Fully Implicit Compositional Modelling of Gas Condensate and Volatile Oil Reservoirs

Abstract

ABSTRACT This work describes an isothermal and two-dimensional fully implicit compositonal model, which has been developed to the modelling of retrograde gas condensate and volatile oil reservoirs. The model considers oil, gas and water phases, and may be used with either cartesian (x-y) or cylindrical (r-z) grids. Water has been considered to be immobile and slightly compressible, and water saturation is a function of pressure. Instantaneous thermodynamic equilibrium has also been considered, with no water dissolved in the hydrocarbon phases and no hydrocarbon dissolved in the water phase. Fluid-rock iteractions have not been considered. Phase equilibrium and fluid properties have been computed by means of the Peng-Robinson6 equation of state. The adjustable coefficients of the equation of state have been previously determined by means of a comercial PVT simulator. The resulting system of partial differential equations has been discretized by the finite difference method, yielding a non-linear system of algebraic equations. The one-point upwind scheme has been selected to compute the molar densities and the saturation dependent properties. The Newton-Raphson method has been selected to solve the resulting non-linear numerical problem. The block penta-diagonal matrix has been solved by Gaussian elimination, which takes advantage of the matrix sparcity. The grid-block saturation pressures are updated at the end of each timestep. Due to the problem complexity, the validation of the model has been provided to the steady-state flow case, which presents a known analytical solution for compositions and saturations. Examples of application of the computer model to depletion process and well testing are presented.