Computer-aided mixture design using molecule superstructures

Computer-aided molecular and process design determines the best molecules together with their optimal process for a given objective function. The nonlinearity of typical thermodynamic models and the discrete nature of molecules lead to the challenge of solving a mixed-integer nonlinear programming problem. The optimization is even more demanding for a mixture design, in which two or more molecules and their composition are degrees of freedom. At the same time, the quality of the solution strongly depends on the accuracy of the thermodynamic model used to predict the thermophysical properties required to determine the process-based objective function and constraints. Today, most molecular design methods employ thermodynamic models based on group counts, resulting in a loss of structural information of the molecule during the optimization. The present work extends the integrated design of mixtures and processes in three areas: (1) Molecule superstructures represent chemical families by graphs that preserve the full adjacency matrix to unlock property prediction methods beyond first-order group-contribution methods. (2) Implicit automatic differentiation of process models determines Jacobians and Hessians needed for the optimization algorithm within machine precision. (3) A fine-tuned outer approximation algorithm efficiently calculates rankings of candidate mixtures for the non-convex integrated molecular and process design problem. In a case study, the design method is used to determine the optimal working fluid mixture for an Organic Rankine cycle.