brake power associated with turbine equipment is similar to the
brake power associated with gas delivery equipment. The gear box brake power
is generally considered to be the shaft power associated with the input shaft.
Furthermore, the motor brake power may not be the same as the gear box brake
power due to the drive or coupling employed between the motor and the gear
reducer (see the previous subsection on Gas Brake Bower).
In a manner similar to gas delivery devices, the gear box brake power is
related to turbine delivered power by a gear box efficiency, e :
turbine gear box brake power = turbine delivered power/e (119)
where e is in decimal percent.
The gear box efficiency is a function of the gear box design (including
the number of gear reductions) and the load. The losses in a gear box are
basically of two different types, a fairly constant churning loss and a bear-
ing loss that is a function of load. Generally speaking, these gear boxes
are very efficient. Rating curves are normally available from the manufac-
turer. A range of full-load gear box efficiencies applicable throughout the
field today might be 0.94 to 0.96. When measurements of the powers in Equation
119 are made directly the efficiency, e , can be calculated.
j
243
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The turbine motor brake power is related to the turbine gear box brake
power by the coupling or drive efficiency, e ,:
turbine motor brake power = turbine gear box brake power/e. (120)
where e, is in decimal percent.
The definition of the term e , as well as its range, is the same as that
discussed in the subsection on Gas Brake Power. Again, e, can be calculated
if the powers in Equation 120 are measured directly.
As with the other power terms, it would be appropriate to define a stan-
dard turbine brake power. The standard turbine brake power could be related
to the standard turbine delivered power by a standard gear box efficiency, e ,
and a standard drive efficiency, edg. Possible values for both of these effi-
ciencies might be 0.95, although many others could be proposed.
Actual measurements of either turbine motor brake power or turbine gear
box brake power can be made with the methods in the Shaft Power Determinations
subsection. The required accuracy on this measurement should be +2 percent.
Turbine (Pump) Hire Power
Turbine wire power can be measured directly with a recording wattmeter.
It is very important, however, that the wattmeter be zeroed and calibrated
accurately before it is used. An ammeter can be used as long as the voltage
and power factor are also measured. An expression for calculating 3-phase
power from current, voltage, and power factor measurements is:
wire horsepower (3 phase! * 1.73 Ei(PF}/746 = 2.32 x 1Q~3 Ei(PF) C12U
where:
E = voltage (volts)
i = current (amperes)
PF = power factor
It is always appropriate to use a recorder when making power measurements.
During the operation of a mechanical device, there are usually fluctuations in
load that can be most easily observed with a recorder. It is recommended that
all wire power measurements be made in accordance with the ASME Power Test
Code and the IEEE Standard. The required accuracy of wire power measurements
244
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should be within +1 percent.
Turbine wire power is related to turbine motor brake power by the motor
efficiency, em:
turbine wire power = turbine motor brake power/em (122)
where e is in decimal percent.
m
As mentioned previously in the subsection on gas power, a range of full-
load motor efficiencies might be 0.90 to 0.95. If the powers in Equation 122
are measured directly, e can be calculated.
As with gas power determinations, it is recommended that a standard effi-
ciency, e ,be used to relate standard turbine wire power to standard turbine
11 lo
power (standard turbine motor brake power). As before, a possible value of
ems might be 0.92.
TOTAL POWER
The summation of the gas and turbine powers is the total power. Thus,
references can be made to total delivered power, total brake power, and total
wire power. When reporting clean water power data, it would be appropriate to
report the gas and turbine power data separately, as well as the combined
total. In the case of data to be used for advertising or comparison purposes,
all power results should be reported in terms of standard conditions.
MECHANICAL AERATOR POWER
This subsection describes the procedures to predict installed aerator
power based on a single-sample field or factory test. The calculated instal-
led power has two components, the most likely value and the range of uncer-
tainty. The uncertainty is a function of the measuring technique and the
ability to define power losses in each appropriate drive component.
In practice, a precise factory test can be as accurate as a field test.
Most often the primary power is used as the basis of comparison. The results
described below could also be applied to a shaft power comparison.
Measurements
Electric Power—
These measurment techniques were covered previously in this section.
245
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Rotating Shaft Torque--
There are several manufacturers of torque measuring devices for rotating
shafts. The two most common devices are inductance and strain gage torque
indicators.
For measured torques at the upper limit of the instrument, the true value
can be determined with +0.3 percent. In most applications, a measurement
uncertainty of +J.5 percent is attainable.
It is possible to custom build torque instrumentation by mounting a
strain gage bridge on a shaft. Precautions are required to identify slip ring
noise and other errors. For example, strain gage torque measurements are sub-
ject to errors induced by bending. Therefore, care must be exercised in in-
terpreting aerator shaft torque measurements. A custom device must have a
certified calibration, similar to commercial units.
Reaction Loads--
A common method for measuring laboratory-scale power is a reaction dyna-
mometer. The drive unit is mounted on a low friction bearing. The torque
required to prevent drive rotation is equal to the impeller torque applied to
the fluid plus the bearing torque. This approach can also be applied to
large-scale drive units.
A related technique would involve strain gaging the drive support struc-
ture. The structural design and location of the strain gages could be opti-
mized to indicate torque, thrust, and bending loads.
In each case, certified calibration is essential. These data must
include any special corrections related to operating losses. These correc-
tions will probably have a complex dependence on shaft speed, delivered power,
shaft/impeller weight, etc.
Shaft Speed--
Speed should be measured with a tachometer or stroboscope having an
accuracy of +1 percent. For low-speed shafts, counting revolutions and mea-
suring elapsed time should be done in a fashion yielding similar accuracy.
Power Calculations
246
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General Relationships--
SHP = BHP nRnM (123)
BMP = PHP np (124)
where:
SHP = shaft power (hp), Lf/t
BHP = brake (output) power of prime mover (hp), Lf/t
PHP = prime mover power (hp), Lf/t
nR = reducer efficiency in decimal percent
nM = miscellaneous (bearings, etc.) efficiency of special factory hard-
ware in decimal percent
n[! = prime mover efficiency in decimal percent
Rotating Torque Device—
P = 2irT N/33,000 = 1.904 x 10"4 T N (116)
where:
P = power (hp), Lf/t
N = shaft speed (rpm), t"
T = torque (ft-lb), Lf
Reaction Load Device--
The measurements made with a reaction load device can be directly related
to shaft torque. The appropriate conversion should be applied to calculate
torque, T . Measurements should also be made with the impeller operating in
air to provide an accurate estimate of zero-load torque, T . Since the
weight density difference between air and water is so great, the air-induced
power on the impeller should be no more than 0.1 percent of that in water. An
appreciable torque measurement, however, can be attributed to system tare.
The tare or zero-load torque value should be subtracted from the torque value
measured in water to calculate shaft horsepower:
SHP = 1.904 x 10"4 N(T - T ) (125)
A tare calculation should not be applied for measurements of BHP or PHP.
At zero load, electric motors draw 5 to 9 percent of full-load power. Current
draw will be 25 to 35 percent of full-load amperes. Motor power (3 phase, a-c)
is not directly proportional to the product of current and voltage since the
247
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power factor (see Equation 121) can vary significantly depending on motor
load. The power factor can be obtained from the manufacturer's motor curve.
Similar relations are probably available for other prime movers. Reducers and
variable speed drives also have significant losses at zero-load conditions.
If the calibrated efficiency curves are used, proper corrections are auto-
matically made for unit efficiencies.
Reducer and Variable Speed Drives
Power losses for these devices can be considered as having two nearly
independent components. Part of the losses are speed dependent. The second
loss element is dependent on output torque or power. The total unit loss is
the sum of these terms. If component efficiency has been determined as a
function of speed and load, these factors are properly considered and the
remainder of this subsection is not applicable.
For a gear-type reducer, power losses are separated into churning and
gear loading components. Chruning losses are dependent almost exclusively on
rotating speed. A slight dependence on transmitted loads is related to oil
temperature changes. Gear loading losses at a specific speed are linearly
dependent on delivered torque (.or power).
For illustrative purposes, consider a hypotehtical reducer that is 95
percent efficient at its 100-BHP rated capacity. Thus, the mixer drive will
generate 95 SHP at rated capacity. An applicable rule-of-thumb is that losses
are split 50-50 between churning and gear loading. For this example, churning
losses would be 2.5 hp irrespective of the magnitude of the load on the
reducer. Gear loading losses, however, vary directly with output load and
would only reach 2.5 hp at rated capacity. Total gear reducer losses are
equal to the sum of churning and gear loading losses, which for this hypothet-
ical unit can be calculated as:
u~ -i,.,.™,. o c x o cf$HP for test aerator V
hpQR losses = 2.5 + 2.5^SHp at rated capacityj
For a factory test on a 20-SHP aerator:
hpGR losses = 2.5 + 2.5(20/95)
= 2.5 + 0.5
= 3.0
248
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and:
BMP = SHP + gear reducer losses (126)
= 20 + 3
= 23
Gear reducer efficiency can then be determined from Equation 119:
Assuming nM = 1.0:
nR = SHP/(BHP nM) (123)
nR = 20/(23 x 1.0)
= 0.87
The above example demonstrates the importance of specifying efficiency as a
function of speed and loading. This precaution can be particularly important
in a factory test where the reducer is operated well below its design point.
