Linear viscous fingering: New experimental results, direct simulation and the evaluation of averaged models

Abstract

In this paper, miscible viscous fingering results have been presented for almost homogeneous “two-dimensional linear” (relatively long and narrow) displacement experiments at mobility ratios of approximately M = 4, 11 and 30. Both effluent profiles (recoveries) and pressure drops along the fingers have been measured and the reproducibility of these in each of the experimental cycles in repacked beds is very good. These viscous unstable experiments have been modelled by direct simulation using a high-accuracy numerical model. A comparison is made between experiment and direct numerical simulation for the effluent concentration and oil production profile as well as pressure behaviour and the viscous fingering patterns. A number of averaged models of viscous fingering have been evaluated using the experimental pressure data including the Koval, Todd and Longstaff, Fayers and the Odeh and Cohen models. It has been found that direct numerical simulation reproduces both the experimental effluent concentration profiles and the observed pressure drop behaviour very well. Numerically simulated viscous fingering patterns match the main features of the experimental observation. The numerical model used only measured laboratory data together with a random mechanism for initiating fingers in the simulation. However, of the averaged model approaches, the Todd and Longstaff and an equivalent mixing model give the most satisfactory agreement with the observed effective in situ mobilities (pressure drops) in the fingering zone. Both the original Koval model and the modification proposed by Odeh and Cohen do not give good agreement with experimental pressure drop measurements. The approach of Fayers also has some shortcomings in that it predicts a viscosity in the finger zone that is too low (i.e. effective mobility is too high) due to the presence of an unphysical shock front behaviour which this model exhibits.