A general thermodynamic law for multi-phase systems without turbulences in the non-linear regime and its application to separation processes

Abstract

Prigogine's principle of minimum entropy production is valid only for single-phase thermodynamic systems with non-equilibrium stationary states in the linear regime. We will show that it can be generalized to a more general law in the non-linear regime for multi-phase thermodynamic systems without turbulences in the flow quantities. We take the example of fluid-mixture separation of the binary fluid mixture benzene-trichloroethylene in a distillation column, which is driven always with constant power in the various rectification processes. We will demonstrate that there are lots of stationary states depending on the additional free parameter of the return ratio of the liquid and vapor flow. We will show further that there is always one stationary state with minimum entropy production. This state corresponds to the optimum separation condition of the column and it is the one, which has the longest setting time. Although engineers use well-known, empirically found relations and equations for their calculations to optimize rectification processes, this new fundamental law of non-equilibrium thermodynamics for non-linear multi-phase systems with laminar flow quantities rationalizes the engineers' empirical knowledge. We will demonstrate that optimizing non-linear non-equilibrium multi-phase thermodynamic processes is based on maximization of entropy flow and minimization of entropy production, which corresponds to maximum reversible separation work for all kinds of separation processes. All performed calculations are based on rigorous thermodynamics. In following papers, we will show that this new discovery is valid for a broad range of non-linear open thermodynamic multi-phase processes and can be beneficially used, e.g. for optimizing chemical and biochemical processes.