cp = product concentration in electrodialysis, equiv/m3 c, = reference concentration, equiv/m3; for electrodialysis, c, ( c f c p ) / 2 D = salt diffusion coefficient, m2/sec f = E X1I3 Re, modified friction factor f* = defined in eq 13; for electrodialysis, in eq 28 F = Faraday's constant, 9.649 x IO4 C/equiv h = system width as in Figure 1, m; in electrodialysis system, width of dialysate channel as in Figure 7 j = average current density over current-carrying area, A/m2 j l l m = limiting value of j k = product cost per coulomb of charge passed through the system, $ / C k , = capital (or ownership) cost coefficient, $/m2 of current-carrying area per sec of operation k , = electrical energy cost, $ / J k , = cost of pumping energy delivered to fluid, $ / J K , = cost per unit volume of product water in electrodialysis $/m3 1 = length, in flow direction, of current-carrying section, m A1 = separation between successive eddy promoters (Figure 8) n = index in performance characteristic, eq 20 A p = pressure drop, in flow direction, along currentcarrying section, N/m2 R = universal gas constant, 8.31J/"K mol Re = p V h l p , Reynolds number p / p D , Schmidt number Sc = Sh = Sherwood number, defined in eq 5 Sh* = defined in eq 12 or 16; for electrodialysis, eq 27 T = absolute temperature of fluid, "K V = superficial flow speed of fluid, m/sec 2 = ion charge number, assumed same for positive and negative ions in electrodialysis
+
Greek Letters cy = a safety factor, defined with regard to eq 3 0 = a dimensionless hydrodynamic performance parameter defined in eq 22
X = conventional friction factor, defined by eq 6
= fluid viscosity coefficient, kg/m sec = fluid density, kg/m3 = average electrical conductivity of working fluid, ohm-1 m - l 9 = potential drop across channel pair in electrodialysis, V 90 = an electrode activation potential, eq 14
p p u
Subscripts opt = optimum value, that is, value which minimizes product cost opt,ideal = optimum value which would be attained under hydrodynamically ideal conditions Literature Cited Belfort, G., Guter, G. A., DesaIination, 10, 221 (1972). Grossman, G., Sonin, A. A,, Desalination, 10, 157 (1972). Hicks, R. E., Mandersloot, W. G. B., Chem. €ng. Sci.. 23, 1201 (1968). Ibl, N., Adam, E., Chem. Ing. Tech.. 37, 573 (1965). Isaacson, M.. Sonin, A. A,, in preparation, 1974. Kitamoto, A,, Takashima, Y . , Desalinafion, 9, 51 (1971). Levich, V . G., "Physiocochemical Hydrodynamics," Prentice-Hall, Englewood Cliffs, N. J. 1962. Lynch, M. A,, Jr., Mintz. M . S., J . Amer. Water Works Ass., 64, 711 (1972). Mandersloot. W. G. B., Hicks, R. E., Ind. Eng. Chem., Process Des. Develop.. 4, 304 (1965). McRae, W., lonics Inc., Watertown. Mass., private communication. 1973. Probstein, R. F., Sonin, A . A,, Gur-Arie, E.. Desaiinafion, 11, 165 (1972). (In this reference there is a slight numerical error: the coefficient 0.013 in eq 7.1 and 7.2 should be replaced by 0.011.) Process Research, Inc., Office of Saline Water Research and Development Progress Report No. 325 (1968). Rosenberg, N. W., Tirrell, C. E., lnd. Eng. Chem.. 49,,780 (1957). Schlichting, H., "Boundary-Layer Theory," 6th ed, McGraw-Hill, New York, N. Y., 1968. Solan, A,, Winograd, Y . , Katz, U., Desalination, 9, 89 (1971). Sonin. A . A,, Probstein, R . F . , Desalination, 5 , 293 (1968). Sonin. A . A,, Probstein, R. F . , Desalination. 6, 270 (1969). Spiegler, K. S., Ed., "Principlesof Desalination;" pp 200-289, Academic Press, New York, N. Y.. 1966. Winograd, Y., Solan, A,, Toren. M., Desalination. 13, 171 (1973).
