Different Pressure Grids for Reservoir Simulation in Heterogeneous Reservoirs

Abstract

SPE Members Abstract 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. Introduction 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. P. 563

A New Experimental Method To Determine Interval of Confidence for Capillary Pressure and Relative-Permeability Curves

“…The principle of the Dual Mesh Method (DMM) is to solve the pressure equation on the coarse grid and the saturation equation on the fine grid. The pressure data are then interpolated on the fine grid to better reproduce the saturation profile evolutions (Guerillot and Verdière, 1995). From a mathematical point of view, the DMM approach is justified by the parabolical (or elliptical) nature of the pressure equation (long range forces) compared with the hyperbolical nature of the saturation equation.…”

Validation of the multiscale mixed finite‐element method

“…Quite a number of such multiscale methods have been presented in the literature, including dualgrid methods [3][4][5][6], finite-element methods [7], mixed finite-element [8][9][10][11], and finite-volume methods [12][13][14][15][16][17]. Apart from algorithmic differences, all of these methods share the same basic concept of incorporating fine-scale information into the coarse-scale equations via some sort of numerically constructed functions.…”

Multiscale method for simulating two and three-phase flow in porous media

“…The literature contains a wide range of multiscale methods that are applicable to reservoir simulation, including dual-grid methods (Guerillot and Verdiere 1995;Audigane and Blunt 2004;Arbogast 2002;Arbogast and Bryant 2002), (adaptive) localglobal methods (Chen et al 2003;Chen and Durlofsky 2006), finite-element methods (Hou and Wu 1997), mixed finite-element methods (Chen and Hou 2002;Aarnes 2004;Aarnes and Efendiev 2008;Alpak et al 2011;Pal et al 2012), and finite-volume multiscale methods (Jenny et al 2003;Lee et al 2008;Jenny 2009, 2011;Parramore et al 2012). Although the methods have certain algorithmic differences, they share a common basic concept for incorporating fine-scale into coarse-scale flow equations.…”