一个新的考虑启动压力梯度的三项式产能方程

A Novel Trinomial Deliverability Equation with Threshold Pressure Gradient

在Forchheimer提出的二项式非达西渗流方程的基础上,考虑启动压力梯度对低渗气藏气井渗流规律的影响,建立了考虑启动压力梯度的三项式非达西渗流方程。结合常规二项式产能方程,建立了考虑启动压力梯度的三项式产能方程。由于启动压力校正系数与启动压力梯度有关,而启动压力梯度很难确定,需采用试算法求取校正系数和产能方程。实例分析表明:对于存在启动压力梯度的修正等时试井数据,用常规产能分析方法得到的(p2e-p2wf)/qsc与qsc直线的斜率小于0;用本文的产能分析方法得到的(p2e-p2wf-c)/qsc与qsc关系直线的相关系数为0.9975,可用于分析气井的产能。这一新的产能分析方法可用于分析存在启动压力梯度的低渗气井产能,由此确定单井合理产量。

On the basis of Forchheimer's binomial non-Darcy flow equation, trinomial deliverability equation is constructed by taking into account the threshold pressure gradient that influences the seepage law of low permeability gas well. Moreover, combining with the LIT equation, trinomial deliverability equation is constructed by taking into account the threshold pressure gradient. Because the correction coefficient of threshold pressure c is related to threshold pressure gradient, which is difficult to determine, a trial-and-error process is used to determine the correction coefficient c and the deliverability equation. Case studies show that, for modified isochronal test data with the threshold pressure gradient, conventional deliverability analysis results in negative slope of (P^2_e-P^2_ wf )/q_ sc —q_ sc ; the new method based on trinomial deliverability equation can lead to a correlation coefficient of 0.9975 of (P^2_e-P^2_ wf -c)/q_ sc —q_ sc . This indicates that the new method can be used to analyze low permeability gas well deliverability with the threshold pressure gradient to determine a reasonable rate.