RECOMMENDED STANDARDIZATION
The recommended standards for power measurements made during a clean
water test are shown in Tables 24 (Section 9), 25, 26, 27, and 28. It is
recommended that standard power be used whenever data are to be reported for
advertising or comparison purposes. The procedures for determining standard
pump, gas, and turbine delivered power are summarized in Tables 26, 27, and
28, respectively. Standard pump and gas delivered power should be determined
by a calculation procedure; standard turbine delivered power can be determined
either by direct or indirect measurement.
Standard pump delivered power should be determined using the equation
shown in Table 26. The power should be calculated for water at 68°F. The
measured parameters should conform to the accuracies shown.
Standard gas delivered power should be determined using the adiabatic
compression equation given in Table 27. The following standard conditions
would apply:
Standard air (68°F, 14.70 psia, 36 percent relative humidity)
Diffuser headless corrected to 68°F
Discharge line loss of 1.0 psi
Blower inlet suction loss of 0.1 psi
249
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TABLE 25. RECOMMENDED EQUIPMENT EFFICIENCIES TO BE
USED FOR STANDARD POWER DETERMINATIONS
Recommended Standard
Present Efficiency Range* Efficiency
Item (decimal percent) (decimal percent)
Compressor 0.50 - 0.80 0.70
Gear box 0.94 - 0.96 0.95
Coupling or drive 0.90 - 1.00 0.95
Motor 0.90 - 0.95 (most) 0.92
*
Efficiencies quoted are for full-load conditions.
TABLE 26. STANDARD PUMP DELIVERED POWER
Pump delivered power should be calculated using the following equation:
pump delivered power = QHS /3960 (118)
where:
Q = liquid flow rate (gpm)
H = total pump head (ft of water)
S = water specific gravity at temperature T
The flow rate, Q, should be determined from a manufacturers H-Q curve for
the pump used. The pump head should be based on actual measurement and should
be accurate to +] percent. The standard pump delivered power should be
referenced to water at 68°F.
The measured parameters should conform to the accuracies shown in Table 24.
Standard turbine delivered power can be determined either by direct or
indirect measurement. Direct methods include cradled dynamometers and trans-
mission dynamometers. Indirect measurements include electrical and shaft
horsepower determinations made on other components in the aeration system,
such as a motor, as long as the appropriate efficiencies are known. Power
measurements should be related to water at 68°F, if possible. The accuracy
of all wire power measurements should be within +1 percent.
When standard brake and wire power values are determined based on
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TABLE 27. STANDARD GAS DELIVERED POWER
Gas delivered power should be calculated using a variation of Equation
106 that excludes the blower, drive, and motor efficiency terms:
gas delivered power = [wRT1/(550K)][(p2/p1 )K - 1]
For air at standard conditions of 68°F, 14.70 psia, and 36 percent relative
humidity, this equation reduces to:
0 2R3
standard air delivered power = 0.227 Qj(p9c/P1c) " - 1] (A)
a i-b IS
where p2s and p, refer to standard discharge and inlet pressures, respec-
tively, such that:
P2 = standard + actual + standard + standard
atmos- static diffuser pipe loss
pheric head loss at (1.0 psia)
pressure (H) 68°F
(14.70 (h.)
psia)
= 15.70 psia + H + hL, and (B)
P, = standard - standard
atmos- suction
pheric loss
pressure (0.1 psia)
(14.70
psia)
= 14.60 psia (C)
Equations A, B and C are recommended for standard air delivered power. The
air flow rate, Qa, should be accurate to +2 percent. The static head, H,
d __
and diffuser headless, hL, measurements should be accurate to +1 percent and
+5 percent, respectively.
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TABLE 28. STANDARD TURBINE DELIVERED POWER
Turbine delivered power (actually the turbine shaft horsepower) may be
determined by direct measurement or by indirect measurement when the appro-
priate efficiency information is available on the motor, coupling (drive),
and gear box. Standard turbine delivered power should be obtained by refer-
encing turbine shaft power draw to water at standard conditions of temperature
and pressure.
Direct Measurement
The following techniques are appropriate for the direct measurement
approach:
1. Cradled dynamometers (i.e., cradled motors, generators, and Prony
brakes).
2. Transmission dynamometers (.i.e., surface strain types and angular
twist types).
All shaft power measurements should be accurate to +2 percent.
Indirect Measurements
The following techniques are appropriate for the indirect measurement
approach:
1. Measurement gear box input shaft horsepower, knowing the gear box
efficiency.
2. Measurement of motor shaft horsepower, knowing the gear box and
coupling efficiencies.
3. Measurement of motor wire horsepower, knowing the gear box coupling,
and motor efficiencies.
4. Other methods.
All shaft power measurements should be accurate to +2 percent. All wire
power measurements should be accurate to +1 percent.
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delivered power data, the recommended equipment efficiencies shown in Table
25 should be used. This recommendation applied to gas, pump, and turbine
power. The basic relationships between delivered, brake, and wire power have
been discussed previously.
For the various types of power measurements, whether for the determina-
tion of standard power or not, it is strongly recommended that the following
performance codes be adhered to:
Shaft power measurement - ASME Power Test Codes #19.7, #9, and #10.4
4
Electrical power measurement - ASME Power Test Codes #19.6, #9, and #10;
IEEE Standards #5, #7, and #9.
Air flow measurement - ASME Power Test Codes #19.5, #19, and #10.
4
Pressure measurement - ASME Power Test Code #19.2.
4
Temperature measurement - ASME Power Test Code #19.3.
4
Rotary speed measurement - ASME Power Test Code #19.3.
Additional reference that may prove valuable include Intersoll-Rand's
1
7
Compressed Air and Gas Data and the Compressed Air and Gas Institute's
Compressed Air and Gas Handbook.
REFERENCES
1. Fair, G.M. and J.C. Geyer, Water Supply and Wastewater Disposal, John
Wiley & Sons, Inc., New York City, 1956.
2. Metcalf and Eddy, Inc., Wastewater Engineering, McGraw-Hill, New York
City, 1972.
3. Holman, J.P., Experimental Methods for Engineers, McGraw-Hill, New York
City, 1966.
4. ASME, Power Test Codes #9, 10, 19.2, 19.3, 19.5, 19.6, 19.7, and 19.13.
5. IEEE, Standards #5, 7, and 9.
6. Gibbs, C.W., Compressed Air and Gas Data, Ingersoll-Rand Co., Woodcliff
Lake, New Jersey, 1971.
7. Compressed Air and Gas Handbook, Compressed Air and Gas Institute, New
York City, Undated.
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SECTION 11
PROPOSED EVALUATION PROCEDURE FOR THE RECOMMENDED
CLEAN WATER OXYGEN TRANSFER TEST
The various techniques employed to date for clean water testing, data
analysis, and design application of test results for oxygen transfer systems
have important similarities and differences. These techniques are similar in
that they all include deoxygenation, reaeration, data collection, and data
analysis to estimate SOTR and OTRf. However, subtle differences in the de-
tails of each step can markedly affect the calculated values of SOTR and OTR-.
The ASCE Subcommittee on Oxygen Transfer Standards in this report has
reviewed current practices and recommended procedures that have been judged
to be the most desirable and workable for the clean water evaluation of
oxygen transfer systems. The next logical step is for these recommended pro-
cedures to be tested experimentally and evaluated in practice by manufac-
turers, consulting engineers, and others involved in producing, specifying,
testing, and using oxygen transfer systems. It is proposed that this evalua-
tion be conducted using a two-part program. The first part would consist of
an Experimental Research Evaluation, whereas the second part would consist of
a Comparative Practical Evaluation. Although the parts are related and com-
plement each other, either part could stand alone.
EXPERIMENTAL RESEARCH EVALUATION
Although the Subcommittee drew upon a wealth of talent and experience in
developing recommended procedures for clean water testing, some areas of
uncertainty remained and had to be handled by reasonable assumptions. Conse-
quently, the accuracy and precision of these recommended procedures need to
be comprehensively field evaluated to determine their applicability in
achieving the desired goal of realistic prediction of actual oxygen transfer
rates, OTR,., under process conditions.
254
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The Experimental Research Evaluation would evaluate the OTRf values
predicted from the clean water test by comparing them with values measured
directly in both clean and process water using the radioactive tracer tech-
nique. General features of the proposed Experimental Research Evaluation are
outlined in Table 29.
COMPARATIVE PRACTICAL EVALUATION
In addition to determining the accuracy of the recommended clean water
test procedures as a predictor of OTRf, it would be useful to evaluate these
procedures relative to the various other methods currently in use. This
evaluation could be accomplished at two levels.
One level would rely strictly on voluntary participation in the evalua-
tion program by manufacturers and others involved in aerator testing. The
voluntary participants would agree to report their results to the Subcommit-
tee. An advantage of this level is that it could be implemented without
external funding. However, there might be a tendency for some participants
to withhold certain data.
