Power Yield and Power Consumption in Thermo-Electro-Chemical Systems – A Synthesizing Approach

Abstract

In this synthesizing research methods of mathematical programming and dynamic optimization are applied to determine limits on power yield or power consumption in various energy systems, such as thermal engines, heat pumps, solar dryers, electrolysers, and fuel cells. Methodological similarities are enunciated when treating power limits in engines, separators, and heat pumps. Numerical approaches to multistage systems are based on the methods of dynamic programming (DP) or Pontryagin’s maximum principle. The first method searches for properties of optimal work and is limited to systems with low dimensionality of state vector, whereas the second investigates properties of differential (canonical) equations derived from the process Hamiltonian. In this paper a relatively unknown symmetry in behaviour of power producers (engines) and power consumers is shown. An approximate evaluation shows that, at least 1/4 of power dissipated in the natural transfer process must be added to a separator or heat pump in order to assure a required process rate.Applications include drying systems which, by nature, require a large amount of thermal or solar energy. We search for minimum power consumed in one-stage and multistage operation of fluidized drying. This multistage system is supported by heat pumps. We outline the related dynamic programming procedure, and also point out a link between the present irreversible approach and the classical problem of minimum reversible work driving the system.