Rate-controlled constrained-equilibrium method using constraint potentials

A method called rate-controlled constrained equilibrium has been developed. It is based on the assumption that complex chemical systems evolve through a sequence of quasi-equilibrium states determined by the instantaneous values of internal constraints on the system's composition. These constraints are imposed by slow rate-limiting reactions. The technique involves direct integration of the rate equations for the constraint potentials (Lagrange multipliers conjugate to the constraints). The method has been tested for stoichiometric mixtures of hydrogen and air in an adiabatic constant-volume chamber for a range of initial pressures between 0.01 and 1000 atm and initial temperatures between 900 and 1500 K. The state of the system was determined by imposing constraints on the total number of moles, the moles of active valence and the moles of free oxygen. The rate equations for constraint potentials were integrated in conjunction with conservation equations for a constant volume and energy mixture. The results were in good agreement with those obtained by integration of a full set of nine rate equations over a wide range of temperature and pressure.