A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting

Chang, Cheng; Xu, Fanxiang; Liang, Hongbin; Zeng, Huangben; Ji, Xiaojing; Wanyan, Ze; Qiu, Ziqi

doi:10.3390/pr14132210

This is an early access version, the complete PDF, HTML, and XML versions will be available soon.

Open AccessArticle

A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting

by

Cheng Chang

¹,

Fanxiang Xu

^1,*,

Hongbin Liang

²,

Huangben Zeng

²,

Xiaojing Ji

¹,

Ze Wanyan

¹ and

Ziqi Qiu

¹

Shale Gas Research Institute, PetroChina Southwest Oil & Gas Field Company, Chengdu 610051, China

²

School of Petroleum Engineering, Chongqing University of Science & Technology, Chongqing 401331, China

^*

Author to whom correspondence should be addressed.

Processes 2026, 14(13), 2210; https://doi.org/10.3390/pr14132210

Submission received: 9 June 2026 / Revised: 1 July 2026 / Accepted: 3 July 2026 / Published: 6 July 2026

(This article belongs to the Special Issue Advances in Enhancing Unconventional Oil/Gas Recovery, 3rd Edition)

Download Versions Notes

Abstract

Shale gas production is governed by complex geological and engineering factors, and its production dynamics are often highly variable. Conventional methods, which can incorporate only a limited number of production-related variables, often struggle to provide accurate forecasts under fluctuating operating conditions. Focusing on the natural flowing stage of shale gas wells, this study proposes a probabilistic forecasting framework that integrates physical decline characteristics with dynamic production data. A dual-branch TCN–LSTM network constrained by decline features is constructed, and Student’s t-distribution is introduced to quantify the uncertainty caused by short-term production fluctuations. The results show that embedding physical decline constraints into the deep learning architecture helps bridge the gap between conventional models with limited parameter representation and purely data-driven models with insufficient interpretability. The proposed method improves forecasting accuracy while preserving the physical meaning of the predictions, and it can generate noise-robust confidence intervals with stable coverage. This method provides decision support for short-term production tracking and production-regime adjustment in shale gas wells.

Keywords: shale gas well; production forecast; physical constraint; uncertainty analysis; data-driven

Share and Cite

MDPI and ACS Style

Chang, C.; Xu, F.; Liang, H.; Zeng, H.; Ji, X.; Wanyan, Z.; Qiu, Z. A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting. Processes 2026, 14, 2210. https://doi.org/10.3390/pr14132210

AMA Style

Chang C, Xu F, Liang H, Zeng H, Ji X, Wanyan Z, Qiu Z. A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting. Processes. 2026; 14(13):2210. https://doi.org/10.3390/pr14132210

Chicago/Turabian Style

Chang, Cheng, Fanxiang Xu, Hongbin Liang, Huangben Zeng, Xiaojing Ji, Ze Wanyan, and Ziqi Qiu. 2026. "A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting" Processes 14, no. 13: 2210. https://doi.org/10.3390/pr14132210

APA Style

Chang, C., Xu, F., Liang, H., Zeng, H., Ji, X., Wanyan, Z., & Qiu, Z. (2026). A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting. Processes, 14(13), 2210. https://doi.org/10.3390/pr14132210

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

A Physically Constrained Deep Learning Method for Shale Gas Well Production Forecasting

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI