Inertial Effects on Dynamics of Immiscible Viscous Fingering in Homogenous Porous Media

Rabbani Rabbani,Sassi Sassi,Abderrahmane Abderrahmane

doi:10.3390/fluids4020079

Rabbani Rabbani, Sassi Sassi + Show 1 more

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https://doi.org/10.3390/fluids4020079

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Abstract

We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy’s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers—which are important parameters for Enhanced Oil Recovery (EOR)—are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy’s law.

Highlights

Viscous Fingering (VF) is a form of hydrodynamic instability which evolves when two fluids of unequal viscosities meet such that the less viscous fluid tries to push or penetrate into the more viscous fluid
Researchers have focused on various aspects of fingering dynamics and its suppression, it is noticeable that during numerical modelling and their validation with experiments, they have relied on the empirically formulated Darcy’s law which was introduced in 1856 [8] and does not take into account inertial effects
Apart from the Forchheimer equation, several other models have been presented to incorporate the effect of inertial forces in porous media flow

Summary

Introduction

Viscous Fingering (VF) is a form of hydrodynamic instability which evolves when two fluids of unequal viscosities meet such that the less viscous fluid tries to push or penetrate into the more viscous fluid. Apart from the Forchheimer equation, several other models have been presented to incorporate the effect of inertial forces in porous media flow. To take into account the non-linear convective term along with inertial effects in porous media flow, we found two models which were developed purely on theoretical basis. We include inertial corrections along with the convective acceleration These applications include costly operations of oil/gas flow near well-bore, liquid waste injection [31], in porous media flow and present comparative analysis of viscous fingering phenomenon for and flow through packed bed reactors which are used in downstream operations [32]. Weviscous formulate a 2D numerical model, both with and without inertial effects and investigate the effect of different Reynolds numbers on different aspects of the viscous

Mathematical

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