&EPA
United States
Environmental Protection
Agency
Municipal Environmental Research EPA-600/2-78-141
Laboratory August 1978
Cincinnati OH 45268
Research and Development
Sludge Dewatering
and Drying
on Sand Beds
-------
RESEARCH REPORTING SERIES
Research reports of the Oftice of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document ts available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
-------
EPA-600/2-78-141
August 1978
SLUDGE DEWATERING AND DRYING ON SAND BEDS
by
Donald Dean Adrian
Environmental Engineering Program
Department of Civil Engineering
University of Massachusetts/Amherst
Amherst, Massachusetts 01003
Grant No. WP 01239/17070 DZS
Project Officers
James E. Smith, Jr.
Roland V. Villiers
Ultimate Disposal Section
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
-------
DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, Cincinnati, Ohio, U. S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the contents
necessarily reflect the views, and policies of the U. S. Environmental
Protection Agency, nor does the mention of trade names or commercial products
constitute endorsement or recommendation for use.
11
-------
FOREWORD
The Environmental Protection Agency was created because of increasing
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 testimony to the deterioration of our natural environment.
The complexity of that environment and the interplay between its components
require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem
solution and it involves defining the problem, measuring its impact, and
searching for solutions. The Municipal Environmental Research Laboratory
develops new and improved technology and systems for the prevention, treat-
ment, and management of wastewater and solid and hazardous waste pollutant
discharges from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and to minimize the adverse
economic, social, health, and aesthetic effects of pollution. This publi-
cation is one of the products of that research; a most vital communications
link between the researcher and the user community.
This report summarizes the results of water and wastewater treatment
sludge dewatering studies in which a computer simulation procedure is
developed to investigate sludge dewatering time and to optimize the size of
sand beds. Such a procedure provides a useful means by which water pollution
control agencies may realize greater efficiencies in their efforts to protect
the environment.
Francis T. Mayo
Director
Municipal Environmental
Research Laboratory
-------
ABSTRACT
The research program presented in this report was developed to examine
sludge dewatering through both theoretical and experimental work. Its
various components include formulation of mathematical models for sludge
drainage and drying on sand beds, preparation of input data for mathematical
models, validation of simulation experiments, and analysis of the outputs
generated by simulation so as to prescribe an optimum system design.
Drainage and drying studies were conducted under controlled conditions
on a variety of sludges. In some cases water content profiles of sludge
cakes and supporting sand layers were determined by a gamma-ray attenuation
method. Chemical analyses were performed on sludge, filtrate and decant
samples.
A theoretical analysis of gravity dewatering of wastewater sludge is
presented, and an equation describing the drainage rate developed. The
equation relates the depth of sludge with time, using the parameters of
solids content, specific resistance, coefficient of compressibility, dynamic
viscosity and density of the filtrate. Extensive bench-scale tests sub-
stantiated the theory. The concept of media factor is introduced to account
for the role of the supporting media. Potential applications of the equation
are discussed.
Computer simulation studies were conducted of water and wastewater
treatment sludges. The output of this 20-year simulation under six weather
conditions is a random variable, the required dewatering time, and its asso-
ciated frequency distribution. Of the parameters describing sludge charac-
teristics, solids content had the most important effect on dewatering time
and in most cases dominated the effects of specific resistance.
Economic analyses were applied to the outputs of simulation for
finding an optimum system design. Two different approaches were used: the
first finds an optimum design that fulfills the target output at a minimum
cost among known alternatives; the second uses the concept of marginal
analysis to assign a cash value to the end product (dry solids) of the de-
watering process, resulting in an optimum design obtained at the point where
the cost of inputs (land and operation) is just equal to the marginal value
of output.
The criteria developed may be used by an engineer to design beds on
the basis of climatic conditions and the nature of sludge to be dewatered,
while assuring that the system will be economically efficient.
IV
-------
This report was submitted in fulfillment of Grant No. WP 01239/17070 DZS
by the Department of Civil Engineering, University of Massachusetts at
Amherst, under the sponsorship of the U. S, Environmental Protection Agency.
The report covers a period from June 1, 1967 to April 1, 1977. Experimental
work was completed as of June 30, 1972.
-------
CONTENTS
Foreword iii
Abstract iv
Figures ix
Tables xiv
Acknowledgments xvii
I. Introduction 1
References 4
II. Conclusions and Recommendations 5
Conclusions 5
Recommendations 6
III. Review of the Literature . 8
References 19
IV. Theoretical Considerations 20
Moisture 20
Derivation of specific resistance. .... 21
Derivation of mathematical model for the gravity
drainage rate 29
Evaporation of water 33
Drying 35
Diffusion of moisture 38
Drying rate 41
Critical moisture content 43
References 46
V. Materials and Apparatus 49
Types of sludge examined 49
Equipment for the gravity drainage study 50
Equipment for drying, evaporation and complex dewatering
studies 50
Moisture measurement apparatus . 53
Scintillation counting equipment 53
References 57
VI. Methodology 58
Sludge characteristics ..... 58
Gravity drainage study 58
Evaporation and drying studies 60
Complex sludge dewatering studies 62
Moisture profile 63
Diffusion 69
Discussion of the method 70
Discussion of the results 72
References 78
vn
-------
VII. Results 81
Chemical characteristics ^'
Results of the gravity drainage study 86
Results of the evaporation and drying studies ^4
Results of drying 98
Results of the complex sludge dewatering studies 105
Moisture and solids profile H3
References 121
VIII. The Effect of Rainfall on Sludge Dewatering on Sand Beds 122
The effect of rainfall on drying 131
References 136
IX. Simulation of Dewatering on Sand Beds 137
Scope of the simulation 137
Estimation of the simulation sample size 140
Simulation procedure 141
Verification of simulation 142
Output of simulation 143
References ..... 147
X. Performance of Sand Drying Beds 148
An application of statistical decision theory 148
Performance index 150
References 151
XI. Economic Analysis for Sludge Dewatering on Sand Beds 152
Introduction 152
Simulation approach 152
Marginal analysis approach 158
References , 168
Appendix: Experimental Determination of Specific Resistance and
Coefficient of Compressibility 169
Equipment 169
Laboratory procedures. , 172
Data analysis 174
Calculation of specific resistance 174
Calculation of coefficient of compressibility 176
vm
-------
FIGURES
Number Page
1 Loading rate of wastewater sludge at various treatment
plants in the United States 10
2 A plot of Haseltine's data of net bed loading versus
initial solids content 10
3 A comparison of a typical soil permeameter to Jeffrey's
drainometer 13
4 Jeffrey's drainage data 14
O
5 A plot of sludge moisture content w versus (w/100) /(l-w/100)
showing that K/L is not constant with a change in moisture
content 15
6 The Swanwick relationship of bed loading to specific
resistance 16
7 A plot of data accumulated by Logsdon and Jeffrey with
dewatering time by gravity versus dewatering time using
a vacuum 16
8 Illustration of use of a graphical calculator for predicting
time required to dewater sludge on sand drying beds 18
9 Relationship of relative humidity versus moisture content. . . 22
10 Definition sketch for a stratified filter 25
11 Schematic representation of filtration of a compressible
material on a porous medium 26
12 A typical graph used to determine the specific resistance of
a wastewater sludge at three different vacuums 28
13 Schematic representation of the different terms used in
derivation of the mathematical model 29
14 Lake evaporation relation 36
-------
Number Page,
15 Mean annual evaporation (inches) from shallow lakes and
reservoirs 37
16 Drying rate curves for various substances 39
17 Sludge drying relationships, various parameters 41
18 Moisture content versus slab thickness 44
19 Gravity drainage apparatus with piezometer tubes 51
20 Diagram of environmental chamber 52
21 Schematic diagram of gamma-ray attenuation system 55
22 Diagram of source shielding and collimation 56
23 Attenuation relations used in moisture profile measurements. . 64
24 Results obtained from specific resistance tests at each of a
range of pressures. (Performed with the same sludge sample
at constant temperaturee.) 71
25 Effect of conditioner dosage on digested sludge from Amherst . 77
26 Effect of conditioner dosage on digested sludge from
Pittsfield 77
27 Experiment IV, triplicate tests with 20 cm of sludge on
Franklin sand 91
28 Experiment IV, triplicate tests with 20 cm of sludge on
Ottawa sand , 91
29 Experiment IV, triplicate tests with 20 cm of sludge on
Hermitage sand , . 92
30 Experiment V, 11 cm of sludge applied on three different sands 92
31 Experiment V, 41 cm of sludge applied on three different sands 93
32 Experiment V, 81 cm of sludge applied on three different sands 93
33 Location of containers in evaporation study 95
34 Sample mass versus time for Bill erica sludge drying at 22° C
(72° F) and 38% relative humidity 97
-------
Number Page
35 Drying rate curves for Bill erica sludge drying at 22° C
(72 F) and 38% relative humidity 98
36 Four types of water treatment sludge at various solids
contents 99
37 Sample mass versus time curves for sludges (D-3) drying at
24° C (75° F) and 60% relative humidity 101
38 Sample mass versus time curves for sludges (D-3) drying at
24° C (75° F) and 60% relative humidity 101
39 Drying rate curves for sludges (D-3) drying at 24° C (75° F)
and 60% relative humidity 104
40 Drying rate curves for sludges (D-3) drying at 24° C (75° F)
and 60% relative humidity 104
41 Sample mass versus time curves for Albany sludge dewatering
at 24° C (75° F) and 46% relative humidity 106
42 Change in depth of Albany sludge dewatering at 24° C (75° F)
and 46% relative humidity 106
43 Sample mass versus time curves for drying period of dewater-
ing study DW-2 108
44 Cumulative volume of filtrate versus time for Albany sludge
dewatering on Ottawa sand (DW-2) 109
45 Drainage curves for 45.7 cm of Albany sludge (DW-2) dewater-
ing on Ottawa sand Ill
46 Sample mass versus time curves for sludges (DW-3) dewatering
at 24° C (75° F) and 35% relative humidity Ill
47 Sample mass versus time for sludges (DW-3) dewatering at
24° C (75° F) and 35% relative humidity 112
48 Drainage curves for 30.8 cm of sludge (DW-3) dewatering on
Ottawa sand 113
49 Energy spectrum for 250 millicuries Cs-137 source 116
50 Variation of the ratio N/N with thickness of water
at 0.661 Mev 7 116
51 Profile of water content in sand layers (DW03) after
drainage terminated 117
xi
-------
Number
52 Profiles of water content in sand layers for dewatering
study DW-3 ......................... 117
53 Profiles of water content in sand layers (DW-3) after
drainage terminated ..................... ^8
54 Variation of solids content with depth for Billerica sludge. 119
55 Error analysis ....................... H9
56 Variation of solids profiles with time for Albany sludge
(DW-3) drying on Ottawa sand ................ 120
57 Variation of solids profile with time for Billerica sludge
(DW-3) drying on Ottawa sand ................ 121
58 Definition sketch of mixing drainage ............ 123
59 Definition sketch of ponding drainage ............ 128
60 Comparison between mixing and ponding models ........ 130
61 Comparison between mixing drainage model and experimental
data ............................ 131
62 Sample operation of drainage and drying models ....... 142
63 An input/output relation showing the law of diminishing
returns ........................... 160
64 Determination of the optimum input and output ........ 162
65 Iso-quant curve showing five different combinations of An
and Ar which yield a constant output of 95% performance
index ............................ 164
66 Curves of i so-cost lines .................. 165
67 Diagram illustrating procedure for locating the points of
optimum proportions ..................... 166
A-l Vacuum adaptor ....................... 169
A-2a Funnel adaptor ....................... 170
A-2b Adaptor in place on Buchner funnel (with epoxy cement seal). 170
A-3 Vacuum plug (optional) ................... 170
xii
-------
Number Page
A-4 Schematic flow diagram for specific resistance testing ... 171
A-5 Sample data and data format for specific resistance test . . 173
A-6 Plot of sample specific resistance data 174
A-7 Graph for calculating coefficient of compressibility .... 176
xiii
-------
TABLES
Number
1 Properties of water treatment and wastewater sludges 74,75
2 Average values for color, pH, and turbidity for the
sludge, filtrate, and decant samples 82
3 Average values for solids for the sludge, filtrate
and decant samples 82
4 Average values for total acidity and total alkalinity
for the sludge, filtrate and decant samples , . , . 84
5 Total hardness, calcium, and magnesium for the sludge,
filtrate and decant samples 84
6 Average values for manganese and iron for the sludge,
filtrate and decant samples 85
7 Average nitrogen values for the sludge, filtrate and decant
samples 85
8 Average values of phosphate and sulfate for the sludge,
filtrate, and decant samples , . . 87
9 Biochemical oxygen demand and chemical oxygen demand for
sludge, filtrate, and decant samples 87
10 Physical characteristics of supporting sand 90
11 Rate of water loss (gm/hr) of de-ionized water at 24°C
(75 F) and 47 percent relative humidity 96
12 Analysis of variance for evaporation data 96
13 Results of Billerica sludge, at two different solids
contents, dried at 22 C (72 F) and 38 percent relative
humidity for 3.0 cm (1.2 in) initial depths 96
14 Experimental arrangement for drying study D-3 conducted
at 24 C (75 F) and 60 percent relative humidity ...,.., 100
xiv
-------
Number Page
15 Summary of results for drying study D-3 conducted at
24°C (75°F) and 60% relative humidity- 102
16 Results of Albany sludge, DW-1, dewatering at 24°C
(75 F) and 46 percent relative humidity 107
17 Dewatering study DW-3, results for four sludges de-
watering at 24°C (75 F) and 35% relative humidity 110
18 Attenuation coefficients at 0.661 Mev for the various
materials 114
3
19 Particle density values, g/cm , for water treatment sludge
solids and Ottawa sand.. . 114
20 Summary of water content measurements for Ottawa sand
by the attenuation method 115
21 The effect of rainfall on wastewater sludge drying during
the falling rate period 134
22 The effect of rainfall on water treatment sludge drying
during the falling rate period 135
23 Characteristics of sludges 138
24 Normal monthly weather data -- selected cities 139
25 Occurrence of freezing at selected cities 140
26 Comparison between computer simulation and field
observations for covered beds at various locations 144
27 Comparison between 20-year computer simulation results and
Haseltine's field observation for open sand beds at
Grove City, PA 145
28 Comparison between 20-year computer simulation results and
Haseltine's field observation for covered sand beds at
Grove City, PA 145
29 The output of simulation of mixed digested primary and
activated sludge dewatering on sand beds at Boise, Idaho
with 20 cm application 146
30 Annual cost of sludge dried in Boise, Idaho, at different
application depths (sludge removed by hand) 156
31 Annual cost of sludge dried in Boise, Idaho, for different
application depths (sludge removed by machine) 157
xv
-------
.. , Page
Number
32 An input/output relation showing the law of diminishing
returns. •
33 The results of optimum sand bed dewatering in Boston with ^
a fixed bed area per capita
34 The cost of sludge dewatering
xvi
-------
ACKNOWLEDGEMENTS
The author is indebted to a number of persons for their assistance in
this research project. Dr. John H. Nebiker introduced him to research on
sludge dewatering, served as co-principal investigator from 1967-1969, and
served as a sounding board for various research ideas until distance made
this impractical. His imprint on the research remained long after he was no
longer an active participant. Philip A. Lutin served enterprisingly as a
full time research associate during initiation of the project and established
many of the early laboratory practices. He was followed by John F. Ramsay
who later changed roles from full time research associate to that of graduate
student and research assistant.
The dedicated participation of several graduate students is acknowledged
with thanks. PhD candidates Edward E. Clark and Kuang-mei (Bob) Lo made
major contributions to the research through their dissertation work. Other
PhD candidates Thomas G. Sanders, Donald L. Ray, Peter Meier and Peter Kos
contributed to the research in their MS and PhD studies. MS candidates who
worked on various aspects of the research were Paul Cummings and George Wan.
Undergraduates Thomas Belevieu and Thomas Roule assisted in some of the de-
watering studies. Christopher C. Clarkson provided valuable assistance in
preparing and editing the final report.
Faculty associates who assisted in development of the project include
Dr. Tsuan Hua Feng, Professor of Civil Engineering, Dr. Chin Shu Chen,
former Assistant Professor of Agricultural Engineering and Bernard B. Berger,
Director of the Water Resources Research Center.
Valuable counsel and advice has been provided by EPA Project Officers:
Dr. Robert B. Dean who enlarged the author's knowledge of sludge and its
properties; Dr. James E. Smith, Jr. who quietly and sympathetically offered
his insights on research programs; and Roland V. Villiers who saw the final
report to completion.
Personnel at water treatment plants in Bill erica, Lowell, Lawrence, and
Amesbury, Massachusetts; Albany, New York; Lebanon and Nashville, Tennessee;
and Kankakee, Illinois, were most helpful in providing sludge samples for
analysis. Sewage sludge was obtained from Amherst and Pittsfield,
Massachusetts.
The persons acknowledged above undoubtedly can see their contributions
reflected in portions of this report. Needless to say the author bears
responsibility for errors which may appear.
xv n
-------
SECTION I
INTRODUCTION
Water for domestic and other general municipal use has traditionally
been obtained from the best available supplies consistent with economy. With
the advent of physical and chemical water treatment late in the nineteenth
century, raw water supplies of lower quality could be upgraded to acceptable
levels. The chemical dosage was roughly inversely proportional to the raw
water quality while the amount of sludge produced varied with the amount of
chemical required.
The central concern of the water utility was the production of ample
supplies of potable treated water under the constraint that this production
be achieved at a minimum cost. Scant attention was paid to treatment by-
products such as filter wash water and sludge from the sedimentation basin.
A convenient and low cost disposal site for filter wash water was often the
supplying stream. Sludge from the sedimentation basin may also have been
discharged to the stream, or, if the stream capacity was low, discharged to
a lagoon.
The occasional usage of a sludge lagoon, rather than direct discharge
of the sludge to the stream, attested to some concern over degradation of the
receiving water quality. However, this mode of operation was subject to the
whim of the utility. Moreover, the stream was always available as a disposal
site should the lagoon capacity become exhausted. In fact, a report by
Louis R. Howson in 1966 indicated that over 90 percent of all water treatment
wastes were being returned to the raw water source(l). Gradually, water
treatment sludge discharged to a stream has come to be recognized as a pollu-
tant. The concern over water pollution necessitates a re-examination of
water treatment sludge handling and disposal methodologies. Lagoon disposal
may be a satisfactory solution provided additional lagoon sites are available
to replace those which are filled, or provided that the compacted solids can
be removed and the lagoon reused. Recent studies point out, however, that
lagoons are not well suited to the processing of water treatment clarifier
sludges due to the high water content of compacted solids which renders them
difficult to handle (2).
In many cases the sludge may be discharged directly to a sanitary sewer
where it becomes the concern of the wastewater treatment plant. Unfortu-
nately, lime sludge becomes less acceptable to the wastewater treatment plant
as the level of treatment increases. While lime sludge is acceptable to a
primary treatment plant, it may be unacceptable to a secondary treatment
1
-------
plant (3), unless incorporated into a phosphate removal process (4).
The relative merits of the choice between augmenting treated supplies
by drawing upon waters of lower quality, or conserving existing supplies by
concentrating on reduction of water usage have recently become more clearly
delineated (5). In many instances an immediate but temporary solution to an
insufficiently treated water supply is attained by marked reduction in con-
sumption achieved by eliminating waste or by altering industrial processes.
However, long range demand trends have focused increased attention on water
renovation, with some processes envisioned as forming a closed system such
that complete reuse will be achieved. Complete renovation of a municipal
wastewater is beyond the capability of secondary treatment. High quality
product water is obtained at the expense of the production of voluminous
amounts of dilute sludge or brine, the disposal of which vastly increases the
now formidable solids handling problem. Today, water renovation in the sense
of complete recycling of wastewater through successive treatment steps until
it can be returned to the domestic water supply is accomplished in laboratory
and pilot systems. Technological advances suggest that wastewater renovation
may be practicable on a large scale in water deficient areas. As treatment
methods evolve and are put into practice, the alternatives between development
of lower quality new raw water sources or renovation of wastewater for reuse
will become more clearly defined, enabling a more informed economic choice.
Wastewater renovation and utilization of lower quality raw waters will
become more commonplace in the future. Either choice will increase sludge
handling problems. Based on the present day production figures of 6.8 kg
(15 lb)/capita/year of dry solids from water treatment plants and 59 kg
(130 lb)/capita/year of dry solids from wastewater treatment plants, the
per capita quantity of sludge requiring handling will be greater with water
renovation than with conventional water treatment (3). The solids from either
process will be accompanied by vast quantities of water so that on a wet
basis, assuming sludges of 3 percent solids content, a water treatment plant
would produce nearly 227 kg (500 Ib) of sludge per capita per year while a
wastewater treatment plant would produce 1900 kg (4,200 Ib) of sludge per
capita per year.
Ultimate disposal of the sludge solids requires their discharge to the
atmosphere, to the ocean, or to the land. Organic compounds which are
oxidizable to carbon dioxide and water vapor are most amenable to atmospheric
disposal. Water treatment sludges are low in organic content so that incin-
eration will leave a substantial fraction of ash. Soluble compounds may be
carried by streamflow to the ocean. For communities near the shore, direct
discharge of sludge into the ocean may be practiced. For the overwhelming
majority of communities in the United States, water treatment sludge solids
are disposed of on land. Prior to their disposal, volume and weight reduc-
tion are necessary to reduce the weight from some 227 kg (500 lb)/capita/
year on a wet basis to approximately 6.8 kg (15 lb)/capita/year on a dry
basis. This can be achieved by removing water from the sludge.
Reduction of the water content of sludge may be carried out by a variety
of mechanical or non-mechanical methods such as compaction and decantation
in lagoons, or gravity drainage and evaporation on drying beds. Selection
-------
among these alternatives is based on economics. Exhaustive studies by the
city of Chicago on wastewater sludge shows the cost of various combinations
of dewatering, drying, and disposal methods varies from approximately $12/ton
(900 kg) to $80/ton on a dry solids basis (6). The most economic method was
dewatering, drying, and disposing of the solids on land.
Although land disposal is widely utilized at small treatment plants,
there is a paucity of reliable design data available with which to design a
sand dewatering and drying bed for sludge. Mechanical dewatering methods,
although less economic than sand beds, have become increasingly popular with
design engineers because of the ready availability of design data. A typical
example is the vacuum filter for sludge dewatering. Sludge solids content,
specific resistance of the sludge cake, and its coefficient of compressibility
are related to the desired dewatered sludge cake characteristics through the
machine operating variables. Variation of the machine operating parameters
permits selection of the optimum vacuum filter. No such procedure is avail-
able to the engineer faced with designing a sand dewatering bed. Mhile he
can resort to some empirical rules-of-thumb or practice at operating instal-
lations or intuition, none of these are as satisfactory as a functioning
mathematical model, verified adequately for reliability, which clearly de-
lineates the role of each parameter. There is a great need for such a mathe-
matical model describing the operation of a sludge dewatering and drying bed.
Additionally, rigorous economic analysis is not feasible without a satisfac-
tory model«
The purpose of the study herein reported was to develop methods of ap-
proach applicable to the previously cited problems of land disposal of water
treatment sludges. The general objective was to develop rational design
formulations which would enable an engineer to design dewatering and drying
beds for water treatment sludges.
To this end, liaison was established with several water treatment plants
treating raw water from several sources by a variety of treatment methods.
Sludge samples were characterized by such classification tests as specific
resistance, coefficient of compressibility, and solids content. The problem
of sludge dewatering and drying was analyzed under a variety of meteorologi-
cal conditions in order to postulate hypotheses which would permit formula-
tion of mathematical models describing these processes.
Formulation of the relation between loading rates of water treatment
sludge applied to filter beds and to subsequent drainage and drying of the
sludge'forms the core of the engineering analysis reported in this study.
The sections which follow present the essential aspects of filtration theory
of a compressible material, drainage theory, evaporation and drying theory,
dewatering practice, current design practice, effect of rainfall on sludge
dewatering, and simulation of dewatering on sand beds.
-------
REFERENCES
1. Howson, L. R. Problems of Pollution. In: Waste Disposal-Water Treat-
ment Plants, Joint Discussion. Journal American Water Works Association,
September, 1966.
2. McWain, J. D. Dewatering by Lagoons and Drying Beds. In: Proceedings
of the Tenth Sanitary Engineering Conference- University of Illinois,
Urbana, Illinois, February, 1968.
3. Hudson, H. E., Jr. How Serious is the Problem? In: Proceedings of the
Tenth Sanitary Engineering Conference. University of Illinois,
Urbana, Illinois, February, 1968.
4. Dean, R. B. Disposal to the Environment. In: Proceedings of the Tenth
Sanitary Engineering Conference. University of Illinois, Urbana,
Illinois, February, 1968.
5. Stephan, D. G. and Weinberger, L. W. Wastewater Reuse—Has It Arrived?
Paper presented at the 40th Annual Conference of the Water Pollution
Control Federation, New York, New York, October, 1967.
6. Dalton, F. E., et al. Land Reclamation—Possibly the Complete Solution
of the Sludge and Solids Disposal Problem. Paper presented at the 40th
Annual Conference of the Water Pollution Control Federation, New York,
New York, October, 1967.
-------
SECTION II
CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS
A theoretical model (Equation 47) developed in this research and verified
experimentally describes gravity dewatering of wastewater sludge. Experi-
ments also suggest the existence of a dimensionless media factor which re-
lates sludge dewaterability on sand and other filter media, to dewaterability
in the Buchner funnel. It is not clear whether the media factor is a
multiplier, as used in this research, or if it applies better in the model
as an additive factor. The model can be used to calculate bed loadings, and
to determine the area needed to dewater a given amount of sludge by gravity
drainage alone. Used in conjunction with models describing evaporation and
drying, the environmental engineer is provided with a rational means by
which to determine sand bed areas. Additionally, it provides a basis upon
which to compare drying bed performance with other means of dewatering, and
a means by which to measure the effectiveness of the many chemical coagulants.
Drainage times of water treatment sludges may also be predicted which
provide a good estimate for design purposes. Drying durations can be calcu-
lated from the drying equations examined (Eq. 134). Evaporation ratios for
each particular type of sludge and average local weather conditions provide
drying rates for any locality or climate. The moisture gradient in water
treatment sludge is constant during most of the drying period, indicating
that evaporation from the surface—not internal diffusion—presents the major
resistance to drying. Under normal conditions, water treatment sludges can
be removed from drying beds while in the constant rate drying period.
The gamma-ray attenuation method is applicable to sludge drying studies
but needs some refinement to cover the dewatering period after lateral shrink-
age of the sludge cake becomes pronounced. After the critical moisture con-
tent is reached the moisture profile provides information on the moisture
content and the moisture transport mechanisms during the falling-rate period.
Although the water treatment sludges tested resulted in a wide range of
values for specific resistance, they were all within one order of magnitude.
The water treatment sludges tested were homogeneous, inorganic, and void of
filamentous binders, thus it is not unreasonable to expect that water treat-
ment sludges will lend themselves to a variety of dewatering techniques.
Somewhat higher coefficients of compressibility were obtained for the water
treatment sludges than are cited in the literature for wastewater sludges.
This indicates that water treatment sludges produce a more compressible cake
than wastewater sludges.
-------
Computer simulation techniques were utilized to develop design Criteria
with which an engineer can design dewatering beds based upon climatic con-
ditions and the nature of sludge to be dewatered. Economic analyses are
applied to the outputs of simulation in developing an optimum system design:
the first explores the optimum system design which fulfills projected output
at minimum cost among known alternatives; the second utilizes marginal
analysis to assign a cash value to the end product (dry solids) of the de-
watering process to determine the point at which cost of inputs equals the
marginal value of output.
Further work in this area would be enhanced by more rigorous scientific
evaluation of the quality of water drainable from different sludges, and by
a greater availability of sand dewatering bed construction cost and operating
cost data which would enable more accurate evaluation of the costs of sand
bed dewatering.
RECOMMENDATIONS
To obtain improved sand bed system design, it is recommended that:
1. the results of the computer simulation be incorporated into
standards for dewatering bed design,
2. the simulation model (or computer program) be included as an alter-
native to other methods of sludge dewatering determination in any
systems analysis approach for water and wastewatef treatment plant
design,
3. a performance index of 95 percent be adopted as a design criterion
for sludge dewatering beds, and,
4. the environmental engineering profession re-evaluate its traditional
design approach so as to foster an effective union of engineering
and economic analysis.
In addition, this investigation points out areas in which further
research is required. Future studies should concentrate on the quantities
of sludge produced by waters of various qualities being treated in different
ways, and the method of removal of sludge from sedimentation basins.
Thickening of certain types of sludge--such as softening sludge—by
sedimentation and decantation could remove large amounts of relatively clear
water. A study of sludge particle size would lead to development of relation-
ships suitable for determining media factors for the drainage model.
There are not now many wastewater treatment plants able to afford the
time or expense required to measure the most effective coagulant dose for
sludges to be applied to sand drainage beds. However, with future expansion
and centralization of wastewater treatment plants, economies to scale will
be enjoyed which will be made possible through more sophisticated plant
operation. The mathematical model developed in this research could con-
ceivably be used to determine optimum coagulant dosage at a cost far less
-------
than the savings to be realized. Availability of a nomograph (whose develop-
ment is based on the mathematical model presented) would enable treatment
plant operators to make more effective use of available sand beds, with only
a modicum of experimental work.
-------
SECTION III
REVIEW OF THE LITERATURE
In 1907, Spillner, one of the early researchers on drying beds (1), dis-
covered that digested sludge from an Imhoff tank dewatered more rapidly than
raw sludge. He found that 80.9 percent of the moisture reduction in digested
sludge was due to drainage as compared with only 44.4 percent for fresh
sludge and concluded that the better drainage of the decomposed sludge was
due to a decrease in viscosity, destruction of hydrophilic colloids and
organic matter, and the formation of gas bubbles. ' The effect of gas bubbles
lifting the sludge to promote formation of a subnatant was probably the
singlemost important factor in improving the drainage rate of digested sludge.
The gases allowed the rapid release of filtrate by unclogging pores at the
sand surface which would otherwise remain blocked by the sludge floe.
During the 1920's, covering drying beds with greenhouse structures be-
came popular. This increased the rate of drying of the sludge by preven-
ting problems with precipitation and by maintaining higher temperatures. How-
ever, enclosure prevented the flow of air which could remove water vapor
directly above the sludge. In 1931 Skinner (2) published a paper which ques-
tioned the economic feasibility of covered sand beds. He stated that open
beds had less construction cost per unit area, and entailed no cqsts for heat,
insurance for glass breakage and maintenance of a fragile superstructure.
On the other hand, covered beds needed up to 50 percent less area per capita,
reduced the odor nuisance, and had a better appearance.
Skinner developed one of the first empirical equations for the computa-
tion of drying bed requirements, covered or uncovered, i.e.,
rAverage Annual
LPrecipitation:
in
]
rSuspended Sewage-i
LSolids: ppm J
rNumber of Months-,
Lin Drying Season-1
rMean Annual n
LTemp. : F J
Mean Wind
[Velocity:]
' mph
Area of Sand Bed = (Constant)
per capita
where the constant depends on the sewage treatment process. For cpvered beds,
the area calculated above is divided by 2. The formula points out the dif-
ferent factors that affect sludge drying.
In 1934, Jones (3) made a survey of existing treatment plants to see how
effective the sand beds were for the dewatering and drying of sludge. He
found that plant records were reliable and concise for every phase of
treatment plant operation except sludge dewatering and disposal. As an
example:
8
-------
"A total of 44 beds of sludge were drawn off from the tanks during
this year and a total of 75 beds of scum. All sludge drawn off was
well digested, dried out quickly and had no prominent odor."
There was no mention of depth of application, solids content of sludge from
digester, or solids content of sludge when removed from the beds. Jones in-
dicated that economic advantages could not be characterized and cost per
unit area estimates for sand beds could not be made until more complete
records were kept at the treatment plants. Based upon the data available
to him, Jones concluded that the degree of treatment, type of process, and
character of sludge not only affected the volume of sludge produced, but
also the rate of dewatering.
During the same years that Jones was doing research on sand beds,
Rudolfs and Heukelekian (4) were studying the drainability of sludge versus
the degree of digestion. It was found that well digested sludge dewatered
faster than a poorly digested sludge, or a well digested sludge which had
been stored before being placed on the sand beds: The resulting conclusion,
substantiating the work of Spillner, was that the well digested sludge had
a large amount of gas which "buoyed" the sludge solids, allowing the subna-
tant water to drain more rapidly.
For so-called dead sludges (a sludge without entrained or dissolved
gases), alum could be added to increase the drainability of the sludge. The
alum would react with the carbonates in the sludge forming CCL gas which
would buoy the sludge solids and increase drainability. Copper sulfate
and even dilute sulfuric acid would have the same effect on the sludge. How-
ever, addition of alum or any other chemical to a freely gaseous sludge would
have no effect on drainability (5). Ferric chloride was tested as a sludge
conditioner because of its minimal cost (6), however, the ferric salts were
oxidized, clogging the sand pores and allowing less drainage.
It was found in Aurora, Illinois in 1939 (6) that differences in
drainage characteristics for the same sludge with the same amount of alum
were attributable to the method of adding alum to the sludge. If the alum
were completely mixed with prolonged stirring, the sludge would not drain
as well as the sludge subjected to a minimum of stirring. This problem was
due to a build-up of fines from shearing of the floccules (the same occurs
with prolonged pumping). Therefore, in order to minimize stirring but
obtain complete mixing, alum was first dissolved in water and then added to
the sludge a few feet from the sand bed outlet. Because of turbulence in
the pipe, adequate mixing was assured.
The major disadvantage to the use of sand beds as a means of sludge
dewatering is the cost of removing dried sludge from the beds. In small
sewage treatment plants the removal costs may be inconsequential, being
merely an occasional task. However, in a larger plant which may treat
1500-2300 cubic meters (2000-3000 cubic yards) of sludge every day, the cost
of sludge removal becomes considerable. As early as 1931, the Sanitation
District of Chicago, concerned at the cost of manually removing sludge
from drainage beds constructed a self-propelled sludge removing machine (7).
The device was capable of removing 3.8 cubic meters (5 cubic yards) of
-------
2.0
>
O
z ,_
Q ^
1.5
CD
O
cc
0.5 -
N
O
1.00
0.75
< o
° ^ 0.50
0.25
e
Q ^
LU O>
CD H
LL)
o oo
12
16
INITIAL SOLIDS CONTENT s0 (%)
Figure 1: Loading rate of wastewater sludge
at various treatment plants in the United
States. Shown as a function of the initial
solids content , the points and straight line
represent the results of Haseltine. The
curve is from Vater (10).
