A numerical model for simulating two-phase flow through porous media

Kukreti, Anant R.; Rajapaksa, Yatendra

doi:10.1016/0307-904x(89)90070-x

Cited by 6 publications

(10 citation statements)

References 9 publications

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“…In the following, the mathematical model composed of Eqs. (14) and (18) for two-phase flow in porous media would be considered.…”

Section: Mathematical Model For Two-phase Flow In Porous Mediamentioning

confidence: 99%

“…(19) is iterated to reach a steady state such that the pressure P satisfying Eq. (14) can be obtained at the physical time t. f…”

Section: Lattice Boltzmann Model For Two-phase Flow In Porous Mediamentioning

confidence: 99%

“…In this part, we continue to consider another benchmark problem where the governing equations for pressure and saturation, i.e., Eqs. (14) and (18), are nonlinearly coupled. Following the previous works [65,66], some parameters appeared in Eqs.…”

Section: Example 2: a Coupled Benchmark Problemmentioning

confidence: 99%

“…The last problem we considered is the classical five spot problem [2,[13][14][15], which is more complicated, and there is no analytical solution available.…”

Section: Example 3: the Classical Five-spot Problemmentioning

confidence: 99%

“…Based on the previous works [14,15], the problem (see Fig. 12) can be described by the following simplified mathematical model,…”

Section: Example 3: the Classical Five-spot Problemmentioning

confidence: 99%

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A Lattice Boltzmann Model for Two-Phase Flow in Porous Media

Chai¹,

Liang²,

Du³

et al. 2019

SIAM J. Sci. Comput.

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In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal secondorder finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for ve- * locity are accurate and also have a second-order convergence rate in space.Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems.

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“…In the following, the mathematical model composed of Eqs. (14) and (18) for two-phase flow in porous media would be considered.…”

Section: Mathematical Model For Two-phase Flow In Porous Mediamentioning

confidence: 99%

“…(19) is iterated to reach a steady state such that the pressure P satisfying Eq. (14) can be obtained at the physical time t. f…”

Section: Lattice Boltzmann Model For Two-phase Flow In Porous Mediamentioning

confidence: 99%

Section: Example 2: a Coupled Benchmark Problemmentioning

confidence: 99%

“…The last problem we considered is the classical five spot problem [2,[13][14][15], which is more complicated, and there is no analytical solution available.…”

Section: Example 3: the Classical Five-spot Problemmentioning

confidence: 99%

“…Based on the previous works [14,15], the problem (see Fig. 12) can be described by the following simplified mathematical model,…”

Section: Example 3: the Classical Five-spot Problemmentioning

confidence: 99%

See 3 more Smart Citations