Chemical Reaction Equilibrium Analysis: Theory and by William R. Smith PDF

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Additional info for Chemical Reaction Equilibrium Analysis: Theory and Algorithms

Sample text

For these algo­ rithms, the nurnber of variables is (N' + M), a1though for ideal systems, 119 Structul"e of Otaptcr this number is usually effectively reduced to (lI! number of phases in the system. + 7T), where rr is the In summary, equilibrium algorithms can be examined from several points of view. This chapter is structured to focus on the fourth classification, but reference is also made to the others where appropriate. We have adopted the philosophy that, by taking various points of view into account and by studying the structures of some representative algorithms, we can better understal1d the basic features of any equilibrium algorithm.

2 algorithm. = In n,. ". :'nlm) S '1r-'(( " l l k -'-- b(rn)t: } lml . = b} - bJ ' j = 1. 2, .... 3-36) Flow chart for the RAND and satisfies the element-abundance constraints, and iterations proceed until the equilibrium conditions are satisfied. In contrast, in the Brinkley variation, n(m) satisfies the equilibrium conditions on each iteration, and iterations proceed until the element-abundance constraints are satisfied. Since In n i are the independent variables. it is convenient to set (cf.

3-16, and the algorithm may iterate to satisfy both theseconditions simultaneously. It is usually called a jree-energy-minimization method. Finally, the RAND algorithm solves a numerical problem in which there are essential1y (M + 7T) variables that must be ultimately determined. These are the M Lagrange multipliers and the 7T values of the total number of moles in each phase. 3-27. We have demonstrated the reduction for the case 7T = 1. In general, for nonideal systems (Chapter 7), we carmot reduce the number of equations in the set.

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