Lift-gas allocation under precedence constraints: 1-configuration inequalities

Lift-gas allocation concerns the distribution of a limited rate of high pressure gas to oil wells with the aim of maximizing profit from hydrocarbon selling. The problem is becoming more complex as oil fields mature and constraints are imposed to deliver near-optimal operations. Today, systems engineers take account of bounds on gas injection, discontinuous production functions, and activation precedence constraints. To this end, this paper discusses a mixed-integer linear formulation obtained from a piecewise linear reformulation of well performance curves for lift-gas allocation under activation precedence constraints. The model handles injection bounds, a limited lift-gas rate, and can be extended to incorporate facility constraints. A somewhat rigorous analysis of the integer polyhedron is carried out to produce valid inequalities based on 1-configurations. Not only can these inequalities be used in cutting-plane and branch-and-cut algorithms, but also applied in combination with evolutionary algorithms to produce upper bounds.