Another level would place the Comparative Practical Evaluation directly
under the control of the Subcommittee. In this plan, the Subcommittee would
determine the techniques and devices to be compared and would retain a con-
sultant to perform the testing. This approach would obviously require
external funding and might easily be combined with work sponsored under the
Experimental Research Evaluation.
It is proposed that, as a minimum, the Subcommittee pursue the voluntary
level of Comparative Practical Evaluation. This activity could be coordinated
by a new subgroup within the Subcommittee. Simultaneously the Subcommittee
should investigate the possibility of obtaining funds for the Experimental
Research Evaluation and/or the second level of the Comparative Practical
Evaluation.
255
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TABLE 29. GENERAL FEATURES OF PROPOSED EXPERIMENTAL RESEARCH EVALUATION
Test Facilities
o Small to medium size aeration systems located in operating
facilities where process wastewater is available should be used.
o Total operating facility should be large enough to unload
one aeration unit or tank for testing.
o Number and types of systems selected should cover various generic
aeration equipment, e.g., one surface aeration system, one
diffused air aeration system, and one other submerged aeration
system.
Test Program
o Clean water unsteady state test should be performed according
to recommended procedures.
o a, g, and 6 should be measured according to recommended proce-
dures.
o SOTR and OTRf should be calculated using recommended methods.
o SOTR and OTRf should be measured by radioactive tracer technique.
o OTRf values obtained with above two methods should be compared.
Program Administration
o Program should be administered by ASCE Subcommittee on Oxygen
Transfer Standards with external funding.
o Actual testing should be performed by consultants under Sub-
committee direction.
256
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APPENDIX A
NONLINEAR ESTIMATION PROGRAM
Most nonlinear least squares parameter estimation procedures involve
iterative techniques for solution. The linearization method uses a Taylor
series expansion of the model about some initial parameter estimates. The
expansion is truncated after the first derivative, resulting in a linear
approximation to the nonlinear model. Linear least squares is then applied
to the approximate linear model in successive steps until convergence to the
least square estimate is obtained.
For the exponential form of the oxygen transfer model, the expansion
proceeds as follows. First, write the model in terms of general parameters,
e.g., K.:
C = K1 - (^ - K2) exp(-K3t) (Al)
where:
K3 - KLa'
The partial derivatives of the model, Equation Al , with respect to the para-
meters are computed as:
Z] = aC/aKj = 1 - exp(-K3t) (A2a)
Z2 = aC/aK2 = exp(-K3t) (A2b)
= (t)(exp(-K3t))(K1 - K2) (A2c)
The Taylor series expansion of Equation Al about the parameters K.. then
becomes:
r - r° 4. 7°IK k^ + 7°^ K°\ + 7°(K - K0} (A^
L • - L __i_ + i.n\l\i ~ l^n > * '•oV^o ~ ^9' '•O\PVO No/ V«J/
obs calc 11 i 2 L c 66 6
257
-------
where:
C . = the observed DO concentration value,
Ccalc = tlie calculated D0 concentration value using the parameter
values K?,
and the superscript (°) indicates the values of the parameters about
which the expansion occurs.
Equation A3 can be written in the following linear form:
W° = 2° + bZ° + bZ° (A4)
where:
W° = C - C°
W obs Ucalc
b. = K. - K°
Z. = the partial derivatives of the model evaluated at the parameter
values K?
To begin the estimation procedure, initial values of the model para-
meters, K.. , must be provided. These initial parameter values are used to
calculate the values W° and Z? in Equation A4. Because Equation A4 is linear
in the parameters b. , the linear least squares technique is used to calculate
estimates of b.. . The least squares estimates of b. provide updated estimates
of the model parameters, K., by the following relationship:
Ki = b1 + K° (A5)
where K. are the prior estimates of the model parameters and K. are the
updated estimates. The values of b. can be viewed as corrections applied to
the prior estimates of the model parameters.
The estimation procedure continues. The new values of K. are used to
calculate new values of Z. and W. in Equation A4. The linear least squares
estimates of b. {Equation A4) are used to provide the next update for the
model parameters (Equation A5). This iterative calculation continues until
the values of the model parameters converge. For models that are only
moderately nonlinear, this linearization estimation procedure usually works
quite well and convergence will be obtained in a few iterations.
258
-------
SOLUTION OF THE NORMAL EQUATIONS
For the linearization method to work, the least squares estimates of b.
in Equation A4 must be obtained. Omitting the superscripts, the sum of
squares function, S, to be minimized is:
S = I (W - b, Z - b? Z - b- Z )2 (A6)
data ' 6 J
where the summation is performed over all the data values of concentration
versus time. Minimization of S with respect to the parameters b. leads to
the following set of normal equations:
(A7a)
(A7b)
(A7c)
Equations A7a, b, and c can be written in more compact form as:
allbl + 312b2 + 313b3 = Cl (A8a)
a b + a b + a«»b, = c? (A8b)
a31b1 + a32b2 + a33b3 = c3 (A8c)
where:
. _ r,2
a!2 a21
a!3 a;
a23 = a32
a33
259
-------
c3 -
Solution of Equations A8a, b, and c by forward elimination and back substitu-
tion yields the following equations for the least squares estimates of b,,
b2, and b_:
b3 = (d1d2 - d3d5)/(d1d4 - d3d3) (A9a)
b2 = (d5 - d3b3)/dl (A9b)
bl = (cl " a!2b2 ' a!3b3)/all (A9c)
where the values of d are given by:
dl = a22all ' a!2a!2
d2 = allc3 * a!3cl
d3 = alla23 " a!3a!2
d4 = alla33 " a!3a!3
d5 = allc2 - a!2Cl
CONVERGENCE
Once the least squares estimates of b. are computed (Equations A9), the
updated values of the model parameters, K., are calculated as follows:
K. = b. + K° (A5)
If the new values of K. are within some specified tolerance of the prior
values, then the solution is assumed to have converged and iteration stops.
If the new values are not within tolerance, then the iterations continue with
the new parameter values serving as the point of the next Taylor series
expansion of the model.
STANDARD DEVIATIONS
Estimates of the precision (standard deviation) of the least squares
parameter estimates can be obtained. These values are computed from the
260
-------
inverse of the coefficient matrix (A-matrix) of the linearized form of the
model (Equation A8) and the residual mean square. The equations for this
calculation are given below:
) = (En/D)(RMS) (AlOa)
Var(K2) = (E22/D)(RMS) (A10b)
Var(K3) = (E33/D)(RMS) (AlOc)
where :
Var(K. ) = variance of the parameters, K.
E.. = cofactors of a., in the coefficient matrix
D = determinant of the coefficient matrix
RMS = residual mean square from the fitted model
The standard deviations of the parameter estimates are obtained from the
square root of the variances in Equations A10.
FORTRAN PROGRAM
The FORTRAN computer program that follows in this appendix is a non-
linear estimation of the parameters in the exponential form of the oxygen
transfer model. The program uses the Taylor series linearization method and
is in two parts. For greatest user ease, the computational and output por-
tions are written in subroutine form (subroutine KLANL). The user-supplied
MAIN program serves as an interface between the system constraints of the
user's computer and the regression computational algorithm in the subroutine.
The MAIN program must perform the following tasks. A sample MAIN
program is shown in the FORTRAN listing:
1. Read in the data to be fitted: concentration (C) versus time (T).
2. Read in initial parameter estimates (CS, CO, XKLA).
3. Provide a descriptive name for the data set (INAME).
4. Provide the logical device number for output (NOUT).
Subroutine KLANL performs all the computations for the nonlinear
estimation and controls the output of the results. The notation in the sub-
routine is consistent with that in this appendix. The estimation and output
proceeds in the following steps:
261
-------
1. Write titles, name of data set, and headings for the iterations.
2. Initialize internal variables, and compute the fitted values and
residual sum of squares based on the initial parameter estimates.
3. Set up the normal equations using current parameter estimates.
4. Solve normal equations for the corrections to the parameter esti-
mates.
5. Update parameter estimates and calculate new fitted values and
residual sum of squares.
6. Test for convergence. The convergence criteria are:
a. Relative change in parameters less than 0.00001.
b. Relative change in sum of squares less than 0.000001.
c. The algorithm will also exit from the iteration loop if more
than 10 iterations are required for convergence. A diagnostic
message is printed.
7. Calculate the estimated standard deviations of the model parameters.
8. Write out a summary of the data, fitted values (F), and residuals(R)
An example estimation problem follows the FORTRAN listing.
