A GENERIC GLOBAL OPTIMIZATION ALGORITHM FOR THE CHEMICAL AND PHASE-EQUILIBRIUM PROBLEM

This paper addresses the problem of finding the number, K, of phases p resent at equilibrium and their composition, in a chemical mixture of n(s) substances. This corresponds to the global minimum of the Gibbs f ree energy of the system, subject to constraints representing mb indep endent conserved quantities, where m(b) = n(s) when no reaction is pos sible and m(b) less than or equal to n(e) + 1 when reaction is possibl e and n(e) is the number of elements present. After surveying previous work in the field and pointing out the main issues, we extend the nec essary and sufficient condition for global optimality based on the ''r eaction tangent-plane criterion'', to the case involving different the rmodynamical models (multiple phase classes). We then present an algor ithmic approach that reduces this global optimization problem (involvi ng a search space of m(b) (n(s) - 1) dimensions) to a finite sequence of local optimization steps in K(n(s) - 1)-space, K less than or equal to m(b), and global optimization steps in (n(s) - 1)-space. The globa l step uses the tangent-plane criterion to determine whether the curre nt solution is optimal, and, if it is not, it finds an improved feasib le solution either with the same number of phases or with one added ph ase. The global step also determines what class of phase (e.g. liquid or vapour) is to be added, if any phase is to be added. Given a local minimization procedure returning a Kuhn-Tucker point and a global opti mization procedure (for a lower-dimensional search space) returning a global minimum, the algorithm is proved to converge to a global minimu m in a finite number of the above local and global steps. The theory i s supported by encouraging computational results.