Computing Chemical Equilibrium Compositions in Multiphase Systems

Abstract

The first-order free energy minimization technique has been adapted for use in multiphase systems. It has been found that the number of phases that maybe included in a computation is independent of the phase rule.Recently, Samuels (1971) and Smith (1972) have discussed the maximum number of phases which may be included in immiscible solid-gas equilibrium computations using the

The Computation of Chemical Equilibria in Complex Systems

“…We will confine our discussion to the RAND algorithm (30), eq 8-11 of section 3.2, although is is clear that similar remarks apply to the algorithms of Brinkley (2)(3)(4)(5)(6)(7) and of Huff et al (29). We consider gas-solids problems (see section 1), since this type of system occurs frequently in metallurgical applications (16)(17)(18)(19)(20) and illustrates the difficulties involved.…”

“…Madeley and Toguri (18,19) have proposed solving such problems in a different way, by using a first-order nonstoichiometric algorithm due to Storey and Van Zeggeren (86) in the early stages of the calculation to eliminate the appropriate solids. Ma and Shipman (87) have suggested a related approach.…”

“…Recent interest in nonideality (13)(14)(15) has been primarily theoretical rather than computational, although it is clear that further developments can be expected for such problems. The late development of interest in multiphase problems (16)(17)(18)(19)(20) In this review, we first concisely formulate the mathematical problem in several equivalent ways and discuss its general properties in section 2. In section 3 we discuss algorithms for ideal systems in the light of the formulations of section 2.…”

“…He also incorporated the choice of an optimal stoichiometric matrix following Browne et al (49). Hutchinson (50), Stone (51), and Bos and Meershoek (52) suggested using the full Newton-Raphson method on eq 15, yielding = (aG/alWG/a^o (18) This entails the solution of a set of R linear equations in as many unknowns on each iteration. Since R is usually very large compared to C + 1, the number of linear equations occurring in the nonstoichiometric methods discussed in section 3.2, this approach is not especially worthwhile.…”

Some Remarks on the Calculation of Complex Chemical Equilibria by General Methods

“…Recently, a number of articles have appeared in this journal suggesting that difficulties may be encountered for specific types of equilibrium problems when such methods are used (Samuels, 1971; Madeley and Toguri, 1973a;Bjornbom, 1975). Samuels (1971) and Balzhiser et al (1972) suggested that the RAND "free-energy minimization method" (White et al, 1958) fails when too many solids are included in the compu-tation.…”