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Entropy 2013, 15(2), 650-677; doi:10.3390/e15020650
Article

An Unified Approach to Limits on Power Generation and Power Consumption in Thermo-Electro-Chemical Systems

Faculty of Chemical and Process Engineering, Warsaw University of Technology, Waryńskiego Street No. 1, Warsaw 00-645, Poland
Received: 20 November 2012 / Revised: 16 January 2013 / Accepted: 5 February 2013 / Published: 11 February 2013
(This article belongs to the Special Issue Entropy and Energy Extraction)
Download PDF [370 KB, 24 February 2015; original version 24 February 2015]

Abstract

This research presents a unified approach to power limits in power producing and power consuming systems, in particular those using renewable resources. As a benchmark system which generates or consumes power, a well-known standardized arrangement is considered, in which two different reservoirs are separated by an engine or a heat pump. Either of these units is located between a resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Power yield or power consumption is determined in terms of conductivities, reservoir temperatures and internal irreversibility coefficient, F. While bulk temperatures Ti of reservoirs’ are the only necessary state coordinates describing purely thermal units, in chemical (electrochemical) engines, heat pumps or separators it is necessary to use both temperatures and chemical potentials mk. 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, fuel cells, etc. Methodological similarities when treating power limits in engines, separators, and heat pumps are shown. Numerical approaches to multistage systems are based on methods of dynamic programming (DP) or on 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. A relatively unknown symmetry in behaviour of power producers (engines) and power consumers is enunciated in this paper. An approximate evaluation shows that, at least ¼ of power dissipated in the natural transfer process must be added to a separator or a heat pump in order to assure a required process rate. Applications focus on drying systems which, by nature, require a large amount of thermal or solar energy. We search for minimum power consumed in one-stage and multi-stage operation of fluidized drying. This multi-stage 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.
Keywords: engines; heat pumps; separators; dryers; solar energy; power limits; energy consumption engines; heat pumps; separators; dryers; solar energy; power limits; energy consumption
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sieniutycz, S. An Unified Approach to Limits on Power Generation and Power Consumption in Thermo-Electro-Chemical Systems. Entropy 2013, 15, 650-677.

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