Due to the variation in pressure drawdown along a well, a pressure drop can occur in a vertical well. A mathematical model is described to study how perforation distribution affects production in a vertical well under steady state inflow. Two types of optimisation problems are established which consider the effects of perforation density on the productivity of a vertical well, where the vertical well production is treated as an objective function and the perforation distribution is considered to be a decision-making variable. A programming algorithm is applied to the vertical well optimisation models established under finite and infinite conductivity, respectively. A 7100?m HTHP (high-temperature-high-pressure) gas well is studied to demonstrate how the model could be used to determine the optimal perforation distribution. The results show that inflow rate profiles are effectively improved through optimising the perforation position and there is a reasonable perforation density distribution. (c) 2011 Canadian Society for Chemical Engineering