Immiscible two-phase Darcy flow model accounting for vanishing and discontinuous capillary pressures: application to the flow in fractured porous media

Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since...

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Bibliographic Details
Published in:Computational geosciences 2017-12, Vol.21 (5-6), p.1075-1094
Main Authors: Brenner, Konstantin, Groza, Mayya, Jeannin, Laurent, Masson, Roland, Pellerin, Jeanne
Format: Article
Language:English
Subjects:
Capillary pressure
Earth and Environmental Science
Earth Sciences
Formulations
Fractures
Frameworks
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Interfaces
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Methods
Multiphase flow
Nonlinear equations
Nonlinear systems
Original Paper
Porous materials
Porous media
Pressure
Saturation
Soil Science & Conservation
Two phase flow
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Summary:Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom.
ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-017-9675-7