The Effects of Small-Scale Heterogeneities on the Effective Dispersivity of Porous Medium

Abstract

ABSTRACT Dispersivity affects the displacement and sweep efficiencies and the required slug size of a displacing fluid. Unfortunately, the dispersivity values estimated from field tests are a few orders of magnitude greater than the values obtained in laboratory tests. This investigation studies the effect of small scale (or core scale) heterogeneities on the effective dispersivity value in a typical gridblock size used in a reservoir simulator. The study is restricted to contact miscible displacements with unit mobility ratio. A finite element simulator is used to investigate these effects. Physical dispersion is explicitly included in the simulator. Results show that the effective dispersivity is affected by the degree of heterogeneity, the average length of heterogeneity, the length of the system, and the manner in which the permeability values are spatially distributed. The effect of heterogeneity becomes significant if the coefficient of variance is greater than 0.4. The effect of dimensionless scale length (ratio of average length of heterogeneity to length of the system) on effective dispersivity is insignificant for dimensionless scale values less than .01; above that value dispersivity increases with an increase in the scale length. The effective dispersivity increases almost linearly with an increase in the length of the system for constant dimensionless scale length. This provides an explanation for the similar trend reported for field dispersivity data. A simple correlation is proposed to calculate the effective dispersivity of the porous medium. The effect of the way in which given permeability values are distributed across the medium on the dispersivity cannot be correlated with the parameters investigated, probably indicating that the effective dispersivity is a unique function of the manner in which permeability values are distributed. This effect was not noted previously in the literature; however, it does not affect the general trends.