Transient Pressure Behavior of CBM Wells during the Injection Fall-Off Test Considering the Quadratic Pressure Gradient

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.