A nonequilibrium heat and mass transfer model is presented for the steady-state operation of a rectifying column, employed in ammonia-water absorption refrigeration systems to dehumidify the ammonia vapor leaving the generator. The thermodynamic state relations of the mixture are derived from two equations representing the Gibbs free energy in terms of temperature, pressure and concentration for the liquid and the vapor phases. Two of the transport properties, surface tension and liquid diffusivity required original relations, as presented here in. The resulting nonlinear system of equations is solved by efficient use of the Newton-Raphson code that minimizes the order of the Jacobian matrix without losing any model information or the quadratic order of convergence of the numerical method. Accuracy tests are performed by grid refinement and by comparison with results in the literature. A sensitivity study is presented showing the influence of some alternative methods for estimation of the transport properties on the temperature and concentration profiles.

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.