Experimental Testing of Mobility Predictions in Averaged Models of Viscous Fingering

Abstract

Abstract Averaged empirical models of viscous fingering are frequently used in order to incorporate the effects of miscible viscous instability into coarse grid simulations of processes involving adverse mobility ratio displacements. However, in order to evaluate these models, it is not sufficient to compare the predictions which they make with effluent profiles in 1D displacement experiments since this only tests the transport properties of the model. It is also necessary to compare the predictions of effective mobility of these models with experiment in order to evaluate their use for application in the modelling of multidimensional displacements. The effective mobility can only be assessed directly when the pressure drops are measured along the fingering zone in miscible unstable displacements and such experiments have not previously been reported. In this paper, miscible viscous fingering results have been presented for "2D linear" 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. The effluent and pressure behaviour has been modelled using direct fine grid numerical simulation and 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. 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.