A Numerical Study of Viscous Instabilities: Effect of Controlling Parameters and Scaling Considerations

Summary An accurate finite-element simulator with a very fine 2D grid was used in this study of viscous instabilities. The simulator has negligible grid-orientation and numerical-dispersion effects and treats longitudinal and transverse dispersivities separately. The simulator was validated by comparing numerical results with the analytical solution for unit-mobility-ratio miscible displacements under varying longitudinal and transverse dispersivities and was further tested by simulating the results of published laboratory displacements under adverse-mobility-ratio conditions. A good match was obtained between the simulated and experimental results for recovery and effluent-concentration profiles for adverse-mobility-ratio displacements. A permeability variance of only 0.1 or an inlet concentration perturbation for a homogeneous system was enough to initiate the effects of viscous fingers seen in laboratory displacements. Results showed that the parameters that control unstable displacements are the permeability variance (Dykstra-Parsons coefficient), the size of heterogeneity (scale length), the mobility ratio, and the dimensionless transverse Peclet number, NPet. It was concluded that the instabilities increase with increases in the permeability variance, the scale length, and the mobility ratio. With increased instability, the recovery decreases and the breakthrough time decreases. For NPer< 0.01, the displacement remains unstable. In addition, the effect of longitudinal dispersivity is negligible. As long as the parameters (mobility ratio, permeability variance, and size of heterogeneities, NPer<0.01) were the same, the effect of the size of the modeled medium on recovery and effluent profiles was insignificant. This implies that the effects of viscous instabilities can be scaled within the range of parameters investigated.