Received for review July 13, 1973 Accepted J a n u a r y 31, 1974
Reaction of Sulfur Dioxide with Limestone and the Influence of Pore Structure Miloslav Hartman and Robert W. Coughlin*' Institute of Chemical Process Fundamentals. Czechoslovak Academy of Science. 165 02 Prague, Czechoslovakia
A simple structural model has been developed and used to correlate experimental results for the reaction of porous particles of limestone with SOn and oxygen in flue gas at high temperature. The model incorporates parameters such as the porosity of the natural rock, its true theoretical density, the content of calcium carbonate, and its conversion to sulfate. The agreement between the model and the experiments implies that the reaction is strongly influenced by reduction in porosity caused by the sulfation reaction, with both the reaction rate and the porosity becoming very small at conversions of about 50%. The pore-size distributions of unsulfated calcines and sulfated samples are remarkably different. The pores with radius larger than 3980 A are probably responsible for the high capacity of limestone to react with Son. Incomplete conversion of calcium oxide results from the strong diffusional resistance developed in the interior of the particles owing to reduction in porosity as the reaction proceeds.
Introduction The widespread availability and low cost of limestone and dolomite underlie their consideration as sorbents in
'
Address correspondence to this author at the Department of Chemical Engineering, Lehigh University, Bethlehem, Pa. 18015.
248
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974
processes for SO2 removal from flue gas (Hartman, e t al., 1969). There has been considerable interest in dry hightemperature processes, such as the reaction between limestone and sulfur dioxide in combustion gas at high temperature and in the presence of excess oxygen as follows CaC03(s) + SOp(g) ' / 2 0 2 ( gf ) CaSO,(s) + C02(g) (I)
+
Contact between solid and gas can be readily attained by injecting finely powdered limestone into the boiler combustion chamber, by passing combustion gases through a fluidized bed of limestone, or by burning fuel within such a bed (Zielke, et al. 1970). A major obstacle to the practical feasibility of dry limestone processes is the important fact that limestone reacts only partially. For example, in Potter’s experiments (1969), in which 86 carbonate rock samples reacted with sulfur dioxide in flue gas, the carbonate stones had practically ceased reacting at a conversion of calcium oxide equal to only 45%. Wide variations in capacity of the samples was best explained as due to differing porosity among the individual limestones. Using limestone that had first been calcined to calcium oxide, Borgwardt (1970) and Borgwardt and Harvey (1972) found that the rate of reaction decreased rapidly as sulfation proceeded. They observed decreasing rates in spite of the fact that the time duration of exposure of CaO to SO2 in their experiments was only on the order of seconds or minutes, in contrast to residence times much longer than a minute for solids in fluidized beds of practical interest. Reaction I, the heterogeneous reaction of solid calcium carbonate with gaseous sulfur dioxide and oxygen, can be accompanied by or involve the prior calcination of calcium carbonate CaCO,(s) f CaO(s)
+ COi(g)
+ SO,(g) + l/nOz(g)
-
CaSO,(s)
+
+
+
(la) Vso,id = v c c vco vcs VIM where impurities occupying volume V I , are also accounted for. The total fraction of calcium carbonate decomposed or converted by any reaction is defined as
where the unconverted state has ncc = n, and XC = 0, and the fractional conversions of calcium to sulfate and oxide are defined as nco. n cs xc = x c o (3) xco = = -; nl ’ nt Designating as ex the void fraction after some extent of reaction given by X and X c
+x
x
T I
and substituting the quantities defined above and in the Nomenclature section gives the general relation between the porosity of the reacting particle and the progress of reaction designated by X C and X
(11)
Reaction I1 is usuaTly fast at high temperature and the results reported below suggest that the overall reaction I may proceed, to some extent, by reaction I1 followed by reaction III CaO(s)
solid phase Vso,ia we write
(In)
Other mechanisms for reaction I, which is the composite of reactions I1 and 111, are of course ruled out. The development which follows provides a simple quantitative model which describes the incomplete conversions of limestone particles by reactions 1,11, and III. Agreement is also explored between experimental results and the predictions of this model. The approach presented here can be applied to other heterogeneous gas-solid reactions as well.