04 8 12 16
INITIAL SOLIDS CONTENT s0 (%)
Figure 2: A plot of Haseltine's data of net
bed loading versus initial solids content.
Data is from American plants. Net bed loading
is defined as gross bed loading multiplied by
the water content of the sludge removed (9, 10)
-------
sludge per minute and thus could replace the 350-400 men who would have been
needed to remove equal amounts of sludge. More recently, a mechanical sludge
removing process was installed in 1961 at London's Maple Lodge Works, result-
ing in a substantial decrease in labor costs (8).
One of the first empirical relationships describing the time required
for sludge to dewater on sand drainage beds was developed by Haseltine (9).
From field data collected at different treatment plants, he plotted the
gross bed loading (kg/m2/day) versus solids content of the sludge. The
resulting equation was determined to be:
Y = 0.157 SQ - 0.286 (1)
o
where Y = gross bed loading of solids (kg/m /day)
S = solids content (%)
Vater (10) analyzed the same data used by Haseltine and found that a
curve may be fitted using a regression analysis (Figure 1). The relation-
ship thus became exponential and defined by the empirical equation:
Y = 0.033 S 1-6 (2)
where Y = gross bed loading of solids
SQ = solids content (wt %) of sludge charged to the bed
Although both Haseltine's and Vater's relationships appear to fit the
data, the curve drawn by Vater seems more realistic since it goes through
the origin whereas Haseltine's straight line does not. Clearly, a sludge
of zero solids content will yield zero bed loading.
Since final moisture content of the sludge was also to be a determining
factor of the sludge drainage and drying capacity of a sand bed, Haseltine
defined the term "net bed loading" as the gross bed loading multiplied by
the final water content of the dried sludge. The relationship between net
bed loading and solids content was found to be (Figure 2):
Z = 0.057 SQ - 0.082 (3)
2
where Z = net bed loading of solids (kg/m /day)
SQ = solids content (%) of sludge charged to the bed
Although Haseltine's equations are strictly empirical, they have been
used for the dimensioning of sludge drying beds. Note that the water con-
tent is defined as (100 - solids content)/100.
During the first half of the twentieth century there was little
progress in formulating drainage and drying relationships which took into
account the parameters of sludge characteristics and quantity, and external
11
-------
factors such as the evaporation potential of the air.
Just as there are a number of dewatering methods, there are also a
number of types of sludge. However, the differences are usually related to
the treatment process without any other classification than solids content.
Since primary and secondary sludges with the same solids content but from
different treatment plants will not dewater at the same rate, other drainage
characteristics intrinsic to each sludge must be present.
Jeffrey (11) studied the relationship between permeability of the sludge,
initial head, and time. For his experiment he designed a drainometer
(Figure 3) which consisted of a lucite tube 45.7 cm (18 inches) in length
covered with a polyethylene film to prevent evaporation. A layer of gravel
followed by a 2.2 cm (7/8 inch) layer of sand was placed in the bottom of
the lucite tube to simulate a sand drainage bed. An inverted "U" tube drain
with a siphon breaker was inserted between the sand and gravel to maintain
a water table. Sludge was poured into the column, after which the volume of
subnatant collected and the time were noted. Jeffrey observed the relation^
ship for flow through a soil permeameter (see Fig. 3):
In H/HQ = -kt/L (4)
where H = initial head at t = 0
H = head at any time t
K = permeability coefficient of soil sample
L = length of soil sample
t = time
He then determined from his experiments that the following equation was valid
for sludge drainage:
In W1/WQ = -Kt/L (5)
where W1 = quantity of filtrate = V - V (see Figure 3)
WQ = total quantity of liquor discharged from a drainometer at the
time the quantity of discharge over a 24 hour period falls
to 1 percent of the total discharge.
K = permeability coefficient of the sludge
L = depth of sludge
t = time
Jeffrey stated that "...the coefficient of permeability, K, is not fixed.
Both K and L change with time and apparently at such a rate that the ratio
K/L is constant."
12
-------
Ho
Vo
H
SOIL
SAMPLE
SAND
L
r
SLUDGE
SAND
PERMEAMETER
DRAINOMETER
Figure 3, A comparison of a typical soil permeameter to
Jeffrey's drainometer (11).
In Figure 4 it is readily apparent that Jeffrey's theoretical curves
coincide closely to the actual drainage curves for all three different
solids contents. However, it should be noted that the theoretical curve
could not be drawn until the actual drainage experiments were near comple-
tion since the value of WQ could not be found until the 24 hour drainage in
the column was less than one percent of the total filtrate volume.
Jeffrey based his conclusion, that the ratio K/L was a constant, on
his experimental data. The plot of log W,/W was constant. However, Sanders
(12) has shown that K/L is not constant but instead i;
water content of the sludge, such that
is proportional to the
K/L = B w°/(l-w)
where B = constant
(6)
w = moisture content (%}
A plot of w versus w /(1-w) produced the curve shown in Figure 5. A small
change in w produces a large change in w3/(l-w) and, by Equation 6, in K/L.
Thus, the ratio K/L does not remain constant but instead is a function of
water content. Therefore, even though one of Jeffrey's conclusions appears
13.
-------
theoretically unjustifiable, he was the first to develop a relationship be-
tween head and time.
0.2
INITIAL SOLIDS CONTENT
n
A
o
2.03
4.30
5.75
lrfWi\__
111 iwoj-
-*£•
10 20 30 40
TIME (days)
50 60
Figure 4: Jeffrey's drainage data. The curves represent
Jeffrey's empirically derived equation (11).
14
-------
0
(w/IOO)V(l-w/lOO)
Figure 5: A plot of sludge moisture content W versus
(W/100)3/(1-W/100) showing that K/L is not constant
with a change in moisture content.
Pilot plant studies in England on sludge dewatering yielded the con-
clusion that specific resistance (an intrinsic characteristic of sludge
which0will be discussed in greater detail later) is related to bed loading
(kg/m2/year). Specific resistance has long been recognized as a functional
parameter for use in describing the dewatering rates of sludge submitted to
vacuum filtration, but this was the first time that specific resistance was
tested as a functional parameter to describe gravity drainage. This is not
unreasonable since the processes of vacuum dewatering and gravity drainage
differ only in type of pressure exerted on the sludge. In vacuum filtration,
the vacuum is constant; and in gravity drainage, the pressure (a function of
head) is continually decreasing. A plot of Swanwick's data results in the
curve of Figure 6 which is described by the equation (10,13;
15
-------
o»
o
o
Q
UJ
CD
200 r~o
150
100
50
10
SPECIFIC
R
2O 30
RESISTANCE-10
(sec/gm)
40
"9
Figure 6: The Swanwick relationship of bed
loading to specific resistance. Each point
represents the mean of a group of loading
values (10, 13).
5 30 -
cr
i
UJ
20
10
o TEST 3
D TEST 4
A TEST 5
• TEST 6
• a
A
• D
Aa
An
20 40 60
TIME (min) - VACUUM
80
100
Figure 7: A plot of data accumulated by Losgdon
and Jeffrey with dewatering time by gravity versus
dewatering time using a vacuum. Solids content
of sludge rarvges from 2,08% in-Jest 6 to 3.13% in
lest 3
-------
Y1 = 107/R1/2 (7)
where Y' = bed loading (kg dry solids/m2/year)
R = specific resistance at 36.9 cm of mercury (sec /gm)
Although it is quite possible that a relationship exists between bed
loading and specific resistance, it is highly improbable that this relation-
ship is precisely described by Swanwick's formulation. Other factors which
are related to bed loading and unrelated to specific resistance, such as
evaporation and freezing temperatures, most certainly play a considerable
role in the dewatering of the sludge. Each value plotted in Figure 6 was
an average of three tests run in the course of one year, thus establishing
some uncertainty as to the reliability of the relationship.
Specific resistance does not take into account moisture removing mech-
anisms other than drainage. Therefore, evaporation and freezing temperatures
must be eliminated from scientific studies for proper correlation of specific
resistance with bed loading or other drainage rate parameters.
Logsdon and Jeffrey (14) conducted research to study the relationship
between the dewatering time of a sludge on sand, and the vacuum dewatering
time (a function of specific resistance) of the same sludge using the Buchner
funnel test. Sludges with four different solids contents ranging from 2.08
percent to 3.13 percent total solids were investigated. The times required
to remove equal amounts of water by gravity drainage and by filtration were
plotted yielding the curves in Figure 7. Even though the vacuum applied to
the four sludges varied from 30.5-61.0 cm of mercury, Jeffrey concluded that
the vacuums in this range dewatered the sludge at equal rates; therefore,
Test 3 through Test 6 could be compared. Since these points on the graph
appear to approach a straight line asymptotically, Logsdon and Jeffrey con-
cluded that the dewatering relationship was a straight line with the general
equation:
d = km + i (8)
where: d = number of days the drainometer operates
m = number of minutes the vacuum operates
k = constant = slope of line
i = intercept of abscissa
Weeks are needed to determine the appropriate constants and unfortunately,
each sludge must be re-evaluated by these methods to determine the effect of
sludge conditioning.
In a 1965 British Water Pollution Research Report (15), the dewatering
time for 12 inches (30 cm) of digested sludge was reported as ranging from
12 days to 111 days due to the effects of rainfall on the performance of the
17
-------
drying bed. In order to take this weather effect into account, the Report
suggested a graphical method to determine the required bed area. This
method depended on estimating the portion of the rainfall drained through the
sludge and the portion evaporated. For example, the reported mean values of
15 separate observations suggested that 43 percent of the rainfall drained_
through the sludge and 57 percent evaporated. In order to predict the drying
time, a plot was made of 0.57 x cumulative rainfall against time; the re-
sulting curve then represented the amount of rainfall which would be^evapor-
ated from the sludge. Another plot was made on the same (monthly) time scale
of 0.75 X cumulative evaporation from a free water surface; this curve repre-
sented the evaporation from sludge where the pan evaporation factor was 0.75.
From the two plots a graphical calculator was made by cutting away the portion
of the evaporation graph below the curve and placing the remaining portion
on the rainfall graph. The time scales of both curves are kept coincident
and the upper curve is moved in a direction parallel to the rainfall (or
evaporation) axis until the two curves cross on the date on which sludge was
applied to the bed. The drying time would be found by observing the subse-
quent date when the two were separated by a distance representing the amount
of water to be evaporated from the sludge. The use of this method is illus-
trated in Figure 8.
?l8
u
g 16
13
« 14
o
cc 12
u. "•
2 10
CE p
O 8
Q.
§«
LJ
> 4
I I
I I
M
M J J
MONTH
I
20
18-2
16
or
12 UJ
I0
-------
REFERENCES
1. Spillner, F. The Drying of Sludge. Sewage Sludge, London, 1912.
2. Skinner, J. F. Sludge Drying Beds. Sewage Works Journal, 3, No. 3,
July, 1931.
3. Jones, F. W. Sludge Dewatering—Sand Filters and Vacuum Filters, Sewage
Works Journal, No. 6, November 1934.
4. Rudolfs, W. and Heukelekian, H. Relation Between Drainability of Sludge
and Degree of Digestion. Sewage Works Journal, No. 6, November, 1934.
5. Quon, J. E. and Tatnblyn, T. A. Intensity of Radiation and Rate of
Sludge Drying. Journal of the Sanitary Engineering Division, ASCE,
91, No. SA2, April, 1965.
6. Sperry, W. A. Alum Treatment of Digested Sludge to Hasten Dewatering.
Sewage Works Journal, 13, No. 5, September, 1941.
7. Kane, L. P. and Pearse, L. Cleaning'Machines for Large Air Drying
Sewage Beds. Engineering News Record, January, 1932.
8. Kershaw, M. A. and Wood, R. Sludge Treatment and Disposal at Maple
Lodge. J. Proc. Inst. Sew. Purif., 1966.
9. Haseltine, T. R. Measurement of Sludge Drying Bed Performance. Sewage
Works Journal, 23, No. 9, September, 1951.
10. Vater, W. Die Entwasserung, Trocknung und Beseitigung von Stadischen
KTa'rschlamm. Doctoral dissertation, Hannover Institute of Technology,
Hannover, Germany, 1956.
11. Jeffrey, E. A. Laboratory Study of the Dewatering Rates for Digested
Sludge in Lagoons. Industrial Waste Conference, Purdue University,
May, 1959.
12. Sanders, T. G. Dewatering of Sewage Sludge on Granular Materials.
M.S. Thesis in Civil Engineering, University of Massachusetts, Amherst,
J968.
13. Report of the Director, Water Pollution Research, 1962. London, 1962.
14. Logsdon, G. A. and Jeffrey, E. A. Estimating the Gravity Dewatering Rates
of Sludge by Vacuum Filtration. Journal HPCF, 38(2), February, 1966.
15. Ministry of Technology. Dewatering of Sludge. Water Pollution Research
Report. Ministry of Technology, United Kingdom, 1965.
19
-------
SECTION IV
THEORETICAL CONSIDERATIONS
Dewatering of water treatment sludge involves several basic operations,
not all of which are fully understood. The dewatering process consists of
gravity drainage and drying over a wide range of moisture and solids concen-
tration. Sludge initially at 0.5 percent solids (99.5 percent water) under-
going drying and drainage simultaneously may behave as a dilute suspension.
The water loss rate by evaporation will approximate that of a free water
surface, especially if some sedimentation has occurred exposing clear super-
natant to the drying atmosphere. Drainage alone may concentrate the sludge
to a gelatin-like mass of 5 to 15 percent solids content in a relatively
short time. Drying will further concentrate the sludge causing it to behave
like a solid. This stage is accompanied by compression and shrinkage with
cracks appearing throughout the sludge cake. Continued drying to equilibrium
produces a hard, dry solid having characteristics ranging from those of a dry
sand bed to a ceramic. The transition between the various stages is not pro-
nounced and more than one basic mechanism may be present at any one time.
MOISTURE
Different classifications of moisture and water content are used by
different disciplines. In environmental engineering the term water content
is usually associated with large amounts of water and is defined as the mass
of water divided by the total mass (solids plus liquid). Moisture content
refers to much smaller amounts of water and is defined as the mass of water
per mass of dry solids. The term water content is convenient during the
drainage and early stages of water treatment sludge drying, whereas the term
moisture content is more convenient during the later stages of drying. The
term solids content is also frequently used in sludge dewatering studies.
Solids content is defined as the mass of solids divided by the total mass.
Thus solids content plus water content is unity.
There is no agreement on the nomenclature of the various kinds of water
involved in the various disciplines. According to Spangler (1) one method of
classification is the Briggs classification of soil water. Each class of
water is referred to according the kind of force primarily controlling its
movement. The three types are:
1. Hygroscopic water - water tightly adhering to solid particles in
thin films which can be removed only as a vapor.
20
-------
2. Capillary water - water which is held by cohesion as a continuous
film around the soil particles and in the capillary spaces.
3. Gravitational water - water which exists in large pores of soil and
which the force of gravity will remove from the soil when conditions
for free drainage exist.
Chemical engineering literature usually refers to four types of moisture.
The four types as listed by Treybal (2) are:
1. Bound moisture - moisture contained by a substance which exerts an
equilibrium vapor pressure less than that of the pure liquid at the
same temperature.
2. Unbound moisture - moisture contained by a substance which exerts an
equilibrium vapor pressure equal to that of the pure liquid at the
same temperature.
3. Equilibrium moisture - the moisture content of a substance when at
equilibrium with a given partial pressure of the vapor.
4. Free moisture - that moisture contained by a substance in excess of
the equilibrium moisture.
These relationships are shown in Figure 9 for a material exposed to an atmos^
phere of relative humidity A. Bound water may exist in several conditions.
Liquid water in fine capillaries exerts an abnormally low vapor pressure be-
cause of the highly concave curvature at the surface. Bound moisture in cell
or fiber walls may have a lower vapor pressure due to dissolved solids. Water
in many substances is bound by both physical and chemical combination, the
nature and strength of which vary with the nature and moisture content of the
solid. Unbound water, however, exerts its full vapor pressure and is largely
held in the voids of the solid. McCabe and Smith (3) state that the distinc-
tion between bound and unbound water depends on the material itself, while
the distinction between free and equilibrium moisture depends on the drying
conditions.
DERIVATION OF SPECIFIC RESISTANCE
The well known concept of specific resistance initially developed by
Carmen and later refined by Coackley and Jones (4), has been proven to
adequately describe the dewatering of a compressible material by means of a
vacuum filtration unit. Therefore, since the only difference between de-
watering by vacuum filtration and dewatering by gravity drainage is that a
constant pressure is applied on the sludge in the former and a continually
decreasing pressure is applied on the sludge in the latter, the specific
resistance concept could well be the basis for a mathematical model describing
gravity drainage on a sand bed.
The concept of specific resistance can be developed starting with the
classic Darcy-Weisbach equation for the head loss of a fluid moving through
21
-------
100
>
H
Q
^
ID
X
LU
>
LU
or
o
EQUILIBRIUM MOISTURE CONTENT
CURVE
^UKVt 1
BOUND
-MOISTURE
MOISTURE AT
RELATIVE HUMIDITY
OF
MOISTURE
FREE MOISTURE AT
RELATIVE HUMIDITY OF A
U.
MOISTURE CONTENT, %
Figure 9: Relationship of relative humidity vs
moisture content.
a pipe.
hf = AP/pg = f1(L/D)V2/2g
(9)
where
hf = head loss (L)
12
AP = pressure drop in pipe (M L T )
o
p = mass density (M L~ )
L = length of pipe (L)
V = mean velocity (L T )
D = diameter of pipe (L)
2
g = acceleration due to gravity (L T )
f] = friction factor (M° L° T°)
Since the fluid velocity through the pores of a sand bed will be very slow,
it is reasonable to conclude that a state of laminar flow will exist. The
friction factor in the laminar flow region is related to the Reynolds number:
22
-------
fl - 64/Rp (TO)
where: Rn = Reynolds Number = DVp/y (M°L°T0) (11)
y = dynamic viscosity (ML T )
For noncircular conduits the hydraulic radius is defined as:
Rh - A/P
where: R. = hydraulic radius (L)
A = area (L2)
P = wetted perimeter (L)
Substituting the area and perimeter of a circular cross section
Rh = (irD2/4)/iTD = D/4
D = 4Rh (12)
Substituting Equations 10, 11 and 12 into Equation 9,
hf = (64/Rp) (Rnu/DVP)(L/4Rh) (V2/2g) (13)
hf = 2pLV"2/VRh2pg
The derivation thus far has been for the head loss through a cross
section of measurable dimensions. For flow through incompressible porous
media, the conduit cross section must be expressed in terms of the porosity:
Ap = eA (14)
where: A = cross-sectional area of pores available to flow. This area
P 2
is assumed constant throughout the column of sand (L )
e = porosity = V /V = Void Volume/Total Volume (M°L°T0)
v
Assuming all particles in the porous material to be identical and defining
N = number of particles (M°L°T°)
2
S = surface area of each particle (L )
P 3
V = volume of each particle (L ),
the hydraulic radius may be written as
Rh = Ap/P = A-L/P-L = Vv/NSp (15)
Note that:
23
-------
= VVtot
Hence
Vv =
Therefore:
Rh = eAL/NS = eNV /(l-s)NS = eV /(l-e)-S (16)
The relationship of actual velocity and superficial velocity (Total Flow/
Area of Total Cross Section) is required. From continuity considerations;
V A = VA
s p
s p p
where V = superficial velocity (L T~ )
Combining equations 16, 17, and 13,
V
% f_S_\ ,22 , 2 ?
{2yL)le '(1-eT $n 2 l-eT VcyLS ^ Ap
n = P_ = s P = __
f 2—2 32
P9 e Vp e gVp p pg
Set
£..
3 2
e V
where R = media or filter resistance (L"2), and
hfpg AP
T- = T=pVsR (20)
Solving for V
v - AP _ 1 dV
s LyR " A dt
where dV/dt - Flowrate (L3 T"1 )
Therefore:
dV/dt = AAP/pLR (2])
Equation 21 may be used for stratified filters where there are two different
depths (L) and two different resistances.
24
-------
FILTER (1)
dv A AP
Mt'l H.L.R,
FILTER (2)
A . Vfe
dl 2 H24,R2
Figure 10. Definition sketch for a stratified filter.
Since water is incompressible
( QL} -A - dV
Mt;l " vdt;2 " dt
A-, - A0 = A
AAP AAP, AAP2
yLR yL, K-j yLoR'
AP AP1 AP2
TD" ~ 1 5~ ~ I 5
L. r\ I*, l\1 I—nf\f\
AP2 =
AP
where AP = AP + AP
L =
AP = AP, +
I
AP
,
I
If the filter consists of n number of strata
AP,
L2R2 LR
AP0 ~ AP"
25
-------
AP
LR =
= (APn
hi
APn
LR = UR, + L9R9 + I L -Rn
II f. t n=3 n n
Combining equations 21 and 22,
dV _ AAP _ AAP _ AAP
(22)
dt yLR
(23)
n=l
Filtration of a compressible material on a porous medium may be
described by using the specific resistance concept. The initial filtration
rate is governed by the support medium resistance, then a cake gradually
forms on the support surface and contributes to the resistance to flow. This
cake increases in thickness with increasing volume of filtrate; as each
volume of filtrate is separated from the sludge, a portion of this volume
(solids) will remain to form a sludge cake with a thickness equal to L,
(Figure 11). '
Suspended Solids
Filter Cake
Supporting Media
Filtrate
Figure 11: Schematic representation of
filtration of a compressible material on a
porous medium.
The relationship is expressed as:
L] = W/A
(24)
26
-------
where: V = volume of filtrate (L )
2
A = area of surface (L )
v = volume of cake deposited per unit volume of filtrate
(L°M°T0)
This accumulation of sludge particles, however, may be more easily ex-
pressed and determined if v is replaced by f, the weight of cake solids per
unit volume of filtrate (F l_-3). Therefore, substitution into (Eq. 23) will
give:
dV AAP
dt /fVR
(25)
1_2 and R_ refer to the supporting medium. The resistance of the cake, R,
called "specific resistance," has units of T2M~'.
The characteristics of the supporting incompressible medium may be com-
bined by substituting Rf for the constant L?Rp and rearranging
yfVR + yARf
dt = ( * r-)d\l (26)
A^AP
If AP remains constant, the following integration can be made:
ft
H+- -
at -
0 -
1
f f
(A2
0 A
1
t —
-
2
VR
AP
yfR
A2AP
yARf
A2AP
-V2 +
dV
yRf
AAP
V
(27)
The experimental data, plotted as (t/V) versus V will yield a straight line on
arithmetic paper. The slope b allows calculation of the specific resistance
R (Figure 12):
R = (28)
where R = specific resistance of compressible material subjected to a
vacuum of AP (T2M-1)
_2
AP = pressure loss across sludge cake (F L )
2
A = area of filtration surface (L )
y = dynamic viscosity of filtrate (ML T )
o
f = weight of solids per unit volume of filtrate (F L" )
b = slope from t/v versus V plot (T L" )
27
-------
ro
E
o
o
4)
80
60
UJ 40
5
ID
_l
O
UJ 20
5
I-
HEAD-cm water
o 56.4
A 151.0
D 310.0
10 15
VOLUME (cm3)
20
Figure 12: A typical graph used to determine the
specific resistance of a wastewater sludge at
three different vacuums.
Similarly, the t/v intercept of the line of slope b at V = 0 determines
the resistance of the supporting media
R _ (t/v intercept) AAP
f y
The relationship of specific resistance to head was studied and found to
be empirically described by the following equation (5,6) :
R = Rc(h/hcf
(29)
where R = specific resistance of sludge at head h (T2 M"1)
R_ = specific resistance when head = h (T M"1)
c c '
a = coefficient of compressibility (L°M°T°)
A plot of the log of specific resistance as the ordinate versus the log
of the head will yield a straight line with a slope equal to the coefficient
of compressibility a.
28
-------
DERIVATION OF MATHEMATICAL MODEL FOR THE GRAVITY DRAINAGE RATE
Using the specific resistance concept, a mathematical model can be de-
rived for determining the gravity drainage rate of a sludge or other compres-
sible material on a drainage bed. Referring to Equation 23
dV _
dt "
AAP
y(L1R1
(23)
and knowing that
99 ~" -F
LI = fV/A and
AP = phg
substitution of R (Eq. 29) for R, (Eq. 23) and rearrangement gives;
dV
A2 phg
dt y[fVRc(h/hc)a + ARf]
(30)
Because the specific resistance of a wastewater sludge is much greater than
the resistance of the supporting sand or soil media, (R»Rf) the term AR,. can
be assumed negligible. Therefore it follows that
dV
dt
Since
dV
dt
And
V =
H =
0
_ A2Phg
ufVRr (h/hja ;
\+ \*
- Adh
" Adt
HO
A(HQ-h)
initial head (L)
i
(
I
h
f
(
/
V
V
'"•'**'. '• '•
• .
' " ' ' t '
s^£%$$
e.*&£
-------
dh
yfRc(HQ-h)
(31)
Reorganizing and integrating to the proper limits will yield
dt - C
U L - -
r. pg(h^)
L) C
yR f
t ~ ^
pg(hc)°
yR f
t ~
Pg(hc)a
,
yR f
i- — C
•n
(l^-h^dh
H
0
~HonGih rh°
a H a+
H
0 /ha M a\
\n ~ "„ /
0
a
l.a+1 a+1 u .
C - \ ii iii
pg(hc)a(a+i) ( a °
+1]h
•I M
h°+1 - Ho*+1
a+1
a I, a+1 a+1
— n i
0 a
(32)
(33)
The value of f, solids deposited per unit volume of filtrate, requires further
analysis in order to simplify Equation 33.
If no solids are lost during filtration the volume of filtrate is
(W4
tot
V =
pg
(34)
-3,
where p = mass density of filtrate (M L~ )
g = acceleration due to gravity (L T~ )
W
tot
tot
= weight of unfiltered sludge (M L T )
o
= weight of filtered cake (M L T )
Referring to the total weight in terms of solids content:
W
tot
WTS/Fo
(35)
-2,
\ot = total wei'9ht of sludge (M L T )
2,
WTS = weight of solids in unfiltered sludge (M L T ) = W.
o o
WTC. = weight of solids in filtered cake (M L T ) = WT
ibf I
JS
30
-------
F = solids content
Therefore the volume of filtrate may be written as:
WT--100 WTQ.100
V = (— 4= --- ^ - )/Pg (36)
ho hf
where PQ = solids content of sludge at beginning of test (%)
Ff = solids content of sludge at end of test (%)
which simplifies to
(37)
It has been previously defined that f is equal to the weight of dry solids
deposited per unit volume of filtrate.
f = WTS/V (38)
Therefore, by substitution of (Eq. 37) into (Eq. 38)
100 MTC 1 1
f - "rs/t-V1 ^ - f7>] <39a)
which reduces to
f ,/100 100\ /OQU\
f = pg/(c -- F — ) (39t>)
ho hf
F will be much less than Ff since dewatering will decrease the solids content
or a dilute sludge 10-15 times. Therefore, the term 100/Ff may be neglected.
Dropping the subscript:
f = pgF/100 , (40)
Equation 40 may now be substituted into Equation 33, resulting in
t = -^ - [ cr+1 _ o+I H ha _ H a+1 + a±l H a+1-, (4] }
100(hc)a (a+1) a 0 o
Equation 41 is dimensional ly correct with the gravity drainage time defined
by basic parameters -- specific resistance R at a given head loss h , co-
efficient of compressibility a, initial solias content F, initial head HQ,
and dynamic viscosity of the filtrate y.
Equation 41 has been used to predict the drainage times for wastewater
sludges. Laboratory determinations of a, FQ, and R comprise the laboratory
31
-------
operations. It is the basic equation used by Sanders (28) and Nebiker et al.
(29) in predicting drainage times for wastewater sludges.
The specific resistance, R, in Equation 41 is determined by the Buchner
funnel or fritted glass funnel method. Standard laboratory procedures for
measuring specific resistance by the various methods have been reported by:
Lutin et al. (30). An adjustment to the specific resistance so determined
is necessary to account for the pressure variation across the cake in the
funnel. In the Buchner or fritted glass funnel the specific resistance is a
function of pressure where
R(P) = R (p-)° (42)
c
-1 -2
where P = pressure at time t (ML t~ )
l -?
P = reference pressure at R (ML~ t" )
The pressure varies from near zero at the surface of the cake to AP at the
outlet of the testing funnel. An average value R is measured by the funnel
and could be defined as:
fAP
R(P) dP (43)
where R(P) is the local specific resistance at each horizon in the sludge
cake. Substituting the value of R(P) from Equation 42 into Equation 43 and
performing the integration
(44)
c
or rearranging,
Rc
Then from Equation 42, Equation 45 may be written as
(46)
This indicates that the values for t determined from Equation 41 should be
multiplied by the term I/ (a + 1) so that proper account is taken of the
specific resistance of the sludge cake.
It is interesting to note that Nebiker et al . (29) in a study of the
drainage time required for sludge applied to sand columns found it necessary
to multiply the drainage times predicted from Equation 41 by a media factor,
a function of the ratio of the size of the sludge particle to the size of
the sand particle. Media factors of magnitude 0.45, 0.60 and 0.75 for three
different sands were used so that the theoretical equation would agree with
experimental values. They used the unadjusted specific resistance values inr
stead of R. The sludges studied had coefficients of compressibility ranging
32
-------
from 0.63 to 0.64, which would yield values of the correction l/(o + 1) of
0.62. Clearly much of the discrepancy between the theoretical formulation
and their experimental values was due not to the media used, but to using
the unadjusted specific resistance.
The assumption that the final solids content term can be ignored in
Equation 39 may be invalid for water treatment sludges. In water treatment
sludges the initial and final solids content may be on the order of 0.5 and
1.5 percent, respectively. Using Equation 39 for f, employing the media
factor, and correcting for the variation of specific resistance with pressure,
the equation for drainage of water treatment sludge may be expressed as
t =
m Rc FQ F u
H
a+l
o+l
_
(100Ff - 100FQ)
(47)
where: m = media factor (dimensionless).
EVAPORATION OF MATER
A net input of thermal energy to a flat free-water surface increases the
free kinetic energy of the water molecules to the point where some are able
to escape across the liquid-gas interface. The amount of heat absorbed by a
unit mass of water while passing from the liquid to the vapor state at con-
stant temperature is called the latent heat of evaporation or latent heat of
vaporization (7). Molecules of water that leave the liquid surface cannot
readily re-enter due to a decrease in kinetic energy. Under equilibrium con-
ditions water vapor may be treated as an ideal gas yielding the following
equation:
P s
(48)
where
p = partial pressure of water vapor (ML" T )
o
p = mass density of water vapor (ML" )
221
RV = gas constant for water (L T T )
T = absolute temperature (T)
Further vaporization causes a continued increase in p in the air above the
liquid until condensation begins. When the rate of condensation and the rate
of vaporization become equal the air is saturated with vapor and molecules
cross the interface in both directions at the same rate. The partial pres-
sure of the vapor in the air at which this equilibrium takes place is known as
the saturation vapor pressure, or simply the vapor pressure of the liquid.
This vapor pressure is an increasing function of the liquid temperature.
Equilibrium never exists under natural conditions since the volume of air
into which vaporization takes place is essentially infinite. Also, various
convective transport processes will operate to transport the vapor both
parallel and perpendicular to the liquid surface, thus preventing equilibrium
33
-------
from occurring.
Laboratory studies on evaporation from free water surfaces have been
reported by many investigators in various disciplines. Boelter et al . (8)
presented the following empirical equation, developed under laboratory
conditions, for evaporation rate into a quiescent atmosphere.
Eu=Ke(Pj-pg) (49)
where E = evaporation rate (ML~ T" )
K = evaporation transfer coefficient (T~ )
-1 -2
p. = partial pressure of water at interface (ML T )
i _1 _p
p = partial pressure of water in main gas (ML" T" )
The value of K is 0.054 when pressures are reported in inches of mercury.
Other investigators found similar values for K .
When evaporation is taking place from a free-water surface, it is helpful
to assume that a thin film of vapor saturated air forms adjacent to the water
surface. The film temperature is assumed to be the temperature of the water.
Whenever the saturation vapor pressure at film temperature is greater than
the partial pressure of the water vapor in the air immediately above the film
a gradient in vapor pressure will exist. The evaporation function may be
written as
Er = -K dpg/dZ (50)
where E = evaporation rate (LT~ )
Z = elevation(L)
K = transfer coefficient (M"]L3T)
The dependence of E upon total atmospheric pressure and salinity as
well as upon tempera tureris implied through variation of p with these vari-
ables. The presence of wind will have a major effect on E , since by convec-
tion it will remove the vapor-laden air, thereby keeping tine film thin and
maintaining a high transfer rate. Other factors influencing the evaporation
rate, either directly or indirectly, are solar radiation, air temperature,
and vapor pressure.
The depression of the evaporation rate due to salinity or dissolved
solids can be formulated by Henry's law which may be written as
Pa=Chx (51)
-1 -2
where P = partial pressure of component a (ML~ T~ )
Ch = Henry's law constant (ML~V2)
x = mole fraction of component a in liquid phase (dimensionless)
34
-------
Since x is defined as the ratio of moles of component a (in this case water)
to the total moles, a dilute solution will exert a higher vapor pressure and
the driving force (p. - p ) in Equation 49 will approach the maximum (that of
pure water). For increasing values of x (dense solutions), the driving force
decreases, hence the evaporation rate decreases.
According to Eagleson (7) there are two fundamental approaches to the
theoretical study of evaporation from a free water surface. The diffusion
method involves a mass-transfer process by which vapor is removed from the
liquid surface. The energy-balance method involves determining an average
rate of water loss by evaporation over a given time interval. Penman(9)
first utilized the best features of both of the theoretical approaches in
order to derive a water-surface evaporation relation which is dependent upon
a limited number of fairly easily measured meteorological variables. Kohler
et al. (10) further developed Penman's model to obtain a graphical method as
shown in Figure 14 which allows prediction of daily water surface evaporation.
In order to apply the concepts of Figure 14 to natural water bodies,
adjustments must be made for advected energy and for changes in heat storage.
This adjustment is in the form of a pan coefficient which is the ratio of
the rate of evaporation in a pan of water to the rate of evaporation in a
large body of water. Measurements are somewhat simplified by using a stan-
dard circular pan which may be installed on the ground (land pan) or in the
water (floating pan). The average coefficient for the land pan is about 0.7
and for the floating pan, 0.8. Complete instructions for making these measure-
ments are given by the U. S. Weather Bureau (11).
Average annual evaporation rates for lakes in the United States have
been compiled by the U. S. Weather Bureau. The average annual lake evapora-
tion, in inches, for the period 1946-1955 is presented in Figure 15 as taken
from Kohler et al. (12).
