基于序列二次规划算法的射孔水平井孔眼分布优化

Optimization of perforation distribution of perforated horizontal well based on sequential quadratic programming algorithm

基于Landman稳态渗流模型和Su井筒压降模型,考虑射孔密度对水平井产能的影响,建立以水平井产能为目标函数、孔眼位置分布为优化设计变量的两类产能优化模型。采用序列二次规划算法求解优化模型,并对无限导流和有限导流水平井的射孔密度分布进行优化。结果表明:优化射孔能有效地改善沿井筒入流剖面;射孔水平井存在最佳的射孔密度分布;为得到最大产量,无限导流井的射孔密度呈'U'型分布,有限导流水平井的射孔密度沿跟部到趾部方向逐渐降低,约在井筒长度的3/4位置处取得最小值;若要使沿井筒入流剖面尽可能均匀,则无限导流井的射孔密度呈'∩'型分布,有限导流井的射孔密度沿跟部到趾部方向逐渐升高,约在井筒长度的3/4位置处取得最大值,但最大产量略有降低。

Based on Landman model of steady state inflow and Su model of pressure drawdown along the wellbore, two types of optimization models were established considering the effect of perforation density on productivity of horizontal well, in which the production of the horizontal well was treated as an objective function and the perforation distribution as a decision-making varia- ble. The sequential quadratic programming algorithm was applied to the optimization models of horizontal well established under the conditions of infinite and finite conductivity respectively. The results indicate that the profiles of inflow rate are improved ef- fectively through optimizing perforation positions and there exists a reasonable perforation density distribution. For a given ex- ample, the perforation density distribution with a shape of ＂U＂ leads to maximum production for the infinite conductive horizon- tal well. However, the perforation density decreases from the heel of the wellbore to the toe and reaches the minimum at the lo- cation of 3/4 length of the well from the heel. Under the constraint of uniform inflow flux, the perforation density distribution shows a shape of ＂ f3＂ for the infinite conductive horizontal well. For the finite conductive horizontal well, the perforation den- sity increases toward the toe of the wellbore and reaches the maximum at the location of 3/4 length of the well. The constraint of uniform inflow flux leads to the decrease in the maximum production of the perforated horizontal well.