Generalized Analytical Well-Test Solutions for Vertically Fractured Wells in Commingled Reservoirs

Abstract

Layered zones with vertical fracture are often found in analyzing well-test data of deep/ultra-deep reservoirs and tight reservoirs. Analyzing and modeling the well-test data in a computation-accurate and easy-program manner have been a challenge for these problems due to the lack of suitable solutions. This work thus presents the generalized analytical well-test solutions for vertically fractured wells in infinite and bounded commingled reservoirs with computation accuracy and functional simplicity. These solutions are derived based on the early-time approximate solution of the infinite/finite-conductivity fracture model, Laplace and Fourier cosine transformation, pressure superposition principle, and Duhamel principle. Subsequently, model validation is carried out by comparing the pressure and derivative results with those of commercial saphir software. The results show that the average absolute percent deviation between the presented analytical solutions and saphir for three kinds of outer boundaries is ∼2% for pressure results and ∼4% for pressure derivative results. Finally, a field case in Xinjiang oilfield is interpreted, indicating that the proposed analytical well-test solutions are feasible to interpret the parameters of commingled reservoirs.