Exergy Representations in Thermodynamics

The paper reviews various representations of exergy and exergy losses in energy systems going from simple heat exchanger (heat transfer, dissipation and embedded exergy) to the exergy of full energy systems from fossil or non fossil resources (including the diffusion exergy). The systems shown include shell in tube heat exchangers, thermal power cycles, cogeneration, heat pump direct heating systems and cryogenic systems. The representations include simple gravitational analogies to extended exergy pinch diagrams and finally to the exergy bowl with the dead states corresponding, for example, to different oxidation products. The transformation from hydrocarbons to CO2 and H20 is shown in particular, highlighting the diffusion exergy of CO2, which is important when dealing with concepts of CO2 capture. INTRODUCTION Exergy is recognized as the best way to analyse energy systems, be it at the component, process, whole site or country levels. It is, however, also often seen as too complex by practitioners, who are used to work around processes and technologies they think to know well. Experience shows that both at the teaching level and the conceptual design level it is often useful to rely on a graphical representation of the concepts. The success of pinch technology [1,2] for example, can also be attributed to having an easier representation of the application of Second Law to the heat transfer in integrated processes. Similar representations can be extended, to more holistically illustrate the other exergy losses like the dissipation exergy losses and the embedded exergy losses [3]. Other only qualitative approaches are cartoon type of representations of energy conversion phenomena [4]. The decomposition of exergy efficiency in the subsystems can help the policy makers to coherently rank technologies like those for heating or air-conditioning [5]. They can also help scholars to better grasp the meaning of concepts, like the need to differentiate between the thermo-mechanical and physicochemical equilibria or dead states when reactive flows are involved [4]. Other approaches inspired by the van’t Hoff box can help in properly identifying the different aspects involved in the calculation of the exergy value of a fuel [4,6]. The objective here is to expose these representations in a comprehensive manner in a single paper. NOMENCLATURE T [K] Temperature P [N/m] Pressure P [N/m] Partial pressure at the thermo-mechanical equilibrium P [N/m] Partial pressure at the physico-chemical equilibrium Δk! [J//kmol] Molar isobaric exergy value of a fuel Δg! [J/kmol] Molar free enthalpy of formation (Gibbs free energy) e! [J/kmol] Molar exergy of diffusion N [kmol/s] Molar flow r [J kmol K] Molar Universal gas constant L [W] Exergy loss j [J/kg] Specific coenthalpy (=u+Pav-Tas)=specific mass exergy Special characters Θ [-] Carnot factor Subscripts r Dissipation T Heat transfer f Fabrication (or embedded) a Atmospheric tu Turbine p Pump 0 Ambient or reference F Fuel i Input or reactant j Output or product evap Evaporator cond Condenser REPRESENTATION OF EXERGY LOSSES IN ENERGY INTEGRATION From the basic composite representation in a (Temperature Heat rate) pinch technology diagram a simple step is to convert the surfaces in exergy values by exchanging the temperature scale by a Carnot factor scale (1-Ta/T). In that way the surfaces below the hot and cold composites represent their exergy values and the surface in-between [2,3,5] represent the exergy losses. Staine in [3] further extended these surface representations by adding: a) a surface on top of the hot composite and below the cold composite representing the exergy losses due the dissipation phenomena (pressure drop) in the streams of the heat exchangers as shown in Figure 1 for a countercurrent heat exchanger b) Complementary surfaces representing the exergy losses due to exergy used during the fabrication of the heat exchangers themselves. In that case the fabrication exergy amount (the embedded exergy) is divided by the expected lifetime of the equipment to get an exergy rate that can also be represented by surfaces in the extended composite diagram. In Figure 1 the surface LT represents the heat transfer exergy loss, the surfaces Lr the dissipation exergy losses in each of the channels and Lf the exergy losses of fabrication. c) An additional diagram on top of the extended composite diagram, representing vertically the electricity consumed or produced and horizontally a pseudo-Carnot factor. The latter is calculated in such way that we visualize the representative surfaces of the exergy losses occurring in power units like turbines or compressors. Figure 2 shows a representation of a simple Rankine cycle for the conversion from heat or waste heat to electricity. The surfaces horizontally oriented in the lower diagram show the extended exergy losses in the evaporator and in the condenser. The coloured surfaces in the upper diagram illustrate the exergy losses in the turbine Lrtu, the surface of the fabrication exergy losses of the turbine itself Lftu as well as the similar surfaces corresponding to the feed pump Lrp and Lfp. The electricity balance can be read on the vertical axis showing a net production of electricity as expected. The advantage of this approach is to provide a visual representation of the sum of the exergy losses and where they occur in the process. Figure 1 Extended exergy composites of a countercurrent heat exchanger Another approach from Marechal [2] and shown in Figure 3 is to extend the concept of grand composite used in pinch technology to include the utilities. In figure 3 we see the grand composite of a given process with one self-satisfied pocket shown in red. The latter indicates a possibility to incorporate an Organic Rankine cycle using process streams themselves and not a utility stream. In this case the utility stream exergy is shown with the surfaces blue, green and yellow, typical of a boiler supply where the blue surface represent the exergy loss of combustion and the green one the heat transfer exergy losses between the combustion gas and the process streams to be heated. Figure 2 Extended exergy composites of a Rankine cycle Figure 3 Grand composite of a process including a boiler as hot utility [2] Figure 4 shows another representation of the opportunities to introduce heat pumps or ORC in the exergy grand composite diagram of a process [6]. L .