Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 411
Influence of Porosity of Calcium Carbonates on Their Reactivity with Sulfur Dioxide Miloslav Hartman, Jaroslav Pata, and Robert W. Coughlin" Institute of Chemical Process Fundamentals, Czechoslovak Academy of Science, 165 02 Prague, Czechoslovakia
An extended grain theory that takes into account local reductions in porosity of reacting particles has been employed to correlate their capacities to react with sulfur dioxide in flue gas. This approach provides better agreement with experimental results than the application of a simpler structural model based on uniform conditions throughout the
particle. Experimental measurements show that the natural porosity persists during the calcination process and that the carbonate rocks already porous prior to their calcination are, in general, better suited for the sulfation reaction than common, dense limestones.
Introduction The main drawback of the dry processes using a fluidized bed of inexpensive limestone for sulfur dioxide removal from flue gas is that the limestone reacts only partially. The major rationale for enhancing the potential of such processes lies in improving limestone utilization. Increased utilization of limestone particles may be attained by using small particle size, long exposure time, reaction a t optimum temperature, and by properly selecting the reactive sorbent (Hartman, 1976). Each of these individual approaches toward increasing limestone utilization is somewhat limited and, therefore, their simultaneous and combined use should be considered in any effort for improving dry limestone SOz sorption processes. Additional pilot-plant studies are needed for estimation of the optimum operating variables of a fluidized-bed contactor which is designed to burn coal and also operate as a chemical reactor. Nevertheless, considerable work has already been done on the kinetics of the sulfation reaction and on the reactivity of carbonate rocks. It is believed that the results of such work now provide some broader principles for selection of natural limestones for sorbing sulfur dioxide. Early kinetic studies indicated wide variation in high-temperature SO2 reactivity of different geological types of carbonate rocks (Harrington et al., 1968; Potter, 1969; Borgwardt, 1970a). The term limestone is frequently used to describe minerals containing not only calcium carbonate but it also usually includes stones with varying contents of magnesium carbonate. There are conflicting results on the effect of the content of magnesium carbonate on reactivity for SOz sorption. While Borgwardt (1970a) found dolomitic carbonate most reactive, Falkenberry and Slack (1969) report that the high-calcium limestones are more reactive than dolomites. In our previous investigation (Hartman, 1975) into the reactivity of commercial limestones we found that a rock containing 19% by weight MgO displayed an approximately median activity within a group of ten limestones. Furthermore, a significant content of silica is undesirable because it can substantially lower the fusion temperature. For example, a chalky limestone containing about 25% of SiOz by weight was completely fused at 1000 "C. 'Address correspondence to this author a t the Department of Chemical Engineering, University of Connecticut, Storrs, Conn. 06268. 0019-7882/78/1117-0411$01.00/0
More generally, however, the chemical composition of limestones is of only minor importance in SO2 sorption, whereas a number of experiments demonstrate that wide variations in reactivity can be related to differences in the physical properties of the calcines of the stones. In addition to such structural features as the poor size distribution, surface area, and grain size, the pore volume of reacting particles has a strong influence upon the sorption of sulfur dioxide (Potter, 1969; Falkenberry and Slack, 1969; Borgwardt and Harvey, 1972; McClellan et al., 1970). Experimental findings clearly suggest that both the rate of reaction and the attainable conversions or SO2 sorption capacity is closely related to the initial porosity of limestone particles. The course of the sulfation reaction is also significantly affected by grain size, chemical activity of the grains, and pore-size distribution (Hartman, 1975) but our experimental results suggest that the chemical composition of the stone may be less important. The chemical activity and size of grains of CaO in calcines will depend on calcination conditions and the nature of the parent rock. Although some general trends are apparent, little effort has yet been made to establish quantitative relationships. A relationship between the porosity of calcined particles and the characteristics of the original natural limestone has been noted previously (Borgward and Harvey, 1972). The present paper develops this conclusion further and more explicitely. In our recent work we investigated structural changes of reacting limestone particles (Hartman and Coughlin, 1974) and developed a mathematical model for the sulfation reaction (Hartman and Coughlin, 1976). This model satisfactorily correlates the experimental data and quantitatively predicts the effect of particle size, gas concentration, and exposure time on the rate of reaction. In the present paper we quantitatively elucidate the role which the porosity of particles plays in this important gas-solid reaction system. Our analysis is extended to include not only the porosity of calcined particles but also the initial porosity of the natural rock before calcination. Our effort is oriented toward better understanding of the basic factors limiting the sorptive utilization of limestone. Experimental work has already shown that the sulfated particles of larger size are enriched in sulfate primarily within the outer portions. Local porosities, therefore, should be considered in the analysis of the reaction rather than the mean values. We believe that the present approach can suggest possible methods to increase attainable limestone conversions and thus improve the economic
0 1978 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
Table I. Expansion Factors of Sulfation Reactions
teomp, C
reaction Na,CO, + SO, Na,SO, + CO,
-f
cuo + so,
t
cuso, Mn20, t 2 SO, + l/zO, 2 MnSO, 1/20,
-+
-f
