考虑流动边界影响的低速非达西渗流试井解释模型

流体流动边界不断向外扩展是低速非达西渗流压力波传播的特点。针对这种情况,建立了考虑井筒储存和表皮效应影响的低速非达西渗流定产量生产的固定边界数学模型,用格林函数法求出井底压力的拉普拉斯空间解,根据流体从静止到流动所需的启动压差确定不同时刻的流动边界半径,用固定边界模型计算井底压力与时间的关系,以此作为流动边界模型的一种数值逼近。用Stehfest数值反演算法绘制了井底无因次压力与无因次时间关系曲线,讨论了流动边界、启动压力梯度、井筒储集和表皮效应的影响及非达西渗流与达西渗流井底压力动态的差别。

Study on Well Flowrate Performance of Low Velocity Non- Darcy Percolation with Flowing Boundary

The fluid flowing boundary extends outwards continuously is the feature of pressure propagation with low velocity Non-Darcy percolation.Based on this situation,a fixed boundary mathematical model based on the pattern of low velocity Non-Darcy percolation with wellbore storage and skin effect is presented,and solutions of wellbore pressure in Laplace domain is worked out with Green′s function.The radius of flowing boundary of different time interval is then determined in accordance with the starting differential pressure needed by fluid from static to flowing condition,analytical solution of fixed boundary model is then used to calculate the correlation of wellbore pressure vs time,which is regarded as a numerical approximation of flowing boundary model.The wellbore pressure vs time curves have been developed by Stehfest method,and the influences of flowing boundary,starting pressure gradient,wellbore storage,skin effect and difference between Darcy percolation and Non-Darcy percolation were also discussed.