Simplified forms of eq 5 can be written, depending on the particular case under consideration. The effect of each of the chemical reactions I, II, and ID on porosity may be described by the partial derivations obtained from eq 5 as follows. For reaction I
Y (Vic - Vi,) = M cc
-1532
Y Mcc
-35.32
= (1 - eLs)pLs
For reaction I1
For reaction 111 Theory The system of a limestone particle at high temperature exposed to flue gas containing sulfur dioxide in a reactor is considered here under the following assumptions. (1) The reacted particle retains its original gross external volume. Microscopic examination of samples of raw limestone, calcines, and sulfated particles confirmed this assumption. Considerable disintegration of particles after reaction was observed for only one specimen of raw limestone. (2) Impurities such as silica, iron oxide, alumina, etc., present in limestone do not take part in the reaction and are not subject to volume changes. (3) Calcium sulfate is the exclusive sulfation product. Only traces of sulfite were detected by chemical analysis in the samples reacted at 850°C. (4) Conditions are uniform throughout the interior of the particle. In the course of reaction calcium carbonate, calcium oxide, and calcium sulfate can occur simultaneously. The mass balance equation for the limestone particle under consideration is then
n, =
+ nco +
~ C C
~ C S
(1)
where n,, the total moles of combined calcium, is constant but the other values of n in eq 1 will depend on conversion by reactions I, 11, and III. Similarly, for the volume of
= (1 - eLs)pLs- (V’,
- Vi,)
=
(1
)
Numerical values for the molar volumes reported by Weast (1968) have been incorporated into these expressions as follows: Vcc = 36.9 cm3/mol, Vc0 = 16.9 cm3/ mol, and Vcs = 52.2 cm3/mol. The defined quantity, 2,is inherently positive and depends only on the initial porosity, density, and composition of the limestone. According to the partial derivatives (6), an extensive pore structure develops during calcination (reaction 11) of limestone. However, the formation of calcium sulfate, whether by reaction I or reaction 11, is accompanied by a net decrease in porosity. From the foregoing it is evident that the direct sulfation of limestone by reaction I causes a net decrease in pore volume. Although it is possible to make limestone more porous by calcining it (reaction 11), subsequent sulfation (reaction 111) causes large decreases in porosity, with attainment of porosities lower than that of the original limestone if reaction I11 proceeds to a sufficient extent. On a molar basis, the pore volume consumed as Cas04 is formed by reaction I11 is greater than the pore volume developed by calcination reaction 11. This analysis, therefore, suggests that owing to a decrease in porosity considerable diffusional resi8tances can develop within Ind. Eng. Chem., Process
Des. Develop., Vol. 13, No. 3,1974
249
limestone particles during exposure to SOz-containing flue gases; as a result, incomplete conversion to Cas04 is likely. Experimental Section The apparatus, including a differential reactor used for the kinetics studies, is shown schematically in Figure 1. The flue gas fed to the reactor was generated by combustion of propane with a moderate excess of air. To ensure complete combustion, the combustion tube (46 mm i.d.1 was packed to a depth of 15 cm with spheres of alumina impregnated with cobalt oxide. Sulfur dioxide was added from a cylinder to the gases leaving the combustor. The composition of the gas entering the differential reactor was 12.6% HzO, 10.1% COz, 3.5% 0 2 , 0.29% SO2 by v01ume, with the remainder consisting of Nz. The concentration of SO2 in the gas was determined by absorption in diluted HzOz solution and titrating the sulfuric acid thereby formed with 0.1 NKOH solution. The combustion gases passed through an annular preheat section 100 cm long and 4.6 cm in diameter and then contacted the limestone in the inner tube which was 18 mm in i.d. The limestone particles were uniformly dispersed on quartz gauze in a removable cup, the bottom of which was perforated to permit the flue gases to flow through. To ensure that measured reaction rates were not influenced by mass transfer to the surface of solid a high flow rate of gas was used in each experiment. The superficial velocity in the inner tube of the reactor was 2.5 m/sec at 850°C and very small changes in gas composition (to approximate a “differential-reactor”) were realized by using small samples (about 50 mg) of dried, uncalcined limestone. This velocity is within the range 2.25-24.0 m/sec used by Borgwardt (1970) and over which he found only a 5% increase in sulfation. Larger samples were used for a porosity study during which the rate of reaction was not determined. The reactor was heated using a Kanthal A 1 resistance wire. Temperature in the reactor was measured by a Calibrated PtRh-Pt thermocouple located 1 cm above the sample cup. Temperature was maintained constant within a few centigrade degrees. Samples exposed to the flue gas in the reactor were analyzed for sulfate by first dissolving them in distilled water in contact with an excess of cation-exchange resin. The amount of sulfate was determined by titration of the filtrate with 0.05 N Ba(C104)Z solution in 80% isopropyl alcohol using a mixture of thorin and methylene blue as indicator, Porosities of the limestone samples were determined by helium and mercury displacement. Pore size distributions were determined by measuring the volume of mercury penetrating the pore volume at increasing pressure using the Carlo Erba Porosimeter. Five different high-grade limestones from various quarries were used in this study, the chemical compositions of which are shown in Table I. The hand-picked samples were crushed and sieved and the fractions of particles within size ranges 0.50-0.63 mm (DP= 0.565 mm) and 1.00-1.40 mm ( D , = 1.20 mm) were investigated in this study. Calculated and experimental values of e x are also recorded in this table, except for sample CI which contained considerable clay impurity and therefore was not subject to the assumption pLs = pcc used in the calculation. Results a n d Discussion At first, an effort was made to explore agreement be250
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 3,1974
AIR
4
l
7-1 I
6
PRO
4
r
Figure 1. Schematic diagram of the apparatus: 1, rotameter; 2, combustor; 3, 8, thermocouples; 4, heating spiral; 5, valve; 6, differential reactor; 7, capillary flowmeter.
