Streamline method for resolving sharp fronts for complex two-phase flow in porous media

In order to study the efficiency of the various forms of trapping including mineral trapping scenarios for CO2 storage behavior in deep layers of porous media, highly nonlinear coupled diffusion-advection-reaction partial differential equations (PDEs) including kinetic and equilibrium reactions modeling the miscible multiphase multicomponent flow have to be solved. We apply the globally fully implicit PDE reduction method (PRM) developed 2007 by Kräutle and Knabner for one-phase flow, which was extended 2019 to the case of two-phase flow with a pure gas in the study of Brunner and Knabner. We extend the method to the case of an arbitrary number of gases in gaseous phase, because CO2 is not the only gas that threats the climate, and usually is accompanied by other climate killing gases. The application of the PRM leads to an equation system consisting of PDEs, ordinary differential equations, and algebraic equations. The Finite Element discretized / Finite Volume stabilized equations are separated into a local and a global system but nevertheless coupled by the resolution function and evaluated with the aid of a nested Newton solver, so our solver is fully global implicit. For the phase disappearance, we use persistent variables which lead to a semismooth formulation that is solved with a semismooth Newton method. We present scenarios of the injection of a mixture of various gases into deep layers, we investigate phase change effects in the context of various gases, and study the mineral trapping effects of the storage technique. The technical framework also applies to other fields such as nuclear waste storage or oil recovery.

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Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions

Knodel

Kräutle

Knabner

2022

Comput Geosci

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Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method

Kong,

Rui,

Zhao

2024

J Sci Comput

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Finite-volume flux reconstruction and semi-analytical particle tracking on triangular prisms for finite-element-type models of variably-saturated flow

Selzer

Allgeier

Therrien

et al. 2021

Advances in Water Resources

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Streamline method for resolving sharp fronts for complex two-phase flow in porous media

Cited by 3 publications

References 68 publications

Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions

Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions

Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method

Finite-volume flux reconstruction and semi-analytical particle tracking on triangular prisms for finite-element-type models of variably-saturated flow

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