Ind. Eng. Chem. Res. 1988,27, 836-845
836
for induction and displacement avoids a further complication in the adsorption process, as the additional compounds have to be separated from the isomers. Conclusion Inductive adsorption is a new separation method of geometrical and optical isomers of amines, alcohols, and amino acids. Compounds to be separated are coadsorbed with an inductive agent on a commercially available adsorbent such as silica or sulfonic resin. The selectivity is created by steric interaction between the carboneous chains of the adsorbed molecules. As far as the separation of optical isomers is concerned, the enantioselectivity comes from the inductive agent chirality. Inductive adsorption does not need support chirality and works for monofunctional compounds. In an inductive adsorption process, such as chromatography or simulated moving bed, the inductive agent can at the same time play the role of a displacement agent in charge of desorption. It has been verified, by mathematical modeling of a simulated moving bed process (Duprat, 1986) that, at any stage of the column, the amount of inductive agent is sufficient to maintain a good separation factor and a good adsorption/desorption equilibrium. Moreover, this simulation has shown that, independently of the structure requirements to induce the selectivity, the inductive agent must have a heat of adsorption close to the one of the isomers. According to Ruthven (1984), this result is consistent with the accepted principle that the the displacement agent would ideally be adsorbed with an affinity intermediate between that of the strongly and weakly adsorbed products. Registry No. Amberlyst 15, 9037-24-5; pyridine, 110-86-1; 2-picoline7109-06-8; Cpicoline, 108-89-4; 4-ethylpyridine, 536-75-4; 4tert-butylpyridine, 3978-81-2; 2,&1utidine, 108485; pentylamine, 110-58-7;2-aminopentane, 625-30-9; 2-methylbutylamine, 96-15-1; isobutylamine, 78-81-9; 1-butanol, 71-36-3; 2-butanol, 78-92-2;
methylbenzylamine, 103-67-3;2-aminoheptane, 123-82-0;nicotine, 54-11-5; silica, 7631-86-9.
Literature Cited Allenmark, S.J . Biochem. Biophys. Meth. 1984, 9, 1. Arnett, E. M.; Haaksma, R. A.; Chawla, B.; Healy, M. H. J . Am. Chem. SOC.1986,108, 4888. Benecke, I.; Konig, W. A. Angew. Chem., Znt. Ed. Engl. 1982,21,709. Bieser, H. J.; de Rosset, A. J. Die Stiirke 1977, 11, 392. Curthoys, G.; Davydov, V. Y.; Kiselev, A. V.; Kiselev, S.A,; Kuznetzov, B. V. J . Colloid Interface Sci. 1974, 48, 58. de Rosset, A. J.; Neuzil, R. W.; Tajbl, D. G.; Braband, J. M. Sep. Sci. Technol. 1980, 15, 637. Duprat, F. “La SBparation RBactive”. These de Doctorat d’Etat, Universite Aix-Marseille 111, 1986. Gates, B. C.; Lieto, J. Encyclopedia of Polymer Science and Engineering; Wiley: New-York, 1985; Vol. 2, pp 706-730. Gassend, R.; Duprat, F.; Gau, G. J. Chromatogr. 1987, 404, 87. Horvath, C. J . Chromatogr. Libr. 1985, 32, 179. Konig, W. A.; Benecke, I.; Sievers, S. J. Chromatogr. 1982,238,427. Lochmuller, C. H.; Colborn, A. S.; Hunnicutt, M. L.; Harris, J. M. Anal. Chem. 1983,55, 1344. Neuzil, R. W.; Rosback, D. H.; Jensen, R. H.; Teague, J. R.; de Rosset, A. J. CHEMTECH 1980, 10, 498. Rahman, M. A.; Ghosh, A. K. J . Colloid Interface Sci. 1980, 77, 50. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984; pp 1-27, 86-123. Seko, M.; Miyake, T.; Inada, K. Znd. Eng. Chem. Prod. Res. Deu. 1979, 18, 263. Seko, M.; Takeuchi, H.; Inada, T. Znd. Eng. Chem. Prod. Res. Deu. 1982, 21, 656. Santacesaria, E.; Morbidelli, M.; Danise, P.; Mercenari, M.; CarrB, S.Ind. Eng. Chem. Process Des. Deu. 1982,21, 440. Snyder, L. R. Principles of Adsorption Chromatography. The Separation of Non-Zonic Organic Compounds”; Marcel-Dekker: New York, 1968; pp 285-333. Snyder, L. R. J . Chromatogr. 1983, 255, 3. Snyder, L. R.; Poppe, H. J. Chromatogr. Chromatogr. Reu. 1980,184, 363. Thornton, D. P. Hydrocarbon Process. 1970, 11, 151. Tomasik, P.; Zalewski, R. Chem. Zuesti 1977, 31, 246. Received for review June 4, 1987 Revised manuscript received November 30, 1987 Accepted December 14, 1987
GENERAL RESEARCH Overlapping Grain Models for Gas-Solid Reactions with Solid Product Stratis V. Sotirchos* and Huei-Chung Y u Department of Chemical Engineering, University of Rochester, Rochester, New York 14627
General overlapping grain models were developed for gas-solid reactions with solid product. The development of the models was based on the assumption that the pore and reaction surfaces of the reacting solid may be represented by two populations of overlapping grains which share the same centers (spherical grains), axes (cylindrical grains),or planes (platelike grains) of symmetry. Specific model equations were formulated for randomly overlapping grains and applied to the sulfation of calcined limestone. The results obtained revealed strong dependence of the overall reactivity of the porous solid on grain overlapping and the type of the grain size distribution. Comparison of the results with the predictions of random pore models showed that capillary structures exhibit, in general, higher reactivities than grainy ones. 1. Introduction
Grain models have been extensively used to model structural changes in porous media undergoing reaction 0888-5885/88/2627-0836$01.50/0
with a gaseous mixture. In grain structural models, the solid phase of the porous medium is visualized as a matrix of dense solid grains of some geometrical shape (usually 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988 837 of cylindrical, spherical, or platelike geometry) which do not overlap and react in a shrinking core fashion. Grains of other shapes have also been considered. For instance, in one of the first papers describing a grain model, Barner and Mantel1 (1968) employed a matrix of dense cubes of uniform edge to model structural changes in the hydrogen reduction of manganese dioxide. Extensive work on the grain model was done by Szekely and co-workers (Szekeley and Evans, 1970, 1971; Sohn and Szekely, 1972, 1973; Szekely et al., 1973; Szekely and Propster, 1975) who applied the grain model to study gas-solid reactions with solid product using a variety of kinetic expressions. Several studies followed or appeared concurrently in the literature with the work of the above investigators. When the grain models are applied to gas-solid reactions with solid product, it is assumed that the shrinking grains of solid reactant are surrounded by a dense layer of solid product of uniform thickness. Most of the early grain models assumed that the overall grain size remained constant in the course of the reaction, but Georgakis et al. (1978) showed that density differences between the solid product and the solid reactant may readily be incorporated in the grain model by means of an equation relating the overall grain size to the local conversion. Most grain models presented in the literature and used to analyze reactivity and surface area evolution data for gas-olid reactions consider populations of nonoverlapping grains of uniform size. Structural models, for grain structures of distributed grain size were presented by Bartlett et ai. (1973) and Szekely and Propster (1975). Extensive computations performed by these authors for a variety of distributions of grain size revealed marked effects of the type of the grain size distribution on the conversion vs time behavior of gas-solid reactions. Specifically, it