Petroleum reservoirs are made of highly heterogeneous rocks. These reservoirs could be described by geostatistical models composed of millions of cells. Currently, fluid flow simulations performed within these media need upscaling (or averaging) techniques. Hence, their results are given by averaging on cells which are much larger than the geological model cells.
To overcome this problem, the Dual Mesh Method is proposed here, whose purpose is to solve the pressure equation on a low resolution grid, and then to interpolate pressure over the fine mesh by taking into account small scale heterogeneities of the medium.
The aim of this paper is this interpolation step; its implementation is presented and illustrated in a five- spot pattern for three different rock characteristics.
More and more geological models are available to describe the internal structure of oil and gas reservoirs. These models are the results of geoscientific work to integrate the data and knowledge about the field. Generally these models are represented on a very high resolution grid. It is not unusual to obtain a grid with millions of cells.
Petrophysical parameters, like porosity, absolute permeability tensors, relative and capillary curves are associated to one or to a group of cells. For simulating fluid flow in a reservoir described by such models, several problems have to be solved: optimal gridding, upscaling of petrophysical parameters, efficient and robust linear solvers, etc. The conventional method is to coarsen the mesh to obtain a lower resolution grid. The motivation of this coarsening is generally to perform fluid flow simulations at a reasonable cost. The results are averaged phase pressures and saturations, and, for compositional modelling, components of the oil or gas. The aim of this paper is to propose a method to obtain more information on the areal distribution of these results.