Element Variables and the Solution of Complex Chemical Equilibrium Problems

Abstract

— A dramatic simplification of the chemical equilibrium problem is obtained through the introduction of "element variables." Element variables formalize an algebraic reduction of the polynomial equations for chemical equilibrium. Their use is one part of a methodology which includes scaling of the equations and solving them by a modification of Newton's method. The solution technique we propose converges to the physical solution from virtually any starting point. This methodology is a significant advance in solving chemical equilibrium problems. It does not require the specification of equilibrium reactions or the choice of component species. It is especially suited to the development of equilibrium solvers for large computer models of physical systems. an application where speed and reliability are important.