Reservoir heterogeneities exhibit a wide range of length scales, and their interaction with various transport mechanisms control the performance of subsurface flow and transport processes. Modeling these processes at large-scales requires proper scale up of heterogeneity and its interaction with underlying transport mechanisms. This paper demonstrates a procedure for quantifying the scaling characteristics of a given recovery process accounting for sub-scale heterogeneities based on the volume averaging approach. Although treatment of transport problems with the volume averaging technique have been published in the past, application to real geological systems exhibiting complex heterogeneity is lacking. 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 can be integrated with the volume averaging technique to provide effective description of transport at the coarse scale. We studied the scaling characteristics of effective transport coefficient for a tracer injection process corresponding to different reservoir heterogeneity correlation lengths as well as different transport mechanisms (e.g. convection, dispersion, and diffusion). Our results show 1) mean and variance of the effective transport coefficient decrease with length scale, similar in the fashion of recovery statistics (e.g. variances in tracer breakthrough time and recovery); 2) the scaling of effective transport coefficients is extremely non-linear; 3) heterogeneity affects the scaling characteristics of transport mechanisms significantly.