A Mathematical Modelling of the Plunger Lift Considering Effects of Fluid Friction and Plunger Travel Velocity

Abstract

Plunger lift technique is a well-known, widely accepted and economical artificial lift alternative, especially in deliquification of gas wells and to increase the efficiency of intermittently flowing oil wells. This study includes impact of fluid friction losses and variable plunger travel velocity in mathematical modelling of plunger lift design. The design of plunger lift system, in most models, is simulated by a fix value of fluid friction losses based on plunger velocity, which does not consider the variable effects of the friction factor calculation based on Colebrook equation or complex multiphase flow. To consider these effects, other equations must be solved simultaneously with the well-known Foss and Gaul equations. Solution of the plunger lift design equation becomes even more complicated if the fluid friction properties are not uniform. Foss and Gaul suggested an approximation for gas and liquid friction are constant for a given tubing size and a plunger velocity of 1,000 ft/min. Plunger travel velocity is the important parameter in design. The velocity at which the plunger travels up the tubing also affects the plunger efficiency. Very low velocity of plunger increases gas slippage and subsequently lead to inefficient operation. Whereas, high plunger velocities tend to push the plunger through the liquids. A steady state mathematical modelling and sensitivity analysis considering broad estimates, has been done using Python language. This approach can simulate any combination of associated parameters for plunger lift design in a relatively simple and effective manner. The numerical results are compared to the actual available data. Analysis of the numerical results shows that the effects of fluid friction losses and plunger travel velocity are important for accurate modelling and design of the plunger lift system.