Miscible Viscous Fingering in Porous Media With Multiple Pore-networks

Most of the porous media models assume that the pore spaces have same size with single porosity and permeability. However, in real porous materials, distribution of pore sizes with more than single porosity can be clearly distinguished. In this study, we consider miscible displacement and viscous fingering in a geo-material with two dominant permeabilities for micro-scale and macro-scale structures so-called double porosity/permeability. We will assume two pore-networks with different anisotropic permeability in which there are mass and chemical species transfer between the micro- and macro-network [1]. Moreover, the governing equations for each network is Darcy and pore-structures are continuum.Following our previous study on double diffusive miscible viscous fingering [2], herein, linear stability analysis and numerical solutions of viscous fingering in porous media with double permeability are conducted. To do so, we will investigate instability of coupled porous media flows and advection-diffusion models. For linear stability analysis we will utilize the quasi-steady state approximation (QSSA) and predict the growth rate of instabilities. Then, numerical simulation of double permeability viscous fingering is performed by employing a stabilized finite element framework. We will show that the results of stability analysis are in very good agreement with those obtained from numerical solutions. We will also show in our analysis that the Darcy model under single porosity/permeability assumption is a special case of the proposed model in current study. References:[1] K. B. Nakshatrala, S. H. S. Joodat, and R. Ballarini. Modeling flow in porous media with double porosity/permeability: Mathematical model, properties, and analytical solutions. Available on arXiv: 1605.07658, 2016. [2] M. Shabouei and K. B. Nakshatrala. Effect of temperature and numerical stabilization on viscous fingering and mixing. Under preparation, 2016.