Abstract

This work describes an isothermal and two-dimensional fully implicit compositional model, which has been developed to the modelling of retrograde to 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 interactions have not been considered. Phase equilibrium and fluid properties have been computed by means of the Peng-Robinson equation of state. The adjustable coefficients of the equation of state have been previously determined by means of a commercial PVT simulator. previously determined by means of a commercial PVT simulator. The resulting system of partial differential equations has been discretized by the finite difference method, yielding a nonlinear 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 pentadiagonal matrix has been solved by Gaussian elimination, pentadiagonal 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.

Introduction

Numerical reservoir simulation is a very important tool in the petroleum industry. This technique can be used to planning the exploitation of new reservoirs, forecasting the behavior of old fields, to make single well studies and in researching methods to improve hydrocarbons recovery. The early models for production forecasting were based on analysis of declining curves, followed in time by material balance methods, general black oil finite difference simulators, pseudo- compositional and compositional models. In the beginning, the numerical models were built considering three phases in the reservoir (oil, gas and water), but were not able to treat the compositional variations occurring in each phase. Due to the increasing occurrence of volatile oil and retry grade gas condensate pools, reservoir studies considering compositional variation of the fluids became necessary, and the development of compositional models started. In such models, the phase equilibrium and fluid properties are obtained with an equation of state, as function of pressure, temperature and composition. These models are general and can be used to simulate several recovery process, like water injection, gas injection, gas cycling, miscible displacement, and so on. Due to its great complexity, these models require more computational efforts than the black-oil or pseudo compositional simulator. Although a semi-implicit approach can minimize this problem, the disadvantage of such formulation is that the process may become very unstable. This can restrict the model application in reservoir studies where radial geometry has to be considered or in situations where great composition variations occur. In this work, with the objective of obtaining an efficient compositional model to study volatile oil and retrograde gas condensate reservoirs, a fully implicit formulation has been selected.

This content is only available via PDF.
You can access this article if you purchase or spend a download.