Partial-equilibrium-combined flux

To avoid solving Equation (3) for each of the ten species present, the partial-equilibrium/ combined flux technique described by Gallagher et aL (25) is used to reduce the model to a set of seven differential and three algebraic equations. The algebraic equations describe the three (equilibrium) protonation reactions. The differential equations describe the conservation of the seven invariants, where an invariant is a linear combination of species that are independent of the equilibrium reactions (25). The invariants used here are (S), (M+), (X ), (H++AH+AHS+AHS2), (A+AH), (AS+AHS), and (AS2+AHS2). The first three are species which do not participate in equilibrium reactions. The fourth encompasses all protonated species, and each of the final three includes the protonated and nonprotonated forms of the carrier or of a complex. 

Gallagher, P. M. Athayde, A. L. Ivory, C. F. "The Combined Flux Technique for Diffusion-Related Problems in Partial Equilibrium Application to the Facilitated Transport of Carbon Dioxide in Aqueous Bicarbonate Solutions" Chem. Eng. Sci., 1986b, 41(3), p. 567. 

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