In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic -hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases. Mathematics Subject Classification (1991): 65M60

More and more computerized models provide reservoir descriptions of million ceIls, which correspond to the complexity of the heterogeneities met in natural rocks. Huid flow simulations within these media need upscaling techniques. The Dual Mesh Method considering specific discretisation for each unknown allows to solve this upscaling problem by doing adaptive homogeneisation. In this paper, non linear problems are addressed and time steps different for each resolution are considered. Applications in heterogeneous media with different mobility ratios are given and show that the dual mesh method could be applied to full field simulations with more accurate solutions than with an a priori upscaling.

C+Yr@ht 1SS5, Society of Petroleum Enginesrs, Inc This pap w prepared fcf presentation at the lSth SPE Symposium on Reaervc4r Slmulatbn heM In San Antonb, TX, U. S.A., 12-15 February 1SS5, Thle p@perwaa sslected for presentation by an SPE program CemmHtes lollowing review of infwmatbn contained in an atelmct 8ubmHted by the auttw(s), Oontents of the paper, =~nti, Mw not been revieti by the Society of Pewteum Engineers end are subject to correction by the author(s). The material, -presented, do-m nec-ariiy reflwt any pwltion d the Society of Petroleum Engineers, Its offkem, w membem, Papers presented al SPE maetl~am aubjecl to publkation review by Editorial Cemmfltaes cdthe Society 01P6trc4eumEnginaws. Permiwica to cc+y is mtdcted tOM~dtimti~tis.lll~s mytib~.~~*Mtin_w~ti .X where and by wham the papw Lspresented. Write I.ibmrian, SPE, P.O. Sox SSSRS6, Rkhardaon, TX 7!WSMSSS, U.S.A. Telex, 1SS245 SPEUT. Abstract Petroleum reservoirs are made of hi hly heterogeneous rocks. J These reservoirs COUI be described by geostatistical models composed of millions of cells. Currently, fluid flow simulations performed within these media need upscalingo(or averaging) techniques. Hence, their results are given by averaging on cells which are much larger than the geologicalmodelcells.To overcome this problem, the Dual Mesh Method is proposed here, whose purpose is to solve the pressure equation on a low resolutiongrid, and then to interpolate pressure over the fine mesh by taking into accountsmall scale heterogeneitiesof the medium. The aim of this paper is this interpolation step; its implementation is presented and illustrated in a fivespot pattern for three differentrock characteristics.References and Illustrationsat end of paper

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