MgO t SO, t '/zOZ -t &SO, CaO + SO, + 1/,0, -+ CaSO,
exPansion ratio
reference
120-150 1.14 Marec'ek et al. (1970a, b ) 400 3.57 Yates and Best (1976) 475 2.65 Van Den Bosch and De Jong (1974) 7 50 4.02 Hartman and Pata ( 1 9 7 7 ) 850-950 3.09 Borgwardt and Harvey (1970a, b; 1972), Hartman and Coughlin (1974,1976)
feasibility of dry limestone processes for desulfurization of flue gas. Theory At temperatures of practical interest (850-950 "C) the thermal decomposition of small particles of calcium carbonate is essentially instantaneous. Thus, a t these temperatures sulfur dioxide may be assumed to react with calcium oxide to produce calcium sulfate exclusively in the presence of excess oxygen. A characteristic feature of this noncatalytic gas-solid reaction is that it is accompanied by a substantial expansion of the volume of the solid phase. The expansion factor, defined as the ratio of the molar volume of calcium sulfate to the molar volume of calcium oxide, is equal to 3.09. Similar ratios of molar volume of a solid sulfation product to solid sorbent are compared in Table I for various other potential solid sorbents for SOz. All the reactions mentioned in this table have their potential for reducing the level of atmospheric pollution caused by sulfur dioxide emissions. As is evident in Table I, the expansion ratios are greater than unity for all the sulfation reactions; when oxidation also occurs as part of the reaction pathway the expansion ratios are significantly larger. Because the reacting particles usually retain their original gross external volume, their reaction with sulfur dioxide in flue gas causes decreases in porosity. We developed (Hartman and Coughlin, 1974) a quantitative structural model which describes both the reduction in volume of the solid phase caused by calcination and the expansion of the solid phase due to the sulfation reaction when limestone is exposed to flue gas a t elevated temperatures. This model leads to a relation between the porosity of the reacting particle and the progress of the calcination and sulfation reactions expressed as Xc and X , respectively. Parameters such as the initial porosity of the natural carbonate rock, its true density, and the conten$ of calcium carbonate are incorporated in the relation. If we assume that the limestone density equals the true density of calcium carbonate, this equation takes the form ex = 1 - (1 - eLs) X
- x c vccv,, - vco)
+ll
(PLS
= Pcc) (1)
If numerical values for the molar volumes (Hartman and Coughlin, 1974) are incorporated into this expression, it immediately becomes evident that the limestone particle is made more porous by calcining it. Subsequent sulfation,
however, causes a correspondingly large decrease in porosity of the reacting particle with the result that a porosity lower than that of the particle prior to its calcination can be attained. A similar equation can be deduced for the sulfation of a precalcined particle wherein the porous structure is fully developed before sulfation begins
( X , = 1) (2) Here the initial porosity of the precalcined particle (ec) appears as one of the parameters. The rapid decrease in porosity of the particle during the course of the sulfation reaction as expressed by eq 1 and 2 has been incorporated in our previously cited version of grain theory for this reaction system. The formulation includes intraparticle transport and chemical reaction within the particle. The model equations can be summarized as follows a2C 2 aC - - - F(r)C = 0 (3) aR2 R aR and
+
+
ar = E(r)C at The functions F(r) and E(r) are given by F(r) = -3K(1 - ec) r2 DS 1 rg 3 Ds + Kr(1 - r / r g ) K
E(r) = -p
(4)
( 5)
DS Ds+ Kr(1 - r/rJ
where the porosity of the reacting particle, ex, is expressed by eq 1. The boundary and initial conditions are C = Co at R = R,
-aC= o
aR r=rg
atR=O
(7)
att=O
The local (XL)and overall conversion (XO) may be expressed in terms of the position of the reaction interface within the individual grains of the reacting particle. The local extent of reaction has been used in evaluating the porosity of the sulfated interior of the particle by using eq 1. The details may be found in the paper by Hartman and Coughlin (1976). Results and Discussion Porosity of the Lime Particles. In this section we examine the consequences of the above theory and confront them with the experimental data where it is possible. We first consider the matter of possible shrinking of the limestone particles during the calcination process. A simplified form of eq 1 for the case of complete calcination but with no sulfation is
High-calcium crystalline limestones are usually nonporous (eLs = 0). The porosities of the calcines of four such limestones prepared at 820 "C and measured in the present work are close to the values predicted by eq 8 and they are plotted in Figure 1. In their extensive survey of porous natural calcium carbonates, Harvey et al. (1973) measured
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 413 Table 11. Studies of Sulfur Dioxide Capacity of Carbonates in Fixed-Bed Reactors -~ concn of time of SO, in gas, % by vol. exposure, h type of reactor particle size, m m temp, "C -0.27 4.0
integral differential
0.92 0.07-0.7 1
980 920-940
3.5 0.5
differential
0.25
980
2.0
0.30
differential
0.56
850
2.0
0.29
reference Potter (1969) Mullins and Hatfield (1970) Borgwardt and Harvey (197 2) this work
calcine formed to be determined with reasonable accuracy by eq 8. Capacity of the Lime Particles for Sorption of Sulfur Dioxide. It is a well documented fact that the rate at which porous particles of limestone react with sulfur dioxide and oxygen decreases exponentially as the reaction progresses. During the course of the reaction the porosity of the reacting particles also decreases rapidly. If conditions are uniform throughout the interior of the particles, eq 2 predicts the extent of conversion to sulfate, X,,, at which porosity reaches the value of zero
x,, 0 50 0
02
0.1
06
Porosity of Natural Rock, eLs
Figure 1. Dependence of the porosity of calcined particles on their porosity prior to calcination: 0 ,mark 0,chalks and chalky limestones; data of Harvey, Frost and Thomas (1973);a, this work. The straight lines show the values predicted by eq 8 for differentcontents of calcium carbonate in the rocks.
