Numerical Simulation of Steam Displacement of Oil in Naturally Fractured ReservoirsUsing Fully Implicit Compositional Formulation: A Comparative Analysis of the Effectsof Capillary and Gravitational Forces in Matrix/Fracture Exchange Term

摘要

A numerical simulator for steam displacement of oil fromrnnaturally fractured reservoirs is developed and tested. Thernthree-dimensional and three phase field scale model employs arncompositional dual-porosity/dual-permeability mathematicalrnformulation. Capillary, gravitational and viscous forces arernaccounted for in the mathematical model. Using a fullyrnimplicit solution scheme, the model solves for (2nHC+10)rnprimary variables simultaneously, where nHC is the number ofrnhydrocarbon components. All reservoir parameters arernformulated as functions of all the primary variables. Thernmodel is linearized using Newton-Raphson method, and thernsystem of linear equations is solved by a direct and an iterativernsolver. The model is verified against the Fourth and SixthrnSPE Comparative Solution Projects. The model is highlyrnstable for the studied extremely dynamic and stiff problems,rnaccommodating large time steps with two to three Newtonianrniterations. The simulations are carried out up to ten years torntest the features of the model for long periods of steamrninjection in naturally fractured systems.rnFluid exchange between the fracture and the matrixrnblocks due to the gravitational, capillary and viscous forces isrninvestigated for a range of naturally fractured reservoirs withrndifferent matrix block sizes and capillary pressures. Relativerneffects and relative magnitutes of these acting forces on therndisplacement of the matrix oil are analysed in these naturallyrnfractured systems undergoing steam injection. Thisrncomprehensive and comparative analysis is conducted usingrndifferent realizations of the studied naturally fractured systemsrnsuch as the dual-permeability and the dual-porosity models.rnThe steam injection operations are carried out forrnlong periods of time. The low initial pressures in the studiedrnfractured systems facilitate zooming in on and observing how,rnin particular, the capillary and gravitational forces work, and testing the model under more strained conditions in a naturallyrnfractured reservoir undergoing a steam injection operation.