Investigation of scale-dependent dispersivity and its impact on upscaling misicble displacements

Mixing of miscible gas with oil in a reservoir decreases the effective strength of the gas, which can adversely affect miscibility and recovery efficiency. The mixing that occurs in a reservoir, however, is widely debated and often ignored in reservoir simulation, where very large grid blocks are used. Large grid blocks create artificially large mixing that can cause errors in predicted oil recovery.
Reservoir mixing, or dispersion, is caused by diffusion of particles across streamlines of varying velocities. Mixing is enhanced by any mechanism that increases the area of contact between the gas and the oil, thereby allowing the effects of diffusion to be magnified. This is, in essence, the cause of scale-dependent dispersion. The contact area grows primarily because of variations in streamlines and their velocities around grains and through layers of various permeabilities (heterogeneity). Mixing can also be enhanced by crossflow, such as that caused by gravity and by the effects of other neighboring wells. This dissertation focuses on estimation of the level of effective local mixing at the field scale and its impact on oil recovery from miscible gas floods. Pore-level simulation was performed using the Navier-Stokes and convection-diffusion equations to examine the origin of scale dependent dispersion. We then estimated dispersivity at the macro scale as a function of key scaling groups in heterogeneous reservoirs. Lastly, we upscaled grid blocks to match the level of mixing at the pattern scale. Once the contact area ceases to grow with distance traveled, dispersion has reached its asymptotic limit. This generally occurs when the fluids are well mixed in transverse direction. We investigated a variety of pore-scale models to understand the nature of scale dependency. From the pore-scale study, we found that reservoir mixing or dispersion is caused by diffusion of particles across streamlines. Diffusion can be significantly enhanced if the surface area of contact between the reservoir and injected fluid are increased as fluids propagate through the reservoir. Echo and transmission dispersivities are scale dependent. They may or may not reach an asymptotic limit depending on the scale of heterogeneities encountered. The scale dependence results from an increase in the contact area between solute (gas) and resident fluid (oil) as heterogeneities are encountered, either at the pore or pattern-scale. The key scaling groups for first-contact miscible (FCM) flow are derived and their impact on mixing is analyzed. We examine only local mixing, not apparent mixing caused by variations in streamline path lengths (convective spreading). Local mixing is important because it affects the strength of the injected fluid, and can cause an otherwise multicontact miscible (MCM) flood to become immiscible.
We then showed how to upscale miscible floods considering reservoir mixing. The sum of numerical dispersion and physical dispersion associated with the reservoir heterogeneities, geometry and fluid properties must be equal at both the fine- and large-scales. The maximum grid-block size allowed in both the x- and z-directions is determined from the scaling groups. Small grid-blocks must be used for reservoirs with uncorrelated permeabilities, while larger grid blocks can be used for more layered reservoirs. The predicted level of mixing for first-contact miscible floods can be extended with good accuracy to multicontact miscible (MCM) gas floods.