Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model

Marchand, Estelle; Müller, Torsten; Knabner, Peter

doi:10.1007/s10596-013-9341-7

Cited by 14 publications

(15 citation statements)

References 25 publications

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“…Heterogeneity, anisotropy, and discontinuity of medium properties require special treatment for computationally efficient approximation of advection, diffusion, dispersion, and chemical reactions. [142], and many others. In general, using mixed finite-element method (MFEM) and finite volume methods in reservoir simulation and transport in porous media is required as they are locally mass conservative.…”

Section: Numerical Methods For Solving the Governing Lawsmentioning

confidence: 97%

Flow and Transport in Tight and Shale Formations: A Review

et al. 2017

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A review on the recent advances of the flow and transport phenomena in tight and shale formations is presented in this work. Exploration of oil and gas in resources that were once considered inaccessible opened the door to highlight interesting phenomena that require attention and understanding. The length scales associated with transport phenomena in tight and shale formations are rich. From nanoscale phenomena to field-scale applications, a unified frame that is able to encounter the varieties of phenomena associated with each scale may not be possible. Each scale has its own tools and limitations that may not, probably, be suitable at other scales. Multiscale algorithms that effectively couple simulations among various scales of porous media are therefore important. In this article, a review of the different length scales and the tools associated with each scale is introduced. Highlights on the different phenomena pertinent to each scale are summarized. Furthermore, the governing equations describing flow and transport phenomena at different scales are investigated. In addition, methods to solve these equations using numerical techniques are introduced. Cross-scale analysis and derivation of linear and nonlinear Darcy's scale laws from pore-scale governing equations are described. Phenomena occurring at molecular scales and their thermodynamics are discussed. Flow slippage at the nanosize pores and its upscaling to Darcy's scale are highlighted. Pore network models are discussed as a viable tool to estimate macroscopic parameters that are otherwise difficult to measure. Then, the environmental aspects associated with the different technologies used in stimulating the gas stored in tight and shale formations are briefly discussed.

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Section: Numerical Methods For Solving the Governing Lawsmentioning

confidence: 97%

Flow and Transport in Tight and Shale Formations: A Review

et al. 2017

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“…Note that this system is decoupled, in the sense that Eqs. (16)- (17) and (14)- (15) can be solved sequentially. Thus, only one global (elliptic or parabolic) system needs to be solved at a time.…”

Section: Iterative Approachmentioning

confidence: 99%

“…This method is of a higher algorithmic complexity and requires additional reformulation of the model by adding so called complementary conditions. The semismooth Newton method can be applied to two-phase flow or multicomponent transport with much better results compared to Newton's method (see [14][15][16]). …”

Section: Introductionmentioning

confidence: 99%

A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

Radu

Nordbotten

Pop

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results.

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“…The drawback of Neumann's approach is that it can only handle the disappearance of the non-wetting phase, not its appearance. As a supplement, Marchand et al (2013) suggested to use mean pressure and molar fraction of the light component as primary variables. This allows both of the primary variables to be constructed independently of the phase status and allows the appearance and disappearance of any of the two phases.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, as the first step of building a multi-component multi-phase reactive transport model for geothermal reservoir simulation, we extend Marchand's componentbased multi-phase flow approach (Marchand et al 2013) to the non-isothermal condition. The extended governing equations ('Governing equations' section), together with the Equation of State (EOS) ('Constitutive laws' section), were solved by nested Newton iterations ('Numerical solution of the global equation system' section).…”

Section: Introductionmentioning

confidence: 99%

Extending the persistent primary variable algorithm to simulate non-isothermal two-phase two-component flow with phase change phenomena

2015

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In high-enthalpy geothermal reservoirs and many other geo-technical applications, coupled non-isothermal multiphase flow is considered to be the underlying governing process that controls the system behavior. Under the high temperature and high pressure environment, the phase change phenomena such as evaporation and condensation have a great impact on the heat distribution, as well as the pattern of fluid flow. In this work, we have extended the persistent primary variable algorithm proposed by (Marchand et al. Comput Geosci 17(2):431-442) to the non-isothermal conditions. The extended method has been implemented into the OpenGeoSys code, which allows the numerical simulation of multiphase flow processes with phase change phenomena. This new feature has been verified by two benchmark cases. The first one simulates the isothermal migration of H 2 through the bentonite formation in a waste repository. The second one models the non-isothermal multiphase flow of heat-pipe problem. The OpenGeoSys simulation results have been successfully verified by closely fitting results from other codes and also against analytical solution.

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Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model

Cited by 14 publications

References 25 publications

Flow and Transport in Tight and Shale Formations: A Review

Flow and Transport in Tight and Shale Formations: A Review

A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

Extending the persistent primary variable algorithm to simulate non-isothermal two-phase two-component flow with phase change phenomena

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