Lagrangian Relaxation Based Production Optimization of Tight-formation Wells*

Dry and semi-dry tight formation gas wells normally share the characteristic production profile defined by an initial high production, with an early steep decline and subsequent low pseudo steady-state gas rates. Small volumes of co-produced liquids will, even for dry gas wells, eventually bring the wells into the state of liquid loading, causing erratic unpredictable production rates deteriorating the performance of the wells. This state of the wells can be prevented by performing short shut-ins when the gas rate falls below the minimum rate needed to avoid liquid loading. Multi-well shut-ins may however lead to very high and low peak rates, possibly causing problems for the capacity of shared surface systems or lower and upper bounds on the total rate in a production plan. This paper presents a Lagrangian relaxation based scheme for scheduling of shut-in times for late-life tight formation gas wells with a shared gathering system. The proposed scheme includes a QP formulation for solving the Lagrangian dual, together with an aggregated construction and improvement heuristic for generating primal feasible solutions from the solution of the Lagrangian. We include several test examples to demonstrate the efficiency of the proposed decomposable scheme.