Title : From empirical decline to intelligent forecasting: A hybrid deep learning framework embedding arps physics for unconventional tight-gas reservoir production prediction
Abstract:
Accurate production forecasting is a cornerstone of reservoir management, field development planning, and economic evaluation in unconventional tight-gas plays. Classical decline curve analysis (DCA) models—including exponential, hyperbolic, Duong, stretched exponential, and power-law exponential formulations—provide physically interpretable production decline characterization but are constrained by restrictive parametric assumptions that limit their applicability to heterogeneous well populations. Meanwhile, purely data-driven deep learning approaches, while powerful in capturing complex nonlinear patterns, frequently generate non-physical forecasts such as production rate increases during terminal decline periods and exhibit poor generalization to wells outside the training distribution.
In this paper, we present a comprehensive hybrid physics-informed deep learning framework that systematically addresses these limitations. We conduct a large-scale empirical investigation using 25 years of monthly production data (2000–2024) from 864 tight-gas wells in the Mancos Shale interval of the Piceance Basin, Colorado, encompassing 232,307 production records. The study introduces three methodological contributions: (1) a Hybrid Physics-Informed Neural Network (Hybrid-PINN) that couples Arps decline equations with neural network residual corrections, achieving a 4.9% mean RMSE reduction over the best classical model on 95.0% of wells; (2) PyTorch-based Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) recurrent architectures for 24-month multi-step forecasting, with the LSTM model achieving R² = 0.834 and RMSE = 39.15 MCF/day—a 29.7% improvement over the naïve persistence baseline; and (3) a novel Physics-Augmented Encoder-Decoder (PAED) architecture that fuses temporal production sequences with 37 enriched static features spanning completion design parameters, petrophysical properties, and DCA-derived decline parameters under monotonic decline regularization (R² = 0.807, RMSE = 43.04 MCF/day).
A weighted ensemble of five neural network architectures yields R² = 0.811 and RMSE = 41.78 MCF/day with calibrated uncertainty bounds suitable for probabilistic reserve estimation. Our results demonstrate that embedding established decline physics as soft constraints within deep learning loss functions and network architectures produces forecasts that are more accurate, physically consistent, and operationally reliable than either purely physics-based or purely data-driven approaches. The framework is directly transferable to other unconventional basins worldwide and offers a practical methodology for integrating domain knowledge with artificial intelligence in modern reservoir engineering workflows.
Keywords: physics-informed neural networks; decline curve analysis; production forecasting; LSTM; GRU; encoder-decoder; hybrid modeling; unconventional tight gas; Piceance Basin; Mancos Shale; deep learning; reservoir engineering