was found that significant differences, both qualitative and quantitative, may exist between conversion evolution results based on a grain size distribution and those obtained from a structural model for uniformly sized grains using some average grain size. Since each grain is assumed to react independently, the grain model predicts that the area of the reaction surface (reacted-unreacted solid interface for reactions with solid product or pore surfce for gasification reactions) decreases monotonically with the progress of the reaction. For a number of gas-solid systems, this behavior contradicts the experimental evidence that suggests a maximum in the variation of the reaction surface area with the conversion. Lindner and Simonsson (1981) showed that the above drawback of the grain models may be overcome if the grains in the structure are allowed to overlap. A system of infinitely long, cylindrical rods of uniform size with random intersections (“inversed” Petersen’s (1957) model) and an aggregate of uniformly sized truncated spheres in contact with each other were used by the above authors to model structural changes in gas-solid reactions with formation of solid product. The notion of overlapping grain models was further pursued by Sotirchos (1987) who showed that Avrami’s (1940) analysis of phase transformation reactions may be used to derive analytical or semianalytical expressions for the structural properties of porous media whose solid phase is represented by a population of randomly overlapping grains of uniform or distributed size. These expressions were used to derive equations for the evolution of the structural properties of porous solids undergoing gasification reactions. Because of the formation of the solid product and its deposition on the surface of the unreacted solid, the extension of the random overlapping grain models to gas-
solid reactions with solid product is not straightforward. After reaction starts and formation of solid product takes place, the porous solid is essentially characterized by a three-phase structure which is described by two receding surfaces, the solid reactant-solid product interface and the pore surface. Although the diffusion distance in the product layer is considerably smaller than the length scale for diffusion in the porous structure, the diffusivity in the product layer is also smaller, by some orders of magnitude, than the effective diffusivity in the intraparticle region. Consequently, significant concentration gradients may exist in the product layer even if there are no appreciable gradients in the gas phase. Under such conditions, the concentration of the gaseous reactant a t the reaction interface is not uniform, and different reaction rates may be exhibited by grains of different size. More complications arise if the solid product occupies more volume than a stoichiometrically equivalent amount of solid reactant, in which case pore plugging, incomplete conversion, and formation of inaccessible void space may occur. In addition to the various grain models, several pore models have been presented in the literature for gas-solid reactions with solid product (e.g., Calvelo and Cunningham (1970),Bhatia and Perlmutter, 1983; Christman and Edgar, 1983; Yortsos and Sharma, 1984; Bhatia, 1985). Pore models represent the void space of the solid particles by a population of cylindrical, usually, capillaries, and consequently they are not of diret interest to our study. A general class of random pore models for solids with a pore size distribution was formulated by our research group (Sotirchos and Yu, 1985; Yu and Sotirchos, 1987) for use under reaction conditions controlled by intrinsic kinetics and diffusion in the product layer. The models take into account the effects of pore overlap on the diffusion flux in the product layer and on the evolution of the reaction and pore surfaces and can describe almost all phenomena arising in gas-solid reactions with solid product including that of the formation of inaccessible pore space. Random overlapping grain models for gas-solid reactions with solid product are presented in the present study. The development of the structural models proceeds along the general lines of a random pore model for the above type of gas-solid reactions that was developed by Sotirchos and Yu (1985). The development of the model equations is kept general enough so that with minor modifications they can be applied to any population of overlapping grains. The models are applied to the investigation of the sulfation of calcined limestone, a gas-solid reaction that enjoys extensive use in the control of SOz emissions from fluidized-bed coal combustors. Particular emphasis is placed on the study of the effects of grain overlapping on the transient behavior of the reacting particles in conjunction with the effects of the grain size distribution. 2. Development of the Mathematical Model We consider that the solid phase of the initial porous structure can be represented by a population of grains of some geometry in the size range [Rot,Ro*],randomly distributed in the three-dimensional space. The grains are assumed to be of platelike, cylindrical, or spherical geometry, but our analysis can also be applied to populations of grains of other shapes. A population of grains of plate geometry is described by the distribution density ao(Ro),where ao(Ro)dRo is the surface area per unit volume of grains in the size range [Ro,RO+dRO]. For cylindrical grains we use the length density function lo&), where lo(Ro)dRo is the length per Fiunit volume of grains in the size range [Ro,Ro+dRo]. nally, a population of spherical grains is described by the
838 Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988
number density no(Ro),where no(Ro)dRo is the number of spherical grains per unit volume that belong to the size range [Ro,Ro+dRo](Sotirchos, 1987). We can unify the analysis for all three geometries by defining, arbitrarily, an average surface- area for parallel-plate grains, A, and an average length, L, for cylindrical grains. Following these definitions, the population of plate-shaped or cylindrical grains may also be described by the number density used for spherical grains, but now no(Ro)dRodenotes the number of grains of average surface area, A, or of average length, L , in the range [Ro,Ro+dRo]. The total volume, vox,and total surface area, SOX,of grains per unit volume are obviously given by the expressions
general class of distributed grain models (or even pore models). To this end, we define the internal reaction or pore surface area density function, u,(Ro,t) or up(RO,t), where ur,,(RO,t)dRo is the reaction or pore surface area per unit volume that belongs to grains originating from the initial pore size range [Ro,Ro+dRo].Let the intrinsic rate of the reaction, expressed in (kmol of solid S/(m2reaction surface area-s)) be denoted by R,. I t is a function of the concentration of gas A and of temperature, but the latter is assumed to be uniform throughout the volume of the solid sample. In terms of the change in R,, the reaction rate at a point of curvature R, is written, in accordance with the above assumptions, as aR,/at = -U~R,(C,,T) (4)
