THE M. W. KELLOGG COMPANY
of Pullman Incorporated
MWKLG-RED-72-1271
REVIEW OF THE DRY LIMESTONE
INJECTION PROCESS
TASKW3 FINAL REPORT FOR PHASE 1
Submitted to
ENVIRONMENTAL PROTECTION AGENCY
AIR POLLUTION CONTROL OFFICE
DIVISION OF PROCESS CONTROL ENGINEERING
Contract No CPA 70-68
May 1,1972
ESEARCH * ENGINEERING DEVELOPMENT
-------
RESEARCH AND ENGINEERING DEVELOPMENT
REVIEW OF THE DRY LIMESTONE
INJECTION PROCESS
TASK #3 FINAL REPORT FOR PHASE I
Submitted to
ENVIRONMENTAL PROTECTION AGENCY
AIR POLLUTION CONTROL OFFICE
DIVISION OF PROCESS CONTROL ENGINEERING
Contract No. CPA 70-68
APPROVED:
fl4- ~ !:/;r
Project ~rec r
~(~/
Chemical Engineering Development
~JL~
Development Engineering Department
-------
~ 6 EO 20 ~A~ 3-68
THE M. W. KELLOGG COMPANY
A DIVISION OF PUllMAM INCORPORATED
~
Page 11o.
RED-72-1271
Report ~o.
Research & Engineering Deve\opment
Sta ff:
Per i od Covered:
l. O. Mo.
Distribution:
OAP
L. C.
A. B.
C. W.
A. L.
J. B.
A. N.
R. H.
J. J.
REVIEW OF THE DRY LIMESTONE
INJECTION PROCESS
TASK #3 FINAL REPORT FOR
EPA- OAP-DCS CONTRACT NO"
May 31, 1971
PHASE I
CPA 70-68
J.A. Bellott, G.M. Drissel, C.J. Roycep
L.J. Scotti, AoG. Sliger
September 1970 to May 1971
4092
Copy No"
Copy No.
Axelrod
Cassidy
Crady
Dowling
Dwyer
Holmberg
Multhaup
O'Donnell
L. E. Scholer
w. C. Schreiner
F.. H. Shipman
A. G. Sliger
M. J. Wall
T. H. Wasp
R.I.D. (4)
AUTHORS:
'.
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MWKLG-RED-72-1271
REVIEW OF THE DRY LIMESTONE
INJECTION PROCESS
TASK #3 FINAL REPORT FOR PHASE I
CONTRACT NO. CPA 70-68
Submitted to
ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF AIR PROGRAMS
DIVISION OF CONTROL SYSTEMS
by
THE M. W. KELLOGG COMPANY
RESEARCH & ENGINEERING DEVELOPMENT
PISCATAWAY, N.J.
May 31, 1971
Rev. December 14, 1971
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1-
II..
III.
IV.
REVIEW OF THE DRY LIMESTONE INJECTION PROCESS
PHASE I FINAL REPORT
TABLE OF CONTENTS
I.
INTRODUCTION
SUMMARY AND CONCLUSIONS
RECOMMENDATIONS
DISCUSSION OF RESULTS
A.
B.
Pilot Plant Sulfation Data
1.
Battelle Studies
a. Battelle Reactor Design and
Conditions of Operation
b. Battelle Data
2.
Babcock and Wilcox Studies
a. Data for Limestone Additives
b. Data with Dolomites
3.
Peabody Coal Studies
a. Description of Reactor and
Conditions of Operation
b. Test Results
4.
Shawnee Plant Data
Bench Scale Sulfation Data
1.
OAP
Research Studies
2.
TVA Studies
i
Page
No.
1
6
11
12
12-
12
12
14
21
22
27
34
34
35
39
42
42
45
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IV.
TABLE OF CONTENTS
Page
No.
DISCUSSION OF RESULTS (Cont'd)
C.
D.
E.
Evaluation of Process Models
55
1.
Kellogg Shrinking Core Model
a. Theory and Development
b. Model Parameters and Constants
55
55
63
65
(1)
Effect of ~nitial S02
Concentration
Effect of Temperature
Effect of Limestone Surface
Area
74
74
(2 )
(3)
(4 )
(5)
74
77
Effect of Particle Size
Comparisons with Other Data
2.
OAP Model
83
83
95
104
a.
General Model Development
Evaluation of Model Constants
b.
3.
Wen Model
4.
MIT Model
113
Calcination Studies
117
1.
particle Heat-up Calculations
117
2.
Deadburning Studies
122
3.
Battelle Calcination Data
125
4.
TVA Calcination Data
132
Gas-Particle Mass Transfer
135
135
1.
Kellogg Calculations
2.
Comparison with Other Studies
Comparison with Initial S02 Reaction
Rates
149
148
3.
ii
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TABLE OF CONTENTS
page
No.
IV. DISCUSSION OF RESULTS (Cont'd)
F. Thermochemical and Physical Property Data 152
1. Thermodynamic Data 152
2. Stone Property Data 155
a. R.D. Harvey Report 155
b. G.R. McClellan Report 164
G. Process Effects on Equipment Performance 170
1. Electrostatic Precipitator Efficiency 170
Studies
a. Summary 170
b. Discussion of Test Results 171
2. Coal Ash Deposition Studies 179
a. Summary 179
b. Fused-Slag Deposits 183
c. Bonded Deposits 184
3. Water Quality Control Studies 187
V. REFERENCES 197
APPENDICES
A.
Thermochemical Values for Basic Reactions
in Flue Gas Sulfur Fixation
201
B.
Summary of Experimental Studies of S02
Removal Systems
Shrinking Core Model Development
217
C.
230
iii
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Table No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
LIST OF TABLES
Title
DRY LIMESTONE PROJECT - TEST RESULTS
USING REVISED CALCULATIONS
SHAWNEE STEAM PLANT
SURFACE AREAS OF CALCINED AND HYDRATED
COLBERT COUNTY LIMESTONE CALCULATED
FROM PORE VOLUMES
OAP MODEL SYSTEM PARAMETERS FOR
DIFFERENT STONES
A COMPARISON OF THE OAP MODEL TO THE
BENCH SCALE DATA FOR A HIGH PURITY
DOLOMITE
VALUES OF APCO MODEL CONSTANTS OBTAINED
BY NON-LINEAR REGRESSION ANALYSIS USING
THE BATTELLE DATA
DATA KEY FOR WEN'S MODELING STUDIES
THE EFFECT OF TEMPERATURE ON REACTION
PARAMETERS AND EFFECTIVE STRUCTURAL
PROPERTIES OF CALCINE 9
PROPERTIES OF LIMESTONE NUMBER 2061
SET I, 70/140 MESH PARTICLE SIZE RANGE
BATTELLE CALCINATION DATA (No S02
Present) - LIMESTONE NO. 2061
BATTELLE CALCINATION DATA (In Situ
Su1fation) - LIMESTONE NO. 2061
EFFECT OF INJECTION TEMPERATURE ON
SURFACE AREA
TVA CALCINATION CORRELATION PREDICTIONS
ACTIVATION ENERGY 30 KCAL/GM MOL
MASS TRANSFER CALCULATIONS
COMPARISON OF SOLIDS CONCENTRATION
EQUILIBRIUM CONCENTRATION OF S02
VERSUS TEMPERATURE
iv
Page No.
40
49
87
88-89
101
106
114
123
128
129
131
133
139
144
153
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Table No.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
LIST OF TABLES (Cont'd)
Title
Page No.
PETROGRAPHIC DESCRIPTION AND SOURCE
OF SAMPLES
156
MINERALOGY OF TYPE SAMPLES IN WEIGlIT
PERCENTAGE
157
CHEMICAL ANALYSES IN WEIGHT
PERCENTAGE
158
TRACE ELEMENT ANALYSES OF TYPE
CARBONATE ROCKS DETERMINED BY
NEUTRON ACTIVATION METHODS
159
RESULTS OF OUANTIMET STUDIES OF THE
PORE STRUCTURE OF CARBONATE ROCK
TYPES
160
GRAIN-SIZE DISTRIBUTION
160
DESCRIPTION OF THE CALCINES
161
S02 SORPTION CAPACITY OF TYPE SAMPLES
AND STATISTICAL LINEAR CORRELATION
COEFFICIENTS BETWEEN S02 SORPTION AND
VARIOUS CHEMICAL ELEMENTS AND PETRO-
GRAPHIC PROPERTIES
163
CORRELATION OF POROSIMETER AND
SCANNING ELECTRON MICROSCOPE
MEASUREMENTS
165
SURFACE AREAS OF CALCINES CALCULATED
FROM POROSIMETER MEASUREMENTS
166-167
PROPERTIES OF SULFATION PRODUCTS
168
RESULTS OF ANALYSIS OF ASH POND
EFFLUENT FROM TYPICAL PLANTS
190
SLUICE WATER QUALITY - NORMAL PLANT
OPERATION
191
SLUICE WATER QUALITY - LIMESTONE
INJECTION
192
SLUICE WATER QUALITY - NORMAL PLANT
OPERATION
SLUICE WATER QUALITY - LIMESTONE
INJECTION
195
195
v
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;......;0....1
Figure No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
LIST OF FIGURES
Title
TEMPERATURE PROFILE IN DISPERSED
PHASE REACTOR
EFFECT OF TEMPERATURE AND RESIDENCE
TIME ON FRACTIONAL CONVERSION OF CaO
EFFECT OF TEMPERATURE AND RESIDENCE
TIME ON FRACTIONAL CONVERSION OF CaO
EFFECT OF S02 CONCENTRATION AND
RESIDENCE TIME ON FRACTIONAL
CONVERSION OF CaO
EFFECT OF TEMPERATURE AND RESIDENCE
TIME ON FRACTIONAL CONVERSION OF CaO
EFFECT OF TEMPERATURE AND RESIDENCE
TIME ON FRACTIONAL CONVERSION OF CaO
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
EFFECT OF S02 CONCENTRATION ON S02
REMOVAL
EFFECT OF RESIDENCE TIME ON CaO
UTILIZATION
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
EFFECT OF RESIDENCE TIME ON CaO
UTILIZATION
EFFECT OF RESIDENCE TIME ON CaO
UTILIZATION
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
EFFECT OF RESIDENCE TIME ON CaO
UTILIZATION
SORPTION OF S02 FROM SIMULATED STACK
GAS BY CALCINE OF -24+28 MESH COLBERT
LIMESTONE
vi
Page No.
13
16
17
18
19
20
24
26
27
28
29
30
32
33
36
37
46
-------
Figure No.
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
32-A
LIST OF FIGURES (Cont'd)
Title
PORE VOLUMES OF COLBERT LIMESTONE,
-24+28 MESH
EFFECT OF PARTICLE SIZE ON THE REACTION
OF CALCINED LIMESTONE WITH S02 AND 02
EFFECT OF S02 AND 02 ON REACTION
VELOCITY WITH -24+28 MESH COLBERT
LIMESTONE
EFFECT OF CALCINATION CONDITIONS ON
REACTIVITY OF CALCINE
MODEL SOLUTION FOR DIMENSIONLESS
ABSORPTION RATE
MODEL SOLUTION FOR DIMENSIONLESS
CUMULATIVE S02 PICK-UP
THE DEPENDENCY OF THE SHRINKING CORE
MODEL K ON S02 CONCENTRATION
SHRINKING CORE MODEL PREDICTIONS FOR
LIMESTONE 2061---74 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
74 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
74 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
74 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
74 MICRON PARTICLES
EFFECT OF TEMPERATURE PROFILE ON THE
SHRINKING CORE MODEL PREDICTION
EFFECT OF TOTAL PARTICLE SURFACE ON
THE SHRINKING CORE MODEL PREDICTION
SHRINKING CORE MODEL PREDICTIONS FOR
LIMESTONE 2061--50 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS FOR
LIMESTONE 2061--EFFECT OF PARTI~LE SIZE
vii
Page No.
47
50
52
54
61
62
66
67
69
70
71
72
73
75
76
78
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Figure No.
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
47-A
48
LIST OF FIGURES (Cont'd)
Title
SHRINKING CORE MODEL PREDICTIONS--
50 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
50 MICRON PARTICLES
SHRINKING CORE MODEL PREDICTIONS--
50 MICRON PARTICLES
FRACTIONAL CALCINE CONVERSION VERSUS
TIME
EFFECT OF TIME AND TEMPERATURE OF
CALCINATION ON REACTIVITY OF CALCINES
REACTION RATE VERSUS TEMPERATURE
DIFFUSION EFFECT UPON REACTION RATE
REACTION RATE VERSUS PARTICLE SIZE
REACTION RATE CONSTANT VERSUS GRAIN
RADIUS
REACTION RATE VERSUS RECIPROCAL
TEMPERATURE
PARTICLE HEAT-UP TIME FOR LIMESTONE
BATTELLE CALCINATION DATA -
LIMESTONE NO.2061
S02 CONVERSION VERSUS STOICHIOMETRIC
CaO FOR VARIOUS PARTICLE DIAMETERS
HEAT TRANSFER TO CLOUDS OF PARTICLES
IN AIR
PARTICLE-GAS MASS TRANSFER CALCULATIONS
S02 REMOVAL VERSUS ADDITIVE INJECTION
RATE
INITIAL REACTION RATE VERSUS B.E.T.
SURFACE AREA OF CALCINE
GAS VOLUME FLOW VERSUS PRECIPITATOR
COLLECTION EFFICIENCY
viii
Page No.
79
80
81
91
93
105
108
109
110
112
121
126
138
142
146
150
172
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Figure No.
49
50
51
52
LIST OF FIGURES (Cont'd)
Title
ELECTROSTATIC PRECIPITATOR COLLECTION
EFFICIENCY VERSUS PERCENT OF RATED
CAPACITY
RATIO OF ESP AREA WITH ADDITIVES TO
ESP AREA WITHOUT ADDITIVES VERSUS
PERCENT OF RATED CAPACITY
THEORETICAL TOTAL ASH BURDEN AND
SLUICE FLOW - LIMESTONE INJECTION
WATER QUALITY OF RECEIVING STRE~1 AT
CRITICAL PLANT LOAD AND STREAM FLOWS
ix
Page No.
175
176
189
194
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I.
INTRODUCTION
The M. W. Kellogg Company has undertaken a review of the
Dry Limestone Injection Process under OAP* Contract No. CPA
70-68 (Task Order #3, Phase I). The Dry Limestone Process
referred to in this particular study is the process scheme
developed and evaluated in the TVA conceptual design study
report prepared for OAP and issued in 1968. This concept
involves injection of the pulverized additive stone directly
into the radiation section of the boiler proper to effect the
vapor phase calcination and sulfation reactions. The resulting
reaction products and unreacted stone are collected with the
fly ash in the dust removal equipment downstream of the boiler.
The increased quantity of particulates and changes in electrical
properties (resistivity) have been reported to result in a
substantial (-2 to 3-fold) increase in the size of electrostatic
precipitator dust collection equipment under normal operation.
Solids disposal problems are also aggravated and boiler deposit-
ion problems have been reported. Details of the initial specific
process design conditions and assumptions can be obtained directly
from the TVA design report.
The basic objective of the Kellogg Task Order was to
provide an independent assessment of the status of the Dry
Limestone Process Technology and to up-date the design bases
used in the TVA study to reflect any additional process
information developed since that time. Unfortunately, the
timing of the Kellogg study was not ideal, as an OAP full
scale test program to evaluate the process has been in
progress at the TVA Shawnee Steam Plant (Unit No. 10) simul-
taneously with the Kellogg effort and is still continuing.
The TVA plant test data are included as much as possible but
programs were not sufficiently complete to permit incorpor-
ation of all their results into the Kellogg evaluation.
Therefore, the approach taken in the present study was to
*or a precursor
-------
review all available information on the Dry Limestone Injection
Process and to derive pertinent correlations and equipment
design recommendations wherever possible.
The Kellogg task effort was initiated in September, 1970
by assimilating all OAP and contractor reports, published
articles and other technical information pertinent to the
subject process. A review of this material revealed that a
substantial experimental effort had been devoted to studies
of the basic process chemistry and parameters which affect
the limestone physical properties in numerous reaction systems.
Most of this work, however, had been carried out in small scale
equipment with long term exposuye of the stone to calcination
and subsequent sulfation conditions. A reasonable degree of
success was achieved in developing reaction models to fit
the laboratory data for a specific experimental configuration,
e.g., reactor type, temperature, etc. However, a comparison
of results from different bench scale studies was not par-
ticularly satisfactory. This observation is believed attributable
to differences in experimental test conditions, particularly
with precalcined stones, and the resultant effects on stone
properties and sorption characteristics.
It was decided at this point in the project review that
the bench scale data taken with relatively long residence
times would not be applicable to the actual boiler in-
jection system. Investigators had found that different
reaction mechanisms seemed to be controlling in studies
taken over a wide range of residence times, and time-tem-
perature effects on critical limestone physical properties
(e.g., internal surface area pore volume, etc) were a
-2-
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major factor limiting reaction rates. The emphasis in
the Kellogg study, therefore, was placed on the evaluation
of data from in situ calcination-sulfation studies taken
in flow reactors designed to simulate commercial boilers.
Pilot plant data for flow reactors were obtained from the
studies of Battelle, Babcock and Wilcox, Peabody Coal and
Ishihara. It was again found that a comparison of results
from these investigators exhibited wide discrepancies.
Attempts to resolve these variations were unsuccessful
because of the generally incomplete status of reported
test data, e.g., insufficient analyses to permit verification
of material balances and incomplete information on additive
properties to permit comparisons between different stone
types. Kellogg concluded that the Battelle test data should
be used to develop correlations for the reaction system
since it exhibited a high degree of internal consistency,
and the pilot studies used the same stone (predonia Valley
Limestone No. 2061), and had equivalent residence times
and similar time-temperature relationships as the initial
screening Shawnee tests.
A number of feasible gas-solid reaction models have
been proposed by various investigators to describe the
S02-CaO system kinetics. The correlation approach used
by Kellogg in this study was developed for a "shrinking
core" model, i. e., where S02 gas must diffuse through a
reaction product layer (CaS04) to reach the shrinking
inner core of available reactant (CaO). This concept
was favored because it has plausible physical and theoret-
ical significance for the system of interest. The specific
shrinking core model developed by Kellogg with the as-
sistance of Kellogg's consultant, Prof. R. L. Pigford
-3-
-------
l.
I
(Univ. of California), assumes that a combined diffusional
resistance limits the overall reaction rate. Kellogg de-
veloped constants for the proposed model to fit the Battelle
data with Limestone No. 2061, and a high degree of correlation
was obtained with different additive particle sizes and at
different reactor operating conditions.
Attempts were then made to test the Kellogg reaction
system model against data obtained in other flow reactor
studies. This effort was not fruitful, mainly because of
the scatter in available experimental information and a
lack of complete stone physical property data. Efforts
were also made to compare the model with some initial test
data from the Shawnee boiler using Limestone 2061. The
experimentally measured CaO conversions were substantially
lower (factor of 2-3) than predicted. In these particular
tests, the additive was injected at a boiler plane cor-
responding to high gas temperatures (>2300°F), and it is
probable that the occurrence of stone deadburning gave
rise to low lime utilization. It is also quite possible
that other parameters in the full scale boiler, e.g.,
limestone distribution problems (see Section IV A.4.) and
mass transfer effects, could be the reason for the apparent
inability to duplicate pilot plant results. One expects that
additional insight should be developed from tests currently
in progress using a boiler plane corresponding to lower gas
temperatures, i.e., -2100°F gas temperature. It is believed
that the Kellogg model is as accurate as any proposed to
describe the CaO-S02 reaction system; however, further
verification against full scale boiler tests is obviously
required.
-4-
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The remaining effort in the overall Kellogg review of
the Dry Limestone Injection Process entailed an analysis
of process effects on the operability of a standard pul-
verized coal-fired boiler. Available information was re-
viewed for the obvious important equipment performance para-
meters, e.g., effect of additives on slagging character-
istics, efficiency of dust removal equipment, and sluice
water quality control. The results of this particular
study were disappointing in that much of the equipment
performance know-how has not been studied in sufficient detail
or exists mainly as proprietary information, with little
useful published design data. For example, published studies
of coal ash deposition tendencies give directional effects of
certain parameters; however, no quantitative correlation is
available to predict operability ranges for ash-limestone
mixtures.
The boiler operability questions are critical and must
be resolved before the Dry Limestone Injection Process can
ever be installed commercially as a continuous control pro-
cess. It is hoped that detailed equipment design information
will be obtained from the TVA Shawnee tests on an actual
boiler. The preliminary Shawnee test data that were avail-
able as of this writing exhibited considerable scatter,
apparently partly explainable from problems of controlling
the boiler operation. Initial full scale data on the electro-
static precipitator showed wide variation in the effect of
limestone additive on collection efficiency and dust resis-
tivity. The long term demonstration tests planned for the
latter part of 1971 should resolve the data discrepancies and
provide useful information in other areas concerning boiler
operability.
-5-
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II.
SUMMARY AND CONCLUSIONS
A. A comparison of CaO-S02 reaction system data from
various pilot plant studies shows a wide divergence in results.
The following represent typical CaO utilizations measured
for approximately the same reaction conditions, e.g., l8500F
injection temperature, 2.0 second gas residence time, stoich-
iometric ratio (cao/s02) of unity and 74-l05M particle size
calcite:
Battelle Studies
Babcock & Wilcox studies
Peabody Coal Studies
10-15% CaO utilization
10-30% CaO utilization
20-40% CaO utilization
The discrepancy is believed attributable to differences in
reactor configuration, experimental techniques, operating
conditions, different types of stone, etc. The Battelle
flow reactor data were chosen for modeling work on the
basis of completeness of information and best degree of
internal consistency and closest simulation of Shawnee test
conditions with regard to time-temperature. Available data
from Shawnee indicate utilizations in the range reported
by Battelle.
B. A "shrinking core" diffusion-reaction model was
developed and pertinent constants were derived to fit the
available Battelle data with Fredonia Valley Limestone No.
2061. A good fit was obtained for the following experimental
conditions: 50-74M average particle size; 1600op-2100oF
gas temperature; 0.025-0.95 mol % S02 in inlet gas. The
reaction system modeling approach is similar to models
developed by Dr. Wen and MIT in other OAP sponsored studies.
C. The Kellogg model could not be adequately tested
against data from other pilot plant studies because of
-6-
-------
incomplete stone physical property data.
this model against initial full scale TVA
with Limestone No. 2061 showed much lower
Attempts to test
Shawnee tests
measured CaO
conversions, possibly due to high additive injection tem-
peratures (>23000F) and resultant deadburning.
D. The extensive bench scale studies of the CaO-S02
system revealed major effects of the calcination time-tem-
perature relationships on stone properties and sorption
characteristics. Reaction models developed from the bench
scale studies could not be extrapolated to the actual
flow system because of the much greater available B.E.T.
surface area from in situ calcination-sulfation at low
residence times (1-2 seconds). The. time-temperature-surface
area relation is not known and probably it will never be possible
to determine this relation for a commercial system. The
shrinking core model groups these variables together so the
relation per se is not needed.
E. Limestone calcination studies showed that a high
degree of calcination (60-70%) could be achieved in approx-
imately 0.2 seconds at temperatures of 1900-2100°F in the actual
boiler system. It was concluded that the calcination step
is relatively fast in the overall sequence, hence it was decided
to develop a model based on sulfation only since it appeared
that such a model might adequately describe the system. Battelle
and Dr. Wen are developing simultaneous calcination/sulfation
models.
F. The effect on 502 absorption of major process
variables is indicated as follows:
1.
Additive properties - - numerous additives with
a wide range of properties have been tested but
no correlations relating additive properties to
502 removal have been developed. However,
excellent correlations between initial reaction
rate and surface area exist.
-7-
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2.
Temperature - - conflicting results from different
investigations with some showing increased 502
absorption as temperature increases while others
show no effect. If the temperature is high enough
to cause deadburning, however, the removal ef-
ficiency falls off in all cases. Temperature
above about 23000F generally produce deadburning
with the severity increasing with temperature.
Time-temperature relationships are important as
described in D. above.
3.
Particle size/specific surface - - decreasing particle
size and increasing specific surface apparently in-
creases 502 removal to a point and then further
changes have little effect. The point at which
decreasing the particle size affects 502 absorption
is not clearly defined, however, ranging from about
50 microns down to about 10 microns. Determination
of the actual particle size is difficult and frag-
mentation or aggregation of the particles in the
reaction zone may be a factor such that below a
certain size, the size of the particles taking part
in the reaction are independent of initial size.
4.
502 Concentration - - The apparent rate of reaction
is dependent on 502 concentration and sulfate loading
on the calcine, but further work is required in this
area to better define the mechanism. It should be
noted, however, that the existing shrinking core model
is valid with respect to the most recent Battelle
data available when the present work was done.
5.
02 - - the majority of investigators have found that
increasing the oxygen concentration (i.e., increasing
excess air) generally increases the 502 absorption
within the range studied (0.2% to 6%) but other
factors (e.g., sulfate loading, alteration of time/
temperature) have a significant effect. No cor-
relations for 02 effect on 502 absorption have been
developed.
6.
Pore size - - data have been obtained which in-
dicate that pore diameter of the absorbent is a
-8-
-------
significant factor in both absorption capacity and rate.
The total S02 sorption capacity increases with increasing
pore size and has been correlated with pore areas greater
than 0.3 microns. The rate of reaction increa~es with decreasing
pore size until a critical pore diameter of about 0.1 micron
is reached.
G. Mass transfer predictions based on generalized
theory revealed that the diff~sional resistance in the gas-
to-solid transfer process can be a major factor in the overall
sulfation reaction. The mass transfer process effects. could
not be derived from the Battelle pilot reactor studies owing
to the use of unrealistically lotl stone injection rates. The
problem requires additional experimental investigation, involving
actual boiler tests supplemented by gas-solid mass transfer
studies at a low particle Reynolds number.
H. The effect of limestone addition on the stack gas
dust resistivity and electrostatic precipitator (ESP) col-
lection efficiency was investigated. Initial TVA tests on
the Shawnee plant precipitator indicated considerable scatter
in the measured precipitator efficiency as shown below:
ESP
Efficiency
w/Additive
87-91%
68-88%
Gas Flow Capacity
(% Design)
76-82%
94-106%
Required ESP Area Factor to Maintain
Baseline Outlet Loading
(Area with Additive/Base Case Area)
1.1-1. 4
1. 3-2.25
It is evident that additional ESP test data are required to
determine a more reliable design efficiency value in the
presence of limestone. OAP has contracted Cottrell Environmental
Systems to perform additional testing on the effects of lime-
stone addition on solids collection efficiency.
-9-
-------
I.
A review of available information on the effects
of boiler additives on coal ash deposition tendencies
indicates directional trends but no general quantitative
correlations. It appears that the ash sintering strength
will be lowered in the presence of limestone, which should
minimize problems resulting from the build-up of bonded
deposits on tube surfaces. There also appears to be a relation-
ship between tendency to deposit and tube temperature regime.
Again, it will be necessary to obtain more useful design in-
formation from the full scale plant test program.
J. Preliminary test data from Shawnee have shown
that water quality control problems will be a critical
consideration in limiting the applicability of the Dry
Limestone Injection Process. A 10-30 fold increase in the
total dissolved solids content of the ash sluice water
has been measured with limestone injection, along with
an increase in disposal pond pH resulting from the hydration
of excess CaO.
-10-
-------
III.
RECOMMENDATIONS
A. Final conclusions regarding applicability of the
Dry Limestone Injection Process to full scale utility boilers
should await completion of the Shawnee test program. The
following items are of particular importance:
1.
Additional data must be generated and evaluated
when stone injection plane A-A corresponding to
the reported optimum injection temperature of
approximately 2l00oP gas temperature is being
used. The Shawnee test program should be designed
to obtain data on different additive types with
different average particle sizes at the injection
location.
2.
Additional information must be generated to permit
a more reliable assessment of effects on the
following equipment performance considerations:
. Electrostatic Precipitator Efficiency
. Boiler Operability and Deposition Problems
. Sluice Water Quality Control Problems
B. The shrinking core model developed by Kellogg to
describe the caO-so2 reaction system should be tested by
correlation with injection plane A-A data.
C. To use the Kellogg reaction model, or other proposed
models with a theoretical basis, the available limestone
internal surface area generated in the calcination-sulfation
processes must be known. Recent studies in the Battelle test
reactor have provided some data on B.E.T. surface area for
in situ calcination conditions. It is recommended that ad-
ditional studies be undertaken to generate similar data for
other stone types.
D. Theoretical predictions indicate that gas-to-particle
mass transfer can contribute a major resistance in the overall
sulfation reaction process. A test program should be developed,
either for the full scale boiler or a pilot flow reactor, to
measure transfer coefficients in the actual system at low
particle Reynolds numbers.
-11-
-------
IV.
DISCUSSION OF RESULTS
A.
Pilot Plant Sulfation Data
1.
Battelle Studies
a.
Battelle Reactor Design and Conditions
of Operation
The Battelle dispersed-phase reactor con-
sisted of a vertical tube with a gas-fired burner at the
bottom. Limestone was injected through one of a series of
ports in the bottom portion of the reactor, was carried
upward by the flue gas stream, and was subsequently ex-
tracted through another of a series of ports in the upper
part of the reactor. Very low particle dispersions, on
the order of 1 to 2 particles per cubic foot of flue gas,
were used in order that each particle might experience
an environment of essentially constant S02 concentration.
This situation, of course, may not exist in commercial
boilers where possible interparticle effects and significant
502 concentration gradients may affect the efficiency of
the mass transfer operation.
The 502 concentration in the flue gas
was continuously monitored by an IR analyzer, and temperatures
throughout the reaction system were continuously monitored
by a multipoint recorder. Gas temperatures at the top,
middle and bottom of the reactor were recorded to provide
an indication of vertical temperature gradients while the
wall temperatures indicated temperatures usually 100° to
200°F cooler than the centerline temperatures. Figure 1,
from the Battelle final report (1), shows a typical tem-
perature profile along and normal to the axis of the
-12-
-------
2100
2000
1900
1800
1700
1600
1500
FIGURE I
TEMPERATURE PROFILE IN DISPERSED-PHASE REACTOR
CENTERLINE
LEGEND
+ CENTERLINE
. +2 INCHES, -2 INCHES
o +4 INCHES, -4 INCHES
IJ..
o
CENTERLINE :t4 INCHES
~
lLI
a::
::>
~
c:r
a::
lLI
a..
~
lLI
~
'" ,
ARE NORMALLY RECORDED AT THREE ~~
LOCATIONS INDICATED BY X. '" "'-
, ."'~
"-
". O~
"-
"
CENTERLINE :t2 INCHES
o
DISTANCE FROM BOTTOM PORT, FT
X X X
1400 -f I. I I I I I I I I I I ,
o 2 3 4 5 6 7 8 9 10 II 12 13
-13-
-------
dispersed-phase reactor. The profiles in either direction
appear to be fairly flat. Velocity gradients along the
reactor were also measured and found to be nearly flat
over the cross-section. In Battelle's residence time cal-
culation, both the known temperature gradient and the
flow profile were considered. Detailed test data received
directly from Battelle showed revised residence times which
were slightly different than the values presented in the
Battelle final report.
Limestone 2061 (Fredonia Valley White) ,
with an analysis of 90.17 percent CaC03, was used ex-
clusively by Battelle in their recent studies. In all but
one calcination run, the particle size range utilized was
-140+200 u.s. Standard mesh (74-105 microns). Battelle's
data were reported in terms of CaO utilization based on
chemical analysis of the reacted stone. The samples were
first hydrated after which a thermogravimetric analysis
determined the carbonate and hydroxide content while total
sulfur was determined by colorimetry. Battelle did not
attempt a material balance over the reactor in order to
check the consistency of their solids analysis data, al-
though the success of such an attempt may be seriously
limited in this case by the extremely low stoichiometric
ratios (approximately 7 to 14 percent) employed.
b. Battelle Data
Sulfation data for the Battelle dispersed-
phase reactor appear in the Battelle final report entitled
"Investigation of The Reactivity of Limestone and Dolomite
for Capturing S02 From Flue Gas,,(l). These data were
plotted as fractional CaO conversion versus residence
-14-
-------
time, and the results can be seen in Figure 2 through
Figure 6 for reported mean temperatures ranging from
l600°F to 2l48°F. Although one might anticipate increased
CaO conversion with. increased temperature over the entire
range of residence times studied, there is no distinct
evidence of this effect within the Battelle data. The
higher temperature runs do, however, exhibit higher initial
rates of reaction as demonstrated by the slope of the
curve at time equal to zero. The Battelle data plots do
show that reactor time-temperature effects are critical
in controlling CaO conversion, and the higher temperature
results undoubtedly reflect some degree of stone dead-
burning.
Also included on Figure 3 are data showing
the effect of 02 concentration on CaO conversion. As can
be seen from the curves, increasing the oxygen concentration
from 0~4% to 6% increases the conversion, other condi-
tions being constant. For example, at 1.5 secondsresidence
time and a temperature of about l7l5°F, CaO conversions are
5.5%, 7.1% and 8.7% for oxygen concentrations of 0.4%, 3.0%
and 6% respectively. Thus, it appears that increasing the
amount of excess air in the boiler has the potential of
increasing S02 removal.
Figure 4 is an excellent illustration of
the effect of initial S02 gas concentration on overall
CaO conversion. Higher S02 concentrations do indeed effect
more efficient utilization of the limestone. Some of the
apparent scatter within the Battelle data could be attrib-
uted to variations in reaction temperature profiles between
different test runs. In spite of these apparent anomalies,
however, considerable weight has been given to the Battelle
data in the development of a reaction system model since
the dispersed-phase reactor studies do reasonably simulate
the Shawnee boiler and since the same limestone (No. 2061)
was used in both tests.
-15-
-------
0.24
0.22
0.20
0.18 z
o
CJ)
0.16 c:::
w
>
z
0.14 0
u
o
0.12 c
u
..J
0.10 «
z
o
0.08 .....
u
«
a:
0.06 LL
0.04
0.02
o
o
FIGURE 2
EFFECT OF TEMPERATURE AND RESIDENCE TIME
ON
-
FRACTIONAL CONVERSION OF CaO
BATTELLE DATA (STONE 2061)
. RUN 2 - 5 (C-W)
o RUN 2-18 (A-Y)
X RUN 3-25 (B-W)
Yso = 0.003
2
.
RESIDENCE TIME, SEC
0.2 0.4 0.6 0.8 1.0 1.2
1.4 1.6
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
-16-
-------
FIGURE 3
EFFECT OF TEMPERATURE AND RESIDENCE TIME
ON
-
FRACTIONAL CONVERSION OF CaO
0.24
0.22
0.20
0.18 z
0
en
0.16 a::
ILl
>
z
0.14 0
u
0
0.12 0
u
..J
0.10 «
z
0
0.08 I-
u fJ,fi";)0'f
« .... \9
a:: '''' -
0.06 IJ..
X
0.04
BATTELLE DATA (STONE 2061)
. RUN 4-16 (B-V)
o RUN 4-15 (B-V)
X RUN 4-10 (B-Y)
o RUN 4- 9 (B-V)
YS02 = 0.003
T M = 1717°F
o
&°/0 0'2.
. 0
- 1717 of :;%02
TM -
-3%0~ ~ TM = 1711°F
[J
0.02
X
X X X
~0.40/0 02
o
o
o
o
0.2 0.4 0.6. 0.8 1.0 1.2
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
-17-
-------
0.24
0.22
0.20
0.18 :z
o
en
0.16 a::
I.&J
>
:z
0.14 0
(,)
o
0.12 ~
(,)
...J
0.10
-------
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
FIGURE 5
EFFECT OF TEMPERATURE AND RESIDENCE TIME
ON
-
FRACTIONAL CONVERSION OF CaO
BATTELLE DATA (STONE 2061)
. RUN 2-17 (A-W)
X RUN 2-19 (B-X)
z
Q
en
Q:
w
>
z
o
u
o
d
U
Yso = 0.003
2
...J
-------
EFFECT
FIGU RE 6
OF TEMPERATURE AND RESIDENCE TIM E
ON
-
FRACTIONAL CONVERSION OF CaO
0.24
0.22 z
Q
(f)
Q:
0.20 ILl
>
z
0.18 0
u
0
0.16 c
u
...J
0.14 <
z
0
0.12 I-
u
-------
2.
Babcock and Wilcox Studies
The Babcock and Wilcox (B & W) dispersed-
phase reactor consisted of a vertical reaction chamber
followed by a vertical heat exchanger which cooled the
gases down to exit conditions. Both coal and limestone
were fed into the top of the downflow reactor through
separate injection ports. Residence times in the reactor
were varied by (1) altering the coal firing rate, or (2)
changing the vertical position and/or angle of the lime-
stone injection port. The latter method, however, introduces
the additional effect of temperature. The following injection
ports along with their respective average injection tem-
peratures were used with the B & W reactor:
Port A
Port 1
Port 2
Port 3
Port 4
2700°F
2300°F
19000F
l700°F
lSOO°F
(It should be noted,
quantity of air used
enough to reduce the
however, that according to B & W the
to convey the additive was large
flue gas temperature by about 40QoF).
The reaction zone was assumed to extend from
the point of injection down to the point in the vertical
heat exchanger at which the temperature was approximately
l400oF. Most of the B & W data were taken from runs which
utilized either injection port A or port 1. The data are
reported in terms of stoichiometry and S02 removal which
is determined by IR monitoring. Although wet chemical
-21-
-------
and X-ray analyses were made for most of the reacted-ad-
ditive-fly ash mixtures, the reported 802-removal data
are based on gas-phase analysis. No material balances
are reported. The analyses of the solids apparently were
made only to determine if there was any reaction between
coal ash and additive. Had natural balances been determined,
perhaps some of the inconsistencies within the data could
have been explained.
The B & W study(2) made use of a large
variety of limestones and dolomites, but only the lime-
stones with a Ca content exceeding 87 percent were con-
sidered for analysis along with the dolomites. In some
cases, the limestones and dolomites were precalcined to
yield greater surface areas, or hydrated to give even
larger surface areas. Greater surface was also effected
by utilization of marls--limestones with characteristically
high surface areas.
a.
Data for Limestone Additions
An attempt to correlate 802 removal with
specific external surface (cm2jgm)* of the raw limestones
proved unsuccessful because of the wide scatter of the
data. A plot of 802 removal versus total external surface
(obtained from both specific surface and stoichiometry)
also revealed no apparent correlation for a specific set
*The reader is reminded that the specific surface measured
by B & W represents only the outside surface of the lime-
stone particles and should be related to particle size
distribution of the stone and not internal surface area.
..--- .
-22-
-------
of operating conditions. For any fixed residence time,
however, runs made with stones of very high specific ex-
ternal surface areas, representing the marls (-15,000
cm2/gm), the hydrates (-17,000 cm2/gm) and, in some cases,
the calcines (-8,000 cm2/gm), did exhibit higher S02
removals than those made with raw limestones (specific
surfaces ranging from approximately 3,000 to 4,000 cm2/gm)
of larger average particle size.
The effect of residence time on .s02 re-
moval was also explored. Since, at anyone injection
port, there existed insufficient data over an appreciable
residence time range, this correlation had to be attempted
using data from both injection ports A and 1. The result
indicated a trend of increased S02 removal with increased
residence time, but too much scatter was inherent in the
data for any conclusive correlation. An explanation for
some of the scatter may lie in the above mentioned tem-
perature effect between the two injection ports.
Stoichiometry appeared to correlate well
with S02 removal for limestone injection at port A and
for coal firing rates ranging from 6.0 lb/hr down to 4.4
lb/hr (approximately 1.7 to 2.4 seconds residence time).
Figure 7 illustrates this correlation. No particular
trend was obtained, however, from similar data at higher
coal rates representing shorter residence times. The
stoichiometry range covered by the Battelle studies is
also included in Figure 7 to illustrate the narrow range
used in these tests and to show the difference in stoich-
iometry between the Battelle and B & W tests.