tween porosities obtained by experiments and those predicted by eq 5. Samples of the various limestones, of mean particle size D, = 1.20 mm, were exposed for 2 hr to the flue gas in the reactor at 850°C. The conversion of calwas determined in each case. cium oxide to sulfate, Other samples were exposed under the same conditions to the flue gas without sulfur dioxide and then analyzed to obtain X c = X c o (X = 0). The porosity of each sample was also measured after each exposure. The fractional porosities of calcined but unsulfated samples ranged from 0.485 to 0.529 cm3/cm3. If no sulfation takes place, i.e., X = 0, and the calcination is completed, i.e., X c = 1, eq 5 simplifies to
x,
e,
= 1
-
tC)’
(1 - eLs) ypLs
[
-
PCC
+ 11
( X = 0;xc = 1) (7) Assuming pLs = pcc and eLs = 0 for the four high-purity crystalline limestones in Table I, the porosities of unsulfated, calcined limestones predicted by eq 7 range from 0.515 to 0.531 cm3/cm3. Thus the experimental and the theoretical porosities agree satisfactorily for the unsulfated, calcined samples. The somewhat lower experimental values suggest that slight shrinkage of the limestone particles might have occurred. Murray, et al. (1950), reported a decrease of limestone porosity from 0.484 to 0.198 cm3/ cm3 as the temperature of calcination increased from 931 to 1283°C. In Figure 2 are plotted the results of the sulfation experiments reported here as well as similar data of Borgwardt and Harvey (1972). It is obvious that there are considerable differences in the conversions of limestone samples from the various quarries. These differences can be related neither to differences in chemical composition of the samples nor to the porosity of the calcined limestone. The porosities of the fully calcined limestones do not differ much among themselves. The straight line in Figure 2 represents the porosities predicted by eq 5 for the limestone which Borgwardt and Harvey (1972) used in their study. In these calculations it was assumed that X c = 1 ( i e . , complete conversion of the limestone by reactions I and 11) but X < 1 (only partial conversion of CaO to sulfate by reaction 111); the following values were used to evaluate the coefficients in eq 5 : y = 0.952, eLs = 0.051, p L s = pcc = 2.71, V’CO= 16.9 cm3/ mol and VCc = 52.2 cm3/mol. Here y and eLs are values measured by Borgwardt (1972); the densities and molar volumes are from Weast (1968). As shown in Figure 2, rather good agreement between theory and experiment was achieved. It is interesting to note that the porosity falls rapidly as the sulfation proceeds. Extrapolating the
Table I. Chemical Composition of Limestones
Limestone analysis (% by wt) Limestone
CaO
MgO
SiOz
A1203
Fez03
W t loss on ignition
CD CI
54.6 42.4 54.9 53.4 55.0
0.42 0.63 0.42 1.26 0.21
1.00 15.01 0.27 0.53 0.29
0.15 3.57 0.09 0.31 0.10
0.11 1.40 0.11 0.24 0.08
43.2 35.5 43.6 43.5 43.4
MO PI VI [L
(ex)o a ~ cad 0.53
...
