This paper presents a consistent implicit in pressure and saturations approach for solving the equations of a fully compositional, isothermal, three phase, numerical simulator. It is based on an original choice of the primary variables for which the partial derivatives for all the pertinent equations are written. For three phase flow (oil, gas, and water) of water plus Nc hydrocarbon components, the primary variables are the pressure P, the water and gas saturations Sw and Sg (Sw and one compositional variable Co for single phase oil or gas), plus Nc-2 compositional variables Ci. A given set of Ci variables characterizes the composition of the oil and gas phases in thermodynamic equilibrium at pressure P, in the Nc component system. Their choice as well as their use with a cubic equation of state are discussed in the paper.
This new approach is supported by a simulation test and is shown to be a suitable compromise between the explicit scheme, which lacks numerical stability, and the fully implicit scheme for which computer time and memory requirements may be prohibitive as the number of hydrocarbon components increases.