the pore volume of a number of such materials before and after calcination carried out at 850 "C. Their data provide a test of eq 8, particularly with respect to eLs. Included in this work are typical examples of the natural calcium carbonates with considerable pore volume prior to calcination, e.g., mark and chalks or chalky limestones. These rocks are the fine-grained varieties of partly or completely amorphous limestones which are especially porous. The pore volume of chalks varies from 0.1 to 0.45 cm3 g, whereas the pore volume of marls is about 0.30 cm /g greater than that of chalks. Several tests indicated that it was reasonable that the true densities of the natural rock and its calcine are equal to the respective Handbook values of 2.71 g/cm3 for pure calcium carbonate and 3.34 g/cm3 for calcium oxide. Using these values of density the pore volumes given by Harvey et al. (1973) were converted to dimensionless porosities, em which can be used to compute the porosity of the corresponding calcines via eq 8. Calcine porosities so computed are plotted in Figure 1 vs. the porosity of the natural rocks. The weight fraction of calcium Carbonate in the rocks selected for this study varies from 0.80 to 0.99; most of the rocks contained about 99% of carbonate. The straight lines shown in Figure 1 represent the values computed from eq 8 for different contents of calcium carbonate (y = 1.0, 0.9, and 0.8) and these computed porosities are generally in fairly good agreement with the experimental values. The porosities of the calcined marls fall slightly higher than those calculated, possibly because of the presence of organic matter. From this analysis it is evident that, it the calcination process takes place a t moderate temperatures such as around 850 "C,shrinkage of the particles does not occur and the pore volume of the natural rock is preserved during its thermal decomposition, thereby permitting the porosity of the
/
Mco
1
YCPC
vcs -
=-
eC v c o 1 - ec
( X c = 1, e x = 0) (9)
At this stage the solid is virtually impervious to the reacting gases and the reaction effectively ceases for practical purposes. This extent of reaction, X,, as given by eq 9 can be viewed as the maximum conversion that can be attained. As shown by eq 9 the maximum attainable conversion (or sulfur dioxide saturation capacity) of the limestone particles is strongly influenced by the porosity of their unsulfated calcines, ec. Reported experimental measurements of sorption capacities for various types of carbonates are not numerous. Those found in the literature (Potter, 1969; Borgwardt and Harvey, 1972; Mullins and Hatfield, 1970) have been used along with our own experimental data for comparison with the theoretical predictions of eq 9. For the latter measurements, a differential reactor containing limestone particles was fed with flue gas generated by combustion of propane. Sulfur dioxide was metered into the flue gas which passed through a thin layer (about 50 mg) of dried, uncalcined particles. The amount of sulfate accumulated in the reacted particles was determined by titration. Further details on the experiments can be found elsewhere (Hartman and Coughlin, 1974). The pore volumes of calcined particles (produced by exposure at 850 "C to flue gas containing no sulfur dioxide) were determined by helium and mercury displacement. The values of saturation capacity of the limestones are plotted against the pore volume of their unsulfated calcines in Figure 2, where previously reported data are included together with measurements from the present work. The experimental conditions under which all these sorption tests were performed are summarized in Table 11. The scatter of the data points plotted in Figure 2 may be attributed to wide variability of the natural materials and different conditions of experiment. Despite the scatter of the data, it appears that the saturation capacity for sorption of sulfur dioxide by limestones generally increases rapidly with the pore volume of their unsulfated calcines. The data of Figure 2 also show that the utilization of calcium oxide is rather low in that the sorption capacities vary from 0.1 to 0.63 g of S03/g of calcine, whereas the stoichiometric saturation value for pure calcium oxide is 1.42 g of S03/g of calcine. Equation 9 can be easily rewritten for the units in which the experimental data are presented. Inserting Handbook
414
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
I
I
I
0.0,
/ '
I
1
I
1 0.4
I
I
I
m 0
f
W
.+
I
e
e
e
I
1 0.2
01
0,l
I 0.4
0.3
0
Pore Volume of Calcine,Vp,(cm'/g)
Fractional
Figure 2. Saturation capacity of limestones for sorption of sulfur dioxide as a function of the pore volume of unsulfated calcines: e , Potter (1969);mean particle size Dz = 0.92 mm; 0,Mullins and Hatfield (1970), D,= 0.074-0.71 mm; 0 , Borgwardt and Harvey (1972), Dz= 0.25 mm; 8,this work D,= 0.565 mm. The straight line shows the values predicted by eq 10. 0.71
0.1
10 2
I 0.5
I
0.8 Mean Particle Size, dp,(mml
I 1.1
J
Figure 3. Dependence of the saturation capacity on the particle size: 1, concentration of SOz, 0.30% by volume; 2, concentration of SOz, 0.05% by volume; limestone VI; temperature, 850 "C; time of exposure, 2 h.
values for VCo and Vcs gives a very simple linear relationship between the sorption capacity of lime particles and their pore volume
S = 2.27 V,
(pc =
pco)
02
(10)
It is evident that the large majority of the experimental sorption capacities are considerably lower than the values predicted by eq 10 which is plotted in Figure 2. These theoretical predictions are based on the assumption of uniform conditions throughout the interior of the particles. Moreover, analysis by the electron microprobe has shown that the sulfation also takes place in the very center of the particles. Unfortunately, because of the scatter in the microprobe data, the concentration profiles of calcium sulfate could not be determined conclusively. In order to explore whether a significant gradient of sulfate concentration exists, the sorption capacities of particles of different size were measured and are plotted in Figure 3. As seen, the saturation capacities attained after 2 h of exposure to the flue gas increased with decreasing particle size, although the reaction occurred throughout the interior of all particles tested. The calcines for the porosity
\ I \ Oh
h
Y
OB
10
Conversion o f CaO, X
Figure 4. Dependence of the porosity of sulfated solid on the conversion to sulfate, X,and natural porosity eLs as predicted by eq 1 for completely calcined pure calcium carbonate (X,= 1, y = 1).
