A pore-scale model of two-phase flow in water-wet rock

Silin, Dmitriy; Patzek, Tadeusz W

doi:10.2172/949046

Cited by 2 publications

(8 citation statements)

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“…The same Poisson solver used to calculate pressure is also used in this stage, with the respective components of pressure gradients as the forcing function. Next, this intermediate solution for velocity is used as an initial guess for Equation (44) in order to calculate the incompressible velocity field. The coefficient matrix L T L + λ 2 D T D is now symmetric, allowing to use the conjugate gradient method [76] as the linear solver.…”

Section: Minimizing the Velocity Field Divergencementioning

confidence: 99%

“…The finite difference method (FDM) also forms a well established discretization technique for computational fluid dynamics. It has been used to estimate permeability in digitized porous media [42,43], including multiphase flow simulations [44]. It allows very efficient use of computational resources, leading to the possibility of investigating larger and more representative samples.…”

Section: Introductionmentioning

confidence: 99%

“…Permeability is then calculated via Darcy's equation and velocity field volumetric averages. Staggered grid, with pressure defined at the voxel center and velocity components defined at the voxel faces, has been the common approach, from early works like Schwartz et al [45], relating electrical conductivity and hydraulic permeability in packings of spherical grains, until more recent fluid flow simulations using µ-CT images from real rocks [13,[42][43][44]. The use of FDM with collocated (non-staggered) grid has also been reported [46,47].…”

Section: Introductionmentioning

confidence: 99%

“…The existence and uniqueness of the problem of incompressible flow under Dirichlet pressure boundary conditions requires adding restrictions on velocities at the inlet and outlet boundaries [53]. Different methods have been proposed to tackle this limitation: high order finite difference schemes [54]; an iterative pressure correction algorithm with periodic velocity boundary conditions [43]; artificial compressibility with zero spatial derivative velocity boundary conditions [44,55]; and treating boundary nodes as internal nodes for normal velocity with zero tangent velocity and the explicit method of incomplete approximation [53]. Immerse boundary method [56][57][58] was introduced in biological fluid mechanics to handle the interaction of incompressible fluid and elastic boundaries, and has been used to simulate fluid flow in porous media [59,60].…”

Section: Introductionmentioning

confidence: 99%

“…Invasion scenarios are then created by cluster search on these radius map. This method is used by Silin and Patzek to calculate relative permeability [44]. Another similar method is called the capillary drainage transform [62], which simulates drainage by letting a non-wetting phase invade a pore region if a sphere with radius given by Young-Laplace equation can be moved from a non-wetting saturated region to the target region.…”

Section: Introductionmentioning

confidence: 99%

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Minimum divergence viscous flow simulation through finite difference and regularization techniques

Victor

Mirabolghasemi

Bryant

et al. 2016

Advances in Water Resources

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We develop a new algorithm to simulate single-and two-phase viscous flow through a three-dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use the finite difference method to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under zero Neumann boundary conditions for the velocity components. Finite difference formulation leads to fast parallel implementation through linear solvers for sparse matrices, allowing relatively fast simulations, while regularization techniques used on solving inverse problems lead to the desired incompressible fluid flow. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Additional tests are run on Bentheimer and Buff Berea sandstone samples with available laboratory measurements. We compare the results from our new method, based on finite differences, with an open source finite volume implementation as well as experimental results, specifically to evaluate the benefits and drawbacks of each method. Finally, we calculate relative permeability by using this modified finite difference technique together with a level set based algorithm for multi-phase fluid distribution in the pore space. To our knowledge this is the first time regularization techniques are used in combination with finite difference fluid flow simulations.

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Section: Minimizing the Velocity Field Divergencementioning

confidence: 99%