Vertical thermosyphon reboilers (VTRs) are widely used in distillation due to their high heat transfer efficiency and low fouling tendency. However, conventional design approaches and commercial tools often treat two-phase heat transfer, geometry, and pressure balance in isolation and depend on extensive manual tuning, which may yield low solution quality. To address this gap, a rigorous mixed integer nonlinear programming (MINLP) optimization framework is established for VTR design that couples thermodynamic, hydraulic, and geometric decisions simultaneously. A two-stage heat transfer modelling approach is proposed to capture the convective boiling transition by integrating sensible heating and boiling heat transfer mechanisms. Within this approach, a dynamic switching scheme selects heat transfer correlations according to the vapor fraction, which improves accuracy across different operating conditions. Moreover, a comprehensive pressure balance model is established that spans the external piping, the reboiler, and the column sump liquid level to ensure the resulting natural circulation is stable. Geometric and operating variables are optimized simultaneously to deliver coordinated design choices under duty and layout constraints. The optimization is implemented in GAMS/48 and solved using SCIP solver. To demonstrate engineering applicability, the thermodynamic modelling results are compared with Aspen EDR simulations, revealing relative errors ranging from 3.8 % to 15.6 %. The optimized design increases the overall heat transfer coefficient by 16.60 % and reduces the required area by 13.86 %. Furthermore, stability analysis under varying heat duties reveals clear operational boundaries, highlighting the importance of coordinating liquid level and skirt height to maintain feasible natural circulation.

Retrofitting industrial heat recovery systems is a key pathway toward low-carbon and resource-efficient manufacturing. Integrating waste heat recovery (WR) with multiple utility (MU) networks can significantly improve energy efficiency, but also creates strong coupling between process heat recovery, waste heat utilisation, and utility allocation. However, existing approaches often address these elements separately or sequentially, limiting the ability to identify optimal system-level retrofit solutions. This study aims to develop a system-level optimisation framework to resolve trade-offs between waste heat recovery and multiple utility integration in industrial retrofit. The framework allows for (i) modifying existing exchangers, (ii) installing new process-to-process units to enhance heat recovery, (iii) integrating waste heat recovery systems for generating high-pressure steam, low-pressure steam, and hot water, and (iv) incorporating optimal utilisation of multiple utilities. The framework is validated through two large-scale industrial case studies. In Case 1, WR and MU integration reduce utility cost to 9.8E+06 $/y (64.6% below the original design) and GHG emissions from 1.7E+08 to 1.2E+08 kg/y CO2 (30.3% reduction), with hot water generation contributing 82.7% of savings. In Case 2, the same strategy achieves a 45.6% GHG reduction relative to the baseline and lowers operation costs by 28.9%. This work provides a practical, system-level retrofit framework to support sustainable production and low-carbon transition in industrial processes.