Use of Corner Point Geometry in Reservoir Simulation

Abstract

Abstract At the present time, field-scale reservoir simulations are usually carried out with Cartesian grids. However, the use of these grids does not permit a good representation of reservoir geological features and reservoir description. Different approaches have been investigated to overcome the disadvantages of Cartesian grids. The corner point geometry (distorted grids) is often used as an alternative for complex full-field studies. This approach can better adapt the grid to reservoir boundaries, faults, horizontal wells and flow patterns and is easily used in standard finite difference reservoir simulators. The key problems for this technique are the preservation of the accuracy of fluid flow modelling and well treatment. In this paper, we will present a technique well suited to the corner point geometry and discuss its application range. Results are presented for test cases, comparing different control- volume type approximations. Introduction In reservoir simulation, the use of rectangular grids associated with the standard finite difference method does not permit a good representation of reservoir geological features and reservoir description, especially for faults, cross stratified beds, heterogeneities and wells. Flexible grids, such as corner point geometry, triangular grids or Voronoi grids, can be used to improve the accuracy. Among these flexible grids, the corner point geometry is the most used with the advantage of easy implementation in standard reservoir simulators and of CPU time gain due to regular matrix structure. The corner point geometry can represent complex reservoir geometries by specifying the corners of each grid block in grid building. It is well known that the use of the five-point scheme for distorted grids yields erroneous results. More accurate numerical schemes are needed with the ability to handle cross derivative terms. Several nine-point schemes, based on control volume methods, have been derived for distorted grids but no comparison is mentioned in the literature. These methods will be discussed in the paper and some examples are presented. In addition to the description of geological features, another major application of flexible grid is well modelling. However, as presented by Ding et al., caution should be used as regards the well region gridding. A sophisticated grid may not give better results if radial flow is not well approximated. In this paper, we will present the techniques for handling well in distorted grids, independently of the well location within the grid block. The technique of implementation in a 3-D reservoir simulator is also presented and some problems, such as heterogeneity modelling, are discussed. P. 451