Distillation plays a major role in chemical process engineering, enabling the separation of liquid mixtures into pure components. However, this process is very energy-intensive. To identify operating points with minimal energy demand that still meet product specifications, it is necessary to solve the MESH equations - a challenging, strongly nonlinear and high-dimensional system.



In this thesis, this problem is tackled by presenting a numerically more stable approach based on a nonlinear reduction method using stage-to-stage computations, combined with homotopy continuation methods. The new approach is rigorously analyzed and, for the first time, convergence guarantees for solving the MESH equations are established under standard modeling assumptions. Numerical case studies demonstrate the robustness in identifying low-energy operating points while avoiding unphysical solutions that can arise with conventional methods.