6.6 EXPEDITING THE SOLUTION OF SYSTEMS OF NONLINEAR ALGEBRAIC EQUATIONS 6.6.1 Concepts Demonstrated Complex chemical equilibrium calculations. 6.6.2 Numerical Methods Utilized Solution of systems of nonlinear algebraic equations, and techniques useful for effective solutions and for examining possible multiple solutions of such systems. 6.6.3 Problem Statement The following reactions are taking place in a constant volume, gas-phase batch reactor: A+BC+DB+CX+YA+XZ A system of algebraic equations describes the equilibrium of the preceding reactions. The nonlinear equilibrium relationships utilize the thermodynamic equilibrium expressions, and the linear relationships have been obtained from the stoichiometry of the reactions. KC1=CACBCCCDKC2=CBCCCXCYKC3=CACXCZ