where s is the shape factor of the grain (0 for a plate, 1for a cylinder, and 2 for a sphere) and f is its geometric factor (2A for a plate, TLfor a cylinder, and 4u/3 for a sphere). The quantities given by eq 1 and 2 are larger than the volume fraction of the solid phase and the internal surface area of the porous solid, respectively, since their derivation does not take into consideration grain overlapping. The solid phase consists of solid S which reacts with a gaseous species A according to the general relation s(S) + VAA(g) + ... VpP(S) + ... (3)
where c, is the concentration of A at the reaction surface (at points of curvature R J . Because of very slow diffusion of species A in the product layer, its concentration at the reaction interface, cr, is lower than that in the pore network, c,. In order for points of the same radius of curvature, R,, to recede with the same velocity, the concentration of species A must be the same at such points, viz. eq 4. This assumption obviously introduces a contradiction at the intersections of grains of different size where two concentration values are ascribed to the same point. However, we should bear in mind that the assumption of uniform growth or shrinkage of grains of the same size is definitely an idealization that helps us to obtain a set of structural equations for the system. To derive the value of c, at the reaction interface of grains of size [R,,R,+dR,], we consider the diffusion of species A in the product layer surrounding grains originating from the initial size range [Ro,Ro+dRo].Using the definition of ur,,(RO,t),we have that (see also Sotirchos and Yu (1985)) a/aR [g,(Ro,t')eo a c / a ~ =] o R 5 R, (5a)
-+
producing a solid product, solid P, which is deposited on the reaction surface as a thin layer. In eq 3, ... denotes other gaseous species participating in the reaction as reactants or products. Because of the formation of the solid product, the internal structure of the reacting medium is characterized by two receding interfaces, defining the reaction and pore surfaces of the solid. Each point of the reaction surface moves in the direction normal to it with velocity proportional to the local reaction rate. In order to simplify the analysis of the pore structure evolution problem, we assume that points of the reaction surface (reacted-unreacted solid interface) of the same radius of curvature recede with the same velocity. A similar assumption was used by Sotirchos and Yu (1985) for the random pore models. Similarly, points of the pore surface of the same curvature recede with the same velocity. A direct consequence of the above assumption is that the reaction and pore surfaces of the porous solid are described by populations of overlapping grains that are concentric (spheres) to, coaxial (cylinders) to, or have the same plane of symmetry (plates) as the grains used to represent the original pore structure. A grain of initial size Ro, therefore, gives birth to two grains, one with size R,(Ro,t),smaller than Ro,that represents the reaction surface and another with size R,(Ro,t) that corresponds to the pore surface. R, may be less than or greater than Ro depending on the value of the stoichiometric volume ratio of the system, 2, which is defined as the ratio of stoichiometrically equivalent volumes of solid product to solid reactant (2 = vpup/us). Obviously, for 2 greater than one, the produced solid product occupies more space than the solid reactant it replaces, and consequently R, increases with time, while the porosity of the solid structure decreases. The development of equations describing the evolution of R, and R, with time proceeds in a similar manner as that followed by Sotirchos and Yu (1985) in their random pore model. However, a more general approach is followed here so that the derived equations may be applied to a more
a/aR [u,(Ro,t') d~~a c / a ~ =] o
R I R~ ( i f 2 > 1 )
(5b) with R, < R < R, and the following boundary conditions: c = cp at R = R, (64
Dp ac/aR = vAR,(c,,T) at R = R,
(6b)
Solving eq 5 and 6, we get
where ur,p(RO,t') dRo is the reaction or pore surface area at time t 'when R,,p(Ro,t') = R. Equations 4 and 7 describe the evolution of R, with time. For simple rate expressions, e.g., zero, first, or second order with respect to e,, eq 4 and 7 may be reduced to one equation by eliminating c,. For instance, for first-order intrinsic kinetics, we have that
The equations for the change of R, are derived by assuming that the solid product formed from reaction at the reacted-unreacted solid interface belonging to grains originating from the initial size range [Ro,Ro+dRo]is deposited as a thin layer on grains of the pore structure originating from the same initial range. A differential mass balance on the solid product gives -(z - l)(ur(Ro,t)dRo)hRo = (U,(Ro,t) & J A R , (9)
Dividing by At and taking the limit as At
-
Ind. Eng. Chem. Res., Vol. 27, No. 5 , 1988 839 0, we get that
aR, -_
--UsksCp
(19)
at
It is almost obvious from the procedure followed for the derivation of eq 4, 7, 8, and 10 that these equations are generally valid for any population of geometrical objects in the initial size range Ro. < Ro < Ro*, grains as well as pores. (Note that for pores the right-hand sides of eq 4, 7, and 8, as well as the second term in the denominator of eq 8, must be multiplied by -1.) The size of the grains used to represent the reaction surface decreases with time. Since we have a distribution of grain size, the core of different size grains will van‘ish at different times; the smaller they are, the earlier their core will vanish. Thus, after the unreacted cores of the smallest grains, of initial size Ror,vanish, eq 4,7,8, and 10 can apply only over the initial size range [Y(t),Ro*] where Y ( t )is the lower limit of the initial size range from which grains of the reaction surface of non-zero size originate. An equation for the change of Y ( t )is derived by noticing that R,(Y(t),t)= 0. Differentiating, we get w v d t = -[(a~,/at)/(a~,/a~,)i~~,=~~~~ (11) A similar expression holds for the active pore size range in the distributed random pore model of Sotirchos and Yu (1985). Equations 4, 7,8, 10, and 11 hold for any population of grains regardless of how they overlap with each other. We only need the expression for the internal surface area density function in order to obtain the specific form of these equations that applies to a given grain system. For the system of randomly overlapping grains considered in this study, Avrami’s (1940) analysis of phase transformation reactions (see Sotirchos (1987)) is used to relate the quantities given by (1)and (2) to to and So. We have that €0 = exp(-cpox) (12)
so = t o s o x
(13) The expression for ur,p(RO,t) is found by considering the expressions for the porosity and the reaction and pore surface areas of the grain structure a t time t. We have from eq 12 and 13 that
where E, is the “porosity” of the structure of the unreacted cores of the grains (i.e., the volume fraction of reacted solid and void space) and S, is its corresponding surface area. It follows from the definition of u,(Ro,t)that a,(Ro,t) = as,(>Ro)/aRo (16) where S,(>Ro)is the internal surface area that belongs to grains of initial size greater than Ro. Using eq 14 and 15, we can show that &*
Sp(>Ro)= (s + l)ftrLo R:(R0’,t)nO(RO’) mo’
(17)
and using eq 16, we finally get the expression
a,(Ro,t) = (5 + l)fe$,8(Ro,t)no(RJ (18) A similar expression, with subscript p replacing r, holds for a,(Ro,t). Introducing (18) in (8) and (lo), we obtain
