Methods to Quantitatively Evaluate the Effect of Shale Gas Fracturing Stimulation Based on Least Squares - DENG Cai; SUN Kexin; WEN Huan; HU Chaolang (工程科学与技术, 2025)
ObjectiveShale gas fracturing constitutes the cornerstone of contemporary energy extraction, with horizontal well-staged multi-cluster fracturing technology emerging as a pivotal technique for achieving efficient shale gas development. Despite its critical role in meeting global energy demands, the industry faces a persistent challenge: the lack of cost-effective, quantifiable methodologies to assess the effectiveness of fracturing. Conventional approaches rely predominantly on post-fracturing active perforation counts as a proxy for stimulation effectiveness. Although empirical evidence indicates a positive correlation between the number of active perforations and production enhancement, this oversimplified metric fails to capture the inherent complexity of hydraulic fracturing dynamics. The process involves complex interactions among geological formations, fluid rheology, wellbore configurations, and operational parameters. Practical limitations at field sites, where only total friction and flow rate are measurable, further compel engineers to neglect quantitative analysis of individual friction components (wellbore friction vs. perforation friction). Hence, traditional methods rely heavily on subjective experiential judgment, resulting in compromised accuracy in active perforation assessment and suboptimal fracturing design. This study develops a comprehensive, physics-based quantitative model to accurately evaluate the effectiveness of fracturing stimulation, enabling data-driven optimization of shale gas extraction processes.MethodsThis study established a novel quantitative evaluation model based on principles of fluid mechanics and mathematical optimization theory. The methodology utilized nonlinear least squares optimization and proceeded through two integrated computational phases: 1) Friction coefficient fitting: A dedicated nonlinear least squares objective function was constructed to resolve friction components during staged multi-cluster fracturing. Using data obtained from step-down discharge tests, the model analyzed the relationship between total friction (comprising wellbore friction, perforation friction, and near-wellbore friction) and the fracturing fluid flow rate. The optimization targeted the perforation friction coefficient kperf as the primary unknown variable. Engineering-informed constraints, such as realistic friction ranges and fluid behavior boundaries, were incorporated to ensure physically meaningful solutions. Advanced global optimization algorithms, including the Levenberg-Marquardt method, were applied to effectively address this non-convex problem. 2) Active perforation assessment: A computational method was developed based on the fitted perforation friction coefficient and established perforation erosion equations. This method identified the precise number of active perforations and calculated their average diameter after erosion during the fracturing process. Advanced optimization algorithms were employed to efficiently address both the fitting and calculation tasks. The model integrated comprehensive fluid mechanics theories related to downhole friction with existing perforation erosion models.Results and DiscussionsThe model was deployed in shale gas wells across the Sichuan Basin in China. During the step-down tests, a high level of agreement was observed between the predicted and measured friction pressure curves, confirming the model's robustness under complex field conditions. It delivered accurate quantitative outputs for both the number of active perforations and their average diameter after abrasion, overcoming the subjectivity and inaccuracy associated with traditional methods. The proposed model demonstrated several advantages over conventional approaches: 1) Enhanced accuracy and relevance: The model ensured highly accurate and practically applicable results by carefully defining fitting parameters and incorporating engineering constraints. 2) Robust theoretical foundation: It was grounded in established mathematical theory and principles of fluid mechanics. 3) Practicality and efficiency: The model featured low implementation costs and high computational efficiency, presenting a viable and promising alternative for field evaluations. Its significance to the industry lay in addressing the major challenge of the absence of a cost-effective, quantifiable assessment method. It offered detailed insights into the effectiveness of fracturing (in terms of the number and quality of perforations), enabling engineers to improve the fracturing stimulation process for improved production results. As the demand for shale gas continued to increase, this innovative approach proved critical to improving industry efficiency and sustainability. The model established a foundation for future developments, supporting more efficient and environmentally sustainable shale gas extraction practices by enabling a deeper understanding of the fracturing process and its results.