Relaxations of thermodynamic property and costing models in process engineering

Abstract

Deterministic global optimization finds many applications in the field of process engineering, e.g., in chemical equilibrium problems, heat exchanger networks, or process synthesis. The optimization models often contain nonconvex functions describing, e.g., physical properties of pure components and mixtures, or equipment purchase costs. We derive convex and concave envelopes or tight relaxations for several functions found in process engineering applications including equipment cost correlations, functions in common mixture models including the NRTL model, and more. For model classes including saturation pressure models and pure component enthalpy models, we determine monotonicity and convexity properties based on the physical interpretation or empirical evidence regarding the phenomena being modeled. These relaxations are hence expected to hold for any correlation modeling the same phenomenon.