DRYING
When asoliddries, two fundamental and simultaneous processes occur.
These are: transfer of heat to evaporate liquid and transfer of mass as
internal moisture and evaporated liquid. Drying of solids encompasses two
different types of material: porous and nonporous. It is customary to assume
that a drying solid is either porous or nonporous although McCabe and Smith
(3) state that most solids are intermediate between the two extremes. Either
type may also be hygroscopic or nonhygroscopic. The drying of a solid may
be studied from the standpoint of how the drying rate varies with external
conditions such as temperature and humidity or with changes in moisture in
the interior,of the solid. Internal liquid flow may occur by several
mechanisms, depending on the structure of the solid. Some of the possible
mechanisms as listed by Marshall and Friedman (13) are as follows: (1) dif-
fusion in continuous homogeneous solids, (2) capillary flow in granular or
porous solids, (3) flow caused by shrinkage and pressure gradients, (4) flow
caused by gravity, and (5) flow caused by a vaporization-condensation sequence.
In general, one mechanism predominates at a given time during drying in a
solid and it is not uncommon to find different mechanisms predominating at
35
-------
OJ
01
Figure 14: Lake evaporation relation (adapted from Figure 6 of Ref. 12)
-------
00
Wot. 2. AVERAGE ANNUAL LAKE EVAPORATION IN INCHES
(PERIOD W4609U)
YWKJlOGiC (NV(SHO»TK)NS SfCliON
H»MOtOGlC MIVCIS DIVISION
VEATttft KuBiAU
Figure 15: Mean annual evaporation (inches) from shallow lakes and reservoirs(Ref. 12).
-------
different times during the drying cycle. Drying theories vary somewhat, how-
ever, the theories presented by Sherwood (14,15) are generally accepted and
their applicability toward sludge drying will be briefly reviewed.
The initial stages of water treatment sludge drying would be expected to
approximate that of a free water surface. Ample water is available for
evaporation and some sedimentation may take place. It is not uncommon to see
relatively clear supernatant on some types of water treatment sludges. As
drying continues the volume changes in proportion to the amount of water lost.
A thin film of water at the surface is replenished from within as fast as it
can evaporate. Eventually a solid cake forms and the internal resistance to
moisture movement becomes large enough that the rate of replenishing the water
at the surface is less than the rate the air can absorb it. The moisture
content at which this occurs is called the first critical moisture content.
Additional drying continues at the solid surface but at a decreased rate.
The zone of evaporation may gradually move into the sludge mass and into the
pores of the walls of any cracks that develop. At this stage the rate of
vapor transport through the empty pores becomes a major factor. A second
critical moisture content is often reached at which evaporation takes place
solely within the interior of the solid. At this point and beyond, resist-
ance to evaporation from surfaces of individual solids dominates. Some
water such as hygroscopic water and hydrate water cannot be removed at atmos-
pheric temperature even though the solid may be considered to be dry.
Significant elevation of temperature is required to remove this moisture.
During the falling rate drying period the rate may be determined either by the
resistance to water removal at the surface or by the resistance to moisture
movement within the material. A plot of drying rate versus moisture content
for the falling rate period will vary significantly with different materials.
Sherwood (16) presented drying curves for various substances as shown in
Figure 16. Curve A is for porous ceramic plate and follows the drying pro-
cess as described above. Curve B represents the drying-rate curve obtained
in the drying of soap and wood. This case is typical where internal dif-
fusion predominates throughout the falling-rate period. Curves C and D
represent drying-rate curves which may be obtained in cases where vapor re-
moval predominates throughout the falling-rate period. Curve C is for sul-
fite pulp slab. Curve D represents the drying of newsprint, bond, or blot-
ting papers, where vapor removal and not internal diffusion controls the
drying.
DIFFUSION OF MOISTURE
Drying of nonporous solids such as soap, glue and plastic clay have been
described by diffusion. These substances are essentially colloidal gels of
solids and water which retain considerable amounts of bound water.
Sherwood (17), Newman (18) and Luikov (19) studied the movement of
moisture during the drying process for various drying conditions and
materials. The general flux equation for moisture movement can be pre-
sented as:
38
-------
CM
'_!
s
UJ
5
cr
, POJROUS
^CERAMIC PLATE
UJ
5
tr
DC
o
B
SOAP OR
WOOD
MOISTURE CONTENT, % MOISTURE CONTENT, %
UJ
5
or
rSULFITE
>APER SLAB
MOISTURE CONTENT, % MOISTURE CONTENT,%
Figure 16: Drying rate curves for various substances,
T w _ n au
1 = • A -at -Dp af
_p _i
where I = drying rate (ML" T" )
A = area (L )
W = mass of water (M)
w
t = time
2 -1
D = constant diffusion coefficient (L T )
p = density (ML"3)
U = average moisture content, dimension!ess
x * distance (L)
(52)
39
-------
The general partial differential equation for variation in moisture con-
tent with time for unidirectional flow is given by the diffusion equation
^ = D 4f (53)
9t ax^
The solutions of Equation 47 for several boundary and initial conditions
have been presented by Carslaw and Jaeger (20), Crank (21), and Ozisik (22).
All solutions assume a slab of thickness 2£ drying from both surfaces, where
Shrinkage is negligible, the diffusion coefficient is a constant, and all
moisture is subject to diffusion. Two common cases encountered in the
literature are cited. When the initial moisture content, U , is uniform and
where the surface moisture content, U , is constant, a solution of Equation
53 is given by Equation 54. When the rate of drying at the surface is con-
stant, I , and the initial moisture content, U , is uniform, the solution of
Equation 52 given by Gil li land and Sherwood (23) is Equation 55.
U-U 4 2 1
= > ] - cos
3 IT
exp[-9Dt(^)2J + 1 cos Sjjf (54)
(U-U)
0
0 c 2)
2 2 Dt
n ir ^-)cos-(mr (x-x.)/£>] (55)
The main limitations to describing moisture movement by diffusion during
drying are the assumptions of constant diffusion coefficient and negligible
Shrinkage (constant thickness). Hougen et al. (24) and Ceaglske and Hougen
(25) found that diffusivity varied with moisture content for various solids
such as paper pulp and sand. Variable diffusivities for wood and other
building materials are also reported by Luikov
If diffusivity is a function of the moisture content, the moisture trans-
port rate may be written
Moisture Flux Rate = -D(U)|^ (56)
oX
which, when combined into a conservation of mass equation, yields
as the concentration dependent diffusion equation. The variation of the
40
-------
diffusion coefficient with moisture content must be evaluated from experi-
mental data.
DRYING RATE
The drying-rate approach presents a less fundamental study of internal
moisture conditions, however, it is experimentally straight-forward and its
application is not sensitive to problems of shrinkage.
The drying-rate method makes calculation of drying times straight-
forward. Drying studies can often be conducted under conditions identical to
those the materials will be exposed to during actual processing. Moisture-
time curves can be constructed requiring only an initial moisture content
measurement and measurements of the loss of water at various times. The time
to dry the material to any desired moisture concentration can then be read
from the moisture-time curve directly. Such a curve is shown in Figure 17.
Note that the sludge mass-time curve is the only experimental curve, the others
being constructed from the data. The general case involves predicting drying
times for materials under a variety of drying conditions only a few of which
need be simulated in the laboratory.
CO
CO
UJ
CD
Q
_l
CO
TIME (t)
UJ
8
UJ
K
h-
co
o
TIME(t)
CM
u
UJ
B
TIME(t) MOISTURE CONTENT,%
Figure 17. Sludge drying relationships, various parameters.
41
-------
The evaporation of unbound moisture from a solid exposed to constant
drying conditions has been explained by Treybal (2). Since evaporation of
moisture absorbs latent heat, the liquid surface will come to and remain at
an equilibrium temperature such that the rate of heat flow from the surround-
ings to the surface equals the rate of heat absorption. If the solid and
liquid surface are at a different temperature than the surroundings, the
evaporation rate will vary until equilibrium conditions are reached as shown
by points A and B. The vapor pressure at the surface thereafter remains
constant causing the rate of evaporation to remain constant. This period is
the constant-rate drying period previously described and shown between points
B and C.
When the average moisture content reaches the first critical moisture
content (point C), the surface film of moisture is so reduced by evaporation
that dry spots appear upon the surface. This gives rise to the first falling-
rateperiod (point C to point D). The moisture content at point D is the
second critical moisture content and the second falling-rate period is shown
between points C and D, The moisture content at point E is the equilibrium
moisture content and is the minimum moisture content obtained under this
drying condition.
This method was used by Nebiker (26) to describe the drying of digested
sewage sludges on open air drying beds. Since the expression for moisture
content is
W
U-IOOT^— (58)
WTS
where WTS = mass of dry solids (M)
the rate of drying is
dW WTC ...
T = _w = TS dU ,_ .
1 " Adt " 100A dt lby;
Rearranging and integrating over the time interval while the moisture content
changes from its initial value U to its final value U. ,
W
TS
' J
100A
o
Ut
(60)
If the drying takes place entirely in the constant rate period so that U
and U. > U~D and 1=1, Equation 60 becomes
L UK C
If the entire falling rate period is taken as a straight line then
(u-u )
CR>Ut>Ue (62)
42
-------
V
where Ue = equilibrium moisture content (dimensionless).
Upon substitution of Equation 62 into Equation 60 the following is
derived:
WTS(UCR - u ) (u -u )
t = _]_£ LK e in IK f
Tf A I 100 (Ut-U )
If the equilibrium moisture content is negligibly small, Equation 63 may be
written as
WTS UCR UCR
*f = A~T TOO ln D^~ ' f°r UCR > Ut > Ue (64)
For a material drying in both the constant and falling rate periods, the
total drying time would be
t = tc + tf
CUo-UCR + UCR ln Ut
CRITICAL MOISTURE CONTENT
The importance of the first critical moisture content is evident from
inspection of the previous equations. Most of the relationships to predict
the critical moisture content were derived using the diffusion method of
moisture movement in the interior of the solid. Methods to calculate the
critical moisture content have been presented by Sherwood and Gilliland (23),
Luikov (19), and Broughton (27).
Broughton derived a relationship for the critical moisture content on
the assumption that the surface-free moisture concentration at the critical
point is dependent on the nature of the material but not the drying con-
ditions. If the constant-rate period is long enough the steady state is
achieved and Equation 53 results in a parabolic moisture distribution across
the slab as shown in Figure 18, the equation for which is
U -Ux (x-£)2
W= -T <66)
where U = moisture control at the surface (dimensionless)
U = moisture content at the midplane (dimensionless)
Differentiating and substituting x = 0 and x = 2a gives gradients at the
surface as
43
-------
SLAB THICKNESS (L)
Figure 18. Moisture content vs. slab
thickness.
(67)
U can be determined from
Uxdx
where Ux = moisture content at a specific location (dimensionless)
Substituting U from Equation 66 into Equation 68 and integrating,
U-Us = I
-------
where Ug = equilibrium moisture content (dimensionless) .
Upon substitution of Equation 62 into Equation 60 the following is
derived:
WTS(UCR - u ) (uCR-u )
e I •
• . .
f A I 100 (U.-UJ
\f U c
If the equilibrium moisture content is negligibly small, Equation 63 may be
written as
W U U
'f-ri^ W1nu 'forUCR>Ut>Ue (64)
For a material drying in both the constant and falling rate periods, the
total drying time would be
t = tc + tf
tVUCR + UCR in (j)], for UQ > UCR > Ut (65)
CRITICAL MOISTURE CONTENT
The importance of the first critical moisture content is evident from
inspection of the previous equations. Most of the relationships to predict
the critical moisture content were derived using the diffusion method of
moisture movement in the interior of the solid. Methods to calculate the
critical moisture content have been presented by Sherwood and Gilliland (23),
Luikov (19), and Broughton (27).
Broughton derived a relationship for the critical moisture content on
the assumption that the surface-free moisture concentration at the critical
point is dependent on the nature of the material but not the drying con-
ditions. If the constant-rate period is long enough the steady state is
achieved and Equation 53 results in a parabolic moisture distribution across
the slab as shown in Figure 18, the equation for which is
U -Uy (x-£)2
^= —
where U = moisture control at the surface (dimensionless)
U = moisture content at the midplane (dimensionless)
Differentiating and substituting x = 0 and x = 2i gives gradients at the
surface as
43
-------
SLAB THICKNESS (L)
Figure 18. Moisture content vs. slab
thickness.
x s =
(67)
U can be determined from
Uxdx
where U = moisture content at a specific location (dimensionless)
/\
Substituting U from Equation 66 into Equation 68 and integrating,
U-u = 1 (u -U )
Equations 52, 58, 67, and 69 may be combined to give
(68)
(69)
44
-------
dU 3D(U-U )
*p dt = — T^ (70)
which when integrated results in
7 1
where I = the constant drying rate (ML T )
{+
The diffusion coefficient, D, would be expected to depend on the nature of
the material and the viscosity of the liquid. Assuming that D varies in-
versely as the viscosity and using the fact that the variation of viscosity
of water is inversely proportional with temperature
D = £= K(a + b Ta) (72)
where v = dynamic viscosity (ML" T )
K = constant (MLT~2)
a = constant (M-1LT)
b = constant (M^LTe"1)
T, = temperature (0)
a
Using the dry bulb temperature of the air and substituting for D in
Equation 71 ,
I (I ) U -U
UCR = Uo
os
The main limitations to Equation 71 are the assumptions of no shrinkage
and mechanism of diffusion. The applicability of this to predicting the
critical moisture content in water treatment sludge drying is questionable.
Nebiker (26) simplified the above procedure by assuming thickness to be
a function of the mass of solids, allowing Equation 71 to be expressed as
UCR = f (Ic> WTS/A) (74)
Nebiker also assumed a constant diffusivity and a negligible equilibrium
moisture content. For open-air drying of wastewater sludges the following
empirical equation was developed from Equation 74:
UCR = 500 (Ic-WTS/A)1/2 (75)
Values of ILR from Equation 75 when used with Equation 65 gave calculated
drying times which compared favorably with actual drying times.
45
-------
REFERENCES
1. Spangler, M. G. Soil Water. Soil Engineering. 2nd Ed., International
Textbook Co., Scranton, PA, 1960, pp. 84-90.
2. Treybal, R. £. Drying. Mass-Transfer Operations. McGraw-Hill Co.,
New York, 1955, pp. 524-583.
3. McCabe, W. L., and Smith, J. C. Unit Operations of Chemical Engineering,
2nd Ed., McGraw-Hill Co., New York, 1967, pp. 512-515.
4. Coackley, P. and Jones,B. R. S. Interpretation of Results by the
Concept of Specific Resistance. Sewage and Industrial Wastes, August,
1956.
5. Eckenfelder, W. A. and O'Connor, D. J. Biological Waste Treatment.
Pergamon Press Ltd., New York, 1961.
6. Rich, L. G. Unit Operations of Sanitary Engineering. John Wiley &
Sons, Inc., New York, 1961.
7. Eagleson, P. S. Evaporation and Transpiration. Dynamic Hydrology.
McGraw-Hill Co., New York, 1970, pp. 211-241.
8. Boelter, L.M.K., et al. Free Evaporation into Air of Water from a
Free Horizontal Quiet Surface. Industrial and Engineering Chemistry,
38(6), June, 1946.
9. Penman, H. L. Natural Evaporation from Open Water, Bare Soil, and
Grass. Proceedings, Royal Society (London), Ser. A, Vol. 193, 1948,
pp. 120-145.
10. Kohler, M. A., et al. Evaporation from Pans and Lakes. Research
Paper No. 38. U.S. Weather Bureau, 1955.
11. Instructions for Climatological Observers. U.S. Department of
Commerce, Weather Bureau, Circular B, 10th Ed., Washington, D.C.,
October, 1955.
12. Kohler, M. A. et al. Evaporation Maps for the United States.
Technical Paper No. 37, U.S. Department of Commerce, Weather Bureau,
Washington, D. C., 1959.
46
-------
13. Marshall, VI. R., and Friedman, S. J. Drying. Chemical Engineers
Handbook. 3rd ed., J. H. Perry, ed., McGraw-Hill Co., New York, 1950,
pp. 799-884.
14. Sherwood, T. K. The Drying of Solids--!. Industrial and Engineering
Chemistry, 21(1):12-16, January, 1929.
15. . The Drying of Solids —II. Industrial and Engineering Chemistry,
2T[TO):976-980, October, 1929.
16. . The Air Drying of Solids. Transactions, American Institute of
Chemical Engineers, 32:150-168, 1936.
17. . Application of Theoretical Diffusion Equations to the Drying
of Solids. Transactions, American Institute of Chemical Engineers,
27:190-202, 1931.
18. Newman, A. B. The Drying of Porous Solids: Diffusion and Surface
Emission Equations. Transactions, American Institute of Chemical
Engineers, 27:203-217, 1931.
19. Luikov, A. V. Heat and Mass Transfer in Some Engineering Processes.
Heat and Mass Transfer in Capillary-Porous Bodies, 1st English ed.,
Pergamon Press, New York, 1966, pp. 341-376.
20. Carslaw, H. S. and Jaeger, J. C. Conduction of Heat in Solids, 2nd
ed., Oxford University Press, London, 1959.
21. Crank, J. The Mathematics of Diffusion. Oxford University Press,
London, 1956.
22. Ozisik, M. N. Boundary Value Problems of Heat Conduction.
International Textbook Co., Scranton, PA, 1968.
23. Gilliland, E. R. and Sherwood, T. K. The Drying of Solids—VI:
Diffusion Equations for the Period of Constant Drying Rate. Industrial
and Engineering Chemistry, 25(10):1134-1136, October, 1933.
24. Hougen, D. A., et a1. Limitations of Diffusion Equations in Drying.
Transactions, American Institute of Chemical Engineers, 36:183-209,
1940.
25. Ceaglske, N. H. and Hougen, D. A. The Drying of Granular Solids.
Transactions, American Institute of Chemical Engineers, 33:283-312,
1937.
26. Nebiker, J. H. The Drying of Wastewater Sludge in the Open Air.
Journal WPCF, 39(4):608-626, April, 1967.
27. Broughton, D. B. The Drying of Solids--Prediction of Critical Moisture
Content. Industrial and Engineering Chemistry, 37(12):1184-1185,
December, 1945.
47
-------
28. Sanders, T. G. A Mathematical Model Describing the Gravity Dewatering
of Wastewater Sludge on Sand Drainage Beds. Master's Degree thesis,
University of Massachusetts, Amherst, 1968.
29. Nebiker, 0. H., et a!. An Investigation of Sludge Dewatering Rates.
Presented at the 23rd Annual Meeting of the Purdue Industrial Waste
Conference, Purdue University, Lafayette, Indiana, May, 1968.
30. Lutin, P. A., et al. Experimental Refinements in the Determination
of Specific Resistance and Coefficient of Compressibility.
Proceedings, 1st Annual New England Anti-Pollution Conference,
University of Rhode Island, Kingston, Rhode Island, 1968.
48
-------
SECTION V
MATERIALS AND APPARATUS
TYPES OF SLUDGE EXAMINED
Sludge resulting from four different types of water treatment was used
for drying and complex dewatering studies. Various wastewater treatment
sludges were also used for detailed study of gravity drainage. The four
different types of water treatment sludge studied represented the following
treatment processes: softening, alum coagulation, alum coagulation with iron
removal, and alum collection with activated carbon. A brief description of
each plant follows.
Albany. The raw water supply for Albany, New York, consists of two im-
pounding reservoirs, Alcove and Basic, which contain 47.4 and 3.79 million
cubic meters (12.5 and 1.0 billion gallons), respectively. The Alcove water-
shed has an area of 8370 hectares (32.33 square miles) with a flooded area
of 580 hectares (1440 acres). The Basic watershed has a drainage area of
4200 hectares (16.37 square miles) with a flooded area of 107 hectares
(265 acres). Water from the Basic reservoir passes into the Alcove reservoir
by means of a tunnel 975 meters (3200 feet) long. The impounding reservoirs
are treated with copper sulfate at times of sudden onset of algal blooms.
The filtration plant in Fuera Bush is of the conventional rapid sand
type, with aeration, alum coagulation-flocculation and sedimentation, and
filtration followed by chlorination. There is provision for pH stabiliza-
tion with lime, and taste and odor control with activated carbon, however,
the sludge samples collected for this investigation contained only alum.
Sludge is stored in sedimentation tanks for approximately 6 months and then
discharged to a nearby receiving stream.
Amesbury. The raw water supply for the Town of Amesbury, Massachusetts,
is a well field consisting of some 300 shallow wells of 5 to 23 cm (2 to 9
inches) diameter. The raw water contains an abundance of iron and treatment
thus consists of aeration; flocculation with alum and caustic soda followed
by addition of activated carbon; sedimentation in a manually cleaned basin;
filtration through manually cleaned slow sand filters; and chlorination.
The sludge is decanted before being discharged twice a year into a nearby
lagoon where it dewaters for approximately six months.
Bill erica. The raw water for the Bill erica, Massachusetts, water
treatment plant is the Concord River. Various industrial wastes are dis-
charged into the river causing the water to be very turbid and to promote
49
-------
algal growth. Treatment consists of flocculation with alum and activated
carbon, sedimentation in a continuously mechanically cleaned basin, rapid
sand filtration, and chlorination. The sludge is discharged daily to a near-
by lagoon. The capacity of the lagoon is exceeded by the sludge discharges.
The overflowing sludge flows directly into the Concord River.
Murfreesboro. The raw water supply for Murfreesboro, Tennessee, is
the East Fork of Stones River. The intake is on the back water from Walter
Hill Dam which marks the beginning of Percy Priest Reservoir. The raw
water contains a hardness of approximately 67 mg/1. The treatment process
includes softening, sedimentation, rapid sand filtration and chlorination.
Chemicals added during the treatment process include ferric sulfate, lime,
soda ash, and activated carbon. Sludge is continuously transferred from the
softening and settling basins to two lagoons. The lagoons are used alter-
nately, each having approximately two years capacity. Supernatant is with-
drawn from the lagoons by means of an overflow weir and discharged to the
river.
EQUIPMENT FOR THE GRAVITY DRAINAGE STUDY
In order to obtain statistically significant and accurate results,nine
columns (Figure 19) were fabricated for the first phase of the research
project. The column diameter, not a determining factor in the results as
pointed out by previous investigators (1), was 10.2 cm (4.0 in) I.D., large
enough to insert a hand but small enough so that only a minimal amount of
sludge would be needed for the experiment. The corrosion resistant acrylic
columns were 0.6 cm (.25 in) thick and 91.5 cm (36 in) long. Flanges were
fastened at each end of the columns, so that acrylic plates could be bolted
in place with an 0-ring seal to prevent leakage of water and air. Nickel-
plated nozzles attached to the plates connected at each end of the column
were the only outlets. 0-ring seals were also used to prevent leakage from
the nozzle connection.
Placed directly below each column were 1000 ml lucite cylinders, gradu-
ated to 2 milliliters. A No. 12 rubber stopper with two holes was placed in
each graduated cylinder with 0.6 cm (1/4 in) I.D. Tygon tubing connected
to a glass tube in the stopper and to the lower nozzle of the column. Tygon
tubing was also connected to the top nozzle of the column which ran to
another glass tube in the stopper, thus preventing evaporation and maintain-
ing a saturated humidity. No pressure differences could exist in the column
and the cylinder, for the filtrate displaced the same volume of air in the
graduated cylinder as would be needed by the volume vacated by the filtrate
in the column.
EQUIPMENT FOR DRYING, EVAPORATION, AND COMPLEX
DEWATERING STUDIES
Two types of containers were used in the drying and evaporation studies,
Drying studies utilized glass pans, 0.5cm (0.2 in) thick. The inside
dimensions of the pans were 22 x 35 x 4.5 cm (8.7 x 13.8 x 1.8 in) and
50
-------
10 GLASS
TUBES
SAND DEPTH 2.5 cm
1
1-
1.5cm
5 cm
i
3ER
ff .
1
__ L
V
x_
X—
v^
v —
V— _ .
i
* •
.. ' >
87,9
TUBING-
TUBING
-1000 ml
GRADUATED
CYLINDER
Figure 19. Gravity drainage apparatus with piezometer tubes. The
supporting filter media consists of 2.5 cm of sand underlain by
approximately 1.5 cm of coarse gravel. The top sand surface lies
30.9 cm above the datum. All dimensions are in centimeters.
51
-------
19 x 30 x 4.5 cm (7,5 x 11.8 x 1.8 in). Evaporation studies were conducted
in plastic pails, 27.5 cm (10.8 in diameter) and 35.5 cm (14.0 in}'high (in-
side dimensions).
Plastic columns were fabricated for the complex dewatering studies._
The column walls were 1.3 cm (1/2 in) thick and were connected with machine
screws. The inside dimensions of the columns were 12.7 x 12.7 x 91.4 cm
(5 x 5 x 36 in). The columns were arranged continuously and supported by
a metal stand. This arrangement permitted measurements of the filtrate
volume and facilitated other measurements and observations.
In order to maintain constant known environmental conditions, an en-
vironmental chamber was constructed and utilized for all evaporation, drying,
and dewatering studies. This chamber consisted of a room approximately 4.3 x
4.9 x 3 m (14 x 16 x 10 ft), specially modified to minimize heat and moisture
losses. Constant temperature and low relative humidities were maintained by
a 31,000 BTU/hr air conditioner with electric heat and reheat capabilities.
High relative humidities were maintained by two humidifiers, each with a
capacity of 36,4 kg (80 Ibs) per day. An electronic control system was cap-
able of maintaining relative humidity between 30 and 80 ± 2 percent and
temperature between 18.3 and 29.4 + 1.1 C (65 and 85 + 2 F). A continuous
record of both temperature and relative humidity was maintained by a wall-
mounted recorder. A schematic diagram of the environmental chamber is
show in Figure 20.
1 —
/
ELECTRIC,
HEATER ><
AIR „
CONDITIONER
/
m
•*•
s*
/
/
/•
/•
/•
/
/
/
s*
/•
/
/
/
/*
s
/
/
/
^
/
/
/
AIR FLOW — - — v \
*1 ti * ^ACOUSTICAL
^
kj
I5
1
i
^ CEILING
HUMIDIFIER
ITY /
VATER *
RECORDER
a — *•
CONTROLS
'WASTE
L/
/
/
/
/
/•
/
S
/
/
x"
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
1
Figure 20. Diagram of environmental chamber.
52
-------
Some of the drying experiments were conducted with slight wind velo-
cities in order to facilitate drying and enhance air circulation in the
tall dewatering columns. Air was provided by a 0.04 cubic meters per minute
(1.5 cfm) blower and an 11.4 x 3,8 cm (4-1/2 x 1-1/2 in) duct served as a
manifold supply. Equally spaced 1 cm (3/8 in) diameter holes provided a
uniform air stream to each column.
MOISTURE MEASUREMENT APPARATUS
The basic equipment for measuring moisture profiles by gamma-ray attenu-
ation included scintillation, detection, and counting equipment; shielding;
and auxiliary equipment arranged as shown in Figure 21.
A rigid structural truss assured alignment of the detector with the
source beam. All were mounted on a hydraulic fork lift, permitting measure-
ments at any elevation desired. The entire apparatus could be moved forward
manually along the support for measurement at the various columns.
In order to assure repetitive measurements at a particular vertical
location on a column, machined metal spacers of various thicknesses were
placed on the vertical shaft of the hydraulic cylinder of the fork lift.
The weight of the apparatus would be supported by the spacers when hydraulic
pressure was released, thus fixing the vertical position of the source and
detector. A tape measure mounted on the side of the fork lift allowed
measurements of the vertical elevation to millimeter accuracy.
Five plastic boxes were fabricated to obtain attenuation coefficient
measurements of sludge and water. These boxes were constructed of 1.3 cm
(0.5 in) plastic, carefully machined, with all connections made with machine
screws. The plastic boxes had inside dimensions of 12.7 x 10.2 cm (5 x 4 in),
with widths of 3.8, 7.6, 11.4, 15.2, and 19.1 cm (1.5, 3.0, 4.5, 6.0 and
7.5 in).
SCINTILLATION COUNTING EQUIPMENT
The scintillation counting system included a scintillation-photomulti-
plier assembly, high voltage supply, voltage stabilizer, linear amplifier,
discriminator, and sealer-timer.
A gamma-ray photon, or ionizing event, struck the crystal in the detec-
tor and generated photons which caused a flash of light. These photons were
reflected by the crystal housing to the photocathode of the photomultiplier
tube. The photomultiplier multiplied the initial number of electrons by a
factor of about one million and delivered a charge proportional to the radi-
ant energy spent in the scintillator. The preamplifier received the charge
from the photomultiplier, gave it added gain, and served as an impedance
matching device to assure the maximum transfer of the signal from the detec-
tor to the amplifier. The amplifier accepted the voltage input pulse and
increased it in a linear manner, thus the relative sizes of the pulses were
53
-------
preserved. A differential discriminator followed the linear amplifier and
provided analysis of the pulse height information, sorted out pulses which
satisfied the present requirements, and rejected those which did not. The
difference in energy levels between the upper limit and the baseline was the
window width. The sealer-timer served as the point for all the information
from the detector. The timer determined the interval during which pulses
from the discriminator were collected. The high voltage supply furnished the
required dynode voltages to the photomultiplier tube.
The amplifier, single channel analyzer, and sealer-timer were of the
RIDL series, manufactured by Nuclear-Chicago Corporation. The amplifier was
a model 30-23. The sealer-timer was a model 49-25. The sealer portion was
composed of three cascaded transistorized decades which drove a four-digit
mechanical register with a total storage of up to 10 counts. The register
responded to a maximum input rate of 20,000 pulses per second on a continuous
basis. A mechanical timing dial could be set manually for any desired time,
and then operated electrically to return its indicators to zero during the
elapsed time for which it was set.
The voltage stabilizer, manufactured by the Raytheon Corporation, had an
input voltage range of 95-130 volts, with an output voltage of 115 volts.
The high voltage supply was of the 2 KV type, manufactured by the Harshaw
Company. The scintillator-photomultiplier system, a 5.1 x 5.1 cm (2inx
2 in) Na(Tl) crystal, also was manufactured by the Harshaw Company. A Baird-
Atomic survey meter and Nuclibadge film-badge service provided additional
monitoring devices.
Shielding and Collimation
The shielding consisted of a specially constructed lead block for col-
limating the gamma beam and providing radiation safety to operating person-
nel. The shielding and scintillation detection equipment were positioned by
means of the hydraulic fork lift previously described.
Since the weight of the lead shield was not an important factor, the
shielding was designed to reduce the radiation to values only slightly
greater than background levels. According to Gardner (2) normal background
varies from 0.01 to 0.03 mR (milliroentgen) per hour. One milliroentgen is
approximately equal to one millirad (mrad), the unit of physical radiation
dose. The dose rate in mrad per hour at a distance z in cm from a point
source of gamma radiation at strength A in me (millicuries) is calculated
by S
fi ^a Ac
D.R.(z.z') = 2.134 x 10° B(y,z)-^ E —^- exp (-yz1) (76)
2 3
where D.R. = radiation dose rate (L T )
B(y ,z) = buildup factor
a
-1 2
y /p = mass-attenuation coefficient (M L )
a
54
-------
Timer
Figure 21.
system.
Scalar
Single Channel
Analyzer
Amplifier
Lead
Collimation
Detector and
Preamplifier
110 Volt AC
Supply
Voltage
Stabilizer
High Voltage
Supply
,Column
Source
Lead Shielding
and Collimation
Schematic diagram of gamma-ray attenuation
55
-------
y = attenuation coefficient (M~ L )
2 -2
E = energy, Mev (ML T~ )
A - radiation strength (T~ )
z = distance, cm (L)
z' = shield thickness, cm(L)
For gamma radiation from a Cs-137 source the energy, EQ, is primarily 0.661
Mev. The mass attenuation coefficient measured in tissue is about 0.031/
cm2/gm, y is 1.134 cnH and the buildup factor (B ,z') for lead (from 3 to
20 cm thick) is approximated by Blizard's (3) relationship
B(y, z1) = 1.2 + 0.13Z1
Therefore, the dose rate in mrad/hr is:
1 Ac:
D.R.(z.z') = (4.27 + O^eSz'jlO-3 -4 exp(-l .134z')
(77)
(78)
NO.
1
2
3
4
5
6
PART NAME
HANDLE
DOOR
COLLIMATION BLOCKS
SLEEVE
SHIELD
SOURCE HOLDER
MAT
STEEL
LEAD
LEAD
STEEL
LEAD
LEAD
Figure 22. Diagram of source shielding and collimation.
56
-------
For the 250-mc Cs-137 source with 14 cm minimum lead thickness, the
radiation at the surface was approximately 0.017 mrad/hr, well below normal
background values (0.01 to 0.03 mrad/hr). In addition to adequate thickness,
care must be exercised in the design to minimize radiation leakage. A dia-
gram of the shielding used in this method is shown in Figure 22. "Good
Geometry" conditions are required for successful gamma-ray attenuation
measurements. Gamma rays from the source should be collimated so that only
a narrow beam strikes the absorber. A collimation slit of 0.1 x 1.9 cm
(0.04 x 0.75 inches) provided a narrow beam from the source, and a detector
collimation slit of 0.2 x 1.9 cm (0.08 x 0.75 inches) minimized buildup due
to scatter.
REFERENCES
1. Quon, J. E. and Tambyln, T. A. Intensity of Radiation and Rate of Sludge
Drying. Journal of the Sanitary Engineering Division, ASCE, 91, No. SA2,
April, 1965.
2. Gardner, W. H. Water Content. Methods of Soil Analysis: Part 1,
C. A.Black, ed., Academic Press, Madison, Wisconsin, 1965, pp. 82-127.
3. Blizard, E. P. Nuclear Radiation Shielding. Nuclear Engineering Hand-
book, H. Etherington, ed., McGraw-Hill Co., New York, 1958.
57
-------
SECTION VI
METHODOLOGY
A number of sludge related character!sties were measured in this
investigation. Chemical analyses were performed on sludge, decant, and fil-
trate samples. Dewatering studies required measurement of gravity drainage
rates, evaporation rates of water, drying rates of thin layers of sludge,
drying rates of thick layers of sludge on sand, and dewatering (drying plus
drainage) rates of sludge on sand. All ^tudies were conducted in the
environmental chamber under controlled temperature, relative humidity, and
wind conditions.
Moisture profile studies required refinements in the gamma-ray attenua-
tion method and determination of required physical parameters. These para-
meters were attenuation coefficients of dry sand, dry sludge solids and water
as well as particle densities of the sand and sludge.
