Upscaling of miscible floods in heterogeneous reservoirs considering reservoir mixing

Inaccurate modeling of reservoir mixing by using large grid blocks in compositional simulation can significantly affect recoveries in miscible gas floods and lead to inaccurate predictions of recovery performance. Reservoir mixing or dispersion is caused by diffusion of particles across streamlines; mixing can be significantly enhanced if the surface area of contact between the reservoir and injected fluid are increased as fluids propagate through the reservoir. A common way to convert geological models into simulation models is to upscale permeabilities based on reservoir heterogeneity. Upscaling affects the degree of mixing that is modeled, but the importance of reservoir mixing in upscaling is largely ignored. This paper shows how to estimate the level of mixing in a reservoir and how to incorporate mixing into the upscaling procedure. We derive the key scaling groups for first-contact miscible (FCM) flow and show how they impact reservoir mixing. 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. Over 800 2-D numerical simulations are carried out using experimental design to estimate dispersivity as a function of the derived scaling groups. We show that reservoir mixing is enhanced owing to fluid propagation through heterogeneous media. Because mixing is dependent on heterogeneities, upscaling is an iterative process where the level of mixing in both the longitudinal and transverse directions must be matched from the fine to coarse scale. The most important groups that affect mixing are the mobility ratio, dispersion number, correlation lengths, and the Dykstra-Parson's coefficient. Large dispersion numbers yield greater dispersivities away from the injection well. We show through simulations of both FCM and multi-contact miscible (MCM) floods that grid-block size can be significantly increased when reservoir mixing is large. Heterogeneous reservoirs with large longitudinal correlation lengths can be upscaled to larger grid blocks than reservoirs with random permeability fields. This paper shows how to determine a priori the maximum grid-block size allowed in both the x- and z-directions to predict accurately the oil recovery from miscible gas floods.