The governing equations of a compositional model for three-phase multicomponent fluid flow in multi-dimensional petroleum reservoirs are cast in terms of a pressure equation and a set of component mass balance equations in this paper. The procedure is based on a pore volume constraint for component partial molar volumes, which is different from earlier techniques utilizing an equation of state for phase fluid volumes or saturations. The present technique simplifies the pressure equation, which is written in terms of various pressures such as phase, weighted fluid, global, and pseudo-global pressures. The different formulations resulting from these pressures are numerically solved; the numerical computations use a scheme based on the mixed finite element method for the pressure equation and the finite volume method for the component mass balance equations. A qualitative analysis of these formulations is also carried out. The analysis yields that the differential system of these formulations is of mixed parabolic-hyperbolic type, typical for fluid flow equations in petroleum reservoirs. Numerical experiments based on the benchmark problem of the third comparative solution project organized by the society of petroleum engineers are presented.