临界产量Dupuit公式的讨论及一种新的方法

临界产量的确定对底水油藏的高效开发起着重要作用. 然而,临界产量Dupuit 公式反映临界产量随着打开程度的降低而单调增加,存在不合理的地方. 本文与一些学者的研究表明,Dupuit 公式推导过程暗含的“当临界状态时水锥正好处于井底” 的假设不合理,水锥不能稳定在井底位置. 在不作水锥到达井底的假设,假设油井上部为径向流,井底周围为半球形流动的情况下,推导出了一种新的底水临界产量方程. 算例与工程实例表明,该方法比较符合实际,能够求得临界水锥高度和对打开程度进行优化. 

DISCUSSION ON DUPUIT FORMULA OF BOTTOM-WATER CRITICAL RATE AND A NEW COMPUTATIONAL METHOD

The determination of critical rate is a key issue of high-efficient development of bottom-water reservoirs, while in the Dupuit formula of bottom-water reservoirs' critical rate, it is unreasonable that the critical rate monotonously increase with the reduction of perforating level. In fact, checking the derivation process of Dupuit formula, there is an implied condition that the top of water cone just at the well bottom. However, it is found that it can't keep a stable water cone at well-bottom when producing with the critical rate computed by Dupuit formula. In the paper, a new computational method has been established without the assumption of water-cone top at well bottom. It assumes that it is a kind of radial flow at the upper and a kind of hemispherical flow at the lower around the well bottom. The example shows that the new method could optimize the perforating level and gain the critical water-cone height. The project case demonstrates that the method gained in this study is more correspond to reality.