0.53 0.52 0.53
(ex)exptl 0.49 0.52 0.53 0.51 0.52
(ex)o.,lcd was computed from eq 7. (ex)exptl was determined experimentally.
01 0
1 0.l
1
0.i
!
03
8.0
05.
0.6
Fractional Conversion of CaO, X
Figure 2. Dependence of the porosity of sulfated particles on the conversion to sulfate, X: e,limestone VI; A , limestone PI; 0 , limestone MO; e,limestone CI; X , limestone CD; 0 ,data of Borgwardt and Harvey (1972). The straight line shows the values predicted by eq 16 for the limestone of Borgwardt and Harvey, assuming Xc = 1 ( i e . , complete conversion of the limestone by reactions I and 11).
straight line in Figure 2 to zero porosity suggests an upper limit to sulfate conversion of about 60%. At this stage the original limestone is 40% calcined to oxide and 60% converted to sulfate. Further conversion of oxide to sulfate is thereafter impossible, however, because the solid is now nonporous and thus virtually impervious to the reacting gases. Since diffusion in the solid is then very small, the reaction essentially ceases. The maximum conversions attainable according to this theory can then be expressed by solving eq 5 for X with porosity set equal to zero
As can be seen from eq 8 the maximum conversions to increase with the pore volume developed by sulfate, X,,,, calcination alone, [X,( V C c - V’co)],as well as due to the initial pore volume, (eLS),of particles prior to sulfation or calcination. However, probably special conditions such as long exposure time, high concentration of sulfur dioxide, optimum temperature, and small particle size would be required to attain the maximum conversion predicted by eq 8. Conversions of the samples from five different quarries with 1.2-mm particles exposed a t 850°C for 2 hr to the flue gas containing 0.29% SO2 ranged from 0.15 to 0.30 as shown in Figure 2. With 0.9-mm particles of different limestones Potter achieved an average saturation conversion 0.45 after 3.5 hr of exposure at 980°C.
I
Pwe radius, log R
[I]
Figure 3. Pore-size distribution of the calcined (1) and sulfated (2) sample VI.
It follows from eq 5 and its graphical form in Figure 2 that the higher the porosity of unsulfated calcined particles, i e . , e, at X = 0, the greater the ultimate conversion to sulfate that can be attained. This prediction agrees well with the results of Potter, who tested a wide spectrum of carbonate rocks. Potter concludedsthat the saturation sulfation conversions of the samples correlated well with the pore volume of the unsulfated calcines. The pore size distributions of the calcined and sulfated samples VI and PI from different quarries were also determined. The conversions of the sulfated samples are shown in Figure 2. The calcined samples were exposed for 2 hr to the flue gas without SO2 a t 850°C. The pore-size distributions of the samples are illustrated in Figures 3 and 4. The curves indicate that the radii of pores are distributed over the 75-75,000 8, range. The derivative curve obtained from curve 1 in Figure 3 shows two peaks a t the radii of 290 and 10,200 A as the most probable pore sizes in calcine VI. The pores within the size range 158-630 A account for 44% of the total pore volume and those within the size range 3980-19,950 A occupy 30% of the total pore volume. The pronounced effect of the sulfation on the pore size distribution is evident from the curves for the calcined and sulfated samples in Figure 3. Two differences in trends of the individual curves are obvious. Pores larger than 1780 A are virtually nonexistent in the sulfated particles, although the most probable pore size in these particles, the value of which is 1350 A, is shifted toward larger pore sizes. Satisfactory explanation of this phenomenon has not been found. o n e possibility is that the structural transformations occurring as limestone is converted to lime are different if reaction I also takes place. The pore-size distribution of the calcined and sulfated Ind. Eng. Chern.,
Process Des.
Develop., Vol. 13, No. 3,1974
251
aio;
’ 6
11
16
1
21
31
26
Exposure Time. t,(min)
, x2
38
u
I
5.0
Figure 5. Dependence of the conversion of calcium oxide to sulfate on the exposure time: temperature, 850°C; concentration of SOz, 0.29% by volume; particle size, 0.565 mm.
