A New Theoretical Approach to the Mathematical Determination of the Relationship Between Cumulative Gas Production Versus Time in a Hydraulic Fracturing Unconventional Gas Well

Abstract The decline curve analysis technique assumes that past production trends can be mathematically characterized to predict future performance. Historically, various models have been developed as alternatives to the traditional Arps' decline model, all based on empirical observations of specific scenarios. This study introduces a new theoretical and mathematical approach, the Lead Coefficient Theoretical Polynomial Model (EWO), derived from 11 physical and theoretical assumptions. This model formulates the trend equation for cumulative gas production versus production time in hydraulically fractured unconventional gas wells, independent of the geometry of the Stimulated Volume of Rock (SVR) and its inherent heterogeneities. The findings indicate that, contrary to conventional practices that promote elevated drawdown pressure to enhance recovery, this approach mathematically suggests a long-term reduction in methane recovery under such conditions. This regression-based method serves as a complementary tool to existing decline curve models, incorporating both statistical and analytical components. By employing polynomials of appropriate degree, the model achieves a more precise fit to actual production data, offering an alternative to Arps and other decline models for estimating future production and EUR in certain cases. Furthermore, this study provides an interdisciplinary contribution to reserves estimation, supported by validation using real production data from a well in the Sichuan Basin, China, demonstrating a high degree of confidence in the model's applicability to real-world scenarios.