The Establishment and Application of Binomial Deliverability Equation for Horizontal Gas Well
Authors: Li X. , Huang B. , Hu Y. 
Published: July 2010

Abstract
Based on gas flow theory in porous media, this paper has considered the formation damage and non-Darcy flow effect and obtained binomial productivity equation in the form of pressure square. Therefore, we can predict inflow performance relationship (IPR) curve, the absolute open flow potential, and production performance of horizontal gas wells by binomial productivity equation. At the same time we study the influences of the gas reservoir bed thickness, anisotropism of the gas reservoir on the IPR curve, and the absolute open flow potential for the example horizontal gas well.

Introduction
In the past few years, many scholars(1–4) such as Joshi and Babu have researched the productivity of horizontal oil wells, but no analysis method of the productivity for the horizontal gas wells has been reported. Based on gas flow theory in porous media, this article has considered formation damage and non-Darcy flow effect and establishes binomial productivity equations with form of pressure square. Therefore, we can predict inflow performance relationship (IPR) curve, the absolute open flow potential, and production performance of horizontal gas wells by them. At the same time, we have studied the influences of the gas reservoir bed thickness, anisotropism of gas reservoir on the IPR curve, and the absolute open flow potential for the example horizontal gas well.

Binomial Deliverability Equation for Horizontal Gas Well
Considering formation damage and non-Darcy effect(5, 6), the production rate equation will be expressed by(7):
Equations (available in full paper)

Factor Analysis of Influencing Inflow Performance of Horizontal Gas Well
Figure 2 shows the IPR curves of a horizontal gas well under different conditions of reservoir thickness. The following are the basic parameters of the horizontal gas well: drainage area is 0.785 km2; the radius of the horizontal gas well equals 0.12 m; the well length equals 500 m; Kh = Kv = 0.1 µm2; i.e., anisotropy ratio is 1; the gas viscosity equals 0.0124 mPa.s; the gas gravity equals 0.6042, deviation factor equals 0.9; temperature of gas reservoir equals 353.15 K; the initial pressure equals 20 MPa; the well is located at the center of the gas reservoir; and, the formation damage is neglected.
The IPR curve shown in Figure 2 of a horizontal gas well is similar to the curve of a vertical gas well. The IPR curve of the horizontal gas well moves right accordingly per the increase of gas reservoir thickness. If the bottom pressure is equal to zero, absolute open flow qAOF of horizontal gas well could be obtained. For example, qAOF = 280.3812 ? 104 m3/d when the thickness of the gas reservoirs equals 10 m.
Figure 3 shows the IPR curves of a horizontal gas well with the effect of gas reservoir anisotropy. The basic parameters of the horizontal gas well are the same as Figure 2. The vertical permeability equals 0.1 µm2; ratios of the gas reservoir anisotropy are 0.316, 1, 3.16, 7.07.
The IPR curve shown in Figure 3 of a horizontal gas well is similar to the curve of a vertical one.