Analysis of bottom hole pressure of unsteady flow in dual-medium fracturing vertical well

Abstract

AbstractIn order to improve the validity of bottom hole pressure model, and simplify its calculation process, a mathematical model of instantaneous pressure for unsteady flow was established by considering the crossflow between the fractures and matrix. Different conditions, including the reservoir top has constant pressure, were considered. The basis for obtaining bottom hole pressure is to solve diffusivity equation with the integration of axisymmetric transformation and similar methods, which is presented for the first time. Different from the traditional method of using the Green’s function and source solution, this paper uses Laplace transformation, axisymmetric transformation and similar methods, separation of variables to obtain the analytical solution of Laplace domain. Then, the Stephenson Numerical method was used to obtain the numerical solution in a real domain. The results of this method agree with the numerical simulations and actual test data, suggesting the validity and accuracy of this method. Finally, the sensitivity analysis revealed that the pressure curve can be divided into eight stages, namely, early linear flow, continuous flow transition section, fracture linear flow, formation linear flow, crossflow, transitional flow, pseudo-radial flow and boundary control flow. The advantage of the analytical solution utilized in this paper is to incorporate exchange coefficient and skin factor efficiently, providing a theoretical basis for optimizing production pressure difference and determining the reasonable productivity.