垂直裂缝井开发低渗透气藏产能方程求解新方法

为更加有效地表征气藏压裂后地层流体渗流规律的变化,得到预测更接近实际的产能动态方程,进而得到更加准确的绝对无阻流量值。基于稳定流理论,根据低渗透气藏压裂后气井的渗流特征,引入椭圆坐标的拉梅系数;并采用椭圆积分方法重新推导、建立了考虑启动压力梯度影响的低渗透气藏垂直裂缝井的产能动态预测方程。研究结果表明:气体渗流中启动压力梯度是一种附加阻力,其越大气井产量越低;裂缝导流能力越强、裂缝越长,整个渗流过程总压降越小,气井产量越高。低渗透气藏压裂设计中,当裂缝达到极限导流能力后,限制低渗透气藏产量的重要因素之一是椭圆渗流能力的大小,此时增加裂缝长度对增产更有效。某压裂气井实例计算得绝对无阻流量值与试井结果的相对误差为2.8%。

A New Solution of Productivity Equation for Vertically Fractured Gas Wells in Low-Permeability Reservoirs

In order to characterize the changes of fluid flow rule more effectively in the fractured gas reservoir and obtain a more predictable and applicable productivity equation which can forecast a more precise AOF (absolute open flow)c, this paper has studied a new solution of the productivity prediction equation for vertically fractured gas wells in low-permeability gas reservoir. Based on the steady flow theory and the percolation characteristics of gas well with vertical fracture, by introducing the Lamé coefficient and the method of elliptic integral and considering the starting pressure gradient, the equation is proposed. The result indicates that as for the gas flow the starting pressure gradient is an additional resistance. The greater its value, the less the gas production is. Besides, the stronger the fracture conductivity and longer the fracture length, the less the overall pressure dropdown is, thus the greater the gas production is. Furthermore, in designing of fracturing process for the low-permeability gas reservoir, one of the key factors restricting gas production when the fracture conductivity reaches its peak, is elliptic flow ability. At this point, fracture length increasing is more important for purpose of enhancing recovery. The result of case study shows that the relative error of AOF is 2.8%, compared with well testing method.