Designing shale-well proxy models for field development and production optimization problems

• A semi-physical shale-well proxy model.
• A novel parameter-estimation scheme with prediction-error filtering.
• Integration of model tuning and the choice of model size.
• The reduced-order proxy model is applicable to a wide range of field design and production optimization problems.

The surge to maintain a high and sustainable gas supply causes shale-gas fields to be developed with a high number of wells and an extensive infrastructure. This may result in large and complex optimization problems in order to utilize shared infrastructure, optimize the field design, and improve the recovery of the natural-gas resource. Solving large-scale, field-wide shale-gas optimization problems put different requirements on the well and reservoir models than conventional history matching, as it is crucial that the models are low ordered, numerically efficient and adaptable to changing operating conditions. To this end, using appropriately designed proxy models is critical. In this paper, we construct a dynamic shale-well proxy model based on the first principles for gas flow in dry shale-gas reservoirs, rendering a semi-physical modeling approach between purely data-driven black-box models and detailed numerical models. To tune proxy models, we propose a parameter-estimation scheme that incorporates prefiltering of prediction errors between the proxy model and reference data. The prefiltering approach provides a means for emphasizing certain ranges of the dynamics in the model, and thus constitutes a structured approach for defining weights in the accompanying weighted least-squares problem. Further, we show how the proposed approach allows for considering the model tuning and spatial grid design as a joint problem with respect to the purpose of the proxy model.