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24 H. Zhang et al./Progress in Energy and Combustion Science 53 (2016) 1–40 Table 17 Screening parameters for a selection of reaction pairs. Reaction Mg(OH)2 ↔ MgO + H2O MgCO3 ↔ MgO + CO2 Ca(OH)2 ↔ CaO + H2O CaMg(CO3)2 ↔ MgO + CaO + 2CO2 CaCO3 + H2O ↔ Ca(OH)2 + CO2 CaCO3 ↔ CaO + CO2 2Co3O4 ↔ 6CoO + O2 6Mn2O3 ↔ 4Mn3O4 + O2 Teq (P = 1 atm) (°C) 259 303 479 490 573 839 870 906 ηwmax (30–120 °C) –) 0.28–0.43 0.34–0.48 0.47–0.60 0.49–0.61 0.55–0.64 0.64–0.73 0.73–0.82 0.64–0.74 Fig. 23. Equilibrium temperature versus pressure for selected reaction pairs. hence proceed so that chemical equilibrium is maintained at all tem- peratures. All the reaction heat and all heat imbalances in the heat exchanger must be converted into maximum work by use of a Carnot cycle available throughout the temperature range. The advantage of both T* and ηwmax is that they may be estimated to a fair approx- imation for a given reaction by use of standard reference data alone. 4.2.2. Calculationresults From the calculations, Figs. 23 and 24 illustrate both screening parameters, T* and ηwmax, for the selected reaction pairs. Fig. 23 plots the equilibrium temperature versus the equilibrium pressure for the different reactions in Table 17. The maximum work efficiency versus the sink temperature is plotted in Fig. 24. To make a selection between the reactions, different aspects need to be taken into consideration. Firstly, the temperature should pref- erably be as close as possible to 500–900 °C. Secondly a higher maximum work recovery efficiency is preferred. But also the prac- tical aspects need to be considered, because adding water vapour is easier than collecting, storing and injecting carbon dioxide, whilst O2 reactions are most favourable since air can be the reactant of the reverse reaction. Oxides and hydroxides are thus favoured above carbonates. Fig. 24 shows that the temperature is not very dependent on the pressure for most of the systems selected except at low partial pres- sures of the gas/vapour phase, as commonly encountered when a separate gas carrier is used to exhaust the gas/vapour reaction prod- ucts. For Mn2O3 the temperature is a more outspoken function of pressure for all pressures. The work efficiency is rather low for car- bonates and hydroxides. Oxides provide the higher value of work efficiency in the selected range of sink temperatures. 4.3. Kineticsfromthermogravimetricanalysis Thermogravimetry (TGA) measures the weight of the sample every second, recording M0, Mt and M∞, at the initial measure- ment time t0, time t and the time for completing the reaction t∞. The conversion is calculated as α = M0 −Mt (10) M0 −M∞ The reaction rate constant can be derived within the complete time and/or temperature scale, as described in detail for other chem- ical process by Brems et al. [172,173]. For example, typical TGA plots for Mg(OH)2 are illustrated in Fig. 25. The decomposition rate is slightly dependent on the tem- perature ramp, β. Similar weight loss curves were obtained for all reaction pairs tested. Additional TGA plots are illustrated in Figs. 26 and 27 for the re- versible reactions of Mn2O3 ↔ Mn3O4 and Co3O4 ↔ CoO, respectively. Clearly, the oxidation reaction is slower than the reduction and incomplete, assumed to be the results of compaction of the reduced reaction compound, hence hampering diffusion of O2 during the reverse reaction [170,174]. This is also illustrated in the BET ad- sorption curves of Mn2O3 and Mn3O4 (Fig. 28) [170]. A fair approximation of the reaction kinetics is obtained by trans- forming the TGA data, using the Arrhenius equation of the reaction rate constant, k: k=Aexp⎛−EA ⎞ (11) Plotting ln(k) versus 1/T provides –EA/R as the slope of the linear fit, and ln(A) as ln(k) at 1/T = 0. In this equation k is the reaction rate constant; A the pre- exponential factor with same units as k; Ea the activation energy, J/mol; R the universal gas constant, 8.314 J/mol K; and T the tem- perature, K. The rate of reaction, dα/dt, is a function of the rate constant k (dependent on temperature) and a function of conversion f(α) (in- dependent on temperature). This results in: Fig. 24. Maximum work efficiency vs. sink temperature for the selected reaction pairs. Since k is described by the Arrhenius expression, the overall ex- pression of the reaction rate is: dα =k(T)f (α) dt (12) ⎜⎝ R T ⎟⎠PDF Image | Thermal energy storage: Recent developments
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