低速非达西渗流流量动态规律研究

流体流动边界不断向外扩展是低速非达西渗流压力传播的特点。针对这种情况，首先建立了考虑表皮效应影响的低速非达西渗流定井底流压生产的固定边界数学模型，用格林函数法求出了流量和累积流量的拉普拉斯空间解；然后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，再用固定边界模型计算流量和累积流量与时间的关系，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流量和累积流量变化曲线，讨论了流动边界、启动压力梯度和表皮效应的影响及非达西渗流与达西渗流流量动态的差别．

Well Flowrate Performance for Low Velocity Nondarcy Percolation with Flowing Boundary

Fluid flowing barrier extends outwards continuously, which is a feature of pressure propagation in low velocity nondarcy percolation. In views of such character, a fixed boundary mathematical model based on the pattern of low velocity nondarcy percolation with skin effect is presented, and solutions of flow rate and cumulative production in Laplace domain is worked out with Green's function. The radius of flowing boundary corresponding to different time intervals is determined according to the starting differential pressure needed by fluid from static to flowing condition. The analytical solution of the fixed boundary model is then used to calculate the correlation of flow rate and cumulative production versus time, which is regarded as a numerical approximation of flowing boundary model.Stehfest method is used to obtain the flow rate and cumulative production curves. Discussion is presented on the influence of flowing boundary, starting pressure gradient, skin effect and difference between darcy percolation and nondarcy percolation.