measurements were prepared at 850 "C by exposing dried particles of natural limestone VI to flue gas containing no sulfur dioxide for 2 h. The pore volumes of these calcines showed no dependence on particle size and the mean value was 0.330 cm3/g. Equation 10 predicts that the saturation capacity corresponding to this value is as large as 0.749 g of SO,/g of calcine. Extrapolating line 1 in Figure 3 to small particle sizes suggests a capacity which is quite close to the prediction of the theoretical model as embodied in eq 10. Figure 3 also shows that lower concentrations of sulfur dioxide in the flue gas have an adverse effect on the saturation capacity. This behavior is in accord with the data of Mullins and Hatfield (1970), who worked with higher concentrations of SO2 in the flue gas and with particles of comparable pore volume observed more reaction than did the other authors listed in Table 11. Local Porosities of the Reacting Particles. The results presented above show that the assumption of uniform conditions throughout the interior of the particle may not be justified, particularly for common, dense limestones of particle size on the order of several tenths of millimeters. The extended grain model comprising eq 1 and 3-7 describes not only the concentration profiles of sulfur dioxide and calcium sulfate but also the local porosity within a spherical limestone particle during the course of reaction. In our previous work (1974) we found that eq 1 predicts rapid reduction in overall porosity of the reacting particles as sulfation progresses, in good agreement with experiment. We have calculated overall porosities as a function of the extent of sulfation reaction for selected initial values of the natural porosity and calcium carbonate content in the limestone. These results plotted in Figures 4 and 5 show how rapidly the porosity falls as the sulfation reaction proceeds. For comparison data on the porosity of a natural carbonate (Travertine 1; see Table IV and Figure 11) as a function of conversion are also plotted in Figure 5 and the agreement with the prediction of eq 1is seen to be reasonably good. It is seen that the pore volume produced by calcination alone (eLs = 0) is filled with the reaction product well before all calcium oxide is converted to sulfate. The presence of pores in the natural carbonate (eLs > 0) increases the porosity of its calcine, thereby providing additional space for accumulation of calcium sulfate. For a pure natural limestone material an initial porosity of 0.3 is further increased by calcination to about 0.64-0.68 as shown in
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 415 I
L - 04 02
oo
I
I
1
06
C8
10
I
I
1
1
00705
0141
o 212
o 282
f
Fracttonal Conversion of C0O.X
Figure 5. Dependence of the porosity of sulfated solid ex on the conversion to sulfate, X, and natural porosity em; solid line represents the behavior predicted by eq 1for completely calcined limestone with a lower content of calcium carbonate (X,= 1,y = 0.8). Data points are the results of experiments with travertine 1 of Table IV under conditions of Figure 11.
Figure 1. It can be seen from Figure 4 that these porosities are sufficient to accommodate the product even if all calcium oxide is converted to sulfate. An electron microprobe was employed to investigate the distribution of sulfur within sulfated limestone spheres (Hartman and Coughlin, 1976). The local conversions measured in this way throughout the particle interior were in general agreement with the values computed from the mathematical model. It is hardly possible to measure the local porosities within such small particles, but it seems that on the basis of the general experimental verification herein, it is feasible to investigate local porosity reductions throughout the particle interior by means of the model formulated by eq 1 and 3-7. Using reactive, high-grade limestone VI in a kinetic study (Hartman and Coughlin, 1976) we were able to quantitatively describe the effects of particle size, gaseous sulfur dioxide concentration, and reaction time on the progress of the chemical sulfation reaction with reasonable accuracy. Details on how the parameters in the model equations describing the processes of diffusion and reaction within the particle were evaluated are contained in the reference. Computed porosity profiles within the particles of mean size D = 0.565 mm for three times of exposure are plotted in Figure 6, where it is seen that the sulfation reaction takes place preferentially in the outer zone of the particles. Because of this the reduction in porosity is substantially greater in the outer zone than that in the center of the particles. When the time of exposure amounts to about 880 s the pores become essentially completely filled and sealed. Our microscopic examinations revealed that most of the pores were filled with the reaction product. But some open pore mouths could still be found even on the particles exposed to the flue gas for long periods of time and their origin may be ascribed to local nonuniformities. The sulfation reaction is not completely halted at this stage, but its rate is too low for practical use. The sulfation also occurs in the very center of the particle, but to a smaller extent. The pores close when the conversion at the outer edge is about 0.57 whereafter the reacting gases can hardly continue to penetrate into the particle interior as shown in Figure 7; as a result most of the internal calcium oxide then remains unreacted. When the theoretical local porosity profiles plotted in Figure 6 are integrated and compared with the experimental total porosities of partially sulfated particles re-
0
Distance from Centre of Particle, (mm)
Figure 6. Time development of porosity profiles throughout the particle interior: nonporous limestone VI; eLs = 0; R, = 0.282 mm; C, = 1.43 X lo-* mol/cm3; temperature, 850 "C; K = 6.6 cm/s; rB = 1X cm; D = 7.5 X cm2/s; D, = 6 X cm2/s. 0.8,
I f
02t-
H
I
\ I
L
I ~~
0
750
1500 2250 E x p o s u r e Time,t, ( 5 )
~
30a3
Figure 7. Dependence of the relative point, gas-phase concentration of sulfur dioxide in the outer zone of the particle a t r = 0.254 mm on the time of exposure for nonporous (eLs = 0 ) and porous limestone (eLs = 0.2). The values of the model parameters are the same as in Figure 6.
