Accurate Calibration of Empirical Viscous Fingering Models

We review the use and calibration of empirical models for viscous fingering. The choice of parameters for the three principal approaches (Koval, Todd and Longstaff, and Fayers methods) is outlined. The methods all give similar levels of accuracy when compared with linear ex-periments, but differ in performance in two-dimensional applications. This arises from differences in the formulation of the total mobility terms. The superiority of the Todd and Longstaff and Fayers methods is demonstrated for two-dimensional and gravity influenced flows by comparison with experiments and high resolution simulation. The use of high resolution simulation to calibrate empirical models in a systematic manner is described. Results from detailed simulation demonstrate the sensitivity of empirical model parameters to viscous to gravity ratio, recovery process (secondary, tertiary or WAG), and geological heterogeneity. It is shown that for large amplitude heterogeneities with short correlation lengths, the accuracy of the empirical models is not satisfactory, but is improved by the addition of a diffusive term.