i P A U-S- Environmental Protection Agency Industrial Environmental Research EPA-600/7"78~072
"* Office of Research and Development Laboratory . .. ^ Q-TQ
Research Triangle Park, North Carolina 27711 Apfll tyfO
DEVELOPMENT
OF A MATHEMATICAL BASIS
FOR RELATING SLUDGE
PROPERTIES TO FGD-SCRUBBER
OPERATING VARIABLES
Interagency
Energy-Environment
Research and Development
Program Report
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EPA-600/7-78-072
April 1978
DEVELOPMENT OF A MATHEMATICAL
BASIS FOR RELATING SLUDGE
PROPERTIES TO FGD-SCRUBBER
OPERATING VARIABLES
by
J.L. Phillips, J.C. Terry, K.C. Wilde,
G.P. Behrens, P.S. Lowell, J.L. Skloss, and K.W. Luke
Radian Corporation
8500 Shoal Creek Boulevard
Austin, Texas 78766
Contract No. 68-02-2608
Task 11
Program Element No. EHE624
EPA Project Officer: Robert H. Borgwardt
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, N.C. 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D.C. 20460
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CONTENTS
Section Page
1 Introduction and Summary 1
2 Conclusions 3
3 Recommendations 4
4 Continuous Crystallization Theory 6
Mathematical Basis 6
Nucleation Rate 7
Growth Rate 9
Material Balances 9
5 Modeling the Calcium Sulfite Crystal Size Distribution (CSD)... 11
The "Typical" Process Arrangement 11
The Scrubber/Hold Tank Equations 11
The Hold Tank/Clarifier Model 14
Parameter Sensitivity Study 16
6 Analytical Methods for Sludge Quality 22
Settling Rate and Settled Density 22
Crystal Size Distribution 26
7 Test Plan 30
Objectives 30
Test Sequence and Operating Conditions 31
Analytical Requirements 34
NOMENCLATURE 37
REFERENCES 39
APPENDIX A - AN APPROACH TO PREDICTING CALCIUM SULFITE
CRYSTAL SIZE DISTRIBUTION IN LIME/LIMESTONE WET SCRUBBING
SYSTEMS (Technical Note #200-187-11-1) A-i
APPENDIX B - AN ANALYSIS OF CRYSTALLIZATION DYNAMICS
AND PARAMETER SENSITIVITY IN LIME/LIMESTONE WET SCRUBBING
SYSTEMS (Technical Note #200-187-11-3) B-i
APPENDIX C - STANDARD METHODS DEVELOPMENT FOR THE DETER-
MINATION OF SLUDGE QUALITY (Technical Note #200-187-11-2) C-i
iii
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CONTENTS (continued)
Section ?*£*
APPENDIX D - COMPARISON OF METHODS FOR MEASURING THE
PARTICLE SIZE DISTRIBUTION OF SMALL PARTICLES
(Technical Note #200-187-11-5) D~1
APPENDIX E - TEST PLAN DOCUMENT (Technical Note
#200-187-11-4) E~i
IV
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FIGURES
Figure Page
5-1 Process Flow Sheet for a Lime or Limestone Scrubbing
System 12
5-2 Simplified Crystallization Model 15
5-3 Mass Average Crystal Size and Relative Saturation Versus
Solids Residence Time (Hold Tank Volume) at Constant SOa
Removal, 10 Weight Percent Solids 19
5-4 Mass Average Crystal Size and Calcium Sulfite Relative
Saturation Weight Percent Versus Solids in Clarifier
Feed Wn_ at Constant SOa Removal and Hold Tank Volume 20
Lr
6-1 Photomicrograph of Sludge Platelets Taken from Limestone
Scrubber, 200X 23
6-2 Photomicrograph of Sludge Granules Taken from Lime
Scrubber, 200X 24
6-3 Settling Rates of Sludges Versus Weight % Solids at
25°C and 50°C 25
6-4 Sludge Granules from Lime Scrubber: Cumulative Percent
of Particles Versus Diameter 27
6-5 Sludge Platelets from Limestone Scrubber: Cumulative
Percent of Particles Versus Width 28
7-1 Size Distribution Data for Limestone Scrubber Slurry.
(Coulter Counter) n(L) versus L 35
TABLES
Table Page
5-1 Sample Print Out for Simplified Hold Tank/Clarifier
Model -^g
7-1 Phase I - Test Schedule 32
7-2 Phase II - Test Schedule 33
v
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SECTION 1
INTRODUCTION AND SUMMARY
Sludge disposal represents a significant operating cost in most
applications of lime/limestone or dual alkali scrubbing processes. In
systems where calcium sulfite is the major product, the waste sludge
generally settles slowly and has a low settled density. The objectives
of this work are to examine prospects for increasing the average particle
size of calcium sulfite produced in these SOz removal systems in order to
improve settling rate and settled density and ultimately to be able to
correlate sludge quality with design and operating conditions.
The approach taken to meet this objective includes four work packages:
literature survey and development of a mathematical
basis for predicting the sulfite size distribution,
computer solution of the size distribution model to
determine parameter sensitivity,
literature survey and screening of analytical methods
for measuring settling rate, settled density, and particle
size distribution, and
planning a test program to investigate parameters expected
to improve settling rate and settled density by in-
creasing the average particle size.
Section 3 of this report describes a mathematical basis for predicting
the size distribution of calcium sulfite crystals produced in lime/limestone
scrubbing systems. The crystal population balance concept is introduced
and size distribution relationships are derived. This approach requires
nucleation and crystal growth rate expressions. These must be obtained from
experimental data. Expected forms for these rate expressions were selected
from the literature. Experimental data from pilot and full-scale scrubbers
were used where applicable to increase the usefulness of the theoretical
development.
The relationships derived in Section 3 are solved for a specific
process configuration in Section 4. An approximate solution to the
problem was obtained by assuming that the crystal size distribution does
not change in the scrubber. This assumption is expected to be realistic
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for supersaturated scrubber operation. It may not apply to operations
where scrubber alkalinity is buffered by dissolution of calcium sulfite.
A computer routine was written to permit convenient parameter sensitivity
studies using the size distribution model. Size distributions were pre-
dicted that were in order of magnitude agreement with experimental measurements.
Verification of the crystal size distribution model requires further
experimental data. Analytical methods are discussed in Section 5. Potential
methods for measuring calcium sulfite size distribution, settling rate, and
settled density were selected based on a literature survey. Reproducible
settling rate and settling density methods are described. Four size distri-
bution techniques were compared. Manual counting by optical microscope
was in good agreement with micromesh sieve data. Two instrumental techniques,
the Coulter Counter and Micromeritics Sedigraph, showed much smaller size
distributions than the microscope or sieves. Further work will be necessary
to select the best method.
A pilot-scale test program is described in Section 6 of this report.
The approach and objectives are based on the literature survey and size
distribution model. Major emphasis is placed on identifying calcium sulfite
nucleation sources in an operating pilot unit. Tests are described which
will aid in quantifying rate parameters used in the crystal size distri-
bution model.
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SECTION 2
CONCLUSIONS
A model has been developed to predict the crystal size distribution of
calcium sulfite produced in limestone wet scrubbing systems. The model
computes size distributions comparable to those observed in operating scrub-
ber systems. The present model may not apply as well to lime systems,
but the approach used here can be adapted as necessary data are obtained.
The model has been used to examine the sensitivity of the product
crystal size distribution to changes in process variables. Prospects for
improving the size distribution depend on further investigation of nucleation
kinetics in the system. Changes in hold tank size or slurry solids content
may lead to an increase or decrease in crystal size, depending on the specific
form of the nucleation and growth rate expressions. The present growth rate
expression is based on a fair amount of experimental data for limestone sys-
tems. No definite correlations relating nucleation phenomena to design and
operating conditions were found in the present data, however.
Several methods for measuring the size distribution of scrubber sludge
were compared. Two instrumental methods indicated much finer size distri-
butions than the optical microscope or micromesh sieves. Additional work
needs to be done to resolve observed differences in results for the crystal
size distribution measurement.
Since the behavior of the crystal size distribution depends on the
nucleation rate expressions, the test program developed in this work needs
to be pursued at the RTF laboratory pilot unit. The proposed tests are
intended to provide more information about sources and rates of nucleation
in the system. The model developed here can be used both to interpret
experimental results and to predict favorable operating conditions for other
process configurations.
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SECTION 3
RECOMMENDATIONS
The CSD data suggests two mechanisms for particle generation in FGD
scrubber systems. The optical microscope and micromesh sieve CSD curves
on a number basis suggest that particle breakage or attrition is the major
or at least a significant mechanism for new particle generation. The Coul-
ter Counter and Micromeritics Sedigraph CSD curves are consistent with
particle generation by nucleation. The Coulter Counter and Micromeritics
Sedigraph methods also indicate much finer crystal size distributions than
the optical microscope and micromesh sieves. Additional work is recom-
mended to resolve these observed differences. Areas which should be in-
vestigated are effects of sample preparation, background noise in the
instrumental methods, use of scanning electron micrographs, and multiple
magnification overlap techniques with the optical microscope.
More bench and pilot scale work is needed to define both nucleation
and growth rate parameters. We recommend that the test plan document pro-
duced during this program be pursued at the RTF laboratory pilot unit.
Crystal size distributions must be measured to have useful data. The
bench and pilot unit data should be correlated with the model. The
computer program should be used as a subroutine of widely available non-
linear curve-fitting programs. Then rate parameters can be deduced from
crystal size distributions and total solids concentration.
The model should be extended to include growth rate-size relations
intermediate between constant and linear in particle size. Incorporation
of the model into complete SOa scrubbing system simulations should be ex-
plored .
Scrubber dissolution of fines could be examined as a possibility of
increased sludge particle size. Further definition of this aspect will
require considerably more work, both experimental and modeling. Since
dissolution is much faster than precipitation, its study on a pilot scale
may not be feasible. The best approach may be bench scale dissolution
rate studies to provide data for resolution of the present model's pro-
blems with the dissolution case.
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The basis of hold tank sizing should be reexamined. The present model
provides a better basis for system design than conventional methods. Al-
though rate parameters in the model are not yet known, a better use of
available information should be possible.
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SECTION 4
CONTINUOUS CRYSTALLIZATION THEORY
The objective of this program is ultimately to be able to correlate
waste sludge quality of lime/limestone scrubbing processes with design
and operating conditions. It is assumed that the size distribution of
calcium sulfite crystals can be adequately used to predict sludge quality
for most systems. While settling rates and settled density are also of
interest in equipment design, the crystal size distribution is more easily
related to process conditions. In this discussion, the term "calcium
sulfite" also includes any coprecipitated sulfate.
MATHEMATICAL BASIS
The size distribution of crystals leaving a scrubbing system is
determined by the relative rates of nucleation and growth sustained in the
process vessels and by the residence time characteristics of these vessels.
Prediction of the crystal size distribution requires:
a nucleation (crystal birth-death) rate expression,
a growth rate expression,
a description of the environment in the process vessels,
and
a description of the process streams.
A simultaneous solution of the crystal population balance and process
material balances is required for a complete description of the process.
The mathematical approach used in this work to describe calcium sulfite
crystallization is based primarily on the particle balance concepts of
Randolph and Larson (1). The first step is to define a crystal size
distribution function, n(L) (meter "*), such that n(L)AL is equal to the
number of crystals in the size range L to L + AL per unit volume of slurry
It is assumed that a single characteristic dimension, L, can be used to
describe a crystal. The crystal population balance states that-
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Rate of accumulation of crystals of size L per
unit volume of slurry is equal to the net input
of crystals of size L via convection plus the
net input via growth plus the net generation of
crystals of size L via other mechanism (e.g.,
breakage) .
Application of this principle to a well-mixed process vessel leads to a
mathematical statement of the problem:
D(L) =i + B(L) (4-1)
_
where the T's are time constants equal to the vessel volume divided by inlet
(i's) and outlet (j's) stream flow rates, R(L) is the crystal growth rate,
D(L) and B(L) are crystal death and birth functions other than nucleation
and n(L) is the size distribution defined above. The nucleation rate, B
o i O
(meter sec ) is equal to the limit of the product nR as L approaches zero,
B = lim n(L)R(L) (4-2)
L -> 0
Tne nucleation rate, B , enters the solution of Equation (4-1) as a boundary
condition. The terms §(L) an D(L) will be assumed to be negligible for the
time being. Details of the derivation of Equation (4-1) are given in
Appendix A.
Solution of Equation (4-1) requires a description of B and R(L) for
all conditions in the process volume V. This information is normally
contained in nucleation and growth rate correlations based on experimental
data. A detailed literature survey was conducted to determine the most
appropriate form for these correlations.
NUCLEATION RATE
Recent literature pertaining to nucleation in continuous crystalliza-
tion processes has focused on the mechanism and kinetics of "secondary"
nucleation. This is defined as the formation of new crystals of negligible
size in the presence of a suspension of existing seed crystals of the same
solute. Secondary nucleation is generally thought to be the most important
source of new crystals in processes where a substantial slurry density is
maintained. Secondary nucleation is also known to occur at much lower
supersaturations than those necessary to produce new crystals from a clear
solution.
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There is some disagreement among investigators as to the exact
mechanisms of secondary nucleation. Some feel that "micro-attrition" or
physical removal of microscopic particles occurs while others hypothesize
that nuclei merely form from the solution near or at the surface of seed
crystals. Judging from reported experimental results, the following
variables are most important in fixing the secondary nucleation rate for a
given crystallizer situation:
temperature,
supersaturation,
slurry solids content, and
factors affecting the energy of collisions or liquid shear
at the crystal surface in the system (e.g., impeller speed
and material, crystal size).
More detailed discussion of variable effects on secondary nucleation is
presented in Appendix A.
Based on this literature survey, the following is proposed as a
nucleation rate expression for use in the mathematical model:
BQ (meter~3 sec'1) = (nR)^ Q = ^(r-1) SNMT SN (4-3)
Here, M (moles/liter) is the slurry solids content and r is the relative
saturation. In this simplified expression, the temperature and collision
energy and crystal size effects are implicit in the rate constant k
oN
Use of Equation (4-3) to describe calcium sulfite nucleation in lime/
limestone scrubbing systems requires values for the exponents i and j
and the nucleation rate constant k . The nucleation rate may be estimated
from the crystal size distribution in an operating system, but no consis-
tent complete data relating product size distribution to process operating
conditions were available in the literature. This is primarily due to the
difficulty of the size distribution measurements (see Section 5 of this
report). Crystal size distribution measurements performed during the present
contract show that "typical" scrubber sludge contains on the order of 1010
crystals per gram of calcium sulfite. This information can be used to fix
an "average" nucleation rate for purposes of modeling, but examination of'
the individual rate parameters used in Equation (4-3) must await furth
experimental data.
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GROWTH RATE
Several crystal growth rate correlations have been described in the
literature. Furthermore, some data correlating calcium sulfite growth rates
with process conditions in actual lime and limestone scrubbing systems are
available. The literature referred to in Appendix A was reviewed to select
the most useful correlation form for the calcium sulfite growth rate.
The growth rate R (meter/sec) appearing in the crystal population
balance (Equation 4-1) is the rate of change of the characteristic dimension
L. It may also be a function of crystal size. Crystals are assumed to
maintain the same shape as they grow. Some data were obtained in this
study and in previous related work that suggest an increasing linear growth
rate with crystal size for calcium sulfite. Most available experimental
data, however, are in the form of an average molar growth rate for crystals
of all sizes. An "average" linear growth rate can be calculated from
existing experimental data by assuming all of the crystals ultimately have
the same size and shape.
For limestone systems calcium sulfite growth rate data from three
widely different pilot units (TCA, marble bed, and spray tower) were in close
agreement considering that no direct comparison of the size distributions
in these studies was available. The data are represented by a linear growth
rate expression that is a function of crystal size and relative saturation:
VR
R = 3x10 12(1 + 5xl05L) (r-D meter/sec (4-4)
The exponent ipR is expected to be one for normal operating levels of rela-
tive saturation.
For lime systems, no definite relationship between calcium sulfite
growth rate and process conditions was obtained. Pilot plant and full
scale data showed growth rates varying by a factor of ten at similar levels
of relative saturation. This behavior may be a result of locally high
supersaturations existing near dissolving lime particles.
MATERIAL BALANCES
The nucleation and growth rate expressions discussed above both include
calcium sulfite relative saturation as a variable. Relative saturation
is in turn a function of the liquid phase concentrations of the precipi-
tating calcium and sulfite. As a result, the crystal population balance
and the solid-liquid mass balances for a crystallizer must be solved simul-
taneously.
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An equation relating the molar crystallization rate per volume of
slurry to the linear growth rate and crystal size distribution may be
written:
CO
Crystallization Rate (mole/meter sec) = k' I nL2RdL (4-5)
Here, k' (mole/meter3) is a shape factor relating the number of moles
v
in a crystal to its characteristic length L. This relationship can be
used in material balance calculations for a given process volume:
T.Q. C. - 10 C = Crystallization Rate (4-6)
in in out out
where C. and C are the liquid phase concentrations of calcium or sulfite
entering and leaving the volume of interest and Q. and.Q are the volu-
metric flow rates (£/sec). in out
Equations (4-1) through (4-6) are the basis for calculating a calcium
sulfite size distribution for a given set of conditions. Solution of the
equations for a particular equipment configuration and various process
operating conditions is addressed in Section 5 of this report.
A better physical understanding of the crystal population balance may
be gained by looking at the overall steady-state balances for a system.
The mass balance recjuijres that the system S02 removal rate be proportional
to the product of N(& 1sec 1), the rate at which crystals leave the system,
and (L ) , the mass mean crystal size to the third power:
m
AS02 = k-N(L )3 (4-7)
sec v m v ''
The population balance requires that the rate of removal of crystals from
the process be equal to the rate of generation (the nucleation rate) of
crystals within the process:
N = BQ (4-8)
Thus, the mass mean size of crystals leaving the system is completely
dependent on the nucleation rate. Correlation of nucleation rates with
process conditions will be an important aspect of the proposed test program
(see Section 7).
10
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SECTION 5
MODELING THE CALCIUM SULFITE CRYSTAL SIZE DISTRIBUTION
In the previous section, the theoretical approach and existing experi-
mental basis for predicting calcium sulfite crystal size distribution (CSD)
were examined. The particle balance Equation (3-1) and nucleation and growth
rate correlations (3-2, 3-4) are the core of the resulting model. The
nucleation and growth rates are coupled to the process liquor composition
through their dependence on the relative saturation r. Application of
these equations to lime/limestone scrubbing systems is described below.
Quantitative solutions to the size distribution problem are discussed for
a simplified process scheme.
THE "TYPICAL" PROCESS ARRANGEMENT
Figure 5-1 represents a typical process flowsheet for a lime or lime-
stone scrubbing system. Flue gas (FG) enters the scrubber and is contacted
with liquor (SF) recirculated from the hold tank. Spent scrubbing liquor
(SB) enters the hold tank and is combined with the lime or limestone addi-
tive (LA) . A slurry stream (CF) is fed from the hold tank to the clari-
fier. Some or all of the solids are removed from this stream and discarded
with the clarifier underflow (CU) stream. The remaining liquor and some
solids are returned to the hold tank with the clarifier overflow (CO)
stream. Four different size distributions may be present in the system.
These are indicated as n , n , n , and n on the flowsheet. Nucleation
may occur in both scrubber and hold tank. Sulfite must precipitate in
the hold tank but may dissolve in the scrubber.
For modeling purposes, all calcium sulfite crystals are assumed to
originate through nucleation at zero size. This is equivalent to letting
B(L) and D(L) be zero in the particle balance Equation (4-1). The clarifier
is modeled as a solids separation unit with no significant chemical reaction.
THE SCRUBBER/HOLD TANK EQUATIONS
The essential behavior of the scrubber/hold tank loop may be examined
most easily by assuming for the time being that n = 0. That is, there are
11
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FG
LA
\
1 SG
A A
Scrubber
PSB
[ SB
Hold
Tank
r
SF
*
^^^M^MMH
nCF
CO
-V
k
CF
nc
0
Clarif ier
CU
"Cu
overall
X system
boundary
.
Figure 5-1. Process Flow Sheet for a Lime or Limestone Scrubbing
System.
12
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no solids in the clarifier overflow. This is a good approximation in
many operating units.
A set of simultaneous particle balance equations may be written for
the scrubber and hold tank:
d(R n )
V
S d
d(R n
Vt "I- + Vt - ^SBnS 5-2
The boundary conditions for the size distribution equations are obtained
from the nucleation rate and growth rate expressions:
n (o) = (B /R ) uu (5-3)
s o o scrubber
n (o) = (B /R ), . . ^ . (5-4)
t o o hold tank
B and R are evaluated at conditions in the scrubber or hold tank as
indicated.
Equations (5-1) through (5-4) represent the crystal population balance
for the scrubber/hold tank loop. The process material balances and chemical
equilibria in the system also enter into the solution through their effects
on the relative saturation, r. This quantity appears in both the nucleation
and growth rate correlations (Equations 4-3 and 4-4).
An unsuccessful attempt was made to solve the entire set of population
balance, material balance, and chemical equilibrium equations with a standard
numerical technique. Because of the apparent complexity of the overall
simulation, it was decided to solve the crystal population balance in terms
of the relative saturation, r. The usefulness of the model is not seriously
jeopardized since relative saturation may be measured or calculated inde-
pendently for a system using an available chemical equilibrium computer
routine (2).
An analytical solution to the scrubber/hold tank population balance
is discussed in Appendix B. Examination of the roots of the characteristic
equations shows that for the case of precipitation in both the scrubber and
hold tank, the scrubber contribution is negligible. This appears to be the
source of problems encountered in the numerical solution of the complete
equation set. For the case of constant dissolution rate (R < o) in the
13
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scrubber, the integral of the resulting crystal size distribution does not
converge for large values of crystal size L. More information about the
dissolution rate as a function of size would be required to solve this case.
THE HOLD TANK/CLARIFIER MODEL
For cases where significant sulfite dissolution does not occur in
the scrubber, the effect of the scrubber on the sulfite size distribution
was found to be small. Thus, the size distribution in the system may be
estimated using a simplified hold tank/clarifier model. This is shown in
Figure 5-2.
Crystallization of calcium sulfite occurs in the hold tank when
SOa from the scrubber and calcium from the additive are combined. The
slurry stream leaving the hold tank has a size distribution n and a
flow rate QrF- The clarifier splits the Q stream into a nearly clear
overflow stream, Qrn, and a thickened underflow stream, Qru- The overflow
has a size distribution n and the underflow n . Since we have assumed
that the scrubber does not change the size distribution, the scrubber loop
does not appear in the model.
The clarifier size distributions may be expressed in terms of the
hold tank size distribution by defining a cutoff size, L . Crystals
larger than L all report to the underflow. Crystals smaller than L
are divided between the two streams according to their relative clear liquor
flow rates. The resulting size distributions are:
nCO = (1-fCL) Q^ V L< Lc (5-5)
nCO = ° > L> Lc
nCU = ^LQ^nt ' L Lc
The quantity f is a function which depends on the crystal density and
the stream flofr-'rates (see Appendix B for derivation) .
14
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S02
CaO
Hold
Tank
n (L)
n
CO
' L>L
Clarifier
L(
Figure 5-2. Simplified Crystallization Model.
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The population balance for the model shown in Figure 5-2 is:
n.
TT(n R)
CF
^-c
CO
0 , L>L
(5-7)
Equation.(5-7) may be integrated using the growth rate expression, R =
k (r-l)lGR (1+ YL). The solution is:
n = n
t o
Lc)
, L> L
(5-8)
n
nt = nQ(l
n , the zero size population density, is calculated using the nucleation and
growth rate expressions:
Bo kSN , T^SN ~ ^R M ^SN ,c _,
no = R- - k~
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Tcu - VQcu' minutes
L = clarifier cut-off size, microns
c
The program calculates the following:
OUTPUT
n = population density, particles/£/micron
N ,N (AL) = number and volume of particles in a size range
G-^ = net precipitation rate, moles/Ji/min
Cr
W , WrT = weight % solids, clarifier feed and underflow
d-t L»U
W = ppm solids in the clarifier overflow
\s\J
L , L Lpr)=: mass average particle sizes
B = nucleation rate, particles/£/min
The program may be used without process material balances since the relative
saturation is contained explicitly in the model. Iterative calculation may
also be done to calculate the inputs for specified values of outputs.
A sample print out for the model is shown in Table 5-1. The inputs
are listed first, then the various calculated quantities are printed along
with the crystal size distribution. The case shown here is for operation at
ten weight percent solids in the clarifier feed. The relative saturation
was set at 4.0 and the solids residence time (V , /Q ) at one day (1440
minutes). For these conditions, using appropriate values for the nucleation
and growth rate parameters, a size distribution is predicted which is in
reasonable agreement with experimental data discussed in Section 6 of this
report (see Figure 6-5).
Predicted changes in crystal size distribution with changes in process
conditions are illustrated in Figures 5-3 and 5-4. The curves shown here
were generated by solving the size distribution model for a range of input
relative saturations and solids residence times (^r and T ) . Cases having
equal slurry solids content but different solids residence times were
selected and plotted in Figure 5-4. The crystal size distribution is repre-
sented for convenience using the calculated mass average crystal size.
Corresponding changes in relative saturation are also plotted in both figures.
Curve I in Figure 5-3 shows that the mean crystal size (ITTT) increases
with increasing solids residence time (T ) when the relative saturation
exponent in the growth expression is less than that in the nucleation ex-
pression (i,-,R = 1.0, i = 2.0). Increasing the solids residence time
increases the total crystal inventory and thus decreases the required
17
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TABLE 5-1. SAMPLE PRINT OUT FOR SIMPLIFIED HOLD TANK/CLARIFIER MODEL
CRYSTALLIZATION SATES
SIMPLIFIED MOLO TANK/CLARIFIER MODEL
RELATIVE SATURATION a.000
HOLD TANK VQL/CLAHIFIER FEED RATE.HIN 1440.
HOLD TANK VOL/CLARIFIES UNOERFLO*,MIN 1.500+01
CLAKIFIEK CUT-OFF SIZE,^ICPON3 -j' 1.00
SLOPE,SWU^TH RATE/SIZE RELATION micron .so
GROWTH RATE CONSTANT,MICRQNS/MIN
REL.3AT. EXPONENT,GROWTH SATE
NUCLEATIQN RATE CONSTANT
REL.3AT. EXPONENT,NUCLEATION HATE
CRYSTAL CONC. EXP.,NUCLEATION RATE
NUCLEATION RATE,PAWT./L/NIN
PPT. RATE, MOLES/L/MIN
»T PCT SOLIDS, CLARIFIES FEED
UNDERFLOW
PPM SOLIDS, OVERFLOW
MASS AVG. P. SIZE, MICRONS, CLARIFIER FEED
UNDERFLOW
OVERFLOW
3.135+07
1.152-06
,024
.223
33.8
1.060
1.557
.591
6.000-05
1.00
2.400+06
1.00
.50
CLARIFIES FEED PARTICLE SIZE DISTRIBUTION
3IZE,*IC»ON3 POP.D£NSITY,PA»TS/L/MICSON
.00 .174+12
.10 .162+12
.20 .150+12
.50 .140+12
.40 .132+12
.50 .124+12
.60 .116+12
.70 .110+12
.90 .104+12
.90 .983+11
1.10 .933+11
1.10 .701+11
1.20 .532+11
1.30 .407+11
I.40 .314+11
1.50 .244+11
1.60 .191+11
1.70 .150+11
1.80 .119+11
1.90 .948+10
NO. PCT
.00
10.19
19.66
26.49
36.75
U4.49
51.77
59.64
65.12
71.26
77.07
82.OU
85,78
88.63
90.82
92.51
93.83
94.86
95.68
96.32
CUMUL VOL PCT
.00
.00
.02
.12
.37
.87
1.73
3.06
5.00
7.66
11.19
15.26
19.28
23.22
27.03
30.67
31,15
37,43
40.53
43.43
0£L VOL PCT
.00
.00
.02
.10
.25
.50
.86
1.33
1,93
2.67
3.53
4.06
a.03
3.9«
3.81
3.65
3.47
3.29
3.10
2.91
2.00
J.UO
4,00
5.00
6.On
7.00
8.00
9.00
10.00
15.00
20.00
25.00
.7*1+10
.109+10
.222+09
.579+08
.181+0*
.648+07
.259+07
.113+07
.528+06
.254+05
.268+04
.450+03
96.8
-------
2 4
0)
S
It-J
-------
5-1
0)
4J
0)
3
0)
N
H
C/3
CO
u
w
>>
i-l
o
0)
to
CO
M
OJ
>
en
0)
03
S-i
0)
T3
fi
-------
relative saturation at constant SOa removal. Since the nucleation rate
decreases more sharply than the growth rate, the size distribution increases.
Curve II in Figure 5-3 shows that the size distribution decreases
with increasing T when i > ipN- Thus, the same process change_ may have
the opposite effect on the crystal size distribution depending on the form
of nucleation and growth rate expressions. Firm values for i and i
will have to be obtained from a test plan such as that proposed in Section
7. If i_n = ic,.T, little change in the size distribution would be expected.
GR SN
Curve I in Figure 5-4 shows an increase in average crystal size with
increasing slurry solids content and constant hold tank size. This change
is again attributed to the drop in relative saturation caused by increasing
the total crystal inventory. Curve II represents an interesting case.
The decrease in nucleation caused by lowering the supersaturation is counter-
balanced by the increase due to increasing solids content. The net
change in average particle size is negligible for this case.
The size distribution changes predicted above are related to changes
in hold tank size or slurry solids content. Either of these changes amounts
to a change in relative saturation at constant SOa removal. One can see
from these figures that the size distribution may not change substantially
even with large changes in operating conditions. For the cases where
operation at low relative saturation is favorable (Type I behavior)
limitations on tank size and slurry solids content will set a practical
limit for the average crystal size. For Type II, cases where high relative
saturation is favored, scaling limits will constrain the maximum attainable
crystal size.
In Section 4, it was noted that the secondary nucleation rate is expected
to be a function of the energy of crystal/crystal and crystal/impeller
collisions in the system. These variables are not considered explicitly in
the present model. From the overall material/population balances at constant
SOa removal, we know that the mass mean particle size must be inversely
proportional to the nucleation rate to the one third power:
(5-10)
B
Changes in the size distribution may thus be expected with changes in
variables other than T or W if the net nucleation rate is changed.
These effects can be included in the nucleation rate constant, k , as
information is developed during the test program.
21
-------
SECTION 6.
ANALYTICAL METHODS FOR SLUDGE QUALITY
Verification of the mathematical model requires experimental measure-
ment of calcium sulfite size distribution. The settling rate and settled
density of the sludge are also important mechanical design parameters.
Potential analytical methods for particle size, settling rate, and settled
density were selected for evaluation from those described in the literature.
Settling rate and settled density measurements are straight forward. The
particle sizing techniques agreed well for crystals larger than about 5 to 10
microns, but poor agreement was found in the submicron range. Results of
the analytical methods evaluation are presented here. Details of the
literature survey are included in Appendix C .
Two types of sludge were used in the evaluation; a limestone process
sludge from a pilot unit operated at Pennsylvania Power and Light Company,
and lime process sludge from the full-scale system at Louisville Gas
and Electric. The limestone sludge contained sulfite crystals with the flat
platelet habit. Calcium sulfite crystals in the lime system sludge appeared
as spherical granules with a dendritic surface. Optical photomicrographs
of the two sludge samples are shown in Figure 6-1 and 6-2.
SETTLING RATE AND SETTLED DENSITY
Settling tests were conducted in a series of glass graduated cylinders.
The settling medium was water saturated with sludge and then filtered.
Figure 6-3 shows calculated settling rate data for lime and limestone sludge
at various levels of temperature and slurry solids content. Settling rate
increases with temperature due to the decrease in viscosity. This is in
accordance with Stokes' Law- Settling rate decreases with increasing solids
content as expected for hindered settling. The effect of cylinder size
(250 ml, 500 ml, 1000 ml) was not important.
Settled density for the lime sludge tests averaged 1.25 g/cm3 (34%
solids) and for the limestone sludge 1.39 g/cm3 (48% solids). The fact
that the granules settled more slowly than the platelets and attained a
lower settled solids content may indicate that the effective density of
the granules is less than that of the platelets. The dendritic habit of
the "granules" may promote entrapment of process liquor.
22
-------
FIGURE 6-1 PHOTOMICROGRAPH OF SLUDGE PLATELETS TAKEN
FROM LIMESTONE SCRUBBER, 200 X
02-2070-1
-------
w. *f"T* r^.
Vf?^*:*'*.-^
wirestjS
wF,"»AlF^r £ *'.
jw * * lP*TB^,«i ' ^A.
j»* Wffct '""
^ ' 4l .'ti1 - 4 -* jkl* m- * *
^3bV-*^ ^fW|.
,^m.m ^^^"«'"? *t *',ji
isS^I
'-*F»_1. ft. mkak '.^, ^^
FIGURE 6-2 PHOTOMICROGRAPH OF SLUDGE GRANULES
TAKEN FROM LIME SCRUBBER, 200 X
02-2069-1
-------
4.0
3.0
c
H
"e
o
01
4J
cd
o 2.0
1.0
O Platelets @ 25 C
O Platelets @ 50° C
Granules @
Granules @ 50C
i l I I
0 2 4 6 8 10 12 14 16 18 20
Weight % Solids
Figure 6-3. Settling Rates of Sludges Versus
Weight % Solids at 25°C and 50°C
25
-------
CRYSTAL SIZE DISTRIBUTION
Several methods were used to measure the size distribution of the
granular (lime) and platelet (limestone) sludges. Optical microscopy is
generally thought to be reliable and accurate. Microscopy also provides
information about particle shape. Optical microscopy is practically limited
to particles about five microns or larger. Other methods measure only a
single characteristic length, but are potentially much faster than the
tedious optical counting. The working size range may be extended down to
about 0.3 microns.
The Coulter Counter and Micromeritics Sedigraph 5000 instrumental
methods were compared to the optical size distribution. The Coulter in-
strument measures a signal proportional to the volume of a particle as it
passes through a small aperture. The particle size may be calculated by
assuming a particle shape. The Micromeritics instrument measures the
settling rate of a suspension of particles and calculates an equivalent
particle diameter using Stokes' Law- Since these methods do not measure
particle shape, some care must be taken in comparing their results with the
optical method.
Micromesh sieves were also evaluated. The smallest sieve had two micron
openings. The sieve procedure was not significantly faster than the optical
microscope.
Results of all of the size distribution measurements are compared for
the granular sludge in Figure 6-4 and for the platelet sludge in Figure
6-5.
With the granular sludge the optical method and sieve results are in
fair agreement. According to these methods, the mean particle size on a
number basis is about seven to ten microns. Both the Coulter Counter and
the Sedigraph data show a much smaller size distribution with a mean
particle size less than one micron.
Even if the large number of fine particles indicated by the instru-
mental methods were not detected by the microscope, they should have posed
no problem to the sieve analysis. The weight fraction of granules passing
through the 5 micron sieve was less than 1% of the total. The Coulter Counter
shows more than 27% of the mass was less than 5 microns in diameter. The
Sedigraph indicates up to 70% of the mass is less than 5 microns. No firm
explanation for this discrepancy was found. It is possible that the ultra-
sonic dispersion technique used in preparing samples for these instruments
was sufficient to break up the spherical agglomerates present in the original
sample.
26
-------
C3
cfl
en
en
0)
C
0)
a
M
0)
CM
I
3
U
"O
a)
1-1
3
en
eo
Sedimentation
100 ..
Coulter Counter.
4
Coulter Counter Truncated at 2 microns
__
Micromesh Sieve
90
80
70 £
60
50
40
30 .
20
10
Optical Microscope
^ Sedimentation
Q] Coulter Counter
Q Sieve
<§ Optical Microscope
10 15 20 25 30 35
Diameter, Micrometers
40 45 50 55
60
Figure 6-4. Sludge Granules from Lime Scrubber: Cumulative Percent of Particles
Versus Diameter.
-------
Typical Predicted Size Distribution from Table 4-1
00
c
nJ
w
w
OJ
(-)
4J
c
OJ
CL,
H
n)
w
0)
100
90 -
70 -
60 ,
50
30
20
10
A Estimated Platelet Width-Sedimen-ation
9 Platelet Width-Optical Microscope
[7] Platelet Width-Coulter Counter
0 Sieve Results
10 15 20 25 30 35 40
Length and Width, Micrometers
45
50
55
60
Figure 6-5. Sludge Platelets from Limestone Scrubber: Cumulative Percent
of Particles Versus Width.
-------
Figure 6~-5 shows results for the platelet sludge. Since the Coulter
Counter and Sedigraph both report equivalent spherical diameter, some ad-
justment of the raw data was required for comparison of the platelet size
distributions. The Coulter Counter data were converted from equivalent
spherical diameter based on a volume proportional signal to platelet width
(W) by multiplying by 1.9. This is the ratio of width of a platelet with
dimentions W x 1.5W x W/20 to the diameter of a sphere of equal volume.
The equivalent diameter reported by the Sedigraph is based on the
terminal settling velocity of a sphere. To convert from equivalent spherical
diameter to platelet width in this case, an expression for the velocity of a
falling body may be used (3):
2gm (p -pf)
PfppAPCd
meter/sec (6-1)
Here, U is the terminal velocity of a particle with mass m , density p ,
and projected area A , falling in a medium with density p. under gravity g.
C, is a drag coefficient describing the fluid forces on trie particle.
Drag coefficients for a sphere and disc are nearly equal at the same
Reynolds number for N < 0.3 (3):
C = ^- (6'2)
Re
If we assume that a platelet will behave approximately the same as a disc,
Equation (6-2) may be used with Equation (6-1) to estimate the size of plate-
let having the same settling velocity as a sphere of diameter D . The
resulting conversion factor is:
D , , = 3.6 D . (6-3)
platelet sphere
As shown in Figure (6-5), size distribution data for the platelet sludge
are again strongly sensitive to the method used. The correction factors
move the Coulter Counter data and Sedigraph data tox^ards the distributions
of the optical and sieve methods, but the overall agreement is still poor.
Additional work with the instrumental methods will be required to
investigate the above discrepancy before selecting a method for use in the
test plan. Different methods of sample preparation should be checked for
their effect on measured size distribution.
29
-------
SECTION 7
TEST PLAN
EPA has been operating a pilot scale SOa scrubbing unit at their
Research Triangle Park laboratory in support of full-scale process develop-
ment efforts. The test plan described here is specifically intended for
this unit. The scrubber is a one to three-stage TCA type with a nominal
gas flow of 500 meter3/hour. The inlet SQz concentration can be fixed at
any desired level. Several hold tank sizes and arrangements are possible.
For purposes of this test program, continuous operation for a five-day period
is required. The test plan objectives and test conditions described here
are based on the literature survey and mathematical development presented
in Sections 3 and 4 of this report.
OBJECTIVES
The major objective of the test plan will be to identify and characterize
nucleation sources in lime/limestone wet scrubbing systems for the purpose
of increasing the average crystal size to improve settleability of solids.
The modeling effort has shown that correlations describing nucleation and
growth as a function of operating conditions can be used to predict a
calcium sulfite size distribution. Some data pertaining to the growth
rate are available, but the nucleation phenomena in this crystal system
have not yet been investigated.
Once the predominant sources of calcium sulfite nuclei have been iden-
tified, a series of tests will be conducted to define the effects of important
process variables on both the nucleation rate and growth rate. The results
of these tests will be used to improve the accuracy and usefulness of the
size distribution model by quantifying the rate parameters used (k , k
-: -; ) GR SN
SN' JSN''
The tests described below are intended for a limestone system Analy-
sis of available data indicated that this system may be more easily modeled
than the lime process.
30
-------
TEST SEQUENCE AND OPERATING CONDITIONS
The proposed test plan is divided into three phases. The purpose of
this strategy is to make full use of experimental data as it is obtained so
that subsequent experiments move operationally towards improved sludge
quality. Test conditions for Phases I and II are presented in Tables 7-1
and 7-2 reproduced from Appendix E .
Phase I includes eight individual five-day tests. In each test, a
single set of operating conditions is maintained for the entire period.
The first test period establishes "base case" operating conditions. Then,
changes are made to try to identify important nucleation sources in the
system. Tests 2, 3, 6, and 7 examine the effects of changes in the mechani-
cal energy sources in the system. In these experiments, the pump and mixer
impeller materials and operating speeds are varied. Tests 4, 5, and 8
screen for chemical nucleation in the scrubber or hold tank.
The most important dependent variable in the Phase I tests will be the
calcium sulfite crystal size distribution. It is expected that changes
in variables affecting nucleation rate will lead to measurable changes in
the steady-state size distribution. Settling properties of the crystallized
product will also be measured as an indication of changes in the sludge
quality.
The mechanical and process configuration of Phase II tests will be based
on results of Phase I. Operating conditions producing the best sludge
quality will be selected. A series of ten five-day experiments will be run
to further correlate calcium sulfite nucleation and growth rates with
process operating conditions.
Tests 10 and 11 involve changes in the slurry solids content. If
secondary nucleation involves crystal-crystal collisions, this may lead to
measureable changes in the sulfite size distribution. Tests 12 through 15
investigate the effect of scrubbing liquor composition by changing levels
of soluble magnesium, chloride, and sodium. Tests 16, 17, and 18 involve
changes in hold tank size and use of a slurry grinder to promote mechanical
nucleation.
As the results of Phases I and II become available, the usefulness
of the computer model should be increased. The constants and exponents
in the nucleation and growth rate expressions can be adjusted to agree with
experimental results. If the physical basis for the model is realistic,
the model can then be used to look at design and operating changes to im-
prove sludge quality. Phase III of the recommended test program includes
eight five-day tests to verify the computer model and demonstrate improved
sludge quality.
31
-------
TABLE 7-1. PHASE I - TEST SCHEDULE
Teat 0
1
Days
5
Objectiv
e
Obtain base case
Variable Changed
None
system operation
2
3
6
5
5
5
5
5
Observe effect
impeller materi
Observe effect
pump speed
Observe higher
supersaturatlon
of
.,i
of
scrubber
Observe scrubber
Switch to steel
impel ler
Reduce pump RPM's,
maintain constant L/C,
residence times.
Reduce scrubber feed flow, raise "
S02 inlet, (constant SOj pickup)
Scrubber feed pH 4.5 '
Reason
Basis for further
comparison
Determine effect of
pump energy on P.S.D.
,
Determine effects of scrubber
conditions on P.S.D.
suhsaturated operation
6
5
Observe mechanical
features of hn]d tank
7
8
5
5
40-
Same as 06
Same as 06
Switch to steel
agitator
Lowe r agitator spaed
Mix additive, clarlfier overflow
and scrubber bottoms together
Determine effect of hold
tank conditions on P.S.D.
(1) Base Case - Low oxygen content in flue gas (<3X), 3000 PPM S02, feed rate 83 fcpm, 10Z solids. 10 hour solids retention time.
Valve positions and nozzles are not to be changed during the study.
-------
TABLE 7-2. PHASE II - TEST SCHEDULE
Test It
9
10
11
12
13
14
15
16
I/
18
Days
5
5
5
5
5
5
5
3
5
5
53
Objective
Base Caa
,(1>
Change number of
crystals in system
Same as 1 10
Change scrubbing
liquor quality
Same as
Same as
Same as
It 12
# 12
» 12
Variable Changed
'Best' configuration from Phase I
5% solids, keep SOa pickup constant >
by raising inlet concentration
15% solids, keep S02 pickup constant
by lowering inlet concentration
Low positive scrubbing liquor
(2MK + Na - Cl)
High posi :ive liquor
Low negative liquor
High nega:ive liquor
System purge
Add seed
Increase
time to
16-hour
grinding
crystals
solids retention
16 hours
S.R.T. and
Grind 1% jf clarifler underflow
stream
Increase hold tank size
Sane as tf i6 and #17
Reason
Future reference
Determine effect of solids
level on nucleation
Determine effect of liquor
quality and nucleation and
growth rates
Eliminate high soluble species
concentration
Increase number of growth
sites
Lower relative saturation
Same as 016 and 1/17
(1) Base Case - Configuration from Phase I yielding lowest amount of mechaniral nucleatiim.
-------
ANALYTICAL REQUIREMENTS
The data obtained here are to be used in modeling the calcium sulfite
size distribution. The model itself depends on nucleation and growth rate
parameters, thus these are quantities requiring experimental measurement.
The nucleation rate can be measured only by measuring the size distri-
bution of the calcium sulfite crystals. The growth rate can be determined
from both the size distribution data and the chemical species balances for
the system. This material balance will provide an independent check on the
size distribution measurement.
Figure 7-1 shows a size distribution for sludge obtained from a lime-
stone scrubbing pilot unit. The size versus count data were obtained using
a Coulter Counter. The linear growth rate, R, may be determined using
the slope of the size distribution, d^nn and the solids residence time, T.
If the distribution is curved , the growth rate varies with crystal size
In this case, the term dR must t,e included in the calculation using an
iterative approach to evaluate both R and 4^ such that:
dL
R =
n n)
dL
The nucleation rate, B , is the product of the growth rate and number
density at zero size. The intercept of the distribution at zero size can
be estimated by extrapolating the small size range data,
B0 = lim (nR) (7-2)
L -» 0 .
The importance of a reliable particle sizing method for the fine size range
is easily seen. Available particle sizing methods were discussed in Section
6 of this report. In view of their uncertainty in the submicron range, some
additional effort may need to be devoted to analytical methods development
prior to or during the test program. An alternate approach to data analysis
would be to use the model described in the previous section as a subroutine
in a curve fitting program using the growth rate and nucleation rate
parameters.
34
-------
O.W
IO6
io5
1 1
1
0)
1 i
OJ
G
° if
IJ 10 .
3
4J
CO
H
Q
a)
f
is 10 .
io2.
10
X
X
X
X
X Pennsylvania Power and Light Limestone
Pilot Unit
X
X
X
X
X
X
X
X
X
10
15
20
25
30
35
Particle Size (Meter x 10 )
Figure 7-1. Size Distribution Data for Limestone Scrubber Slurry.
Counter) n (L) versus L
(Coulter
35
-------
Chemical analytical methods for important liquid and solid phase
species are well-established. Details of these procedures are included
in Appendix E . Sufficient chemical and operating data should be obtained
to complete individual calcium and sulfur balances for the process vessels
as well as calculate the relative saturation of the process liquor.
36
-------
NOMENCLATURE
A - Particle surface area (cm2)
B - Rate of birth of particles, no/£/min
C - Concentration (moles/liter)
C^ - Drag coefficient
cm - Centimeters
D - Rate of disappearance, no
fp-r - Factor defining clarifier particle
size split
G - Molar precipitation rate, moles/£/min
g - Gram
i - Experimental exponent
j - Experimental exponent
k - Rate constant
k,k ,k",ki,k2,ka - Experimental constants
k - Shape factor
v r
L - Characteristic particle length (m)
L - Clarifier cut-off size, microns
c
£ - Liters
L - Mass average length (m)
m - Meters
m - Mass of a particle
P
M - Total slurry solids, moles/£
N - Number of particles per slurry volume
(A"1)
n - Number of particles of size L volume
OT1 m'1)
N - Number of particles of size L ger
volume leaving system (i sec )
M - Reynolds number
Re
Q - Volumetric flow rate (£/sec)
37
-------
NOMENCLATURE (continued)
R - Linear crystal growth rate (m/sec)
r - Relative saturation
AS02 - SO2 pickup (moles/sec)
U - Terminal velocity of a falling particle
V - Slurry volume
W - Weight fraction solids
y - slope of R vs_ L straight line, microns)
F - Gamma function
p - Density, gm/cc
T - Characteristic time = vessel volume/
flow rate, min.
SUBSCRIPTS
CL - Clarifier
CF - Clarifier feed
CO - Clarifier overflow
CU - Clarifier underflow
GR - Growth
i - Input stream
j - Output stream
n - No (particle)
o - Zero size
p - Particle (crystal)
S - Scrubber
SB - Scrubber bottoms
SF - Scrubber feed
SN - Secondary nucleation
T - Hold tank
T - Total
v - Volume
38
-------
REFERENCES
Randolph, Alan D. and Maurice A. Larson, Theory of Particulate Pro-
cesses. Analysis and Techniques of Continuous Crystallization.