For reaction rates that are not first order with respect to the gaseous reactant, eq 19 is replaced by eq 4 and 7 with U , , ~ ( Rgiven ~ , ~ )by eq 18. The “porosity” of the reaction surface structure, cr, needed in eq 19 and 20, is obtained from eq 14. The porosity of the system, cp, may be found either from an equation similar to (14) or by using the expression tp = €0 - (Z - 1)(€, - €0) (21) Finally, the conversion is obtained from the relation
The model equations may be modified for discrete distributions of grain size in a straightforward manner by use of the density functions N
no(R0) = Cn0,G(Ro- Rot) i=l
N
‘T,,p(RO,t) = f(s
+ l ) ~ ~k =,1p C n o , ~ , , ”-~ ROJ Ro
The structural model developed above consists of two partial integrodifferential equations (eq 19 and 20, for a fist-order reaction) describingthe evolution of R,(Ro,t)and Rp(Ro,t)with time, one ordinary differential equation for Y (eq ll),and eq 14 and 21 that give the values of the porosities of the reaction surface and pore surface grain structures. The model equations are thus qualitatively equivalent to those describing the random pore model for gas-solid reactions with solid product (Sotirchos and Yu, 1985),and consequently the numerical procedure used in that article can also be employed here. It consists of treating the integral that appears in the denominator of eq 11as a dependent variable, immobilizing the boundaries of the problem by introducing a new set of coordinates, and discretizing the integral and derivatives appearing in the model equations using cubic spline interpolation and collocation. The resulting set of algebraic and ordinary differential equations is then integrated in time using an appropriate integrator. 3. Results and Discussion In this section, results are presented and discussed for calcined limestone particles (CaO) reacting in an environment of sulfur dioxide and oxygen according to the reaction
-
CaO(s) + SOz + 1/z02 CaS04(s) As we mentioned in section 1,this reaction finds extensive use in the control of SO2emissions from coal-fired power plants. Based on a number of experimental reports (e.g. Borgwardt (1970),Borgwardt and Harvey (1972),Hartman and Coughlin (1974)), the reaction rate is considered of first order with respect to the concentration of sulfur dioxide. The following values were used for the kinetic and physical parameters of the system: k,’ = uSks = 4 X m4/ m2/s, us = 16.9 X m3/kmol, (kmol-s),D p = 2 X up = 52.2 X m3/kmol, eo = 0.5. These represent av-
840 Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988
x ................
a
So= 8.397 x 106m2/m3
' v?
- Overlopping Grain Model
3 v e i opptng Grain Model
so= 8 397 x
:
to= 0
00
106mZ/m
5
30 0
60 0
JiME (min)
Figure 1. Comparison of overlapping and nonoverlapping grain models. Overlapping grain sizes: spheres, 1238 A; cylinders, 825 A; plates, 413 A. Nonoverlapping grain sizes: spheres, 1786 A; cylinders, 1191 A; plates, 595 A.
erage values that were compiled by Sotirchos and Yu (1985) from a number of experimental studies. The calcined limestone particles are assumed to react at atmospheric pressure and 850 " C with 0.3% SOz (mol/mol). These are typical reaction conditions in fluidized-bed combustors or sulfation experiments. Let po(Ro) be the distribution density of the volume fraction of the solid phase; that is, @(Ro)dRo is the volume fraction occupied by grains in the size range [Ro,RO+dRo], including the overlap volume with smaller grains. If is known instead of the number density no(Ro), the latter may be determined from the former by means of the relation
For a grain system of N discrete sizes with distribution densities no(Ro)= Cz1noiS(R0 - Roil and PO(RO)= CglpoiS(Ro - R0J,eq 23 becomes
Equations 23 and 24 are derived using eq 12 and 13, written for the range [RO,RO*]. The structural model developed in section 2 suffices for the description of the transient behavior of the reacting limestone particles provided that the reaction conditions are controlled by the intrinsic kinetics of the reaction and the mass transport resistance in the product layer. If significant intraparticle concentration gradients exist in the interior of the reacting particles, an appropriate diffusion and reaction model is also needed. 3.1. Insignificant Intraparticle Concentration Gradients. Figure 1 compares the reaction trajectories (conversion vs time curves) predicted by the conventional nonoverlapping grain model with those predicted by the random overlapping grain models for three different grain geometries. The total initial porosity and surface area are the same for all cases, and uniform grain size is assumed. (The value of initial surface area shown in the figure (8.397 x lo6 m2/m3or 2.5 m2/g) was used as reference value by Sotirchos and Yu (1985) in their random pore model computations. It characterizes a calcined limestone whose pore structure is represented by a random pore system of discrete bimodal pore size distribution (500 and loo00 A),
Figure 2. Variation of the pore surface area with the conversion for the grain structures (spheres and plates) of Figure 1.
. - Nonoveriapp~ngGrain Made,
co= 0.5
d
Spherical Groins
......... .........
cr, Plale-like Grains
yx1 000
0 25
0 50
CONVERSiON
Figure 3. Variation of the reaction surface area with the conversion for the grain structure (spheres and plates) of Figure 1.
with total porosity equal to 0.5 and equally distributed between the two pore sizes.) The stoichiometric volume ratio of the CaS04-Ca0 pair is greater than one (about 3.09), and hence incomplete conversion is observed. As it can be found from eq 22 by setting E , equal to zero, the maximum conversion that can be reached by a calcined limestone with total porosity equal to 0.5 is about 48%. It is interesting to observe that, in contrast to the conventional grain model, the results from the random overlapping grain model do not exhibit a sudden interruption of the reaction at the point where plugging of the pore space takes place, a behavior that agrees with the experimental evidence. It is seen in Figure 1 that the nonoverlapping grain model predicts higher conversion at all times for all geometries. The main reason for this behavior lies in the fact that the pore surface area, S,, given by the nonoverlapping grain model at conversions different from zero is larger than that corresponding to a structure of overlapping grains (see Figure 21, and consequently, the surface area that is available for diffusion of the gaseous reactant toward the unreacted-reacted solid interface is also larger. Depending on the value of the total porosity and the geometry of the grains, the reaction surface area, S,, for overlapping grains may be larger or smaller than that for nonoverlapping grains (Figure 3). However, the available reaction surface area does not influence significantly the conversion trajectories for the CaO-S02 system since, as the simulation results of Sotirchos and Yu (1985) revealed, the overall reaction rate is mostly controlled by diffusion in the product layer. For similar reasons, the overall reactivity of the porous solid increases as the shape factor of the grain increases. For instance, notice in Figure 1that the porous solid with overlapping platelike grains exhibits the lowest reaction rate despite the fact that the corre-
Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988 841 0 0
2
?
