A nonlinear domain decomposition method to couple compositional gas liquid Darcy and free gas flows

International audienceA domain decomposition algorithm is proposed to couple at the interface a gas liquid compositional Darcy flow and a compositional free gas flow. At each time step, our algorithm solves iteratively the nonlinear system coupling the compositional Darcy flow in the porous medium, the RANS gas flow in the free flow domain, and the convection diffusion of the species in the free flow domain. In order to speed up the convergence of the algorithm, the transmission conditions at the interface are replaced by Robin boundary conditions. Each Robin coefficient is obtained from a diagonal approximation of the Dirichlet to Neumann operator related to a scalar simplified model in the neighbouring subdomain. The efficiency of our domain decomposition algorithm is assessed in the case of the modelling of the mass exchanges at the interface between the geological formation and the ventilation galleries of geological radioactive waste disposal

Formulations of two phase liquid gas compositional Darcy flows with phase transitions

International audienceIn this article, three formulations of two phase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so called natural variable formulation commonly used in reservoir simulation, the second has been introduced in [14] and uses the phase pressures, saturations and component fugacities as main unknowns, and the third is an extension to general compositional two phase flows of the pressure pressure formulation introduced in [2] in the case of two compo-nents. The three formulations are shown to lead to equivalent definitions of the phase transitions for our gas liquid thermodynamical model. Then, they are compared numerically in terms of solution and convergence of the Newton type non linear solver on several 1D and 3D test cases including gas appearance and liquid disappearance. The 3D discretization is based on the Vertex Approximate Gradient (VAG) scheme [10] and takes into account discontinuous capillary pressures

Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces

We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled by the fluids and small deformations with a linear elastic constitutive law are considered in the matrix. As opposed to [10], the phase pressures are not assumed continuous at matrix fracture interfaces, which raises new challenges in the convergence analysis related to the additional interfacial equations and unknowns for the flow. As shown in [16, 2], unlike single phase flow, discontinuous pressure models for two-phase flows provide a better accuracy than continuous pressure models even for highly permeable fractures. This is due to the fact that fractures fully filled by one phase can act as barriers for the other phase, resulting in a pressure discontinuity at the matrix fracture interface. The model is discretized using the gradient discretization method [22], which covers a large class of conforming and non conforming schemes. This framework allows for a generic convergence analysis of the coupled model using a combination of discrete functional tools. In this work, the gradient discretization of [10] is extended to the discontinuous pressure model and the convergence to a weak solution is proved. Numerical solutions provided by the continuous and discontinuous pressure models are compared on gas injection and suction test cases using a Two-Point Flux Approximation (TPFA) finite volume scheme for the flows and $P_2$ finite elements for the mechanics.Comment: 32 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2004.0986

Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow

International audienceA model coupling a three dimensional gas liquid compositional Darcy flow and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous medium account for the molar normal fluxes continuity for each component, the gas liquid thermodynamical equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository. The spatial discretization is essentially nodal and based on the Vertex Approximate Gradient (VAG) scheme. Compared with classical nodal approaches such as the Control Volume Finite Element method, the VAG scheme has the advantage to avoid the mixture of different material properties and models in the control volumes located at the interfaces. The discrete model is validated using a quasi analytical solution for the stationary state, and the convergence of the VAG discretization is analysed for a simplified model coupling the Richards approximation in the porous medium and the gas pressure equation in the gallery

Two-phase Discrete Fracture Matrix models with linear and nonlinear transmission conditions

International audienceThis work deals with two-phase Discrete Fracture Matrix models coupling the two-phase Darcy flow in the matrix domain to the two-phase Darcy flow in the network of fractures represented as co-dimension one surfaces. Two classes of such hybrid-dimensional models are investigated either based on nonlinear or linear transmission conditions at the matrix-fracture interfaces. The linear transmission conditions include the cell-centred upwind approximation of the phase mobilities classicaly used in the porous media flow community as well as a basic extension of the continuous phase pressure model accounting for fractures acting as drains. The nonlinear transmission conditions at the matrix-fracture interfaces are based on the normal flux continuity equation for each phase using additional interface phase pressure unknowns. They are compared both in terms of accuracy and numerical efficiency to a reference equi-dimensional model for which the fractures are represented as full-dimensional subdomains. The discretization focuses on Finite Volume cell-centred Two-Point Flux Approximation which is combined with a local nonlinear solver allowing to eliminate efficiently the additional matrix-fracture interfacial unknowns together with the non-linear transmission conditions. 2D numerical experiments illustrate the better accuracy provided by the nonlinear transmission conditions compared to their linear approximations with a moderate computational overhead obtained thanks to the local nonlinear elimination at the matrix-fracture interfaces. The numerical section is complemented by a comparison of the reduced models on a 3D test case using the Vertex Approximate Gradient scheme