-23-
-------
60
40
FIGURE 7
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
LIMESTONE> 870/0 CaO - 8 AND W DATA
70
50
/ .
/
/
/
./
/
/
/ .
/
.....
z
w
u
a::
LLI
a.
30
..
...J
~
~ . "r
o /
U) !.
/ .
/
/
/ BATTELLE
/ STUDIES
RANGE
STOICHIOMETRY, PERCENT
4.4 - 6.0 LB/HR COAL FIRING RATE
3400-5520 CM2/GM STONE SURFACE
--3500 PPM S02 CONCENTRATION
INJECTION AT 27000F
20
10
o
o
100
200
300
400
500
600
700
800
-24-
-------
Figure 8 is a plot of initial S02 con-
centration in the gas phase correlated against S02 re-
moval for limestone injected through port A. Although the
data are scattered, the graph indicates increased S02
removal with increased S02 concentration. This trend
was compared with the correlation provided by Battelle in
their final report. For a comparable residence time (ap-
proximately 1.2 seconds), the effect of initial S02 con-
centration on S02 pickup is approximately the same for
both the Battelle and the B & W studies.
The S02 removal data were converted to CaO
utilization terms (determined from the ratio of S02 removal
to stoichiometric fraction) for purposes of comparison
with the Battelle data. Only the B & W data for runs
with stoichiometric rates varying between 80 and 100
percent were considered. Figure 9 shows CaO utilization as
a function of residence time for the B & W limestone data,
and for Battelle data on a run in which the average temperature
was approximately l850°F (one of the best Battelle runs in
terms of CaO utilization). Both sets of data cover runs in
which the initial S02 concentration ranged between 3000 and
3500 molar ppm. From the graph, it is apparent that the B & W
data for approximately 100 percent stoichiometry show sig-
nificantly greater CaO utilization than do the Battelle data
for which the Ca/S stoichiometry did not exceed about 14 percent.
The validity of an analogy such as this, however, is questionable
owing to the following differences between the two reactor
conditions:
(1)
The temperatures in the Battelle reactor
ranqed from about 24500F to l600oF, whereas
that of B & W maintain~d a reaction temperature
-25-
-------
I
9
8
7
6
5
4
o
x
X 3
3
2
I
9
8
7
6
5
4
2
2
h
FIGURE 8
EFFECT OF 802 CONCENTRATION ON 802 REMOVAL
LIMESTONE> 87% C_oO - BAND W DATA
~
:z
w
(,)
a::
w
a..
8
---
8 ,....""- 8
8........."
.........
8/ :
8 ./8 88
8/
/
/
,
/
..
...J
o
::!:
w
a::
8
8
8
N
o
C/)
5.6 - 6.1 LB/HR COAL FIRING RATE
3800 - 4300 CM2/GM STONE SURFACE
INJECTION AT 27000F
S02 CONCENTRATION, PPM
3
4567891
4567891
2
4567891
3
2
3
X 102
.J.
~
~
X 104
X 103
-26-
-------
60
50
40
30
20
FIGURE 9
EFFECT OF RESIDENCE TIME ON CoO UTiliZATION
LIMESTONE> 81% CaO
~
Z
ILl
U
D::
ILl
a..
. BATTELLE DATA (TAV = 1'8500F)
X BAND W DATA (T = 1400-27000F)
80 -120% STOICHIOMETRY
3000 - 4000 CM2/GM STONE SURFACE
-3500 PPM 502 CONCENTRATION
~
z
o
~
o
o
U
x
10
x
X _X
~ ....-X ---
....-
,.....
//X
", X X
X ,/
X X/
X
Xx/x
X
/' .
X
XXx
TIME, SEC
o
o
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
-27-
-------
profile ranging from 27000F down to
approximately 1400oF.
(2)
The B & W data are extracted from runs
utilizing limestones from several
sources; the Battelle studies utilized
limestone No. 2061 (Fredonia Valley
White) exclusively.
b.
Data with Dolomites
B & W data for runs with dolomite in-
jection show slightly less scatter than those runs with
limestone injection, although an appreciable amount of
data scatter persists. As with limestones, dolomite sur-
face also exhibited no apparent correlation with S02
removal.
Stoichiometry of the dolomitic runs*
(injection at port A) correlated fairly linearly with
removal at coal rates of 4.5 to 6.7 1bjhr and for raw
external surfaces ranging from 2200 to 2900 cm2jgm.
Figure 10 illustrates this relationship which exhibits
approximately the same slope as the corresponding plot
for limestones. A similar graph for data at higher coal
firing rates was impossible because of insufficient data
over an appreciable range of stoichiometry. Another plot
was made, however, for higher coal rate runs in which
dolomite was injected into the reaction system at port 1
(Figure 11). This plot indicates increased S02 removal
with increased stoichiometry, although any definite cor-
relation is excluded due to the limited stoichiometric
range of the data available. Figure 12 illustrates the
effect of stoichiometry on S02 removal for runs in which
S02
stone
*Stoichiometry and utilization in the B & W dolomite runs
were calculated on the basis of CaO+MgO as reactive
species.
-27-
-------
FIGURE 10
EFFECT OF STOICHIOMETRY ON 502 REMOVAL
DOLOMITES - BAND W DATA
80
/
I.
70 /
/
. I
60 /
./
I- /
50 z I..
UJ
u
a: /
w
a..
~ /
40 .-J
~ /
0
~ /
UJ
a::
30 C\I ./ .
0
(f) I .
.
r
I. 4.5 - 6.7 LB/HR COAL FIRING RATE
20 2200 - 2900 CM2/GM STONE SURFACE
/ ....., 3500 PPM S02 CONCENTRATION
I INJECTION AT 27000F
10 I
I
/ STOICHIOMETRY, PERCENT
0
0 100 200 300 400 500 600 700 800
-28-
-------
FIGURE II
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
DOLOMITES - BAND W DATA
60
50 8.0-10.9 LB/HR COAL FIRING RATE
2100 - 2830 CM2/GM STONE SURFACE
3500 PPM S02 CONCENTRATION
~ INJECTION AT 23000F
40 z
UJ
(.)
a::
UJ
Q.
~
30 ..J
«
> /
0 ..
~ /
UJ . .
a:: ~ .
20 C\/ .
0 /
en
.'/
10 {.
,/8.
/ .
/ STOICHIOMETRY, PERCENT
0
0 100 200 300 400 500 600 700 800
. 29..-
-------
FIGURE I 2
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
DOLOMITES - 8 AND W DATA
60
50
....
:J z
w
0
a::
w .
a..
... .
...J
30 «
>
0
~
UJ
a:: 7.3 -10.0 LB/HR COAL FIRING RATE
C\I
20 0 . 1560 -1630 CM2/GM STONE SURFACE
en / -3500 PPM S02 CONCENTRATION
/ . INJECTION AT 23000F
/
10 /
/
I STOICHIOMETRY, PERCENT
0
0 100 200 300 400 500 600 700 800 900
I
--30-
-------
the coal rate varied between 7.3 and 10.0 lbjhr, for
specific surfaces of approximately 1600 cm2jgm, and for
injection at port 1. The effect of stoichiometry on 802
removal in this case is much smaller than that shown on
Figure 10. The difference between the two curves results
from a combination of: (1) a residence time effect re-
sulting from varying coal firing rates, (2) a combined
residence time and temperature effect stemming from
stone injection at two different ports, and (3) an extent-
of-reaction effect arising from the difference in total
surface available.
It was assumed that B & W reported their
data on the basis that both CaO and MgO are equally re-
active. Plots of (CaO + MgO) utilization at low (80%-
120%) and high (>120%) stoichiometries are illustrated
in Figures 13 and 14, respectively. These graphs, al-
though exhibiting wide data scatter, show approximately
the same trend as the corresponding plot for limestone
(Figure 9). It is also significant to note from Figures
13 and 14 that a stoichiometric rate in the range of 80
percent and greater has little or no effect on (CaO + MgO)
utilization for any specified residence time.
In general, the B & W data tend to be
less consistent than the Battelle data for a specified set
of conditions, although the B & W data do, in fact, tend
to indicate higher stone utilizations.
-31-
-------
FIGURE 13
EFFECT OF RESIDENCE TIME ON CaO UTILIZATION
DOLOMITES - BAND W DATA
60
50
20
I-
2:
W
U
cr
w
a.
~
2:
0
I-
«
N
-.J
I-
:J
0
CI
~
+ .
.
80 -120% STOICHIOMETRY
2100 - 3400 CM2/GM STONE SURFACE
-3500 PPM S02 CONCENTRATION
40
30
.
.
.
10
.
.
.
-
RESIDENCE TIME, SEC
o
o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
"32-
-------
"
60
50
40
30
20
FIGURE 14
EFFECT OF RESIDENCE TIME ON CaO UTILIZATION
DOLOM ITES - B ANQ W DATA'
~
z
w
U
Q:
W
0..
>120% STOICHIOMETRY
2000 - 4000 CM2/GM STONE SURFACE
.......3500 PPM S02 CONCENTRATION
10
..
z
o
~
-------
3.
Peabody Coal Studies
a.
Description of Reactor and Conditions
of Operation
The reactor used by Peabody Coal consis-
ted of a pilot-scale coke furnace with a moving chain
grate through which primary combustion air passed normally
to the coal. Secondary air was also added directly to
the flame area above the fire bed. The resulting flue
gas then passed through a rectangular refractory duct
followed by a cylindrical duct, after which it was quenched
with water and bypassed to the atmosphere. The gas was
continuously monitored through sampling points prior to
the spray cooling section. In order to make possible a
sulfur material balance around the reactor, Peabody also
sampled the particulate matter prior to the water quench.
Since the furnace was not equipped with a standard ash
discharge, the ash was sampled before it was dumped from
the moving grate.
Temperature was monitored at various
places throughout the unit, and temperature profiles for
various feed rates were determined and are presented in
the Peabody Final Report(3). The injection ports were
located vertically in the rectangular section above the
flame with additional high temperature (2400° to 25000F)
injection ports toward the front. Peabody defined their
residence time calculation basis as beginning at the point
of injection and terminating at the water quench point
(not less than 12000F), assuming that the particles travel
at combustion gas velocity. Although six different injection
-34-
-------
materials were tested, the data for Aragonite Stone No.
1683, is emphasized here since its composition was con-
sidered to be closest to that of the stones utilized
in the other flow reactor studies. It should be noted
that two other stones (1359 and 1684) with similar com-
positions were tested and gave essentially the same results
as did No. 1683.
b.
Test Results
Figure 15 shows graphically the correla-
tion between S02 removal and stoichiometry for three dif-
ferent particle sizes of Limestone No. l683--the as-
received sample size which contained approximately 20 per-
cent -100 mesh material, a-140+200 mesh sample and a -200
mesh sample. The data are scattered, but a straight line
was approximated through each set of points. The as-
received sample gives a correlation in good agreement with
that obtained from the B & W data for limestones and dolo-
mites which were ground to pass 100 percent through a 60
mesh screen. From Figure 15, there appears to be very
little difference between the sets of data representing
the -140+200 and the -200 mesh samples, and they appear
to exhibit a twofold improvement over the as-received
sample with respect to S02 removal.
In Figure 16, the CaO utilization of
Peabody's Limestone No. 1683 (-140+200 mesh and -200 mesh
samples) is plotted against residence time of the, gas in
the reactor. Although the points do not show any clear-
cut relation within themselves, they do indicate much
higher utilizations than do the data points of Battelle
and B & W which appear on the same plot. One possible
explanation for this discrepancy lies in the fact that
the Peabody test runs used very high excess oxygen levels
-35-
-------
FIGURE 15
EFFECT OF STOICHIOMETRY ON S02 REMOVAL
PEABODY DATA - LIMESTONE 1683
100
80
INJECTION AT 2100° - 23800F
. AS RECEIVED (AR) SAMPLE
o -140 + 200 MESH SAMPLE
X -200 MESH SAMPLE
90
70
-200 AND -140 + 200
~
60 z
IJJ
U 0
a::
w x
a..
50 ...J X
ex
> 0
o
~
IJJ
a:: ~
40 C\I AR
o
en
10
.
30
20
STOICHIOMETRY, PERCENT
o
o
20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
-36-
-------
FIGURE 16
EFFECT OF RESIDENCE TIME ON CaO UTILIZATION
100
90
80
70
I-
Z
60 w
u
a::
w
a..
-
z
50 0 0
I- 00
«
N
-' 0
I- 0
:J
40 0
o
CI 0
U
0
30 0
O~
o
OX
20
X
X x
10 ~ X
X
X
.
o
o
LIMESTONE> 81% CoO
. BATTELLE DATA (TAV = 18500F)
X BAND W DATA (T = 1400 - 27000F)
80 -120% STOICHIOMETRY
3000 - 4000 CM2/GM STONE SURFACE
-3500 PPM S02 CONCENTRATION
o PEABODY DATA
-140 +200 AND -200 MESH
ALL STOICHIOMETRIES
o
0 X
X
0 X X
o ~ X
X
X X
XXX
RESIDENCE TIME, SEC
0.2 0.4 0.6 0.8 1.0 1.2
-37-
1.8 2.0 2.2 2.4 2.6 2.8 3.0
1.4 1.6
-------
ranging as high as 130 percent. Although there is no con-
sistent evidence within the data to support this con-
clusion, it is considered a possible explanation for the
high CaO utilizations observed. That is, based on diffusion
controlling, higher excess oxygen levels would give higher
utilizations by increasing the rate of diffusion and subsequent
reaction for the same residence time. Note that most investi-
gators have found that 502 absorption increases with increasing
oxygen concentration. It should be noted also that good sulfur
balances generally were not obtained; for example, the average
of 5 test runs for stone 1683 is 70% accountability (after
correction for fly ash dilution), 83.6% accountability for
1359 .(6 points), and 79.5% accountability for 1684 (5 points).
This may account for some of the high CaO utilizations reported.
-38-
-------
4.
Shawnee Plant Data
Results from the first 35 tests run on the
full-scale boiler at different injection locations, in-
jection velocities and injection angles were rather scattered
(see Table I). Limestone utilizations for S02 gas con-
centrations of 3000 ppm lie in the range of some of the pilot
studies; e.g., at a residence time of approximately 1.5
seconds, CaO utilization ranged from about 7 to 18 percent.
However, the particle size range reported for the Limestone
No. 2061 used at Shawnee (50% less than 16 microns) was
considerably smaller than that employed in the pilot studies
(50-90 microns average particle). According to previous
correlations of stone utilization with particle size, the
Shawnee data should indicate much higher utilizations for
its smaller particle size. The shrinking core model developed
by M. W. Kellogg predicts CaO utilizations for 16 micron
particles of Limestone No. 2061 to be more than threefold
the actual values reported.
This apparent anomaly could possibly be
attributed to the fact that, if indeed the actual additive
particle size range is as small as that reported, there may
be an appreciable amount of particle dead-burning occurring
since injection temperatures at the coolest injection location
(upper rear) exceed 2300°F. Although the shrinking core
model has not been validated for particle sizes smaller than
50 microns, it is felt that the discrepancy obtained with
the Shawnee data is far too great for considering the model's
inadequacies as the explanation.
-39-
-------
TABLE I
DRY LIMESTONE PROJECT
PFASE I TEST RESULTS
SHAWlj~F STEAM PLANT
Avg. Initial
Part Limestone
Test Injection Coal Injection Excess Air injection Size S02 L"ve1-ppm ~ RemoVal. Utilization
~ Location Stoich. , S Velocity ~ E{'6)* W\%)+ Angle Index E* W+ E* W+ E* W+
(fps)
1 Lower Rear 1.86 2.4 130 140 26.5 24.3 0 4.0 1840 1840 15.1 10.8 11.3 11.7
2 Upper Rear 1.55 2.6 132 140 35.5 33.3 0 4.0 1600 1640 23.0 20.1 11.4 15.1
3 upper Rear 1.84 2.2 59 143 27.3 20.0 0 4.5 1400 1500 15.2 7.3 6.8 7.7
4 Upper Rear 3.10 1.6 127 144 25.0 20.0 0 4.4 1190 1190 14.9 14.9 9.4 10.1
5 Upper Rear 3.68 1.4 67 142 18.0 16.7 0 4.2 1240 1240 14.7 7.2 6.3
6 Lower Rear 2.11 1.8 68 142 21.7 23.9 0 4.2 1480.' 1540 11.5 10.4 6.2 6.6
7 Lower Rear 2.30 2.0 130 140 18.3 19.2 0 4.6 2040 2120 11.2 9.4 5.2 6.5
8 Lower Rear 2.43 2.1 68 140 23.5 20.0 0 4.5 1900 1840 12.0 10.9 7.3 5.7
9 upper Rear 1.47 2.5 940 140 14.1 18.0 0 4.7 2240 2160 13.1 14.1 10.4 9.0
10R2 Upper Rear 1.33 3.8 940 139 35.5 32.9 0 5.0 2400 2480 13.1 11.7 9.4 10.0
11 Front 1.53 3.3 195 139 29.6 31.3 0 5.0 2400 2440 4.7 11.0 7 . 9 ---'1f':b
12R3 Front 1.11 3.6 198 139 37.7 35.0 0 5.0 2360 2400 6.1 12.4 15.1 13.9
13 Front 1. 76 2.2 101 142 37.7 37.7 0 4.7 1600 1600 14.2 12.9 7.1 9.1
14 Front 1.46 3.3 192 144 37.7 37.7 0 4.6 1800 1800 16.7 16.7 5.9 7.2
15 Upper Rear 1.75 2.2 945 142 40.0 33.3 0 4.8 1600 1520 27.4 26.7 9.9 12.8
16 Upper Rear 1.50 3.2 940 142 29.b 31.3 0 4.7 2680 2680 15.3 13.7 20.1 16.5
17 Upper Rear 1.01 3.5 131 142 29.6 31.3 +45 4.8 2520 2400 8.1 16.0 14.5 13.0
18 Upper Rear 1.77 2.4 131 141 29.6 37.3 +45 4.7 2680 2480 11.2 17.4 11.9 13.7
19 Upper Rear 1.16 3.0 132 142 38.2 39.1 -45 4.7 2200 2200 13.3 11.9 11.1 12.5
20 Upper Rear 1.69 3.0 132 142 38.2 39.1 -45 4.7 2400 2160 14.3 14.2 9.0 9.0
21 Upper Rear 0.87 2.9 134 138 16.0 16.6 -45 5.1 2200 2080 8.2 6.6 7.2 10.1
22 Upper Rear 1.76 1.7 131 140 25.0 15.4 0 4.8 1600 1680 17.2 15.3 11.8 11.1
23 upper Rear 1.07 3.7 68 140 33.8 28.8 0 4.4 2720 2760 9.4 5.8 11.0 12.5
24 Upper Rear 1. 70 3.2 67 139 32.9 39.1 -45 4.6 2480 2480 6.5 4.6 5.6 7.6
25 Upper Rear 1.29 4.0 68 116 22.1 23.5 0 5.2 3000 2920 8.7 8.9 6.7 5.1
26 Upper Rear 1.29 4.2 131 118 30.4 30.4 -45 4.8 3200 3200 4.4 5.7 7.9 8.7
27 Upper Rear 1.10 2.3 69 120 11.9 11.0 -45 5.7 1960 2000 8.6 11.5 10.2 11.3
28 Upper Rear 1.13 2.5 135 117 26.5 28.2 0 5.7 1800 1900 11.1 11.9 12.4 13.8
6A Lower Rear 1.19 2.6 69 137 22.8 23.5 0 4.4 2400 2360 6.8 4.3 9.5 8.6
7A Lower Rear 1.72 2.3 132 139 17.3 21.6 0 4.8 2080 1960 11.2 10.9 6.9 6.1
8A Lower Rear 2.01 2.4 68 140 22.1 23.5 0 4.5 2080 2000 11.2 10.8 6.5 7.4
2A Upper Rear 1.11 2.1 133 138 35.5 32.1 0 5.1 1620 1520 11.3 17.0 10.3 12.2
4A Upper Rear 1.39 1.9 132 139 27.3 20.7 0 4.3 1760 1660 14.5 21.7 6.9 8.0
29 Upper Rear 0.86 1.7 136 78 27.0 28.0 0 5.0 1560 1440 13.0 14.5 12.3 17.0
1A Lower Rear 1.44 2.7 133 138 25.4 29.2 0 5.1 2440 2480 11.0 8.6 7.4 6.1
*I=East Half of boiler
+V=West Half of boiler
-40-
-------
Another parameter which could have an effect
on the CaO utilization in the full scale boiler is limestone
distribution within the boiler. The model makes no allowance
for nonuniform distribution of either limestone or S02
in the flue gas; that is, it is ass~ed that both S02 and
CaO are distributed uniformly over the boiler cross sectional
area. In actual practice, however, the Shawnee tests have
shown nonuniform distributions are obtained for both S02
and limestone. Thus, even if completely uniform distribution
of limestone in the boiler flue, gas is obtained, uniform
distribution with respect to S02 will not be realized owing
to the variation in S02 concentration from point to point
within a given plane. The effect on CaO utilization of
this nonuniformity in S02 and CaO distribution is difficult
to determine but possibly could account for some of the
discrepancy between the model prediction and actual data.
Hopefully, the studies in progress as of this writing
utilizing lower injection temperatures and improved lime-
~ . -
stone distribution will yield more optimistic results.
-41-
-------
B. Bench Scale Sulfation Data
1.
OAP Research Studies
The in-house OAP Research studies investi-
gated the S02 sorption characteristics of ten diverse
types of limestones. In these studies, differential
reactor techniques were used to measure the rate of reaction
of sulfur dioxide with ten species of naturally occurring
limestones after calcination at standardized conditions.
The rates were measured as a function of particle size,
S02 concentration, CaO conversion and temperature, and
then correlated to these variables and the physical prop-
erties of the stones.
The calcines used in these studies were
prepared by a 2-hour kiln calcination at l796°F. The
calcined samples were then crushed and screened into three
particle size ranges, i.e., 12/16 mesh, 42/65 mesh and
150/170 mesh. The samples were then placed in the dif-
ferential reactor where they were exposed to a flue gas
containing about 3000 ppm S02. The sulfation tests were
undertaken at reaction temperatures of l202°F, l400oF,
l598°F and l796°F.
While tabular experimental data for the
particle loading versus time are not presented, the report(4)
does contain a.series of plots of loading versus time for
the conditions studied. Further data presented in this
report include the following properties: pore volume,
mean pore diameter and B.E.T. surface area, by type and
particle size, as well as the raw stone composition and
ignition loss-by stone type. Using these data, the OAP
-42-
-------
Research group developed a sorption rate model which in-
corporates empirical constants to relate the physical
properties and system parameters to the sorption rate.
These empirical constants are tabulated in the OAP pub-
lished report by stone size and type(4).
However, because of the nature of the ex-
perimental procedures used, some of the conclusions and
results indicated in the OAP report are open to question.
There are two primary areas which have caused such specu-
lation to arise:
(1)
(2 )
the calcination technique
the range of residence times
studied
One of the primary conclusions drawn from the experimental
data was that the rate of reaction was linearly related
to the B.E.T. surface area of the calcine. However, there
is a significant time-temperature relationship to the stone
surface area. While this effect will be discussed in more
detail in a later section of this report, (Section IV, C.2.,
D.2.,3; E.3;F.2.b), it is important to note that the flash
calcination which would be experienced in a commercial
system could result in calcines with surface areas in the
range of one to two orders of magnitude higher than measured
in the OAP bench scale tests. Thus, the surface area
effects seen in this study might not be comparable to those
which may occur in a commercial boiler system.
The second source of possible difficulty
is the residence time range used in the OAP studies. The
range investigated was from 5 to 140 seconds, whereas
commercial pulverized coal boilers would offer a maximum
-43-
-------
residence time in the order of 2 to 4 seconds. Therefore,
the mechanisms of sorption which are represented by the
empirical model and data of the bench studies may not be
those which come into play in a commercial system. These
comments are intended to point out some of the inherent
limitations involved in this type of bench scale work,
and to caution subsequent investigators as to possible
difficulties which may be encountered in trying to adapt
the resulting data to their particular needs.
-44-
-------
2.
TVA Studies
The Fundamental Research Branch of TVA has
performed numerous sorption studies in an attempt to re-
late the physical properties of various stones to their
sorption characteristics. Most of these sulfation tests
utilized calcines which were prepared by long duration cal-
cination, as were the stones in the OAP studies.
One of the most significant finds of the
TVA experimentation was the relationship of pore volume
or surface area to the rate of S02 removal. By comparing
the sulfation data of a calcined sample to that of a
sample which had been calcined, hydrated, and dehydrated,
the results in Figure 17 were obtained(6). The curves in
Figure 17 reflect a significantly higher degree of sorption
for the hydrated sample than for the anhydrous one. At
25 minutes run duration, the capacity of the former sample
was 40% greater than that of the latter. Figure 18 demon-
strates that the cumulative pore volume of hydrated material
is 40% greater than the "calcined only" sample, which is in
line with the difference in capacity. Furthermore, the
rapid absorption of S02 by the hydrated sample in the first
5 minutes of the absorption test, Figure 17, may be explained
by the difference in the distributions of pores in the two
samples as shown in Figure 18. Forty percent of the pores
in the hydrated sample have diameters greater than 1.75
microns, whereas the calcine has only 18% pores in this
range. The larger pores should be more accessible to the
S02' and samples with high percentages of large pores should
react faster if other conditions are the same. Obviously
a trade-off between large pores and greater capacity and
small pores and greater rates is necessary to optimize
for a specific application. When reaction times are very short,
as when lime is injected in a combustion gas stream,
reaction rate is probably most important.
-45-
-------
FIGURE I 7
SORPTION OF S02 FROM SIMULATED STACK GAS
BY
-
CALCINE OF -24 +28 MESH COLBERT LIMESTONE
lIJ
Z
U
...J 50
«
u
CI
E
o
o
...... 40
CI
E
~
z
«
(!)
~
:I: 30
(!)
w
3;
80
70
60
20
TEMPERATURE,
°C
o
6.
792
800
INPUT
CALCINE
ANHYDROUS
HYDRATED
10
o
o
5
10 15
TIME, MINUTES
-46-
20
25
-------
0.50
0.40
0.30
0.20
0.10
0.00
98
FIGURE 18
PORE VOLUMES OF COLBERT LIMESTONE,
-24 +28 MESH
~
..J
o
>
w
a::
o
a..
IJJ
>
~
~
::>
u
PORE DIAMETER, fL
17.5
1.75
0.175
0.035
-47-
-------
To investigate this possibility, TVA recal-
culated the total available surface area by the method of
Rootare and prenzlow(5). As shown in Table 2, the dif-
ferences between surface areas for the calcined and
hydrated samples exist only in the larger pores. The
larger surface area in the large pores of the hydrated
sample could account for the more rapid initial absorp-
tion of 502 by this sample in the test shown in Figure
17. The ratio of the surface areas of the two samples
at 0.2 micron pores or larger is the same as the ratio
of weights of 502 absorbed in 25 minutes. This suggests
that although small pores may contain a large fraction
of the total surface area, they are not significant in
the total absorption of 502.
In an attempt to relate the particle size
of a calcine to its sorption rate, the data in Figure 19
were obtained and plotted on a log-log basis. It is evident
that there are two distinct reaction stages with different
slopes in this relationship. The first stage consists of
parallel lines of slope approximately unity; the curves
for the smaller particles lie above those of the larger
ones, that is, the intercept at ! = 1 (log! = 0) is
inversely related to the particle size with the exception
of the minus 325-mesh samples. An explanation of this
discrepancy might be that there has been some aggregation
of the very fine particles in this size range, as suggested
by others.
The second stage of the reaction starts at
3 to 5 minutes under these conditions, and the slopes of
the lines are inversely related to the particle size of
the calcine. The intersection of the two stages, found
by extrapolating the two straight portions of the curves,
-48-
-------
TABLE 2
-SURFACE AREAS OF CALCINED AND HYDRATED
COLBERT COUNTY LIMESTONE CALCUATED FROM PORE VOLUMES
Pore Diameter,
microns
Cumulative Surface Area, m2/gm
Hydrated. Calcined
17.5
5.0
1.0
0.5
0.2
0.1
0.05
0.035
0.008
0.03
0.14
0.26
0.75
2.5
7.6
10.0
0.003
0~:007
0.04
0.14
0.53
2.4
7.6
10.6
-49-
-------
60
w
z
U
..J
«
u 40
~
E SIZE, MESH
o
0 30 . -48 +60
......
~ 0 -80+100
E
~ \l -150+170
z -250+270
« A
(!) 20 0 -325
~
I I
U1 (!)
a W
I 3:
15
80
10
1.5
6 8
TIME, MINUTES
10
20
15
2
3
4
FIGURE 19
EFFECT OF PARTICLE SIZE
ON
-
THE REACTION OF CALCINED LIMESTONE WITH S02 AND 02
30
40
-------
II
was found to be at about the same value ,for all particle
sizes in weight gain per unit weight of calcine, 48 ~
2 mg/lOO mg calcine. This indicates that the proportion
of the reaction during the first stage is independent of
the particle size of the calcine, and that about 40% of the
CaO reacts during the first stage. This would also indicate
that in the injection of limestone into a boiler, a maximum
of 40% utilization of the CaO can be expected by the first
reaction mechanism, and 250% of the stoichiometric amount
of limestone would be required to obtain complete removal
of 502 from the flue gas if the first-stage mechanism can
be carried to completion in the boiler. The second stage
is so much slower than the first stage that the retention
times in the boiler practically eliminate this diffusion-
through-product mechanism from consideration. The signifi-
cance of these results is that the loading of 502 on the
calcine is insignificant for the first-stage reaction rate
as long as there is abundant surface for reaction.
To test the effect of 502 gas concentration,
the previous experimentation was re-run, this time varying
the 502 concentration in the flue gas. The results, as
shown on Figure 20, are similar to those obtained for the
different particle size runs in that two distinct sorption
regions are evident, and the intercept of the two straight
portions was again about 48 mg 503/100 mg calcine or-40%
utilization of the CaO in the first stage. In other test-
ing, TVA found that 02 had little effect upon sorption
in the primary reaction zone, and that H20 did not affect
the soprtion or calcination kinetics of limestone.
To test the effects of calcination time and
temperature, an experiment was performed in which the
limestone was rapidly calcined and transferred to a TGA
-51-
-------
w 30
z
(,)
...J
~
(,)
~ 20
o
o
.......
CI
E
..
z
~
C)
I- 10
~
C)
~ 8
FIGURE 20
EFFECT OF S02 AND 02 ON REACTION VELOCITY
WITH
-24 +28 MESH COLBERT LIMESTONE
60
40
NUMBERS ON CURVES DENOTE
PERCENT S02 IN GAS WITH
4.5 PERCENT O2.
8AQ CONTAINED NO 02.
6
4
2
4 6
TIME, MINUTES
8
10
20
-52-
-------
.(thermogravimetric analyzer) apparatus for sorption test-
ing in a typical flue gas mixture. As shown in Figure 21,
the reactivity of the calcine decreased very rapidly as
the calcination temperature was raised, and this loss in
reactivity also increased as the time of calcination was
lengthened. Based upon these results, it was estimated
that the percent loss in reactivity was related to the
one-half power of the calcination time and the reciprocal
of the absolute temperature by the formula:
(%) = (445 - 5.7 x 105) tl/2
T
The conclusions drawn by TVA regarding the sorption of S02
by limestone calcines may be summarized as follows:
(a) The sulfation reaction is influenced
greatly by the conditions of calcina-
tion as well as the type of stone and
the degree of grinding prior to cal-
cination.
Loss of reactivity
(b) Sulfation of CaO takes place in two
stages: reaction of sulfur dioxide
with oxygen on the surface of the
lime, followed by diffusion of the re-
actants through the resultant CaS04
shell into the unreacted lime core.
(c) Pores in the calcine smaller than 0.1
micron do not admit sulfur dioxide
rapidly enough to have a significant
effect upon sorption at short residence
times.
(d) From bench scale testing, there appear
to be many interactions between param-
eters. These effects may be related
to the scale of experimentation and it
is likely that definitive information
will only be obtained under actual con-
ditions simulating the boiler injection
process.
-53-
-------
.-
z
w
<.>
D:
~ 60
.;
.-
>
.....
<.>
I
-------
C.
Evaluation of" Process Models
1.
Kellogg Shrinking' Core Mod'el (sulfation reaction)
a.
Theory and Development
The shrinking core model was developed by
Kellogg with assistance from consultant Dr. R. L. Pigford
(Univ. California)*. This model considers a single CaO particle
of radius, R , which consists of tiny nonpQrous micropellets
s
of radius, R , the void spaces between these micropellets being
s
the pores of the larger particles. 802 in the gas phase dif-
fuses through these pores to the surface of the micropellets
where reaction with 802 occurs. As reaction proceeds, a
shell of reaction product uniformly accumulates around the
surface of the CaO spherical micropellets. Further reaction
occurs only after gas diffuses through pore structure of the
particle and then through the reaction product layer
around the micropellets to their inner core of fresh unre-
acted CaO which gradually shrinks in size until ideally only
a pellet of reaction product remains.
The model is therefore valid under the
assumption that chemical reaction is rapid relative to
the diffusional process in the form of (1) bulk gas dif-
fusion, (2) pore or Knudsen diffusion, and (3) diffusion
of the gas through the cracks and pores of the reaction
product. The following expression describes the rela-
tionship between the rate of diffusion of S02 through the
reaction product and the radial velocity of the reaction
*
See Appendix C for details of model deve~opment.
I
I
i
-55-
-------
surface:
K
(CH-O)
\r-x
where
K
C
H
*r
x
rX
ps
t
41T rX
d
-at
~s j .x3)
Eq. (1)
=
=
diffusion coefficient representing
transfer of gas through the solid
reaction product, cm21sec
=
802 gas concentration, gm-moles/cc
=
A Henry's law coefficient representing
equilibrium between the 802 and the
solid reaction product
=
micropellet radius, cm
=
radius of CaO core of micropellet, cm
=
square of the geometric mean radius of
the spherical shell of reaction
product, cm2
=
molal density of reaction product,
lb mols/cc
=
time, sec
Diffusion through the pores of the large particles is
given by
D
-rRL
where
D
-r =
R =
*8 =
v
a
oR
e2 ~~
=
oC
IT
+
8v
y
(Rate of reaction)
~er unit area Eq. (2)
=
diffusion coefficient depicting bulk
gas phase and/or pore (Knudsen)
diffusion, cm2/sec
particle tortuosity
radial position in the larger particle, cm
total calcined particle surface to
volume ratio, cm2/cc
* y = porosity of the calcined particle, cc/cc
* These parameters were assumed to remain constant during
the sulfation reaction.
-56-
-------
The first term on the right-hand side of equation (2)
accounts for accumulation of gas in the pores and is
considered negligible. By appropriate mathematical man-
ipulation of equations (1) and (2), the following rela-
tionship results:
D
- 8
""'(
1 q (R2 JC) -
RZ8;sR JR-
V tCdt
oc.C
Eq 8 (3 )
where
(j..=
1y ~P.!
For simplification purposes, a set of dimensionless var-
iables is introduced at this point:
c
=
C/Ci
1
i=
R/RS
.
,
9= ~u.t
~4
s
where
Ci =
502 gas concentration at the surface
of the large particle, qm-moles/cc
radius of the large particle, em
RS =
In dimensionless terms, equation (3) now becomes
1 d
?~
(~) c
cS!5 = Vlode
Eg. (4)
with the following boundary limitations:
c ( 5, 0) = 0 , c (1 , (j) = 1 1 iI (0 ,9) = 0
-57-
-------
-,
Equation
and must
solution
(4) is a nonlinear, partial differential equation
be solved by a finite differencing technique. The
will be of the form
c
=
F (i;,B)
Eq . ( 5 )
It is noted that the solution indicated by equation (5)
contains no parameters, i.e., the dimensionless concen-
tration, c, is a function of dimensionless position (~)
and time (e) only. There will consequently be a unique
solution to equation (5) for !l! values of the system
parameters (Rs, Ci, D, etc.).
The rate of passage of 502 into the large particle is ob-
tained from
N (gm-moles/sec) ~ Q1 (41TRs2) igR/
' o~ R=Rs
Eq. ( 6 )
or, in terms of dimensionless variables,
N = D 't C i '411 Rs 2) J c I
1;'Rs "'dr e= 1
Eq. (7)
A dimensionless instantaneous rate of S02 consumption
may now be defined as
G ,e) =
N
tD ~~i,) (4 tT'Rs2)
=
~F I
d~ ~= 1
Eq. (8)
Similarly, a dimensionless variable 0(8) representing
the total cumulative take-up of S02 is
Q(9 )
D !G1e> dB
Eq. (9)
-58-
-------
A computer program has been developed to solve equation
(4), by a finite differencing technique, on the IBM 1130
computer. The one and only solution to equation (4) is
exhibited in Figure 22 and is of the form
G(e)
=
k'S -0.25
Eq. (10)
In terms of the dimensionless total 502 consumption,
O(e), the solution which is shown in Figure 23 is
O( 8)
=
k90.75
Eq. (11)
where
k =
a constant
Returning for the moment to dimensional terms, the
total cumulative take-up of 502 in gm-moles is
q(t)
= it
N dt
Eq. (12)
Converting the right-hand side of equation (12) to in-
clude the dimensionless variables, and utilizing equation
(9), the expression for the total gm-moles of 502 consumed
per particle becomes
q (t) = 21T"Rs5 5v2 '1'1< H f!. Q ( 6 )
'JD
Eq. ( 13 )
By application of the definition of dimensionless
B, along with equations (l~) and (13), the total
consumed by one limestone particle is determined.
time,
5°2
The
-59-
-------
overall CaO utilization is then computed from
CaO utilization
.
q(t)
4/31T Rs'" cr=-n ('C
where
f'c
=
molal density of CaO, qm-moles/cc
It is worthy of mention that the unique
model solution of equation (10) is an approximate one
applicable to dimensionless times approaching zero. There
does exist, however, an exact solution which mathematically
is the same as that in the case of the poisoning of a cat-
alyst pellet. Although the exact solution is being
attempted, it is felt that since the dimensionless times
are very small as indicated in Figures 22 and 23, the
result will not exhibit any appreciable discrepancy from
the existing solution.
The model, as it is presented here, is
an extrapolation of the behavior of one limestone particle.
Its applicability to the performance of a commercial
boiler may in fact be limited by the inherent model assump-
tion that no horizontal or vertical S02 concentration grad-
ients exist within the reactor, or, in other words, the
Ca/S stoichiometry is constant throughout. Whether or not
the shrinking core model will accurately predict large-
scale boiler performance will therefore depend on the
degree of homogeneity of the atmosphere within the boiler.
-60-
-------
n
o 4
3
X
1
~
7
6
5
- 4
X 3
~ l~
2
CJ)
::>
0-
w(J)
z-
«C>
I- ~
zZ
«0
I-J-
CJ)Q..
Za::
-0
CJ)CJ)
CJ)m
W«
...Ju..
Zo
o
(j)W
ZI-
w«
~a::
c
SLOPE = -0.25
DIMENSIONLESS TIME, e
I..
2
3 4 5 6 7891
X 10-8
~~
2
34567891
2
34567891
2
34567891
2
3 4 5 67891
X 10-7
-I..
~
~,.
~I..
X 10-6
X 10-5
X 10-4
FIGURE 22
MODEL SOLUTION
FOR
-
DIMENSIONLESS ABSORPTION. RATE
-------
FIGURE 23
MODEL SOLUTION
FOR
DIMENSIONLESS CUMULATIVE 502 PICKUP
T~
It) 4
I
~ 3 -
(J)
-
X "
2 a:-
:::>
~
u
1 a..
A C\I
0 SLOPE = 0.75
7 CI)
6
5 W
>
v 4
I ~
~ 3
..J
X :::>
~
2 ::>
U
CI)
CI)
1 W
a ..J
z
7 0
6 CI)
5 Z
W
It) 4 ::!:
I
~ 3 Q
X
l~
I..
DIMENSIONLESS TIME, a
2
34567891
X 10-7 . .1--.
