Optimal Design of Energy–Water Systems Under the Energy–Water–Carbon Nexus Using Probability-Pinch Analysis

The energy–water–carbon (EWC) nexus has become a critical concern for industrial systems seeking sustainable development, yet existing assessment approaches often require intensive computation and lack practical adaptability. This study proposes a probability-pinch analysis (P-PA) framework that enhances conventional pinch analysis (PA) by integrating allocation-based correction factors to account for system inefficiencies across all time intervals explicitly. The framework incorporates PA tools, specifically the Power Cascade Table (PCT), Water Cascade Table (WCT), and Energy Planning Pinch Diagram (EPPD), to design ideal energy–water systems that do not consider losses. Correction factors based on probable energy and water flows are then incorporated to capture system inefficiencies, with design modifications proposed to meet annual carbon reduction targets. Results from an industrial plant case study validate the effectiveness of P-PA in establishing minimum resource targets while achieving a 46% reduction in carbon emissions through system modifications. Deviations from conventional PA were within 10%, confirming the framework’s accuracy and reliability in designing integrated energy–water systems within the EWC nexus. It could serve as a handy tool for designing large-scale energy–water systems that require substantial computational effort, but it may be less accurate for small-scale applications. Nevertheless, compared with conventional PA-based approaches, P-PA offers a balanced combination of rigor, simplicity, and adaptability, making it well-suited for industrial EWC nexus analysis and decision support in sustainable process design.