Quantifying of the Impact of Reservoir Heterogeneity on Recovery Using Shear and Vorticity

We have used the vorticity of the displacement velocity, as defined by Heller (1966), to derive dimensionless numbers to be used to quantify the relative impact of viscosity ratio, gravity, diffusion and dispersion, and permeability heterogeneity on reservoir flow behaviour. We have used this approach to introduce a new objective measure of the impact of permeability and porosity heterogeneity on reservoir flow behaviour. Buoyancy forces are quantified using a gravity to viscous ratio (G) and diffusion/dispersion using the transverse dispersion number. Detailed simulation of first contact miscible gas/solvent displacements through a range of geologically realistic reservoir models is used to show that the new heterogeneity number, in conjunction with the dimensionless numbers, can be used to provide meaningful results for real non-linear reservoir flows. 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.