A new approach and a comparative study of numerical solution strategies for slightly compressible and immiscible two-phase flow in oil reservoirs with the finite volume method

Mayksoel Medeiros de Freitas¹; Leonardo Figueira Werneck¹; Grazione de Souza¹; Helio Pedro Amaral Souto¹

¹ Polytechnic Institute, Rio de Janeiro State University

doi:10.20906/CPS/CILAMCE2017-0849

Resumo

We introduced a new approach and performed a comparative study of some of the most well-known strategies for solving the algebraic equations system arising from the space and time discretization of the governing equations for a three-dimensional slightly compressible two-phase (water-oil), in a heterogeneous oil reservoir. The flow is considered to be isothermal, the fluids immiscible and we take into account the compressibility of the fluids and the porous matrix. A model is also used for the well-reservoir coupling considering specified flow rates of injection and production. The resolution strategies considered were the Fully Implicit method (Newton's method), the IMPES method (IMplicit for Pressure and Explicit for Saturation), the Sequential method (implicit for pressure and saturation) and a new Hybrid method (implicit for pressure and the Newton's method for saturation), which represents the main contribution of this work. Verification of the numerical approaches was done considering the Buckley-Leverett problem. As an application example, we considered the problem of production in a Five-Spot well arrangement. For all tests considered in this work the Hybrid method presented the best performance results.

Palavras-chave: Oil reservoir; Finite Volume Method; Two-phase Flow; Resolution Strategies; Fully Implicit Method; IMPES Method; Sequential Method; Hybrid Method