262
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FORTRAN COMPUTER PROGRAM
00100
00200
00300
00400
00500
00600
00700
00800
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C
C
C
C
1
2
10
15
19
C
C
C
C
C
C
C
20
21
C
C
C
50
99
MAIN PROGRAM FOR NONLINEAR ESTIMATION OF OXYGEN
TRANSFER PARAMETERS
DIMENSION C(100)J(100),F(100),R(100)
WRITE(5,1)
FORMATC NAME OF INPUT DATA FILE: ' $)
READ(5,2) INAME
FORMAT(A5)
OPEN(UNIT=20,MODE='ASCII1,ACCESS='SEQIN',FILE=INAME)
READ(20,10) CS,CO,XKLA
FORM AT OF)
N=l
READ(20,10,END=19) T(N),C(N)
N = N+l
GO TO 15
CONTINUE
NOB = N-l
NOUT = 5
CALL KLANL(C,T,F,R,NOB,CS,CO,XKLA,INAME,NOUT)
CALL EXIT
END
SUBROUTINE KLANL PERFORMS NONLINEAR ESTIMATION COMPUTATIONS
AND CONTROLS OUTPUT SUMMARIES
SUBROUTINE KLANL(C,T,F,R,NOB,CS,CO,XKLA,INAME,NOUT)
DIMENSION C(100),T(100),F(100),R(100)
REAL K1,K2,K3
STEP 1 - WRITE TITLES
WRITE(NOUT,20) INAME
FORMAT(//20X,'NON LINEAR ESTIMATION'/
115X,'UNSTEADY STATE OXYGEN TRANSFER1/
223X,'DATA SET ',A5)
WRITE(NOUT,21)
FORMAT(///' ITERATION1,29X,'KLA',8X,'SUM OF'/
12X,'NUMBER',6X,'C-STAR',6X,'C-ZERO',6X,'PRIME',6X,'SQUARES'/)
STEP 2 - INITIALIZATION OF VARIABLES
K=0
OSSQ =0.0
DO 50 I-l.NOB
F(I) = CS-(CS-CO)*EXP(-XLA*T(I))
R(D = C(I) - F(I)
OSSQ = OSSQ + R(I)*R(I)
WRITE(NOUT,30) K,CS,CO,XKLA,OSSQ
K=K+1
All=0.0
A12=0.0
A13=0.0
263
-------
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09500
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10000
10100
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10400
10500
10600
10700
C
C
C
C
100
C
C
C
C
C
C
C
120
C
A22=0.0
A23=0.0
A33=0.0
Cl=0.0
C2=0.0
C3=0.0
SSQ=0.0
STEP 3 - SET UP NORMAL EQUATIONS FOR LINEARIZED MODEL
USING CURRENT LEAST SQUARES ESTIMATES.
DO 100 1=1,NOB
Z2=EXP(-XKLA*T(I))
Z1=1.0-Z2
Z3 = T(I)*Z2*(CS-CO)
All
A12
A13 :
A22 =
A23 =
A33 =
R(D
Cl =
All
A12
A13
A22
A23
Z1*Z1
Z1*Z2
Z1*Z3
Z2*Z2
Z2*Z3
= A33 + Z3*Z3
= CS - (CS-CO)*Z2
Cl + R(I
C2 = C2 +
C3 = C3 +
CONTINUE
*Z1
*Z2
*Z3
STEP 4 - SOLUTION OF NORMAL EQUATIONS FOR CORRECTIONS TO
THE PRIOR LEAST SQUARES ESTIMATES
Dl = A11*A22 - A12*A12
D2 = A11*C3 - A13*C1
D3 = A11*A23 - A13*A12
D4 = A33*A11 - A13*A13
D5 = A11*C2 - A12*C1
BN3 = D1*D2 - D3 *D5
BD3 = D1*D4 - D3*D3
B3 = BN3/BD3
BN2 = D5 - D3*B3
B2 = BN2/D1
Bl = (Cl - A12*B2 - A13*B3)/A11
STEP 5 - UPDATE ESTIMATES, SUM OF SQUARES
Kl = Bl + CS
K2 = B2 + CO
K3 = B3 + XKLA
DO 120 1=1, NOB
= Kl -(K1-K2)*EXP(-K3*T(I))
SSQ = SSQ + R{I)*R(I)
264
-------
10800
10900
11000
11100
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15800
C
c
C
c
c
150
30
C
C
C
200
C
C
C
C
300
22
23
C
C
C
STEP 6 - TEST FOR CONVERGENCE - PARAMETERS
IF(B1/K1.GE.0.00001) GO TO 200
IF(B2/K2.GE.0.00001) GO TO 200
IF(B3/K3.GE.0.00001) GO TO 200
ITERATIONS CONVERGED
WRITE(NOUT,30) K,K1,K2,K3,SSQ
FORMAT(3X,I4,3X,4E12.4)
GO TO 300
PARAMETERS NOT CONVERGED, TEST SUM OF SQUARES
IF(ABS((OSSQ-SSQ).LE.0.000001) GO TO 150
SUM OF SQUARES NOT CONVERGED, TEST ITERATIONS
IF(K.GT.IO) GO TO 350
WRITE(NOUT,30) K,K1,K2,K3,SSQ
NEW ESTIMATES
CS = Kl
CO = K2
XKLA = K3
OSSQ = SSQ
GO TO 99
CONTINUE
XDF = NOB - 3
RSM = SSQ/XDF
ERROR = SQRT(RSM)
WRITE(NOUT),22) ERROR
FORMAT(/' ESTIMATE OF ERROR FROM RESIDUAL MEAN SQUARE ',F6.2)
WRITE(NOUT,23)
FORMAT(//17X,'STANDARD DEVIATIONS1/
116X,'OF PARAMETER ESTIMATES1//)
STEP 7 - COMPUTE STANDARD DEVIATIONS OF THE PARAMETER ESTIMATES
DETP = A11*A22*A33 + 2.0*A12*A13*A23
DETN = A11*A23*A23 + A22*A13*A13 + A33*A12*A12
DET = DETP-DETN
Ell = A22*A33 - A23*A23
E22 = A11*A33 - A13*A13
E33 = A11*A22 - A12*A12
VARK1 = (E11/DET)*RSM
VARK2 = (E22/DET)*RSM
VARK3 = (E33/DET)*RSM
SIGCS = SQRT(VARKl)
SIGCO = SQRT(VARK2)
SIGKL = SQRT(VARKS)
WRITE(NOUT,31) SIGCS,SIGCO,SIGKL
265
-------
15900 31 FORMATC ABSOLUTE'/3X'UNITS',2X,3E12.4)
16000 SIGCS = SIGCS/CS*100.0
16100 SIGCO = SIGCO/CO*100.0
16200 SIGKL = SIGKL/XKLA*100.0
16300 WRITE(NOUT,32) SIGCS.SIGCO,SIGKL
16400 32 FORMAT(/' PER CENT'/2X'OF LSE',2X,3F12.1)
16500 C
16600 C STEP 8 - WRITE FINAL SUMMARY
16700 C
16800 WRITE(NOUT,33)
16900 33 FORMAT(//15X,'SUMMARY OF DATA1//
17000 110X,'TIME',6X,'CONC',5X,'FITTED1,3X,1RESIDUAL'/
17100 230X,1VALUE1/}
17200 DO 370 I=1,NOB
17300 370 WRITE(NOUT,34) I,T(I),C(I),F(I),R(I)
17400 34 FORMAT(I5,4F10.2)
17500 GO TO 400
17600 350 WRITE(NOUT,35)
17700 35 FORMAT(//3X,'SOLUTION NOT CONVERGED IN 10 ITERATIONS!'//)
17800 400 RETURN
17900 END
266
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EXAMPLE ESTIMATION PROBLEM
FORTRAN: KLANLN
MAIN.
KLANL
LINK: Loading
CLNKXCT KLANLN execution
NAME OF INPUT DATA FILE: COMB
NON LINEAR ESTIMATION
UNSTEADY STATE OXYGEN TRANSFER
DATA SET COMB
ITERATION
NUMBER
0
1
2
3
4
5
0.
0.
0.
0.
0.
0.
C-STAR
1200E+01
1116E+02
1133E+02
1143E+02
1143E+02
1143E+02
0.
0.
0.
0.
0.
0.
C-ZERO
5000E+00
1935E+01
1186E+01
1122E+01
1122E+01
1122E+01
0,
0,
0.
0.
0.
0,
KLA
PRIME
.1500E+00
.6928E-01
.8733E-01
.8691E-01
.8692E-01
.8692E-01
0.
0.
0.
0.
0.
0.
SUM OF
SQUARES
4893E+02
6109E+01
7795E-01
1617E-01
1617E-01
1617E-01
ESTIMATE OF ERROR FORM RESIDUAL MEAN SQUARE
STANDARD DEVIATIONS
OF PARAMETER ESTIMATES
ABSOLUTE
UNITS 0.1822E-01 0.3769E-01 0.6443E-03
0.03
PER CENT
OF LSE
0.2
3.4
0.7
1
2
3
a.
5
6
7
8
9
10
11
12
13
14
15
16
17
18
SUMMARY OF DATA
TIME CONC FITTED
VALUE
2.77
4.15
5.31
6.29
7.11
7.80
8.37
8.86
9.27
9.61
9.90
10.25
10.67
10.93
11.11
11.22
11.29
11.34
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
22.00
25.00
30.00
35.00
40.00
45.00
50.00
55.00
2.77
4.15
5.35
6.25
7.08
7.80
8.34
8.85
9.28
9.62
9.93
10.24
10.70
11.00
11.14
11.20
11.25
11.30
RESIDUAL
0.00
0.00
0.04
-0.04
-0.03
0.00
-0.03
-0.01
0.01
0.01
0.03
-0.01
0.03
0.07
0.03
-0.02
-0.04
-0.04
267
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APPENDIX B
BASIC NONLINEAR ESTIMATION PROGRAM
This appendix presents the BASIC computer language adaptation of the
FORTRAN nonlinear estimation program discussed in Appendix A. Also given are
examples of output obtained by applying the BASIC program to typical data
sets using an Apple II Microcomputer.
