Parallel Finite Element Simulation of Tracer lnjection in Oil Reservoirs
Resumo
In this work, parallel finite element techniques for the simulation of tracer injection in oil reservoirs are addressed. The pressure equation is approximated by Galerkin's method and the velocity field computed through a post-processing approach to recover the required accuracy. The concentration equation is approximated in space by the Streamline Upwind Petrov Galerkin (SUPG) plus a discontinuity-capturing operator. The resulting semi-discrete equations are approximated in time by a predictor-multicorrector algorithm. The pressure, velocity and concentration linear systems of equations are solved with parallel element-by-element iterative techniques. Performance measurements on the CRAY YMP and the CRAY C90 for the injection of tracer on a five-spot pattem with random small scale permeability variations are performed to demonstrate that the numerical techniques employed are accurate and result in a fast code.
Referências
Young, L.C. and Hemanth-Kumar, K.: "Parallel Reservoir Computations", Proc. 13th SPE Symposium on Reservoir Simulation, SPE 29104, (1995), 101-10.
Fung, L. S-K., Hiebert, A.D. and Nghiem, L.X.: "Reservoir Simulation with a Control-Volume Finite Element Method", SPERE, (Aug. 1992), 349-57.
Loula, A.F.D., Guerreiro, J.N.C., Ribeiro, F.L.B. and Landau, L.: "Tracer Injection Simulations by Finite Element Methods", 3rd Latin American/Caribbean Petroleum Engineering Conference, SPE21041, (1994), 403-410.
Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., and Mittal, S. :"Parallel Finite Element Computation of 3D Flows", IEE Computer, October (1993) 27-36.
Behr, M., and Tezduyar, T. :"Finite Element Solution Strategies for Large-Scale Flow Simulations", Comp. Meth. Appl. Mech. Engng., (1994), 112, 3-24.
Coutinho, A.L.G.A., Alves, J.L.D., Garcia, E.L.M. and Loula, A.F.D.: "Solution of Miscible and Immiscible Flows Employing Element-by-Element lterative Strategies", 3rd Latin American/Caribbean Petroleum Engineering Conference, SPE21050, (1994), 431-444.
Chavent, G. and Jaffre, J. : Mathematical Models and Finile Elements for Reservoir Simulation, Elsevier Science Publishers B.V., Amsterdam, (1986).
Brooks, A.N. and Hughes, T.J.R.: "Streamline Upwind/Petrov-Galerkin Formulation for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations", Comp. Me/h. Appl. Mech. Engng., (1982), 32, 199-259.
Hughes, T.J.R., Mallet, M and Mizukami, A.: "A New Finite Element Formulation for Computational Fluid Dynamics: II. Beyond SUPG", Comp. Meths. Appl. Mech. Engng., (1986), 54, 341-55.
Hughes, T.J.R.: The Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, (1987),803.
Gustafsson, K.: "Using Control Theory to Improve Stepsize Selection in Numerical Integration of ODE",Proc. 11th/FAC World Congress, Tallinn, Estonia, Vol.1, (1989), 139-44.
Shakib, F.,Hughes, T.J.R. and Johan, Z.: "A Multi-Element Group Preconditioned GMRES Algorithm for Nonsymmetric Systems Arising in Finite Element Analysis", Comp. Meths. Appl. Mech. Engng., (1989), 75, 415-56.
Crowl, L.A.: "How to Measure, Present, and Compare Parallel Performance", IEE Parallel and Distributed Technology., Spring (1994), 9-25.
Douglas, J., Jr., Wheeler, M.F., Darlow, B.L. and Kendall, R.P.:"Self-Adaptive Finite Element Simulation of Miscible Displacement in Porous Media", Comp. Meth. Appl. Mech Engng., (1 984), 47, 131-59.
Abbaszadeh-Dehghani, M. and Brigham, W.E.: "Analysis of Unit Mobility Ratio Well-to-Well Tracer Flow to Determine Reservoir Heterogeneity", Stanford University Technical Report, SUPRI TR-36, Stanford, CA, (1983).
Bailey, D.H., Barszcz, E., Dagum, L. and Simon, H.D.: "NAS Parallel Benchmark Results", IEE Parallel and Distributed Technology., February (1993), 43-51.
Simon, H.D., Van Dalsem, W.R. and Dagum, L. : "Parallel CFD: Current Status and Future Requirements", Parallel Computational Fluid Dynamics: Implementation and Results, Edt. H.D. Simon, MIT Press (1992), 1-32.