Natural Cross-flow Rate Modeling in Complex Reservoirs

During fluid injection into a complex reservoir, different pressure gradients are generated in the sandface of each layer because of differences in reservoir properties such as permeability, compressibility, thickness, porosity and depletion. Upon shut-in, these differences cause flow from high-pressure layers, usually of lower permeability, to low-pressure layers, usually of higher permeability, a process known as natural cross-flow. Cross-flow may lead to sanding problems [e.g. Santarelli et al. 1998]. In this study, one-dimensional (axisymmetric) natural cross-flow in a complex reservoir is simulated using a finite difference approach. The problem is solved for multiple layers with different permeabilities, separated by impermeable layers. In the paper we emphasize various means of establishing input parameters and apply the model to several well-documented field cases, demonstrating its capacity to predict accurately measured cross-flow.