The widely used Cartesian coordinate grid has some disadvantages in the description of boundaries, faults and discontinuities. In addition, a five-point scheme can cause significant grid orientation effects. A ninepoint scheme reduces this effect but makes the treatment of boundaries and heterogeneities more difficult.Orthogonal curvilinear coordinate systems have improved the modeling of reservoir shape and flow geometry. Mathematically they are based on a coordinate transformation and discretization of the transformed equations in the usual manner. Due to the lack of orthogonality additional mixed derivative terms are introduced which are difficult to discretize and therefore are usually neglected. However, because grid lines have to be coordinate lines, strictly orthogonal systems are not flexible enough to describe reservoirs of complicated shape. This paper describes a practical method for using irregular or locally irregular grids in reservoir simulation with the advantages of flexible approximation of reservoir geometry, simple treatment of boundary conditions and reduced grid orientation effects.Finite difference equations are set up by the so-called balance method. This method uses an integral formulation of the reservoir model equations equivalent to the commonly used differential equations. Integrating over grid blocks results in "balance equations" for each References and illustrations at end of paper 37 block. This can be done for various types of networks formed by triangles, convex quadrangles, polar meshes, curvilinear or locally refined grids. HEINRICHS 1 has proved consistence for this discretization scheme. The mesh can be refined locally. Well locations can be selected as mesh points to ensure that they are situated in the center of grid blocks. For triangular grids, the more isotropic distribution of grid points diminishes the orientation effect significantly.Numerical examples are presented comparing the proposed difference scheme with a nine-point Cartesian scheme . The performance of the method is illustrated by symmetry elements and complex simulation problems.
This paper describes a practical method in which irregular or locally irregular grids are used in reservoir simulation with the advantages of flexible approximation of reservoir geometry and reduced grid-orientation effects. Finite-difference equations are derived from an integral formulation of the reservoir model equations equivalent to the commonly used differential equations. Integrating over gridblocks results in material-balance equations for each block. This leads to a finite-volume method that combines the advantages of finite-element methods (flexible grids) with those of finite-difference methods (intuitive interpretation of flow terms). Grid-orientation effects are investigated. For grids based on triangular elements, the more isotropic distribution of gridpoints diminishes the orientation effect significantly. Numerical examples show that the regions of interest in a reservoir can be simulated efficiently and that well flow can be represented accurately.
Copynghl 1986, Society of Petroleum EngineersThis pa~er was prepared for presentation at the 56th Calilorma Regional Meeting of me Society of Petroleum Engineers held m Oakland. CA. April2-4, 1986.Thm paper was selected for presenlat,on by an SPE Program Commmee Iollowmg review of in!ormal!oncontained m an abstract submmed by the author(s).Contents of the paper, as presented, have not been rewewed by Ihe Soc!ety of Petroleum Engmeera and are sublecl to correctionby the author(s).The malenal, as presanted, dose not necessarily reflect any poamonof the Soc!etyof Petroleum Engineers. IISofflcera, or members. Papers presented at SPE meetmga are subject to publication review by Eddonal CommMees of the SOCIetyof Petroleum Engmears. Permlaalon 10 copy IS restrictedto an abalract of not more than 300 words. Illustrationsmay not be copted.The abatract shouldcontain coneplcuousacknowledgmanlof where and by whom the papar IS presanted. Write PubhcationsManager. SPE, P O Box 833836. R!chard%m. TX 75083-3836. Telex, 730989. SPEDAL
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.