Non-isothermal Compositional Two-Phase Darcy Flow: Formulation and Outflow Boundary Condition

Beaude, Laurence; Brenner, Konstantin; López, Simón; Masson, Roland; Smaï, Farid

doi:10.1007/978-3-319-57394-6_34

Cited by 1 publication

(1 citation statement)

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“…Subsequent works by Ben Gharbia [6], Ben Gharbia and Jaffré [10], Masson et al [26,27] and Beaude et al [4] testified to the superiority of the unified formulation over the variable-switching one regarding computational time in simple cases, i.e., with Henry's law for fugacity coeffients. Another series of works at IFPEN [7,8,24,31] seem to reach the opposite conclusion for realistic fugacity coefficients given by cubic equations of state, such as Peng-Robinson's law.…”

Section: Motivation and Objectivesmentioning

confidence: 99%

A new approach for solving nonlinear algebraic systems with complementarity conditions. Application to compositional multiphase equilibrium problems

Gharbia

Haddou

et al. 2021

Mathematics and Computers in Simulation

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We present a new method to solve general systems of equations containing complementarity conditions, with a special focus on those arising in the thermodynamics of multicomponent multiphase mixtures at equilibrium. Indeed, the unified formulation introduced by Lauser et al. [Adv. Water Res. 34 (2011), 957-966] has recently emerged as a promising way to automatically handle the appearance and disappearance of phases in porous media compositional multiphase flows. From a mathematical viewpoint and after discretization in space and time, this leads to a system consisting of algebraic equations and nonlinear complementarity equations. Such a system exhibit serious convergence difficulties for the existing semismooth and smoothing methods. This observation led us to design a new strategy called NPIPM (Non-Parametric Interior-Point Method ). Inspired from interior-point methods in optimization, the technique we propose avoids any parameter management while ensuring good theoretical convergence results. These are validated by extensive numerical tests, in which we compare NPIPM to the Newton-min method.

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