2
X 10-6
34567891
~~
2 3 4 5 67891 2 3 4
x 10-5-+X 10-4~
-62-
-------
b.
Model Parameters and Constants
The gas-phase diffusivity, D, is in-
cluded in the model as a function of both Knudsen dif-
fusion which involves a square-root dependency on tem-
perature and bulk gas diffusion which depends on tempera-
ture to the three-halves power. The former accounts for
collision of the gas molecules with the pore walls while
the latter deals with diffusion of S02 through the gas.
The two diffusivities are combined, according to
Satterfield and Sherwood(7), in the following manner re-
sUlting in an overall effective diffusivity, Deff, which
describes gas transfer in the pores of the particles
1
Deff =
1
Dbulk
+
1
DKnudsen
The individual diffusivities are incorporated into the
model program as follows:
Dbu1k
=
6.75 x 10-7
)"Tl.S
;:
and
DKnudsen
=
14,460 )'2
'Sv
v ~
where
T
M
-
gas temperature, oR
molecular weight of gas
=
The S02 gas concentration, Ci, at the particle surface
-63-
-------
was converted to mole fraction by
YS02
8:
Pg Ci
R T
where
Pg
YS02
=
gas pressure, atm
S02 mole fraction in the gas at the
surface of the particle
gas constant in consistent units
temperature, oR
=
R
T
=
=
The existing model assumes the 502 concentration at the
surface of the particle to be constant and an isothermal
reactor. The user of the model computer program has the
option of maintaining the above temperature constant,
thereby simulating an isothermal reactor, or of including
temperature as a linear function of time.
For convenience, the diffusivity, K,
representing gas transfer through the solid reaction prod-
uct, and the Henry's Law constant, H, depicting any equil-
ibrium between the S02 and the solid reaction product were
consolidated into a single constant, k.
-64-
-------
(1)
Effect of Initial s02Concentration
Data from the Battelle dispersed-
phase reactor runs with varying S02 concentrations appear
in their final report (1) . By varying the previously dis-
cussed constant k, the model was fit to some of the better
Battelle runs (See Figures 26-29). Subsequently, a graph
of k versus initial S02 mol fraction was plotted (Figure 24),
yielding a straight line on log-log paper. The constant k
was then incorporated into the computer program as the
following function of initial S02 concentration:
k
=
e (-19.56-1.15 In YS02)
The above equation suggests that diffusion of gas into
the solid reaction product is S02 concentration dependent.
A feasible explanation for this phenomenon may be the fol-
lowing: If S02 is adsorbed strongly onto the surface of
the reaction product, then until this surface becomes
saturated with S02' the diffusivity will appear to de-
crease with increasing S02 concentration, owing to in-
creased adsorption at greater concentrations. It should be
emphasized that the above explanation is offered solely as
a possibility.
After the constant, k, was
programmed as a funct~on of S02 concentration, model
predictions. for the behavior of 74 and 105 micron par-
ticles were made at various S02 concentrations. The pre-
dictions for the 74 micron particles appear in Figure
25 and are based on the following stone and system
-65-
-------
FIGURE 24
THE DEPENDENCY OF THE SHRINKING CORE MODEL CONSTANT K
ON
-
S02 CONCENTRATION
I
9
8
7
6
5
It) 4
I
o
- 3
x
2.
I
9
8
7
6 ~
5 t-
Z
4 «
CD t-
I en
o 3 Z
- 0
X U
-.J
2 UJ
C
o
:!:
1
9
8
7
6
5
,.. 4
I
0
- 3
X
2
~..
502 MOLE FRACTION, YS02
2
3
4567891
2
34567891 2 34
X 10-3 ...~ X 10-2-.J
X 10-4
~..
-66-
-------
0.24
0.22
0.20
0.18 z
o
(/)
0.16 a::
w
>
z
0.14 0
u
o
0.12 a
u
..J
0.10
-------
properties:
Gas pressure, Pg
CaO molal density, pc
Particle porosity, y
Particle tortuosity, 1
Ca804 molal density, ps
Particle radius, R
s
Temperature, T
Particle surface/volume, 8
v
= 1 atm
= 0.0484 gm-mole/cc
= 0.45 cc/cc
= 3.0
= 0.0218 gm-mole/cc
= 0.0037 cm
= 1850°F
= 635,000 cm2/cc
The above properties were utilized in all of the model pre-
dictions except where otherwise noted. Figures 26 through
29 illustrates the fit of the resulting model predictions
to the Battelle data for 802 mole fractions of 0.0004,
0.0030, 0.0075, and 0.0095. Note that in Figures 26-29
two curves are shown for each 802 concentration that is com-
pared to actual data, corresponding to the upper and lower
limit of the particle size. Battelle used their test work,
viz, 105 and 74 microns respectively (-140+200-mesh). The
limits are shown for two reasons: 1) to illustrate the effect
of particle size on the model predictions, and 2) because
the particle size distribution for the Battelle test material
was not available and therefore the average particle size
was not known. The arithmetic average (i.e., 90 microns)
would apply only if the particles had a linear distribution
between the two sizes. It is obvious that the fit is quite
good for this particular set of data.
An isothermal reaction system was assumed
in all of the predictions. From Figure 30 one sees the
validity of this particular assumption. The non-isothermal
prediction, assuming a linear temperature profile with time.
does not deviate appreciably from the isothermal case up to
residence times of approximately 1.5 seconds. Commercial
boilers would not involve residence times much greater than
this value.
-68-
-------
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
o
o
FIGURE 26
SHRINKING CORE MODEL PREDICTIONS
MODEL......74fL PARTICLES
BATTELLE DATA..... 74 - I05fL PARTICLES
z
o
(f)
a:
ILl
>
Z
o
u
o
t:I
U
...J
-------
--- ~,-'
FIGURE 27
SHRINKING CORE MODEL PREDICTIONS
MODEL...... 74 J-L PARTICLES
BATTELLE DATA.... 74 - I05fL PARTICLES
0.30
0.28
0.26
0.24
0.22
z
0.20 0
C/)
0::
LLI
0.18 >
z
o
0.16 u
o
. '0
0.14 u
...J
-------
0.24
0.22
0.20
0./8
0.16
0.14
0.12
0.08
0.06
0.04
0.02
FIGURE 28
SHRINKING CORE MODEL PREDICTIONS
MODEL....... 74 fL PARTICLES
BATTELLE DATA.... 74 -I05fL PARTICLES
0.10
z
o
en
cr
I.&.J
>
Z
o
()
o
~
()
x BATTELLE RUN 4-17 (BB -yy)
YS02 ;::; 0.0075
y ::: 0.0004
o
o
0.2 0.4 0.6 0.8 1.0 1.2
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-71-
-------
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
FIGURE 29
SHRINKING CORE MODEL PREDICTIONS
MODEL...... 74 fL PARTICLES
BATTELLE DATA.... 74 - I05fL PARTICLES
z
o
(i)
Q:
W
>
Z
o
u
o
d
U
~
<[
z
o
.....
u
<[
Q:
LL
x BATTELLE RUN 4-17 (B-Y)
YS02 = 0.0095
y ::: 0.0004
o
o 0.2 OA 0.6 0.8 1.0 1.2 I A 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-72-
-------
0.24
0.22
0.20
0.18
0./6
0.14
0.12
0.10
0.08
0.06
0.04
0.02
FIGURE 30
EFFECT OF TEMPERATURE PROFILE
ON
THE SHRINKING CORE MODEL PREDICTION
- T = 21600R
-- - T = 2560 - 500.t (OR)
z
o
(f)
£r
I.1J
>
Z
o
u
o
t:!
U
...J
<[
z
o
....
u
<[
a::
u..
o
o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
. 73-
-------
(2)
Effect of Temperature
Over the particular temperature
range of interest in the Battelle reactor (14000F-2300°F),
the model is essentially independent of temperature. This
implies that the following two temperature functions in
the model are counteractive: (1) the temperature effect on
the gas-phase diffusivity and (2) the temperature effect on
the initial S02 mole fraction. A check of the Battelle data
plots discussed earlier supports the above observation in
that the actual dispersed-phase reactor data also did not
exhibit any apparent temperature effect other than the
low conversions at high temperatures which is evidently a
result of deadburning.
(3)
Effect of Limestone Surface Area
The limestone surface area is included
in the model with the factor S which represents the total
v
surface area of a particle per unit volume. Figure 31 ill-
ustrates the predicted effect of changing this surface area
factor. Surface to volume ratios were varied from
286,000 cm2/cc to 858,000 cm2/cc, corresponding to a B.E.T.
surface area range of approximately 20 m2/gm to 60 m2/gm.
CaO utilization varies with the square root of the surface
to volume ratio, S , in the model. Therefore, as the sur-
v
face area is increased, its effect on utilization becomes
less significant.
(4)
Effect of Particle Size
Model predictions for 50 micron par-
ticles and four different inlet gas s02 mole fractions are
given in Figure 32. A comparison of this plot with the pre-
dictions illustrated in Figure 25 for 74 micron particles
demonstrates the predicted particle size effect for a spec-
-74-
-------
,----- -
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
FIGURE 3 I
EFFECT OF TOTAL PARTICLE SURFACE
ON
-
THE SHRINKING CORE MODEL PREDICTION
(I) Sv = 286,000 CM2/cc
(B.E.T. SURFACE = 20 M2/GM)
(2) Sv = 635,000 CM2/CC
(B.E.T. SURFACE = 44 M2/GM)
z
o (3) Sv = 858,000 CM2/CC
~ (B.E.T. SURFACE = 60 M2/GM)
w
>
z
o
(.) YS02 = 0.0030
o T = 18500F
d
(.)
...J
-------
FIGURE 32
SHRINKING CORE MODEL PREDICTIONS
FOR
LIMESTONE 2061
50 MICRON PARTICLES
0.34
0.32
0.30
0.28
0.26
0.24
z
0.22 0
(f)
Ir
w
0.20 >
z
o
u
0.18 0
~
0.16 u
-oJ
«
z
0.14 0
~
u
0.12 «
a:::
LL
0.10
0.08
0.06
0.02
I y = 502 CONCENTRATION I
~~
00
O.
9
'\
'J ::: 0.0002.5
0.04
o
o 0.2 0.4 0~6 0.8 1.0 1.2
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-76-
-------
ific S02 concentration. To further illustrate the effect
of particle size, Figure 32-A shows the model predictions
of CaO utilization for a gas concentration of 0.3% S02' a
temperature of 1850°F, and residence times of 0.5, 1.0
and 1.5 seconds. One can see, therefore, that CaO utili-
zation varies inversely with the first power of particle
radius according to the existing model. Figures 33 through
35 compare the predictions for 50 micron particles with
the recent Battelle data for inlet S02 mole fractions of
0.0025, 0.00398, and 0.0099 for particles in the size
range of 44-53 microns. It is obvious that the existing
shrinking core model is also valid with respect to the
most recent Battelle data.
(5 )
Comparisons with Other Data
In order to accurately test the valid-
ity of the model with any particular set of data, complete
physical properties of the calcined limestone must have been
determined, i. e., density, porosity, tortuosity, and B.E.T.
surface area. In the recent Battelle study which utilized
limestone 2061 (Fredonia Valley White) exclusively, all ex-
cept tortuosity had been determined. For the purposes of
this study an assumed average tortuosity of 3.0 was found
satisfactory. Other existing data, however, such as that
of B & W, Ishihara, and Peabody do not include complete
physical properties of limestone calcines as a function of
time and temperature in their respective studies, thus
making an accurate test of the model an impossiblity. An
attempt was made to approximate stone properties by compar-
ison with the corresponding properties of limestone 2061,
but the results proved to be incongruous. Still another
attempt, this time to compare the OAP bench scale extended
residence time data with the model, met with little success
-77-
-------
FIGURE 32 - A
SHRINKING CORE MODEL PREDICTIONS FOR LIMESTONE 2061
EFFECT OF PARTICLE SIZE
GAS CONCENTRATION 0.3°/0
TEMPERATURE 1850°F
0.24
0.22
0.20
0.18 2
0
I-
0.16 «
N ~
...J
0.14' I- ~
::> ()~
0.12 0 1-"
d ~
U ~~
...J
0.10 « ~
z I 8~C'
0 °I\1D
0.08 I- ,$
u
«
0.06 a::
u.
0.04
0.02
PARTICLE DIAMETER, MICRONS
0
0 ro 20 30 40 50 60 70 80 90 100 110 120
-78..
-------
FIGURE :3:3
SHRINKING CORE MODEL PREDICTIONS
MODEL...... 50 fL. PARTICLES
BATTELLE DATA.... 44 - 53fL PARTICLES
0.34
0.32
0.30 X BATTELLE RUN 1123
0.28 YS02 = 0.00025 C?J"J
00
0.26 O.
~
'\
0.24
z
0.22 0
CJ)
Q:
w
0.20 >
z
0 00.
<.>
0.18 0 O~
a -:-
<.> i
0.16 ...J
<[
0.14 z
0
....
<.>
0.12 <[
Q:
1.1..
0.10
0.08
0.06 - 0 00025
'J - .
0.04 X
X~ X_X X
0.02 X X X -£ XX
0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
.-79-
-------
FIGURE 34
SHRINKING CORE MODEL PREDICTIONS
MODEL.....50fL PARTICLES
BATTELLE DATA.... 44 - 5'3J.L PARTICLES
0.34
0.32
0.30
0.28
0.26
0.24
z
0.22 0
Cf)
a::
iLl
0.20 >
z
o
u
0.18 0
o
u
0.16 ...J
«
z
0.14 0
I-
u
0.12 «
a::
LL
0.10
0.08
0.06
x BATTELLE RUN 1210
Yso2 = 0.00398
~';)
00
o.
~
"\
- 0 00025
'j - .
0.04
0.02
o
o 0.2 0.4 0:6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-80-
-------
FIGURE :3 5
SHRINKING CORE MODEL PREDICTIONS
MODEL.... 50 jJ- PARTICLES
BATTELLE DATA.... 44 - 53jJ- PARTICLES
0.34
0.32
0.30
0.28
0.26
0.24
z
o
0.22 CJ)
a:
w
0.20 >
z
o
o
0.18 0
~
o
0.16 ...J
~
0.14 z
o
t-
O
0.12 ~
a:
LL..
0.10
0.08
0.06
0.04
0.02
x BATTELLE RUN 1208
YS02 = 0.0099
OJ"
t:P
o.
~
"\
x
X ~ >,X X
~ X Xfi. X
/
X
X/
- 0 0002.5
'/ - .
o
o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
-81-
-------
and indicated that this particular model is not valid at
these extremely high residence times.
Data which are currently being
obtained from TVA power plant at Shawnee should be helpful
in validating the proposed Kellogg shrinking core model.
All other available data, however, are apparently incom-
plete with respect to the model requirements.
-82-
-------
2.
OAP Model
a.
General Model Development
In June of 1970, R. H. Borgwardt of OAP
presented a paper entitled, "Isothermal Reactivity of
Selected Calcined Limestones with S02"' at the International
Dry Limestone Injection Process Symposium (4) . In this paper,
a sorption model for a limestone removal scheme for S02 was
developed and the system parameters required by the model
for various limestone types were evaluated.
In evaluating the procedure used in the
development of the model, two inconsistencies were en-
countered: (1) the rate of reaction, as expressed in
equation (3) of the report, is only a partial representa-
tion of the reaction rate, not the total rate; and (2) the
Sg (B.E.T. surface area) term was omitted from the final
equation (equation (4) of the report). This term is re-
quired to satisfy the model development from both a theore-
tical and dimensional viewpoint. After consultation with
Mr. Borgwardt (OAP), it was agreed that these changes should
be incorporated in the development of the model.
The equation representing the dry lime-
stone sorption of S02 is:
1
-W
dnl
at
=
A -Bnl/W
o e
-E/RTC
e SO
2
11 S
g
where
A
o
=
frequency factor, em/see
CSO
2
=
gas phase concentration of sulfur dioxide,
gm mols/cc
-83-
-------
E
R
5
g
T
W
dnl/dt
e
1
n
t
B
~
=
activation energy, cal/gm mol
o
gas constant, 1.987 cal/gm mol K
2
B.E.T. surface area of the calcine, cm /gm
o
temperature, K
weight of the calcine sample, gm
=
=
=
=
=
rate of change of 503 on the solid, gm mols/sec
base of the Napierian logarithm, dimensionless
=
=
sulfate in solid as 503' gm mols
time, sec
empirical correlation coefficient, gm/gm mol
effectiveness factor, ratio of the reaction
=
=
=
rate to the rate that would be obtained if
the entire volume of the particle partici-
pated equally in the reaction, dimensionless
Additionally, it was agreed by Mr. Borgwardt
that the most useful form of this equation would be the inte-
grated form in which particle loading could be represented as
a function of time and the various system parameters. Since
the data upon which the OAP model is based were obtained in
a differential reactor, the gas concentration and reaction
temperature are essentially constant. The rate equation was
integrated with these constraints to give the following
form:
1
A
o
where
B
BL
e
-E/RT 5 C
e g 502 ~ t + K
=
K
=
constant of integration
sulfate loading
to the original
gm mols/gm
L
=
on the solid as 503' with respect
weight of calcine sample,
-84-
-------
If the loading at time zero is assumed to be negligible,
the constant of integration can be evaluated. Substi-
tuting this boundary condition, the constant becomes:
K =
1
B
Substituting for K and rearranging the equation in
of L, the following equation is obtained:
L = ~ In [-E/RT 5 C 11 BAt + 1. J
B ~ g 5°2 0 :J
terms
stants which
in Table 3.
The system parameters and empirical con-
are required to satisfy the model are given
Initial evaluation of the model consisted of
comparing the OAP bench scale loading versus time data to
the loading values predicted by the model upon substitution
of the appropriate constants. The results of the comparison
indicated that the model predictions agreed fairly well with
the graphical loading data presented by Mr. Borgwardt. A
typical comparison of predicted versus experimental 503
loading data is given in Table 4. While the correlation is
good, there is a noticeable trend for the model to predict
lower than the actual loadings. For the 52 data points in
Table 4, an average percent deviation of -17.97 is obtained.
Upon further inspection of Table 4, it was noted that these
deviations appeared to increase in a negative direction as
the time variable increased; while this trend is not evident
in the data at 980°C, the data sets for operation at 870°C,
760°C and 650°C all display the trend. Therefore, it was
assumed that the increasing negative differences between the
actual and calculated values were caused by the empirical
-86-
-------
TABLE 3
APCO HODEL SYSTEM PARAMETERS FOR DIFFERENT STONES
Act. Energy
Cal/Gm Mol
Freq. Factor(Ao)
Cm/Sec
Correl. Factor(B)
GIn/Gm Mol
B.E.T. Surface
Sq. 1>1/Gm
Effect. Factor
Dimensionless
Init. CaO
Percent
Calcining Nt. Loss
Percent
Part. Size
Mesh
Iceland S ar Colorless Near Perfect
8.50 O. 53.50 43.39
8.50 3040 9.90 0.21 53.50 43.39
8.50 1340 10.20 1.00 53.50 43.39
Translucent in Color Cr stalline 1m erfections
0.8 O. 55.50 43.15
0.70 0.85 55.50 43.15
0.70 °1.00 55.50 43.15
Limestone and Porous Few Fine Grained Gra
O. 53.40 43.67
42/65 1.60 0.79 53.40 43.67
I 150/170 1.80 1.00 53.40 43.67
00
-.J
I
Limestone and Dense Li ht Brownish Gra
. 7 54.80 43.15
42/65 12500 31. 20 480 2.10 0.74 54.80 43.15
150/170 12500 31. 20 289 2.40 1.00 54.80 43.15
Grained Granular and Porous e
0.32 30.30 47.24
42/65 19500 484.00 393 3.40 0.49 30.30 47.24
150/170 19500 484.00 303 3.90 1.00 30.30 47.24
Dolomite Grain Granular Micro orous Non-Reef T e
O. . 0 40.46
42/65 9200 2.78 300 3.90 0.63 26.50 40.46
150/170 9200 2.78 192 4.10 1.00 26.50 40.46
Calcite Banded Structure of Fibrous Ara onite
2 O. 5 .00 55.20 43.33
150/170 2 0.79 1.00 55.20 43.33
-------
TABLE 4
A COMPARISON OF THE APCO MODEL TO THE BENCH SCALE DATA
FOR A HIGH PURITY DOLOMITE, MEDIUM GRAINED GRANULAR AND POROUS, GRAY REEF TYPE
Part. Size
Mesh
150/170
Act. Energy
Ca1/GrnMol
19500
Freq. Factor (Ao)
Cm/Sec
484.00
Correl. Factor(B)
GmlGmMol
303
B.E. T. Surface
Sq. M/Gm
3.9
Effect. Factor
Dimensionless
1.00
Init. CaO
Percent
30.30
Calcining Wt. Loss
Percent
47.24
Temperature Time Actual Loading Calculated Loading Deviation Percent Deviation
0c ~ GmMols S03/Gm GmMols S03/Gm GmHols S03/Gm Percent
980 5 0.1082E-02 0.9437E-03 0.1387E-03 12.82-
980 10 0.1457E-02 0.1676E-02 -0.2196E-03 -15.07
980 20 0.2373E-02 O. 2783E-02 -0.4102E-03 -17.23
980 30 0.35801::-02 0.3610E-02 -0.3014£:-04 -0.1:J4
980 40 0.4121E-02 0.4271E-02 -0.1498;:;-03 -3.63
980 50 0.4517E-02 0.4821E-02 -0.3046E-03 -6.74
980 60 0.4621E-02 0.5293E-02 -0.6721E-03 -14.54
980 70 0.5349E-02 0.5706E-02 -0.J561E-03 -6.65
980 80 0.5870E-02 O. 6072E-02 -0.2023E-03 -3.44
980 90 0.5995E-02 0.6402E-02 -0.4074£:-03 -6.79
I 980 100 0.6702E-02 O. 6702E-02 O.3883E-06 0.00
co 980 120 0.6911E-02 0.7231E-02 -0.3201E-03 -4.63
co
I
870 10 0.8951E-03 O. 9697E-03 -0.7462£:-04 -8.33
870 10 0.9159E-03 0.9697E-03 -0.5380E-04 -5.07
870 20 0.1373E-02 0.1718E-02 -0.3444E-03 -25.06
870 20 0.1519E-02 0.1718E-02 -0.1936E-03 -13 . 07
870 30 0.1727E-02 0.2328E-02 -0. 600n-03 -34.74
870 30 0.1935E-02 0.2328E-02 -0.3921E-03 -<:0.25
870 40 0.2123E-02 0.2842E-02 -0. 7192E-03 -33.87
870 40 0.2248E-02 0.2842E-02 -0.5943E-03 -26.43
870 50 0.2498£-02 0.3287E-02 -0.7895E-03 -31.60
870 50 0.2581E-02 O. 3287E-02 -0.7062E-03 -27 36
870 60 0.2622E-02 0.3679E-02 -0.1056;::-02 -40.28
870 60 0.27891::-02 0.3679E-02 -0.3901E-03 -31.91
870 70 0.2955E-02 0.4030E-02 -0.1074E-02 -36.33
870 70 0.27891::-02 0.4030E-02 -0.1240E-02 -44.47
870 80 0.2789E-02 0.4346E-02 -0 1557E-02 -55 8'J
870 80 0.2747E-02 0.4346E-02 -0.1598E-02 -58.19
870 90 0.3122E-02 0.4635E-02 -0.1513E-02 -4J.46
870 90 O. 3164E-02 0.4635E-02 -0.1471E-02 -46.50
870 100 0.3372E-02 0.4901E-02 -~.1529E-02 -45.34
870 100 0.3413E-02 0.4901E-02 -0 1487E-02 -43.57
870 110 0.37881::-02 0.5147E-02 -0.1358E-02 -35.36
870 110 0.40801::-02 0.5147:.;:-02 -0.1067E-02 -26.15
870 120 0.3747E-02 0.5376E-02 -0.1629E-02 -43.47
870 120 0.3788E-02 0.5376L-02 -0.1537E-02 -41.90
-------
TABLE 4 (Cont 'd)
Temperature Time Actual Loading Calculated Loading Deviation Percent Deviation
OC Sec. GmHols S03/Gm GrnMols S03/Gm GmMols S03/Gm Percent
760 10 0.7494E-03 0.4654E-03 0.2839E-03 37.88
760 20 0.1290E-02 0.8733E-03 O. 4172E-03 32.33
760 30 0.1623E-02 0.1236E-02 0.3873E-03 23.85
760 50 0.1998E-02 0.1860E-02 a .1376E-03 6.83
760 80 0.2539E-02 0.2619E-02 -0.8017E-04 -3.15
760 90 0.2706E-02 0.2838£:-02 -0 .1322E-03 -.488
760 100 0.2872E-02 0.3043E-02 -0.1707E-03 -5.94
760 110 0.2955E-02 0.3236E-02 -0.2805E-03 -9.49
760 130 0.3247E-02 0.3591E-02 -0.3442;:;-03 -10.60
650 20 0.4787E-03 0.3422E-03 0.1364£-03 28.50
650 40 0.7077E-03 0.6523E-03 O. 5537I:-04 7.82
650 60 0.9783E-03 0.9358E-03 0.4253E-04 4.34
650 80 0.1020E-02 0.1196E-02 -0.1768E-03 -17.33
650 100 0.1061E-02 0.1438E-02 -0.3770E-03 -35.52
650 120 0.1165E-02 0.1664E-02 -0.4983E-03 -42.75
I 650 140 0.1207E-02 0.1875E-02 -0.6676E-03 -55.30
(X)
'"
Average Absolute Percent Deviation
Standard Deviation of Actual Loading
88.85
0.1544E-02
Standard Error of Estimate
0.4933E-02
Coefficient of Correlation
Imaginary
-------
evaluation of the constants. If, for example, the value
for the correlation coefficient, B, is raised from 303 to
450, the statistical coeffecient of correlation, r, would
be raised from 0.86 to 0.94 while the average percent devia-
tion would be lowered from -17.97 to -1.52 percent. For a
truly definitive evaluation of the proposed model in terms
of the OAP data, the constants would have to be redeter-
mined to reflect the inclusion of the B. E. T. surface effect.
Before proceeding to re-evaluate the em-
pirical model constants, it was decided to check the OAP
model predictions against the short residence time Battelle
test data to see if the same trend was indicated. Figure 36
presents the fractional conversion of the Battelle limestone,
No. 2061, versus time for two runs at fairly similar condi-
tions. The third plot represents the fractional conversion
predicted by the OAP model for a stone type of similar
composition which was given in the Borgwardt report. The
plotted results indicate an order of magnitude difference
in the calcine conversion when the model is compared to the
Battelle data. The major difference between the two results
has been postulated to be caused by the method and extent
of calcination. The data taken by OAP were obtained in a
differential balance reactor using pre-calcined stone. The
Battelle data are based upon in situ calcination of the
finely ground stone in the furnace. In the former case the
raw stone was calcined in a small rotary kiln for two hours
at 980°C (1796°F). The calcine was then crushed and
screened before charging to the reactor. In the latter
testing the raw stone was crushed, screened, and injected
into the reactor where both calcination and reaction
occurred.
-90-
-------
0.16
AT 16910F
0.14 ...J
«
I-
z
0
c::I
0.12 <..>
0
UJ
...J
0
:J:
.......
C\J
0.10 0
(J)
UJ
...J
0
~
I 0.08 z
\0 0
I-' (J)
r a:
UJ
>
Z
0
0.06 <..> BATTELLE RUN 2-18 (A-Y)
o
UJ
z b. BATTELLE RUN 3-25 (B-W)
<..> 8 BORGWARDT MODEL PREDICTIONS
...J
« FOR A SIMILAR STONE AT THE
<..>
0.04 SAME OPERATING CONDITIONS.
0.02
1::1
AT 1691°F
TIME, SECONDS
o
o
0.4
0.8
1.2
1.6
2.4
2.8
3.2
3.6
4.0
2.0
FIGURE 36
FRACTIONAL CALCINE CONVERSION VS TIME
J-'
-------
I
I --
I
One of the basic premises of the OAP
model is that reaction rate increases linearly with sur-
face area for a particular stone. Therefore, it is im-
portant to determine what effect the variation in these
testing procedures would have upon the surface area of
the reactor charge. In Boynton's book (8), "Chemistry and
Technology of Lime and Limestone", on page 148, a plot is
given of the time-temperature relationship to stone sur-
face area, which is based upon the data of Staley and
Greenfield (9) . While these data were obtained on fairly
large diameter stone, they do indicate a significant less-
ening of the B.E.T. surface area with increasing calcina-
tion time. The minimum time of calcination used in this
study was 1 hour, however, while the residence time of a
limestone particle in a furnace would be in the order of
1 to 2 seconds.
While it is known that the surface area
of calcines is extremely time-temperature dependent,
there are no known studies which investigate this effect
for systems similar to those which would be encountered in
a commercial boiler. However, a series of bench scale ex-
periments performed by researchers at TVA has shown that
the sorption characteristics of a typical limestone are
severely diminished with increasing time and temperature.
Based upon the results obtained in this study, the curves
shown in Figure 37 were developed. The curves developed
represent extrapolations of the TVA bench scale data to
the residence times of interest in a commercial system.
Since there appears to be a direct relatio~ship between
sorption rate and surface area, and since independent
research has verified the time-temperature dependency of
both these parameters, and a significant time interval
-92-
-------
(2732)
1500
NUMBERS ON CURVES ARE
LOSS OF REACTIVITY,
PERCENT.
-24 +28 MESH LIMESTONE
(2552)
1400
-
LL
(2372) ~
1300 u
o
~
1LI
a::
::::>
I ~
\0
-------
-----
I
passes before analysis, the surface areas measured may
not be the same as those which would be observed on an in
situ measurement (if one were possible). Because of
this time dependency, it may be required that samples for
surface area measurements be rapidly quenched after ex-
posure to insure a representative sample. Although a
rapid quench might also alter the measured stone proper-
ties, it is felt that such a procedure would yield the most
applicable measurement of the actual, in situ calcine sur-
face area.
Because of the time-temperature relation-
ship upon surface area caused by the calcination method
employed and its intrinsic effect upon the empirical con-
stants required in the GAP model, the proposed re-
evaluation of these constants to satisfy the adjusted
model as a predictor of the GAP bench scale data was
abandoned. For subsequent evaluation of this model, it
was decided to investigate only those systems which would
provide for in situ calcination and residence times com-
parable to those which would be experienced in a commer-
cial boiler operation. Similarly, a unique set of con-
stants would be calculated for each set of experimental
data, and then be compared for consistency with constants
derived from other sets of data.
-94-
-------
L
I
b.
Evaluation of Model Constants
Since the model developed by OAP Research
was based upon an essentially isothermal test system with
constant S02 gas concentration, the form of the model was
varied to handle the non-isothermal, varying s02 concentra-
tion systems investigated in the flow reactors of B & Wand
Battelle. The model may be defined as follows:
cL
m--
=
-E
A . RT -BL
o.e e . n.Sg.CS02
where L is defined as the loading of S02 on the sorbent in
gm mol S02/gm CaO. This term, L, replaces the earlier term,
nl/w, which was Mr. Borgwardt's expression for loading. The
equation as written is a function of five variables: t, L,
T, CS02 and Sg, and four
the following discussion
tegrated and analyzed as
system constants Ao, B, n, and R. In
the equation will be simplified, in-
a potential design model.
The first variable to be considered is Sg,
the B. E. T. surface area. While numerous studies have been
made to measure the surface areas of calcines and uncalcined
stones, no techniques are available to measure the surface
of in situ stone. Results based on surface area data which
are obtained from the product or reactant material can be
misleading owing to the severe thermal shock calcination
undergone by the raw limestone upon injection into a furnace.
This rapid calcination, coupled with the time and temp~rature
dependent structural relaxation which is undergone by the
stone after calcination, make it virtually impossible to
measure the actual stone surface area as it exists in the
reactor. Furthermore, since the residence time within the
furnace is relatively short, say 3 seconds maximum, it will
be assumed that the in situ surface area of a particular
stone will be a constant.
-95-
-------
The second variable to be considered is
CS02' the gas phase concentration of S02. First, eliminate
Cs02by replacing it with an equivalent term, YS02 . pGas
where YS02 is the mole fraction of s02 in the gas and pGas
is the molar gas density. The latter term is a function of
temperature only since the pressure effects in the system
are negligible; thus, pGas is equal to P/RT where P is the
absolute pressure in atmospheres and R is the gas constan~
The YS02 term can be related to the loading, L, through the
system stoichiometry by the relationship:
YS02
= Y
°S02
( 1- S . MW . L)
where Y is the initial mol fraction of S02' MW is the
°S02
molecular weight
stoichimoetry of
of CaO (56.08 gm/gm mol) and S. is the
the system as gm mol CaO fed/gm mol S02
fed.
The third variable to be considered is T,
the reaction temperature. By measuring the temperature pro-
file in the reactor, and establishing the gas velocity in
the reactor as a function of T and reactor geometry, the
temperature versus time profile of the flue gas can be
established. Therefore, T = F(t) for a particular reactor.
For the purpose of the following calculation, a linear pro-
file will be used for simplicity; however, any relationship
which satisfied T may be employed without affecting the
form of the solution. After elimination of the variables
T, CS02 and Sg, the rate expression may be rewritten as:
dL
-------
I - --~-----
,
relationship is obtainedt
MW:S L (eBIMW'S+l) 'In(l-MW'S'L) +
c::I:> -
- ~ &;,?sf . N:NJ = ~02 .:.Sg'Ao'T) . f (t)
C1:}
~ (B.MW.S.L-B)N
1. \: MW.S
. 1
N.N:
where
- c::I:>
f (t) =~ ~n (T:~mt) + ~( R1;~-mt;r
1
N.N:
~(~)N N:NJ
The arbitrary system constants S9' Ao and ~ cannot be iso-
lated in this form of the equation and therefore can be
combined to give a single constant K. Thus, the system is
defined...in terms of two variables t and L, three arbitrary
system constants B, E and K, three boundary conditions
YOS02' To and S, and the true constants P, Rand MW. It
should be noted that a series expansion form will result
for the time variable if any polynomial functional rela-
tionship is used to relate T to t. Use of a model in this
form is extremely difficult since the dependent variable L
is given in an implicit form rather than the normally found
explicit one. Therefore, if suitable system constants can
be obtained, the value for the loading at a particular time
would have to be determined by a trial and error procedure.
Before proceeding with an evaluation of
the model, the constants E, K and B must be determined.
In this regard, the. fOllowing published discussion is appli-
cablet ."There are two procedures for analyzing experimental
kinetic data, the integral and the differential method. . .
There are specific advantages and disadvantages to each of
-97-
-------
these methods. The integral method is easy to use and is
recommended when testing specific mechanisms, when fitting
relatively simple mechanisms, or when the data are so scat-
tered that we cannot reliably find the derivatives needed
in the differential method. The differential method may
be more useful in more complicated situations but requires
more accurate or larger amounts of data" (10) .
Ideally, therefore, the system constants
could be evaluated from the rate expression, which implies
the differential method. However, the experimental procedure
and the significant scatter exhibited by the data virtually
preclude this type of analysis. While the integrated form
is more difficult to handle from a calculational viewpoint,
the results will be significantly more reliable when applied
to a design equation. It may be argued from a mechanistic
point of view, that the loading relationship e-BL is not
correct, but rather is a simplification of the effect of
a series of kinetic resistances. However, since we are in-
terested in a design equation, the empirical relationship
should be sufficient for the purposes of this study. Fur-
thermore, a simplification of this type will avoid the
arduous solution techniques required by the mechanistic
series resistance equations which are also under consider-
ation.
Two sets of data were investigated in an
attempt to develop constants which would satisfy the OAP
model. The first data set evaluated was that of Babcock
and Wilcox (2) . In these data, the sorption of 502 by var-
ious stone types was investigated for system parameters of
residence time, loading, stoichiometry and temperature.
However, because of the nature of the system, only two
effective inlet temperatures were studies. This factor,
-98-
-------
II
coupled with the rather large degree of scatter exhibited
by the B & W data, precluded any attempts to correlate con-
stants for the OAP sulfation model.
The second data set to be evaluated was
that of Battelle (1) . The reportrd CaO utilization data
plus additive injection rate dati received from R. W.
Coutant of Battelle on March 12r 1971, were compiled and
grouped for analysis. However, one important data criter-
ion was missing, namely, the gas temperature at the stone
injection point. However, the data did provide the mean
reactor temperature and a gas temperature profile versus
reactor length. Using this information, the reported
Reynold's number, and the assumption of an equal residence
time profile around the center of the reactor, a temperature
profile versus residence time was obtained. The following
equation represents the derived temperature profile:
T = TM exp(-3.779xlO-S.Re.tl)
where TMis the reactor midpoint temperature, Re is the
Reynold's number calculated at the reactor midpoint tem-
perature, and tl is the modified residence time dictated
by the half-range formula such that tl varies from -6t/2
to +6t/2 where 6t is the reported residence time.
Since for this system, the relationship
of T to t is by an exponential rather than a polynomial
expression, an explicit relationship can be developed for
the time function in the integrated OAP model. This time
-99-
-------
function may be defined as follows:
f (t)
=
-52579 r: -5*
E.Re L:XP (-E*EXP (.3779xlO Re* 6t/2)
exp (-E.eXP(-3.779Xlo-5'Re'At/2)/RT~
/RTM)
Upon substitution into the OAP model the relationship
becomes:
1
MW.S
E(B'L)
+
n(B~
=
K
f (E,6t)
The constants Band K were evaluated by
performing a non-linear regression analysis using an assumed
value for E based on experimental values as follows:
Source
E, kcal/mol
e TVA, 1/68 monthly report
e Borgwardt, Table 1, Paducah*
paper, 9.2+26.5, 9 stone average
eIshihara, Paducah*paper, 14 runs,
range 18+50, average
16.7
14.0
28.0
eBattelle, Paducah*paper
eIshida & Wen, Paducah*paper
Average
Range
22.0
17.5
19.6
14 - 28
The results of the regression analyses are given in Table 5.
The high correlation coefficients indicate that the model
is internally consistent with the results from each individ-
ual Battelle test run, with the exception of Run 4-9. How-
ever, when an attempt was made to develop a unique set of
* Fourth International Symposium on Dry Limestone Injection
Process, Paducah, Kentucky, June 22-26 (1970).
-100-
-------
TABLE 5
VALUES OF APCO MODEL CONSTANTS
OBTAINED BY NON-LINEAR REGRESSION ANALYSIS USING THE BATTELLE DATA
Feed Activation S02
Battelle Run Stoichiometry Energy Concentration Correlation
No. (qrn CaO/gm mol S02) (cal/gm mol) ppm B K Coefficient
2-17 7.493 20,000 2770 2.959 2.738x106 0.841
3-25 10.335 20,000 3010 1.769 2.201x106 0.941
4-9 10.318 20,000 3050 1.881 1.777x106 0.381
4-16 7.382 20,000 3000 2.139 2.745x106 0.944
I 4-17 (A) 1.887 20,000 9540 18.634 1.174x101g 0.946
~ 4-17(AA) 2.392 20,000 7480 23.645 1.370x101 0.932
o 2-17 7.493 15,000 2770 2.618 3.858x105 0.848
.....
I 3-25 10.335 15,000 3010 1.109 2.762x105 0.957
4-9 10.318 15,000 3050 1.488 2.183x105 0.523
4-16 7.382 15,000 3000 2.076 3.560x105 0.956
4-17 (A) 1.887 15,000 9540 22.328 1.048x1010 0.959
4-17 (AA) 2.392 15,000 7480 24.613 2.598X10~ 0.949
2-17 thru 4-16 varies 20,000 -' 3000 1.778 2.172x10 0.774
2-17 thru 4-16 varies 15,000 ~ 3000 1.683 2.620x105 0.770
-------
constants to satisfy the total body of the Battelle data,
no significant correlation could be obtained. A second
attempt was made to correlate the grouped data by re-
gressing the Battelle runs tabulated which were made at
approximately 3000 ppm S02. This attempt succeeded and
provided a fairly high correlation coefficient of 0.77.
