RESEARCH REPORT
INVESTIGATION OF THE REACTIVITY OF
LIMESTONE AND DOLOMITE FOR
CAPTURING S02 FROM FLUE GAS
Contract No. CPA 70-111
to
DIVISION OF CONTROL SYSTEMS
OFFICE OF AIR PROGRAMS
ENVIRONMENTAL PROTECTION AGENCY
4%
OBalteiie
umbus Laborat
-------
FINAL REPORT
on
INVESTIGATION OF THE REACTIVITY OF
LIMESTONE AND DOLOMITE FOR
CAPTURING S02 FROM FLUE GAS
Contract No. CPA 70-111
to
DIVISION OF CONTROL SYSTEMS
OFFICE OF AIR PROGRAMS
ENVIRONMENTAL PROTECTION AGENCY
October 1, 1971
by
R. W. Coutant, R. Simon,
B. Campbell, and R. E. Barrett
BATTELLE
Columbus Laboratories
505 King Avenue
Columbus, Ohio 43201
Franklin County
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INVESTIGATION OF THE REACTIVITY OF
LIMESTONE AND DOLOMITE FOR
CAPTURING SO FROM FLUE GAS
MANAGEMENT SUMMARY
The objective of this research program was to develop a better
understanding of the reaction between limestone and SO as applied to
the dry-limestone injection process for SO- control in conventional
power-generating boilers. This has been accomplished through study of
some of the fundamental characteristics of this reaction under laboratory
conditions simulating the time-temperature profile of the superheater/
economizer section of a boiler. This work is an extension of earlier
efforts conducted under Contract No. PH 86-67-115, "Investigation of the
Reactivity of Limestone and Dolomite for Capturing S0_ from Flue Gas".
During this contract period of June, 1970,through July, 1971:
e An empirical model was developed for the limestone-
SO- reaction, and this model was used for correlation
of previous data as well as in discussion of current
data.
• Changes in reactivity caused by variation in time-
temperature profile were shown to be predominantly
related to residence time.
• It was shown that the maximum utilization of a lime-
stone is proportional to the square root of the
S02 concentration, which is consistent with ob-
servations of other workers studying the reaction
under simulated boiler conditions.
• It was shown that calcination under simulated boiler
conditions leads to generation of relatively small
pores and high surface areas, and that the reactivity
of a particular limestone is directly proportional to
the surface area developed by a given reaction condition,
provided that other factors, such as particle size,
are taken into account.
• The theoretical model of the calcination process,
previously developed under Contract No. PH 86-67-115,
was extended to enable prediction of calcination rates,
particle temperatures, circumferential stresses, and
pressures within a limestone particle during calcination
under simulated boiler conditions.
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TABLE OF CONTENTS
Page
INTRODUCTION 1
SUMMARY 3
Experimental Work 3
Conclusions 5
EXPERIMENTAL METHODS AND MATERIALS 6
Dispersed-Phase Reactor 6
Limestones .' . . , 7
Chemical Analyses 7
Surface Areas and Porosities. .......... 11
EXPERIMENTAL RESULTS AND DISCUSSION 12
Reaction of Limestone with S0? 12
Correlation of Previous Data 12
Effect of Temperature Gradient 16
Effect of Particle Size 18
Effect of SO Concentration 21
Surface Areas and Porosities ... 27
Effect of Time and Temperature on
Pore Structure. 28
Surface Area and Reactivity . 33
Calcination of Limestone 42
Application of the Model 43
REFERENCES. . 54
APPENDIX A - STONE ANALYSIS
APPENDIX B - REACTOR DATA
APPENDIX C - PORE SIZE DISTRIBUTIONS
APPENDIX D - COMPUTER PROGRAM - CALNOW
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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INVESTIGATION OF THE REACTIVITY OF
LIMESTONE AND DOLOMITE FOR
CAPTURING S02 FROM FLUE GAS
to
DIVISION OF CONTROL SYSTEMS
OFFICE OF AIR PROGRAMS
ENVIRONMENTAL PROTECTION AGENCY
by
R. W. Coutant, R. Simon,
B. Campbell, and R. E. Barrett
October 1, 1971
INTRODUCTION
Emission of sulfur dioxide by power plants and process industries
using coal and residual oil as fuels constitutes a major contribution to
air pollution in the United States. Ideally, the most positive approach
to control of these emissions is to burn low sulfur fuels. However, al-
though this approach is being investigated and developed, the burning of
low sulfur fuels is currently not technically or economically feasible in
most cases. The other alternative is the development of processes to re-
move the sulfur dioxide from the flue gas before emission into the atmos-
phere. A large number of such processes have been suggested. One of the
most attractive of these because of its relative simplicity and low cost
is the dry-limestone injection process.
Use of the dry-limestone injection process involves the use of
the boiler itself as a reaction chamber, and thus imposes certain limi-
tations on temperature and residence time. Generally, residence times
in a useful temperature zone are of the order of 2 seconds. Furthermore,
injection of the limestone close to the fireball, for the purpose of ob-
taining maximum residence, involves the risk of everburning of the lime,
which greatly reduces its reactivity. It is therefore highly important
that the chemistry and kinetics of calcination of the limestone, over-
burning or sintering of the lime, and reaction of S02 with the lime be
well understood in order to make optimum use of this process.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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The current program is one of several sponsored by EPA for the
purpose of elucidation of various aspects of the dry-limestone injection
(1 2 3)
process. This program is closely related to work previously reported ' '
under Contract No. PH 86-67-115, and has been directed at clarification of
previous observations as well as towards development of new information
relevant to the process. Using Stone No. 2061 (a limestone being used
(4)
by TVA in full-scale demonstration of the process) under simulated
boiler conditions, previous work showed that:
(1) Under standard conditions of 0.3 and 3 percent S02
and 02, respectively, the maximum utilization of
90-micron particles of the limestone is about 20
percent.
(2) Maximum limestone utilization is achieved at mean
gas temperatures of 1900-2000 F for 90-micron
particles-
(3) The maximum utilization of CaO is proportional to
the square root of the S09 concentration.
(4) The efficiency of utilization of the CaO is in-
creased by increasing the excess air level.
(5) Precalcination of the limestone before injection
into the flue gas generally results in lower
overall utilization of the CaO-
(6) The kinetics of calcination of limestone under
simulated boiler conditions can adequately be
modeled in terms of the heat and mass transport
characteristics of the system.
Primary emphasis of the current work has been on clarification
of some of the features of the process and on the effect of physical para-
meters of the stones and limes, e.g., surface area, porosity, and particle
size and of system variables such as temperature of injection, time-
temperature profile, and S0_ concentration on the reactivities of selected
limestones and dolomites.
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SUMMARY
Experimental Work
During the current contract period, it has been shown that:
(1) Maximum reactivity is also obtained at 1900-2000 F
for 48-micron particles.
(2) The maximum utilization of CaO is proportional
to the square root of the 862 concentration.
This is equivalent to saying that the amount
of S(>2 which can be removed from the flue gas
is proportional to the 3/2 power of the SOo
concentration.
(3) Steeper time-temperature profiles are beneficial
in reducing the time spent by the limestone in
higher temperature regions, but generally lead
to lower overall CaO utilization because of re-
duced overall residence times.
(4) Calcination of limestone under the relatively
short time (less than 2 seconds) conditions
of exposure encountered with boiler simulation
leads to much smaller pore sizes and much
higher surface areas than are observed with
the usually long-term calcination in kilns.
(5) The generally high rates of reaction observed
under conditions of boiler simulation can be
related to the higher surface areas generated
under these conditions.
(6) The reactivities of limestones, in general,
can be correlated with surface areas, pro-
viding other factors such as particle size
remain constant.
(7) Reduction in particle size in situ, as occurs
naturally upon rapid calcination of many stones,
may lead to increased rates of calcination, S02
reaction, and everburning, which can result in
high apparent reactivities per unit area when
surface area is not measured until after the
fact.
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An empirical model has been developed which is consistent with
these observations. This model can be expressed in the form of the
equation
S = b(l-e"kt)
where S is the sulfur pickup in SO^/g, b is associated with maximum value
of S obtainable under boiler simulation conditions, k is a rate constant,
Vi-
and t is the residence time. For -140 + 200 mesh Stone No. 2061 and
SCL and (X concentrations of 0.3 and 3 percent, respectively,
k = exp (14.563 - 18734/T )
m
and
b = exp (-2.982 + 10139/T )
m
where T is the mean gas temperature in degrees Kelvin. These equations
are valid over the range of mean gas temperatures from 1600 to 2148 F.
A theoretical model of the calcination process has been extended
to permit calculation of calcination rates, particle temperature, circum-
ferential stress, and pressure within a limestone particle during calcina-
tion under simulated boiler conditions. This model is based on nonsteady
heat and mass transfer within a limestone particle. Results of application
of this model indicate that:
(1) The rate of calcination is controlled primarily
by two factors: the rate of heat transfer to the
surface of the particle, and the rate of escape
of CO. through the relatively small pores of the
limestone.
(2) Particle temperatures are moderated somewhat by
the thermal requirements of the calcination process
with the result that use of the mean gas temperature
in place of the true particle temperature is a
reasonable approximation at residence times of about
1 to 1.5 seconds at a mean gas temperature of 1600 F,
At higher mean gas temperatures and longer residence
times, the mean gas temperature is less valid as an
approximation to the true particle temperature.
* Average size of 90 microns.
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(3) Pressure buildup within the calcining particle can
be appreciable, especially during the initial por-
tion of the process, with the result that circum-
ferential stresses which exceed the tensile strength
expected for the stone are predicted by the model.
This must result either in opening of cracks or, as
is observed in some cases, fragmentation of the stone.
Conclusions
As has been recognized in preliminary field testing of the dry-
(4)
limestone injection process by TVA , this process is relatively in-
efficient for removal of SO- from flue gas. The fact that only a
relatively short time period is available in a boiler at temperatures
favorable for the reaction does not explain why the process is in-
efficient,, Laboratory investigations of the process under simulated
boiler conditions indicate high enough initial reaction rates that apprec-
iably greater efficiencies would be obtainable if these high rates could
be maintained. The reason for these low efficiencies lies in the funda-
mental nature of this heterogeneous reaction.
Results of this work, and that of Borgwardt , show that the
rate of reaction is proportional to the amount of surface area generated
as a result of calcination of the limestone. But surface is continuously
formed by calcination and destroyed by sintering of the lime. This
sintering is manifested through growth of the pores during the process.
Very small pores, less than 0.01 micron, are associated with very high
surface areas, and hence high rates of reaction. However, since the
molar volume of the reaction product, calcium sulfate, is about twice
that of the lime, the pores tend to fill upon reaction. Furthermore,
small pores are associated with appreciable diffusional resistance so
that reaction tends to take place near the pore mouth. The result is
confinement of the reaction to the outer portion of large particles, and
eventual sealing off of the pore mouth by reaction product. With larger
pores, say 0.1-0.3 micron as found with many commercially burnt limes,
the interior of a limestone particle is more accessible, but the reaction
rate is lower because of smaller surface area.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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For limes calcined under simulated boiler conditions, pore
radii are of the order of 0.01 micron. Appreciable everburning of the
lime takes place at injection temperatures above about 2200 F and it
appears that the dynamics of this deactivating process are important
even at lower temperatures. It might be expected that increased utili-
zation could be obtained with smaller, say 5-micron particles, but
smaller particles also calcine faster, and hence the true particle
temperature can rise more rapidly to temperatures where the sintering
process is important. There is therefore a compromise between the
dynamics of calcination, sintering, and reaction with S0~, with the
net result that reduction of particle size below, say 45-microns, does
not greatly increase utilization.
That the percentage of S02 removed is proportional to the
1/2 power of the initial SO- concentration implies that the dry-
limestone process would be relatively more effective in application
with flue gas containing high concentrations of SO .
EXPERIMENTAL METHODS AND MATERIALS
Experimental procedures used for this work have been described
in detail in earlier reports. ' ' Briefly, limestone is exposed to
flue gas under conditions closely simulating the time and temperature
history in the superheater/exonomizer section of a power-boiler. The
partly calcined, partly reacted limestone is then analyzed for degree
of calcination and extent of reaction with SO..
Dispersed-Phase Reactor
The basic design of the dispersed-phase reactor (DPR), and
the evolution of techniques employed with this reactor have been des-
(123)
cribed in detail previously. ' ' Only relatively minor changes in
the apparatus have been made during this contract period to enable more
flexibility in controlling the time-temperature profile. Modifications
consisted mainly of the addition of a water-cooled jacket to each section
of the DPR. Each of the three sections can now be operated independently
BATTELLE MEMOKIAL INSTITUTE - COLUMBUS LABORATORIES
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with walls either cooled or uncooled to obtain the desired time-temper-
ature profile for the system.
A photograph of the DPR is shown in Figure 1, and a line
drawing indicating the construction elements is given in Figure 2.
Figure 3 shows the effect of addition of the cooling jackets. The net
result of this increased flexibility is that average time-temperature
profiles expected in a steam-generating boiler can be simulated reasonably
well.
