Solving a gas-lift optimization problem by dynamic programming

Gas lift is a costly, however indispensable means to recover oil from high-depth reservoirs that entails solving the gas-lift optimization problem, GOP, often in response to variations in the dynamics of the reservoir and economic oscillations. GOP can be cast as a mixed integer nonlinear programming problem whose integer variables decide which oil wells should produce, while the continuous variables allocate the gas-compressing capacity to the active ones. This paper extends the GOP formulation to encompass uncertainties in the oil outflow and precedence constraints imposed on the activation of wells. Recursive solutions are suggested for instances devoid of precedence constraints, as well as instances arising from precedence constraints induced by forests and general acyclic graphs. For the first two classes, pseudo-polynomial algorithms are developed to solve a discretized version of GOP, while the most general version is shown to be NP-Hard in the strong sense. Numerical experiments provide evidence that the approximate algorithms obtained by solving the recurrences produce near-optimal solutions. Further, the family of cover inequalities of the knapsack problem is extended to the gas-lift optimization problem.