Scale-up of mass transfer and recovery performance in heterogeneous reservoirs

Reservoir heterogeneities occur over a wide range of length scales, and transport process modeling at large-scales requires proper scale-up of heterogeneity and its interaction with underlying transport mechanisms. This paper demonstrates a new technique to systematically quantify the scaling characteristics of mass transfer in heterogeneous reservoirs based on the volume averaging approach. Although treatment of transport problems with the volume averaging technique has been published in the past, application of those methods to geological systems exhibiting realistic spatial variability is lacking due to various restrictive assumptions in the conventional formulation. We propose a new procedure where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a small sub-volume of the reservoir are integrated with the volume averaging technique to provide effective description of transport properties and to derive scaling relationships of mass transfer coefficient (Keff) in reservoirs exhibiting anisotropic spatial variability. Our results present promising potential for application to other complex geologic medium. The method is further extended to describe transport in systems involving inter-phase transport between multiple flowing phases. ticular, the scaling characteristics of Keff for a tracer injection process corresponding to different reservoir heterogeneity correlation lengths as well as different transport mechanisms were studied. Our results show that scaling of recovery responses (e.g., variances in tracer breakthrough time and recovery) can be described by the scaling of Keff; in particular, mean and variance of Keff decrease with length scale, similar in the fashion of recovery statistics.