1 Introduction
1.1 Energy consumption and CO2 emission
1.2 Renewable energy and energy storage
1.3 Thermal energy storage
1.3.1 Classification according to energy storage mechanism
1.3.2 Classification according to temperature range and other classifications
1.4 Objectives and structure of the paper
Fig. 2 Layout of the review paper |
2 Sensible heat storage
2.1 Classification by temperature
2.2 Classification by material
2.2.1 Liquid material
2.2.2 Solid materials
2.2.3 Material comparison
Table 1 Main characteristics of different SHS materials |
Materials | Temperature | cp(kJ/kg∙K) | Average Cost(\$/kW·h) | Refs | |
---|---|---|---|---|---|
Low (°C) | High (°C) | ||||
Water | 0 | 100 | 4.183 | - | [48] |
Mineral oil | 200 | 300 | 2.6 | 4.2 | [19] |
Synthetic oil | 250 | 350 | 2.3 | 43 | [19] |
Rocks | - | - | 0.96 | - | [29] |
Sand | - | - | 0.83 | 4.2 | [29] |
Cast steel | 200 | 700 | 0.60 | 60 | [19] |
Reinforced concrete | 200 | 400 | 0.85 | 1.0 | [19] |
Solar salt | 220 | 565 | 1.5 | 5.8 | [49] |
Hitec salt | 142 | 535 | 1.4 | 10.7 | [49] |
Nitrite salts | 250 | 450 | 1.5 | 12 | [19] |
Nitrate salts | 265 | 565 | 1.6 | 3.7 | [19] |
Carbonate salts | 450 | 850 | 1.8 | 11.0 | [19] |
2.3 Summary
3 Latent heat storageenergy
3.1 PCM classification based on melting temperature
3.2 PCMs classification based on material composition
3.2.1 Organic compounds
Type | Material | Ρ kg/m3 | Tm °C | Δh kJ/kg | K W/mK | cp kJ/kgK | Corrosive | Toxicity |
---|---|---|---|---|---|---|---|---|
Paraffin wax | n-Tridecane | 755 | -5 | 160 | - | - | Slight | |
n-Hexadecane | 773 | 18 | 237 | - | - | slight | ||
n-Heneicosane | 787 | 40.2 | 200 | - | - | Non-toxic | ||
n-Tetracosane | 799 | 50.6 | 255 | - | - | NA | ||
n-Hexacosane | 778 | 56.3 | 256 | - | - | NA | ||
n-Octacosane | 804 | 61.6 | 253 | - | - | Slight | ||
Non-paraffins | Acetic acid | 1002 | 16.7 | 184 | 0.16 | 2.04 (l) | Mild | Non-toxic |
Lauric acid | 1007 | 44 | 218 | 0.22 | 2.15 (l) | Mild | Acute | |
Palmitic acid | 989 | 61 | 222 | 0.21 | 2.20 (l) | Moderate | Non-toxic | |
Thiosinamine | 1167 | 77 | 140 | - | - | Non-corrosive | High | |
Catechol | 1149 | 104.3 | 207 | - | - | Strong | Slight | |
Benzamide | 1341 | 127.2 | 169.4 | - | - | Non-corrosive | Acute |
Fig. 3 Experimental layout for thermal management of photovoltaic panels using paraffins [59] |
3.2.2 Inorganic materials
Table 3 Thermophysical properties of selected salt hydrates as PCMs |
Material | ρ kg/m3 | Tm °C | Δh kJ/kg | k W/mK | cp kJ/kgK | Refs |
---|---|---|---|---|---|---|
Na2SO4·10H2O | 1485 (s) | 31-32.4 | 251.1-254 | 0.544 | 1.93(s) | [62] |
Mn(NO3)2·6H2O | 1795 (s) | 25.5-25.8 | 125.9-148 | - | - | [63] |
CaCl2·6H2O | 1682.4-1802 (s) | 27.45-30 | 161.15-192 | 1.088(s) | 1.4(s) | [56, 64] |
LiNO3·3H2O | 1550 (s) | 29.6-29.9 | 296 | 0.8 (s) | 1.8 (s) | [65] |
Zn(NO3)2·6H2O | 1937-2065 (s) | 36-36.4 | 134-147 | 0.464-0.469(l) | 1.34(s) | [62] |
Fe(NO3)3·9H2O | 1684 (s) | 47-47.2 | 155 | - | - | [65] |
Na(CH3COO)·3H2O | - | 58-58.4 | 226-264 | - | - | [54, 66] |
