Abstract

Based on principle of mass conservation, this paper sets up a new mathematical model of gas-water two-phase underground percolation, and the model includes the influences of formation damage and non-darcy eflect. Theoretically, we first obtain the production rate equations of gas-water well with the forms of pseudo-pressure. On the basis of the production rate equations, we deduced the binomial productivity equation, thus, the IPR curve of gaswater well can be calculated by the binomial productivity equation, at the same time, the influences of gas-water ratio on IPR curve is studied. This paper also describes the calculation method of IPR curve #and expounds how to use the IPR curve to determine gas and water production rate from gas-water well.

By the end IPR curve of an example gas-water well is calculated and analyzed. The research in this paper supplies a new way for the productivity analysis and performance prediction in gas-water well.

Introduction

Inflow performance relationship curve(IPR) is an important means of predicting gas behavior, productivity of gas well and reasonable working system are determined by using Inflow performance relationship curve(IPR). The IPR curve of pure gas well is obtained usually by productivity test. Many paper[1][5] has reported research methods of the IPR curve of gas well. Under the condition of gas and water simultaneous production, if we use the IPR curve of pure gas well to predict production performance of gas-water well(two-phase flay condition exist simultaneous in both gas reservoir and wellbore), it is inevitable necessary to generate erroneous. There has no report on IPR curve of gaswater well in gas reservoirs undergoing simultaneous water production yet.

This paper deduced the binomial productivity equation of gas-water well, thus, the IPR curve of gas-water well can be calculated by the binomial productivity equation, at the same time, the influences of gas-water ratio on IPR curve is studied. This paper also describes the calculation method of IPR curve and expounds how to use the IPR curve to determine gas and water production rate from gas-water well.

By the end, IPR curve of an example gas-water well is calculated and analyzed. The research in this paper supplies a new way for the productivity analysis and performance prediction in gas-water well.

MATHMETICAL MODEL

To set up mathematical model of gas-water well steady flow, we establish the following additional hypotheses: the gas reservoir are both horizontal and homogeneous with uniform thickness, constant porosity, and the initial pressure is equal to constant. Gas-water two-phase flow appears in gas reservoir, flow of gsa-water obeies Darcy law, Gravitational effect is neglected. Mathematical model is expressed as follows: diffusivity equation:

Equation (1) (Available in full paper)

Equation (2) (Available in full paper)

Equation (3) (Available in full paper)

Equation (4) (Available in full paper)

Equation (5) (Available in full paper)

Equation (6) (Available in full paper)

Equation (7) (Available in full paper)

Equation (8) (Available in full paper)1

Equation (9) (Available in full paper)

Equation (10) (Available in full paper)

This content is only available via PDF.