Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media

Shaheryar T. Hussain, Klaus Regenauer-Lieb, Aleksandr Zhuravljov, Furqan Hussain, Sheik S. Rahman

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This paper presents a novel technique for upscaling multiphase fluid flow in complex porous materials that combines asymptotic homogenization approach with hydrodynamicand thermodynamic bounds. Computational asymptotic homogenization has been widely utilised in solid mechanics as a method for analysing multiscale expansion and convergence coefficients in heterogeneous systems. Computations are performed over several volumes by increasing the size until convergence of the material parameters under different load scenarios is achieved. It works by simplifying the problem with a homogenization method and is ideally suited for estimating the representative elementary volume of microporous material by expanding algorithms. The validity of the method to include complex multiphase hydrodynamic processes and their interaction with the matrix structure of porous media lacks a sound theoretical foundation. To overcome this problem, a variational thermodynamic approach is used. Upper and lower bounds of entropy production are proposed to provide effective material properties with uncertainties. This allows multiple possibilities to address dynamics via thermodynamically linked processes. This work utilizes volume of fluid approach to model multiphase porous media flow in models based on micro-computerized tomography x-ray data of Bentheimer sandstone and Savonnieres carbonate. It is found that the representative elementary volume sizes obtained by the conventional asymptotic homogenization methods do not satisfy thermodynamic bounds which consistently require larger representative elementary volume sizes. For the Savonnieres carbonate the entropic bounds have not converged fully questioning the reliability of the effective properties obtained from the classical method.

Document Type: Original article

Cited as: Hussain, S. T., Regenauer-Lieb, K., Zhuravljov, A., Hussain, F., Rahman, S. S. Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media. Advances in Geo-Energy Research, 2023, 9(1): 38-53.


Uncertainty bounds, entropy production, multiphase REV, volume of fluid, pore scale modelling

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