268
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10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
RINT
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
0$ = CRR$ (4)
REM
REM NON-LINEAR LEAST SQUARES PROGRAM IN APPLE II BASIC
REM FOR OXYGEN TRANSFER PARAMETERS
REM OUTPUT SETUP FOR 40 POSITION CRT/MONITOR
TEXT : CALL - 936: REM CLEARS SCREEN
REM
REM ::::::::::::::::::::::
REM STEP 1
REM WRITE TITLES
REM ::::::::::::::::::::::
REM
PRINT '
PRINT '
PRINT '
PRINT '
PRINT '
***************************************"
NON-LINEAR ESTIMATION FOR"
UNSTEADY-STATE OXYGEN TRANSFER"
*************************************** n
BY"
PRINT 'LINFIELD C. BROWN & GEORGE R. FISETTE"
PRINT 'VERSION 1.0-NOVEMBER 11, 1979"
PRINT
INVERSE : PRINT "THE VALUES ARE TRUNCATED": PRINT "AND NOT ROUNDED OFF.
: NORMAL
REM
REM PROGRAM HAS MAXIMUM LIMIT OF 30 DATA POINTS
REF1
DIM C(30),T(30),R30),R(30)
INPUT "IS DATA IN DISK FILE;Y/N?";A$
INPUT "INPUT NAME OF DATE FILL?";N$
IF AS = " " GOTO 650: REM GET DATA FROM DISK FILL
INPUT "DO YOU ANT INPUT DATA SAVED ON DISK,Y/N?";AS
PRINT "INPUT DATA IN TIME,DO DATA PAIRS"
PRINT "INPUT 999,999 AS LAST DATA PAIR"
FOR I = 1 TO 30
INPUT T(I),C(I)
IF T(I) = 999.0 GOTO 360
NEXT I
ND = I - 1.0
INPUT "BEST ESTIMATE FOR C-STAR OR USE 10.0 MG/L?";CS
INPUT "BEST ESTIMATE FOR C-ZERO OR USE 0.0 MG/L?";CO
INPUT "BEST ESTIMATE FOR KLA-PRIME OR USE 4.0 1/HR?";XK
XK = XK / 60.0
IF AS = "N" GOTO 790
REM
REM WRITE DATA TO DISK FILE
REM SPECIFIC FOR APPLE/MICROSOFT BASIC
REM
PRINT D$;"OPEN "N$;" ,VO,L15"
FOR I = 1 to ND
PRINT D$;"WRITE "NS;",BO,R";I
PRINT T(I): PRINT C(I)
NEXT I
PRINT D$;"WRITE "N$;",BO,RO"
PRINT ND
PRINT D$;"WRITE "N$;",BO,R";ND + 1.
PRINT CS
269
-------
550 PRINT D$;"WRITE "N$;",BO,R";ND + 2.
560 PRINT CO
570 PRINT DS;"WRITE "N$;" ,BO,R";ND + 3.
580 PRINT XK
590 PRINT D$;"CLOSE "N$
600 ' GOTO 790
610 REM
620 REM READ DISK FILE FOR DATA
630 REM SPECIFIC FOR APPLE/MICROSOFT BASIC
640 REM
650 PRINT DS;"OPEN "N$;" ,VO,L15"
660 PRINT DS;"READ "NS;",BO,RO"
670 INPUT NO
680 FOR I = 1 TO NO
690 PRINT DS;"READ "NS;",BO,R";I
700 INPUT T(I),C(I)
710 NEXT I
720 PRINT D$:"READ "N$;" ,BO,R";ND + 1.
730 INPUT CS
740 PRINT DS;"READ "N$;" ,BO,R";ND + 2.
750 INPUT CO
760 PRINT DS;"READ "N$;" ,80,R";ND + 3.
770 INPUT XK
780 PRINT D$;"CLOSE "NS
790 PRINT : FLASH : INPUT "HIT RETURN FOR ITERATIONS.";I$: NORMAL
800 CALL 936: PRINT : PRINT " DATA SLT ";NS: PRINT
810 PRINT "ITERATION" TAB( 11}"C-STAR" TAB( 18)"C-ZERO" TAB( 26)"KLA" TAB ( 33)"
SUM OF"
820 PRINT TAB( 2)"NUMBER" TAB( 26)"PRIME" TAB( 33)"SQUARES"
830 PRINT TAB ( 11)"(MG/L)" TAB( 18)"{MG/L)" TAB ( 26)"(1/HR"
840 PRINT
850 REM
860 REM ::::::::::::::::::::::
870 REM STEP 2
880 REM INITIALIZATION OF VARIABLES
890 REM DO ITERATION CALCULATIONS
900 REM ::::::::::::::::::::::
910 REM
920 K% = 0
930 OS = 0.0
940 FOR I = 1 TO ND
950 F(I) = CS - (CS - CO) * EXP ( - XK * T(I))
960 R(I) = C(I) - F(I)
970 OS = OS + R(I) * R(I)
980 NEXT I
990 ZZ$ = STRS (CS) :VA = 5.: GOSUB 2900
1000 CSS = ZZ$:ZZ$ = STRS (CO): GOSUB 2900
1010 COS = ZZS:ZZS = STRS (XK * 60.): GOSUB 2900
1020 XK$ = ZZS:ZZ$ = STRS (OS): GOSUB 2900
1030 OSS = ZZS
1040 PRINT TAB( 4)K% TAB( 10)CS$ TAB( 18)COS TAB( 26)XK$ TAB( 33)OS$
1050 GOTO 1070
1060 REM
1070 REM CALCULATION LOOP - INITILIZE VARIABLES
270
-------
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
i ?in
1 L. 1U
1220
1230
1240
i ?^n
1 £OU
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
i Aan
1H4-U
1450
1460
1470
i/isn
IHOU
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
1600
1610
REM
Kci =
Al =
A2 =
A3 =
A4 =
A5 =
A6 =
Cl =
C2 =
C3 =
SQ =
REM
RFM
r\Lj i
REM
REM
REM
RFM
f\Ll 1
REM
FOR
Z2 =
Zl =
Z3 =
Al =
A2 =
A3 =
A4 =
A5 =
A6 =
F(D
R(D
Cl =
C2 =
C3 =
NEXT
REH
PPM
r\L.rl
REM
REM
REM
RFM
f\dl
REM
Dl =
D2 =
D3 =
D4 =
D5 =
XN =
XD =
X3 =
YN =
X2 =
XI =
REM
K°; + 1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
STEP 3
SETUP NORMAL EQUATIONS FOR LINEARIZED MODEL
USING CURRENT LEAST SQUARE ESTIMATES
I = 1 TO ND
EXP ( - XK * T(I))
1.0 - Z2
T(I) * Z2 * (CS - CO)
Al + Zl * Zl
A2 + Zl Z2
A3 + Zl Z3
A4 + Z2 Z2
A5 + Z2 Z3
A6 + Z3 Z3
= CS - (CS - CO) * Z2
= C(I) - F(I)
Cl + R(I) * Zl
C2 + R(I) * Z2
C3 + R(I) * Z3
I
STEP 4
SOLUTION OF NORMAL EQUATIONS FOR CORRECTIONS
TO THE PRIOR LEAST SQUARES ESTIMATES
Al * A4 - A2 * A2
Al * C3 - A3 * Cl
Al * A5 - A3 * A2
A6 * Al - A3 * A3
Al * C2 - A2 * Cl
Dl * D2 - D3 * D5
Dl * D4 - D3 * D3
XN / XD
D5 - D3 * X3
YN / Dl
(Cl - A2 * X2 - A3 * X3) / Al
271
-------
1620 REK ::::::::::::::::::::::
1630 REM STEP 5
1640 REM UPDATE ESTIMATES, SUM OF SQUARES
1650 REM ::::::::::::::::::::::
1660 REH
1670 Tl - XI + CS
1680 T2 » X2 + CO
1690 T3 » X3 + XK
1700 FOR I • 1 TO NO
1710 F(I) * Tl - (Tl - T2) * EXP ( - T3 * T(I))
1720 R(I) * C(I) - F(I)
1730 SQ » SQ + R(I) * R(I)
1740 NEXT I
1750 SEN
1760 REM ::::::::::::::::::::::
1770 REM STEP 6
1730 REM TEST FOR CONVERGENCE - PARAMETERS 1 PART IN 100,000
1790 REM :::::::::::::::::::::
1800 REM
1810 IF (XI / Tl a 0.00001) AND (X2 / T2 a 0.00001) AND (X3 / T3 BO.00001) GOT
0 2160 .
