Nonlinear Optimization Applied to Chemical-Equilibrium Problems

摘要

The purpoe of this study was to investigate computational procedures for solving nonlinear complex chemical-equilibrium problems. Two problems were chosen. Problem 1 dealt with the methanation reaction and the water-gas shift reaction. Problem 2 dealt with three coal-gasification reactions, hydrogen and oxygen reacting with pure carbon. The problem solution is equilibrium composition at a given temperature and pressure. Each problem was posed in three different ways: (1) the K-value method solved by Newton's method; (2) minimization of Gibbs free energy as a constrained minimization problem with Lagrange multipliers using Newton's method to find the roots; and (3) minimization of the system Gibbs free energy as an unconstrained optimization problem, with constraints added as penalty functions. The function minimum was sought using a quasi-Newton method. Problem 1 was solved by Methods 1 and 2, but could not be solved by Method 3. Problem 2 was solved by Method 1 only if simplifying assumptions were made. Method 2 solved Problem 2 if the initial guess was close to the solution. Method 3 sometimes found an approximate solution to Problem 2. 2 figures, 3 tables. (ERA citation 08:025325)