Conventional coalbed methane (CBM) reservoir models for injection fall-off testing often disregard the quadratic pressure gradient’s impact. This omission leads to discrepancies in simulating the transient behavior of formation fluids and extracting critical reservoir properties. Accurate determination of permeability, storability, and other properties is crucial for effective reservoir characterization and production forecasting. Inaccurate estimations can lead to suboptimal well placement, ineffective production strategies, and ultimately, missed economic opportunities. To address this shortcoming, we present a novel analytical model that explicitly incorporates the complexities of the quadratic pressure gradient and dual-permeability flow mechanisms, prevalent in many CBM formations where nanopores are rich, presenting a kind of natural nanomaterial. This model offers significant advantages over traditional approaches. By leveraging variable substitution, it facilitates the derivation of analytical solutions in the Laplace domain, subsequently converted to real-space solutions for practical application. These solutions empower reservoir engineers to generate novel type curves, a valuable tool for analyzing wellbore pressure responses during injection fall-off tests. By identifying distinct flow regimes within the reservoir based on these type curves, engineers gain valuable insights into the dynamic behavior of formation fluids. This model goes beyond traditional approaches by investigating the influence of the quadratic pressure gradient coefficient, inter-porosity flow coefficient, and storability ratio on the pressure response. A quantitative comparison with traditional models further elucidates the key discrepancies caused by neglecting the quadratic pressure gradient. The results demonstrate the proposed model’s ability to accurately depict the non-linear flow behavior observed in CBM wells. This translates to more reliable pressure and pressure derivative curves that account for the impact of the quadratic pressure gradient.

Tight sandstone gas reservoirs are characterized by low single-well productivity, rapid natural decline, and generally low recovery rates, which limit the effectiveness of conventional development strategies. The injection of CO₂ into tight gas reservoirs offers broad prospects for both enhanced gas recovery (EGR) and integrated CO₂ capture, utilization, and storage (CCUS). However, during the depletion and CO₂ injection processes, fracture conductivity, reservoir fluid distribution, and gas–water relative permeability evolve continuously, exhibiting pronounced time-varying behavior. Conventional models have certain limitations in characterizing these time-varying mechanisms, often resulting in significant discrepancies between predicted performance and actual conditions. To address this, we develop a robust and generic model that explicitly incorporates the time-varying mechanisms and stress sensitivity. This model also accounts for the non-equilibrium flash (NEF) behavior of the gas–liquid mixture during CO₂ injection into tight gas reservoirs. The successive substitution iteration method is adopted for non-equilibrium flash calculation, and the Newton–Raphson iteration (NRI) method is used for obtaining a fully implicit solution of the reservoir flow equations. The accuracy and reliability of the proposed model are verified through comparisons with commercial simulator results, and a quantitative comparison with traditional models highlights the key discrepancies caused by neglecting time-varying mechanisms. Parametric analyses further clarify the impacts of time-varying behavior and stress sensitivity on CO₂-EGR performance and CO₂ sequestration efficiency. The results show that the displacement process of CO₂ in tight gas reservoirs can be divided into four characteristic stages. The results also indicate that if the time-varying effects and the stress sensitivity of the reservoir permeability are ignored, the calculations tend to overestimate the true gas production capacity of the reservoir and underestimate the CO₂ sequestration performance.