Since the constants developed by regress-
ion analysis are not true constants, but apparently are
dependent upon the system stoichiometry, it must be con-
cluded that either the model must be modified in some way,
or that the constants derived at the different stoichio-
metry levels are related to differences in stone proper-
ties or experimental operating conditions. The latter
possibility could reflect an abnormal experimental stone
size distribution, unusual reactor temperature profile,
or other system variations which are not evident from
the reported data. On the other hand, if these data do
give a complete representation of the system, then the
proposed OAP Research model as it is presently constituted
must be modified to satisfy the data presented by Battelle.
This modeling modification may be required
to satisfy potential reaction mechanism differences between
the bench scale data, upon which the model was developed,
and the pilot plant data upon which the model was tested.
As was discussed in an earlier section of this report,
such differences are possible due to the calcination
techniques, as well as the different residence time ranges
used by OAP and Battelle. When further data for flow re-
actors or simulated commercial systems become available,
-102-
-------
r- ----
they should be tested against the constants developed for
the Battelle data to determine concretely the applicability
of the OAP model. However, until such time as any future
data confirm or reject the present form of the proposed
model, it remains as one of the more desirable of the
proposed sulfation models because of its relative simpli-
city and adaptability to a commercial system.
~~l010-
-------
3.
Wen Model
The rate of sorption of S02 by an agglo-
merated single sphere of calcium oxide powder has been
investigated by Dr. C. Y. Wen of the University of West
Virginia. Based upon this investigation and the investi-
gations of OAP, TVA and Battelle, Dr. Wen has proposed that
the kinetics of limestone sorption can be represented by a
series resistance type model in which one or a combination
of resistances represents the rate controlling mechanism.
The "zone-reaction" model which Dr. Wen proposes defines the
relationship between the chemical reaction rate of each grain
contained in the solid particle, the diffusion rate and the
overall reaction rate. A general development for this type
of model has been presented by Ishida and Wen in several
published articles(11,12). However, a specific design
model proposed for the non-isothermal CaO-S02 reaction sys-
tem and pertinent rate constants have not been made avail-
able to Kellogg at the time of this evaluation.
In the initial analysis of the model's appli-
cability to the dry limestone process, the reaction rates
per unit concentration of S02 were plotted versus tempera-
ture, as shown in Figure 38. Table 6 is provided as a key
to the data used in Wen's studies. In the low temperature
regions, the rate is shown to be less sensitive to particle
size than in the high temperature region. This plot demon-
strates that diffusion resistances are controlling the reac-
tion at high temperatures, while in the lower temperature
region, the system is chemical reaction rate controlled.
Furthermore, the effect of particle size is demonstrated by
the increase of diffusion resistance with increasing particle
size at a given temperature.
-104-
-------
50
20
10
FIGURE 38
REACTION RATE VS TEMPERATURE
6
1100/0 SOLID CONVERSION I
~ RAW LIMESTONE
T.V.A.
181: RAW 0: CALCINED
COUTANT, 61 al.
R = 0.0045 em
(9 9 () -0-
BORGWARDT
CALCINED LIMESTONE
R = 0.0048 em
~ 0 @
WEN'S DATA
AGGLOMERATED PARTICLE
OF CALCIUM OXIDE
5
u
L&J ~,
(J)
CD 2
.-
0
E
I
t:J)
"
It)
e
0 ~,
-
It)
I 0.5
0
-
x
t\I
0
en
U 0.2
"
-
....
"d
"
X
'd 0.1
0.05
0.02
0.01
0.005
0.6
RATE CONTROLLED
BY DIFFUSION
o
0.8
1.0
1.2
I IT X 103 (OK-I)
1.4
1.6
1.8
~olO.r:-~
-------
TABLE 6
DATA KEY FOR WEN'S MODELING STUDIES
Key Stone*
C9 C
CD C
G) C
€) C
Investigator
CaO
~ (Wt. , in Calcine)
1337 55
1351 54
1343 94
1360 81
Borgwardt
e C T2 98
~ C T3 95
Ct C T4 96
() Borgwardt
C TS 58
-0 C T8 97
cp C Marl 88
D C 2061 90
t8I Coutant, et a1
R 2061 90
~
R
T.V.A.
o
o
@
C
\'len
Agglom-
erated
CaO
100
C
C
* C denotes calcined stone, R denotes raw stone
-106-
-------
Figure 39 was developed to demonstrate the
effect of diffusion upon reaction rate. This plot illus-
trates the effect of diffusion upon the overall reaction
rate at different calcine conversions for the forms of
the model which represent volumetric and grain reaction.
At initiation, where solid conversion (X) equals zero,
both models give the same curve, and the effect of dif-
fusion on overall rate is small for small values of ~v.
(~v is a Thiele modulus based upon the effective diffus-
ivity.) For the curves shown on Figure 39, the effective
diffusivity, DeA' was assumed constant. If DeA changes,
the rate representation would also change, but since no
data are available to investigate this variable, it was
decided to compare the various experimental results at
low conversions to minimize any diffusional effects.
This comparison is shown in Figure 40, where
the upper curve represents the data of Wen while the
lower curve reflects the OAP bench scale data. If the rate
is extrapolated toward zero particle radius, as rep-
resented by the horizontal dashed lines, the reaction
rate constant for the chemical reaction controlling region
may be obtained. Since s02 concentration is constant in
this region, the value of k's/R' may be calculated from
the rate data, where k's is the reaction rate constant
based on the surface area in the grain, and R' is the
radius of the spherical grain. Using this ratio, and the
function defined for the Thiele modulus (11) , an effective
diffusivity may be obtained. Furthermore, by plotting
this ratio versus the grain radius using sulfation data
of many investigators (Figure 41), Wen concludes that
the rate constant (k's) is practically independent of
particle size and is a function of temperature only. The
-107-
-------
0.5
~
u 0.2
LLI
IL.
LL
UJ
Z
LLlO
~ (j) 0.1
a::~
...J~
~
~::>
~ 0 0.05
::r:
~
::
LLI
~
-------
FIGURE 40
REACTION RATE VS PARTICLE SIZE
-------
1'00/0 SOLID CONVERSION I
WEN'S DATA
AGGLOMERATED PARTICLE
OF
CALCIUM OXIDE
T = 700°C
3
2
0.5
-
u
w
en
~ fdv = 1.66
o
E
I
CI
"-
~E BORGWARDT
~ CALCINATED LIMESTONE
10
b
TYPE 4
T = 980°C
0.2
X
N
o
(/)
U
"-
-
-
'C
"-
X
'C
-
RADIUS OF PARTICLE, R (cm)
0.1
0.002
0.005
0.01
0.02
0.05
0.1
0.2
-109-
2
u
w
en
0.5
Q)
-"
o
E
I
t:J)
"-
~
E
o
-
0.2
f
o
x
0.1
N
o
(/)
U
"-
-
-
'C
"-
X
'tJ
-
0.05
0.02
0.01
0.5
-------
-
(.)
w
en
CD
....
o
E
I
CII
~1
o
-
It)
I
o
x
-
a::
.....
'"
~ 0.3
FIGURE 4 I
REACTION RATE CONSTANT VS GRAIN RADIUS
7
3
1100/0 SOLID CONVERSION ,
T = 980°C
CaO: 54 ,..., 100%
<9
G
E!)
e
KEY: SEE TABLE 6
0.1
0.03
0.1 0.3
RADIUS OF GRAIN, R' X 104 (cm)
2
-110-
-------
1__-
same conclusion is demonstrated on Figure 42
Arrhenius approach, i.e., a plot of reaction
versus reciprocal absolute temperature.
by a standard
rate constant
As of this writing, the reaction modeling by
Dr. Wen is continuing. The grain reaction model which he
proposes appears to answer many of the questions which
arose over the order of magnitude deviations in reaction
rate data of OAP and Battelle. Present efforts by Dr.
Wen involve the modeling of the calcination of the raw
limestone, and integration of the calcination reaction
and sulfation reaction models into a single non-isothermal
model to simulate the design conditions which would exist
in a commercial boiler system.
-111-
-------
FIGURE 42
ARRHENIUS PLOT
10
5 .1100/0 SOLID CONVERSION I
G
I)
2 @
e I) AVERAGE LINE
/Ek's = 17.5 Kcal/g-moLe
D@
Ei)
-
(,) 0.5
LLI
(J)
CD
-' ~
0
E
I
CI 0.2
......
v
E
(,) - WEN'S DATA
-
(J) 0.1 ~
-oX:
0.05
,.,0.02
0.01
KEY: SEE TABLE 6
0.005
0.6
0.7
0.8
0.9 1.0 1.I 1.2
lIT X 103 (oK-I)
1.5
-112-
1.3
1.4
-------
4 .
M.I.T. Model
The proposed MIT model represents a solution
of a series resistance type approach to the sorption of 802
by calcines. A report published by Dr. J. B. Howard and co-
workers at MIT(13) presents a discussion of the development
and testing of this model. The model includes the follow-
ing steps: mass transfer from the ambient gas to the par-
ticle, diffusion and reaction within the pores of the par-
ticle, and solid diffusion within the calcium oxide grains.
To represent the internal structure of the calcine particle,
a simple geometric model was developed.
In order to evaluate the accuracy of the pro-
posed MIT model, the model's constants had to be evaluated.
This was accomplished in studies at MIT by the simultaneous
solution of the partial differential equation representing
the previously discussed series resistances. The solution
method presented in the MIT report employs a finite differ-
ence technique. and requires a computer solution. In this
manner, the model calculated values for the pore diffusion
coefficient, reaction rate constant, solid diffusional co-
efficient and the effective structural properties of the
calcine. The data used in the development of the model
constants are those which were published by Mr. Borgwardt
of OAP(14). Using the OAP bench scale data, the con-
stants shown in Table 7 were developed to represent the
sorption characteristics of "Calcine 9", a calcitic dolo-
mite (70% dolomite, 18% calcite). These particular con-
stants are the only ones presented in support of the
model by the MIT report.
In an attempt to verify the development of
the MIT model constants, and to obtain constants for the
-113-
-------
TABLE 7
THE EFFECT OF TEMPERATURE ON REACTION PARAMETERS
AND EFFECTIVE STRUCTURAL PROPERTIES OF CALCINE 9
Temperature, of 1796 1598 140"0 1202
Pore Diffusion Coefficient, cm2/sec 0.23 0.21 0.20 0.18
I Reaction Rate Constant, em/see 27.5 5.5 0.78 0.067
I-'
I-' Solid Diffusion Coefficient, cm2/sec x 1010 0.87 0.073
~ 1.12 1.00
I
Effective Surface Area per Unit Volume, cm-1 x 10-6 0.235 0.765 6.52 199
Effective CaO Grain Radius, em 0.7 0.5 0.1 0.02
-------
other calcines studied by OAP, the MIT modeling procedure
was adapted to the Kellogg Laboratory IBM-ll30 computer.
However, considerable difficulty was encountered in this
endeavor due to the size of the program's calculational
matrix. The original MIT modeling program was developed
for use on an IBM 360-65 machine and utilizes some 88,000
programming words. The Kellogg machine has only 5,500
words available for use, thus necessitating a decrease in
the time and space steps required by the iterative solu-
tion. One further problem arose in attempting to simu-
late the MIT program on the smaller machine, viz., a loss
of calculational precision. The IBM-360 uses 12 signifi-
cant figures to represent a number, whereas the 1130 com-
puter uses only 6. In the finite difference calculational
technique, the determining factor for a solution is the
representation of the slope of a function by the differ-
ence between two adjacent values. Because of the two
computing limitations encountered, a suitable representa-
tion of the MIT model could not be made on the Kellogg
Laboratory computer.
Since the MIT model constants presented in
their final report were for only one of the 11 calcines
studied by OAP, and since the bench scale experimental
data may not sufficiently describe the mechanisms en-
countered in a commercial boiler system, no judgments as
to the accuracy of the proposed MIT model can be made at
this time. The Kellogg effort to study the MIT method of
analysis for other sets of experimental data has been lim-
ited by the lack of sufficient computer size. Since
other experimental models using the series resistance
technique are being investigated, further work on the MIT
-115-
-------
modeling procedure has been discontinued. Should the
other proposed models prove insufficient in their descrip-
tion of the process system, further system analysis may be
required using the more complex MIT modeling.
-116-
-------
D.
Calcination Studies
1.
Particle Heat-up Calculations
Particle heat-up time was estimated by making
a heat transfer calculation on a single calcine particle.
This calculation consisted of an isothermal heat balance
around the particle, i.e., it was assumed that no tempera-
ture gradient exists throughout the particle itself. The
following heat balance was used:
Accumulation
=
input - output + generation
The differential accumulation term for a spherical particle
of diameter Dp is
Accumulation
= (11'~p3) f'p cp (~ :,
where
=
particle density, lb/ft3
solid specific heat, Btu/lb, of
particle temperature, of
time, hr
pp
cp
Tp
e
=
=
=
Heat input to the particle occurs by convec-
tion and is given as follows:
qc
=
hc ( ""'Dp2) (Tg - Tp)
where
=
convective heat, Btu/hr
convective heat transfer
gas temperature, of
coefficient, Btu/hr, ft2, of
qc
he
Tg
=
=
-117-
-------
The output term in the heat balance equation is represented
by radiation heat loss terms. In the system considered,
there are two radiation terms--(l) radiation between the
particle and the steam-jacketed boiler wall, and (2) rad-
iation between the particle and the furnace flame. The
two radiation terms are additive, and are thus lumped into
one radiation heat loss term as follows:
qr
=
hrw (11' Dp2) (Tp-Tw) + hrf (1'f Dp2) (Tp-Tf)
where
Tw
Tf
=
radiation heat, Btu/hr
wall radiation heat transfer coefficient,
Btu/hr, ft2, OF
flame radiation heat transfer coefficient,
Btu/hr, ft2, of
wall temperature, of
flame temperature, of
qr
hrw
=
=
hrf
=
=
The generation term in the heat balance equation represents
the heats of reaction and is assumed to be zero. The basis
for this assumption lies in the fact that the decomposition
of the carbonate is endothermic while the reaction of 502
with CaO is exothermic. Thus the heats of reaction tend to
cancel each other.
with the above assumptions, the heat balance
equation for a single particle becomes
~ = ( ppc:OP2) [NU kg(Tg-Tpl
- hrwDp(Tp-Tw)
- hrfDp (Tp-Tf)]
-118-
-------
where
'I
I
kg
Nu
=
thermal conductivity of the gas (assumed
to be pure N2)' Btu/hr, ft2, 0F/ft
=
Nusselt number
Other terms as previously defined
The above equation was programmed on the Kellogg IBM 1130
computer. The variation of the gas temperature, Tg, was
assumed to be linear with respect to time, the relationship
of which was obtained from the Battelle project report of
June 30, 1966(15). The following conditions were used in
obtaining a solution to the differential heat balance
equation:
1.
2 .
3.
4.
5.
Particle injection temperature = 150°F
Gas temperature at the injection point =
Wall temperature was assumed constant at
Flame temperature was assumed constant at
kg and Cp were programmed as functions of
and Tp, respectively
hrw and hrf were programmed as functions
pp was assumed constant at 102.9 lb/ft3
(porosity = 0.45 cc/cc)
of Tp
24000F
700°F
3000°F
Tg
6.
7 .
Figure 43 illustrates the Kellogg computer
solution graphically showing particle temperature as a
function of time for particle diameters of 44, 74 and 100
microns. As would be expected, the heat-up time increases
with increasing particle size, e.g., the heat-up time for
44 micron limestone particles is approximately one-third
that for 100 micron particles. The effect of the Nusselt
number on heat transfer has also been determined, and it
-119-
-------
also is shown on Figure 43 that i~creasing the Nusselt
number by a factor of ten (from 0.2 to 2.0) approximately
halves the particle heat-up time. Even for 100 micron
particles, however, the heat-up time of 0.07 seconds is
small compared to the actual total residence time of
approximately one to two seconds available in a boiler.
It is, therefore, reasonable to assume that particle
heat-up time is not a limiting factor in the overall
limestone sulfaction reaction.
-l~O-
-------
FIGURE 43
PARTICLE HEAT-UP TIME FOR LIMESTONE
2600
44f-L 74 f-L
~~:>O
u.. 100 f-L
o
2200
2000
1800
1600
: ~ JO
1200
- Nu = 0.2
1000 --- Nu = 2.0
800
400
200
TIME, SECONDS
o
o
0.'01
0.02
0.03
0.04
0.05
0.06
0.07
-121-
-------
2.
Deadburning Studies
Studies aimed at evaluating the degree of
deadburning of limestones and dolomites were published by
Dr. Drehmel of OAP(16). It previously had been noted
that as limestones are calcined for longer times and at
higher temperatures, they lose reactivity and experience
a shrinkage in volume along with a loss of surface area
and porosity. In this study, Limestones No. 2061 and
No. 2062, and Dolomite No. 2069 were calcined in a rotary
kiln for two hours at temperatures of 1700, 2000, 2300,
2600 and 3200oF. The resultant calcined samples were sub-
sequently analyzed for B.E.T. surface area, density, por-
osity, distribution of pore volume, and median pore size.
Along with physical property measurements, the following
chemical reactivity experiments were conducted on the
calcines:
1. Absorption of sulfur dioxide from flue gas
2. Absorption of sulfur dioxide from pure S02
3. Absorption of carbon dioxide
4 . Absorption of steam
5. Modified coarse-grain acid titration
6. Hydration-weight gain.
Table 8 is a typical example of the results
obtained in OAP's published study. As expected, density
increased with increasing calcination temperature, while
B.E.T. surface area, pore volume, and chemical reactivity
each decreased. It can be noted from Table 8 that except
for C02 absorption, all of the physical properties tested
-122-
-------
TABLE 8
PROPERTIES OF LIMESTONE NUMBER 2061
SET I, 70/140 MESH PARTICLE SIZE RANGE
Calcine Tem~eratureb of
1700 2000 2 00 26 0 3200
Flue Gas Absorption 8.6 5.9 2.5 1.6 1.0
18000F, 2 min, mg/30 mg
Pure S02 Absorption* 66.0 40.7 21.9 10.4 8.0
18000F, 30 min, , gain
Pure C02 Absorption* 37.4 8.7 5.8 2.6 1.7
1400oF, 60 min, , gain
Steam Absorption 29.7 22.5 12.5 10.8 7.2
500°C, 5 min, , gain
B.E.T. Surface Area 3.1 1.6 1.0 0.8 0.3
m2/g
Total Pore Volume 0.61 0.51 0.33 0.25 0.33
cc/g
Small Pore Volume 0.28 0.14 0.09 0.04 0.04
cc/g
Density by Mercury 2.82 2.44 3.23 3.34 3.30
Intrusion, g/cc
*'Note: Listed values for 140/200 mesh
-123-
-------
plus the reactivities change in approximately the same
manner between successive calcination temperatures. C02
absorption drops sharply at 2000°F, and this behavior has
been attributed to the shrinking, melting, and fusing of
the crystals, thus obstructing carbon dioxide penetration
into the lime(17).
1-
The following conclusions regarding parameter
effects on limestone reactivity were drawn from this partic-
ular study:
1.
C02 absorption was
particle size, but
slightly lower for
size ranges.
nearly independent of
802 absorption was
the largest particle
2.
C02 absorption was affected drastically
by calcination temperature, but 802 absorption
was not.
3.
Both C02 and 802 absorption were independent
of gas tlow and weakly dependent on reaction
time.
A statistical analysis by Dr. Drehmel supported the fact
that the loss in surface area and pore volume at higher
calcination temperatures accounted for the loss in reac-
tivity. No explicit conclusion concerning an optimum temp-
erature of limestone injection is obvious from this study.
From Table 8, however, it appears that the best calcination
temperature lies somewhere between 17000F and 2000°F. In
order to allow sufficient time for sulfation to occur, the
overall optimum injection temperature would probably be
clos~r to 2000°F.
-124-
-------
3.
Battelle Calcination Data
The calcination results discussed in this
section are obtained from the data presented in the
Battelle final project report (1) . Figure 44 is a plot of
the Battelle data for Limestone No. 2061, and shows the
percentage calcination as a function of gas residence time
over the temperature range l604°F to 2068°F. Curves A, C
and D represent calcination data for -140+200 mesh par-
ticles (74-l05~). Curve B illustrates the data for
-270+325 mesh particles (44-53~) calcined at a gas temp-
erature of l770°F. Battelle originally reported data for
the -140+200 mesh particles at a temperature of l770°F;
however, in their final report they stated that this par-
ticular set of data is unreliable. Hence, while there is
no direct effect of particle size derivable from the data,
interpolation of the above curves would indicate a very
minor effect.
The initial rate of calcination evidenced
from the initial slope of the above curves, increases with
increasing gas temperature as expected. The extent of
calcination at a reactor residence time of two seconds
ranges from about 70% to about 90% in the temperature range
of l600-2068°F. It should also be noted that the curves
extrapolate to a residence time of approximately 0.1 second
at zero conversion of the stone. This value is in good
agreement with a particle heat-up time of 0.07 seconds
which was estimated from heat transfer calculations.
Some recent Battelle experimental studies
presented in their monthly project reports to OAP (Sept.
1970 to Nov. 1970) also were reviewed. The results of
-125-
,
-------
1----- - -------.
100
....
Z
iLl
o
90 a:::
iLl
Q..
....
80 :z:
(,!)
UJ
3:
70 ~
z
o
60 ~
z
o
...J
-------
calcination tests carried out with -270+325 mesh (44-53M)
Limestone No. 2061 are summarized in Table 9. The flow
reactor inlet and outlet gas temperatures are listed along
with the average gas residence time. The measured extent
of calcination cannot be compared directly with the earlier
plot of data (Figure 44), because of the different particle
size and non-isothermal reactor profiles. The most signi-
ficant aspect of the recent Battelle work is that B.E.T.
surface area determinations have been made on stones cal-
cined under short residence time conditions.
The surface
2
area values tabulated generally range from 20 to 60 m /gm '
CaD. This range is significantly higher than the values of
1 to 10 m2/gm CaD reported by DAP(4) and TVA(18) from
bench scale tests involving longer calcination times, i.e.,
1 to 120 minutes, which illustrates the potential problem
of decreased intraparticle surface area and loss of reactiv-
ity due to deadburning. The data of Table 9 do not exhibit
any obvious correlation with residence time: however, there
does appear to be a loss of surface area at high injection
temperatures (>2000°F) coupled with the higher residence
times.
The results of additional limestone calcination
measurements from the recent Battelle monthly reports for
simultaneous calcination-sulfation tests in their dispersed-
phase reactor are shown in Table 10. The most interesting
observation from the data is the fact that the percentage
calcination at low residence times with in situ sulfation
of the calcine is much greater than indicated by Figure 44.
For example, 58-65% calcination is indicated for a 1900-
20000F injection temperature and 0.2 second gas residence
time, whereas the above cited plot would predict about
-127-
-------
TABLE 9
BATTELLE CALCINATION DATA (NO 502 PRESENT)
LIMESTONE NO. 2061
PARTICLE SIZEs -270+325 MESH (44-5311)
Gas Temperature Residence Percentage Surface
~ Collection Time Calcination Area
(wt. %) (m2/gm CaO)
F ~ (seconds)
- -
1830 1440 1.82 73.0 61.3
1830 1765 0.23 19.0 44.2
1849 1782 0.18 45.0 42.9
1920 1500 1.35 78.0 36.6
1996 1920 0.17 28.0 67.8
2156 2073 0.16 45.0 66.7
2224 1440 2.86 86.0 21.3
2224 1765 1.27 83.0 21.3
2243 2156 0.15 40.0 52.9
2243 1500 1.99 85.0 7.6
-128-
-------
TABLE 10
BATTELLE CALCINATION DATA (IN SITU SULFATION)
LIMESTONE NO. 2061
PARTICLE SIZE: -270+325 MESH (44-53 M)
Residence Percentage
Time Calcination
(seconds) (wt. %)
-
1908 1842 0.17 58.0
1974 1567 1.28 88.0
2046 1974 0.16 65.0
2197 2120 0.15 71.0
2277 2197 0.15 72.0
2277 1567 1.90 95.0
-129~
-------
30-40%. One possible explanation for the increased cal-
cination rate in the presence of 802 is offered by Ishida
and Wen (Univeristy of West Virginia) who postulate that
it is caused by the exothermic heat of sulfate formation.
It appears that this question does merit further study.
Effect of injection temperature on surface
area of the calcines is illustrated in Table 11 taken
from a recent Battelle project report. Battelle has tak~n
three different limestones and injected them into a pilot
reactor at three different temperatures while maintaining
the gas residence time approximately constant. Inspection
of Table 11 reveals that with respect to surface area,
the optimum injection temperature appears to be approxi-
mately 2000oF. This result is consistent with other
studies discussed in this section of the report. It should
also be noted that different stones (IG8-4 and No. 1336)
yield similar surface areas at the optimum injection temper-
ature whereas significant difference exist at other in-
jection temperatures. In all cases shown in Table 11
marl has much less area than the other stones, possibly
indicating that it dead burns easier than the other stones.
-130-
-------
....
TABLE 11
EFFECT OF INJECTION TEMPERATURE ON SURFACE AREA
Residence
Stone Temperature Time Percentage Area
Run Type (a) Injection Collection (seconds) Calcination m2/gm(b)
317-A Mich. Marl 2155 1785 1.17 66 7.5
317-B IGS-4 2155 1785 1.17 80 16.3
j17-C No. 1336 2155 1785 1.17 83 23.7
I
,...... 318-A Mich. Marl 2006 1712 1.03 52 13.6
"'"
I-' 318-B IGS-4 2006 1712 1.03 72 24.8
I
318-C No. 1336 2006 1712 1.03 71 26.4
318-D Mich. Marl 2263 1828 1.14 74 5.9
318-E IGS-4 2263 1828 1.14 81 8.2
318-F No. 1336 2263 1828 1.14 84 14.1
(a) -140+200 mesh
(b) area per gram of sample
-------
~
I
4.
T.V.A. Calcination Data
Extensive bench scale experimental studies
of limestone calcination rates have been carried out by
the TVA Fundamental Research Branch. The work entailed
fixed bed studies of limestone calcination at long resi-
dence times (1 to 30 minutes) in an inert gas atmosphere.
The TVA final correlation of the calcination reaction
rate is presented in their October 1969 monthly project
report to OAP. The correlation equation was used to cal-
culate Table 12, which gives the time required for 75%
calcination for different particle sizes and gas temper-
atures. An assumed activation energy of 30 kcal/gm mole
is incorporated into these calculations. The results do
indicate that for an average particle diameter less than
100 microns, and a gas temperature of 1900°F or greater,
the time required for 75% calcination will be under 0.20
seconds. The TVA correlation yields a higher predicted
percentage calcination at low residence times than the
plot of the Battelle calcination data. However, the dis-
crepancy may merely reflect a loss of accuracy inherent
in extrapolating the TVA bench scale data to much lower
residence times (less than 1 second).
The principal conclusion from the analysis
of both the Battelle and TVA data is that at least 40%
stone calcination can be achieved in 0.2 second residence
time .in a boiler with a minimum injection temperature of
1900°F. Also, as Battelle(l) point out, the sulfation
reaction apparently begins immediately upon injection of
the stone into the reactor which, coupled with the in-
creased calcination rates obtained in the presence of 802'
indicates that the calcination step does not appear to
be critical in the overall sulfation process, and detailed
-132-
-------
TABLE 12
TVA CALCINATION CORRELATION PREDICTIONS.
ACTIVATION ENERGY 30 kcal/qm mole (Assumedl
Particle Time Required (Seconds) For 75' Calcination At
Size Indicated Temperature
(microns) 18320F 20120F 20190F 23700F
57 0.14 0.061 0.029 0.015
99 0.24 0.10 0.049 0.025
161 0.41 0.17 0.081 0.042
. TVA Monthly Project Report to OAP
(October 1969)
-133-
-------
kinetic modeling of the limestone calcination reaction
does not appear to be justified at this time. Prelimi-
nary surface area measurements from the Battelle flow
reactor indicate an optimum additive injection point
corresponding to a gas temperature range of 19000F to
2l00oF. The most useful aspect of future experimental
-studies of limestone calcination would appear to lie in
the analysis of parameters that control the particle
surface area to pore volume characteristics.
-134-
-------
E.
Gas-Particle Mass Transfer
1.
Kello9g Calculations
A relationship describing the mass transfer
of sulfur dioxide can be derived by utilizing the j-factor
analogy between heat and mass transfer as follows:
In the case of heat transfer, the j-factor is defined as
jn
==
Nu
Re pr
(pr) 2/3
where
Nu
Re
=
Nusselt Number
Reynolds Number
Prandtl Number
==
Pr
=
By a direct analogy to heat transfer, the mass transfer
j-factor can be expressed as
jM
==
Gz' (Sc) 2/3
Re Pro
where
Gz'
==
Modified Graetz Number
Zenz and Othmer(19) give an expression for the modified
Graetz Number for the case of fluid flow around a sphere as
Gz'
=
11'Dp Mm Pm Kq Cp
kg
-135-
.'~
-------
where
Dp =
Kg =
Pm =
Mm =
cp =
kg =
Particle diameter
Overall mass transfer coefficient
Mean pressure of non-transferring gas
Mean gas molecular weight
Specific heat of non-transferring gas
Thermal conductivity of non-transferring gas
An expression for the mass transfer coefficient is obtained
by solving the above equation for Kg:
Kg
Gz' (~p)J 1fD/ Mm Pm)
=
Equating the j-factor equations then results in an express-
ion for the modified Graetz Number, from which a numerical
value may be obtained for use in the above equation to
find the mass transfer coefficient:
pressed as
Gz'
(pr)2/3
Nu -
Sc
=
The rate of mass transfer of S02 is now ex-
Nt
9
;; (Kg At) PS02 de
=
Nt
18 (' 6 W )
o Kg f'p D; PS02 de
=
-136-
-------
where
Nt = Rate of S02 transferred
At = Total external surface area of all particles
PS02 = Local partial pressure of S02 in the gas
a = time
Wp = Weight rate of solids injection
pp = particle density of calcine
After substituting the previously derived expression for
the mass transfer coefficient, Kg, into the above equation,
the final relationship describing the rate of mass trans-
fer of S02 is
Nt = [zo (~p)g (~~J
( 6 Wp)
1TD2
P p
PSO de
2
This equation is the same as that used by Battelle (15)
their mass transfer calculations.
in
Based on the above relationship, mass transfer
calculations were made assuming that the caO-S02 reaction
is relatively fast compared with the diffusion of sulfur
dioxide through the inert gas. Sulfur dioxide conversion
in a typical stack gas (0.3 mole percent S02) was calculated
as a function of the stoichiometric Ca/S ratio using a typ-
ical limestone additive (94% CaC03' 45% porosity). The
active boiler injection zone for the desulfurization re-
action was assumed to have an average temperature of l600°F
and to provide a gas residence time of 2.0 seconds. Re-
sults of this calculation are presented on Figure 45 for
particle sizes of 44 microns (325 mesh), 74 microns (200
mesh) and 100 microns (140 mesh). The calculated conver-
sion increases with Ca/S ratio since more total particle
-137-
-------
~ 40
w
u
c::
I.LJ
a..
~
z
o
U; 30
c::
I.LJ
>
Z
o
u
C\J
~ 20
FIGURE 45
S02 CONVERSION VS STOICHIOMETRIC CaO
FOR
-
VARIOUS PARTICLE DIAMETERS
60
50
CALCULATION BASES
LIMESTONE = 94% CaO
POROSITY = 0.45 cc/cc
NUSSELT NO = 0.2
RESIDENCE TIME = 2 SECONDS
AVERAGE TEMPERATURE = 16000F
FOR CaO/S02 = I MOLE/MOLE,
FLUE GAS/LIMESTONE = 168 LB/LB
10
44fL (-325 MESH)
74?- (-200 MESH)
100}-L (-140 MESH)
o
o
100 200 300 400
STOICHIOMETRIC CaO INJECTED, PERCENT
500
-138--
-------
TABLE 13
GAS-PARTICLE MASS TRN~SFER CALCULATIONS
Stone
CaO Injection Flue Gas Skeletal Particle Stoich. Average Residence 502
Content Rate Rate D D Porosity Densit~ Densit) CaO Temp. Time Conversion
Stone (wt. %) (1b/hr) (lb/hr) .& (ftx~04) (cc/cc) (lb/ft) (lb/ft) % Nu (OF) (see) (%)
Dolomite 54 115,526 1.08xl07 74 2.43 0.56 187 82.3 100 0.2 1600 2 5.2
n 54 115,526 1.08xl07 74 2.43 0.56 187 82.3 100 0.2 900 2 3.5
54 115,526 1.08xl07 74 2.43 0.56 187 82.3 100 0.2 1600&900 4 8.7
54 115,526 1.08x107 74 2.43 0.56 187 82.3 100 2.0 1600 2 51.9
54 115,526 1.08x107 74 2.43 0.45 187 102.9 100 0.2 1600 2 4.1
II 54 115,526 1.08x10'l 74 2.43 0.56 212 93.4 100 0.2 1600 2 4.6
54 231,052 1.08x107 74 2.43 0.56 187 82.3 200 0.2 1600 2 10.4
54 346,578 1.08X104 74 2.43 0.56 187 82.3 300 0.2 1600 2 15.6
I 54 115,526 1. 08x10 100 3.28 0.56 187 82.3 100 0.2 1600 2 2.9
f-'
w 54 231,052 1.08x107 100 3.28 0.56 187 82.3 200 0.2 1600 2 5.8
'"' ,. 54 346,578 1.08x101 100 3.28 0.56 187 82.3 300 0.2 1600 2 8.7
I
54 115,526 1.08x107 44 1.44 0.56 187 82.3 100 0.2 1600 2 14.2
54 231,052 1.08x107 44 1.44 0.56 187 82.3 200 0.2 1600 2 29.4
54 346,578 1.08x107 44 1.44 0.56 187 82.3 300 0.2 1600 2 44.1
Limestone 94 66,366 1.08x107 74 2.43 0.45 187 102.9 100 0.2 1600 2 2.4
n 94 132,732 1.08x107 74 2.43 0.45 187 102.9 200 0.2 1600 2 4.8
94 199,098 1.08x107 74 2.43 0.45 187 102.9 300 0.2 1600 2 7.2
94 66,366 1.08x107 100 3.28 0.45 187 102.9 100 0.2 1600 2 1.3
94 132,732 1.08x107 100 3.28 0.45 187 102.9 200 0.2 1600 2 2.6
94 199,098 1.08x101 100 3.28 0.45 187 102.9 300 0.2 1600 2 3.9
94 66,366 1.08x107 44 1.44 0.45 187 102.9 100 0.2 1600 2 6.8
94 132,732 1.08x107 44 1.44 0.45 187 102.9 200 0.2 1600 2 13.6
94 199,098 1.08x107 44 1.44 0.45 187 102.9 300 0.2 1600 2 20.4
-------
I:
[
surface is available at higher' additive injection rates.
However, the results do indicate extremely low potential
502 conversions (6% maximum) at practical additive rates
(100-250% stoichiometric Cao/502) for a standard 140-200
mesh particle size range. The curves also illustrate
the substantial benefit attainable from fine grinding to
325 mesh if mass transfer were the controlling mechanism.
[ [
Table 13 illustrates the effect of a few of
the parameters on overall 502 conversion. The parameters
involved include particle porosity, skeletal density,
particle density, stoichiometric ratio, particle diameter,
and CaO content of the stone. From the equation utilized,
overall 502 conversion is directly proportional to the
stone injection rate and inversely related to both particle
density and the square root of particle diameter. It is
interesting to note that these mass transfer calculation
results differ from those obtained when the shrinking core
model is used in that the latter shows utilization varying
inversely as the first power of the particle diameter.
The calculations shown for the dolomitic stone assume that
the MgO content is not reactive with 502 under boiler
conditions in accordance with the Battelle results (20) .
The specific dolomite and limestone used for this case
are stone types 1351 and 1343, respectively, taken from
Borgwardt's published studies (14) . A flue gas rate of
5,400 tons/hr and a sulfur dioxide mole fraction of
3xlO-3 were used as assumed in the Battelle mass transfer
predictions (15) .
A major limitation in the accuracy of the
above calculational results exists because of a lack of
basic heat transfer data for gas-to-dilute dispersions of
solid particles in a small size range (10M-100~). A good
discussion of the problem, including available background
information, is presented in the literature (19) . The im-
plications of this problem and inherent related calcula-
tional uncertainties when applied to The Dry Limestone
-140-
-------
I
I
I
Process are presented and discussed below.
A substantial number of experimental studies
have been carried out to determine heat and mass transfer
to single spherical particles suspended in flowing gas
streams. Unfortunately, there are very few analogous in-
vestigations which tested very dilute dispersions of par-
ticles, i.e., bed voidage greater than 99%. The most per-
tinent published study. appears to be the work of Johnstone,
et al(21) on heat transfer to clouds of particles. In
this particular investigation, measurements of the tempera-
ture rise of particles falling through a stagnant gas (air
or C02) were made. The particle size range of 326M-545M
was evaluated for the test materials, viz. sand, aloxite
and carborundum.
I'
I
I
I
The results of the published study are shown
in Figure 46 as a plot of the average particle Nusselt
Number versus the average particle Reynolds Number. The
Johnstone data include Reynolds Numbers ranging from 10
to 100 with a corresponding Nusselt Number range of 1 to
10. The dashed curve shown on the plot represents a
somewhat arbitrary extrapolation of the data to a Reynolds
Number of 1.0. Also shown on this figure is a generalized
correlation for heat transfer to single spherical parti-
cles(19), which approaches an asymptotic Nusselt Number of
2.0 at very low Reynolds Numbers. It is apparent that the
Johnstone study of heat transfer to dilute dispersions re-
sulted in particle-to-gas convective heat transfer coef-
ficients which are an order of magnitude lower than pre-
dicted from the accepted correlation for single spheres.
The literature tends to rationalize this discrepancy as
the result of interparticle hindrance effects, which
appears to be a plausible explanation.
-141-
-------
X 3
I
9
8
7
6
5
4
2
I
9
8
7
6
5
4
I
n
3
X
L
I,
I
I
FIGURE 46
HEAT TRANSFER TO CLOUDS OF PARTICLES IN AIR
/'
0/
/
/
/
,/
/'
,/
,/
,/
"
/
'"
,."
..",.
.JIC
.......
Q.
a
&.
..
o
z
~
LLI
CJ)
CJ)
~
Z
LLI
...J
(.)
~
a:
-------
For comparison purposes, Table 14 was pre-
pared showing solids concentrations and particle Reynolds
Numbers for the Johnstone data, Battelle reactor data and
predictions for the full-size boiler at Ca/S ratios of 1.0
and 2.0. The calculated particle Reynolds Number is based
on the slip velocity as calculated from a published equa-
tion(22). There are valid questions concerning the accur-
acy of this slip velocity correlation in a multiple par-
ticle system. Nevertheless, the calculated Reynolds
Number for the Battelle reactor conditions and commercial
boiler will be about unity. It is thus apparent that a
major extrapolation of existing data will be required to
predict heat transfer coefficients in the Battelle reac-
tion system or the commercial injection system.