Limestones
The majority of experiments performed during both this contract
period and the previous one involved the use of Stone No. 2061, the same
stone which is being used in the TVA full-scale demonstration of the dry-
limestone injection process. During the course of this work, at least
three distinctly different batches of Stone No. 2061 have been examined
at least briefly. Analyses for two of these are given in Table A-l of
Appendix.A. The third material was found to decrepitate severely upon
heating to about 690 F and was not considered to be representative of
the general type of Stone No. 2061.
Ten other stones were also studied in this work. These stones
were typical of distinctly different types of limestones and dolomites
as classified by Richard Harvey of the Illinois State Geological
Survey. They ranged in type from Iceland Spar to magnesite. Analyses
for these materials are listed in Table A-l of Appendix A.
Chemical Analyses
This experimental work included exposure of stones in the DPR
both with and without SO. in the flue gas. For those samples where no
sulfur was present, the samples, as received, were composed of calcium
oxide, calcium carbonate, some calcium hydroxide originating from partial
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Exhaust
Coolant expansion
tanks
Thermocouple probe
Gas sampling probes
Particle and water
filters for SQ2
analysis
Cyclone
collector
Vacuum and
coolant manifolds
(hidden)
Thermocouple probe
Control panel
Thermocouple pr
oolant pumps
d ballast
tacks
FIGURE 1. DISPERSED-PHASE REACTOR
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14'
i
6'
2f
i-
I
4-
Reactor:
Castable refractory
poured in place
6-inch stainless
steel pipe
3-inch insulation
(not shown)
Injection and sampling parts
Stainless steel
flanges
Annular water jacket
3/4-inch gap
Combustor:
16-inch stainless pipe cast
with refractory to 11-inch ID
Fuel, air, H S inlet
Figure 2. REACTOR CONFIGURATION
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10
2500
2300
2100
1900
A. No water in jacket
-1700
Ol
a
£
1300
I 100
B. Water in jacket
900
C. Water in jacket
700
0.0 0.8
1.6
2.4 3.2 4.0
Residence Time,seconds
4.8 5.6
FIGURE 3. TIME-TEMPERATURE PROFILES IN MODIFIED REACTOR
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11
hydration by water vapor in the flue gas, and various other non-reactive
components depending on the composition of the original stone. These
samples were first exposed to steam at approximately one atmosphere
pressure and 250 F to convert the calcium oxide to calcium hydroxide
and thereby simplify chemical analyses. Samples were then analyzed by
a thermogravimetric method for hydroxide and carbonate content.
When samples had been exposed to SO in the flue gas, a similar
procedure of steam hydration and thermogravimetric analysis was followed.
However, these samples also were analyzed for sulfate and, generally,
for sulfite content. The procedure followed for sulfur analyses has been
(3)
reported previously . Basically, this procedure consists of (1) digestion
of sample using ion-exchange resin, followed by (2) colorimetric
determination of sulfate using barium chloranilate as the reagent.
Surface Areas and Porosities
Surface area and porosity measurements were made on appropriate
samples of both sulfurized and unsulfurized stones after exposure in the
DPR. Area measurements were made using the dynamic BET method. Porosity
measurements were made with a mercury porosimeter.
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EXPERIMENTAL RESULTS AND DISCUSSION
A considerable body of data has been developed relevant to the
reaction of limestone with SO in the dry-limestone injection process.
The main purpose of this current work has been to organize and clarify
previous data through correlation of data, development of supplemental
information, and formulation of reaction models. Specifically, the
following facets of the process have been considered and are discussed
further belox^:
o The effect of time and temperature on reactivity
0 The effect of SCL concentration on reactivity
0 The effects of physical factors such as particle
size, surface area, and pore size, on reactivity
0 The effect of physical factors on calcination rates .
Reaction of Limestone with S09
Correlation of Previous Data
A number of different approaches can be taken to correlate the
experimental data, and several empirical and theoretical models have been
developed. However, the majority of the models have been based either
on isothermal experimental data or on non-isothermal representations
employing the time-temperature profile of the flue gas rather than that
of the limestone. Either of these approaches is capable, in principle,
of providing adequate representation of the limestone-SO reaction if
enoueh information concerning the effects of Drocess variables is avail-
able. For example, it can be seen qualitatively from Figure 17 that the
temperature of a limestone particle rises rather sharply upon injection
into the flue gas to a temperature which is relatively stable for a con-
siderable portion of its residence time in the flue gas. The particle
* Details of reaction conditions and analytical results are listed in
Appendix B under headings corresponding to appropriate sections of text.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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13
temperature tends to follow the gas temperature after the initial heatup
but at a slightly lower rate. Because of this, the process might be
equally well represented either as an isothermal process at some inter-
mediate temperature, or as a nonisothermal process using gas temperatures
after the first half second or so. Departures from nonisothermal approxi-
mation are most serious with high injection temperatures, long residence
times, and small particles.
Data gained with the DPR are expected to be more closely related
to the process as it occurs in a boiler because of the similarities in
time-temperature profile. It is therefore believed that empirical re-
presentation of DPR data may provide a slightly better representation of
the limestone-SCL reaction in a boiler. Some work of this type was re-
(3)
ported in the November, 1970, Summary Report , but the equations used
were not developed to the point where any physical significance could be
attached to the adjustable parameters used.
In general, the most outstanding characteristics of the reaction
at any given temperature are the rapid decrease in reaction rate with
increased loading and approach to some limiting extent .of reaction which
is dependent on temperature and particle size. This suggests that the
rate equation should be expressed in terms of the loading, i.e., that the
rate is a function of the amount of lime actually available for reaction.
The correlation between reactivity and surface area as developed by
Borgwardt and as confirmed by other work also implies that the r
equation should be expressed in terms of loading.
Both the dependence of rate on loading and the concept of some
limiting value of reactivity is expressed by
ff = k(b-S) (1)
where S is the loading (sulfur pickup in mg S0_/g), k is a rate constant,
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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14
and b is the maximum loading. Integration of Equation 1 yields
S = b(l-exp(-kt)) . (2)
If this equation is expanded in series form, the result is similar to
the polynomial used to correlate data in the November 20, 1970 Summary
S = b(kt - k2t2/2l + ) (3)
(3)
Report , i.e
It is expected therefore that Equation 2 would fit the experimental data
at least as well as the truncated polynomial used in the Summary Report.
Furthermore, use of Equation 2 permits attachment of some physical signifi-
cance to the parameters b and k.
A least-squares fit of Equation 2 to the SO,,- limestone reaction
data from the Summary Report consistently yielded smaller standard devia-
tions than had been obtained in any previous attempts at correlation of
this data. Furthermore, Equation 2 was applicable at mean reactor
temperatures above 1845 F, where the maximum loading decreases with
increasing temperature. All of the data can be organized in a relatively
straightforward fashion using Equation 2. Figure 4 shows semi-log .plots
of b and k versus the reciprocal of the absolute mean reactor temperature
for the data for -140+200 mesh Stone No. 2061 at C = 3000 ppm and
so2
C =3 percent. This plot shows that, within the limits of the experi-
mental work, both k and b can be expressed in terms of Arrhenius-type
functions of temperature
and
k = exp(14.563 - 18734/T ) (4)
b = exp(-2.982 + 10139/T ) (5)
where T is the mean reaction temperature in degrees Kelvin. These
m
expressions for k and b are consistent with the fact that the amount of
lime available for reaction decreases at the higher temperatures and
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15
that rate constants are normally expected to increase exponentially
with temperature. It should be noted that Equation 5 cannot be used
for b at temperatures below about 1500-1600 F because b is allowed
to increase without limit. This is,of course, of little consequence
in a practical sense since reaction rates are too low to be of practical
value below these temperatures.
o
X
10.0
8.0
6.0
4.0
3.0
2.0
1.0
0.8
0.6
0.4
0.3
0.2
0.1
0.6
0.7
b x 10
-2
0.8
10 /T K
m
0.9
FIGURE 4. DEPENDENCE OF k AND b ON MEAN GAS TEMPERATURE
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(3)
In the Summary Report , it was shown that the apparent order
of reaction with respect to SO- concentration changes during the course
of the reaction. Further examination of these data in terms of the
expression given in Equation 2 reveals that k is independent of S00 con-
1/2
centration and the value of b is proportional to C . Since the rate
so2
of reaction is proportional to (b-S), the apparent order of reaction,
(d In (dS/dt)/d In C ), depends on loading. This square-root dependence
bU2
of the maximum loading has been further confirmed by recent work which
is discussed on Page 21.
According to Equation 4, the activation energy for the process
is 37.2 kcal/mole. However, the apparent activation energy,
2
RT (d ln(dS/dt)/dT), reflects both the temperature dependence of k and
that of b, and is dependent on time. For example, at very short times,
the apparent activation energy approaches 17.1 kcal/mole at all temper-
atures, but at t = 0.1 sec at 1950 F, the apparent activation energy is
10.5 kcal/mole. At higher temperatures and longer residence times, the
apparent activation energy can even become negative, reflecting the de-
creased overall reactivity with increased temperature due to loss of
surface area by overburning.
Effect of Temperature Gradient
"The average time-temperature profile of a boiler is dependent
on the specific design and size of the unit, so that different boilers
are apt to be characterized by different time-temperature profiles.
Furthermore, the time-temperature profile in any given boiler will vary
depending upon load. Therefore, there is some need to know how the per-
formance of a given limestone may vary with a change in temperature
gradient.
Two series of injections in the DPR were made with -270+325
mesh Stone No. 2061 operating the reactor with two different time-temper-
ature profiles. Profiles for these series are shown in Figure 5. Results
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[V,
Cl
D.
2600
2500
2400
2300
2200
2100
H 2000
1900
1800
1700
1600
.Scries 1015
I
I
I
I
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Residence Time, seconds
FIGURE 5. TIME TEMPERATURE PROFILES
1.4
1.6
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18
of these runs are summarized in Table 1. For each series, a maximum in
reactivity was found for injection at 2100-2200 F (mean temperature =
1950 F) as indicated in Figure 6. However, with the steeper time-temper-
ature profile (Series 1022), higher injection temperatures appear less
detrimental, possibly because of the reduced time of exposure at these
high temperatures.
The most serious effect of increasing the temperature gradient
is of course a decrease in the time available for reaction at favorable
temperatures. This shows up in comparison of the results obtained for
these two series. However, if comparisons are made between pairs of
samples having approximately common mean temperatures and residence times,
little difference in reactivity is seen beyond that which might be
attributed to the slight differences in residence time.
In principle, the response curves shown in Figure 6 could be
calculated from Equation 2 of the previous section of this report pro-
viding adequate knowledge of the dependence of b and k on particle size
were available. Equation 2 predicts a maximum reactivity at temperatures
in agreement with Figure 6, but the dependence of b and k on particle
size is not fully known. Furthermore, the particular batch of Stone No.
2061 used in these experiments was slightly different in composition
from that used in the previous work, and it is not known how strongly
this factor influences the reactivity.
Effect of Particle Size
To obtain some idea of the effect of particle size on the
factors b and k of Equation 2, a single series of runs was made in the
DPR at constant mean temperature (1930 F). For this series, the particle
v?
size was -270+325 mesh, and the batch of Stone No. 2061 used was similar
in composition to that used previously for the -140+200 mesh material.
* Average size 48 microns.
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TABLE 1. EFFECT OF TIME-TEMPERATURE PROFILE
Run
No,
1015-B
1015-C
1015-E
1015 -G
1015-K
1015-L
1015-N
1015 -P
1015 -S
102 2 -A
1022-C
1022-E
1022-G
1022-J
1022-L
1022 -N
1022-P
1022-R
Temperature
, F
Iniection Collection
2402
2402
2179
2345
2179
2070
2014
1901
1843
2565
2565
2216
2565
2216
2138
1996
1865
1805
2179
2014
2014
1730
1730
1730
1730
1730
1730
2216
1996
1996
1693
1693
1693
1693
1693
1693
Residence
Time,
seconds
0.45
0.82
0.37
1.38
1.04
0.80
0.67
0.41
0.28
0.27
0,49
0.22
0.91
0.64
0.57
0.42
0.26
0.17
Sulfur Pickup,
mg SO /g Sample
55
87
124
136
175
175
163
156
142
96
89
154
115
167
150
150
122
79
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180
, 120
o
CO
ep 100
Q.
3 80
60
40
20
0
o
•^
0<
M
3
3
CO
Series 1015
Collection Temperature = 1730 F
(
1
Series 1022
Collection Temperature = 1693 F
I
I
2600 2400 2200 2000 1800 1600 2600 2400 2200 2000
Injection Temperature, F
FIGURE 6. EFFECT OF TIME-TEMPERATURE PROFILE ON REACTIVITY
1800
1600
-------
21
A least-squares fit of the data to Equation 2 yields values of
b and k of 135 mg SO /g and 3.09 sec respectively. These may be compared
with calculated values of b = 105 and k = 1.56 for the larger particle
size at the same temperature. Thus, approximate halving of the particle
size had only a minor effect on b, the maximum loading, but the rate
constant was approximately doubled. This is consistent with the observa-
tions made in the previous section of this report, but, again, because
of the potential differences between the two batches of stone, no
quantitative comparison seems warranted. These data are also consistent
with observations of Ishihara whose work indicated higher initial
rates of reaction for smaller particles but only a relatively minor effect
of particle size on overall utilization.
