Two-Dimensional Analytical Solution of Ideal Perforation Flow

Abstract

AbstractCore flow efficiency (CFE) is defined to quantitatively evaluate the flow performance of single-shot perforation. To calculate CFE, the flow rate of the ideal perforation flow in the core target is needed. The ideal flow rate is typically calculated with numerical simulators, but the computation may be time-consuming and costly.This paper presents the two-dimensional analytical solution of the steady state flow model (mass conservation equation) for the ideal single-shot perforation in a cylindrical core sample. The separation of variable method is used to solve the partial differential equation of the flow model. Pressure and velocity distributions in (r, z) space are obtained, as well as the flow rate distribution along the perforation tunnel.The accuracy and convergence of the analytical solution for the ideal single-shot perforation flow are investigated and compared with those of the numerical solution of the commercial software ANSYS FLUENT. The analytical solution for the governing equation of the ideal perforation flow is composed of the infinite number of Bessel functions. To compute the CFE by making use of this analytical solution, the analytical solution is approximated with a limited number of Bessel functions. The approximated analytical solution is analyzed and compared with the numerical solutions from ANSYS FLUENT.Further, the axial, radial, and radial-axial flow geometries of the ideal shingle-shot perforation are characterized with their approximated analytical solutions. Interactions between the boundary condition, perforation parameters, and core parameters are investigated for these flow geometries.The analysis results show that: 1) the analytical solution has no grid effects; 2) the boundary condition of the perforated core is the dominant factor to the ideal flow rate of the perforated core; 3) the penetration depth and anisotropic permeability are the significant factors to the flow performance of the perforated core.