SLUDGE CHARACTERISTICS
Representative sludge samples were used to determine chemical charac-
teristics of the sludge, decant, and filtrate. Physical properties such as
total solids, particle density and specific resistance were determined for
each individual study. Samples of the clear supernatant which resulted from
sedimentation were taken as representative decant samples. Filtrate samples
were collected during the drainage studies. The filtrate had passed through
9.0 cm of Ottawa sand. Unless otherwise specified, all analyses were per-
formed according to Standard Methods (1) and FWPCA Methods for Chemical
Analysis of Water and Hastes (2).Tn some cases standard procedures were not
available and it was necessary to develop suitable methods of analysis.
Six separate experiments were undertaken for which the average value of
triplicate analyses is reported.
Solids analyses were determined by heating the samples for 8 hours at
103 C to determine total solids and 20 minutes at 600 C to determine total
volatile solids. Experimental determination of specific resistance and
coefficient of compressibility is presented in detail.
GRAVITY DRAINAGE STUDY
In order to demonstrate that the drainage rate of sludge on a sand bed
is a function of specific resistance, coefficient of compressibility, initial
58
-------
solids content, and initial head, interference from outside factors which
affect the rate of moisture removal but which are unrelated to gravity
drainage had to be eliminated. These factors include evaporation and
flotation.
Evaporation, if not eliminated, would reduce the moisture of the sludge
at some unknown rate so that determination of head from the volume of filtrate
collected would be impossible. Therefore, the experimental apparatus was
designed as a closed system to prevent the entrance or exit of moisture.
Each column was initially calibrated with water by noting the time re-
quired for the water surface elevation to drop from 110 cm (43 in) to 30 cm
(11.8 in). Minor adjustments were made until the time deviation between
columns was 1.9 oercent. Addition of the sand, gravel, and the chromel 16
mesh (24 B&S gage) wire screen decreased discharge rates in each column
equally. Total drainage time using water was approximately 2 minutes, hence,
permeability of the supporting media was so large relative to the permeabil-
ity of the sludge that it could be disregarded in the computations.
It is important to note that the effective drainage head was the
distance from the upper sludge surface to the tip of the discharge tube. The
distance from the discharge tube to the sand surface approximated the stan-
dard design depths for sand in a drying bed. The additional head created is
thought realistically to approach the operation of properly constructed dry-
ing beds in which, as the sand becomes rapidly saturated, a vacuum tends to
form on the bottom of the sludge-sand interface, as was created also by the
discharge system of the experimental columns.
Three different sands were utilized for the experiments. To provide a
basis for later corroboration by other researchers, A.S.T.M. Standard
Ottawa sand was used. To develop information of practical value, sands from
drying beds of two treatment plants (Hermitage Hills, and Franklin,Tennessee)
were tested. These sands were coded as types 0, H, and F, and were sieve
analyzed.
Prior to each of the six experiments, all equipment including the
acrylic columns, graduated cylinders, and Tygon tubing was thoroughly washed
and rinsed with distilled water to avoid the possible problem of biological
or chemical contamination. Furthermore, all sand and gravel used in previous
experiments was replaced with clean material. Lastly, to prevent impedance
of flow due to the presence of air pockets, sand in the column was saturated
with distilled water before addition of sludge.
Experiments I-III were designed to test a settled sludge condition.
Sludges were introduced to the columns with an additional depth of super-
natant applied, thus providing a greater potential filtrate volume, and, in
essence, simulating conditions in a lagoon.
Experiments IV-VI used a homogeneous charge of sludge without an
applied supernatant. All nine columns of Experiment IV had an initial
head of 54 cm, with Franklin, Ottawa, and Hermitage sands used as the
supporting media in columns 1-3, 4-6, and 7-9, respectively. In Experiment V,
59
-------
Franklin sand was again the supporting media for columns 1, 2, and 3;
Ottawa sand for columns 4, 5, and 6; and Hermitage sand forcolumns 7, 8, and
9. However, the initial head varied--44 cm for columns 1, 4, and 7; 74 cm
for columns 2, 5, and 8; and 114 cm for columns 3, 6, and 9.
Once all nine columns were brought up to the proper head, the stoppers
were released so that drainage could begin. During the course of the six
experiments the volume of filtrate drained from the sludge in each column
was measured and recorded three times daily. The length of each experiment
varied from 20 to 57 days depending upon the time required for the drainage
of filtrate to cease in the majority of the columns and leave a dewatered
sludge cake.
For Experiment VI, only one column was used. Nine piezometer tubes
were placed along the length of the column so that the pressure at different
depths of sludge could be studied. To prevent the sludge from clogging the
piezometer tubes, the column was filled with distilled water, thereby fill-
ing the piezometer tubes. The tubes were stoppered, causing the distilled
water to remain in them after the column had been emptied. Sludge was then
poured into the column after which the stoppers on the piezometer tubes were
released. The initial head was 96 cm.
EVAPORATION AND DRYING STUDIES
To establish a control, evaporation studies were conducted to determine
evaporation rates from free water surfaces. Cylindrical plastic pails 27.5 cm
(10.8 in) diameter and 35.5 cm (14 in) high (inside dimensions) were filled
with water at depths of 9.6, 19.3, and 29.1 cm (3.8, 7.6 and 11.5 in). The
pails were placed at three locations within the environmental chamber. The
mass of containers plus water was determined to the nearest gram on a triple-
beam balance at intervals of approximately 1.5 days.
Since a plot of mass of water versus time is linear for constant drying
conditions,the slope is equal to the drying rate (MT~i). This allows com-
parison of drying rates using the method of comparison of regression lines.
The procedure utilized was taken from Hald (3). Straight lines were fitted
to the data by linear regression analysis. The hypothesis that the theoreti-
cal variances of the two populations are equal was tested by means of the
variance ratio. If the test did not reveal a significant difference between
the two variances, the slopes of the two regression lines were compared by
means of a t-test of f = N, + N2 - 4 degrees of freedom, such that
T _ M2_/[B1_ + 551__]V2 (?9)
1 2
where SSD. = zN(t.-I)2
U • I
$ = slope (80)
IfT exceeded the significance limit the test hypothesis was rejected and
60
-------
the two lines were considered to have different slopes.
If T was not significant the two regression lines were considered paral
lel. A common estimate of the slope 0 was obtained by forming the weighted
mean of the two slopes g-, and e?5 using the reciprocal values of the
variances as
SPDt w
SSDt H
SPD
V
+ SPD
h SSDt
Vi - Z(trt)
(w..-w)
where SPDt w = z(t.-t) (wrw) (82)
and t = 1 sti (83)
An analysis of variance was also performed which considered average evapora-
tion ratesas variables.
Two methods were considered in the data analyses of water treatment
sludge drying studies. The first method consisted of taking the derivative
of the sludge mass-time data. Various relationships were then fitted to
certain portions of the data. The second method considered the sludge mass-
time curve only.
The first method is the traditional one for analyzing drying data in
environmental and chemical engineering equations. The equation for obtaining
the derivative of a function W = f(t) for unequal spacing of the independent
variable t, as given by Salvadori and Baron (4) may be written:
% (tn> ' - ^ - (1-a - A-l . (84)
t , written as:
where a is the ratio between the spacings of the three points tn_-j , tn,
' (85)
and
• Vl • *n (86)
Moisture content may be obtained from the relationship
(y
W-WT<. W
U = (-rr^)lOO = 100(— - 1) (87)
TS
where WJS = mass of sludge solids (M).
The evaporation ratio E, in percent, is defined as the rate of evaporation
of sludge divided by the rate of evaporation of water. The shape of the
61
-------
drying rate curve and the rate of change of moisture content curve are the
same since
WTC dU
1 - (88)
when WTS and A are assumed constant.
It is known from theory that a constant-rate drying period should occur
under certain conditions. Thus the mass of water, W , is a direct function
of time,
dVI d(W-W,<0
dt
= B(constant) (89)
The mass versus time curve is therefore the integral of Equation 89 or a
straight line of the form
W = A + Bt (90)
In some cases the falling rate portion of the drying curve has been shown to
be approximately linear in the form
dW
^=D + Et (91)
Equation 91 indicates that the weight-time curve for the falling-rate portion
should be of the form
Jw = f(D+Et)dt (92)
therefore
ww = C + Dt + Et2 (93)
Statistical analyses of the constant-rate portions of the curves were
conducted by the same procedure used for the evaporation studies.
COMPLEX SLUDGE DEWATERING STUDIES
The primary methodology for complex sludge dewatering studies was to
determine the amount of water lost by gravity drainage, the solids content
at the end of drainage, and the solids content at the end of dewatering
(drainage plus drying).
All dewatering studies were conducted in plastic columns supported by a
metal frame. Temperature and relative humidity were carefully controlled
during the experiments. All sludges were dewatered on an 8.9 cm (3.5 in)
layer of saturated Ottawa sand, supported by a 2.5 cm (1 in) layer of washed
stone. Each sludge was thoroughly mixed in large quantities in a 115 liter
62
-------
(30 gallon) capacity concrete mixer for a minimum of 20 minutes. The sludge
was carefully placed in the columns by means of a specially constructed splash
rod which prevented damage to the sand bed while charging the columns. (Ali-
quot samples were taken simultaneously for laboratory analyses). Initial
mass of container (tare), tare plus mass of dry sand, and tare plus mass of
saturated sand were recorded. Sludge surface elevations, volume of filtrate,
and mass of sludge were recorded at various intervals. The sludge mass and
time were both recorded when drainage stopped. Samples of the filtrate were
taken for chemical analyses after drainage had continued for some time. This
insured a more representative sample since the sand and other media were pre-
viously saturated with distilled water.
The columns were permitted to drain throughout the entire dewatering
study. The total filtrate collected when drainage ceased consisted of water
drained from the sludge and the distilled water used to saturate the sand
beds initially. The procedure for calculating the solids content at the end
of drainage was as follows: the percentage of the total filtrate which came
from the sludge (excluding the water to saturate the support media) was
determined from
Vf = 100(l-V/Vt) (94)
o
where V,, = volume of filtrate (L )
3
V = volume of distilled water (L )
3
V, = total volume collected (L )
The corresponding drainage time for Vf was then determined from the cumula-
tive filtrate-time curve and the corresponding sludge mass was determined
from the sludge mass-time curve. The solids content at the end of sludge
drainage was calculated as the mass of total solids (previously determined)
to the total sludge mass.
MOISTURE PROFILE
Gamma-ray attenuation techniques have been used widely to follow the
rapid water content change in soil columns undergoing wetting (5,6,7,8).
More recently, this method was used by Tang (9) to determine moisture pro-
files in sewage sludges. Because gamma-ray attenuation provides a conven-
ient, rapid, non-destructive method for repeatedly measuring the solids or
moisture content of sludges, it was selected for determining in situ the
solids and moisture profiles in columns of water treatment sludge undergoing
dewatering.
Attenuation Equations. Evans (10) relates the intensity of monoener-
getic gamma rays after passing through several layers of material to their
incident intensity:
N = NQ exp (-£ v. p. I.)
where N = intensity of transmitted beam (dimensionless)
63
-------
N - intensity of incident beam (dimensionless)
-1 2
y. = attenuation coefficient of material i (M L )
q
p. = density of material i (ML )
L. = thickness of material i (L)
As an example, consider a plastic column which contains sludge and is sub-
jected to a monoenergetic beam of gamma rays as shown in Figure 23. The
gamma ray beam traverses the two column walls, each of thickness L , and the
sludge of thickness L . The applicable attenuation relation is
N = NQ exp - (2 ypPpLp
.-1,2,
where u = attenuation coefficient of plastic (M L )
_
p = density of plastic (ML~ )
-12
~
-
= attenuation coefficient of sludge (M~ L )
(96)
_
p = density of sludge (ML" ).
o
EMPTY COLUMN
Figure 23: Attenuation relations used in moisture profile
measurements.
to
Since sludge consists of water and solids, Equation 96 can be expanded
eXp -(2ypPpLp
(97)
where the subscripts p, w, and d refer to plastic, water and solids, respec-
tively. Attenuation of the plastic is described by the equation
Np = NQ exp
(98)
64
-------
where Np = intensity of beam transmitted through plastic (M°L°T0)
Division of Equation 97 by Equation 98 results in a simplified form:
N = Np exp - (VwLw + udPdLd) ' (99)
Adrian (11) showed that a relationship between L , L,, !_<., and the water
content, w, can be derived from the basic relationship
Ls • Lw + Ld
and the definition of solids content
S WTq p. V,
_ i o a • a
where S = percent solids content (dimensionless)
WTS = mass of solids (M)
Ww = mass of water (M)
3
V . = volume of solids (L )
o
V = volume of water (L ).
Solving Equation 101 for Vd results in
S p V
V = w w
V
_
d 100 pd (1 - S/100)
The respective volumes are related by Area A and Equation 100, by the rela-
tion
V, = ALS = A(Lw + Ld) = Vw + V, (103)
so the distance through the water may be expressed as
P(J(1 - S/100)
Lw = Ls [(S/100)pw + pd (r-S/100)] (104)
The distance through the solids becomes
(S/100pw)
Ld = Ls [(S/100)pw + pd (1-S/100)] (105)
The distance L can be readily measured. Therefore, a combination of
Equations 102,S104, and 105 are related to the counting measurements N and
N through the equation
65
-------
P
exp
P.JP...L
dws pd + S/100 (Pw-Pd)
(106)
Equation 106 can be rearranged as
)1
(107)
100 (P^- Pd) ln VN) + pwpdLs%- V
and since moisture content
U = 100(°-- 1) (108)
Equation 107 may be expressed in terms of moisture content as
N
U _ r
-------
The relative standard deviation, R.S.D. is defined as
Since the number of observed counts depends on the counting interval, the
R.S.D. can be decreased by extending the counting time.
The counting rate observed during a time t was defined as
n=f (112)
where n = counting rate (T )
Excluding errors in the measurement of time t, the standard deviation of the
counting rate would be
A counting time of 16 minutes was chosen for this study and provided a
standard deviation of (n)l/2/4 for the counting rate. To reduce the standard
deviation by half, i.e., to (n)l/2/8, would have required a counting time of
64 minutes.
The radioactivity detection instruments have finite resolving times with-
in which two occurring events may be distinguished and recorded separately.
Thus some counts are missed; the fraction lost increases with increasing
counting rate. A coincidence correction allows the mean number of counts
occurring to be calculated by the method given by Kohl et al . (14) as
where n = mean count rate occurring (T )
n = mean count rate recorded (T )
t = resolving time (T)
The number of lost counts is
nQ - n = n nQ tr
and
n
max
All count rates in this investigation were corrected for coincidence
losses using the previous equations and the published value for the counting
equipment of t = ly sec.
Attenuation Coefficient Measurements. Values for the attenuation
67
-------
coefficients for water and dry solids are needed in the gamma-ray attenuation
equations. The basic attenuation equation as used by Davidson et al . (6) can
be written as
N = Np exp [- (ydpb + uwe)L] (117)
_o
where p, = bulk density of the dry material (ML" )
p
,
_o
e = water content (ML )
L = thickness of sample (L).
For distilled water, Equation 117 reduces to
N = Np exp (-WWPW0 (118)
_2
where p = density of water (ML )
Equation 118 can be written as
ln N/Np = -VwL (119)
or in linear fashion
Y = BX (120)
where Y = ln(N/N )
x = PWL = L
since the density of water in the cgs system is approximately 1,0.
Plastic boxes of various thicknesses were used for making several
measurements of Y. The term B was found by regression analysis for a line
passing through the origin (15):
E X. Y
B = - V1 (121)
EX.2
the variance
°2 = ih~E(Yi " BXi)2 (122)
and the correlation coefficient r from
IX Y
r = —L- j - 2~172~ (123)
(E X.2 E Y.2)1/2
68
-------
Attenuation coefficients for dry sludge solids or dry sand required
measuring the attenuation of the dry material for a constant thickness at
various bulk densities. To this end the sludges were slowly dried on a
water bath, pulverized with a mortar and pestle, placed in uniform layers,
and compacted by shaking or with a standard number of strokes with a blunt
instrument. The bulk density was the weight of material divided by the
volume of the box. Counting times for both the dry material and the empty
box were 16 minutes, with counts taken at various locations.
Particle Density. Particle density measurements were made on all sludges
studied as well as the Ottawa sand used for drainage media. Particle density,
the mass of solid per unit volume, is numerically equivalent to the specific
gravity of a soil, and is defined by Lambe (16) as the ratio of the weight in
air of a given volume of soil particles to the weight in air of an equal
volume of distilled water at 4 C. The specific gravities of the sludges
were determined using laboratory procedures presented by Lambe (16).
Moisture Profile Determinations, The moisture profiles of both sludge
and supporting sand layers were determined periodically during the dewatering
studies. Equations 107 and 109 were used to obtain moisture or solids pro-
files in the sludge layers. The method for determining the moisture content
of the sand was identical to that of sludge, however, the amount of water
in the sand was calculated differently, because when water left the sand
layer the pores were filled with air, changing the effective thickness of
the sample. Equation 107and 109 were thus not valid for drying sand since the
derivation assumed the entire sample to be either solid or water. Equation
117 was used to determine the water content of sand.
DIFFUSION
Measurements of the diffusion coefficient were made in order to deter-
mine the applicability of the diffusion model to water treatment sludge dry-
ing. Recent work in the soil sciences examining moisture movement in
soils found the diffusion coefficient to be a function of the moisture con-
tent. Covey (17) and Wakabayashi (18,19) reported experimental values for
D(U) for soils.
Where D is a function of U only, Boltzman (20) has shown that if U=U(n),
where n = xt"1^2, the concentration dependent diffusion equation
!iU _3. [D(U) y.] (124)
at ax L v ' sxj
can be written as an ordinary nonlinear differential equation
dU , 1 dD(U
dn 2D(U) dn D(U) dU dn
The initial and boundary conditions for Equation (124)
(125)
U (x,0) = ly, U(0,t) = Us and U (»,t) = Uj (126)
69
-------
transform to two conditions for Equation 125
U(0) = Us and U(») = U. (127)
Equation 125 may be written as
- (128)
dn L v ' dnj 2 dn
and upon integration, rearranged as
fUx
nfn\ _ 1 /dX\
x dU (129)
Ui
Obtaining D(U) requires measurements of U vs. X for t constant, or nearly
constant. These measurements must be made experimentally by determining
the moisture content along a column containing drying sludge.
After evaluating the variation of the diffusion coefficient with
moisture content and using the proper boundary conditions the basic diffu-
sion equation, Equation 124, can be solved for U at any time t by numerical
techniques. This also permits calculation of the time required to dry the
material to any desired moisture content.
DISCUSSION OF THE METHOD
In order to obtain reliable results for both specific resistance and the
coefficient of compressibility, computer handling of data was employed when-
ever possible. One aspect, however, which is hardly applicable to computer
techniques is human variation in basic specific resistance testing.
Although Swanwick and Davidson (21) noted very high replicability in
their experimentation, a series of tests was devised to measure the repro-
ducibility of results on the newly designed equipment and techniques being
employed. Triplicate specific resistance tests were performed on the same
sludge, at each of three different pressures in a constant temperature room.
The elapsed time from the beginning of the first test to the end of the last
was held to an absolute minimum.
The results as shown in Figure 24 are indeed gratifying because in
addition to corroborating the work of Swanwick and Davidson (21) the reli-
ability of past and future testing with later generation equipment and tech-
niques has been substantiated.
Swanwick et al. (21) have proposed several refinements to the testing
methods. Of primary concern was the determination of the filter area of a
Buchner funnel. It was reasoned that the entire filter paper area was not
the effective filter area because of the relatively wide spacing of the drain
holes in the filter paper support plate of the funnel. Swanwick noted that
the filter area appears as a squared term in the evaluation of specific
resistance, and hence a faulty evaluation of area could lead to a significant
70
-------
I0
20 30 40 50 60 70 80
(cm Hg)
Correlation
Coefficient
Std. Error of
Computed R
0.87401
0.99880
0.03436
Pressure (cm Hg)
Computed R (sec /gm) 95% Confidence Limits
50.8
20.0
8.0
7.44 x
3.30 x
1.48 x
Legend
108
108
108
• Regression Line
Q^"/. rnnfiHpnre
Upper
7.97 x 108
3.53 x 108
1.59 x 108
1 inn t<;
Lower
6.95 x 108
3.08 x 108
1.38 x 108
Figure 24: Results obtained from triplicate specific resistance tests at
each of a range of pressures. (Performed with the same sludge sample at
constant temperature.)
error. He corrected the apparatus by placing a gauze wire mesh between the
paper and plate and delineating the filter area using Perspex rings clamped
onto the filter paper. However, no difference in results was found using
71
-------
this arrangement over the previous method. However, Swanwick did notice a
difference in specific resistance values using different types of filter
paper.
The consulting firm of O'Brien and Gere (22) modified the testing pro-
cedure by placing diatomaceous earth onto the filter plate. The reasoning
here apparently was that a more representative test for sand bed drainage
could be made.
Baskerville and Gale (23) have attempted to reduce the time required
to determine specific resistance, A simple automatic capillary suction
apparatus is used for which the readings indicate sludge filterability.
These readings can be correlated with specific resistance units. However,
accuracy was apparently low, and no method for coefficient of compressi-
bility determination was included.
The approach of O'Brien and Gere (22) appears to have considerable merit
for measuring specific resistance and coefficient of compressibility of
sludges to be gravity drained, Nebiker, Sanders, and Adrian (24) noted that
the classic Buchner funnel results required a correlation factor for use
with their gravity dewatering equation. This factor, the so-called media
factor, approximated 75 percent, and depended on the characteristics of the
filter in the Buchner funnel test, and on the characteristics of the sup-
porting media used in gravity dewatering. A closer analysis of the media
factor'appeared justified. A promising procedure would be to test the actual
drainage media along with the sludge in the Buchner funnel apparatus. This
may then allow elimination of the media factor in the computations required
to predict gravity dewatering rates,
The results of preliminary filtrations made through the standard fun-
nel with a dilute slurry of sludge indicated a concentration of solids on the
filter paper around each individual perforation in the filter disk. Since,
as previously described, this was not a true representation of gravity
thickening, alternative filtration equipment was sought. A simple solution
was found by substituting for a perforated filter disk a fritted glass disk
which allows filtration across the entire filter surface, thus eliminating
the localized phenomenon observed in the standard funnel (25). An additional
advantage of the fritted funnel is the transparency of the filter walls which
allows observation of the entire filtration process.
In the technique employed in specific resistance testing on bulk fil-
ter media the fritted funnel is filled to a predetermined depth with media.
The sand is then washed, repacked, and flooded with sludge. A vacuum is
then applied to the system. With a coarse media such as Ottawa sand, there
is likely to be some penetration of sludge into the media at higher vacuums.
The sand depth is experimentally adjusted to insure against sludge penetra-
tion through the filter disk.
*
DISCUSSION OF THE RESULTS
72
-------
Units
As pointed out by Swanwick and Davidson (21), early investigators report-
ed specific resistance in units of sec2/gm. These units resulted from in-
terpreting pressure in units of gm/cm rather than dynes/cm2. The laboratory
data presented in Table 1 is in a form for ready comparison to results re-
ported by previous investigators. These units are dimensionally correct
when considering c as the WEIGHT of sludge solids per unit volume of filtrate
(rather than the MASS of sludge solids per unit volume of filtrate). Simple
multiplication of specific resistance Cin sec2/gm) by g (980 cm/sec2) results
in units of cm/gm and implies that'c is considered as the mass of sludge
solids per unit volume of filtrate.
The laboratory data of specific resistance and coefficient of compress-
ibility obtained for various sludges are compared with the data published
by other authors in Table 1.
Specific Resistance
It is evident from the laboratory data and the results from O'Brien
and Gere (22) presented in Table 1 that for the most part water treatment
sludges have lower specific resistance values than wastewater sludges. The
water treatment sludges tested were homogeneous, inorganic, and devoid of
filamentous binders.
The specific resistances of the pulp and paper activated sludge (2 per-
cent FeClo) reported by O'Brien and Gere (22) point out the fact that chemi-
cal conditioning may be of significant value in lessening the resistance of
sludge to filtration.
Although the water treatment sludges tested resulted in a wide range
of values for specific resistance, they were all within one order of magni-
tude. The specific resistances of Billerica and Lawrence sludges determined
using 100 ml filter samples compare favorably with those obtained using
250 ml filter samples.
Coefficient of Compressibility
O'Brien and Gere (22) do not report values for the coefficients of
compressibility of water treatment sludges tested, so no comparable data
are available with which to compare values obtained with Massachusetts water
treatment sludges. Somewhat higher coefficients of compressibility were
obtained for the water treatment sludges than are cited in the literature for
wastewater sludges. This indicates that water treatment sludges produce a
more compressible cake than wastewater sludges.
Sludge Conditioning
Efforts to improve gravity dewatering by conditioning date back over
half a century. Alum, ferric salts, and lime all had been used to accelerate
dewatering rates of what was then solely primary sludge. Ferric salts were
reported to oxidize and clog the sand beds. The most successful conditioner,
73
-------
TABLE 1. PROPERTIES OF WATER TREATMENT AND WASTEWATER SLUDGES
Solids Sample
Sludge Content Volume
% (ml )
Digested
Wastewater 15.0 NA
Digested
Wastewater 15.0 NA
Digested
Wastewater 4.9 NA
Raw
Wastewater NA NA
Pulp & Paper
Activated Sludge
2% FeCl3 NA NA
Digested
Wastewater 6.35 100
Digested
Wastewater 4.89 100
Digested
Wastewater 3.70 100
Water Treatment
3.0 mg/1 Lime 1.00 NA
Water Treatment
2.0 mg/1 Lime 1.00 NA
R @ &P =
Coefficient of 38.1?cm Hg
Compressibility (sec /gm)
Q
0.63 23.8 x 10y
Q
0.56 18.7 x 10y
q
0.76 4.07 x 10y
rt
0.54 4.70 x 10y
q
0.80 0.165 x 10y
q
0.51 72.4 x 10y
q
0.74 14.0 x 10y
q
0.66 48.0 x 10
q
NA 0.098 x 10
Q
NA 1.29 x 10y
Reference
Coackley (29)
Coackley (29)
Niemitz (30)
Eckenf elder & O'Connor (31)
Eckenfelder & O'Connor (31)
Nebiker, Sanders, & Adrian
(24)
Nebiker, Sanders, & Adrian
(24)
Nebiker, Sanders, & Adrian
(24)
O'Brien & Gere (22)
O'Brien and Gere (22)
-------
TABLE 1. PROPERTIES OF WATER TREATMENT AND WASTEWATER SLUDGES (continued)
Solids
Sludge Content
%
Water Treatment 1.00
Water Treatment
Billerica (x) 4.65
Water Treatment
Lawrence (y) 0.944
Water Treatment
Lowell (z) 3.81
Water Treatment
Amesbury 2.06
Water Treatment
Billerica 4.65
Water Treatment
Lawrence 0.944
Sample
Volume
(ml)
NA
100
100
100
250
250
250
R (3 AP=-=
Coefficient of 38.12cm Hg
Compressibility (sec /gm) Reference
NA 1.85 x 109 O'Brien & Gere (22)
1.21 2.49 x 109 Laboratory Data
Q
1.02 10.4 x 10 Laboratory Data
0.886 4.23 x 109 Laboratory Data
0.802 1.04 x 109 Laboratory Data
0.831 3.48 x 109 Laboratory Data
1.32 9.85 x 109 Laboratory Data
x = average of 3 sets
y = average of 5 sets
z = average of 4 sets
-------
alum, in addition to providing larger floe, hence larger pores and easier
paths of egress for the filtrate, provided additional flotation by produc-
tion of carbon dioxide (26).
The effect of conditioning on drainage was noted most vividly by
Templeton (27). Here aluminum chlorohydrate was added to one sample at a
dosage of 10 percent based on dry solids. During the first ten days, the
treated sludge dewatered at twice the rate of the untreated sludge. Further-
more, the treated sludge dewatered from 6.7 percent solids to 14.3 percent,
whereas the untreated sludge dewatered to but 7.6 percent solids.
In spite of such impressive results, few treatment plants presently
utilize chemical conditioning to aid gravity dewatering. A powerful deter-
rent to chemical use resides in the belief that the metals in conditioned
sludge are deleterious to certain plant life, hence proscribing sludge dis-
posal on farmland (28). The use of organic polymer conditioners promises
to quiet such objections; thus, the role of conditioning in gravity dewater-
ing bears closer scrutiny in the future. Evaluation of conditioner perfor-
mance must be simplified, however, over methods such as outlined by
Templeton (27). In this regard, the applicability of the specific resistance
concept to gravity dewatering can prove of great value.
Two wastewater sludges were selected for experimentation to determine
conditioner performance. The Amherst, Massachusetts treatment plant pro-
vided a primary digested sludge. Pittsfield, Massachusetts, served as a
source of a digested mixed primary and trickling filter sludge. Samples of
each sludge were flash mixed with doses of polymer conditioners at 100 rpm
for one minute. The effectiveness of each dosage and conditioner was noted
qualitatively after one minute of gentle stirring at 30 rpm, with attention
being paid to floe structure and depth of supernatant. Two conditioners
were eventually selected as being sufficiently effective to warrant specific
resistance tests.
Samples of each sludge were prepared with conditioner dosages of 0, 100,
200, 300, 400, and 500 mg/£, each sample being readied according to the manu-
facturer's instructions. One hundred ml of sludge was then poured into a
12 cm I.D. Buchnerfunnel, previously fitted with a wetted Whatman No.5
filter paper. The vacuums applied were 18, 38, and 60 cm of mercury, each
held constant during each separate filter run. Three repetitions were run
throughout. The duration of each run was never in excess of 17 minutes, which
was sufficient at the higher vacuums to provide a solid cake. Cakes generally
did not develop at the lowest pressures, and because of theoretical justifi-
cation, the top liquid sludge was poured off and the solids content of the
remaining cake measured.
Regression analysis provided the values for specific resistance and the
coefficient of compressibility in Figures 25 and 26, As can be seen, the
specific resistance decreased in both cases with increasing conditioner con-
centration. Statistical tests proved the variation of specific resistance
with concentration was significant (>90 percent certainty). The apparent
increase in the coefficient of compressibility with dosage, however, could
not be statistically proven. This was believed to be caused by the erratic
76
-------
values of specific resistance measured at the lowest heads, possibly re-
sulting from unrepresentative cake samples. For instance, if cake material
were to be poured off with the unfiltered sludge at the end of the experi-
ment, the final solids content of the cake would be too high, with inflated
values of specific resistance resulting. Nonetheless, all regression lines
had a correlation coefficient of better than 0.98.
O SPECIFIC RESISTANCE '
AGO-EFFICIENT OF
COMPRESSIBILITY
0.5-10
100 200 300 400 500
DOSAGE, mg/l
Figure 25: Effect of conditioner dosage on digested sludge
from Amherst. The specific resistance values are at a
vacuum of 38.1 cm of mercury. Initial solids content = 9.5%.
7-10
10
3-10
O SPECIFIC RESISTANCE
A COEFFICIENT OF
COMPRESSIBILITY
m
55
1.0
0.9
0.8°
u_
O
200 300
DOSAGE, mg/l
Figure 26: Effect of conditioner dosage on digested sludge
from Pittsfield. Specific resistance values are for vacuums
of 38.1 cm of mercury, initial solids content of 4.9%.
77
-------
REFERENCES
1. Standard Methods for the Examination of Water and Wastewater,
12th Ed., American Public Health Association, New York, iybb«
2. FWPCA Methods for Chemical Analysis of Water and Wastes, Federal
Water Pollution Control Administration, U.S. Department of the
Interior, Washington, D.C., November 1969.
3. Hald, A. Statistical Theory With Engineering Applications, John
Wiley and Sons, Inc., New York, 1952, pp. 571-584.
4. Salvadori, M. G., and Baron, M, L. Finite Differences and Their
Applications. Numerical Methods in Engineering. Prentice-Hall Inc.,
New York, 1952, pp. 45-75,
5. Reginato, R. J. and Van Bavel, C.H.M. Soil Measurement with Gamma
Attenuation. Proceedings, Soil Science Society of America, 28(6);721-
724, 1964.
6. Davidson, J. M. et al. Gamma Radiation Intensity for Measuring Bulk
Density and Transient Water Flow in Porous Materials. Journal of
Geophysical Research, 68(16):4777-4783, 1963.
7. Ferguson, H. and Gardner, W. H, Water Content Measurement in Soil
Columns by Gamma Ray Adsorption. Proceedings, Soil Science Society
of American, 26(1):11-14, 1962.
8. Gurr, C. G. Use of Gamma Rays in Measuring Water Content and
Permeability in Unsaturated Columns of Soil., Soil Science, 94:224-
229, 1962.
9. Tang, W. Moisture Transport in Sludge Dewatering and Drying on
Sand Beds. Ph.D.Thesis, Vanderbilt University, 1969.
10. Evans, R. D. Attenuation and Absorption of Electromagnetic Radiation.
The Atomic Nucleus, McGraw-Hill Co., New York, 1955, pp. 224-229.
11. Adrian, D. D., et al. Source Control of Water Treatment Waste
Solids. Report No. EVE-7-58-1, Department of Civil Engineering,
University of Massachusetts, Amherst, April, 1968.
12. Van Bavel, C. H. M. et al. Transmission of Gamma Radiation by Soils and
Soil Densitometry. Proceedings, Soil Science Society of America,
21:588-591, 1957.
78
-------
13. Chase, C. G. and Rabinowitz, j. [_. Scintillation Techniques of
Nuclear Emulsions. Principles of Radjoisotope Methodology, 3rd
Ed., Burgess, Minneapolis, 1967, pp. 283-323.
14. Kohl, J., et al. Radioisotope Applications Engineering, Van Nostrand
Co., New York, 1961.
15. Steel, R.G.D. and Torrie, J. H. Principles and Procedures of
Statistics, McGraw-Hill Co., New York, 1951, pp. 15-19.
16. Lambe, T. W. Specific Gravity Test. Soil Testing for Engineers,
John Wiley and Sons, New York, 1951, pp. 15-19.
17. Covey, W. Mathematical Study of the First Stage of Drying of a
Moist Soil. Proceedings, Soil Science Society of America, 27(2):
130-134, 1963.
18. Wakabayashi, K. Moisture Diffusion Coefficient of Solids During
Drying Process. Kagaku Kogaku (abridged ed.), 2(2):132-136, 1964.
19. . Calculation of Moisture Distribution in Clay
During Drying Process. Kagaku Kogaku, 2(2):146-149, 1964.
20. Ames, W. F. Nonlinear Partial Differential Equations in Engineering.
Academic Press, New York, 1965, p. 34.
21. Swanwick, J. D. and Davidson, M. F. Determination of Specific
Resistance to Filtration. The Water and Waste Treatment Journal,
July/August, 1961.