Pore radius, log R [ i ]
Figure 4. Pore-size distribution of the calcined (1) and sulfated (2) sample PI.
samples PI is shown in Figure 4. The most probable pore size in the calcine is 570 A and 80% of the total pore volume is occupied by the pores within the range 355-1260 A in contrast to the distribution of calcine VI. While the pore-size distributions of calcined samples VI and PI are considerably different, the distributions of sulfated samples VI and PI are very close. The most probable pore sizes are 1350 and 1550 A, respectively. The pores ranging from 890 to 2290 A account for 80 and 90% of the total pore volume, respectively. It is of interest to note that limestone VI, the calcine of which comprised a considerable volume of pores larger than 3980 A, showed a significantly higher capacity to react with SO2 than did limestone PI. Pores of this size were scarce in calcine PI. The results of pore-size distribution measurement also indicate that an impervious shell of reaction product was not formed on the sulfated particles. In a preliminary study the reactivity of ten high-grade, commercial limestones was also tested. Some of them are listed in Table I. As the most reactive sample proved to be limestone VI, this limestone was selected to measure the rate of overall reaction I. Series of experiments were carried out at 850°C with particles of 0.565 mm average size. The concentration of sulfur dioxide in the gas was 0.29% by volume. The times of exposure of the solid to the gas were varied from 2 min to 8 hr. Except for the large exposure durations these reaction conditions of exposure time and concentration are presumed to be of practical interest for fluidized bed application in sulfur dioxide removal. In the preliminary experiments the rate of simple calcination, reaction 11, of the limestone was measured in the flue gas containing no SOZ. By following the weight loss of samples it was found that calcination was complete within 2 min of exposure. It is obvious from the curve in Figure 5 that the sulfation reaction is very rapid in its initial stage. As the exposure time continues, however, the rate of reaction decreases rapidly. After about 10-11 min of exposure about 31% of the total amount of calcium oxide in the particles was converted to sulfate with rather slow conversion thereafter. After 30 min, for example, a conversion of only 35% was attained. By graphical differentiation of the curve in Figure 5 the reaction rates dx/dt were evaluated and these results are 252
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974
b
B
i
l 5t or
Fractional Conversion of Co0.X
Figure 6. Dependence of the sulfation reaction rate on the conversion of calcium oxide: temperature, 850°C; concentration of SOz, 0.29%by volume; particle size 0.565 mm.
plotted us. conversion in Figure 6. Although the values represented by the points in Figure 6 can be taken as approximate only, it is clear that the rate of reaction plotted logarithmically decreases approximately linearly (suggesting first-order reaction rate) until the conversion reaches the value of about 30%. When conversions become higher the rate of the reaction falls very rapidly. As the conversion rose from 11.5% to 35% the reaction rate dropped by the factor of l/go. Because of differences in experimental conditions only a rough comparison can be made with the results of Borgwardt (1970) and Murthi, et al. (1971). Under comparable circumstances Murthi estimated an initial rate that was about ten times lower than that determined by Borgwardt. The initial reaction rate of limestone VI reported here lies between the values given by these authors. The conversions of the particles exposed to the flue gas for very long times are shown in Figure 7. After exposure for 2 hr to the flue gas only slight further increase of the conversion can be seen. The maximum conversion of calcium oxide obtained at an exposure time of 8 hr was 42.5%. Practically no increase of the conversion can be expected with further prolongation of the exposure time. The theoretical maximum conversion predicted by eq 8 is greater than 50%. Even under favorable conditions of reaction this value of maximum conversion was not attained in the experiments. The possible explanation can be found using the concept of “grain theory” introduced by Szekely and Evans (1970, 1971) and further developed and applied by Pigford
K
b 0.38-
4
I . 6
I I 8
Exposure Time,t.(hr)
F i g u r e 7. Dependence of s u l f a t i o n conversion of c a l c i u m oxide on t h e exposure t i m e : temperature, 850°C; c o n c e n t r a t i o n of SOz, 0.29% by volume; p a r t i c l e size, 0.565 mm.
and Sliger (1973). The theory assumes that the porous particles are comprised of grains separated by pores through which the reacting gases diffuse. The reaction starts on the fresh surface of the subparticles a t high rate. The reaction product accumulates on the surface of the grains and the diffusional resistance increases rapidly as the reaction proceeds. The volume of each subparticle grows and the porosity of the particle decreases as described here. After some elapsed time the resistance of the product shell is so large that SO2 can no longer reach the active CaO in the grain. Although the particle can still show some porosity at this stage and SO2 can slowly penetrate its interior, the reaction effectively ceases for practical purposes. There is some parallel between the present case of reaction in porous limestone and the growth of oxide layers on metals, in that the relative molar volumes of reactant and product can determine the protective qualities or porous structure of the oxide film (Pilling and Bedworth, 1923j , Selected sulfate-loaded samples were also examined by a scanning electron microscope. The microphotographs of the surfaces and the interiors of the particles show that the structure of the sulfated samples is denser than that of the calcines. Unfortunately, the technical quality of the photographs does not permit their reproduction here. The photographs are available from the authors.