9 i (col= 0.1,
22
RO,= 358 i)
2
8
......
Cylindrical Pore Model
- Spherical Grain Model
_ _Cylindrical Grain Model Plate-like Groin Model
cO= 0.5 so= 8.397 106m2/m3 RO2= 10,000 i
0
x
,
Spherical Gruins 0
0.0
,
I
30.0
60.0
TIME (min)
pore model
Figgre 4. Variation of conversion with time for a solid with discrete bimodal distribution of grain size and fixed initial porosity and surface area.
0
2
0
X I
I
2
52 2
8
$ 2z
2 0 2
' '
I'
/
8
/ -A: CGS Grain Size Dislribulian
; /
0
x
00
/
E:
Uniform Groin Size
So(m2/m3)
- Spherical Grains
1.4 x lo7
.....
Cylindrical Groins
9.5 x IO6
- Plate-like Groins
4.7 x lo6
30 0
60 0
TIME (min) 0
i
0 1
00
30 0
60 0
T/M€ (min)
Figure 5. Effect of the distribution of grain volume on the conversion vs time results for a solid with discrete bimodal distribution of grain size.
sponding reaction surface (see Figure 3) is greater than that for overlapping spherical grains. Figures 4 and 5 present simulation results for a solid with discrete bimodal distribution of grain size. We use the sizes and the volume fractions to describe the distribution, and we employ eq 24 to obtain the distribution density no(Ro),on which the development of the model equations is based. In Figure 4, the initial values of total porosity, surface area, and large grain size are kept constant, while we allow the distribution of grain volume, and hence the small grain size, to change. Because of the very low contribution of the large grains to the total surface area, the reaction rate decreases significantly after the small grains of solid reactant vanish. As the volume fraction of the small grains increases, the conversion at which the unreacted core of the small grains vanish also increases and eventually both small and large grains exist when the maximum conversion is reached (at about cpol = 0.3). Increasing the volume fraction of the small grains further leads to slightly lower reactivities for the calcined limestone particles mainly because of the increasing size of the small grains. In Figure 5, the distribution of grain volume between the two sizes is varied while the initial porosity and grain sizes are kept constant. Since the initial internal surface area increases with increasing volume fraction of small grains (see eq 13), the calcium oxide particles become less reactive with increasing volume fraction of large grains. Figure 6 compares the reaction trajectories predicted by the random overlapping grain model for three grain geometries with the conversion vs time results given by the
Figure 7. Conversion trajectories for a continuous distribution of grain size.
cylindrical random pore model for gassolid reactions with solid product developed by Sotirchos and Yu (1985). Like in Figure 1,we use the same initial porosity and surface area and assume uniform pore or grain size. The results show that random capillary structures are more reactive than random grain structures, and consequently identification of the type of porous structure of a given solidwhether it is grainy or capillary-may be needed before modeling of its reaction with a gaseous mixture is attempted. Conversion trajectories for a solid with continuous distribution of grain size are depicted in Figure 7. We employ the Gates-Gaudin-Schuhmann (GGS) size distribution which has been used by many investigators to describe particle mixtures resulting from crushing and grinding operations. It has also been employed by Bartlett trt al. (1973) and Szekely and Propster (1975) to represent the grain size distribution in distributed nonoverlapping grain models. The GGS distribution states that the cumulative volume fraction of grains with size smaller than Ro is given by (Ro/Ro*Im, where 0.7 < m I 1.0, and Ro* is the maximum grain size. In order to allow for finite lower limits of the grain size range, we modify the GGS distribution and write it in the form
where ao(R0)is the volume fraction of the porous solid occupied by grains smaller than R,,. If the above equation is differentiated, the following expression is obtained for ~o(Ro):
842 Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988
The corresponding number density function no(Ro)is found by introducting eq 26 in eq 23. The results of Figure 7 were obtained for m = 1 and the grain size range [200, 2000 A]. Once again we observe that the transient behavior of the reacting particles depends not only on the initial values of porosity and surface area but also on the grain size distribution. There are two reasons for which the porous solid with uniform grain size exhibits higher reactivity than the one with continuous grain size distribution. First, the slower growth of grains with size greater than the uniform grain size offsets the faster growth of the smaller grains (for spherical or cylindrical grains). Second, after the unreacted core of the smallest grains (of size Ro,) vanishes, the pore surface area that belongs to exhausted grains does not participate, according to our assumptions, in the diffusion process in the product layer, It should be pointed out that, if no unreacted cores vanish before the maximum conversion is reached, the conversion trajectories for plate-shaped grains would be independent of the form of the pore size distribution. The random pore model equations developed by Sotirchos and Yu (1985) were further simplified by assuming that the pore and reaction surfaces recede with a uniform average velocity in the direction normal to their surface. A similar simplification can also be followed for the overlapping grain model. We introduce the average growth variables qr and qp, where (27) Rr,p(Ro,t) = Ro + qr,p(t)
Uniform Growth Modei Nonuniform Growlh Model Spherical Grains
30
30.0
60.0
TIME (min)
Figure 8. Effects of nonuniform grain growth for a solid with discrete bimodal distribution of grain size. 0
(2000
A,
(R,,~=
1000 A,
1.71
107m2/m3)
so= 1.38 x IO^^^/^^)
......
