Study On Deliverability Equations Of Natural Gas Wells

This paper starts with analyzing unstable-flow mathematical model of natural gas. Linearize the non-linear flow equation by using the pseudo-pressure function and pseudo-time function, simplify the unsteady-stage flow equation into steady-state equation by advantage of the characteristics of "pseudo-steady state ", then solve the steady-state equation in order to get deliverability equation of gas well. Finally, analyzing the deliverability equation of gas well and comparing three other improved deliverability equations of gas well.On the basis of the definition of pseudo-pressure function and pseudo-time function, we presents the calculation methods and results of the pseudo-pressure function in conventional reservoir and pressure sensitive reservoir, traditional pseudo-time function and “material balance” pseudo-time function. And then show the curves and results in Cartesian coordinate. Besides, we present the relationship of recovery and parameters(μgcg).For unstable flowing model of circular homogeneous gas reservoir, Laplace transform, Bessel function addition theorem and asymptotic analysis is adopted to solve the model. Then we obtain the pseudo-steady-state deliverability equation. Analysis of the influence of eccentricity on gas well productivity shows that eccentricity boundary effect has been brought forward due to the existence of eccentricity in advance, plane radial flow duration becomes shorter than before, dimensionless pressure derivative upturns produced in the late. The upturn is similar with the effect of single line fault, but the essence is different--there is no Radius to the flow line segment in the curve of pressure derivative; for a given reservoir, the greater the eccentricity is, the faster the production decreases; in the condition of elastic, it is inversely proportional to the elastic production and eccentricity except in the late period.For unstable flowing model of rectangle homogeneous pressure-sensitive gas reservoir, combining Newman product method with the point source function results in the analytic solution. By redefining the pressure-sensitive pseudo-pressure function and pressure-sensitive pseudo-time function and using asymptotic analysis, we obtain the pseudo-steady-state deliverability equation of gas well in the late period. Results show that with the increase of the permeability sensitivity, in constant production condition wellbore pressure decline increased, and production decrease in constant bottom-hole flow pressure, which indicating that the flow resistance caused by permeability reduction increases.The results of this paper can be used for the analysis and prediction of production and providing basic data for the production decision of gas wells.