基于拟时间函数的气井不稳定生产数据分析

Analysis of the unsteady production data of a gas well based on pseudo-time function

将气井不稳定流动阶段的产量、压力等生产数据处理为产量修正的拟压力差与拟时间,利用两者间的线性关系可以确定出裂缝长度、地层渗透率等参数,据此评价气井压裂效果、预测气井生产动态。为了准确计算拟时间值,通过引入动边界概念,将探测边界视为压力扰动的外边缘,利用积分方法求解渗流偏微分方程,得到由气井生产引起的探测边界传播规律,结合物质平衡方程获得探测范围内的平均地层压力,并借助迭代算法确定不同生产时刻对应的气体拟时间。结果表明:与拟时间相比,直接使用真实时间分析生产数据,定压生产时引起直线斜率偏小,且生产压差越大偏差程度越明显,定产生产时导致数据线性相关性变差,气井产量越高相关系数越低;在变产量生产时,利用物质平衡拟时间能够消除气体高压物性和变产量带来的非线性影响,明确生产数据间的线性关系,压裂参数的计算结果更为合理。

The per-well performance data like productivity,pressure,etc.at the unsteady stage of the well production are processed as rate-normalized pseudo pressure and pseudo time.In order to evaluate the fracturing effect and predict the per-well performance,we need to determine the fracture length and formation permeability,etc.through utilizing the slope of a square-root-time plot （a plot of rate-normalized pressure vs.square root of pseudo time）.But the actual value of pseudo time is hard to obtain.Therefore,based on the concept of moving boundary,the distance of investigation was regarded as the region obviously affected by pressure disturbance.An approximate solution to the propagation rule of investigation boundary was obtained by an integral method at a variable rate condition,which was used to calculate the average pressure within the investigation region.The pseudo time value was thus calculated with the help of the corresponding iterated algorithm.The results showed that the slope of a square root time plot is smaller than that of a square root pseudo time plot at constant pressure conditions,while the plot of square root time derivates from the expected straight line at constant rate conditions,where the degree of these deviations is determined respectively by flowing pressure drop and production rate.At variable rate conditions,a distinct linear relationship in the plot could be observed by incorporating the material balance pseudo time,which results in a reliable calculated result of fracture length.