Uniform Growth Modei - Nonuniform Growth Model Spherical Groins
:
0 0
Working in a similar manner as Sotirchos and Yu (1985), for a first-order reaction, we obtain the equations dqr
USkeCp
where Sr,p(Rc,q)is the reaction or surface area that belongs to grains in the initial size range [Rc,R0*3at the time instant that qr,p= q. With the exception of the negative sign that appears in the right side of eq 28 and in front of the second term of its denominator, eq 28 and 29 are identical with those describing uniformly growing or shrinking pores (Sotirchos and Yu, 1985). For the lower limit of the active grain size range, we have that Y(t) = max [Ro*,-qr(t)]. I t follows from the expression for O ~ , ~ ( R eq~18, , ~that ), for a system of overlapping grains Sr,p(Rc,q) =
(8
+ l)f~r,pJyRo*(Ro + q)'no(Ro) ~ R o (30)
The porosities of the grain structures, t, and ep, are given by eq 14 and 21, respectively, with R, given by eq 27. Needless to say, the uniform grain growth model is markedly simpler than the general model. It is described by two ordinary differential equations only (eq 28 and 29), but eq 29 is independent of eq 28, and consequently it can be integrated independently of eq 28 to give qp as a function of qr. The integration of eq 28 then follows. The effect of nonuniform grain growth on the reaction trajectories may be seen in Figures 8 and 9 for a porous solid with discrete bimodal distribution of grain size (see Figures 4 and 5 ) . We mentioned before-it can be easily shown by using eq 19-that the smaller a spherical or cylindrical grain is the faster it reacts. (The reaction rate of a platelike grain is independent of its size, and consequently the predictions of the uniform growth model are
30 0
00
60 0
TIME (min)
Figure 9. Effects of nonuniform grain growth for a solid with discrete bimodal distribution of grain size.
for structures of plate-shaped grains identical with those of the distributed growth model developed in section 2.) Therefore, the conversion at which the unreacted core of the small grains vanishes increases if uniform growth is assumed, and this eventually leads to higher reaction rates. This situation is seen in Figure 7 where under conditions of uniform grain growth all grains are active when pore plugging takes place, while the small grains of unreacted solid vanish before the maximum conversion is reached if the grains are let to react according to the general model. If all grains have non-zero core at maximum conversion, the differences in the predictions of the uniform and nonuniform growth models are not very large (see Figure 9). 3.2. Reaction with Significant Intraparticle Concentration Gradients. A diffusion and reaction model must be used along with the structural model developed in section 2 if the diffusional limitations in the intraparticle region are important. The mass balances of the gaseous reactant and solid reactant are written (Sotirchos and Yu, 1985) as
with the following boundary and initial conditions: r = 0: acp/ar = o (33) r = 1:
t = 0:
(34)
c,=o
[ = O
(35)
Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988 843 0
2
0
7l=2
1
............ .,'x A I _ .
I'
/
\
0
c c o
Experimental Dala by Harfman and Coughlin (1976)
-
Model Prediclions
0.25 mm
2
..........
0
5"?
$2
0.5 mm
..............................
....................
2
J.......................... Overlapping Grain Modei .... Nonoverlapping Groin Model
0
30.0
0
0.0282
O
0,0450
Q
0.0560 Spherical Grains
x
0
I
0
0.0
Particle Radius (cm)
8
...........
60.0
T/ME (min)
Figure 10. Effects of intraparticle diffusional limitations. The structural parameters are the same as in Figure 1for spherical grains. A, conversion vs time curves without intraparticle concentration gradients.
The porosity is given by eq 14, and the effective diffusion coefficient is computed from
where DAis the diffusion coefficient in a pore of radius 2tp/Sp,and q is the tortuosity factor of the porous structure. The reaction rate per unit volume, Bv, is found from
which is obtained by averaging the reaction rate for a grain of initial size Ro (eq 8 or 19) over all active grains. Equations 31-37 are solved numerically by using a procedure similar to that followed by Sotirchos and Yu (1985) for the random pore model. Figure 10 shows the effect of particle size on the reaction trajectories of calcined limestone particles whose porous structure is represented by spherical grains of uniform size, randomly overlapping (solid curves) or nonoverlapping (dashed curves). Curves A give the conversion vs time results without intraparticle diffusional limitations, which are also shown in Figure 1. The tortuosity factor was set equal to 2, a value that agrees with experimental reports of the literature (Huizenga and Smith, 1986), and the external diffusional limitations were neglected. Because of strong intraparticle diffusional limitations, significant concentration gradients appear in the interior of the particles, and the local reaction rate in the vicinity of their external surface is much higher than that a t the center. As a result, complete plugging of the porous structure may first occur a t the external surface and prevent further reaction in the interior, thus reducing the ultimate capacity of the calcined limestone particles for SO2 removal. Since the solid with nonoverlapping grains is more reactive (compare curves A), it is not unexpected that its external surface becomes plugged at lower conversions. The predictions of our mathematical model are compared in Figure 11 with experimental reactivity data reported by Hartman and Coughlin (1974, 1976) for limestone VI particles reacting a t 850 "C with 0.29% SOz by volume. The initial porosity and surface area used in our computations (0.52 and 1.194 X lo7 m2/m3,respectively) were calculated using the pore size distribution data of the above authors, and spherical grains of uniform size (854 A) were used. The diffusivity in the product layer was treated as a free parameter, and the best curve fitting was m2/s. If nonoverlapping grains obtained for Dp = 1 x
0.0
30.0
60.0
T/M€ (min)
Figure 11. Model predictions vs experimental reactivity data.
are assumed, a much smaller value for the product layer diffusivity is needed to approximate the experimental data. 4. Summary and F u r t h e r Remarks
A general structural model was developed for the description of structural charges in porous solids undergoing a reaction with solid product. The solid phase of the porous medium is visualized as a population of overlapping grains of spherical, cylindrical, or platelike geometry that react in a shrinking core fashion. The chief assumption involved in the construction of the mathematical model is that the reaction and pore surfaces of the porous solid can be represented by populations of overlapping grains which originate from those used to represent the original porous structure; that is, they share the same centers (spheres), axes (cylinders), or planes (plates) of symmetry. Specific model equations were formulated for porous structures represented by randomly overlapping grains and applied to study the reaction of calcined limestone with sulfur dioxide. Our numerical computations revealed strong effects of the type of the grain size distribution and of grain overlapping on the reactivity of calcined limestone, even for solids of the same initial porosity and surface area. Allowing for grain overlapping leads to smaller values of pore surface area at conversions different from zero and hence to lower mass transport rates in the product layer and lower reactivities. Comparison of the predictions of the overlapping grain model with those of the random pore model of the authors (Sotirchos and Yu, 1985) showed that a grainy structure reacts in a different manner from a capillary one. Consequently, it may be necessary to identify the type of the structure of a given solid (grainy or capillary), possibly by photomicrographic methods, before modeling of its reaction with a gaseous mixture is undertaken. The development of our structural models is based on the assumption that, after the unreacted cores of grains of some size vanish, the corresponding pore surface area does not contribute anymore to the mass transport problem in the product layer, an assumption that is rigorously valid only for nonoverlapping grains. For overlapping grain structures, the reaction surface of active grains can still be accessed by diffusing molecules that originate from the pore surface that belongs to grains without active core. Nevertheless, the diffusion path that has to be traveled by such molecules is considerably larger, and therefore this is not expected to enhance significantly the reaction rate. Of course, this observation does not apply to grain structures of uniformly sized grains. A final remark refers to the application of the developed models to gas-solid reactions with pore closure behavior.
