Numerical Simulation of the Imbibition Process in Fractured Reservoirs

Abstract

This paper describes an algorithm for simulating matrix fractured reservoirs. Response curves for individual matrix blocks developed by numerically simulating the inhibition processes in individual blocks for several sets of boundary conditions are coupled in an iterative process to describe vertical water movement and oil production in the simulator. This simulator can be used to estimate the efficiency of waterflooding in matrix fractured reservoirs as a function of reservoir and matrix block description and planned waterflooding rates. The simulator has been used on an example reservoir to develop some general results and conclusions. For matrix fractured reservoirs, ultimate recoveries will be greater if there are relative few blocks in the vertical direction and flooding rates are kept low. If individual blocks are tall and flooding rates are high low recoveries can be expected. The water oil ratio increases more rapidly in matrix fractured reservoirs after water breakthrough than in homogeneous reservoirs. Introduction The objective of this study is to investigate the importance of the inhibition phenomenon in fractured reservoirs. The performance of such reservoirs is difficult to predict because of the presence, within the reservoir of high permeability regions where the flow velocity is large and the potential gradient negligible. The injection of water in this case raises some important questions such as the efficiency of this process and the final recovery of oil. Among the numerous papers treating reservoir engineering problems by numerical methods, only few concern heterogeneous reservoirs. Despite the effectiveness of the implicit and semi-implicit numerical methods used, discontinuities in the reservoir characteristics make it difficult to numerically study the displacement of oil by water in fractured reservoirs. After a review of the literature, the prototype of fractured reservoirs used is described. The simulation of the flow in the matrix as well as in the fractures is very difficult when the fracture permeability is large because of numerical stability. To avoid this problem, a different approach is used here. Only the problem, a different approach is used here. Only the flow in the matrix is taken into account while the fractures are considered as boundaries for the system. This assumes of course that the fractures permeability is infinite. During the injection of water in a fractured reservoir, the matrix block production of oil by imbibition depends on the situation of the block at each time step. A block entirely surrounded by water produces less oil than a block invaded by water from produces less oil than a block invaded by water from only one side for example. In this study, it is assumed that the behavior of the matrix blocks producing by imbibition is known. Particularly it is assumed that the matrix block Particularly it is assumed that the matrix block production of oil by imbibition is given as function production of oil by imbibition is given as function of time for different situations of the block by reference to the water level. The model described in this paper uses these functions to simulate fractured reservoirs by an iterative method. An application is given in the last part to illustrate the utilization of this method in a hypothetical fractured reservoir case. II - STATEMENT OF THE PROBLEM Most of the methods known for solving reservoir engineering problems concern homogeneous and isotropic porous media, despite the fact that all petroleum porous media, despite the fact that all petroleum reservoirs are more or less heterogeneous. Stratified reservoirs are one example of heterogeneous reservoirs that have been studied in the literature. Another important class of heterogeneous reservoirs is what has been called two porosity systems such as naturally fractured or vugular reservoirs. In this kind of system, the primary porosity which is intergranular is the matrix porosity. The secondary porosity is constituted of fractures randomly distributed and sometimes well interconnected.