Table 14 illustrates an important difference
in the comparison between various reactor systems. It is
noted that the concentration of particles in the Battelle
dispersed-phase reactor (5,700 particles/cu ft) is apprec-
iably lower than in the Johnstone study (476,000 particles/
cu ft) or the commercial boiler design (146,000-292,000
particles/cu ft). The low density in the Battelle reactor
reflects the fact that a much lower additive injection
rate was used (approximately 7-14% stoichiometric Ca/S)
than that required in the full scale installation. The
Kellogg predictions of mass transfer in the boiler system
utilized a low coefficient, corresponding to a Nusselt
Number of 0.2, to offset uncertainties in the Johnstone
data extrapolation. If the Nusselt Number is influenced
by particle density and hindrance effects as postulated
earlier, it is possible that transfer coefficients in the
Battelle reactor could approach the single particle corre-
lation, and thus be an order of magnitude higher than val-
ues predicted for the commercial design. The importance
-143-
-------
TABLE 14
COMPARISON OF SOLIDS CONCENTRATION
A B C D
Particle Diameter, ,q 326 90 74 74
Gas Velocity, ft/sec 0 7 62.5 62.5
Slip Velocity, ft/sec* 6.2 1.1 9.3 9.3
Reynolds No. (slip) 3.8 0.2 1.4 1.4
I Lb Solids/cu ft 5.04xlO-2 8.0xlO-6 11.2xlO-5 22.4xlO-5
f-'
.c:>. 145,700 291,400
.c:>. Particles/cu ft 476,500 5,740
I
A =
B =
C =
D =
Data of Johnstone, et al
Battelle data
Commercial-scale operation, 100% stoichiometry
Commercial-scale operation, 200% stoichiometry
* Calculated using the correlation given, for horizontal ducts, by
in Fluidization, McGraw-Hill (1959). Since the terminal falling
of small diameter particles is low (e.g., inches per second), it
assumed that the correlation will apply also to vertical travel.
Leva,
velocity
is
-------
-,
of this question in the calculation of mass transfer limi-
tations in The Dry Limestone Process is explored below.
The basis of the mass transfer predictions is
an assumption that the CaO-S02 reaction is relatively fast
compared with the diffusional processes: that is, the lim-
iting step is taken to be the gas phase mass transfer of
S02 to the particle surface, and this basis would represent
the upper limit of potential S02 removal. The gas-to-
partible mass transfer coeffecients were obtained directly
from the Chilton-Colburn j-factor analogy using the par-
ticle heat transfer data discussed above (Figure 46). The
following additional calculational bases were used:
limestone composition 94% CaC03
calcine porosity 45%
average particle size 74M
reactor residence time 2.25 sec
average temperature 1900°F
The results of mass transfer calculations are
presented on Figure 47 as the percentage S02 removal versus
the additive injection rate (% stoichiometric). The S02 re-
moval will increase proportionally at higher additive rates
in this calculation since greater total particle surface area
will be available. Two curves are plotted representing the
extremes in the range of the predicted mass transfer coef-
ficient, corresponding to particle Nusselt Number values of
2.0 and 0.2. The calculated S02 removal will vary directly
with the mass transfer coefficient which explains the wide
range attainable from the curves plotted. For example, at
a stoichiometric injection rate of 2.0 (Ca/S), the maximum
possible removal is 60%, and the minimum is 6%.
-145-
-------
FIGURE 47
PARTICLE-GAS MASS TRANSFER CALCULATIONS
502 REMOVAL V5 ADDITIVE INJECTION RATE
80
70
CALCULATION BASES
LIMESTONE = 94% CaO
POROSITY = 45%
PARTICLE SIZE = 74 fL
RESIDENCE TIME = 2.25 SECONDS
AVERAGE TEMPERATURE = 19000F
NUSSELT NO. = 2.0
60
10
NUSSELT NO. = 0.2
....
50 l&J
-I
Z
....
Z
l&J
U
D::
l&J
40 a..
~
-I
<[
>
o
~
l&J
D::
30 N
o
en
20
ADDITIVE RATE, PERCENT STOICHIOMETRIC
o
o
50
100
150
200
250
-146-
-------
It is possible that for the Battelle dispersed-
phase reactors, where the additive rates and resulting par-
ticle concentrations are low, relatively high transfer coef-
ficients could be realized. This could imply that heat and
mass transfer limitations were unimportant in the Battelle
tests, and the results should provide some data on the sys-
tem kinetics. On the other hand, the transfer coefficients
could be much lower in the full scale boiler system because
of higher injection rates, which would result in signifi-
cant mass transfer limitations. The key point is that en-
tirely different mechanisms could be governing the perform-
ance of the commercial boiler, and the information developed
in the pilot reactor would be of limited utility to the pro-
cess designer due to an inadequate simulation of the actual
reaction system.
-147-
-------
2.
Comparison with Other Studies
Thomas (23) carried out a study on gas-solid
mass transfer for the reaction of S02 and limestone in
which he compiled mass transfer data from several sources
and correlated them on a plot of Sherwood Number versus
particle Reynolds Number. For the particular Reynolds
Number range calculated in the previous section of this re-
port (0.2 to 3.8) and for a tubular reactor, the Thomas
correlation indicates a Sherwood Number of 2.0 which is the
expected lower limit in diffusion involving a single
ticle. This value is also applicable to the Nusselt
which is the heat transfer equivalent of the Sherwood
Number.
par-
Number
In a similar study on fluidized beds, Kato,
Kubota and wen(24) show that for a particle Reynolds Number
of approximately 1.0, the Sherwood Number lies in the range
of 0.1 to 0.5, depending on the particular study and the
particle size utilized. This study and that of Thomas,
therefore, continue to support the prior conclusion that
the appropriate value of the Nusselt Number (for heat trans-
fer) or the Sherwood Number (for mass transfer) lies some-
where between 0.2 and 2.0, with the use of 0.2 yielding
the most conservative results.
-148-
-------
3.
Comparison with Initial 802 Reaction Rates
In a recent study by Borgwardt and Harvey(2S)
is presented for the initial reaction rates
with their measured B.E.T. surface area.
a correlation
of limestones
This correlation indicates a linear relationship on a log-log
plot, Figure 47-A, from which it is concluded that chemical
reaction is the controlling mechanism.
The data shown on Figure 47-A are for a
wide range of calcination times, viz., from fractions of
seconds up to and including two hours. The shorter times
correspond to the dispersed reactor used in the Battelle
tests while the longer residence times represent stones
calcined in a kiln for the OAP evaluations. Note that
flash calcination produces surface areas an order of
magnitude higher than obtained by calcining in a kiln for
long residence times. However, all of the data correlate
well with the OAP B.E.T. surface area - initial rate concept,
thus leading to the conclusion that chemical reaction is
the controlling mechanism.
The average B.E.T. surface area of the calcined
limestones used in the Battelle study is approximately 40 m2/gm
for which Borgwardt's plot indicates an initial reaction
rate of 0.002 gm moles 802/gm CaO, sec. Assuming this
reaction rate applies and is constant over the entire range
of sulfate loading, then for a two-second residence time,
100 percent stoichiometry and 100 micron particle, the
802 removal is calculated to be 22.4 percent. From the
results of the mass transfer calculations presented in
Table 13, the 802 conversion for the same physical properties,
but assuming gas-particle mass transfer to be limiting,
is 1.3 percent using the lower limit of the Nusselt Number
(0.2). This value is much lower than that obtained when
chemical reaction is assumed to control.
-149-
-------
FIGURE
47-A
INITIAL REACTION RATE VS B.E.T. SURFACE AREA
300
100
II)
0
)( .
- /
(,)
Q)
en .
I
o
0
(,) y.
CP
"
o
E ..
10 CP
- /
*0
~
~
LLJ
to-
-------
Although the first calculation described above
may yield a result which appears higher than the actual
value of S02 conversion since the initial reaction rate
was utilized, it is felt that the size of the decrease in
reaction rate over a time interval as small as two seconds
would not alter the result significantly. On the other
hand, the mass transfer calculation gives a result which
tends to be too low, but even if the upper limit of the
Nusselt Number (2.0) were utilized, the mass transfer
calculation would still yield only 13% S02 conversion.
Battelle's data in Figure 10(1) for an S02 concentration of
0.3%, 74-105 micron particles, and a residence time of two
seconds, shows about 118 mg S03/g calcine which is equivalent
to 9.1% CaO utilization. Thus, for the two extremes of
mass transfer calculations cited (Nusselt Numbers of 0.2
and 2), the conversions of 1.3% and 13% range from about
15% to 150% of the actual data reported by Battelle.
Since the Nusselt Number is 0.2 as the Reynolds Number
approaches 0 (for dilute suspension), and since the Reynolds
in this case is about 1, then the mass transfer calculation
that applies is closer to 1.3% than 13%. The obvious con-
clusion therefore is that mass transfer, which indicates
much lower S02 conversions, should not be totally disregarded
as playing a role in the overall controlling mechanism of
the S02-CaO reaction.
-151-
-------
F.
Thermochemical and Physical Property Data
1.
Thermodynamic Data
In a report entitled "Fundamental Study of Sul-
fur Fixation by Lime and Magnesia" (15), Battelle has com-
piled and analyzed the thermodynamic free energy data for
the reaction of limestones and dolomites in boiler atomos-
pheres. The free energy data used in the Battelle study are
presented in Appendix A of the report, and thermodynamic
equilibrium calculations were performed based upon these
data. In this manner, the extent to which many of the pro-
posed sulfation and calcination reactions might proceed was
determined.
The major reactions investigated were those of
CaO and MgO with S02 and 02. For these two systems, at an
assumed 02 level of 2.7 vol. % and a solid activity ratio of
unity,the equilibrium partial pressures of S02 were calcu-
lated versus temperature and are reported in Table 15. The
calculated results indicate that S02 sorption is only pos-
sible below temperatures of ~2250°F for CaO and ~1550oF
for MgO. However, it must be remembered that these calcu-
lations represent the theoretical equilibrium conversions,
whereas reaction kinetics will dictate the actual S02 con-
centration within a practical reactor system.
Other conclusions concerning reaction equilibria
which have been drawn from the free energy data are:
(1) CaO will tend to recombine with C02 to form CaC03 at
temperatures below l415°F.
(2) CaC03 can desulfurize flue gas at temperatures below
its calcination temperature.
(3) Compared to the formation of CaS04' producing CaS03
has no advantages.
-152-
-------
TABLE 15
EQUILIBRIUM CONCENTRATION OF S02 VERSUS TEMPERATURE
FOR THE REACTIONS a:
Reaction 1. CaO + S02 + 1/2 02 ( » CaS04
Reaction 2. MgO + 502 + 1/2 02 ~ Mg504
Temperature 502 Conc. by S02 Conc. by
(OF) Reaction 1 (ppm) Reaction 2 (ppm)
1000 1.66xlO-ll 1.3xlO-3
1200 1.09xlO-7 1.0
1400 1.01xlO-4 1.8xl02
1600 2.34xlO-2 1.lxl04
1800 1.95 3.2x10Sb
2000 7.47xlOl )106C
2060 2.l2xl02
2240 2.95xl03
2420 2.87xl04
2500 6.30xl05b
3000 >106c
a
b
Basis 2.7 vol. % 02 and unit activity of the solids
Insufficient sulfur in the fuel to supply this level
of 502
Implies an S02 concentration greater than 100% is
required for equilibrium
c
-153-
-------
(4)
(5)
(6)
(7)
(8)
502 will tend to react with 02 in the flue gas at
temperatures up to .-l400oF.
Calcium and magnesium sulfates can be reduced by
CO at temperatures greater than SOOOF.
The iron oxides and calcium silicates present in
the ash do not appear significant from a desul-
furization point of view.
Na2CO) and alumina (constituents of ash) can react
with 502 throughout the range of boiler tempera-
tures.
Hydration of lime by steam in the flue gas will
not occur.
-154-
-------
2.
Stone Property Data
a.
R. D. Harvey Report(26)
Dr. Harvey of the Illinois State Geological
Survey has investigated the physical properties of a cross-
section of limestone-bearing materials under an OAP funded
contract. The basic petrography of the materi~ls studied is
given in Table 16 and the mineralogy is contained in Table
17. Included in the Harvey Report are the chemical composi-
tion of the limestone samples and the trace elements con-
tained therein, which are presented in Tables 18 and 19, re-
specitvely.
Further petrographic analyses are presented
in the report to relate the grains, grain size and shape dis-
tributions, and pore structure of the samples. 'rhe proced-
ures employed involved the use of a scanning electron micro-
scope and a Quantimet (QTM), an image-analyzing computer
with a polarizing microscope. Sample resolutions were ob-
tained with this equipment at magnifications of up to 20,000
times, and the results of this investigation are given in
Tables 20 and 21.
Similar studies were then performed on sam-
ples of the stones which had been calcined by the Process
Research Section of OAP. The mineralogical studies do not
show significant or consistent differences between the cal-
cine samples for different size frac'cions as can be observed
from Table 22. In an attempt to correlate the results ob-
tained from Dr. Harvey's study to the 802 sorption character-
istics measured by OAP, the following conclusions were
-155-
-------
Sample
Type
No.
I
I-'
V1
'"
I
Rock or
Mineral
Classif.
1
Calcite
2
Calcite
3
Limestone
4
Limestone
5
Dolomite
6
Dolomite
7
Magnesite
8
Aragonite
9
Dolomite
Distinguishing
Characteristics
Iceland spar
Abundant crystal
defects
Coarse-grained,
high purity
Fine-grained,
high purity
Reef type,
high purity
Nonreef type,
clayey and
silty
Fine-grained,
high purity
Oolitic and
strontium-
bearing
Limonite- and
calcite-
bearing
10
Dolomite' Strontianite- &
. calcite-bearing
TABLE 16
PETROGRAPHIC DESCRIPTION AND SOURCE OF SAMPLE~
color
Clear
Milky
Gray
Gray
Gray
Buff
Milky
Light
buff to
milky
Brown'
gray
Buff-
gray
Relative
Grain
Size
Very
coarse
Very
coarse
Coarse
Fine
Medium
Fine
Fine
Fine
Fine
Medium
Grain
Shape
Cleavage
rhombs
Cleavage
rhombs
Anhedral
Anhedral
Anhedral
Anhedral'
rhombic
Anhedral &
rhombic
Fibrous &
bladed
Anhedral &
rhombic
Anhedral
Degree of
Grain
Inter-
lockina
None
None
High
High
High
Low
Low
High
Low
Low
Other Textural Features
Nearly perfect crystals
Abundant intracrystalline voids,
solid inclusions, and twin
lamellaei subgrains present ift
some specimens
Inequigranularl crinoid and
bryozoan fossil fragments;
intragranular voids abundant
Equigranular and densei a few
vein lets occur with medium-
sized grains of clear calcite
Recrystallized granular and
microporousi abundant intra-
granular voids
Equigranular and microporousi
grains adjacent to pores are
rhombic. Clay occurs along
bedding planes, iron oxide
along dolomite qrain
boundaries
Equigranular and microporous
Elliptical and cylindrical re-
mains of marine organisms abun-
danti very smooth exterior sur-
facesi most microporous
Equigranular and microporousi
rhombic grains along poresi
fibrous limonite (?) occurs
along dolomite grain boundariesi
abundant intragranular voids
Inequigranulari fibrous stron-
tianite crystallites alonq
pores
Source of
samples
Ecjunqo, Durango,
Mexico
Hillside mine
dump, Rosiclare,
Illinois
Columbia Quarry
Co. mine, Val-
.meyer, Illinois
Allied Stone Co.
Quarry, Milan,
Illinois
Midway Stone
Quarry, Osborne,
Illinois
Abandoned quarry
near Bourbon-
nais, Illinois
Red Mountain Dist~
Santa Clara Co.,
California
North Cat Cay,
Bahama Islands
Jeffrey Limestone
Co. Quarry,
Parma, Michiaan
Abandoned Quarry
near Ida,
~lichiqan
-------
TABLE 17
MINERALOGY OF TYPE SAMPLES IN WEIGHT PERCENTAGE
Sample
Type 1
Type 2
Type 3
Type 4
Type 5
Type 6
Type 7
Type 8
Type 9
Major
Component 'i)
100 calcite
100 calcite
91 calcite
98 calcite
99 dolomite
81 dolomite
99 magnesite
96+ aragonite
70 dolomite
Minor and Trace
Components
None detected
Traces of soluble
salts of Cl and S03
8% dolomite and <1%
limonite
<2% quartz
<1% calcite, approxi-
mately 0.3 mol % FeC03
is present in the
dolomite
9% quartz, 4% calcite,
5% clay, approximately
0.8 mol % FeC03 is pres-
ent in the dolomite
<0.5% quartz and clay,
approximately 0.26 mol %
FeC03 and 4.51 mol % CaC03
are present in the
magnesite
Approximately 3% Mg-
calcite and <1% clay,
approximately 1.38 mol %
SrC03 is present in the
aragonite
18% calcite, 5% quartz,
2% clay, 5% limonite
-157-
Insoluble
Residue (%)
0.0
0.1
0.2
0.9
0.1
14.4
0.1
0.4
4.08
-------
TABLE 18
CHEMICAL ANALYSES IN WEIGHT PERCENTAGE
(Analyses by Analytical Chemistry Section of the Illinois State Geological Survey)
Oxides
I
I-'
In
ex>
I
Si02
Ti02
A1203
Fe203
Fe
MnO
MgO
CaO
Na20
K20
1"2°5
C02
S03
SrO
Cl
Ign.Loss
1
NDa
ND
ND
ND
0.13
ND
ND
55.3
0.003
0.02
traceD
43.95
0.01
0.014
ND
43.49
2
(69-104)
ND
ND
0.01
0.19c
0.06
ND
55.5
0.015
0.02
43.35
0.17
0.002
0.04
43.15
3
(69-103)
ND
ND
ND
0.20c
0.10
1.86
53.4
0.015
0.02
43.75
0.20
0.009
0.03
43.67
Sample Type Number
5 6
(69-102)
4
(69-101)
1.53
ND
0.01
0.31c
0.09
0.00
54.8
0.047
0.04
43.35
0.15
0.019
ND
43.15
0.03
ND
0.02
0.34c
0.02
21.40
30.30
0.008
0.03
47.30
0.13
0.019
0.09
47.24
11.8
0.02
1.77
0.13
0.41
0.02
17.4
26.5
0.040
0.90
0.02
40.27
0.03
0.04
trace
40.46d
7
0.47
ND
0.08
ND
0.07
ND
44.2
2.93
0.026
0.03
trace
50.96
0.01
0.01
ND
51.56e
8
0.19
ND
0.27
ND
0.01
ND
ND
55.2
0.53
0.03
0.01
42.10
0.37
0.10
0.24
43.33
9
(BCR-1701)
5.88
0.15
0.69
2.82
1.75
0.21
15.33
30.82
0.16
0.22
0.10
40.68
0.42
0.04
ND
41.85
10
(IDA)
1.95
0.23
0.09c
5.06
26.31
trace
trace
36.54
0.14
27.23
36.71
a ND - not detected: Limits of detection for Si02, 0.031 Ti02 and MnO, 0.011 A1203, 0.051
Fe203, 0.011 MgO, 0.101 C1, 0.02.
b Trace of P205' approximately 0.005%.
c Percentage of total iron expressed as Fe203.
d Includes 0.30\ H20+.
e Includes 0.61\ H20+.
-------
TABLE 19
TRACE ELEMENT ANALYSES OF TYPE CARBONATE ROCKS
DETERMINED BY NEUTRON ACTIVATION METHODS
~alyses by Dr. R.R. Ruch of the Analytical
Chemistry Section of the Illinois State
Geological Survey)
Element (Pt~)
~ CU Br La Sc As Ga Cr
1 lS <2 <0.3 0.03 < 0.03 2 <1 <2
2 44 <2 3.3 0.35 5.2 <2 <7 <11
3 <7 <3 1.6 0.16 <0.07 2 <2 <5
4 <3 17 <1 0.10 <0.2 a <6 <2
5 11 <1 1.2 0.23 < 0.05 <0.8 <2 <4
6 <25 <5 9.6 1.4 <0.3 <4 <6 35
7 <8 <0.9 <0.2 0.06 <0.1 <0.7 <3 127
8 b 17 <1 0.05 b a b <12
9 25 <1 3.4 1.0 <0.7 <2 <14 <31
a
b
Not determined, excessive interference from Br
Not determined, excessive interference from Na
-159-
-------
~
2
3
4
5
6
7
8
9
TABLE 20
RESULTS OF QUANTIMET (QTM) STUDIES OF THE PORE STRUCTURE OF CARBONATE ROCK TYPES*
QTM
Pore Volume'
Mean 'i) S.D.**
0.19 0.17
10.43 2.18
18.42 16.99
9.65 3.34
24.46 9.22
43.98 6.88
35.66 4.22
4.69 4.79
24.81 6.06
I
I-'
'"
a
I
**
Magnification of X1300
Standard deviation
*
QTM Pore Boundary
M LPro~ S.D.**
ean enAfh ,rom)
0.19 0.12
9.547 1.59
4.814 1.99
6.615 2.02
9.728 2.22
8.005 3.84
18.040 3.73
2.975 2.68
5.410 1.41
Frequency of
cepts Within
1-8 8-16
97.98 1.52
98.64 1.13
78.21 12.11
95.31 4.37
85.03 10.95
57.19 21.64
90.35 8.71
91.06 6.69
64.62 20.55
TABLE 21
GRAIN-SIZE DISTRIBUTION
QTM Pore Chord Inter-
Micron Intervals
16-31 31-63
0.51 0
0.21 0.03
5.32 3.10
0.32 0
3.23 0.53
15.88 4.97
0.93 0.01
1.95 0.30
11.96 2.74
63
o
o
1.27
o
0.26
0.32
o
o
0.13
Mean QTM
Surf.Area
(mm2 ~mm3 )
o
1610
890
1110
1950
21-60
4220
480
1090
Size Interval Fre~Uency of Grains (%)
(Ll) Type13 Type 4 Type Type 6 Type 7 Type B Type 9
250-4000 o. 0 0.1 0 0 0 0
125-250 1.7 0 0.5 0 0 0 0.1
63-125 2.4 0.1 1.1 2.1 0 0.1 0.3
32-63 2.3 0 10.4 2.7 0 0.1 1.9
16-32 4.9 0.1 33.8 34.3 0.1 0.5 24.2
8-16 4.8 4.2 33.1 30.8 4.9 1.0 33.7
4-8 12.6 32.8 16.4 27.4 33.2 1.6 25.8
1-4 71.2 62.7 4.7 2.7 61.8 96.7 ),~, GO
Arithmetic mean* (4) 44 4 81 17 4 3 13
Arithmetic standard
deviation* (Lf) 136 8 99 15 2 4 23
* Statistical methods of Krumbein and Pettijohn (1938, p. 240 for mean and p. 248 for
standard deviation).
-------
TABLE 22
DESCRIPTION OF THE CALCINES
Sample Temp. Minerals Particle Relative
Type (OF) Present Size* (AA) Texture Porosity
1 1700 Lime 0.1 to 0.5** Granular Very low
1800 Lime 1 to 2 Rounded Moderate
2 1700 Lime and 2 to 4 Partly spongy Low to moderate
mino~ calcite
1800 Lime 2 to 5 Spongy Low
1900 Lime 2 to 10 Blocky Low
3 1800 Lime, minor 1 to 2 Spongy, partly rounded Moderate to high
peric1ase
I
..... 4 1800 Lime 0.5 to 1 Granular, partly spongy Low to moderate
'"
.....
I
5 1800 Lime and 0.2 to 1 Granular-agglomeratic Moderate
peric1ase
6 1800 Lime, peri- 0.2 to 1 Granular-agglomeratic High
clase, and
quartz
7 1800 Periclase 0.1 to 0.5 Granular Very low
8 1800 Lime 2 to 10 Spongy, partly blocky Low to moderate
9 1800 Lime and 0.5 to 2 Granular-agg1omeratic Moderate
periclase
* Determined from scanning electron micrographs.
** These particles are subgrains of 1 rom grains that are anisotropic and laminated.
other samples are isotropic limes.
All
-------
drawn:
(1)
(3)
No correlation is apparent between the 802 sorption
and the mineralogy of the sample.
Only one significant correlation could be obtained
between the chemical composition of the samples
and the measured sorption capacity.
Little or no correlation is apparent between the
surface areas determined by QTM data and sorption
capacity, but a significant correlation was ob-
tained when pore volume data were compared.
(2)
A tabulation of 802 sorption capacity for
various stone types and attempted correlations thereof is
presented in Table 23. The logarithm of Na20 concentration
is seen to have a high correlation coefficient (0.84). In
this correlation method, the sodium is considered only as an
index, not as an element which reacts with 802. Dr. Harvey
hypothesizes, however, that Na20 may be promoting a cata-
lytic or fluxing effect to account for the higher reactivity
of the calcine.
-162-
-------
I--
I
TABLE 23
S02 SORPTION CAPACITY OF TYPE SAMPLES* AND STATISTICAL
LINEAR CORRELATION COEFFICIENTS BETWEEN S02 SORPTION AND
VARIOUS CHEMICAL ELEMENTS AND PETROGRAPHIC PROPERTIES
S02 Sorption Linear Correlation
Sample Capacity** Chemical Element Coefficient with S02
Type (in grams) Or Property Sorption Capacity***
1 5.46 5i02, A1203 0.37
2 11.65 MnO 0.30
3 10.73 Fe20J (total Fe) 0.35
4 6.97 Na20 (log) 0.84a
5 9.03 CU 0.18
Br 0.32
6 13.68 La 0.45
Sc 0.46
7 1.78 As 0.19
Ga 0.25
8 18.30 Cr -0.44
Mean pore volume 0.74b
determined by QTM
9 14.91 Frequency of 8-16 fJ 0.77b
pore chord lengths (QTM)
10 10.2 Mean grain size (log) 0.51a
*
Test data of R. Borgwardt, Process Research Section, OAP.,
Cincinnati, Ohio.
Reaction temperature was 18000F for all samples except type 1,
which was 17000F.
For a confidence level of 95% the critical correlation coef-
ficient is 0.532 for the number of the samples considered in
this analysis (D.C. Drehmel, Division of Process Control
Engineering, OAP, - personal communication).
Excludes data on type 7.
Excludes data on types 7 and 8.
**
***
a
b
-163-
-------
b.
G. H. McClellan Report(27)
In this report, Dr. McClellan of TVA ex-
amines the differences in limestone physical properties re-
sulting from differences in calcination temperature, and the
effect of these properties upon the reactivity of calcines
with sulfur dioxide. The procedures used in determining
properties include X-ray diffraction analysis, petrographic
analysis by means of scanning electron microscopy, and por-
osity analysis via mercury intrusion techniques.
A comparison of the data obtained by mer-
cury intrusion and electron microscopy for stone surface
area is presented in Table 24. The relatively good agreement
between the two methods over the range of calcination tem-
peratures studied supports the accuracy of the pore size dis-
tribution measurements which were made by the mercury intru-
sion technique. The data of Table 25 show the effective con-
tribution of pore surface area to the total stone surface
area for limestone and Iceland spar calcines. It can be
seen that the largest contributor to the stone surface area
is the pores of 0.05 to 2.0 micron diameter size range.
, I
The reaction of calcines with 802 was then
investigated at 1382°P, 1922°P, and 2192°P under two differ-
ent experimental conditions--calcination for 16 hours and subse-
quent sulfation, and simultaneous calcination and sulfation.
The crystallite size of calcium sulfate grew larger with in-
creasing temperature, and crystallite sizes for the lime-
stone calcines were consistently larger than those for the
Iceland spar, as shown in Table 26. Purthermore, the sam-
ples calcined and sulfated simultaneously at 1382°P for 15
minutes, were found to have undergone virtually no calcina-
tion. However, at the other temperature levels studied,
the limestone did undergo sulfation to a larger degree than
the Iceland spar.
-164-
-------
TABLE 24
CORRELATION OF POROSIHETER AND SCANNING
ELECTRON MICROSCOPE MEASUREMENTS
Calcination
Temp., of
Porosimeter
Surface Pore
Area, m2 /gm Size,.Lt ma
Scanning Electron Microscope
Surface Pore No. of
Area, m2/gm Size, Mm poresb
Limestone 89
1382
1562
1742
1832
2012
36.0
20.3
4.7
6.8
1.2
0.05
0.09
0.37
0.26
1.44
27.4
14.6
4.2
6.7
1.4
0.06
0.12
0.42
0.26
1.27
Iceland Spar
1382
1562
1742
1832
2012
62.9
32.2
0.03
0.05
0.25
1.58
66.5
46.4
46.0
10.8
0.9
0.03
0.04
0.04
0.16
1.92
7.0
1.1
a
Calculated from the relation A = 6/D.P, where A = surface area,
m2/gmJ D = mean diameter, ~mj of pores assumed to be sphericalJ
P = absolute density, gm/cm .
b
Number of pores measured for calculation of pore size.
-165-
-,
482
514
471
502
188
477
470
348
368
75
-------
TABLE 25
SURFACE AREAS OF CALCINES CALCULATED FROM POROSIMETER MEASUREMENTS
Surface Areaa Surface Areaa Surface Areaa
Pore Size, , of , of , of
Microns m2/gm Total m2/gm Total m2/gm Total
Limestone 89
13820F Calcine 1562 OF Calcine 1742°F Calcine
17.5 0.12 0.3 0.08 0.04 0.07 1.5
5.0 0.17 0.5 0.12 0.6 0.11 2.4
1.75 0.22 0.6 0.16 0.8 0.19 4.0
1.0 0.36 1.0 0.26 1.3 0.28 5.9
0.5 0.54 1.5 0.43 2.1 1.15 24.5
0.4 0.71 2.0 0.84 4.1 1.87 39.8
0.2 3.72 10.3 8.62 42.4 3.76 80.0
0.1 26.26 72.9 20.17 99.3 4.70 100.0
0.05 35.68 99.0 20.31 100.0 4.70 100.0
0.035 36.03 100.0 20.31 100.0 4.70 100.0
1832°F Calcine 2012 of Calcine 2192 of Calcine
17.5 0.04 0.6 0.06 5.2 0.03 5.9
5.0 0.08 1.1 0.09 7.3 0.05 9.7
1.75 0.15 2.2 0.17 13.7 0.09 16.1
1.0 0.32 4.7 0.37 29.2 0.31 57.6
0.5 0.67 9.9 0.82 65.4 0.50 92.3
0.4 0.96 14.1 0.92 73.2 0.54 100.0
0.2 4.88 71.8 1.06 84.5 0.54 100.0
0.1 6.79 100.0 1.12 89.6 0.54 100.0
0.05 6.79 100.0 1.25 100.0 0.54 100.0
0.035 6.79 100.0 1.25 100.0 0.54 100.0
Iceland Spar
l~OF Calcine 1562 of Calcine 1832°F Calcine
17.5 . 1 0.0 0.01 0.0 0.01 0.1
5.0 0.03 0.0 0.01 0.0 0.01 0.1
1.75 0.09 0.1 0.04 0.1 0.02 0.3
1.0 0.19 0.3 0.06 0.2 0.05 0.7
0.5 0.25 0.4 0.06 0.2 0.05 0.7
0.4 0.28 0.4 0.06 0.2 0.05 0.7
0.2 0.38 0.6 0.06 0.2 0.08 1.2
0.1 0.38 0.6 4.26 13.2 1.02 14.5
0.05 47.38 75.3 29.86 92.7 5.95 84.3
0.035 62.93 100.0 32.20 100.0 7.06 100.0
a Area contributed by pores of indicated and all larger sizes
-166-
-------
TABLE 25 (Cont'd)
SURFACE AREAS OF CALCINES CALCULATED FROM POROSIMETER MEASUREMENTS
Surface Areaa Surface Areaa Surface Areaa
Pore Size, , of , of , Of
Microns m2/gm Total m2/gm Total m2/gm Total
Iceland Spar
20120p Calcine 21920P Calcine ~op Calcine
17.5 0.00 0.0 0.00 0.1 . 0 2.0
5.0 0.01 0.7 0.01 0.4 0.01 5.0
1.75 0.01 0.7 0.01 .0.6 0.02 11.6
1.0 0.03 2.5 0.02 1.0 0.03 15.6
0.5 0.04 3.4 0.02 1.0 0.06 29.1
0.4 0.05 5.0 0.04 1.9 0.10 50.8
0.2 0.08 7.6 1.14 56.6 0.20 100.0
0.1 0.40 37.9 1.89 93.8 0.20 100.0
0.05 0.69 65.2 2.02 100.0 0.20 100.0
0.035 1.06 100.0 2.02 100.0 0.20 100.0
a Area contributed by pores of indicated and all larger sizes.
-167-
-------
TABLE 26
PROPERTIES OF SULFATION PRODUCTS
Su1fation Conditions Crystallite
Temp. Time, Size of Ratio of Areas of
of Min. caS04.t..1L CaC03 CaO CaS04
-
Sulfation of Limestone Calcines
1382 1.5 1725 0 1.00 2.20
1922 5 2950 0 1.00 0.35
1922 15 2325 0 1.00 0.42
1922 30 2450 0 1.00 0.68
2192 15 3075 0 1.00 0.13
Su1fation of Iceland Spar Calcines
1382 15 1350 0 1.00 0.48
1922 5 1600 0 1.00 0.05
1922 15 2050 0 1.00 0.03
1922 30 1950 0 1.00 0.35
2192 lS 2275 0 1.00 0.07
Simultaneous Calcination and Sulfation of Limestone
1382 lS 2400 1.00 0.02 0.07
1922 15 2550 1.00 0.03 0.65
2192 lS 3150 0 1.00 1.73
Simultaneous Calcination and Su1fation of Iceland Spar
1382 15 0 1.00 0 0
1922 lS 2825 1.00 0.24 0.19
2192 15 1950 0 1.00 0.33
-168-
-------
Further examination of the sulfated samples
was then performed to determine the growth pattern and dis-
tribution of the sulfate grains in the hope of ascertaining
the mechanism of the sulfation reaction with calcines. The
following conclusions were drawn by Dr. McClellan from this
study:
(1)
Sulfation of lime occurs in two stages--reaction of
the sulfur dioxide and oxygen with the exposed sur-
face of lime, followed by diffusion of the gaseous
reactants through the resultant shell of calcium
sulfate to the core of unreacted lime. Pores in
the calcine smaller than about 0.1 micron do not
admit sulfur dioxide rapidly enough to have sig-
nificant effect on the sulfation reaction at short
retention times.
(2 )
Calcines react best with sulfur dioxide at tem-
peratures below 1922°F, but simultaneous calcin-
ation and sulfation, which is required when pow-
dered limestone is injected into power plant fur-
naces, occurs best at temperatures of 1922°F and
above.
It can be inferred from these results that
solid-gas reactivity is Correlated with pore distribution
and surface area. The pores provide the reactant gas with
access to the surface area. If diffusion of the gas in small
pores is slow, then each stone has some optimum time and
temperature of calcination for development of a favorable pore
size distribution and surface area that results in a reac-
tive lime. Furthermore, the physical and chemical properties
of a calcine are influenced markedly by the crystallite size
of the parent limestone. The high thermal stability of
Iceland spar reflects its relatively large crystallite size,
and its calcines react slowly with sulfur dioxide. In addi-
tion to the decomposition of the calcium carbonate, calcina-
tion effects a recrystallization of the resultant calcium
oxide which is accelerated by rising temperature and which
decreases the reactivity of the calcine with sulfur dioxide.
-169-
-------
G.
Process Effects on Equipment Performance
1.
Electrostatic Precipitator Efficiency Studies
a. Summary
The results of the tests performed
on TVA Shawnee Steam Plant Unit 10 Precipitator A and Research
Cottrell studies, as reported in References 28,29 and 30
respectively, are summarized in the attached graphs,
Figures 48-50. Conclusions which can be drawn from the
reported data are as follows:
(1)
(2)
(3)
In 1969 TVA performance tests without additives
indicate that the electrostatic precipitator (ESP)
was operating at a high efficiency level, along
the predicted upper limit curve, about 3 to 5%
above the ESP guarantee efficiency value.
The 1970 TVA performance tests without additives
indicate that the ESP performance had deter-
iorated compared to 1969 performance data. The
test results are scattered, but in general, in-
dicate a lower ESP collection efficiency. Several
of the test points fall 3 to 5% below the minimum
predicted ESP operating line or guarantee efficiency
curve.
The 1970 performance tests with additives give
widely scattered results; however, the majority
of test runs showed performance considerably
better than had been predicted. The decrease
in efficiency due to the introduction of addi-
tives was roughly half of the predicted decrease
in a majority of the runs. Eighteen of the twenty
two ESP tests were run at 94% to 106% of the
rated gas flow capacity, and show a collection
efficiency varying from 68% to 88%. Four of the
tests were run at 76% to 82% of rated capacity,
and these runs show a collection efficiency of
87% to 91%.
(4)
The tests were run at limestone additive rates
varying from 2,600 Ib/hr to 20,000 Ib/hr. There
is no detectable trend in ESP collection efficiency
attributable to variations in the additive rate.
-170-
-------
(5)
EPA has contracted Cottrell Environmental Systems
(a Division of Research Cottrell) to conduct additional,
more detailed, testing and evaluation of the effects
of additives on ESP performance. The study will
include evaluation of possible operating modes and
other potential solutions to minimize or eliminate
the observed effects. In addition, the effects of
additives on mechanical collector performance also
will be assessed.
b.
Discussion of Test Results
(1)
Figure 48 - Gas Volume Flow Versus
Precipitator Collection Efficiency
Figure 48 includes predicted ESP
performance ranges for operation with and without additives
(Reference No. 30), and ESP collection efficiencies obtained
during performance tests run in 1969 and 1970, both with
and without additives (References No. 28 and 29). The pre-
installation collection efficiency for this ESP was predicted
by Research-Cottrell to be 90-94.6% at rated design capacity
without addivites, decreasing to 70.3-74.7% with additives.
The initial TVA performance tests carried out during Ju1y-
August 1969 without additives indicated that the measured
ESP collection efficiencies fell along the upper limit of
the predicted performance range, which was 3 to 5% above
the guarantee curve. Individual test runs deviated only
slightly from the predicted performance curve over the
entire operating range from 75% to 106% of rated flow
capacity.
The performance tests run during June-
July 1970 without additives showed a considerable deterior-
ation in the ESP collection efficiency when compared to the
-171-
-------
I-
Z
W
()
::i 85
Q.
l-
X
C)
W
~
>=
~ 80
w
()
u..
u..
w
z
o
I-
() 75
w
...J
...J
o
()
It:
o
I-
~
I-
~ 70
()
W
It:
Q.
FIGURE 48
GAS VOLUME FLOW VS PRECIPITATOR COLLECTION EFFICIENCY
TV A SHAWNEE STEAM PLANT UNIT 10, PRECIPITATOR A
100
95
UPPER AND LOWER LIMITS OF PREDICTED
EFFICIENCY WITHOUT ADDITIVES,
REFERENCE NO.30.
90
'7
\l
\10
o
o
AREA OF ACTUAL OPERATiON
DURING PERFORMANCE TESTS
WITH ADDITIVES, REFERENCE
NO. 29.
UPPER AND LOWER LIMITS OF
PREDICTED EFFICIENCY WITH
ADDITIVES, REFERENCE NO.
30.
65
o 1969 PERFORMANCE TESTS WITHOUT
ADDITIVES, REFERENCE NO. 28.
o 1970 PERFORMANCE TESTS WITHOUT
ADDITIVES, REFERENCE NO. 29.
!Q] 1970 PERFORMANCE TESTS WITHOUT
ADDITIVES WHICH FELL BELOW THE
LOWER LIMIT OF THE PREDICTED
EFFICIENCY.
o /970 PERFORMANCE TESTS WITH
2,600 TO 10,000 LB/HR LIMESTONE
INJECTION RATE.
\} 1970 PERFORMANCE TESTS WITH
20,000 LB/HR LIMESTONE
INJECTION RATE.
w
:!:
::I u..
...J 0
o 0
> 0
rt)
o I-
~ ~
~
It:
60
\l
55
200 210
220 230
240 250 260 270 280 290 300
GAS VOLUME FLOW, ACFM IN THOUSANDS
310 320
330 340
-172-
-------
1969 test results.
The 1970 test results exhibit consider-
able scatter, and the collection efficiencies fell below
the upper limit of the predicted efficiency range. Several
test points fell considerably below the minimum predicted
performance curve for no apparent reason. The 1970 tests
run with additive amounts varying from 2,600 lb/hr to 20,000
lb/hr showed widely scattered results with no evident pat-
tern attributable to variation in additive rate. Of the
twenty two acceptable tests run with additives, eighteen
were run in the narrow range of 94-106% of rated flow capac-
ity. These tests showed ESP collection efficiencies vary-
ing from 68-88%. The four remaining tests which were run
at 76-82% of rated capacity showed collection efficiencies
varying from 87-91%.
