A piecewise linear-quadratic approximation for production optimization of gas-lifted oil fields

The optimization of oil wells operated by gas-lift under facility, routing and pressure constraints is a problem that has been addressed in technical literature. Due to the presence of unknown functions that are not given in explicit form, two methods are commonly used to approximate such relations: nonlinear and piecewise-linear models. The nonlinear methods fall into derivative-free or black-box approaches, or make use of surrogates obtained by curve fitting procedures, which can entail solving challenging problems. In this work, it is proposed a hybrid approach relying on concave quadratic approximations for well production curves and piecewise-linear functions for pressure drops. The result is a Mixed-Integer Convex Programming (MICP) formulation which is more compact and allows the global optimum to be reached. Two MICP formulations were developed and their performance were assessed by means of computational analysis for a representative synthetic oil field.