Shale gas production forecasting is an ill-posed inverse problem and requires regularization

Abstract

Abstract Decline curve analysis (DCA)—the extrapolation of a production curve model fitted to a well’s past production—remains the standard approach for forecasting unconventional oil and gas production. A scaling curve based on a fractured shale gas reservoir model was recently proposed as a way of connecting this approach with underlying physics but as this paper shows, it actually generates worse predictions than the traditional non-physical modified Arps curve. DCA is fundamentally an ill-posed inverse problem with the defining characteristic of model sloppiness, or parameter correlation. Today’s unconventional resource forecasts can be substantially improved by using information from offset wells to reduce ill-posedness through Tikhonov regularization. This versatile approach nearly matches a deep neural network approach introduced here, which has practical limitations but offers a model-neutral benchmark of achievable extrapolation accuracy. There is a natural connection between regularization and a Bayesian formulation which is also highlighted. This paper evaluates long-term forecasting accuracy for these techniques using historic production data from 4457 Barnett shale wells, and reveals that the overlooked step of regularization is more critical than choice of model.