水平井射孔优化设计的增广拉格朗日乘子法

AUGMENTED LAGRANGE MULTIPLIER METHOD FOR PERFORATION OPTIMIZATION DESIGN OF HORIZONTAL WELL

射孔参数优化能提高水平井开发效果。考虑射孔分布对水平井产能的影响,以Landman油藏稳态渗流模型为基础,以孔眼位置为优化设计变量,分别建立了以水平井产量最大和水平井生产端压力降最小为目标函数的优化模型。利用增广拉格朗日乘子法具有收敛速度快和求解精度高的特点,对无限导流水平井射孔分布进行优化研究。结果表明,优化射孔分布能有效地改善沿水平井井筒流入流量剖面;对一定的井底流压和产量,射孔水平井存在最佳的射孔分布。算例中,为得到最大产量或最小井底流压,射孔密度沿水平井井筒呈"U"型分布;若考虑沿水平井井筒流入流量剖面均匀,则射孔密度沿水平井井筒呈"∩"型分布,但产能略有降低。上述研究为水平井射孔分布优化设计提供了新方法。

The optimum perforation distribution is of great benefit to enhance the exploitation effect of horizontal wells.Considering the effect of perforation distribution on productivity of horizontal wells,based on the Landman model of steady state inflow,the optimization models were established,in which production or bottom hole pressure was treated as an objective function,positions of perforations as the decision-making variable.Perforation distribution of an infinite conductivity well was studied by virtue of augmented Lagrange multiplier method with rapid convergence and high precision.The results indicated that the profiles of inflow rate were improved effectively through optimizing perforation positions.For a given bottom hole pressure or production rate,there exists a reasonable perforation distribution.For the given example,perforation density distribution showed a shape of 'U' on the horizontal wellbore in order to obtain maximum production or minimum bottom-hole pressure.However,aimed to maximize production or minimize bottom-hole pressure,the perforation density was distributed like a shape of '∩' on the horizontal wellbore considering the constraint of uniform inflow rate which leads to decreasing the productivity a little of the horizontal well.The above research provided a new method for optimization of perforation parameters of horizontal wells.