A comparative study on some methods for computing equilibrium concentrations

Abstract It is demonstrated that almost all the methods applied to computing equilibrium concentrations in ideal systems of a given number of phases can be derived via applying Newton's iteration formula to the system of equations describing equilibrium and mass-balance. In practical realization either concentrations or their logarithms are treated as unknowns; this results in two mathematically different types of algorithms. Proper transformations of the inverses of the Jacobians give various numerically different versions. Most of these may be identified with well-known literature methods, some of which result from applying Newton's treatment and some resulting from free-energy minimization (RAND). An important property of the algorithms which use concentrations as unknowns is that, regardless of the initial approximations, the mass-balance equations should hold from the second iteration. For algorithms which use logarithms of concentrations, the equilibrium equations should hold. However, in making use of these properties and thus omitting unnecessary terms the result can be perturbed solutions because of round-off error. The efficiency and stability of the algorthims under consideration is discussed on the bases of numerical examples.