These test results indicate that the
decrease in ESP collection efficiency caused by introducing
additives is less when operating below the ~ated design cap-
acity than it is when operating near the rated capacity. It
is possible however, that a greater number of tests run in
the lower capacity region would show a wider scatter pattern.
The reported collection efficiencies pertain to the ESP only.
The TVA Shawnee Unit No. 10 installation consists of a me-
chanical separator followed by the ESP, consequently overall
solids collection efficiencies are higher. No data are
available to permit calculation of the mechanical collector
efficiency or the overall solids removal efficiency for dif-
ferent loadings.
-1.71-
-------
(2)
Figure 49 - Electrostatic Precipitator
Collection Efficiency Versus Percent
of Rated Capacity
Figure 49 represents a simplification
of Figure 48 which is intended to show the extent of the ESP
operating region with additives, in relation to the guaranteed
performance curve wi thout addi ti ves, .as a function of
. rated flow capacity. The curve showing predicted mechanical
separator efficiency was derived from Reference No. 30, and
corresponds to the specific mechanical separator used in
conjunction with Precipitator A on Shawnee Unit 10.
(3)
Figure 50 -
~ Precipe Area with additives
Ratio Al Precipe Area without additives
Versus Percent of Rated Capacity
The required collecting electrode sur-
face area (A2) calculated for use with additives is based on
maintaining the same outlet gas solids concentration as
would be obtained by the base case electrode area without
additives. The required area was calculated from the equation:
-A
Co V W
11 = l-Ci = 1- e
where:
11 = collection efficiency - fractional
Co = outlet concentration
Ci = inlet concentration
A = collecting electrode surface area
V = volumetric flow rate
W = effective migration velocity
W was obtai~ed from the test results.
-174-
-------
FIGURE 49
ELECTROSTATIC PRECIPITATOR COLLECTION EFFICIENCY
VS
PERCENT OF RATED CAPACITY
TVA SHAWNEE STEAM PLANT UNIT 10, PRECIPITATOR A
98
96
94
92
90
...
z
88 LaJ
(,)
a::
w
Q..
86 ...
:I:
~
W
84 ~
.;
(,)
82 z
LaJ
(,)
lL.
80 lL.
LaJ
Z
o
78 ...
(,)
LaJ
...J
...J
76 0
(,)
0::
74 0
...
«
...
Q..
72 (,)
LaJ
0::
Q.
70
68
66
64
CSp
GU4
J?4
(WI"'/j tv"'CCD
°U.,. PCI?
4DD ~OJ?
1.,./ v 11141\1
CS) Cc
c,'
\
-------
2.5
2.4
0 1970 PERFORMANCE TESTS WITH
2.3 2600 TO 10000 LB/HR LIMESTONE
INJECTION RATE.
2.2 en [] 1970 PERFORMANCE TESTS WITH
LLJ 20000 LB/HR LIMESTONE
en >
LLJ I- INJECTION RATE.
2.1 > \)
0 REFERENCE NO. 29
I- 0 8
0
0
I- :I:
1.9 ~ I-
-------
L
Inlet dust loadings studied ranged from 1.260 to 2.173
grains/standard cubic foot (gr/SCF) for the tests using
limestone injection while the range for tests without
injection was 1.119 to 1.737 gr/SCF. Concentrations in
the effluent gas from the ESP ranged from 0.162 to 0.674
gr/SCF with additives and from 0.0728 to 0.214 gr/SCF
without additives.Results are plotted for the 22 test runs
with additives calculated on the same basis as the results
obtained from the 12 tests run without additives.
Individ-
ual test points are widely scattered showing the same
general configuration as Figure 48. In the operating region
of 76-82% of rated capacity, the area ratio (A2/Al) is
about 1.1 to 1.4, while in the region of 94-106% of rated
capacity, the area ratio varies from 1.3 to 2.25. If this
difference in collection efficiency is valid for the gen-
eral case, it may be more economical to design the ESP for
a higher rated gas volume capacity and operate at 75% of
rated capacity, than to design for and operate at the nor-
mal rated capacity.
The results of these tests are appli-
cable only to comparable modern ESP units designed specific-
ally for a high solids collection effeciency, which are
maintained and operated with a high degree of efficiency. In
comparison, the data reported in Reference No. 30 for the
Detroit Edison St. Clair station ESP tests show a collection
efficiency with additives of only 55%. This requires an
area ratio of 3.15 to maintain the same outlet dust loading as
the base case where the ESP test efficiency was 80%. This
type of performance is more indicative of existing ESP units
which were not originally designed for high collection
efficiency.
-177-
-------
L---- - ---
(4)
Effect of Additives on Dust Resistivity
The effect of additives on dust resis-
tivity and consequently on ESP collection efficiency is dis-
cussed in Reference No. 30. It was pointed out that all
limestone or dolomite additives would result in high dust
resistivity values, above the critical range of 1010 to lOll
ohm-em. The increased resistivity results in a lower parti-
cle migration velocity and a lower electrode collection
efficiency. The resistivity values reported in Reference No.
29 show a relatively smaller increase in resistivity from
the use of additives than is predicted in Reference No. 30.
One composite limestone-fly ash sample indicated a decrease
in resistivity for an additive injection rate of 20,000 lb/hr
as compared to zero additive. Assuming that the other re-
ported resistivity values are truly representative of lime-
stone-fly ash mixtures, the decrease in ESP collection ef-
ficiency would be less than predicted from the use of lime-
stone additive. Figure 48 shows that this was the case
for the TVA tests. This reduced sensitivity of the dust
particle resistivity is probably due to a conditioning
effect caused by the presence of S03 or some other chemical
in the flue gas.
-178-
-------
2.
Coal Ash Deposition Studies
a.
Summary
The effect of additives on ash deposition
on boiler surfaces has been reviewed following the guide-
lines presented in the B & W Report(2). This review was
carried out with the aim of establishing generalized corre-
lations relating the B , W data to both types of ash deposi-
tion at various additive to ash ratios. The two types of
ash deposition under consideration are: (1) fused-slag
deposits which form mainly on the furnace radiant section
surfaces; and (2) bonded deposits which form on the convec-
tion section heating surfaces. These two types of ash de-
posits are treated separately since the tendency for such
deposits to form is related to different physical charac-
teristics of the coal ash. Fused-slag deposits are related
to ash fusion temperature and ash viscosity which are in
turn greatly influenced by the ambient atmosphere in the
area of the deposit. The atmosphere can be either oxidiz-
ing or reducing depending on furnace operating character-
istics. Bonded deposits are related to the fly 'ash sinter-
ing strength which is dependent on the ash composition and
would therefore be directly influenced by additives.
A review of the published literature re-
lating to ash deposition on boiler surfaces has turned up
only one paper (Reference No. 31) which attempts to corre-
late quantitatively the physical and chemical properties of
a coal ash (without additives) with the tendency to form
fused-slag deposits and bonded deposits. It developed that
the correlations contained in Reference 31 had very limited
applicability to the data contained in Reference 2. Conse-
quently, the slagging problem was referred back to B & W to
-179-
-------
i---n- .
!
I
obtain further clarification of their published correlations,
and any other information relating to the possibility of cor-
relating the data on slag viscosity contained in Reference 2
with slagging tendency. Results achieved in this effort have
been negative, and it must be concluded that the type of
generalized correlations which were originally planned are
beyond the present state of the art.
It should be noted that Energopomiar (Power
Metrology Research Organization, Poland) are investigating
the effect of limestone additives on ash deposition on boiler
surfaces and,based on results reported in reference 36,
concluded that no correlation could be developed relating
fouling tendencies to mixture properties. The Energopomiar
work comprised the following determinations (taken from
reference 36):
1.
The effect of the quantity of additive on the
laboratory ash fusion.
2.
The effect of the quantity of additive on the fly
ash fusion.
3.
The effect of the quantity of additive on the
laboratory ash viscosity in the pyroplastic state.
4.
The effect of the quantity of additive on the fly
ash viscosity in the pyroplastic state.
Although it was found that additives changed the ash fusion
temperatures (raising it in a reducing atmosphere and lowering
it in an oxidizing one) no correlations with fouling ten-
dencies were developed. Similar results were obtained for
ash viscosity, i.e., additives changed the viscosity, (in
some cases increasing it, in others lowering it) but no
correlations with fouling tendencies were found. This work
is continuing to develop data for possible correlation with
fouling tendencies, particularly with respect to coal composition.
Although no correlations have been developed
to relate increased ash deposits with additives injected into
-180-
-------
the boiler, it should be noted that such increased deposits
have been observed in the full-scale tests at TVA's unit
37
No. 10, Shawnee Steam Plant, Paducah, Kentucky. In
these tests, heavy deposits have been observed in the re-
heat steam superheater section which compr~ses a bank of
2-inch diameter tubes spaced on 3-inch centers. Heavy
deposits accumulated on these tubes after injection of
only 592 tons of limestone resulting in a unit outage to
rod out the material. Following the outage, a tube leak
caused a forced outage (about four weeks after the first
outage) which revealed heavy deposits had accumulated in
the same section as before. About 322 tons of limestone
had been injected during these four weeks. The deposit
was very hard and although steam soot blowing frequency
was increased by 25%, it may not be possible to control
buildup by these techniques. Coal composition and process
. and operating variables will be studied during the test
program for possible correlation and solution to the problem
of deposition.
The present technology can be summed up by
quoting a statement from the summary of the B & W Report:
"In the study of ash deposition, the results indicate
that general statements concerning the effects of additives
on furnace wall slagging and tube bank fouling would be
misleading". It would be possible for an experienced
boiler designer to analyze, at least directionally if
not quantitatively, the effects of additive injection on ash
deposition utilizing the type of data contained in Reference 2.
This analysis, when used in conjunction with other operating
and design variables, such as method of firing, furnace
and steam generator design, coal ash composition, soot
blower effectiveness, deposit conditions and combustion
conditions, would enable the designe~ to modify the furnace
to obtain improved performance. The following discussion
-181-
-------
will review the general significance of the data presented
in Reference 2 relating to ash fusion temperatures, slag
viscosity characteristics, sintering strength and chemical
composition of the ash.
-182-
-------
b.
Fused-Slag Deposits
Fused-slag deposits form on furnace walls
and other areas which are predominantly exposed to radiant
heat. This type of deposit is mainly due to molten ash
particles carried in the flue gas, but can be caused by se-
lective condensation of ash constituents vaporized during
the combustion process. Such selective condensation causes
enrichment of certain components on cooler surfaces making
it relatively more difficult to predict slagging tendencies.
Ash fusion temperatures can sometimes be used as a means of
roughly approximating the slagging tendency of a coal ash.
When the initial deformation temperature (ASTM-DI857-66T)
is above the 2500-2600oF range, the slagging tendency should
be very low. If the initial deformation temperature is be-
low the 2000-2l00oF range, slagging problems can be expected.
Between these temperature limits, the slagging tendency is
variable and depends largely on the boiler characteristics
and operating conditions. Many coal ashes with similar
chemical analyses and ash fusion temperatures have been
found to exhibit widely divergent slagging tendencies.
The ash fusion temperature data contained
in Reference 2 are presented as plots against the percentage
additive for both oxidizing and reducing atmospheres. The
following comments on the reported B , W data refer to gen-
eral distinct trends exhibited by a majority, but not nec-
essarily all of the samples tested. The inclusion of addi-
tives in the ash initially causes the ash deformation tem-
perature to decrease to a minimum value corresponding
roughly to an ash with an additive content of 20 to 40%.
As the additive percentage is increased further, the ash
deformation temperature increases fairly rapidly exceeding
the 26000F level at high additive percentages. The minimum
-183-
-------
I~
initial deformation temperature occurs in the general range
of 100-200\ stoichiometric CaO/S02 ratio. Since this is the
most likely operating range for the Dry Limestone Injection
Process, most boiler operations will be carried out in the
lower ash fusion temperature region, where slagging tenden-
cy is determined largely by boiler characteristics and opera-
ting conditions, and therefore is less amenable to predic-
tion. The B & W data further show that additive amounts
varying from 250-800% of stoichiometric were required to
raise ash fusion temperatures above the 2S00-2600oF range
where slagging would not be expected to occur.
Slag viscosity has been found to be the
most reliable criterion for predicting the slagging tenden-
cy of a coal ash (Reference 31). The slag viscosity data
of Reference 2 are presented in the form of graphs of slag
viscosity versus temperature for both oxidizing and reduc-
ing atmospheres. As a general statement, large overall
plastic ranges (....,500 poises to solid slag), and a rela-
tively greater sensitivity of the ash to either oxidizing
or reducing conditions, requires special furnace design.
There are no available guidelines unfortunately, relating
plastic range extent with the degree of slagging tendency.
A comparison of the viscosity characteristics of ash samples
containing additives, with coal ash samples without addi-
tives, shows that the introduction of additives results in
a pronounced reduction in the extent of the plastic region
for both oxidizing and reducing atmospheres. This indicates
directionally, a potentially smaller zone wherein slagging
would be expected to occur, and consequently a reduced need
for special furnace design considerations.
-184-
-------
Aslagging index (RS) can be used to pre-
dict slagging tendency in the absence of other data. This
type of correlation was developed(3l) for bituminous coals
without additives, which normally have a Base/Acid ratio
less than 1.0. The correlation is convenient to use since
it requires only a knowledge of the chemical composition of
the coal ash. However, it gives completely erroneous re-
sults when applied to a ~oal ash-limestone additive mix-
ture which generally will have a Base/Acid ratio greater
t.han 1.0.
c.
Bonded Deposits
The tendency of an ash obtained from bi-
tuminous type coals to form hard bonded deposits on the
convection tube banks of boilers has been related to the
sintering strength of the ash by means of a standard test(32).
A correlat.ion applicable to bituminous coals without addi-
tives relating sintering strength, ash fouling index (RF)
and chemical composition has been empirically developed
(Reference 31, Figure 5). The fouling index and sintering
strength are then related to fouling category as follows:
Sintering
st.rength, psi
< 1000
1000-5000
5000-17000
> 17000
Fouling Category
Low
Medium
High
Severe
Fouling Index, RF
< 0.2
0.2-0.5
0.5-1.0
> 1.0
Reference 2 presents sintering strength data*
for six coal samples without additives and 13 coal samples
with additives. The sintering strengths of 11 samples were
very substantially reduced by the additives, and for 2 sam-
ples which had very low initial sintering st.rengt.hs, were
increased by the additives. The indication is st.rong that
additives will have a tendency to lower ash sintering
*Based on pilot plant tests.
-185-
-------
strength thereby reducing the tendency to form bonded de-
posits. However, due to the limited sampling and the unex-
plained exceptions, this conclusion may not be valid for
every case.
Fouling categories calculated using the
ash chemical composition were in fair agreement with the
categories obtained from sintering strength data for the
six coal samples without additives. However, for the 13
samples with additives, there appears to be no correlation
between the two methods. For 12 of the samples, the cal-
culated fouling index is much higher, indicating an in-
creased fouling tendency due to the introduction of addi-
tives. This is true even for those samples where the
Base/Acid ratio with additives is substantially below 1.0.
Since the calculated trends obtained from the fouling index
are in contradiction to the results obtained from sintering
strength test data, it is concluded that the correlation
relating fouling index and chemical composition is not
applicable to coal ash in the presence of limestone
additives.
-186-
-------
3.
Water Quality Control Studies
In a typical coal-fired thermal power plant,
water is used to sluice collected fly ash to a disposal
area, and after the solids have settled from it, is dis-
charged to a watercourse. Consequently, any water soluble
compounds in the fly ash will be dissolved in the sluice
water and discharged into the watercourse. Alternatively,
if a dry solids handling system were used, the soluble com-
pounds eventually would be leached out of the fly ash dis-
posal pile by rain water. In either case a potential water
pollution problem exists. Only the wet disposal system is
considered here.
The quantity of water discharged from the ash
sluice system of coal-fired power plants is a function of
the type of fuel-feed system, the ash content of the coal,
the type and efficiency of the ash-collection system, the
type of pumping system, and the quantity of coal burned.
The following data are typical of pulverized fuel type
plants (these and other data shown in this report are taken
from a paper presented by J.S. Morris, TVA(33»:
Ash Collector System Percent Ash Average Flow
System Efficiency In Coal Gals/Ton Coal
Mechanical 60-68 11-14 1600 :t ~25%
Electrostatic Precipe 90-98 11-14 1900 "
Mechanical-Electrostatic 96-98 11-14 2000 "
The above data represent typical power plant con-
ditions and do not include the effects of adding on a process
for controlling S02. Installing a system such as the lime-
stone injection process, either wet or dry, will appreciably
increase the quantities of water and of solid wastes dis-
charged. In the dry process, the fly ash, reaction products,
and unreacted lime are removed via the ash sluice system.
-187-
-------
Additional water is required since the total quantity of
solids to be removed i~ increased by limestone injection.
Figure 51 shows the theoretical increase in ash pond flow
and solid waste produced as a function of stoichiometric
limestone injected into the boiler. Calculations have
been made based on preliminary test data from TVA's
Shawnee plant (1.7 stoichiometric = 0.16 lb limestone/lb
coal) and the results indicate an 82% increase in the quan-
tity of fly ash-limestone requiring disposal.
The sluice water from a power plant normally
is discharged to a receiving stream after the solids have
been removed by settling. The generally large receiving
streams usually provide ample dilution to reduce the var-
ious water quality parameters to acceptable limits (beyond
a short mixing zone) even though the ash pond discharge
often exceeds the standards. Table 27 lists water quality
analyses from typical steam plant ash pond discharges.
(The present recommended limit for sulfate in drinking
water is 250 ppm but recent proposals have included reduc-
tion to 150 ppm. The present limit on total dissolved
solids is 500 ppm.) The concentration in sluice water of
a few selected parameters is shown in Table 28 for normal
plant operation and in Table 29 for operation with limestone
injection. It should be noted that while these latter re-
sults are preliminary, they are based on actual tests at
the Shawnee plant. One important point to note is that the
Shawnee tests are based on a high calcium limestone contain-
ing very little magnesium. A high magnesium limestone (e.g.,
dolomite) would probably increase the dissolved solids since
the magnesium compounds involved are more soluble than the
calcium compounds.
-188-
-------
FIGURE 5 I
THEORETICAL TOTAL ASH BURDEN AND SLUICE FLOW
LIMESTONE INJECTION
4.4
550
ASSUMED BASES
500 3.5% SULFUR 4.0
I 2 % ASH
30% S02 REMOVAL AT 1.0 STOICHIOMETRY ..J
50% S02 REMOVAL AT 2.0 STOICHIOMETRY <[
0
...J u
~50 <[ 3.6
o LL
U 0
LL Z
0 0
z ~
0 ........
400 ~ (/) 3.2
........ z
(/) 0
C ..J
Z ...J
::> <[
0 (!)
a.. 0
350 .. 0 2.8
z 0
I.1J -
C ~
Q:
::> o
m ...J
:I: LL
300 (/) I.1J 2.4
<[ u
=>
...J
(/)
250 2.0
STOICHIOMETRIC RATIO: LIMESTONE FEED
200
o
1.0
1.6
2.0
-189--
-------
TABLE 27
RESULTS OF ANALYSIS OF ASH POND EFFLUENT FROM TYPICAL PLANTS
Constituents Plant
(mgjl except as noted) A B C D E
Average flow (mgd) 7.0 5.0 10.0 19.0 12.0
Dissolved oxygen 9.33 9.98 8.4 9.0 8.6
pH 11.8 12.0 9.6 11.0 9.0
, Alkalinity (pheno) 259 186 14.0 5.0
Alkalinity (total) 279 204 40.0 163 74.0
Solids (total) 464 388 422 786 237
Hardness (CaC03) 296 276 183 338 128
Calcium 114 106 65.3 130 43.6
Magnesium 3.0 3.0 5.0 3.17 4.63
Iron (ferrous) 0.0 0.01 0.0 0.02 0.0
Iron (total) 0.21 0.10 1.12 0.50 0.55
Manganese (total) 0.08 0.03 0.17 0.03 0.02
Silica 6.9 13.7 4.94 51.9 1.91
Chloride 21.9 5.69 70.4 71.6 20.6
Sulfate 84.5 69.5 93.5 145 6.7
Specific 1260 1110 551 870 332
conductance (umbos)
-190-
-------
TABLE 28
SLUICE WATER QUALITY
NORMAL PLANT OPERATION
Mean Range of
Type of Concen. Concen.
Sluice Parameter (mg/l)- ~
Mechanical Ca 232 44-480
.. Mg 51 0-144
" Hardness 790* 130-1700*
" pH 120** 10.4-12.2**
n Total Alkalinity 820 150-1700
n S04 130 22-460
" Total Dissolved Solids 2800 300-5600
Electrostatic Ca 66 23-140
It Mg 28 5-58
.. Hardness 282* 120-520*
n pH 9.8** 7.5-11.5**
" Total Alkalinity 125 44-270
" S04 150 31-430
" Total Dissolved Solids 450 150-900
Bottom Ca 128 64-272
II Mg 19 0-48
n Hardness 400* 270-440*
II pH 10.7** 7.3-11.6**
It Total Alkalinity 180 92-340
Q S04 250 50-570
II Total Dissolved Solids 700 380-1100
pyr i te Ca 53 21-104
.. Mg 10 0-24
II Hardness 176* 100-280*
.. pH 7.8** 7.5-8.1**
" Total Alkalinity 55 50-62
II S04 29 24-42
.. Total Dissolved Solids 132 120-150
*
**
As CaC03
Median Value, Units
-191-
-------
TABLE 29
SLUICE WATER QUALITY
LIMESTONE INJECTION
Mean , of Mean
Type of Concen. Concen. of
Sluice Parameter (mg/l) Normal Opera.
Mechanical Ca 520 220
" Mg 390 770
.. Hardness 2900* 370
.. pH 12.6** Not applicable
n Total Alkalinity 2900 350
.. S04 320 250
It Total Dissolved Solids 16,000 570
Electrostatic Ca 360 550
" Mg 530 1900
.. Hardness 3100* 1100
.. pH 12.6* Not applicable
" Total Alkalinity 2400 1900
" S04 620 410
" Total Dissolved Solids 14,000 3100
* As CaC03
** Median Value, Units
-192-
-------
1- -
The preliminary data from the Shawnee tests
have been projected to an actual steam plant burning a
large quantity of coal and having low receiving stream
flows available for dilution. Figure 52 shows the effects
on the receiving stream of limestone injection. The allow-
able loads are based on maximum concentrations in the stream
of:
. dissolved solids - 500 mg/l
. S04 - 150 mg/l
. hardness - 50% rise in concentration
above 100 mg/l
. ph - 8.5 units
The assumed available flow for dilution is one-half the aver-
age flow. These results, while of a preliminary nature,
clearly show that further consideration must be given to
the water quality aspects of the limestone injection
process before the process can be considered ready for wide-
spread ~ommercial application. Indeed, water pollution
ultimately may be the most severe problem facing the lime-
stone injection process.
The above discussion ~nd tables presented were
extracted from the Morris paper and were based on preliminary
Dry Limestone Process data from TVA's Shawnee plant. Addi-
tional process data have recently been made available in the
TVA October-December 1970 Progress Report(34) on the Shawnee
plant test results. Typical ash sluice water quality data
from the mechanical and electrostatic collectors correspond-
ing to the more recent information is presented in Table 30.
The effect of the limestone injection tests on three water
quality parameters is shown in Table 31. Comparison of
these results with the earlier test data (Tables 28 and 29)
-193-
-------
DISSOLVED
SOLIDS
HARDNESS
I
I-'
I.D
~
S04
r77I MECHANICAL AND ELECTOSTATIC
~ FLY ASH COLLECTORS
1>:-:-:1 LIMESTONE INJECTION
. . . ADDED
pH
""""'" ,..... I'" II'" ......... ...... .
.. ,.,... .... . .... ,....., ,.. ... ,... If "" 8f'
. '8'" 'f... ""'" 8', ,.... If"" If. .8.. " .
... If. 8" 8'- . ,. 8f..', ,..... '8"""""'"
............ 1"8""""'" ",.8f......... .
8"""'" " . f" '8" ,.... 'f"""" ........ .
...-..... 8" f"'" ..". ff" ..... ff"""" .
., If"" .... ........ ,..... ..... If.. '8""
I..."... .f.' ...... ........ .... f',. f.. ..... .
",.8.... ,... f""
. of" ,. ""'" ..,
...-.... """'"
""'" ..... If ...
"-"" .,.. ..,..
....... ... ,. "'"
.,. .f... 'f"" f,..
.,. 8f" .. """ If
.,. '8"""'" .......
. . . . . . . . . . . . . .. .......
....... ........ ... ....
. . . .. .. . . . . . . .. .......
. . . . . . . . . . . . . . . . . . . . . .
.............. .......
. . . . . . . . . . . . . .. ... . . . .
. . . . . . . . . . . . . . . . . . . . .. .
. . . . . . . . .. . . .. .......
o
20 40 60 80 100
PERCENT OF ALLOWABLE STREAM CONCENTRATION
120
FIGURE 52
WATER QUALITY OF RECEIVING STREAM
AT
-
CRITICAL PLANT LOAD AND STREAMFLOWS
-------
TABLE 30
SLUICE WATER QUALITY - NORMAL PLANT OPERATION
Concentration
Type Sluice Parameter Mean Med. Standard
Mechanical pH 11.5 11.6 6.0-9.0
Mechanical Dis. Solids 2000 1550 500
Mechanical Hardness 680 480 200
Electrostatic pH 9.9 10.0 6.0-9.0
Electrostatic Dis. Solids 610 525 500
Electrostatic Hardness 300 265 200
TABLE 31
SLUICE WATER QUALITY - LIMESTONE INJECTION
Concentration
Without With %
Type Sluice Parameter Limestone Limestone Increase
Electrostatic Calcium 200 1180 490
Electrostatic pH 10.0 12.2
Electrostatic Dis. Solids 300 11,500 3730
Mechanical Calcium 430 1310 205
Mechanical pH 11.5 12.4
Mechanical Dis. Solids 680 12,100 1680
-195-
-------
r-
shows that a large increase in the total dissolved solids
content is still being experienced. In fact, the reported
values indicate that a high degree of dilution (--25 to 1)
will be necessary to avoid excessive concentration in the
receiving stream.
As cited previously, the overall solids dis-
posal problem for the limestone injection process is a
major one, and TVA studies in this area are continuing.
Some aspects of the problem still under investigation are:
the effect of heavy metal contaminants on effluent stan-
dards, the effect of limestone reaction products on ash
pond settling characteristics, and overall effects on
water recycle costs and problems. Firm design recommenda-
tions for the disposal system cannot be derived until the
completion of the TVA Shawnee plant test program.
-196-
-------
V.
REFERENCES
(1)
(2)
(3 )
(4)
(5)
(6)
(7)
(8)
(9 )
(10)
(11)
(12)
"Investigation of The Reactivity of Limestone
and Dolomite for Capturing S02 from Flue
Gas", Battelle Memorial Institute Final
Report (November 20, 1970)
"Additive Injection for Sulfur Dioxide Control -
A Pilot Plant Study", The Babcock and Wilcox
Company Final Report (March 27, 1970)
"Pilot Plant Moving Grate Furnace Study of
Limestone-Dolomite for Control of Sulfur
Dioxide in Combustion Flue Gas", Peabody
Coal Company Final Rt~~~~ (May 27,1969)
Borgwardt, R.H., "Isothermal Reactivity of
Selected Calcined Limestones With S02",
Paper presented at the Fourth Dry Limestone
Process Symposium (June 22-26, 1970)
Rootare, H.M., and Prenzlow, C.F.
J. Phys. Chem., Z!, 2733 (1967)
TVA Fundamental Research Branch, Monthly
Project Report, "Removal of Sulfur Dioxide
from Stack Gases" (May 1968)
Satterfield, C.N., and Sherwood, T.K.,
The Role of Diffusion in Catal~,
Addison-Wesley Publishing Co. Inc. (1963)
Boynton, R.S., "Chemistry and Technology
of Lime and Limestone", 148, Interscie~ce
Publishers (1966) .
Staley, H.R., and Greenfeld, S.H.,
Ind. Eng. Chem.!!, 520 (1949)
Levenspiel, 0., Chemical Reaction Engineering,
John Wiley & Sons, Inc., New York, 43 (1962)
Ishida, M., and Wen, C.Y., A.I.Ch.E. Journal,
!i, 311 (1968)
Ishida, M., and Wen, C.Y., Chem. Eng. Sci., ~,
125 (1968)
-197-
-------
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
Howard, J.B., M.I.T. Final Report to APCO
under Contract No. CPA-22-69-44:
"Mathematical Model of The Reaction Between
Sulfur Dioxide and Calcine Particles",
(Nov. 1970)
Borgwardt, R.H., "Kinetics of The Reaction
of S02 with Calcined Limestone", Environ-
mental Science and Technology, 4, No.1, 59
(1970) -
"Fundamental Study of Fixation by Lime and
Magnesia", Battelle Memorial Institute
Report (June 30, 1966) .
Drehmel, D.C., "Test to Evaluate The Over-
burning of Carbonate Rocks", Paper presented
at the Fourth International Symposium on
Dry Limestone for S02 Control, Paducah,
Kentucky (June 22-26, 1970)
.Ohno, Y., "The Direct Adsorption of C02 by
Quicklime", Gypsum and Lime, No. 28,
22-28 (1957)
TVA Fundamental Research Branch, Monthly
project Report, "Removal of Sulfur Dioxide
from Stack Gases" (July, 1968)
Zenz, F.A., and Othmer, D.F., Fluidization
and Fluid-Particle Systems, Reinhold
Publishing Corp., New York, 421-436 (1960)
"Investigation of The Reactivity of Limestone
and Dolomite for Capturing S02 from Flue Gas",
. Battelle Memorial Institute Report (August 30, 1968)
JOhnstone, H.F., pigford, R.L., and Chapin, J.H.,
"Heat Transfer to Clouds of Falling Particles",
Trans. A.I.Ch.E., IL, 95 (1941)
Leva, M., Fluidization, McGraw-Hill PUblishing
Co., New York (1959) .
Thomas, David G., "Dry Limestone Injection:
Factors Affecting The Reaction of S02 with
Limestone Particles", Oak Ridge National
Laboratory, Oak Ridge, Tennessee (August, 1970)
.
-198-
-------
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
Kato, Kunio, Hiroshi, Kubota and Wen, C.Y.,
"Mass Transfer in Fixed and Fluidized Beds",
Chemical Engineering Symposium Series, 66,
Number 105 (1970) --
Borgwardt, Robert H., and Harvey, Richard D.,
"Physical properties of Carbonate Rocks
Related to S02 Reactivity" (1971)
Harvey, R.D., Interim Report to APCO under
Contract No. CPA 22-69-65: "Petrographic
and Mineralogical Characteristics of
Carbonate Rocks Related to Sorption of
Sulfur Oxides in Flue Gas", (June 22, 1970)
McClellan, G.H., "Physical Characterization
of Calcined and Sulfated Limestones",
Paper presented at the Fourth Dry Limestone
Process Symposium (June 22-26, 1970)
Pickett, J.L., TVA Report No. 54:
"Electrostatic Fly Ash Collector Performance
Test - Shawnee Stearn Plant Unit 10"
(July 9-August 6, 1969) .
McDonald, W.M., TVA Report No. 62:
"Electrostatic Fly Ash Collector Performance
With Limestone Injection - Shawnee Steam
Plant Unit 10 precipitator A" (June 9-July 15,
1970)
Brown, R.F., Research-Cottrell Inc., Final Report
Technical Memorandum CES 70-1: "Determination
of Bulk Electrical Resistivity Characteristics
of Boiler Flue Gas Desulfurization Additives
and Their Reaction Products" (Jan. 19, 1970)
Attig, R.C., and Duzy, A.F., "Coal Deposition
Studies and Application to Boiler Design",
Vol. 31, Proceedings of the American Power
Conference (1969)
Barnhart, D.H., and Williams, p.e., "The
Sintering Test - An Index to Ash Fouling
Tendency", Transactions of the ASHE (August 1956)
-199-
-------
(33)
(34)
(35)
(36)
(37)
Morris, J.S.", "The Dry Limestone Injection
Process for S02 Control - Solid Waste and
Water Quality Considerations", Paper pre-
sented at the Fourth Dry Limestone Process
Symposium (June 22-26, 1970)
Reese, J.T., TVA Quarterly Progress Report,
October-December 1970, Dry Limestone Injection
Project 2438 (Feb. 19, 1971)
TVA Conceptual Design and Cost Study, "Sulfur
Dioxide Removal from Power Plant Stack Gas -
Sorption by Limestone or Lime - Dry Process",
Prepared for the National Center for Air
Pollution Control (1968).
Chrusciel, R. T., "Investigation of American
Coal and Limestone Shipped to Energopomiar",
letter report to D. T. Clay (OAP)", December 14,
1970.
Womble, T. D., Jr., Reese, J. T., "The Dry
Limestone Injection Process For S02 Control",
Paper presented at the Fourth International
Symposium on Dry Limestone Injection Process
June 22-26, 1970.
"\. . ).,
~ . "."
<' ". ,
- ) :
-200-
-------
BATTELLE MEMORIAL INSTITUTE, COLUMBUS
LABORATORIESs "FUNDAMENTAL STUDY OF
SULFUR FIXATION BY LIME AND MAGNESIA",
(June 30, 1966)
APPENDIX A
THERMOCHEMICAL VALUES FOR BASIC
REACTIONS IN FLUE GAS SULFUR FIXATION
-201-
-------
TABLE A-I.
TABLE A-2.
TABLE A-3.
fABLE A-4.
~ABLE A-5.
~ABLE A-6.
'.
~ABLE A-7.
TA13LE A-S.
R EAC 'nO;\;S CI V ).;t,; IN TAl \ 1..,.;:;
CaO(c) + ~ S2(/':) + 2 02(g) :: C"S04(C)
. 1
CaO(c) + 502(g) -I- '2 0z(g) :: CaSO 4(c)
1 3
MgO(c) + Z S2(g) + l 02.(g) :;: Mt:S0'1(c)
~gO(c) + S02(g) + ~ 02 (g) :: MgS0'1 (c)
CaMg(Co)z(c) :: CaC03(c) + MgC03(c)
CaMg(C03)Z :: CaCO) (c) + MgO(c) + C02(g)
1
Caso) (c) + Z 0z(g) == CaSO'1 (c)
CaS04(c) ::: CaS(c) + 20l(g)
MgS04(C} :: MgS(c) + 20l(g)
1
MgS03(c) + Z 0l :: MgS0'1(c)
MgC03(c) + SOl (g) :: MgS03{c) + COl{g)
CaC03(c) + SOl (g) :: CaS03(c) + COl(g)
CaO(c) + SOl(g) :: CaS03 (c)
CaO(c) + COl(g) :: CaC03(c)
MgO(c) + SOl(g) = MgS03 (c)
MgO(c).+ COz(g) = MgC03 (c)
-202-
-------
TABLE A-9.
TABLE A-IO.
.. ~
-------
;. -"'!....
TAB.T..E A-l?
. f
TABLE A-lS.
TABLE A-19.
REACT!O~S GIVE~ IN TABLES
(Continued)
1
Na2S04(c) ~ Na20(c) + S02(S) + 2.' 02(g)
"
. . 3
A12(SO 4)3 (c) :: AiZO) (c) + 3S02(g) + Z 0Z(g)
1 1
FeS04(c) :: 2: Fe203 (c) + S02(g) + 4 02(g)
1 1
FeSO 4(c) :: 3' Fe) 04 (c) + SOZ(g) + "2 02(G)
1
FeS04(c) :: FeO(c) + S02(g) + Z 0Z(g)
.'.
-204-
-------
TABLE A-I. THE THEIt\1QCBEMISTRY 0;: 5UU"l;R f1XATiO~ BY CALCIU~,! OX!L)E
.----
C;\Q(.:) + ~. $'i(g) -t ~ O:C.lSo.(C)(.1)
~ 2 .
T.:IU?, AfoR' cal m<>!.:-1 t\FoR' cal mole-1 Tenia'.
f Lobl0 K LoSlO K K
300 -170,005 88. O:~5 . -91,036 41.122 4~';:.2
.100 -165,391 15.6.14 -81,291 39.926 417.8
500 -1GO, GS3 65.846 -83.566 34.245 533.3
liOO -155,981 51.881 -';9.843 29.630 583.9
700 -1.51,317 51. 311 -16, 154 25.821 6.... .4
SOU -146,1358 45.181 -72,464 22.C~3 700.0
900 -10;2,023 41.017 -68,816 19.904 755.6
1000 -131,421 37.026 -65,185 11.5G'3 811.1
1100 -132,839 33.496 -61,587 15.523 86u.7
1200 -128,295 30.403 -58,018 13.74~ 922.2
1300 -123,770 27.664 -54,476 12.175 971.6
1..00 -119.293 25.231 -50,971 10.7132 lC3a.3
1500 -11':',1343 23.050 -47,496 9.532 1033.9
1(;00 -110,443 21. 091 -44,073 8.,a6 114-:. . ..
1700 -106,063 19.311 -40,658 7.404 1200.0
1S00 -101.734 17.707 -27,311 6.494 1255.6
1900 -97,'446 16.243 -33,985 5.665 1311.1
2000 -93,192 14.902 -30,711 4.911 1366.7
2500 -72, GOO(b) 9.648 -14,94g(b) 1.981 1644.4
:;000 -53,152 6.043 -216 0.031 1922.2
(a) Da:a b.1~cd 0., App~aJix Reicrcnce. (1, 7).
(b) Mcl:i.,S ?\)int of CaSO.. = 1123 K.
TABLE A-2. THI: THEiU,,1OCHEMISTRY OF 5U12UR F1XATIO~ BY MAG~r:SIUM OXIDE
Temp, MgO(c).. S02(g)-t % 0zw= MgSO..(C)(a)
F t\FoR' cal mole -1 Log10 K
300 -f;2,020 32.103
400 -58,245 26.641
500 -54.4SB 22.329
600 -50,733 18.827
700 -..1,003 15.941
8iJO " . -43,271 13.509
000 -39,571 11. 445
10:>0 -35,885 9.669
1100 -32,224 8.125
1~iJO -28,598 6.775
1300 -24,973 . 5.581
1400 -21,3!>2 4.524
1.500 -17,823 3.577
16C1D -14,30(; 2.732
1700 -10,793 1.966
lSiiO -7,339 1.211
1900 -3,903 0,651
2000 -511 0.082
25:'0 15,9iJ5 -2.114
3iJvO 31,332 -3.562
1 3 'a)
MgO(c)+- 52(g)+- 0;2(g) = Mg50.;(c)\
2 2 Temp.
t\FoR' cal mole-1 LoS10 K
-133,867 69,293 422.2
-130,091 . 59.502 477.8
-126,299 51. 756 533.3
-122,483 45.453 588.9
-118,660 40.242 13.:4 ,.1
-114,827 35. 8.~9 700.0
-112,787 32.621 755.6
-108,125 29. 133 811. 1
-103,486 29.094 8136.7
-98,874 23.431 922.2
-94,281 21.072 911.8
-89,726 18.911 1033.3
-85,181 17.096 105S.a
-80,690 15.409 lltA, 4
-76,203 13.878 1200.0
-71.116 12.493 1255.6
-67,370 11.229 13 ~ 1. 1
-63,OOi(b) 10.075 132'::.7
-41,962 5.577 lc"~.~~
-21,138 2.411 192'2.~
(.1) D:'I.1 bas.;c.I un A~i1cr.Jix R-:::'cr~.\e~ (2).
(D) :-'~::50.~ c.I':c<>l1Iposo.:s .11 13!>1 K.
. ~... ..
-205-
-------
TABLE A-3. THE THERMOCHEMISTRY OF DOW:-"iI7E DISSOCIATION
Tem?,
F
CaM£(CO:j)-';cC) = CaCO:.\Cc) + ~lbC03(C)(a)
a~R' cal molc-l LoSI0 K
CaMgCC03)Z(C):;: C.1C03(c) + }'ioO(c);- C02(ja)
6~R' cal mole-I LoSlO K
T~In~1
K
300.
