Summary An improved heterogeneity/homogeneity index is introduced that uses the shear-strain rate of the single-phase-velocity field to characterize heterogeneity and rank geological realizations in terms of their impact on secondary-recovery performance. The index is compared with the Dykstra-Parsons coefficient (Dykstra and Parsons 1950) and the dynamic Lorenz coefficient (Shook and Mitchell 2009). The results show that the index's ranking ability is preserved for miscible and immiscible displacements at different viscosity/mobility ratios. Neither the Dykstra-Parsons coefficient (Dykstra and Parsons 1950) nor the dynamic Lorenz coefficient (Shook and Mitchell 2009) can consistently discriminate between different realizations in terms of breakthrough time and oil recovery at 1 pore volume injected (PVI) for tracer flow or adverse-viscosity-ratio miscible and immiscible floods.

A new and improved heterogeneity index is introduced that uses the shear-strain rate of the single phase velocity field to characterise heterogeneity in terms of its impact on performance. This index's ability to rank heterogeneous reservoir models is compared with that of the Dykstra-Parsons coefficient and the dynamic Lorenz coefficient. The new index is able to rank reservoirs, both accurately and quickly, based on performance for both miscible and immiscible fluids at a range of different mobility ratios. In contrast both the Dykstra-Parsons coefficient and the dynamic Lorenz coefficient are found to lack the sensitivity needed to be able to estimate the time to breakthrough of the displacing fluid and the recovery of oil at one pore volume injected.

The vorticity of the displacement velocity is used to derive dimensionless numbers that can be used to quantify the relative importance of viscosity ratio, gravity, diffusion/dispersion and permeability heterogeneity on secondary hydrocarbon recovery. Using this approach, a new objective measure of the impact of permeability and porosity heterogeneity on reservoir performance is obtained. This is used, in conjunction with other dimensionless numbers, to analyse the relative impact of heterogeneity, buoyancy effects, mobility ratio and dispersion on breakthrough time and recovery at 1 pore volume injected during first contact miscible gas injection. This is achieved using results obtained from detailed simulation of miscible displacements through a range of geologically realistic reservoir models. This study goes some way towards developing a unified mathematical framework to determine under which flow conditions reservoir heterogeneity becomes more important than other physical processes. We propose that comparison of these dimensionless numbers can be used to identify the key factors controlling recovery and thus assist the engineer in determining appropriate enhanced oil recovery techniques to improve recovery.

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