Characterizing the Impact of Heterogeneity on Miscible Gas Injection

The performance of miscible gas injection processes is typically adversely affected by geological heterogeneity and viscous fingering. It is well known that very high grid resolutions are needed to model viscous fingering explicitly so most field scale simulations will use an empirical model such as the Todd and Longstaff (1972) model to describe the average effects of viscous fingering on recovery. In homogeneous reservoirs it is usual to assume to use a Todd and Longstaff mixing parameter with a value of 2/3 in these simulations. It is, however, unclear how to model the influence of heterogeneities on the viscous fingering. Previous work by Fayers et al. (1992) identified that there are two flow regimes associated with heterogeneity – diffusive when the permeability distribution is uncorrelated and random tending to advective as the permeability distribution has a larger standard deviation and a greater correlation length. In the former case the effect of heterogeneity can be modelled using a dispersivity whilst in the latter case it can be modelled by an effective viscosity ratio of heterogeneity factor (Koval, 1963). In this work we identify a third heterogeneity controlled flow regime – that of channelized flow. In this regime the effect of heterogeneity can best be modelled using a bypassed oil volume. We propose the use of a phase diagram for identifying which of these three flow regimes is dominant in a given heterogeneous reservoir and hence which method of upscaling flow is best suited to that reservoir. This phase diagram uses only static measures of the permeability distribution. We further provide a simple method for estimating the effective mobility ratio for use when the heterogeneity can be modelled by a Koval heterogeneity factor. The results are benchmarked against high resolution, finite-difference, first-contact miscibility simulation using SPE 10 Model 2 and synthetic permeability fields.