844 Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988
If the solid product occupies stoichiometrically more volume than the solid reactant, the size of the grains used to represent the pore surface, as well as the extent of grain overlap, increases with the conversion, and consequently regions of inaccessible pore space may be formed in the interior of the reacting particles. However, the models developed in the present study consider that the total surface area of the reacting solid remains accessible to the gaseous reactants from the outset of the reaction until complete closure of the porous structure takes place. If a relation between the fraction of inaccessible pore space and solid conversion is available, the overlapping grain models may readily be modified to account for inaccessible pore volume formation by use of percolation theory concepts in a manner similar to that followed by Yu and Sotirchos (1987) for random pore models. Acknowledgment This work has partially been supported by grants from NSF and DOE. Nomenclature a_ = particle radius A = average surface area of a platelike grain c = concentration of the gas cf = concentration of the gas in the surrounding gas phase Dp = diffusion coefficient in the product layer De = effective diffusion coefficient D A = diffusion coefficient in a pore of radius (2tp/S ) f = geometric factor of grain (4a/3for a sphere, ai! for a cylinder, and A for a plate) k, = mass-transfer coefficient k,, k,’ = reaction rate constants L = average length of a cylindrical grain no(Ro)dRo = number of grains per unit volume with size in the initial size range [Ro,RO+dRo] q = uniform growth variable (see eq 27) R = distance from the center (sphere),axis (cylinder),or plane of symmetry (plate) of the grain Ro = grain size (half thickness for plates or radius for cylinders and spheres) Roe = lower limit of the grain size range Ro* = upper limit of the grain size range R,(Ro,t) = size of a grain of initial size Ro at the reaction surface at time t Rp(Ro,t)= size of a grain of initial size Ro at the pore surface at time t R, = intrinsic reaction rate, per unit of reaction surface area R, = average local reaction rate, per unit volume S = surface area per unit volume of a grain structure Sox= total surface area of grains per unit volume at time t = 0, without correction for overlapping s = shape factor of a grain ( 2 for a sphere, 1 for a cylinder, and 0 for a plate) t = time u, = specific molar volume of ith solid Y = lower limit of the size range of active grains 2 = stoichiometric volume ratio (solid product to solid reactant) Greek Symbols 6 = delta function to = initial porosity t = porosity of a grain structure tr = volume fraction of void space and reacted solid tp = porosity of the solid 7 = tortuosity factor v, = stoichiometric coefficient of the ith species = solid conversion
U ~ , ~ ( RdRo ~ , ~=)reaction or pore surface area per unit volume at time t that belongs to grains originating from the initial size range [Ro,Ro+dRo] p0= volume fraction of the solid phase cpor = total volume of grains per unit volume at time t = 0, without correction for overlapping cpg(Ro)dRo = initial volume fraction that belongs to grains in the size range [Ro,RO+dRO]
Subscripts 1,..., N = refer to the ith grain size in a discrete distribution A = refers to gaseous reactant p = refers to values at the pore surface or to its properties P = refers to solid product r, p = r or p, in this order r = refers to values at the reaction surface or to its properties S = refers to solid reactant 0 = refers to t = 0 Registry No. SO2, 7446-09-5; CaO, 1305-78-8 Literature Cited Avrami, M. “Kinetics of Phase Change. 11. Transformation-Time Relations for Random Distribution of Nuclei”. J . Chem. Phys. 1940,8, 212-224. Barner, H. E.; Mantell, C. L. “Kinetics of Hydrogen Reduction of Manganese Dioxide”. Ind. Eng. Chem. Process Des. Deu. 1968, 7, 285-294. Bartlett, R. W.; Krishnan, N. G.; Van Hecke, M. C. “Micrograin Models of Reacting Porous Solids with Approximations to Logarithmic Solid Conversion”, Chem. Eng. Sci. 1973, 28, 2179-2186. Bhatia, S. K. “Analysis of Distributed Pore Closure in Gas-Solid Reactions”. AIChE J . 1985, 31, 642-649. Bhatia, S. K.; Perlmutter, D. D. “Unified Treatment of Structural Effects in Fluid-Solid Reactions“, AIChE J . 1983, 29, 281-289. Borgwardt, R. H. “Kinetics of the Reaction of SO2 with Calcined Limestone“. Enuiron. Sei. Technol. 1970, 4, 59-63. Borgwardt, R. H.; Harvey, R. D. ”Properties of Carbonate Rocks Related to SO2 Reactivity”. Environ. Sci. Technol. 1972, 6, 350-360. Calvelo, A.; Cunningham, R. E. “Kinetics of Gas-Solid Reactions. Influence of Surface Area and Effective Diffusivity Profiles”. J . Catal. 1970, 17, 1-9. Christman, P. G.; Edgar, T. F. “Distributed Pore-Size Model for Sulphation of Limestone”. AIChE J . 1983, 29, 388-395. Costa, E. C.; Smith, J. M. “Kinetics of Noncatalytic, Nonisothermal, Gas-Solid Reactions: Hydrofluorization of Uranium Dioxide”. AIChE J . 1971,17, 947-958. Georgakis, C.; Chang, C. W.; Szekely, J. “A Changing Grain Size Model for Gas-Solid Reactions”. Chem. Eng. Sci. 1978, 34, 1072. Hartman, M.; Coughlin, R. W. “Reactions of Sulfur Dioxide with Limestone and the Influence of Pore Structure”. Ind. Eng. Chem. Process Des. Dev. 1974, 13, 248-253. Hartman, M.; Coughlin, R. W. “Reactions of Sulfur Dioxide with Limestone and the Grain Model”. AIChE J. 1976,22,490-498. Huizenga, D. G.; Smith, D. M. “Knudsen Diffusion in Random Assemblages of Uniform Spheres-. AIChE J. 1986,32, 1-6. Lindner, B.; Simonsson, D. “Comparison of Structural Models for Gas-Solid Reactions in Porous Solids undergoing Structural Changes”. Chem. Eng. Sci. 1981,36, 1519-1527. Petersen, E. E. “Reaction of Porous Solids”. AIChE J . 1957, 3, 443-448. Sohn, H. Y.; Szekely, J. “A Structural Model for Gas-Solid Reactions with a Moving Boundary-111”. Chem. Eng. Sci. 1972,27,763-778. S o b , H. Y.; Szekely, J. “A Structural Model for Gas-Solid Reactions with a Moving Boundary-IV”. Chem. Eng. Sci. 1973, 28, 1169-1177. Sotirchos, S. V. “On a Class of Random Pore and Grain Models for Gas-Solid Reactions”. Chem. Eng. Sci. 1987, 42, 1262-1265. Sotirchos, S. V.; Yu, H. C. “Mathematical Modeling of Gas-Solid Reactions with Solid Product”. Chem. Ene. Sci. 1985., 40., 2039-2052. Szekelv. J.: Evans. J. W. “A Structural Model for Gas-Solid Reactioni’with a Moving Boundary”. Chem. Eng. Sci. 1970, 25, 1091-1107. Szekely, J.; Evans, J. W. “A Structural Model for Gas-Solid Reaction with a Moving Boundary-11”. Chem. Eng. Sci. 1971, 26, 1901-1913. I
Znd. Eng. Chem. Res. 1988, 27,845-847 Szekely, J.; Propster, M. “A Structural Model for Gas-Solid Reaction with a Moving Boundary-VI”. Chem. Eng. Sci. 1975, 30,
1049-1055.
