Practical pressure-transient analysis solutions for a well intercepted by finite conductivity vertical fracture in naturally fractured reservoirs

The semi-analytical or numerical solutions are the most used for pressure-transient analysis (PTA) for finiteconductivity fractured wells in naturally fractured reservoir now. However, the semi-analytical solutions are time-consuming and easily lead to inaccuracy at low fracture conductivity with less discretized segments. The numerical solutions are more time-consuming and usually face convergence and stability problems. These solutions are not convenient for practical well test analysis in Oilfield. Our motivation for this paper is to develop simply, quickly and stably analytical PTA solutions for finite-conductivity fractured wells in naturally fractured reservoir that can serve the well test analysis in Oilfield. We first derive a transformation method which can extend finite-conductivity fracture solutions in homogeneous reservoir to dual-porosity reservoir. Thereafter, analytical solutions for finite-conductivity fractured wells in homogeneous reservoir are presented. Then we provide a series of analytical finite-conductivity fracture solutions in dual-porosity reservoir under different boundary conditions based on the transformation method and homogeneous reservoir solutions. Six solutions given in the published literatures are used to verify the proposed solutions under different dimensionless fracture conductivity (FcD). Results indicate that (a) the proposed solutions are valid for FcD>1 with maximum error (5%) and this error will quickly decreases to around 1%; (b) the proposed solutions are applicable for infinite, closed and constant-pressure boundary conditions; (c) the proposed solutions can be extended to triple-porosity naturally fractured reservoirs after changing the f(s) function; (d) the proposed solutions are accurate and can greatly shorten the time of well test interpretation comparing to conventional solutions. Finally, the pressure-buildup data from Shunbei Oilfield is interpreted using the proposed solutions to verify its feasibility and practicability. The findings of this work can help for better understanding of its potential in quick well test analysis for field cases.