1820 RBI
1830 REM PARAMETERS NOT CONVERGED,
1840 REM TEST SUM OF SQUARES - 1 PART IN 1,000,000
1850 REM
1860 IF ABS ((OS - SQ) / SQ) a 0.000001 GOTO 2160
1870 REM
1880 REM SUM OF SQUARES NOT CONVERGED,
1890 REM TEST flO. OF ITERATIONS
1900 REM
1910 IF (KS > 10) GOTO 2090
1920 ZZS » STRS (Tl) : GOSU8 2900
1930 T1S - ZZS:ZZS « STRS (T2) : GOSU8 2900
1940 T2S » ZZS:ZZS • STRS (T3 * 60.): GOSUB 2900
1950 T3$ * ZZS:ZZS - STRS (SQ) : GOSUB 2900
1960 SQ$ * ZZS
1970 PRINT TA8( 4)KS TAB( 10)T1S TAB( 18)T2S TAB( 26)T3S TAB( 33)SQS
1980 REfl
1990 REM NEW ESTIMATES
200Q REM
2010 CS * Tl
2020 CO » T2
2030 XK * T3
2040 OS * SQ
2050 GOTO 1090
2060 REM
2070 REM OUTPUTS
2080 REM
2090 PRINT
2100 PRINT "SOLUTION NOT CONVERGED IN 10 ITERATIONS'"
2110 PRINT "CHANGE VALUE IN LINE 2670 to TRY MORE ITERATIONS."
2120 END
2130 REM
2140 REM OUTPUT PARAMETER ESTIMATES
272
-------
2150 REM
2160 ZZS = SIRS (Tl): GOSUB 2900
2170 Tl$ = ZZ$:ZZS = SIRS (T2): GOSUB 2900
2180 T2$ = ZZ$:ZZ$ = SIRS (T3 * 60.): SOSUB 2900
2190 T3S = ZZS:ZZS = SIRS (SQ): GOSUB 2900
2200 SQS = ZZ$
2210 PRINT TAB( 4)K% TAB( 10)T1$ TAB( 18}T2$ TAB( 26)T3S TAB( 33)SQ$
2220 PRINT
2230 REM
2240 REM ::::::::::::::::::::::
2250 REM STEP 7
2260 REM COMPUTE STANDARD DEVIATIONS OF PARAMETER ESTIMATES
2270 REM ::::::::::::::::::::::
2280 REM
2290 XF = ND - 3.0
2300 RS = SQ / XF
2310 BR = SQR (RS)
2320 PRINT "STD DEVIATIONS OF PARAMETER ESTIMATES"
2330 PRINT
2340 DP = Al * A4 * A6 + 2.0 * A2 * A3 * A5
2350 DN = Al * A5 * A5 + A4 * A3 * A3 + A6 * A2 * A2
2360 DT = DP - DN
2370 Fl = A4 * A6 - A5 * A5
2380 F2 = Al * A6 - A3 * A3
2390 F3 = Al * A4 - A2 * A2
2400 VI = (Fl / DT) * RS
2410 V2 = (F2 / DT) * RS
2420 V3 = (F3 / DT) * RS
2430 SI = SQR (VI)
2440 S2 = SQR (V2)
2450 S3 = SQR (V3)
2460 ZZS = STRS (S1):VA = 5.: GOSUB 2900
2470 SIS = ZZS'.ZZS = STRS (S2)< GOSUB 2900
2480 S2S = ZZS:ZZS = STRS (S3 * 60.): GOSUB 2900
2490 S3S = ZZS
2500 PRINT " UNITS" TAB( 10)51$ TAB( 18)52$ TAB( 26)S3$
2510 SI = SI / CS * 100.0
2520 S2 = S2 / CO * 100.0
2530 S3 = S3 / XK * 100.0
2540 ZZS = STRS (S1):VA = 3.: GOSUB 2900
2550 SIS = ZZ$:ZZS = STR$ (52): GOSUB 2900
2560 S2$ = ZZS:ZZ$ = STRS (s3): GOSUB 2900
2570 S3S = ZZS
2580 PRINT "% OF LSE" TAB( 10)51$ TAB( 18)52$ TAB( 26)S3$
2590 PRINT
2600 ZZS = STRS (ER):VA = 4.: GOSUB 2900
2610 ERS = ZZS
2620 PRINT "ESTIMATE OF ERROR = ";FR$
2630 REM
2640 REM ::::::::::::::::::::::
2650 REH STEP 8
2660 REM WRITE SUMMARY
2670 REM I:::::::::::::::::::::
2680 REM
2690 PRINT
2700 FLASH : INPUT "HIT RETURN FOR SUMMARY OF DATA.«;I$: NORMAL
273
-------
2710 CALL - 936: PRINT : PRINT : REM CLEARS SCREEN
2720 PRINT TAB( 13)"SUMMARY OF DATA"
2730 PRINT : PRINT
2740 PRINT TAB( 8)"TIME" TAB( 16)"CONC" TAB( 22)"FIT VALUE" TAB( 32)"RESIDUAL"
2750 PRINT TAB( 8)"(MIN}" TAB( 15)"(MG/L)" TAB( Z3)"MG/L"
2760 PRINT
2770 FOR I = 1 TO ND
2780 ZZ$ = STRS (F(I)):VA = 4.: GOSUB 2900
2790 HIS = ZZ$:ZZ$ = STRS (R(I)): GOSUB 2900
2800 H2$ = ZZ$
2810 PRINT TAB( 2)1 TAB( 8)T(I) TAB( 16)C(I) TAB( 25)H1$ TAB( 33)H2$
2820 NEXT I
2830 PRINT : PRINT
2840 PRINT "***************************************"
2850 END
2860 REM
2870 REM OUTPUT FORMATTING ROUTINES
2880 REM SPECIFIC FOR APPLE/MICROSOFT BASIC
2890 REM
2900 LL = LEN (ZZS)
2910 IF LL«=12 THEN ZZS = LEFTS (ZZ$,VA): RETURN
2920 IF MIDS (ZZS.LL - 2,1) = "+" THEN ZZS = LEFTS (ZZ$,VA - 3) + RIGHTS (ZZ
S3): RETURN
2930 CC = 2.: IF LEFTS (ZZS.l) - "-" THEN CC = 1.
2940 IF MIDS (ZZS.LL - 3,1) = "R" THEN RL = VAL (RIGHTS (ZZS,2)):NNS = MIDS
(ZZ$,CC,1): FOR J = 1 TO BE:NN$ = "0" + NN$:: NEXT J:ZZS = "." NN$ + MIDS (Z
ZS,CC + 2,LL - 4): IF CC = 2. THEN ZZS = "-" + ZZS
2950 ZZS = LEFTS (ZZ$,VA): RETURN
2960 REM
2970 REM NON-LINEAR LEAST SQUARES PROGRAM FOR
2980 REM UNSTEADY-STATE OXYGEN TRANSFER
2990 REM LY LINFIELD C. BROWN & GEORGE R. FISETTE
3000 REM VERSION 1.0-NOVEMBER 11, 1979
3010 REM COPYRIGHT BY ASCE
274
-------
RUN
*******************************************************************************
NON-LINEAR ESTIMATION FOR UNSTEADY-STATE OXYGEN TRANSFER
*******************************************************************************
BY
LINFIELD C. BROWN & GEORGE R. FISETTE
VERSION 1.0-NOVEMBER 11, 1979
IS DATA IN DISK FILE; Y/NPY
INPUT NAME OF DATA FILE7TEST2
ITERATION
NUMBER
0
1
2
3
C-STAR
10
10.1592458
10.1889055
10.1893432
DATA SET TEST2
C-ZERO
.1
.713872799
.694460338
.694630637
KLA
PRIME
.07
.0601645437
.0603440105
.0603354201
SUM OF
SQUARES
.869733335
.189522011
.185289531
.185289365
STANDARD DEVIATIONS OF PARAMETER ESTIMATES
ABSOLUTE UNITS .195594007
PERCENT OF LSE 1.91967633
.111803446
16.0993277
3.18746727E-03
5.28216013
ESTIMATE OF ERROR = .152187945
SUMMARY OF DATA
1
2
3
4
5
6
7
8
9
10
11
TIME
.77
1.75
2.67
5.08
7.77
10.65
13.3
17.88
23.4
34.52
49.13
CONC
1.25
1.75
05
.1
.25
.85
.1
8.1
8.9
9.65
FIT VALUE
1.12564889
1.64603691
2.10734213
3.20108643
4.24803791
5.19571448
5.93358056
6.96110108
7.87555468
9.00645823
9.69943839
@ RESIDUAL
.124351112
.103963087
-.0573421288
-.201086428
-.148037907
.0542855244
-.0835805573
.138898922
.224445321
-.106458228
-.0494383909
********************************************************************************
275
-------
APPENDIX C
ALPHA-BETA TEST PROCEDURE
EQUIPMENT AND CHEMICALS
Equipment
Test Apparatus --
The required test apparatus consists of two non-metallic tanks each with
a liquid capacity of 35 gal, 18 in. in diameter by 48 in. high; two air flow
meters equal to Dwyer Model RMC-102-SSV (10-100 scfh); two air spargers with
four 1/8-in. orifices (spargers may be constructed of 1/2-in. stainless steel
pipe); plastic tubing for air piping; and an air supply source. A schematic
of the test apparatus is presented in Figure C-l.
