Modelling Viscous Fingering During Reinjection in Geothermal Reservoirs

Abstract

Viscous fingering is a hydrodynamic instability that can be caused by a viscosity difference across a travelling thermal front. The equations governing the instability of radial flow through porous media are cast, and a linear perturbation analysis was performed numerically. Transient growth of temperature perturbations show which wave number, and hence fingering displacement shape, will be most unstable. Results illustrate that there are two parameters that define the stability: the Peclet number and the log-mobility ratio (for homogeneous media). These critical parameters provide limits on reinjection temperature and flow rate for a given reservoir temperature that will cause thermal stability. In addition, the TOUGH2.2 numerical simulator was used to model fluid flow displacement patterns that occur during reinjection in geothermal reservoirs. Results show that a critical Peclet number and log-mobility ratio exist for the onset of viscous fingering. Moreover, in cases where the porous medium is heterogeneous, fingering displacements are dominated by the permeability structure for heterogeneity indices beyond some critical value (the precise value of which should factor in inherent numerical dispersion present in the TOUGH2.2 simulator.