New York, Academic, 1971.
Ottmers, D. M., Jr., et al., A Theoretical and Experimental Study
of the Lime/Limestone Wet Scrubbing Process. EPA 650/2-75-006,
NTIS #PB 243-399/AS EPA Contract No. 68-02-0023. Austin, Texas,
Radian Corporation, 1974.
Perry, John H., Chemical Engineers Handbook, 5th edition. New York,
McGraw-Hill, 1973.
39
-------
DCN #77-200-187-11-04
APPENDIX A
AN APPROACH TO PREDICTING CALCIUM
SULFITE CRYSTAL SIZE DISTRIBUTION
IN LIME/LIMESTONE WET SCRUBBING SYSTEMS
Technical Note 200-187-11-01
28 November 1977
Prepared for:
Robert H. Borgwardt
Industrial Environmental Research Laboratory/RTP (MD-61)
U. S. Environmental Protection Agency
Research Triangle Park,
North Carolina 27711
Prepared by:
James L. Phillips
Grep P. Behrens
Reviewed by:
Philip S. Lowell
A-i
-------
TABLE OF CONTENTS
Pae
1.0 INTRODUCTION ................................. A~l
2.0 THEORY OF CONTINUOUS CRYSTALLIZATION ......... A- 3
3 . 0 APPLICATION OF CRYSTALLIZATION THEORY TO
LIME/LIMESTONE SCRUBBING SYSTEMS ............. A-10
3.1 The Overall Scrubbing System ............ A-ll
3.2 Simulation of the Scrubbing System ...... A-14
4.0 NUCLEATION AND GROWTH FUNCTIONS .............. A-16
4.1 Nucleation .............................. A-16
4.2 Crystal Growth .......................... A-26
4.3 Experimental Data for Calcium Sulfite
Precipitation ........................... A-31
5 . 0 SUMMARY AND RECOMMENDATIONS .................. A-49
NOMENCLATURE ................................. A-53
REFERENCES ................................... A-56
A-ii
-------
LIST OF FIGURES
Figure Page
2-1 Limestone Platelets A-4
2-2 Lime Rosettes A-4
4-1 Comparison of Calculated Sulfite Precipitation
Rates for Lime and Limestone Scrubbing
Systems A-33
4-2 Comparison of Seed Crystal Sizes for Two Labora-
tory Experiments Having Similar Molar Growth
Rates A-40
4-3 Size Distribution Data for Lime and Limestone
Scrubber Slurries (Coulter Counter) A-43
LIST OF TABLES
Table page
4-1 Results of Lime/Limestone Scrubbing Tests at
Combusion Engineering Pilot Units A-34
4-2 Results of Lime/Limestone Scrubbing Tests at
EPA/RTP Pilot Unit A-36
4-3 Results of Lime Scrubbing Tests at Louisville
Gas and Electric A-38
A-iii
-------
LIST OF TABLES (continued)
Table Page
4-4 Comparison of Liquor Compositions and Preci-
pitation Rates for Two Lime Scrubbing
Systems A-45
A-iv
-------
1.0 INTRODUCTION
Concentration and disposal of waste slurry is an
important aspect of lime/limestone wet scrubbing technology.
Most research and development efforts in the past have been
directed towards improving SOa removal and preventing scale
formation in these systems. Solution of these problems is
crucial to successful process application. Theoretical and
experimental studies at Radian Corporation (OT-023, JO-R-214),
EPA's Research Triangle Park facility (BO-144, BO-147, BO-241),
and the EPA/TVA prototype scrubbing system at Shawnee have
related scaling potential and SOz removal efficiency to
important system design and operating parameters. These
advances have helped make continuous operation of lime/
limestone scrubbers a practical reality.
Given an operable process, the quality of waste material
produced assumes greater importance. Such parameters as slurry
settling rate and settled density may have a significant impact
on waste disposal costs over the life of a system. The purpose
of this technical note is to outline a quantitative basis for
predicting the size distribution of calcium sulfite solids pro-
duced in lime/limestone scrubbers. This appears to be a logical
first step in designing for optimum waste sludge quality. It is
believed that sulfite crystal size distribution can ultimately be
related to slurry settling and dewatering properties. In the
following development, the term "calcium sulfite solids" will
include any coprecipitated sulfate, but gypsum precipitation
will not be considered.
Our approach will first examine the general mathemati-
cal relationships regarding conservation of particles in continuous
crystallization. Section 2.0 describes this "particle balance"
A-l
-------
concept based primarily on the work of Randolph and Larson
(RA-060). A general equation is derived and then simplified
for the application of interest here.
In Section 3.0, the general particle balance relation-
ships are more specifically applied to lime/limestone wet scrub-
bing. In addition, a qualitative discussion of the possible
effects of system design and operating parameters on waste
product particle size is presented.
Section 4.0 examines the physical and mathematical
description of particle birth, death, and growth functions
necessary for solution of the particle balance equations.
Correlation of nucleation and growth rates with the physical
and chemical environment in various parts of the system will
be central to quantitative application of the proposal model.
A-2
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2.0 THEORY OF CONTINUOUS CRYSTALLIZATION
Many quantitative investigations of particle size
distributions in laboratory and industrial crystallizers are
described in recent chemical engineering literature. Nearly
all of these have used a mathematical approach derived from the
principle of particle conservation. For crystallization from
solution this may be stated as follows (RA-050):
Rate of accumulation of crystals of size L per
unit volume of slurry is equal to the net input
of crystals of size L via convection plus the
net input via growth plus the net generation
of crystals of size L via other mechanisms
(e.g., breakage).
In this statement, L (meters) is a characteristic length which
completely describes all three dimensions of each crystal. This
is equivalent to assuming that all crystals are geometrically
similar. Recent experimental work by TVA using sludge from the
Shawnee test facility has shown that nucleation and/or growth
mechanisms in lime and limestone scrubbing systems produce
different predominant crystal shapes. Flat platelets with a
length-to-width-to-thickness ratio of about 25:20:1 predominate
in limestone systems while rosettes are more characteristic of
lime scrubbing systems (CR-163). Figures 2-1 and 2-2 are
electronmicrographs of limestone platelets and lime rosettes.
The mathematical development in this technical note will be
limited to a single characteristic length L. Different crystal
habits may be dealt with later by specifying an applicable
"shape factor" for each case. This shape factor is normally
defined by the relationship between crystal volume and the
characteristic length:
A-3
-------
FIGURE 2-1
LIMESTONE PLATELETS (COURTESY TVA)
FIGURE 2-2
LIME ROSETTES (COURTESY TVA)
-------
V = k LJ
P v
(2-1)
The possibility exists that more than one shape factor may be
necessary to describe the crystals formed in a single process
configuration. This can presumably be handled by calculating a
separate size distribution for crystals of each shape.
A reasonably general mathematical form for the particle
balance principle can be derived by considering the differential
element of slurry shown in Figure 2- 3.
AY
,1
AX
AxAYAz = Av
AZ
X,Y,Z
Figure 2-3.
First, define the crystal size distribution n(L,X,Y,Z) such that
nAL is equal to the number of crystals in the size range AL
per unit volume of slurry. The dimensions of n are thus m~".
The rate of accumulation of crystals in the size range AL
in the slurry element may then be written as:
accumulation =
-^-(n(L)ALAV) (sec'1)
at
(2-2)
Here n(L) is an average value of n(L,X,Y,Z) over the small volume
element.
A-5
-------
For convection in the X direction, the net input of
crystals in the size range AL is:
net input via X convection= -
(uxn(L)
- (uvn(L)
A
'x
ALAYAZ
(sec"1)
(2-3)
where uv is the X component of slurry velocity averaged over the
A
AYAZ plane. Strictly speaking, this term should deal with con-
vection of crystals, not slurry. The derivation is simplified
by assuming that the slurry velocity and crystal velocity are
identical. This appears to be a reasonable assumption for the
small crystals typical of lime/limestone wet scrubbing systems.
(This assumption would not apply to a clarifier, but very little
change in size distribution would be expected in this vessel for
any case.) Similar convection terms may be written for the Y
and Z directions.
The net imput of crystals via growth to the size range
AL in element AV may be written:
net input via growth =
(n(L) R(L))L - (n(L) R(L))
L+AL
AV (2-4)
where R(L) (meter/sec) is the growth rate of the L dimension for
crystals of size L. This growth rate may be size dependent. The
entire particle balance expression is obtained by combining
Equations 2-2, 2-3, and 2-4. Thus:
3
9t
n(L)ALAV
X+AX
- (uvn(L))
X
ALAYAZ
(2-5)
ALAXAZ
ALAXAY
A-6
-------
(n(L) R(L))|T - (n(L) R(L)
AV
'L+AL
+ net generation by mechanisms other than growth
Dividing both sides of Equation 2-5 by ALAXAYAZ and taking the
limit as the "A" values go to zero yields a partial differential
equation. The "average" values n and u become point values.
3n
9t
_3_(u n) _ 9_(u n) _ ^_(u7n) _ S_(nR(L)) + G(L,X,Y,Z) (2-6)
8X 3Y * 8Z 9LV /
The term G represents net formation of crystals of size L from
mechanisms other than growth and convection. For example, a
single large crystal might break to form two or more smaller
crystals. Breakage has been addressed in the ball mill litera-
ture (AU-013 , BO-272 ). It is itself a rather complex phenomenon.
G will in general be some function of L, X, Y, Z and must be
dimensionally consistent with the remaining terms in the particle
balance .
It should be noted that the G term does not include
nucleation, which is defined as formation of particles of a
length L near zero. Instead this is included in solutions to
Equation 2-6 by specifying as a boundary condition the number
concentration of nuclei, n , as L approaches zero. The nuclea-
tion rate, n , is related to the nuclei concentration n by an
expression similar to that used for the rate of appearance of
crystals at larger sizes of L (see Equation 2-4) :
n = (n(L) R(L) ) | evaluated as L becomes small (2-7a)
o
=< Lim n(L)R(L) ! (2-7b)
- L->o
A-7
-------
It should be realized that not all nuclei grow to mature
crystals. A death rate term is implicit in an overall system
nucleation rate. For example, in lime scrubbing systems, an
increase in liquid phase calcium concentrations is often seen
across the scrubber. This is due to the demand for extra alka-
linity by the scrubbing liquor. As the calcium sulfite goes into
solution, two possibilities exist. Either the fine particles
dissolve first or mass is removed from each crystal in proportion
to its volume. It is possible that fines dissolution is the
major mechanism for extra alkalinity. This death of fine parti-
cles in the scrubber must be more than offset by the nucleation
rate, in order to satisfy the overall particle balance.
Practical application of Equation 2-6 requires detailed
information about the functionality of crystal nucleation rate
and growth rate for a particular system. Nucleation rate is
typically a function of liquid composition and may also be in-
fluenced by crystal collisions in agitated slurries. Growth rate
is affected by liquid composition, crystal size, and in some cases,
level of agitation. Both nucleation and growth are temperature
dependent. If the other particle generation term, G, is signifi-
cant, its variation with supersaturation and crystal size must
also be known. Possible forms for these functions are discussed
in later sections of this technical note.
Some additional simplification of the general particle
balance equation is desirable before applying it to lime/limestone
scrubbing systems. First of all, it seems reasonable to limit
the present discussion to steady-state conditions. Mathemati-
cally, at steady state,
3n(L) = 0 for all values of L, X, Y, Z (2-8)
9t
A-8
-------
Equation 2-6 may now be written
(2-9)
For application of Equation 2-9 to systems of fixed volume, the
convection terms may be converted to entrance and exit stream
flow rates and particle concentrations by integrating both sides
of 2-9 over the volume of the system and applying Gauss' Theorem
to the right-hand side. In vector notation, Equation 2-9 becomes
;
v
dV
v
(Vun)dV
(2-10)
In Equation 2-10, the right hand side is identically equal
volumetric
Thus, our final
to ZCWnout
- E. n.
in in
where Q. and Q are volumetric flow
rates of entering and exiting slurry streams.
form of the particle balance equation becomes
f I 3
ZQoutnout - EQinnin= V ~ 3L
+ G dv
(2-11)
A-9
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3.0
APPLICATION OF CRYSTALLIZATION THEORY TO LIME/LIMESTONE
SCRUBBING SYSTEMS
In the previous section a general appraoch to predicting
crystal size distribution was derived. It was pointed out that
application of Equation 2-6 requires definition of suitable
functions for nucleation rate (or nuclei density) and crystal
growth rate. In this section, the generalized particle balance
is applied to lime/limestone scrubbing systems. The qualitative
effects of various process parameters on the particle balance
equation will be discussed. Information required for quantitative
solutions will be identified for further investigation. Mass
balance equations will also be introduced so that interactions
between the particle size distribution and overall material
balance can be seen.
A "typical" process flow sheet for a lime or limestone
scrubbing system is shown in Figure 3-1. A physical description
overall
system
boundary
Figure 3-1.
A-10
-------
of the process units and their possible effects on sulfite
particle size distribution will aid in developing a suitable
mathematical model. First, the overall system is discussed.
Then the combination of individual process units on sulfite
particle size distribution are considered.
3.1 The Overall Scrubbing System
Referring to Figure 3-1, S02 enters the system in the
flue gas (FG) stream. Most of this inlet SC2 is absorbed by the
scrubber feed liquor (SF). Some of the absorbed SOa is oxidized in
the scrubber. Depending on the specific system design, sufficient
residence time and supersaturation may exist in the scrubber to
form sulfite nuclei or to provide additional growth on sulfite
crystals entering with the scrubber feed (OT-023). In other systems,
for example the lime scrubber at Paddy's Run, sulfite crystals
may dissolve in the scrubber to provide alkalinity for S02
absorption (HA-696). For many systems, particularly those
with short slurry residence time in the scrubber, little solid-
liquid mass transfer would occur until the dissolved SOa
enters the hold tank with the scrubber bottom (SB) stream.
In the hold tank, dissolved sulfite and sulfate react
with dissolved calcium from the alkaline additive to precipitate
calcium sulfite and sulfate solids. Recent experimental work has
shown that calcium sulfite precipitated in lime or limestone
scrubbing systems may coprecipitate a limited amount of sulfate
ion. A solid phase with the formula Ca(S03), V(SCU) V*%H20
L~ji. X
has been identified (JO-R-214). Depending on system operating
conditions, the value of x ranges from zero to about .2.
For purposes of the present discussion, "calcium sulfite"
crystals will include coprecipitated sulfate.
A-ll
-------
A waste stream ±s taken from the hold tank and pumped
to a dewatering area (pond, filter or clarifier) . The remaining
slurry is recirculated to the scrubber. Nearly all of the solids
are typically removed from the waste slurry stream and some or
all of the clear liquor is recycled. The "dewatered solids"
(actually containing up to 60 wt . 7a water) are contained in a suita-
ble permanent storage area such as an ash pond or land fill. The
dewatering properties of this waste slurry stream and the physical
properties of the dewatered solids should be related in some way
to the particle size distribution and shape of the sulfite
crystals .
The overall scrubbing system may be treated as a "black
box" which combines calcium from lime or limestone additive with
SOa from the flue gas to form calcium sulfite crystals. The
number and size of these crystals depends on the mechanisms and
rates of nucleation and growth in the system. At steady-state
or for conditions averaged over a suitable time period, the
total number of moles of SOz removed from the gas is approximately
equal to the total number of tnoles of sulfite + sulfate appearing
in the waste slurry. This can be expressed mathematically by an
overall mass balance:
S\
n
sec J Vsec/ s\kj Vmole
(3-1)
x '
In this equation CU is the clarifier underflow rate, m the con-
centration of coprecipitate solids in the slurry, and MW the
molecular weight of the sulfite/ sulfate coprecipitate. The contri
bution of dissolved sulfur to the overall mass balance is assumed
to be negligible. This relationship shows that changes in S02
removal rate will ultimately require a corresponding change in
the slurry waste rate or slurry solids concentration.
The overall system S02 balance can also be related to
the particle size distribution n(L) by recognizing that the sum
A-12
-------
of the individual crystals leaving the system must also account
for the molar 862 removal rate. Thus:
k p CU f00 n(L)L3dL (3-2)
v s J
MW °
The particle concentration leaving the system is :
oo
N = £ n(L)dL (3_3)
If we define a mass average length L such that
L3 = JS(L)L3dL//S(L)dL (3-4)
m o / o
then Equation (3-2) may be written as
kvpsCU N
-------
3.2 Simulation of the Scrubbing System
While the system mass balance equations constrain the
weighted integral of the crystal size distribution, the residence
times and environments of the individual process units will
control the function n(L). At this point in the program, we
expect that individual models for the scrubber, hold tank, and
possibly the clarifier will be combined to predict the overall
particle size distribution for slurry leaving the system. This
approach will be more complex than developing "average" nuclea-
tion and growth functions for an entire system, but should more
closely describe reality. The flexibility of the model would be
improved by considering crystallization phenomenon in each process
unit. If model verification studies show that the impact of the
scrubber and clarifier on particle size distribution are negligi-
ble the model can be simplified accordingly.
The solution of the particle balance around each indi-
vidual process unit (scrubber, hold tank, and clarifier) involves
input from the other process units. The incoming distribution
must be known in order to calculate the outgoing stream. In a
scrubbing system, the feed to the scrubber is the effluent of
the hold tank. Conversely, the scrubber effluent enters the
hold tank. The clarifier overflow, which is a fraction of the
hold tank effluent, is also returned as part of the hold tank
feed. An accurate model of these distributions involves the
solution of several simultaneous differential equations. For a
complete description of the mathematical development of these
equations and the calculational scheme proposed by Radian to
obtain predicted particle size distributions, the reader is
referred to Radian Technical Note 200-187-11-03.
A-14
-------
One objective of the model verification portion of this
program will be to arrive at the simplest approach to the overall
simulation that will still predict observed data. Hopefully,
some simplifying assumptions can be applied that will reduce
computational time without decreasing the utility of the simula-
tion. These simplifying assumptions will probably center on the
nucleation and growth functions appearing in the particle balance
equations. In particular, the relationships between nucleation,
growth, and solution composition need to be as simple as possible
so that accurate simulations can be made without excessive nest-
ing of material balance and particle balance calculations.
Another important part of the overall simulation will
be arriving at a good initial guess for the calculated particle
size distributions. Field data may be very important in meeting
this objective.
In the following section the nucleation and growth
rate functions are discussed. The impact of various forms for
these on the overall simulation is also considered.
A-15
-------
4.0 NUCLEATION AND GROWTH FUNCTIONS
In this section, some possible forms for calcium
sulfite nucleation and growth functions are examined. Our
objective is to select a model that adequately describes these
phenomena in the scrubbing environment and can be easily re-
lated to system mass balances. A brief discussion of nucleation
and growth studies appearing in the literature is followed
by detailed examination of data for calcium sulfite precipita-
tion.
4.1 Nucleation
For purposes of this study, nucleation has been de-
fined mathematically as the rate of appearance of crystals of
"zero" size. Normally, all crystals of size L greater than
zero are considered to have been produced through the mechanism
of growth on nuclei. Appearance of crystals of non-zero size
via mechanisms other than growth (e.g. breakage) will not be
considered at this point.
Nucleation phenomena are traditionally separated into
three classes depending on the mechanism and circumstances
of particle formation (WA-339). These are:
a. Homogeneous - spontaneous formation of
solute particles from a clear super-
saturated solution,
b. Heterogeneous - formation of solute
particles from a supersaturated solution
in the presence of a second solid phase,
and
A-16
-------
c. Secondary - formation of solute particles
from a supersaturated solution in the
presence of existing solute particles.
A general t he rmo dynamic description of nucleation
phenomena was developed by Gibbs and modified by Volmer (MO-311)
For any phase change to occur, a net decrease "in free energy is
required. The total free energy change (AGrr,) for nucleation
is the sum of free energy changes associated with the volume
(AGr,) and the surface (AGS) of the solid phase:
AGT = AGS + AGy (4-1)
The surface free energy change, AG^, is assumed to be propor-
tional to the surface area of the nuclei:
(4-2)
For one mole transferred from the liquid phase to form solid
particles solid particles, the volume free energy change,
AGy, is equal to the difference in chemical potentials between the
solid and liquid phases.
AGV = -
-------
y = u + RTn a ^
s * sat
Thus, the volume free energy change may be written in terms
of solute activities by combining Equations 4-3, 4-4, and 4-5
AG = _ (y y ) = -RT£n - (4-6)
s sat
At equilibrium, the total free energy change between liquid
and solid phases must be zero. Thus, the equilibrium state is
described thermodynamically by:
RTJln - - + A a = 0 (4-7)
asat P
The surface area formed by one mole of precipitate may be deter-
mined by the volumetric and area shape factors :
MW k a
A = ' a (4-8)
P PL v
Combining Equations 4-7 and 4-8, we can see that the equilibrium
size of a nucleus, L , is related to the surface energy of the
solid phase and the activity or supersaturation of solute:
Lea = ° m -a <4~9>
eq k p RT£n
v s a
sat
According to Equation 4-9, an increase in the activity of the
solute will decrease the size at which nuclei are stable. At
a given level of supersaturation (a/ao .), particles smaller
S 3.U
than L will te'nd to dissolve while particles larger than L
will grow to become crystals.
Equation 4-9 describes the critical size at which a nucleus
begins to grow into a crystal. The rate at which nuclei of this
critical size appear should be proportional to the probability
A-18
-------
of their formation. The probability of formation is related to
the work of formation by an exponential function (KH-034). Thus
nQ = K exp f-(work)/RTj (4-10)
The work term in Equation 4-10 can be evaluated in terms of
the free energy change as the nucleus "grows" from zero size
to Leq:
L
eq
WORK = f AG_(3L2k p /MW)dL (4-11)
J
v s
The term in parentheses relates the change in number of moles
to the change in crystal size L. If the proper relationship
for AGrr, versus L is substituted into Equation 4-11 and the
integration carried out, the result is
_ 3 f,rr T 2
WORK = = k
27 "v p *rizilnza ~ (4-12)
s
a
sat
and the nucleation rate becomes:
(4-13)
n = K exp - (4=k Q3MW2) / (p2R3T3£n2a )
O I Z. I V S ^
L asat
Equation 4-12 predicts a very rapid rise in nucleation
rate with supersaturation. For example, Mullin summarized
Volmer's calculations for nucleation of water droplets in super
cooled vapor (MU-001):
A-19
-------
(nuclei/sec liter) r = a/a
So, L
1
10 68 2
_9
10 3
10 4
1013 5
The functionality of Equation 4-12 is consistent with the
appearance of "showers" of nuclei at certain "critical" levels
of supersaturation in various systems. The region of. super-
saturation below the critical level for nucleation is termed
the "metastable" region.
Attempts at experimental verification of Equation 4-12
for homogeneous nucleation have led to many complications.
Early work by Ting and McCabe (TI-006) showed that for nuclea-
tion of magnesium chloride, the critical supersaturation for
spontaneous nucleation depended on such things as the rate of
stirring and the rate of increase of supersaturation. Other
variable effects on "homogeneous" nucleation are summarized
by Khamskii (KH-034 ).
Experiments showing the effect of solid impurities in
a nucleating system led to the concept of "heterogeneous"
nucleation. The amount of work required to form critical
nuclei is apparently much less when other solid surfaces are
available. If the nucleating system is seeded with crystals
of the precipitating substance itself, "secondary" nucleation
takes place. This can occur at levels of supersaturation
approaching equilibrium. In typical industrial crsytallizers
where substantial slurry densities are maintained, secondary
nucleation appears to be the predominant mechanism for new
particle formation. (Strickland-Constable in ES-003).
A-20
-------
Clontz and McCabe (in LA-035) have demonstrated
some important aspects of secondary nucleation in a study
using single crystals of HgSO^'7E20. In their work, single
crystals of MgSO^yHaO were fixed in a flowing supersaturated
solution and struck with either a rod or a second crystal.
They found that the number of nuclei formed during crystal-
crystal or crystal-surface collisions was a function of both
supersaturation and the energy dissipated in the collisions.
A correlation of the form:
f=k1(r-l)E (4-14)
c
was proposed where N is the number of nuclei produced by a
crystal-crystal collision. A_ is the surface area involved in the
collision, E is the contact energy, and r is the relative satura-
tion (a/a ,_) . For contact of crystals with other solid surfaces,
sai.
the number of nuclei generated was less but still significant.
A slightly different correlation form was found:
(4-15)
The actual number of nuclei produced by single
collisions in Clontz and McCabe's study ranged from zero to
approximately 600. The region of supersaturation studied was 0-12%,
and contact energy ranged from 10 to 2600 ergs. The nucleation
mechanism did not appear to require a critical level of either
supersaturation or contact energy.
In an extension of this initial work on single-crystal
secondary nucleation, Johnson et.al. (in ES-003) demonstrated
that the number of nuclei formed in crystal-surface contacts
depended on the hardness of the surface used. The initial
experiments had been conducted using a stainless steel rod.
A-21
-------
Further tests xvith soft rubber and hard polypropylene yielded no
detectable nucleation at comparable levels of supersaturation and
contact energy. This observation could be of substantial impor-
tance in situations where low levels of secondary nucleation
are desired.
Other investigators have studied secondary nucleation
phenomena in experimental situations more closely related to
continuous mixed-suspension crystallizers. Cise and Randolph
(ES-003, RA-432) measured secondary nucleation in agitated
suspensions of KaSOi* with a continuous-liquid/batch-solids
reactor. An empirical correlation of their data showed that
the nucleation rate was proportional to supersaturation to the
.56 power, seed crystal size to the 4.1 power and stirrer speed
to the 5.78 power. The strong dependence of the secondary nu-
cleation rate on stirrer speed and crystal size is consistent
with a mechanism which depends on the energy of stirrer/crystal
collisions.
Rousseau, et.al. (in RO-344) studied the-, effects of crystal
size on nucleation rate using MgSCU«7H20 crystals. When a single
seed crystal was placed in an agitated vessel, nucleation oc-
curred only for crystals larger than approximately 200 microns.
Above this lower limit, the secondary nucleation rate increased
exponentially with seed crystal size.
Ness and White (in RO-344) also studied secondary
nucleation effects with MgSOi>-7H20 crystals. They counted the
number of nuclei produced in an agitated suspension of closely-
sized crystals. At a given impeller speed and supersaturation,
the observed nucleation rate was directly proportional to the
number of seed crystals. This is consistent with a mechanism
dependent on crystal-impeller contacts rather than crystal-
crystal collisions. Their slurry density was very low, however;
about .5 grams solids/liter. Thus the importance of
A-22
-------
crystal-crystal collisions at higher slurry densities was not
ruled out.
The effects of stirrer speed and crystal size observed
by Ness and White were similar to other studies. The nucleation
rate was proportional to the fourth power of both stirrer speed
and crystal size. The observed effect of supersaturation on
nucleation rate in this study was substantially greater than seen
in previous work, however. An exponent of 2.5 was used to fit
their data.
When the steel impeller used for most of their experi-
ments was replaced with polypropylene, nucleation was reduced
by up to a factor of ten. Furthermore, the effect of the
number of seed crystals increased over the linear relationship
noted for the steel impeller. The influence of crystal-crystal
collisions was thought to account for this increased dependence
on slurry density.
The significance of secondary nucleation in lime/lime-
stone wet scrubbing systems has yet to be established. Clontz
and McCabe point out that in order to satisfy the particle balance
constraint in a continuous crystallizer, it is only necessary
for each crystal in the system to provide one nucleus before
it leaves the system. Since mean solids residence times in
lime/limestone scrubbing systems are typically on the order of
one day, even a very low collision probability and nucleation
rate would suffice.
The crystal size necessary to produce a collision
energy on the order of 10 erg may be estimated for calcium
sulfite. Assuming a shape factor k = .025 based on length,
the mass of a sulfite crystal of length L will be:
A-23
-------
m(grams) = PS -025 L
3 (4-16)
= .06L3
The maximum approach velocity for a collision with
an impeller will be on the order of 100 feet/sec or 3000 cm/sec
An erg is equal to one gram cm2 /sec2. To produce a collision
energy of 10 ergs :
10 gm cm2/sec2 = %4V2 = .03L3(3000)2 (4-17)
Solving Equation 4-17 for L yields Lmin^ °3 cm or 30° microns.
The maximum observed size for sulfite crystals in lime /lime stone
wet scrubbing processes is about 100 microns . Contact energy
for a 100 micron crystal would be on the order of 0.4 erg.
This is substantially less than the contact energy studied by
Clontz and McCabe, but secondary nucleation remains a possibility,
particularly since the sulfite supersaturations in limestone
scrubbing systems are up to 30 times the range considered by
Clontz and McCabe and can be even higher for lime systems. In
fact, the phenomena discussed above could well make production
of large sulfite crystals impossible under realistic process
conditions.
The discovery of the importance of secondary nucleation
at moderate to low supersaturations has precluded the use of
classical nucleatiori theories in industrial crystallization.
Nearly all recent quantitative studies of nucleation kinetics
in agitated suspensions have used simple "power law" correlations
of the form:
A-24
-------
n = kr m-* (nuclei/sec liter) (4-18)
o g
In Equation 4-18, r is the relative supersaturation and m
S
is the slurry solids content. This type of correlation can be
used to express observed effects of slurry density and super-
saturation, but must be used with care because of its obvious
empirical basis. In particular, one would not expect this type
of correlation to be useful over a wide range of supersaturation,
since the mechanism of nucleation changes from secondary to
heterogeneous to homogeneous as supersaturation increases. Also,
Equation 4-18 does not explicitly include the well documented
effect of crystal size on nucleation rate. The "constant"
kin Equation 4-18 will also depend on other factors influencing
the quality and quantity of crystal collisions, such as impeller
speed.
For simulation of systems where large changes in
supersaturation occur, a correlation which includes both secon-
dary and homogeneous nucleation effects seems desirable.
This will probably be the case for lime scrubbers and possibly
for limestone scrubbers. An expression which sums the effects
described by Equations 4-13 and 4-18 would be:
n (particles/liter-sec) = (nR)T = ki (r-1) m 1LJ + k2exp -k3/£n2r (4-19)
o IrK) s n I
In Equation 4-19, Ln, the number average crystal size has been
added as an explicit parameter. The constants would be
selected based on experimental data. At present, little informa-
tion is known about the source of nuclei in lime/limestone
scrubbing systems. Thus, explicit terms describing energy input
to the nucleation source have not been included in 4-19. It
should be recognized that the nucleation rate may depend on such
things as agitator or pump impeller speeds and materials of
construction.
A-25
-------
Recalling Equation 3-4, the combined mass balance
and particle balance for the scrubbing system is:
(3-4)
This states that the mass mean particle size for the system is
completely dependent on the nucleation rate under the constraint
of constant S02 removal. Thus, correlation of nucleation rates
may be the most important aspect of the current modeling effort.
It should be noted, however, that nucleation rates and growth
rates are coupled for a given system by their mutual dependence
on relative saturation. Thus, the form of the growth rate
expression is also important.
4.2 Crystal Growth
Once nuclei larger than the initial size have been
formed in a supersaturated solution, they will grow to form
macroscopic crystals. The relationship between growth rate,
crystal properties, and solution properties has been the subject
of many studies reported in the literature. The results of these
studies have not supported any one specific concept of crystal
growth kinetics. Instead, a large number of difficult-to-explain
variable effects have been noted. Most problems in experimental
data analysis are thought to result from using macroscopic
models to describe events taking place at an undefined crystal/
solution interface. Some established aspects of crystal growth
kinetics are outlined below.
In order for a crystal to grow, the ionic or molecular
components of the precipitating substance must first diffuse
from the bulk solution to the solid-liquid interface and then
A-26
-------
be incorporated into the crystal lattice. The overall rate of
crystal growth may be limited by diffusion, surface reaction,
or both.
The diffusion step is conventionally described by the
product of a mass transfer coefficient, the crystal surface
area, and a concentration driving force:
G (mole/sec) = t^ACCi) (4-20)
In equation 4-20, 1^, the mass transfer coefficient is a function
of the diffusivity of the species of interest and the hydrodynamic
conditions that affect the fluid boundary layer near the crystal
surface. A is the crystal surface area. The driving force term
^Cb~CP is the difference between the solute concentration in the
bulk phase and at the solid-liquid interface.
Levins, et al, (LE-305) have conducted an extensive
review of solid-liquid mass transfer rates in agitated vessels.
Their own experimental data were used to arrive at a general
correlation for predicting 1^ as a function of important system
variables. For small particles (<100y) with specific gravity
less than three, the proposed mass transfer correlation is:
_
D \ U / \Dt
.36 (4-21)
In equation 4-21, D is the diffusivity of the solute, E the
agitation power per unit mass of slurry, o the kinematic
viscosity, and Ds/Dt is the ratio of stirrer and tank diameters.
For a given solid liquid system with fixed mechanical configura-
tion, Equation 4-21 may be simplified:
2 + aL'82 (4-22)
A-27
-------
Equation 4-22 shows that 1%, the mass transfer coefficient
increases as particle size decreases. In the limiting case
of very small particles, the second term on the right hand
side of 4-22 goes to zero and
_ (4-23)
D
This equation is exactly true for diffusion through a stagnant
liquid surrounding the solid particle.
The mechanism and kinetics for integration of ions
ir.to the crystal lattice are less well understood than the diffu-
sion step. As a result, there is no consistent approach in the
literature for predicting the rate of surface reaction. Khamskii
(KH- 034) summarizes several of the more important theoretical
approaches to crystal growth kinetics. Buckley (BU-090) and
Nielsen (NI- 001) review a wide range of experimental data for
various systems in their comprehensive discussions of crystal
growth. The rate of the surface reaction is generally held to
be a function of temperature, solution composition, and surface
characteristics of the crystals.
Many experimental investigators (CO-020, DA-006,
IS-001, LU-006,MC-012, NA-015, NA-016, GA-236) have used an em-
pirical rate expression of the form
k°a(C " °s) = k0a(r~1) mole/£-sec (4-24)
to correlate overall rates of crystal growth in supersaturated
solutions. Since the rate of bulk diffusion depends on agitation
parameters but the surface reaction rate does not, experiments
A-28
-------
at different levels of agitation can be used to distinguish
between these two possible rate-controlling mechanisms. As would
be expected, the overall rate constant k for a given crystal-
lization system can exhibit variable effects typical of diffusion
or surface reaction depending on the particular levels of tem-
perature and agitation studied. The exponent, p , of the driving
force term in Equation 4-24 will be 1 for the diffusion limited
case but may be greater than 1 for cases where the surface
reaction rate is important.
If the surface reaction rate is found to be first order
with respect to supersaturation, (p=l), then a combined expression
may be written for the overall reaction rate using the individual
rate constants for mass transfer and surface reaction:
G = k a(C - C ) = a(C - C ) = a(r-l) (4-25)
m ° s 1/k + 1/k s l/k'+l/k'
ro r m r
In this expression, k will be a function of the variables in-
cluded in Equation 4-21 while k is normally assumed to be a
function of temperature only.
The term a in Equation 4-24 is related in some manner
to the. surface properties of the crystal. For a diffusion-limited
system, a would be equal to A , the crystal surface area. ?or the
surface reaction, the situation is unclear. Many engineering
studies, particularly those using the MSMPR approach of Randolph
and Larson have assumed that the surface reaction rate is also
prcpcrtional to crystal surface area. This is equivalent to
assuming that the linear growth rate is independent of particle
size; the so-called "McCabe AL Rule" (CA-003). On the other hand,
several recent investigators have reported systems where the
linear growth rate due to surface reaction is strongly size
dependent (GA-234, WE-331, GA-236, PH-050). Specifically, the
surface reaction rate was observed to decrease with crystal size
A-29
-------
for nickel sulfate, and potassium sulfate. A size dependent
surface reaction rate could be included in Equation 4-25 by
developing a suitable correlation for kr versus crystal size.
This would allow the use ofa= A for both diffusion and surface
P
reaction.
Cise and Randolph in their previously discussed study
of secondary nucleation also estimated the linear growth rates
of very small K2S(\ crystals using measured size distribution
data. Growth rate was found to increase rapidly with crystal
size. Crystals in the 2-3 micron range grew only one tenth
as fast as those larger than 25 microns . They point out that
this effect is opposite to that which might be expected from dif-
fusion limited mechanism even if the effect of increasing solu-
bility with decreasing crystal size is considered. An empirical
correlation of their data showed that:
k = k exp (-k//L) meter/sec (4-26)
In a later study, White, et.al. (in RO-344) confirmed
the strong size dependence for growth rates of K2SOu crystals.
They suggested a growth rate expression of the form:
kr/kr = 1 + 2L2/3 (4-27)
o
Larson and Bendig (in RO-344) on the other hand, were unable to
detect a size-dependent growth rate for MgSO^-yHaO crystals.
Whatever the observed form of the relationship between
growth rate and crystal size, some care must be exercised in
applying empirical correlation for use in particle balance
calculations . Wey and Terwilliger (WE-331) have discussed
A-30
-------
application of various growth rate expressions appearing in the
literature. They caution that the system mass balance requires
the integral of individual particle growth rates over all particle
sizes to be equal to the total precipitation rate:
CO
k P f
(mole/liter sec) = ^- |n(L) L2R(L) dL (4-28)
total MW
If R(L) is infinite as L -> o or L -> °°, then the integral in
4-28 may not converge. Also, if R(L) is zero as L -> o, it is
obvious that nuclei cannot grow to form macroscopic crystals.
4.3 Experimental Data for Calcium Sulfite Precipitation
Data describing the precipitation kinetics of calcium
sulfite in lime/limestone wet scrubbing systems are available from
several sources. These data are summarized and discussed below.
Our objective is to quantify, to the extent possible, the nucleation
and growth rates of calcium sulfite as a function of the variables
discussed in Sections 4.1 and 4.2. Gaps in existing data will
be pointed out so that they may be addressed in the test plan por-
tion of this program.
The earliest reported data for growth of CaS03-% H20
crystals are those reported by Ottmers, et.al. (OT-023) under EPA
contract 68-02-0023. Overall growth rates for an agitated suspension
of seed crystals were measured in a continuous-liquid, batch-solids
reactor. Supersaturated solutions were prepared by mixing Na2S03
and CaCl2 feed streams. For supersaturations below 3 x K , the
overall growth rate was correlated by:
Rate (mole/min-gram) = 1.2 x 1C exp (-21,000/RT)(r-1) (4-29)
A-31
-------
At low supersaturations these sulfite crystals assumed the familiar
flat platelet habit with a length/width/thickness rates of roughly
30:20:1. For supersaturations above 3 x K , the growth mechanism
sp
changed to surface nucleation and the overall growth rate increased
rapidly. Crystals grown at high rates showed a multi-directional
dendritic habit and tended to form agglomerates.
The overall growth rate was unaffected by stirrer speed
and was estimated to be less than one fourth that expected for
difussion limited growth. No apparent change in overall growth rate
was observed during experiments where the mass average size of the
initial seed charge increased by ^40%. Nucleation was not observed
in these experiments at supersaturations below 3 x K .
sp
Results of a series of pilot scale lime/limestone wet
scrubbing tests were also reported by Ottmers (01-023) . The tests
were conducted using a pilot-scale scrubbing system built by
Combustion Engineering Company. Overall growth rates for calcium
sulfite* were calculated using liquid phase or solid phase
material balances across the major process vessels in a more
realistic scrubbing environment. The process arrangement consisted
of a one or two-stage marble bed scrubber with a cross-sectional
2
area of 25 ft followed by a 6000 gallon effluent hold tank and a
20,000 gallon clarifier. Two major test series were conducted;
the first using boiler calcined lime introduced with the flue gas,
and the second using commercial limestone added to the effluent
hold tank. Results for the lime and limestone test series are
summarized in Table 4-1.
Figure 4-1 compares early laboratory results with these
pilot-scale observations. On the graph, all data have been adjusted
to equivalent rates a.: 45°C on the basis of the exponent in
* The actual precipitating crystals were most likely
Ca(S03), v- (SOOV'%H20 in this case.
1 A. A
A-32
-------
X
i cd
w U
.,-1
o
0)
PM
QJ 100 -
4 1
H
iii
rH 80
cn
60
40
20
0
V *-" * -*-& J_L1(-1 _U J-Jtilj'kj'i.tAW-'^-y IX - Lime - RTF
+ - Limestone - RTF
f
I
.
1
/
/
/
y
/
/ PP&L data (40 points)
Least Square Fit
/ <$> Corrected to 45 C <£>
1^23 4 5 6 7 8 9 10 11
Sulfite Relative Saturation
Figure 4-1. Comparison of Calculated Sulfite Precipitation Rates for Lime and Limestone
Scrubbing Systems.
-------
TABLE 4-1. RESULTS OF IJMF./LIMESTONE SCRUBBING TESTS AT COMBUSTION ENGINEERING PILOT UNIT*
Test No.
18-1
18-2
19-1
19-2
20-1
20-2
> 21-1
CO 22-1
"* 1A-1
2 A- 2
3A-1
1B-1
2B-1
2B-2
Hd.Tk. Vol.
Reactant (liter)
Ltme
Lime
Lime
Lime
Lime
Lime
Lime
Lime
Limes t.
Llmest.
Llmest.
Limes t.
LJmest.
Llmest.
22,700
22,700
22,700
22,700
22,700
22,700
11,350
20,000
22,700
22,700
22,700
22,700
22,700
22,700
Tot. Solids
in Slurry
(Em/1)
46
38
14
15
7.4
6.7
84
91
77
66
82
64
88
93
Liquor pH
Scr. Hd.Tk.
6.0
6.0
4.6
4.8
4.6
4.6
5.6
6.0
5.3
5.2
5.3
5.7
5.6
5.6
10.7
10.6
5.4
5.5
5.7
5.7
8.5
5.6
6.0
6.1
6.0
6.3
6.0
6.0
Liq.Temp.
46
46
39
39
40
40
45
46
48
47
49
50
51
50
Calcium SulTIte
Sulfite Solids Cal. Sulflte Precipitation Rate In
in Slurry Rel. Saturations Hold Tank
(gm/1) Scr.** Hd.Tk. (g rao]e/gm-mln)
14
11
3.1
3.0
1.5
1.2
25
28
27
28
35
26
38
41
5-8
7-11
3-5
4-7
2
2-3
4-6
5
11
8.6
9.6
13
6.3
6.7
2.7
4.4
9.9
11.4
7.8
10.4
3.0
4.0
3.5
4.8
8.4
5.9
4.9
4.2
5.7 x
9.6 x
7.8 x
.7.3 x
1.2 x
1.0 x
4.6 x
1.9 x
6.5 x
1.4 x
1.3 x
1.4 x
9.4 x
1.1 x
-6
10
-6
10
-5
10
-5
10
-It
10
10
-f,
10
10
-(,
10
10
-5
10
-5
10
10
- 5
10
* Boiler-calcined lime introduced via flue gas stream, Limestone introduced via hold tank.
** Range of calculated relative saturation for observed pH range.
-------
Equation 4-29. At low supersaturations, the lime and limestone
data are roughly comparable and correspond to a rate constant of
^7 x 108 versus 1.2 x 1010 for the laboratory data. No good ex-
planation for this factor of 17 difference is available. It
should be noted that the results are reported on a "per gram" of
seed crystal and not on a "per cm2" of seed crystal area basis.
At higher supersaturations, precipitation rates for the lime
system increase rapidly. The level of supersaturation at which
this occurs is much greater than the 3 x K limit observed in
sp
the laboratory study however.
Borgwardt has reported a large number of lime and lime-
stone scrubbing experiments in a series of EPA progress reports.
(BO-146, BO-247). Several sets of results from this pilot unit
have also been included on Figure 4-1 for comparison to the data
discussed above. Pertinent calculated results based on reported
data for this pilot unit are summarized in Table 4-2. Calculated
calcium sulfite precipitation rates for the limestone system are
comparable to other reported pilot unit data. Precipitation rates
per unit mass of seed crystals for the lime system are more scat-
tered and again some points lie considerably above the limestone
data.
Additional pilot scale measurements of calcium sulfite
precipitation rates were obtained by Phillips, et al. , during
Radian Corporation's large pilot-scale limestone scrubbing study
at Pennsylvania Power and Light Company (internal Radian report).
This unit was a high L/G spray tower operating at 80-90% S02 re-
moval when treating 300 tn3/min. of gas with inlet S02 levels near
2,000 ppm. For most of the test program, the hold tank volume
for this unit was approximately 60,000 liters and the slurry
solids content was maintained at 10 weight percent. The scrubber
effluent pH ranged typically from 5-5.5 while the hold tank pH
was normally about 6.0. Calcium sulfite relative saturations
A-35
-------
TABLE 4-2. RESULTS OF LIME/LIMESTONE SCRUBBING TESTS AT EPA/RTP PILOT UNIT
Test Date
(1973)
1/18
1/19
1/23
10/16-19
10/19-23
10/29-11/2
11/26-30
12/10-14
Reactant
Limestone
Limestone
Limestone
Lime
Lime
Lime
Lime
Lime
Hd.Tk. Vol.
(liter)
300
300
300
370
370
370
370
370
Tot. Solids
in Slurry
(gm/1)
176
176
176
41
41
95
106
106
Sulflte Solids
Liquor pH In Slurry
Scr. Hd.Tk. (gm/1)
5.8
5.6
5.7
4.8
5.0
4.9
5.0
6.0
6.3
6.2
6.3
6.0
6.7
7.0
7.1
8.4
50
80
65
35
35
86
82
8.1
Cal. Sulflte
Rel. Saturations
Scr. Hd.Tk.
6.
6.
5.
2.
6.
4.
8.
10.
7
8
9
2
1
1
2
5
Calcium Sulfite
Precipitation Rate
In Hold Tank
(g mole/gm-min)
1.
1.
1.
6.
8.
3.
2.
2.
6 x
2 x
7 x
9 x
3 x
1 x
9 x
4 x
-5
10
- 5
10
~ 5
10
_ 5
10
-5
10
-5
10
-5
10
-5
10
-------
ranged from 2 to 6 with most tests falling in the 3-5 region.
A least squares fit of more than forty steady-state closed loop
tests is shown by the dashed line on Figure 4-1. These data are
in close agreement with data taken at comparable levels of super-
saturation at the other pilot units.
As a final check on the magnitude of sulfite precipita-
tion rates in a full-scale scurbbing unit, some recent test data
obtained by Radian during EPA's current Louisville Gas and Electric
test program were used. This unit is a full-scale Combustion
Engineering design using a two-stage marble bed scrubber followed
by a hold tank with a capacity of approximately 106 liters.
During normal operation, scrubber effluent liquor is
introduced to the hold tank via a small "draft tube" section of
approximately 10 "* liters capacity. The lime additive is also
added to this small section of the tank and pre-mixed with the
scrubber effluent before entering the main tank. During the EPA
test series at this unit the piping and tank arrangement was
modified so that the additive could be introduced to the main
tank rather than the draft tube. Also, the main tank could be
eliminated completely so that the entire precipitation reaction
would be forced to occur in the small draft tube section.
Table 4-3 summarizes tests for this lime scrubbing
system. Calculated precipitation rates are shown for both the
draft tube and main sections of the hold tank where applicable.
According to the data, nearly all of the observed sulfite precipi-
tation occured in the draft tube portion of the hold tank even
in tests where the lime additive was added to the main portion
of the vessel. As a result, calculated values for calcium sulfite
precipitation rate per unit mass of seed crystals are five to ten
times those observed at either the CE/Windsor pilot unit of EPA/
RTF unit when using lime. In the final two tests shown, the
the major portion of the hold tank was physically isolated from
A-37
-------
TABLE 4-3. RESULTS OF LIME SCRUBBINC TESTS AT LOUISVILLE RAS AND ELECTRIC
Tank Volumes
(liter)
\
OJ
OO
Tost Date
7/7/77*
7/B/77*
7/26/77*
8/1/77**
8/8/77**
8/22/77*
8/2')/77*
Hold Tank
9.
9,
9.
9.
9.
. 6xios
. GxlO5
6xlOs
,6xll)5
. 6x1 O5
not In use
not In use
Draft Tube
1
1
I
1
1,
1.
1.
. 1x10"
.1x10"
.1x10"
.1x10"
, IxlO'1
1x10*
,ixio"
Total Solids
In Slurry
Liquor pi!
(gram/liter) Scrubber
43
45
74
84
58
59
73
6
6
6,
6.
