An Efficient Fully Implicit Simulator

Abstract

ABSTRACT This paper describes PORES, an efficient general purpose implicit three-phase three-dimensional black oil reservoir simulator. Efficiency is achieved by solving the coupled equations using a new sequential method which automatically ensures material balance. A new iterative method for the solution of the linear equations is described. This method also conserves material and uses a truncated conjugate gradient technique to accelerate convergence. Simultaneous and direct solution options are also provided. PORES contains an extensive well model which is numerically stable, meets production targets precisely, and apportions flows accurately to individual layers of the reservoir model. Other practical features include a numerical aquifer model, flexible pseudo function facilities, and a two-point upstream option for the control of numerical dispersion. Two examples are presented to illustrate the use of the fully-implicit sequential method. INTRODUCTION PORES (Program for Oil Reservoir Simulation) is a new general purpose three-phase fully-implicit finite-difference oil reservoir simulator, which has been developed over the last three years on behalf of the Department of Energy, the British National Oil Corporation and the British Gas Corporation, for use in planning, developing and monitoring the operation of North Sea fields. Ouraim has been to exploit the inherent stability of the fully-implicit method and to develop new techniques to make it computationally efficient. The result is a highly flexible and robust tool which can deal with widely differing types of problem with minimum inconvenience to the user. The advantages of the fully-implicit method have long been recognised. It allows large time steps to be taken, even for traditionally difficult problems, such as those with high permeability contrasts, strong gravity segregation, small reservoir blocks with high flow rates, wells completed in many layers of the reservoir model, coning studies, etc. However, fully-implicit simulators are often assumed to be computationally expensive, partly because of the need to iterate non-linearities to convergence, and partly because the coupled sets of equations for each phase are usually solved simultaneously.