Rate transient analysis of infinite-acting linear flow by use of piecewise constant diffusivity coefficients

Abstract

Rate transient analysis (RTA) techniques are developed based on the analytical solutions to the hydraulic diffusivity equation. The diffusivity equation is subject to nonlinearity caused by the dependency of the rock and fluid properties to pressure. In this study, first, we develop a semi-analytical model to solve a nonlinear diffusivity equation for transient linear flow under the constant bottom-hole pressure condition. We use piecewise constant diffusivity coefficients to linearize the diffusivity equation. The domain under consideration is divided into an arbitrary number of subdomains. Each subdomain is assigned with a constant hydraulic diffusivity coefficient. As a result, the nonlinear diffusivity equation is reduced into a set of piecewise linear equations. Further, we propose a new RTA approach using the developed semi-analytical model. We then validate both the semi-analytical model and the RTA approach against direct numerical simulation. The comparison reveals the high accuracy of the developed model in the estimation of reservoir properties, pressure profiles, and flow rates, including the cases with highly pressure-dependent properties. Finally, we apply the proposed RTA approach to the flowback and long-term production data obtained from two horizontal wells to determine the reservoir properties, such as the cross-sectional area to flow and initial permeability. The field applications demonstrate that the proposed RTA approach provides a rigorous avenue for production data analysis of pressure-sensitive formations during transient linear flow.