Globally convergent computation of chemical equilibrium composition

We report the Newton-Raphson based globally convergent computational method for determination of chemical equilibrium composition. In the computation of chemical equilibrium composition, an appearance of nonpositive value of number of moles of any component leads to discrepancy. The process of conditional backtracking and adaptive set of refining factors for Newton-Raphson steps are employed to resolve the problem. The mathematical formulation proposed by Heuze et al. (J Chem Phys 1985, 83, 4734) has been solved using proposed computational method, instead of empirical iterative formulation, as proposed by them. Results for the same numerical example, used by Heuze et al. (J Chem Phys 1985, 83, 4734) and White et al. (J Chem Phys 1958, 28, 751) are presented in addition to decomposition of Cyclotrimethylenetrinitramine for fixed temperature and pressure. It is observed that the proposed method is efficient and globally convergent. An even noteworthy finding is that the set of refining factors can be chosen from the range 0.1 to eta, where eta may be greater than one depending on how smoothly system of nonlinear equations is dependant on corresponding variable. Related analysis and results are discussed.