A semi-analytical rate-transient analysis model for light oil reservoirs exhibiting reservoir heterogeneity and multiphase flow

Abstract

Rate-transient analysis (RTA) has been widely applied to extract estimates of reservoir/hydraulic fracture properties. However, the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously. This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, and improve the evaluation of reservoir/fracture properties. A new, general, semi-analytical model is proposed that explicitly accounts for multiphase flow, fractal-based reservoir heterogeneity, anomalous diffusion, and pressure-dependent fluid properties. This is achieved by introducing a new Boltzmann-type transformation, the exponent of which includes reservoir heterogeneity and anomalous diffusion. In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, the modified Boltzmann variable allows the conversion of three partial differential equations (PDE's) (i.e., oil, gas and water diffusion equations) into ordinary differential equations (ODE's) that are easily solved using the Runge-Kutta (RK) method. A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties, recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously. Using the slope of the straight line on the modified time-power-law plot, the linear flow parameter can be estimated with more confidence. Moreover, because of the new Boltzmann-type transformation, reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations. Using the new semi-analytical model, the effects of multiphase flow, reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated. For the case of approximately constant flowing pressure, multiphase flow impacts initial oil rate, which is a function of oil relative permeability and well flowing pressure. However, multiphase flow has a minor effect on the oil production decline exponent. Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent. The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only. The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios, leading to more accurate production forecasting and better-informed capital planning.