Multiphase Flow and Transport Processes in the Subsurface

Helmig, Rainer

doi:10.1007/978-3-642-60763-9

Cited by 620 publications

(530 citation statements)

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“…It is widely known that because of the inherent instability for the first-order derivatives in space, the C-FEM is not suitable for mild to the highly nonlinear convective-dominated immiscible displacement problems [Lewis et al, 1974;Lemmonier, 1979;Rabbani and Warner, 1994]. The SUPG-FEM [Brooks and Hughes, 1982;Hughes and Mallet, 1986] overcomes the instability of the C-FEM, but recent works have shown that this method can produce unphysical results when used for the simulation of two-phase flow in highly contrasted heterogeneous porous media [Helmig, 1997;Helmig and Huber, 1998]. …”

Section: Introductionmentioning

confidence: 99%

“…(An analysis of the FU-FEM is given by Helmig [1997].) In this method the computation of the FEM stiffness matrix in 2-D Delaunay mesh is modified by assembling a nodebalance flow system of equations.…”

Section: Introductionmentioning

confidence: 99%

“…Some authors [Forsyth, 1990[Forsyth, , 1991Letniowski and Forsyth, 1991;Helmig, 1997] refer to the FU-FEM as the control-volume finite element method and to the CV method as the controlvolume box method.…”

Section: Introductionmentioning

confidence: 99%

“…[16] Because of these features, the CV method has been used mainly to solve the saturation equation of the twophase immiscible flow in porous media [Verma, 1996;Helmig, 1997]. The convergence of the CV numerical method for two-phase immiscible flow in porous media has been recently proved by Michel [2003].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Monteagudo

Firoozabadi

2004

Water Resources Research

198

111

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[1] We provide a numerical procedure for the simulation of two-phase immiscible and incompressible flow in two-and three-dimensional discrete-fractured media. The concept of cross-flow equilibrium is used to reduce the fracture dimension from n to (n-1) in the calculation of flow in the fractures. This concept, which is often referred to as the discrete-fracture model, has a significant effect on the reduction of computational time. The spatial discretization is performed with the control-volume method. This method is locally conservative and allows the use of unstructured grids to represent complex geometries, such as discrete-fracture configurations. The relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes, which is consistent with the physics of fluid flow. The system of partial differential equations is decoupled and solved using the implicit-pressure, explicitsaturation (IMPES) approach. The algorithm has been successfully tested in two-and three-dimensional numerical simulations of wetting phase fluid injection (such as water) in discrete-fractured media saturated by a nonwetting phase (such as nonaqueous phase liquid or oil) with mild to high nonlinearity in relative permeability and capillary pressure. To the best of our knowledge, results for simulations of two-phase immiscible and incompressible flow in three-dimensional discrete-fractured media, including capillary and gravity effects, are the first to appear in the literature.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Monteagudo

Firoozabadi

2004

Water Resources Research

198

111

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“…For example, oil and gas reservoir, nuclear waste disposal in sedimentary stratum, coastal excavation when meeting much gas flow, immiscible contamination in soil and subsurface water remediation, geothermal heat extraction with steam production, carbon dioxide sequestration into coal seams and its enhanced oil, natural gas/coal bed methane recovery, and carbon dioxide storage in deep saline aquifer. On the contrary, there are few available text books (Helmig, 1997;Chen, Huan and Ma, 2006) to meet these growing demands, especially on the fundamentals of numerical computation of multiphase flows specific to new engineering advancement.…”

Section: Introductionmentioning

confidence: 99%

Development of a 3D Fem Simulator on Multiphase Seepage Flows and its Applications

Ranjith

Yamaguchi

et al. 2007

Engineering Applications of Computational Fluid Mechanics

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This paper introduces a 3D FEM simulator for multiphase flows in porous media and its applications through consecutive consulting projects in the past three years. Based on the three-dimensional finite element method for two-phase flow of a liquid (underground water) and an immiscible or partly soluble gas (air, methane, CO 2 , etc.) seepage flows in porous media, the corresponding partial differential simultaneous equations and their numerical discretization method as well as the sorption/diffusion formulations are described. The simulator has been mainly applied to simulate both the combustible gas and water flows induced by a step-wise excavation process in sedimentary rock for disaster prevention during underground excavation for nuclear waste disposal. Furthermore, the simulator has been applied to predict the coal mine gas and water flows induced by face advancement in coal mining. These practical application examples are given in this paper.

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Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach

Huber

Helmig

1999

Int. J. Numer. Meth. Fluids

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Multiphase Flow and Transport Processes in the Subsurface

Cited by 620 publications

References 0 publications

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Development of a 3D Fem Simulator on Multiphase Seepage Flows and its Applications

Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach

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