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

Key words:  horizontal wells  perforation distribution  optimization model  sequential quadratic programming algorithm

Abstract:

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 variable. 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 effectively through optimizing perforation positions and there exists a reasonable perforation density distribution. For a given example, the perforation density distribution with a shape of “U” leads to maximum production for the infinite conductive horizontal well. However, the perforation density decreases from the heel of the wellbore to the toe and reaches the minimum at the location 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 “∩” for the infinite conductive horizontal well. For the finite conductive horizontal well, the perforation density 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.