In this paper, we investigate power production in complex multireaction systems propelled by either uncoupled or coupled multicomponent mass transfer. The considered system contains two mass ...reservoirs, one supplying and one taking out the species, and a power-producing reactor undergoing the chemical transformations characterized by multiple (vector) efficiencies. To establish a suitable basis for these efficiencies, an approach is applied that implements balances of molar flows and reaction invariants to complex chemical systems with power production. Reaction invariants, i.e., quantities that take the same values during a reaction, follow by linear transformations of molar flows of the species. Flux balances for the reacting mixture may be written down by equating these reaction invariants before and after the reactor. Obtained efficiency formulas are applied for steady-state chemical machines working at the maximum production of power. Total output of produced power is maximized at constraints which take into account the (coupled or uncoupled) mass transport and efficiency of power generation. Special attention is given to non-isothermal power systems, stoichiometric mixtures and internal dissipation within the chemical reactor. Optimization models lead to optimal functions that describe thermokinetic limits on power production or consumption and extend reversible chemical work
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rev to situations in which reduction of chemical efficiencies, caused by finite rates, is essential. The classical thermostatic theory of reversible work is recovered from the present thermokinetic theory in the case of quasistatic rates and vanishing dissipation.
Despite the vast research on energy optimization and process integration, there has to date been no synthesis linking these together. This book fills the gap, presenting optimization and integration ...in energy and process engineering. The content is based on the current literature and includes novel approaches developed by the authors.
Various thermal and chemical systems (heat and mass exchangers, thermal and water networks, energy converters, recovery units, solar collectors, and separators) are considered. Thermodynamics, kinetics and economics are used to formulate and solve problems with constraints on process rates, equipment size, environmental parameters, and costs.
Comprehensive coverage of dynamic optimization of energy conversion systems and separation units is provided along with suitable computational algorithms for deterministic and stochastic optimization approaches based on: nonlinear programming, dynamic programming, variational calculus, Hamilton-Jacobi-Bellman theory, Pontryagin's maximum principles, and special methods of process integration.
Integration of heat energy and process water within a total site is shown to be a significant factor reducing production costs, in particular costs of utilities for the chemical industry. This integration involves systematic design and optimization of heat exchangers and water networks (HEN and WN). After presenting basic, insight-based Pinch Technology, systematic, optimization-based sequential and simultaneous approaches to design HEN and WN are described. Special consideration is given to the HEN design problem targeting stage, in view of its importance at various levels of system design. Selected, advanced methods for HEN synthesis and retrofit are presented. For WN design a novel approach based on stochastic optimization is described that accounts for both grassroots and revamp design scenarios.
We consider typical problems of the field called the finite time thermodynamics (also called the optimization thermodynamics). We also outline selected formal methods applied to solve these problems ...and discuss some results obtained. It is shown that by introducing constraints imposed on the intensity of fluxes and on the magnitude of coefficients in kinetic equations, it is possible not only to investigate limiting possibilities of thermodynamic systems within the considered class of irreversible processes, but also to state and solve problems whose formulation has no meaning in the class of reversible processes.
This article is part of the themed issue ‘Horizons of cybernetical physics’.
► A unique synthesis of power yield or consumption based on thermodynamic optimization. ► Common methodology when describing engines, separators, solar units, and heat pumps. ► Original, in-depth ...study of power maxima and minima in practical and industrial systems. ► Includes fuel cells to a common class of thermodynamic power systems.
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.
We present a synthesizing thermodynamic approach to modeling and power maximization in various energy converters, such as thermal, solar and chemical engines and fuel cells. Static and dynamical ...systems are investigated. Thermodynamic analyses lead to converters’ efficiencies in terms of propelling fluxes. Efficiency equations are applied to find maximum power points in static systems. These efficiency equations are also applied to determine maxima of integrated power (work) in dynamical systems, which work with upgrading and downgrading of a resource medium. While optimization of static systems requires using of differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting mixtures balances of mass and energy are applied to derive power yield in terms of an active part of chemical affinity. Power maximization approach is finally applied for fuel cells treated as flow engines driven by fluxes of chemical reagents and electrochemical mechanism of electric current generation. The efficiency decrease is linked with thermodynamic and electrochemical irreversibilities expressed in terms of polarizations (activation, concentration and ohmic). Maximum power data provide bounds for SOFC energy generators, which are more exact and informative than reversible bounds for electrochemical transformation.