Effect of S09 Concentration
Reaction Rates. Rate data summarized in the Summary Report of
(3)
November 20, 1970 indicated that the rate of reaction of Limestone No,
2061 wiLh SG~ iii flue gas was proportional to the square root of the S0_
concentration during the initial stages of the reaction, and that the
apparent order of reaction increased to unity or greater as the reaction
proceeded. Further work has now been done to clarify this seemingly
complex behavior.
Firstly, the previous data have been treated in terms of
Equation 2 given above to determine the specific dependencies of k and b
on concentration. This treatment of the previous data reveals that the
rate constant, k, is essentially independent of the S09 concentration at
a mean reactor temperature of 1770 F. However, the maximum loading,
b, depends on the square root of the concentration. Inspection of the
form of Equation 2 shows that comparison of rates at common values of S
along the response curves for various concentrations, will lead to a
complex and varying apparent order. However, if the rates are compared
at constant times, the apparent order is constant at one-half.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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22
A second clarification of apparent reaction order was made through a
series of additional runs in the reactor at concentrations of 125, 255,
650, 1600, 3980, and 9900 ppm. These runs included injection and col-
lection of samples under various temperature and residence conditions,
but most of the data were taken in the plateau region of the response
curve so that the data more generally represent b.
In each of these runs limestone injection rates were approxi-
mately 1 gram per minute. This means that, with the lowest SO con-
centration, the effective stoichiometry of the system was about one, i.e.,
the molar throughputs of limestone and SO were approximately equal.
However, the maximum lime utilization observed was only 3 percent, and,
for all practical purposes, the SO concentration can be considered
constant. At higher concentrations, the effective stoichiometric ratios
were less than one and the net S09 removal achieved in each case was less
than 3 percent. This means that these data can be considered as valid
tests of reactivity at the stated concentrations.
It will be noted from the data cited in Table B-3 of Appendix B
that similar time and temperature conditions were used for corresponding
samples at each SO concentration. Comparison can thus be made on a
point-by-point basis. Also, since most of the data were taken in the
plateau region of the reaction trajectory, averages of the results at
each concentration can be used to represent the effect of concentration
on overall reactivity. Either the point-by-point comparison or the'
comparison of average reactivities leads to the same conclusion, as
indicated in Figure 7.
Figure 7 shows clearly that the overall reactivity is proportional
to the square root of the S00 concentration, which is entirely in agreement
(3)
with data of the Summary Report . This fact is seemingly in conflict
/•o \
with results obtained by Babcock & Wilcox . It must be recognized,
however, that the B6W data represent a different type of experimental
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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Q)
c
(0
o
00
00
o
CO
200
100
80
60
40
20
100
200
A
Slope = 0.48
I I
I
1 1 1
400
6(50 800 1000
t-o
u>
2000
4000 6000 8000 10000
S02 Concentration, ppm
FIGURE 7. EFFECT OF S02 CONCENTRATION OF OVERALL SULFUR PICKUP
-------
24
approach. Their data show the amount of S0? removed from the flue gas
stream as a function of initial SO concentration. The current data can
L *
be transformed into this form by multiplying the percentage SO removal
at unit stoichiometry by the SCL concentration, in which case the apparent
order of the concentration dependence should be 1.5. It can be readily
seen.from Figure 8 that when the data are represented in this fashion
the apparent order is 1.5. Although the B&W report cites an apparent
order of about 1 for their data, a least squares treatment of the B&W
data reveals an apparent order of 1.4. Hence these two pieces of work
are in agreement.
Equilibria. Some comment is warranted on the effect of the
SO. concentration on the dissociation of calcium sulfate and the relation
of this, process to the observed maximum in reactivity. Consider the
following reaction
kf
CaO + S00 + 1/2 or 1/2 00 £ CaSO. .
t- 2,4
K
r
Although this expression may not necessarily represent the actual chemical
reaction mechanisms, it does represent the essential chemistry involved
in the dry-limestone injection process. Here, k and k are the forward
and reverse rate constants. Taking constant oxygen partial pressure of
0.03 atm, a typical value for boiler operation, the equilibrium partial
pressure of SO- over pure calcium sulfate can be calculated as shown in
(9)
Table 2 from the thermodynamic data of Reid, et al. . It can be seen
from this Table that at particle temperatures above about 2150 F, the
driving force for reaction of lime with SO- will be decreased appreciably
by virtue of the increasing instability of the sulfate.
In a boiler, particle temperatures could conceivably reach this
value momentarily if the stone were injected at temperatures above about
2350 F, but since the temperature gradients in a boiler are rather steep
it is unlikely that this temperature would persist in the stone particles
* Assumed to be equal to the CaO utilization.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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25
6
ex
10"
9
7
5
Q)
E
o
O
• ,-4
O
U
1/1
• ,-1
c
9
7
5
Slope = 1.5
TO
O
-------
26
TABLE 2. EQUILIBRIUM PARTIAL PRESSURE OF S02
CaSO. = CaO + 1/2 (X, + S00 (00 = 0.03 atm)
4 L L L
P (torr) = exp (37.4556 - 55440/T°K)
T°F
1600
1650
1700
1750
1800
1850
1900
1950
2000
2050
2100
2150
2200
2250
2300
2350
2400
2500
2600
P,
1.67
5.26
1.57
4.48
1.22
3.17
1.90
1.90
4.42
9.91
2.16
4.55
9.34
1.87
3.64
6.92
12.9
41.9
126.
torr
x 10"5
x 10~5
x 10~4
x 10~4
_3
x 10
x 10"3
_3
x 10
x 10"2
x 10"2
x 10"2
_i
x 10
_i
x 10
x 10"1
P, ppm
2.20 x 10"2
6.92 x 10"2
2.07 x 10"1
5.89 x 10"1
1.61
4.17
10.4
25.0
58.2
130
284
599
12.3 x 102
24.6 x 102
47.9 x 102
91.1 x 102
17.0 x 103
55.1 x 103
16.6 x 104
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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27
for very long. Even if it is assumed that the particle temperature pre-
cisely follows the gas temperature, there is a maximum in reactivity pre-
dicted by rate equations implied by the chemical equation above, but the
decreased reactivity above 2100 F does not compare with that observed
experimentally. It is therefore unlikely that the instability of the
sulfate can be blamed for decreased reactivity at high injection temperatures,
Surface Areas and Porosities
The results of Borgwardt have indicated that the most important
factors in determining the reactivity of a given limestone are the surface
area and porosity developed during the course of calcination. These
factors directly determine the availability of lime for reaction,the
accessibility of the lime, and the space which is available within a given
particle for occupancy by reaction products. The surface area and
porosity are determined by calcination rate and sintering rate, of which
the latter is apparently more important in determining the decreased
reactivity of limestones at high temperatures. Sintering itself is a
complex process, depending on grain size, impurity content, and temperature
of the lime and time. Kuczynski has identified at least four distinct
mechanisms for the sintering process, and, in view of this complexity,
it is necessary to rely upon direct measurements of surface area and
porosity and empirical correlation with reactivity as a means of identi-
fying reaction conditions and particular limestones which could be of
interest in the dry-limestone injection process or related limestone-
SO removal schemes.
Surface areas of kiln-calcined limes are generally of the order
of a few square meters per gram or less depending on the degree of over-
burning of the lime. Average pore diameters in these same materials are
generally of the order of a few tenths of microns. Borgwardt has
shown that the isothermal reaction rates of such kiln-calcined limes are
directly proportional to surface areas.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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28
The process of pore formation during calcination involves con-
tinuous growth of the pores from essentially molecular dimensions to some
final state which is determined largely by temperature, when calcination
times are of the order of minutes to hours. But insufficient information
is available to determine how important the dynamics of the process may
be at short times, say seconds or less, which are important in considera-
tion of the calcination and reaction of limestone either in a boiler or
in the DPR. If the dynamics of the process are important on this time
scale, the use of a correlation of reactivity with surface area measured
after completion of the process could be subject to question.
To clarify this point, two series of experiments were run using
the DPR. The first series was directed at examining the time and temper-
ature dependence of surface area in the DPR. The second series was con-
cerned with the question of correlating surface area with reactivity in
the DPR.
Effect of Time and Temperature
on Pore Structure
Data shown in Table 3 summarize the results of surface area
and porosimetry measurements made on Stone No. 2061 calcined in the DPR
under a variety of temperature and residence time conditions. A typical
pore distribution for DPR-calcined Stone No. 2061 is shown in Figure 9.
Note that most of the apparent pore volume at pore diameters greater than
10 (j, is probably interparticle space rather than true pore volume.
Complete pore distribution data for these samples are given in Appendix C,
Series 925 was run with -140+200 mesh stone and series 106 was run using
-270+325 mesh stone.
Pore volumes and surface areas cited in Table 3 are listed
relative to the weight of CaO formed during the partial calcination.
Pore diameters listed are calculated from the surface area and pore
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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TABLE 3. POROSITY AND SURFACE AREA DATA
Sample
Number
925-B
925-A
925-D
925-C
106-A
106-B
106-C
106-F
106-E
106-D
Temperature,
F
Injection Collection
2224
2224
1830
1830
2243
2156
1996
1920
1849
2243
1440
1765
1440
1765
2156
2073
1920
1500
1782
1500
Residence
Time,
seconds
2.86
1.27
1.82
0.23
0.15
0.16
0.17
1.35
0.18
0.99
Percentage
Calcination
86
83
73 .
19
40
45
28
78
45
85
Pore . ,
Volume , ^
cc/g CaO
0.187
0.203
0.337
0.575
0.133
0.226
0.411
0.164
0.166
0.100
Surface Area
2
m /g CaO
21.3
21.5
61.3
44.2
52.9
66.7
67.8
36.6
42.9
7.6
Average
Pore
Diameter,
microns
0.044
0.048
0.028
0.066
0.013
0.017
0.030
0.022
0.019
0.066
(a) Series 925 is -140+200 mesh, Series 106 is -270+325 mesh.
(b) For pores with d < 2 ^.
N>
-------
1.0
E
o
0:8
0.6
Stone No. 2061
-140 + 200 mesh
65% Calcined
Aye « 0.02
•3
o
o
o
|
_J
O
0.2
Inter part icle space
J I
I I
J I
10-
10'
10' IOU
Pore Dicimeter, microns
FIGURE 9. PORE SIZE DISTRIBUTION
10"
10
.-2
-------
31
volume data using the equation
d = 5V /A,
P
where V and A are the pore volume and surface area respectively. This
equation is only an approximation; the actual relationship between volume
and area depends on the specific pore shape. However, the calculated
values can serve to determine whether any significant contribution to the
surface area is made by pores smaller than those observed in the porosimetry
measurements. With these samples, the calculated diameters agree well
with the pore size distribution shown in Appendix C, indicating that no
significant pore structure exists at diameters less than about 0,01 micron.
The porosity data indicate a bidisperse system of pores with a
minor pore distribution having diameters of the order of a few tenths of
microns. This second pore distribution is especially evident in samples
having larger pore volumes than might be expected for a soft-burned lime,
0.36 cc/gCaO. This may indicate that the second pore distribution is due
to cracks in the lime caused by the violent nature of the calcination
process, or it may be caused by pore inclusion in the original limestone
sample. It should be noted also that many of the samples have pore
volumes smaller than 0.36 cc/gCaO, implying that a significant amount of
sintering has already taken place in the relatively short time of exposure.
Maximum surface areas in these runs appear to be developed with
injection temperatures in the neighborhood of 1900-2000 F, implying the
everburning of the lime is significant at higher temperatures.
The surface area data also reflect the importance of the dynamics
of the sintering process. Comparing sample 106-A with Sample 106-F, it
can be seen that although the injection temperatures were the same for
these two samples, the longer exposure of Sample F resulted in a much
lower surface area. This is also evident in comparison of Samples 106-C
and 106-D. Although the injection temperature for Sample C was slightly
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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32
higher than that for Sample D, the shorter exposure time for C resulted in a
higher surface area per unit weight of CaO formed.
Some additional experiments with other stones were performed to
determine the effect of temperature on surface area development,, This in-
volved use of three selected members of a set of ten stones provided by APCO,
all ten of which were used in tests of the correlation between area and re-
activity, discussed below. The results of study of the effect of temperature
on area of these materials is shown in Table 4. These results clearly show
that the surface area developed during a given residence time decreases with
increasing temperature.
TABLE 4. EFFECT OF TEMPERATURE ON SURFACE AREA
Run
318-A
318-B
318-C
317-A
317-B
317-C
318-D
318-E
318-F
Stone^'
Type
Mich. Marl
IGS-4
No. 1336
Mich .Marl
IGS-4
No. 1336
Mich .Marl
IGS-4
No. 1336
Temperature Residence Time
Injection
2006
2006
2006
2155
2155
2155
2263
2263
2263
Collection
1712
1712
1712
1785
1785
1785
1828
1828
1828
sec
1.03
1.03
1.03
1.17
1.17
1.17
1.14
1.14
1.14
, Percentage
Calcination
52
72
71
66
80
83
74
81
84
Area,
13.6
24.8
26.4
7.5
16.3
23.7
5.9
8.2
14.1
(a) -140+200 mesh-
(b) Area per gram of sample >
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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Surface Area and Reactivity
In a further attempt to clarify the validity of correlation of
surface area with reactivity, ten stones selected by APCO as representative
of the spectrum of limestone classes were tested in the DPR both for sur-
face area development and reactivity. The mineralogical characteristics
of these ten stones have been examined irv detail by Harvey , and identi-
fication numbers used in discussing the data refer to Harvey's classifica-
tion. All of the stones were -270+325 U.S. Standard mesh.