Ba(OH)2·8H2O | 2070-2180 (s) | 78 | 265.7-301 | 1.255(s) | 1.17(s) | [65] |
Mg(NO3)2·6H2O | 1636-1640 (s) | 89-95 | 254-267 | 0.611-0.669(s) | 0.9(s) | [66] |
MgCl2·6H2O | 1560-1570 (s) | 115-117 | 195-172 | 0.694-0.704(s) | 1.72-2.25(s) | [65] |
In addition to the above phase separation problem, another main problem of salt hydrate is supercooling. Mechanical stirring, adding thickening agents, encapsulating PCMs [67], and modifying the chemical composition to make materials congruent [68] are effective methods to solve these problems. Kazemi and Mortazafi [69] used sodium tetra borate as a nucleating agent and successfully minimized the supercooling of Glauber’s salt. Similarly, nitro aluminum was used as a nucleating agent to reduce supercooling [70], as were Si3N4, ZrB2 and SiO2, silver nanoparticles [71]. |
Material | ρ kg/m3 | Tm °C | Δh kJ/kg | k W/mK | cp kJ/kgK | Refs |
---|---|---|---|---|---|---|
Na2SO4·10H2O | 1485 (s) | 31-32.4 | 251.1-254 | 0.544 | 1.93(s) | [62] |
Mn(NO3)2·6H2O | 1795 (s) | 25.5-25.8 | 125.9-148 | - | - | [63] |
CaCl2·6H2O | 1682.4-1802 (s) | 27.45-30 | 161.15-192 | 1.088(s) | 1.4(s) | [56, 64] |
LiNO3·3H2O | 1550 (s) | 29.6-29.9 | 296 | 0.8 (s) | 1.8 (s) | [65] |
Zn(NO3)2·6H2O | 1937-2065 (s) | 36-36.4 | 134-147 | 0.464-0.469(l) | 1.34(s) | [62] |
Fe(NO3)3·9H2O | 1684 (s) | 47-47.2 | 155 | - | - | [65] |
Na(CH3COO)·3H2O | - | 58-58.4 | 226-264 | - | - | [54, 66] |
Ba(OH)2·8H2O | 2070-2180 (s) | 78 | 265.7-301 | 1.255(s) | 1.17(s) | [65] |
Mg(NO3)2·6H2O | 1636-1640 (s) | 89-95 | 254-267 | 0.611-0.669(s) | 0.9(s) | [66] |
MgCl2·6H2O | 1560-1570 (s) | 115-117 | 195-172 | 0.694-0.704(s) | 1.72-2.25(s) | [65] |
Table 5 Thermophysical properties of selected pure inorganic salts as PCMs |
Material | ρ kg/m3 | Tm °C | Δh kJ/kg | K W/mK | cp kJ/kgK | Refs |
---|---|---|---|---|---|---|
AlCl3 | 2440 | 192 | 272-280 | - | - | [56] |
LiNO3 | 2380 | 250-254 | 360-373 | - | - | [56, 73] |
ZnCl2 | 2907 | 280 | 75 | 0.5 (s) | 0.74 (l) | [76] |
NaNO3 | 2257-2261 | 306-310 | 172-199 | 0.5 (s) | 1.1 (l) | [63] |
KNO3 | 2109-2110 | 330-336 | 88-266 | 0.5 (s) | 0.935 (s) | [63] |
MgCl2 | 2140 | 714 | 452-454 | - | - | [63, 73] |
NaCl | 2160 | 800-802 | 466.7-492 | 5 (s) | - | [63, 73] |
LiF | - | 848-868 | 932-1041 | - | - | [56] |
NaCO3 | 2533 | 854-858 | 165-275.7 | 2 (s) | - | [63] |
KF | 2370 | 857-858 | 452-507 | - | - | [63, 77] |
K2CO3 | 2290 | 897-900 | 200-235.8 | 2 (s) | - | [73, 77] |
Table 6 Representative studies of the cycling and thermal stability of carbonates, nitrates and chlorides |
Material | Heating conditions | Atmosphere | Cycles | Comments | Refs |
---|---|---|---|---|---|
LiKCO3 | 480-535 °C | - | 129 | Suitable for 8 kWh thermal energy storage application | [88] |
Na2CO3 - Li2CO3 | 600 °C | CO2 | 500 | Without weight loss, great thermal and chemical stability | [89] |
N2 | 0.8% weight loss | ||||
32.1 wt% Li2CO3 - 33.4 wt% Na2CO3 - 34.5 wt% K2CO3 | Up to 1000 °C | CO2 | - | Stable | [90] |
Ar | Decompose at 710-715 °C | ||||
