The assumption of constant reservoir permeability is not strictly applicable to reservoirs where rock properties undergo changes, such as stress-sensitive porous media. Most researches on the permeability stress sensitivity mainly concentrated on experimental approach, physical modeling or pressure transient analysis, whereas rate transient analysis does not attract much attention. Based on source/sink function method, this paper develops a seepage model of multi-fractured horizontal well incorporating stress-sensitive permeability. The model is semi-analytically solved by fracture discretization, Pedrosa’s transformation, perturbation theory, and integration transformation method. Not only pressure transient analysis, but also rate transient analysis is separately performed with relevant parameters. The model presented here can provide some insights into well dynamic forecasting during exploiting such reservoirs, and contribute to establish the theoretical basic for transient analysis efficiently.

Natural gas is an eco-friendly energy source with low carbon emissions, making it attractive globally. Understanding gas reservoirs is crucial for sustainable extraction and optimizing potential. However, the complicated fluid flow and production dynamics within intricate gas reservoirs, particularly those characterized by abnormally high pressures and tight porous media, remain partially understood and demand further investigation. In a tight porous medium subjected to high pressure, the assumption of constant permeability is no longer valid. Consequently, a novel composite seepage model has been developed in this study, which considers the responsiveness of permeability to stress. Perturbation theory is employed to address the inherent non-linearity demonstrated by the permeability modulus. The solution of dimensionless pressure responses under constant production conditions is accomplished in the Laplace domain by implementing integral transformation methods. Overall, a comprehensive model is provided to understand the production behaviors of tight gas reservoirs. Moreover, in order to comprehend the transient flow characteristics of tight gas reservoirs, log–log plots are generated through the Stehfest numerical inversion approach, with the flow regimes categorized based on the normalized time phases of the pressure curves. Parametric investigations reveal that stress sensitivity detrimentally affects permeability, resulting in more pronounced pressure declines during the intermediate and late flow phases. The transient seepage model elaborated in this study is able to consider the pertinent formation and well parameters. These interpreted parameters bear significance in designing hydraulic fracturing operations, assessing the potential of tight gas reservoirs, and ultimately enhancing gas production. The presented model not only enhances our understanding of the behavior of horizontal wells in stress-sensitive tight gas reservoirs but also makes a valuable contribution to the broader discussion on transient flow phenomena in petroleum engineering.

Natural gas stands out as a cleaner source of energy due to its relatively lower carbon emissions, making it an appealing choice for numerous countries. Therefore, it is essential to gain a deeper understanding of natural gas reservoirs to ensure sustainable extraction and unlock their full potential. The behavior of fluid flow and production in complex gas reservoirs, especially those characterized by abnormal high-pressure and tight porous media, is not yet fully comprehended, necessitating further investigation. Traditional Darcy's law is no longer applicable in tight porous media with high pressure. To overcome this challenge, a new composite seepage model was developed. The model incorporates stress-sensitive permeability and threshold pressure gradient. We employed perturbation theory for permeability modulus and the Green function method for the inhomogeneous special solution, effectively addressing its nonlinearity. Through integration transformation methods, a dimensionless rate solution under constant bottom-hole pressure was derived in the Laplace domain. Eventually, a new model involving multiple factors has been proposed for production prediction in such gas reservoirs. Studying unsteady gas flow dynamics in tight formations provides valuable insights into flow patterns. To investigate transient flow characteristics in tight gas reservoirs, log-log figures were generated through Stehfest numerical inversion. Flow periods were classified based on standardized time stages for rate curves. A parametric study revealed that stress sensitivity damages permeability, causing a larger pressure drop in intermediate and late flow regimes. This effect is reflected in upward tendencies in rate derivative curves. A higher threshold pressure gradient indicates poorer reservoir properties, making fluid flow more difficult, as evidenced by steeper downwarping in production rate curves. The combined impact of stress-sensitivity and threshold pressure gradient accentuates the variation trend in these curves. Multi-stage hydraulic fracturing can effectively address the negative impacts of these two factors, which impede seepage. Enhancing fracture conductivity can decrease even eliminate the threshold pressure gradient, while increasing proppant strength can slow down elastic and plastic deformation of reservoir rock, thereby reducing the loss of permeability. The transient seepage model developed in this paper serves not only for production prediction but also to explain the related formation and well parameters. It functions as a traditional well test interpretation tool, particularly remarkable as it relies solely on daily production data, enhancing workflow efficiency and reducing testing time. The interpreted parameters are valuable for designing hydraulic fracturing operations, evaluating the potential of tight gas reservoirs, and ultimately increasing gas production rates.