利用δ函数计算间歇试采井压力分布

Calculation of pressure distribution in intermittent producing test well with δ Function

δ函数是一个用于描述非连续分布物理量的数学工具,利用δ函数的相关理论和性质,采用密度方程求解瞬时注入或采出δm量流体后(集中分布的物理量)的地层压力分布,对这个集中分布量的地层压力进行叠加,模拟了间歇采油井的压力分布和井底压力。利用井底压力的表达式进行间歇采油井的压力历史拟合,为间歇采油井的试井分析和产能评价提供了依据。对大庆油田一口间歇井进行了实例计算,并与实测数据进行了对比,该方法的计算结果符合间断流动状态地层压力分布的实际情况。

The intermittent pumping technique is often used in the low-permeability reservoir with poor deliverability. In this case, the downhole pressure transforms discontinuously. δ function is a mathematical tool to describe the discontinuous distribution of physics quantity. On the basis of δ function theory, the formation pressure distribution of instantaneous injection or after producing certain quantity of fluid were calculated with the density equations. The calculated pressure distribution and downhole pressure were superposed and simulated under the intermittent pumping condition. The downhole pressure expression was used to match the intermittent pumping pressure history. This method can provide the basis for well testing analysis and production evaluation. The calculation case of an intermittent producing well in Daqing Oilfield is presented. The comparison of calculated data with field data proved that this method is possible.