22. O'Brien and Gere. Waste Alum Sludge Characteristics and Treatment.
Research Report No. 15, New York State Department of Health, 1966.
23. Baskerville, R. C. and Gale, R. S. A Simple Automatic Instrument for
Determining the Filterability of Sewage Sludges. Journal of the
Institute of Water Pollution Control, 2, 1968.
24. Nebiker, J. H. et al. An Investigation of Sludge Dewatering Rates.
Proceedings of the 23rd Purdue Industrial Waste Conference, May, 1968.
25. Lutin, P. A., Nebiker, J. H. and Adrian, D. D. Experimental Refinements
in the Determination of Specific Resistance and Coefficient of
Compressibility. Proceedings of the Annual North Eastern Regional Anti-
Pollution Conference, University of Rhode Island, Kingston, July, 1968.
26. Sperry, W. A. Sewage Works Journal, September, 1941, pp. 855-867.
27. Templeton, W. E. J. Proc. Inst. Sew. Purif., 1959, pp. 223-226.
28. Downing, A. L. and Swanwick, J. D. J. Instn. Municipal Engineers,
94:81-86, March, 1967.
79
-------
29. Coackley, P. and Jones, B.R.S. Interpretation of Results by the Concept
of Specific Resistance. Sewage and Industrial Wastes, August, 1956.
30. von Niemitz, W. and Fuss, K. "Der spezifische Filterwiderstand und die
Kompressibilitat von Klarschlammen," Wasser-Abwasser 106 Jahrg, Jeft 28,
16 (Juli, 1965).
31. Eckenfelder, W. A. and O'Connor, D. J. Biological Waste Treatment.
Pergamon Press Ltd., New York, 1961.
80
-------
SECTION VII
RESULTS
CHEMICAL CHARACTERISTICS
Chemical characteristics of the sludge, decant, and filtrate samples
are presented for four water treatment sludges. Physical properties such as
particle density, specific resistance, and total solids were determined for
each individual study and are not included here. Samples of the clear super-
natant which resulted from sedimentation were taken as representative decant
samples. Filtrate samples were collected during the dewatering studies from
the column effluent. The average value of triplicate analyses is reported.
Color-turbidity-pH. Color, turbidity, and pH were determined for all
samples. The average values are tabulated in Table 2.
Color was determined by a Helige Aqua Tester on unfiltered samples.
This method gave values for the apparent color. The sludges exhibited a
dark black color with the exception of the softening sludge. The softening
sludge was reddish-brown. The dark color of the three clarifier sludges
was probably due to the activated carbon and minute amounts of organic
material. Both the filtrate and decant were relatively clear, exhibiting
low color values.
Turbidity was determined by the Jackson turbidity meter. The presence
in the sludge of suspended solids which could settle out rapidly may have
given false high readings. The turbidity values for the sludges therefore
have less significance than the values for decant and filtrate. Relatively
low turbidity values were obtained for the filtrate samples with the excep-
tion of Billerica sludge which had an average pH of 4.3. During the time
interval of transferring samples from the treatment plants to the laboratory
and subsequent handling, neutralization, such as from loss of C02, could
have taken place.
Solids. Total solids, total volatile solids, and suspended solids were
determined. No established procedure for determining solids in sludge
samples exists, however Standard Methods (1) and extensive solids analysis
investigations at the University of Massachusetts (2) served as guidelines.
Total solids were determined by heating the samples for 8 hours at 103°C and
total volatile solids were determined by heating the total solids residue at
600°C for 20 minutes. Samples for the suspended (nonfilterable solids deter-
minations were processed by filtering through a standard glass fiber filter.
The results of the solids determinations are presented in Table 3.
81
-------
TABLE 2. AVERAGE VALUES FOR COLOR, pH, AND TURBIDITY FOR
THE SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Ames bury
Sludge
Filtrate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
TABLE
Sample
Albany
Sludge
Filtrate
Decant
Ames bury
Sludge
Filtrete
Decant
Billerica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
Color,
(color units)
black
0.03
0.10
black
0.01
0.02
black
0.10
0.12
reddish-brown
0.02
0.02
3, AVERAGE VALUES
FILTRATE, AND
Total
Solids, %
1.45
0.029
0.024
3.83
0.041
0.029
6.30
0.104
0.050
4.80
0.036
0.326
PH
7.0
7.5
7.7
8.0
8.3
7.9
4.3
7.4
8.3
8.0
7.6
7.6
FOR SOLIDS FOR THE
DECANT SAMPLES
Volatile
Solids as a %
of Total Solids
46.0
40.0
53.0
43.8
12.5
11.0
58.0
34.8
40.8
2.2
26.0
19.0
Turbidity,
(JTU)
1200
6.0
36
3600
4.0
3.0
2200
65
22
1700
8.0
2.0
SLUDGE,
Suspended
Solids,
mg/1
13500
1.5
2.0
37200
0.11
0.08
62000
2.14
2.58
47000
1.44
0.90
82
-------
The four sludges had a wide variation in total solids, the range extend-
ing from 1.45 percent for Albany sludge to 6.30 percent for Billerica sludge.
The sludges were approximately 50 percent volatile solids with the exception
of Murfreesboro (softening) sludge which was only 2.15 percent volatile
solids. A portion of the high values (50 percent) for volatile solids may
be attributed to bound water which would be retained on the solid particle
at lower temperatures but driven off at higher temperatures. Suspended
material accounted for 98.5 percent of the total solids for the four sludges.
The filtrate and decant samples were relatively clear. Note that suspended
solids cannot be compared directly with total solids since two different
analytical methods were utilized. The total solids are reported on a mass-
mass (percent) basis while the suspended solids are reported as mass-volume
(mg/1). The two are comparable only when the specific gravity of the sample
is unity. Values for specific gravity for the sludges ranged from 1.95 to
2.75.
Acidity and Alkalinity. Total acidity and total alkalinity were deter-
mined by potentiometric titration. The results are tabulated in Table 4.
Billerica sludge had total acidity of 2753 mg/1 (as CaCOoK the maximum ob-
tained. The maximum alkalinity obtained was for the Murfreesboro (softening)
sludge and was 12,950 mg/1 (as CaC03).
Calcium-Magnesiurn-Total Hardness. Total hardness and calcium were
determined by the EDTA titrimetric method. Magnesium was determined by
subtracting calcium from total hardness since hardness is usually considered
to be primarily composed of calcium and magnesium. The results are presented
in Table 5.
Iron and Manganese. Iron and manganese were determined for the samples
and the results are shown in Table 6. The Amesbury and Murfreesboro sludges
contained the highest concentrations of iron, 3080 and 1990 mg/1, respec-
tively. The Amesbury water treatment plant practices iron removal by oxi-
dizing ferrous iron to the insoluble ferric state. A similar removal pro-
cess would be produced during softening at the Murfreesboro plant. As shown
by the low values for iron in the filtrate and decant samples, most of the
iron was in the insoluble ferric state. Manganese often is present with
iron in surface water supplies and is generally removed concurrently with
iron. A large percentage of manganese in the Albany and Billerica sludges
was in the insoluble form.
Nitrogen. Nitrogen analysis consisted of organic nitrogen, ammonia,
nitrite, and nitrate. Ammonia was analyzed by the direct nesslerization
method. Organic nitrogen was determined by performing total Kjeldahl and
then subtracting the value obtained for ammonia. Nitrate was obtained by
the phenoldisulfonic acid method which determined both nitrate and nitrite.
The values for nitrate were then determined by subtracting the values pre-
viously obtained for nitrite. The results of the nitrogen analyses are
presented in Table 7.
The Albany and Bill erica sludges contained 479 and 612 mg/1 organic
nitrogen, respectively. The filtrate and decant for both sludges contained
significantly less organic nitrogen, indicating the organic nitrogen was
83
-------
TABLE 4. AVERAGE VALUES FOR TOTAL ACIDITY AND TOTAL ALKALINITY
FOR THE SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Amesbury
Sludge
Filtrate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
TABLE
Total
mg/1
2,
Acidity,
as CaCO~
360
44.2
25.2
612
16.7
-
753
14.0
253.5
-
6.0
7.5
5. TOTAL HARDNESS, CALCIUM, AND
Total Alkalinity,
mg/1 as CaCO~
832
147
87.4
1,975
158.5
-
-
88.0
2.6
12,950
74.5
82.5
MAGNESIUM FOR
THE SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Amesbury
Sludge
Filtrate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
Total Hardness,
mg/1 as CaC03
12,900
195
153
2,360
182
165
10,900
458
452
15,100
180
182
Calcium
mg/1 as Ca
3,960
68
58
790
68
64
2,560
172
170
3,990
62
62
Magnesium
mg/1 as mg
715
6
2
92
3
1
1,100
7
7
1,240
6
7
84
-------
-TABLE 6. AVERAGE VALUES FOR MANGANESE AND IRON
FOR THE SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Al bany
Sludge
Filtrate
Decant
Amesbury
Sludge
Filtrate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
Manganese,
mg/1
70.0
12.3
13.8
57.6
5.4
0
31.0
7.4
18.8
5.6
0
0
Iron,
mg/1
89.2
0.07
1.27
308
0
541
2.38
5.55
1990
0
0
TABLE 7. AVERAGE NITROGEN VALUES FOR THE SLUDGE,
FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Amesbury
Sludge
Fi 1 trate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
Organic N
479
41.8
25.3
4.70
1.50
1.06
612
10.6
15.2
35.8
9.1
15.0
mq/1 Nitrogen found
Free NH3
58.8
12.6
24.8
('
10.5
10.7
8.49
89.2
41.4
72.8
2.00
1.65
3.66
as
N02
0.126
3.15
11.2
0.019
0.004
0.004
0.002
0.065
0.011
0.019
0.027
0.006
N03
2.65
0.450
2.80
0.13
0.22
0.38
0.98
0.22
0.27
0.23
0.15
0.37
85
-------
adsorbed to the sludge solids. The organic nitrogen in the Amesbury and
Murfreesboro sludges was considerably less at 4.70 and 35.8 mg/1, respec-
tively. The Albany, Amesbury, and Billerica samples contained significant
amounts of free ammonia. Nitrite and nitrate values of all samples were
comparatively small. The decant samples in general contained more nitrogen
than the filtrate samples. The two might normally be considered equal except
for the amount adsorbed to any suspended particles in the decant. Filtrate
and decant samples for Albany and Bill erica had a higher concentration of NCL
than the sludge samples. The filtrate and decant samples were separated from
any bacteria that was present in the original sludge samples. Since the
amount of each of the different forms of nitrogen is greatly influenced by
microbial activity, the rates of oxidation reduction of the filtrate and
decant samples were not equal to the oxidation reduction rates of the sludge
samples.
Phosphate. Phosphate determinations consisted of orthophosphate and
polyphosphate analyses. Orthophosphate was determined by the stannous
chloride method. Polyphosphates were determined by subtracting orthophosphate
from the total inorganic phosphate. The phosphate results are summarized in
Table 8.
Polyphosphate comprised the larger portion of phosphates in all samples
except for the Murfreesboro sludge sample. The filtrate and decant samples
contained much less phosphate than the sludge samples which indicates that
phosphates were adsorbed to the sludge particles.
Sulfate. Sulfate analyses were performed according to Standard Methods
(1), Method B: Gravimetric Method with Drying or Residue. Billerica sludge
had the maximum value of 1240 mg/1 SO*. The results are tabulated in Table 8.
BOD-COD. Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand(COD)
results are presented in Table 9. The BOD values for the filtrate and decant
samples were low. The Murfreesboro sludge had the lowest BOD, 7.8 mg/1. The
maximum BOD was in Billerica sludge which also had the highest total solids
content.
The COD values ranged from a minimum value of 3330 mg/1 for Albany sludge
to a maximum of 440,000 mg/1 for Billerica. The large amounts of activated
carbon present and the high (6.30 percent) total solids content are two
possible explanations for the high COD value for Billerica sludge. The COD
values for the decant and filtrate samples ranged from 124 to 289 mg/1.
RESULTS OF THE GRAVITY DRAINAGE STUDY
The theoretical formula (Equation 40) previously derived relates the
drainage rate of a wastewater sludge on sand or other highly permeable mate-
rial to the solids content of the sludge, the head, specific resistance, coef-
ficent of compressibility, filtrate density, and dynamic viscosity of the
filtrate. The degree of accuracy with which this formula fits the experi-
mental data will in part be dependent upon the accuracy with which the
86
-------
TABLE 8. AVERAGE VALUES OF PHOSPHATE AND SULFATE FOR THE
SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Amesbury
Sludge
Filtrate
Decant
Bill erica
Sludge
Filtrate
Decant
Murfreesboro
Sludge
Filtrate
Decant
Orthophosphate,
mg/1 P04
2.64
0.34
0.08
1.4
0.15
0.15
2.6
0.15
0.40
134
0.24
0.25
Polyphosphate,
mg/1 P04
54.0
0.83
5.4
395
1.6
1.2
1803
1.6
4.45
61
0.88
1.25
Sulfate,
mg/1
209
18.2
5.35
150
7.20
33.8
1240
23.8
51.2
156
128
69.0
TABLE 9. BIOCHEMICAL OXYGEN DEMAND AND CHEMICAL OXYGEN
DEMAND FOR SLUDGE, FILTRATE, AND DECANT SAMPLES
Sample
Albany
Sludge
Filtrate
Decant
Amesbury
Sludge
Filtrate
Decant
Billerica
Sludge
Fi 1 trate
Decant
Murfreesboro
Sludge
Filtrate
Decant
BOD,
mg/1
160
9.6
7.9
180
2.7
1.2
190
2.0
2.0
7.8
0
7.1
COD,
mg/1
3,330
160
240
18,500
124
98
440,000
167
289
3,350
134
124
87
-------
dependent variables are measured.
Experimental errors incurred in the determination of the solids content
must be considered minimal (<5 percent) since the procedure utilized multiple
samples. The solids determinations were used in both Equation 40 and in the
determination of specific resistance, and values inserted here were in fact
approximations for the volume of filtrate per unit weight of solids.
Greater accuracy in laboratory determinations for solids content was thus
not justified.
The initial head was directly measured to 1 mm. Instantaneous values
for head were calculated from the initial head and the instantaneous volume
of filtrate. The volume could be measured to within 2 ml which represented
a head interval of 2.5 mm, certainly not a source of significant error. A
greater error occurred occasionally with the appearance of bubbles in the
filtrate discharge tubes below the nozzles. Sometimes the bubbles attained
2-3 cm (.8-1.2 in) length, thus causing a corresponding reduction in the
calculated head. However, the heads were invariably greater than 30 cm
(11.8 in), hence the bubbles created minimum disturbance.
Values for filtrate density and dynamic viscosity were originally
checked and judged to be identical to values for water at the same tempera-
ture. A series of preliminary tests indicated this conclusion was sound
since any deviations of filtrate characteristics from water were clearly
smaller than the effects of temperature fluctuation. These fluctuations,
minimized by the air-conditioning system in the laboratory, approximated
+ 3 C during the course of an experiment. Mean temperatures were 24 C, ,
leading to values of 0.00919 gm/cm-sec for dynamic viscosity, and 1.0 gm/cm
for density, which appear in both the calculations for gravity dewatering
time and specific resistance.
In Experiments I-III, a phenomenon of "surging" occurred whereby an
extremely high rate of dewatering occurred with a penetration of solids into
the sand. Also, great difficulty was encountered with the placing of super-
natant on top of the thick sludge. Turbulence caused a mixing of the two,
with a poor, partial separation developing after 24 hours at which time each
experiment began. The initial solids content, specific resistance, and
coefficient of compressibility were determined from the sludge initially
applied, and as shown, these values were to be used in the theoretical
equation. Unfortunately they were clearly altered by the addition of super-
natant. It might also be mentioned that additional settling after drainage
began did not improve the data. Additional settling was minor due to the
short drainage times, and also due to temperature currents. Experiments
I-III were run in late summer with the columns some 61 cm (2 feet) from an
external wall. The outdoor heat created a warmer backside on the columns
leading to a flow pattern inimical to settling. Later experiments run in
the fall were not influenced by this problem.
Quon (3) witnessed surges which he believed were caused by the adsorp-
tion of air in the sand by the filtrate, thus increasing the effective
porosity which in turn increased the rate of drainage. Since the supporting
media was saturated with water before each experiment, the phenomenon which
88
-------
Quon observed did not appear to apply.
Visual observations of surging which did occur indicated that the
filtrate turbidity sharply increased as a result. Further, it was noted
that larger sludge particles penetrated into the sand at the edges of the
column-sand interface. This leads one to suspect that the sand-column
interface served as an easier exit for particles and that the column dia-
meter may influence the occurrence if not magnitude of the surges. The re-
latively thin layers of sludge in Experiments I-III exhibited a "punching11
of the surface near the edges, adding credence to this theory.
Further substantiation was indicated by Experiments IV-VI, which were
charged with homogeneous mixtures providing thicker sludge cakes. Surging
was significantly reduced, and it may be assumed that this was due to lower
pressure gradients across the sludge cakes. It should also be mentioned that
disturbance of the sand surface during the filling with sludge alone was
definitely less than in those cases where supernatant was then later added.
An uneven sand surface would probably encourage surging, for a cake would
build of uneven thickness.
In Experiment VI 10 piezometer tubes spaced along the length of a single
column were used as a measure of pressure differences in the sludge column.
Initial head of the sludge on the Ottawa sand was 96 cm. During the experi-
ment it was proven that a large pressure difference which is proportional to
the head loss occurs at the sludge-sand interface. Therefore, the build-up
of a thin sludge cake was responsible for most of the head loss in the column
and would thus be the determining factor which controlled drainage rates.
This follows standard filter theory for compressible materials, hence justify-
ing the assumption made in developing the theoretical derivation that the
drainage rate is proportional to the build-up of a thin sludge cake.
Based upon Experiment VI which provided proof of the existence of a thin
sludge layer at the sludge-sand interface, a theory was proposed to explain
the surging phenomenon, namely, that this layer structurally bridged the
distance between individual sand particles. If the distance between parti-
cles were large, a small amount of stress (from viscous drag) would cause a
break in the sludge cake to occur, allowing an early release of filtrate.
As the liquor passed through, new sludge particles would eventually heal the
break and stop the surge. However, this may await a low drainage rate
at which viscous drag is at a minimum, i.e., possibly the passages were
plugged only at the end of dewatering. If the distances between individual
sand particles were small, more stress would be needed to collapse the
bridging sludge cake, and once a break occurred less solids would be needed
to fill the break.
To explore the rigid sludge cake theory, the effective size of each
sand was measured. The effective size is an approximate measure of the
sand grain diameters. A small effective size would indicate a small
distance between individual sand particles and a large effective size
would indicate a large distance between particles. Table 10 indicates
that Franklin sand possessed the smallest effective size and Hermitage
sand the largest. The sludge supported by Franklin sand in Experiment IV
89
-------
TABLE 10. PHYSICAL CHARACTERISTICS OF SUPPORTING SAND
Sand Source
>anc
Designation
D10(mm)
D60/D10
Media
Factor
Franklin Treatment Plant F
Ottawa Standard Sand 0
Hermitage Hill Treatment H
Plant
0.16
0.60
0.78
1.25
1.23
1.41
0.75
0.60
0.45
did not surge in the twenty-five days (Figure 27) of the experiment except
for column 3 on the 14th day. The sludge supported by the Ottawa sand
(Figure 28) surged in all three columns around the 17th day of the experi-
ments. And finally, the sludge supported by the Hermitage sand surged
in the vicinity of the 14th day (Figure 29).
Data from Experiments IV and V, plotted in Figures 27-32, presented
sufficient data before surging to test the validity of Equation 40. The
theory, however, predicted longer drainage times in all cases, but a study
revealed that a constant correction factor applied for each type of sand.
One would not expect the value of R , calculated from Buchner funnel
testing, to fully represent a value of specific resistance of a sludge on
different supporting media such as a sand. Approximately 40-50 percent
of the gross sand surface is porous; that of a Buchner funnel less so, even
though filter paper is used. To illustrate extreme cases of the role of the
supporting media, it is clear that impermeable supporting media will allow
no dewatering, whereas very coarse supporting media will retain no solids,
resulting in a zero resistance to flow,
To account for the relationship between the sludge and the supporting
media, but mindful of dimensional correctness, a media factor must be intro-
uced into Equation 40. This media factor can be considered as a function of
the ratio of a representative sludge floe diameter to an equivalent diameter
of a sand grain: the sand grain representing the effect of the supporting
media or some equivalent parameter of the Buchner funnel, or filter leaf,
or any other dewatering device. The value of the media factor, m, would be
larger for finer sands and smaller for coarse sands. As a function of ratio
of diameters, m would be dimensionless.
The values found for the media factor by curve fitting, and listed in
Table 10 exhibit the correct directional relationship with the corresponding
D,Q size; that is, the decrease in media factor (or drainage time) results
from an increase in the sand size. However, such an increase in sand size
inevitably increases the turbidity and color of the filtrate.
A plot of the experimental data and theoretical data (Figure 30,
90
-------
oo
t
53
51
1"
,0,
§ 49
UJ
47
45
43
(
1 i i i
L
i. o COLUMN 1
^ A COLUMN 2
\ D COLUMN 3
_ £v — THEORETICAL
"A
v^
^^™=a75
^S-o
i i i i
D 5 10 15 20 2
21 55
/
19 53
17 51
1 I
— • o
15 x Q 49
Q- <
UJ UJ
0 X
13 47
II 45
9 43
5 C
1 1 1 1
k
r ° COLUMN 4
\ A COLUMN 5
\ D COLUMN 6
_R\ — THEORETICAL
Q
2-&J
^A
m=0.60 "-^
t ( 1 t
) 5 10 15 20 2
£i
19
17
"?
15 x
a_
UJ
Q
13
II
9
5
TIME (days) TIME (days)
Figure 27. Experiment IV, triplicate tests
with 20 cm of sludge on Franklin sand.
Figure 28: Experiment IV, triplicate tests
with 20 cm of sludge on Ottawa sand.
-------
ro
O COLUMN 7
A COLUMN 8
D COLUMN 9
— THEORETICAL
10 15
TIME (days)
20
E
o
a.
UJ
- 13
- II
25
Figure 29; Experiment IV, triplicate tests
with 20 cm of sludge on Hermitage sand.
45
o SAND F
A SAND 0
a SAND H
THEORETICAL -
10 15
TIME (days)
20
12
10
8
o
QL
Ul
Q
25
0
Figure 30: Experiment V, 11 cm of sludge
applied on three different sands.
-------
47
IQ
CO
LU
O
10 15
TIME (days)
25
Figure 31: Experiment V, 41 cm of sludge
applied on three different sands.
"*£•
o SAND F
A SAND 0
0 SAND H
— THEORETICAL
82
77
72
E
o
67 3T
Q.
UJ
Q
62
57
10 15
TIME (days)
20
25
52
Figure 32: Experiment V, 31 cm of sludge
applied on three different sands.
-------
Figure 31, and Figure 32) substantiated the conclusions drawn from Experiment
IV that the mathematical model (Eq. 40) incorporating the media factor could
approximate the actual drainage rate of a sludge on a sand bed and that the
type of sand did effect the initial filtrate volume and the time of surge.
The results obtained from Experiments IV and V proved the applicability
of Equation 40 in predicting the drainage rates of a sludge on a sand bed.
The sludge supported by the Franklin sand in Experiment IV drained according
to the theoretical curve (Figure 27). The sludge supported by the Ottawa
sand, because of an initial filtrate release, drained at the rate determined
by Equation 40 but plotted below the theoretical curve in the first few days
(Figure 28). If the volume of initial filtrate released divided by column
area were added to each point plotted in Figure 28, the experimental curves
would coincide with the theoretical curve. The sludge supported by the
Hermitage sand also had an initial unpredicted filtrate release or surge,
which offset the experimental curve from the theoretical curve.
The initial high drainage rates resulted from an initial retarded cake
formation due to some of the solids being drawn into the supporting media
instead of being retained above the sand interface. During the course of
six experiments, there was strong evidence that the initial filtrate release
as well as the time of surging was related to the supporting media. The
sludge supported by the Franklin sand not only had very little filtrate
release but also did not surge in 25 days. However, the same sludge suppor-
ted by the Hermitage sand did release a sizeable amount of filtrate at the
beginning of the experiment and surging occurred at approximately 14 days.
As previously mentioned, if head loss due to the initial filtrate
release were added to each point on the head versus time curves for the
Ottawa and Hermitage sands respectively, the curves would then coincide
with the head versus time curve for the Franklin sand with the same initial
head, thus justifying identical media factors for all the sands tested.
RESULTS OF THE EVAPORATION AND DRYING STUDIES
Preliminary Results of Evaporation and Drying
Evaporation of Hater. Preliminary studies on the evaporation of water
were conducted in the environmental chamber to determine if there was any
significant effect on evaporation rates attributable to either location
in the environmental chamber or to liqliid depth. Deionized water was
evaporated in three sets of three cylindrical plastic pails (27.5 cm diameter
and 35.5 cm depth, 11 in and 14 in respectively, which were filled to
depths of 9.6, 19.3 and 29.1 cm (3.8, 7.6, 11.5 in). A set was placed at
each of three locations: on the floor near the control panel, on a table
in the center of the room, and on the floor near the door, as shown in
Figure 33. Relative humidity and temperature were controlled at 47
percent and 24 C (76°F), respectively. The containers were weighed to the
nearest gram at intervals of approximately 1.5 days.
The average rate of water loss (gm/hr) was calculated by fitting a
94
-------
CONTROL PANEL
(A) (B)
LOCATION I
LOCATION 2
LOCATION 3
©@©
AIR CONDITIONER
Figure 33: Location of containers in
evaporation study.
straight line to the weight-time data, the slope of which was obtained from
linear regression analysis. The data are summarized in Table 11. A two-way
analysis of variance of the drying rates showed no significant difference be-
tween depths and locations at the 5 percent level. A summary of the analysis
of variance is shown in Table 12.
Drying Studies, Two preliminary drying studies were conducted using
Billerica sludge. Sludges with solids content of 2.35 and .6.12 percent
were dried in glass pans .5 cm thick with inside dimensions of 35 x 22 x
4.5 cm (13.8, 8.7, 1.8 in). The initial sludge depths were 3.0 cm (1.2 in).
Pans of distilled water were evaporated as controls. Temperature and rela-
tive humidity were controlled at 22 + 1°C (72 + 0.5°F) and 38 +_ 1 percent,
respectively. The sludge mass was determined on a triple-beam balance at
intervals of approximately one day. When the change in mass was less than
one gram per day, the sludges were assumed to be at equilibrium. Results
of the two drying studies are summarized in Table 13.
Curves showing the sludge mass-time relationships are shown in Figure
34. The constant-rate drying period accounted for approximately 75 percent
of the water loss and 75 percent of the total drying duration for each
sample. During the early stages of drying sample D-l appeared to have a
thin film of moisture on the surface while sample D-2, of lower solids
content, had clear supernatant present. The first critical moisture content
95
-------
TABLE 11. RATE OF WATER LOSS (gm/hr) OF DE-IONIZED WATER
AT 24°C (76°F) AND 47 PERCENT RELATIVE HUMIDITY
Location
9.6 cm
Water Depth
19.3 cm 29.1 cm
1
2
3
3.77
2.74
2.77
4.05
3.53
3.18
4.39
4.36
3.67
TABLE 12. ANALYSIS OF VARIANCE FOR EVAPORATION DATA
Source of
Variation
Location
Depth
Error
Totals
Sum of
Squares
2.1
1.6
0.7
4.4
Degrees of
Freedom
2
2
4
8
Mean
Squares
1.05
0.80
0.17
F
Test
6.20
4.70
TABLE 13. RESULTS OF BILLERICA SLUDGE, AT TWO DIFFERENT SOLIDS
CONTENTS, DRIED AT 22°C (72°F) AND 38 PERCENT RELATIVE
HUMIDITY FOR 3.0 cm (1.2 in) INITIAL DEPTHS
Sample Number
Initial Solids, %
Critical Moisture Content, %
Critical Solids Content, %
Solids at Equilibrium, %
Moisture at Equilibrium, %
2
I , gm/cm -hr
d/^»^/%^«^4-T/^iri v» n 4- T rt ®l
D-l
6.12
400
20.0
90.0
11.0
0.0062
76.5
D-2
2.35
350
22.2
79.5
26.0
0.0070
86.5
96
-------
was not reached, however, until after the sludges had appeared very dry and
many cracks had formed. The equilibrium moisture contents were low with an
average value of only 18 percent. At equilibrium, the sludges had shrunk
to only a few small, warped pieces, approximately 0.5 cm (0.2 in) thick.
LEGEND
D-DI
0-D2
100
200 300
TIME (hrs)
400
500
Figure 34: Sample mass versus time for Billerica
sludge drying at 22°C (72 F) and 38% relative humidity.
The average drying rate for a long constant-rate drying period was
determined by fitting straight lines to the sludge mass-time data. The 2
average drying rates for samples D-l and D-2 were 0.0062 and 0.0070 gm/cm -
hr, respectively. When tested by comparison of regression lines the two
drying rates were shown to be most affected by the initial solids concentra-
tions. The average evaporation rate of water for the same conditions was
0.0081 gm/hr-cm2. The evaporation ratios (the ratio of sludge drying inten-
sity to evaporation rate of water) for samples D-l and D-2 were therefore
76.5 and 86.5 percent, respectively.
Drying-rates for the entire drying duration were calculated by Equation
84 and are shown in Figure 35. The initial decrease in the drying rate was
due to the samples having been stored at a higher temperature than the experi-
mental drying conditions. The drying rate decreased while the surface
temperature fell to the ultimate value. This initial adjustment period was
so short that it was ignored in subsequent analysis of the drying times.
The first critical moisture content was reached at a higher moisture
content (shorter drying time) for the sample (D-l) with the higher proportion
of solids. This conforms with the general theory for critical moisture con-
tent in that sample D-l had a higher solids content, therefore a higher value
for mass of total solids, WT$. A second critical moisture content could not
97
-------
be clearly established for either sample.
LEGEND
o D-l (S0=6.I2%)
a D-2 (So=2.35%)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
MOISTURE CONTENT, %
Figure 35: Drying rate curves for Billerica sludge drying at
22°C (72°F) and 38% relative humidity.
RESULTS OF DRYING
Drying studies were conducted to determine the drying rates and evapora-
tion ratios of thin layers of sludge under controlled drying conditions.
During the drying of water treatment sludges, shrinkage and formation of
cracks occurred which changed the drying surface area. In order to show the
relative magnitude of shrinkage, pans containing the four types of sludge
were dried in the oven at 103°C (2170F) for approximately two days. Sludge
mass was determined periodically to provide values for solids content. The
relative amount of shrinkage and crack formation is shown in Figure 36. The
softening sludge (Murfreesboro) settled rapidly leaving a clear supernatant
to be evaporated during most of the drying period. The Billerica sludge had
98
-------
Murfreesboro
/I.84?
B i 11 e r i c a
21.50%
Albany
7.66%
Amesbury
24.84%
>95;,
32.69% 12.30%
52.30%
All S > 95?
Figure 36: Four types of water treatment sludge at various solids contents
99
-------
less shrinkage, probably due to the large amounts of activated carbon
present.
Drying-Rate Studies. Drying-rate study D-3 was conducted to study the
drying and evaporation ratios of thin layers of sludge under controlled
drying conditions. Albany, Bill erica, and Amesbury sludges were dried at
depths of 2 and 4 cm (0.8 and 1.6 in) in heavy glass pans. The pans had walls
0.5 cm (0.2 in) thick and were 22 x 35 x 4.5 and 19 x 30 x 4.5 cm (0.8, 13.8,
1.8 and 7.5, 11.8, 1.8 in) inside dimensions, respectively. Temperature and
relative humidity were controlled at 24°C (75°F) and 65 percent, respectively.
All Billerica samples had an initial solids content of 6.20 percent. Two
different solids contents were studied for Amesbury and Albany sludge. The
higher solids content was obtained by decanting some of the clear supernatant
from the original sludge samples. The experimental conditions are tabulated
in Table 14.
TABLE 14. EXPERIMENTAL ARRANGEMENT FOR DRYING STUDY D-3
CONDUCTED AT 24°C (75°F) AND 60 PERCENT RELATIVE
HUMIDITY
Sample
Number
1A
IB
1C
ID
2A
2B
2C
2D
3
4
5
6
Material
Amesbury
Bill erica
Albany
Water
Amesbury
Billerica
Albany
Water
Albany
Albany
Amesbury
Amesbury
Initial
Depth, cm
2
2
2
2
4
4
4
4
2
4
4
2
Area
cm
770
770
770
770
570
570
770
770
570
570
570
570
c y
V /0
3.15
6.20
0.92
-
3.15
6.20
0.92
-
1.40
1.40
4.47
4.47
The sludge mass-time curves for the samples are shown in Figure 37 and
Figure 38. Two control pans of water filled to 2 cm (0.8 in) depth for ease
of handling served as controls. Toward the end of the drying run, water had
to be added to the control pans to prevent them from becoming dry. This was
due to evaporation of the 2 cm (0.8 in) initial depth of water in less time
than some of the pans containing 4 cm (1.6 in) of sludge. The pans of sludge
were divided between two tables located near the center of the environmental
chamber. Each table contained one control pan of water. No difference in
drying rates could be attributed to the different locations; however, as a
precautionary measure, the evaporation ratios for sludge samples on a given
table were calculated using as the denominator the values of the control pan
of that table. Results are presented in Table 15.
100
-------
4500
4000
o» 3500
co~
V)
<
5 3000
2500
2000
1500
1000
UJ
0.
.Cracks
Crack
10 15 20 25
TIME, days
30
35
40
Figure 37: Sample mass versus time curves for sludges
(D-3) drying at 240C (75°F) and 60% relative humidity.
CO
4000
3500
3000
UJ 2500
Q.
to 2000
1500
1000
10
15
20
25
30
35
40
45
TIME, days
Figure 38. Sample mass versus time curves for sludges
(D-3) drying at 24°C (75°F) and 60% relative humidity.
101
-------
TABLE 15. SUMMARY OF RESULTS FOR DRYING STUDY D-3 CONDUCTED AT 24°C (75°F) AND
60% RELATIVE HUMIDITY.
o
ro
Column
Number
1A
IB
1C
ID
2A
2B
2C
2D
3
4
5
6
Initial
Material Depth, cm
Ames bury
Bill erica
Al bany
Water
Ames bury
Bill erica
Albany
Water
Al bany
Albany
Ames bury
Ames bury
2
2
2
2
4
4
4
4
2
4
4
2
3
6
0
3
6
0
1
1
4
4
S
0
.15
.20
.92
-
.15
.20
.92
-
.40
.40
.47
.47
Solids,
SCR
16
21
6
-
15
23
13
-
14
24
15
17
.1
.8
.1
.4
.6
.2
.3
.4
.4
.2
°/
h
Se
76.5
81.1
75.0
-
76.5
82.5
80.8
-
75.0
78.8
75.3
73.5
1 1 °/
UCR, /0
640
360
840
-
600
270
780
-
460
380
480
440
Constant-Rate Drying
r F "/
C , £ f- , h
gm/hr-cm
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0045
0039
0038
0038
0044
0042
0043
0045
0038
0040
0042
0038
118
103
84
-
116
93
96
-
84
105
93
84
-------
_ As indicated in the sludge mass-time curves, the constant-rate drying
period was dominant. The constant-rate period accounted for 80 to 85 percent
of water loss and 65 to 75 percent of the drying duration.