The type of data obtained in this series of tests must be dis-
tinguished from the area-reactivity data of Borgwardt. Borgwardt showed
that the isothermal reaction rates of prccalcined limes were proportional
to their surface areas. Because of the nature of the DPR experiments,
however, it was not possible to determine actual surface areas existing
during the course of reaction with SCL . In these experiments, only the
terminal surface area, i.e., that area existing after completion of calci-
nation and sintering, could be determined. It is recognized that the SCL.
reaction occurs simultaneously with calcination and sintering in the DPR.
Hence correlation between SCL pickup and terminal surface area is not
necessarily expected. The purpose of this work was therefore to explore
the possibility of correlation of reactivity with terminal surface area.
Table 5 shows a summary of terminal area data for samples of the
ten stones calcined in the DPR in the absence of SO.. Table 6 shows the
reactivities of these same materials exposed in the DPR under similar tem-
perature and residence time conditions with an SCL concentration of 3000
ppm. Also indicated in Table 6 is the effect of reaction on lowering the
area due to filling of pore space during reaction.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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34
TABLE 5. SURFACE AREAS OF TEN CALCINES
Stone Temperature Residence Time,
Run
226 -A
226-B
226-C
226-D
226-E
32-A
32-B
32-C
32-D
32-E
Type Injection
Mich. Marl
No. 1336
IGS-1
IGS -2
ICS-3
IGS -4
1GS-5
IGS -6
IGS-7
IGS-8
2140
2140
2140
2140
2140
2140
2140
2140
2140
2140
Collection
1495
1495
1495
1495
1495
1495
1495
1495
1495
1495
sec
2.08
2.08
2.08
2.08
2.08
2.08
2.08
2.08
2.08
2,08
Terminal
Percentage Area.
Calcination m^/g'- '
67
83
83
81
81
82
(c)-
(c)
(c)
76
5.4
14.2
18.4
11.0
18.3
8.6
21.9
14.7
23.6
15.1
(a) -2704-325 mesh.
(b) Area per gram of sample.
(c) Approximately SO percent calcinal
TABLE 6. REACTIVITY AND SURFACE AREA
Stone
Marl
1336
IGS 1
IGS 2
IGS 3
IGS 4
IGS 5
IGS 6
IGS 7
IGS 8
Terminal,
Area, m /g
5.4
14.2
' 18.4
11.0
18.3 (6.7)(b)
8.6 (2.5)(b)
21.9
14.7
23.6
15.1
Sulfur Pickup , v
mg SO /g-calcinea'
260
126
115
132
178 (179)(c)
274 (260)(c)
259
246
85
168
(a) Reaction temperatures and times similar to those
given in Table 5.
(b) Area of sample after reaction.
(c) Repeat values on separately injected samples.
-------
35
It is readily apparent from Figure 10 that no linear correlation
exists between reactivity and terminal surface area for these samples.
Five of the test stones (IGS-2,8,3,5, and No. 1336) could conceivably
display a linear correlation. IGS-7 is almost pure magnesite, and since
MgO is relatively unreactive, this material probably should not be in-
cluded in the correlation., However, the very high reactivities of the
two materials showing the lowest terminal surface areas, IGS-4 and Michigan
Marl, strongly mitigates against the general validity of a correlation,
unless other factors are taken into consideration.
Although all of the ten stones were initially sieved to -270+325
mesh, microscopic examination of samples recovered from the DPR indicates
severe disintegration of particles for some of the stones. Figures 11 a-J
show photomicrographs of these ten stones before and after injection into
the DPR. It is readily apparent from these photos that five of the stones,
105-4,5,6,7 and Michigan Marl underwent severe size reduction in the re-
actor,, With Michigan Marl even those few large particles remaining are
really agglomerates of fine particles„ Reexamination of Figure 10 reveals
that these are all materials for which the reactivity was higher than that
expected from the terminal surface area. This is especially true for IGS-5,
6, and 7 because of the fact that these stones contain relatively little
CaO per gram of calcine; IGS-5 and 6 are dolomites and IGS-7 is a magnesite
having about 3 percent CaCO as an impurity,, In each case, the reactivity
of these three materials is greater than the 10-15 percent utilization of
the CaO usually observed with other -270+325 mesh limestones„ Since MgSO,
is not thermodynamically stable under the conditions of these experiments,
little of the increased reactivity can be attributed to reaction with MgO.
There is therefore some reason to believe that the reactivity-
terminal area correlation may be valid, providing all other factors are
equal. By the same token, a low-terminal surface area does not necessarily
imply low reactivity if the stone is one which does undergo decrepitation
upon exposure to the severe thermal stresses imposed in the DPR or in a
boiler.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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36
280
0)
c
240
?nn
CO
60
E
ex
3
^
y
3
CO
120
80
(M)
(4)
(4)
(5)
(6)
(7)
6 8 10 12 14 16 18 20 22 24 26
Terminal Surface Area of Lime, m /g calcine
FIGURE 10. REACTIVITY vs SURFACE AREA
-------
37
Scale: 1 in. = 435
Before Reaction After Reaction
a. Michigan Marl
Before Reaction After Reaction
b. No. 1336
FIGURE 11. PHOTOMICROGRAPHS OF TEN STONES BEFORE AND AFTER REACTION
-------
38
Scale: 1 in. = 435 ju
Before Reaction After Reaction
c. IGS 1
Before Reaction After Reaction
d. IGS 2
FIGURE 11. (Continued)
-------
Scale: 1 in. = 435
Before Reaction
After Reaction
e. IGS 3
Before Reaction After Reaction
f. IGS 4
FIGURE 11. (Continued)
-------
40
Scale: 1 in. = 435
Before Reaction
Before Reaction
After Reaction
g. IGS 5
After Reaction
h. IGS 6
FIGURE 11. (Continued)
-------
41
Scale: 1 in. = 435
Before Reaction
i. IGS 7
After Reaction
Before Reaction After Reaction
j. IGS 8
FIGURE 11. (Continued)
-------
42
These data could also be taken as a reflection of the importance
of the relative dynamics of the calcination, sintering and reaction
processes. The calcination process does act as a thermal buffer in
protecting the particles from reaching too high a temperature (see
Figure 1?.). The smaller the particles, the more rapid the calcination
process, and hence the higher will be the maximum particle temperature.
Thus the rate of sintering is also expected to be greater for small
particles. At the same time, the rate of reaction is also greater for
small particles*, but most of the reaction takes place while calcination
is still occurring. That is, most of the reaction with SO oc.curs before
high temperatures and hence rapid sintering is encountered. It is there-
fore highly probable that additional sintering of small particles, such
as those produced by fragmentation in the DPR, took place after essentially
all of the SO reaction had occurred. In other words, the measured terminal
surface areas are not representative of areas available during the actual
course of reaction. This is also shown by comparison of data in Tables 4
and 5 where it is indicated that surface areas depend on the time of
exposure in the DPR.
Calcination of Limestone
A theoretical model of the calcination of limestone was pre-
(3)
sented in the November 20, 1970, Summary Report. This model was
based on a representation of the heat and mass transfer processes oc-
curring during calcination. The model has now been extended to permit
simulation of the calcination process under non-isothermal conditions
similar to those encountered in the DPR or a boiler. To accomplish this,
the original computer program given in the Summary Report has been modi-
fied in several ways:
* As indicated on Page 21 the maximum loading, b, is influenced
only slightly by decreased particle size, but the rate constant,
k, is approximately inversely proportional to particle size.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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43
(1) The model now takes into account the effects of
the actual variation in gas temperature from the
injection point to the collection point in the
DPR. This replaces the previous approximation of
constant gas temperature at some mean value. This
change has made an appreciable difference in the
results, particularly for the longer residence
times. The percentage calcination was found to be
much more sensitive to the higher rates of calci-
nation obtained for gas temperatures near the
injection point.
(2) The computer output format was modified from that
given in Appendix D of the Summary Report to show
the position of the particle between points and
the gas temperature at this position as functions
of time. In addition, the following information
is printed out regarding the calcination front at
each time: calcination front radius, calcination
temperature, calcination pressure, and circumferential
tensile stress. When the particle has reached the
sampling point, the profile of temperature, pressure
and stress as functions of radial position are also
printed out.
(3) The model was made completely dynamic by including
the effects of the time rate of change in gas
density in the gas flow continuity equation and
also of the inertia term in the gas-diffusion
equation. Closer attention was also given to more
accurate representations of the effects of porosity
and also of the boundary conditions at the
calcination front. A listing of the modified
program is given in Appendix D.
Application of the Model
Comparison With Experimental Work. Comparison of the computed
results of the extended model has been made with experimental results
cited in the Summary Report. In doing this, more realistic values of
pore radii have been used based on the porosimetry results cited earlier
in this report.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
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44
The encircled points on Figure 12 are the computed values of
percentage calcination as a function of residence time for the central
o
port (nominal) gas temperature of 1600 F, assuming values of 100 A for
the pore radius and 90 jj, for the particle diameter. These computed
points are seen to alternate in vertical position about some average
curve, which is not drawn, probably because the extent of calcination
is more sensitive to the value of the initial port temperature than to
the final port temperature. Lower lying points correspond to the same
initial port temperature, but to a lower final port temperature than
those for their neighboring points to the left.
The smooth curve on Figure 12 is drawn through the experimental
data for the nominal gas temperature of 1604 F. Except for the initial
point, there is considerable disagreement between the experimental and
computed results.
Variation of Pore Radius and Particle Diameter. Figure 13
shows the effects of altering the values .of either the pore radius or
particle diameter alone on the computed calcination percentage values.
Here again, the smooth curve represents the experimental data. Although
o
best agreement is obtained for the pore radius value of 400 A, all
computed variations of calcination percentage with residence time exhibit
a much more gradual decrease in slope with increased residence time than
is obtained experimentally.
Figure 14 indicates that a reasonably good agreement can be
obtained by adjusting both the pore radius and particle diameter. It is
difficult to justify the combination of 16 times the nominal pore radius
and the 50 percent increase over the nominal particle diameter. An
effective particle diameter that is somewhat smaller than actual can be
justified in terms of the increased ratio of surface area to volume
characteristic of departures of the particle shapes from the perfect
sphericity assumed for the computations.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
-------
100
90
§
c
•H
O
i-l
CO
00
CO
4J
c
0)
u
n
0)
O-i
80
70
60
50
40
30
20
10
Experimental I
* 1
O O
Calculated
Pore radius = 100
Particle diameter
90
0
0.5
1.0
1.5
2.0
Time, seconds
2.5
3.0
3.5
FIGURE 12. CALCINATION OF LIMESTONE AT 1600 F
-------
100I-
o
§
o>
00
e
0)
u
90
80
70
60
50
40
30
20
10
0
Particle Diameter
0.5
1.0
2.5
1.5 2.0
Time, seconds
FIGURE 13. EFFECT OF VARIATION OF PORE RADIUS AND PARTICLE SIZE ON CALCINATION AT 1600 F
3.0
3.5
-------
u
CJ
0)
60
rt
J-)
c
-------
48
The encircled points on Figure 15 are for the case of the
nominal value of 90 ^ for the particle diameter in combination with 8
times the nominal pore radius. Except for the two uppermost points at
somewhat over 80 percent calcination, it is evident that agreement with
the experimental curve would be good if the experimental curve were
shifted about 0.2 second to the left. A time delay in the onset of
calcination of this amount would account for the discrepancy, such as
could possibly correspond to the time required to inject the particles
into the gas stream and for the injection gas to disperse.
Variation of Heat Transfer Coefficient. Another possible cause
of the discrepancy is an actual value for the heat transfer coefficient
for the boundary layer between flue gas and particle surface that is
smaller than the theoretical one because of departures from the assumed
sphericity. The points enclosed by triangles on Figure 15" are computed
values for which the heat transfer coefficient has been reduced by 50
percent. Agreement with the experimental curve is good, except for the
two uppermost curves which predict about 10 percent more calcination
than is actually observed.
The true situation may well correspond to an effective particle
diameter near the nominal average particle diameter, an effective pore
size between 4 to 8 times the nominal pore size, and some combination of
a reduced value of the boundary-layer heat-transfer coefficient and
delay in the onset of calcination. The effective value of the pore radius
may well be several times that of the observed pore size because of the
presence of cracks in the particle. Even a few small cracks extending
partially in the radial direction could reduce greatly the effective
value of the diffusion constant. The circumferential stresses produced
in the particle by the radial pressure gradient, to be discussed later,
are such as to tend to open radial cracks.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
-------
100
90
80
70
g 60
T4
4-1
n)
7J 50
40
rt
O
rt
u
-------
50
Variation of Other Parameters. Several additional computations
were made to ascertain the effects of altering other parameters whose
assumed valued could be questioned. Changing the thermal conductivity
value for the limestone by as much as a factor of two had little effect
on the computed calcination values. Also, little effect was obtained
by varying the specific heats of the calcined or uncalcined portions of
the limestone particle. Likewise, altering the assumed initial particle
temperature had little effect. Thus, the transfer of heat into the
particle is largely controlled by the thermal conductance of the boundary
layer.
