Differential Gibbs and Helmholtz reactor models for ideal and non-ideal gases: Applications to the SMR and methanol processes

Abstract

This work unifies the concepts of chemical reaction equilibrium and transport phenomena applied to fluid flow of reactive gas mixtures over solid catalysts. Different from accurate modeling of reactions, which in the outset relies on reaction kinetics, the current approach is rather based on calculation of thermodynamic equilibrium thus requiring far fewer model parameters. Here, minimization of Gibbs or Helmholtz energy is solved in an inner loop inside the transport equations for heat, mass, and momentum. In addition to ideal gas, the non-ideal virial expansion and Soave-Redlich-Kwong equations of state have been used to model the gas mixture. The use of thermodynamic energy potentials ensures that all the derived properties like e.g. heat capacity, density, reaction enthalpy and equilibrium composition are derived from one fundamental relation only. The complete model framework is exemplified using the steam methane reforming and methanol synthesis processes. Herein, different combinations of energy potential (Gibbs versus Helmholtz) and numerical solution method for solving the transport equations (finite volume versus orthogonal collocation) have been studied with focus on model complexity, and efficiency and robustness of the solver. Orthogonal collocation is shown to be more efficient than finite volume, and Gibbs energy is shown to be more efficient than Helmholtz energy. The last statement depends on both flow conditions and implementation details and is therefore not a general result. The proposed model framework is a novel tool for calculating industrial reactors which operate quite close to equilibrium and might as such be useful for process design studies, albeit not for accurate simulation.