Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

Vandita Sharma,Manoranjan Mishra,Satyajit Pramanik

doi:10.3390/fluids2020032

Abstract

Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO2 sequestration. The viscosity contrasts between heavy oil and water is several orders of magnitude larger than typical viscosity contrasts considered in the majority of the literature. We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts. Our numerical model is suitable for a wide range of viscosity contrasts covering chromatographic separation as well as heavy oil recovery. We have successfully captured some interesting and previously unexplored dynamics of miscible blobs with very large viscosity contrasts in homogeneous porous media. We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob. Spreading (variance of transversely averaged concentration) follows the power law t 3 . 34 for the blobs with viscosity ∼ O ( 10 2 ) and higher, while degree of mixing is found to vary non-monotonically with log-mobility ratio. Moreover, in the limit of very large viscosity contrast, the circular blob behaves like an erodible solid body and the degree of mixing approaches the viscosity-matched case.

Highlights

Displacement of a less mobile fluid by a more mobile one in a porous medium results in a hydrodynamic instability, viscous fingering (VF)
We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob
The majority of the studies are focused on the case when the defending fluid is separated from the invading fluid by a flat interface

Summary

Introduction

Displacement of a less mobile fluid by a more mobile one in a porous medium results in a hydrodynamic instability, viscous fingering (VF). Depending upon the blob dynamics, R-Pe plane was demarcated into three regions: lump-, comet-shaped deformations, and VF Their studies were restricted to R ≤ 2.5, and Pe ≤ 2500, due to the limitations of the numerical convergence of the semi-implicit time integration of the pseudo-spectral method. The fluid velocity at the interface has sharp gradients In these cases, one needs to solve a stiff system [20] that limits the numerical convergence [6].

Physical Description of the Problem

COMSOL Multiphsysics Simulations

Results

Discussion and Conclusions