_ The sludges shrunk vertically and appeared to have a free water surface
in the early stages of drying. When a solids content of 7 to 10 percent was
reached, cracks formed which increased the exposed surface area The in-
creased surface area would increase the drying rate, possibly offsetting
any decrease in the drying rate due to the surface becoming dry. After cracks
were formed in the sludge samples, horizontal shrinkage became more pronounced,
At equilibrium the sludge samples had shrunk to irregularly shaped pieces
approximately 0.5 cm thick (0.2 in) with a maximum dimension of 2 cm (0.8 in).
The pieces appeared completely dry and were warped, exposing the bottom and
therefore exposing a maximum surface area.
Evaporation ratios ranged from 84 to 118 percent. Pans with lower
initial solids content generally dried at a faster rate than samples with
higher initial solids. The larger evaporation ratios can be attributed to
heat advection since these samples generally contained a larger amount of
solids, WTS.
Curves showing the drying rate-moisture content relationship are shown
in Figures 39 and 40. After the initial temperature adjustment, the sludges
remained in the constant-rate drying period while 80 to 85 percent of the
water was lost. Only 15 to 20 percent of the water was lost during the
falling-rate drying period. The falling-rate period was studied for theoreti-
cal interest only since the sludges could have been removed from a drying bed
before the critical moisture content was reached. No distinct second criti-
cal moisture content was established, therefore, the entire falling-rate dry-
ing period was considered as one period. Both a straight line and a parabola
were fitted to the falling rate portion by regression analysis. As a rule,
the parabola was associated with a higher correlation coefficient. Values for
the first critical moisture content ranged from 270 to 840.
Critical Moisture Content. Both straight lines and parabolas were
fitted by regression analysis to the drying intensity-moisture content data in
order to obtain values for the first critical moisture content. As a rule,
the parabola provided a better fit and gave a higher correlation coefficient.
The intersection of the parabola with the constant rate curve was taken as the
critical moisture content.
Relationship for Drying Time. A relationship for calculating the drying
duration in the falling-rate portion was developed assuming the relationship
between drying intensity and moisture content was parabolic. This relation-
ship can be expressed as
I2 = 4pU (130)
or
I = 2P1/2U1/2 (131)
103
-------
TO.O05
o
CT
cn
liT
!5 0.003
J 0.002
g
0.001
n
r i i i i i i I 1
2C
A ^ A-^> ^A o-A° 4 " A-AX-
V30/£c -""^ D 1C 8 3 "
/ / / /'{r-
A/ x/7 .' IC
7 // X" LEGEND
. /^//' a - 1C
/J"' °"2C
V 0-3
§ A-4
MOISTURE CONTENT, %
Figure 39. Drying rate curves for sludges (D-3) drying at
24°C (75°F) and 60% relative humidity.
0.005 -
0 200 400 600 800 1000 1200 1400 1600 1800 2000
MOISTURE CONTENT, %
Figure 40: Drying rate curves for sludges (D-3) drying at
24°C (75°F) and 60% relative humidity.
104
-------
CR
where
From Equation 54,
= Constant
(132)
W
t =
'TS
100A
o dU
I
(54)
U
Substituting Equation 131 into Equation 54 and performing the integration
gives the drying duration in the falling-rate period as
2WTS U
TOO A I
-------
LJ
Z
o
o
LU
or
=3
14000
13000
12000 -
;IIOOO -
"lOOOO
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
LEGEND
o Col I- (Dry a drainage)
a Col 2-(Drying only)
^-Drainage ended
"oo
200 400 600
800 1000 1200 1400 1600 1800 2000
TIME, hrs
Figure 41: Sample mass versus time curves for Albany
sludge dewatering at 24 C (75 F) and 46% relative humidity.
Col I- (Dry 8 drainage)
o Col 2- (Drying only)
200 400 600
800 1000 1200
TIME, hrs
1400 1600 1800 2000
Figure 42. Change in depth of Albany sludge dewatering
at 240C (75°F) and 46% relative humidity.
106
-------
2 2
gm/hr-cm as compared to 0.0063 gm/hr-cm for Column 2.
Column
TABLE 16. RESULTS OF ALBANY SLUDGE, DW-1, DEWATERING AT
24°C (75°F) AND 46 PERCENT RELATIVE HUMIDITY
Drainage permitted
Initial solids, %
Initial sludge depth, cm
Final solids content, %
2
I , gm/cm -hr
c
Support media
Yes
1.22
13.5
75.5
0.0057
sand-stone
No
1.22
13.5
73.8
0.0063
none
Shrinkage-time curves for both samples are shown in Figure 42. The
depth-time curve for Column 2 was linear over most of the dewatering period,
indicating constant-rate drying. Vertical shrinkage in Column 2 diminished
at a solids content of 4.6 percent and horizontal shrinkage began with cracks
forming throughout the depth of the sludge cake.
Dewatering Study DM-2. Dewatering study DW-2 consisted of three columns
of Albany sludge draining and drying simultaneously and one column of water
used as a control. In addition, three large pails of water in various loca-
tions within the environmental chamber were evaporated concurrently as cgn-
trols. Temperature and relative humidity remained constant at 24° +_ 0.5 C
(75 + 1°F) and 30 ± 2 percent, respectively.
The dewatering columns contained 45.7 cm (18 in) of sludge on 11.5 cm
(4.5 in) of Ottawa sand supported by 3.8 cm (1.5 in) of stone. The initial
solids content of the sludge was 1.3 percent. The initial depth of water in
the control column was adjusted to 30 cm (11.8 in) in order to eliminate any
"freeboard" effects caused by the surfaces of the columns being at different
elevations after drainage had occurred in the sludge columns. No significant
difference in evaporation rates was seen in the three large pails of water,
thus indicating constant drying conditions. The average evaporation rate
for the three pails was 0.0064 gm/hr-cnf.
The mass of the dewatering columns was determined periodically after
drainage ended. The sludge mass-time curves for the columns are shown in
Figure 43. Column 3 was omitted from the data analysis since some water was
accidentally lost early in the study. The sludge columns remained in the
constant rate drying period throughout the drying run. 2The average drying
rate for the two columns of sludge was 0.00524 gm/hr-cm and the average
evaporation ratio was 87.5 percent. At the end of the drying run the columns
were dismantled and the sludge cakes carefully removed. The sludge cakes
appeared dry and could be readily picked up by hand. However, the average
107
-------
14,500
14,000
CO
CO
LJ
_J
CL
2
<
CO
13,500
13,000
12,500
LEGEND
o Column I
A Column 3
o Water
50 100 150 200
TIME AFTER DRAINAGE TERMINATED, hrs
250 275
Figure 43: Sample mass versus time curves for drying period
of dewatering study DW-2.
solids content was only 10-12 percent, demonstrating that this particular
sludge contained large amounts of bound water. A thin layer approximately
5 mm thick and lighter in color encased the sludge mass causing the sludge
cake to appear to be drier on the outside than in the interior. This layer
was removed from one cake, cut into small pieces and a gravimetric solids
content analysis performed. The solids content was 10.7 percent in the
interior and 12.3 percent in the outer layer.
The accumulated volume of filtrate for each of the three sludge columns
is shown in Figure 44 and the variation of total head (H ) is shown in
Figure 45. The predicted head values using empirical meaia factors and
Equation 46 are shown as solid lines.
Dewatering Study DW-3. Dewatering study DW-3 consisted of 9 columns of
sludge and 2 columns of water dewatering under controlled conditions. Tempera-
ture and relative humidity were maintained at 25 + 1°C and 35 i 2 percent.
Air was uniformly supplied to each column to expedite the dewatering process.
Each column contained 9 cm of Ottawa sand supported by 2,5 cm of stone. The
experimental conditions and results are shown in Table 17,
The two columns of water (columns 4 and 8) had an average drying rate of
0.0097 gm/hr-cm2 as calculated from the slope of the sludge mass-time data.
There was no significant difference in the drying rates of the two columns
of water, thus indicating constant drying conditions. The evaporation rate
for water at 24°C (75 F) and 35 percent relative humidity, with negligible
wind and sunlight, is 0.05 cm/day from Figure 14. Converted to comparable
108
-------
OVJUU
K.r\r\f\
4000
"^ ir\r\r\
LTRATE, rr
r
3 C
I i
1, IUUU
900
£800
0 700
^ 600
d 50°
uj 400
>
£ 300
_i
Z3
2
3 200
100
/
/
A
3
o/
~3Jj^
CD
¥
.La*
^
£
— Q— fi
LEGEND
o Column 1
a Column 2
A Column 3
0 100 200 300 400 500 600
TIME, hrs
Figure 44: Cumulative volume of filtrate versus
time for Albany sludge dewatering on Ottawa sand
(DW-2).
2
units, this would be 0.0021 am/cm -hr, considerably less than the control
column value of 0.0097 gm/cm^. If the vertical air stream alone accounted
for the difference in drying rates, the equivalent horizontal wind velocity
from Figure 14 would be 12 km per hour (7.5 mi per hour) for the control
columns.
Dewatering with and without drainage was studied with Bill erica sludge
in columns 5 and 6, and column 1, respectively. The drying rates for columns
5 and 6 (drying and drainage) were lower than column 1 (drying only). This
could have resulted from the higher solids content in columns 5 and 6 due to
drainage or the larger amount of freeboard due to the smaller initial depth.
Columns 5 and 6 differed significantly in their drying rates, column 6
109
-------
TABLE 17. DEWATERING STUDY DW-3, RESULTS OF FOUR SLUDGES DEWATERING
AT 24°C (75°F) AND 35% RELATIVE HUMIDITY
Column
Number
1*
2*
3
4*
5
6
7
8*
9
10
11
Material
Bill erica
Albany
Albany
Water
Bill erica
Bill erica
Amesbury
Water
Amesbury
Murfreesboro
Murfreesboro
Initial
depth
inches
18
18
12
12
12
12
12
12
12
12
12
Initial
6.10
1.86
1.86
-
6.10
6.10
3.67
-
3.67
4.80
4.80
Solids, %
After
Drainage
-
-
5.8
-
10.4
9.1
7.1
-
6.2
41.0
29.2
Final
12.4
3.7
15.2
-
20.6
22.8
20.6
-
33.4
81.0
92.5
c 2
gm/cm -hr
0.0128
0.0120
0.0070
0.0093
0.0075
0.0085
0.0115
0.0096
0.0148
0.0055
0.0060
r c/
h, h
136
128
74
-
79
91
122
-
157
58
64
Denotes Drying Only.
-------
LEGEND
o Column I
A Column 2
20
40
60 80
TIME, hrs
Figure 45: Drainage curves for 45.7 cm of Albany
sludge (DW-2) dewatering on Ottawa sand.
17,500
17,000
LEGEND
o Coll-Bill«rica(dryonly)
& Coi 5-Billerica (drainage)
0 a Col6-Bill«rico (drying a-
droinage)
• Col 10-Murfrecsboro
Col Il-Murfre*»boro
(drying 8 drainage)
10,500
20O 4OO 600 800 1000 1200 1400 1600 1800 2000
TIME, hrt
Figure 46: Sample mass versus time curves for
sludges (DW-3) dewatering at 24 C (75QF) and 35%
relative humidity.
Ill
-------
having
column
solids
of 137
fer to
the faster rate. The amount of water lost by drainage was larger for
5 than the dmnage volume from column 6. This resulted in_a higher
content and a lower drying rate for column 5. The evaporation ratio
percent for column 1 was due partially to the high rate of heat trans-
the dark sludge surface by radiation and conduction. The sludge mass-
time curves for columns 1, 5, and 6 are shown in Figure 46.
Dewatering of Albany sludge with and without drainage was studied in
columns 3 and 2, respectively. The drying rates were significantly different,
column 2 having the larger rate. Again, the lower drying rate occurred in
the column with the higher solids content. The average evaporation ratios
for columns 2 and 3 were 128 percent and 74 percent, respectively. Sludge
mass-time curves for columns 2 and 3 are shown in Figure 47.
17,500
O Col 2-Alfoany (drying only)
A Col 3-Albany (drying 8
drainage)
Q Col 7-Amesbury
• Col 9-Amesbury (drying &
drainage)
"-Drainage ended
iOOO 1200
TIME, hrs
1600 1800 2000
Figure 47: Sample mass versus time for sludges (DW-3)
dewatering at 24°C (75°F) and 35% relative humidity.
Columns 7 and 9 contained Amesbury sludge dewatering by simultaneous
drying and drainage. These two sludges had an average evaporation rate of
140 percent. Immediately after drainage stopped,, the sludge cakes shrunk
horizontally, pulling away from the container walls. The shrinkage left
a large exposed porous surface which greatly increased the drying area. The
sludge was dark in color, thus, some of the increased drying rate may be
attributed to heat advection. The mass-time curves for columns 7 and 9 are
shown in Figure 47.
Murfreesboro sludge was dewatered by drying and drainage in columns 10
112
-------
and 11, respectively. The sludge dewatered very rapidly, drainage being
completed in approximately 20 hours. Although the sludge initially contained
4.8 percent total solids, the solids settled rapidly to a dense layer approxi-
mately 3 centimeters thick, leaving a large clear supernatant. The solids
content was approximately 35 percent and the depth of sludge cake was 2.3 cm
when drainage ended. Although some vertical cracks appeared, the sludge
cake did not have a large exposed drying surface. The average evaporation
rate was 62 percent, the smallest of any sludges investigated. The sludge
mass-time curves for columns 10 and 11 are shown in Figure 46.
The variation of total head (HQ) for the sludge samples is shown in
Figure 48 along with predicted H0 values from Equation 47. The time span
covered by Equation 47 is considerably less than the total time span for total
drainage. This is due to two factors: first, approximately 25 percent of
the filtrate came from the distilled water used initially to saturate the
sand columns; second, Equation 47 does not cover the entire drainage period
but is valid only until the decreasing sludge surface coincides with the
increasing sludge cake. The remaining drainage, affected by consolidation
and shrinkage, is unaccounted for by the drainage model.
75
e
o
70
X
o
Ul
>65
60
< 55
O
(-
50
45
LEGEND
Col 3- Albony
Col 5- Billeriea
Col 6- Billeriea
Col 7- Amesbury
Col 9 - Amesbury
0
50
too
TIME, hrs
150
ZOO
250
Figure 48: Drainage curves for 30.8 cm of sludge (DW-3)
dewatering on Ottawa sand.
MOISTURE AND SOLIDS PROFILES
Preliminary Measurements. The gamma-ray attenuation method of moisture
and solids profile measurement required prior determination of attenuation
113
-------
TABLE 18. ATTENUATION COEFFICIENTS AT 0.661 Mev FOR THE VARIOUS
MATERIALS
Material
Albany sludge
Arnesbury sludge
Bill erica sludge
Average value for si
Ottawa sand
Water
Water
Water
Soil (average value)
TABLE 19.
Source
Bill erica
Ames bury
Albany
Murfreesboro
Ottawa sand
2, Standard
w' cm /gm Deviation
0.0780 0.0048
0.0792 0.0050
0.0781 0.0031
udges 0.0784
0.0765 0.0060
0.0842 0.0007
0.0839
0.0815 0.0008
0.0775
PARTICLE DENSITY VALUES, g/cm3,
SLUDGE SOLIDS AND OTTAWA SAND
p, grci/cni
1.95
2.64
2.36
2.75
2.64
Reference
Data
Data
Data
Data
Data
Data
Adrian
Davidson, et al .
Reginato and
Van Bavel
FOR WATER TREATMENT
Standard
Deviation
0.025
0.049
0.023
0.019
0.009
114
-------
coefficients and particle densities. The energy spectrum of the Cs-137
source was determined as a check on the calibration and performance of the
counting equipment. The familiar Cs-137 spectrum, as shown in Figure 49 was
determined.
The attenuation coefficients were determined by measuring the attenuation
of the gamma beam through water in the small plastic boxes. A plot of N/N
for 16 minute counts through water is shown in Figure 50. The slope of thi
line is equal to yp. The values for attenuation coefficients obtained are
shown in Table 18 along with the values from the literature.
Particle density measurements of sand and dry sludge solids were made
by the specific gravity method. The results are presented in Table 19.
Moisture Movement in Sand. Moisture profiles were determined for the
sand layers of the dewatering columns by the attenuation method. The sand
layers remained saturated until drainage from the sludge layers terminated.
After drying caused cracks to appear in the sludge layer, or the sludge cake
receded from the column walls, the water in the sand layer was lost. The
sand layers were devoid of water at the termination of the drying period.
The method for measuring water content in sand was tested using Ottawa
sand in the small plastic boxes. Values of water content in the sand as
determined from Equation 117 are shown in Table 20 along with values obtained
by volumetric measurement. There was a 2.6 percent difference between the
two methods. The sludge variation in water content (e) at various depths
was attributed to differences in the bulk density of the compacted sand.
TABLE 20. SUMMARY OF WATER CONTENT MEASUREMENTS FOR
OTTAWA SAND BY THE ATTENUATION METHOD
Ratio of distance from bottom
to total length, x/L
0.20
0.40
0.60
0.80
Average (Attenuation Values)
Average (Volumetric Measurement)
Difference in two methods, %
Water content (e) ,
/ 3
gm/cm
0.36
0.34
0.37
0.42
0,37
0,38
2.6
Profiles of water content in the supporting sand layers were vertical
during the initial dewatering stages, as shown for column 3 in Figure 51
and column 5 in Figure 52. Water content remained constant, during the
115
-------
2x10
100 200 300 400 500 600 700 800
BASE-LINE DISCRIMINATOR (KEV) OR CHANNEL NUMBER
Figure 49: Energy spectrum for 250 millicuries
Cs-137 source.
0.0
0.9
0.8
0.7
0.6
0.4
N
0.2
0.
X
\
\
X
0 12345678
THICKNESS L, inches
10
Figure 50: Variation of the ratio N/N with
thickness of water at 0.661 Mev. p
-------
X
D Time, in days, after drainage terminated
COLUMN 7
COLUMN 3
COLUMN II
.1 .2 .3 .4 0 .1 .2 .3 A 0
WATER CONTENT (9) g/cm3
.2 .3 .4
Figure 51: Profile of water content in sand layers
(DW-3) after drainage terminated.
o Time in days, after drainage terminated
Q Elapsed time, in doyt
0.9
0.8
0.7
0.6
o.5
0.4
0.3
0.2
O.I
COLUMN I
COLUMN 2
I
COLUMN 5
0 0.1 0.2 0.3 0.4 0 OJ 0.2 0.3 0.4 0 O.I 0.2 0.3 0.4
WATER CONTENT (6), g/cm3
Figure 52. Profiles of water content in sand layers
for dewatering study DW-3.
117
-------
drying of sludge when drainage was not permitted, as shown in column 2 in
Figure 52, when dewatering occurred by drying only. After enough water was
lost from the sludge to cause the sludge cake to recede from the container
walls, water was lost from the sand layer as shown in Figures 52 and 53.
Column 2, containing a lower initial solids content (1.86 compared to 6.1 per-
cent for column 1) did not dry sufficiently during this study to shrink hori-
zontally, thus the sand layer remained saturated.
i.o
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
O.I
Figure
(DW-3)
D Time, in days, after drainage terminated
COLUMN 6
COLUMN 9
COLUMN 10
0 OJ 0.2 0.3 O.4 0 OJ 0.2 0.3 0.4 0 OJ 0.2 0.3 0.4
WATER CONTENT (9), Q/cm3
53: Profiles of water content in sand layers
after drainage terminated.
Moisture and Solids Profiles in Sludge. The moisture and solids profiles
of sludge undergoing drying and dewatering were measured periodically by the
attenuation method. Since the mass of the samples had been determined peri-
odically, the average values for solids and moisture content could be calcu-
lated. Measurements obtained in the early stages of dewatering agreed well
with gravimetric measurements and showed no significant variations in the
moisture and solids profile. As dewatering progressed, the sluge cake re-
ceded from the column walls and horizontal and vertical cracks appeared.
Since theoretical equations for the solids content had been derived on the
basis of the column being filled with water or solids, the net result of
shrinkage and formation of cracks was to change the sludge thickness, making
the gamma ray attenuation method inapplicable during the final stages of de-
watering.
The method for measuring moisture and solids content was tested using
Billerica sludge in the small plastic boxes. The sludge was thoroughly mixed
initially and an aliquot taken for solids content measurement by the gravi-
metric method (oven drying). The solids profile as determined by the atten-
uation method is shown in Figure 54 along with the average solids content
118
-------
X
L
I.U
0T9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
r\
- 1
Attenuation values — o — ^
\
1
1
I
\
\
\
i
10
SOLIDS CONTENT, %
Figure 54: Variation of solids content with
depth for Billerica sludge.
0
0
10
20 30
40 50 60
SOLIDS, %
80
90 100
Figure 55: Error analysis.
119
-------
determined by gravimetric methods. The difference between the average solids
content determined gravimetrically and by gamma-ray attenuation was 6.0 per-
cent. Since the profile determination required some 1.5 hours, some sedi-
mentation occurred causing higher solids concentrations near the bottom of the
sample. An analysis of error in the attenuation method was performed and is
described in Clark (4). The method was found to be very accurate for high
values of solids content with the accuracy diminishing as solids content
decreased. The results of the error analysis for Billerica sludge are shown
in Figure 55.
Solids profiles for sludge dewatering by drying only are shown in Figure
56 for Albany sludge (DW-3). The initial depth and solids content were 40=6
cm and 1.86 percent, respectively. Calculated average values of the solids
content are shown for comparison. During the initial stages of drying, the
solids profile was uniform with somewhat higher values near the bottom of
the column due to sedimentation. As the drying time increased the solids
became more varied due to shrinkage and consolidation. The final profile
shows the solids content after horizontal and vertical cracks had formed.
Values for solids content near the top of the column could not be determined
after the sludge cake had receded from the sludge surface, changing the
thickness.
o_
UJ
Q
26
24
22
20
18
16
14
12
10 '
8-
6-
4-
2 •
0
Cafcuiated average value -----
Attenuation values —en-
Sludge surface V
.Elapsed fim®, days Q
0123401 23401
SOLiDH CO.NTLNT, %
6 7
Figure 56: Variation of solids profiles with time
for Albany sludge (DW-3) drying on Ottawa sand.
Solio- profiles for Billerica sludge (DW-3) dewatering by drying only
are rh>:n in Figure 57. The initial depth and solids content were 40.6 cm
and 6.10 percent, respectively. The sludge cake shrunk both horizontally and
120
-------
vertically during dewatering.
E
o
Q.
LU
Q
Calculated average value
Attenuation values
Sludge surface
Elapsed time, days
II 12 13 14 15
Figure 57. Variation of solids profile with time for
Billerica sludge (DW-3) drying on Ottawa Sand.
REFERENCES
1. Standard Methods for the Examination of Mater and VJastewater. 12th
ed., American Public Health Association, New York, 1965.
2. Nebiker, J. H., Sanders, T. G., and Adrian, D. D. An Investigation of
Sludge Dewatering Rates. Journal Hater Pollution Control Federation,
August, 1969, Part 2.
3. Quon, J. E. and Tamblyn,T. A. Intensity of Radiation and Rate of Sludge
Drying. Journal of the Sanitary Engineering Division, A.S.C.E., 91,
No. SA2, April, 1965.
4. Clark, E. E. Water Treatment Sludge Drying and Drainage on Sand Beds.
Ph.D. dissertation, University of Massachusetts, Amherst, 1970.
121
-------
SECTION VIII
THE EFFECT OF RAINFALL ON SLUDGE DEWATERING
ON SAND BEDS
The fundamental gravity drainage equation, discussed by Lo (1), which
is used to describe liquid flow through a compressible sludge cake is:
t = —£ [H a+1 + 0H0+1 - (a + 1) H Ha] (136)
where
gs s
c = c
ioo(sc-s0)
y = filtrate viscosity (poises)
2
R = specific resistance of cake at reference head loss, H (T /M)
a = coefficient of compressibility
H = initial hydraulic head (L)
H = reference hydraulic head (L)
L>
H = hydraulic head at time t (L)
2
p = density of water (M/L )
S = initial solids content of sludge (%)
S = solids content of cake (%)
\r
In this section, the effect of rainfall on the rate of drainage is incor-
porated into the drainage equation in order to establish a drainage model with
daily rainfall as a stochastic input.
The addition of rainfall on the surface of sludge may not only prolong
the drainage time but may also dilute the suspended sludge. According to
the basic equations, this diluting effect will increase the rate of drainage,
As a result, the following assumptions are important to the behaviour of the
dewatering system. For simplicity in analysis, two models (mixing and ponding)
were studied to represent two extreme conditions of water on the surface of
122
-------
the sludge, In the ponding model it was assumed that water and sludge were
immiscible, resulting in ponding of rainfall on the surface as supernatant.
Mixing model for sludge drainage. It is assumed that R, units of rain-
fall are added to the surface of draining sludge at time t,, in which a
cake has been formed at sludge depth H, as shown in Figure 58.
I
J
F
i
H0
r
H,
*
L
D
' *•
• '
-. .' . ••. . . .• .••. .-••.. '
.• !. • '•' •.•''- ; : '' '
'•'•••
• < >
'*
'-.
:
^
' * * * * *. * *
•» L . - _ ' •'> •*"
Sand ' '
Rainfall
Suspended
Sludge
V
Cake
-Free Water
Surface into
Sand Bed
j^A.^--— -Underdrain
M"-*"1
Figure 58: Definition sketch of mixing drainage.
It is seen that filter resistance after time t, will gradually nncrease
as filtration proceeds and the amount of cake formed increases Based on
the basic drainage equation, friction losses can be written in terms of
specific resistance and the discharged filtrates. If Hf, represents the
fHcllw loss of the formed cake and Hf2 the friction l5ss of the forming
cake, these two equations will be:
_ C R (HQ + D - H)/ (PgA)]
(137)
123
-------
Hf2 = ^ [y C R1 (H1 + D + R] - H)/(p g A)] (138)
C =Pg SQ SC/(SC-S0MOO (139)
C1 = p g S'Q SC/CSC-S^)-100 (140)
H
R = Rc C/)c (141)
R1 = R ({j-)° (142)
o
where
S = solids content in the suspended sludge before raining
S' = solids content in the suspended sludge after raining
S = solids content in the cake
D = depth of free water surface on the sand bed
Since total friction loss H,: = Hf-, + H^
ft = P 9 A Hf/{(y CR) (HQ + D - Hj) + (u C1 R') (H] + D + R] - H)} (143)
The term dv/dt may be rewritten in terms of the head as -AdH/dt and the total
friction loss Hf is none other than the head, H. Then Equation 143 becomes:
$:= - P9 H/{(y CR) (HQ + D- H] ) + (y C1 R1) (H] + D + R] - H)} (144)
This equation can be integrated from H = H, + R, - E, at t = t, to H = H at
t = t2 where E, is the height of sludge lost due to evaporation during the
perioa t, . The equation becomes
y R S S
°
100H%(a+l) (S-SJ
\f CO
H, + D + R, - E1 S' S
log (-J - n - ! - H + (a+l)^c (H + D + R
M ^'^ '
((H, H- D + R - E,
1 ' '
S1 S
(^
co
(145)
124
-------
Where S', the solids content in the suspended sludge after raining, will
depend on the amount of rainfall, the height of suspended sludge and the
initial solids content. An attempt has been made to express this post-rain
solids content in terms of known parameters.
By definition, the post-rain solids contentcanbe written as
W 100
S_ = S
o Ww + P g A R1 + Ws
or
-(>9AR) (146>
where W = the weight of dry solid material in the suspension after raining
o
W = the weight of water in the suspension before raining.
Since the solid material will be the same before or after raining, the W may
also be expressed in terms of the initial solids content as:
" (147)
Substituting the above equation into Equation 146 gives
=?— (W +pg A R^ (148)
o
W , the amount of water in the suspension, can be expressed as the total
amount of water on the drying bed minus the amount of water in the cake and
the amount discharged as filtrate. Since the total volume of water in the
sludge was found to be
S
P, (1 - T§n-)
A H (-=—? 1^0 )
0 op n Io N
100 ps ( 100;
therefore
ps (1 ^_) 100 - S
Ww = p 9 A Ho So + n So SC
loop+ps (1 -Too)
- A p g (HQ - H)
125
_ w
(149)
-------
where W denotes the dry solid material in the cake, and P the density
of totaTcsolids. Since C has been defined in the previous section as the
dry solid material in the cake per unit volume of filtrate, W can be re-
placed by the term CQ A (HQ - H). Equation 149 then becomes
o
ii n u / ° uvj \ /•> ft /ii LJ i
W = p g A H (c c ) - C A (H - H,;-
W 0 o i> 001
ISO p + ps (1 " TOO5
100 - S^
( 5 -) - A p g (HQ - H^ (150)
P 9 S S
Inserting CQ = 1QQ /j: _g \ into Equation 150
PeO ~ TS?T) P 9 Sn A
- « n fl U I '"-" 1 4- <
* P 9 * "O ^ S ^ + 1WVS-
100 D Ds u 100J
(H^) (100-Sc) - A p g (H^H^ (151)
Substituting Equation 151 into Equation 148 yields
-c) (v"]) .
_c \ ill
100-SQ 100-S^ LV"1 SQ p + PS (100-S^ 100(So-SQ)
S P H Srt(100-S^) (H -H,)
r/u 0 0 Ov C' \Q r v-i
1 " So p + ps(100'So) 100 (SC-SQ) ;J
c, ,HO-HI,
1 S p + pTTlOO-S ) 100 (S -S )
o s o co
S G
Then S' = —^ = (153)
Equation 153 is an expression of the post-rain solids content in terms of
known parameters S , H , H,, R,, p , p.
For the general case, the above drainage equation can easily be extended
to the condition in which there are many rainy days adding various amounts of
rainfall to the surface of the sludge.
126
-------
each
H = hfl + hf2 + ..... + hfn
= dv/dt [y CQ Rc (H1/Hc)a(HQ + D + R^) +
y ci Rc (H2/HC)0 (H! + D + R2 - HZ) +
' • ' ' + ..... + (154)
MCn-l Rc
-------
of the sludge is derived below.
H,
D
Sand
Rainfall
Suspended
Sludge
Cake
"T
^ Free Water
Surface into
Sand Bed
Underdrain
Gravel
Figure 59: Definition sketch of ponding drainage.
Let R-, units of rainfall be ponded on the surface of sludge at time t,
while the sludge depth is known as H,, shown on Figure 59. It is seen that the
resistance to the flow of supernatant will include resistance from the sludge
suspension, from the formed cake and from the supporting material. If the
resistance from the suspended sludge and the supporting material are neglected,
the rate of drainage can be expressed as:
dt
P9 A hf
u C RV/A
(158)
where
5
dt
= -A-
d(H
dt
(159)
128
-------
if HI is considered as a constant for a short period, then
dVs = -A dR1 (160)
and
then
dR, -p g (H + D)
l. 3 (161)
dt y C R^/H/ (H0+D - HI)
Integrating the above equation from R, = R, at t = 0, to RI = R at t = t,
yields,
P g (H, + D)t
R = R ! (162)
MC Rc (H^)0 (Ho + D - HI)
P g So Sc
where C =
(SC-SQ)100
P 9 (H, + D) t
or R, - R = AR = - - -
v C Rc(H1/Hc)a (HQ + D - H^
(H, + D) t
or AR = — ~ - (163)
100(Sp-Sn) cc0 -l
L. o
Equation 163 allows determination of the amount of supernatant drained at a
certain period of time, while the depth of the sludge is assumed constant.
This means that the dewatering of sludge is temporarily halted during the
course of draining the supernatant. Of course this is not true in a real
sense, but the error may be not significant if the time of drainage is chosen
to be smal 1 .
Verification of drainage models. After developing the mixing and ponding
models, tests were made to see if these two models yielded the sanie results
under various rainfall conditions. The aim of this investigation was to
test the sensitivity of the assumption about mixing and ponding models which
represented two extreme conditions of rainwater on the surface of sludge.
The results indicated that under identical conditions the ponding model
usually had a more rapid drainage rate than the mixing model. The reason is
simply that the mixing model treated rainwater as sludge while the ponding
model did not. A representative comparison is shown in Figure 60. The over-
all results indicate that the difference in most cases was within 5 percent,
demonstrating that the assumption of miscibility of rainwater and sludge does
129
-------
not significantly affect the final results. In the real condition of
course, rainwater in sludge will behave somewhat in between these two models.
E - _
'
.10
E
o
CL
UJ
Q
UJ
C/5
Mixing model
Ponding model
R*= I010, S0=5%
cr= l.O
* at 38 cm of Hg
I
468
DEWATERING TIME (DAY)
10
12
Figure 60: Comparison between mixing and
ponding models.
Since the mixing drainage model gives a conservative drainage rate, it
lends itself well to computer applications, thus it was chosen as the drain-
age model to be used to predict the required drainage for water and waste-
water sludge in the rest of the study.
To test whether or not this model really describes the behavior of sludge
drainage on a sand bed, the mixing model was further investigated, in the
laboratory by means of column tests. Results shown in Figure 61 indicate
that the observed sludge heads on sand beds were very close to that predicted
by the mixing model equation, and proved that the model was verified experi-
mentally, provided a media factor of 0.36 and the adjusted specific resistance
130
-------
were used.
Theoretical
Exp. Col.
Exp. Col. 2.
Exp. Col. 3.
Rc=8.0 x 10 at 38 cm of Hg
= 0.49
M.F= 0.36
Sand + Gravel = 10 cm
DEWATERING TIME (DAY)
Figure 61: Comparison between mixing drainage
model and experimental data.
THE EFFECT OF RAINFALL ON DRYING
The effects of rainfall on the rate of drainage during the constant
rate drying period may be determined by the models discussed previously.
However, very little information exists which describes the effects of rain-
water on the process of drying during the falling rate drying period. In all
cases, rainfall will prolong the length of time a drying sludge must remain
on the sand bed. A previous investigation (2) indicated that this effect
varied considerably, depending upon the time, intensity, and duration of the
131
-------
rainfall. If rain occurs during the falling rate drying period, a portion
of the rainwater is absorbed by the sludge. The remainder depending upon
such factors as number and depth of cracks, cake moisture content and
sludge cake permeability may be drained through the sludge cake to appear
as filtrate, or may pond on the surface as supernatant.