5,
5.
5.
.1-7
.3-7
.0-7
.1-7
.1-5
.9-6
,6-6
.1
.2
.2
.0
.6
.9
.8
Hold Tan1
7.9
7.9
8.0
8.1
8.5
7.9
7.5
Liquor Temp.
k °C
5C-53
50-53
5C-53
49-52
51-53
51-52
50-53
Sulflte Solids
In Slurry
Calcium Sulflte
Relative Saturation
(gram/liter) Scrubber
35
36
60
68
47
48
59
2.1-2
2.6-2
1 .7-2
2.1-2
1.3-3
2.5-3
1.4-2
.5
.9
.1
.8
.6
.2
.9
Calcium Sulflte
Precipitation Rate
Onole/gram-minxlO )
Hold Tank Draft Tube
Hold Tank Draft Tube
2.5 3
2.8 3
2.3 3
1.7 2
3.7
4
3
.2
.2
.6
.6
^
.2
.5
vl) 980
^0 1450
<0 RIO
2.7 240
1- t
850
670
I Insufficient data
* Lime added to draft tube
** Lime added to hold tank
-------
the draft tube section. In this case, the high calculated pre-
cipitation rates should be correct in spite of the difficulty of
obtaining a representative sample from the draft tube effluent.
It should be emphasized at this point that the above
comparison of measured calcium sulfite precipitation rates has
not included information regarding the size distribution of the
seed crystal mass in suspension. If the linear growth rate, R,
is constant with crystal size, then the molar growth rate per
unit mass of crystals should be inversely proportional to the
crystal size:
k p
v s
G (mole/gram min) = __. f n(L)L2RdL (mole/liter-min) (4-30)
g MW J
o
k p / n(L)L3dL (grams/liter)
\T O *
S
O
If R increases with size as suggested by some of the previous
work discussed in Section 4.2, then the molar growth rate per
unit mass would be less sensitive to changes in size.
Some qualitative information on the effect of crystal
size on growth rate for calcium sulfite is available as a result
of work conducted at Radian Corporation under EPA contract
68-02-1883 (JO-R-214 ). A series of bench-scale experiments
was conducted to investigate variables affecting the composition
of sulfite/sulfate coprecipitate formed in lime/limestone wet
scrubbing systems. The size distribution of the growing crystals
was not of specific interest in this work, but photomicrographs
were taken of product crystals from several kinetic experiments
to document the presence or absence of gypsum. Figures 4-2a
and 4-2b are photographs of product crystals from Runs K-13
and K-20. Even though there appears to be a dramatic difference
in the crystal size distributions for these two experiments, the
A-39
-------
RUN 13
4-2a
10X20
RUN 20
4-2b
10X20
FIGURE 4-2 COMPARISON OF SEED CRYSTAL SIZES FOR
TWO LABORATORY EXPERIMENTS HAVING SIMILAR MOLAR GROWTH RATES.
-------
reported molar growth rates per unit mass of solids were comparable
This observation implies that the linear growth rate of the small
crystals is much less than that of larger crystals.
The effect of crystal size on the linear growth rate
can also be inferred from the shape of the product crystal size
distribution. If the scrubbing system approximates MSMPR crystal-
lizer conditions, Equation 3-12, the particle balance for a well
mixed vessel can be simplified to yield:
~ d(nR) = n
dL T (4-31)
where T is the mean solids residence time in the system. After
multiplying the right side by R/R, the variables may be separated
and the equation integrated.
d(nR) = -dL
~rtT~ IF (4-32)
/R \ r i
lo \ -1 f
n = no\R07/ exp[T J
L j
dx
(4-33)
Examination of equation 4-33 shows that the number of particles of
size L is directly related to the number of zero size particles.
The ratio of R to R(L) based on experimental observations is less
than one. This is due to faster growth rates for larger crystals.
Even if the growth term continues to increase with size, the ex-
ponential term will limit the number of larger particles seen in
a size distribution.
Equation 4-31 can also be expanded to isolate the term
dln(n).
d ln(n) = d ln(R) - 1
~dL ~dL
A-41
-------
If the linear growth rate is constant, = 0 , then a plot
of In n(L) versus L should be a straight line with slope equal to
- . If the growth rate increases with size, (^ ^ j > 0 then
RT
the curve will be concave upward.
Figure 4-3 shows size distributions for product crystals
from the LG&E lime and PP&L limestone scrubbing systems calculated
from Coulter Counter data. Both distributions are clearly concave
upward, indicating an increasing growth rate with increasing size.
Equation 4-32 can be rearranged to calculate the
growth rate R using the slope of the size distribution:
I + IE
R = - T dL (4-35)
d(lnn)
dL
The change in growth rates with crystal size indicated by the
data in Figure 4-3 can be estimated by approximating the size
distribution with the straight lines indicated on the figure.
Along these lines, dR/dL = 0, and
R - - - - (4-36)
dL
For the lime data from LG&E, T was approximately 1300 minutes.
Using this number and the slopes of the indicated lines:
- 1 o
R ,, = 2.4 x 10 meter/min
-9
Rlar = 2.2 x 10 meter/min
Thus, the larger crystals grow about ten times faster than the
smaller crystals. This is consistant with our previous observa-
tions that the molar growth rate per unit crystal mass appears
to be independent of crystal size over the range of interest.
A-42
-------
107
10s
10s
10*
-------
The above discussion suggests that changes in particle
size distribution should not cause large changes in precipitation
rate per unit mass of seed crystals. In this case, an alternate
explanation for the widely different rates observed for lime
systems must be found. One possible mechanism for the extremely
high precipitation rates calculated for the lime system at LG&E
would be the existence of locally high supersaturation in the
liquid phase due to additive dissolution. The tendency for this
to occur should be far greater in a lime system than a limestone
system since the lime additive is much more reactive and more
soluble than limestone. Thus, results from different pilot
units would be similar for limestone systems, as observed, but
would depend on certain aspects of the liquor composition and
additive arrangement in the lime systems.
Some evidence is available to support the hypothesis
that precipitation rates in lime systems are influenced more by
localized conditions than by bulk liquor supersaturation. Table
4-4 summarizes reported liquor compositions and calculated pre-
cipitation rates for lime tests at EPA's RTF pilot unit and the
LG&E full-scale system. As previously noted, the calculated
sulfite precipitation rates for the LG&E system are ten to twenty
times those observed at the RTF pilot unit at comparable levels
of bulk supersaturation. A substantial difference in the liquor
composition between these two sets of tests is evident, however.
During this period at LG&E, the magnesium content of the liquor
was maintained at a relatively high level, causing the dissolved
calcium concentrations to be lowered. Under these circumstances,
one would expect any effects due to localized additive dissolution
to be maximized since large relative increases in calcium con-
centration are possible.
Equilibrium calculations have been used in a previous
study (HA-696) to estimate the maximum calcium concentration and
A-44
-------
TABLE 4-4. COMPARISON OF LIQUOR COMPOSITIONS AND PRECIPITATION RATES FOR TWO LIME SCRUBBING SYSTEMS
>
Ln
Liquid Phase Composition (mole/liter) Sulf ite Relative
System Test Date
RTF 10/16/73
10/19/73
10/29/73
11/26/73
12/10/73
LG&E 7/7/77
7/8/77
7/26/77
8/22/77
8/29/77
Ca
.016
.011
.0053
.016
.017
.0013-18
.0014-19
.0010-16
.0010-15
.0020-30
Mg
.0054
.024
.047
.034
.017
.17
.17
.14
.13
.14
Cl
.0076
.0096
.013
.015
.011
.006
.007
.02
.01
.08
S02
.0017
.0040
.0057
.0041
.0038
.05
.05
.05-. 07
.05-. 06
.03-. 05
Saturation
2.2
6.1
4.1
8.2
10.5
3.2
3.2
3.6
4.2
3.5
Sulf ite Precipitation
(Rate (raole/grara-min)
6.9xlO~5
8.3xlO"5
3.1xlO~5
2.9xlO~5
2.4xlO~5
9.8xlO~"
1.4xlO~3
S.lxlO'1*
S.SxlO'11
6.7x10^
-------
sulfite supersaturation attained by saturating a scrubbing liquor
with lime. A calcium concentration of .03 mole/liter would be
near the solubility limit for lime in scrubbing liquor. Thus,
lime dissolution in a high magnesium liquor where the bulk
concentration of dissolved calcium is only .001 mole/liter
could lead to much higher localized precipitation rates than in
a liquor where the bulk concentration is already .015 mole/liter.
If this effect is significant, mixing differences between pilot
scale and full-scale units might also be important. Explanation
of these substantial differences in precipitation rates among
lime systems will be one important objective of the proposed test
plan.
Another, and perhaps the most important objective, will
be to determine the nucleation rate function. Existing literature
on this subject is sketchy at best. Some qualitative relation-
ships have been observed, however, and the test plan will attempt
to quantify these observations.
The TVA Report, Lime/Limestone Sludge Characterization
-- Shawnee Test Facility (CR-163) possibly comes the closest to
determining nucleation rates in a scrubbing system. No firm
conclusions are offered, however, several observations are made.
First, in limestone systems, the average particle size is noted
to decrease with higher stoichiometry. For better filtration and
clarification, the stoichiometry should approach 1. This would
indicate that stoichiometry, which influences the relative satur-
ation, also affects nucleation. The less excess calcium present,
the lower the chance of nucleation occurring.
Solids surface area measurements made by TVA show an
average of 5.4 square meters/gram for lime crystals and 3.3 for
limestone. At this time TVA has not correlated this measurement
with process variables. This could potentially provide some
indication of the relationships involved.
A-46
-------
The Aerospace Report, Disposal of By-Products from
Non-Regenerable Flue Gas Desulfurization Systems: Second Progress
Report (RO-362) deals mainly with the leaching of trace elements
from sludges. The most important process variable for trace
element leaching was determined to be scrubber pH. Physical
properties of solids studied were permeability, pumpability,
bulk density, compaction, and compressive strength. No data or
correlation was given with these measured properties and process
variables.
Some photomicrographs for nine different scrubbing
systems are shown in the Appendix of the Aerospace Report. These
are meant to be representative samples from typical operation,
however, and cannot be used to determine a correlation between
operating parameters and particle size since sufficient quanti-
tative data are not reported.
The Final Report, Dual Alkali Test and Evaluation Pro-
gram (LA-324), prepared by A. D. Little, is also primarily
concerned with leaching effects. Only three solid samples were
analyzed, one from a concentrated dual alkali sludge, a dilute
alkali sludge and a limestone sludge. The usual bulk physical
tests were made. Even if the nucleation rate had been determined
with only one data point from each system no relationship could
have been derived including all the process variables which
influence crystal size.
These reports and other literature which has been
examined have failed to yield data from which nucleation rates
can be calculatd. In even fewer instances, process variables
have been connected with resultant sludge properties. For this
reason, the first step in optimizing sludge quality will be
detailed investigation of relationships which have only previously
been qualitatively observed. The first phases of the test plan
A-47
-------
are geared therefore to providing a quantitative understanding
of calcium sulfite nucleation and growth.
A-48
-------
5.0 SUMMARY AND RECOMMENDATIONS
A mathematical approach to predicting calcium sulfite
crystal size distributions in lime/limestone wet scrubbing sys-
tems has been formulated. The model is based primarily on the
particle balance theory of Randolph and Larson. A size distri-
bution n(L) is defined such that the number of particles per
unit volume of slurry in a small size range L is equal to the
product n(L) L. The general partial differential equation for
n as a function of size L and position (X,Y,Z), is:
- IL (nR) + G = Ix
-------
liquor composition in a vessel where precipitation takes place
may be related to the inlet liquor compositions by a mass balance
for the components of interest:
Precipitation Rate ^ - IQ.n Cin - IQ^C^ - JnL2RdL (5-2)
o
In Equation 5-2, C is the liquid phase concentration of" the
precipitating species and k is a constant relating crystal
surface area to the square of the linear dimension L.
The overall modeling problem requires simultaneous
solution of the mass balance and particle balance for each pro-
cess vessel where precipitation (or dissolution) takes place.
To perform this computation, a relationship between growth rate,
nucleation rate, and conditions in the vessel are required.
A literature survey was conducted to determine the
expected form of the nucleation and growth functions. Process
variables expected to influence nucleation include relative
saturation, slurry solids content, crystal size, and energy
dissipation rates in pumps or mixers. An empirical correlation
of the form:
* h i i
n (particles/liter-sec) = (nR) = ki (r-1) m LJ + kaexp
~+
o L~+o s n
(4-19)
is suggested for the nucleation rate. In this equation, r is
the relative saturation, mg the slurry solids content, and L
the number average crystal size. No experimental data are
available at this time to determine the values of the exponents
h, i, and j, or the constants ki, k2) and k3.
Some data describing the total average nucleation rate
in lime and limestone systems were expected to be derived from
A-50
-------
particle size distribution analysis of slurry samples from
operating units. Optical size distribution data suggest that
lime and limestone scrubbing solids contain on the order of 109
particles per gram. Coulter Counter data for the same samples
show particle counts in the range of 1011 particles per gram
(see Radian Technical Note # 200-187-11-2 for further discussion
of these results). Until the discrepancy between these two
methods is resolved, an average nucleation rate of 1010 particles
per gram of sludge produced can be used in the modeling effort.
For crystal growth a general rate equation of the form:
R(meter/sec) -* + 1/fc (r-l)P (5-3)
m r
is suggested by the literature. Experimental data from labora-
tory and pilot scale scrubbings systems show that k , the bulk
mass transfer rate constant, is much larger than k , the surface
reaction rate constant. Also, k appears to be a function of
particle size. For modeling purposes the following growth rate
expression will be used:
R(meter/sec) = k (1 + 5 L) (r - 1)P (5-4)
r
For limestone systems, sufficient experimental data were available
to estimate values for the constants in Equation 5-4. kr is
approximately equal to 3xlO~12 meter/sec with & equal to
5x105 meter ~l. At normal levels of supersaturation the exponent
p is expected to be one.
For lime systems, Equation 5-4 does not adequately
describe crystal growth. Additional data will be required to
examine effects of liquor composition on growth rate of particles
in lime systems.
A-51
-------
After reviewing both theoretical and experimental
aspects of calcium sulfite particle size distribution in lime/
limestone wet scrubbing systems, we have found that sufficient
information is not presently available to predict what process
variables can be used to improve sludge quality. Specifically,
the mechanism of particle generation must be identified before
any rational approach to controlling particle size distribution
can be devised. Thus, we recommend that the test plan document
produced during this program be directed towards correlating
nucleation rate as a function of important process variables
identified in the present literature survey.
A-52
-------
NOMENCLATURE
a - Chemical Activity
a .- Chemical Activity at Saturation
S 3. U
a - Interfacial Area (m2/m3)
A - Crystal-Crystal Contact Area (cm2)
A - Particle Surface Area (cm2)
p
C - Concentration (moles/liter)
Ci - Concentration in Bulk Phase (moles/liter)
CF - Clarifier Feed (liters/sec)
C. - Concentration at Solid-Liquid Interface (moles/liter)
cm - Centimeters
CO - Clarifier Overflow (liters/sec)
C - Saturation Concentration (moles/2-)
S
CU - Clarifier Underflow (liters/sec)
D - Diffusivity (m2/sec)
D - Stirrer Diameter (m)
S
D - Hold Tank Diameter (m)
E - Collision Contact Energy (ergs)
E - Agitation Power per Unit Mass of Slurry (ergs/gram)
FG - Flue Gas Rate (m3/hr)
G
Particle Generation Term other than growth and convection
(S.'1 sec'1)
g - gram
G - Molar Diffusion Rate (moles/sec)
Gg - Molar Growth Rate per Unit mass (moles/g sec)
Gm - Molar Growth Rate (moles/£ sec)
AGg - Surface Free Energy Change (ergs)
AG - Total Free Energy Change (ergs)
AG - Volume Free Energy Change (ergs)
h - Experimental Exponent
A-53
-------
NOMENCLATURE (continued)
i - Experimental Exponent
j - Experimental Exponent
K - Pre-exponential Constant (&"1 sec"1)
k,k ,k',ki,k2,k3- Experimental Constants
k - Constant Relating Surface Area to the Square of the
3.
Characteristic Length, L2
kg - Kilogram
k - Diffusion Rate Constant (m2/sec)
k - Surface Reaction Rate Constant (m2/sec)
K - Solubility Product
sp J
k - Shape Factor
L - Characteristic Particle Length (m)
I - Liters
LA - Limestone Additive Rate (H/sec)
L - Equilibrium Particle Length (m)
L - Mass Average Length (m)
L - Number Average Length (m)
m - Meters
mg - Calcium Sulfite Coprecipitate Solids Concentration (g/£)
MW - Molecular Weight (g/mole)
N - Number of Particles Per Slurry Volume (A"1)
n - Number of Particles of Size L Volume (H~l m"1)
N - Number of Particles of Size L per Volume Leaving System
(JT1 sec"1)
N - Number of Nuclei Produced by Crystal-Crystal Collisions
(collision"1)
n - Nuclei Concentration U"1)
n - Nucleation Rate (Jl^sec"1)
An - Change in Number of Moles
p - Experimental Exponent
A-54
-------
NOMENCLATURE (continued)
Q - Volumetric Flow Rate (£/sec)
R - Linear Crystal Growth Rate (m/sec)
r - Relative Saturation
R - Gas Constant (atm 5,/mole K°)
SB - Scrubber Bottoms Flow Rate (£/sec)
SF - Scrubber Feed Flow Rate (2,/sec)
SG - Stack Gas Flow Rate (m3 /hr)
AS02- S02 Pickup (moles/sec)
T - Temperature (K°)
u. - Slurry Velocity in the ith direction (m/sec)
V - Slurry Volume
V - Particle Volume (m )
X - Length Dimension (m)
Y - Length Dimension (m)
Z - Length Dimension (m)
a - Experimental Constant
6 - Growth Constant (m~ l )
a - Surface Energy (ergs/m2)
P0 - Slurry Density (g/£)
s
y - Liquid Phase Chemical Potential
yo - Standard State Liquid Phase Chemical Potential
X/
yo - Solid Phase Chemical Potential
S
v - Kingmatic Viscosity (m2/sec)
T - Mean Solids Residence Time (sec)
A-55
-------
REFERENCES
AU-013 Austin, L. G., "Understanding Ball Mill Sizing",
Ind. Eng. Chem., Process Des. Develop. 12(2) , 121
(1973).
BO-144 Borgwardt, Robert H., Sulfate Scale Control in Lime/
Limestone Scrubbers by Unsaturated Operation, Draft
Report. Research Triangle Park, N. C., EPA, May 1974.
BO-146 Borgwardt, Robert H., Limestone Scrubbing of S02 at
EPA Pilot Scrubber. Progress Report 15. Research
Triangle Park, N.C., EPA, Feb. 1974.
BO-147 Borgwardt, Robert H., "EPA Pilot Plant Support at
Research Triangle Park, N.C. Summary of research
related to process improvement", Presented at the
Industry Briefing on Progress at Shawnee Lime/Limestone
Wet Scrubbing Prototype Facility, NERC, Research Triangle
Park, N.C., Dec. 1973.
BO-272 Bond, Fred C., "Crushing and Grinding Calculations",
2 parts. Milwaukee, WS, Allis-Chalmers Manufacturing
Company, Jan. 1961.
BO-241 Borgwardt, Robert H., "EPA/RTP Pilot Studies Related
to Unsaturated Operation of Lime and Limestone
Scrubbers", Combustion 47(4). 37-42 (1975).
BO-247 Borgwardt, Robert H., Limestone Scrubbing of S02 at
EPA Pilot Plant. Progress Report 9. St. Louis, Mo.,
Monsanto Research Corp., April 1973.
A-56
-------
BU-090 Buckley, H. E., Crystal Growth. Chapman and Hall,
1958.
CA-003 Canning, T. F. and A. D. Randolph, "Some Aspects of
Crystallization Theory: Systems that Violate McCabe's
Delta L Law", AIChEJ 13 (1), 5-10 (1967).
CO-020 Collins, F. C. and J. P. Leineweber "The Kinetics of
the Homogeneous Precipitation of Barium Sulfate",
J. Phys Chem. 60, 389-94 (1956).
CR-163 Crowe, J. L. and S. K. Seale, Processing Sludge:
Lime/Limestone Sludge Characterization -- Shawnee
Test Facility, draft report. Chattanooga, TN and
Muscle Shoals, AL, TVA, June 1977.
DA-006 Davies and Nancollas, "The Precipitation of Silver
Chloride from Aqueous Solutions. Part 3. Temperature
Coefficients of Growth and Solution", Trans. Faraday
Soc. 51, 818-23 (1955).
ES-003 Estrin, Joseph, ed., Crystallization From Solution:
Nucleation Phenomena in Growing Crystal Systems.
AIChE Symposium Series 68(121). N.Y., AIChE, 1972.
GA-234 Garside, John, et al., "On Size-Dependent Crystal Growth",
I&EC Fund. 15(3), 230-33 (1976).
GA-236 Garside, John, John W. Mullin, and Sibendu N.
Das, "Growth and Dissolution Kinetics of Potassium
Sulfate Crystals in an Agitated Vessel", I&EC Fund.
13(4), 299 (1974).
A-57
-------
HA-696 Hargrove, 0. W. and D. M. Ottmers, Review and
Analysis of Louisville Gas and Electric Scrubbing
System Data, final report. EPA Contract No. 68-02-1319,
Task 30, Radian Project No. 200-045-30, Reviewed,by
W. E. Corbett and J. L. Phillips. Austin, Tx., Radian
Corporation, December 1975.
IS-001 Ishii, T. and S. Fugita, Chem. Engr. (Japan 3(2),
236-81 (1965).
JO-R-214 Jones, Benjamin F., Philip S. Lowell, and Frank
B. Meserole, Experimental and Theoretical Studies
of Solid Solution Formation in Lime and Limestone SOa
Scrubbers, final report. EPA 600/2-76-273a, EPA
Contract No. 68-02-1883, Radian Project No. 200-144.
Austin, Tx., Radian Corp., Oct. 1976.
KH-034 Khamskii, Eugenu V., Crystallization from Solutions.
New York, Consultants Bureau, 1969. Translated1by
Alvin Tybulewicz.
LA-035 Larson, M. A., ed. Crystallization from Solution:
Factors Influencing Size Distribution, CEP Symp. 67
(110), (1971)
LA-324 LaMantia, C. R. , et al. , Dual Alkali Test and Evalua-
tion Program Vol. II. Laboratory and Pilot Plant
Programs, final report. EPA Contract No. 68-02-1071,
EPA 600/7-77-050b. Cambridge, MA, Arthur D. Little,
Inc., May 1977.
A-58
-------
LE-305 Levins, D. M. and J. R. Glastonbury, "Particle-Liquid
Hydrodynamics and Mass Transfer in a Stirred Vessel"
2 pts. Trans. Inst. Chem. Engrs. 50. 32 (1972),
pt. 1; Trans. Inst. Chem. Engrs. 50. 132 (1972), pt. 2.
LU-006 Lucchesi, Peter S., "Oscillometric Investigation of
Precipitation and Dissolution Rates of Sparingly Soluble
Sulfates", J. Colloid Sci 11; 113-123 (1956).
MC-012 HcCabe, W. L. , and P.. P. Stevens, "Rate of Grwoth of
Crystals in Aqueous Solutions", CEP 47 (4), 168-74
(1951)
MO-311 Moore, Walter J., Physical Chemistry, 4th edition.
Englewood Cliffs, NJ, Prentice-Hall, 1972.
MU-001 Mullin, J. W. , Crystallization, Butterworths, London,
1961.
NA-015 Nancollas and Purdie, "Crystallization of Barium Sul-
fate in Aqueous Solution", Trans. Farad. Soc. 59, 735
(1963).
NA-016 Nancollas and Purdie, Trans. Farad. Soc. 57, 2272
(1961).
NI-001 Nielsen, A. E. , Kinetics of Precipitation. Pergamon
Press, Oxford, 1964.
OT-R-023 Ottmers, D. M. , Jr., et al. , A Theoretical and Experi-
mental Study of the Lime/Limestone Wet Scrubbing Process
PB 243-399/AS, EPA 650/2-75-006, EPA Contract No.
68-02-0023. Austin, Tx., Radian Corp., 1974
A-59
-------
PH-050 Phillips, V. Roger and Norman Epstein, "Growth of
Nickel Sulfate in a Laboratory-Scale Fluidized-Bed
Crystallizer", AIChE 20(4), 678 (1974).
RA-060 Randolph, Alan D. and Maurice A. Larson, Theory of
Particulate Processes. Analysis and Techniques of
Continuous Crystallization. New York, Academic, 1971,
RA-432 Randolph, Alan D. and Michael D. Cise, "Nucleation
Kinetics of the Potassium Sulfate-Water System",
AIChE J. 18(4), 798 (1972).
RO-344 Rousseau, R. W. and M. A. Larson, eds., Analysis
and Design of Crystallization Processes. AIChE
Symposium Series 72(153). NY, AIChE, 1976.
RO-362 Rossoff, J., et al., Disposal of By-Products From
Nonregenerable Flue Gas Desulfurization Systems,
second progress report. EPA Contract No. 68-02-1010,
EPA-600/7-77-052. Los Angeles, CA, Aerospace Corpora-
tion, Environment and Energy Conservation Division,
May 1977.
TI-006 Ting, H. H., and W. L. McCabe "Supersaturation
and Crystal Formation in Seeded Solutions", I&EC
26, 1201-07 (1934).
WA-339 Walton, A. G., "Principles of Precipitation of Fine
Particles", in Dispersion Powders and Liquids. 2nd
ed., G. D. Parfitt, ed. New York, Halsted Press,
1973, pp. 175-220
A-60
-------
WE-331 Wey, J. S. and J. P. Terwilliger, "On Size-Dependent
Crystal Growth Rates", AIChE J. 20(6), 1219 (1974).
A-61
-------
DON #78-200-187-11-12
APPENDIX B
AN ANALYSIS OF CRYSTALLIZATION
DYNAMICS AND PARAMETER SENSITIVITY IN
LIME/LIMESTONE WET SCRUBBING
SYSTEMS
Technical Note 200-187-11-03
17 February 1978
Prepared for:
Robert H. Borgwardt
Industrial Environmental Research Laboratory RTP (MD-61)
U. S. Environmental Protection Agency
Research Triangle Park,
North Carolina 27711
Prepared by:
Kenneth A. Wilde
Reviewed by:
Philip S. Lowell
D. M. Ottmers, Jr.
B-i
-------
TABLE OF CONTENTS
Page
1.0 SUMMARY B-l
2 . 0 RECOMMENDATIONS B-7
3. 0 DISCUSSION OF MODELS B-8
3.1 Scrubber/Hold Tank/Clarifier Model B-8
3.2 Simplified Hold Tank/Clarifier Model B-17
4. 0 MODEL PARAMETER SENSITIVITY STUDIES B-31
4.1 Computer Program B-31
4.2 Discussion of Input Parameters B-32
4. 3 Parameter Variation Studies B-35
5 . 0 REFERENCES B-50
6 . 0 NOMENCLATURE B-51
APPENDIX A - PROGRAM DESCRIPTION B-53
B-ii
-------
LIST OF FIGURES
. Page
3-1 Process Flow Sheet for a Lime or Limestone
Scrubbing System ............................. g-9
3-2 Simplified Cyrstallization Model ............... B-18
4-1 Population Density vs_ Particle Size ............ B-38
4-2 Average Particle Size vs Growth Rate Para-
meter, pCF ..................................... B-39
4-3 Average Particle Size vs_ Clarifier Cut-off
Size ........................................... B-40
4-4 Relative Saturation, Particle Size and Preci-
pitation Rate vs Solids Residence Time ......... B-42
4-5 Mass Average Crystal Size and Relative Satura-
tion vs_ Solids Residence Time (Hold Tank Volume)
at Constant SOa Removal, 10 Weight Percent
Solids ......................................... B-43
4-6 Mass Average Crystal Size and Calcium Sulfite
Relative Saturation Weight Percent v£ Solids
in Clarifier Feed WCF at Constant S02 Removal
and Hold Tank Volume ........................... B~44
4-7 Particle Size and Precipitation Rate vs Growth
Rate-Size Slope ................................ B"46
4-8 Precipitation Rate vs Growth Rate Constant
B-iii
-------
LIST OF FIGURES (continued)
Figure Page
4-9 Particle Size and Precipitation Rate vs
Nucleation Rate Constant B-48
LIST OF TABLES
Table page
4-1 Sample Computer Program Output, Typical
Particle Size B-36
4-2 Sample Computer Program Output, Small
Particle Size B-37
B-iv
-------
1.0 SUMMARY
This technical note presents a study of models for
calculating calcium sulfite particle size distribution in lime/
limestone SOa scrubbing systems. Particle size plays a key
role in determining sludge handling and disposal characteristics.
The objective of this study was to explore the feasibility
of predicting the effects of system parameters on sludge pro-
perties. Equations were developed for the particle size
distributions in a coupled scrubber/hold tank/clarifier. For
the case of precipitation in the scrubber, the general model
could be simplified. In this case just the hold tank and clari-
fier were considered since precipitation was negligible in the
scrubber. Closed analytical solutions were possible.
A computer program was written to implement the simpli-
fied model equations. A limited parameter study of the model
characteristics was made. The lack of applicable rate data
prevented definitive evaluation of the model. The rate para-
meters in the model must be determined to assess its ultimate
utility and indicate possible refinements.
The basic particle balance equations which determine
particle size distribution were discussed in Technical Note
(#200-187-11-01). Nucleation and growth rate phenomena were
also discussed. This current note is a continuation and
implementation of those ideas. The basic model structure in-
volves equations for all process units considered together.
Critical unit interactions can then be studied. Closed analy-
tical solutions of the equations are thus more likely than in
a separate unit approach.
The system equations have markedly different behavior
depending on whether there is precipitation or dissolution of
B-l
-------
calcium sulfite in the scrubber. These two cases occur when
the scrubber is supersaturated or subsaturated with respect to
calcium sulfite. Other general model features include a
clarifier which separates particles at a given size, without
precipitation or reaction. Particle growth rate is considered
to be either constant or a linear function of particle size.
The case of supersaturation with precipitation of
calcium sulfite in the scrubber was considered for a well-mixed
scrubber. It was found that precipitation in the scrubber was
negligible compared to that in the hold tank. The well-mixed
approximation is best for longer residence time scrubbers such
as the marble bed or turbulent contacting type. Thus, preci-
pitation for shorter residence time scrubbers should also be
negligible. The added complexity of another variable to describe
precipitation and SOa pick-up along the scrubber is avoided.
The case of subsaturation with dissolution of calcium
sulfite in the scrubber presents some special problems. There
is an almost total lack of data on particle dissolution rates.
The nature of the solutions of the particle balance equations
for dissolution in the scrubber also presents some mathematical
problems. In particular, more must be known of the particle
size dependence of dissolution rate to resolve the problems
with the theory. The possibility of smaller particles dissolving
faster than larger ones in the scrubber is suggested. Larger
particle sizes in the clarifier underflow sludge could result
from dissolution of small particles in the scrubber. It
was not possible to pursue the dissolution case any further,
due to limitations in the data and scope of effort.
The model which has been developed and tested is a
simplified one for just the hold tank and clarifier. It is
applicable to the case of negligible precipitation in the scrubber.
B-2
-------
It is not applicable to subsaturation and dissolution of
calcium sulfite in the scrubber. The model is defined by the
following features and assumptions:
there is negligible change in solids in
the scrubber,
the clarifier divides particles at a
given size, with no precipitation,
growth rate is either a linear function
of particle size or is constant,
zero-size growth rate is a power function
of relative saturation, and
nucleation rate is a power function of
relative saturation and molar solids
concentration.
It was possible to derive closed analytical solutions
for all quantities of interest. The case of constant growth
rate could not be derived by specialization of the results for
the linear case. Separation equations were necessary. Equa-
tions were derived for the clarifier feed particle size distri-
bution, average particle size, total solid concentration, and
total precipitation rate.
The equations for the general case of non-clear clari-
fier overflow are algebraically cumbersome. To illustrate the
properties of the model, some simplified equations for the case
of clear clarifier overflow will be given. A basic result is
the relationship for the number of particles of a given size,
B-3
-------
the particle size distribution. For particle growth rate as a
linear function of size, the result is
T
CF
where:
n = number of particles per unit volume of a given
size, L, no./^/micron,
n = particles of zero size, no./£/micron,
L = particle size, microns,
Y = slope of the growth rate - particle size relation,
R = growth rate at zero size, and
Tp^ = solids residence time.
The number of particles, n, decreases monotonically with in-
creasing particle size, L, starting at essentially zero size.
These zero size particles come from nucleation. The rapidity
of this decrease is greater for smaller values of y, R , and
Trp. The average particle size would be correspondingly smaller,
An expression for the mass average particle size of
the clarifier feed, L^' i-s :
If the growth rate R is independent of particle size, Y=0, and
Equation (1-2) reduces to
Lcf -
B-4
-------
Thus, larger particle sizes are favored by longer solids resi-
dence times and higher particle growth rates. The same result
is true for y ^ o, except dependence is stronger for larger
positive values for y.
Another significant result is a relation between the
total precipitation rate, G, moles/£/min, and the total solids
concentration, M, moles/H:
G/MT = 1/TCF d-4)
The relation of G/MT to the growth rate can be shown by substitu-
ting for T^-p, from Equation (1-3) :
G/MT = 61/3RQ/L (1-5)
Most of the data on calcium sulfite precipitation is reported as
correlations of G/M versus relative saturation. The present
results indicate that meaningful rate parameters cannot be
found unless particle sizes are measured.
The simplified hold tank/clarifier model has been pro-
grammed, including non-clear clarifier overflow and both constant
and linear growth rate laws. The program is a relatively simple
one since analytical solutions are possible. The input parameters
include relative saturation, solids residence time, and nucleation
and growth rate parameters. Outputs include average particle size
molar precipitation rate, and particle size distribution. The
program can be used along with data-fitting programs to deduce
crystallization rate parameters. Given the rate parameters, it
3-5
-------
can be used in an iterative fashion to find inputs such as rela-
tive saturation and solids residence time for required outputs
such as net precipitation rate (S02 pick-up). The program can
also be used as a subroutine of a complete S02 scrubbing system
simulation.
Almost no rate data were available either for nuclea-
tion or growth. Physically reasonable results for particle sizes
were obtained with typical system parameters and order of magni-
tude rate parameters. Additional data are required to verify
the model further.
Parameter studies were made to illustrate the use
of the model and the interrelations of the rate and system
parameters. An example is given of determination of hold
tank size for a given maximum relative saturation and total
SOa pick-up rate.
B-6
-------
2.0 RECOMMENDATIONS
More bench and pilot scale work is needed to define
both nucleation and growth rate parameters. Particle size dis-
tributions must be measured to have useful data.
The bench and pilot unit data should be correlated with
the model. The computer program should be used as a subroutine
of widely available non-linear curve-fitting programs. Then rate
parameters can be deduced from particle size distributions and
total solids concentrations.
The model should be extended to include growth rate-
size relations intermediate between constant and linear in particle
size. Incorporation of the model into complete SOa scrubbing
system simulations should be explored.
Scrubber dissolution of fines could be examined as a
possibility of increased sludge particle size. Further definition
of this aspect will require considerably more work, both experi-
mental and modeling. Since dissolution is much faster than
precipitation, its study on a pilot scale may not be feasible.
The best approach may be bench scale dissolution rate studies
to provide data for resolution of the present model's problems
with the dissolution case.
The basis of hold tank sizing should be reexamined.
The present model provides a better basis for system design than
conventional methods. Although rate parameters in the model
are not yet known, a better use of available information should
be possible.
B-7
-------
3.0 DISCUSSION OF MODELS
The coupled scrubber/hold tank/clarifier system forms
the basis of the first model. Two sub-cases for this model
will be discussed: precipitation or dissolution of calcium
sulfite in the scrubber. The system equations for these two
possibilities have a different nature. Examination of the case
of precipitation in the scrubber indicates that precipitation
of CaSOs in the scrubber is negligible compared to precipitation
in the hold tank. The case,of negligible precipitation in the
scrubber leads to a simplified model for just the hold tank
and clarifier. Equations for the quantities of interest for
this simplified model will be derived. Implementation of the
simplified model is discussed in Section 4.
3.1 Scrubber/Hold Tank/Clarifjer Model
The "typical" lime or limestone scrubbing system dis-
cussed in Technical Note #200-187-11-01 will be the basis for
this section. A schematic flow sheet is shown in Figure 3-1.
Both the scrubber and hold tank will be modeled as "perfectly
stirred tanks". That is, the mixing will be rapid enough compared
to reaction and crystallization so that an essentially uniform
composition prevails. This idealization will usually be reason-
able for hold tanks. It is also reasonable for certain types of
scrubbers such as the turbulent contacting adsorbers (TCA).
Residence times for TCA scrubbers are considerably
longer than for Venturi scrubbers, for example. The result
found for negligible precipitation in a well-mixed scrubber
would certainly hold true for those which are not well-mixed
but have lesser residence times. Thus, the problem is avoided
of modeling scrubbers with an added variable for precipitation
along the length of the scrubber. The model in that case would
be much more difficult to solve computationally.
B-8
-------
FG
LA
1
A
Scrub
1
bG
A
ber
f
SF
'
. SB I
Hold
Tank
(MM
nt
/
CO n
*v °
»
__ Clarifier CU
Lr
nout
overall
* system
boundary
__._ L
Figure 3-1. Process Flow Sheet for a Lime or Limestone Scrubbing
System.
.B-9
-------
The basic particle balance equations have been discussed
in the Technical Note # 200-187-11-01. Oxidation will not be
considered explicitly. An amount of calcium sulfate up to the co-
precipitation limit of about 15 mole "L can be considered by using
the appropriate molecular weight for the precipitated crystals.
The clarifier will be treated as just a size separations device
with negligible reaction or precipitation. All particles greater
than a given size will go in the underflow. Smaller particles
will be divided according to the relative volumes of the over-
flow and underflow streams. The growth rate will be considered
as either constant or as a linear function of particle size.
3.1.1 General Particle Balance Equation
The particle balance equation for a well-mixed vessel
is (RA-060):
+D(L)=Z+B(L) (3-1)
where:
R = linear growth rate, microns/min
n = particle population density, no./liter/micron
L = length (size) characterizing particle growth,
microns
J = characteristic time for output stream j, minutes
j_ = time for input stream i, minutes
B = rate of birth of particles, no./liter/micron/min
D = rate of disappearance of particles, no./liter/
micron/min
B-10
-------
The formation of crystals of size L by other than growth and
convection has been divided into birth and death functions
B and D. The lefthand terms are the output from the slurry
volume of particles of a size L by crystal growth, bulk convection
and particle death. The righthand side has terms for inputs by
convection and birth.
The characteristic times, T, are defined as V/Q, the
vessel volume divided by the volumetric flow rate of the parti-
cular stream. They are not necessarily residence times. Equation
(3-1) is a steady-state balance in the (single) dimension of
particle size. The vessel is also assumed to be at steady-state
with respect to the conventional material balances, including
numbers of particles. However, in this Note the term particle
balance will refer to relations such as Equation (3-1).
The birth and death functions represent the effects of
crystal breakage and attrition. They are even less well charac-
terized than other aspects of crystallization. Randolph and
Larson (RA-060, p. 121) considered in a general approximate way
the case of breakage into equal pieces. This produces the maxi-
mum effect on the form of the crystal size distribution. The
relative number of smaller particles remained about the same,
while larger particle numbers were appreciably reduced. The
limit of smaller and smaller fragments breaking off represents
crystal attrition. The net effects of attrition were an apparent
increase in nucleation, decrease in growth rate, possible rounding
of crystals, and no major change in the form of the crystal size
distribution.
The birth and death functions, B and D, will be taken
as zero. The particle size change effects considered will be
net effects including such terms. Separate consideration is not
feasible within the scope of this work.
B-ll
-------
3.1.2 Scrubber/Hold Tank Equations
It is essential in modeling the scrubber/hold tank
combination to recognize that the output of one is the input of
the other. The conventional approach is to consider separate
models and equations for each process unit. Here the close
interaction of the equations for scrubber and hold tank would
cause vital model details to be lost in the separate unit approach.
Also, the opportunity for closed analytical solutions without
iteration would be lost.
In order to demonstrate the nature of the model in-
cluding the scrubber, two further simplifications will be made:
growth rate independent of particle size and no particles in the
clarifier overflow, i.e., perfect clarification. Implications
of these approximations will be noted. There is an equation
of the form of (3-1) for both the scrubber and hold tank:
d(R n )
d(R n )
where the subscripts s and T are for scrubber and hold tank. SB
and SF represent scrubber bottoms and feed. If the clarifier
overflow were not clear, a term Qconco would be added to the
right hand side of (3-3). The overflow particle size distribu-
tion would be some fraction of the clarifier feed n^ (or n )
CF T
For constant growth rates R, Equations (3-2) and (3-3) can be
written as :
dnc
S + an -an
T: s T
B-12
-------
(3_5)
where:
a = QSB/RSVS =
a' = QSF/RSVS = 1/RSTSF
b = QT/RTVT = 1/RTTT
C -
We thus have two first-order ordinary differential
equations in the two particle size distributions ns and n , for
the scrubber and hold tank. The boundary conditions nc(o) and
O
nT(o) are found from the nucleation rate B and the zero size
growth rate RQ (RA-060, p. 70):
n(o) = BO/RQ (3-6)
For R independent of L, the coefficients a, a', b and c are
constants. Then the equations have a relatively simple analytical
solution. If R is a function of the particle size, L, the
coefficients are functions of the dependent variable, L. Then
they have no general analytical solution.
3.1.3 Nature of the Solutions and Characteristic Roots
The solution of a set of simultaneous linear first-
order differential equations can be found by several standard
methods (PE-030, p. 38, MA-766) . It involves a sum of exponen-
tial terms:
B-13
-------
(3-7)
ClemiL C2em2L
n = T- (mi + a) + - (m2 + a) (3-8)
T a a
where Ci and C 2 are constants to be determined from the boundary
conditions nc(0) and n (0) :
O T
n° > ng(0) - Ci +C2 (3-9)
° - n (0) - -. [ci(mi + a) + CzCma + a)~| (3-10)
nT T a L_ J
Solving Equations (3-9) and (3-10) f or C i and C 2 ,
(m2 + a) n - a" n
Ci = - 2 - 1 (3-11)
mz ~ mi
a"* n - C i (mi + a)
mi and m2 are the roots of a quadratic involving the
coefficients of the original differential Equations (3 -4) and
(3-5):
-(a + b) ±V(a + b)2 - 4(ab-a^c) (3-13)
m = _
Thus, the complete solution for the particle size distributions
is contained in Equations (3-7, 8, 11, 12, 13). Neither of the
exponential terms or roots mi and ma can be identified with the
scrubber or hold tank. Both are necessary for both process
units. The nature of the solutions is profoundly affected by
the signs of the roots mi and ma in the exponents. From the
general expression for the product of the roots of any quadratic,
. - QSB(QT - QSF) , 1/N
mim2 = ab - a c = y (3-14)
S S T T
B-14
-------
Since QT is the total hold tank outflow and Qs is that part
going to the scrubber, QT - QSF must always be positive. Thus,
the sign of the proudct mnn2 depends on the particle size change
rates RT and Rg. Precipitation must occur in the hold tank for
the system to work at all, i.e. , RT must be positive. The root
product mim2 must then have the same sign as Rq, the scrubber
O
growth (R is +) or dissolution (R is -) rate.
s s
It can also be shown that the roots mi and m2 cannot be
imaginary. The quantity under the radical in Equation (3-13) can
be written as:
2
(a - b)z + 4 a'c, (3-15)
which cannot be negative for Rq>0, since a" and c are positive.
If RQ
-------
(a + b)2, since ab - a'c is positive. Therefore, the root for
the plus radical sign must also be negative, as well as the
other one for the negative sign. We are thus assured that the
particle size distributions will decrease monotonically with
increasing particle size, L, and approach zero as L approaches
infinity. This aspect is important in integration of particle
size distributions to obtain other quantities.
The foregoing equations can be used to relate crystal-
lization to process conditions. Overall material balances provide
other relations. The relation between solution supersaturation
is provided by an aqueous ionic equilibrium computer program, such
as those developed by Radian (LO-007) . The complete scrubbing
system can then be simulated, at least insofar as the crystalli-
zation is concerned.
A computer program was written to solve the resulting
set of non-linear algebraic equations. The equations for constant
R were used for varying R by dividing the size range into a number
of parts, each with a different constant R. A pair of constants
Ci and C2 results for each size division. The resulting addi-
tional computation is still much less than a numerical solution.
Details will not be given here as complete solutions were not
obtained. It was discovered that the precipitation in the scrub-
ber is small enough compared to the hold tank to prevent numerical
solution of the complete problem. In any case, the problem can
be simplified by considering only the hold tank and clarifier, as
shown in Section 3.2.
3.1.5 Dissolution in the Scrubber
It has been recognized in practice that sometimes
the scrubber may be subsaturated with respect to CaSOa. Dis-
solution would then take place in the scrubber with precipitation
B-16
-------
in the supersaturated hold tank still occurring. Returning to
the product of roots, Equation (3-14), mi and m2 must be of
opposite sign if Rg is negative for dissolution in the scrubber
This means that one of the exponential terms will increase with
increasing L. There would be no bounds on integrals over the
particle size distribution as L goes to infinity. Unfortunately
very little is known about dissolution rates except that they
are presumably much faster than precipitation. Thus there could
be appreciable dissolution in the short residence times in
scrubbers. Also, it appears that dissolution cannot continue
to larger sizes for finite particle size distributions. An
intriguing possibility is that smaller sizes may dissolve more
rapidly than large ones. Operation of the scrubber subsaturated
would then be a means to increase particle size and sludge quali-
ties. More definitive data on dissolution rates are needed to
investigate this possibility. It could not be pursued further
in this program.
3.2 Simplified Hold Tank/Clarifier Model
The model in this section is depicted in Figure 3-2.
It has the following characteristics:
negligible solids change in the scrubber,
clarifier divides particles at given size,
growth rate a linear function of L (or
constant), and
relative saturation a given input quantity.
B-17
-------
n
L(
Clarifier
Q* "CO
n - r CF nT L
-------
- The hold tank has two feeds: (1) a sulfite stream
from the S02 picked up in the scrubber and (2) calcium from
the lime or limestone addition. Thus, the key species in the
feed streams are total sulfite (S02), total calcium (CaO)
and water (H20). Precipitation takes place to form calcium
sulfite hemihydrate, CaS03*%H20.
The circulating loop between the scrubber and hold
tank is ignored. No material balances are used. The model is
intended to display the interrelationships of the parameters.
If enough of the parameters can be defined by future experimental
programs, the present model can be used with other relations to
simulate hold tank precipitation and clarifier underflow sludge
qualities. From Equation (3-1), the hold tank particle balance
is
d(nR)
dL
n
CF
n
CO
, LL.
V
CF
- T
co
x:o
The subscript T on n and R is dropped in this section
3.2.1
Clarifier Model
The clarifier particle size distribution for particles
less than LQ is found by dividing them according to the ratio of
clear overflow and underflow volumes. Particles greater than LC
B-19
-------
all go to the underflow. Since n is a concentration, the particle
distribution greater than LC in the underflow is described by:
QCF (3-18)
nCU - V L>LC
The nrTT less than Lr is less than that in Equation (3-18) by the
L U Li
ratio of the clear liquid volumes, approximately:
(Qcu) clear . QQP L< (3.19)
nCU (QCF) clear QCU T' C
The ratio of clear volumes is found from the clear volume fraction
in the clarifier underflow, Y^:
(3-20a)
w
1 +f - wcu\ p
V WrV ?
(Qcu) clear QCU Ycu (3-20b)
(QCF) clear ' (QCF - ^ + q^ ^
It is assumed in Equation (3-20b) that the volume of solids in
the clarifier overflow is negligible. Wfu is the overall weight
fraction solids in the clarifier underflow. p is the particle
(crystal) density. If the complete Equation (3-20) were used,
the model would have to be solved iteratively. Wrn is an
output and would require an initial estimate to be corrected
and converged on. Since the clarifier separation is arbitrary
anyway, it was decided to simplify Equation (3-20) to eliminate
B-20
-------
w
cu
by using a typical value of 0.5. The split of the small
particles is not sensitive to the value of WGU and a reasonable
approximation will result:
n
CU
r p>
i +
QCF .
