An Analytical Method for Predicting the Performance of Gravitationally-unstable Flow in Porous Media

摘要

unstable flow in porous media. The Koval model is analogous to the Buckley-Leverett method and multiplies the heterogeneit index of the system as an input (H-factor) with the fluid-flow (here gravity) induced instability factor, E to obtain the Koval facto KG = HE. This paper only considers the gravity induced instability factor E (H=1). The Koval factor is implemented in a modifie fractional flow function that includes a dilution effect when the CO2 moves away from the interface to describe countercurren gravity flow. The pseudo two-phase flow problem provides the average concentration of CO2 in the brine as a function of distance The KG-factor can be used in commercial simulators to account for the density-driven natural convection, which cannot b currently captured because the grid cells are typically orders of magnitude larger than the wavelength of the initial fingers. Suc natural convection effects occur in storage of greenhouse gases in aquifers and EOR processes using carbon dioxide or othe solvents. A comparison of the analytical model with the horizontally-averaged concentrations obtained from 2-D numerical simulation provides a correlation for calculation of the KG-factor for different Rayleigh numbers. The model shows a rarefaction followed b shock-like behavior because the CO2 concentration decreases away from the gaseous CO2-liquid interface. The agreement betwee the analytical model and full numerical simulation is practically acceptable. We leave the introduction of the heterogeneity facto for future work.