DO Apparatus --
Fast response DO probes and a DO analyzer, such as Weston & Stack Model
3000 S6A analyzer with Model 60 DO probes and Model 18 agitator, are required.
DO may also be determined using the Azide Modified Winkler procedure.
Wet Chemistry Apparatus --
All necessary laboratory equipment for DO, pH, and temperature determina-
tions of grab samples taken from the aeration tanks shall be provided.
Water Supply
Tap Water --
An approved drinking water source that has no surface active chemical
interference present shall be provided.
Wastewater --
Settled supernatant from the activated sludge mixed liquor shall be
obtained or, if this is not available, settled composited raw wastewater is
276
-------
ro
AIR IN
B
A DISTILLED WATER TANK (PLASTIO.35-GALLON CAPACITY
B TEST WATER TANK (PLASTIC), 35-GALLON CAPACITY
C DUPLICATE FLOW METERS
D PRESSURE REGULATOR
E PRESSURE GUAGE
F PLASTIC TUBING
Figure C-l. Schematic of alpha test apparatus.
-------
the second choice.
Reaeration Test Water --
The reaeration test water shall be a representative sample of the fluid
to be aerated.
Chemicals
Cobalt Chloride Hexahydrate --
Technical grade or better CoCl2-6H20 shall be provided. Prepare the
stock solution by adding 15.2 g of CoCl2'6H20 to 1 I of water. The addition
of a 12.5-ml aliquot of this solution to 25 gal of test water will yield a
cobalt ion concentration of 0.5 mg/£.
Sodium Sulfite --
Technical grade, cobalt free, or better Na2SO- shall be provided.
Prepare the stock solution by dissolving 200 g of Na2SO~ in 1 £ of water.
The amount of sodium sulfite solution required is calculated as follows:
fi nn 4. °i FY!
ml of solution required = (4.65)(C*) -|QQ (Cl)
where:
C* = DO saturation concentration in the test tank in mg/£
% EX = excess amount of chemical (above the stoichiometric requirement)
to be used. % EX ranges from 10 to 25 percent, depending on
testing requirements.
Sulfuric Acid --
Technical grade or better H2SO. shall be provided. Add as required to
neutralize the water in each tank.
Sodium Hydroxide --
Technical grade or better NaOH shall be provided. Add as required to
neutralize the water in each tank.
Reagents for Azide Modified Winkler Analysis --
Use premeasured reagents, such as sold by Hach Chemical Company.
278
-------
DATA MEASUREMENTS AND RECORDING
Probe Calibration and Interference Determination
Probes shall be calibrated against the results of the Azide Modified
Winkler procedure before the start of each test. Three water samples shall
be taken from the aeration tanks after the oxygen saturation concentration
has been reached. Only pH adjustment chemicals shall have been added to the
test water up to this point. The DO probes shall be adjusted as necessary to
within + 0.1 mg/£ of the average Winkler value.
Cobalt chloride interference shall be determined by a "blank correction"
for each Winkler test. The "blank correction" sample shall be titrated using
the standard Winkler procedure except manganous sulfate shall not be added to
the sample. Any apparent DO titrated is the interference caused by cobalt
oxide reacting with iodide to form iodine. The "blank correction" shall be
subtracted from all DO measurements made during the test.
Cobalt chloride shall then be added to the test water and mixed. A
second set of three samples shall be taken and Winkler DO analyses performed.
If any cobalt chloride interference is present in the Winkler procedure, it
shall be noted at this time.
At the end of each test, a set of three additional samples shall be
taken and Winkler DO analyses performed. Test results shall then be compared
with probe values for verification of the terminal saturation concentration.
In the event that DO probes are not used, samples shall be taken from
each tank and analyzed for DO concentration by the Azide Modified Winkler
procedure.
Sample Location and Pmcedure
The sample location shall be at the mid-depth of the test tank, half way
between the aeration device and tank side wall. DO probes shall be placed at
this location, and sample tubes for Winkler analysis shall also be placed at
this location.
Samples for Winkler analysis shall be siphoned into the bottom of a
300-ml BOD bottle. Sample water flow to the BOD bottle shall continue until
the BOD bottle has overflowed at least twice to ensure that oxygenation of
the sample has not occurred during the filling of the BOD bottle.
279
-------
DO Measurements
\
DO shall be measured and recorded continuously throughout the test if a
recorder is available. The test recorder strip chart shall serve as the raw
experimental data base from which K. a and C* are determined.
If samples are taken for Winkler analysis or for remote DO probe reading,
the sampling frequency shall be not greater than 5 min between collections
per tank. The following sampling sequence is suggested:
Sample Point Tap Water Waste or Test
Number Time (min) Water Time (min)
1 5 6
2 10 11
3 15 16
4 20 21
5 25 26
6 30 31
7 35 36
8 40 41
9 45 46
10 50 51
11 55 56
12 60 61
13 65 66
14 70 71
Seventy min should be sufficient time to acquire enough data to deter-
mine K. a for each water sample at the end of the test. However, the test tap
water should be approximately 95 percent saturated. If this does not occur
within 70 min, sampling should be continued until this saturation level is
achieved. The testing shall then be continued until saturation of the tap
water has occurred, at which time samples shall be taken from each tank for
the beta factor determination.
Air Flow Measurements
The air flow rate shall be noted and recorded at the start of the test,
after every 10 min,and at the end of the test.
The degree of mixing and aeration in the tap water test tank should be
adjusted so that the test will yield essentially the same KLa as in the full-
scale design at standard test conditions. Use of the same KLa values gives
the same degree of tank turbulence for aeration in both the laboratory unit
280
-------
and in the design unit. Under these conditions, the alpha value will be
close to that in the design unit.
A number of aeration tests with varying air flow should be conducted on
the tap water sample to determine the relationship between air flow rate and
K.a. Once this relationship is established, the proper air flow can be
selected that will duplicate KLa in the tap water laboratory test and KLa in
the full-scale design. The alpha and beta tests shall be conducted at this
predetermined air flow rate.
TESTING SEQUENCE
Neutralize biological activity of the wastewater sample by autoclaving or
disinfection. Filter the wastewater sample if necessary.
Fill each tank with 25 gal of sample. Keep the temperature constant at
the wastewater or test water value. Turn on the air supply, and set the air
flow rates equal to a predetermined value for duplicating K.a in the tap water
tank and K,a in the full-scale design at standard conditions.
Check the pH of each water sample and adjust to pH 7.0 ± 0.2 as required.
Aerate the samples until saturation has been reached; C* should be con-
stant' (± 0.1 mg/£) for at least 15 min when DO probes are used. When DO
probes are not used, the samples should be aerated to the handbook saturation
value, adjusted for temperature and pressure at test conditions.
Take samples for Winkler analysis, DO probe calibration, and "blank
correction".
Add cobalt chloride to the test tanks and mix thoroughly.
Take samples for Winkler analysis and "blank correction".
Calculate the amount of sodium sulfite required, based on percent excess
solution to be used and C*.
CO
Check the air flow rate to each tank and adjust if necessary; take air
flow readings for the beginning of the test.
Simultaneously add the sodium sulfite solution to each tank.
Take samples in accordance with the previously defined technique.
Continue sampling for at least 70 min or until 95 percent saturation has
been achieved in the tap water tank.
Continue aeration until saturation has again been reached in the test
tanks, take samples for beta factor determinations, and check and record the
281
-------
air flow rate to each tank.
EVALUATION OF TEST DATA
Determination of the Alpha Factor
Alpha is the ratio of K.a of the wastewater sample to K. a of the tap
water sample:
alpha = K|_a (wastewater )/K. a(tap water) (C2)
Determination of K.a
K.a should be calculated using the method presented in Section 4.
Temperature Correction
KLa at the test temperature, K.a,., shall be corrected to standard condi-
tions (20°C) by use of the following equation:
KLa20 = KLaT/1
Determination of the Beta Factor
Beta is the ratio of C* of the wastewater sample to C* of the tap water:
beta = C*(wastewater)/C*(tap water) (C4)
282
-------
APPENDIX D
DETERMINATION OF OXYGEN UPTAKE RATES
FOR A CONTINUOUS SYSTEM
The rate of oxygen uptake of a continuously-fed mixed liquor begins
changing as soon as the sample is removed from the aeration basin for testing.
For this reason, the oxygen uptake rate must be determined as quickly as
possible. The testing should be performed as near the aeration basin as
feasible to avoid time delays. The required steps for the determination are
given below:
1. Remove a sample of mixed liquor from the aeration basin. Note the
time the sample was taken as time zero.
2. Quickly aerate the sample by shaking vigorously or bubbling air or
oxygen through the sample. If the initial DO level of the sample is
sufficient (4 to 6 mg/£), perform the test on the sample so as to
avoid reaeration of the sample.
