TY - JOUR
A2 - Chen, Kue-Hong
AU - Hu, Chaolang
AU - Lu, Jing
AU - He, Xiaoming
PY - 2012
DA - 2012/08/14
TI - Productivity Formulae of an Infinite-Conductivity Hydraulically Fractured Well Producing at Constant Wellbore Pressure Based on Numerical Solutions of a Weakly Singular Integral Equation of the First Kind
SP - 428596
VL - 2012
AB - In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these two methods are in accordance with each other. And then the solutions of the weakly singular integral equation are utilized for the productivity formula of hydraulic fractured wells producing at constant pressure, which provide fast analytical tools to evaluate production performance of infinite-conductivity fractured wells. The paper also shows equipotential threads, which are generated from the numerical results, with different fluid potential values. These threads can be approximately taken as a family of ellipses whose focuses are the two endpoints of the fracture, which is in accordance with the regular assumption in Kuchuk and Brigham, 1979.
SN - 1024-123X
UR - https://doi.org/10.1155/2012/428596
DO - 10.1155/2012/428596
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -