Henry’ Law and Gas Phase Disappearance

Jaffré, Jérôme; Sboui, Amel

doi:10.1007/s11242-009-9407-0

Cited by 29 publications

(14 citation statements)

References 3 publications

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“…Two of the participating teams :INRIA-Rocquencourt, France (Jérôme Jaffré, Ibtihel Ben Gharbia) and Friedrich-Alexander Universitat FAU, Erlangen-Nurnberg, Germany (Peter Knabner, Estelle Marchand, Torsten Muller)) ; are using the total hydrogen concentration and the pressure for "persistent" variables ; but they formulate the solubility conditions as complementary conditions, which complement the conservation law equations (see [23] and [32]). Namely : they add the "complementary solubility constraints" to the nonlinear algebraic equations, coming from the discretization of the conservation laws and the constitutive equations.…”

Section: Choice Of the Primary Variablesmentioning

confidence: 99%

Compositional two-phase flow in saturated–unsaturated porous media: benchmarks for phase appearance/disappearance

Bourgeat

Smaï

Granet³

2013

Simulation of Flow in Porous Media

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The two test cases presented herein aimed at simulating the transport migration of nuclides around a nuclear waste repository and belong to the "Two-Phases Numerical Test Data Base" presented in [1], [2]. They were initially designed in the framework of the French research group MoMaS [3]. The starting point in designing all the test cases presented in [1] comes from some of the main challenges the traditional simulators for multiphase flow in porous media are facing when attempting to simulate gas migration in deep geological repositories for long-lived high-level nuclear waste; particularly with low permeability argillites host rocks, as considered by most European radioactive waste management organisations and regulators (see for instance: [4]). The gas migration in this type of porous media is driven by a compressible two-phase partially miscible flow, and is described by a system of nonlinear parabolic PDE's (see [5]). The aim of the test-cases presented below and in [1] is to address some of the specific problems encountered when numerically simulating gas migration in such underground nuclear waste repositories. But, because we are interested in the difficulties inherent to physical modeling , and less in the ones coming from numerical methods, we kept in all these test cases a simple geometry corresponding to a quasi 1-D flow. The first test case is motivated by simulating the gas-phase appearance/disappearance in a two-phase flow, produced by injection of H 2 in a homogeneous porous medium initially fully saturated with pure water. The aim of the second test case is to simulate the evolution of a compressible and partially miscible two-phase flow, starting from an out of equilibrium initial state, made up of two adjacent partially liquid saturated zones with two different uniform pressures .

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Section: Choice Of the Primary Variablesmentioning

confidence: 99%

Compositional two-phase flow in saturated–unsaturated porous media: benchmarks for phase appearance/disappearance

Bourgeat

Smaï

Granet³

2013

Simulation of Flow in Porous Media

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“…Using complementarity constraints (see [11]). p n , (S w or X b w ) Switching primary variables depending on present phases (see [12], [13]).…”

Section: Choice Of Primary Variablesmentioning

confidence: 99%

Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase

2012

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Carbon Capture and Storage (CCS) is a recently discussed new technology, aimed at allowing an ongoing use of fossil fuels while preventing the produced CO 2 to be released to the atmosphere. CSS can be modeled with two components (water and CO 2 ) in two phases (liquid and CO 2 ). To simulate the process, a multiphase flow equation with equilibrium phase exchange is used. One of the big problems arising in two-phase twocomponent flow simulations is the disappearance of the nonwetting phase, which leads to a degeneration of the equations satisfied by the saturation. A standard choice of primary variables, which is the pressure of one phase and the saturation of the other phase, cannot be applied here.We developed a new approach using the pressure of the nonwetting phase and the capillary pressure as primary variables. One important advantage of this approach is the fact that we have only one set of primary variables that can be used for the biphasic as well as the monophasic case. We implemented this new choice of primary variables in the DUNE simulation framework and present numerical results for some test cases. arXiv:1209.4752v1 [physics.comp-ph]

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“…For applications related to hydrogen migration in underground repositories, typical values are p 0 = 1 MPa, C h p 0 = 1.5×10 −2 kg/m 3 , and using the values listed in Table 1, we obtain the estimates (in square meters per second) 22 , only the second term is used for the estimate, but the first term can take much larger values if the gas phase is present). Hence, condition 18 holds true.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…This choice is motivated by the fact that the liquid phase is always present in the whole domain, while the dissolved hydrogen density is always well-defined, regardless of the presence of a gas phase. As observed in [22], Henry's law can be used within a formulation with complementary constraints to determine the presence of the gas phase. Here, as in [8,32], we adopt the simpler approach where the gasphase saturation is recovered from the main unknowns using the reciprocal function of the capillary pressure extended by zero.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin method for two-component liquid–gas porous media flows

Ern

Mozolevski

2012

Comput Geosci

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We consider two-component (typically, water and hydrogen) compressible liquid-gas porous media flows including mass exchange between phases possibly leading to gas-phase (dis)appearance, as motivated by hydrogen production in underground repositories of radioactive waste. Following recent work by Bourgeat, Jurak, and Smaï, we formulate the governing equations in terms of liquid pressure and dissolved hydrogen density as main unknowns, leading mathematically to a nonlinear elliptic-parabolic system of partial differential equations, in which the equations degenerate when the gas phase disappears. We develop a discontinuous Galerkin method for space discretization, combined with a backward Euler scheme for time discretization and an incomplete Newton method for linearization. Numerical examples deal with gas-phase (dis)appearance, ill-prepared initial conditions, and heterogeneous problem with different rock types.

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Henry’ Law and Gas Phase Disappearance

Cited by 29 publications

References 3 publications

Compositional two-phase flow in saturated–unsaturated porous media: benchmarks for phase appearance/disappearance

Compositional two-phase flow in saturated–unsaturated porous media: benchmarks for phase appearance/disappearance

Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase

Discontinuous Galerkin method for two-component liquid–gas porous media flows

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