ported previously (Hartman and Coughlin, 1974) the agreement is good. More sensitive tests of theory, however, are provided by the influence of total porosity on overall conversion (Hartman and Coughlin, 1974) and by measuring local extents of sulfation reaction within the particles by electron microprobe analysis (Hartman and Coughlin, 1976). Overall conversions attained at the moment when the pores become closed were measured after exposing particles of sizes 0.282, 0.565,0.900 and 1.12 mm to the flue gas for 2 h. The conversion attained are compared in Figure 8 with values computed from the model. Although the experimental conversions are somewhat higher than those computed, nevertheless, the agreement is good. It is worthy of mention that the time of pore closing in the mathematical simulations is on the order of 10-20 min and this is much less than the reaction time in the experiments. These results show that the maximum conversions or saturation sorption capacities of the particles are, in principle, those attained at the moment of pore closing ( t = tclosing). It follows from a comparison of Figures 2 and 8 that the sorption capacities predicted by computation
416
Ind. Eng. Chem. Process
0.2' 0.2
Des. Dev., Vol. 17, No. 4, 1978
I
1
0.5
0.8
11
Mean Particle Size, 6p,(rnrn)
Figure 8. Maximum attainable utilization of calcium oxide in the particles of different size: limestone VI; temperature, 850 "C; concentration of SO2, 0.295% by volume; exposure time, 2 h. The solid line shows the overall conversions predicted by the grain theory for the time when the pores become closed ( t = tClah). The values of the model parameters are the same as in Figure 6.
using the grain theory are closer to experimental reality than the values predicted by the simple structural model assuming uniform concentration of sulfate throughout the particle interior. The curve in Figure 8 shows the overall conversions computed from the theory; this is different from curve 1 of Figure 3 which is the best fit of experimental values. The discussion above is oriented toward dense, finegrained limestones represented by the reactive stone VI, the pore-size distribution of which was determined in our earlier work (Hartman and Coughlin, 1974). In general, a more complete analysis of the sulfation reaction would also take into consideration pore or grain-size distribution which is affected by calcination conditions and the nature of the original carbonate (Borgwardt and Harvey, 1970b, 1972). Several parameters or coefficients which appear in the equations of the model describing the process of diffusion and reaction within the particle may be regrouped into two parameters such as a Thiele-type modulus and a Biot number which determine the overall course of reaction (Calvelo and Smith, 1970). Due to the gradual changes in the pore structure during the course of reaction, the Thiele-type modulus varies both with time and radial position. Aside from its geologic origin and grain size, the porosity of a rock is apparently the most important factor in the sulfation process. That is why the influence of porosity has been explored separately rather than in combination with the other parameters as in a Thielegroup modulus. The optimum temperature observed for the sulfation reaction of three different natural limestones is near 850-900 "C. A t such temperatures shrinkage of the limestone particles does not occur and the volume of voids in the natural material is effectively added to the pores formed by calcination as shown above. A favorable influence of high natural porosity in maintaining high gas-phase concentrations of sulfur dioxide within the interior of the particle is depicted in Figure 7. The higher porosity provides more space for the reaction product to accumulate and the time of exposure at which the pore mouths become closed is greatly prolonged by increasing porosity, as shown by the curve in Figure 9. If the mean residence time of the solid in a practical fluidized bed is
1800ao
0.1
6
02 0
0
0.3 1
Porosity of Natural R o c k , q S
Figure 9. Sensitivity of the time of exposure at which the pore mouths become closed to the initial porosity of natural limestone. The values of the model parameters and variables are the same as in Figure 6. I
I
01
02
/ /
0.9
0
0
Distance from Centre
Of
03 Particle, (rnrn)
Figure 10. Sensitivity of the local extent of reaction within the particle to the initial porosity of natural limestone. The curves show the concentration profiles developed at the time of pore closing ( t = td*). The values of the model parameters are the same as in Figure 6.