PP
, PP
1 + p
P.
n
(3-21)
The quantity in brackets is subsequently defined as f
particle distribution in the overflow is then:
The
'CO
"CL'
n
(3-22)
3.2.2
Solution for Particle Size Distribution
For the linear growth rate law,
R - R (1 + yL)
the particle balance, Equation (3-17) becomes
(3-23)
dn n
dL 1
CL
(3-24)
where y is the slope of the R vs. L relation, in (microns) l, and
fpT = 1 for L > L^. The time Trt, is the ratio of hold tank volume
^.L L/ <-*
and clarifier feed rate. It is often referred to as the solids
residence time. It is the important time parameter, rather
than the residence time as determined by the total circulating
liquor volume.
B-21
-------
Equation (3-24) is readily integrated to give the
particle size distribution of the clarifier feed.
n = n
n = nQ(l +
PCF
PCF "PCU
PCF + 1
, L > L,
. L < L
PCU ~ fCLPCF
(3-25a)
(3-25b)
(3-25c)
Equation (3-25) is a power law relationship rather than the
usual exponential one for constant R. This is a consequence of
the linear growth rate, Equation (3-23). The n - L relation is
monotonically decreasing but not a straight line on a semi-log
plot. The zero size growth rate is taken as an empirical function
of relative saturation, r, of CaS03*%H20:
R
GR
(3-26)
where kGR and iGR are growth rate constants. A similar function
is used for the nucleation rate, B , with an added term for the
total CaSOa crystal density, M_, in moles/liter:
- »
sSB
(3-27)
where SN represents secondary nucleation, the presumably pre-
dominant nuclei formation mode. The zero-size population density
is given by Equation (3-6), B /R :
r _
JSN
(3-28)
B-22
-------
Other quantities of interest derived from the particle
size distribution include Hp, total crystal concentration in moles/
liter, precipitation rate, G, in moles/£/min, and mass average
particle size, L, in microns. Expressions for these quantities
will be derived for the particle size distribution, n(L) , given
by Equations (3-25).
3.2.3
Total Crystal Concentration
is found by integrating n(L) times the mass of an
individual particle:
MW
L3n(L)dL
(3-29)
where k is the factor converting L3 to particle volume. kv
is TT/6 for a sphere. The integration is carried out from zero
to LC using Equation (3-25a) and from LC to infinity using
Equation (3-25b).
= f n
P o
/L3dL _ , ,-, , ,,L \
+ U -i- Y^c;
(1 + YD1 + Pcu
o
YL) CF
,PCF " pcu
(3-30)
where f is a factor lumping together p kv/MW. The result is
B-23
-------
T =
- fpn°
YL
'(X3~PCU - 1) 3(X2"PCU
3CX1 PCU
c
-p
cu
(2 - p
CU
- p
cu
(X PCU -
c
PCU
XPCU
,3
C
3X'
3X
(3 - PCF)
-PCF}
cp
(3-31)
where X =l+yL. If L =0 (clear clarifier overflow), a
c c c
simpler equation for Mr, can be found:
L3dL
(3-32)
o (1 +
The integral in Equation (3-32) can be written in terms of the
Gamma and Beta functions (MA-766, DW-006):
°° m-l,
u du
(1 + u)
nrin
^ - r(m)«r(n)
(m'n) - r(m+n)
(3-33)
where the Beta function B is defined in Equation (3-33) in terms
of the Gamma function, r, which is defined as
T(p)
/CO
p-1 -U,
u e du
(3-34)
- (p-l)'» if p is an integer.
The parameters in Equation (3-32) can be identified with those
in the integral in (3-33):
m = 4, p = PCF-3, u = yL.
B-24
-------
The results for H is
6f n
The dependence of (secondary) nucleation on crystal
density, Hj,, means that Hj, occurs in both input and output.
However, it can be isolated to avoid iterations. From Equation
(3-32) for H, we have:
"r = > CF (3-36)
Re
where I is the integral over L3dL, and n is replaced by
Bo/Ro. Substituting Equation (3-27) , the power law, for BQ
and solving for Mp _1
'(r _ 1)±SNI (YJ p n^
**T =L i * (3-37)
PT? ^ ^~-*-/ pr,
olx Orv
3.2.4 Average Particle Size
The mass average particle size, L is defined through
and N, the total number of particle/liter:
r
N = / n
(3-38b)
ndL
B-25
-------
The particle concentration in the clarifier feed is found using
nPT? = n from Equation (3-25) in (3-36b) :
or T
m
TCF
p
= n R
'CL" - *;PCU«cL-' - "I (3-39>
r
F/
, L = 0 (3-41)
f n R TPWJ ' c
p o o CF
The average sizes in the overflow and underflow are similarly
found.
A check on the internal consistency of the model can
be made by expressing the net nucleation rate as the particle
concentration in the clarifier underflow times the underflow
volumetric flow rate, divided by the hold tank volume:
NrnQrn
BQ = v CU (3-42)
t
If the expression in Equation (3-40) is evaluated for any L ,
we find
BQ = VV (3-43)
as expected.
B-26
-------
3.2.5 Total Precipitation Rate
The total precipitation rate, G, moles/ A/ min, is found
by integrating the particle size distribution times the particle
area times the growth rate. The volume of a particle, v is
v = k L /"> / / \
p v (J-44)
The single particle volumetric growth rate, dv /dt, is found as:
dv d(k L3)
_ P v _, T 2 dL
dT = Tt - = 3kvL d^ (3-45)
The characteristic dimension L is usually taken as the particle
diameter. The growth rate, dL/dt, is twice that needed to multi-
ply the surface area to get the volume change. This is because
the crystal diameter is growing twice as fast as the radius.
We can define a factor k for area analogous to k
a = k L2 ^3
P a
For spheres and other regular shapes, kfl = 6kv, if L is the dia-
meter. The volume change rate is then given by
dv k Ra
dL/dt has been replaced by R. The factor of two appears because
the growth rate defined in terms of particle diameter is twice
that needed to go with particle surface area. Thus G can be
written as
G = ^, /°n(L) L2R(L)dL <3-*8)
B-27
-------
For the linear growth rate and clear clarifier overflow, an
expression similar to that for Rj can be derived:
k p n R
a P o ° (3-4Q1
k ^
_
(MW)Y3(pCF-l)(pCF-2)(pCF-3)
Since ka = 6kv> the ratio of G to Hp from Equations (3-47)
and (3-35) is
G/MT = l/TCF (3-50)
The same result is obtained for constant growth rate. A
different result is found for the case of L ^ 0. However,
the same considerations would apply to the net particle pro-
duction, and are used in the equations for the parameter study
in Section 3.
Equation (3-48) states that the total precipitation
rate divided by the total crystal concentration is a function
only of the solids residence time TCF. This is unfortunate,
since much of the crystallization rates reported for CaSOs are
as the rate per unit mass of crystals, moles/gm/min. This quanti
ty has ostensibly been correlated with relative saturation. The
rate per unit mass would be different only by dividing the
right-hand side of Equation (3-48) by the molecular weight.
If the particles did not follow the relation k = 6 k , we would
cl V
have
k /6k
where the subscript m on M is for mass concentration. The
reported quantity, G/M^, is not expressable only in terms of either
B-28
-------
growth or nucleation rate. The relationship to growth rate can
be shown by substituting a relation between average particle
size and growth rate, such as Equation (3-39). For simplicity
using a constant growth rate,
61/3R
f(L)l (3-52)
One conclusion from the above results is that particle
sizes must be determined in precipitation kinetics studies to
deduce useful parameters. Another is that apparent correlations
of G/M with relative saturations that do not have specific
surface included are in fact reflections of residence time,
variation of k/6k. or other factors not considered in the
cL V
basic models.
3.2.6 Growth Rate Independent of Particle S:Lze
The constant rate case cannot be deduced by specializing
the linear one, but similar integrations are involved. The re-
sulting equations are given below. Computations and parameter
studies with both cases are given in Section 4 .
n =
(3-53)
(pCF~PCU)Lc ~PCFL, L> L (3-54)
-
n = n e -e
o
re e "PCULC /Lc
"° L^cu" " e \pcu
P ° I Pr,u \pcu v,u ^ «« (3-55)
L3 3L2
c -
PCF
B-29
-------
G -
G/MT =
» L =
= 0
(3-56)
(3-57)
(3-58)
B-30
-------
4.0 MODEL PARAMETER SENSITIVITY STUDIES
The equations derived in the previous section comprise
closed analytical solutions to the particle balance equations.
A computer program was written based upon these analytical solu-
tions to specialized cases of the particle balance equation.
This section discusses the model input and output quantities.
Examples of use of the model are also discussed. The sensitivity
of the model to both system and rate parameters is illustrated.
Possible refinements to the model are indicated.
4.1 Computer Program
A computer program has been written in FORTRAN language
for the equations of the hold tank/clarifier model of Section 3.2.
The inputs and outputs are defined as follows:
INPUT
r = relative saturation with respect to CaSOs-%H20
k/-m> i~r> constants in the growth rate
bK OK
kSN' iSN' -^SN = constants in the nucleation rate
Y = slope of growth rate/size function, (microns) l
T£p = VT/QQ-P, minutes
T/-TT = V /Q^TT, minutes
^U T wU
L£ = clarifier cut-off size, microns
OUTPUT
n(L) = population density, particles/Vmicron
N (AL) = number of particles per liter in a size range AL
/(AL) = volume of particles per liter in a size range AL
B-31
-------
GCF = net precipitation rate, moles/2,/min
WCF WGU = weight % solids, clarifier feed and underflow
WpQ = ppm solids in the clarifier overflow
L, Lgg, LCQ = mass average particle sizes , microns
BQ = nucleation rate, particles/£/min
The above choice of dependent and independent variables
was made to obtain a straight-forward, noniterative calculation.
Thus, the program and equations can serve both to indicate
relative parameter sensitivity and as a building block for
further work. If some of the output variables were measured in
a bench or pilot scale, the unknown nucleation and growth
constants could be found. The present program would then be
used as a subroutine in a nonlinear curve fitting program.
Another application would be the determination of
required residence times and relative saturations for given
values of precipitation rate (SO2 pick-up) and circulating
solids concentration. This would be an iterative calculation
It would require knowledge of the input rate constants. Scrubber
system behavior would be more closely simulated. A discussion
of the input parameters will be followed by the results of the
parameter variation runs. Further details of the program and
a FORTRAN listing are given in the Appendix.
4. 2 Discussion of Input Parameters
The equations for the model are set up without
reference to any particular scrubbing system. The input
parameters can be divided into two classes: operational and
rate. The operational ones are relative saturation, r, solids
residence time, TCF; underflow residence time, Tnj; and clarifier
overflow maximum size, Lp The relative saturation will be
\j
B-32
-------
treated as a free parameter here. In applications of the model,
it would come from experimental data, material balances or
other auxiliary conditions. A typical TCF of one day was used
in most of the present results. The TCU value in practice
might be determined by that necessary to give the desired solids
content in the clarifier underflow. It affects the model only
through the clarifier split factor, fCL. A typical range value
of 7-10 times TCF was mainly used. The clarifier size Lf will,
of course, be a function of the flows and times in the clarifier
Perhaps typical values of one-half to one micron were used,
along with consideration of values down to zero.
The only direct information available on the rate
parameters is that given in Technical Note #200-187-11-01
on the linear growth rate law. R and y in Equation (3-23),
R = R (1 + yL) (3-23)
o
were deduced from experimental sludge particle size distributions.
However, the approximate nature of both the data and the deduction
of rate parameters from the data makes the result of only order-
of-magnitude significance. It is encouraging that these rough
values, along with typical other parameters, do give reasonable
results for particle sizes. The value of gamma of 0.5 is
similar to values in the literature for other crystals (RA-543).
The relative saturation dependence of both the growth
and nucleation rates is not well-defined. As discussed in
B-33
-------
Section 3.2, the reported linear correlations of precipitation
rates with relative saturation are not meaningful. The dependence
may be more or less linear, as indicated by some literature data
on other crystals.
Also, the CaS03 relative saturation values are actually
maximum ones based on limiting cases of aqueous ionic equilibrium
programs. The linearity of the relationship between theoretical
maximum relative saturations and actual values is a question which
has not as yet been addressed. The relative saturation exponents
for growth, IGR, and nucleation, ISN, were taken to be unity for
most cases. The exponent on MT, jgN (as defined in Equation 3-28),
is an important parameter, especially if it approaches one. The
exponent of the RHS of Equation (3-37) is 1/(1 - jCM) which
approaches infinity as j SN approaches 1. In fact, it cannot
approach one unless there are compensating changes in the other
parameters, so that Equation (3-37) is not the only one involving
those variables to be satisfied.
One recent study reported a value of j ., about 0.5
(RA-543). Others have suggested a value of unity (HE-287,
RA-060). The full implications of a value of or near unity
have not been addressed in CaSOs crystallization kinetics and
modeling. A "standard" value of jSN = 0.5 has been used here.
The dependence of nucleation rate on hold tank momentum
transfer was not included in this study. It has been reported
for a laboratory study that the nucleation rate is a function of
the 2.5 power of the stirrer RPM (RA-543). This aspect should
be considered in any treatment of data or scale-up considerations.
B-34
-------
4.3 Parameter Variation Studies
Program outputs for two typical cases are shown in
Tables 4-1 and 4-2. The semi-log plots of n versus particle
size in Figure 4-1 are concave upward at larger particle sizes,
as with the experimental data in Figure 4-3 of Technical Note
#200-187-11-01. Calculated numbers for n cannot be compared to
experimental as the experimental slurry particle concentrations
are unknown. There is an abrupt change of slope in the curves
at the particle size of one micron. This is due to the sharp
cut-off of one micron for the clarifier overflow.
The mass average particle size, LCF is plotted vs
1/pp-p in Figure 4-2. The constant growth rate case does not
include y in p/-p, of course. The constant R used was taken to be
the value of R for the linear case at five microns. The sharp
upswing in L as 1/p approaches the limiting value of 1/3
is an artifact of the simple linear growth law. The rate R
probably does not continue to increase linearly to very large
particle sizes. Values of 1/p greater than 1/3 have no physical
significance.
The foregoing results illustrated the use of the pro-
gram in a noniterative fashion. Some parameter studies were
also made with some of the outputs held constant and inputs
varied. The desired values of the outputs were found by inter-
polation and cross-plotting of a series of noniterative runs.
In order to find the effect of varying clarifier cut-
off size, Lc, the total precipitation rate G (S02 pick-up)
was held constant by varying the relative saturation. The
B-35
-------
TABLE 4-1. SAMPLE COMPUTER PROGRAM OUTPUT, TYPICAL PARTICLE SIZE
TA*K/CL*RIFIER
o. D T»>« VOL/CLARIFJER FEED R»TE,HII
HO.D U"l< YOL/CLARIFIER JSOE»F,Ow,MY
:LARIFIE* :JT-O«, SIZE, MICRONS
R»T£/5IZE
7,330
1443,
2,403+34
i.aa
»PT,
»V
S3LI3S, Ci.*R!FIER FEED
JNOE^FLOX
3VERFUOW
SIZE, tIC*tm,
RuTE CONSTANT,HICSOMS/^IN
Uu.SAT, EXPONENT,JRQWTH RATE
-------
TABLE 4-2. SAMPLE COMPUTER PROGRAM OUTPUT, SMALL PARTICLE SIZE
CRYSTALLIZATION RATES
SIMPLIFIED MOLD TANK/CLARIFIER MODEL
SATURATION 1.000
MULD TANK VOL/CLARIFIER FEED RATE,*IN 1110.
HULO TANK VUL/CLARIF1ER UNOtHF LCM, MIN 1.500+01
CLAWIFIS> CUT-OFF 31 ZE , Ml CKlNS 1.00
3LOPE,G«0«TH RATE/SIZE RELATION .50
GCOHTH RATE CONSTANT,
frtL.SAT. EXPONENT,t,RU»TH HATE
NUCLEM10'. HATE COI.STAST
KtL.SAT. Expn>itM,MjCLEATION HATE
CONC. EXP,,NUCLEATIO* RATE
6.000-DJ
1.00
2,UOO»OB
1.00
NUCLEATION »ATF,PAHT./L/"IN
PfT. HATE. HClLES/L/nI*
»T PCT SOLIDS, CLARIFIER FEED
UNDERFLOW
PPM SOLIDS, OvE»FLO»
HASS AVC. P. SIZE, HICRONS, CLARIFIER FEED
OVERFLOW
3.1J5+07
1.152-Of,
.024
.221
53.8
1.060
1.557
.591
CLARIFIER FEED PARTICLE SIZE DISTRIBUTION
JIZE.KICRONS
.00
.10
.20
.30
.10
.50
.60
.70
.80
.90
.00
.10
.20
.30
.10
.50
.60
.70
.80
.90
2.00
3.00
i.OO
5.00
6.00
7.00
8.00
9.00
10.00
15.00
20.00
25.00
POP. DENSITY, PARTS/L/MICRON
.162+12
.150+12
.110+12
.132+12
.121+12
.116+12
.110+12
.101+12
.983+11
.933+11
.701+11
.532+11
.107+11
.311+11
.191+11
.150+11
.119+11
.918+10
.761+10
.109+10
.222+09
.579+08
.181+08
.618+07
.259+07
.113+07
.528+06
.251+05
.268+01
.150+03
CUHUL NO. PCT
.00
10.19
19.66
28,19
36.75
11.19
51.77
56.61
65.12
71,26
77.07
62.01
85.78
88.63
90.62
92.51
93.63
91.86
95.68
96,32
96.64
99.16
99.88
99.96
99.99
99,99
100.00
100.00
100.00
100.00
100.00
100.00
CU1UL VOL PCT
.00
.00
.02
.12
.37
.87
1.73
3.06
5.00
7.66
11.19
15.26
19.28
23.22
27.03
30.67
31.15
37.13
10.53
13.13
16.16
75.33
87.38
92.86
95.58
97.02
97.85
98.3«
98.61
99.80
99.96
100.00
DEL VOL PCT
.00
.00
.02
.10
.25
.50
.86
1.33
1.93
2.67
3.53
1.06
1.03
3.91
3.81
3.65
3.17
3.29
3.10
2.91
2.72
29,17
12.06
5.18
2.72
1.15
.82
.19
.30
1.16
.16
.04
B-37
-------
0.259
129
10 15 2iD 25
Particle Size, microns
30
35
Figure 4-1. Population Density vs Particle Size.
B-38
-------
10
-------
3.8 .
3.7
3.6
3.5
3.4
2.7
2.6
Underflow
Y * 0.5 (microns)
"1
R = 4.2(10"*) microns /min
TCF° " 144° min
3 .2 .4 .6 .8 1.0
L , microns
Figure 4-3. Average Particle Size vs Clarifier Cut-off Size.
B-40
-------
results are shown in Figure 4-3. Improving clarifier perfor-
mance by decreasing .Lc increases the feed particle size The
underflow (sludge) particle size does not change as much. It
goes through a slight maximum with decreasing Lr and then de-
(j
creases .
The effect of solids residence time, TCF is shown in
Figure 4-4. Here the clarifier feed solids content was held
constant while relative saturation was varied. Particle sizes
remain constant since the group PCF determining particle size
remains constant, and the exponents IGR and iSN are equal. From
Equation (3-37) for M^ it is seen that the relative saturation
cancels out of the nucleation and growth rate terms in brackets
if these two exponents are equal (one in this case) . Then
relative saturation appears only in the parameter p.-,,., in the
integral. When solids residence time T__ is varied to keep Mp
and W^y constant, relative saturation varies inversely with
TC_ and p,,p is constant. Thus, particle size remains constant.
This will not be true for unequal values of ! and ig^- This
possibility is illustrated in Figures (4-5) and (4-6) for
iGR = 1 and igN = 2 and 0.5. It is seen that for igN = 2
(igN > iGR) particle size increases with increasing solids
residence time. The opposite is true for igN = 0.5 (igN
<
Plots such as Figures 4-4 can be used to illustrate the
possible use of the model in a design problem. Suppose one had
a given S02 removal rate in moles/min and wished to find the
required hold tank size. A maximum relative saturation of six
might be determined from other system considerations. From
Figure 4-4 at this relative saturation we find a solids resi-
dence TCF of 1750 minutes and precipitation rate G of 4.7 x 10
moles/Jl/min. The hold tank size, VT , is then found from the
ratio of the required total S02 removal rate and the precipitation
rate. The clarifier feed rate can then be found from the hold
tank volume and solids residence time.
B-41
-------
8
4
8
7.5.
7
6.5.
6
5.5.
5
4.5
4
3.5
107»
1.0 microns
Average Clarifier Underflow
Particle Size, Microns
1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
TCF, min
Figure 4-4. Relative Saturation, Particle Size and
Precipitation Rate yjs Solids Residence
Time.
B-42
-------
M
4) 5
U J
4)
3
HI
N
o
41
00
19
eg
o)
I
rl
O
, H
3
-------
J
U
oj
CO
I
B)
rH
0)
«
(9
U
3
Figure 4-6.
5678
WCF Weight Percent Solids
10
11
Mass Average Crystal Size and Calcium Sulfite Relative
Saturation Weight Percent Versus Solids in Clarifier
Feed WCF at Constant SOz Removal and Hold Tank Volume
B-44
-------
The next three figures, Figures 4-7 through 4-9 dis-
play sensitivity of outputs to some of the rate parameters in
the model. Weight percent solids in the clarifier feed was
held constant at 10 per cent by varying solids residence time,
TCF'
The values of the rate parameters used were chosen to
give physically reasonable model output values. The use of the
model to predict the effect of system parameters on particle
size distributions must be based on experimentally determined
rate parameters. The exponents IGR> igN, and jgN are unknown
but critical to model behavior. There are six rate parameters
in the model which must be determined from experimental data:
kGR' ^GR' kSN' "^SN' ^SN ancl r' Ttie amount and quality of data
necessary to determine these parameters cannot be judged at this
time.
Another rate parameter which should be added to the
present model is one involving the stirring and mass transfer
characteristics of the hold tank, as they affect the nucleation
rate. This dependence will be necessary if it is desired to
transfer information from one size of equipment or type of
stirring to another.
A desirable extension to the model would be growth
rate laws intermediate between the linear and constant cases
considered here. These represent two limiting cases. The
particle size dependence probably falls in between. One
possibility is to have an exponent less than one in the growth
rate equation:
B-45
-------
3.8.
Clarifier
Underflow
2.0
. 5.5
. 5
rl
e
4.5 «
o
3.5 S
3.0
2.5
Figure 4-7. Particle Size and Precipitation Rate v£ Growth Rate-Size
Slope.
B-46
-------
Figure 4-8.
6 8 10 12 14
kGR(105), microns/min
Precipitation Rate vs_ Growth Rate Constant.
T
16
B-47
-------
7 _
6 _
5 -
JSN= 0.50
3 -
0(10"),
moles/i/niin
I microns
L__, microns
1 .
.5
1.0
1.5
kSN(ioa)
2.0
2.5
Figure 4-9. Particle Size and Precipitation Rate vs Nucleation
Rate Constant.
B-48
-------
where $ is still another parameter to be determined. Its value
would be between zero (constant case) and one (linear case)
With Equation (4-1) an analytical solution for the particle size
distribution would still be possible. But numerical integration
would be necessary for the total solids concentration, M_.
Another possible rate law would be to stop the increase
in R at some size Lmax beyond which the growth rate would be
constant:
R = R (1 + vL), L < L
o ' max
R = R(L ) , L > L
max max
(4-2)
This rate law would allow all analytical solutions as with the
present model. The solutions would be algebraically more complex.
Either of the above rate laws would give finite particle
sizes over the whole range of parameters. The present linear
growth rate cannot be used beyond a maximum value of p^F of
1/3.
B-49
-------
5.0 REFERENCES
DW-006 Dwight, H. Bristol, Tables of Integrals and Other
Mathematical Data, revised. New York, MacMillian,
1947
HE-287 Kelt, James E. and Maurice A. Larson, "Effects of
Temperature on the Crystallization of Potassium Nitrate
by Direct Measurement of Supersaturation", AIChE J.
23(6), 822 (1977).
LO-R-007 Lowell, P. S., et al., A Theoretical Description of the
Limestone Injection Wet Scrubbing Process, final report,
2 vols. PB 193-029, PB 193-030, Contract No. CPA-22-
69-138. Radian Project No. 200-002. Austin, Texas,
Radian Corporation, June 1970.
MA-766 Margenau, Henry and George M. Murphy, The Mathematics
of Physics in Chemistry, New York, Van Nostrand, 1943
OT-A-56 Ottens, Erroll P. K. and Esso J. deJong, "A Model for
Secondary Nucleation in a Stirred Vessel Cooling
Crystallizer", I&EC, Fund. 12(2), 179 (1973).
PE-030 Perry, John H., Chemical Engineers Handbook, 4th ed.
New York, McGraw-Hill, 1963.
RA-060 Randolph, Alan D. and Maurice A. Larson, Theory of
Particulate Processes. Analysis and Techniques of
Continuous Crystallization. New York, Academic, 1971.
RA-543 Randolph, Alan D. and Subhas K. Sikdar, "Creation
and Survival of Secondary Crystal Nuclei. The Potas-
sium Sulfate-Water System", I&EC, Fund. 15(1). 64
(1976).
B-50
-------
6.0 NOMENCLATURE
a =QSB/RSVS = 1/RS TSB' also Particle area (a )
1/RS TSF
B = rate of birth of particles, no/fc/min
b =QT/RTVT = I/RTVT
c =QSB/RTVT - I/VST
C = Arbitrary constant of Equation (2-7)
D = Rate of disappearance, no/£/min
f = Define as ppky/MW
fCL = Factor defining clarifier particle size split,
Equation (2-21)
G = Molar precipitation rate, molesA/min
i = Exponent on relative saturation
I = Integral defined in Equation (3-1)
j = Exponent on MT> nucleation rate
k = Factor converting L2 to area
3-
k = Factor converting L3 to particle volume
k = Rate constant
L = Particle size, microns
m = Characteristic root, Equation (2-13)
M = Crystal concentration moles/liter slurry
MW = Molecular weight of crystals
N = Particle concentration, no/liter
n = Particle population density, no/£/micron
P = Parameter in growth rate, Equation (2-25)
Q = Volumetric total slurry flow rate, liters/min
r = Relative saturation
R = One- dimensional particle growth rate, microns/min
v = Particle volume
v = Vessel volume, liters
w = Weight fraction solids
Xc = 14- YLc
Y = Volume fraction clear liquor
B-51
-------
3 - Exponent in general growth rate, Equation (4-1)
Y = Slope of R vs_ L straight line, (microns)"1
T = Gamma function, Equation (2-34)
p = Density, gm/cc
T = characteristic time = vessel volume/flow rate, min
SUBSCRIPTS
C = Clarifier
CF = Clarifier feed
CO = Clarifier overflow
CU = Clarifier underflow
GR = Growth
i = Input stream
j = Output stream
n = No (particle)
o = Zero size
p = Particle (crystal)
S = Scrubber
SB = Scrubber bottoms
SF = Scrubber feed
SN = Secondary nucleation
T = Hold tank
T = Total
v - Vo lume
SUPERSCRIPTS
Average
B-52
-------
APPENDIX A
PROGRAM DESCRIPTION
The program was written in FORTRAN V for a Univac
1108. However, no sophisticated hardware or compiler features
were used. The program should be essentially machine independent
and transferable to any computer system with FORTRAN capability.
For maximum flexibility and ease of use, NAME LIST input
is used, except for an initial alphanumeric identification card.
NAME LIST input is of the form
VRBNAM = xx.xx ,
The variables can be in any order. The beginning and end of data
sets are indicated by the master NAME LIST name (here INPUT)
and END cards. Any or all parameters can be changed in serial
runs. The user is referred to the FORTRAN manual for implemen-
tation details for the computer used. The variable names in the
input are shown below with their standard or default values.
These numbers are stored internally in the program and are used
unless other values are assigned in the input data.
Variable NAME LIST Name Default Value
k.v KV */6
p RHOP 24
MW WTMOL 129-
r RELSAT
kGR GRK
iGR GRI I-"
kSN SNK
iSN
JSN SNJ °'>
Y GAMMA
(continued)
B-53
-------
Variable NAME LIST Name Default Value
TCF TAUCF
TCU TAUCU
L LC
CALCN
The last name, CALCN, is an array of up to ten numbers
controlling the particle sizes computed and printed out in the
output. The odd values are size intervals in microns. The
even values are sizes to stop the preceding interval and switch
to the next. Thus the combination:
.1, 2., 1., 10., 5., 50.,
would give results every 0.1 microns up to 2 microns, then- 1
micron intervals to 10, then 5. to 50., and so on up to 5 changes.
The program names for the output parameters are as
follows:
Program Name Definition
N - Population density
- Percent particles less
than a given size
- Volume (mass) percent
less than a given size
- Volume (mass) percent
in a given size range
CUM - Net precipitation rate
WCF - Weight percent solids
in the clarifier feed
wcu - Weight percent solids
in the clarifier underflow
B-54
-------
Program Name Definition
CFL - Average particle sizes
CUL - in the clarifier feed,
COL - underflow and overflow
The particle size distribution will be computed until
the increment in the volume, NV, is less than 10~3 of the
total. Or to a maximum of 200 increments, where a warning message
to that effect is printed. The results are printed anyway, as
they may be useful.
An error message is printed if the value of pCF
is less than 3.0, the minimum value for the linear growth rate
law.
The FORTRAN listing is given on the next pages.
B-55
-------
bd
i
Oi
00100 1* C CRYSTALLIZATION HATE , HOLD TANK/CLARIFIER ONLY
00100 2* C GROWTH HATE LINEAR IN PARTICLE SIZE
00101 3* WEAL NPZ,NZ»N(20Q),KV,LC,MT,L(200) ,MTEJ
0010} 0* DIMENSION CALCN(IO)»CU1N(200),VOL(200),PCN(200),PCV(200),DELV(200)
0010U 5* OATA KHUP/2.40/,KV/.5236/,l'irMOL/129./,GRI/l./,SNI/l./,SNJ/.5/
.0011* 6* NAME LIST/INPUT/ KV,RHOP,WT>10L,RELSAT,GRK,GUI,SNK,SNI,SNJ,GAMMA,
00113 7* 1 TAUCF,TAUCU,LC,CALCN ,DELTA
OOlla 8* 1 REAO(5,2)
UOllfc 9* 2 FORMAT ( '
00116 10* 1 ')
00117 11* 5 READ(5,INPUT,END=60)
00122 12* 501 KKITF.(6»?)
00124 13* w»ITF(h,(>) RELSAT,GRK, TAUCF, GRI,TAUCU,SNK,LC,SNI, GAMMA, SNJ
001«0 10* 6 FflHNAT ('ORELATlVE SATUR ATIOM' , T «0, F 1 0 . 3,
OOlaO IS* 1T60,'GKOwTH RATE CONST ANT,MICKONS/MIN',T100,1PE10.3/
ooi«o ifc* a1 HOLO TANK VOL/CLARIFIER FEED RATE,MIN<,Tao,oPFio.o,
001«0 17* 3T60,'REL.SAT. EXPONENT,GROWTH HATE',T100,F10,2/
OOlaO IB* U' HOLD TANK VUL/CL ARIF IER UNOF.RFLOW, MI N T10, 1PE 1 0 .3,
001UO 19* 5T60,'NUCLFATION HATE CONSTAMT',T100,E10.3/
OOIUO 20* 6' CLAKlFIfcR CUT-OFF SIZE,MICRONS',T«0,OPF10.2,
OOluo 21* 7T60,'WEL.SAT. EXPONENT,NUCLEATION RATE',Tl00,F10,2/
OOl'lO 22* 8' SLOPE,GROWTH HATE/SIZE KEL ATION , T UQ,F 1 0.2,
OOluo 23* 9T60,'CRYSTAL CHNC. ExP .,NUCLEATION RATE',Tl00,F10.2)
00111 2«* FRHO = hHOP*KV/*ITMOL*l .E-12
001«2 25* «RP = RMOf/d. + HHOP)
001^3 26* FCL = RKP/CTAIJCLi/TAUCF - 1. + RRP)
,jni«4 27* WZ = GHK*(UtLSAT - l.)**GRI
001^5 26* MPZ = SM<*(RELSAT - l.)**SNI/HZ
00l«h 29* JF(GA*MA ,GT. l.E-5) GO TO 8
00150 30* PCF = l./RZ/TAUCF
00151 31* PCU = PCF*FCL
00152 32* FM = FRHQ*NPZ
00)53 33* CO^P = FM*(6./PCIJ**4 - EXPC-PCU*LC)*(LC**3/PCU f 3.*LC**2/PCU**2
00153 3
-------
i
Ln
00161
00164
00165
00166
00167
00170
00171
00172
00172
00173
00173
00174
00175
00176
00177
00200
00201
00202
00202
00203
00204
01)205
00206
00207
00210
00212
00213
0^214
00215
Of>2 1 h
00217
00220
0.1221
00222
00223
00225
0022b
002P7
0023D
002^2
00233
00234
00235
an*
41*
42*
U3*
44*
45*
46*
47*
48*
49*
50*
51*
52*
53*
54*
55*
56*
57*
58*
59*
60*
61*
62*
63*
64*
65*
66*
67*
68*
6"*
70*
71*
72*
73*
74*
75*
76*
77*
7H*
79*
HO*
ei*
«2*
W«ITE(6,15) PCF
15 FORMATCOPCF LESS THAN MJN OF 3., '.F10.3)
GO TO 5
20 PCll = PCF*FCL
XC = 1. + GAMMA*LC
FM = FHHO*»-IPZ/GAMMA**4
XEPCIJ = XOM-PCU)
COMP = FM*((XC**3*XEPCU - l.)/(3.-PCU) - 3.*(XC**2*XEPCU I.)/
1 (2.-PCU) + 3.*(XC*XEPCU - !.)/(!.-PCU) + {XEPCU - l.J/PCU)
CUMP = FM*XEPCU*(XC**3/(PCF-3.) * 3. *XC**2/(2.-PCF) - 3,*XC/
1 (1, PCF) - l./PCF)
25 MT = CCUMP t COMP)**(1./(1.-SNJ))
WCF = MT/(MT*(1. - l./RHOP) + 1000,/WTMOL)*100,
"TEJ = MT**SN,J
MZ = NPZ*MTEJ
PZ = NZ*«Z
CFN = BZ*TAUCF*(1./FCL - XEPCU*{J,/FCL - 1.))
COM = (CFN/TAUCF - 8Z)
C******** CON = NCO/TAUCO, CUN/TAUCU » SZ
CFL = (MT/FHHO/CFN)**.33333333
COM = COMP*HTEJ*(1. - FCD/TAUCF
COL = (COM/FWHO/CON)**.33333333
FNUC = XC**(PCF - PCU)
IF(GAMMA ,LT. l.E-5) FNLC = EXP({PCF - PCU)*LC)
ZN = NZ
P = PCU
K = 2
I = 1
KLC = 0
L(l) = .0
. CUHN(l) s .0
V"L(1) = .0
29 L(K) = L(K-l) * CALCN(2*1-1)
JF(L(K) ,Lt. LC .OR. KLC .GT. 0) GO TO 30
KLC = 1
ZN = ZN*FNLC
P s PCF
30 IF(GA!1MA .GT. l.E-5) GO TO 31
MK) = .ZN*tXP(-P*L(K))
r,l) TU 32
31 N(K) = ZN/U. + GAMMA*L(K))**( 1 . + P)
32 DELN s (N(K) -f N(K-1 ) ) *C ALCN ( 2* I-1 ) X2.
-------
00
00236
002"0
002^1
0 0 2 " 2
002^3
002^7
00251
00252
002S3
0025U
00255
00260
00261
00262
0026U
00265
00266
00267
00270
00302
00302
00302
00302
00302
0030?
00302
00302
0030?
00305
00306
00307
00310
00311
R3*
flu*
«5*
«6*
h7*
H9*
90*
91*
92*
93*
9tl*
95*
96*
97*
98*
99*
100*
101*
102*
103*
104*
105*
106*
107*
10ft*
109*
110*
111*
112*
113*
110*
115*
1 16*
IF U(K) ,<;E. CALCNC2*!)) I a I + 1
CllhN(K) = CUMN(K-l) + DELN
OfclV(K) = OELN*((I_(K) + L(K-l))/2.)**3
VOL(K) = VOL(K-l) + DELV(K)
IF(OELV(K) ,LT. 1,E"3*VOL(K)) GO TO «0
TF (K ,LT. 200) GO TO 35
*HITEC6,34)
31 FOHMiJCONO CONVF.HGENCE OF MASS/VOL IN 200 INCREMENTS')
GO TO «0
35 K = K + 1
GO TO 29
UO PO «5 J = 1,K
PCN(J) = CUMN(J)/CUMH(K)*100.
CELV(J) = DtLV(J)/VOL(K)*100.
«5 PCV(J) = VUL(J)/VOL(K)*100.
CUM = Ml/TAUCF - COM
CUL = (CUM/t-KHd/B^)**.33333333
t.CU = CUM*TAUCU/(CUM*TAUCU*(1. l./RHOP) + 1 000./HTMQL) * 1 00 .
«CO = COM*1000.*WT*OL/(1. /TAUCF - l./TAUCU)
k.RITFC6,50) PZ,CUM,WCF>WCU,WCO,CFL,CUL,COL
50 FOHHAT('0'iT28,'NUCUEATIONJ S4TE,PART./L/*IN',T77t1PE10,3/T27»
1' PPT. KATE, MOLES/I/MIN',T77,E10 .3/T27f
2' fc'T PCI SOLIDS, CLAWIFIEU FEED',T77,OPF10,3X
3 T<46, lU^4Dt«FLf)Ht,T77>F10.3/T^7,
X ' PPM SOLIDS, OVERFLOW', T77,F10.1/T27,
«' MASS AVG. P. SIZE, MICRONS, CLARIFIES FEED,T77,F10.3/
5 Tfcl, ILINOF.KFLOW',T77,F10.3/
6 T62, '(IVEWFLO*1 ,177,F10.3)
IF(wCF .GT. 10.) GO TO 5
TAUCF = TAUCF + DELTA
TAUCU = TAUCU + DELTAM0.2
r,n TO 501
60 CALL EXIT
END
END OF UNIVAC 1108 FORTRAN V COMPILATION.
0 ^DIAGNOSTIC* MESSAGE(S)
-------
DCN #77-200-187-11-07
APPENDIX C
STANDARD METHODS DEVELOPMENT FOR
THE DETERMINATION OF SLUDGE QUALITY
Technical Note #200-187-11-02
1 December 1977
Prepared for:
Robert H. Borgwardt
Industrial Environmental Research Laboratory/RTF (MD-61)
U. S. Environmental Protection Agency
Research Triangle Park,
North Carolina 27711
Prepared by
K. W. Luke
J. L. Skloss
C-i
-------
TABLE OF CONTENTS
Page
1. 0 INTRODUCTION C-l
2 . 0 SUMMARY OF° RESULTS ' C-2
3 . 0 RECOMMENDATIONS C-4
4.0 EXPERIMENTAL PROCEDURES AND RESULTS C-6
4.1 Particle Size Distribution by
Visual Microscopy C-6
4.2 Particle Size Distribution by
Wet Sieving C-ll
4. 3 PSD by Coulter Counter C-25
4.4 Standardization of Settling Rate
and Settled Density Tests C-27
5 . 0 RESULTS OF THE LITERATURE SURVEY C-35
5.1 Methods for Particle Size
Determination C-35
5.2 Methods for Settling Rate and
Density Measurements C-50
REFERENCES C-51
C-ii
-------
LIST OF FIGURES
Figure
Paee
4-1 Photomicrograph of Sludge Granules
Taken from Lime Scrubber, 200 X C-I2
4-2 Photomicrograph of Sludge Platelets
Taken from Limestone Scrubber, 200 X C-13
4-3 Sludge Granules from Lime Scrubber:
Cumulative Percent of Particles Versus
Diameter C-15
4-4 Sludge Platelets from Limestone Scrubber.-
Cumulative Percent of Particles Versus
Length and Width C-16
4-5 Sieved Sludge Granules: Average Cumulative
Percent of Particles Versus Diameter C-23
4-6 Sieved Sludge Platelets: Average Cumulative
Percent of Particles Versus Width C-24
4-7 Sieved Sludge Platelets: Corrected
Cumulative Percent of Particles Versus
Width C'26
4-8 Settling Rates of Sludges Versus Weight
% Solids at 25°C and 20°C
Or, i onOp C-34
C-iii
-------
LIST OF TABLES
Table
4-1 Particle Size Distribution by
Microscopic Method C-14
4-2 Particle Size Determination by
Wet Sieving of Granules C-21
4-3 Particle Size Distribution by
Wet Sieving of Platelets C-22
4-4 Coulter Counter Data for the
Sludge Granules C-28
4-5 Coulter Counter Data for the
Sludge Platelets C-29
4-6 Settling Rate of Sludges Versus Weight
7o Solids at 25°C and 50°C C-33
5-1 Particle Size Determination C-36
5-2 Bulk Density and Settling Rate
Measurements C-47
C-iv
-------
1.0 INTRODUCTION
The flue gas desulfurization (FGD) sludges produced
in lime, limestone, and double alkali systems generally are
difficult to settle. Radian Corporation was contracted by the
EPA to investigate the prospects for improving the quality of
FGD scrubber sludges. This technical note reports the work
performed to develop standard analytical techniques for measuring
particle size distribution (PSD), settling rate, and settled
density. A literature survey is also presented.
Particle size distribution of the precipitated solids
is an important factor in the settling and dewatering characteris-
tics of FGD sludges. Numerous methods for measuring PSD are
available. However, most of these are time consuming, require
expensive equipment, or give only approximations of the PSD.
A survey of the literature showed that optical micro-
scopic methods have been used to size FGD sludges. Two addi-
tional sizing methods were selected for this study. These
methods are wet micromesh sieving and Coulter Counter analysis.
The results of both of these techniques were compared to the PSD
determined by microscopic measurements . The literature was also
surveyed for methods to measure settling rate and settled
density of sludges. Specific results of the literature survey
are given in Section 5.
The methods development and standardization studies
were carried out using two types of sludges: granular particles
from a lime scrubber and platelet particles from a limestone
scrubber. Tests were also performed to determine the effect
of several variables on settling rates of these sludges. These
included temperature, cylinder size, and weight percent solids
in the slurry.
C-l
-------
2.0 SUMMARY OF RESULTS
The optical microscopic method for the measurement of
PSD worked well for both the granular and platelet sludges.
A representative distribution of particles on a slide was obtained
by filtering a dilute suspension of the particles onto a Milli-
pore (cellulose acetate) filter membrane and rendering the membrane
transparent with acetone. Other methods such as dry or wet
mounting of the particles directly on the slide were also satis-
factory, although these methods do not give as consistently re-
liable particle distributions.
The photomicrographs were taken at 200X magnification.
This offered a compromise between having large, easily measured
particles, and having a sufficient number of particles in each
photograph available for sizing. At this magnification the
smallest particles visible were about 1 micron in size.
The micromesh sieves gave results comparable to those
obtained by the microscopic method when granular particles were
tested. The number of particles retained on each sieve was
calculated from the weight of sludge on each sieve by assuming
an average particle size, shape, and density. The micromesh
sieve and optical microscope results were then compared on
the basis of a population distribution as a function of average
particle diameter. The sieves worked equally well for the plate-
lets. Comparison of the sieve data for platelets with the micro-
scopic results was possible by making some assumptions about the
relative dimensions of the particles and their orientation as
they passed through the sieves. Specifically, it was assumed
that the platelets passed through the square holes of the sieves
in a lengthwise fashion such that the diagonal width of the
square opening was equal to the width of the thin platelet
C-2
-------
particle. With the above assumption the optical and sieve
results agreed fairly well for particles in the range of 10-
40 microns.
The Coulter Counter method generally observed and mea-
sured particles much smaller in size than the other two methods
for both types of sludges. Reasonable agreement between results
for all three methods was obtained, however, when comparing PSD's
for particles greater than 2y diameter only.
Settling rates were found to be dependent on the weight
percent of solids in the slurry, the temperature, and the type
of particles. The settling rate is independent of cylinder size
in the range tested. An increase in weight percent solids
resulted in a significant decrease in the settling rate. A
50 to 60 percent increase in the settling rate was observed
when the temperature was increased from 25 to 50°C. This in-
crease was attributed to a decrease in the viscosity of the
liquid. The granular particles settled slower than the plate-
lets, indicating that the granules had an effectively smaller
particle size.
The settled density was found to be dependent on
particles type with the granules having the lower settled density.
C-3
-------
3.0 RECOMMENDATIONS
The microscopic method for determining particle size
distribution is recommended based on the results of this work.
The method has the following advantages:
The individual particles are visible.
Using good mounting techniques, the
accuracy of PSD is dependent only on the
visual measuring technique.
A permanent record is obtained in the
form of a photograph.
The morphology of the particles can
be seen.
Results are on a population basis.
The main problem encountered in the microscopic method
was obtaining a representative distribution of particles on the
microscope slide. This x^as overcome by slurrying the solids in
an alcohol-water solution and filtering the slurry on a thin
membrane. After mounting, the membrane was rendered transparent
with acetone vapors making the sludge particles clearly visible.
Best results were obtained at 200X magnification. The
images were sufficiently magnified to see the ly particles, and
a total of 250 particles could easily be included in the photo-
micrograph field. In this work the particle size was measured
with a transparent ruler. However, another good and perhaps
faster method would be to use a template with circles or holes
of a known size. The circles or holes could be placed over the
C-4
-------
particles on the photomicrograph until a proper match was located
This method would be most applicable to spherical or granular-
shaped particles.
The micromesh sieves gave satisfactory particle size
distributions on a weight basis. No significant saving of time
compared to optical microscopic methods was noticed, however,
because of time required for the weighing, drying, and sieving
procedural steps. Because of their small size and weight, the
sieves may be useful in the field where an expensive microscope
is not available.
The Coulter Counter method for sizing FGD sludges
may have great potential. It is faster than the other methods,
and a large number of samples may be run to determine relative
PSD. More work needs to be done to obtain proper calibration
and optimization of the method, particularly for particles less
than l-2y.
The settling rates for slurries should all be measured
at constant weight percent solids and constant temperature if
meaningful comparisons are to be made. Any selected constant
concentration between 3 and 10 percent solids should be satis-
factory. The recommended liquor temperature is any specific
value between 25 and 50°C which simulates the FGD scrubber
operational mode for settling solids. After the solids have
settled overnight the settled density may be calculated.
C-5
-------
4.0 EXPERIMENTAL PROCEDURES AND RESULTS
As a result of the literature survey, several methods
of solids characterization were chosen for further investigation.
These included particle size distribution by visual microscopy,
wet sieving, and Coulter Counter (Sections 4.1, 4.2, and 4.3),
and the standardization of settling rate and settled density
measurements (Section 4.4).
The standard method for particle size determination
is currently visual microscopy. The purpose of this study was
to compare the results obtained by wet micromesh sieving and
Coulter Counter to the results obtained by optical microscopy.
Also, the effects of cylinder size, temperature, and weight per-
cent solids on settling rate was determined and a standard pro-
cedure recommended.
There are two main types of sludge to be considered:
1) those produced from limestone scrubbing processes, which
consist of thin plates of approximate dimensions 30:20:1, and
2) those produced from lime scrubbers which are granular and
approximate a spherical shape. Because of this great difference
in shape, tests were performed on both types of sludge.
4.1 Particle Size Distribution by Visual Microscopy
Visual microscopy is the standard to which the other
methods will be compared. A description of the method develop-
ment and results follows.
4.1.1 Microscopic Method Development
The ASTM E-20 Method was used as a reference in this
study to determine particle size distribution. This method
consists of mounting the sludge solids on a glass microscope
C-6
-------
slide and taking photomicrographs to include a total of 250
particles. Measurement of the particle sizes is made on the
photomicrographs with a finely divided transparent ruler. The
microscopic method allows direct viewing of the individual
particles. The photomicrograph provides a record of the sludge
solids, and further qualitative observations of the crystal form,
size, and texture of the solids may be made.
