Reservoir heterogeneities exhibit a wide range of length scales, and their interaction with various transport mechanisms control the overall performance of subsurface flow and transport processes. Modeling these processes at large-scales requires proper scale-up of both heterogeneity and the underlying transport mechanisms. This research demonstrates a new reservoir modeling procedure to systematically quantify the scaling characteristics of transport processes by accounting for sub-scale heterogeneities and their interaction with various transport mechanisms based on the volume averaging approach.

Although treatments of transport problems with the volume averaging technique have been published in the past, application to real geological systems exhibiting complex heterogeneity is lacking. A novel 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, can be integrated with the volume averaging technique to provide effective description of transport at the coarse scale. In a volume averaging procedure, scaled up equations describing solute transport in single-phase flow are developed. Scaling characteristics of effective transport coefficient corresponding to different reservoir heterogeneity correlation lengths as well as different transport mechanisms including convection, dispersion, and diffusion are studied. The method is subsequently extended to describe transport in multiphase systems to study scaling characteristics of processes involving adsorption and inter-phase transport.

Key conclusions drawn from this dissertation show that 1) variance of reservoir properties and flow responses generally decrease with scale;​ 2) scaling of recovery processes can be described by the scaling of effective mass transfer coefficient (Keff);​ in particular, mean and variance of Keff decrease with length scale, similar in the fashion of recovery statistics (e.g., variances in tracer breakthrough time and recovery);​ 3) the scaling of Keff depends on the underlying heterogeneity and is influenced by the dominant transport mechanisms. To show the versatility of the approach for studying scale-up of other transport mechanisms, it is also applied to derive scaled up formulations of non-Newtonian polymer flow to investigate the scaling characteristics of the apparent viscosity and effective shear rate in porous media.