APPENDIXThe geometric model ( Figure 7 ) and theory for twodimensional diffusion through a cluster of aligned elliptic cylinders are completely analogous to those for a bed of aligned spheroidal particles (Neale and Nader, 1976). Consequently, the present theory is summarized only very briefly here. Elliptic coordinates [t, q] which are related to Cartesian coordinates byequation vzc = 0 is sought which satisfies the following boundary conditions: at t = to, qe = 0 (A4) at = f l , qc = -Q cose (A51 where qc is given by the appropriate form of Fick's law; namely (A61 1 ac q e = -D adsinh2 f + sin2 q and, from basic geometry (A71 cosh t sin q dsinh2 t + sin2 q cose = -General solutions of Equation (A3) in elliptic coordinates are available in the literature (Moon and Spencer, 1961). The particular solution which satisfies Equations (A3) to (A7) may be verified to be cosh ttanh (0 sinh [ tanh 51tanh to c = co -(Qa/D) [ ]sing (A81 The effective diffusivity D, is determined (Neale and Nader, 1976) by applying the macroscopic form of Fick's law to the unit cell depicted in Figure 7; namely Q = DACA -CB)/L (AS) where L = 2a sinh sing. Combining Equations (A9) and(A8), we get the sought prediction tor U,, which is presented in liquation ( 9 ) of the main text (note that E = tanh to and I' = tanh & ) . The porosity of the unit cell must be equal to the porosity E of the original system (Neale and Nader, 1976) in order to ensure macroscopic homogeneity of the modelled system; thus ~inh to cash €0 sinh €1 cash 61

H A chemical model is described that predicts thermodynamic equilibria for aqueous magnesium-sulfite-sulfate solutions in the range 15-60 "C. If three of the following variables are specified, then the other three are predicted: partial pressure of sulfur dioxide, pH, degree of saturation with solid magnesium sulfite hexahydrate, molality of dissolved magnesium, molality of dissolved sulfite, and fraction of dissolved sulfur species oxidized to sulfate. Published experimental data are used to test the model. The model predicts that the solubility of magnesium sulfite hexahydrate is independent of liquor composition for dissolved mole ratios of sulfite to active magnesium between 1.0 and 2.0, and that the solubility increases with increasing temperature. A simple set of correlations derived from the model predicts liquor composition and sulfur dioxide partial pressure for solutions saturated with magnesium sulfite.A variety of wet sulfur dioxide (S02) scrubbing processes using magnesium have been applied or proposed (1-6). The design and operation of such magnesia-based scrubbing processes require an understanding of the lic,uor chemistry. Experimental data are available for sulfur dioxide partial pressure, pH, and magnesium sulfite solubility in some aqueous magnesium-sulfite-sulfate solutions (7-15). The chemical model described here predicts equilibria. The model can be simplified for solutions saturated with magnesium sulfite hexahydrate (MgS03~6H20); for this special case, a set of correlations derived from the model predicts liquor composition and SO2 partial pressure. The model has also been used to prepare parametric plots. Variables i n the ModelIn the formulation employed here for the Mg-SOZ-SO3system, there are 13 species: H+, Mg2+, SO,'-, HSO;, SO,(aq), SO:-, MgSOg, MgSO:, OH-, MgOH+, H20(1), SOz(g), andOther species that were considered but not retained in the model are HSO,, MgHSO;, and MgS03-3H20(s). Use of a value of 0.0104 for the dissociation constant of HSO; at 25 "C (16) indicated that dissociation is complete for magnesia-SO2 scrubbing. The ion complex MgHS0; had no significance in explaining experimental data. The hexahydrate solid form of MgS03 is thermodynamically stable, or lower in solubility than trihydrate, at temperatures as high as 59 "C (17). Although trihydrate solid is occasionally encountered at temperatures of 50-60 "C ( I ) , it is assumed here that compositions of liquors saturated with MgS03 at temperatures below 60 "C are adequately predicted from hexahydrate solubilities.The activity coefficients of the three minor ionic species included in the modei, X+, OH-, and MgOH+, are arbitrarily set equal to unity, because the concentrations of these species are too low to affect the ionic and mass balances. The equations given below to describe the system determine the activity of each of these minor species.The individual activity coefficients of the neutral dissolved species SOAaq), MgSO:, and MgSO! are also set equal to unity because data for such coefficients are scarce and repo...

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