3. Place the sample in a flask or BOD bottle. Immediately begin moni-
toring the'decline in DO at regular time increments, 0.25 to 1.0 min
intervals, depending on the oxygen uptake rate of the sample. The
time data must be related to the zero time noted earlier.
4. When the oxygen content of the sample approaches 1 mg/£, discontinue
DO monitoring'and quickly reaerate the sample as before. Resume
monitoring the decline in DO with time, continuing the time notations
from time zero. Measure the sample temperature at the beginning and
end of each test.
5. Repeat Step 4 until the endogenous respiration rate has been
established, i.e., when the rate remains relatively constant for
successive determinations. Repeat Steps 1 through 5 at least twice
to enhance the validity of the data. Replicate tests should be per-
formed on samples taken from the same point in the aeration volume.
283
-------
6. Calculate the oxygen uptake rate for each set of oxygen readings and
plot them against time on semi-logarithmic graph paper as shown in
Figure D-l. The linear portion of the curve, representing oxygen
uptake as a result of endogenous respiration, is extended to time
zero. The value of oxygen uptake at time zero represents the en-
dogenous respiration rate of the mixed liquor in the aeration basin.
In the example indicated in Figure D-l, this value is 33 mg/£/hr.
g (40-40-
(33) —
«v
o>
E
UJ
5
tr
UJ
a,
ID
UJ
X
o
LEGEND
O TEST NO. 1
A TEST NO. 2
0 TEST NO. 3
i—SYNTHESIS RESPIRATION RATE
0 10 20 30 40 50 60 70 80 90 100
TIME (min)
Figure D-l. Estimation of oxygen uptake rate.
284
-------
7. Subtract the oxygen uptake due to endogenous respiration from the
data points on the curved portion of the plot, and plot these differ-
ences against their respective time values as indicated in
Figure D-l. This line represents oxygen uptake resulting from
synthesis. Extension of the line to time zero results in the synthe-
sis oxygen uptake of the mixed liquor in the aeration basin. In the
example of Figure D-l, this value is 41 mg/£/hr.
8. Add the endogenous respiration and synthesis oxygen uptake values
together to determine the total oxygen uptake rate of the mixed
liquor in the aeration basin. In the example of Figure D-l, this
value is 74 mg/£/hr.
9. If the average temperature of the sample during testing is different
from that of the mixed liquor in the aeration basin, the resulting
value for R should be corrected to the mixed liquor temperature by
Note that the synthesis respiration rate at time zero, determined
according to Step 7, is double the highest value determined by subtracting the
endogenous uptake rate from the total oxygen uptake rate (t = 3 min). The
possible errors in such a procedure necessitate that the results be considered
no more than an estimate of the actual oxygen uptake rate in the aeration
basin.
285
-------
APPENDIX E
BATCH DESORPTION TESTING - PEROXIDE ADDITION DETAILS
DIFFUSED AERATION
Peroxide should be added simultaneously at points along the tank at a
distance about equal to the tank width, but with not less than one addition
2
point for each 250 to 300 ft of tank surface (Figure E-l). The release
points should be at mid-depth for spiral flow aeration systems and close to
the bottom for systems where the aerators are evenly distributed over the
tank bottom.
SURFACE AERATION AND TURBINE AERATION (FIGURE E-2)
Peroxide should be injected simultaneously at points located half the
distance between the wall and aerator and between aerators (Figure E-2). At
p
least one injection point for each 250 to 300 ft of tank surface is recom-
mended.
BRUSH AERATORS
Measure the flow velocity and calculate the flow time from one rotor to
the next. The period of peroxide injection should approximate the flow time.
The peroxide should be injected close to the bottom and at mid-width of the
tank (Figure E-3).
286
-------
DIFFUSERS
W
MID-DEPTH INJECTION
-—w
W
rv>
oo
BOTTOM
INJECTION
250—" 300 sq ft
Figure E-l. Diffused aeration —peroxide addition locations
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ro
CO
CO
D
MID-DEPTH
INJECTION POINT
Figure E-2. Surface or turbine aeration - peroxide addition locations.
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-*• V = I ft/sec
/ *
H202 INJECTION*--^ VDO PROBE
ft
VS|-2 ft/sec
D 0 PROBES7 ^- H202 INJECTION
'NOTE' SLOW BOTTOM INJECTION UNTIL DO PROBE
SHOWS INCREASE
Figure E-3. Brush aerators in extended aeration oxidation ditches
peroxide addition locations.
289
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APPENDIX F
INDIVIDUAL SAMPLE POINT ANALYSIS
The clean water reaeration test can be used to evaluate DO dispersion.
Data from each point are analyzed to evaluate the local uptake rate. Using
the equation:
f=KLa(C*-C) (Fl)
a nonlinear curve fit is used to estimate the values for K. a and C*. The
L °°
values are corrected to standard conditions and are identified as K,a2Q and
C*2Q. The procedures for this analysis are detailed in Section 4. The
product of these terms is the uptake at zero DO.
To demonstrate the evaluation procedure, test results for three aeration
systems are presented (Tables F-l, F-2 and F-3). Each test includes three
replicate runs with six sample points. These tables also illustrate the
types of limits associated with data reproducibility for the reaeration test.
For the high uptake system, samples were collected every minute during
the initial period. For some tests, this time is reduced to 45 or 30 sec.
Thus, a split-second delay in sample reading causes measurable variation.
The coefficient of variation, CV, for all the data was 9.4 percent. Dis-
carding the three highest and three lowest values (one-third the data) changed
the mean uptake rate by only 0.3 percent. CV, however, was reduced by one-
third to 6.2 percent.
The standard uptake system (Table F-2) produced the most consistent data.
The sample times were spaced 3 min apart. A slight error in timing the
sample is not as critical as with the high uptake system. Using all the data,
CV was only 5.4 percent. Excluding the three highest and three lowest values
reduced CV to 3.4 percent. Once again, there was no significant change in
the mean uptake rate.
290
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TABLE F-l. HIGH UPTAKE SYSTEM
Run
1
2
3
A
90.0
81.4
74.7
dC/dt at
82
96
87
zero DO in
B
.8
.1 1
.5
mg/£/hr
85
00
86
C
.3
.1
.8
for
1
Indicated
D
80.7
04.2
92.3
Sample
E
83.
100.
96.
Points
5
8
5
F
77.1
85.7
96.3
Con si
dering all
data points
:
Discarding three highest and
three lowest data points:
TABLE F-2.
Avg.
CV =
Avg.
CV =
dC/dt = 89.0 ±
9.4 percent
dC/dt = 88.7 ±
6.2 percent
STANDARD
8.5 mg/£/hr
5.5 mg/£/hr
UPTAKE SYSTEM
Run
1
2
3
A
38.0
38.5
39.9
dC/dt at
37
40
39
zero DO in
B
.3
.6
.1
mg/£/hr
38
41
41
C
.7
.2
.2
for
Indicated
D
39.7
44.7
41.0
Sample
E
39.
43.
44.
Points
1
0
5
F
42.3
43.8
42.0
Considering all data points:
Discarding three highest and
three lowest data points:
TABLE F-
3.
Avg.
CV =
Avg.
CV =
LOW
dC/dt = 40.8 ±
5.4 percent
dC/dt = 40.7 ±
3.4 percent
2.2 mg/£/hr
1.4 mg/£/hr
UPTAKE SYSTEM
Run
1
2
3
A
7.4
6.5
7.0
dC/dt at
zero DO in
B
8.4
7
6
.4
.2
mg/£/hr
6
6
6
C
.3
.9
.5
for
Indicated
D
7.4
5.8
8.3
Sample
E
6.
7.
6.
Points
8
2
2
F
8.1
6.5
6.9
Considering all data points: Avg. dC/dt = 7.0 ±0.7 mg/£/hr
CV = 10 percent
Discarding three highest and
three lowest data points: Avg. dC/dt = 6.9 ± 0.4 mg/£/hr
CV = 6 percent
291
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The low uptake system (Table F-3) exhibited the impact of data precision.
The uptake in mg/£/hr has only one significant digit to the right of the deci-
mal point. Hence, scatter is introduced by the limits of the ability to dis-
tinguish the numerical value for the uptake rate. For extremely low uptake
rates, this factor would control data variation. For the test reported in
Table F-3, CV was 10 percent. Elimination of the three highest and .three
lowest values reduced CV to 6 percent.
Using these analysis procedures, all of the tests demonstrated adequate
mixing. No single uptake rate value was consistently higher or lower than
the mean value. The observed variations, point to point and run to run, were
within the prescribed limits.
DO gradients are not a good indicator of mixing. For the reaeration
test, DO gradients are directly proportional to the uptake rate and inversely
proportional to the aerator pumping rate. For the example of Table F-l
(high uptake system), the gradients at the start of the test were quite
severe. As an example, the gradients between sample points B and F were
typically 1.0 to 1.5 mg/£. Yet for the three tests, the average uptake rates
at these points were within 3 percent of one another. The gradients were
progressively less severe for the lower uptake systems.
292 *us GOVERNMENT PRINTING OFFICE 1983- 759-102/0775
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