Most attention in this study was directed to finding
a suitable method to mount the sludge solids on a microscope
slide such that a representative distribution of the particles
was obtained and sharply contrasted photomicrographs could be
taken. The various mounting techniques tried were:
spreading dried solids over a microscope
slide,
pressing slurried solids between two
microscope slides, and
filtering slurried solids on a filter
membrane and clearing the membrane while
on the microscope slide.
Spreading Dried Solids Over Microslide
The dried solids when spread over a microscope slide
with a spatula or pointer provided excellent visibility and con-
trast for taking photomicrographs. However, the distribution of
particles was not sufficiently uniform to determine particle
size distribution. Better results were obtained when the^solids
were smeared over the microscope slide with a smooth fabric.
Also, uniform distribution of particles was accomplished by
mixing the solids in methanol-water solution and filtering on
Nuclepore polycarbonate filter membrane. After drying, the
C-7
-------
membrane containing the solids was inverted on a dry microscope
slide and gently smeared. This procedure gave acceptable results.
Pressing Slurried Solids Between Two Microscope Slides_
Various materials were mixed with the dried sludge to
make slurries which were smeared on microscope slides. These
were:
water,
water plus surfactants,
water plus glycerol,
glycerol,
mineral oil,
silicone grease, and
silicone glue.
Each slurry was smeared on a microscope slide, and another
microscope slide was placed on top. When the two slides were
pressed together, a thin film of the slurry spread between the
slides.
Best results were obtained with the silicone grease
and silicone glue. These materials afforded good mounting charac-
teristics, and sufficient contrast was present in the photomicro-
graph to allow particle measurement. The other materials listed
above for making slurries are not recommended, because the smaller
particles tended to move about on the slide when handled. Even
C-8
-------
while being viewed the slurries were set in motion by the heat
from the microscope objective light which shined through the
microscope slide. Also, contrast was poor between the crystals
and the background in most cases.
Filtering Slurried Solids on a Membrane
The sludge sample was slurried in methanol-water
solution and was filtered and dried on filter membranes. Two
types of membranes were tried - Nuclepore and Millipore. The
filter membranes used were 47 mm diameter and 0.8u pore size.
It was assumed that the majority of particles exceeded ly.
The Nuclepore polycarbonate membrane was thin, smooth,
and transparent to the light. However, when viewed at 200X
magnification, the pores in the filter membrane cast an etched
background which blended with some of the sludge particles.
Repeated attempts to render the membrane transparent without
losing particles from the smooth surface were not successful.
The Millipore membrane made of cellulose acetate was
preferred in these tests for their handling ease. The cellu-
lose acetate membranes were thicker and provide a coarser surface
for holding the particles. After the solids were filtered and
dried on the membrane, the membrane was placed on the microscope
slide and rendered transparent with acetone vapors. Reliable
particle size distributions were obtained by this recommended
procedure.
4.1.2 Recommended Millipore Membrane-Acetone Vapor Method
for Mounting Solids on Microslides
A 2-8 mg sample of dried sludge solids is placed on a
Piece of smooth, water resistant paper. Two-three drops of
C-9
-------
5070 methanol-water solution are added to the solids, and the
slurry is gently mixed with a spatula or pointer to separate
any clumps into individual particles. The slurry is quantita-
tively transferred using a wash bottle to a 125 ml flask con-
taining 50 ml of 50% by volume methanol-water solution.
(If the original FGD sludge slurry is available, it is necessary
only to transfer an aliquot containing 2-8 mg of solids to the
methanol-water solution.)
The flask is swirled to insure uniform mixing, and
the slurry is filtered on a 47 mm Millipore membrane using a
suction filtering assembly. The membrane is the plain white
cellulose acetate, O.Sp pore size variety (Millipore Catalog
No. AAWP-04700). After filtering, the membrane is placed in a
petridish to dry for 15-30 minutes in an oven set at 50°C.
The dried membrane containing the solids is removed
from the petridish, and a 1 cm strip is cut with scissors and
placed on a microscope slide (1x3 inch). Warm acetone
vapor is directed over the membrane until it turns clear.
Acetone vapor is supplied from a heated side arm flask containing
acetone.
Another microscope slide is placed over the first slide
and membrane, and the two microscope slides are taped together
and labeled. The slides are ready for microscopic examination
and taking photomicrographs. 200X magnification works well for
including 250 particles in a single photomicrograph field.
4.1.3 Equipment and Materials for the Millipore-Acetone
Method
Microscope and camera attachment
Glass microscope slides, 1x3 inch , 1 mm thick
C-10
-------
Oven set at 50°C
Hot plate
Suction flask assembly, 47 mm filter
Millipore filter membranes, white plain, 47 mm
diameter, 0.8 pore size
50-50% by volume methanol-water solution
125 ml erlenmeyer flask
Wash bottle
Spatula
Smooth, water-resistant paper
Petridishes, 50 mm
Side arm flask and stopper
Acetone
Scissors and transparent tape
4.1.4 Optical Microscope PSD Results
The two types of sludge solids were mounted on microscope
slides using the filter membrane-acetone method described in
Section 4.1.3. Several photomicrographs were taken at 200X
magnification of each sample. Figure 4-1 is an example of the
sludge granules from a lime scrubber; Figure 4-2 is an example
of the sludge platelets from a limestone scrubber. Ruler
measurements were made on sufficient photos to include at least
250 particles of each sample. The results are shown in Table
4-1. Diameters are reported for the granules, and both the
length and width are reported for the platelets. The cumulative
percent of particles less than the largest size in each range
is plotted in Figure 4-3 and 4-4 on a number basis.
4-2 Particle Size Distribution by Wet Sieving
A set of six micromesh sieves was obtained from the
Buckbee Hears Company of St. Paul Minnesota. The sieves measured
C-ll
-------
FIGURE 4-1 PHOTOMICROGRAPH OF SLUDGE GRANULES
TAKEN FROM LIME SCRUBBER, 200 X
-------
>&. **& "I*
", ,''-£( ' ..-*" / ; ^-t,|
FIGURE 4-2 PHOTOMICROGRAPH OF SLUDGE PLATELETS TAKEN
FROM LIMESTONE SCRUBBER, 200 X
-------
TABLE 4-1. PARTICLE SIZE DISTRIBUTION BY MICROSCOPIC METHOD
O
i
Size
Range (vO
1-5
5-10
10 - 15
15 - 20
20 - 25
25 - 30
30 - 35
35 - 40
40 - 45
45 - 50
Granules
// Of
Particles
56
121
77
56
26
6
3
0
Cumulative %
Less Than
16.2
51.3
73.6
89.8
97.4
99.1
99.9
VLOO
Platelets
Length
# Of Particles
5
35
79
78
54
36
18
9
2
4
Cumulative %
Less Than
1.6
12.5
37.2
61.6
78.4
89.7
95.3
98.1
98.7
^99.9
Width
# Of Particles
45
117
72
48
27
8
3
2
Cumulative %
Less Than
13.9
50.3
72.7
87.6
95.9
98.4
99.4
^99.9
-------
o
100
I 90
(0 80
HI
Z 70
LU
O
LU 60
Q.
LU
50
40
O
D3°
Ul
CC
W20
<
LU
10
15
50
55
Figure 4-3.
20 25 30 35 40 45
DIAMETER, MICROMETERS
Sludge Granules from Lime Scrubber: Cumulative Percent of
Particles Versus Diameter.
60
-------
o
I
100
2 90
X
to 80
CO
ui
H 7°
Z
UI
o ftn
a: 60
ui
a.
uj 50
H
-J 40
D
O 30
a
UJ
20
CO
10
Q PLATELET LENGTH
A PLATELET WIDTH
10 15 20 25 30 35 40 45
LENGTH AND WIDTH. MICROMETERS
50
55
GO
Figure 4-4. Sludge Platelets from Limestone Scrubber: Cumulative Percent
of Particles Versus Length and Width.
-------
3 inches in diameter and about 1 inch in depth. The mesh had
precision electro-formed square openings with sides of 2, 5
8, 13, 20 and 35 microns in length. The tolerance for aach'opening
was ±2 microns which limited the accuracy of the smaller sieves
relative to the larger ones.
4.2.1 Wet Sieving Method Development
There are several steps in the sieving procedure which
deserve special attention. These are sample preparation, sieve
preparation, the actual sieving, and calculations of results
and are described in the following sections.
Sample Preparation
A dried representative sludge sample is required.
The slurry cannot be filtered directly because the aqueous
slurry liquor is too viscous to permit rapid filtration through
the micromesh sieve. If the sample is taken as a slurry it is
filtered and then dried at 40-50°C. The sample is allowed to
equilibrate with the atmosphere at room temperature before
weighing because the sludge solids tends to absorb some moisture
from the atmosphere. The dry sludge should be free of clumps
and have a consistency similar to that of flour. A sample size
of 500 to 700 mg is used. If the sample is unusually fine-
grained a smaller sample may be more desirable.
Sieve Preparation
The sieves are thoroughly cleaned before use. The
best method for cleaning them is by ultrasonic cleaning, since
compressed air jets and brushes may damage the mesh. A mixture
of methanol and water is used in the cleaner with the solution
completely covering the sieves. The small size of the sieves
C-17
-------
usually allows several of them to be cleaned at the same time.
The time required to clean the sieves varies according to the
efficiency of the cleaner. When clean, the sieves are removed,
rinsed on both sides with methanol, and dried at 40-50 C. They
are then weighed on an analytical balance capable of an accuracy
of at least 1 milligram. The sieves weigh about eighty grams
each.
Sieving Procedure
Because of the small size of the particles, dry sieving
is impractical. The smallest particles become airborne when the
sample is shaken. Therefore, the particles are washed through
the screens with methanol delivered in a jet from a polyethylene
wash bottle. Other liquids may be used if they have a low
viscosity and surface tension and do not dissolve calcium sulfite.
The sieves were stacked with the largest screen openings
(35u) placed on top. The sludge sample may be added directly
to the top sieve from a piece of weighing paper. The particles
are washed through until the effluent from the first sieve is
clear, which may be observed by lifting and tilting the sieve
slightly. Then it is washed once more to make sure all of the
undersize particles reach the next sieve. The top sieve is
removed and the process is repeated for the next one, and so on.
A tapping up and down motion of the sieve while rotating
it will help to prevent blinding of the holes and will speed up
the particle sizing separation. The liquid drains through the
smaller sized sieves very slowly, so they should be checked often
to avoid over filling and thus spillage and sample loss. The
drainage through the smaller sieves was increased by the applica-
tion of a light vacuum from a water aspirator. The filtrate was
C-18
-------
collected in a filter flask and saved to pour through the
next smaller sized sieve.
The entire sieving procedure uses about 500 ml of metha-
nol and takes about two hours, not including weighing, cleaning
or sample preparation. After all of the particles were sized,
the sieves were dried and weighed in the same manner as. before.
They are then ready to be cleaned for sieving the next sample.
Calculations
After the weight of particles on each sieve has been
determined, the data may be compiled in several ways : cumulative
percent greater than or less than each sieve size, or percent
between sievessizes. Data is usually plotted on probability
graph paper as cumulative percent less than or greater than a
size.
When attempting to compare sieving results to those
of photomicrographs , problems were encountered because sieve
results are based on the weight of particles in a size range
and photomicrographs give the number of particles in a size
range. In order to compare these two methods, the weights of
particles retained on each of the sieves were converted to the
number of particles contained in that mass. This was done as
follows:
# of particles - weight (g)/[density (g / cm3)-volume (cm3):
Clearly, to compute the volume of a particle, its shape must be
known. The granular particles are assumed to be spheres and
C-19
-------
platelets are given dimensions of 30:20:1. For example, if 0.2
grams of sludge are retained on the 13 y sieve, following a 20y
sieve, the average diameter of a spherical particle is calculated
to be 16.5 microns. This would give an average volume of
2.35 x 10"9 cm3. If the sludge density is assumed to be
2.5 g/cm , then the number of particles is
0.200/(2.35 x 10~9 x 2.5) = 3.4 x 107
particles between 20 and 13 microns. The data is then graphed
in the usual manner.
It was found that the best agreement between micromesh
sieve and optical microscope PSD's for platelets was obtained
when the platelets were assumed to pass through the sieve holes
lengthwise. In this case the PSD is more a measure of the plate-
let width than of the length or thickness. Also, assuming that
the platelets pass through the square sieve holes according to
the diagonal width of the hole further improves the agreement
between sieve and optical data.
For the example given above the average width of a
platelet would be 16.5 x i/2~microns; the length and height are
calculated using the ratios of length 30:width 20:height 1.
4.2.2 Results of Sieving Tests
Duplicate sieving tests were performed on each type
of sludge, granules and platelets. The weights of particles
retained on each screen were converted to the number of
particles. The percent of particles smaller than each sieve
size was calculated and the average values were used for plotting
the data. The data are shown in Table 4-2 for granules and
Table 4-3 for platelets. The graphs are shown in Figure 4-5 and
4-6 on a number basis.
C-20
-------
TABLE 4-2. PARTICLE SIZE DETERMINATION BY WET SIEVING OF GRANULES
Sieve
Size
U
2
5
8
13
20
35
Weight of
Particles
R
0.00293
0.07999
0.06963
0.39921
0.39908
0.05850
Test //I
Est. // of
Particles
5.24xl07
2.23xl08
4.59xl07
6.79xl07
1.47xl07
6.99xl05
Cumulative*
% Less Than
%3
13.0
67.9
79.3
96.1
99.7
Weight of
Particles
g
0.00216'
0.06991
0.07933
0.33543
0.22033
0.03839
Test #2
Est. # of
Particles
3.86xl07
1.95xl08
5.23xl07
5.71xl07
S.lOxlO6
4.58xl05
Cumulative *
% Less Than
2
11.0
66.4
81.2
97.4
99.7
Average
Cumulative*
% Less Than
2.5
12.0
67.2
80.2
96.8
99.7
o
I
ro
On a number basis
-------
TABLE 4-3. PARTICLE SIZE DISTRIBUTION BY WET SIEVING OF PLATELETS
O
i
Sieve
Size
u
2
5
8
13
20
35
Weight of
Particles
g
0.00036
0.06670
0.05789
0.14245
0.17920
0.22119
i
Test #1
Est. # of
Particles
4.49x10 7
1.29xl09
2.67xl08
1. 69x10 8
4.59x10 7
1.84x10 7
Cumulative *
% Less Than
0
2.5
72.5
87.1
96.2
98.7
Weight of
Particles
g
0.00128
0.08436
0.04723
0.15773
0.16790
0.20637
Test //2
Est. // of
Particles
1. 60x10 8
1. 64x10 9
2. 18x10 8
1. 87x10 8
4.31x10 7
1. 72x10 7
Cumulative*
% Less Than
2
7.1
79.6
89.3
97.6
99.5
Average
Cumulative *
% Less Than
1
4.8
76.1
88.2
96.9
99.1
* On a number basis.
-------
o
I
100
90
80
I
I-
S 70
UJ
_l
H 60
UJ
O
OC 50
UJ
0.
UJ
0
40
30
20
10
O
> 5 10 15 20 25 30 35 40 45 50 55 60
DIAMETER. MICROMETERS
Figure 4-5. Sieved Sludge Granules: Average Cumulative Percent of
Particles Versus Diameter.
-------
100
90
80
I
I-
CO
<0
UJ
70
60
o
i
ho
50
z
UJ
o
or
UJ
D.
UJ
> 30
40
s
3
O
20
10
10 15 20 25 30 35 40
WIDTH, MICROMETERS
45
50 55
60
Figure 4-6. Sieved Sludge Platelets: Average Cumulative Percent of
Particles Versus Width.
-------
sieve
in-
If it is assumed that the plates pass through the
holes diagonally then the apparent size of the openings is
creased by a factor of 1.414 (VI). This made the particle Tize
distribution larger and the data agree better with the photo-
micrographs. A plot of this data may be found in Figure 4-7
4.3 PSD by Coulter Counter
Two samples were sent to an independent laboratory
for particle size distribution analysis by Coulter Counter.
This instrument measures the number and diameter of
particles in an electrically conductive fluid. As a suspension
of the particles is drawn through a small aperture the resis-
tance across it is measured by electrodes on both sides. The
resistance change across the aperture is proportioned to the size
of the particle passing through it.
4.3.1 Procedure
A small amount of the sample was dispersed in Coulter
isoton solution with Triton X-100 added as a surfactant to
reduce particles agglomeration. Dispersion of particles was
completed by ultrasonic vibration. After 1:10 dilution the samples
were then analyzed in a Coulter Counter Model TA with aperture
setting at 70y. The PSD data was recorded as the number of
particles in each size range. The particle sizes are expressed
as diameters in microns.
Because the particle sizes are reported as diameters,
the data may be sized as is for granular or spherical-shaped
particles. The platelets sample cannot be treated this way.
Assuming dimensions of 30:20:1, the diameter was converted to
the width of the particle as follows:
C-25
-------
o
100r
90
to
w
UJ
z
Ul
o
cc
UJ
Q.
UJ
80
70
6 Of
50^
4 Of
O
D
UJ
H
O
UJ
CC
cc
o
o
30
20
10
0 5 10 15 20 25 30 35 40 45 50 55 60
WIDTH, MICROMETERS
Figure 4-7. Sieved Sludge Platelets: Corrected Cumulative Percent of
Particles Versus Width.
-------
20 x 3 Vvolume of particle/600 = width of
a particle.
The width dimension was chosen to allow comparison with
the sieve and optical microscope data.
4.3.2 Results
The results of the Coulter Counter sizing are found
in Table 4-4 and 4-5. The size distributions obtained by this
method were lower than those obtained by the other two methods. Best
comparisons were obtained by considering only the Coulter Counter
data above 2y for the granules diameters and above 3y for the
platelets widths. Below these limits a large number of particles
were reported by the Coulter Counter method that were not observed
in either the photomicrographs or the scanning electron micro-
graphs of the same sludge samples. The ultrasonic dispersion
step may have broken the sludge crystals, however, there is no
evidence that this occurred.
4.4 Standardization of Settling Rate and Settled Density
Tests
The purpose of this work was to determine the effect
of cylinder size, weight percent solids, temperature, and
particle size on settling rates and settled bulk density of
FGD sludges.
4.4.1 Procedure
Settling Rate
A sample of dry sludge was added to a weighed graduated
cylinder and sufficient water was added to bring the slurry to
:-27
-------
TABLE 4-4. COULTER COUNTER DATA FOR THE SLUDGE GRANULES
Diameter
y
2.00-2.52
2.52-3.17
3.17-4.00
4.00-5.04
5.04-6.35
6.35-8.00
8.00-10.1
10.1-12.7
12.7-16.0
16.0-20.2
20.2-25.4
25.4-32.0
% Volume
2.5
2.0
2.5
3.9
6.7
11.9
16.7
18.1
16.2
12.4
4.9
2.2
Number
12467
4987
3116
2415
2103
1805
1305
706
316
120
23
5
% Number
42.4
17.0
10.6
8.2
7.1
6.3
4.4
2.4
1.1
0.41
0.08
0.02
Cumulative *
% Less Than
42.4
59.4
70.0
78.2
85.3
91.6
96.0
98.4
99.5
99.9
100
100
* On a number basis.
C-28
-------
TABLE 4-5. COULTER COUNTER DATA FOR THE SLUDGE PLATELETS
Diameter
y
3.8-4.8
4.8-6.1
6.1-7.6
7.6-9.6
9.6-12.1
12.1-15.3
15.3-19.3
19.3-24.3
24.3-30.6
30.6-38.6
38.6-48.5
48.5-61.2
- ' ^-^-
% Volume
8.0
4.7
4.7
4.7
5.6
8.0
8.7
13.1
15.9
18.7
5.6
2.3
Number
8134
2392
1196
598
358
254
138
104
63
37
5
1
% Number
61.2
18.0
9.0
4.5
2.7
1.9
1.0
0.78
0.47
0.28
0.04
0.01
Cumulative
% Less Than
61.2
79.2
88.2
92.7
95.4
97.3
98.3
99.1
99.4
99.4
99.4
99.4
* On a number basis.
C-29
-------
the desired weight percent solids. The water used to make the
slurry was previously equilibrated with similar scrubber solids
and filtered. This helped prevent any of the crystals from
dissolving. The slurry was mixed thoroughly by repeated inversion
of the cylinder. A ruler graduated in centimeters was attached
to the cylinder. A timer was then started and the height of
the liquid solids interface was measured at one minute intervals
for 10 to 15 minutes.
If the settling tests are to be performed in the field,
a more convenient way to prepare the sample might be to determine
the weight percent solids of the slurry, and then dilute it to
the desired value obviating the need for slurry filtration.
The data is plotted on regular graph paper. The
settling rate is determined from the slope of the line for the
first 5 or 6 minutes of settling. This region of the settling
rate curve is for the hindered settling mode.
Settled Density
After the slurry has settled for at least six hours, but
preferably overnight, the density of the settled fraction is cal-
culated from the following equation:
WtT - p£(VT - Vs)
Settled density =
V
s
where,
Wt = total slurry weight (grams)
V^ = total slurry volume (mis)
V = volume of settled solids (mis)
o
p. = supernatant density (g/ml)
C-30
-------
The measurement of p£ was made with a hydrometer calibrated over
the range of 1.000 to 1.200 g/mJl.
By knowing or assuming a solids density, p , the weight
percent solid in the settled fraction can also be calculated using
the the following equation:
Weight % Solids f_ga_ VWtT " pgVT
in Settled = \P - Pt - p V
Fraction
4.4.2 Results
S , T p v
Effect of Cylinder Size
Tests were performed to determine the effect of container
diameter on settling rates. Settling data were recorded as a
function of time in three containers of different diameters. The
cylinders used were 250 ml, 500 ml and 1000 ml capacity each.
Although the initial height of the slurry in each cylinder was dif-
ferent for a constant slurry volume, the observed settling rates
were constant, indicating that settling rate is not a function of
container size within the size range tested.
Effect of Percent Solids
The weight percent solids was varied over the range of
1% to 20% and was found to have a large effect on settling rates.
For the platelet sludge sample the settling rate at 25 C
ranged from 3.4 cm/min at 1% solids to 0.18 cm/min at 20% solids.
The granular sludge sample which consisted of smaller particles
showed a range of 2.45 cm/min at 2% solids to 0.10 cm/min at 15%
solids at 25°C. By extrapolating these results it is estimated
that the two sludges will have approximately equal settling rates
at about 25% solids. The results of these tests are shown in
Table 4-6 and in Figure 4-8.
C-31
-------
Effect of Temperature
It was found that upon increasing the slurry tempera-
ture from 25°C to 50°C the solids settling rate increased by
50-60% for both types of samples over the entire range of
weight 7o solids investigated (Table 4-6 and Figure 4-8) . The
difference in settling rate was attributed to changes in the
viscosity of the water and agrees with rate changes predicted
from Stoke's Law calculations.
Effect of Particle Size
The smaller granular particles settled slower than the
platelet particles at all the weight 7* solids concentrations
that were compared.
Results of Settled Density Tests
The settled density was calculated for each type of
sample. The settled density for the platelet-type particles
was 1.39 g/cm3 and for the granules the settled density was
1.25 g/cm3 .
C-32
-------
TABLE 4-6. SETTLING RATE OF SLUDGES VERSUS WEIGHT % SOLIDS AT 25°C AND 50°C
Weight %
Solids
1
2
3
4
5
6
7
8
9
10
12.5
15
20
Granules
Settling Rate (cm/hr)
25°C 50°C
2.38
1.64 2.64
1.30 2.04
0.74 1.10
0.42
0.30 0.45
0.10
Platelets
Settling Rate
25°C
3.35
2.95
2.51
2.34
1.95
1.70
1.50
1.30
1.15
0.98
0.65
0.44
0.18
(cm/hr)
50°C
3.03
1.48
0.60
C-33
-------
4.0
3.0
rt
-------
5.0 RESULTS OF THE LITERATURE SURVEY
The literature was searched for methods to determine
particle size distribution, settling rate, and settled density
of fine powders. The results are given in Tables 5-1 and 5-2.
5.1 Methods for Particle Size Determination
There are a large number of methods which have been
used for particle size determination. These methods fall into
the following broad categories:
direct measurement with the aid of a
visual or electron microscope (or a
hologram),
sieving,
sedimentation in a fluid,
measurements based upon particle
trajectories,
measurements based upon radiation
scattering, and
electrical measurements.
More detailed descriptions of the principles involved,
the apparatus required and the applicability of these methods
are given in Table 5-1.
Optical methods (visible light microscopy, electron
microscopy, and holography) provide a direct measure of the
C-35
-------
TABLE 5-1. PARTICLE SIZE DETERMINATION
Method
Principle
1.0
1.1
Microscopic
Visible Light
>!anual Scan
l
LO
1.2
Visible Light
Automatic
Scan
A prepared sample is observed
visually under a microscope.
Particles are counted and
sized individually usually by
comparison with'circles of a
known size on a transparent
plate, or by measurement of a
horizontal or verticle linear
dimension combined with statis-
tical data treatment. ASTM
E20-68 calls for measurement
of at least 250 particles in
each of three randomly select-
ed fields to insure calcula-
tion of a statistically re-
liable size distribution.
Counting and sizing may also
be done using a photomicro-
graph projected on a grided
Apparatus
In this method, the human
observer is replaced by an
automatic counting and siz-
ing system. These systems
scan the -sample slide or
photograph using a narrow slit
or dot of light. Interception
of this light by a particle
is detected photometrically.
The problem of meaningful
interpretation of scanning
results is not simple. The
information derived is depen-
dent on the number and shapes
of the scanning beams. Also,
the concentration of the sam-
ple being scanned affects
errors caused by overlapping
or coincident particles.
Sophisticated electronics are
required to provide particle
size readout.
A good quality
microscope is re-
quired. The
instrument charac-
teristics, pri-
marily aperture
and magnification,
must be sufficient
to resolve the
edges of the
smallest particle
class size of in-
terest.
Commercial Instru-
ments such as the
Quantimet are avail-
able. These con-
sist of scanning
and photometric
equipment along
with a minicompu-
ter for interpre-
tation of raw
output.
Applicability and Constraints
Microscopy is generally con-
sidered as a standard method
for absolute particle size
measurement. Unfortunately,
manual microscopy is tedious
and time consuming, about 3-4
hours are usually required
for one sample. An operator
must be skilled in sample
preparation as well as count-
ing and size determination.
This method is applicable to
nearly any particulate matter
ranging in size from ,2^i to
~ 74|_i. The measurement of
only two dimensions (those In
the plane of the field) may
lead to serious errors in case
of disc-like particles. Nor-
mally, the assumption is made
that a randomly sampled field
will contain particles with no
preferred orientation.
Primary constraints on the use
of automatic scanning are the
effects of particle size,
shape, and concentration on
results. Irregularly shaped
particles or particles too
close together in the field
may lead to counting and siz-
ing errors. The lower parti-
cle size limit for automatic
scanning is generally higher
than for manual scanning,
about .8[j. Proper form is
essential as in manual scan-
ing.
As many as 100 fields may be
counted in 2 minutes with one
commercial instrument (Quanti-
met) .
Accuracy and Precision
The accur-cy and pr^^lsion of
microscopic sizing (assuming
an adequate instrument) are
dependent primarily on three
factors: 1) the skill and ex-
perience of the operator, 2)
the representative character
of the prepared sample, and
3) the number of particles
counted. The statistical re-
liability of the results
increases as (n)^ where n is
the number of particles coun-
ted. To obtain the number of
particles of a given size in
a sample within ± 2"L, ~ 10,000
particles would have to be
counted. ASTM E20-63 recom-
mends a count of at least 250
particles in each of three
randomly sampled fields.
Reference
AM-011
CA-040
HA-044
KI-014
LA-022
SI-010
sr-040
su-ou
MO-016
OR-006
SC-R-141
IR-016
CA-040
HA-044
KA-021
MO-016
OR-006
SM-007
WA-022
IR-016
(continued)
-------
TABLE 5-1. (Cont'd.)
Method
1.3 Electron Micro-
scope
Principle
O
I
1.4 Holography
2.0
2.1
Sieving
Sieving
The electron microscope ex-
tends the range of microscopic
size determination to as low
as .001 u by using electrons
instead of visible light as
the image producing beam. A
sample of particles is usually
fixed in a very thin membrane
by methods similar to those
used in visible microscopy.
The image rcay be viewed
directly on a cathode ray tube,
or photographed for measure-
ment and sizing.
Apparatus
The electron
microscope ia a
sophisticated
instrument requir-
ing skilled opera-
tors. It is also
a relatively ex-
pensive particle
sizing technique
($50,000 +).
Holography ia a means of
imaging an object by photo-
graphing interference patterns
forced when a volume of small
particles is illuminated with
laser light. An image of the
sample is reconstructed when
the resulting hologram is
illuminated by a second laser.
The reconstructed volume is a
perfect r.odsl of the original
volume with uniform magnifica-
tion throughout and ell objects
located at coordinates corres-
ponding to their original posi-
tion. Particles may then be
counted and sized as in standard
microscopy. In theory, the
particles irust be stationary,
but in practice a rapid pulsed
laser can be used to "stop" a
dynamic situation.
A pulsed ruby
laser with a
colliroator and
a camera with a
common longitudi-
nal axis are
required to re-
cord the hologram.
The image is
reconstructed us-
ing a second
laser.
This method is conceptually one
of the simplest particle sizing
techniques. A sample of partic-
ulate is passed through a series
of sieves of decreasing grid
size so that particle size frac-
tions are separated. These
fractions arc collected and
weighed to calculate a size dis-
tribution. Actually, size sepa-
ration by sieving is a probabil-
istic process depending on both
(cont.)
Standard sieves
are employed
usually having
grid sizes with
a lower limit
of 37 u and
ascending in ,
the ratio (2)^:1
[or (2)<-:i].'
A mechanical
shaker is pre-
ferred for
(cont.)
Applicability and Constraints
Particles as small as .001 u
may be sized via electron
microscopy. The upper limit
of the sizing range is approx-
imately 10 u since particles
larger than this will block
the field. A distribution
requiring both electron and
visible microscopy, presents
some problem since the greater
resolution of the former in
the 1-10 u range results in a
curve which docs not "mesh"
with the visibly determined
distribution for the upper
range. Time required for im-
ap.e analysis is similar to
visible microscopy (manual or
automatic image analysis is
available).
The equipment required for
this method is obviously not
justified except where stop
action" in-situ imaging of
fasc moving particles is re-
'quired. Determination of
particle size distribution
from a hologram is as time
consuming as from a photo-
micrograph. The system dis-
cribed by Zinley records
particle sizes in the range
3.5-100 u mean diameter.
Sieving is normally used for
particles greater than 50 u in
size. Electroformed "micro-
mesh" sieves are available in
sizes as fine as 5 u, however.
Probably the greatest single
drawback in sieve analysis is
the dependence of results on
shape and sieving time. In
general, sieve analyses do not
agree well with microscopic or
sedimentation techniques.
(cont.)
Accuracy and Precision
The precision of this method
is similar to that of visible
microscopy.
When a mechanical shaker is
used with a specified sieving
time, rep'roducibility between
runs should be within 27. for
standard sieves. Standard
deviations from 37, to 25% have
been reported using electro-
formed micromesh sieves in the
30 to 5 u range.
Reference
CA-040
JO-019
OR-006
ST-039
IR-016
ZI-003
BR-023
CA-040
DA-019
GR-016
WJ-012
LA-022
LU-012
OR-006
RO-014
SC-027
SU-005
AM-275
PR-091
DA-264
-------
TABLE 5-1. (Cont'd.)
Method
2.1 Sieving (cont.)
Principle
3.0 Methods Based
or. Particle
Settling
Velocity
3.1 Gravity Sedi-
mentation in
Liquid
O
Co
oo
size and shape. A particle
shaped like a square flat
plate, for example, has only
a small probability of passing
through a square grid of the
same or nearly the same width.
This means that the end point
for a sieve test must be an
arbitrary time limit, usually
7-9 minutes.
Apparatus
In general, these methods
measure an "equivalent" diam-
eter by observing the settling
rate of the sample in a vis-
cous fluid. Stoke 's law for
viscous flow around a spheri-
cal body is used as a basis
for calculation of particle
size distribution. This is
given by:
Where Ut is the terminal
settling velocity, D, the
Stoke' s particle diameter,
Of and p, the fluid and parti-
cal densities respectively,
and p the fluid viscosity.
The relationship between
actual particle shape and di-
mensions and Stoke' s diameter
is not known in general.
Different methods use differ-
ent means of measuring settl-
ing rates and extracting
particle size data from these
measurements t It should be
noted that the particles must
be of uniform density in order
for accurate particle size
data to result.
improved accuracy.
Equipment for
normal sieve sizes
is inexpensive,
about $1000 in-
cluding a mechan-
ical shaker.
Equipment for
micromesh sieving
would cost an
additional $1000
(sonic sifter" +
sieves).
L Applicability and Constraints
On the other hand, this meth-
od is fast (-V hour) and inex-
pensive. A relatively large
sample is required compared
to the other methods (50-
100 gms).
Accuracy and Precision
Reference
IR-016
LA-159
LO-089
AM-269
AM-270
Accumulative or fixed level
sensing methods require up to
24 hours for small (< 1 u)
particles to settle. More
sophisticated scanning instru-
ments reduce this to as little
as one hour.
The accuracy and reproducibil-
Ity of all sedimentation de-
vices- depends strongly on the
care with which the sample is
dispersed before settling.
CA-040
HE-010
HI-020
OR-006
PH-002
SH-006
SO-010
IR-016
-------
TABLE 5-1 (Cont'd.)
Method
3.1.1 Pipette Method
Principle
O
I
(jO
3.1.2 Balance Method
A sample of particulate Is
dispersed and suspended In a
graduated cylinder In which
a pipette is mounted at a
fixed level. After uniform
suspension is achieved by
shaking, the particles are
allowed to settle. Samples
are withdrawn using the pi-
pette at various times over
the test period. These sam-
ples are dried and weighed,
providing a measure of con-
centration vs. time at the
pipette level in the cylinder.
These data are easily con-
verted to a cumulative wcight-
undersize plot via the Stoke's
equation and a knowledge of
the distance from the top of
the suspension cylinder to the
pipette mouth.
Apparatus
The settling rate of a sample
is measured by cumulative
collection and in situ "weigh-
ing" of the settled particles.
This is accomplished by plac-
ing a balance pan or other
force transducer at the bottom
of a settling tube. Two
methods of introducing the
sample have been used. In
one, the sample is dispersed
throughout the tube by shak-
ing. In the other, the sam-
ple is introduced at the top
of the tube at time zero. The
former method requires graphi-
cal differentiation of the
weight settled vs. time plot
to extract a particle size dis-
tribution. The latter does not
(cont.)
The apparatus for
this method is
quite simple. It
consists of a
sedimentation
vessel graduated
from 0-20 cm. in
height and holding
approximately 500
ml of sample sus-
pension. A 10 ml.
pipette is fitted
to the top with a
ground glass joint
so that the tip
extends down to a
fixed level in the
vessel. For pre-
cise work, a con-
stant temperature
bath is desirable.
A drying oven and
precision balance
are also required.
Multiple pipettes
fixed at different
levels have been
used to shorten
overall time re-
quired for a given
size distribution.
A fluid must be
selected that will
have no effect on
the size and den-
sity o£ the settl-
ing particles.
Apparatus consists
of a settling tube
(in a constant
temperature bath
for precise work
with small parti-
cles) with a sen-
sitive force
transducing appa-
ratus at the bottom.
An amplifier/meter
recorder combina-
tion may be used
to provide direct
readout of data,
after calibration.
Commercial apparat-
us (Calm) is avail-
able for about
$3,000.
Applicability and Constraints
As with other gravity settling
methods, the particle size
range for which this method Is
convenient is determined by
the settling velocities of the
largest and smallest particles.
For example, a one u sphere
with a specific gravity of two
would settle at a ~ 5.4xlO~s
cm/sec, in water requiring
over 100 hours to settle 20 cm
A 100 u particle on the other
hand would settle this far in
only 37 seconds, giving rise to
great variation in a method us-
ing a 10-20 second pipette
sample time (large particles
also may settle outside the
Stoke's law range of velocity).
The sample must be well dis-
persed usually with an agent
added to reduce agglomeration
tendencies. Sample concentra-
tion must be low to avoid
particle interaction (hindered
settling).
Problems are similar to
other sedimentation methods.
In addition, sample size must
be selected with the sensi-
tivity of the balance in mind.
Accuracy and Precision
If performed carefully, the
method is quite reproducible.
Grindrod (GR-016) reports a
standard deviation of 1-27.
on repetitive tests with
Portland cement particles.
Results are similar to other
sedimentation methods. In the
very fine particle (< 5 u)
range, however, standard de-
viations up to 10-2070 have
been noted. In this range,
turbulence caused by sampling
or convection can effect re-
sults. Error is also intro-
duced by non-instantaneous
sampling and variation in
operator technique.
Reference
CA-040
GR-016
HU-012
OR-006
SI-010
IR-016
Accuracy and precision compare
to those of the pipette method
CA-040
BO-016
FE-009
JA-011
OR-006
RA-025
SI-010
SM-005
SU-011
-------
TABLE 5-1. (Cont'd.)
Method
3.12 Ealar.ee Method
(cont.)
3.1.3 Hydrometer
Method
Principle
3.1A Diver Method
i
.£-
O
3.2 Gravity Sedi-
mentation in
Air
and is more amenable to
inexpensive direct reading and
recording devices.
A sample is mixed with an
appropriate fluid and disper-
sant in a settling tube as in
other gravity settling methods.
In this case, the concentra-
tion of suspension at a given
level and time is determined
by insertion of a calibrated
hydrometer into the fluid.
Once the concentration at a
level is known, particle size
distribution data are obtained
in the same manner as the
pipette method using Stoke's
law. The results are obtained
in the form of a weight frac-
tion-oversize vs. size plot.
This technique is similar in
principle to the hydrometer
method except that the den-
sity of the suspension at
different times and levels
is determined by carefully
inserting "divers" of known
density into the suspension.
The diver will sink to a level
at which the suspension den-
sity is equal to its own.
This level is measured Compu-
tation of particle size distri-
bution from density data is
straightforward.
These methods are similar to
sedimentation techniques us-
ing liquids. Cumulative deter-
mination of settled weight by
balance pan is the roost practi-
cal route to data reduction.
Apparatus
The apparatus con-
sists of a cali-
brated hydrometer,
a settling tube,
and a constant
temperature bath.
Applicability and Constraints
Accuracy and Precision
Reference
Apparatus is
similar to other
settling methods
with the hydro-
meter or pipette
exchanged for
calibrated glass
spheres of known
density.
Air settling tubes
are usually quite
long compared to
their liquid coun-
terparts. One
commercial appara-
tus employs a tube
about 90 inches
long. A means of
dispersing a samfie
in air is not
straightforward.
One instrument
uses a blase of
compressed air. A
precision record-
ing balance is
required.
This method generally agrees
with other sedimentation
methods. Some error arises
from disturbances caused by
manipulating the hydrometer.
Additional error is intro-
duced in reading it and esti-
mating an equivalent level to
which the reading corresponds.
The minimum particle size
class measurable by this tech-
nique is on the order of one
micron. This lower limit is
fixed by error in hydrometer
readings arising from convec-
tion, vibration, and Brownian
movement. The maximum size is
limited by rapid settling of
large particles as in the
other settling methods. A
rather concentrated suspension
is required, making deviation
from free settling likely.
The particle size distribution
must be fairly uniform since
the hydrometer covers a finite
level in the settling tube.
Similar to hydrometer method, Similar to hydrometer method.
This technique is capable of
measuring small particles
(< 5 u) in much less time
than that required for liquid
settling. It is also useful
for very light materials which
settle very slowly in liquid
media. Large particles (> 50
u) settling in air deviate
significantly from Stoke's
law, making some correction
necessary.
A commercial instrument,
the Sharpies Microtnerograph
claims an accuracy of ± 37..
It is doubtful whether this
can be achieved for particles
smaller than 5 u or larger
than 50 u. Wall losses with
small particles may be sig-
nificant.
CA-040
LE-013
MA-057
KC-019
OR-006
LA-159
IR-016
AM-275
CA-040
OR-006
IR-016
CA-040
OR-006
SO-010
-------
TABLE 5-1. (Cont'd.)
Method
3.3
O
I
-P-
4.0 Particle
Trajectories
4.1 Elutriation
4.2 Combined Cen-
tr Ifugation/
Elutriation
(Bahco Class-
ifier)
Principle
Centrifugal
Sedimentation
The limitations imposed by
slow settling of very fine
particles may be overcome by
use of a centrifuge. The "g"
in Stoke1s equation is re-
placed by Ri2 where R is the
radius of rotation and >jj the
angular velocity of the cen-
trifuge. The variation in R
as the particle settles leads
to
1 [18u ln(X,/X, ;
iw I (p,-
D
as a modified version of
Stoke's law. Here, u> is the
angular velocity, Xj is the
distance from the center of
rotation to the liquid sur-
face, and X,; the distance
from the center to the point
to which the particle settles.
Instead of allowing particles
to settle in a fluid, parti-
cles of a given diameter are
removed from a sample by a
flowing fluid with its velo-
city equivalent to the Stoke's
velocity of' a particular size
particle. All particles
smaller than this size will
be carried away. Repeated
fraction at ions at different
velocities followed by collec-
tion and weighing of the frac-
tions yields a size distribu-
tion.
This method combines air
elutriation with centrifu-
gal sedimentation in a
manner which both decreases
classification time and
improves the separation be-
tween successive size frac-
tions. The resulting size
fractions are weighed to
yield a weight-undersize
plot.
Apparatus
For small particles
(< 1 u), a high
speed centrifuge
Is required.
An clutrlator con-
sists,, in general,
of a tube, a means
of controlling
fluid flow through
this tube, and a
means of introduc-
ing a sample and
collecting elu-
triated fractions.
This equipment can
range considerably
in complexity and
cost.
A relatively in-
expensive commer-
cial instrument
($3300) is
available.
Applicability and Constraints
Centrifugation to determine
particle size distribution can
extend the range of sedimenta-
tion methods to particles as
small as .05 u.
Accuracy and Precision
Separation of a number of
particle size fractions by
elutriation is time consum-
ing. Also, the existence
of a parbolic velocity profile
in the tube tends to make the
distribution within fractions
relatively broad. AdditionUl
errors arise from selection
of an arbitrary end point
(as in sieving) and deposi-
tion of material on the e]u-
triator walls. About 30 min-
utes are required to separate
one fraction.
Elutriation combined with
centrifugal separation of
fractions enables a single
size cut to be made in 15
minutes.
Reference
LE-013
MU-010
OR-006
SO-010
1R-016
CA-040
HU-012
OR-006
IR-016
In tests with fly ash
reproducabllity is reported
to be better than 17,. For
a given material, accuracy
is improved by calibration
of each size fraction against
a slower sedimentation method.
CR-012
DI-021.
GR-032
SI-010
TO-008
IR-016
-------
Table 5-1. (Cont'd.)
Method
Principle
4.3
Inertial
Inpaction
O
-O
ro
5.0 Methods Based
on Radiation
Transmission
or Scatter-
Particles suspended In air are
drawn through a series of jets
or slots of decreasing size,
each of which is followed by a
flat plate. As the high velo-
city air stream flows around a
plate, particles larger than a
given size will be separated
from the gas stream since
their inertia prevents them
from following the air stream.
The collected particles may be
sized independently or the
instrument Day be calibrated
so that after weighing the
fractions, a mass-undersize
plot is obtained directly.
The minimum size particle re-
moved by a given stage (jet/
plate combination) is given
Apparatus
min
TTDU
when ID' is the half width of
the jet vena contracta, p is
the fluid viscosity, p the
particle density, and u the
particle velocity.
A basic cascade
Iropactor is quite
simple in construc-
tion, consisting
of an airtight
container with
jets and iropac-
tion plates mount-
ed within. Asso-
ciated equipment
includes a pump,
valve, and flow
tneter arrange-
ment to reproduce
sampling condi-
tions. Prices
range from $100-
$2000).
Applicability and Constraints
This method is normally used
in situ to size particles sus-
pended in air. The possibil-
ity exists of redispersing a
bulk solids sample so that it
can be sized by impaction.
Impaction may be used to class-
ify particles from .1 to 100 u.
in diameter. Operating time
is dependent on concentration
of particles in the sample
stream. Sufficient sample
must be collected for accurate
weighing.
Accuracy and Precision Reference
Accuracy varies with instru- CA-040
ments. Some sources of OR-006
error include secondary depo-
sition and wall deposition.
These can be minimized by
proper design and operation.
5.1 Radiation
Scattering
(Visible
Light Range)
These methods use the princi-
ples of radiation scattering
as a means of counting and
sizing particles. When a
narrow beam of incident radia-
tion is intercepted by a parti-
cle, a portion of the energy
is absorbed and a portion
scattered. The remainder is
transmitted. The intensity of
scattered energy is a function
of scattering angle, particle
shape, size, and optical prop-
erties, and the wavelength of
incident radiation. For par-
ticle size determinations it
is desirable that the parti-
cles not absorb light at the
wavelength of the incident
radiation. Complex indices
of refraction also cause errors
in interpretation o£ data.
This type of
instrument re-
quires complex and
precise means of
transmitting and
detecting narrow
beams or slits of
the detecting
radiation. If
direct readout is
desired, con-
siderable elec-
tronic sophistica-
tion results.
The primary constraint associa-
ted with scattering methods is
the difficulty in relating
measured intensity to particle
size and concentration. Theory
is well developed only for
monodispersed spherical parti-
cles of uniform optical proper-
ties. A second consideration
is sample concentration. Too
many particles per unit volume
cause interactions that are not
easily interpreted. Particle
size may range from .2 to 100
p, although background noise
may cause significant devia-
tions in the lower range.
The real-time,.on-line capabil-
ity of this method is attractive
For most applications this
method measures a rather
qualitative "equivalent"
diameter which may differ
widely from that determined
by other methods. Counts for
particles less than 1 u in
diameter may be seriously in
error (on the low side) in
some circumstances.
AP-004
AU-003
CA-026
DI-012
LI-019
NA-059
MU-013
MU-014
OR-OC6
RI-007
WE-022
ZI-003
-------
TABLE 5-1. (Cont'd.)
Method
Principle
5.2
Turbidimetric
Methods
O
I
-P-
u>
These methods measure photo-
metrically extinction of
light by a settling suspension
to determine particle size
distribution. The intensity
of transmitted light, I, is
given for monodispersed
spherical particles by:
Apparatus
Applicability and Constraints
where I0 in the incident in-
tensity, K is a scattering
coefficient, r the particle
radius, n the number of par-
ticles per unit volume, and I
the path length. For non-
spherical particles having a
wide range of sizes, this
equation is not useful in
practice, thus the turbidi-
metric method requires cali-
bration with a known distri-
bution of the particular
material of interest.
Beginning with a uniform
suspension and a transverse
light beara at a fixed depth
below the surface, no change
in absorbance of 'the suspen-
sion will occur until the
largest particles in the
suspension have fallen from .
the surface to the level of
the measuring beam. At this
time the absorbance will de-
crease by an amount propor-
tional to the concentration
of the largest particles.
Any point on the absorbance
vs. time curve then repre-
sents the concentration of
particles smaller than a size
of particle which would fall
the distance "h" from the
surface to the measuring beara
in a time "t". Thus a size-
distribution curve is obtained
with the "y" or absorbance
ordinate representing concen-
tration of particles less than
stated size and the "x" or
time ordinate representing
particle size in terms of
Stoke's diameter. This method
has the capability of rapid
measurement at several levels
in a settling tube, thus shorten-
ing the time required for a wide
size distribution.
The apparatus Is
not very complex.
It consists of a
settling cell
surrounded by a
barrier through
which a narrow
colliraated beam
of light may pass.
The extinction is
measured photo-
metrically and can
be recorded, A
vertical adjust-
ment for the cell
platform permits
rapid measurements
at different
levels.
An elegant var-
iation in approach
using the princi-
ples of the block-
ing of radiation
by solid particles
is described by
Ricci and Cooper
(RI-009). A
scanning laser
beam is directed
at a flowing slur-
ry under condi-
tions such that
settling will not
occur. Sophisti-
cated electronic
circuitry converts
the output of a
photodetector to
particle size
distribution
information.
