Volume 5, Issue 3
Numerical Solutions of a Hypersingular Integral Equation with Application to Productivity Formulae o

CHAOLANG HU, JING LU, AND XIAOMING HE

Int. J. Numer. Anal. Mod. B,5 (2014), pp. 269-288

Published online: 2014-05

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  • 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.
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65R20

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@Article{IJNAMB-5-269, author = {CHAOLANG HU, JING LU, AND XIAOMING HE}, 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} }
TY - JOUR T1 - Numerical Solutions of a Hypersingular Integral Equation with Application to Productivity Formulae o AU - CHAOLANG HU, JING LU, AND XIAOMING HE JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 269 EP - 288 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/234.html KW - Hypersingular Integral Equation KW - Quadrature method KW - Horizontal Well KW - Constant Wellbore Pressure AB - 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.
CHAOLANG HU, JING LU, AND XIAOMING HE. (2014). Numerical Solutions of a Hypersingular Integral Equation with Application to Productivity Formulae o. International Journal of Numerical Analysis Modeling Series B. 5 (3). 269-288. doi:
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