Calcination at Higher Temperature. Figure 16 shows the results
o
of computations for the 1770 F nominal temperature case, using 800 A for
the pore radius, for both the nominal and reduced values of the boundary
layer heat transfer coefficient. The latter yields good agreement with
experiment except for the prediction of about 10 percent more calcination
for the uppermost points, as was also obtained at the lower nominal
temperature.
Particle Temperature, Pressure, and Stress. Figure 17 shows a
typical set of computed points for the nominal gas temperature of 1600 F.
The gas temperature, Curve (a), is assumed to decrease linearly with
time from 1825 F at the injection port to 1425 F at the particle sampling
port. Curve (b) shows the particle temperature at the calcination front.
The temperature on the outer surface of the particle never differs from
this value by more than a fraction of a degree. Calcination begins at
0.064 second after injection, when the particle temperature is 1383 F,
the calcination temperature corresponding to the 76 torr partial pressure
of CO . The particle temperature quickly reaches a flat maximum value of
1643 F and then slowly declines, approaching the gas temperature asymptot-
ically. Near the removal port, at 2.12 sec after injection, Curves (a)
and (b) cross. At removal, the particle temperature is actually 2.6 F
above the gas temperature.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
-------
100
§
u
i-i
(0
O
00
rt
4J
-------
1900
1800
1700
1600
1500
1400
1300
1200
(d) Calcination (?„) -*
Gas
Temperature (F)
(a)
(c) Pressure (torr/10) —»
(b)
*—Particle
Temperature (F)
(e) Stress (psi) -*
Pore radius = 800 A
Particle diameter = 90u
90
80
70
60
50
40
30
20
10
0.5
1.0
1.5
2.0
2.5
Time, sec
FIGURE 17. CALCINATION VARIABLES
-------
53
Curve (c) of Figure 16 shows the variation in gas pressure at
the calcination front. This gas pressure rises to a maximum value of
885 torr when the particle temperature reaches its maximum. The ordinates
of Curves (b) and (c) are functionally related, since the calcination
temperature is a function of pressure. Curve (d), the percentage calci-
nation, increases rapidly with time at first and then slows down con-
siderably as the particle temperature approaches gas temperature. The
calcination process does not stop, but continues at a low rate, as the
gas temperature drops below particle temperature. A portion of the out-
ward flowing heat then also contributes to advancing the calcination front.
Calcination does not cease altogether until the particle temperature has
dropped below 1383 F, the calcination temperature at 76 torr.
Curve (e) of Figure 16 shows the circumferential stress in psi
at the calcination front as a function of time. This is a tensile stress
resulting from the high pressure gradient. Its value at any radial
position is given by
„ = . I rf £2>|
CT 2r{br)
where r is the radius and (dp/dr) is the pressure gradient. The maximum
tensile stress of almost 68 psi is reached soon after calcination begins.
Later, it declines rapidly even though the pressure is increasing, be-
cause of the decreasing value of the pressure gradient resulting from
the increasing distance between the calcination fraction and the outer
surface of the particle. This more than compensates for the increasing
pressure. Since the tensile strength of limestone is several hundred
psi, the maximum circumferential stress is nowhere near great enough to
rupture the limestone particle in this case. However, it would, affect
significantly the degree of opening of radial cracks, and hence the
effective value of the diffusion constant. Closing of these radial cracks
as this stress decreases may account for the lower calcination percentages
obtained experimentally for the higher residence times than are predicted
theoretically in Figures 14 and 15 for assumed effective pore radii of
o
800 A. In other words, the theory should be modified to incorporate a
decreasing value of effective pore radius, corresponding to a decreasing
diffusion coefficient as the circumferential tensile stress decreases.
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
-------
REFERENCES
(1) R. Coutant, R. E. Barrett, and E. H. Lougher, Summary Report on
"Investigation of the Reactivity of Limestone and Dolomite for
Capturing SO From Flue Gas", to NAPCA, August 30, 1968,
Contract No. PH 86-67-115.
(2) R. Coutant, R. E. Barrett, and E. H. Lougher, Summary Report on
"Investigation of the Reactivity of Limestone and Dolomite for
Capturing SO From Flue Gas", to NAPCA, June 27, 1969,
Contract No. PH 86-67-115.
(3) R. Coutant, R. E.' Barrett, and E. H. Lougher, Summary Report on
"Investigation of the Reactivity of Limestone and Dolomite for
Capturing SO From Flue Gas", to NAPCA, November 20, 1970,
Contract No. PH 86-67-115.
(4) T. D. Womble, et al., "Presentation of Full-Scale Dry Limestone
Injection Project at Shawnee Steam Plant", paper presented at the
Dry Limestone Injection Process Symposium, Gilbertsville, Ky.,
June 22-26, 1970.
(5) R. H. Borgwardt, et al., "Alkaline Additives for Sulfur Dioxide
Control", Annual Report from Division of Control Systems to APCO,
EPA, March 29, 1971.
(6) R, D. Harvey, "Petrographic and Mineralogical Characteristics of
Carbonate Rocks Related to Sorption of Sulfur Oxides in Flue Gases",
Interim Report to NAPCA, June 22, 1970.
(7) Y. Ishihara, "Kinetics of the Reaction of Calcined Limestone with
Sulfur Dioxide in Combustion Gases", paper presented at the Dry
Limestone Injection Process Symposium, Gilbertsville, Ky.
June 22-26, 1970.
(8) R. C. Attig and P. Sedor, "Additive Injection for Sulfur Dioxide
Control, A Pilot Plant Study", Research Center Report 5460 from
The Babcock & Wilcox Company to NAPCA, March 27, 1970.
(9) W. T. Reid, et al., "Fundamental Study of Sulfur Fixation by Lime
and Magnesia", Final Report to Robert A. Taft Engineering Center,
PHS, June 30, 1966.
(10) G. C. Kuczynski, Trans. AIME, 185. 169 (1949).
RWC:RS:ao
BATTELLE MEMORIAL INSTITUTE - COLUMBUS LABORATORIES
-------
APPENDIX A
STONE ANALYSES
-------
A-l
TABLE 1. CHEMICAL ANALYSES DATA
Stone No.
IGS 1
IGS 2
IGS 3
IGS 4
IGS 5
IGS 6
IGS 7
IGS 8
BCR 1336
Michigan
Marl
2 061 (new)
2061(old)
Percentage
MgC03
0.16
0.70
7.89
0.45
44.2
41.3
97.8
98.3
2.66
2.58
3.72
2.57
4.00
1.87
0.75
Percentage
CaCO
99.9
99.3
92.4
99.0
55.7
49.9
3.08
3.00
94.8
94.6
97.4
98.8
80.7
99.0
93.9
Weight Loss
Percentage
Calculated
44.04
43.94
44.49
43.78
46.56
42.52
50.02
42.95
44.65
37.46
44.49
41.6
Weight Loss
Percentage
Measured
44.17
43.80
44.76
44.23
48.88
42.48
48.10
41.03
42.95
37.95
43.68
41.5
P g/cc
2.57+0.03
2.6410.01
2.71+0.01
2.73+0.01
2.86
• 2.77*0.1
2.82+0.01
2.48+0.02
2.70
2.05+0.1
2.67+0.04
2.58
-------
APPENDIX B
REACTOR DATA
o Effect of Time-Temperature Profile
o Effect of Particle Size
o Effect of SCL Concentration
o Effect of Time and Temperature on Pore Structure
o Reactivities of Ten Stones
-------
TABLE B-l.
EFFECT OF TIME-TEMPERATURE PROFILE
F.un
No.
101.5-B
10 15 -C
10J.5-E
101.5-G
10 15 -K
1015-L
1015-N
10i.5-P
10 1.5 -S
1022-A
1022-C
1022-E
1022-G
1022-J
1022-L
1022-N
1022-P
1022-R
Gas
Temperature
Injec-
tion
2402
2402
2179
2345
2179
2070
2014
1901
1843
2565
2565
2216
2565
2216
2138
1996
1865
1805
(a) Weight percent as
(b) Thermogravimetric
F
Collect-
tion
2179
2114
2114
1730
1730
1730
1730
1730
1730
2216
1996
1996
1693
1693
1693
1693
1693
1693
CaSO, •
weight
(c) Based on actual amount of
Residence
Time,
sec
0.45
0.82
0.37
1.38
1.04
0.80
0.67
0.41
0.28
0.27
0.49
0.30
0.91
0.64
0.57
0.42
0.26
0.17
2H20.
losses o
CaO formed «
Product Analysis;
Weight
mg
10.08
10.00
10.09
10.07
10.10
10.62
10.03
10.12
10.02
9.97
9.90
10.03
10.78
10.06
11.60
10.19
10.23
10.01
Total^ SOA=V£
Sulfur
7.0
11.3
16.1
18.0
22.4
21.6
20.9
19.7
18.0
12.0
11.7
19.3
15.0
21.4
19.5
19.4
15.5
9.6
5.4
9.1
13.2
16.9
19.6
19.8
17.2
15.5
12.8
10.8
10.1
17.1
13.8
19.9
18.4
17.5
11.4
7.3.
l' CO.,^
mg"
0.20
0.15
0.19
0.15
0.20
0.36
0.20
0.55
1.00
0.14
0.15
0.41
0.55
0.35
0.38
0.54
1.06
2.34
mg
1.75
1.75
1.69
1.73
1.60
1.56
1.61
1.46
1.28
1.63
1.71
1.45
1.65
1.50
1.80
1.48
1.28
0.71
Pei
1 Ut:
Actual(C°
4.1
6.3
9.1
9.9
12.9
13.3
12.0
12.5
12.9
7.1
6.6
12.3
9.3
13.1
11.6
12.3
11.5
12.4
rcentage
Llization
(d)
Apparent
3.9
6.1
8.8
9.6
12.3
12.3
11.5
11.0
10.1
6.9
6.4
11.1
8.3
12.1
10.8
10.9
8.8
5.7
mg SO,
Per
— Gram
Calcine
54.9
86.8
124
136
175
175
163
156
142
95.8
88.8
154
115
167
150
150
122
78.7
Percentage
Calcination
96.2
97.1
96.4
97.1
96.1
93.2
96.1
89.1
79.8
97.3
97.1
91.6
89.9
93.0
93.5
89.3
78.8
49.4
Gas Analysis ,
volume percent
so2 co2 o2
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
0.306 10.0 3.0
t
0.294 10.0 3iO *"*
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
0.294 10.0 3.0
(d) Based on total CaO content of sample*
(e) Dry basis.
-------
TABLE B-2 EFFECT OF PARTICLE SIZE
(-270+325 mesh No.2061)
Gas
Run Temperature F
No. Inject
421-A 1967
421-B 1967
421-C 2030
421-D 2030
421-E 2095
421-F 2095
421-G 2157
421-H 2157
421-J 2220
421-K 2220
Collect
.1906
1843
1843
1776
1776
1712
1712
1646
1645
1582
(a) Weight percent as CaSO^-
(b) Thermogravimetric weight
(c) Based on actual amount of
(d) Based on total
Residence
Time,
sec
0.15
0.31 '
0.45
0.61
0..75
0.92
1.06
1.23
1.36
1.54
losses .
CaO formed .
Product Analysis
Weight,
mg
9.98
9.93
10.08
10.20
10.14
10.09
10.04
9.80
10.25
10.04
Total*"' CO^0
Sulfur mg
6.5
10.6
15.2
14.3
16.4
18.2
17.2
20.1
18.2
17.8
2.23
0.70
0.30
0.26
0.20
0.33
0.20
0.20
0.16
0.25
rag
0.76
1.66
1.71
1.70
1.75
1.66
l.EO
l.£5
1.S3
1.75
Percentage
Utilization
Actual'0'
8.20
6.22
8.57
8.24
9.05
10.38
9.12
11.11
9.64
9.66
1 Q 1
Apparent
3.90
5.36
8.04
7.79
8.68
9.67
8.76
10.64
9.34
9.17
mg blj.
Per
Gram
Calcine
54.1
74.2
111
108
120
134
121
147
129
127
Percentage
Calcination
47.6
86.1
93.8
94.6
95.9
93.2
96.0
95.8
96.9
95.0
Gas Analysis,
volume percent
so2 co2 o2
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
0.303 10.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
i
CaO content of sample .
(e) Dry basis.
-------
TABLE B-3
EFFECT OF SO, CONCENTRATION
Gas
Temoeraturp F
Run
No.