The requirement that this
. method be calibrated with a
known sample of the same mate"
rial may-be i\ serious handi-
cap when particle size analy-
ses of nonuniform materials
is necessary, since results
can be affected by color and
shape and even initial sus-
pension concentration as well
as size. The total analysis
time of approximately one hour
is attractive. Also very
small samples are needed as
compared to gravimetric tech-
niques. A .01% suspension is
used vs. 1-2% for other settl-
ing methods. The photometric
output is amenable to auto-
matic readout.
The apparatus described by
Ricci and Cooper (see Appara-
tus column) must still be
calibrated for each particu-
late system. It is designed
to monitor particle size dis-
tribution in the range 5 u
to 2000 u on an on-stream,
real-time basis.
Accuracy and Precision Reference
Reproduclblllty Is reported to AM-006
be In the range of ± 2%. In CA-040
view of questionable theoreti- BE-035
cal basis for this method, BR-023
there is some question as to LA-021
what "size" is actually meas- OR-006
ured. RI-009
This method does not in TA-012
general give similar results
to most other particle sizing
methods, especially for
smaller particles.
-------
Table 5-1. (Cont'd.)
Method
Principle
5.3
X-Ray Absorp-
tion Detection
O
5.4
X-Ray Fluo-
rescence
Similar in principle Co tur-
bidimetry, small angle X-ray
scattering can be used to
determine the concentration
of a settling suspension at
a given level and time. A
particle size distribution can
easily be extracted from these
data. Ebel, et al., (EB-001)
discuss the theory involved.
Apparatus
The intensity of fluorescent
X-rays from an element in a
particle is dependent on
particle size. The effect can
be expressed by the intensity
ratio R, the ratio of the
intensity from a sample con-
taining particles of size S
to the intensity from a sam-
ple containing particles of
zero size, both samples hav-
ing the same concentration
of the fluorescing elements.
The X-ray scatter-
ing apparatus is
wore complex than
the visible light
extinction method.
A very finely
collitnated X-ray
beam is directed
through the sample
cell and small
angle scattering
intensity is de-
tected by a Gei-
ger counter.
Electronic con-
version of raw
data directly to
particle size
distribution is
possible. A com-
mercial instrument
(Micromeritics) Is
available for
$14,000.
X-ray fluores-
ence spectro-
meter.
Applicability and Constraints
Small angle X-ray scattering
is more accurate than light
extinction since the optical
properties of the sample do
not affect results. Also, the
capability of a multilevel
scan as in turbidimetry re-
duces the time required and
extends the particle size range
to ~ .5-100 u.
Accuracy and Precision
Precision of a commercial
instrument by Microtneritics
is reported to be ± 17,.
The following requirements
must be met in order for this
method to be applicable.
1. The concentration of the
element for which the
fluorescent radiation is
being measured must be
known.
2, The X-ray properties of the
unknown sample must be
close to those of the com-
parison sample.
3. The desired information is
average particle size.
4. The matrix cannot contain
the same element as the
particle element whose
fluorescence is being meas-
ured .
5. The particles must contain
an element above atomic
number 11.
6. The particles must be dis-
tributed randomly in the
sample.
The particle size - Intensity
effect is greatest for parti-
cles in the 1-20O u size range.
Reference
EB-001
KA-026
MI-024 '
OR-006
BU-259
HO-024
IR-016
-------
TABLE 5-1.
Method
(Cont'd.)
5.5 X-Ray Scatter-
6.0 Electrical
6.1 Coulter Coun-
ter
Principle
Apparatus
X-ray source and
detector system.
X-ray scattering at very
small angles, i.e., scattering
in the forward direction of
propagation of the radiation
is employed for particle size
measurement.
If a single small spherical
particle is irradiated by a
narrow monochromatic beam of
X-rays, the radiation will be
scattered when normalized
(intensity is unity for r=0)
in accordance with the rela-
tion:
I = C}=kp
where I is the scattered in-
tensity; 0 a constant depend-
ing on electron charge, den-
sity, number of electrons in
the particle, etc.; p the
radius of gyration of the par-
ticle; k = A^ sin(Y/2)/X;
Y the scattering angle; \ the
wavelength of the radiation;
arid $ the Scattering function
of spherical particles.
This instrumental method mea- The apparatus con-
sures the number and "diameter" sists of a sample
of particles in an electrical- cell and aperture
ly conductive system. A sus-
pension of the material to be
measured is drawn through a
small aperture having an im-
rersed electrode on each side.
with arrangements
for drawing the
sample through it,
an amplifier and
pulse height an-
As each particle passes through alyzer, and an
the aperture it displaces a
volume of solution proportion-
al to its own volume. This
displacement momentarily pro-
duces a change in resistance
between the electrodes creat-
ing a voltage pulse the
magnitude of which is related
to the volume of the passing
particle. The pulses are
electronically counted and
scaled. A direct fraction under-
size distribution may be obtained
by setting different "threshold"
limits for the largest or small-
est particle size to be counted.
oscilloscope dis-
play and or x-y
plotter. The basic
unit costs ~ $5000.
An automatic plotter
is an additional
$2000.
Applicability and Constraints
This method gives average
particle size in the range
0.005 to 0.05 u. If X-rays
in the wavelengths requiring
evacuated systems are used
larger particles may be exam-
ined.
A primary source of error in
this method is coincidental
passage of more than one
particle through the aperture.
Additional error results from
electrical noise and some
variation of response with
particle shape.
Aperture blockage may occur
when large particles are pres-
ent. On the other hand, use
of a larger aperture leads to
errors in the small particle
size range.
Applicable size range is
.5-100 u.
Accuracy and Precision
Since response is nearly
linear with particle volume,
particle size is inferred
only by assuming a shape.
The instrument must be cal-
ibrated with a known parti-
cle size sample. Standard
deviation of repetative
counts is reported to be
l-57o depending upon particle
size, shape, and concentra-
tion. In general, smaller
particles are subject to
larger variation in count.
Reference
BR-027
OR-006
BR-023
DI-012
EC-002
ED-004
GR-014
GR-015
HU-010
HU-012
KE-025
RO-014
SC-018
IR-016
-------
TABLE 5-1.
Method
6.2 Electrostatic
(Cont'd.)
Principle
Particles are charged accord-
ing to their size in a corona
discharge and then precipitated
by an electric field.
O
i
Apparatus
The device des-
cribed basically
consists of a
chamber in which
the particles
acquire charges
upon traversing a
corona discharge
from a length of
wire. The aero-
sol then goes in-
to a cylindrical
condenser with
the inner rod
maintained on a
fixed potential
and the outer
cylinder ground-
ed. The electric
field causes the
charged particles
to follow differ-
ent trajectories
and be precipita-
ted on the cylin-
der wall.
Applicability and Constraints
Applicable to aerosols in the
1-20 micron size range.
Accuracy and Precision
Reference
YO-004
CPi
-------
TABLE 5-2. BULK DENSITY AND SETTLING RATE MEASUREMENTS
Method
Principle
n
-P-
1. Slurry Bulk A representative sample of the
Density slurry is added to a preweighed
volumetric flask. Small devia-
tions from the full mark can
be made up with water. The
flask and contents are then
reweighed. The bulk density
is calculated from the follow-
ing equation:
D =
-------
TABLE 5-2. (Cont'd.) - BULK DEHSITY AND SETTLING RATE MEASUREMENTS
Method
3.
Solids Con-
tent,
"Quick
Method"
O
I
-P>
00
Solids Con-
tent,
"Standard
Method"
5.
Settling
Rate,
Visual
Principle
water content, Peak bulk den-
sities are usually found at
between 20Z and 40/i water
content.
If the specific gravity of
the scrubber solids
(CaSO,-2H20, CaSO,-%H20,
and fly ash) is assumed to be
2.47, then the solids content
of the slurry in grams per
liter of slurry is calculated
as:
W -Wp-V,,
where:
Weight of Sample -t flask
(g)
Weight of empty flash (g)
Volume of Slurry (ml)
A known weight and volume of
the slurry is drawn through a
weighed filter by application
of a vacuum. The filter and
solids are dried in an oven at
40-50°C and then reweighed.
The solids content can then
be calculated as the percent
solids or in grams of solids/
liter of slurry.
Settling rates are determined
by visual observation of the
liquid-solids interface
during settling in a 1000 ml
graduated cylinder. The
height of the interface
(cm) is plotted versus time
(min.). The settling rate is
determined from the slope of
the graph.
Apparatus
Analytical balance and
volumetric flasks.
Drying oven, vacuum
filtration apparatus,
analytical balance,
volumetric flasks.
1000 ml Graduated
Cylinder, timer
Applicability
and Constraints
Accuracy and
PrL-ci sion
This method is quick in that This method is
it does not require filtering convenient when
or drying the solids. the solids content
of the slurry need
only be determined
within a +107.
accuracy.
When drying the solids,
the oven temperature
should not exceed 50°C
which will drive off the
water of hydration of
the sulfite crystals.
The settling rate is a
function of weight percent
solids, temperature, and
particle morphology For
a valid comparison of
sludges, the temperature
and weight percent solids
should be held constant.
Settllr.R rates for sludges
of less than 'i°L solids by
weight are difficult to
measure because of the
indistincLnpss of the
i ntcrface.
References
AU-063
This is a very AU-063,
accurate method MI-262,
when sufficient PR-091
care is taken during SC-R-141
the filtration not
to lose any of the
solids.
Dependent on the TE"
care with which the
sample is dispersed PR~
before settling.
-------
size and shape of the particles present. Many indirect methods
require calibration and occasional checking by microscopic
measurements.
Separation of particle fractions by sieving is an
inexpensive and fast method for measuring size distribution for
relatively large particles. Sieves are available for small
particles but the separations are not as satisfactory as for
large particles.
The various sedimentation procedures are very popular
for routine work and give satisfactory particle size distributions
on many samples when properly calibrated. In order to obtain
satisfactory results the sample should be fairly homogeneous.
Elutriation is a very valuable tool for particle size
determination. In combination with other techniques (e.g.,
screening, centrifugation) phase separation of particles with
differing densities may also be effected. Inertial impaction
requires that the particles be suspended in air. It is not use-
ful for particles larger than lOOy in diameter.
Scattered light measurements can be useful for deter-
minating an "average diameter" for small particles. Transmission
or "turbidity" measurements are ususally used when the particles
are considerably larger than the wavelength of the incident
radiation. Very small angle X-ray scattering can be applied
to the estimation of average particle size in the range 0.005
to 0.05u.
The Coulter counter electrically measures the volume
of individual particles as they displace a conducting medium
in an aperture. Some disagreement exists in the literature
as to the speed and reliability of this method. Electrostatic
C-49
-------
charging of small particles may be used to determine particle
sizes in some cases.
5.2 Methods for Settling Rate and Density Measurements
The settling rate and settled density are both affected
by the particle size and morphology. If the settling rate and
settled density are known, then estimates of the relative particle
sizes of different sludges can be made. The methods for measuring
these quantites are presented in Table 5-2 along with several
other related measurements.
C-50
-------
REFERENCES
AM-006 American Society for Testing and Materials, 1970
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AM-011 American Society for Testing and Materials, "Recommended
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AM-270 American Society for Testing and Materials, Committee
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C-51
-------
REFERENCES (Cont'd.)
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BR-027 Brusset, H. and J. R. Donati, "Un Nouvel Aspect du
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C-52
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REFERENCES (Cont'd.)
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Formed Sieves", Powder Tech. 2, 349-55 (1969).
DA-264 Daeschner, H. W., E. E. Siebert, and E. D. Peters,
"Application of Electroformed Precision Micromesh
Sieves to the Determination of Particle Size Distri-
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DI-012 DiGrado, C. Joseph, "Panel Discussion: Liquid-Borne
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(2), 62-67 (1970).
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Centrifugally", Company Brochure SL-52.
EB-001 Ebel, Horst, et al. , "Die Pulverkorngrossenbestimmung
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C-53
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REFERENCES (Cont'd.)
EC-002 Eckhoff, R. K., "Experimental Indication of the
Volume Proportional Response of the Coulter Counter
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648-49 (1967).
ED-004 Edward, Victor H. and Charles R. Wilke, "Electronic
Sizing and Counting of Bacteria", Biotechn. Bioeng. 9,
559-74 (1967).
EN-269 Environmental Protection Agency, (Office of Research
and Development), Symposium on Flue Gas Desulfurization,
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74-126 a,b. Research Triangle Park, N. C.,
Dec. 1974.
GR-014 Grover, N. B. et al., "Electrical Sizing of Particles
in Suspension. I. Theory." Biophysical J. 9, 1398-
414 (1969).
GR-015 Grover, N. B., et al., "Electrical Sizing of Particles
in Suspensions. II. Experiments with Rigid Spheres,"
Biophysical J. 9, 1415-25 (1969).
GR-032 Graham, A. L. and T. H. Hanna, "The Micro-Particle
Classifier", Preprint. Ceramic Age, 1962 (Sept.)
HA-044 Hawksley, P. G. W. and J. H. Blackett, "The Design and
Construction of a Photoelectronic Scanning Machine for
Sizing Microscopic Particles", Brit. J. Appl. Phys.
Supp. 3, 165-73 (1954).
C-54
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REFSRENCES (Cont'd.)
HE-010 Heiss, John F. and James Coull, "The Effect of Orien-
tation and Shape on the Settling Velocity of Non-
Isometric Particles in a Viscous Medium", CEP 48 (3),
133-40 (1952).
HI-020 Hime, W. G. , "ASTM Method for the Surface Area Analysis
of Portland Cement", in Fineness of Cement. STP 473.
Philadelphia, ASTM, 1970, pp. 3-19.
HO-024 Hockings, W. A., "Particle- and Grain-Size Measurement
by X-Ray Fluorescence", Powder Tech. 3, 29-40 (1969).
HU-012 Hunt, C. M. , and A. R. Woolf, "Comparison of Some
Different Methods for Measuring Particle Size Using
Microscopically Calibrated Glass Beads", Powder Tech.
3, 9-23 (1969).
IR-016 Irani, Riyad R. and Clayton F. Callis, Particle Size:
Measurement, Interpretation, and Application. New
York, Wiley, 1963.
JA-011 Jacobsen, A. E. and W. F. Sullivan, "Method for Particle
Size Distribution for the Entire Subsieve Range",
Anal. Chem. 19 (11), 855-60 (1947).
JO-019 Johari, 0., and S. Bhattacharyya, "The Application of
Scanning Electron Microscopy for the Characterization
of Powders", Powder. Tech. 2, 225-48 (1969).
C-55
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REFERENCES (Cont'd.)
JO-083 Jones, Julian W. and Richard D. Stern, "Waste Products
from Throwaway Flue Gas Cleaning Processes - Ecologi-
cally Sound Treatment and Disposal", Presented at
the Flue Gas Desulfurization Symp., New Orleans, May
1973.
KA-021 Kaye, B. H., "Automatic Microscopes for the Paint
Technologist, Part II. Particle System Evaluation
Using the Quantimer.", Paint, Oil Colour J., 1968
(Aug. 30), 372-75 (1968).
KA-026 Karansek, F. W., "Micromeritics" R/D, 59-62 (1970).
(Sept.)
KE-025 Kendall, C. E., "Comparative Data and Requirements
for Determination of Particle Size Distribution
in Australian Pharmaceuticals", Ann. N. Y. Acad.
Sci. 158, 640-50 (1969).
KI-014 Kirnbauer, Erwin, Panel Discussion: Liquid-Borne
Particle Counting in the Pharmaceutical Industry. I
Microscopic Counting.", Bull. Parenteral Drug Assoc., 24
(2), 53-58 (1970).
LA-021 Lamar, Richard S., "Particle-Size Distribution Analysis
by a Modification of the Turbidimetric Procedure of
Musgrave and Horner", J. Am. Cer. Soc. 37, 386-90
(1954).
LA-022 Lapple, C. E., "Particle-Size Analysis and Analyzers",
Chem. Eng. 1968 (May 20), 149-56 (1968).
C-56
-------
REFERENCES (Contd'.)
LA-159 Lambe, T. William, Soil Testing for Engineers.
N.Y., Wiley, 1951.
LE-013 Lester, R. H. , "Subsieve Particle Size Measurements on
Porcelain Materials", Am. Cer. Soc. Bull. 37, 129-34
(1958).
LI-019 Livesy, P. J. and F. W. Billmeyer, Jr., "Particle
Size Determination by Low-Angle Light Scattering: New
Instrumentation and Rapid Method of Interpreting Data",
J. Colloid Interface Sci. 30 (4), 447-72 (1969).
LO-089 Lord, William H., "FGD Sludge Fixation and Disposal",
Presented at the Flue Gas Desulfurization Symposium,
Atlanta, Ga., Nov. 1974.
LU-012 Ludwick, John C. and Patricia L. Henderson "Particle
Shape and Inference of Size from Sieving", Sedimentology
11, 197-235 (1968).
MA-057 Maguire, S. G., Jr. and G. W. Phelps, "Practical
Particle-Size Analysis of Clays: II, a Simplified
Procedure", J. Am. Cer. Soc. 40, 403-49 (1957).
MA-059 Martens, Alexander H., "Measurement of Small Particles
Using Light-Scattering: A Survey of the Current
State of the Art", Ann. N. Y. Acad. Sci. 158, 690-702
MC-019 McCann, C. , "The Measurement of the Sizes of Non-
spherical Particles by the Hydrometer Method," Sedi-
mentology 13, 307-9 (1969).
C-57
-------
REFERENCES (Cont'd.)
MI-024 Micromeritics Instrument Corp., "Sedigraph 5000 Particle
Size Analyzer", Company brochure.
MI-262 Mijares-Lopez, C., Dynamics of the Continuous Settling
of Discrete-Particle Slurries. Doctoral Thesis,
University of Colorado, 1976.
MO-016 Morgan, B. B., "Automatic Particle Counting and Sizing",
Research 10, 271-79.
MU-010 Murley, R. D., "An Improved Method of Calculating
Particle Size Distribution from Centrifugal Sedimenta-
tion Experiments", Nature 207 (5001), 1089-90 (1965).
MU-013 Mullaney, P. F. and P. N. Dean, "Cell Sizing: A
Small-Angle Light-Scattering Method for Sizing Particles
at Low Relative Refractive Index", App1. Opt. 8,
2361-62 (1969).
MU-014 Muslin, Lawrence, "Panel Discussion: Liquid-Borne
Particle Counting in the Pharmacuetical Industry. II.
Light-Scattering Instruments", Bull. Parenteral Drug
Assoc. 249(2). 59-63 (1970).
OR-006 Orr, Clyde, Fine Particle Measurement: Size, Surface,
and Pore Volume. New York, Macmillan, 1959.
PH-002 Phelps, G. W. and S. G. Maguire, Jr., "Practical
Particle-Size Analysis of Clay, I, Sample Preparation",
J. Am. Cer. Soc. 40, 399-402 (1957).
1-58
-------
REFERENCES (Cont'd.)
PR-091 Princiotta, Frank T., Sulfur Oxide Throwaway Sludge
Evaluation Panel (SOTSEP). 2 vols. EPA 650/2-75-010
a, b. Research Triangle Park, N.C., Control Systems
Lab., NERC, 1975.
RA-025 Rabatin, J. G. and R. H. Gale, "Determination of
Particle Size with a Simple Recording Sedimentation
Balance", Anal. Chem. 28 (8), 1314-16 (1956).
RI-007 Rimburg, D. and D. Keafer, "Accuracy of Measuring
Aerosol Concentration with Particle Counters", J.
Colloid Interface Sci. 33 (4), 628 (1970).
RI-009 Ricci, R. J., and H. R. Cooper, "A Method for Moni-
toring Particle Size Distribution in Process Slurries",
ISA Trans. 9, 28-36 (1970).
RO-014 Rosen, Howard N. and Hugh M. Hulburt, "Size Analysis
of Irregular Shaped Particles in Sieving. Comparison
with the Coulter Counter". I&EC Fundam. 9 (4), 658-61
(1970).
RO-133 Rossoff, J. and R. C. Rossi, Disposal of By-Products
From Nonregenerable Flue Gas Desulfurization Systems:
Initial Report. EPA-650/2-74-037-a. El Sugundo, Ca.,
Aerospace Corp., 1974.
SC-018 Scrag, K. R., and M. Corn., "Comparison of Particle
Size Determined with the Coulter Counter and by Optical
Microscopy", Amer. Ind. Hyg. Assoc. J. 31 (4), 446-53
1970.
C-59
-------
REFERENCES (Cont'd.)
SC-027 "Screening and Size Analysis", Ceramic Age, 1969
(July), 66-70 (1969).
SC-R-141 Schwitzgebel, Klaus and F. B. Meserole, Determination
of the Molecular Parameters Important to the Performance
of Scaling Inhibitors, Final Report. Contract No.
14-30-2914. Radian Project No. 400-012, Austin, Tx. ,
Radian Corp., 1973.
SI-010 Simecek, Jaroslav, "Vergleichende Untersuchung Von
Methoden Zur Korngrossenbestimmung", Staub-Reinhalt.
Luft 26 (9), 372-79 (1966).
SM-005 Smith, George B. and G. V. Downing Jr., "Objective
Method of Data Reduction for Particle Size Analysis by
Cumulative Sedimentation Method.", Anal. Chem. 42 (1),
136-38 (1970).
SM-006 Smith, T. N., "The Differential Sedimentation of Particles
of Two Different Species", Trans. Instn. Chem. Engrs.
43, T69-73(1965).
SM-007 Smith, M. J., "A Quantitative Evaluation of Pigment
Dispersions", Microscope 16, 123-35 (1968).
SI-010 Society for Analytical Chemistry, Particle Size
Analysis Sub-Committee. The Determination of Particle
Size. I. A Critical Review of Sedimentation Methods.
London, 1968.
C-60
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ST-039 Strang, A., "Direct Image Analysis in the Electron
Microscope", J. Sci. Instr. 2. 45-47 (1969).
ST-040 Stein, Felix, "Particle Size Measurements With
Phase-Contrast Microscopy", Powder Tech. 2. 327-34
(1969).
SU-005 Suhm, H. 0., "Oscillating Air Column Method for
the Dry Separation of Fine and Subsieve Particle
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SU-011 Suito, H. et al., "The Effect of Particle Shape on
the Measurement of Particle-Size Distribution",
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TA-012 Talvite, N. A. and H. J. Paulus, "Recording, Photo-
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C-61
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C-62
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DCN #78-200-187-11-14
APPENDIX D
COMPARISON OF METHODS FOR
MEASURING THE PARTICLE SIZE
DISTRIBUTION OF SMALL PARTICLES
Technical Note #200-187-11-05
1 February 1978
Prepared for:
Mr. Robert H. Borgwardt, Task Officer
Industrial Environmental Research Laboratory/RTF
U. S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
Prepared by:
J. C. Terry
D-i
-------
TABLE OF CONTENTS
Page
1. 0 INTRODUCTION D-l
2.0 SUMMARY OF RESULTS AND CONCLUSIONS D-3
3 . 0 RECOMMENDATIONS D-5
4.0 EXPERIMENTAL PROCEDURES AND RESULTS D-6
4.1 Particle Size Distribution by Coulter
Counter D-6
4.2 Particle Size Distribution by Sedimen-
tation D-17
4. 3 Comparison of Results D-20
D-ii
-------
LIST OF FIGURES
Figure
4-1 Sludge Granules: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Single Tube Method. D-ll
4-2 Sludge Granules: Cumulative Volume Percent
of Particles Versus Equivalent Spherical Dia-
meter Measured by Coulter Counter Single Tube
Method .- D-12
4-3 Sludge Platelets: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Single Tube
Method D-13
4-4 Sludge Platelets: Cumulative Volume Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Single Tube
Method D-14
4-5 Sludge Platelets: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Multiple Tube
Method D-15
4-6 Sludge Platelets: Cumulative Volume Percent
of Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Multiple Tube
Method D-16
D-iii
-------
LIST OF FIGURES (continued)
Figure
4-7 Sludge Granules: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Sedimentation Method D-21
4-8 Sludge Granules: Cumulative Volume Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Sedimentation Method D-22
4-9 Sludge Platelets: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Sedimentation Method D-23
4-10 Sludge Platelets: Cumulative Volume Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Sedimentation Method D-24
4-11 Sludge Granules: Number Percent of Particles
Versus Equivalent Spherical Diameter Measured
by Optical Microscopy and Wet Micromesh
Sieve Methods D-29
4-12 Sludge Granules: Number Percent of Particles
Versus Equivalent Spherical Diameter Measured
by Single Tube Coulter Counter and Sedimentation
Methods D-30
4-13 Sludge Platelets: Number Percent of Particles
Versus Equivalent Spherical Diameter Measured
by Optical Microscopy and Wet Micromesh Sieve
Methods D-31
D-iv
-------
LIST OF FIGURES (continued)
Figure Page
4-14 Sludge Platelets: Number Percent of Particle
Versus Equivalent Spherical Diameter Measured
by Single Tube Coulter Counter and Sedimenta-
tion Methods D-32
D-v
-------
LIST OF TABLES
Table
4-1 Particle Size Distribution of the Sludge Granules
by the Coulter Counter Single Tube Method D-8
4-2 Particle Size Distribution of the Sludge Platelets
by the Coulter Counter Single Tube Method D-9
4-3 Particle Size Distribution of the Sludge Platelets
by the Coulter Counter Multiple Tube Method D-10
4-4 Particle Size Distribution of the Sludge Granules
by the Sedimentation Method D-18
4-5 Particle Size Distribution of the Sludge Platelets
by the Sedimentation Method D-19
4-6 Mean Particle Diameter on Volume Basis D-25
4-7 Mean Particle Diameter on Number Basis D-25
4-8 Particle Size Distribution of Sludge Granules
on a Number Percent Basis D-27
4-9 Particle Size Distribution of Sludge Platelets
on a Number Percent Basis D-28
D-vi
-------
1.0 INTRODUCTION
The flue gas desulfurization (FGD) sludges produced in
Lime, limestone and double alkali systems generally are difficult
to settle and dewater. Sludge disposal therefore is a problem
and represents a significant operating cost in scrubbing pro-
cesses. Radian Corporation was contracted by the EPA to investi-
gate the prospects for improving the quality of FGD scrubber
sludges. Briefly, the approach taken was to develop a mathe-
matical basis for relating sludge quality to scrubber operating
conditions. Scrubber sludge quality was defined as the particle
size distribution (PSD) of calcium sulfite hemihdyrate.
One phase of the project was the development of standard
analytical techniques for measuring sludge properties. It was
found that optical microscopy and wet micromesh sieve methods
for measuring the particle size distribution of sludge resulted
in PSD data which was not in agreement with Coulter Counter
results. Specifically, it was found that the optical and sieve
PSD curves showed maxima in the range of about 5 to 10 microns
whereas the Coulter Counter PSD curve continued to increase
smoothly with decreasing particle size. This difference sugges-
ted two possible mechanisms for new particle generation, attri-
tion and nucleation. The Coulter Counter results showed a large
number of small and submicron size particles which were not
observed by the optical and sieve methods.
These differences in the FGD scrubber sludge PSD's
are important in the formulation, verification, and refinement
of the scrubber model. In order to understand the origin of
the differences in the PSD data and to provide a basis for
selecting an accurate particle sizing method, it was felt that
additional study was needed.
D-l
-------
The methods selected for additional study of small and
submicron size particles were Coulter Counter and sedimentation.
This report presents the results of PSD studies on FGD sludge
granules and platelets down to 0.3 microns in size. A comparison
of optical, sieve, Coulter Counter, and sedimentation results
are given.
D-2
-------
2.0 SUMMARY OF RESULTS AND CONCLUSIONS
The FGD sludge granule and platelet samples were analyzed
by Coulter Counter and sedimentation methods down to a lower
particle cut off size of about 0.3 microns. These results were
compared to those previously obtained by optical microscopy
and wet micromesh sieves.
On a mass or volume basis the mean particle size of the
granule and platelet samples varied widely as measured by
Coulter Counter, sedimentation, optical microscopy, and sieve
techniques. Generally, the optical and sieve methods tended to
give larger PSD's than did the Coulter Counter and sedimentation
methods. The optical and sieve methods used a lower cut-off
limit which was larger but this should not have significantly
effected the PSD on a volume or mass basis since the bulk of the
particle mass and volume are represented by the larger particles.
The mean equivalent spherical diameter for the granular sample
varied between 1.7 and 18.5 microns and the platelet sample
varied between 1.8 and 10.2 microns on a volume or mass basis.
The Coulter Counter and sedimentation results on a
number basis agreed reasonably well. Likewise, the optical and
sieve results were in good mutual agreement. The equivalent
spherical diameters measured by the optical and sieve methods,
however, were much larger than those measured by sedimentation
and Coulter Counter. This is a result of using a 1-2 micron
lower cut off size for the optical and sieve methods whereas
the sedimentation and Coulter Counter methods had cut-off sizes
down to 0.3 microns. The mean equivalent spherical diameters
for the granular sample varied between 0.4 and 7.5 microns and
the platelet sample varied between 0.4 and 4.0 microns on a
number basis.
D-3
-------
Graphs of the optical and sieve number percent of parti-
cles versus size data for both granule and platelet samples
show a maximum in the PSD curve. This suggests that particle
breakage or attrition is a major or at least a significant
mechanism for new particle generation. The PSD curves for the
Coulter Counter and sedimentation data decrease monotonically
with increasing particle size and do not show any maxima. The
range of particle sizes covered by the two groups of methods
do not overlap well and provides for the possibility of both
sets of data being correct. That is, there could be two
mechanisms for new particle generation, nucleation and attrition.
The preponderance of the data does not support this two mechanism
theory, however, and the maxima in the optical and sieve data
curves are probably due to limitations in the methods to measure
small particles. The maxima in the PSD curves occurred at 6
to 8 microns. This further suggests that optical and sieve
measurements below 5 to 10 microns are questionable. Measure-
ments in the range of 1 to 2 microns are probably highly inaccurate
and measure far too few particles in the smaller size ranges.
Based on these results, it is not possible to select
any one of the analytical methods as correct. It is clear that
some of the methods have inherent limitations which necessarily
prevent them from giving accurate data on small or submicron
size particles. These are optical microscopy and microsieves.
The necessity of using the same particle size cut off limits is
obvious and is clearly illustrated by comparing the various
particle size data on a number basis. It is also clear that
comparing PSD data between different analytical techniques is
highly questionable. Even comparison of PSD data on different
FGD sludges would be suspect if the particle shape was different
such as granules versus platelets.
D-4
-------
3.0 RECOMMENDATIONS
When comparing particle size distribution data, it is
very important to know the analytical method used and also the
details of how that method was applied. As has been shown,
even particle sizing methods that are generally accepted as
accurate and suitable for small particles can give widely
varying results. Certainly when measuring particle size distri-
bution on a number basis the cut off sizes should be held con-
stant for data comparisons. Also there would be considerable
uncertainty in comparing the results of different analytical PSD
methods.
Although the results of this project have provided
standard analytical methods for determining FGD scrubber sludge
quality, these methods are directed at the bulk mass of sludge.
The data collected have not clearly established a method for
measuring the PSD of submicron size particles. The sedimentation
and Coulter Counter results presented in this technical note
are based on only one or two tests per method and thus cannot
be regarded as definitive indications of the ultimate abilities
of these methods. Additional tests are needed on a wider variety
of scrubber sludges and under highly controlled conditions in order
to more clearly establish the accuracy and limitations of the
methods. Also, PSD measurements using scanning electron micro-
graphs should be studied as this method could prove to be an
accurate and highly accepted technique for submicron particles.
D-5
-------
4.0 EXPERIMENTAL PROCEDURES AND RESULTS
The standard method for measuring particle size distri-
bution is optical microscopy. A problem with this method, however,
is its inability to measure particles less than about 5 microns.
Based on the literature survey presented in Technical Note
#200-187-11-02, there are a number of other methods which appear
to be suitable for accurately sizing submicron particles. The
two methods selected for study were sedimentation and Coulter
Counter. Another method which should also be applicable is
electron microscopy. This method was not specifically studied
in this work.
The sludge samples used to test the analytical methods
were the same as those used for the standard analytical methods
development. Specifically, a platelet sample from a limestone
scrubber and a granular sample from a lime scrubber were utilized.
4.1 Particle Size Distribution by Coulter Counter
The two sludge samples were sent to an independent
laboratory for particle size distribution analysis by Coulter
Counter. In addition, the platelet sample was sent to a second
independent laboratory to obtain comparison results.
The Coulter Counter measures the number and equivalent
spherical diameter of particles in a electrically conductive
fluid. As a suspension of the particles is drawn through a small
aperture the resistance across it is measured by electrodes on
both sides. The resistance change across the aperture is pro-
portional to the volume of the particle passing through it. The
equivalent spherical diameter is calculated from the measured
particle volume assuming spherical particle shape.
D-6
-------
4.1.1 Procedure
The laboratory analyzing both the platelet and
granular sludge samples prepared the samples for analyses by
dispersing a small amount of sludge in Coulter isoton solution
with Triton X-100 added as. a surfactant to reduce particle
agglomeration. Dispersion of particles was completed by ultra-
sonic vibration. After 1:10 dilution the samples were analyzed
on a Coulter Counter Model TA with aperture setting at 70 microns.
The PSD data was recorded as the number and volume percents finer
than each size range.
The platelet sample analyzed at the second independent
laboratory was prepared by dispersion into 30% glycerine/70%
isoton for the 560y aperture and saturated 470 NaCl/FhO electro-
lyte for the 200, 70, and 16u apertures, with 30 second ultrasonic
agitation and Type I-A dispersant. The analysis was conducted
on a Coulter Counter Model TA II using a multiple tube overlap
technique. The data was processed on a Coulter M3 data processor/
calculator system. The PSD was recorded as the number and volume
percents finer than each size range.
4.1.2 Results
The results of the Coulter Counter single tube method
analyses for the granular and platelet sludge samples are in
Tables 4-1 and 4-2. The results of the Coulter Counter multiple
tube analyses for the platelet sample are in Table 4-3. Figures
4-1 through 4-6 are plots of the Coulter Counter data as cumula-
tive number and cumulative volume percent of particles versus
equivalent spherical diameter.
D-7
-------
TABLE 4-1. PARTICLE SIZE DISTRIBUTION OF THE SLUDGE GRANULES BY THE
COULTER COUNTER SINGLE TUBE METHOD
Size Range
E.S.D.*, y
0.80-1.00
1.00-1.26
1.26-1.59
1.59-2.00
2.00-2.52
2.52-3.17
3.17-4.00
4.00-5.04
5.04-6.35
6.35-8.0
8.0-10.1
10.1-12.7
12.7-16.0
16.0-20.2
20.2-25.4
25.4-32.0
Volume
%
4.9
8.0
2.5
3.4
2.0
1.6
2-0
3.1
5.4
9.5
13.4
14.5
13.0
9.9
3.9
1.8
Cum Vol
% Finer
4.9
12.9
15.4
18.8
20.8
22.4
24.4
27.5
32.9
42.4
55.8
70.3
83.3
93.2
97.1
98.9
Number
%
47.8
39.0
6.1
4.2
1.2
0.5
0.3
0.2
0.2
0.2
0.1
0.1
Cum Number
% Finer
47.8
86.8
92.9
97.1
98.3
98.8
99.1
99.3
99.5
99.7
99.8
99.9
* Equivalent spherical diameter
D-8
-------
TABLE 4-2. PARTICLE SIZE DISTRIBUTION OF THE SLUDGE PLATELETS BY THE COULTER
COUNTER SINGLE TUBE METHOD
Size Range
F..S.D.*, U
0.80-1.00
1.00-1.26
1.26-1.59
1.59-2.00
2.00-2.52
2.52-3.17
3.17-4.00
4.00-5.04
5.04-6.35
6.35-8.0
8.0-10.1
10.1-12.7
12.7-16.0
16.0-20.2
20.2-25.4
25.4-32.0
%
12.6
24.3
7.9
11.7
3.4
2.0
2.0
2.0
2.4
3-4
3.7
5.6
6.8
8.0
2.4
1.0
% Finer
12.6
36.9
44.8
56.5
59.9
61.9
63.9
65.9
68.3
71.7
75.4
81.0
87.8
95.8
98.2
99.2
%
44.2
42.6
6.9
5.1
0.7
0.2
0.1
0.1
~ .... .
Cum Number
% Finer
44.2
86.8
93.7
98.8
99.5
99.7
99.8
99.9
~
""~"
============
* Equivalent spherical diameter
D-9
-------
TABLE 4-3. PARTICLE SIZE DISTRIBUTION OF THE SLUDGE PLATELETS BY THE COULTER
COUNTER MULTIPLE TUBE METHOD
Size Range
E.S.D.*, y
0.32-0.40
0.40-0.50
0.50-0.63
0.63-0.80
0.80-1.00
1.00-1.26
1.26-1.59
1.59-2.00
2.00-2.52
2.52-3.17
3.17-4.00
4.00-5.04
5.04-6.35
6.35-8.0
8.0-10.1
10.1-12.7
12.7-16.0
16.0-20.2
20.2-25.4
25.4-32.0
32.0-40.3
40.3-50.8
50.8-65-0
64.0-80.6
80.6-102
102-128
128-161
161-203
203-256
256-
Volume
%
8.3
11.9
11.8
7.7
2.7
1.6
1.5
1.4
1.7
2.0
2.0
2.1
1.9
1.8
2.1
2.6
3.3
3.9
4.7
5.6
6.4
3.9
2.6
1.4
1.1
0.9
1.2
1.0
0.4
0.4
Cum Vol Number
% Finer %
8.3 40.8
20.2 32.7
32.0 18.3
39.7 6.6
42.4 1.0
44.0 0.3
45.5 0.1
46.9 0.1
48.6
50.6
52.6
54.7
56.6
58.4
60.5
63.1
66.4
70.3
75.0
80.6
87.0
90.9
93.5
94 . 9
96.0
96.9
98.1
99.1
99.5
99.9
Cum Number
% Finer
40.8
73.5
91.8
98.4
99.4
99.7
99.8
99-9
D-10
-------
100
90
H
01
ti
rl
En
C
OJ
O
h
0)
(X
80
70
60
a
3
3
O
50
40
30
20
10
10
12
Figure 4-1.
Equivalent Spherical Diameter, Microns
Sludge Granules: Cumulative Number Percent of Particles
Versus Equivalent Spherical Diameter Measured by Coulter
Counter Single Tube Method.
02 2552-1
D-ll
-------
c
Cd
-------
100 _
c
cfl
H
0)
C
H
C
(II
O
90
80
70
60
(U
I
3
U
50
40
30
20
10
I i t i
1 234
Equivalent Spherical Diameter, Microns
Figure 4-3.
Sludge Platelets: Cumulative Number Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Single Tube Method.
02 2554-1
D-13
-------
cd
H
(-1
OJ
c
CL>
O
M
OJ
P-!
100 _
90
80
70
60
50
OJ
40
u
30
20
10
10 20 30
Equivalent Spherical Diameter, Microns
40
Figure 4-4. Sludge Platelets: Cumulative \blume Percent of Particles
\ersus Equivalent Spherical Diameter Measured by Coulter
Counter Single Tube Method.
02 2553-1
D-14
-------
ti
a
100
90
80
E 70
4J
g
o
Jj
01
PH
tJ
-------
-S
Pn
§
O
PH
0)
g
3
0)
H
4J
ed
1-1
100 _
90 -
80 .
70 _
60 .
50 _
40
30
20
10
10
90
100
20 30 40 50 60 70 80
Equivalent Spherical Diameter, Microns
Figure 4-6. Sludge Platelets: Cumulative Volume Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Coulter Counter Multiple Tube
Method.
02 2556-1
D-16
-------
4.2 Particle Size Distribution by Sedimentation
The granular and platelet samples were sent to an
independent laboratory for particle size distribution analysis
by sedimentation.
In general, sedimentation methods measure an equivalent
particle diameter by observing the settling rate of the sample
in a viscous fluid. Stoke's law for viscous flow around a
spherical body is used as the basis for calculation of particle
size distribution. The relationship between actual particle
shape and dimensions and Stoke's diameter is not known in general
Different methods use different means of measuring settling rates
and extracting particle size data from these measurements. The
particles must be of uniform density in order to obtain accurate
particle size data.
4.2.1 Procedure
The sludge samples were analyzed on a Micromeritics
Sedigraph 5000 by adding 1.0 gram of sample to 25 ml Sedispore
"W-ll", an aqueous medium containing 0.05% surfactant. Dis-
persion was accomplished by placing the slurry in an ultrasonic
bath for two minutes. The running time for the samples was
about 50 minutes each with a cell temperature of 32-33 C. The
particle size range cut off levels were 80 to 0.29y for granules
and 70 to 0.25y for the platelets. The PSD data was recorded
as cumulative mass percent finer than each size range where the
particle sizes are calculated as equivalent spherical diameters.
4-2.2 Results
The results of the sedimentation analyses are given in
Tables 4-4 and 4-5. The cumulative number percent finer than
each size range was calculated for the sedimentation analyses
D-17
-------
TABLE 4-4. PARTICLE SIZE DISTRIBUTION OF THE SLUDGE GRANULES BY THE SEDIMENTATION
METHOD
Size Range
E.S.D.*, y
<0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.8
0.8-1.0
1.0-1.2
1.2-1.5
1.5-2.0
2.0-2.5
2.5-3.0
3-4
4-5
5-6
6-8
8-10
10-13
13-16
16-20
Mass**
%
11.5
5.0
5.5
5.0
7.5
5.5
5.0
3.5
4.5
3.5
3.0
5.0
6.5
6.5
14.5
5.0
2.0
0.5
0.4
Cum Mass
% Finer
11.5
16.5
22.0
27.0
34.5
40.0
45.0
48.5
53.0
56.5
59.5
65.5
71.0
77.5
92.0
97.0
99.0
99.5
99.9
Number
%
47.9
24.8
12.4
9.0
3.1
1.6
0.6
0.3
0.1
0.1
Cum Number
% Finer
47.9
72.7
85.1
94.1
97.2
98.8
99.4
99.7
99.8
99.9
* Equivalent spherical diameter
** Mass % = Volume %
D-18
-------
TABLE 4-5. PARTICLE SIZE DISTRIBUTION OF THE SLUDGE PLATELETS BY THE
SEDIMENTATION METHOD
Size Range
E.S.D.*, U
0.25-0,8
0.8-1.0
1.0-1.2
1.2-1.5
1.5-2.0
2.0-2.5
2.5-3.0
3-4
4-5
5-6
6-8
8-10
10-13
13-16
16-20
20-30
30-40
40-50
50-60
Mass**
%
0.5
0.7
0.8
1.0
2.0
2.5
3.5
5.0
7.0
6.0
14.5
11.0
14.0
12.5
9.0
7.5
1.0
1.0
0.4
Cum Mass
% Finer
0.5
1.2
2.0
3.0
5.0
7.5
11.0
16.0
23.0
29.0
43.5
54.5
68.5
81.0
90.0
97.5
98.5
99-5
99.9
Number
%
53.3
14.8
9.3
6.3
5.8
3.4
2.6
1.8
1.2
0.6
0.6
0.2
0.1
_ =
Cum Number
% Finer
53.3
68.1
77.4
83.7
89.5
92.9
95.5
97.3
98.5
99.1
99.7
99.9
======
* Equivalent spherical diameter
** Mass % = Volume %
D-19
-------
and is also given. Figures 4-7 through 4-10 are plots of
cumulative number and volume percent of particles versus equi-
valent spherical diameter.
4.3 Comparison of Sedimentation and Coulter Counter Results
From plots of the data given in Figures 4-1 through
4-10 the mean particle size for the sludge granules and platelets
was determined for each analysis method. The mean particle size
on a volume or mass basis is given in Table 4-6 and on a number
basis in Table 4-7.
Comparison of the mean particle sizes given in Table
4-6 shows a reasonably good agreement between Coulter Counter
results on platelets but a very poor agreement between Coulter
Counter and sedimentation results. Specifically, the granular
sludge sample had a mean equivalent spherical diameter of 9.3
microns by Coulter Counter and 1.7 micron by sedimentation.
The platelet sample had 1.8 and 2.9 micron diameter by Coulter
Counter measurements and 9.2 microns by sedimentation. Based on
these results it would appear that the samples were accidentally
reversed during analysis. This possibility was carefully checked
and was found not to be the case.
The mass mean particle size of the granular sludge
particles measured by micromesh sieves (Technical Note #200-187-11-02
is about 12.5 microns. This is larger than the 9.3 microns
measured by Coulter Counter but is at least directionally more
in agreement than the sedimentation results. The mass mean
diameter of the granular sample calculated from the optical PSD
data is 18.5 microns.
The platelet particles had a mass mean equivalent
spherical diameter of 5.2 microns by sieve measurement and 10.2
D-20
-------
100 _
90
c
03
£ 80
70
4J
C
0)
a 6°
-------
c
.c
H
Li
C
H
ft,
U
C
01
a
£
0)
s
3
O
01
.5
JJ
nj
J
3
e
3
-l.\J V/
90
80
70
60
50
40
30
20
10
0
18
20
2 4 6 8 10 12 14 16
Equivalent Spherical Diameter, Microns
Figure 4-8. Sludge Granules: Cumulative Volume Percent of
Particles Versus Equivalent Spherical Diameter
Measured by Sedimentation Method.
02 2558-1
D-22
-------
100 _
§
QJ
S
90
80
70
01
o
60
3 50
-------
100 _
90
H
0)
c
H
C
OJ
a
>-<
cu
PL,
OJ
e
0)
H
3
3
CJ
80
70
60
50
40
30
20
10
0 10 20 30 40 50 60
Equivalent Spherical Diameter, Microns
Figure 4-10. Sludge Platelets: Cumulative Volume Percent of Particles
Versus Equivalent Spherical Diameter Measured by Sedi-
mentation Method.
02 2560-1
D-24
-------
TABLE 4-6. MEAN PARTICLE DIAMETER ON VOLUME BASIS*
Method of Analysis
Coulter Singletube
Coulter Multitube
Sedimentation
Optical Microscopy
Micromesh Sieve
Granule (y)
9.3
1.7
18.5
12.5
Sludge Type
Platelet (y)
1.8
2.9
9.2
10.2
5.2
TABLE 4-7. MEAN PARTICLE DIAMETER ON NUMBER BASIS*
Method of Analysis
Coulter Singletube
Coulter Multitube
Sedimentation
Optical Microscopy
Micromesh Sieve
Granule (y)
1.0
0.4
7.5
7.0
Sludge Type
Platelet
1.0
0.4
0.7
4.0
3.5
(y)
* Equivalent spherical diameter
D-25
-------
microns calculated from optical measurements. As was the case
with the sludge granules, the optical and sieve results are
higher than the Coulter Counter results. The sedimentation data
is high in the case of the platelets, however, and does not
follow the same trend as with the granules.
Comparing the results given in Table 4-7 for the mean
equivalent spherical diameter on a number basis, the Coulter
Counter and sedimentation results agree much more closely than
did the data on a volume basis. The granules had a mean diameter
of 1.0 and 0.4 microns by the Counter Counter and sedimentation
methods, respectively. The platelets measured 1.0 and 0.4
microns by Coulter Counter and 0.7 microns by sedimentation.
The Coulter Counter and sedimentation results on a number basis
do not compare well to the optical and wet micromesh sieve
results since the latter did not measure any particles less
than about 1-2 microns. Since a large number of particles if
not the vast majority of particles are less than one micron,
the optical and sieve methods necessarily give much larger
mean particle sizes. Similarly, the use of a larger or smaller
lower cut off size for Coulter Counter and sedimentation would
give a correspondingly larger or smaller mean particle size on a
number basis for any given sample.
There is another very significant difference between
the various particle size distributions which is not obvious
from plots of cumulative percent of particles versus size data.
Namely, the optical and sieve data on a number basis show maxima
in their PSD curves but the Coulter Counter and sedimentation
data do not. This is illustrated by the data in Tables 4-8
and 4-9 which are the particle size distributions of sludge
granule and platelet samples on a noncumulative number percent
basis. Plots of these data are given in Figures 4-11 through
4-14. A comparison of Figures 4-11 and 4-12 for granular sludge
D-26
-------
TABLE 4-8. PARTICLE SIZE DISTRIBUTION OF SLUDGE GRANULES ON A NUMBER PERCENT BASIS
l-o
-J
Optical Microscopy
Size ()i)* Percent
3.
