Quantifying the Multidimensional Benefits of Sustainable Shale Gas Development: A Copula–Monte Carlo Integrated Framework

Although shale gas is an important energy source in the energy transition, its development faces multidimensional challenges across economic, environmental, social and technological domains. Traditional evaluation methods struggle to quantify interdependencies among indicators or capture their overall benefits. To address this, we propose a sustainable development evaluation framework for shale gas that integrates 25 indicators across four dimensions: economic, environmental, social and technical. Entropy weighting is used to determine indicator weights, and principal component analysis (PCA) is applied to reduce dimensionality, Gaussian copula functions are then used to model inter-indicator dependencies, and Monte Carlo simulation (10,000 iterations) is used to quantify the distribution of comprehensive benefits under uncertainty. The key findings are as follows: (1) the environmental and technological dimensions carry the highest weights at 29% and 28%, respectively; (2) the PCA–Monte Carlo (PMC) development model achieves a comprehensive benefit score of 0.567, and 22% higher than the traditional model’s score of 0.467 with a 90% confidence interval of [2%, 46%]; and (3) sensitivity analysis identifies the most influential drivers as the hazardous waste compliance rate (impact coefficient 0.92), the community conflict resolution rate (0.367), and community satisfaction (0.26). The marginal benefits of environmental compliance and social governance substantially exceed those of traditional economic indicators, offering scientific guidance for the green transformation of the shale gas industry. The integrated PCA–copula–Monte Carlo framework also provides a methodological reference for the sustainable assessment of other unconventional resources.