@Article{IJNAMB-5-269,
author = {Zichen Deng},
title = {Numerical Solutions of a Hypersingular Integral Equation with Application to Productivity Formulae o},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2014},
volume = {5},
number = {3},
pages = {269--288},
abstract = {The performance of horizontal wells producing at constant wellbore pressure is a critical problem in petroleum engineering. But few articles on the well performance under constant
wellbore pressure can be found in the literature due to the difficulty of hypersingular integral
equations, which are needed for this problem. This article proposes and studies a new model using
a hypersingular integral equation for the productivity of horizontal wells producing at constant
wellbore pressure. An efficient numerical method is developed for this hypersingular integral
equation based on a new expansion with respect to the singularity at arbitrary points. And
numerical examples are provided to illustrate the convergence of the numerical methods. By
using fluid potential superposition principle, productivity equations for a line sink model are
derived from the point sink solution to the diffusivity equation. By solving the hypersingular
integral equation, the authors obtain the productivity formulae of a horizontal well producing at
constant wellbore pressure, which provide fast analytical tools to evaluate production performance
of horizontal wells. Numerical examples are provided to illustrate the features of the model and
the numerical method.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/234.html}
}