111-A
Hl-C
Lll-E
111-G
111-J
Ul-L
Lll-P
111-T
111-V
111-X
111-AA
111-CC
111-DD
123-A
123-C
123-E
123-G
123-J
123-L
Injec-
tion
2341
2341
2341
2341
2341
2341
2263
2263
2263
2191
2191
2191
2191
2321
2321
2321
2321
2321
2321
Collec-
tion
1908
1844
1780
1715
1654
1593
1780
1654
1593
1780
1715
1654
1593
1928
1866
1804
1744
1684
1626
Residence
Time
sec
. 0.74
0.88
1.02
1.16
1.31
1.47
0.90 '
1.20
1.35
0.79
0.93
1.03
1.23
0.71
0.84
0.97
1.10
1.24
1.39
Weight,
mg
10.04
9.99
. 10.04
'10.00
10.01
10.07
10.01
10.04
10.04
10.03
10.03
10.08
10.09
9.99
10.08
9.93
10.00
10.07
9.96
Product
Total
Sulfur
3.0
6.3
3.0
2.6
2.8
4.4
2.6
3.3
3.8
3.6
5.0
4.7
5.1
4.9
5.5
6.8
5.1 :
6.6
6.4
Analysis
S04= 3
3.0
6.3
2.3
1.9
2.4
4.4
2.4
3.1
3.7
3.2
4.3
4.3
4.5
4.5
5.4
4.7
3.8
4.8
5.9'
mg
0.23
0.39
0.20
0.4.5
0.40
0.2.5
0.50
0.60
0.36
0.61
0.35
' 0.70
0.53
0.33
0.51
0.40
0.60
0.54
0.65
mg
1.90
1.70
1.83
1.80
1.73
1.83
1.79
1.75
1.85
1.68
1.85
1.61
1.71
1.85
1.73
1.84
1.79
1.76
1.66
Percentage
Utilization
Actual^
1.63
3.73
1.69
1.49
1.67
2.47
1.50
1.94
2.11
2.20
2.76
2.99
3.05
2.69
3.24
3.70
2.90
3.80
3.86
Apparent
1.54
3.42
1.62
1.35
1.53
2.34
1.35
1.71
1.96
1.92
2.57
2.55 -
2.72
2.52
2.91
3.41
2.56
3.39
3.35
mg SO,
Per
r- Gram
' Calcine
21.4
47.4
22.5
18.7
21.1
32.5
18.7
23.7
27.2
26.6
35.6
35.3
37.7
34.9
40.3
47.2
35.4
47.0
46.4
Percentag
Calcinatic
94.8
92.5
96.2
91.6
92.4
95.3
90.6
88.7
93.2
88.4
93.5
86.6
90.0
93.8
90.4
92.5
88.8
89.9
87.5
Gas Analysis
volume percent
;e
>n SO
0.013
0.013
0.013.
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.025
0.025
0.025
0.025
0.025
0.025
co2
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
92
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0 (_,
3.0 i
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
-------
TABLE B-3 EF:?ECT OF S02 CONCENTRATION
(continued)
Gas
T^mn^T^ ftirp . r
Run
No.
i:!3-N
l:!3-P
i:'.3-R
li!3-T
i:;3-v
i::3-x
i:>.3-AA
i;'.3-cc
l:'.3-EE
121-A
i::i-c
121-E
m-c
121-j
I;:I-L
I;:I-N
I;:I-P
121-R
121 -T
Injec-
tion
2253
2253
2253
2253
2253
2186
2186
2186
2186
2350
•2350
2350
2350
2350
2350 '
2284
2284
2284
2284
Collec-
tion
.1866
1904
1744
1684
1626
1804
1744
1684
1626
1971
1912
1854
1796
1739
1684
1912
1854
1796
1739
Residence
Time
sec
0.73
0.86
0.99
1.13
1.28
0.75
0.88
1.02
1.17
0.76
0.90
1.04
1.19
1.34
1.49
0.78
0.92
1.07
1.22
Weight
rag
10.01
9.94
10.09
10.04
9.93
10.04
10.04
10.00
10.00
9.96
10.01
9.93
10.04
10.01
10.00
9.97
10.06
9.98
10.04
Product
Total^
Sulfur
6.6
6.2
6.3
7.0
7.7
5.1
6.5
6.6
9.4
5.1
4.6
5.0
5.1
5.5
5.5
4.8
5.2
5.5
6.3
Analysis
S04-1"
5.0
5.8
5.5
6.1
6.9
5.0
6.0
5.8
7.9
4.0
4.0
4.3
4.1
4.3
4.9
5.2.
5.0
5.4
5.9
co2(b>
mg
0.31
0.30
0.75
0.63
0.40
0.70
0.48
0.43
0.55
0.51
0.60
0.39
0.55
0.70
0.58
0.65
0.35
0.56
0.56
H20(b>
mg
1.83
1.85
1.63
1.68
1.74
1.66
1.80
1.74
1.70
1.79
1.66
1.85
1.75
1.64
1.70
1.70
1.85
1.70
1.68
Percentage
Utilization
Actual(c)
3.64
3.37
3.92
4.19
4.40
3.13
3.66
3.82
5.47
2.88
2.82
2.73
2.97
3.39
3.27
2.86
2.87
3.27
3.79
Apparent
3.41
3.17
3.32
3.66
4.03
2.68
3.31
3.48
4.86
2.59 '
2.47
2.52
2.64
2.90
2.89
2.48
2.67
2.89
3.35
mg SO,
Per
Gram
Calcine
47.3
43.9
46.0
50.7
55.9
37.1
45.8
48.2
67.4
35.9
34.2
34.9
36.6
40.2
40.0
34.4
37.0
40.1
46.4
Percentage
Calcination
94.2
94.4
85.7
88.0
92.4
86.7
91.0
91.8
89.5
90.4
88.5
92.7
89.7
86.6
89.0
87.6
93.5
89.3
89.3
Gas Analysis ^
volume percent
so2
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.025
0.065
0.065
0.065
0.065
0.065
0.065
0.065
0.065
0.065
0.065
co2
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
10.2
°2
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3'° • T
•C-
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
. 2.8
-------
TABLE B-3 EFFECT OF S02 CONCENTRATION
(continued) .
Gas
Temperature F Residence
Run
No.
121-V
121-X
121-AA
121-CC
121-EE
1
Injec-
tion
2284
2220
2220
2220
2220
Collec- Time
tion sec
1684 1.37
1854 0.80
1796 0.95
1739 1.09
1684 1.25
Product Analysis Percentagw
Weight Total SO = co H 0 Utilization
mg Sulfur mg rog Actual
10.01 6.0 5.7 0.61 1.73 3.51
10.06 6.3 5.8 0.70 1.69 3.78
10.01 7.0 5.6 0.65 1.61 4.36
9.95 7.5 6.7 0.40 1.76 4.25
10.01 7.1 6.0 0.43 1.76 4.05
Apparent
3.08
3.25
3.76
3.90
3.70
Per Gas Analysis
Gram Percentage volume _percent
Calcine Calcination SO- CO- 0
42.6 88.5 0.065
45.0 86.8 0.065
52.1 87.5 0.065
54.1 92.4 0.065
51.3 91.9 0.065
10.2 2.8
10.2 2.8
10.2 2.8
10.2 2.8
10.2 2.8
a
i
-------
TABLE B-3 EFFECT OF S02 CONCENTRATION
(continued)
L>as
Temperature F
Run
No
1210-A .
1210-C
1210-E
1210-G
1210-J
1210-L
1210-N
1210-P
1210-R
1210-T
1210-V .
1210-X
1210-AA
1210-CC
1210-EE
1202-A
1202-C
1202-E
1202 -G
Injec-
tion
2329
2329
2329
2329
2329
2329
2271
2271
2271
2271
. 2271
2213
2213
2213
2213
2368
2368
2368
2368
Collec-
tion
1990
1936
1884
1832
1781
1731
1936
1884
1832
1781
1731
1884
1832
1781
1731
1979
1921
1864
1809
Residence
Time
sec
0.72
0.85
0.98
1.12
1.26
1.40
0.74
0.87
1.01'
1.14
1.29
0.75
0.89
1.03
1.17
0.69
0.71
0.84
0.97
Product Analysis
Weight,
mg
10.80
. 10.21
10.08
9.94
10.03
10.06
9.96
10.40
10.20
10.28
10.20
10.00
10.44
9.97
10.09
10.02
10.35
10.03
9.94
Total
Sulfur
21.3
16.6
15.7
17.9
18.2
19.0
18.4
19.5
19.6
18.2
19.3
18.4
18.7
21.6
19.4
10.5
10.7
11.4
11.6
4
17.7
14.8
14.1
15.3
17.0
17.1
14.9
17.8
17.0
16.9
18.3
18.0
18.2
20.1
17.6
8.7
9.1
9.5
10.3
mg
0.19
0.24
0.31
0.34
0.26
0.4S
0.33
0.36
0.25
0.15
0.24
0.25
0.28
0.46
0.30
0.45
0.26
0.29
0.25
mg
1.81
1.68
1.66
1.75
1.70
1.55
1.68
1.65
1.74
1.81
1.70
1.69
1.73
1.50
1.65
1.70
1.84
1.78
1.73
Percentage
Utilization
Actual(c)
11.7
9.6
9.1
9.6
10.1
11.4
10.3
11.4
10.7
9.8
10.8
10.2
10.6
13.1
11.0
6.08
5.93
6.30
6.52
Apparent '
11.3
9.1
8.5
9.0
9.6
10.3
9.6
10.6
10.2
9.5
10.3
9.7
10.0
11.8 '
10.4
5.52.
5.62
5.93
6.18
me su,
Per 3
Gram Percentage
Calcine Calcination
157
126
118
124
133
142
132
146
141
131
142
134
138
163
144
76.5
77.9
88.2
85.6
96.4
95.0
93.5
93.3
94.7
89.7
93.3
92.7
95.0
97.0
95.1
94.9
94.4
90.2
93.8
90.8
94.8
94.1
94.8
Gas Analysis (e)
volune percent
so2
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.398
0.160
0.160
0.160
0.160
co2 c
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0 ?
o-.
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
-------
TABLE B-3 EFFECT OF SO CONCENTRATION
(c:onl:inucd)
Gas
TpTnnpraf-iirp F
Run
Ho.
1202-J
1202-L
1202-N
1202-P
1201-R
1202-T
1202-V
1202-X
1202-AA
1202 -CC
1202-EE
120E-A
1208 -C
1208-E
1208-G
1208-J
1208-L
1208-N
1208-P
Injec-
tion
2368
2368
2299
2299
2299
2299
2299
2231
2231
. 2231
2231
2320
2320
2320
2320
2320
2320
2245
2245
Collec-
tion
1756
1705
. 1921
1864
1809
1756
1705
1864
1809
1756
1705
1909
1850
1793
1738
1686
1637
1850
1793
Residence
Time,
sec
1.11
1.25
0.71
0.83
0.97
1.10
1.24
0.72 '
0.86
0.99
1.13
0.74
0.88
1.02
1.16
1.31
1.46
0.76
0.90
Product Analysis
. Weight,
mg
..10.05
10.02
10.00
9.99
10.00
9.98
9.95
9.98
9.94
10.00
10.00
10.02
10.04
9.98
10.03
9.99
10.00
9.97
10.03
Total
Sulfur
11.7
14.4
11.4
12.2
11.7
12.6
13.6
11.6
11.5
12.1
13.1
20.2
22.4
24.0
24.8
25.6
26.4
25.2
24.9
so4=a
10.6
13.2
9.6
9.2
9.8
10.4
10.8
9.2
10.8
11.0
12.0
18.6
21.1
22.6
23.2
.24.3
25.4
23.2
24.2
mg
0.13
0.55
0.19
0.20
0.29
0.30
0.24
0.24
0.25
0.21
0.21
0.18
0.16
0.15
0.28
0.20
0.25
0.25
0.21
mg
1.83
1.55
1.81
1.78
1.78
1.75
1.75
1.75
1.75
1.80
1.75
1.65
1.63
1.55
1.50
1.56
1.48
1.53
1.59
Percentage
Utilization
Actual*'0''
6.30
8.88
6.18
6.69
6.44
6.99
7.49
6.47
6.40
6.57
7.26
11.38
12.62
13.92
14.79
14.64
15.73
14.66
14.12
Apparent '
6.07
7.84
5.94
6.41
6.06
6.57
7.12
6.15
6.07
6.29
6.95
10.94 '
12.19
13.46
13.88
14.02
14.87
13.87
13.49
mg SO
Per
Gran
Calcine
84.1
108.6
32.4
88.8
83.9
91.0
98.6
85.2
84.1
87.2
96.3
152
169
187
192
194
206
192
187
Percentage
Calcinat ion
96.4
88.3
96.1
95.9
94.1
93.9
95.1
95.0
94.8
95.7
95.7
96.2
96.6
96.7
93.9
95.7
94.5
94.6
95.9
Gas Analysis^
volume percent
so2
0.160
0.160
0.160
0.160
0.160
0.160
0.160
0.160
0.160
0.160
0.160
0.990
0.990
0.990
0.990
0.990
0.990
0.990
0.990
co2
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
°2
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0 ¥
3.0
3.0
3.0
3.0
3.0
3.0
3.0
. 3.0
3.0
-------
TABLE B-3 EFFECT OF SO- CONCENTRATION
(continued)
Gas
Termerature F
Run
No.
1208-R
1208-T
1208-V
1208-X
1208-AA
1208-CC
1208-EE
(£) Weight
Injec-
tion
2245
2245
2245
2173
2173
2173
2173
percent
Collec-
tion
1738
. 1686
1637
1793
1738
1686
1637
as CaSO •
Residence
Time
sec
1.05
1.19
1.34
0.78
0.93
. 1.07
1.23
2H20.
Product Analysis
Weight , Total
mg Sulfur
10.03
10.28
10 . 16
10.37
10.45
10.36
10.22
27.1
27.5
27.8
23.3
26.1
26.4
29.5
\3)
4
23.9
25.6
25.6
22.1
24.9
25.2
27.2
mg
0.54
0.25
0.^-4
0.50
0.34
O.t-S
o.?.3
mg
1.45
1.50
1.46
1.50
1.58
1.44
1.51
Percentage
Utilization
Actual(c) Apparent^
16.40
16.47
16.84
14.43
15.30
16.58
17.29-
15
15
15
12
14
14
16
.18
.59
.27
.92
.24
.86
.09
mg sO,
Per 3
Gram
Calcine
210
216
212
179
197
206
223
Percentage
Calcination
92.6
94.6
90.7
89.6
93.1
89.6
93.1
Gas . Analysis >
volunje percent
so2
0.990
0.990
0.990
0.990
0.990
0.990
0.990
co2
10.0
10.0
10.0
10.0
10.0
10.0
10.0
°2
3.0
3.0
3.0
3.0
3.0
3.0
3.0 .
W
(b) Thennogravimetric weight losses .
(c) Based on actual amount of CaO formed•
(d) Based on total CaO content of sample •
(e.) Dry basis.
oo
-------
TABLE B-4 REACTOR DATA - EFFECT OF TIKE AND TEMPERATURE ON PORE STRUCTURE
Run
No.
925-A
925-B
925-C
925 -D
106-A
106-B
106-C
106-D
106-E
106-F
Gas Temperature F
Injection
2224
2224
1830
1830
2245
2156
1996
1920
1849
2243
Collection
1440
1765
1440
1765
2156
2073
1920
1500
1782
1500
Residence
Time,
sec
• 2.86
1.27
1.82
0.23
0.15
0.16
0.17
1.35
0.18
1.99
Product Analysis '
Weight ,
~g
10.53
8.05
10.19
9.36
10.55
11.60
10.67
10.00
10.49
10.35
co2,
Dig
0.88
0.81
1.54
3.55
3.08
3.15
3.58
1.18
2.85
0.83
mg
1.73
1.25
1.35
0.19
0.73
0.90
0.54
1.45
0.75
1.83
Percentage
Calcination
85.8
82.6
73.0
19.0
40.0
45.1
28.3
79.0
45.5
85.8
Gas Analysis ,
volurae percent
so2 co2 o2
0
0
0
0
0
0
0
0
0
0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0 ^
3.0
(a) Termogravlmetric analysis data.
(b) Dry basis .
-------
TABLE IJ-5
XEACTIVITIES OF TEN STONES
Gas Residence Product Am lysis
Run
No.
56-A
56-B
56-C
5'J-D
56-E
56-F
56-G
56-H
56-J
56-K
56-L
56-M
Stone
Type
Marl
1336
ICS1
IGS2
IGS3
ICS4
IGS5
IGS6
IGS7
ICS8
IGS4
IGS3
Temperature* F
Inject
2136
2136
2136
' 2136
2136
2136
2136
2136
2136
2136
2136
2136
Collect
1475
1475
1475
1475
1475
1475
1475
1475 •
1475
1475
1475
1475
Time,
Sec
2.27
2.27
2.27
2.27
2.27
2.27
2.27
2.27
2.27
2.27
2.27
2.27
rog
10.16
10.04
10.21
9.99
10.47
10.60
10.81
9.16
9.92
10.35
10.27
10.32
Sulfur
31.2
15.8
15.0
15.8
23.5
31.6
38.4
37.6
15.7
23.0
31.7
24.8
\>')f. w
mg
0.33
0.26
0.21
0.26
0.10
0.28
0.20
0.14
0.0
0.40
0.25
0.18
1^"
0.85
1.58
1.75
1.50
1.63
1.34
0.8!)
0.6(1
0.58
1.50
1.40
1.65
Percentage
UtU I* Hi' Ii'n
Actual*'0
28.07
9.51
8.39
. 9.93
13.66
20.74
32.80
37.53
--
13.77
19.57
13.97
'"* PC?
Apparent Calcine
25.19
8.96
8. 03
9.32
13. 37
19.42
30.89
35.42
./°
12.63
18.49
13.45
260
126
115
132
17H
274
259
246
85
168
260
179
I'crccnt-
C;ilci-
nation
89.8
94.3
95.7
94.0
97.9
93.7
94.2
94.4
-100.
91.7
94.5
96.3
Cns Analysis/6*
volume percent
so2 co2 o2
0.299
0.299
0.299
0.299
0.299
0.299
0.299
0.299
0.299
0.299
0.299
0.299
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0 •
3.0
3.0
3.0 oi
3.0 ±
o
3.0
(n) Weight percent us C;iSO,. 211 0 .
(b) Thcrmogravlmctric weight losses*
(c) Based on natural amount of CaO formed .
(d) Based on total CaO content of sample.
(o) Dry basis .
(f) Utilization of CaO Z 100 percent, utilization of MgO ~ 1.4 percent.
-------
APPENDIX C
PORE SIZE DISTRIBUTIONS
-------
Sample No. - 925-A
2
Surface Area - 13.7 m /g sample
1.0
0.8
es
o
1
i—i
c
CJ
o
o
>
-O-—• 9
o
t
0.4
0.2
JLJ I L
I I I
10-
102
10J
10
0
Pore Dianeter, microns
FIGURE C-l. PORE SIZE DISTRIBUTION
10
-1
10
-2
-------
Sample No. - 925-B
Surface Area - 13.1 ra /g sample
1.0
0.8
-c
-O 0 O C
-9 9-
ra
w
eo
o
u
a
e
3
o
04 0.4
01
•r4
u
re
t-4
o
i
to
0.2
\ I i
I
I I I
J I
10-
10U
Pore Diameter, microns
FIGURE C-2 PORE SIZE DISTRIBUTION
10'
10'
-------
Sample No. - 925-C
Surface Area - 31.8 m /g
1.0
0.8
to
y
o
,: 0.6
-o—o e—<
o
O
fc 0.4
o
o
>
•r-l
I.
0.2
1 I
I 1 1
10-
102
101 10°
Pore Dianeter, microns
10
-1
10
-2
FIGURE C-3. PORE SIZE DISTRIBUTION
-------
Sample No. - 925-D
2
Surface Area - 5.0 m /g
1.0
0.8
M
00
U
u
0.6
, a
o
o
•r-l
AJ
ra
0.4
-------
Sample No. - 106-A
2
Surface Area - 13.1 m /g
1.0
0.8
V-i
00
o
0
oT 0.6
E
O
o
l-l
o
0.4
^ e—«—« —
o
J_J. L
1
Ill
101 . 10°
Pore Diameter, microns
FIGURE C-5. PORE SIZE DISTRIBUTION
10
"1
10
'2
-------
Sample No. - 106-B
2
Surface Area - 18.9 m /g
1.0
0.8
e
o
p
oo
0.6
£
3
i— i
O
t)
' l-i
O
o
3
E.
0.4
-o-
-«—e—«
o
0.2
10
» « » L
102
10J
10
0
Pore Dianeter, microns
FIGUEIE C-6.PORE SIZE DISTRIBUTION
10
-1
10
-2
-------
Sample No. 106-C
2
Surface Area - 11.4 m /g
1.0
0.8
oo
y
o
0.6
E
3
f— I
o
0.4
o
i
D
0.2
0
LI I JL
I I I
III I
10-
101 10°
Pore Diameter, microns
FIGURE C-7. PORE SIZE DISTRIBUTION
10
-1
10
-2
-------
Sample No. - 106-D
2
Surface Area - 20.8 m /g
O
»
00
Cumulative Pore Volume, cc/gram
O O O
• • •
N3 -P* CT>
o
I
oo
10-
III
III
II
102
ioi
Pore Diameter, microns
10
10
"1
10
'2
FIGURE c-8. PORE SIZE DISTRIBUTION
-------
Sample No. - 106-E
Surface Area - 12.4 m /g
1.0
0.8
60
O
0.6
e
,-1
o
0.4
i-H
3
S
0.2
0
I I
10-
I I (
102
I I
_o~ o O © 9 O O 9 •-
I I I
101 10°
Pore Dianeter, microns
10
-1
o
i
I I
10
-2
FIGURE 3-9 . PORE SIZE DISTRIBUTION
-------
Sample No, - 106-F
2
Surface Area - 308 m /g
1.0
0.8
60
U
E
=J
,— i
O
0.4
o
i
i
0.2
I L
I I I
I
I I I
1
I I I
I I
10-
102
10U
Pore Dianeter, microns
FIGURE C-10. PORE SIZE DISTRIBUTION
10
-1
10
-2
-------
APPENDIX D
COMPUTER PROGRAM - CALNOW
Calcination of Limestone Under Simulated Boiler Conditions
-------
D-l
00100
00110
00120
00130
00140
001SO
00160
00170
00180
00190
00200
00210
00220
00230
00240
00250
00260
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
00540
00550
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
REAL L*M*MC*NUMT*NUMF
DIMENSION PZ<21)*PAC21)*PB<21>*FZ<21>*FA<21>*FB(21>*RC2I>
DIMENSION IC0UNTC21)
DOUBLE PRECISION TZC21 >.* TA<21 >* TBC2I >* TB1* TBI* TBJ1*TC* FUNCTC
COMMON L*M,MC*THK*RH02*S2*RH0I*S1* GASC*P0R* ETA* A*RCDA
FUNCDCPF. TF)=A*CA*PF/8/'ETA*3.22E05«-2/3.*SQRTC1.5708*3.22E05
& *GASC*/M>)
FUNCTC(PF)°C40.4E03/1.987/C24. 195-AL0G(PF»-273. >*l*8+32.
FUNCTG(PF) = 40«4E03/1.987*1.8/C24.195-AL0GCPF)>**2/PF
FUNCSG(TF> = . 156*. 194E-03*TF-.056E-06*TF**2
FUNCTD = -GR*RF*FUNCSGCTE>>
& /S1/RH01
FUNCG2CGR*TD*RF*TE*R1)=-2*GR/R1«>>/THK
FUNCHCTl*T2>«sHKG*(.015+. 7E-05*CT1 + T2»*EPS*S1 G*CT1 + T2+920. >
4 *«T1 + 460.)**2-KT2+460.>**2>
FUNCPGCRE* RF* TE* PE,RFD»RFG) = - GASC/M/P0R*CTE+460)*RF/FLNCD(PE» TE>
& -)/P0R/3.22E05
FUNCINTCZl*Z2*Yl*Y2*Y3*Xl«X2)aZl*«Y3*Xl/X2-Yl*X2/Xl)/(Xl*X2>
& -Y2*(X1-X2>/X1/X2> + Z2*((Y3/X2«-Y1/X1>/CX1«-X2>-Y2/X1/X2>
DATA MULT* TERR* RERR, TGERR* FERR
4 /100* l.E-04* l.E-06* l.E-04* l.E-05/
DATA RNE«S2»RH02»SURHei»TO«EPS«SI G
4 /.06*.2*169.».2»95.» 70.* .3* . 1 73E-08/
DATA GASC*ETA,PGAS*THK*R0»A*L*M*MC
6 /5 55. *.l* 76.*. 4* 1. 48E-04*3.28E-08* 710.»44.» 100./
A=26.24E-08
PRINT* ' TNOM*C *
ACCEPT* TN3M*C
HKG=o 5/R0*(2o*.37*RNE**.6)
C=C/3600
P0R=RH01/RH02
Xl=5»5
X2=5.5
TC*FUNCTC(PGAS)
D3 1000 IX-1*12
XIaXl-M0D
X2=X1+IX
TEMP1 = TN0M+ 50* f 6-X1>
TEMP2sTN0M*50*(6-X2)
PRINT 3* XUTEMP1*X2»TEMP2
3 F0RMATC///* Xls»*F4.
1* '*
»*F9.3* * T0
TGAS=f*
fi F9.3/)
IF CXI-5.5) 5* 7* 7
5 IF (X1 + X2-11.5) 7*1000*6
6 DELT=AMIN 1C1*2*DTINT*DETC/ABSCTCDB))
G0 T0 130
7 TIME»0.
XA=X1
TA0=T0
TGASaTN0M* 50* < 6-XA)
H=FUNCH/TDA0/10
10 TB0=TA0*TDA0*DELT
TIME=TIME+DELT
XB=XA*DELT/C
..TGASaTN0M*50*< 6-XB)
-------
D-2
00670 IF CXB-X2) 40*20*20
00680 20 T3600=TIME*3600
00690 PRINT 30* TC*T3600*TB0
00700 30 F0RMATC • CALC TEMP(F)= '* F9« 3* * N0T REACHED AT X2. V
00710 & ° TIME* C*F8.4* « PARTICLE TEMP( F>= ** F9.3/)
00720 60 T0 1000
00730 40 K=FUNCH(TBS*TGAS)