400
~OO
GOO
700
800
900
(a) Data b.1s~d 001 A??\~:idiX Reference (11). Data ~timated by Brewer's approximation, AppenJix Reference (13).
2,G02 -1.347 13,021 -6.740 t,Z2.2
2,558 -1.170 10,670 -<'.880 4.77. 9
2,513 -1.030 8,337 -3. .W; 533.3 .
2,4C9 -0,916 6,019 -2.234 528.9
2,424 -0.822 3,722 -1.2G2 6/..;.4
2,3:50 -0.743 1,442 -0.450, 700.0
2.336 -0.676 -617 +0.23:> 755.6
TABLE A-4. THE THERMOCHEMISTRY 0..7 CALCIUM SULFATE AND CALCIUM SULFIDE FORMA no:,
,
, 1 CaSO,(c) = CaS(c) + 2 02(g)(b) \,
Temp, CaS03(e) + 2' O,tS) . CaS04c) (a)
Tem? I,
F M"R' cal mOle-1 LogI0'!.' &F"R' cal mole-1 LogIO K K
300 -52,182 27.011 191,634 -99.195 422.2
400 -50,875 23.269 186,892 -85,482 477.8
500 -49,515 ' 20.291 182.165 -74.649 533.3
600 -48,115 17.855 177,444 -65.849 586.9
700 -46,699 15.837 172.145 -58.5d5 6-V- .4
800 -45.279 14.136 168,059 -52.468 7DO.O
900 -44.891 12.984 163,423 -47.269 155.6
1000 -43,126 11.181 158,809 '-42.189 811.1
1100 -42.620 10.747 154,172 -38.875 8uQ.7
1200 -41.675 9.876 149,573 -35.445 922.2
13()i) -40,602 9.074 144,998 -32.407 917.8
1';00' . ;~.,. -39,568 8.368 140,498 -29.715 1033.3
1500 . -3S,5GO 7.739 136,048 -21,305 1085.9
1600.' -36,185 7.026 131.599 -25.131 114-}. 4
1700 -35,848 6.528 127,168 -23.159 1200.0
1800 -34.954 6.084 122,834 -21.360 1255.6
1900 -310.077 5.680 118.536 -19.758 1311.1
2000 -33,258 5.318 114.225 -18.265 1360.7
2500 -29,81.5 3.966 93.600 -12.439 16~~~.';
.:!UOO -24.293 2.762 19'22.2
(J.) D.1.:.. oas.:c; on A~~e..dix r..e:'ere:1ces(1~3, 6. 1,9). Data estimateJ by &rewe,'s approximation, A;>pc..dix Rdcr~:i.;e (13).
(b) D;.:;. b:.;;cd 001 A;>;>er,d;x Rcfe.ences (1,4, 7). Data cstimarcd by Brewer's appruximation. Appendix Reference (13).
:-';otc; ~ieltin(; point of CaS:: 1123 K.
, , !..:.
, -206-
-------
TAtlLE A-~. THE 'rHEIt\1OCIIEMISTRY Or MAGt\i:SIUM ~ULFIDi:: AI'D M"G~£SIUM SUlfATE fO:;''.:A7IO~
T..:mjl. M(;SO.;(c) II M;:;S{c) 9 2 02(S)(a)
F 6:°R' cal molc-1 1.0&10 K
300 18~,710 -96.128
~.)O 160.870 -82.728
sea 176.053 -72.144
&\)0 171,236 -63.546
700 166,';~2 -56.450
600 161,665 -50.472
900 158,011 -~5.701
1000 152,051 -~O.968
1100 147,3~3 -37.15~
1~00 142, 6~n{c) -33.8~5
1300 138.172 -30.852
HOO 133.565 -28.N9
1500 128.908 -25. 88~
1600 124.~31 -23.162
1700 119,897 -21.835
1800 115.426 -20.090
1900 110,913 -18.~98
20\)0 106,565 -17.040
2500 85.085 -11.308
3000 64.589 -'.343
MgS03(C) .. 1. 02 . M~50.;(C)(b)
2
tweR' ca\ molc-1
1.01:10 K
27.802
23.887
20.78';
18.258
16.1C4
14. 398
Tern;>,
K
~22.2
477.8
533.3
508.9
~.~
700.0
755.6
811.1
866.7
922.2
S11.8
"1033.3.
. 1038.9
11~.4
1200.0
1255.6
1311.1
1366.7
1~.4
1922.2
(a) D.;t;; bJ~.:d 0:1 App.:r..1uc Rdeccnce (2).
(b) Data b:.~td on Ap;>.;r"Hx Rde;.;nce~ (l-3, 9).
(c) Mellin.. point of M:;S . 923 K. .
-53,111
-52,224
-50.719
-49,199
. -41,662
-4G. lJ. 7
TABLE ".6. THE THZR:,~OCHZ:MISTRY OF SULFUR DIOXIDE FiXATION BY CALCIUM CARDOl>iATE
AND MAGNESIUM CARJONATE
Teli.;>,
F
300
';00
500
600
100
600
900 '
.
100i)
1100
1200
1300
gOO
1500 '
}&OO
1100
1800
gOO
2000
2500
~OOO
CaC03(c) 9 S~(S)&:C..S03~~)+ CO~(3)(b) 7e:np,
~eR' cal mole-1 Lo310 K K
-12,453 6.~5 422.2
-12.103 S.5~0 ';11.8
-11,806 4.833 533.3
-11.539 4.232 583.9
-n.298 3.832 ~.4
-11,OS1 3.450 100.0
-9,796 2.e33 155.6
-9,317 2.510 811.1
-8,'199 2.219 6lio.'/
-8,130 1.921 922.2
-7,606 1. 699 977.8
-7,06S(c) 1. 495 1033.3
-G,513 1. 3';7 1v3S.9
-6,766 1.29'2 11?-1. 4.
-G,177 1.125 l~vv.O
-S.601 0.9i5 1:55.0
-S,013 0.635 1311.1
-4,409 0.705 1:)<3:>,1
-1.131 0.150 IG~~.~
.801 0.091 1~:2.2
~:SC03(c)+ 502(;)= MgSO:;(c)9 COzeS)ea)
6.",oR. cal mole -1 LoS10 K
2.110
2.091
2,056
2,016
1.957
1,908
-1. 092
-0.956
-0.842
-0.748
-0.664
-0.S96
~:J ~.;.cc ur, i.;>;>.;;oJiA Rcfcr.;:r.cc~ (1-3, 1. (1).
(b) Da:J boll':"': 0:1 A:>?c~.diA Rd.~rcr.cc.1 (1-3. 6. 'I. 9).
(c) C:.C03 ~1crffiochcrrJcal1y umtable in (urnace atmo$;>hcre.
-207-
-------
,
'.
TAi3LE A-7. Ti-IE TH:i\.\:OCI-~}l.ISTRY or CALCIUM OXIDE ''11TH SULFU~ DIOXID~ A:-'-o CArDO:.; DIOXlD2
T-.:mp. CaO( c) l' S02(;) = CaS03(C)(a) CaO(c) + C02(g) = C.'lCO:;.(cj(b) Temp.
F N°R' cal molc-l Log10 K N°R' cal mole-l LogI0 K K
300 -33,85~ 20.112 -26.401 13.660 '122.2
~OO -3G.416 16.656 -24.313 11.120 ~77.8
500 -3~.051 13.954 -22.245 9.116 533.3
GOO -31.129 11.175 -20,190 1.432 58a.9
700 -29,454 9.989 -18.156 6.157 e';";.4
SOO -27,185 8.481 -16,134 5.037 700.0
900 -23.925 6.920 -g. 129 4.086 755.6
1000 -21.459 5.182 -12.143 3.272 811.1
1100 -18.SU1 4.183 -10.168 2.564 660.7
1200 -lG.3~3 3.873 -8.213 1. 946 922.2
1300 -13,814 3.101 -6.268 1. 401 911.8
1400 -11,409 2.413 -4,340 0.918 1033.3
1500 -8,936 1. 793 -2.423 0.486 1058.9
1600 -7.289 1.392 -523 0.100 114:..4
1700 -4.810 0.816 1,361 -0.249 1200.0
"1800 -2,357 0.410 3,244 -0.565 1255.6
190~ 92 -0.015 5,105 -0.851 1311.1
2000 2.54S -0.407 6,951 -1.112 13136.7
2500 14,896 -1.980 16.021 -2.130 Ie.;..'..!.
3000 24.01'1 -2.'131 24,818 -2.822 1922.2
(a) Data b..se.:i Oil Ap?cndLx Re:<:rcnces (1-3. 6, 9). Data estirn3ted by Brewer's approximation, Appendix R~icrcnce (13).
(b) Dat.. b.15Cd on Appendix RCIer.;:nces (1. 1).
TABLE A-S. THE THE:tV.OCHEMlSTRY O~ MAGNESIU~1 OXIDE REACTING WI7H SULFUR DIOXIDE: .t..~'D CAREO:-: DiOXW::
T~m? MgO(c) + SOZ(g) ::; :':;SO;)(c)(a) MgO(c) + C02(g) :: },:;CO:(C)(b) Te:rJp.
' .
F ~FoR' cal mole-I LogI0 i< 6. . I -1 LoglO K K
F R' cal mo e
300 -8,309 4.301 -10,419 5.393 I-iI"\t) t')
....-...
400 -6,021 2.754 -8,112 3.710 477.8
500 . -3,769 1.544 -5.525. 2.381 533.3
eoo -1,534 0.569 -3,550 1.317 55.3.9
100 659 -0.223 -1,298 0.440 6';'~.4
800 2.8~6 -0.888 938 -0.293 700.0
900 3,153 -0.912 7~5.6
(a) Do'lt:. o.l:.cd or. A?;>e~.:l1x R.dc:cr.ces (1-3, 9). D..ta cstim.lted by Biewcr's ,::,ppiox:mation. A?P~i,,jLx il.ek;e~ce (13).
(~) Data b..sed 0:1 Ap;>.:nC:ix Rcfc;ences (1. 7).
-208-
-------
TAGLE A~9. THE THER~~OCIJ£~IlSTaY Of MAG:-:ESlU~1 CARf\O~ATC: r-EACTING WITti SULFUR OXIDES
Mc;C0;:j( c) ;- S03(g) .
M~S0-1(c) ;- CO;:(g),a} .
Tcm?
~.
ll.~OR' c.11 mol.:-1
LoglO I(
30'>
.;00
500
600
100
SOil
-37,615
-37,389
-37.151
-36,838
-36, 625
-:>6,331
19.410
17.101
15.224
13.693
12.421
11. 343
1
Mc;C03'c) ;- SO~(b) ;- 2" 02(g) :a
MgS04(c) + COZ(,;)Cb)
Temp,
K
~F.R' cal mole-l
LoSIO K
-51,601
-50,133
-48,663
-41.183
-45,705
-44,209
26.110
22.930
19.942
17.510
15.500
13.802
100.0
~22.2
~77.8
533.3
588.9
644.4
~a) D.1t.1 b.15CC 0:1 A?P~i.dix Rde:c:1ccs (2. 7. 9).
:b) D.1t.1 b.1,;.;:d or: Ap?cr:dix Refcrcnces (2, 7).
TABLE A-10. THE THER.\10Cn2M1STRY Of CALCIUM CARBONATE REACTI~G WITH SULfUR OXID:::S
1
CaC03(c) ;- SOZ(g) ;- 2" 02(g) .
C.1S04(c) ;- C02(g)(.1)
rem?,
F MOR' cal mole-1 LoSI0 K
300 -64,635 33.457
.:.00 -62,978 28.805
500 -61,321 25,129
600 -59,654 22.138
700 . -57,997 19.669
800 -56,330 17.586
900 -54,687 15.817
1000 -53,0':'3 14.292
11CO -51,419 12.965
1200 -49,805 11. 803
1300 ' . -48.20S 10,775
gOO -46. 637(c) 9.864
1500 -45,073 9.0~6
l(;CO -43,551 8.317
1700 -42,025 7.653
1:::00 -40,555 7.059
1:)00 -39,090 6.516
2000 -37,667 6.023
2500 -30,9';'0 4.117
3000 -25.09':' 2.853
CaC03(c) ;- S03(g) .
CaS04(c) ;- COzW(b)
Temp.
~F.R' cal r.;ole-1
Log10 K
K
-50,649
-50,234
-49.809
-49,369
-48.917
-48.452
-49,208
-47,621
-47,216
-46,955
-46,552
-46. 176(c)
-45,810
-45,462
-45,107
-44,782
-44,464
-44,216
26.217
22.970
20.411
18.321
16.589
15.121
14.232
12.831
11. 905
11.121
10.404.
9.766
9.19.~
422.2
411.8
533.3
589.9
6.g...
700.0
755.6
811.1
866.7
9'2'2.2
977.8
1033.3
1083.9
IH~...
1200.0
1255.6
1311.1
13~6.';
8.682
8.215
7.79t.
7.411
7.070
16.....'..4
1922.2
l) Data ba.c.;! un Ap~c..cix R.:fcrcr.c(:. (1, 7).
?) D.:!ta ~.:!s~d oa A?~h~nc!ix Rd~renccs (2, 1, 9).
:) CaC03 them1vchc;-nic.1l1y ur:stablc in fUro101CC atmo~phcre.
-209-
-------
TAuL£ A-ll. Tl-IE TEC:i\..'l.OCHEMISTRY Or' SULFUR A;--;D OXYGi:N AS GASES
T.:m?, ~ S;! (S) + O:;! (£) . S02(g)(a) 503(g) .. 502(1;) + ~ O;:c:;P» Temp,
F MOR' C.11 mule -1 Log10 K N°R' cal molc-1 Log10 K K
300 -71. 9~2 31.239 13,986 -1.239 422.2
400 -71. 9~a 32.8!)9 12. 144 -5.829 ~17.8
500 -11,879 29.455. 11,512 -4.711 533.3
GOO -11,805 26.641 10,285 -3.811' 538.9
100 -11.689 24.313 9.080 -3.0'1J G-h.4
800 -11,562 22.342 1,818 -2"~60 100.0
900 -'73,216 21.1'76 .5,.4'79 -1.584 155.6
1000 -12,240 19.464 5,422 -1.461 811.1
1100 -11,262 1'7.969 4,203 -1.060 86G.1
1200 -'70.434 16.691 2,850 -0.6'75 922.2
1300 -69,400 15.524 1,656 -0.310 91'1.8
1400 -68,4'30 14.485 461 -0.098 1033.3
1500 -61,520 13.551 -'731 0.148 1088.9
11300 -66,552 12.'709 -1,911 0.3C5 11""'.4
1700 -65.582 11. 944 -3,082 0.561 1200.0
1800 -64.61<. 11.246 -4,227 0.136 1255.5
1900 -63,6';1 10.609 -5,314 0,896 1311.1
2000 -62,681 '10.023 -6.549 1.04'1 1300.7
2500 -5'7,86'7 '7.691 16?4.4
3000 -53.010 6.034 192'2.'2
(a) Data bas.:d 0:1 Aj>p':io~ix Rcier.:nce (2).
(b) Data b..s~ 1,)1'\ APi)i~.l'\dix References (2, 9).
TABLE A-1'l, THE THER."Y:OCHEMISTRY OF CALCIUM OXIDE A~ MAG~ESIUM OXIDE ~ITH SUU'0R GAS
CaO(c) + 1 St)(g) . C.1S(c) + l02(8)(.1) 1 1 (~
Temp. 2 .. 2 MgO(c) + '2 52(g). MgS(c)+'2 O'I.(g) Temp.
F 6FoR' cal mole-1 Log10 K MOR' cal mole -I Log10 K K
300 21,539 -11.149 51,'748 -26.186 422.2
400 21,511 -9.839 50,691 -23.188 411.8
500 21.483 -8.804 49,686 -20,361 533.3
600 21,456 -'7.962 48,698 -18.012 588.9
100 21,428 -'7.261 41.'760 -16.191 6" .
...... ..
800 21.400 -6.681 46,832 -14.621 700.0
' .
900 21,400 -6.189 45,224 -13.080 755.6
. 1000 21,388 -5.'763 43.926 -11. '135 811.1
1100 21.333 -5.319 43.862 -11. 059 8~6.7
1200. 21,218 -5.042 43,'799 -10.379 92'2.2
1300 21,222 -4,'143 43,739 -9,176 917.8
gOO 21.200 -4.484 43,683 -9.23~ 1033.3
1500 21.200 -4.255 43,625 -8.'155 1038.9
1r:OO 21,156 -4.040 43.513 -8.322 11.;";...
1'100 21,100 -3,843 43.522 -'1.926 1'20J.0
1800 21,100 ~3,6'73 43.413 -1.5.31 1255.6
1900 21,090 -3,515 43,423 -'7.238 1311.1
~OC/O 21.033 -3.3C3 43,3'13 -6.936 13136.;
2500 21,000 -2. '191 43,123 -5.'131 16.1";. ~
:iC/OO 21,000 -2.383 42,851 -4.8'12 1922. '2
(o.) D:.t~ b:..!.(:d 0:1. A?;c;:d ix R.::f~;~i:c": (t.).
(b) D"ta b:.scd 0:1 Appe:1dix Rde;e:1ce (2).
~Otc: ~:~j,in:; ?oil'\l of c:.s " 1123 K; m~lli:l~ point of MI!5 . 923 K.
-210-
-------
[~~~.~~.~~~~::~:~.~~~~-~~~ r~DUC.ro~~~~~~::.~~~.\TC J~ C:i,~;_~:,:_;:~~;:)- c..~,~~.~~~ ~"';-~~~'~,::~,:~~~
':C (~;) ~ C.\S('-.(:):.o CJ::>(':) l' .:-:::C(g)(.1) 4CO(b)'" C:lSO,;(C)" C.);:,;,') r .;cojd.l) T".i"f).
~1:1? . .------
. ~W'R. .::\1 I;',v:': -1 Logl0 K
~~J 1,~J9 -0.f.05
:':'vv -31. ~32 14.GJO
.. .".. ~lGJ.2~3 20.593
-V'-V
M'R' 01 mole-I
wgl0 K
!(
---.-...--
-~3,821
-.:02. i1?2
-3f'. .:2.3
13.0::1
1.803
5.CO~
7,.0
1 '21.)0
l'/jC
--_._---_.__.~... ~-
- -~- . .-..----
_. .--..---...
;) D.1t.l b.1s,,:J on A?£",..:nJi:'\ :\..::'.;;.;::c.:s (2. ... 7).
ASLE A-~';. TH".:: TEZ,,-\\':X:::::::-.:iSny O~ .nE REDUCTIO}! 0, M.-\G~ESIUM SULFA.'E BY C:iR.:O~~ A};D CAI80:-J },:I.):\O:':Di::
-------.--.
-----. ---- -- ------- ,----
.----------
e;.;?,
4C(b;) l' ~.!::;~v.;:c) .;; :-.:;s(c);- .:co.;dJ)
4CO\g);- },!gSO.;(c) 0: :-':~S(c) ... .;CO;::ii;)(a)
F
\,..' 1 .-1
~. R' CJ ;no;c
LogIIJ K
~F'R' cal m.:>:e-l
LoS\O K
Tc:;;'ip,
K
SCJ
1700
-4,'207
1.313
16.081
-50.503
-50,631
15,7C7
9.221
7\)0
1200
-S8,299
...--..---- -.
.) D.1t.l b.1>cJ o~ A??.:r.Jl:'\ R..:i"crc01ce (2).
TABLE A-IS. THE THERMOCHEMISTRY OF FOi\~lATIO~ O~. CALCIli},! SILIC/\T~S
ex? 2CaC\c) T SiO,,(c) :: Ca"'SiO~(c)(a) CaO(c) ... SiO., . CaSiO~(a)(a) TC:i-:1?,
- .. .. ,)
.' ;... CJl m"lc:-l . I I -I
F DceR- LoglO K R' C3 In" C Log10 K K
-
300 -30, no 15.896 .-21,249 10.999 ..,.., t')
..'" -.....
~J0 -30,770 . '14.074 -21.2.:03 9.716 ';' ,'j, 8
500 -30,S~O 12.638 -21,236 8.702 [.33.3
. 0;)0 -30,910 11.471 -21, 2~!) 7.878 :.iS3.9
':00 -30,910 10.S03 -21,223 1.193 6.~..4
800 ' . -31,C~0 9.691 -21,216 6.624 100.0
900 -31,110 8.998 -21.209 6.134 155,0
1000 -31,110 8.393 -21,203 5.713 SILl
1100 -31.240 7.811 -21,196 5,345 866,'1
1~00 -31,310 7.419 -21.18:1 5.021 S22.'.1
1:;00 -31,370 7.011 -21.183 4.13.~ 977.$
1.;JO -31.4~0 6.649 -21.110 4,419 1033.3
1~00 -31.510 6.324 -21.16~ 4.248 1088.9
1':;00 -31,570 0.028 -21.163 4.0':1 11';";..~
1';'00 -31, 6'~0 5.162 -21,156 3.853 1200.0
1200 -31,110 5.519 -21.1<:.9 3.631 1255.0
'.SjO -31,710 5.296 -21, g3 3.52.. 1311.1
.:,,0 -31,840 5,091 -21,136 3.3'30 13136.7
~OJ -32,173 4.276 164.~. 4
u:.:a ~.'1~~~ 0:1 .~.;->~~:-.~\x K~~'~:~.-.c~ (5). . ... ~- -
-211-
I I
-------
T A13LE A-IG. THE Tl-iZr,,\:OCH~~IISTRY O~ HYDRATION o;~ CALCIUM OXIDE Ah'D MAG:-;C:Sll';~.: "::,iDE
T~m? CaO(.:) + l-bO(g) : C..(Oi'i)..,(C)(3)
.. w
F AFoR' 1:.11 mule-l LogI0 K
300 -10.8;):,1 5.633
1.0" -8,95G 4.096
500 -7.061 2.894
GOO -5.190 1.926
700 -3,347 1.135
SO\) -1,526 0.476
9i>0 272 -0.079
1000 2,042 -0.550
MgO(c) + H~O(o) :; Mg(OH)2(C)(b)
Tem?
AFOR' cal mok-l
Log1u i<
K
-4,165
-2,197
.261
1,658
2.156
1.005
0.107
-0.615
422.2
477.8
533.3
52S.9
6~.~
700.0
755.6
811.1
(a) Dat3 =>J.$.::d 001 A??cn~i:\ Rd.:::.::01CCS (1, 7).
(b) Dat.. b..sed on A;>;>cnc ix RefeceOlce (2).
TABLE A-17. TriE THER.v.OCHE:-..nSTRY OF DISSOCIAT~ON OF SODIUM SUl.i-ATE AND ALUMn,1..i~: 5~t.FATE
T.:mp. N.12S04(c) :: ~a2C(c) + S02(g) T ~Oz(g)(a) AI2(S04>3(c) '" A1Z03(c) T 3Su2(g) + %.:-::: db) TCi::?
F A~R' cal mole-l Log10 K Ar-R. cal molc'! LVb~O K K
300 132,791 -68.736 120,881 -~. 571 422.2
400 125,436 -57.373 109,371 -50.025 (,77. S
5uO 118,081 -48.388 97,967 -~O.14u 533,3
600 .~ . 110,719 -3:.143
-41.088 86,628 599.9
700 103,365 -35.055 75,389 -25. 567 6.;";, t,
800 96,010 -29.974 64,210 -2i>.040 700,0
900 88,655 -25. 642 53.106 .,15.360 755.0
1000 81,300 -21.905 42,096 -11.3.i2 811. 1
1100 73,945 -18.645 31,134 -7.851 8(;13, '7
1200 66,591 -15.781 20,261 -".801 92~.2
1300 59.236 -13.239 9.431 -2.108 977. S
11,00 -I, 316 .0.275 1033,3
(O!) Data bJ.Scd Oi"l A:>?'::01d:x Rd.-:iencc (.1). Data estimated bl Brewer's approximation. A;:>;>endiX Reicrcnce (:;;).
(b) Data b;,seG Oil A;,pcildix RcfciCr.Ces (I, 7).
-212-
-------
1'AGLI: :\-1:;.
TJi:: Tl:l~;(\~0C:!i;:\~ISTRY 0:: f-mRJC S\.1U:A'n iO !'Ei,RjC ()X~;)2 A:\;) rE~f\O-;'i:,;\1C 0;';;;1;:
===.=-.=-.=.=:.::..:.:..==.::.--::-' -.----------.-- -~-:::...~~=====.=.:- ._-~ ._~:-_::.:.~==---:=::...=~:.: :.:.:-:':.-'::== :--=::,:~...- ---
T.:-.:l:P.
F
300
.;00
500
COO
700
$00
900
10::0
nO:l
1~JO
1300
1':00
1':'00
1600
1'iliO
1500
1:).)0
~OOO
~.;oo
3000
F,~~\:(~~ :.::~_:~0;,(') ": !'O'~i!'-) T 1. o.;.:(dA)
af-\. c.,). ;~:,)lc-1 wgJO K
J 1 (")
fcSO.;(c) '" ';:; r,,:;o.\(I:) ~ SOLC~) ~ -~~ \~ ji) "
-----. .",,--- '".. . o. ._-. --- - --_..- ---
(\1"1\, c;,1 11;,):(:' J 1.1\;10 K
.------ - -. -. ~-_.-.". ------ -----.- -_... --.....--- - 0_-
T (,iI1i'.
K
27, ~51
2';,3:1J
21,2S?'
]8,090
14.953
11, SOO
8,6~S
5,501
2,3.;B
-7:)9
-3,951
-7.093
-10,251
-13,397
- -16,55:1
-14,261
-11. j(;0
-8', 70~
-6.'117
-S.to?)
-3. fSlj
34,3%
30,%0
-17. 2u~
-14.10
-11. ~~4
21. :<'i,
2';, ]05
?0.6S1
17, ?':'O
-8.P45
-7.014
-5.3[05
-2. M]
-1. "f.2
-O.S92
O. 189
0.853
1.501
2.057
2.558
3.014
3. ~29
3.809
4.158
~.S4g
6,~7
]3,87.\)
10,3:15
6,~GIi
3,540
110
-3.315
.6,74.3
-10, ]69
- -13.600
-17,030
-20,455
.23,885
-41,020
-5S, 160
-3.~J7
-2.£01
-1. 7d;
-0. 83(J .
-0.024
0.701
l.:JM
1. 9.;?
2.4;7
9..904
'.409
3.819
S,45~
13.(i,~
-19,702
-22,8';~
-26,002
-41. '147
-47,499
D,iI,~ cstima.tcJ by Brew,~r's "'P?WXim,H,.,n, A??end IX R.;::"~rciicc (13).
. "'----'--"'---~--~'.----'''-------'. ~'-_....
.-.--.---...---..---- _. .---.-.-.
(a) D..... b.:is~c 0:1 Ai'lciidix Rd(:h~ii":CS (1, "I).
TABLE A-19. T!E THER.\~C\:!1EMISTRY Oc' D:SSCX::A-no;oJ or FERROUS SUli AiE
TO FERROUS OXIDE
Temp. FeSO.;(c) '"' Ft'o.:c) -+- 50;;(£) -+- ~ 0-;.(',.)") Temp.
F . -1 [.(1£10 K K
&f R' ca.1 mole
300 55,608 -28.'7IH 422.2
.{OO 51.600 -23.fn 477.8
....
. -19.506 533.3
500 47,600
600 43, ~92 -16.177 58S.9
700 39. S92 -13...27 6~;, ,i
SOO 35. 5~.';' -11.10~) 700.0
900 31,475 -9.133 75~.o
1000 27,f:i6 -7.430 811.1
1100 23,S6(J -S.9~3 SS6.7
1200 19,558 -01.637 9'''' "
"40'.-
1300 lS.Sf\) .3.478 977.8
HOO ll,5f~ -2. ~45 1033.3
1500 1,552 -1.516 1053.9
16C.~ 3,552 -0.678 1l';.~.'1
1700 ' -';56 0.OS3 l:!OJ.O
-
DJ~a t.:SL:1,,,j{c.J by tj;~\...~:fS ..:??rOX~t~1.H iCi..
(;.) DJ:a b.HC': ,):] r,??.:.<.iX F;'::;'':!Ci.CCS (1,7).
Ap?.:.n~ix "c:;c~.:.~c, (13).
-213-
4~:?. 2
4'j'j.3
[);33.3
[)~~:1, !)
(.Q.4
,00. (1
7 ;J;). (i
8)]. J
R{;G.7
97?-.2
!I"i7. (1
]0:13. :J
)0811.9
J ]'1':.4
1700.0
J25,'). (i
J:J 1 J. 1
J3l;o.7
J C4/.. 4,
J~?'l.. 2
-------
(1 )
,
(2)
(3)
(4)
(5)
.(6)
(7)
(8 )
(10)
. (11)
REFEREi':CES FOR THERMOCHEMICAL CALCU LA TIO;-:S
Latirncr, Wer.dell M., 9xidation Potentials, Sccond Edition, Prc:1ticc HaJl, Inc.,
New York (1952).
JANAF Thermochemical Data, issued by the'Dow Chemical Company, Midla.r-d,
Michigan.
Stull, D. R., and Sinke, G. C., Thermodynamic Properties of the Elements,
American Chemica.l Society, Washington, D. C. (1956).
Elliott, J. F., and Gleiscr, M., Thermochemistry tor Steel Making, Addison-
Wesley, Reading, Massachusetts (1960), Vol I.
Kubaschewski, 0., and Evans, E. L'I ~etallurgical Thermochemistry,
Pergamon Press, l'\CW York (1958).
Maslov, P. G., "Thermodynamic Characteristics of Calcium, Gallium, lndi\:.m,
and Thallium Compounds", Journal of General Chemiotry of the U. S. S. R.,
V ~ (5), 1387-1397 (1959).
Kelley, K. K., "Contributions to the Datil pft Theoretical Metallurgy", U. S.
Bureau of Mines Bull. No. 584 (1960),
Kelley, K. K. A and King, E. G., "Contributions to the Data on Theoretica.l
Metallurgy", U. S. Bureau of Mines Bull. No. 592 (1961).
(9)
Coughlin, J. P., "Contributions to the Dt\ti}. on Theoretical Metallurgy", U. S.
Bureau of :Mines Bull. No. 5~2. (1954).
'Wagman, D. D., Evans, W. H., Halowj I., Park~t', V. B., Bailey, S. M., and
Schumm, R. H., "Selected Values of ChemiQa1 Thermodynamic Properties",
National Bureau of Standards 'l'ec:hnical Note 270-1, Superintendent of Documents,
Washington, D. C., 1965.
Stout, J. W., and RObie, R. A., "Heat Capacity horn 11 to 3000 K, Entropy,
and Heat of Formation of Dolomite!', J, Phy. Chem., 67, 2248-2252 (1963).
.~. . -
(12)
Halla, F., "Note on the Thermodynamics of Formation of Dolomite", J. Phys.
Chern., ~ (3), 1065 (March, '1965).
(13 )
Quill, L. L., Ed., The Chemistry and Metallurgy of Miscellaneous Matel'iu.ls:
Thermodynamics, Paper 4, McGraw~Hill Book Company, Inc. J ~ew York (1950).
(14 )
Wicks, C. E., and Block, F. E., "Thermodynamic Properties of 65 Elements -
Their Oxides, Halides, Carbides, and Nitrides", U. S. Bureau of Mines Bull.
No. 605 (1963),
(15 )
Kelley, K. K., and Anderson, C, T., "Contributions to the Data on Theoretical
Metallurgy", U. S. Bureau of Mines Bull. No. 384, 1935.
( 16)
Kclley, K. K" "Contributions to the Data on Theoretical Metallurgy", U. S,
Bureau of Mines Bull. No. 406, 1937.
-214-
-------
ADDENDA
,
Dcsulfurizin,<::: Action of Hvdrated Lime
,
Since issuing this report, information has been received suggesting tha.t Ca(OH)2
is beirlg lI:>ea with considerable promise in Germany for the fixation of 502 in flue gas.
Slaked lirn~ had been omitted from the original calculations here because oi its instability
above quit~ moderate temperaturcs. However, in light of this demonstrated ability of
Ca(OH)2. to capture 502., the same sort oi calculations were made for the reaction
Ca(OH)Z + S02 - CaS03 + H20
as wer'c inclu.dcd initially in the report ~or other lime ",nd magnesia reactions.
..
Table A- ZO gives the rcsults of thermochemical ca.lculations for this reaction.
.The free- cnergy change, 6 FR' suggests that there is a good likelihood for the reaction
TABLE A-20.
THE THERMOCHEMISTRY OF CALCIUM HYDROXIDE
REACTING WITH SULFUR DIOXIDE TO FORM
CALCIUM SULFITE AND WATER VAPOR(a)
Ca(OH)2.(c) + SOz(g) ~ CaS03(c) + H2.0(g)
Temperature, ~Fo Temperature,
R'
F 'cal m01e- 1 Log10 K K
300 -2.7,972 +14.478 422..2.
400 -27,460 +12.. 559 477.8
500 -26,990 +11. 060 533. 3
600 -2.6,539 +9.848 588.9
700 -26,107 +8.853 644.4
800 -25,659 +8.010 700.0
900(b) -24,197 +6.998 755. 6
1000 -23,501 +6. 332 811.1
...{a) Data calculated from Tables A-7 and A-16.
(b) Ca(OH)2 is thermochemically unstable above 849 F in steam at 1 atmosphere pres.>urc.
to occur but Table A-16 shows that the upper temperature limits are clearly limited.
, '
As was shown in Table A-lb, Ca(OH)Z is thermodynamically unstable above 8.19 F in
stec:.m at 1 atmosphere pressure. How rapidly this dehydration will occur is not pre-
dictable, but the calculations 'definitely indic.ate that slaked lime should have only
limited usefulness except in relatively cool fluc gases. In fact, data from Table .::"-16
show that the dissociation temperatu:;c of Ca(OH)2 in flue gas will be 682 F wher. the
Huc gaz cor.tains 7.1 percent water vapor. At higher tem?eratures, ?tirticularly with
relz.i:ivcly lor.~ period.'> of exposure, Ca(OH)z would bc converted to CaO, and althousr.
the physical state of the solid might be different, it would behave the:;mochemically a6
CaO.
-215-
-------
l\,\th \.'':>:I~;h'I.:HI:; L\re \.~:-.;tl'cmcl~' ~o\'d dc~nlfurizil\~ "'::;I..'nls if cquiJibrillnl can be
.1~)Pl'l').,..'i.l'(:' H(\\\'('ycr, Ca(OIi)l, h~\s a lowcr lhermod'/J'urnic cificicncy than an c(iuiva-
l..::\t an~lH\J\I oi CaO, as is cyidcnt from the data in Table .(\-21. If C~,(0I-i)2 proves to be
~110::C dic\..tiyc as a desulfurizing agcnt th2.n CaO, thc behavior ca:1 be cxpiained best
on the basis of a more reactivc ph}'sical state of CaO resulting from dehydration of
C.l(OH)2, not one of greater thcrmod~'namic efficiency.
The likely reaction product of CaO or Ca(OH)2 with S02 is
in Table A-'l, CaS03 will be thermocl1cmic.:10-3
.,Iobo\'c Ji.>ociation t.:mp.:ratlirt'. or Ca( OH>2 in (Jue gas.
Reliability of Calc ulations
A question has bccn raised about the reliability of these thermochemical calcula-
tio.ns. How precisely do they define the actual equilibrium concentrations, and how
reliably can the calculations be used?
The thermodynamic working Tables A-I through A-20 were compiled and cal-
culated from the most reliable data given in recent sources, as listed under the
reierence:5 given on pages A-13 and A-14, Because of the need for ariti1metical con-
sistency in this type of study, the number of significant figures in the values repo.:ted
is beyond that which actually exists.
In several of the tables, high-temperature heat-capacity data were not avaib.ble.
In these cases, Bl'cwer's Approximation (Referencc 13) was used. Brcwer's ApiJl"oxi-
:nation gave data comparable with that reported in Table A-I, which is based on ex-
pcrimental values to 2000 F. .It is believed that the calculations listed in the tables can
he rClted as "good" ior evaluating practical temperature limits of the dcsulfurizir.g action
0: the: compounds und.er consideration. By estimating the limits of error for sevc.:~ll
import~nt cases, it was concluded that the S02 concentration calculated at a specific
~cmpcl'ature should not val"}' irom the actual value by more than 10 ppm S02- CO:1sid-
cri:1g that fluc gas nominally contains 2000 ppm to 3000 ppm S02 and that a good de-
sulfurizcr would low(~r the S02 on11' to 200 ppm to 300 ppm, these c<,lculations are con-
sidcrccl to be well within reasonable inacticallimits.
-216-
-------
APPENDIX B
SUMMARY OF EXPERIMENTAL STUDIES
OF S02 REMOVAL SYSTEMS
-217-
-------
II.
I.
TVA (Muscle Shoals, Alabama)
Small Coal Burning Pilot Plant (1955)
A.
Conditions
1.
Limestones I
87.3% CaO (Pelham)
97.5% CaO (Rockwood)
2.
Limestone passed 100% through a 200-
mesh screen
3.
S02 Concentration = 2900 ppm
4.
Residence time = 1 sec.
5.
Exit temperature range = 1150-1370oF
(no temp. profile given)
B.
A plot of S02 removal vs stoichiometry compares
very favorably with the same plots of the B , W
data (Port A injection, low coal firing rates -
residence time = 1.6-2.4 sec., S02 concentration
-'3500 ppm).
C.
Also tests with synthetic stack gases
(N2, C02, 02)
1.
Limestone requirement much higher
2.
No effect of humidity
D.
Best correlation between reactivity with S02 and
physical properties was related to pore volume
of 17.5 to 0.035~ pores of the calcine.
APCO Studies
A.
Fixed Bed Sorption Unit
1.
Ten limestones and dolomites (not listed)
-10+28 mesh particles
2.
3.
Flue gas from burning natural gas
-218-
-------
III.
B.
Results
1.
2.
3.
Measured in terms of time required for
sorbent saturation to the "breakthrough
point" (point at which 20% of sulfur
passes through)
Samples varied from 30-150 min. in
breakthrough time
l6000F and l8000F optimum temperature
4.
No correlation between chemical com-
position and reactivity
Very fast reaction rate (total S02
removal in 0.02 sec. up to the break-
through point)
Standard Operating Conditions:
5.
1.
2.
3.
4.
20 SCFH through 1-1/4" dia. reactor
S02 conc. in gas = 2800 ppm
Flue gas from methane burned at 67%
excess air
S02 content of flue gas by IR
Bergbau-Forschung (Essen, Germany)
A. Small scale tests on non-isothermal kinetics
of decarbonization reaction
B.
C.
Results on non-isothermal study
1.
Calcination and S02 sorption occur
simultaneously
2.
For actual injection conditions,
only 50% conversion under the best
conditions
3.
Limestones vary widely in reactivity
Small pilot plant (isothermal)
1.
Coal combusted (1.5-1.8% S)
-219-
-------
IV.
2.
3.
S02 conc. = 1100-1400 ppm
Velocity = 1-4 meters/sec.
4.
Hydrated dolomites tested
Do-
At 900°C, much higher desulfurization
than at lower temps down to 400°C.
80% S02 removal at 9'00°C and 300%.
stoichiometry.
S02 removal 20% higher with
particles <60~.
Residence times longer than 1.5
to 2.0 sec. do not influence
degree of S02 removal.
Concluded that incomplete utilization
of sorbent due to very rapid coating of
injected particle with a dense sulfate
coating.
a.
b.
c.
d.
E.
Small pilot plant reactor.
1.
2.
7 meters high; 10 ern in diameter
Electrically heated
3.
Constant temperature along length
of reactor.
Pilot plant studies proved limestone to
be the best desulfurizing additive, and
dolomite the poorest.
Landesanstalt (Essen, Germany)
F.
A.
Small scale studies in fixed bed reactor
with 97.4% CaO limestone and 59.9% CaO
dolomite
1.