about 1 h or more, then during most of this period of time the limestone particles will be nonreactive with their pores closed, assuming a common dense limestone (eLs = 0) is employed. Figure 10 illustrates how higher void fractions, which facilitate the transport of the reacting gases, increase the local conversions and make the concentration profiles of sulfate flatter. It is evident then that higher values of porosity, eLs, diminish the effect of particle size on sulfation conversion, a desirable result from the standpoint of an economic desulfurization process. In general agreement with the upper curve (eLs = 0.25) of Figure 10 we have found by electron microprobe investigation that after an exposure of 60 min the distribution of sulfur is practically uniform within reacted particles of Travertine 1 (see Table IV and Figure 11) of particle size 0.565 mm and eLs = 0.273. In any practical situation, however, it, may also be necessary to consider the relationship between the strength and porosity of the particles; very porous particles often abrade easily. Reaction Rates and Sorption Capacities of Porous Carbonate Rocks. The extended grain theory and analysis presented here suggest requirements for carbonate rocks and their calcines to be most reactive with sulfur dioxide, viz. high pore volume and small size. In order to
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 417
Table 111. Comparison of Carbonate Rocks rock
limestone VI travertine marl"
~
content of calcium carbonate, y porosity of natural rock, eLS porosity of calcine, eC, computed from eq 8 porosity of completely reacted material, (e&=,, computed from eq 1 conversion of 1 . 1 2 mm particles after 2-h exposure, X ,
0.982
0.812
0.840
0
0.273
0.706
0.540
0.593
0.840
0 at X = 0.57
0.028
0.604
0.269
0.674
lb
" Tested by Borgwardt and Harvey (1970b, 1972). Exposure Time,t,(min)
Figure 11. DeDendence of the conversion of different carbonate rocks tosulfate on t i e exposure time: temperature, 850 "C; concentration of SOz, 0.29% by volume; 0,dense limestone VI, particle size, 1.12 mm; e,porous, amorphous travertine 1 of Table IV particle size, 1.12 mm;o', porous amorphous travertine 1of Table IV particle size, 0.565 mm; 0 , data of Borgwardt (1970b); temperature, 980 "C; highly porous marl; particle size, 1.3 mm; concentration of SOz, 0.30% by volume.
verify at least the trends outlined by simulation of the reaction system, we have conducted experiments with travertine. It is a microcrystalline, somewhat amorphous mineral containing 45.5% calcium oxide by weight. Its pore volume in the natural state was determined by helium and mercury displacement and is as large as 0.139 cm3/g, which corresponds to a porosity of 0.273 cm3/cm3. Two particle-size ranges, 0.50-0.63 mm (D,= 0.565 mm) and 1.00-1.24 mm (Dp = 1.12 mm), were investigated in this work. The dry, uncalcined samples of the travertine were exposed to flue gas containing 0.295% sulfur dioxide by volume for 5 to 60 rnin at 850 O C . This temperature is near the optimum for the reaction and is sufficiently low that shrinkage of the particles during their calcination is avoided. In Figure 11 are plotted the results of these sulfation experiments as well as similar data obtained by Borgwardt (1970b) and our own results with the finegrained, dense commercial limestone VI. This rock was found to be the most reactive within a group of ten different commercial limestones tested previously (Hartman and Coughlin, 1974). It is obvious from Figure 11that the sorption performance of the porous travertine (eLs= 0.273) is clearly superior to that of the virtually nonporous limestone VI (eLs = 0) in spite of its relatively high reactivity. After 60 min of exposure more than 60% of the calcium oxide in the 1.12-mm particles of the travertine was converted to sulfate. This value is more than two times greater than the conversion of limestone particles attained under the same conditions. A similar comparison made on a weight basis would indicate a conversion ratio which is slightly less than 2 because of the somewhat lower content of calcium oxide in the travertine. Although the conversion curves of the travertine particles also gradually flatten with time as shown in Figure 11, a considerable increase of the conversion can be observed for travertine a t longer exposure times. It is of interest to note that the size of the travertine particles has only a minor effect on the conversions attained; calcium oxide utilization increased by only 7-9% when particle size was reduced from 1.12 to 0.565 mm. The total porosities of sulfated particles of the travertine of Figure 11were determined by helium and mercury displacement as a function of conversion and the results are in reasonable agreement with eq 1as shown in Figure 5.
1.3-mm particles of marl were completely reacted in less than 20 rnin of exposure.
The kinetic data of Borgwardt and Harvey (1970b, 1972) obtained with a marl show extraordinary high reactivity for this rock. Some of these results are also plotted in Figure 11. Borgwardt's marl was a porous, soft and incoherent carbonate composed principally of weakly agglomerated, very fine calcite grains; its pore volume was also unusually large. The natural carbonate had a pore volume of 0.89 cm3/g corresponding to a porosity of 0.706 cm3/cm3prior to calcination. In contrast to the limestone VI and the travertine, the marl particles were completely reacted in less than 20 min. Assuming that calcination is complete, i.e., Xc = 1,the application of eq 1 suggests that the porosity of the particles remains as large as 0.604 cm3/cm3even when completely converted to sulfate. This final porosity is somewhat higher than the initial porosity of unsulfated, calcined ordinary limestones such as the limestone VI. The corresponding, final porosity, ex, of the travertine, Le., ex at X = 1,attains a small value of 0.028 cm3/cm3,substantially less than that of the marl. In the case of the limestone VI, the porosity of the particles approaches zero for conversions close to 0.57. Whereas the conversion of the 1.12-mm particles of travertine attained after 2 h of exposure was 0.674, the utilization of the limestone VI achieved under the same experimental conditions was only 0.269. Borgwardt's data show not only that the marl particles can be easily and completely converted to sulfate but also that the reaction rate is independent of particle