00740 TDB0=H*CTGAS-TB0)*3/R0/S2/RH02
00750 TBT=TA0+ 60*60*50
00770 50 TB03TBT
00780 G0 T0 40
00790 60 IF CTBT-TO 70*80*80
00800 70 TA0aTBT
00810 XA=XB
00820 TDA0=TDB0
00830 G0 T0 10
00840 80 DT=DELT*
00850 TIME^TIME-DT '
00860 XA=XB-DT/C
00870 TGAS3TN0M*50*(6-XA)
00880 RC1)=R0
00890 KC=1
00900 TC0R=1.
00910 FC0R=1.
00920 J=0
00930 N=0
00940 N0°0
00950 HA«FUNCHCTC*TGAS)
00960 SHGAS=FUNCSG(.5*(TC*TGAS))
00970 TGJaHA/THK*(TGAS-TC)/< l.+M/MC*FUNCSG(TC)/L*(TGAS-TO)
00980 FDA=0.
00990 PDA«0.
01000 100 CALL FR0NT(PGAS«PGJ*PDA*PCDA*TC*TGJ*TG2J*TDA»TCDA»FC«FGJ*
01010 & FDA*FCDA«RS*RCDA)
01020 H=HA-FC^SHGAS
01030 TGSTsH/THK*CTGAS-TC)
01040 CALL C0MP
-------
D-3
01240
01250
01260
01270
01280
01290
01300
01310
01320
01330
01340
01350
01360
01370
01380
01390
01400
01410
01420
01430
01440
01450
01460
01470
01480
01490
01500
01510
01520
01530
01540
01550
01560
01570
01580
01590
01600
01610
01620
01630
01640
01650
01660
01670
01680
01690
01 700
01710
01720
01730
01740
01750
01760
01770
01780
01790
01800
PB(I)=PGAS
FZU)nFC
FAU> = FC
127 FBCI)=FC
DELTa-RQ/RCDA/MULT
DTB=DELT
DETODELT*TCDA
130 TIME=TIME*DELT
IF (RCDA) J«J+ 1
J1«=J-H
KC=KO1
FC0R=CKO1»>*FC0R/KC
IF (TIME*. 1*DELT-C*(X2-X1 >> 133*132*132
132 DTINT«=DELT
DELT=DELT-TIME+C*CX2-X1>
TIME=C*CX2-X1>
133 XB^XA+DELT/C
TGAS=TN0M+50*C6-X8>
135 IF (J-2) 136*137*137
136 TB(1>=TA<1)*TDA*DELT
G9 T0 1383
137 JM1=J-1
QP=1*DELT/DTB
QMal-DELT/DTB
00 138 I~1*JM1
FBCI>=FZCI>*QP*(QM**TDA*DEL.T
FB(J)=FA(J)*FDA*DELT
PB(J)=PACJ>*PDA*DELT
1383 IF (J-2) 1385,139*139
1385 TD1=2*-TA<1»/DELT-TDA
FDI=2*(FBC1>-FA(1))/DELT-FDA
G0 T0 1387
139 TDI = FUNCINTCU»2*DELT«TZC1)*TA(1)*TBC1)*DTB,DELT)
FBC1>=AMAX1CO«*FB<1>>
FDIsFUNCINT
H*FUNCH(TBC1)*TGAS)-FB(1)*FLWCSG(.5*CTB(1)+TGAS»
TGI1=H/THK**460)
FGIl = -PaR*M/GASC*P0TD0T-2*FBCl)/R(l)
PGI 1 = FUNCPGCRC 1 )* FB( 1 )» TB( 1 >* PBC 1 >* FDI* FGI 1 )
TD0=TDI
FD0=FDI
PD0=POI
IF (J-l) 189*189*181
181 D0 188 I-2*J
TGI = TGI1*TG2I1*(R(I)-R(I-1»
1815 IF CI-J) 182*183*183
182 TDI = FU,MCINTC1.*2*DELT*TZ*DTB*DELT)
FDIaFUNCINTC 1 .*2*DELT* FZC I )* FA(I>* FB( I )*DTB*DELT)
-------
D-4
01810 PDI*FUNCINT(lo*2*DELT*PZCIJ*PACI>*PB*DTB*DELT>
01820 GO T0 184
01830 183 TDI=2*CTB(I)-TACI))/DELT-TDA
01840 FDIa2*(FBCI>-FAei»/DELT-FDA
01850 PD1»2*-PA*TDI/«-460»/(TB + 460>
01870 FGI=*-P0R*M/GASC*P0TD0T-2*FBU>/RU>
01880 FBCI>=FBCI-1>+CFGI+FGI1>/2*CR-R*TBCI)*R>
01900 TGI=TGI1**/2*>
01920 PGI*FUNCPG*FB*TBCI>*PBU>*FDI*FGI>
01930 PB(I>=PB(I-l)+CPGI+PGIl)/2*CRCi)-R*TERR*IND>
01950 G3 T0 C185*187*186>*IND
01960 185 TB=TBI
01970 60 T0 1815
01980 186 TMPDIFsTBI-TBCI)
01990 PRINT 1865* I*J*TMPDIF
02000 1865 F0RMATC » P00R S0LUTI0N AT I=M5*° J= •# 15*
02010 & • TEMP ERRCF)= *>F8o5/)
02020 187 TB-R/2*CR(J1)-RCJ)>
02110 PBCJ1)=PB(J)+PGI1*(R
02120 CALL FReNT*PGJl*PDI*PCD8«TBCJl>*TGJi*TG2Jl*TDB*TCDB*
02130 & FB(J1)«FGJ1*FDI«FCDB*RCJ1>«RCDB>
02140 IF (RCDA) R< Jl > = R + CRCDA<-RCDB)/2*DELT
02150 £90 TGJlaTGll*(TG2Il + TG2Jl>/2*(R(Jt)-RCJ))
02160 TB=PBCJ) + (PGJ1*PGI1)/2*(R(J1)-RCJ»
02180 PDBs2*-PA(J»/DELT-PCDA-RCDB*PGJl
02190 FDB=2*(FB(J1)-FA»FGJ1«FDB»FCDB»R(J1>»RCDB>
02220 IF (RCDA) RJ1=R(J)*/2*DELT
02230 CALL CBMPC (RJ1-RC J1»/R( 1 >»RERR* IND>
02240 G9 T0 (191/192,1915), INO
02250 191 R(J1)=RJ1
02260 G0 T0 190
02270 1915 N0=N0+1
02280 192 FBJ1=FB(J)*(FGJ1*FGI1>/2*(R(J1)-R(J»
02290 FDIF=FBJ1-FBCJ1)
02300 IF (RCDA) 193,196,196
02310 193 TDIF=TB>
02320 Gfl T0 198
02330 196 TBJ1=TA
02350 198 IF (ABS(TDIF)-TERR) 1985*1985*199
02360 1985 IF (ABS(FOIF)-FERR*FC> 260*260*199
02370 199 N=N+1
-------
D-5
02380
02390
02400
02410
02420
02430
02440
02450
02460
02470
02480
02490
02500
02510
02520
02530
02540
02550
02560
02570
02580
02590
02600
02610
02620
02630
02640
02650
02660
02670
02680
02690
02700
02710
02720
02730
02740
02750
02760
02770
02780
02790
02800
02810
02820
02830
02840
02850
02860
02870
02880
02890
02900
02910
02920
02930
02940
G3 T0 Cl992*1994*1996pl998J* M0D+1
1992 TDIF1=TDIF
FDIFl^FDIF
TBU)=TBU>-TDIF1*TC0R
GO T0 1383
1994 TDIF2=TDIF
FDIF2=FDIF
TBC1)=TB(1)*TDIF1*TC0R
FB(1) = FBC1>-FDIF1*FC0R
63 T0 1383
1996 TDIF3=*TDIF
FDIF3=FDIF
DEN0M=*(FDIF2-FDIFl>
NUMT=TDIF3#FD1F1-TDIF1*FDIF3
NUMF=TDIF1*FDIF2-TDIF2*FDIF1
TBC15°TB<1)-NUMT/DEN0M*TDIF1*TC0R
FB<1> = FB<1)«-C1-NUMF/DEN0M>*FDIF1*FC0R
G0 T0 1383
1998 IF (N-20> 199*200*200
200 IF CN0-IO) 202*202*220
202 IF 210*203*203
203 DELT8DELT*<-RCDA>/(RCDB-RCDA>
TIME»TIME+RCDB/RCDA*DELT
GS T0 215
210 DELT=DELT/1.4
TIME=> TIME-. 4*DELT
215 N6=«N0+i
N=0
G0 T0 133
220 T3600=3600*TIME
PRINT 225* T3600* TDIF*RCDA*RCDB
225 FSRMATC * P00R S0LUTI0N* TIME* •* F7. 4* f TEMP ERR»°*F7.4X
& • RCDA= '*E10.3* • RCDB* f*E10. 3) ' .
TIC0=»3600*C#CX2-XI>
PRINT 298* TIC0
G3 T0 1000
260 N=0
273 DTB=DELT
XAsXB
IF CTCDB) 275*277*275
275 DELT=AMIN1 ( 1 .4*DELT*DETC/ABSCTCDB»
G2> T0 280
277 DELT=U4*DELT
280 PCDAaPCDB
TCDAsTCDB
FCDA=FCDB
RCOA°AMIN1(RCDB*OO
TOA=TOB
FDA=FDB
PDA=PDB
03 290 1=1* Jl
TZ(I)»TA(I)
TACI)=TBCI)
PZ(I)aPAsFA
-------
D-6
02950
02960
02970
02980
02990
03000
03010
03020
03030
03040
03050
03060
03070
03080
03090
03100
03110
03120
03130
03140
03150
03! 60
03170
03180
03290
03200
03210
03220
03230
03240
03250
03260
03270
03280
03290
03300
03310
03320
03330
03340
03350
03360
03370
03380
03390
03400
03410
03420
03430
03440
03450
03460
03470
03480
03490
03500
03510
290
293 PGRaPGJ 1*RC Jl >/2/51 . 71 5
RJR=iOO*(lo-/R0J**3>
RJRO=R(J1)/H9
T3600=3600*TIME
PRINT 295*T3600*XB*T6AS*RJR0*RJR*TB*PBeJl>*PGR
295 F0RMATCF7<,4*F6.2*Fl0.3*F8»4*F6o2*F10«3*F9.l*F9. 1>
IF (ABS(RCDB) + o01*RCDA) 297*297*299
297 TIC0=3600*C*CX2-X1>
PRINT 298* TIC0
298 F0RMATC ' CALCINATION C0MPLETED* TIME AT X2*»>F7. 4*' SEC')
G0 T0 300
299 IF -RCI»/CR(1>-RCJ1>>
IF (IR-IRfl) 308*306*306
306 RIR03RU5/R0
IF CI-2) 3062*3066*3064
3062 STRESS=PGa*R0/I03«43
G0 T0 3068
3064 IF CI-J) 3066*3066*3065
3065 STRESS=PGJ1$R(J!>/103.43
Gfl T0 3068
3066 STRESS* FUNCINT* PBCI >*PBCI- 1>*RC I >-R< !<•!)*
& RCI-1>-R/103«43
3068 PRINT 307* RIR0* TBCI )*PB(D* STRESS
307 F0RMAT(F8o4*F10.3*F9.1*F9«l)
IR0=IR0+1
308 CONTINUE
S3 T0 1000
410 IF (Jl-20) 130*420*420
420 19=2
D8 440 1=2*17
IR=10*(RCl)-R(I»/(R(n-R(18»
IFCIR-I0+1) 440*430*430
430 IC0UNTU0>sI
440 C0NTINUE
00 450 I=18*J1
450 IC0UNTCI-8)=I
J=J-8
JlBj*l
00 460 I=2*JI
I0=IC0UMT(I)
PZ(I)=PZ(I0>
PA(I)=PA(I0)
FZCI)=FZCI0)
FACI)=FACI0)
TZ(I)eTZCI0)
TA
460 RCI)>R(I0)
60 T0 130
1000 CONTINUE
ST0P
-------
. D-7
03520 END
03530 SUBR0UTINE C0MPCRT* ERR* IND)
03540 IF (ABSCRT)-ERR) 50*50*20
03550 20 IF (1-20) 40*40*30
03560 30 IND:--3
03570 1*0
035SO RETURN
03590 40 IND=1
03600 1=1*1
03610 RETURN
03620 50 IND=2
03630 1=0
03640 RETURN
03650 END
03660 SUBROUTINE FR0NTCP* PG* PD*PCO* T* TG* T62* TO* TCD* F* FG* FD* FCD* R* RD>
03670 REAL L*M,MC
03680 C0MM0N L*M*MC* THK*RH02*S2*RH0 1* SI* GASC*P0R* ETA* A*RCDA
03690 TABS=T+460.
03700 TST*0.
03710 D=A*CA*P/8/ETA*3.22E05+2/3.*SQRT< lo5708*3o22E05*GASC*TABS/M>>
03 720 DTCDP= 40400/ 1 o 98 7* 1 •> 8/ C24« 19 5° AL8 G< P) )**2/P
03730 SG=.!56+.194E-03$T-.056E-06*T**2
03740 5 C1 = **2*C4
03780 IF (C5> 10*20*20
03790 10 RD=0«
05500 3& TS 30
03810 20 RDaC3/2-SQRT(C5>
03820 IF (RCDA) 30*25*25
03830 25 RD=AM!NKO.*RD>
03840 30 F=RD*<-M/MC*RH02+P0R*M/GASC*P/TABS>
03850 PG=RD/D**<1*TST)-FD/P0R/3.22E05
03860 TCD=3/R/S2*
03980 RETURN
03990 END
------- |