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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
Joint Authors
He, Xiaoming
Hu, Chaolang
Lu, Jing
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-06-04
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Hu, Chaolang& Lu, Jing& He, Xiaoming. 2012. 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. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-1001591
Modern Language Association (MLA)
Hu, Chaolang…[et al.]. 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. Mathematical Problems in Engineering No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-1001591
American Medical Association (AMA)
Hu, Chaolang& Lu, Jing& He, Xiaoming. 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. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-1001591
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1001591