Gas-Lift Allocation under Precedence Constraints: Piecewise-Linear Formulation and K-Covers

Artificial lifting is a costly, but indispensable means to recover oil from high depth reservoirs. Continuous gas-lift works by injecting high pressure gas at the bottom of the production tubing to gasify the oil column, thereby forcing the flow of fluid to surface facilities. The problem consists in deciding which wells should produce and allocating a limited lift-gas rate to the active ones, subject to lower and upper bounds on gas injection, activation precedence constraints, and nonlinearities and discontinuities of the well performance curves. To this end, this paper develops a piecewise linear formulation of the lift-gas allocation problem that allows the application of powerful integer-programming algorithms. More specifically, it analyzes the constraint polyhedron of the piecewise linear formulation and extends cover inequalities of the knapsack polytope to the problem at hand.