Experimental study of corrosion-induced degradation of reinforced concrete elements

Corrosion of steel reinforcement is the main cause of damage for reinforced concrete structures. Iron oxides produced during the corrosion process can induce concrete cracking, loss of adhesion at the steel-concrete interface, loss of reinforcing bar cross-section and even spalling of the concrete cover. In the presented research, the durability problems related to the corrosion of the reinforcement are investigated by combining experimental and numerical studies. However, this paper particularly focuses on the experimental methodology used for the time evolution of damages (steel corrosion products formation and crack patterns) induced by the accelerated corrosion test. The accelerated corrosion tests were carried out by applying a constant current between reinforcement used as an anode and a counter electrode. To control the corrosion process, electrochemical parameters (such as free corrosion potential, polarization resistance, electrical concrete resistance) were measured. The purpose of this paper is to determine the width and length of the cracks and their orientation according to the current density and time

Corrosion modelling of iron for long term prediction in nuclear waste repository

International audienceThe long-term behavior of nuclear waste canisters in geological repository depends on metallic materials and geochemical features of the surrounding. In clay, H$_2$ and metallic cations induce geochemical transformations which change pH and redox potential. So the 1000-years behavior of canisters could be predicted in linking geochemical and corrosion models.The Diffusion Poisson Coupled Model has been proposed as corrosion model for passive iron. To ensure feedback from geochemistry on corrosion rate backward reactions were introduced. It's a mechanistic model involving 40 parameters to solve the Poisson Fick equations in moving boundaries situation. The purpose of this paper is to present the strategy adopted to set up parameters of DPCM.It has been shown that one half of these parameters could be evaluated from equilibrium considerations. Then specific experiments could be simulated to set up this or that parameters. For instance, dissolution rate of magnetite layer monitored by XANES, layer thickness growth monitored by ellipsometry, potentiostatic and Mott-Schottky experiments have been simulated to set up parameters of dissolution and release processes, inner oxide growth and electrostatic description of outer interface. This strategy was efficient because DPCM can simulated a large panel of stationary and non-stationary experiments

Coupling of a two phase gas liquid 3D Darcy flow in fractured porous media with a 1D free gas flow

A model coupling a three dimensional gas liquid compositional Darcy flow in a frac-tured porous medium, and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous medium account for the molar normal fluxes continuity for each component, the gas liquid thermody-namical equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. The fractures are represented as interfaces of codimension one immersed in the surrounding 3D porous medium, the matrix. Pressure continuity is assumed for both phases at the interfaces between the fracture and the matrix. The spatial discretization is based on the Vertex Approximate Gradient (VAG) scheme in the porous medium coupled with a non conforming control volume finite element discretization in the gallery. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository

Hybrid Finite Volume discretization of two-phase Discrete Fracture Matrix models with nonlinear interface solver

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A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

International audienceThis paper presents an extension of Discrete Fracture Matrix (DFM) models to com-positional two-phase Darcy flow accounting for phase transitions and Fickian diffusion. The hybrid-dimensional model is based on nonlinear transmission conditions at matrix fracture (mf) interfaces designed to be consistent with the physical processes. They account in particular for the saturation jump induced by the different rock types, for the Fickian diffusion in the fracture width, as well as for the thermodynamical equilibrium formulated by complementary constraints. The model is validated by numerical comparison with a reference equi-dimensional model using a TPFA approximation in space and a fully implicit Euler time integration. It is also compared with the usual approach based on an harmonic averaging of the transmissivities at mf interfaces combined with a two-point upwinding of the mobilities jumping over the mf interfaces. Our approach is shown to provide basically the same accuracy than the equi-dimensional model as opposed to the classical harmonic averaging approach which is shown to exhibit physical inconsistency. It is then applied to simulate the desaturation by suction at the interface between a fractured Callovo-Oxfordian argilite storage rock and a ventilation tunnel with data set provided by Andra