Mathematical Structure of the Black-Oil Model for Petroleum Reservoir Simulation

Trangenstein, John A.; Bell, John B.

doi:10.1137/0149044

Cited by 162 publications

(100 citation statements)

References 6 publications

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“…In this section our algorithms are compared with the classical Windowing algorithm on two 3D test cases using a Black Oil type model [12]. A reference solution is obtained using the LGR grid with the global fine time stepping.…”

Section: Numerical Testsmentioning

confidence: 99%

Nearwell local space and time refinement in reservoir simulation

Kheriji

Masson

Moncorgé

2015

Mathematics and Computers in Simulation

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Abstract. In reservoir simulations, nearwell regions usually require finer space and time scales compared with the remaining of the reservoir domain. We present a domain decomposition algorithm for a two phase Darcy flow model coupling nearwell regions locally refined in space and time with a coarser reservoir discretization. The algorithm is based on an optimized Schwarz method using a full overlap at the coarse level. The main advantage of this approach is to apply to fully implicit discretizations of general multiphase flow models and to allow a simple optimization of the interface conditions based on a single phase flow equation.

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Section: Numerical Testsmentioning

confidence: 99%

Nearwell local space and time refinement in reservoir simulation

Kheriji

Masson

Moncorgé

2015

Mathematics and Computers in Simulation

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“…If we use (30) to express the phase mobility, then the phase velocity no longer appears on both sides of (27):…”

Section: Darcy's Lawmentioning

confidence: 99%

“…Other authors have used these techniques for modeling porous media flow; for example, Trangenstein and Bell [26,27] modeled mass transfer between phases and Nelson [18] modeled time-varying porosity.…”

Section: Introductionmentioning

confidence: 99%

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A Numerical Model for Trickle Bed Reactors

Propp¹,

Colella²,

Crutchfield³

et al. 2000

Journal of Computational Physics

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Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

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“…Thus, it places in the general framework of multiphase multicomponent models such as those in [5][6][7] for which accuracy and efficiency have been studied extensively in the past decades. In particular, for the oil-water or black-oil models described e.g., in [8][9][10][11][12][13] the best practice is to use mass-conservative spatial schemes combined either with an implicit treatment of pressures and explicit treatment of saturations/concentrations, or with a fully implicit treatment of all phases and components. Typically, the computational complexity of implicit models is the highest, while other variants are easier to implement.…”

Section: Introductionmentioning

confidence: 99%

Reduced Numerical Model for Methane Hydrate Formation under Conditions of Variable Salinity. Time-Stepping Variants and Sensitivity

et al. 2015

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Abstract:In this paper, we consider a reduced computational model of methane hydrate formation in variable salinity conditions, and give details on the discretization and phase equilibria implementation. We describe three time-stepping variants: Implicit, Semi-implicit, and Sequential, and we compare the accuracy and efficiency of these variants depending on the spatial and temporal discretization parameters. We also study the sensitivity of the model to the simulation parameters and in particular to the reduced phase equilibria model.

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Mathematical Structure of the Black-Oil Model for Petroleum Reservoir Simulation

Cited by 162 publications

References 6 publications

Nearwell local space and time refinement in reservoir simulation

Nearwell local space and time refinement in reservoir simulation

A Numerical Model for Trickle Bed Reactors

Reduced Numerical Model for Methane Hydrate Formation under Conditions of Variable Salinity. Time-Stepping Variants and Sensitivity

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