Lagrangian relaxation based decomposition for well scheduling in shale-gas systems

• A novel formulation for shut-in scheduling in large, multi-well shale-gas systems.
• The scheduling problem is formulated as an MILP and solved using a Lagrangian relaxation scheme.
• A trust-region cutting-plane algorithm for solving the Lagrangian dual.
• A filter-based weighted nonlinear least-squares formulation for tuning of the shale-well proxy model.

Suppressing the effects of liquid loading is a key issue for efficient utilization of mid and late-life wells in shale-gas systems. 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. In this paper, we present a Lagrangian relaxation scheme for shut-in scheduling of distributed shale multi-well systems. The scheme optimizes shut-in times and a reference rate for each multi-well pad, such that the total produced rate tracks a given short-term gas demand for the field. By using simple, frequency-tuned well proxy models, we obtain a compact mixed-integer formulation which by Lagrangian relaxation renders a decomposable structure. A set of computational tests demonstrates the merits of the proposed scheme. This study indicates that the method is capable of solving large field-wide scheduling problems by producing good solutions in reasonable computation times.