Computational investigations of viscous fingering in enhanced oil recovery

Abstract

Viscous fingering is important in many applications and industries and can occur over a wide range of time and length scales. Examples include fluid separation using chromatography and carbon dioxide (CO2) sequestration. The particular type of viscous fingering discussed occurs in first contact miscible (FCM) displacements, which are often encountered in enhanced oil recovery applications such as CO2 injection.

Viscous fingering is a highly non-linear phenomenon with a strong dependence on viscosity contrast, diffusion, dispersion and permeability variation. Its dynamics cannot be described analytically except at early time when the fingers grow independently of their neighbours. Predicting the growth of viscous fingering is challenging as it requires numerical simulation with high resolution to ensure physical diffussion and dispersion dominates over numerical errors.

We begin our investigation with a quantitative assessment on the inherent errors in numerical simulations resulting from truncation of Taylor’s expansion when approximating the governing partial differential equations describing the flow in porous media. We study the effects of grid orientation and different numerical schemes. We show how the truncation error reduces the growth rate of immiscible viscous fingers for wavenumbers greater than 1 in all cases but does not affect the growth rate of higher wavenumber fingers as much as would be seen if capillary pressure were present.

We then proceed to study the life-cycle of miscible fingering, from the early to late time regime. We use simple but effective methods to precisely detect nonlinear phenomena such as finger merging, coalescence and tip-splitting. By investigating the impacts of viscosity ratio and anisotropic dispersion on the fingering patterns, we propose how the scaling of non-linear growth can be made using the results from linear stability analysis. This subsequently allows us to predict when the late time regime will occur.

Next we investigate how spatial variations in the permeability including channelling and highly correlated reservoirs influence the viscous fingering. We study how macroscopic efficiency is reduced due to bypassed-oil in channelised reservoirs, and attempt to capture this using a modified 1D Koval model. We use several metrics to provide demarcations between the type of heterogeneity and resulting flow regimes.

Finally, we perform numerical simulations of polymer slug fingering using FCM simulator and black-oil simulator with Todd-Longstaff model. We show how the latter may suffer excessive numerical dispersion and we present a simple method to overcome this. Finally, we show that the miscible fingering at the back of the slug may be simplified by using a semi-analytical model that allows a rapid estimation of slug size required to maintain the integrity of the polymer slug.