Conclusion A simple structural model has been presented for the reaction of limestone with sulfur dioxide and oxygen a t high temperature. From this a relation is developed and evaluated between the porosity of the solid and the conversion. The model incorporates parameters such as the porosity of natural limestone, its true density, and the content of calcium carbonate. Satisfactory agreement has been obtained between experiment and this model. As the reaction proceeds, both the porosity of the reacting particles and the sulfation reaction rate decrease rapidly. The attainment of zero porosity by the solid corresponds to a theoretical conversion generally near 50%. Under the most favorable experimental conditions of reaction only about 42% of calcium oxide in the solid was ac-
tually converted to sulfate in the experiments, even after an exposure time of 8 hr. The reaction also affects the pore size distribution in the solid. The pores with radius larger than 1780 8, are virtually nonexistent in sulfated samples in contrast to pore distributions of the calcines. Of two samples, a calcine with a considerably greater volume of pores larger than 2980 8, showed higher capacity to react with SO2 than did the other with a smaller volume of pores in this size range. Both theory and experiment indicate that the cause of the low conversion to sulfate is the strong diffusional resistance developed in the interior of particles during the course of reaction.
Acknowledgment The authors wish to thank V. BBzant, Head of The Institute of Chemical Process Fundamentals, for the interest he has shown in this work. Valuable discussions with P. Schneider from the same Institute are gratefully acknowledged. Nomenclature e LS = porosity of natural limestone ex = porosity of sulfate-loaded particle expressed by eq 5 Mi = molecular weight, g/mol n, = number of moles t = time of exposure of solid to gas, min V I= volume, cm3 V', = molar volume of pure component, cm3/mol X = conversion of calcium oxide to sulfate, defined by. eq3, mol/mol X c = degree of calcination of calcium carbonate, defined by eq 2, mol/mol y = content of calcium carbonate in limestone, weight fraction 2 = defined quantity = (1- t L S j pLs(y/Mcc),mol/cm3 pi = true (helium) density, g/cm3
Subscripts CC = calcium carbonate GO = calcium oxide CS = calcium sulfate IM = impurities LS = limestone t = total
Literature Cited Borgwardt, R . H., Environ. Sci. Techno/., 4, 59 (1970). Borgwardt, R. H.. Harvey, R. D., Environ. Sci. Techno/., 6, 350 (1972). Hartman, M., Polek, J. R . , Coughlin, R. W., "Removal of SO2 from Flue Gas by Sorption and Catalytic Reaction on Carbon, Proceedings of the Symposium on Important Chemical Reactions in Air Pollution Control, A.I.Ch.E., Washington, D. C., 1969. Murray, J. A.. Fischer, H. C., Sabean. D. W., Proc. ASTM, 1263 (1950). Murthi, K. S.,Harrison, D., Chan. K. R., €nviron. Sci. Techno/., 5, 776 (1971). Pigford. R. L., Sliger, G., Ind. Eng. Chem., Process Des. Deveiop. 12, 85 (1973). Pilling. N. B., Bedworth, R . E.. J . Inst. Met., 29, 529 (1923). Potter, A. E., Ceram. Bull., 48, 855 (1969). Szekely, J., Evans, J. W., Chem. Eng. Sci., 25, 1091 (1970) Szekely, J., Evans, J. W., Chem. Eng. Sci., 26, 1901 (1971). Weast, R . C., "Handbook of Chemistry and Physics," 49th ed, The Chemical Rubber Co.. Cleveland, Ohio, 1968. Zielke, C. W., Lebowitz. H. E., Struck, R . T., Gorin. E., APCA J . , 20, 164 (1970).
Received for review A u g u s t 6, 1973 Accepted J a n u a r y 21, 1974
Ind. Eng. Chern., Process Des. Develop., Vol. 13,No. 3, 1974
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