Sorption increased up to 900°C (highest
temperature studied).
Calcined limestone exhibited considerably
higher utilizations than did the uncal-
cined stones.
2.
3.
Both calcined and raw limestones gave
better results than the corresponding
dolomi te. .
-220-
-------
B.
C.
4.
Reducing the particle size by a
factor of 2 almost doubled limestone
utilization
5.
6.
02 essential to the sorption
H20 vapor tends to depress loading
capacity of calcined limestones.
Reactor Conditions
L
Quartz tube reactor - 21.5 rom I.D.
with 50-350 liter/hr flow rate.
2.
Artifically-produced flue gas.
Results
1.
Reaction with uncalcined stone began at
700°C
2.
Reaction with stones calcined for 13 hrs
at 1000°C started at 500°C, but only 1%
of lime utilized before breakthrough.
Optimum S02 reactivity between 800 and
900°C.
v.
Resources Research Institute (Kawaguchi-Saitama,Japan)
A.
Fixed bed studies
1.
Optimum calcination temperature about
1000oC.
2.
Optimum S02 sorption temperature about
900°C.
3.
Rapid decline in S02 sorption below
700°C.
4.
Small particle size important.
B. Injection Tests
1.
2.
Residence time = 3 sec.
S02 concentration = 2000-2500 ppm.
3.
Little or no sorption after 1.5 sec.
retention time.
4.
Graph showing effect of particle size
and residence time.
-221-
-------
,
I
I
I
I
I
c.
D.
E.
F.
Absorbents tested
1.
Limestone with diameter = 1-2 rom
2.
Tablet of limestone of 100-200 mesh binded by
1-2% magnesium stearate 1-2 rom diameter
Tablet of limestone under 200 mesh with
same binder
3.
4.
Tablet of same size formed by slaked lime
wi th same binder
s.
Limestones used were calcined in an
electric furnace for 3 hra
Reactor conditions
1.
Silica glass reaction tube of 34 rom diameter
2.
Reaction tube put in electric furnace and
temperature of absorbent was kept at desired
value
3.
Flue gas velocity = 2800-3100 HSV (hourly
space velocity) at temperature of 9000C
Desulfurization tests showed that desulfurization
rate is proportional to d-l/6
Desulfurization by CaC03 found to be inferior to
that by slaked lime
-222-
-------
VI.
Steinkohlen-Elektrizitat A.G. (Essen, Germany)
A.
B.
c.
Boiler with steam production rate of 110 tons/hr
1.
Coal with 1.5% S (1.4-2.2 stoich.)
2.
Injection at 1500OC, 13250C, 1150oC, 10750C,
and 9200C
3.
optimum temperature for hydrated dolomite -
l1500C
4.
other materials used
a.
b.
c.
d.
Hydrated lime (150,000 cm2/gm)
Byproduct lime (107,000 cm2/gm)
Calcined limestone (8000 cm2/gm)
Raw limestone (4000 cm2/gm)
5.
Hydrated lime most efficient -
calcined lime least efficient
6.
Tests showed small particles of limestone
more effective
Electrostatic precipitator operation
Reactor limestone distribution studied
-223-
-------
VII.
VIII.
Technical University of stuttgart, Institute of Process
Technology (Stuttgart, Germany)
A.
B.
Boiler with maximum ste~~ output of 54 tons/hr
1.
Hydrated lime deadburned badly
29
R~Ridence time = ~-5 sec. from 10000C to
aiL heatexo
3.
Better results ~~th injection between
9500 and 10000C
4.
Hydrat~u li~~ considerably more effective
than hydrated dolomite
s.
Better sorption with oil firing
6.
Sorbent reacted with C02 as well as S02
Three-part program
1.
Precalcined lime mixed with pulverized coal
2.
Injection of dolomite and lime hydrates
into a pulverized coal firing power plant
Injection of dolomite and lime hydrates
into the same plant with coal firing
3.
Central Research Institute of Electric Power Industry
(Tokyo, Japan)
A.
pilot plant studies (oil-fired)
1.
Optimum limestone injection temperature
900-12000C
2.
Removal decreased inversely with the one-
fourth power of particle size
3.
Limestones with >1% ferric oxide were -vSO%
more effective than those with
-------
IX.
B.
Plant tests (oil-fired boiler)
1.
Injection at 1100-1200OC
2.
Hydrated lime superior
3.
Trend indicated on graph of 502 removal
vs stoichiometry agrees with that of
B & W data
4.
Boiler consumed 18.5 tons of 2.17%
sulfur fuel oil/hr
Wisconsin Electric Power Company (Milwaukee, Wisconsin)
A.
'Plant consisting of five 80-megawatt units
1.
Dolomitic limestone used
2.
Coal with 2.8% 5 and 8% ash
3.
Tests run at 130% and 65% stoichiometry
Coal-limestone mix about 65% -200 mesh
4.
s.
~50% removal with 135% stoich.1
no appreciable removal for 65% stoich.
6.
Data on effect of limestone on ash
fusion temperature
- 2 2"5-
-------
x.
Combustion Engineering and Detroit Edison
(Detroit, Michigan)
A.
Twin 32S-megawatt furnace
1.
Coal .-v3-4% Sulfur
2.
Stoichiometric amount of dolomite injected
into one side
3.
Over 90% of the injected dust left the
boiler with fly ash rather than bottom
ash
4.
A little data with coal burner tilt a
variable
s.
Dust loading in. stack gas increased about
65% as a result of dolomite injection
6.
High temperature and low temperature
corrosion measurements made
7.
No unusual slagging tendencies although
a 14' ash coal was used
8.
Optimum operating conditions
a.
Dolomite injection at
stoichiometric
Dolomite injection at
tilt of +14 degrees
Coal feed at a burner
-15 degrees
tilt of
106-112%
b.
a burner
c.
-226-
-------
XI.
TVA Colbert Steam Plant
A.
B.
C.
200 megawatt boiler
Static tests
1.
Lumps (3/8 in.) various lime materials
held in boiler for 5 minutes
2.
No 502 sorbed below l2000p
Calcined and hydrated limestones sorbed
C02 below 12000P
3.
4.
Very little 502 sorption unless calcina-
tion was complete
5.
Iron oxide promoted both decarbonation
and 502 sorption
6.
Occasional deadburning in samples
exposed at 19000p
Injection at part stoichiometry
1.
One-sixth stoich. injected by sand-
blasting machine
2.
Erratic injection rates and dilution of
recovered sample by fly ash - not much
significant data
a. Calcined lime more effective
than raw limestone
b. <30' of material was reacted
c. Pine particles reacted to much
higher degree than coarser ones
-227-
-------
XII.
D.
Injection at full stoichiometry
1. Limestone mixed with coal
2. Different feed arrangements used
3. Degree of S02 removal determined
a.
b.
c.
Stack gas analysis
Solids analysis
Petrographic examination of solids
4.
Results
a.
Limestone ground as easily as the
coal and more of it ground to
-200 mesh
Slag accumulation not excessive,
but unusual stringy appearance
Although solids load was doubled,
dust removal equipment was not
overloaded
b.
c.
Central Research Institute of Electric Power Industry
(Tokyo, Japan) - Later Studies
A.
Experimental Set-up
1.
Furnace with inverse U-type reaction tower
2.
Fuel oil was burned, and S02 level was
controlled by injecting S02 from a
cylinder
3.
Pulverized limestone injected with air
4.
S02 removal determined by analysis of
gas at various points
s.
Gas temperatures along with oxygen and
carbon dioxide levels in the gas were
measured
6.
Six different limestones and two hydrated
limes were utilized
-228-
-------
B.
C.
Effect of physical conditions
1.
Reaction determined to be first-order
with respect to S02 concentration
2.
Particle size effect
a.
Initial reaction rate increased with
decreasing particle size
Reaction rate for finer particle sizes
of limestone reduced more rapidly
with progress of the reaction
b.
3.
Effect of injection temperature
4.
Higher reaction rate was obtained at
the beginning of the reaction at
higher injection temperatures
Decrease of reaction rate was more
rapid in cases of injection at
higher temperatures
Effect of limestone used
a.
b.
a.
Sorption efficiency of Tokunoshima
Limestone (coral reef rock) was
about twice that of other limestones
Due to a gentle decrease of reaction
rate, sorption efficiency of the
hydrated lime was much higher than
that of the limestones
b.
Conclusions regarding reaction mechanism
1.
Diffusion of S02 through gas-film boundary
layer on CaO particle was considered not
to be the rate controlling resistance
2.
At the beginning of the S02 reaction,
rate controlling resistance was con-
sidered to be both the diffusion and.
chemical reaction in the pore of the
calc~ne particle
-229-
-------
i -
APPENDIX
C
SHRINKING CORE MODEL DEVELOPMENT
-230-
-------
THE RATE OF A DIFFUSION-CONTROLLED
REACTION BETWEEN A GAS AND A POROUS, SOLID SPHERE--
The reaction of S02 with CaC03
by,
Robert L. Pigford
'University of California
Berkeley, California 94720
June 1971
Sununary
The reaction rate ~s assumed to be governed by two
diffusional processes: the diffusion of S02 through the pores,
and the diffusion of 802 through a layer of solid reaction
product which forms on the active solid surface progressively
as the reaction proceeds. One or the other predominates,
depending on particle size, gas composition, and temperature.
The theory accounts qualitatively for the ob~ervations of
Borgwardt (1970) and Coutant et ale (1970).
--
-231-
:
-------
Introduction
One of the major sources of atmospheric p~llution in the
United States is the coal-fire power plant, which frequently
consumes sulfur-laden fuel and produces flue gas containing a
few thousand parts per million S02.
In recent years there has
been increasing interest in chemical processes for the removal
of sulfur compounds from the flue gas stream. Many of these
involve treatment of the effluent gas stream from the plant
with alkaline liquid reagents in large scrubbers before the gas
.is discharged.
Such processes are capable of nearly complete
recovery of gaseous sulfur but the equipment may be very costly
and may be hard to add to many existing power plants.
A process
which can be applied to existing plants involves the injection
of finely powdered limestone or Dolomite into the fire box of
the boiler, where the solid particles decompose, forming calcium
oxide.
This reacts with ~ulfur dioxide and with excess oxygen,
, .
forming calcium sulfite and calcium sulfate.
The reaction
product must be collected with the fly ash in dust collection
equipment.
In the evaluation of the limestone injection processes it is
necessary to know the rates of the chemical reactions between the
gas and the solid in o~der to determine the quantity of solid
required, its particle size, the temperatures at the injection
point and downstream, and the time of exposure of the solid to the
gas.
Previous studies of the rate phenomena have led to somewhat
confusing results.
-232-
-------
Borgwardt (1970) measured the rates of reaction using beds
of solid particles of CaO through which the gas passed.
His times
of exposure were on the order of one to two minutes, much longer
than those which are of practical interest.
He assumed that the
heterogeneous reaction rate was governed by the speed of a
chemical r~action and evaluated an apparent first-order rate
constant, which he found to vary with the particle size and with
the elapsed time of the reaction. Such ambiguous results are
cause for caution in the application of his data.
Coutant et ale (1970) carried out a more extensive and
--
realistic series of experiments at the Battelle Memorial Institute,
in which particles of limestone particles (type 2061, screened to
average size about 0.00895 cm. diameter) were injected into a
current of hot gas which flowed upward through an insulated tube.
By'varying the height of the particle injection point various
times of exposure could be obtained, from a fraction of a second
to about three seconds.
The particles were collected and analyzed
to determine the extent to which conversion to CaO and to CaS03
and CaS04 had occurred.
The gas concentration of S02 varied
between 0.0004 and 0.009 mole fraction and the temperature between
1600 and 2148 deg. F.
Interpretation of the data was attempted
usi~g an equation apparently borrowed from classical corrosion
theory, according to which the quantity of sulfur picked up
should be proportional to the square root of the reaction time.
Thus the rate was expected to vary inversely with
tl/2
,
evidently because of the changes in thickness of a layer of
-233-
/"
-------
reaction product through which S02 had to diffuse to reach the
active reagent underneath.
It was noted, however, that several
of the sets of data did not follow such a relationship and it
was not possible to find a systematic relationship between the
"rate constants" and gas composition, temperature, or particle
size.
Thus, application of the data to a variety of conditions
may be difficult on the basis chosen.
The idea that the rate of the reaction is governed by
diffusion is an appealing one and some aspects of the Battelle
data suggest that the idea may be correct.
For example, at,
comparable times or extents of reaction the rates did not appear
to vary with temperature as rapidly as would be expected f~om
, typical chemical reaction activation energies.
Moreover,the
plots of amount of sulfur absorbed versus time were concave toward
the time axis, as in most diffusion-controlled processes in which
the build-up of concentration inside the particle reduces the
driving force or the accumulation of a reaction product increases
the resistance.
.
Nevertheless, 'the process could not be represented
as an ordinary, linear diffusion problem because the rate did not
seem to be proportional to the gas con~entration.
A diffusion-pIus-reaction mechanism which suggests itself as
potentially capable of accounting for the data is one in which
each particle of solid. is assumed to be made up ,of many smaller
spherical particles of solid reagent, as indicated by the sketch
in Figure 1.
The sulfur dioxide diffuses through the pores
separating these sub-particles and reacts on their surfaces.
The
speed of tpe reaction is determined by t~e thickness of a solid
reaction product layer which forms on the surface of each
.
-234-
-------
F='IGUt
-------
sub-particle and by the local concentration inside the pores,
The product layer thickness is, in turn, determined by the whole
time history of the local concentration since it represents the
accumulated product, i.e. the integral of the local reaction rate,
at the particular position in the porous solid.
Note that it is
not necessary to assume that the S02 dissolves in the sulfite or
sulfate layer for such a layer could easily develop cracks or
, fissures owing to a mismatch of solid density with the calcium
oxide underneath,
Such a reaction mechanism is not wholly different from the
simple one assumed by Coutant et al,; it is a logical extension
of theirs, including an additional pore diffusion process which
may be important if gaseous diffusion is slow, if the specific
surface of the pores is large, or if the particles are large.
Under these conditions the composite particles should react
principally near their exterior surfaces, their interior regions
being inaccessible to S02',
The following pages present an analysis of the proposed
diffusion theory and compare its predictions with the two sets of
available data,
The Theory of Diffusion Plus Reaction Between a Gas and a Porous
, Solid Sphere:
Consider the material balance reprasenting the transient
diffusion of a gas having concentration C(r,t) through the pores
of a spherical particle of radius
R
, reacting on the surface
of the pores at a rate
v
per unit surface, as in Figure 1.
Let
the intern~l surface area per unit volume of the' particle be
S ,
v
-236-
-------
The equation which results is
(~a )
~ L (r2 ~)
r dr ar
::
dC
at
+
s v
v
(I)
in which
a
represents the fraction by volume of pores,
'["
is their tortuosity, and
D
is the gaseous diffusivity.
The local reaction rate,
v
, can be computed by
considering the diffusion of gaseous reactant through a spherical
,
shell of reaction product of thickness
x
which forms on the
surface of each sub-particle of solid reagent.
We assume that
such diffusion processes are always at steady state and we'
evaluate the diffusion flux in the following equation by
multiplying the solid-phase diffusion coefficient,
D
s
, by the
geometric-mean cross sectional area and the quotient of concentra-
tion difference by film thickness.
r
s
4 u (" - X) 2 (~~)
::
D
XS 4~ aCa-X) CCr,t}.
(2)
If the gaseous reactant must dissolve in the surface of the
reaction product layer we should include d Henry's Law coefficient
~s a factor on the rig~t'multiplying the solid diffusion co-
efficient; if the gas diffuses through cracks in the product
layer the coefficient would be omitted.
Equation C2} is an
ordinary differential equation from which 'XCr,t) can be found
as a function of the sub-particle radius;
~
a
, 'the phys ical
. .
-237-
-------
properties of the solid, and the local value of the integral
of
C
with respect to time.
In order to find an expression for
v(r,t)
we need to
solve explicitl~ for
x
, in order to evaluate the diffusion
flux into the sub-particle,
v(r,t) :: a-xx D C(r,t)
a s
(3)
It is difficult to obtain a simple expression for
v
excep,t
when the thickness of the product layer is small compared with
the sub-particle radius, i.e. only when the fractional conyers ion
of the solid is small.
Then we may take
X«a
and find
X2
::
(2D Ir )
s s
t
Joc
-------
2
VE; c =
('~:B ) ( :;) +
SVTR 2 J D r C B
s s 0
DaC ?
o .
c
J~: cde
Now it is very likely that for the conditions of real
interest the time-derivative term on the right will be in-
significantly small, as in the classical problem of the
(6)
effectiveness factor for a porous catalyst particle. We shall
drop the term by assuming that TR26/Da«1, an assumption
which we can justify a postiori.
Now, if we choose
6 =
2C D2a2
o
D r S 2T2R4
s s V
our mathematical problem reduces to
,
1
2
a
a~
«2 :~)
J 1: cd e
c
=
with the boundary conditions.
e(l,S) = 1 ; c~(O,S)= 0 ; c(~,o) = 0
-239-
(7)
(8)
(9a,b,c)
,.,
-------
Note that Equati.on (8) is not linear; as a result we can
expect that the gas concentration will appear in a non-linear
way in the solution.
In -fact, the characteristic time,
-1
~ ,
depends on the ratio of solid and gas molar concentrations.
After
we have obtained the solution, we shall want to find the ins tan-
taneous rate of passage of S02 across the exterior surface of
the sphere, given by
aDC
N = ---.£
TR
(:~ )
(1,8)
(10)
where Net) is the rate per unit of external surface area.
Then,
we shall want to compute the fraction of the total solid reagent
contained in the particle which has been consumed at any time of
exposure,
F.
3
F = Rr (I-cd
s
t
1 Nat
o
-1
=.Y
a
I C(l,p)dp
o
(11)
where
y ::
2
R r T(l-cd
s
3 DC a
. 0
B ::
2 Da(l-a)
3 R2S 2TD
v s
(12)
The solution of Equation (8) is presented in Appendix I.
Table I gives a few selected values of numerical results,
'0
-240-
-------
including instantaneous values of the dimensionless rate,
(ac/as)(1,8), and the cumulative dimensionless fraction
8
conversion f c~(l,p)dp , versus dimensionless time e .
- Jo
that, for small 8 , the instantaneous rate is very nearly
proportional to 8-1/4 and the reaction fraction is proportional
to 83/4 ; for large 8 the corresponding relationships are
6-1/2 and 61/2 , respectively. Thus, the theory provides
Note
a gradual transition from a situation at small
8 , in which the
reacting region of a particle is near its surface and very little
802 reaches the center, to a different situation at large 8 in
which the 802 is spread nearly uniformly through the pores and all
the particle's interior reacts.
Large
8
therefore corresponds
to the situation assumed by Coutant et al. (1970) and the
calculated time dependence agrees with their assumption.
Figure 2 shows how the ratio of 802 concentrations at the
center and the surface of ~he porous particle depends upon
8 .
Figure 3 is a plot of the instantaneous rate and Figure 4 shows
the cumulative fraction reacted.
When the original expression for the rate of absorption is
evaluated with the theoretical results we obtain
4~R2N = 13.6 (alIi Dl/2 D~/4 s~/2 r~R2 c~/4;'Tl/2 tl/4)
(13)
when.pore Idiffusion is controlling at small
8
and
-241-
! .
-------
,llj
4.R2N = 5.5 (DS1/~ Sv r;/2 R3 C~/2/ t -/2)
(14)
when the diffusional resistance of the pores is small and
e
is large.
Note that, depending on the time constant,
a , the
dependence of the rate on particle Slze can change from
to R3 , the effect of gas concentration from C;/4 to
t-l/4 -1/2
. and the effect of exposure time from to t ,
R2
Cl/2
o '
respectively.
Moreover the effect of temperature, presumably
contained in
D
andD and possibly also in
s
S
v'
can also
vary.
Under the assumption of small conversion which we have
made the only effect of the size of the tiny sub-particles is
through the specific surface as expressed by
Sv = 3(I-a)/a.
-242-
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i :=~i~f~~~~~~g~=;;:~~~~,;;]~~_wir~~];t~~!;';i~ '~'i[~;_1
H=H+ -$~::~ ~-~ *' _:';~~ :-,~~~t=;:: ': . ; ': ,:-;- ~~l~ : ~fi:t. t~-~--- -~'~-x,:l.c!-:-~d2~~1g~~3;';r ~-17~~: -:- -i-: J:
..!..,;...: ~:'~:..L. -"';"'r: '_.f-+p-f-'- ;, I :';-hLr--' I--'e'r-...R-' _.~- '-~C-'--I~-;i.j::,cjls:~:r:t.~~;-+.c_...:..-'--.f
3 ~:." --"--- ~,.:.~ ~~~-- -::..-.. ...." --' .:.. ~._..:..: ---~..'. -,~ . . S -;:- r--~::7~ n "..--:: -'.. .:.. . '. . '.
.~ ___h. '--l_.='-_h._" .., ~ -- -I" ::::::"--E.-".._-t" =-- '-;:::1 "'~:. ';:L'r:.~r=-=-:';r::~::::I=,~f:~': ':"-:"::7','::~: ::: ::,(, -~r'l
. ~i~ ~~~ ~t ~~ i /~~~~ ~ir~j"-~;~~c ~";~ ~,'~t~~~\~~; ~,.~:i~~i~;~r[
+ ~H-' 'Ie:: ",.1t~, it;; :-i:1 1 -; ~~ r .-m+ 'qL~I:i:' -rn', -f4i L,.!lJ + J.:', 'H+~'fl.L' ,t _Lrri ,":C fT" --M,r-j'f'
-t- ~ ./-1 J~ r+(! [[;ri+L~p ~ITi =~ I ~-:f - . :. ~1-. ijj Wi rr-1ffi m: [nit 1 :t T::H+tH+H- rllifni ilJT £f-H rtf:=F '~I't:
I f H-11 r, I :: t ititi I" I r. . + I I \ I -H-t I I. i: Ii r. I I, 'J! I . t I I : r 1 1 I I-~m- rmr i I: ; I ! I Ii: '!, I . '.' ~ I '
2
1.0
9
8
7
IJ,(J /.,
0.01
Z 3 + !> 4> . ~ 9 10 2 3 + !> 6 7 8 9 Ii) 2 a + ~ . . J
~
0.1 (.CI 10
0)' B
R,L.. P.
'-1"'- 7/
-245-
-------
I
I'V
~
m
I
TAB LE I
Numerical Values of Reaction Rate and Fraction Conversion from
Diffusion Theory
,;
Dimensionless Rate Dimensionless Total Quantity
e
8=Bt ~~(l,e) el/4 ~~(1,8) 61/2 ~~(l,e) Absorbed, YF=ioC~(l'P)dP
yF e-3/4yF e-l/2yF
.
0 00 1.287 0 1.717).:
0.02 3.174 1.193 . - 0.0879 1.65
0.04 2.475 1.106 0.1435 1.606
0.05 2.273 1.075 0.1683 1.592
0.1,0 1.728 0.971 0.2666 1.589
0.15 1.462 0.909 0.3447 1.430
0.20 1. 292 0.864 0.4144 1.382
0.30 1.081 0.799 0.5322 1.310
0.40 0.9517 0.757 0.6335 1.260
0.50 0.8603 0.723 0.7239 1.218
0.60 0.7911 0.696 0.8063 1.182
-------
TABLE I Continued'
I
I\J
~
~
I
~
0.70 0.7362 0.673 0.8825 1.151 1.056
0.80 0.6933 0.656 0.9540 1.128 1.067
1. 00 0.6244 0.624 .624 1.0855 1. 0 85 1.085
1.2 0.5733 0.600 .628 1. 205 1.050 1.100
1.5 0.5-160 0.5613 .621 1.368 1.117
.
{:
00 1.188
. .
. .
* By Extrapolation.
-------
Interpretation of the Data of Borgwardt (1970) and Coutant,
et al. 0.970):
The diffusion theory contains two combinations of physical
constants,
8
and
y
, defined in Equations(7) and (12).
Each
contains several quantities, such as the specific surface area
and the solid diffusion coefficient, which are very difficult to
estimate and which must be found from the data themselves.
Note,
however, that the combination
8/Y
contains constants that are
readily accessible from independent measurement or can be estimated
approximately.
. -
3D C a
o
- = 2
Y R r T(l-a)
s
8
(15)
Assuming that the gas diffusivity in the pores is equal to its
bulk value, which varies with the 7/4 power of the absolute
temperature, and taking
a - O~5
and
T .. 1.0,
8/y = 2.29XIO-4(Y/R2)(T/273)3/4
,
-1
sec.
(16)
where
y
--
is the mole fraction of 802 in the gas, R is in em.,
is in deg. K. .Obviously if a is smaller than 0.5 and
and
T
T
is larger than unity
8/y
can be smaller.
In the following,
however, a value found from Equation (16) will be referred to as
a "standard value."
-248-
-------
i-.-~-
.
The procedure for estimating the remairiing parameter from
the data, either
a
or
y , is to compute
Sly
from Equation
(16) (or from the same equation with a multiplying constant)
and to determine
S
50 as to minimize deviations from the theory.
If
at
is sufficiently small it will be possible to determine
S
by dividing each of the measured values of the fraction con-
3/4 . .
version, F , by t , taklng an average value of the quotient,
and referring to Table I to find the appropriate value of F/e3/4
in the expression
F/t3/4 = [e-3/4YF] (S/y)S-1/4
(17)
from which
-1/4
S
and
a
can be .computed.
Similarly, if St
is sufficiently large, an equation like Equation (17) will give
a value of 6-1/2. One sees that, following this procedure,
the data at large values of C t/R4 , corresponding to large
o
e , should give a more reliabl~ value of
a
and of the constants
it contains, such as
y
and S .
v
Note also that by choosing
a/y
smaller than its "the-
oretical value" one can reduce "the value of
a
to be found,
causing the time dependence of the rate to be more nearly as
t-1/4 than as t-1/2 and also changing the effects of R
and
c
o
, as indicated in Equation (13) and (14).
Thus, when data
are available for various gas compositions and various particle
sizes, as well as for varying times of exposure it may be possible
to find best values of both
I
y.
and
a
when all the data are
-249-
-------
. '....
considered.
In general the problem is one of non~linear curve
fitting because of the changing functional behavior of the two
constants, as shown in Table I.
The Effect of Particle Size on the Reaction Rate:
Figure 5 shows the data of Borg~ardt (1970), plotted
logarithmically as suggested by the diffusion theory.
Note that
the straight line drawn through' the points representing the
smallest particles has a slope just greater than 1/2, suggesting
that for these particles there was not much difference in the
S02 concentration at the center and at the surface and negligible
diffusional resistance in the pores.
The data for the largest
particles, however, yields a slope approximately equal to 3/4,
suggesting that these particles were large enough for their
centers to be ineffective.
The instantaneous rates of reaction,
dF/dt, can be evaluated easily as a function of
t
and particle
size.
The results show that the rate at c'onstant
t
is pro-
portional to the -0.29 power of diameter at
t = 10 sec.
and to
the -0.18 power at
t = 60 sec.
These numerical results should
be associated with the intermediate particle size.
The slope
would be zero if all the interior of each particle were reacting
equally and equal to minus one if there were major resistance to '
diffusion through the pores, as indicated in Equation (13) and
(14).
Evidently, part~cles about a quarter of a 'millimeter in
diameter experience some influence of pore diffusion.
By fitting the theoretical results to the Borgwardt data,
using Equation (16) to evaluate
a/y
, the results shown in Table
-250-
-------
II were obtained.
The values of
at
corresponding to t =
60 sec.) the average time of exposure, show that only for the
largest particles was there appreciable pore diffusion resist-
ance.
The last two columns in the table show that the derived
values
a
and
y
vary with particle radius approximately in
, the way expected from the theory.
Although it is possible to determine the product
S2D
v s
-1
40 sec.
from the empirically derived values of either
a
or
y , using estimated values of
a.
and
l' , neither
S
v
nor
Ds
can be determined separately.
Nevertheless, if the ~ure guess
is made that the elementary sub-particles were about 40 microns
in diameter and
a. ... 1/2
and
l' ...
1) D
s
turns out to be about
-6 2
10 cm Isec.
Obviously this is a highly unreliable value
because it is highly sensitive to the assumed value of
a.
If
a.
were off by a factor of ten,
D
s
would be changed by a hundred.
Moreover, the values of
a
computed from the data are
strongly affected by the assumed ratio of the true value of (Sly)
to its "nominal value"
according to Equation (15).
A non-linear
least-squares procedure applied to the same data shows that the
quali ty of fit of the data can be, improved by taking f3 Iy equal
to 0.11 times its nominal value, yielding smaller values of R48
2 -1 5 2
and S D = 50DO sec. , 90rresponding to D ow 10- cm !sec. if
v s s
a ow '40 microns.
The value of such highly speculative estimates lies in the
possibility of attaching significance to the assumptions made in
the derivations of the rate equations.
I
Since none of the diffu-
sivities estimated above for the penetration of the layer of product
CaS04
by
8°2
are as small as expected for diffusion in the
-251-
-------
solid state it seems possible that the diffusional process in
the accumulating layer of product is assisted by cracks or
fissures.
L
'0
-252-
-------
f<~
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-------
TABLE II
Values of Physical Constants Derived from Data of Borgwardt--
Effect of Particle Size
Particle Derived Constants aR4 yR2
Dia. , a, -1 at at t -1 4 2
cm., sec. y ave. sec. cm. cm.
. -
I 0.0096 14 156 820 7xlO-9 -3
t.J 3.6xlO
lJ1 15xlO-9 -3
~ 0.025 0.6 48 37 7.5xlO
I
0.13 6xlO-4 1.3 0.035 llxlO-9 -3
5.5xlO
llxlO-9 -3
averages: 4.1xlO
If
a = 1/2, t = 1, a = 40 microns it follows that D
s
=
-7 2
4xlO cm. /sec.
-------
The Effect of Gas Concentration of 802 on the Reaction Rate:
"
The data of Coutant, et ale (1970) were taken at gas
concentrations ranging from 0.0004 to 0.0095 mole fraction 802
and at various temperatures, although at only one value of the
particle size, 0.009 em.
When the observed values of the frac-
tional conversion of CaO are plotted logaritmically against
times, as in Figure 5, it is once again possible to draw straight
lines through the data, which extend from
t = 0.25 to 3.2 sec.
According to Equation (13) and (14) the logarithmic slope should
vary from 0.75 if pore diffusion is limiting to 0.50 if the
surface reaction rate is limiting.
Table III gives values of
dF/dt at 2 sec., a quantity proportional to the rate of reaction
per unit mass of solid, at the four different gas compositions.
It is seen that the slopes are very nearly within the range ex-
pected.
The values imply that the reaction rate is small enough
at the lowest concentration that po~e diffusion easily keeps the
.
interior of the particles fully supplied with the gaseous reactant,
while, at the highest concentration pore diffusion is limiting.
Figure 6 shows a plot of the slopes against the gas mole fraction.
The straight line through the data has a slope of 0.64, nearly
half way between the possible extremes expected, indicating that,
at least at the intermedi~te concentrations, the data are in a
transition region between limiting pore diffusion and uniform
surface rate.
Values of
a
and
y
derived from the, Coutant data are
listed in Table IV, which shows that
a
is nearly proportional
-255-
-------
TABLE III
r.ffect of Gas Composition on the Slope of
"log F vs. log t ; data of Coutant et ale (1970)
;-_ut T = 1700 deg. -F., particles 0.009 em. diameter
Mole Fraction 802 in Gas
d log Fld log t
0.0004 0.49
-,
- .'.' 0.00302 0.68
0.00748 0.74
0.00954 0.75
- -
_..
.
. ....'
-256-
r"
-------
FiGURE
~
I
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MCJI..E:- FR.4CrION' 502
IN G-A.$
~-r;7
-------
TABLE IV
Values of Physical-Constant Groups, Band y,
Derived from Data of Coutant, et al.(Battelle)
--
Mole Fraction Gas B, s ec. -1 Bly Btav
y
8°2 in Gas Temp. ,oF
A. Effect of Gas Composition:
0.0004 1692 0.32 800 23 0.55
0.00302 1692 6.0 2000 58 8.2
0.00748 1690 12.3 1600 48 19.7
0.00954 1703 16.2 1700 49 25.8
i
I ave. = 1500 45
B. Effect of Tem'Derature:
.
0.00303 1600 . 8. 2 81
0.00302 1692 6.0 58
0.00277 1845 2.5 25
0.00305 2041 3.3' 28
0.00302 2109 6.9 57
0.00306 2148 16 130
-258-
-------
to
y
, as expected from the theory.
One exception is the point
at the smallest value of
y
, at which the determination of
a
is least accurate. If the average value of a/y is used, as
f 2 .
before, to find an apparent value 0 SvDs ' assum1ng a = 1/2
and T = I , the result is 190 sec.-I, which is remarkably close
to the value from the data of Borgwardt.
Once again, as with the
previously considered data, it is statistically possible to
improve the quality of the comparison between theory and data con-
cerning gas compositio~ by choosing a value of
( B IY )
equal to
about 0.1 times the "nominal value."
The result is that the values
of
f3
are reduced below those listed in Table IV and the time
dependence of the observed conversion is matched much better.
When the apparent value of S2D is computed from the results of
v s
the non-linear least squares procedure one obtains S2D 3 x 104
v s
-1
sec.
,.which is substantially greater than the apparent value
obtained from the Borgwardt data.
Note, however, that the data
of Coutant et al. were ob~aineq in 'an experiment in which lime-
--
stone particles were injected into the hot gas containing S02
whereas Borgwardt used limestone that had already been calcined
to CaO.
Thus, in
the experiments which lead to the larger
S~Ds ' C02 evolution occurred simultaneously
apparent value of
with 802 absorption.
Figure 7 shows a comparison of the measured values of the
fraction of CaO converted versus time, based on the data of
Coutant et al. at 1700 deg. F. and 2R = 0.009 em., and theoretical
--
lines based on the diffusion theory.
The two parameters,
B
and
y
, were adjusted to obtain the best fit of the data while
-259- .
I"
-------
~'c.;':'~~:£J ~;.;t..PH1C CC.~4f~Dt5 C(~..;:tG"'Atl~N
Oufro.Jlo. New Yor\
Pr.40-a".lj!: A
snum
1r. I IQ 10 m MIll I~tl
~s ~au.."
I
r-J
~
o
I
::'-r
'--" i"
-= .~.. ::::
"-'.. .
-""""'" .
.,-.-"
- , - 0 .; ~ .
.......,...-
::~_:! ;":.::
,,:'~-.._L
-. -..,.-..
.....,.. -
__0_-
-------
maintaining the dependence of these quantities on particle size
and gas concentration computed in the theory.
The parameters
used corresponded to (a/y) equal to 0.12 times its nominal value and
-1
B/y = 11 sec. .
The smaller value of (a/y) can easily be
accounted for by a pore diffusion coefficient smaller than the
bulk-gas value and tortuosity in the diffusion channels.
One
sees from the figure that the theory is capable of accounting
for effects of composition and time on the conversion in these
experiments.
The Effect of Temperature o~ the Reaction Rate:
Table IV shows some values of
a
and
y
computed from
data of Coutant et ale in which the particle size and the 'gas
--
composition were held constant and the gas temperature was
varied. One expects that an increase in temperature will decrease
B ,because of the probably greater increase in Ds than in D2co;
similar changes should also occur in
y
The table shows,
however, that both
B
and
Y" go through a minimum at a temper-
ature of about 1845 deg. F., corresponding to. the observed max-
imum reaction rate at this temperature.
The increase in the
parameters at higher temperature may be owing to sintering of
the particles and a resulting decrease in . S
v
-261-
-------
Conclusions:
The good qualitative agreement of the theory with data
expressing the effects of particle size and gas concen~ration
a~d the rough agreement of apparent values of physical constants
with accepted ranges indicate that the pore-diffusion theory is
capable of accounting for the main features of the reaction of
gaseous 802 with porous limestone particles.
The theory is not
exact) however, and ought not to be used as a substitute for
experiment.
It can be used for estimates of the effects of
changes in the particle size) the gas composition) and temper-
ature in a narrow range on the rate of absorption of 802 for
adjustment of experimental data. Thus) with the theory avail-
able) costly experimentation may be reduced~ if not eliminated)
and data taken under idealized laboratory conditions can be
applied to the design of practical recovery systems.
-2.62-
-------
References:
Borgwardt, R. H., Environmental Science and Technology, ~,
(1970)
Coutant, R. W., Barrett, E. E., Simon, R., C~npbell, B. E.,
and Lougher, E. H., "Investigation of the Reactivity of
Limestone and Dolomite for Capturing SO from Flue Gas,"
Battelle Memorial Institute, Columbus, 6hio, November 20,
1970.
---
Acknowledgement:
Ass~~~fj ~rom technical
J.. Bellot~Aof the M.W. Kellogg
discussions with L. Scotti and
Company and with L. Hegedus is
gratefully acknowledged.
W. Tang assisted with the computations.
.
-263-
,-
-------
Appendix
Solution of the Differential Equati6n for Diffusion and Reaction
We wish to find the solution of the problem
~- L ;2 dC -
;2 d; d;
c
(A-I)
J~: cCE; ,p)dp
with the boundary conditions
c(;,o) = 0 , c(1,8) = 1 , c;(o,6) = 0
(A-2,a,b;c)
If we let
2
u (;,8)
e
= ~ tc(~'P)dP
(A-3)
we find that Equation (A-I) becomes the third-order equation
d (d2 u2 2;1/2 U),= 0
Fe ~-
(A-4)
(Note that
;1/2 u (;,8)
is proportional to the thickness of the
product layer,
x
. )
Integrating Equation (A-4) with respect to
time,
-264-
-------
a 2u2
3 f,;2
- 2~1/2 u = 0; u(~,o) = 0; u(l,~) = el/2
(A- 5)
Let
u2(~,e) = e F2(~,e)
so that
F(E;,e)
= (~/e) Jr:C(~'P)dP
(Note that this relationship makes F(o,e) = 0.)
is now reduced to
The problem
'\
1/2
a2if - 2(F2Ej8) = 0; F(o,e) = 0; F(l,e) = 1
7
(A- 6)
A numerical solution is possible as follows.
Obviously F depends on both ~ and 6, but one can start the
integration of Equation (A-6) in the E;- direction to obtain
F vs. E;at8fixed 6. The integration begins at E;= 0, where
F = 0, regardless of e, and continues to E;= 1 where F = 1,
regardless of 6. At intermediate points Fdepends on 6.
To begin the integration one must supply a value of aF/aE;(0,6),
say b (6). The correct value of c is the one that yields
F(l,e) = l.Near E;=o, F = E;b(e) and
b(e) = ~ [ c.(o,p)dp
o
from which the concentration of the gaseous reagent at the
center of the porous sphere can be found.
(A-7 )
-265-
-------
Nomenclature:
a
c
D
D
s
F
F
N
r
R
8v
t
T
v
x
y
radius of sub-particle of solid reagent
concentration of reactant gas inside porous particle,
mole/volume; subscript 0 refers to gas outside porous
sphere
Diffusion coefficient of gaseous reactant in pores
diffusivity of 802 through solid product shell
dimensionless fraction conversion, equal to
yF
fraction conversion of solid reagent in porous particle
rate of absorption of gaseous reagent per unit exterior
surface of porous particle
radius in porous particle
radius of porous solid particle
surface area for reaction per unit volume of large particle
time following first exposure of porous particle to gas
gas temperature, deg. K.
reaction rate on interior surface of porous particle,
moles/(sec)(sq.cm.)
thickness of solid produ~t shell
mole fraction 802 in gas outside porous sphere
Greek Letters
a
a
y
fs
fraction by volume of pores in large particle
time constant defined in Equation (7)
combination of physical
used for expressing the
reagent
constants defined in Equation (12),
fraction conversion of the solid
molar concentration of solid reagent, moles/cc
"0
-266-
-------
e dimensionless time, equal to at
E; dimensionless radial distance in porous sphere
or tortuosity of pores
. .
-267-
------- |