The Dispersive-Fingering Transition and Flow Upscaling for Miscible Displacements in Heterogeneous Systems

The nature of fluid flow through porous media is determined by the interaction between the fluid mechanics of the displacement process and the rock heterogeneity. The interplay between the various forces may be described by dimensionless scaling groups e.g. mobility ratio, capillary number, viscous/gravity ratio etc. A quantitative measui~ of rock heterogeneity is more difficult to define in real geological systems but it is central to the prediction of the fluid displacement process. In this work, the permeability heterogeneity is described by a correlated random field which is the simplest model into which we can introduce both variability and structure in a systematic way. We consider mainly viscous displacements at adverse mobility ratios in first contact miscible floods. The various flow regimes that are possible in such fluid displacement-heterogeneity combinations are described and, in particular, we focus on the fingering-dispersive transition. The results presented here extend previously reported work on this topic. In particular, the importance of certain “shape” scaling groups in detennining the global flow regime within the system are demonstrated. These scaling groups are related to the vertical equilibrium concept. The significance of the flow regime is discussed in the light of how the flow parameters in miscible displacement may be scaled up. The pseudo-isation technique, which is commonly used in two phase flow, is applied and some observations are made on the resulting averaged or “upscaled” parameters which relate to the overall flow regime in the displacement process.