Streamline Methodology using An Efficient Operator Splitting for Accurate Modelling of Capillarity and Gravity Effects

Abstract

Abstract The flow of hydrocarbons in a reservoir is a very complex process involving the interaction of several fluids and rock. Accurate and fast modelling of this complex flow is crucial to optimize reservoir exploitation. We have developed a 3D streamline based reservoir simulator for two phase (water and oil) incompressible flow. In this case, the model simplifies to a non-linear elliptic equation for the pressure, coupled to an equation for the evolution of saturation. The streamline method assumes that displacement along any streamline follows a one-dimensional solution, and that there is no communication among streamlines, so that the 3D saturation equation is decomposed into a set of one-dimensional problems. It takes advantage of the fact that the pressure varies slowly compared to saturation and therefore needs to be updated after several steps in the saturation equation. The decoupling of the pressure equation from the saturation equation speeds up the simulation orders of magnitude with respect to the conventional finite difference method, and this increase in speed is very important in modern reservoir engineering. The method is best suited to problems dominated by displacement as opposed to gravity and capillarity. However, these effects can be taken into account in the model and we will show how to use operator splitting techniques to this end. We will describe the main characteristics of the streamline method, analyze different numerical methods to solve the non-linear hyperbolic equation along streamlines, and present numerical results to show the effects of capillarity in the production of the reservoir.