Detailed Validation of an Empirical Model for Viscous Fingering With Gravity Effects

Abstract

This paper extends to two-dimensional (2D) flows the derivation and validation of an empirical model for viscous fingering previously developed. Fine-scale numerical simulations are used to provide basic data for validating the approximations, and these fingering results are also checked against a range of experiments. The flow rate dependence of gravity segregation in vertical section experiments conducted by van der Poel is examined, where the broadly acceptable agreement of the empirical model is limited by some identified additional features.

Investigation of concentration‐dependent diffusion on frontal instabilities and mass transfer in homogeneous porous media

“…This exponential variation can closely characterize the "quarter-power mixing rule" adopted by petroleum engineers. [27,28] m ¼ e Rð1ÀcÞ ð7Þ…”

“…To determine the coefficients in Equation (26), 48 simulations were conducted in which the log mobility ratio R varied from 1 to 3.5 and the Pe varied from 300 to 1000. Through linear regression, the coefficients were calculated and the correlated equation is given by Equation (27). The R-squared in the regression is 0.993 164, indicating an excellent data fitting of simulated breakthrough times.…”

“…With Equation (27), the breakthrough times at any scenarios within the discussed range of variables R and Pe can be predicted. A comparison of predicted breakthrough times calculated with Equation (27) with simulated breakthrough times is shown in Figure 19.…”

“…A comparison of predicted breakthrough times calculated with Equation (27) with simulated breakthrough times is shown in Figure 19. It is found that excellent agreement is achieved.…”

An empirical theory for gravitationally unstable flow in porous media

“…He discussed various expressions for the driving force to optimize agreement with experimental results of [3]. Fayers and Newley [18] and [17] introduced a three-parameter model to obtain a better description of viscous fingering with gravity effects. However, [19] pointed to the poor performance for gravity flow indicated, not only for Koval model itself but also for extensions like the [17,44] models.…”