However, the most important parameter with respect to drying is the
amount of rainwater retained by the sludge in contrast with the amount that
drains away. In this study experiments were run to develop an equation which
would predict the amount of rainwater absorbed by the sludges for different
sludge conditions.
Experimental determination of rainfall effects on drying. These experi-
ments were concerned primarily with characterizing the amount of rainwater
absorbed by a sludge after each rain, under different sludge conditions.
Variables considered were: (1) moisture content of the sludge after rain,
(2) moisture content of the sludge before rain, (3) intensity of rainfall and
(4) duration of rainfall. In order to make the tests representative of field
conditions, initial moisture content of each sludge was intentionally altered
to cover the range that would normally be found during the falling rate drying
period for water and wastewater sludge drying on sand beds.
Rainfall effects were determined through experiments with intensities
of 0.025, 0.125 and 0.25 cm/hr (0.1, 0.5 and 1.0 in/hr) for durations of 1,
2 and 4 hr at each intensity. In the test procedure, 500 ml of well mixed
sludge was poured into a fritted glass funnel after which the sludge was
allowed to dewater until it reached the desired moisture content. After being
weighed, this glass funnel was installed on the testing equipment to receive
artificial rainfall at a designated intensity and duration. After treatment,
the sludge was removed from the test apparatus, and weighed again to measure
the increase of weight due to the absorption of rainfall. The results of the
experiments revealed that only a portion of rainwater was absorbed by the
sludge, the percentage of rainwater retained varied considerably with the
initial cake moisture content and with the intensity and duration of rain-
fall. In general, there was a rapid initial absorption of rainwater by the
sludge during the early stage of testing, then the rate of absorption de-
creased with an increase in the duration of rainfall. The initial intake was
even more significant for higher intensities of rainfall. The occurence of
this phenomenon is attributed to an initially highly porous sludge surface.
Following saturation at the surface, water then migrated from the region of
high surface moisture to inner portions of the sludge.
In order to establish the water-absorbing characteristics of sludge,
moisture content after rainfall was related by multiple regression analysis
to the intensity and duration of rainfall and to the moisture content before
rainfall. In general, statistically significant relationships were shown to
exist, and the signs of the regression coefficients were consistent with
intuitive judgment of cause and effect. The regression equations for water
and wastewater sludge are shown below.
132
-------
(1) Water treatment sludge
M = 3.44 Mo°'812 x I0'008 x D°-012 (164)
R2 = 0.9956 N - 30
(2) Wastewater treatment sludge
M = 5.44 M0°'751 xI°-062xD0.041
R2 = 0.9759 N = 27 (165)
where M = moisture content after rain
M = moisture content before rain
D = duration of rainfall (hr)
I = intensity of rainfall (in/hr)
It is interesting to note that the exponents for intensity and duration
were close to each other for each type of sludge. This suggests that the
effects of intensity on the moisture content after rainfall seemed very
similar to the effects of duration; therefore, these two factors were com-
bined into a new variable: depth of daily rainfall. This combination is
fortuitous in a practical sense because daily rainfall records are more
readily available than are records of continuous rainfall. When the moisture
content after rainfall was related to the parameters of initial moisture
content and daily rainfall, the equations obtained were:
(1) For water treatment sludge
M = 3.55 M00'807 x Rd°-°095
R2 = 0.9953 N = 30 (166)
(2) For wastewater sludge
M - 4.93 M0°'766 x Rd0'056
R2 = 0.9727 N = 27 (167)
Where R. = daily rainfall (inches)
Comparison between moisture contents predicted by Equations 166 and 167 and
the experimental values is shown in Tables 21 and 22-
133
-------
TABLE 21. THE EFFECT OF RAINFALL ON WASTEWATER SLUDGE
DRYING DURING THE FALLING RATE PERIOD
Rainfall
in Inch
(Rd)
.1
.1
.1
.2
.2
.2
.4
.4
.4
.5
.5
.5
1.0
1.0
1.0
2.0
2.0
2.0
1.0
1.0
1.0
2.0
2.0
2.0
4.0
4.0
4.0
Moist. Cont.
Before Rain
(MQ)
267.5
272.2
276.6
243.6
269.6
174.7
289.6
179.1
330.2
250.8
317.2
290.7
257.5
280.0
201.4
195.6
278.4
329.9
272.9
345.0
297.5
285.4
321.6
254.5
245.5
369.6
342.5
Experimental
Moist. Cont.
After Rain
(M)
310.7
326.5
305.3
292.3
338.5
236.7
364-7
243.6
396.3
326.9
381.7
371.7
342.2
381.0
289.3
287.7
383.5
420.9
375.4
436.2
398.8
392.6
463.3
359.6
358.2
469.1
452.9
Calculated
Moist. Cont.
After Rain
(M)
313.3
317.5
321.4
303.2
327.7
235.0
359.8
249.0
397.8
326.4
390.6
365.4
346.2
369.2
286.8
291.5
382.1
435.1
361.9
433.1
386.6
389.4
426.7
356.7
360.7
493.5
465.5
Residual
-2.7
9.1
-16.1
-10.9
10.8
1.6
4.9
-5.4
-1.6
.6
-9.0
6.3
-4.0
11.8
2.6
-3.8
1.5
-14.3
13.5
3.0
12.2
3.2
36.7
2.9
-2.4
-24.3
-12.6
134
-------
TABLE 22: THE EFFECT OF RAINFALL ON WATER TREATMENT
SLUDGE DRYING DURING THE FALLING RATE PERIOD
Rainfall
In Inch
(Rd)
.1
.1
.1
.2
.2
.2
,2
.4
.4
.4
.5
.5
.5
1.0
1.0
1.0
1.0
2.0
2.0
2.0
1.0
1.0
1.0
2.0
2.0
2.0
2.0
4.0
4.0
4.0
Moist. Cont.
Before Rain
(MQ)
580.0
560.0
572.3
548.3
521.7
559.1
362.6
540.0
526.6
508.6
575.4
564.3
571.4
546.3
546.9
556.0
418.6
548.9
544.3
457.4
568.6
564.3
568.6
530.0
544.0
537.7
423.7
538.6
547.7
518.6
Experimental
Moist. Cont.
After Rain
(M)
592.9
578.6
583.7
572.6
548.9
572.3
405.7
569.4
562.0
546.3
596.3
585.7
594.3
576.9
576.3
584.3
466.3
577.4
579.1
505.7
591.4
597.1
595.7
564.9
585.7
577.1
471.4
578.9
584.3
560.3
Calculated
Moist. Cont.
After Rain
(M)
604.6
587.7
598.1
578.1
555.4
587.3
413.9
571.4
559.9
544.4
601.7
592.3
598.3
577.3
577.8
585.6
465.6
579.9
576.0
500.5
596.3
592.7
596.3
563.8
575.8
570.4
470.5
571.5
579.4
554.3
Residual
-11.7
-9.1
-14.4
-5.5
-6.5
-15.1
-8.2
-2.0
2.1
1.9
-5.4
-6.5
-4.0
-.5
-1.5
-1.3
.7
-2.5
3.1
5.2
-4.9
4.5
-.6
1.1
9.9
6.7
.9
7.3
4.9
6.0
135
-------
REFERENCES
Lo, K. Digital Computer Simulation of Water and Wastewater Sludge
Drying on Sand Beds. Ph.D. dissertation, University of Massachusetts,
Amherst, 1971.
Randall, C. W. and Koch, C. T. Dewatering Characteristics of Aerobically
Digested Sludge. Journal of the Water Pollution Control Federation,
Research Supplement, May, 1969.
136
-------
SECTION IX
SIMULATION OF DEWATERING ON SAND BEDS
Because of the stochastic nature of rainfall and its resultant effect on
drainage and drying on open sand beds, a simulation approach was employed to
test the performance of a particular design under conditions representative
of a given area of the country. To achieve this simulation, drainage and
drying models were developed, as discussed previously, which related sludge
characteristics and weather to the amount of water lost by drying and drain-
age. Synthetic rainfalls were used as input to determine the response of the
models.
Local evaporation data were another important input to the models for
they not only represented water losses during the constant rate drying
period but also determined drying rates during the falling rate period.
Therefore, the time required for drainage and drying was treated as a func-
tion of local meteorological conditions and the nature of the sludge.
SCOPE OF THE SIMULATION
The computer simulation included four different types of wastewater
sludge and two types of water treatment sludge. The wastewater sludges
were anaerobically digested primary sludge, primary and trickling filter
digested sludge, primary and activated sludge and aerobically digested
sludge. Alum sludges from the Albany, New York, and Amesbury, Massachusetts
treatment plants were used to represent the water treatment sludges. These
two alum sludges exhibited significant differences in drainage rates permit-
ting them to serve as the upper and lower limits of sludge properties.
Softening sludge was not considered in this study because this sludge settles
so rapidly that a lagoon disposal method might be more suitable. The sludge
parameters related to dewatering are presented in Table 23.
So as to take into account weather conditions encountered across the
United States, six cities were chosen to represent six different meteorolog-
ical conditions. Table 24 shows the normal weather data for these cities,
and indicates the variation they experience in annual precipitation.
In recognition of decreased drainage and drying in cold weather, winter
months at each location were excluded from simulation. The occurrence of
freezing in selected cities, shown in Table 25, is based upon Environmental
Science Service Administration records (7). Excluding the periods during
which freezing occurs is a conservative approach since some drainage and
137
-------
TABLE 23. CHARACTERISTICS OF SLUDGES
Water
Sludge
Types of Sludge
Alum Sludge
(Albany)
Alum Sludge
(Amesbury)
Primary
Anaerobically
Digested
Sludge
Solids
Content
1.3%
1.5%
9.5%
Specific
Resistance*
Sec /gm
8.0 x 109
5.8 x 108
2.6xl010
Coefficient
of
Compressibility
0.49
0.99
0.68
Reference
Lo (1)
Adrian (2)
Nebiker (3)
Anaerobically
Digested Sludge
Waste Mixed with Acti
Water vated Sludge
Sludge
3,6% 4,8 x 10
10
0.66
Sanders (4)
Anaerobically 6.1% 8.25 x 109 0.8
Digested Sludge
Mixed with
Trickling
Filter
Aerobically 4.5% 1.15xl09 0.97
Digested
Sludge
Quon (5)
Cummings(6)
*At pressure P =38.1 cm of Hg
138
-------
TABLE 24. NORMAL MONTHLY WEATHER DATA - SELECTED CITIES
Stations
Phoenix,
Ari zona
San Francisco,
California
Boise,
Idaho
Miami,
Florida
Boston,
Massachusetts
Duluth,
Minnesota
Jan,
2.90
0.61
4.0
1,3
4.03
11.0
0.79
1.33
12.0
3.0
2.15
8.0
0.97
3.50
12.0
0.26
1.01
10.0
Feb.
3,50
0.82
4,0
1,5
3,91
10.0
1.2
1.35
11.0
3.4
1.73
6.0
1.1
2.93
10.0
0.32
1.02
8.0
Mar.
5,40
0.68
3,0
2,1
2.78
10,0
2.4
1.34
10.0
4.1
2.15
6.0
1.4
3.43
12.0
0.69
1.54
10.0
Apr,
7,40
0.37
2.0
2,5
1.49
6.0
3.8
1.10
8.0
4.9
3.44
7.0
2.2
3.46
11.0
1.4
2.21
9.0
May
10.4
0.16
1,0
2,7
0.59
4.0
5.3
1.09
9.0
5.0
4.27
11.0
3.1
2.91
11.0
2.1
2.95
12.0
Jim,
13.5
0.06
1.0
2.9
0.15
2.0
7.1
0.84
7.0
4.8
5.55
13.0
4.2
3.48
10.0
2.4
3.72
13.0
Jul.
14.8
0.68
5.0
2.7
0.01
1.0
10.6
0.18
2.0
5.3
4.36
15.0
5.0
3.18
10.0
3.7
3.31
11.0
Aug.
13.5
0.90
5.0
2.5
0.01
1.0
10.1
0.21
2.0
5.1
5.06
15.0
4.5
3.23
10.0
4.2
3.19
11.0
Sep.
11.7
0.36
2.0
2.9
0.13
1.0
6.3
0.46
3.0
4.3
6.72
18.0
3.6
2.99
9.0
3.6
3.03
11.0
Oct.
8.20
0.40
3.0
2.9
1.07
5.0
3.5
0.94
7.0
4.1
7.88
15.0
2.9
2.79
9.0
2.4
1.96
9.0
Nov.
5.10
0.50
2.0
2.4
2.27
7.0
1.8
1.35
10.0
4.3
2.16
9.0
1.9
3.49
10.0
1.0
1.67
9.0
Dec.
3.10*
0.98**
4.0***
1.7*
4.07**
1 1 . 0***
0.92*
1 . 29**
12.0***
2.7*
1.73**
7 _ o***
1.3*
3.37**
1 1 . 0***
0.31*
1 . 00**
9 . 0***
"Monthly evaporation in inches,
**Monthly precipitation in inches.
***Number of rainy days.
-------
TABLE 25. OCCURRENCE OF FREEZING AT SELECTED CITIES
(Based on records from 1921 to 1950)
Occurrence of Freezing
0°C Mean Number of Days
Mean Mean Minimum
Fall Spring Temperature 0 C
Station Date Date or less
Phoenix Dec. 6 Feb. 2 17
San Francisco Dec. 22 Jan. 17 less than 10
Miami -
Boise Oct. 16 Apr. 29 128
Boston Oct. 25 Apr. 16 94
Duluth Oct. 3 May 13 189
drying still occur during such intervals.
All six sludges were simulated for their performance on sand beds in
various locations with at least six different application depths. The start-
ing depth was 10 cm for each sludge; its value was increased by 5 or 10 cm
increments wherever possible.
ESTIMATION OF THE SIMULATION SAMPLE SIZE
Sample size for a simulation study must not be so large as to be too
costly or so small as to be unreliable. In this study, the sample size (the
number of sludge applications to be generated for the simulation experiment)
was determined according to Equation 168 given by Chow and Ramaseshan (8), for
which levels of precision and confidence are specified.
n > (ya)2[(l-Pn)/Pn] (168)
where Pn = the proportion of the sample from a population that belongs
to the group under consideration
a = percentage of error level
6 = percentage of confidence level
t = the standard normal deviate corresponding to the confidence
B level
140
-------
In this study, a confidence level of 80 percent results in a standard
normal deviate of 0.842 for the equation. With a selected error level of 15
percent, the value of the proportion of generated dewatering times that were
different from the actual dewatering time was 15 percent. The desired sample
size is calculated as:
M - (0-842x2 ,1-0.15^ _ 1Rn
N ~ (0.15 } (~OJ5~) ' 18°
Because the dewatering time varied widely depending upon location, type
of sludge, and applied depth, 180 application times might mean a 20-year simu-
lated operation under one condition and only 10 years under another. The
longer the period of simulation, the greater the chance of encountering higher
intensities of rainfall. The chance of a 10 year simulation having a 20-year
storm history was only 30 percent. Consequently, the use of the number of
applications as the .criterion for sample size was biased based on the hydro-
logical point of view. In order to correct this, the sample size was chosen
to be at least 200 events to be applied over a 20 year simulation period. This
dual criteria for sample size control provided the required level of accuracy
and also ensured that a 20-year storm or higher was considered in the simula-
tion; therefore, a bed design based on the results of this study is expected
to have a useful life of 20 years or more.
SIMULATION PROCEDURE
Input parameters to the sludge dewatering simulation experiment were
the physical properties of the sludge. Output of the stochastic system was
affected by changes in the quantities and types of input. The models were
operated in the computer in accordance with the following rules:
1. The total amount of daily rainfall was considered to fall on the
ground instantaneously at zero hour of each day of rain.
2. The drainage process for wastewater sludge was terminated when
the moisture content reached the first critical point (UCR). For
water treatment sludge the drainage was stopped according to Clark's
expression (1)
S, = 4.3 + 0.7 Sn
d o
where S, = solids content at which drainage stops
a
S = initial solids content
o
3 The final solids content for wastewater sludge was selected as 35
percent, while 20 percent was selected for water treatment sludge.
The values were considered to be representative of past practice.
The simulation started at the beginning of each day with the addition of
the daily rainfall to the sludge surface; if it was not a raimng day, a
zero amount of rainfall was added. Then by applying the drainage model
141
-------
(Eqs. 156 and 157), the depth of sludge on the drying bed at the end of 24
hours of dewatering was obtained. This depth of sludge, after subtracting
the amount of water lost by drying, was used as an entry value for the drain-
age model in the second day's operation. The procedure was repeated until
the drainage-terminate moisture content was obtained. Moisture content of
sludge was calculated by Equations 64 and 133 for wastewater and water sludge
respectively, with Equations 166 and 167 accounting for rainfall effects.
A result of this operation is shown in Figure 62.
6
0
I
I
B
UJ
CD
a
6
4
2
20
15
10
5
i
(
-
1 . i .
10
R
-------
periods corresponding to his field observations of net bed loadings For
this reason the weather pattern existing when Haseltine collected his data
was assumed the same as the average obtained from a 20 year simulation.
The comparison for covered beds is shown in Table 26. The results indi-
cate that the reported net bed loading at the various plants was within
the limit established by the expected dewatering time for the 20 year simu-
lation at different application depths. The results for open beds in Table
27 and 28 show that the reported dewatering times for various application
depths were slightly less than the expected dewatering time from the 20-year
simulation, but the observed values still fell within the range of the simu-
lated dewatering times. Statistical tests between the observed and simulated
values were not considered because of the small sample from which observed
data were drawn.
OUTPUT OF SIMULATION
Theoutputof this simulation was a random variable (the required drying
time) and its associatedprobability distribution. A sample output is
shown in Table 29. Essentially, it describes the natural phenomena of sand
bed dewatering in terms of outcomes of various frequencies. For example,
following application of 20 cm of mixed digested primary and activated sludge
in Boise, Idaho, it would be possible to remove the sludge at 35 percent
solids content twice within fourteen days, forty times within 15 days, and
so on, over a twenty-year period. The mean period for which the sludge
had to remain on the beds was 19.9 days with a standard deviation of five
days. The shape of the frequency distribution shows that the low limit of
dewatering time was 14 days, with short dewatering times occurring more fre-
quently than long ones, suggesting that dewatering time might be described
by the Poisson distribution.
Overall outputs for the entire simulation are presented in summary form
in Lo (1 ). They include the data for mean and range of dewatering times
and their corresponding standard deviations. Net bed loadings calculated
from the mean dewatering time are also included.
143
-------
TABLE 26: COMPARISON BETWEEN COMPUTER SIMULATION AND
FIELD OBSERVATIONS FOR COVERED BEDS AT
VARIOUS LOCATIONS.
Plants
Butler,
PA
Grove City,
PA
Dayton,
Ohio
Huntington,
NY
Rockville,
NY
Salinas,
CA
San Antonio,
Tex.
Springfield,
111.
RC = 8.25 x
M.F. = 0.36
a = 0.66
On
6.1-9.2
3.6-4.8
4-5
8.4
5.4
5.4
4.0
9.2
109 at P =
Net Bed
Off Loading
26.7-37.9 1.05-1.99
38-50 0.66-1.0
36-56 1,04-1.71
27.0 2.92
24.5 1.66
62.8 1.35
45.5 0,86
54.1 2.66
Computer Simulation
Solids(%) Net Bed Loading for
On Off Applied Sludge Depth, in
46 8 10
7.0 35.0 1.42 0.94 0.75 0.63
4.3 40.0 2.14 1.33 1.07 0.85
5.0 40.0 1.79 1.18 0.91 0.81
8.4 27.0 1.44 0.93 0.71 0.66
5.4 24.5 3.35 1.58 1.13 0.89
5.4 62.8 1.49 1.08 0.92 0.83
4.0 45.5 2.14 1.41 1.20 1.0
9.2 54.1 1.08 0.82 0.80 0.74
38 cm of Hg.
-------
TABLE 27. COMPARISON BETWEEN ?0-YEAR COMPUTER SIMULATION RESULTS
AND HASELTINE'S (9) FIELD OBSERVATION FOR OPEN SAND
BEDS AT GROVE CITY, PA
Field Observations 20-yr. Computer Simulation Results
Total Drying
Time(Days)
Total Net ReT
Depth Solids Solids Dry Bed Depth Solids Solids Exp Range of Bed
Applied on off Time Load- Applied on off Dry Dry Load-
(in) (%} (%} (day) ing (in) (%) (%) Time Time
8/12
9
9
Rc =
M.F.
a =
3.4 34.1
3.55 40.1
3.5 34.1
8.25 x 109
= 0.36
0.66
18
19
16
0.86 8 1/2 3.4
1.05 9 3.55
1.05 9 3.5
34.1 22.6 12-59 0.68
40.0 36.6 19-58 0.54
34.1 26.1 15-57 0.64
TABLE 28. COMPARISON BETWEEN 20-YEAR COMPUTER SIMULATION RESULTS
AND HASELTINE'S (9) FIELD OBSERVATION FOR COVERED SAND
BEDS AT GROVE CITY, PA.
Field Observations
Appl i
Depth
(in)
10
10
R -
c
M.F.
o =
ed Solids Solids
on off
(%) U)
3.8 41.8
4.1 42.4
8.25 x 109
= 0.36
0.66
Total
Drying
Time
(day)
20
20
Net
Bed
Load-
ing
1.26
1.37
20-yr. Computer Simulation Results
Total Drying
Time
Applied Solids
Depth on
(in) (%)
10 3.8
10 4.1
Solids Exp.
off Dry
(%} Time
41.8 26.8
42.4 29
Range of
Dry
Time
25-29
29-31
Net
Bed
Load-
ing
0.93
0.94
145
-------
TABLE 29. THE OUTPUT OF SIMULATION OF MIXED DIGESTED
PRIMARY AND ACTIVATED SLUDGE DEWATERING ON
SAND BEDS AT BOISE, IDAHO WITH 20 cm
APPLICATION
Dewatering
Timp
(days)
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
32.0
33.0
34.0
37.0
Frequency of
Occurrence
2.0
38.0
20.0
21.0
24.0
12.0
15.0
9.0
9.0
6.0
4.0
8.0
8.0
7.0
1.0
4.0
2.0
2.0
4.0
1.0
1.0
2.0
Probability
0,01000
0.19000
0.10000
0.10500
0.12000
0.06000
0.07500
0.04500
0.04500
0.03000
0.02000
0.04000
0.04000
0.03500
0.00500
0.02000
0.01000
0.01000
0.02000
0.00500
0.00500
0.01000
Cumulative
Probability
0.01000
0.20000
0.30000
0.40500
0.52500
0.58500
0.66000
0.70500
0.75000
0.78000
0.80000
0.84000
0.88000
0.91500
0.92000
0.94000
0.95000
0.06000
0.98000
0.98500
0.99000
1.00000
The expected mean dewatering time is 19.9 days.
The standard deviation of dewatering time is 5.0 days.
The net bed loading is 0.81 Ib/ft2/30 days. (Based on the
mean dewatering time).
146
-------
REFERENCES
1. Lo, K. Digital Computer Simulation of Water and Wastewater Sludge
Dewatering on Sand Beds. Ph.D. Dissertation, University of Massachusetts,
Amherst, 1971.
2. Adrian, D. D. et al. Source Control of Water Treatment Waste Solids.
Report No. EVE-7-58-1, Environmental Engineering, Department of Civil
Engineering, University of Massachusetts, Amherst, 1968.
3. Nebiker, J. H., Adrian, D. D. and Lo, K. Evaluation of Chemical Condi-
tioning for Gravity Dewatering of Wastewater Sludge. In Report No.
EVE-7-68-1, Environmental Engineering, Department of Civil Engineering,
University of Massachusetts, Amherst, 1968.
4. Sanders, T. G. A Mathematical Model Describing the Gravity Dewatering
of Wastewater Sludge on Sand Drainage Beds. M. S. Thesis in Civil
Engineering, University of Massachusetts, Amherst, 1968.
5. Quon, J. E. and Tamblyn, T. A. Intensity of Radiation and Rate of Sludge
Drying. Journal, Sanitary Engineering Division, ASCE, April, 1965.
6. Cummings, P. W. Digital Computer Simulation of Wastewater Treatment.
M.S. Thesis in Civil Engineering, University of Massachusetts, Amherst,
1969.
7. Statistical Abstract of the United States, 1969. U. S. Department of
Commerce, 1969.
8. Chow, V. T. and Ramaseshan, S. Sequential Generation of Rainfall and
Runoff Data. Journal, Hydraulics Division, ASCE, July, 1965.
9 Haseltine, R. R. Measurement of Sludge Drying Bed Performance. Sewage
and Industrial Wastes, 23(9): 1065-1083, 1951.
147
-------
SECTION X
PEFORMANCE OF SAND DRYING BEDS
In the previous section, dewatering times for various sludges at dif-
ferent locations were determined. Little mention was made of the required
bed area and the expected bed performance under each condition. In general,
knowing the dewatering time, depth of application and solids content of the
applied sludge will enable the design engineer to size the drying bed if
the known dewatering time is a single value variable. Due to the effect of
weather, however, the dewatering time as obtained in the preceeding section
was shown to be a random variable which exhibits a wide range of outcomes
for a given sludge and location. Therefore, the design engineer is required
to choose from a number of courses of action. The practical consequence of
adopting any particular course depends not only upon the choice made but also
upon local meteorological conditions. Referring to the data shown in Table
29 for example, it is shown that the time required to dewater a 20 cm applica-
tion of mixed digested primary and activated sludge in Boise, Idaho ranged
from 14 days to 37 days. If the design engineer chose 15-days as the design
dewatering time, the calculated bed area would be 1.45 square feet per
capita, based on the method suggested by the Water Pollution Control
Federation (1). However, the designed bed would be undersized according to
the data shown in Table 28 in that during a twenty year period the sludge
would have to remain on the bed longer than 15 days, 80 percent of the time.
As a result, the yield of dry solids from the bed, or the bed performance,
would not satisfy the design requirements.
AN APPLICATION OF STATISTICAL DECISION THEORY
Before seeking the relationship between dewatering time, bed area and
bed performance, a new random variable N was introduced to represent the
total number of bed applications per year. N was obtained by substituting
the results of the dewatering time obtained in the previous chapter into the
equation:
N =
(169)
where N = total number of bed applications per year
T = total dewatering time available (day/year)
T, = the required dewatering time per application (day)
T = the required bed preparing time (day)
148
-------
In order to measure the consequence of an engineer selecting a larger
number of bed applications than "Nature" allowed, it was assumed that there
existed a loss function which reflected a penalty for the loss of bed
performance brought about by taking too short a design dewatering time. Con-
sequently, some amount of dry solids was left undewatered. If the amount of
undewatered solids is represented by the random variable Z,
Z(n) =
(An-N) Ar H SQ P
(170)
0 Ap>n
where An = the number of bed applications considered by the designer
N = the random variable of bed applications which represents the
"state of nature"
O
Ar = the required bed area in ft (for wastewater sludge it is the
area needed per capita, per year; for water treatment sludge,
it is the area needed per pound of dry solids per day)
H = the depth of sludge in ft
S = the solids content of the applied sludge
p = the density of sludge
Then the expected value of the total solids left undewatered per year can be
calculated as;
"Jo Z (K) Pn
V1
- Z (An - N) Ar H SQ p Pn (K) +
K=o
z 0 P (K)
= (An Ar HSQp) (P [n
-------
A =12 bed applications per year,
Ar = 0.135 m2(1.45 ft2) per capita,
H = 0.20 m (0.66 ft2),
S = 0.034, and
p = 1000 kg/m3 (62.4 lb/ft3)
a fifteen day design dewatering time results in 2.4 kg (5.3 Ib) per capita
per year as the expected dry solids left undewatered.
PERFORMANCE INDEX
For the purpose of expressing bed performance as a function of inputs
such as bed area, application depth and local weather conditions, a term
called performance index (PI) was introduced to measure the weighted average
of sludge dewatered by drying beds each year under various conditions. It
was defined as
Wt of sludge dewatered x 100
Total wt. of sludge
By applying Equation 171 to the above relationship, the performance
index is written as:
PI(%) = [W, - {An A^ H Srt p (Pn (n < An ,))
a n r o n n~ i
A -1
- A H S p ( I K Pn (K))} x 100]/W (173)
I U ]/ r\ I! Lb
K.-U
where W, = weight of dry solids expected to be dewatered under the design
condition without consideration of "the state of nature". The
terms enclosed in parenthesis { } represent the dry weight of
undewatered sludge.
W. = total dry solids expected per year
In words the equation states that the performance index depends upon
the inputs A , A , and H. The design engineer may increase or decrease
the output by increasing or decreasing the quantities of all inputs used,
or increase it to some maximum level by increasing the quantity of one input
while holding the quantities of other inputs constant. Since this equation
expresses the physical relation between the inputs of resources (such as
the bed area, the number of applications and the applied depth) and their
output (PI-- the percentage of the total dry solids dried on the drying beds)
per unit of time, it is often called a production function. Since this
particular production function also involves a random variable N to describe
150
-------
the "state of nature", the function is then appropriately called a
stochastic production function (2).
The overall performance for sludge dewatering on sand beds at various
locations is shown in tables prepared by Lo (3). In each table, the data
show the corresponding performance index for each possible dewatering time
and bed area.
REFERENCES
1. ASCE & WPCF, Sewage Treatment Plant Design. Manual of Engineering
Practice, No. 36, 1959.
2. Mass, A., et al. Design of Water-Resource Systems, Harvard University
Press, 1962.
3. Lo, K. Digital Computer Simulation of Water and Wastewater Sludge
Dewatering on Sand Beds. Ph.D. Dissertation, University of Massachusetts,
Amherst, 1971.
151
-------
SECTION XI
ECONOMIC ANALYSIS FOR SLUDGE DEWATERING ON SAND BEDS
INTRODUCTION
The objective of this chapter is to utilize computer simulation results
presented in previous sections in order to improve sludge dewatering bed
design methodology, so that an optimal system can be obtained. The conven-
tional rule-of-thumb procedure for designing dewatering beds, based largely
on limited field observations* does not effectively incorporate both
engineering and economic analysis. A typical dewatering bed design basis as
recommended by the American Society of Civil Engineers (1) is 1.0 to 1.5
square feet (.09 to 0.14 m2) per capita for primary digested sludge in the
northern United States. It gives no consideration to the cost of land,
labor and operation. Furthermore, there has been a tendency in engineering
practice to consider these design criteria as professional engineering
standards, and the realities upon which they are based are not commonly
appreciated. Support is presented in this chapter for the belief that design
criteria may be applied more satisfactorily if they are associated with all
relevant cost terms. For example, the engineer might over-design the bed
in low land-cost areas in order to reduce the labor costs of operation. In
high land-cost areas, he might design to minimize land costs.
In order to join engineering and economics more effectively than has
been the case in past, an objective function for sand bed dewatering has been
derived which includes design criteria and the associated cost terms. The
objective function used in this study is basically the same as suggested by
Meier (2) in his study of dewatering bed system design. However, efforts
are made in this section to minimize the objective function by utilizing a
simulation approach and a marginal analysis approach.
SIMULATION APPROACH
Simulation has been used by Meier and Ray (2) to study the optimum de-
watering bed system design. In their study, an objective function Z was
suggested:
Z = C1Ar + C2ArAn (174)
where Z = total cost of sand bed dewatering
C-i = cost associated with the required land area
152
-------
C2 = cost associated with the number of applications to the land area
Ar = area of land required
A = the number of applications
A and An are functions of the dewatering time. Therefore knowing C,,
Cy, the dewatering time and the depth of sludge application, the total colt
of sand bed dewatering can be determined if this dewatering time is a single
value variable. Due to the effects of weather, however, the actual dewater-
ing time for a sludge in a particular location has been shown to be a random
variable with a wide range of outcomes. For example, the dewatering time
shown in Table 29 for 20 cm of digested primary and activated sludge on a
sand bed in Boise, Idaho was found to range from 14 days to 37 days. For
each possible dewatering time, there was a corresponding combination of A
and Ar which in turn yielded a different cost. Therefore, the design n
engineer in this case was left to choose from a large number of possible
outcomes. In order to choose a dewatering time that would best represent
actual field conditions and serve as a basis for design and comparison
between alternatives, the following two criteria were used in this study:
expected value of dewatering time, and performance index (PI).
Expected value of drying time. The entire frequency distribution of
possible dewatering times for the example of 20 cm of mixed digested primary
and activated sludge in Boise, Idaho is shown in Table 29. It indicates
that there were 2 times in 20 years when the required dewatering time was 14
days or less, and 40 times when it was 15 days or less, and so on. This
frequency distribution may be considered to be the probability distribution*
of the random variable, drying time. The expected value of the random
variable is
E(t) = E P.t. (175)
i*l 1 1
where t- = the value of the ith possible outcome of the dewatering time
P. = the probability of occurrence of t...
By applying this equation to the data in Table 29, the expected de-
watering time was found to be 19.9 days. This means that 19.9 days only
represents the average dewatering time for an infinite number of applica-
tions. It should be realized that on a single dewatering, one and only one
of the dewatering times from 14 to 37 days can occur. Therefore, if one uses
this expected dewatering time as a basis of design, it is almost certain
that the bed so designed would not be sufficient for certain periods of time
during a 20-year period. Nevertheless, this expected value of dewatering
time does give a single number which significantly characterizes the random
*By~the law of large numbers, the frequency distribution would approach the
probability distribution as a limit, when the sample size approaches
infinity(3).
153
-------
variable over its range of occurrence. In many cases, it alone is an ade-
quate basis for choice among alternatives, especially when all alternatives
have approximately the same probability distribution. Based on the above
discussion, then, the expected value of drying time is suggested in this
study as one of the criteria to be used in determining the variables Ap and
A . The data concerning these expected drying times for various sludges
dewatered in different locations at different depths of application is found
in Lo (4).
Performance index (PI). In preceeding paragraphs the expected dewater-
ing time was suggested as a criterion for determining the variables An and
A . The advantages of using this familiar statistic are:
1. it makes use of all outcomes, and develops a weighted sum in which
the contribution of each outcome is afforded an equal weight.
2. the assertion drawn from Tchebycheff's inequality (5) regarding any
probability distribution with a finite standard deviation, namely
that the probability that an outcome of dewatering time larger than
K days away from its mean is at most 1/K2,
3. that it is relatively easy and straightforward to determine; also
it gives the option of using only the mean or the mean plus one or
more standard deviations as criteria.
