Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

Abstract

Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO 2 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.

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

“…This phenomenon is also known as the Saffmann-Taylor instability [1]. In recent years, the study of immiscible fingering has been investigated due to its wide range of applications in CO 2 sequestration [2,3], Enhanced Oil Recovery (EOR) [4,5], and separation in chromatography [6,7]. Depending on the application, sometimes the fingering phenomenon is desirable to enhance process productivity, while sometimes it has a detrimental effect on the final yield.…”

Viscous fingering of miscible annular ring

“…Below, we briefly explain how the equations in the TPDL module can be utilised to model the single-phase porous media flow of miscible fluids. A detailed description of the same is available in one of our previous works (Sharma, Pramanik & Mishra 2017). Under the assumption of constant density of the fluids and disregarding the gravity and capillary pressure, the equations in the TPDL module are where is the Darcy velocity, is the hydrodynamic pressure, and are, respectively, the permeability and porosity of the porous medium.…”

“…The time stepping is adaptive, however, to have results independent of the final time, we fix s to be the maximum and the initial time step taken by the solver (Sharma et al. 2017). In the table 1, we give the details about various parameters used throughout the study.…”

“…Time discretisation is set default by the solver in COMSOL using backward differentiation formulae of first and second orders. The time stepping is adaptive, however, to have results independent of the final time, we fix 10 −2 s to be the maximum and the initial time step taken by the solver (Sharma et al 2017). In the table 1, we give the details about various parameters used throughout the study.…”

Inertia Effects in the Dynamics of Viscous Fingering of Miscible Fluids in Porous Media: Circular Hele-Shaw Cell Configuration

“…This instability occurs at the interface between two fluids when a less viscous fluid displaces a more viscous fluid and appears as finger-like patterns. Fingering instability occurs at various scales ranging from micro-scale to several kilometers in fractured reservoirs [3], in chromatography separation [4,5], Enhanced Oil Recovery [6,7], CO 2 sequestration [8,9], and pollutant removal processes [10].…”