7.
12.
17.
22.
27.
32
37
0
5
5
,5
.5
,5
.5
.5
16.
35.
22.
16.
7.
1.
0.
0.
2
1
3
2
6
7
,8
,1
Wet Micromesh Sieve
Size (p)*
3.
6.
10,
16,
27.
5
.5
.5
.5
.5
Percent
26,
68,
9
8.
0.
,9
.8
.9
.7
.7
Coulter
Size (u)*
0.
1.
1.
1.
2.
2.
3.
90
13
43
80
26
85
59
Counter **
Percent
56
35
4
2
0
0
0
.7
.6
.4
.4
.5
.2
.1
Sedimentation
Size (g)*
0
0
0
0
0
1
1
1
.35
.45
.55
.70
.90
.10
.35
.75
Percent
52
26
13
4,
1.
0.
0.
0.
.0
.9
.5
,9
,7
9
1
07
* Equivalent Spherical Diameter
** Single Tube Method
-------
TABLE 4-9.
Ni
00
PARTICLE SIZE DISTRIBUTION OF SLUDGE PLATELETS ON A NUMBER PERCENT
BASIS
Optical Microscopy Wet Micromesh Sieve
Size (u)* Percent Size (M)* Percent
1.
3,
6,
8,
11.
13.
16.
18.
,50
,75
,25
,75
.25
,75
25
,75
13.
36.
27.
14.
8.
2.
1,
0.
.9 1.75 4.4
,4 3.25 82.4
,4 5.25 8.5
.9 8.25 4.3
,3 13.75 0.5
,5
.0
.5
Coulter Counter **
Size (u)*
0
1
1
1
2
2
.90
.13
.43
.80
.26
.85
Percent
52,
39,
5,
1.
0
0
,6
.0
.0
.2
.3
.1
Sedimentation
Size GO*
0
0
1
1
1
2
2
3
4
5
.52
.90
.10
.35
.75
.25
.78
.50
.50
.50
Percent
36.
27.
17.
7.
4.
2.
2.
0.
0.
0.
5
9
5
9
4
6
0
7
4
1
**
Equivalent Spherical Diameter
Single Tube Method
-------
.u
§
o
ij
0)
PU
(-1
0)
J3
3
S3
100
90
80
70
60
50
40
30
20
10
0
10
20
30
40
Equivalent Spherical Diameter, Microns
Figure 4-11. Sludge Granules: Number Percent of
Particles Versus Equivalent Spherical
Diameter Measured by Optical Microscopy
and Wet Micromesh Sieve Methods.
02 2561-1
D-29
-------
c
OJ
o
M
0)
p-l
100 -
90 .
80 _
70 .
60 -
50 _
40 -
30 _
20 _
10 _
0
Coulter
_ Sedimentation
1234
Equivalent Spherical Diameter, Microns
Figure 4-12. Sludge Granules: Number Percent of
Particles Versus Equivalent Spherical
Diameter Measured by Single Tube Coulter
Counter and Sedimentation Methods.
D-30
02 2562-1
-------
0)
CJ
i-l
0)
JO
e
100 _
90
80
70
60
50
40
30
20
10
0
0
is
/ I
Optical
_____ Sieve
18
20
2 4 6 8 10 12 14 16
Equivalent Spherical Diameter, Microns
Figure 4-13. Sludge Platelets: Number Percent of Particles
Versus Equivalent Spherical Diameter Measured
by Optical Microscopy and Wet Micromesh Sieve
Methods.
D-31
02 2563-1
-------
c
0)
o
cu
I
100 _
90 _
80 _
70 _
60 _
50 _
40
30
20 _
10 _
Coulter
_____ Sedimentation
) 1 2 3 4 56
Equivalent Spherical Diameter, Microns
Figure 4-14. Sludge Platelets: Number Percent of Particle Versus Equi-
valent Spherical Diameter Measured by Single Tube Coulter
Counter and Sedimentation Methods.
D-32
02 2564-1
-------
shows maxima in the particle size distribution curves between
6 and 8 microns for the optical and sieve results. The PSD
curves for Coulter Counter and sedimentation data decrease
monotonically with increasing particle size and do not show a
maximum. A comparison of Figures 4-13 and 4-14 shows maxima
in the sieve and optical PSD curves for the platelet sludge
sample but no maxima in the sedimentation and Coulter Counter
platelet curves. The maxima in the sieve and optical PSD
curves for platelets occur between 3 and 4 microns. It will
be recalled that the equivalent spherical diameter of the
platelets is one half the platelet width. Thus, the 3 to 4
micron maxima for platelets are equivalent to 6 to 8 microns
when actual particle shape is considered.
There are a number of different and important inter-
pretations of the differences in the optical and sieve data
versus the sedimentation and Coulter Counter data. The maximum
in the various optical and sieve PSD curves could indicate that
attrition or particle breakage is the major or at least a signi-
ficant mechanism for new particle generation. This maximum
could also be the result of the inherent limitations of optical
and sieve methods to measure small particles.
In the case of the optical methods, the smallest
particle that can be readily seen at 200X magnification is
about 1 to 2 microns. This would appear on a photomicrograph
as 0.2 to 0.4 millimeters which is not only difficult to see
but is certainly difficult to accurately measure visually against
a millimeter ruler. The smallest particle which can be accurately
measured at 200X magnification is probably at least 5 microns
up to perhaps 10 microns. Thus, the decreased number of particles
counted below 5 to 6 microns could simply be a result of not
being able to see the smaller particles.
D-33
-------
The sieve method also has several inherent problems
in the measurement of small particles. One is the rather .large
tolerance for the sieve openings which significantly limits
the accuracy of the smaller mesh sizes compared to the large
sizes. Also, the smaller sizes tend to blind more quickly than
the larger sizes which could significantly reduce the number of
particles reaching the smaller sieve sizes.
It also appears odd that the sludge granule and plate-
let samples have their PSD curve maxima in essentially the same
6 to 8 micron size range. The granules were produced in a lime
scrubber suspected to have very high nucleation rate whereas
the platelets were produced in a limestone system. These dif-
ferences in sludge origin and crystal habit do not seem to support
the theory of particle breakage as the source of the maxima in
the optical and sieve data PSD curves.
The Coulter Counter and sedimentation PSD curves for
granules and platelets do not show maxima. Also, they generally
do not measure many, if any, particles above about 3 to 5
microns in size. Thus, one reconciliation of the data is that
both types of curves are correct and the methods are mutually
exclusive in the size ranges of particles measured. This would
indicate that the vast majority of particles are produced through
nucleation but a small number of larger particles are produced
by particle breakage. This theory breaks down, however, upon
close inspection of the actual Coulter Counter particle count
data given in Tables 4-4 and 4-5 of Technical Note #200-187-11-02.
These data cover the particle size range of 2 to 60 microns and
clearly show no maximum in the PSD curve.
The weight of the data presented supports the maxima
in the optical and sieve PSD curves being a result of limitations
in the methods. The results are not conclusive, however, and
D-34
-------
more work is needed. Identification of a particle sizing method
which could bridge the 1 to 10 micron range with accuracy would
greatly clarify which type of PSD curve shape is correct.
The mathematical model for relating sludge PSD to
scrubber operating conditions predicts a smooth, monotonic PSD
curve as it is currently formulated with constant or linear
growth - particle size relations. This type of crystal size
distribution is considered normal for crystallization processes
and agrees with the predictions of the Coulter Counter and
sedimentation methods. If the true PSD curve does contain a
maximum due to particle attrition or some other mechanism, then
the mathematical model will have to be reformulated to include
more complex crystal growth rate functions and perhaps also
include the possibility of crystal dissolution in the scrubber.
D-35
-------
DCN #77-200-187-11-09
APPENDIX E
TEST PLAN DOCUMENT
Technical Note #200-187-11-04
18 January 1978
Prepared for:
Robert H. Borgwardt
Industrial Environmental Research Laboratory RTF (MD-61)
U. S. Environmental Protection Agency
Research Triangle Park,
North Carolina 27711
Prepared by:
G. P. Behrens
Reviewed by:
P. S. Lowell
E-i
-------
TABLE OF CONTENTS
Page
1. 0 INTRODUCTION E-l
2 . 0 PROCESS DESCRIPTION E- 2
2. 1 Limestone Scrubbing E-4
2.2 Lime Scrubbing E-7
2 . 3 Double Alkali Scrubbing E-8
3.0 TEST OBJECTIVES AND APPROACH .' E-10
3.1 Test Objectives E-10
3.2 Technical Approach E-ll
4.0 TEST PLAN DESCRIPTION E-21
4.1 Phase I - Nucleation Site Determination.. E-21
4.2 Phase II - Particle Size Distribution
Correlation E-25
4.3 Phase III - Sludge Quality Optimization
and Model Verification E-29
5.0 SAMPLING AND ANALYTICAL MEASUREMENTS E-31
5.1 System Characterization Measurements E-31
5 . 2 Line-Out Measurements E- 34
5. 3 Sampling Frequency and Timing E-36
6.0 PROCESS MEASUREMENTS E-38
6.1 Flow Rates E-38
6. 2 Pressure Measurements E-38
6.3 Temperature Measurements E-38
6.4 Other Process Data E-40
E-ii
-------
TABLE OF CONTENTS (Cont'd)
Page
7.0 DATA HANDLING AND ANALYSES PROCEDURES E-41
7.1 Chemical Analyses E-41
7.2 Process Measurements E-55
7. 3 Process Calculations E-55
7.4 Monthly Progress Reports E-69
8.0 POSSIBLE PROBLEM AREAS E-77
8.1 System Operation E-77
8.2 Measurement Problems E-78
8. 3 Engineering Analysis E-80
9.0 SUMMARY E-81
NOMENCLATURE E-82
REFERENCES E- 84
E-iii
-------
LIST OF FIGURES
Figure Page
2-1 RTF Limestone Scrubbing System E-5
3-1 Size Distribution Data for Lime and Lime-
stone Scrubber Slurries (Coulter Counter) E-16
4-1 Proposed Test Schedule E-22
5-1 Limestone Flow Sheet E-33
7-1 Liquid and Solid Phase Chemical Sample
Locations - Characterization Samples E-44
7-2 Proposed Sample Label Format E-46
7-3 Sample Collection Schematic Diagram E-48
7-4 RTP Monthly Operating Log E-70
7-5 RTP Scrubbing Liquor Parameters E-71
7-6 RTP Dissolved Solids Concentrations E-72
7-7 Particle Size Distribution E-76
E-iv
-------
LIST OF TABLES
Table page
4-1 Phase I - Test Schedule E-23
4-2 Phase II - Test Schedule E-26
4-3 Phase III - Test Schedule E-30
5-1 Limestone System Characterization
Measurements - Sample Points and Analysis E-32
5-2 Limestone Line-Out Measurements E-35
5-3 Sample Point Description and Sequence E-37
6-1 Process Data Requirements E-39
7-1 Scrubber System Chemical Analyses Required. . .. E-42
7-2 Sample Handling Flow Sheet E-45
7-3 Proposed Master Log Book Format E-49
7-4 Results of Liquid Phase Analyses E-53
7-5 Results of Solid Phase Analyses E-54
7-6 Process Measurement Documentation E-56
7-7 Typical Equilibrium Program Printout E-58
7-8 Scrubber Rate Calculation Work Sheet E-61
E-v
-------
LIST OF TABLES (Cont'd.)
Table
7-9 Hold Tank Rate Calculation Work Sheet E-62
7-10 Particle Calculation Sheet E-63
7-11 Operating Data Summary E-73
7-12 Chemical Reaction Calculation Summary E-75
E-vi
-------
1.0 INTRODUCTION
Radian Corporation has been contracted by the Environ-
mental Protection Agency to develop a test plan document to eval-
uate the prospects for improving the physical quality of calcium
sulfite sludge without altering its composition. A secondary
test objective will be to verify the accuracy of a Radian-devel-
oped model for prediction of sludge quality.
The model was developed using present day calcium
sulfite crystallization kinetics. Using data produced in EPA
Contract 68-02-0223 and others, the model predicts particle size
distributions based on nucleation and crystal growth rates of
CaS03-%H20. This document presents a series of tests designed
to yield useful information on sludge quality due to various
scrubber operating parameters.
The test plan information which is presented here is
organized into the general categories of: system description,
test objectives and approach, test plan description, sampling
and analytical measurements, process measurements, process
analysis, and problem areas. Each of these subjects is
discussed in detail in separate sections of this report.
E-l
-------
2.0 PROCESS DESCRIPTION
The overall chemical objective of a scrubbing system
is the removal of S02 from flue gases. In throwaway wet systems,
this S02 is reacted with an alkali metal salt, usually calcium
carbonate or oxide, to yield calcium sulfite or sulfate sludge.
The three processes considered for testing produce a sulfite
sludge which has a fraction of sulfate coprecipitated with it.
The three FGD processes considered were: limestone scrubbing,
lime scrubbing, and double alkali scrubbing. Due to the length
of time necessary to test each process, Radian proposes the
limestone system first. If significant results are achieved,
testing of the other two systems may be implemented.
The decision to test limestone scrubbing is based on
several factors:
1) limestone scrubbing has been in
existence the longest and most
operating problems have been solved,
2) lime will continue to increase in
cost as fuel prices rise,
3) double alkali systems in the U.S.
have traditionally used lime as an
additive, and
4) limestone systems are the simplest
in terms of kinetics, precipitation
rates and operability.
The EPA Research Triangle Park pilot unit is a three-
stage, countercurrent turbulent contractor absorber (TCA). The
E-2
-------
scrubber has a 23-cm diameter and is approximately 3.7 meters
tall. The flow diagram and approximate rates are shown in
Figure 2-1.
An oil fired boiler is used to generate 270-510 m3/nr
of flue gas. For this test plan, a gas rate of 510 m3/hr will
be used. S02 is spiked into this stream at specified rates to
provide the desired concentration. Normal concentration will be
3000 ppm. Oxygen in the flue gas is generally 4-6%. Since the
purpose of this test plan is to study calcium sulfite crystals,
factors which reduce the oxidation of sulfite to sulfate will
be employed. Possibly the biggest factor affecting the oxidation
rate is the oxygen concentration in the flue gas. It is recom-
mended that this be kept below 370. Raising the pickup per pass
will also reduce oxidation. A 50-6070 removal efficiency should
significantly reduce oxidation as compared to a 80-90% SOa
removal.
The flue gas enters the scrubber below the bottom
stage. A 10 wt % scrubbing slurry is introduced at the top of
the scrubber. The slurry feed rate is approximately 83 £pm.
This corresponds to a liquid to gas ratio of 9.8 &/m3 (73 gal/
lOOOacf) . The scrubber feed pH is normally 6, and the scrubber
bottoms ranges from 5 to 6. The bottoms stream flows directly
into the reaction tank which has a 400 liter volume.
Reaction tank feed streams include:
1) scrubber bottoms
2) clarifier and filter overflows,
and
3) limestone additive.
E-3
-------
The liquid residence time in the hold tank under these conditions
is 5 minutes and the average solids residence time is approxi-
mately 10 hours. A bleed stream of 0.5-0.6 liters per minute is
taken from the scrubber feed line and sent to the clarifier.
The clarifier underflow is sent batchwise to a vacuum filter and
the overflow is returned to the hold tank.
Limestone is added to the system from the additive
tank. This tank contains a 2570 limestone slurry. The slurry
is kept well mixed by an agitator and is fed to the hold tank
on pH demand. Generally, flow rates will be about 400 milliliters
per minute to keep a pH 6 scrubber feed.
The remaining portion of this section describes the
process chemistry of each of the three FGD processes. As
stated previously, limestone scrubbing will be the only process
tested at this time.
2.1 Limestone Scrubbing
The flow diagram for the limestone scrubbing unit at
Research Triangle Park is given in Figure 2-1. Average flow
rates are also indicated.
The overall reaction in a limestone system is as
follows:
S02(g) + CaC03(s) + %H20 -» CaS03 %H20 (s) + C02 (g)
Some of the sulfite is oxidized to sulfate:
S02(g) + %02(g) + CaC03(s) + 2H20 *
CaS(V2H20(s) + C02(g)
E-4
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510 m3/hr
FG
SG
ill I T
Scrubber
MW
SCB
LA
. 4 £pm
Additive
Hold Tank
vJy
CO
SCF
83 £pm
CF .6 £pm
_J
u
Clarifier
cu
Figure 2-1. RTF Limestone Scrubbing System.
S-5
-------
The overall reaction may be broken down into sorption (scrubber)
and precipitation (hold tank) reactions. The scrubbing slurry
has two components: liquid and solid. Both of these components
can react with the sorbed S02 in its hydrated form, H2S03.
Scrubber:
Liquid Phase
MgS03 (aq.)
MgHC03
\ 2HS03
)
2HS0
H2S03 H>
< + +
\ Mg
^_
HC03~ + HS03'
Solid Phase
CaC03
CaS03 Lu ^ + Ii2SO:
Hold Tank:
CaC03 (s) => Ca++ + C03=
C03~ + KS03 ^ HC03 + S02=
Ca++ + S03= + %H20 ^ CaS03
S03 -
2HS03
H2C03
+ %H20
%H20 (s)
The base in the limestone system is the carbonate ion produced
by limestone dissolution. As a result, there is not a large
pH change between the scrubber and the hold tank.
Recent work (JO-R-214) has indicated that as long as
the oxidation fraction (specific sulfate/total sulfur-solid
E-6
-------
phase) is below .15, the coprecipitation phenomena is capable
of removing calcium sulfate. Scale-free scrubber operation is
then realized. In this test plan, all suldge produced is re-
garded as calcium sulfite hemihydrate (CaS03-%H20).
Limestone dissolution is a rate controlling factor in
this system. It is probable that limestone fines may dissolve
in the scrubber to increase the liquid phase alkalinity. This
effect will change the particle size distribution in a manner
yet to be determined.
2.2 Lime S cr ubb ing
The overall lime scrubbing reaction is:
S02(g) + CaO(s) + %H20 -» CaS03-%H20(s)
Oxidation of sulfite can also occur:
S02(g) + %02(g) + CaO + 2H20 -» CaSO^ 2H20(s)
Dissolution of lime is extremely fast compared to sulfite
precipitation rates or limestone dissolution rates (OT-023).
Therefore most of the alkalinity required to sorb S02 in the
scrubber comes from dissolution of calcium sulfite to form
calcium bisulfite. This phase change will have an effect on
particle size distribution which could be different from a
Limestone system. Furthermore, there is a large pH change be-
tween the scrubber and hold tank that can effect the nucleation
rate.
E-7
-------
2. 3
Double Alkali Scrubbing
The double alkali process utilizes a soluble sodium-
based alkali (NaOH and Na2S03) to absorb S02. The sulfur-oxide
rich effluent is then reacted with lime (Ca[OH]2) to produce cal-
cium sulfite solids and regenerate the scrubbing liquor. The
principle reactions are as follows :
Absorption:
2NaOH + S02 -» Na2S03 + H20
Na2S03 + S03 + H20 -» 2NaHSO 3
Oxidation of sulfite also occurs :
Na2S03 + %02 -> Na2SO,t
Regeneration :
Ca(OH)2 + 2NaHS03 * Na2S03 + CaS03'%H2(H + 3/2 H20
Ca(OH)2 + Na2S03 + %H20 -> NaOH + CaS03'%H2(H
Ca(OH)2 + Na2SCU + 2H20 * 2NaOH + CaS04-2H20
CaC03 + 2NaHS03 + %H20 -» Na2S03 + C02 + H20 + CaS03-%H2Oi
By using sodium compounds to absorb S02 , higher alka-
linity levels can be used than in lime /lime stone scrubbers.
This results in lower L/G ratios. Also scrubber scaling is
avoided due to the high sulfite concentration present. With
the lime added in a special hold tank, greater utilization is
realized. Since the system uses a clear scrubbing liquor,
calcium sulfite solids are not pumped around the scrubbing loop.
Particle size distribution will therefore be different from
E-8
-------
lime or limestone systems. Historically, this process produces
a sludge which has worse characteristics than lime or limestone
systems.
S-9
-------
3.0 TEST OBJECTIVES AND APPROACH
The sludge quality/model verification test program
will be conducted using a limestone scrubbing system. Three
phases of tests are planned for the process. The objectives of
each test phase are discussed in this section. The technical
approach required to meet these objectives is also outlined.
3.1 Test Objectives
The test phases proposed for the limestone FGD process
are listed below:
1) nucleation site determination,
2) particle size distribution
correlation, and
3) sludge quality optimization and
model verification.
The objectives of each of these test phases are discussed in
the following subsections.
3.1.1 Nucleation Site Determination
Phase I testing is intended to locate the major
source of nucleation in the scrubbing system. The three possible
sites for nucleation are the scrubber, the hold tank, and the
pumps. Single parameter tests are planned in this phase.
Coulter counter analysis will be used to determine the particle
size distribution of hold tank slurry. By observing changes
in the number of small particles, varied operating conditions
should reveal the nucleation source.
E-10
-------
A major portion of the initial phase will be spent
studying the effect of equipment on nucleation. Such mechanical
nucleation will interfere with nucleation from other changes.
It will therefore be eliminated from Phase II and III testing
as much as possible once its causes have been identified.
3.1.2 Particle Size Distribution Correlation
The second phase of testing will provide data to cor-
relate the particle size distribution with operational parameters.
Particle size distribution is the result of the interaction be-
tween nucleation, crystal growth, equipment arrangement, and
operational conditions. Four series of tests are planned to
generate results for the model. These are percent solids changes,
scrubbing liquor quality, residence time variations, and slurry
grinding. The data obtained from these parametric studies will
be compared with results predicted by the model. Modifications
to the model will be made where necessary to reach agreement be-
tween predictions and observations.
3.1.3 Sludge Quality Optimization and Model Verification
The final phase will utilize tests proposed by the
developed correlation. Multi-parameter tests will be used to
check the model's accuracy to predict sludge quality. Further
tests will attempt to produce the highest quality sludge pos-
sible by changing the most influential process conditions.
3.2 Technical Approach
Radian believes the most important parameter affecting
sludge quality is the particle size distribution. Large particles
settle and dewater better than small ones. However, larger crys-
tals have smaller area to mass ratios. This can cause a rise in
E-ll
-------
supersaturation. At certain "critical" supersaturation levels,
homogenous nucleation occurs, resulting in the formation of many
new particles. This showering of solids can result in scale
formation in certain circumstances. By using the tests outlined
in Section 4, an understanding of nucleation and crystal growth
will be obtained. The desired result of this test plan is the
production of a high quality sludge obtained by controlling the
particle size distribution.
At steady state, several balances must hold true in
scrubbing systems. By relating these balances to one another,
an understanding of the importance of particle size distribution
can be realized. Since no calcium sulfite crystals enter the
system, those generated within the system must equal the number
of particles leaving the system. This can be expressed as:
no = CF
o
rm
J n(L)dL , (3-1)
where nQ = nucleation rate (particles/5,-second) ,
CF = clarifier feed rate (£/second),
n = number of particles of size L per
unit particle length and per unit
volume (H 1-m~i), and
L = characteristic length of particle
(meters).
The function of n(L) is usually referred to as the
particle size distribution function. The quantitative descrip-
tion of this function is the heart of the problem. Several
other pieces of information are also important. Some of these
E-12
-------
are: the total number of particles, the nucleation rate, and
the size distribution function evaluated at zero size.
The value of the integral in equation (3-1) is N, the
total number of particles per unit volume. As the length ap-
proaches zero, the initial distribution function, n , is defined.
o
n = lim n(L) . (3-2)
L+o
This initial value is important because it is funda-
mentally related to the nucleation rate as shown in equation
(3-3).
n = lim (nR) = n R . (3-3)
0
It is expected that the nucleation rate is dependent
upon relative saturation, solids content, the number average
crystal size, and energy dissipation rate in the solution,
especially in pumps and mixers. These parameters have been in-
cluded in an empirical correlation:
n = ki (r-l)hm *L j + k2 exp[-4c3/£n r] , (3-4)
o s n
where r ^ relative saturation,
m H slurry solids content,
s
L = number average crystal size,
n
h,i,j = undetermined exponents, and
ki,k2,k3 ^ undetermined constants.
E-13
-------
No experimental data exists which would help in the determina-
tion of the six missing constants. Therefore, Phases I and II
will be used to generate these values.
For modeling purposes, the growth function, R, must be
known. One form for the growth rate assumes that it is a linear
function of size.
R(meter/sec) = k (l+6L)(r-l)P , (3-5)
where k = surface reaction rate constant.
At normal levels of supersaturation, experimental data from
PP&L has yielded a kr of 3x10"12 meter/sec and a 5 of 5xl05
meter"1. This correlation does not seem to fit lime crystal
growth data.
Once the functional dependence of the nucleation and
growth rates have been determined, the computer model should be
able to predict the existing particle distribution, given the
incoming distribution and process parameters, A simplification
of the general particle balance equation will be used by the
mo de 1:
+ G(L,X,Y,Z) .
(3-6)
Basically, the equation says; the change in the number of size
L particles with respect to time is equal to the net number of
particles of size L convected into a volume (first three terms)
plus the number in the volume which grow to size L, (nR(L)),
plus particles of size L generated by other mechanisms(G). The
E-14
-------
nucleation rate is not included in the equation per se. It is
actually a boundary condition for the growth term:
nQ =fn(L)R(L)J| evaluated as L-K> . (3-7)
Several assumptions can be made to simplify equation
(3-6). First, steady-state conditions should apply to the num-
ber of particles in an operating system. Therefore, 1^=0.
d t
The convection terms can be considered as entering and exiting
streams when a system component volume is used. Therefore, the
final working form of the particle balance equation becomes:
/[S
v L
dV , (3-8)
where Q = volumetric flow rate (liters/
second), and
G = particle generation term other
than growth and nucleation
(jT'-sec"1).
This equation predicts the change in the particle size distri-
bution, given expressions for the growth, nucleation, and other
particle size changing rates. Obtaining these expressions for
n(L), R(L) and G is therefore part of the objective of this test
plan.
Graphs for n(L) will take the form of Figure 3-1.
The distribution will be plotted as the characteristic length L.
versus the log of the number of particles having that dimension.
E-15
-------
107
1Q6
10s
10"
io3
i
102
10
\
.\
\
\
x Pennsylvania Power and Light Limestone Pilot Unit
Louisville Gas and Electric Lime System
5 10 15 20 25 30
Particle Size (Meter x 10s)
35
Figure 3-1. Size Distribution Data for Lime and Limestone
Scrubber Slurries (Coulter Counter).
E-16
-------
The nucleation rate at steady state will simply be the total
number of particles in the PSD sample times the clarifier under
flow rate. Since the number of particles increases as L ap-
proaches zero, and the technique for measuring sub-micron par-
ticles is not fully developed, changes in the nucleation rate
will be difficult to separate from experimental error unless
extreme care is taken in their analyses. A worksheet for PSD
calculations is given in Table 7-10, based on the results gen-
erated in completion of Figure 7-7.
An alternate method of generating a nucleation rate
can also be used. For a scrubbing system, the material balance
must also be solved. For every mole of S02 absorbed a mole of
sludge is formed. Actually, a small amount of sulfur leaves
dissolved in the adherent water. Since the sludge consists of
calcium sulfite crystals, the material balance is connected to
the particle balance.
For limestone systems, the average length to width to
thickness ratio is generally 25y x 20y x ly. Since all of the
equations developed here are based on a characteristic length
L, definition of a shape factor, kv is necessary.
(3-9)
where V = crystal volume (meters3). A mass balance between the
S02 pickup and the particle volume change can now be made.
CF k,, p
^/"r.(L)L'dL , (3-10)
E-17
-------
where AS02 = S02 pickup (gram mol/second),
CF E clarifier feed rate (liters/second),
p = particle density (grams/cm3), and
s
MW = molecular weight (grams/gram mol)
if we define a mass average length L (meters) such that:
/co .-oo
i(L)L3dL/ /n(L)dL , (3-11)
o o
then equation (3-10) can be rewritten as :
AS02 = CF kv ps N L^/MW (3-12a)
= k p N L/MW , (3-12b)
where N is the total number of crystals per volume of slurry and
N is the total number of crystals leaving the system.
«
In a steady-state situation, N should equal n , the
nucleation rate. Equation (3-12) shows that for a change in the
S02 removal rate, the product of NL3 must change. Consequently,
if the pickup is constant, and the mass average length increases,
the nucleation rate decreases to the third power.
Determination of the net nucleation rate can be done
by either Coulter Counter analysis or sedimentation techniques.
Both methods can analyze to below . 5y. By counting the total
number of particles in a sample, calculations can be made to
determine the number of particles leaving the system. This net
E-18
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rate includes generation of particles by methods other than
nucleation. In order to obtain useful results, it will be
necessary to closely maintain steady-state conditions.
The growth rate function R(L) must also be calculated
for input into the computer model. If the scrubbing system ap-
proximates mixed suspension, mixed product removal (MSMPR) crys-
tallizer conditions, the particle balance for a well mixed vessel
can be simplified to yield:
d(nR) = n
dIT~ T
where T is the mean solids residence time in the system. This
equation can be expanded and solved for the size derivatives of
the distribution n(L). Thus,
n) _ d £n R
__
dL dl Rf
If the linear growth rate is constant, (dl^£R)) = 0, then a plot
of In n(L) versus L should be a straight line with slope equal
to - rr- . If the growth rate increases with size, (gj-) >0,
then the curve will be concave upward.
Figure 3-1 shows size distributions for product
crystals from the LG&E lime and PP&L limestone scrubbing systems
calculated from Coulter Counter data. Both distributions are
clearly concave upward, indicating an increasing growth rate
with increasing size.
E-19
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Equation 3-14 can be rearranged to calculate the
growth rate R using the slope of the size distribution:
dR
dL
The change in growth rates with crystal size indicated by the
data in Figure 3-1 can be estimated by approximating the size
distribution with the straight lines indicated on the figure.
Along these lines, dR/dL = 0, and
dL
For the lime data from LG&E, T was approximately 1300 minutes
Using this number and the slopes of the indicated lines:
R
small - 2.4 x ICT" meter/min
Rlarge = 2-2 x 10"9 meter/min
Thus, the larger crystals grow about ten times faster than the
smaller crystals.
Once the particle size distribution is plotted, a
decision can be made as to how many segments are necessary to
model the growth function accurately.
E-20
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4.0 TEST PLAN DESCRIPTION
In this section, the strategy and sequencing of
individual tests to be conducted during each of the three
planned test phases are discussed. Operating conditions which
are proposed for each specific test run are summarized in Tables
4-1, 4-2, and 4-3. The estimated time duration of each test is
also shown in that set of tables.
The overall test schedule shown in Figure 4-1 is based
upon individual test duration figures given in Tables 4-1 through
4-3 and an estimate of the necessary analytical and operating
manhours required.
4.1 Phase I - Nucleation Site Determination
The eight tests proposed for Phase I are presented in
Table 4-1. The suggested flow arrangement is shown in Figure
4-2. In this configuration, the solids retention time is
approximately 10 hours. Allowing three or four residence times
for the solid phase to line out after a change in operation was
instituted would require two days of steady-state operation. After
this time, full characterization sample sets could be taken.
Allowing for three replicates would make each test run approxi-
mately one week in length. As soon as results confirm a reliable
set of data, the next test parameter will be implemented to
minimize total project length.
The first test will be used as a base case for compar-
ison with further tests. The desired operating and mechanical
parameters are given on Table 4-1. It should be noted that
unless specifically stated, .all. variables return to base case
conditions after a test run. This is to insure that results
E-21
-------
I
N>
to
I. NUCLEATION SITE DETERMINATION
1. Base Case
2. Pump Test
3. Pump Test
4. High Relative Saturation
5. Low Relative Saturation
6. Hold Tank Testing
7. Hold Tank Testing
8. Hold Tank Testing
II. PARTICLE SIZE DISTRIBUTION CORRELATION
9. Base Case
10. Solids Level
.11. Solids Level
12. Low Positive Liquor
13. High Positive Liquor
14. Low Negative Liquor
15. High Negative Liquor
16. Purge - Seed Crystals
17. Increase Retention Time
18. Retention Time and Grinding
III. MODEL VERIFICATION
19. Computer Predicted
20. Computer Predicted
60
80
35
10
15
I 1
Months After Initiation of Testing
Figure 4-1. Proposed Test Schedule
-------
TABLE 4-1. PHASE I - TEST SCHEDULE
i
ho
Test *
1
2
3
4
5
6
7
6
Days
5
5
5
5 .
5
5
5
5
40
Objective
Obtain base case
system operation
Observe effect of
impeller material
Observe effect of "
pump speed
Observe higher scrubber
supersaturation
Observe scrubber
subsaturatcd operation
Observe mechanical
features of hold tank
Same as #6
Same as //6
Variable Changed
None
Switch to steel
impeller
Reduce pump RPM'a,
maintain constant L/C,
residence times.
Seduce scrubber feed flow, raise *
SO; inlet, (constant SO 2 pickup)
Scrubber feed pH 4.5 x
Switch to steel
agitator
Lower agitator speed
Mix additive, clarifier overflow
and scrubber bottoms together
Reason
Basis for further
comparison
Determine effect of
pump energy on P.S.D.
Determine effects of scrubber
conditions on P.S.D.
Determine effect of hold
tank conditions on P.S.D.
(1) Base Case - Low oxygen content in flue gas (<3Z), 3000 PPM S02, feed rate 83 fcpra, 10Z solids, 10 hour solids retention time.
Valve positions and nozzles are not to be changed during the study.
-------
generated will have a common basis for comparison. The purpose
of Phase I testing will be to determine the source of nucleation.
Three possible areas exist where nucleation occurs: the feed
pump, the scrubber and the hold tank. Hopefully, only one area
contributes significantly, so its location can be determined.
Tests two and three will determine the effect of the
feed pump on the particle size distribution. In large pumps,
the tip speed can approach 90-100 fps. The pump tip speed
at RTF should be about 30 fps. At this low speed, changes might
not have a great effect. Test two will use a steel impeller in
place of the rubber-tipped one and Test three will operate the
pump at a lower speed while maintaining the same flow rate to
the scrubber. A Variac or similar device is envisioned to
slow down the pump.
Tests four and five are planned to observe changes
due to scrubber conditions. Test four will attempt to operate
in a higher supersaturated mode than previously. This will be
done by reducing the scrubber feed flow (bypass) and raising
the inlet SOa concentration to a point where the pickup per
pass is the same as in the base case. Test five will be run
at a scrubber feed of pH 4.5. This will cause the scrubber
liquor to be subsaturated with respect to calcium sulfite due
to the shift to bisulfite. The pickup rate should be the same
as previously. If not, the inlet SOz concentration can be
changed to increase the driving force.
Tests six and seven will examine some of the effects
of the hold tank. In line with the reasoning behind Tests two
and three, Test six will use an agitator of steel rather than
polypropylene. Test seven will reduce the agitator speed,
again with a Variac.
E-24
-------
The final test in Phase I, test eight will determine
the effect of adding the scrubber bottoms, limestone additive
and clarifier overflow at the same location. Recent work at
LG&E with lime additive has shown a difference in crystal shape
due to additive point changes. However, due to the size of the
LG&E system, tight control of other variables was not possible.
After these tests are completed, the nucleation site
should be defined. Based on the results obtained, the base
case for Phase II (Test Nine) will consist of the operating condi-
tions and variables which have yielded the lowest nucleation rate.
This will enable changes in the particle size distribution to be
more easily recognized in Phase II.
4.2 Phase II - Particle Size Distribution Correlation
Tests proposed for Phase II are given in Table 4-2
along with variable changes and estimated durations of each test.
At this point, analysis of Phase I data should indicate
the major source of nucleation. The thrust of Phase II will be
to correlate changes in process variables with the nucleation
and growth rates. The equipment configuration and operating
conditions for Phase II should reflect the lowest nucleation rate
features of Phase I testing. An initial estimate on the equipment
arrangement based on previous research (TI-006, KH-034) could be:
polypropylene agitator, low mixing speed, rubber impellers, slow
pump speed, and medium-high L/G ratio. This, or another set of
conditions, will form the base case for further testing. It can
be seen that these conditions should tend to eliminate the mech-
anical sources of nucleation. This will improve the observation
of different nucleation rates and simplify correlation of these
changes with process variations. Four areas of testing are
planned for Phase IT:
E-25
-------
TABLE 4-2. PHASE II - TEST SCHEDULE
Test t
9
10
11
12
13
14
15
16 '
17
18
Days
5
5
5
5
5
5
5
3
5
5
_5
53
Objective
Base Case^
Change number of
crystals in system
Same as
Change
liquor
Same as
Same as
Same as
System
tf 10
scrubbing
quality
012
* 12
# 12
purge
Add seed crystals
Increase solids retention
time to 16 hours
16-hour S.R.T. and
grinding
Variable Changed
'Best' configuration from Phase I
5X solids, keep SOz pickup constant -s
by raising inlet concentration
15% solids, keep SO? pickup constant I
by lowering inlet concentration
Low positive scrubbing liquor
(2Hy 4- Na - Cl)
High positive liquor
Low negative liquor
High negative liquor
Grind 1% of clarifier underflow
stream
Increase hold tank size
Sane as 016 and #17
Reason
Future reference
> Determine effect of solids
level on nucleation
Determine effect of liquor
> quality and nucleation and
growth rates
Eliminate high soluble species
conccntrat ion
Increase number of growth
sites
Longer time for crystal
growth
Same as #16 and till
(1) Base Case - Configuration from Phase I yielding lowest amount of mechanical nucleation.
-------
1) percent slurry solids changes,
2) scrubbing liquor quality changes,
3) residence time variations, and
4) slurry grinding.
Slurry grinding is a proprietary Radian process which has been
patented, stemming from work at the Sunbury S02 pilot unit
(R/J-074-03).
Test 9 will be used as a base case for Phase II.
As stated previously, the configuration will be the combination
of parameters which produced the lowest nucleation rate in Phase
I. Tests 9 and 11 will use 5 and 15% slurry solids levels,
respectively. Changing the solids level will change the number
of crystals in the system and also the super saturation. By
changing both of these parameters, the new size distribution
is not easily predictable.
Tests 12 through 15 will examine the effect of
scrubbing liquor quality on crystal size. In an equilibrium
mixture, the anions and cations will balance leaving no residual
electronegatively. By rearranging into sets of soluble and in-
soluble ion pairs, the following liquid phase groupings at pH
6 can be made: very soluble; magnesium, sodium and chloride, and
slightly soluble;calcium, sulfite, sulfate, bicarbonate, and
carbonate. If the net charge of the very soluble group is
negative, i.e., high chloride levels, the other group must
balance; i.e., high calcium level. This is a poor scrubbing
liquor as the sulfite level is low, due to solubility constraints.
If, on the other handthe very soluble group is positive, (e.g. high
S-27
-------
magnesium levels) , the other grouping must have a net charge.
This means higher sulfite levels. This sulfite provides extra
alkalinity for scrubbing, hence, it is a good liquor. In order
to determine quality, the sum of twice the magnesium level plus
the sodium minus the chloride is evaluated in terms of moles
per liter. The range of +.6 to -.6 is the proposed test band.
I | +
Examples of these liquors could be 7300 ppm Mg , 0 ppm Na and
_ _ _
Cl~ and 0 ppm Mg and Na and 21,000 ppm Cl~. Many other
possibilities also exist. Test 12 will have a low positive read-
ing, Test 13 - high positive, Test 14 - low negative and Test 15 -
high negative. Tests 14 and 15 may cause scaling in the scrubber.
Frequent inspections should be made during these two tests.
Following this set of tests, the system should be operated in an
open loop configuration to purge the soluble species until their
levels return to normal.
Test 16 will observe the effect of grinding a small
portion of the clarifier underflow and returning these crystals
to the hold tank. Mature sulfite crystals range from 15-50
microns. The grinder will process about one milliliter per
minute of underflow. The grinder may produce new crystals by
two mechanisms. The first is breakage of existing crystals. The
second is production of secondary nuclei because of the extremely
high energy dissapation rates. Levins et. al. (LE-305) has shown
that as particle size decreases, the mass transfer coefficient
between the liquid phase and solid surface increases. Other ob-
servations show larger particles growing faster than smaller ones.
Further work in this area is needed to resolve this discrepancy.
Test 17 will utilize a longer residence time, approxi-
mately 16 hours. The longer residence time will provide more
crystal growth opportunity, but will tend to decrease the
super saturation. Test 18 will combine the 16-hour residence time
and ground crystals.
E-28
-------
4-3 Phase III - Sludge Quality Optimization and Model
Verification
Phase III of this test program will be based on analysis
of the results from Phases I and II. The primary objective is
to improve the quality of the sludge produced in limestone
scrubbing systems. The other objective of this phase is to
check the accuracy of the model developed by Radian for predic-
tion of sludge quality.
Analysis of data from Phase II should show relationships
between operational variations and sludge quality. Hopefully,
these changes will fit a correlation. Phase III will use these
correlations to produce a sludge of predetermined characteristics.
By intermeshing chemical and process options, a scan of scrubber
operations can be made. Ideally, the correlation will predict
the resulting sludge product.
Obviously, at this time, a detailed description of
Phase III tests is not possible. Analysis of Phase II data will
show the effects of variables changed in that phase. The extent
of variation will determine each parameter's importance to over-
all sludge quality.
Two months of testing are scheduled for Phase III.
It is recommended that sufficient analysis be given to Phase II
analysis before the system is restarted. A detailed list of
parameter changes for each test should also be made prior to
startup.
E-29
-------
Ui
o
TABLE 4-3. PHASE III - TEST SCHEDULE
fe^t II Days Objective Variable Changed Reason
19,20 37 Optimize sludge quality ?? Primary objective of test
plan
-------
5-0 SAMPLING AND ANALYTICAL MEASUREMENTS
Proposed chemical analysis and sampling schedules are
presented in this section. Two types of sample sets will be
necessary for this test program. Line-out measurements will be
taken to determine system stability after a change in operation
has been made. After three or four solids residence times have
elapsed and the line-out samples indicate steady-state has been
reached, a full set of system characterization samples will be
taken.
In this section, the two schedules are discussed and
related to the test program objectives of Section 4.0. In addi-
tion, the sampling techniques required to obtain meaningful
test results will be discussed.
5.1 System Characterization Measurements
A listing of system characterization sample points and
required analysis is presented in Table 5-1. This table specifies
the complete set of sample points and analyses required to perform
an in-depth engineering evaluation of the tested scrubbing system.
These samples will be gathered once the system has reached steady-
state with respect to both solid and liquid phases. Base case
testing will be duplicated to insure a reliable source of compar-
ison with subsequent perturbations. In other cases, the operating
conditions will be altered immediately after repeatable character-
ization sampling has occurred.
It should be noted that some deviation from the sampling
schedule is expected during the test program. Not all of the
analyses listed in the table will be performed for every sample
point during every sampling period. Some of these deviations
S-31
-------
I
CO
N3
TABLE 5-1. LIMESTONE SYSTEM CHARACTERIZATION MEASUREMENTS-
SAMPLE POINTS AND ANALYSIS
Stream Name
Flue Gas
Stack Gas
Scrubber
Feed
Scrubber
Bottoms
Clarifler
Underflow
Clarlfier
Overflow
Limestone
Additive
f ^
Makeup"'
Water
Designation
FG
SG
SCF
SCB
CLU
CLO
LA
MW
Gas Analyses Liquid Analyses Solids Analyses
II S02 02 C02 H20 Ca** Mg^ Na""' Cl" C02 S02 T.S. Z Ca Mg COz SOz SOa PSD Settling
Solids
1 X X X X
2 x x
3 - XXXXXXX XXXXXXX X
f ]\
A xxxxxxx x
5 XXXXXXX XXXXXXX X
6 x x x x x x x(2) x x(a)
7 xx x xxxx
8 xxxxxxx
d)
(2)
(3)
PSD teat will be discontinued If no difference is observed with SCF.
Necessary only if % solida >.1Z.
Periodic sample sufficient.
-------
FG
SG
nTrr
Scrubber
MW
SCB
LA
Additive
Hold Tank
(6)
CO
SCF
CF
LJ
Clarifier
CU
Figure 5-1. Limestone Flow Sheet.
E-33
-------
are mentioned in the notes attached to the sampling schedules.
Other cases are discussed below.
Some species, such as the magnesium, sodium and
chloride liquor concentrations, are not expected to change
significantly except in certain test runs. For example, no
tests in Phase I should significantly affect these ions. As a
result, these analyses need only be performed periodically during
this phase. Also, these soluble salt levels are not expected
to vary significantly from stream to stream within the scrubbing
loop so they will be measured only in the scrubber feed stream.
Other streams needing only periodic sampling are the
makeup water, and the limestone additive. These should be
checked so accurate additive consumption rates can be calculated.
5.2 Line-Out Measurements
In the initial phase, these systems will have a
solids residence time of approximately 10 hours. Based on a
step change disturbance in a first order system, after three
residence times have passed, the system is within 95 percent
of its new steady-state. Allowing two days for line-out should
therefore be sufficient with the original hold tank volume.
Since the nature of these measurements is that of a monitoring
function, a minimal number of sample points and analyses will
be performed. The primary sample points will be the scrubber
feed and the clarifier underflow. The liquid and solid phases
from each stream should be similar in composition at steady-state,
Table 5-2 lists the tests required for line-out of the limestone
system.
E-34
-------
TABLE 5-2. LIMESTONE LINE-OUT MEASUREMENTS
Liquid Analyses Solids Analyses
Stream Designation // Ca Mg Na Cl C02 S02 TS Ca Mg C02 S02 TS PSD % Solids
Scrubber Feed SCF 3xx xxxx xxxx
Clarifier Underflow CLU 5xx xxxx xxxx
M
l
<-o
Ul
-------
5.3 Sampling Frequency and Timing
With the original system volume, a test period should
last three or four days. After a system perturbation, two days
will be allowed for line-out. At the end of the second day
(35-40 hours after start-up), a set of line-out samples will be
tc'ken. Upon analyzing the results, a decision will be made to
take a characterization set the next day. If the results of the
full set are judged satisfactory, change to a new test condition
will be made. If not, the system will be reanalyzed the next
day.
The recommended sampling sequence is given in Table 5-3.
It should be noted that sample points 2, 3, and 4 are to be
taken simultaneously. Ideally, the whole system should be
sampled at the same time. Due to the volumes involved in the
tanks, sequential sampling is acceptable. However, comparison
between gas and liquid phase SOa depletion/pickup valves are
meaningless if they are not taken at about the same time.
Once scrubber sampling is completed, the rest of the
system can be sampled. A complete sample set should be collectable
in 15-20 minutes. In this amount of time, minor process variations
should not affect conditions in the various tanks.
S-36
-------
TABLE 5-3. SAMPLE POINT DESCRIPTION AND SEQUENCE
(Limestone Systems)
Sample Points
Sample-Sequence Number Description
1 1 Flue Gas Inlet
2 2 Stack Gas Outlet
3 Scrubber Feed
4 Scrubber Bottoms
3 5 Clarifier Bottoms
4 6 Clarifier Overflow
5 (7) Alkaline Additive
6 (8) Makeup Water
( ) Indicates periodic sampling point
E-37
-------
6.0 PROCESS MEASUREMENTS
In order to properly characterize scrubber systems,
certain process measurements must be gathered in conjunction
with the chemical analyses discussed in the previous section.
These process measurements include such variables as slurry and
liquor flow rates, gas flow rates, various tank levels and stream
temperatures and pH's. Table 6-1 indicates which process measure-
ments will be required for system characterization.
6.1 Flow Rates
Measurement of the scrubber feed rate is necessary for
testing purposes. At present, this is done by measuring a
tank level change over a time interval. Installation and cali-
bration of a rotameter would simplify controlling the feed rate.
The gas flow is measured by a differential pressure
cell attached to an orifice plate. Measurement of the SOa addi-
tion rate is performed by hourly weighing of supply gas cylinders.
Due to the small flows involved, the remaining streams (lime-
stone additive, clarifier feed, overflow and bottoms and makeup
water) can be measured with a graduated cylinder..