This paper contributes to the simulation of transients and stability properties of singular states in engineering and environmental gas-solid systems. Qualitative properties of paths around ...equilibrium, quasi-equilibrium and disequilibrium states in closed and open systems are investigated by Lyapunov functions or functionals, V, determined by an original method. The method requires first to assume a constant-sign time derivative of V with respect to perturbed dynamical equations, V, and next to determine V itself from a matrix formula. Such functions V, which may be of an indefinite sign, describe qualitative properties of system paths, and may be derived from the derivatives image attributed to the constant-sign rates of entropy production or related exergy sink. Examples confirming the effectiveness of the approach for testing stability and qualitative properties of paths in non-reacting and reacting gas-solid systems are presented. A nontrivial example of the research benefit is presented in the paper in the form of the original classification of drying-moistening paths, based on the nontrivial saddle form of V in countercurrent systems and the focus form of V in co-current systems.
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.
We apply optimization methods to study power generation limits for various energy converters, such as thermal, solar, chemical, and electrochemical engines. Methodological similarity is observed when ...analysing power limits in thermal machines and fuel cells which are electrochemical flow engines. Operative driving forces and voltage are suitable indicators of imperfect phenomena in energy converters. The results obtained generalize our previous findings for power yield limits in purely thermal systems with finite rates. While temperatures Tᵢ of participating media were only necessary variables in purely thermal systems, in the present work both temperatures and chemical potentials μₖ are essential. This case is associated with engines propelled by fluxes of both energy and substance. In dynamical systems downgrading or upgrading of resources may occur. Energy flux (power) is created in the generator located between the resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Fluid properties, transfer mechanisms and conductance values of dissipative layers or conductors influence the rate of power production. Numerical approaches to the dynamical solutions are based on the dynamic programming or maximum principle. Here we focus especially on the latter method, which involves discrete algorithms of Pontryagin’s type. Downgrading or upgrading of resources may also occur in electrochemical systems of fuel cell type. Yet, in this paper we restrict ourselves to the steady-state fuel cells. We present a simple analysis showing that, in linear systems, only at most ¼ of power dissipated in the natural transfer process can be transformed into the noble form of mechanical power.
For nonlinear steady paths of a fluid in an inhomogeneous isotropic porous medium a Fermat-like principle of minimum time is formulated which shows that the fluid streamlines are curved by a location ...dependent hydraulic conductivity. The principle describes an optimal nature of nonlinear paths in steady Darcy’s flows of fluids. An expression for the total resistance of the path leads to a basic analytical formula for an optimal shape of a steady trajectory. In the physical space an optimal curved path ensures the maximum flux or shortest transition time of the fluid through the porous medium. A sort of “law of bending” holds for the frictional fluid flux in Lagrange coordinates. This law shows that – by minimizing the total resistance – a ray spanned between two given points takes the shape assuring that its relatively large part resides in the region of lower flow resistance (a ‘rarer’ region of the medium). Analogies and dissimilarities with other systems (e.g. optical or thermal ones) are also discussed.
This research continues the thermodynamic analysis of steady-state solid oxide fuel cells initiated in Sieniutycz (Sieniutycz, S., 2010, Thermodynamic aspects of power generation in imperfect fuel ...cells: part I. International Journal of Ambient Energy, 31 (4), 195-202). This analysis focuses on the effect of incomplete conversions in chemical reactions. A general approach is developed that attributes lowering of the cell voltage below its reversible value to polarisations and imperfect chemical conversions. Relevant model, appropriate for systems with complete conversions, is extended to imperfect cases. The performance curves of a fuel cell and the effect of typical design and operating parameters on the cell behaviour are analysed. A general result is obtained for power limits of fuel cells propelled by linear transport phenomena.
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