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<p>The mathematical model describing three-phase flow in porous media involves at least three coupled, nonlinear partial differential equations with position-dependent coefficients, making analytical solutions highly challenging. We explore various numerical solution approaches to handle the nonlinearities and coupling within these equations. This work reviews traditional methods, including fully implicit schemes utilizing the finite volume method for discretization. Furthermore, we investigate an alternative solution strategy, termed the Picard–Newton sequential method, in both simultaneous and segregated versions. The model considers isothermal, immiscible flow of oil, water, and gas, accounting for the compressibility of all three fluids and the slight compressibility of the porous medium. Application examples demonstrate three-phase flow in porous media under diverse scenarios, encompassing production wells, water-alternating gas (WAG) injection, capillary pressure, and gravitational effects. The sequential Picard–Newton method, in both versions, yielded results comparable to the traditional simultaneous solution method, while achieving a significant reduction in simulation time for the numerical experiments presented.</p>

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Numerical simulation of three-phase flow in petroleum reservoirs using a Picard–Newton sequential method

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • João Gabriel Souza Debossam,
  • Mayksoel Medeiros de Freitas,
  • Grazione de Souza,
  • Helio Pedro Amaral Souto

摘要

The mathematical model describing three-phase flow in porous media involves at least three coupled, nonlinear partial differential equations with position-dependent coefficients, making analytical solutions highly challenging. We explore various numerical solution approaches to handle the nonlinearities and coupling within these equations. This work reviews traditional methods, including fully implicit schemes utilizing the finite volume method for discretization. Furthermore, we investigate an alternative solution strategy, termed the Picard–Newton sequential method, in both simultaneous and segregated versions. The model considers isothermal, immiscible flow of oil, water, and gas, accounting for the compressibility of all three fluids and the slight compressibility of the porous medium. Application examples demonstrate three-phase flow in porous media under diverse scenarios, encompassing production wells, water-alternating gas (WAG) injection, capillary pressure, and gravitational effects. The sequential Picard–Newton method, in both versions, yielded results comparable to the traditional simultaneous solution method, while achieving a significant reduction in simulation time for the numerical experiments presented.