size within a range from 0.096 to 1.3 mm. This experimental finding indicates that intraparticle transport does not offer any significant resistance to the sorption of sulfur dioxide within these highly porous calcines and the reaction proceeds uniformly throughout their interior. A comparison of the grain theory model with experimental results such as shown in Figure 11 has been made in a previous paper (Hartman and Coughlin, 1976); the parameters of the model are the same in the present paper as in the earlier paper. Data on the content of calcium carbonate, porosity and conversion of the various stones under comparison are summarized in Table 111. Nine different natural calcium carbonates (seven Czechoslovak travertines, one oolitic limestone from the Persian Gulf, and one Cuban limestone) were also explored as to the effect of their natural porosity on their reactivity with SOz. The characteristics of these stones and the conversions attained after reaction times of 60 min are collected in Table IV. The conversions are also plotted as a function of the natural porosities, eLs, in Figure 12. Although the data are considerably scattered, a generally favorable effect of porosity on reactivity is clearly evident
418
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
Table IV. Characteristics of Different Carbonate Rocks (Temperature, 850 C; Particle Size, 0.565 mm; Concentration of SO,, 0.3%by Volume; Exposure Time, 60 min)
rock
weight fraction of CaCO,
weight loss on ignition at 850 "C
porosity of natural stone, eLS
most probable radius of pores, A
conversion
0.8722
0.4341
0.273
not determined
0.6841
0.9389 0.9212 0.9436 0.8273 0.9379 0.9439 0.8470
0.4276 0.4341 0.4294 0.4043 0.4369 0.4407 0.3739
0.775 0.0879 0.0536 0.0340 0.2242 0.2188 0.2153
27 800 34 000 34 000 4 000 7 200 1300 1300
0.6542 0.4557 0.4337 0.2580 0.5220 0.4886 0.7147
0.9236
0.4406
0.0798
200
0.4044
travertine 1 (see Figures 5 and 11) travertine SJ travertine BP travertine MB travertine KK travertine MO travertine ME oolitic limestone (Persian Gu1f)PZ limestone VA (Cuba)
0
02oJ
0
I
I
0.1
0.2
0.3 eLs
Figure 12. Conversionsof various carbonate rocks of Table IV under the following conditions: T = 850 "C, particle size 0.565 mm, concentration of SO2 0.3% vol/vol, exposure time 60 min. Solid line is the prediction of grain theory model for: C, = 3.2 X lo-* mol/cm3; k = 6.6 cm/s; rg = 1 X cm; D = 0.075 cm2/s;D,= 6 X lo4 cm2/s; t = 60 min.
in Figure 12. The solid line shown in Figure 12 was obtained by computations using grain theory for different values of eLs as a parameter using carbonate content y = 0.9, identical values of chemical reaction rate constant, diffusion coefficient, and grain size as determined for limestone VI of our previous paper. Although three data points are not near the theoretical line in Figure 12 the other points fall quite close. Considering that no effect was made to adjust model parameters to suit each individual stone (so that the theoretical line represents some kind of a typical computed expectation), the agreement evident in Figure 12 seems rather satisfactory. Postlude We wish to emphasize that the very wide variability of natural SOz sorbent materials contributes greatly to the complexities of the sulfation reaction. Because of this, every difference in reactivity or sorption capacity can hardly be explained solely on the basis of porosity without further consideration. In general, however, both the experimental findings and the theory strongly suggest that the pore volume of carbonates and their calcines is a physical parameter of major importance. Conclusion Grain theory has been combined with a simple structural model and employed for the analysis of limestone sulfation. Satisfactory agreement between experiment and this model suggests that at temperatures of 850-900 O C carbonate particles do not shrink and therefore retain their natural
porosity during the calcination process. Experimental results show a close link between the pore volume of calcined particles of the stones examined and their capacity for sorption of sulfur dioxide. The sorption capacity or maximum attainable conversion of the particles can be viewed in terms of the pore volume available to accommodate the reaction product. When uniform conditions are assumed throughout the interior of particles predictions of the simple model are, in general, considerably higher than the experimental values. This discrepancy decreases with decreasing particle size. The expanded grain model reflecting a rapid local decrease in porosity as well as the concentration gradients within the reacting particles is better suited for modeling the heterogeneous sulfation reaction. This grain model predicts that in the case of a common limestone, a dense shell of calcium sulfate and calcium oxide is formed at the outer edge of large particles after an exposure time of about 15 min. In contrast to the predictions of a simple model based on uniform conditions, the overall conversions predicted at this stage by grain theory for the particles of the high-grade limestone are in satisfactory agreement with the corresponding values of the sorption capacity determined by experiment. Simulations of the reaction by the grain theory model indicate a strong influence of the porosity of natural limestone on the concentration profiles developed within particles and the exposure time at which the pores close. The theory suggests that a dense shell should not form on particles of natural porosity larger than 30%. Three carbonate rocks with greatly different pore volume in the initial natural state exhibit a correspondingly different pattern of sulfation reaction. For particles of a limestone nonporous prior to calcination, only 27 % of the calcium oxide was actually converted to sulfate in the experiments after an exposure time of 2 h. With the microporous travertine, the initial porosity of which is 27 70,the conversion attained under the same conditions was 67%. The results of Borgwardt show that all calcium oxide present in his very porous marl can be easily converted to sulfate. This result suggests that the porosity of this completely reacted material should remain as high as 60%. To be well suited for the sorption of sulfur dioxide a carbonate material should have an initial porosity prior to calcination of more than 30% to permit it to accommodate all calcium sulfate formed by the reaction.