On the other hand, the main disadvantage of using this expected de-
watering time is that it is affected by its probability distribution, by
which the expected drying time from a positively skewed distribution (like
the Poisson distribution) is considerably smaller than that from a symmetric
distribution (like the normal distribution) over the same range of occurrence.
Consequently, two outcomes with the same expected dewatering time would not
yield the same performance level (PI) if their probability distributions were
different. In order to avoid this problem, an alternative decision criterion
based upon the concept of performance index was suggested. The actual prob-
ability distribution generated by computer simulation was treated as an
empirical discrete distribution so that the performance index would not be
affected by the shape of the distribution. One may design the bed based on
any expected performance level. However, 100 percent performance index is
not recommended for use because it is overly conservative.
Since the rainfall distribution appeared highly skewed regardless of
geographical location, the shorter dewatering times occurred most frequently,
and longer dewatering times occurred more and more infrequently. As a
result, the performance index determined by the expected dewatering time was
found to be very high. In most cases it was in the range of 90 percent to
95 percent. Based upon the above observation, therefore, it was recommended
that the concepts of expected dewatering time and performance index be used
jointly to design the bed in such a way that the target performance index
is in close agreement with the expected dewatering time.
Economic factors. Upon completing the criteria for determining A and
154
-------
Vrf •!! ![ °n ^s been given to economic parameters C,, the cost associ-
ated with the required land, and C2 the cost associated with the number of
applications per land area. Items which must be included in Ci would be
land construction and maintenance costs as well as the land salvaae value
and rehabilitation cost at the end of the economic life span For example
if one assumes K
land cost $10,000/Acre
construction cost $l'0,000/Acre
maintenance cost $ 1,000/Acre/Year
repair of bed cost $ 5,000/Acre/Year
salvage value $10,000/Acre
rehabilitation cost $ 2,000/Acre/30 Years
economic life 30 years
and selects an appropriate interest rate, the value of C, can be readily
calculated as follows: '
land cost (6%, 30 Years) = $ 726/Acre
construction cost (6%, 30 Years) = $ 726/Acre
maintenance cost = $l,000/Acre
repair cost (6%, every 10 Years) = $ 320/Acre
salvage value (6%, 30 Years) = $ 125/Acre
rehabilitation cost (6%, 30 Years) = $ 25/Acre
Total C,= $2,672/Acre/ Year($6600/Hectare/
'1
Year)
C? considers the costs of applying and removing sludge and varies with
the method of removal. Cake removed by hand requires a low capital invest-
ment, but requires more labor than that removed by machine. In addition,
machine removal causes a greater loss of sand and requires frequent sand
renewal. The depth of application may also affect removal costs. A shallow
application may result in a thin layer of cake which might impede the
removal operation. Unfortunately, there is very little information in the
literature concerning sludge removal. Conversation with the operators
at the Northampton, Massachusetts, sewage treatment plant revealed that it
took 2 man-days to remove sludge from 7 beds by machine. In 2 man-days
sludge could be removed from 2 beds by hand. The dimension of the bed was
25 feet by 150 feet. On the average the bed required sand renewal after
every 8 applications for either machine or hand removal.
Using this information and assuming that the cost of labor is $4/hr,
and that the sand renewal operation is $50/bed, C-j can be determined for a
plant utilizing hand methods to remove sludge as:
Labor Cost:
2
2 man-day x 8 hr/man-dav x 4 $/hr x 43560 ft /AC _ -^/application Acre
2 Bed/day x 25 ft x 150 ft ($914/application/hectare)
155
-------
Sand renewal cost:
50 $/bed x 43560 ft 2/Ac
8 Apply, x 25 ft x 150 ft
= $ 73/application/Acre
($180/application/hectare)
Total C, = $443/application/Acre
($1094/application/hectare)
Determination of optimum system design. By including the calculated C-,
and C? in the objective function of Equation 174, simulation results were
obtained for the optimum application depth of sludge. The method utilized
was to take A and A for different application depths and calculate the
annual cost. nThe glSbal optimum was then determined as the depth which
yielded a minimum cost. The results shown in Table 30 using the output from
Boise, Idaho as an example, indicate that the optimum sludge depth would be
25 cm for a digested primary and activated sludge with 95 percent performance
index as the target output. The required bed area would be 0.22 m2(2.32 ft?)
per capita with 6 applications per year. The annual cost of sand bed drying
would be $0.281/person.
As an alternative, however, the design engineer may chose to use a
mechanical rather than a manual method to remove dry sludge from the bed.
TABLE 30. ANNUAL COST OF SLUDGE DRIED IN BOISE, IDAHO.AT DIFFERENT
APPLICATION DEPTHS (Sludge Removed by Hand)H)
'Application
Depth
(cm)
10
15
20
25
30
35
Dewatering
Time
(day)
5
12
20-21
30-35
44-57
58-81
Bed
Area
(ft2/cap)
1.40
1.66
1.98
2.32
2.90
2.32
No. of
Application
Per Year
26
14
9
6
4
3
Annual
Cost (2)<3)
($/cap)
0.445
0.331
0.299
0.281*
0.293
0.301
(1) Type of Sludge: Digested PKimary and Activated Sludge.
(2) C1 = $ 2672/AC = $ 0.061/ftT
C2 = 443/AC/Applic. = $ 0.01/ft2/Applic.
(3) PI - 95%
*0ptimum Depth.
Under this alternative situation, the cost of ^2 would reduce to:
labor cost:
156
-------
2 man-day x 8 hr/man-day x 4 $/hr x 43560 ft*
7 Bed/day x 15 ft x 150 ft
Ac
— = $105/app1ication/Acre
($26 0/appli cation/hectare)
sand renewal cost:
50 $/Bed x 43560 ft2/Ac
8 Apply, x 25 ft x 150 ft _^_
=,$178/application/Acre
C
_ $ 73/application Acre
($180/app1ication/hectare)
1
($440/application/hectare)
Substituting this cost factor into Equation 174 produces the output
shown in Table 31, indicating that the optimum depth reduces to 20 cm and the
required bed area to 0.18 m2 (1.98 ft2) per capita with an increase in
applications to 9 per year, while a saving of $0.089/cap/year would be
realized by mechanical sludge removal. Therefore the decision of whether
or not to use a machine to remove sludge would depend upon whether this
saving would cover its annual per capita cost.
TABLE 31. ANNUAL COST OF SLUDGE DRIED IN BOISE, IDAHO FOR
DIFFERENT APPLICATION DEPTHS (Dry Sludge Removed
by Machine)"'
Application
Depth
(cm)
10
15
20
25
30
35
Dewatering
Time
(day)
15
12
20-21
30-35
44-57
58-81
Bed
Area
(ft2/cap)
1.40
1.66
1.98
2,32
2.90
3.32
No. of
Application
Per Year
26
14
9
6
4
3
Annual
Cost
•($/cap)(2)(3)
0.230
0.194
0.192*
0.198
0.224
0.242
(1) Type of Sludge: Digested Primary and Activated Sludge
(2) C] = $ 2672/AC = $ 0.061/ft2
C9 = $ 178/AC/Applic. = $ 0.004/ft2/Applic.
(3) PI = 95%
* Optimum Depth.
A method has been illustrated in the above example to determine the
optimum system design from the results of sj™1ajl VVfl'm^hiL? 2
to their associated variables, A and A. Appendix C of Lo (4) shows
the optimum depths of application^ for sfudges dried in various locations
under different cost ratios C2/C-| .
The way in which this information might be used is first to determine
the Jst terms C* and C2 following which the design engineer, using expected
157
-------
drying time and/or performance index as the design criterion, could select
the optimum depth in such a way that it best accounts for local weather and
sludge conditions. After the optimum applied depth and the expected perfor-
mance index have been determined, the required land area and its correspond-
ing number of applications per year can be found from the data presented in
Appendix B of Lo (4) in which ft2/cap was used as the unit for sizing waste-
water sludge dewatering beds and ft2/lb of dry solids was used as the unit
for sizing water treatment sludge dewatering beds.
MARGINAL ANALYSIS APPROACH
A simulation approach has been presented for the determination of opti-
mum dewatering bed system design. An example illustrating this simulation
methodology indicated that the 95 percent performance level could be attained
in Boise, Idaho by using either a bed area of .022 m2 (2.32 ft2) per capita
with 6 applications per year or 0.18 m2(1.98 ft2) per capita with 9 applica-
tions per year. Of course, the applied depth in the latter case was reduced
from 25 to 20 cm in order to shorten the necessary dewatering time and make
the additional 3 applications possible. This demonstrates that a tradeoff
exists between land and labor, since application may be accomplished manually
rather than by machine.
Both land and labor are economic resources which command a price at
a given time and condition. They have long been analyzed in production
theory in order to find an optimum combination that will produce the greatest
amount of product for a given cost outlay. In this section, a production
theory approach is taken to determine the optimum dewatering bed design, in
which the whole process of dewatering is treated from the viewpoint of a
firm that attempts to maximize the produce (dry solids) in relation to any
given cost outlay by way of securing and combining resource inputs (bed area
and applications).
The approach begins with the determination of a production function.
In this study, Equation 173 is used as the production function because it
expresses the physical relation between resource input and output, leaving
price aside. In Equation 173,
= [Wd -
H
(P
n=l
(173)
-A_ H S P ( z K P (K))} x 100]/W
r o k=1 n ts
where
PI = performance index, the percentage of the total dry solids
dewatered
A = applications per year
A = required bed area
H = the applied depth
158
-------
Wd, SQ, p, Wts are parameters
Marginal analysis for one injjut. In many cases, the engineer may face
a restriction on the use of land. For example, it is often desirable to
increase the dewatering capacity of an existing plant in which the bed
area is fixed, and auxiliary means of dewatering must be employed. Before
the results can be analyzed in a least cost fashion, the relationship between
the output and the input of sand bed dewatering must be examined in terms of
the law of diminishing returns.
The following example should illustrate the law of diminishing returns
numerically and graphically. Suppose that for a secondary sewage treatment
plant in the Boston area the dewatering bed was fixed as 0.14 m? (1.5 ft2)
per capita. If different quantites of input and bed applications per year
were applied to the bed, the performance index calculated from Equation 173
would be observed as shown in Table 31. It indicates that the performance
index would increase linearly with an increase in the number of applications
for the first four units. Then, beginning with 6 applications per year, the
law of diminishing returns comes into effect and the marginal physical
product of "application" decreases with an increase of the input resource.
This marginal physical product of a resource is defined by economists (6,7,8)
as the change in total product resulting from a one-unit change in the
quantity of the resource used per unit of time. Thus the law of diminishing
returns is also frequently called the law of diminishing marginal physical
product.
The total product curve of Figure 63 plotted from columns 3 and 4 of
Table 32 illustrates that the law of diminishing returns holds in this
example. Obviously, the reason is that the weather limits the number of
applications allowed each year. For later stages, an increase in number of
bed applications would not yield any significant increase of performance
index simply because there is only a very slight possibility that the "state
of nature" would allow such a high number of applications.
Up to this point, only the physical relation between output and input
has been considered. No mention was made of decision making since any recom-
mendation as to the bed's optimum rate of application would depend upon the
price of the output and the cost of each application. The dry sludge pro-
duced by dewatering beds has no significant cash value in the private market,
thus there is no market price for the output. However, the output can be
assigned a value represented by the cost of dewatering by an alternative
method, or the amount of charge (fine) imposed by a regulatory agency for
discharging untreated sludge. For example, assume that the value of the
output is $1.25/capita/year, and the cost of application is $0.093/capita/
m2/year ($0.026/capita/l.5 ft2/year). If the number of applications is in-
creased from 6 to 8 per year the input-output results in Table 31 would
yield an additional value of
(47.755 - 35.855) x 1.25 = $0.l49/capita/year
159
-------
O
38
X
i
LJ
CC
£
a:
UJ
a.
100 p
90 -
80
70 -
60
50
40
30
20
10
Type of sludge;
Mixed digested primary
activates sludge
Location-.
Boston
Applied depth
10 cm
Bed area=
i.$ft.2/cap
Marginal physical product curve
J L
5 10 15
NO. OF APPLICATIONS PER YEAR
20
(INPUT)
25
Figure 63: An input/output relation showing the
law of diminishing returns.
at an additional cost of
2 x 0.026 = $0.051/capita/yr
As the value per additional unit of input is greater than the additional
unit of input cost, it pays to increase the number of applications and the
output. However, in order to find the optimum output the value of the total
product and the marginal physical product have to be determined. For this
particular example, they were obtained by multiplying 1.25 by the total
product and the marginal physical product, and are shown in columns 5 and 6
of Table 32. Economists have proven that the optimum use of a variable input
is obtained when the value of marginal physical product is equal to the cost
of unit input. The marginal analysis implies (1) that if the last incre-
mental increase in the number of applications does not pay for itself, fewer
applications should be used, (2) that if the last increase of applications
more than pays for itself, additional applications should be considered, and
(3) the number of applications should be stopped at the point at which the
last application just pays for itself.
160
-------
TABLE 32. AN INPUT-OUTPUT* RELATION SHOWING THE
LAW OF DIMINISHING RETURNS
(1) (2)
No. of
Bed Applic.
Area per year
(ft2/Cap) (labor)
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
2
4
6
8
10
12
14
16
18
20
22
24
26
(3) (4)
Marginal
Total Product Physical
(performance) Product
index (labor)
11.954
23.908
35.855
47.755
59.438
70.481
80.211
87.954
93.395
96.729
98.502
99.321
99.651
5.977
5.977
5.972
5.938
5.795
5.404
4.654
3.592
2.433
1.433
0.731
0.324
0.125
(5) (6)
Marginal
Total Value Value
Product Product
($) ($)
0.149
0.299
0.448
0.597
0.743
0.881
1.003
1.099
1.167
1.209
1.231
1.242
1.246
0.075
0.075
0.075
0.074
0.072
0.068
0.058
0.045
0.030
0.018
0.009
0.004
0.002
*Type of Sludge: Mixed digested primary and activated sludge.
Location: Boston
Applied Depth: 10 cm
161
-------
1.3
1.2
I.I
Value of output - i.26/cap./yr.
Cost of input (An) = *o.026/applic.
Marginal value product curve
Cost of input=
marginal value
'product
Cost of input An
5 10 15 20
NUMBER OF APPLICATIONS PER YEAR
Figure 64: Determination of the optimum input and output.
Applying the above concept to an example produces the results shown in
Figure 64 indicating that the optimum number of applications per year is 19
at the applied depth of 10 cm. The results for other application depths are
shown in Table 33. Therefore the optimum operation of dewatering beds in
Boston with a fixed bed area of 0.139 m2(1.5 ft2) per capita is to apply 15
cm sludge on the bed with 13 applications per year at a cost of $0.026/
application. For this optimum condition, the dewatering bed would handle
about 82 percent of the sludge (since the performance index is 82 percent),
and the untreated sludge is more economically treated by other means at a
cost of $1.25/cap. Therefore, if mechanical methods are used as an auxiliary
means of dewatering, the capacity of the equipment should be designed to
handle 18 percent of the sludge. Of course, this optimum condition would
change when the value of the output and the cost of the input varied.
The fundamental difference between this approach and the simulation
approach discussed in the preceding section is that the output in this
approach was assigned a cash value, so that the logical optimum point in this
162
-------
TABLE 33. THE RESULTS OF OPTIMUM SAND BED DEWATERING IN BOSTON
WITH A FIXED BED AREA (0.14 m2/l.5 ft2) PER CAPITA
Applied
Depth
of Sludge
(cm)
5
10
15
20
Optimum Bed
Applications
per Year
34
19
13
9
Optimum
Sand Bed
Dewatering
(Performance
Index)
99%
95%
82%
71%
Cost of
Sand Bed
Dewatering
(at $0.026/
Application)
0.885
0.495
0.325
0.234
Cost of
Mechancial
Dewatering
(at $1.25/
Capita)
0.013
0.063
0.223
0.363
Total
Cost
per
Capita
0.898
0.558
0.548
0.597
(1) Mixed digested primary and activated sludge.
method is the cost of input just equal to the marginal value of output. In
the simulation approach the value of output was not considered. The purpose
was to find a combination of inputs that fulfilled the target (say 95 percent
performance index) at a minimum cost.
Marginal analysis for two inputs. In the previous section, marginal
analysis was introduced to increase the economic efficiency for an existing
plant which had limited land. This section takes up the more complicated
aspect of drying bed optimization including more than one variable.
In designing a new plant, the restriction on land area usually does not
exist, therefore the output (performance index) as shown in Equation 173 is
conceived of as depending upon two important inputs, the total application
per year (An), and the bed area (Ar). When two inputs are combined together
to produce a given output, two questions are likely to be raised concerning
the optimization: the first has to do with the proportion in which the two
inputs should be used, the second has to do with the amount of the two inputs
which would be produced. These two questions are answered by means of mar-
ginal analysis.
Under the concepts of marginal analysis for multi-variables, it is
usually considered that different resources can be technical substitutes.
Leftwich (6) pointed out that if labor and capital were used in digging a
ditch of a certain length, width and depth, they could be substituted for
each other within certain limits. But the more labor and the Jess capital
used to dig the ditch, the more difficult it becomes to substitute additional
labor for capital. Finally, additional units of labor just compensate for
S^st1^^
S3 s&idl.'fflffS:
i ^
the drying season and by the "state of nature". Due to the effects of
163
-------
weather, the allowable number of applications in this study is a random
variable, and the probability of an assumed number of applications will be
realized decreasing with the increase of its value. In addition, for a
given applied depth the calculated performance index will decrease as the
number of applications increases. Therefore, a "trade-off" between the
number of applications and land area at a given depth of sludge application
is not practical in this case because of the complications mentioned above.
Nevertheless, it has been shown that a perfect substitution of land and
applications was possible if the applied depth was reduced for the purpose
of shortening the necessary drying time. A possible increase in bed applica-
tions as a trade-off for a smaller bed area thus results, This substitution
has been demonstrated clearly in Table 30, in which six different combina-
tions of A and A were possible to obtain a constant output of 95 percent
performance1 indexT By drawing the above information as a smooth curve, an
isoquant curve shown in Figure 65 is obtained, with which one can produce
the same amount of output by using A in one direction and A in other
direction. By using information contained in Appendix B of Lo (4), a family
of isoquant lines may be drawn to indicate the different levels of output.
o:
o:
LU
a.
30
25
20
O 15
5
O
a.
Q.
10
5 -
Type of sludge=
Mixed digested primary
and activated sludge
Location:
Boise, Idaho
BED AREA (A,) ft
Figure 65: Iso-quant curve showing six different
combinations of An and Ar which yield a constant
output of 95% performance index.
164
-------
At this point, there is a question concerning how the economizing pro-
cedure can be applied to locate the optimum amount of output and the optimum
proportions in which two_inputs should be used to dry the sludge under given
economic conditions. This question is answered by determining the proportions
in which the two inputs should be combined and by determining the optimum
level of output.
1. Optimum proportion using bed application and bed area. It is obvi-
ous that the best way to spend a given amount of money on two inputs is such
that they will produce the highest output. In order to achieve this, the
cost of drying must first be decided upon before any optimization can be
undertaken. A cost function introduced earlier is:
Z = C]Ar + C2ApAr (174)
in which C, and C2 are costs associated with the inputs A and A , respec-
tively. Based on the above equation, an isocost curve can be determined
which shows the price per unit of each resource, and shows that different
combinations of resources A and Ar can be allocated to produce output at a
given,cost outlay. In Figure 66 each curve represents a given cost outlay.
70
BED AREA(Ar)ft
Figure 66: Curves of iso-cost lines.
165
-------
Up to this point, the problem of optimization was reduced to combining
the isoquant and isocost curves, and identifying the highest possible isoquant
that its isocost curve would allow, so that the concept of deriving the.
greatest amount of product from the given cost outlay on resources might be
realized.
The point at which the isoquant line is tangent to an isocost line
yields the highest value of output attainable for that input. Therefore, it
is the point of optimum combination. In Figure 67 it is easily seen that a
greater cost outlay would be necessary if some non-optimum resource combina-
tion were used to produce the same quantity of output. Since this particular
cost function gives a curved isocost line, it is difficult to determine the
points of tangency. The curves shown in Figure 67 were set by trial, the
isocost curves being drawn in the region of apparent tangency.
70
60
s
cr
UJ
CE
CL
CO
g
Si
o
Q.
CL
40
30
20
10
Performance
Index
AH=IOcm
O H=l5cm
o H=20cm
Iso-quant lines
Iso-cost lines
BED ARE A (Ar) ft2
Figure G7: Diagram illustrating procedure for
locating the points of optimum proportions.
Two important features should be noted in regard to Figure 67;
a. Change in the cost of resources will shift the isocost curve. For
example, an increase in the land cost would shift the curve to the
166
-------
left to favor more applications and less land. When the land cost
decreases, the curve shifts to the right favoring more land use and
fewer applications. However, at any resource cost level, the
tangent point would be the least possible cost of producing the
given output.
b. After locating the optimum point on the isoquant curve, the optimum
application depth is determined by interpolation because the iso^
quant curve is drawn from the points at different applied depths,
2. The optimum^output level. The line which connects the optimum com-
bination points in Figure 67 is called the expansion line by economists. It
indicates the amount of output which should be produced at various investment
levels. Since increased investment will result in a higher performance
index, the optimum level of sand bed dewatering would obviously depend on
the cost of treating the remaining sludge. This may be the cost of mechani-
cally .dewatering the excess sludge, or it may be the charge imposed by a
regulatory agency. However, the optimum performance index is the least-cost
combination of sand bed dewatering and dewatering by other means. The cost
of sand bed dewatering for various performance index levels using Boston as
an example is presented in Table 34. From this table it is readily apparent
that the optimum level for gravity dewatering is at a performance index of
90 percent with the sludge application depth between 15 to 20 cm. At this
level the required bed area is 0.19 m? (2.0 ft2) with 8 bed applications per
year.
TABLE 34- THE COST OF SLUDGE DEWATERING
Performance
Index
0%
60%
70%
80%
90%
95%
The Cost of
The Cost of
**
The Cost of
Cost of*
Sand Bed
Drying
0.546
0.623
0.649
0.728
0.879
Land = $ 0.
Application
Mechanical
Cost of
Mechanical
Dewatering**
1.250
0.500
0.375
0.250
0.125
0.063
Total Cost
per capita
1.250
1.046
1.008
0.899
0.853
0.942
Sludge
Application
depth (cm)
20
20
15-20
15-20
15-20
26/ftZ/yr.
= 0.026/Appli cation
Dewatering = $1 .25/Capita.
167
-------
REFERENCES
1. ASCE & WPCF, Sewage Treatment Plant Design. Manual of Engineering
Practice No. 36, 1959.
2. Meier, P. M. and Ray, D. L. "Optimum System Design," in Report No.
EVE 13-69-1, Source Control of Water Treatment Waste Solids,
Environmental Engineering, Department of Civil Engineering, University
of Massachusetts, Amherst, 1969.
3. Ehrenfeld, S. and Vittaner, S. B. Introduction to Statistical Methods,
McGraw-Hill, 1963.
4. Lo, K. Digital Computer Simulation of Water and Wastewater Sludge De-
watering on Sand Beds. Report No. EVE 26-71-1, Department of Civil
Engineering, University of Massachusetts, Amherst, 1971.
5. Kane, E. J. Economic Statistics and Econometrics, Harper and Row, 1968.
6. Leftwich, R. H. The Price System and Resource Allocation, Holt,
Rinehart and Winston, 1966.
7. Bradford, L. A. and Johnson, G. L. Farm Management Analysis, John Wiley
& Sons, Inc., 1953.
8. Mass, A., et al. Design of Water Resource Systems, Harvard University
Press, 1962.
168
-------
APPENDIX
EXPERIMENTAL DETERMINATION OF SPECIFIC
RESISTANCE AND COEFFICIENT OF COMPRESSIBILITY
Great care was taken to devise an accurate method to determine specific
resistance, the basic sludge characteristic used in formulation of the
mathematical model descriptive of gravity drainage properties. The lack
of standard equipment and a standard procedure for the determination of
specific resistance required development of special equipment, description
of which follows
EQUIPMENT
j|- OD GLASS
TUBING
f|ee5
RING SEAL
Figure A-l: Vacuum adaptor
169
-------
5.'"
6
„-•
v
29 r*r 5
. -^ _- (3(3 5
26
Figure A-2a: Funnel adaptor. Figure A-2b: Adaptor in place on Buchner
funnel (with epoxy cement seal).
Figure A-3: Vacuum plug (optional).
170
-------
a. The following custom glass equipment is fabricated:
(1) Join the female portion of a 24/40 I ground glass joint to the
open end of a 250 ml buret (1.0 ml subdivisions)
(2) Construct a vacuum adaptor as shown in Figure A-l taking
care that the glass in the narrow neck above the ringseal is
not weakened. Anneal the fixture. A small drip extension
(not shown) on the effluent end will be helpful.
(3) Use a short male section of a 29/26 f joint, flair the funnel
adaptor as shown in Figure A-2a. Anneal the fixture. Join
the adaptor to the Buchner funnel with epoxy cement as shown
in Figure A-2b.
b. Assembly of equipment
The components are assembled according to the schematic diagram of
Figure A-4- Two screw clamps (not shown) may be substituted in
series for the pressure control valve. The clamp nearest the mano-
meter may be used to bring the manometer slightly below the desired
pressure setting while the second clamp is used to fine-adjust the
level.
TRAP FLASK
MERCURY
MANOMETER
/
BUCHNER FUNNEL
VACUUM ADAPTOR
BURET
EXTERNAL TIMER
VACUUM CONTROL VALVE
VACUUM PUMP
Figure A-4: Schematic flow diagram for specific resistance
testing.
RUBBER
\TU8ING
171
-------
LABORATORY PROCEDURES
a. Storage of sludge sample.
The bulk samples are stored in a 20°C constant temperature
room in closed containers.
b. Preparation of the test samples.
(1) Bulk samples are thoroughly mixed by gentle stirring to pro-
vide homogeneity.
(2) A smaller 32-ounce (95 ml) polyethylene bottle is filled and
its contents used throughout the testing. This aliquot is
sufficient to perform triplicate solids analysis as well as
three specific resistance tests.
c. Laboratory analysis
(1) Solids Determinations.
Solids determinations are run in triplicate 50 ml samples
according to Standard Methods (12th Edition) part III,
Residue on Evaporation.
(2) Remove the Buchner funnel from the vacuum adaptor and insert
the vacuum plug. By means of the pressure control selected,
adjust the manometer to a constant pressure level. Since
three separate tests will be run in the range from 10 cm Hg to
50 cm Hg, it is suggested that a low pressure test be run first
to become familiar with the equipment.
(3) Wet the porous surface of the Buchner funnel and cover with
Whatman No. 5 filter paper. Smooth out wrinkles and air
bubbles, replace the funnel in the vacuum adaptor, and apply a
vacuum to void the paper of excess water.
(4) Measure 100 ml of wet sludge into a graduated cylinder and
apply to the filter surface of the Buchner funnel.
(5) Apply a vacuum to the system. Since there will be a time lag
between the inception of the vacuum and the actual present
value, the timer is not actuated until the present pressure
value is reached. Record the initial volume on the data sheet
shown in Figure A-5 when the timer is started. Record the
pressure and room temperature at this time.
(6) Remove the Buchner funnel at the end of each test, record the
depth of sludge cake, and perform triplicate residue (total)
tests on the cake as outlined.
172
-------
Do(e
^Specific Resision
Sludge .
Volume
-(ml)
Left
Prpssure
Time
(Sec)
0
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
510
540
570
600
630
660
Volume
Buret Read.
250.0
2«5
Z-f-0
237
111
•Z3/
ZW
227
22$
223
22/
Z/9
Z/6
-2./&.S
2/5
•2/3.5-
2/Z
Z//
2 0*3
2oe
'Zo T- -S
2o&
Zas
(ml)
Cum. R|t. Vol
a
5
SO
/3
/£
/9
2/
23
25
27
23
3/
3Z
33.5
35
3&.S
£8
33
4/
4/
42. S
44-
45
Time s
Volume
Q
6,
6>
<*.
7.5
7.3
&.(,
3./
9. d
/£> ,O
SO. 3
/o.t.
//. 2
//.£
,Z.O
/2.3
/Z.b
/?./
/3.Z
/3.9
//./
Jl-3
/4-.7
Remarks
2# ,.«>»,<, Z^^/^3
^-^3. s/o&/,*3
£^e. Jecowf "or* /«~yy
£>fe:i tfo/^j
(2-e* k £• t? & *" £ /*jf*f/~»y
£u±&/ei 6»->»">f -* Sof
£*^ te^
CsJ^e. c/CjD/Si = o. •{-£•"'
4.65% Cake Solids
\
;
wet pan & sludge p£8.3/£>
dry pan (-) /.4--f627
wet sludge ^ 23683
„ . , /• <3/53/
dry pan 8 sludge *
rtrv nnn M /. 4U27
solids *• **9o#
I
<*/ =
/<=
752
1
/?.^£
2. /i BM
J.4-S/M>
O.CMZ4-
*
3
0
7
%~
«£*)/,,
c
N
0'
^
V
-^
\>X
s
Figure A-5: Sample data and data format for specific resistance test.
173
-------
DATA ANALYSIS
(1) Subtract the succeeding buret readings from the reading at t = 0
and record in the cumulative volume column (see Figure A-5).
(2) At each reading time, divide the time in seconds by the cumulative
volume in ml.
(3) On Cartesian paper plot t/V as the ordinate versus V as the
abcissa. The slope "b" may be directly determined from the line
of best fit. Figure A-6 shows the plot for the sample specific
resistance data provided.
V (sec/ml)
itto
16.0
14.0
12.0
10.0
8.0
6.0
4.0
i 1 i i i i * i i
t/V-vs-V
Billerica Sludge Test ^3
Pressure =48.9 cm Hg
Temperature = 23 C o°
100 ml sludge sample 9^
test run 2/1/68 /y0
^x" «
°X 173 1
/°X
J3 4.2 3
-X^ 173
o cr
i i i i i i i i i
0.0
10 15 20 25 30 35 40 45 50
V (ml)
Figure A-6: Plot of sample specific resistance data.
CALCULATION OF SPECIFIC RESISTANCE
(1) Specific resistance may be calculated according to the following
equation
D - 2 b A2 Ap
R = yc
174
-------
where: R = specific resistance (sec /gm)
b = slope of t/V vs. V (sec/ml2)
A = area of filter paper (cm2)
p
Ap = test pressure (dynes/cm ); p is taken as the average test
pressure in cm Hg X 13333.22 to convert to dynes/cm2.
r\
y = dynamic viscosity (poise) or dyne sec/cm may be found in
various handbooks or calculated by the formula:
2.1482[(t-8.435) + {8078.4 + (t-8.435)2}0'5 -120
where t = test temperature (°C)
ght of solids per i
given by the formula:
C =
c = weight of solids per unit volume of filtrate (gm/cm2-sec2),
100 100
where: p = density of filtrate (assumed water) at the test
temperature (gm/cm3)
2
g = gravitational constant (980.0 cm/sec )
S = initial sludge solids content
Sf = sludge solids content after testing
(2) Sample Calculation
b = 0.243 (see Figure A-6)
diameter of filter paper = 11.1 cm
pressure = 48.9 cm Hg
temperature = 23°C
S = 4.65%
o
Sf = 8.25%
175
-------
12
4x10
3x
o>
9x
8x
7x
6x
5x
3x10
R - vs - Ap
Billerico Sludge
2/1/68
3 4 5 6 7 8 9 10 20 30 40 50 60 70 80
Ap (cmHg)
Figure A-7: Graph for calculating coefficient of
compressibility.
R =
R =
- 2(0.243) (9.364 x 1Q3) (48.9 x 1.33 x 1Q4)
(9.358 x 10J) (0.997538)-(980)
100 } , 100 i
0.0465 '~^0.0825;
3.05 x 109 sec2/gm
CALCULATION OF COEFFICIENT OF COMPRESSIBILITY
It has been experimentally determined that specific resistance is re-
lated to pressure by the following
where R = specific resistance (sec /gm)
specific resistance at a head h
C
test head
coefficient of compressibility (dimensionless)
R =
\f
h
a =
176
-------
(1) Before determining the coefficient of compressibility,
three or more specific resistance tests must be run,
as previously outlined, at pressures of about 10, 20, and
50 cm Hg.
(2) Plot on bi-logarithmic paper each resistance ordinate versus
the pressure at which the resistance was run. Determine the
slope a which is the coefficient of compressibility, as
shown in Figure A-7.
177
-------
TECHNICAL REPORT DATA
(Please read hiuructions on the reverse before completing)
1 RfcPORT\O
EPA-600/2-78-141
: ;TLE AND SUBTITLE
Sludge Dewatering and Drying on Sand Beds
3. RECIPIENT'S ACCESSIO(*NO.
5. REPORT DATE
August 1978 (Issuing
6. PERFORMING ORGANIZATION CODE
7. AUTHORISI
Donald Dean Adrian
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Engineering Program
Department of Civil Engineering
University of Massachusetts
Amherst, Massachusetts 01003
10. PROGRAM ELEMENT NO.
1BC611
11. CONTRACT/GRANT NO.
WP-01239/17070-DZS
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory--Cin.
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
OH
13. TYPE OF REPORT AND PERIOD COVERED
Final 6/1/67 - 6/30/74
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer: Roland
V. Villiers (513) 684-7664
16. ABSTRACT
Dewatering of water and wastewater treatment sludges was examined through mathe-
matical modeling and experimental work. The various components of the research include
(1) chemical analyses of water treatment sludges, (2) drainage and drying studies of
sludges, (3) a mathematical model to describe sludge drainage and drying on sand beds,
and (4) a procedure to optimize the size of sand beds.
Computer simulation studies were conducted of wastewater and water treatment sludge
The output of this 20-year simulation under six weather conditions was a random vari-
able, the required dewatering time, and its associated frequency distribution. Of the
parameters describing sludge characteristics, solids content had the most important
effect on dewatering time, and in most cases dominated the effects of specific
resistance.
Economic analyses were applied to the outputs of simulation for finding an optimum
system design. Two different approaches were used: the first finds an optimum design
that fulfills the target output at a minimum cost among the known alternatives; the
second uses the concept of marginal analysis to assign a cash value to the end product
(dry solids) of the dewatering process, so that the optimum design is obtained at the
point where the cost of inputs (land and operation) is just equal to the marginal
value of output.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Cost analysis
Dewatering
Optimum design
Sludge drying
Waste treatment
Water quality
Water treatment
Drying rates
Sand drying beds
Ultimate disposal
Wastewater treatment
13B
3. DISTRIBUTION STATEMENT
Release to public
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
196
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
178
4 U.S. ISO*EBI(WIITntl«™« OfF1CE 1976—7 57 -140 /1396
------- |