Two-phase darcy flows in fractured and deformable porous media, convergence analysis and iterative coupling

F. Bonaldi, K. Brenner, J. Droniou, R. Masson

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

Abstract

We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is coupled with the mechanical deformation of the matrix assuming that the fractures are open and filled by the fluids, as well as small deformations and a linear elastic constitutive law. In this work, the model is derived and discretized using the gradient discretization method which covers a large class of conforming and non conforming discretizations. This framework allows a generic convergence analysis of the coupled model using a combination of discrete functional tools. The convergence of the discrete solution to a weak solution of the model is proved using a priori and compactness estimates. This is, to our knowledge, the first convergence result for this type of models taking into account two-phase flows and the nonlinear poro-mechanical coupling including the cubic nonlinear dependence of the fracture conductivity on the fracture aperture. Previous related works consider a linear approximation obtained for a single-phase flow by freezing the fracture conductivity. Numerical experiments are presented to illustrate this result using a Two-Point Flux Approximation cell centered finite volume scheme for the flow and a P2 finite element method for the mechanics. Iterative coupling algorithms are investigated to solve the coupled discrete nonlinear systems at each time step of the simulation.

Original languageEnglish
Title of host publicationECMOR 2020 - 17th European Conference on the Mathematics of Oil Recovery
PublisherEuropean Association of Geoscientists and Engineers, EAGE
Number of pages20
ISBN (Electronic)9789462823426
DOIs
Publication statusPublished - Sep 2020
EventEuropean Conference on the Mathematics of Oil Recovery, 2020 - Virtual, Online, United Kingdom
Duration: 14 Sep 202017 Sep 2020
Conference number: 17th
https://eage.eventsair.com/ecmor-xvii/

Conference

ConferenceEuropean Conference on the Mathematics of Oil Recovery, 2020
Abbreviated titleECMOR 2020
CountryUnited Kingdom
CityVirtual, Online
Period14/09/2017/09/20
OtherEuropean Conference on the Mathematics of Oil Recovery gathers applied mathematicians and geoscience engineers from both academia and industry to focus on recent advances in geological and reservoir modelling. The ECMOR conferences started in Cambridge over 30 years ago and through a sequence of meetings in major European centres, continue a tradition of combining high-quality mathematical science with engineering applications. Researchers and engineers from industry, government and academia meet in an informal atmosphere to focus on key technical and mathematical challenges facing the oil industry.
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