Acknowledgment The authors with to thank J. Rathouskg, Head of The Institute of Chemical Process Fundamentals, who has made this work possible. We are grateful to Messrs. Picha
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 419
and Skocek of the Geological Survey, Prague, for providing samples of natural carbonate rocks. Nomenclature C = concentration of reactant gas within pores, mol/cm3 C, = concentration of reactant gas outside spherical particle, mol/cm* D = diffusion coefficient of reactant gas in pores, cm2/s D , = mean particle size, mm Ds = diffusivitiy of reactant gas through product shell of the grain, cm2/s E ( r ) = function defined by eq 6 ec = porosity of calcined limestone eLs = porosity of natural rock ex = porosity of sulfate-loaded particle F(r) = function defined by eq 5 K = chemical reaction rate constant, cm/s M = molecular weight, g/mol R = radial coordinate within spherical particle, cm R, = radius of spherical particle, cm r = radius of reaction interface within spherical grain, cm r = radius of grain, cm 9 = sorption capacity of calcine, g of SO,/^ of calcine t = time of exposure of solid to gas, s Vi = molar volume of pure component, cm3/mol V = pore volume of particle, cm3/g x"= conversion of calcium oxide to sulfate, mol/mol Xc = degree of thermal decomposition of calcium carbonate, mol/mol XL 1 - r3/rg3 = local conversion of calcium oxide to sulfate, mol/mol X o 1 3f R; loR* R2XLdR = overall conversion of calcium oxide to sulfate, mol/mol y = content of calcium carbonate in limestone, weight fraction y c = content of calcium oxide in calcine, weight fraction p = true (helium) density of solid reactant, mole/cm3
True (helium) density, g/cm3 Subscripts C = calcine CC = calcium carbonate CO = calcium oxide CS = calcium sulfate LS = limestone Literature Cited
pi
Borgwardt, R. H., Environ. Sci. Technoi., 4, 59 (1970a). Borgwardt, R. H., "Isothermal Reactivity of Selected Calcined Limestones with SO2",International Dry Limestone Injection Process Symposium, Paducah, Ky., 1970b. Borgwardt, R . H., Harvey, R . D., Environ. Sci. Techno/.,6, 350 (1972). Caivelo, A., Smith, J. M., Proc. Chemeca (1970). Falkenberry, H. L., Slack, A. V., Chem. Eng. Prog., 85 (12),62 (1969). Harrington, R . E., Borgwardt, R . H., Potter, A. E., Am. Ind. Hyg. Assoc. J., 29, 52 (1968). Hartman, M., Coughlin, R. W., Ind. Eng. Chem. Process Des. Dev., 13, 248
(1974). Hartman, M., Collect. Czech. Chem. Commun., 40, 1466 (1975). Hartman, M., Int. Chem. Eng., 16 (l),86 (1976). Hartman, M.. Coughlin, R . W., AICHE J . , 22,490 (1976). Hartman, M., Pata, J., Chem. Prum., 27, 230 (1977). Harvey, R. D., Frost, R. R., Thomas, J., Jr., Petrographic Characteristic and Physical Properties of Marls, Chalks, Shells and Their Calcines Related to Desulfurizationof Flue Gases", Final Report No. 68-02-021 2,Illinois State Geological Survey, Urbana, Ill., 1973. MareEek, J., Mocek, K., Erdos, E., Collect. Czech. Chem. Commun., 35, 154
(1970a). MareEek, J., Erdos, E., Collect. Czech. Chem. Commun., 35, 524 (1970b). McClellan, G.H., Hunter, S. R., Scheib, R. M., Spec. Tech. Publ., No. 472,32, Am. SOC.for Testing and Materials (1970). Mullins, R. C.. Hatfieid, J. D., "Effects of Calcination Conditions on the Properties of Lime", Spec. Tech. Publ., No. 472, 117,Am. SOC.for Testing and Materials
(1970). Potter, A. E., Am. Ceram. SOC.Bull., 48,855 (1969). Van den Bosch, P. J. W. M., De Jong, W. A,, The Third International Symposium on Chemical Reaction Engineering, Evanston, Ill., 1974. Yates, J. G.,Best, R. J., I d . Eng. Chem. Process Des. Dev., 15, 239 (1976).
Receiued for reuiew June 15, 1977 Accepted April 19, 1978
Characterization of Membrane Material, Specification of Membranes, and Predictability of Membrane Performance in Reverse Osmosis Takeshi Matsuura and S. Sourlrajan" Division of Chemistry, National Research Counci/ of Canada. Ottawa, Canada K1A OR9
Liquid-solid chromatography (LSC) data on retention volumes of selected reference solutes offer a means of characterizing membrane materials for reverse osmosis. Using tert-butyl alcohol, sec-butyl alcohol, sodium thiocyanate, and raffinose as reference solutes in LSC, four cellulosic and four noncellulosic polymer materials have been characterized by a parameter called the @-parameter. The values of @ exhibit unique correlations with other parameters governing solute separations in reverse osmosis systems where water is preferentially sorbed at the membrane-solution interface. Using data on @-parameterfor the polymer, and only one set of reverse osmosis data for a reference NaCI-H,O feed solution for any membrane made from the above polymer material, reverse osmosis separations obtainable with the membrane for a number of other solutes can be predicted. This is illustrated in this paper with respect to reverse osmosis systems involving 8 polymer membrane materials, 15 membranes of different surface porosities, and 22 organic and inorganic solutes in single-solute dilute aqueous feed solutions.
Introduction In an earlier work (Matsuura et al., 1976a) polar (a,) and nonpolar (a,) parameters characterizing a variety of cellulosic and noncellulosic polymer materials were generated from liquid-solid chromatography (LSC) data on retention times of selected reference solutes in aqueous 0019-7882/78/1117-0419$01.00/0
solutions. The relevance of the above work to reverse osmosis stems from the principle that the solute-solvent-polymer interactions governing the relative retention times of solutes in LSC are analogous to the interactions prevailing a t the membrane-solution interface under reverse osmosis conditions. Following the same principle, @ 1978 American Chemical Society