6.2 Pressure Measurements
The pressure measurement required will be taken by
the D.P. cell for gas flow determination.
6.3 Temperature Measurements
Table 6-1 indicates that every sampled stream should
have a temperature measurement. Temperature is a required input
to the equilibrium program. After continuous operation has
E-38
-------
TABLE 6-1. PROCESS DATA REQUIREMENTS
Stream Name
Flow Rate
Pressure
SO2 Cone
PH
Temp
Gaj3
Flue Gas (FG)
Stack Gas (SG)
x
x
X
X
Liquid
Scrubber Feed CSCF)
Scrubber Bottoms
(SCB)
Clarifier Feed (CF)
Clarifier Overflow
(CO)
Clarifier Underflow
(CU)
Limestone Additive (LA)
Makeup Water (MW)
Vessel Level Data
Vessel
Hold Tank
Additive Tank
x
x
x
x
x
X
X
X
X
X
X
X
X
X
X
X
X
X
E-39
-------
been established, the variation in temperature may be deemed
minor and readings taken only periodically.
6.4 Other Process Data
Various process data will be gathered on a routine
basis during the test runs. Among these are gas inlet and outlet
S02 concentrations (DuPont on-line analyzer readings), pH's and
tank slurry levels. The DuPont readings should be checked manu-
ally occasionally to maintain reliability.
During sampling, the pH's of all the sampled streams
will be recorded. This measurement will be taken: 1) to check
on-line pH instrumentation for calibration purposes and 2) for
use in the equilibrium program.
Tank levels will be recorded routinely. In combination
with the water makeup rate, the slurry level will determine the
magnitude of the system's water requirement. It is desirable
from a system operation documentation standpoint for the water
rate and tank levels to remain reasonably constant. With constant
slurry volume conditions, changes in liquid or solid phase
chemistry can be attributed to intended changes in system
operation.
E-40
-------
7.0 DATA HANDLING AND ANALYSES PROCEDURES
This section provides documentation of the data hand-
ling and analyses procedures that will be used during the test
program. It includes specifications of chemical analyses to be
performed, various sample and process log book formats, instruc-
tions for sample handling and computational formats for engineer-
ing calculations.
7.1 Chemical Analyses
Table 7-1 lists the analyses which need to be per-
formed on the scrubbing systems. In order to generate all of
the analyses listed in Table 7-1, as many as five different
sample bottles may be needed at each sample point. One sample
bottle will be used to collect slurry for a weight percent solids
determination. The dry solids obtained will be used for further
solids analyses. A second bottle M liters) will collect slurry
for the settling test. The remaining three bottles will be
used for filtered liquid phase analyses. Sulfite analyses will
require a 125 ml bottle containing (1) a known volume of a standard
iodine solution and (2) a sodium acetate buffer solution. Another
filtrate sample MOO ml) will be collected in a sample bottle
containing an EDTA-ammonium hydroxide buffer solution whenever
liquid carbonate analyses are desired. The third filtrate sample
MOO ml) will be caught in a sample bottle containing ^50 mis
of a dilute hydrogen perioxide solution. This sample will be
used for the remaining liquid phase analyses.
Naturally, not all of the five sample bottles dis-
cussed above need to be filled for each sampling port. Only
those sample which are required to obtain the data listed xn
Table 5-1 will be taken during a given test run.
E-41
-------
TABLE 7-1. SCRUBBER SYSTEM CHEMICAL ANALYSES REQUIRED
Gas Liquid Solid
Sulfur Dioxide Calcium Calcium
Carbon Dioxide Magnesium Magnesium
Oxygen Sodium Carbonate
Water Vapor Chloride Sulfite
Carbonate Total Sulfur
Sulfite % Solids
Total Sulfur Particle Size Distri-
bution
Temperature
pH Settling Tests
E-42
-------
Using the analytical data specifications shown in
Table 5-1 and the sample bottle requirements discussed above,
Figure 7-1 was prepared to illustrate which sample bottles are
required at each sample location. The requirements shown in
Figure 7-1 are representative of full characterization sets.
Sampling requirements for system line-out are obviously less
severe than those indicated.
Generation of usable chemical analysis data requires
(1) the use of proper sampling procedures, (2) the employment
of accurate analytical methods, and (3) the evaluation and
presentation of the resulting data. Each of these phases is
detailed in subsections 7.1.1, 7.1.2, and 7.1.3 respectively.
7.1.1 Sample Handling Procedure
Considering the large volume of samples to be handled
and analyzed after each test run, a variety of problems may arise
if proper sample handling procedures are not followed. As many
as thirty separate sample bottles may be needed for one charac-
terization set alone. In this section, Radian's proposed approach
to sample preparation, labeling, actual sample technique, and
sampling logging is outlined.
7.1.1.1 Sample Bottle Preparation
Bottle preparation will depend on the type of sampling
required (line-out, or characterization). For line-out samples,
fewer bottles need preparing. The five different types of sample
bottles will be processed according to the steps outlined in
Table 7-2. In general, bottle "prep" will consist of attaching
a label, adding the necessary reagents, and/or deionized water,
weighing the bottle and recording necessary information. An
example of the proposed label format is shown in Figure 7-2.
E-43
-------
SG
0
FG
i
MW \i
Jv.
\s
fr
i i ' > i
LA Ch
PJ
1
r i
O
o
a
O
i
SCB
(DcLO
\
O
o
a
0
-I
1
U 1
J t
2 X
666
o o o
§ o o
CLU
o
n
o
KEY:
O Slurry (250 mis); He 7, Solids, Particle Size Distribution
O Filtrate (100 mis); Ca, Mg, Na, Cl, T.S.
D Filtrate (125 mis); SOT
O Filtrate (100 mis); C0°
Slurry (2 liters); Settling Test
Figure 7-1. Liquid and Solid Phase Chemical Sample Locations
Characterization Samples.
E-44
-------
TABLE 7-2. SAMPLE HANDLING FLOW SHEET
Ui
Sample
Description
Prepare Sample Bottles
t Rumpling h'-og rollecfoH Rampl »« , Sample Check
Weight X -Q- (1) Attach proper (1) Collect 250 ml (1) Log In master
Solids. label
Slurry
slurry log book
P.S.D. (2) Tare flask (2) Record pH, temperature
Settling -A- (1) Attach proper (1) Collect two liters (1) Log In master
Test label
a lurry log book
Liquid -O- (1) Attach proper (1) Collect 1400 ml (1) Log In master
f- Species label
Filtrate
filtrate log book
(2) Tare bottle (2) Record time
(3) Add Dilute HjOz
(4) Reuelgh bottle
Liquid -Q- O.) Attach proper (1) Collect filtrate (1) Log In master
Sulflte label
until color change log book
(2) Add buffer noted (do not pass
(3) Add 1 2 solution end point).
(4) Weight bottle with
solution
Liquid -<>- (1) Attach proper (1) Collect 100 ml (1) Log In master
Carbonate label
filtrate \ log book
(2) Tare bottle 1
Check to see
that all re-
quired samples
have been
mil r»f f f»H
(3) Add buffer
(4) Rewelgh
bottle
-------
I.D. # x
Sample Type x_
Dilution Factor_
Time /
pH /_
Temperature /
Date x
Prepared by: x
x
Full Weight
Added Weight
Tare Weight
x
Denotes information to be recorded during bottle prep
Denotes information to be recorded during sampling
Denotes information to be recorded after sampling
Figure 7-2. Proposed Sample Label Format,
S-46
-------
The designated symbols for the various types of
sample bottles used in Table 7-2 are related to the required
sample schedule shown in Figure 7-1. The total number of sample
bottles prepared will be sufficient to fulfill the sampling re-
quirements. A suitable number of spares should also be prepared.
7.1.1.2 Sampling Procedure
After the sample bottles have been prepared, the
required samples must be gathered. A schematic of the sample
collection apparatus is presented in Figure 7-3.
Once the apparatus has been set up, the sample port
will be purged. The slurry sample and pH and temperature will
then be taken. Purging of the filter will then be done, allowing
^50 mis of filtrate to pass through. The liquid species, sulfite,
and carbonate samples will then be taken. Finally, two liters
of slurry will be collected for the settling test if necessary.
7.1.1.3 Sample Logging
Upon completion of the sample gathering, all samples
will be taken to the laboratory for logging into the master log
book. To keep a logical sequence of numbers, the following
identification scheme is proposed. The I.D. number will contain
the sample location point, month and date. As an example, the
abbreviation for the scrubber feed is SCF. A sample taken on
April 27th would then be identified by, SCF0427. If a second
scrubber feed sample were taken, an additional letter could be
added, SCF0427A. This method will simplify both labeling and
log in procedures. A suggested format for the master log book
is shown in Table 7-3. Other information deemed useful by
on-site personnel may be incorporated in the master log book.
E-47
-------
Filtrate Samples
i
P-
oo
Sample Port
O-
Millipore
Filter
O *
~M
Sampling Pump
1
Purge Port
»
i , /:
\ \
Slurry Samples
wt % Solids, PSD
Settling Test
O Liquid Species
P Sulfite
Carbonate
Figure 7-3. Sample Collection Schematic Diagram.
-------
TABLE 7-3. PROPOSED MASTER LOG BOOK FORMAT
ID'?
SCF0427
SCB0427
CL00427
CLV0427
LA0427
HW0427
Description
FIL,
FIL
FIL
FIL,
FIL.
FIL
SL
SL
SL
Date
4/27/78
4/27/78
4/27/73
4/27/73
4/27/78
4/27/78
Time
9:
9:
9:
9:
9:
9:
00
05
10
15
20
20
6
4
6
5
10
7
PH
.0
.5
.0
.8
.0
.0
Liquid Analyses (mmoles/JO Solid Arialyses (mmoles/KL Gas A"3.1^5-!?. .
T°C Dll. F. Ca+2 Mg+2 Na+ Cl'1 COs'2 S03~2 T.S. Ca+2 Mg+2 C03~2 SOn'2 T.S. ^ (°2 z
50
52
48
48
25
25
PIL - Filtrate
SL - Solids
Oil. F. - Dilution Factor
-------
7.1.2 Analytical Procedures
Once the samples have been logged in, sample analyses
will begin. This subsection deals with the recommended analysis
procedures and the order of sample analysis. An introduction
to proposed methods of checking data consistency is also furnished.
7.1.2.1 Gas Analyses
Gas phase analyses will use the following procedures.
Sulfur dioxide determination will be made using the DuPont analyzer.
Weekly calibration should be done by the Reich method. Oxygen and
carbon dioxide will employ an Orsat apparatus and water vapor can
be determined by either condensation or wet bulb/dry bulb procedure.
7.1.2.2 Liquid Analysis
O- Solids Content (Wt % Solids) Particle Size Distri-
bution, Solids Analyses)....
The weight percent solids content of the circulating
slurry will be monitored hourly by tracking the slurry density
(weighing a known volume of slurry). Daily slurry samples will
be filtered and the solids dried at 60°C. The dry solids will
be further used for solid phase analyses. Using the weights of
the bottle, slurry sample, and dried solids, the weight percent
solids content of the slurry will be calculated to confirm the
accuracy of the slurry density method.
O- Liquid Species. . . .
Calcium, magnesium, and sodium will be determined by
atomic absorption analyses. Chloride and total sulfur will be
analyzed by a Dionex ion chromatograph.
E-50
-------
- Liquid Carbonate....
A nondispersive infrared technique will be employed
for liquid phase carbonate determination. The samples are acidi-
fied and the carbonate is determined in the gas phase.
A. - Slurry Text....
Qualitative observations of sludge behaviour can be
quickly determined by settling tests. By using a constant 3 per-
cent slurry for all tests, comparison between test conditions
can be made. This test should also be done at the same tempera-
ture each time. The dilutant should be filtered slurry liquor.
7.1.2.3 Solids Analyses
Chemical analyses of the solids will use the same meth-
ods as liquid analyses. The sample will first be dissolved in
peroxide. To obtain a specific sulfate analysis, a sample will
be purged with carbon dioxide in a hydrochloric acid mixture,
and then analyzed on the Dionex. Solid carbonate will be analyzed
by nondispersive I.R. techniques.
Particle size determinations will be done by either
Coulter counter analysis, sedimentation methods, or some other
technique which gives accurate results.
Also scanning electron micrographs (SEM) should be
taken for each test condition. At magnifications of 500X, 1000X,
and 3000X, these provide a method for quick qualitative compari-
son of crystal sizes and shapes.
E-51
-------
7.1.2.4 Analytical Consistency Checks
As a routine procedure, the data for each sample loca-
tion will be checked for analytical consistency. Liquid phase
results will be checked by performing equilibrium calculations.
The Radian aqueous ionic equilibrium program is capable of
generating relative saturations and a percent residual electro-
negativity. Past Radian experience has indicated that data which
show errors of less than 570 are characteristic of a consistent
set of chemical analyses. Certainly a residual electronegativity
in excess of 20% is unreasonable. Repeat analyses will be per-
formed on any sample when this is felt to be justified. These
calculations and their implications to the test program will be
discussed in more detail in Section 7.3.
Periodic repetition of different analyses will be
performed as a general rule throughout the test program.
This duplication of analyses will document the reproducibility
of the analytical results.
7.1.3 Data Handling and Presentation
Analytical results will be reported in formats similar
to those shown in Table 7-4 (Liquid Anaytical Results) and 7-5
(Solid Phase Analytical Results). These results will be presented
in this manner so that engineering evaluations and calculations
can be easily performed.
The results sheets, in combination with the sample
log book entries, will allow on-site personnel to determine
which samples need further processing and which analyses are
complete.
E-52
-------
TABLE 7-4. RESULTS OF LIQUID PHASE ANALYSES
Scrubber System
Total Concentration (nmol/Ilter)
Temp. Charge
Sample Designation (C°) j>H Ca Mg Na Sulfite Sulfate Total S Carbonate Chloride CaSChRS CaSO..RS Imbalance
(-0
Prepared by:_
-------
TABLE 7-5. RESULTS OF SOLID PHASE ANALYSES
Scrubber System
Date_
Test //
Total Concentration (mmol/gram)
Sample Designation % Solids in Slurry Ca Mg Carbonate Specific Sulfite Specific Sulfate Total Sulfur
Ui
O
Prepared by:
-------
7.2 Process Measurements
Enough process measurements will be taken to fulfill
the requirements discussed in Section 6.0 and listed in Table
6-1. Process measurement data for each sample set will be docu-
mented on forms similar to those shown in Table 7-6. While the
pH and temperature of all sampled streams are considered process
measurements, they will not be listed on this form. Temperature
and pH data will be gathered at the time of sampling, and con-
venience dictates that they be recorded on the appropriate diluted
filtrate sample bottle.
The process data gathered at the time of sampling will
be checked to insure that the data are sufficient (1) to docu-
ment system performance and (2) to enable important process
rates to be quantified. The process measurement documentation
table (Table 7-6) should facilitate this procedure.
7.3 Process Calculations
In this section the procedures which will be used to
interpret the analytical and process performance data gathered
by the techniques just discussed are reviewed. Two general
types of activities are covered here. The first level of analysis
which is required will be primarily concerned with a confirmation
of the consistency of the analytical results. This activity, and
a proposed method is discussed in Section 7.3.1.
The second level of data analysis is concerned with
the interpretation of test results. This activity will be the
responsibility of the on-site personnel. It will include all
computational activities required (1) to monitor the day to
day test conditions and (2) to interpret overall test results.
This aspect is discussed in Section 7.3.2.
£-55
-------
TABLE 7-6. PROCESS MEASUREMENT DOCUMENTATION
Scrubber System
Test #
Stream
Flue Gas (FG)
Scrubber Feed (SCF)
Scrubber Bottoms (SCB)
Clarifier Feed (CLF)
Clarifier Overflow (CLO)
Clarifier Underflow (CLU)
Limestone Additive (LA)
Makeup Water (MW)
Date
FLOW RATE DATA
Flow Rate
Units
NroVsec
LPM
LPM
LPM
LPM
KGPM
LPM
LPM
Stream
Flue Gas (FG)
Stack Gas (SG)
PRESSURE DATA
Pressure
Units
Centimeters HaO vacuum
Centimeters H£0 vacuum
Vessel
Scrubber Bottoms
Hold Tank
Additive Tank
LEVEL MEASUREMENT DATA
Level (Centimeters from
Reference)
Inlet SO2 Concentration =
Outlet S02 Concentration =_
Hold Tank pH =
OTHER MEASUREMENTS
ppm
_ppm
Slurry Density =
Underflow Density
Wt % Solid
Wt % Solid
E-56
-------
7.3.1. Analytical Consistency Confirmati
on
Vapor-liquid and liquid-solid mass transfer reactions
in an S02 scrubbing system are generally very slow compared to
the rates at which ionic reactions in the liquid phase take
place. It is therefore reasonable to treat the liquid phase in
an S02 scrubber as an equilibrium mixture.
Analysis of liquid phase equilibrium data involves
many interacting equations which can best be solved by computer.
Radian has developed an aqueous ionic equilibrium program which
is capable of predicting liquid phase activities of the various
ionic speci.es found in a typical scrubber liquor. Inputs re-
quired by the program include total liquid phase concentrations
of sodium, calcium, magnesium, sulfite, sulfate, carbonate, and
chloride, and also the solution pH and temperature. Program
outputs include (1) liquid phase activities and activity coef-
ficients , (2) equilibrium partial pressures of S02 and C02 above
the liquid phase, (3) relative saturations of potential preci-
pitating species, and (4) a calculated value for residual electro-
neutrality, a measure of the solution charge imbalance which is
indicative of the consistency of the analytical input data. A
typical equilibrium program output sheet is shown in Table 7-7.
The interpretation and utilization of these output results are
discussed below.
After all of the required liquid phase analyses for
a given sample are completed, the solution pH and temperature
(determined at the time that the samples are taken) and its
composition will be input to the Radian equilibrium program.
The program output sheet will then be examined to determine
whether the residual electroneutrality figure is within toler-
able limits. They will be done by dividing the charge imbalance
E-57
-------
TABLE 7-7. TYPICAL EQUILIBRIUM PROGRAM PRINTOUT
17 AUC 75 21123118,311
H20 «
CAO »
NSO
NA20 «
INPUT SPECIES
4,10114*94
j ((ifi339*Ut
4.78662*00
3,42131*88
TEMPERATURE 32.129 DEC, C,
(MOLESl
MCL ',12761*00
C02 ,2»6«6*(!0
N203 ,0n?^0
N203 .J3604-01
S02 ,29623*01
S03 .80660*01
SUPERSATURATION ALLOWED
AQUEOUS SOLUTION EQUILIBRIA
COMPONENT MOLALITY
1,946-04
H«
H20
M2C03
HC03-
HN03
H2S03
HS03-
HSQ4.
CA**
CAOH +
CAHC03*
CAC03
CAN03*
CAS03
CASQ4
MC+*
HCOH*
HCC03
MGSQ3
MSS04
MA»
NAOH
NAHC03
NAC03-
NAMQ3
NASQ4-
OH.
cu-
C03--
N03-
303..
804
COMPONENT
CA(OH)2(S)
CAC03C3)
CAS03CS]
CAS04(S}
MGC03C)
MG3Q3C3)
1,733-83
7,283-BS
9,589-39
2,792-84
1,717-82
i.BSS-e4
1,932-82
1,007.10
i.tsa-ee
3,633-11
3.474-03
8.313-83
8,488-83
3'.994-83
4,«83-t0
1,348-27
1,434-11
9,474-aa
2,478-83
9.028.03
7.249-13
3,878-08
2.139-12
2.272-08
2,314.04
4,987-10
1,1*8-32
6,753-12
1,142-03
9.583-U6
1.307.02
0,0110
a,ana
0,000
0,089
a,ana
PC02 9,91*88<9.e2 ATM.
PS02 « 3.64398*04 ATM.
PHNQ3 1,88010-13 ATM,
ACTIVITT ACTIVITY COEFFICIENT
1,811.84
1,761-03
3. S23-BS
9.743-B9
2,837-04
1,323-ez
1,463.04
7.179-B3
7.803-11
8,914-07
3.710.11
2,692-03
8.448-93
8,626-03
1,737-93
3,S3lTl8
1.D43.07
1,457-11
6,579-CS
2.518-03
7.118.03
7,367-13
3,939*08
1.637*12
2,339*06
1,793*04
3,830*10
8,412-03
2,397-12
8,136*04
3. 401, US
4,108-03
ACTIVITY PRODUCT
1.064-21
I, 721» 14
2,440.08
8.941--3
2,604-22
4,193*13
5,930.09
8,2B2.flt
9,986.81
1,016*30
7,718-81
1,016*88
1 ,1116+30
7,718.*!
7,730-«»l
3,7is.ai
7,750-31
7,73fl«01
1, -16*00
7,758.01
1.019*8EI
1.016*00
4,398.01
7,750-01
7,750.01
1.B16+00
1,JI1S«98
1,816*00
7,876-dl
1,016*00
1,016*00
7,750.01
1,~16*08
7,730.01
7,750-01
7,648.91
3,349*01
7,141.01
3,349-01
3,144.01
RELATIVE SATURATION
3.364.16
1,029-03
2,9B4-fli
1,338*08
2.827-11
3,607.18
1.879.94
PH 3.7928
NOLECULAR HATER 7,38790*02 KG3,
IONIC 3TRENGTM 9.27834-02 RES. E.N.
3.169.07
E-58
-------
by the total ionic strength in the analyzed sample. From pre-
vious Radian experience, a 57, or less error indicates reasonable
analytical consistency. If the error ig judged tQ be ^ ^^
some of the analyses may be repeated.
A second analytical consistency check may be used
for the scrubber effluent streams. The equilibrium S02 pres-
sure above the exiting slurry effluent streams will be compared
to the measured S02 partial pressure in the stack gas. If the
measured stack gas S02 concentration does not exceed the cal-
culated SO2 equilibrium partial pressure above the upper bed
downcomer, a gas phase or liquid phase analytical error is
indicated, and the analytical data will be re-examined.
The equilibrium printout also specifies relative satu-
rations (r) for the various solids which may form in a scrubbing
slurry. The solids of major interest are calcium sulfite and
calcium sulfate. The relative saturations calculated from the
most recently gathered data will provide the basis for quick
estimations of current relative saturations during on-site test-
ing. (A method of quick relative saturation estimation is dis-
cussed in detail in Section 7.3.2.) System relative saturation
levels can be used as a measure of the scaling potential of a
given scrubbing liquor. Since previously untried operating con-
ditions will be attempted during the test program, reasonably
accurate relative saturation estimation procedures are vital to
the conduct of the tests. Should critical supersaturation levels
be approached in the scrubbing loop system, operating parameters
must be altered as necessary. Calculated relative saturations
will be compared to both estimated relative saturations and to
information obtained from periodic visual scrubber inspections.
E-59
-------
The liquid phase activities computed by the equilibri-
um program will be useful in the detailed evaluations to be per-
formed at the conclusion of the on-site testing. For example,
it may be possible to correlate sulfate ion activity with the
sulfate to sulfite ratio of the coprecipitated solids. Also,
the activities of chloride and magnesium may provide insight into
the effects of these ions on the coprecipitation phenomenon.
7.3.2 On-Site Calculations
The on-site engineering staff will be responsible for
all calculations required to interpret the test results and to
monitor the daily performance of the system. At a minimum,
this function will include process rate determinations, calcium
sulfite and sulfate relative saturation estimates, and process
variable tracking. Any additional calculations required for re-
sults interpretation or for determination of test program direc-
tion will also be performed on-site.
7.3.2.1 Process Rate Calculations
A detailed discussion of proposed methods and assumptions
involved in calculating the important process rates is presented
in Section 3.0. Basicially, the significant chemical reactions
include the vapor-liquid and solid liquid reactions in the
scrubber and the solid-liquid reactions in the holding tank
system. By employing the assumptions and calculation procedures
presented in Section 3.0, typical worksheets have been prepared
for determination of the hold tank and scrubber chemical reaction
rates as well as the particle distribution and the crystal growth
rate. These example worksheets are shown in Tables 7-8, 7-9,
and 7-10. The calculations will be made as soon as the necessary
data become available.
E-60
-------
TABLE 7-8. SCRUBBER RATE CALCULATION WORK SHEET
Gas Streams
Inlet:
Flue Gas (FG)
Flow Rate (acfm) Temp. ('F) S02 Concentration (ppm)
(G) (I)
SO; Flow Rate (g-moles/min)
(I)
Outlet:
Stack Gas (SG)
Liquor Streams
Flow Rate (J./min)
(L)
Aqueous Species
Concentrations (mg/t)
CCa> (C
Species Flow Rates
(g-rooles/min)
r
Ca
rn
C02
Inlet:
Scrubber Feed (SCF)
Outlet:
Scrubber Bottoms (SB)
S02 Sorptioti Rate I S02(g) - I S02(g)
in out
Sulfite Oxidation Rate*
f S03(3) "I
|S03(s) + S02(s)J
Leaving System
x S02 Sorption Rate
CaSOs Dissolution Rate = I S02 (aq) - £ S02(aq) + Sulfite Oxidation Race* - SOj Sorption Rate
out in
CaSOi, Dissolution Rate = I S03(aq) - I S03(aq) - Sulfite Oxidation Rate*
out in
Dissolution Rate** » i Ca(aq) - I Ca(aq) - CaSOs Dissolution - CaSOw Dissolution
out in
(1) S02 Gas Flow Rate =
(g-moles/nin)
(2) Aqueous Ca Flow Rate
(g-moles/min)
(3) Aqueous S02 Flow Rate
(g-moles/min)
(4) Aqueous SOj Flow Rate
(g-moles/min)
(5) Aqueous C02 Flow Rate
(g-moles/min)
520 1
) + 460)
454 st
379 scf
3 Ca
xlO" mg Qa
g-moles SO; U
-AxlO" mg SOz/J
/_jg;mo_les_cp_2__ U
U.4xlO" mg C02 IJ
* During early phases of the test program
all system oxidation will be assumed Co
occur in Che scrubber. If the accual
scrubber oxidation can be quantified in
later tests, this difference will be
accounted for.
** Calcium carbonate dissolution race will
be calculated assuming all of the Ca(OH)2
dissolves in the hold cank.
E-61
-------
TABLE 7-9. HOLD TANK RATE CALCULATION WORK SHEET
Liquor Screams
Flow Race (i/min)
(L) _
Aqueous Species
Concentrations (mg/g.)
Species Flow Races
(g-moles/min)
) ( 1 1
2 Ca(1}
fal
SOi(O C02
Inlet:
Scrubber Bottoms (SB)
Outlet:
Sciubber Feed CSC?)
CaS03 Precipitation Rate*
I S02(aq) - E S02(aq)
in out
CaSOn Precipitation Race* - I S03(aq) - Z SOs(aq)
in out
CaC03 Precipitation Rate** - E COi(aq) - Z C02(aq)
in out
Ca(OH)2 Dissolution " Z Ca - E + CaS03 Precipitation Rate + CaSO, Precipitation Rate
out in
+ CaC03 Precipitation Rate
NOTE: Several small streams (clarifier and filter effluents for example) may be neglected when performing hold tank
balances because the liquid species flow rates for these are insignificant compared to the stream flows listed
above.
(1) Aqueous Ca Flow Rate
(g-moles/min)
(2) Aqueous SOa Flow Race
(g-moles/min)
(3) Aqueous S03 Flow Rate
(g-moles/min)
(4) Aqueous C02 Flow Rate
(g-moles/min)
( Stoles C0; \l
U?4xlO" mg C02 IJ
* These balances are made assuming negligible
oxidation in Che hold tank. The balances
will be modified should the hold tank oxida-
Cion be quantified.
** The carbonate precipitation rate is made
assuming no desorption of COj from the hold
tank liquor.
E-62
-------
TABLE 7-10. PARTICLE CALCULATION SHEET
N = CU x N s n
-1
small T A log n
A L C2.303)
-1
(<4u)
600 min (3.3-9.4)
4xlO~s(2.303)
2.5x10" meter/min
R.
-1
large
= 6.0x10 8 meter/min (>4y)
600(1-1.3)
36xl(T° (2.303)
Note: This is a hypothetical distribution intended for
explanation purposes only.
24 6 8 io 1* 18 22 26 30 34 38
ci-63
-------
7.3.2.2 Relative Saturation Estimates
Relative saturation levels are important parameters
influencing crystal growth. For most tests, a constant level
will be desired. Therefore, a quick method of estimation or
daily computer predictions will be required. The following
is a method for estimation using liquid species analyses. A
quick turnaround on the chemical analyses for this determination
(calcium, total sulfur, sulfite, temperature, and ionic strength)
will be required. An approximate technique for determining
system relative saturations should therefore be developed prior
to the start of the test program by making a series of equili-
brium runs which cover the regions of expected system operation.
On-site estimates for supersaturation will be based
on a simplified treatment of perturbations about a given solu-
tion to the full set of chemical equilibrium equations. Peri-
odically, complete sets of process data could be input to the
equilibrium computer routine at Radian or a similar program.
These data will include the temperature, pH, calcium, sulfite,
sulfate, chloride, magnesium, sodium, and carbonate
concentrations. Since the magnesium, sodium, and chloride,
concentrations should normally change very slowly with time,
reasonably accurate estimates of supersaturation can be made
based upon measured values of pH, calcium, sulfite, and sulfate.
These quantities can all be conveniently obtained within a few
hours of the time that a sample is taken at a given point.
Estimating techniques for calcium sulfate and sulfite
supersaturations will differ somewhat. The solubility of
CaSOk-2E20 depends primarily on the temperature and ionic
!-64
-------
strength of the liquor as well as the amount of magnesium pre-
sent. Its solubility is not very sensitive to pH changes which
can occur in a limestone scrubbing unit. In most cases, it
should be possible to estimate the sulfate supersaturation by
simply using the ratio of the measured and "base case" concen-
tration products for total calcium (Ca) and total sulfate (S03)
That is,
mr*mcr\ (measured) /-r i
r(estimated) * r(base case) x Ga S0ji . (7-1
m_ mcn (base case)
CaSO,,(s) CaSO^(s) La bUjL
Base case calculations should be run at several temperatures
to provide a basis for interpolation. Temperatures in the
system should not vary substantially with time, however.
Estimates of calcium sulfite supersaturations may
prove more difficult. These will be quite sensitive to pH in
addition to temperature, ionic strength, and magnesium content.
The fraction of total sulfite that is in the form of sulfite
ion may change by several orders of magnitude over the pH
range 5-7.
A semi-empirical form for estimating calcium sulfite
supersaturations may be developed by considering the equilibria
involving the sulfite ion. The most important of these are:
K 3
aS07 (7-2)
E-65
-------
aS03 (7-3)
-
HS03
K
aCaS03(&)
aS03 (7-4)
aS07 (7-5)
aMgS03(£)
An additional relationship is the total sulfite (S02) material
balance for the liquid phase given by Equation 7-6.
mS02 = mH2S03(£) + ^SOl + mCaS03a) + "MgSOaU) + mS07 (7-6)
A simultaneous solution to Equations 7-2 through 7-5
yields an approximate expression for the sulfite ion activity
in terms of the measured quantities of total S02 and pH. Some
simplifications are needed to arrive at this expression, how-
ever. First, the activity coefficients of all species in
Equations 7-2 through 7-5 will be held constant over the range
of solution composition covered by the approximation. These
equations can then be written in terms of concentrations:
aH+ mS07 (7-7)
mH2S03(£)
(7-8)
E-66
-------
mCaS03(£)
mcr =
§2l (7-9)
(7-10)
Two additional variables may be eliminated by
treating the calcium and magnesium ion concentrations as
constants. This should be a reasonable approximation since
percentage variations in calcium and magnesium concentrations
in the system are known to be quite small compared to changes
in total S02 concentration. Thus,
(7-1D
m.
CaS03(&)
mcn-
TTll _ S03
JS-4 -
Equations 7-6, 7-7, 7-8, 7-11, and 7-12 can now be combined to
yield the final expression.
50
Equation 7-13 may be used to compare the sulfite
concentration (or activity if the activity coefficient is
E-67
-------
assumed constant) at one level of pH and total SOa to that at
another. The constants must be evaluated from the base case
computer solutions. The following terms are included:
T
H2S03 (7-14)
3 YHS03 (7-15)
YS03
_ KCaS03q) YCaS03(£) (7-16)
3
YMgS03q) (7-17)
w
where K) KHSQ- , KcaS03a), andK are functions
of temperature.
Finally the estimated calcium sulfite supersaturation
may be taken as the base case supersaturation times the ratio
of the measured and base case concentration products:
m_ m_n= (measured)
r (estimated) = r(base case)
/^ - N
CaS03(s) CaS03(s) mCamSO^base case)
(7-18)
In Equation 7-18, the total calcium concentration,
is measured directly and the sulfite ion concentration,
E-68
-------
nigQ- is obtained using Equation 7-13 along with measured
values for mSQ and pH. The base case values for input to
these equations will be periodically updated. It should be
noted here that this estimation will not be adequate during
certain tests when the magnesium and chloride levels are changed,
Rapid analytical turnaround with subsequent use of the Radian
equilibrium program will probably be required to track relative
saturation during this phase.
7.3.2.3 Process Variable Monitoring
Various system parameters xvill be monitored to assess
scrubbing system operation on a day-to-day basis. At a minimum,
pH's, flows, and circulating solids density will be tracked.
Gas flows and SOa concentrations should be monitored hourly
to insure steady-state operation. By monitoring these and
possibly other variables, their impact upon test results can be
properly interpreted.
7.4 Monthly Progress Reports
Once a month a detailed report should be submitted
to describing the status of the project and to report the
findings of the previous month's tests. A monthly operations
summary will involve the preparation of figures similar to those
shown in Figure 7-4, 7-5, and 7-6. Included in this graphical
summary will be (1) test performed and date, (2) daily average
S02 concentrations and ranges, (3) average S02 removal effi-
ciency, (4) scrubber feed and scrubber bottoms pH, (5) slurry
solids'concentration and (6) dissolved solids concentration.
In addition, Table 7-11 will be presented in the
monthly progress report. This sheet specifies process condi-
E-69
-------
9 10 11 12 13 U IS 16 17 18 19 20 21 22 23 24 2S 26 27 28 29 30 3:
Test #
3000
Inlet SO 2
Concentration
Cppm) .
2500
2000
c
^
Jj
0 100
a
0
0i 100
9 90
a
CO *-> Qrt
U 3* OU |
* 70
T4
0
-T-
I
, i
1
i
^
1
(
I
t
r-5-
1 !
i i
i
-1-
I
-
| |
F" 1
* <
-
i
-5-
'
'
i_
i
<
i
i
»
,
< <
r~j
r,
4
*-
<
.,
<
-i
i
1 i
*T
_
i-
~~"i
i ,
h-
t <
L J
t
i
t
i
i
j
~4
2 3 * 5 « 7 3 > IQ U 12 13 14 15 16 17 18 13 20 21 22 23 24 25 26 27 23 23 30 31
Month
19
Figure 7-4. RTF Monthly Operating Log..
E-70
-------
u
V
.3
.3
2
a
ui
9.0
8.0(
7.0
6.0
5.0
o
CO
11.0
10.0
9.0
8.0
14 l 16 17 13 19 20 21 22 23 21 25 ii 27 23 29 30 31
Figure 7-5. RTP Scrubbing Liquor Parameters.
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3 9 10 11 12 13 U 1! IS 17 13 19 20 21 22 23 21 25 26 27 21 29 30 31
A-SULFITE
* - SULFATE
-CALCIUM
-MAGNESIUM
3 29 30 31
Figure 7-6. RTP Dissolved Solids Concentrations.
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TABLE 7-11. OPERATING DATA SUMMARY
Prepared by
Dace:
Time:
Test No.:
Sample Set No.:
System Operating Time (hrs):
GAS PHASE MEASUREMENTS
Gas Flow Sate (103 acfm)
iP Across Scrubber (inches H20)
Inlet S02 Concentration (ppra):
DuPont Analyzer
Manual Analyzer
Outlet SOj Concentration (ppm):
DuPont Analyzer
Manual Analyzer
S02 Removal Efficiency (%)
LIQUID/SOLID PHASE MEASUREMENTS
Flow Rates
(gpm):
Scrubber Feed
Scrubber Bottoms
Clarifier Feed
Combined Clarifier and Filter Overflows
Filter Bottoms
Limestone Additive
Make-Up Water
Level Measurements:
Scrubber Bottoms
Additive Tank
Reaction Tank
Circulating Slurry Solids Content (% weight)
Filter Bottoms Solids Content (Z weight)
Percent Oxidation
Hold Tank Effluent (pH)
STOICH10METRY [Moles CaC03 Added/Moles SOj Sorbed]
L/G (gal/scf)
COMMENTS:
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tions at the time of each characterization test. Comments on
operating anomalies or difficulties will be noted as they occur,
The more significant operating problems will be discussed in
detail in the progress report.
Completed chemical analysis results will also be
presented in monthly progress letters. The resulting data will
be compiled on forms similar to Table 7-4 and 7-5. These re-
sults should include the computed electroneutrality imbalance
generated by an equilibrium program.
A calculations summary will be furnished for each
characterization set. A proposed format is shown in Table 7-12.
In addition, the relative saturations data will also be docu-
mented in this table. Figure 7-7 will be used to plot the particle
size distribution analysis for the various tests. Transparent
overlays could be made to provide easy comparison of different
test results.
Brief discussions of each test will be given in these
reports among with an interpretation of the results. Should the
results of one test affect the scope of the program or suggest
possible test program alterations, these options will be docu-
mented.
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TABLE 7-12. CHEMICAL REACTION CALCULATION SUMMARY
Scrubber System
Test No.
Date_
Prepared by
Reaction Rate (g-moles/min);
SO2 Sorption
Oxidation
Calcium Sulfite Precipitation
Calcium Sulfate Precipitation
Calcium Carbonate Precipitation
Calcium Hydroxide Dissolution
Effluent Relative Saturations*:
CaSOa
CaSOif
Scrubber
Hold Tank
Particle Size Distribution:
Nucleation Rate (///sec)
Growth Rate (Large)(M/sec)
Growth Rate (Small)(M/sec)
* Based on equilibrium program output data.
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FIGURE 7-7
PARTICLE SIZE DISTRIBUTION
109--
DATE .
TEST*
10°--
107--
5
Hi
p ica4-
03
at
Q
cc
IU
103--
10*--
10 --
3 10 12 14 16 18 20
PARTICLE SIZE (METER X 106>
22 24 26
02-2346-1
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8.0 POSSIBLE PROBLEM AREAS
This section furnishes a discussion of several areas
in which difficulties may be encountered during the execution
of the test program. Three general areas where problems may be
discovered are addressed: 1) system operation, 2) process and
analytical measurements, and 3) engineering analysis.
8.1 System Operation
Several aspects of system operation which may have an
impact upon test results are discussed in this section.
8.1.1 Effect of Unsteady-State Operation
It would be ideal if each of the proposed system tests
could be conducted under specified "steady-state" conditions.
Realistically, it is reasonable to expect that fluctuations in
process conditions will occur.
One possible fluctuation is in the S02 inlet concentra-
tion. Small changes will not seriously affect scrubber conditions,
however, if a large change is noted, the rate should be readjusted
and two hours allowed for the scrubber chemistry to stabilize.
The reason for allowing a stabilization period, is that
for a change in the SOa concentration will change the system
pH. This will affect the limestone additive and alter the
chemical composition of the scrubbing liquor. Any sample taken
during this period would not be representative of the overall test
conditions.
If significant changes are observed in the SO2 concen-
tration or slurry tank levels during sampling, a repeat sample
should be taken to insure accurate results are obtained.
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RADIAN
CORPORATION
8.1.2 Recommended Operating Conditions
Several system configurations and operating conditions
have been proposed in the test plan that are different from the
base case arrangement. Operation in these modes should not be
difficult, however, some potential sources of problems are dis-
cussed in general below.
8.1.2.1 Solids Concentration Changes
Several tests are planned at varied solids levels or
concentration. At the lower level, the clarifier will have to
settle particles faster in order to remove the same amount of
solids. No major problem is envisioned, due to the small size of
the pilot unit and the available extra capacity of the vacuum
filter.
The higher solids level should not provide any major
problems either. Over a longer term, erosion might increase,
but for a week long test, no difficulty is foreseen.
8.1.2.2 Hold Tank Modifications
Various modifications to the hold tank system have been
proposed. Different agitator materials and speeds are planned
along with moving the additive location. Increased residence
time is also planned. None of these changes should cause any
operational problems.
8.2 Measurement Problems
Readily apparent problems with the required measurements
for the test plan are discussed in this section.
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8.2.1 Analytical Problems
Standard chemical analyses of scrubber streams has
been done for quite some time. Accurate, reliable, and quick
methods of chemical analysis are fairly well standardized. At
the present time, the particle size distribution measurement is
the least developed. Reproducibility between microscopic,
scanning electron microscopy and Coulter counter analysis has
not been fully demonstrated. Please see Technical Note
#200-187-11-02 for a description of Radian's recommended method
for determination of the particle size distribution.
8.2.2 Process Measurements
No major problem is seen in the obtaining of process
measurements. The scrubbing facility has been operated for
several years, and as a research facility, accurate measurement
recording procedures were incorporated in its design.
8.2.3 Steady-State Determination
System steady-state determinations are a key to ob-
taining reliable test results in a minimum amount of time. Due
to the nature of the tests in this document, solid phase line-out
is essential for meaningful results. By assuming that the hold
tank is a continuous stirred tank reactor, the solid phase resi-
dence time can be modeled as a first order system. For a step
change in a process variable in a first order system, 95% of
the neweffeet is attained within three residence times. Based
on a ten-hour solids residence time, two days of continuous
operation should be sufficient to insure steady-state conditions.
Analytical tests required to insure steady-state conditions are
given in Section 5.2.
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8.3 Engineering Analysis
As part of the overall engineering analysis effort,
rates of important chemical reactions, crystal growth and
nucleation will be calculated. A discussion of the methods of
calculation is presented in Section 3.0. These rates will be
used in relating the particle size distribution to operating para-
meters. In any correlation effort, exact agreement between the
assumed function and experimental data is unexpected. Hopefully
with accurate process and analytical measurements, the derived
correlations will closely model the physical situation.
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RADIAN
CORPORATION
9.0 SUMMARY
The basic objectives of the test program are to:
develop quantitative relationships
between calcium sulfite particle size
distribution and process variables, and
using the computer model developed
by Radian, determine conditions for
producing an optimum sludge product.
To accomplish these objectives, tests will be conducted to
locate the source of nucleation in the
scrubbing system,
correlate growth and nucleation rates
with process parameters, and
determine if computer predicted test
conditions produce the optimum sludge.
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NOMENCLATURE
a - Chemical Activity
CF - Clarifier Feed (liters/sec)
cm - Centimeters
CLO - Clarifier
CLU - Clarifier Underflow (liters/sec)
FG - Flue Gas Rate (m3/hr)
G - Particle Generation Term other than growth and convection
( C l sec~ *)
g - gram
h - Experimental Exponent
i - Experimental Exponent
j - Experimental Exponent
ki,k2,k3- Undetermined exponents
KI, K2, K3, K4 - equilibrium constants
kg - Kilogram
k - Surface Reaction Rate Constant (m2/sec)
k - Shape Factor
^v r
L - Characteristic Particle Length (m)
£ - Liters
LA - Limestone Additive Rate (^/sec)
L - Mass Average Length (m)
L - Number Average Length (m)
m - Meters
m. - moles of specie i
ms ~ Calcium Sulfite Coprecipitate Solids Concentration (g/&)
MW - Molecular Weight (g/mole)
N - Number of Particles per Slurry Volume (A"1)
n - Number of Particles of Size L per Volume (A"1 m"1)
N - Number of Particles of Size L per Volume Leaving System
(A"1!!!" sec"1)
nQ - Nuclei Concentration (i"1)
n - Nucleation Rate (I'1 sec"1)
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-------
p - Experimental Exponent
Q - Volumetric Flow Rate (A/sec)
R - Linear Crystal Growth Rate (m/sec)
RQ - Crystal Growth Rate at Zero Size (m/sec)
r - Relative Saturation
SCB - Scrubber Bottoms Flow Rate (A/sec)
SCF - Scrubber Feed Flow Rate (A/sec)
SG - Stack Gas Flow Rate (m3/hr)
AS02- SOa Pickup (moles/sec)
T - Temperature (K°)
u. - Slurry Velocity in the ith direction (m/sec)
V - Slurry Volume (A)
X - Length Dimension (m)
Y - Length Dimension (m)
Z - Length Dimension (m)
« - activity coefficient
6 - Growth Constant (m'1)
p - Particle Density (g/cm )
Q
T - Mean Solids Residence Time (sec)
y - Micron (10~6m)
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REFERENCES
JO-R-214 Jones, Benjamin F. , Philip S. Lowell, and Frank B.
Meserole, Experimental and Theoretical Studies of
Solid Solution Formation in Lime and Limestone SQ2
Scrubbers, final report, EPA 600/2-76-273a EPA Con-
tract No. 68-02-1883, Radian Project No. 200-144,
Austin, Texas, Radian Corp., Oct. 1976.
KH-034 Khamskii, Evgenii V., Crystallization from solutions,
New York, Consultants Bureau, 1969.
LE-305 Levins, D.M., and J.R. Glastonbury, "Particle-liquid
hydrodynamics and mass transfer in a stirred vessel",
2 pts, Trans. Inst. Chem. Engrs. 50, 32 (1972),
pt.l; Trans. Inst. Chem. Engrs. 50, 132 (1972),
pt. 2.
LO-R-170 Lowell, Philip S., "Process Removing Sulfur Dioxide
from Gases", U.S. Patent 3,972,980 (Aug. 1976).
OT-023 Ottmers, D. M., Jr., et al., A Theoretical and Experi-
mental Study of the Lime/Limestone Wet Scrubbing Process
PB 243-399/AS, EPA 650/2-75-006. Contract No.
68-02-0023. Austin, Tx., Radian Corp., 197/-.
TI-006 Ting, H.H. and W.L. McCabe, "Supersaturation and
Crystal Formation in Seeded Solutions", I&EC 26,
1201-7 (1934).
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REPORT NO
EPA-6QO/7-78-072
TITLE AND SUBTITLE
for Relating
Operating Variables
6. PERFORMING ORGANIZATION CODE
. AUTHORIS) T
J .
.Phillips, J.C.Terry, K A Wilde G P
Behrens, P.S.Lowell, J.L.Skloss, and K.W.Luke '
8. PERFORMING ORGANIZATION REPORT NO.
9.
Radian Corporation
8500 Shoal Creek Boulevard
Austin, Texas 78766
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
April 1978
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
68-02-2608, Task 11
AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Task Final; Through 1/78
14. SPONSORING AGENCY CODE
EPA/600/13
15. SUPPLEMENTARY NOTES
DrOp 65 ,
16. ABSTRACT
The report gives results of research to investigate prospects for increa-
sing the size of calcium sulfite sludge particles in flue gas desulfurization systems.
The approach included four work packages: a literature survey and development of a
mathematical basis for predicting calcium sulfite sludge distribution; a computer
solution of the size distribution model to determine parameter sensitivity; a liter-
ature survey and screening of analytical methods for measuring settling rate, set-
tled density, and particle size distribution; and planning a test program to investigate
parameters not available from previous work to verify the size distribution model.
The crystal population balance concept was introduced into the mathematical basis
for predicting particle size distribution of calcium sulfite sludge. Relationships were
derived that required nucleation and crystal growth rate expressions which must be
obtained from experimental data. Available pilot and full-scale scrubber data were
used to increase the usefulness of the theoretical model. The relationship derived
was solved for a specific process configuration. An approximate solution was ob-
tained assuming that crystal size distribution does not change in the scrubber. A
computer routine was written to permit convenient parameter sensitivity studies
using the size distribution model.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATl Field/Group
Air Pollution
Flue Gases
Desulfurization
Gas Scrubbing
Calcium Sulfites
e
Slud
I
Properties
Mathematical
Models
Measurement
Crystal Growth
Densit
Air Pollution Control
Stationary Sources
Particulate
13B 14B
21B
07A,07D 12 A
13 H
07B 20B
3. DISTRIBUTION STATEMENT
Unlimited
Unclassified
369
20. SECURITY CLASS (This page/
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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