Szekely, J.; Lin, C. I.; Sohn, H. Y. “A Structural Model for Gas-Solid Reactions with a Moving Boundary-V”. Chem. Eng. Sci. 1973,223, 1975-1989. Yortsos, Y. C.; Sharma, M. ”Application of Percolation Theory to Noncatalytic Gas-Solid Reactions”. AIChE Annual Meeting, San
845
Francisco, 1984. Yu, H. C.; Sotirchos, S. V. “A Generalized Pore Model for Gas-Solid Reactions with Pore Closure Behavior”. AZChE J. 1987, 33,
382-393.
Received for review July 10, 1986 Revised manuscript received August 14, 1987 Accepted October 2, 1987
Effect of the Operating Conditions on the Preparation of Stannous Octanoate from Stannous Oxide Fernando
V. DIez, Herminio Sastre, and Jose Coca*
Department of Chemical Engineering, University of Oviedo, 33071 Oviedo, Spain
Stannous octanoate (stannous 2-ethylhexanoate) has been obtained by reaction of hydrous and anhydrous stannous oxides with 2-ethylhexanoic acid. Results for the precipitation of stannous oxide from a stannous chloride solution with sodium hydroxide are reported, viz., pH, particle size distribution, and form of the particles. The effect of temperature, speed of agitation, and percentage excess of acid in the preparation of stannous odanoate was investigated. The most effective conditions for the industrial production of stannous octanoate using this process are suggested. Stannous octanoate (stannous 2-ethylhexanoate) is among the most important industrial tin catalysts. It is used as a stabilizer of rigid poly(viny1 chloride) (Custack and Smith, 1981), in the production of rigid and flexible polyurethane foams (Karpel, 19801, and as a curing agent in vulcanizing (RTV) silicones (Fuller, 1975). The main industrial manufacturing methods used to obtain stannous octanoate follow two routes depending on the starting material used: stannous chloride (Dietsch, 1973; Rapp, 1963) or stannous oxide (Goldschmidt, 1970; Ashbel et al., 1968). Both compounds can be obtained from stannic chloride which is the final product in the chlorine process for recovering tin from tin-plate scrap (Dubois and Bourgogne, 1981; Ray et al., 1974). Stannous chloride is obtained by treating stannic chloride with granulated tin. When stannous chloride is treated with sodium hydroxide, a white precipitate of hydrous stannous oxide forms: SnC1, 2NaOH SnO-xH20+ 2NaC1
+
-
If the aqueous solution is boiled, this precipitate turns black due to dehydration. Stannous octanoate can be obtained either from hydrous or anhydrous stannous oxide by reacting it with an excess of 2-ethylhexanoicacid in an inert atmosphere: SnOz + 2C,H15COOH Sn(C7H15C00)2+ H 2 0
-
The stannous octanoate dissolved in 2-ethylhexanoicacid can be separated from the solvent by vacuum distillation. In this work, the effect of the operating conditions on the preparation of stannous oxide and stannous octanoate are reported. The particle size distribution of hydrous and anhydrous stannous oxide has been determined as a function of operating conditions. The yield of stannous octanoate has been ascertained as a function of the reaction temperature, speed of agitation, and the percentage excess of 2-ethylhexanoic acid used.
Experimental Section Stannous oxide and stannous octanoate were prepared in a 700-cm3stirred tank reactor provided with a condenser, for heating under reflux or condensing a distillate,
and ports, for adding the reactants, measuring the temperature, introducing nitrogen, or creating a vacuum in the system. The reactor was heated with an electric heater, and the rate of heating was adjusted with a PID controller. The reaction temperature was measured with a Fe-constantan thermocouple immersed in the reactor through a glass well. The particle size distribution of hydrous and anhydrous stannous oxide was determined with a Malvern 2200 apparatus, which operates on the principle of the Fraunhofer diffraction. The electronic analysis of the diffraction patterns gives the particle size distribution of the sample. The particles of stannous oxide were observed under a Lentz Wetzlar microscope with magnifying powers of lOOX, 400X, and 1OOOX. Hydrous stannous oxide was prepared by adding sodium hydroxide solution to an aqueous solution of stannous chloride at room temperature and controlling the final pH. The anhydrous stannous oxide was obtained by boiling this solution for 15 min. If stannous oxide was employed to obtain stannous octanoate, it was washed 3 times with previously boiled water, and the excess water above the precipitate was removed. The stannous oxide was then reacted with an excess of 2-ethylhexanoic acid, while the reaction mixture was heated in a nitrogen atmosphere. The water present in the stannous oxide precipitate was removed by distillation and the mixture heated under reflux at the desired temperature. Once the reaction was completed, the product was filtered and the excess free acid was removed by distillation at reduced pressure. The tin content was determined by atomic absorption (Perkin-Elmer 372 spectrometer). For tin analysis in the aqueous phase during the preparation of stannous oxide a nitrous oxide-acetylene flame was used. The analysis of tin in the organic phase, during the preparation of stannous octanoate, was carried out with an air-acetylene flame. The yield of tin octanoate was approximately taken as the ratio between the concentration of tin in the organic phase (previously filtered) and the concentration of tin in the bulk of the reaction mixture (organic phase and solids), taking into account that the volume of solids is negligible
0888-5885/88/ 2627-0845$01.50/0 0 1988 American Chemical Society
