Abstract

The horizontal gas well has more and more important roles in developing low permeability gas reservoirs, fractured gas reservoirs and bottom-water gas reservoirs. The productivity forecast of horizontal gas well is an important research work in aspect of its gas reservoir engineering. Based on gas underground percolation theory, considering formation damage and non-darcy effect, this article establishes the mathematical model of horizontal gas well production rate analysis, on the basis of obtaining the mathematical model solution, i. e. production rate equation of horizontal gas well, we derive binomial productivity equations with the forms of pressure square, thus, we can forecast inflow performance relationship(IPR) curve absolute open flow potential and production performance of horizontal gas well by using the binomial productivity equations. At the same time, we study the influences of the gas reservoir bed thickness, anisotropism of gas reservoir on the inflow performance relationship(IPR) curve and absolute open flow potential. Inflow performance relationship(IPR) curve of an example horizontal gas well is made in this paper. The binomial productivity equations presented in this paper supply the foundation for calculating and forecasting the productivity performance of horizontal gas well.

Introduction

So far, in the world, more and more special oil and gas reservoirs are developed through the horizontal well, both the horizontal oil well and the horizontal gas well, analysis methods of their productivity are important research content. Recently several years, many scholars[1][2][3][4][5][6][7] studied productivity of the horizontal oil well, their methods contained that method of Joshi[1] and method of Babu[2]. At the present, analysis method of the horizontal gas well is not reported. Based on gas underground percolation theory, considering formation damage and non-darcy effect, this article establishes the mathematical model of horizontal gas well production rate analysis, on the basis of obtaining the mathematical model solution, i.e. production rate equation of horizontal gas well, we derive binomial productivity equations with the forms of pressure square, thus, we can forecast inflow performance relationship(IPR) curve, absolute open flow potential and production performance of horizontal gas well by using the binomial productivity equations. At the same time, we study the influences of the gas reservoir bed thickness, anisotropism of gas reservoir on the inflow performance relationship(IPR) curve and absolute open flow potential. Inflow performance relationship(IPR) curve of an example horizontal gas well is made in this paper. The binomial productivity equations presented in this paper supply the foundation for calculating and forecasting the productivity performance of horizontal gas well.

MATHEMATICAL MODEL OF HORIZONTAL GAS WELL PRODUCTION RATE EQUATION

Fig.1 shows a schematic picture of horizontal well. To set up mathematical model of horizontal gas well steady flow, we establish the following additional hypotheses:

(1) The gas reservoir is horizontal with constant uniform thickness(h), horizontal permeability (Kh) and vertical permeability (Kv), the initial pressure is equal to constant (PR).

(2) Horizontal gas well located at a distance δ z from the gas reservoir center and paralleled with upper and lower impermeable, its length isL.

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