A mathematical program for finding the optimal oil production rates in an oil production system is developed. Each well may be manipulated by injecting lift gas and adjusting a production choke. The oil production from the wells may be restricted with multiple constraints in the maximum oil flow rate, water flow rate, liquid flow rate, and gas flow rate. The wells may also be restricted with a maximum total lift gas rate. In oil production systems with sub sea wells, flow lines are often shared between two or more wells. The pressure in the production manifold will in such configurations be affected by the flow from the wells. The commonly used models based on gas lift performance curves (GLPC) no longer apply to these problems due to changing pressure conditions in the production manifold. Because of this, a model of the flow line is also required to get more accurate results. This work incorporates such a model. A piecewise linear approximation is proposed. This makes it possible to find a proven global optimum, within the approximation, for the optimization problem. The problem is formulated as a mixed integer linear program and solved with a commercial branch and cut solver.

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