Minimum divergence viscous flow simulation through finite difference and regularization techniques. (September 2016)

• Record Type: Journal Article
• Authors: Victor, Rodolfo A.; Mirabolghasemi, Maryam; Bryant, Steven L.; Prodanović, Maša
• Is Part Of: Advances in water resources. Volume 95(2016)
• Page Start: 29
• Page End: 45
• Publication Date: 2016-09
• Subjects: Fluid flow in porous media -- Finite difference method -- Finite volume method -- Absolute permeability -- Relative permeability -- Tikhonov regularization; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2016.02.002
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: A new algorithm to simulate viscous flow through a three-dimensional Cartesian representation of a porous space is proposed. The method adds Tikhonov regularization to finite difference techniques to find a solution with enforced fluid incompressibility. Tests performed using synthetic and real sandstone samples show good agreement with established finite volume technique and experimental/theoretical values. The new technique is used in conjunction with level set methods to estimate relative permeability curves. Abstract: 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.