Compositional Fluid Flow Simulation in Petroleum Reservoirs Using High-Order Locally Conservative Formulations

  • Santos Galindo, Maria Eduarda (Federal University of Pernambuco (UFPE))
  • Vasconcelos Lacerda, Igor (Federal University of Pernambuco (UFPE))
  • Maciel Lyra, Paulo Roberto (Federal University of Pernambuco (UFPE))
  • Elisiário de Carvalho, Darlan Karlo (Federal University of Pernambuco (UFPE))

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In the simulation of oil reservoirs, classic models such as Black-Oil are widely used by commercial simulators. However, for the modelling of fluid flow in complex oil reservoirs, such as in cases where the reservoir fluid is volatile and composed of several pseudo-components with different characteristics, or reservoirs that requires the use of an Enhanced Oil Recovery (EOR) process, these simpler models may not be adequate. Therefore, in those cases it is more appropriate to use a compositional model based in Equations of State (EOS). This model comprises the mass conservation equation, the Darcy´s law and fugacity constraints. In the present work, we consider an isothermal three-phase fluid flow of water, oil, and gas. We also assume that there is no mass transfer between the water and the hydrocarbon phases. Physical dispersion, and capillary effects are also neglected. To solve the system of Partial Differential Equations (PDEs) that arise from the compositional model, we have used the classical IMPEC approach and the Peng-Robinson equation of state (PR-EOS) to describe the complex phase behaviour of the fluids in the reservoir. To discretize the diffusion terms in the pressure equation, we have used the Finite Volume Method. To approximate the advective terms in the transport equation, we have used two high order formulations: the classical 2nd order accurate MUSCL method and the very high order Flux Reconstruction (FR) scheme that can be employed to discretize the hyperbolic conservation laws using general unstructured grids. These schemes can replace low-order approaches, such as the First Order Upwind (FOU) scheme, which is traditionally used in commercial simulators, obtaining more accurate solutions with reduced computational cost. To appraise the robustness of our high order formulations, we have solved some benchmark problems found in literature. Our results are very promising and accurate when compared with other schemes found in literature.