{"title":"The Transformational Decomposition (TD) Method for Compressible Fluid Flow Simulations","authors":"G. Moridis, D. A. McVay","doi":"10.2118/25264-PA","DOIUrl":"https://doi.org/10.2118/25264-PA","url":null,"abstract":"A new method, the Transformational Decomposition (lD) method, is developed for the solution of the Partial Differential Equations (PDE's) of single-phase, compressible liquid now through porous media. The major advantage . of the TD method is that it eliminates the need for time discretization, and significantly reduces space discretization, yielding a solution semi-analytical in time and analytical in space. There are two stages in the lD method: Introduction In transient now through porous media, the Partial Differential Equation (PDE) to be solved is obtained by combining appropriate forms of Darcy's Law and the equation of masS conservation, yielding: a Decomposition stage and a Reconstitution stage. In the Eq. 1 is generally nonlinear, and in all but the siInplest DecompOSition stage the original PDE is decomposed by problems is solved numerically. The basic concept of any using a Laplace transform for time, and successive levels numerical method is the substitution of a set of algebraic of finite integral transforms for space. Each level of finite equations for the original PDE. Instead of solving for the integral transform eliminates one active dimenSion, until a continuous smooth function p(x, y, z, t), the space domain small set of algebraic equations remain. The original PDE (x, y, z) is subdivided in ND subdomains, and the. tinte t is thus oecomposed into much simpler algebraiC equations, is discretized in NT timesteps; NT sets of approximations for which solutions are obtained in the transformed space. p of the solution are obtained at the N D predetermined In the Reconstitution stage, solutions in space and time points in space. A PDE problem with a continuous smooth are obtained by applying succesive levels of inverse transsolution surface is thus reduced to· a set of algebraic forms. In contrast to traditional numerical techniques, the equations, which are easier to solve and provide a solution . lD method requires no discretization of time and only a. arithmetically \"close\" to the true solution, from which they very coarse space discretization for stability and accuracy. differ by the truncation error e = p _ p. _ The TD method is tested against results from oneand Despite their power and flexibility, numerical solutwo-dimensional test cases obtained from a standard Finite tions have some serious drawbacks. Minimization of the Difference (FD) simulator, as well as from analytical moderror introduced by the numerical approximation of the spaels. The TD method may significantly reduce the computer tial derivatives in the PDE's dictates the discretization of memory requirements because discretization in time is not the space domain into a large number of subdomains at all needed, and a very coarse grid corresponding to inhomoof which solutions must be obtained (whether desired or geneous regions suffices for the space discretization.· Exnot). This increases the execution time requirements and ecution times may be substantially reduce","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"59 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132497023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oil/Water Relative Permeability Estimation From Fall Off Tests","authors":"E. Oliveira, K. Serra","doi":"10.2118/26984-PA","DOIUrl":"https://doi.org/10.2118/26984-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"202 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120948782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Polymer-Enhanced Foams Part 1: Laboratory Development and Evaluation","authors":"R. D. Sydansk","doi":"10.2118/25168-PA","DOIUrl":"https://doi.org/10.2118/25168-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124213388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Component Partitioning in CO2/Crude Oil Systems: Effects of Oil Composition on CO2 Displacement Performance","authors":"K. D. Hagedorn, F. Orr","doi":"10.2118/25169-PA","DOIUrl":"https://doi.org/10.2118/25169-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127862223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Procedure for the Phase-Equilibrium Computations in the Compositional Reservoir Simulator","authors":"M. Litvak","doi":"10.2118/25252-PA","DOIUrl":"https://doi.org/10.2118/25252-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"54 33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116985215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Demulsifying the Produced Fluids from Marathon's M-1 Micellar/Polymer Project","authors":"R. B. Duke","doi":"10.2118/24539-PA","DOIUrl":"https://doi.org/10.2118/24539-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"17 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116064285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling Formation Damage Caused by kaolinite From 25 to 300 degrees Centigrade in the Oil Sand Reservoirs of Alberta","authors":"W. Gunter, Z. Zhou, E. Perkins","doi":"10.2118/23786-PA","DOIUrl":"https://doi.org/10.2118/23786-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114490908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Higher Order Flux Update Function Method for Reduction of Numerical Dispersion and Grid Orientation Effect in Reservoir Simulation","authors":"D. Shin, A. R. Merchant","doi":"10.2118/25600-PA","DOIUrl":"https://doi.org/10.2118/25600-PA","url":null,"abstract":"","PeriodicalId":249085,"journal":{"name":"SPE Advanced Technology Series","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126459650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}