Air | Decompose at 530 °C | ||||
28.5 wt% Li2CO3 - 71.5 wt% K2CO3 | 300-600 °C | Air | 40/100 | A weakened sub-cooling | [91] |
35 wt% Li2CO3 - 65 wt% K2CO3 | |||||
22 wt% Li2CO3 - 62 wt% K2CO3 - 16 wt% Na2CO3 | Unnoticeable phase change after a 20-cycle test, a weakened sub-cooling | ||||
NaNO3 | ~ 500 °C | Air | - | Relatively stable over 350 °C, partial salt creeped out in the liquid state, form a little nitrite (NaNO2-NaNO3) | [92] |
Solar Salt | 600 °C | Air | 10-50 | Unchanged latent heat, hardly changed chemical structures, less than 3% weight loss at 500 °C | [93] |
20 mol% Ca(NO3)2 - 80 mol% NaNO3 | 350-750 °C (thermal) 80-350 °C (cycling) | - | 26 | 0.20% mass loss, high reproducibility of DSC curves in heating process | [80] |
30 mol% Ca(NO3)2 - 70 mol% NaNO3 | 0.42% mass loss, better exothermic performance, half the cost of Solar Salt | ||||
KNO3 - NaNO3 - LiNO3 | 30-1000 °C | Ar | - | Formed NO at 325 °C | [94] |
N2 | Formed NO at 425 °C | ||||
Air | Formed NO at 475 °C, limited long-term stability at 500 °C | ||||
O2 | Formed NO at 540 °C | ||||
68 wt% KNO3 - 18 wt% LiNO3 - 14 wt% Ca(NO3)2 | 400-500 °C, 32-72 days (thermal) 100-180 °C (cycling) | Air | 800 | 31.3% reduction in latent heat | [95] |
Same ternary eutectics with 0-0.6 wt% CsNO3 additives | Good thermal stability with 0-0.6 wt% CsNO3 at 400 °C but unstable at 500 °C, improved cycling stability with 0.2-0.38 wt% CsNO3 additives | ||||
64 wt% MgCl2 - 36 wt% KCl | 300-600 °C | Air | 40 | Salts creeped out after 40 cycles | [91] |
52 wt% MgCl2 - 48 wt% NaCl | No significant change | ||||
Na2CO3 - NaCl | 600-650 °C, 2 h | Air | 1000 | No noticeable change in thermophysical properties | [96] |
Na2SO4 - NaCl | 550-680 °C, ≤ 6 h | Air | 100 | Good thermal stability | [97] |
Same sample with α-alumina or mullite additives | Reduced undercooling |
3.3 Heat transfer enhancement methods
3.3.1 Material level
Table 7 Thermal conductivity of some composite PCMs embedded in highly thermal conductive particles |
PCMs | Additives | Thermal conductivity W/mK | Refs | ||||
---|---|---|---|---|---|---|---|
Material | k W/mK | Material | Size | Amount | |||
32.2% Li2CO3 - 33.2% Na2CO3 - 34.5% K2CO3, wt% | 1.33 | Mg | 100-200 meshes | 0.1 wt% | 1.59 | [111] | |
2 wt% | 1.93 | ||||||
Solar Salt | 0.78 | MgO | - | 0.125 wt% | 0.85 | [115] | |
0.25 wt% | 0.88 | ||||||
0.5 wt% | 0.85 | ||||||
1.0 wt% | 0.86 | ||||||
2 wt% | 0.87 | ||||||
32.1% Li2CO3 - 33.4% Na2CO3 - 34.5% K2CO3, wt% | 1.67 | Al2O3 | 20 nm | 1.0 wt% | 2.06 | [116] | |
50 nm | 1.0 wt% | 2.15 | |||||
80 nm | 0.8 wt% | 2.19 | |||||
32.1% Li2CO3 - 33.4% Na2CO3-34.5% K2CO3, wt% | 1.67 | T-ZnOw | - | 0.2 wt% | 2.06 | [117] | |
0.4 wt% | 2.64 | ||||||
0.8 wt% | 3.36 | ||||||
1.0 wt% | 3.89 | ||||||
1.4 wt% | 4.48 | ||||||
2.0 wt% | 4.36 | ||||||
LiNO3 | 0.51 | Graphite | 85 μm | 5 wt% | 0.87 | [118] | |
10 wt% | 1.19 | ||||||
15 wt% | 1.52 | ||||||
20 wt% | 1.86 | ||||||
Na2CO3/MgO | 0.75 @40 °C | MWCNT | l = 10 μm | 0.1 wt% | 0.90 | @40 °C | [119] |
0.83 @75 °C | d = 11 nm | 1.03 | @75 °C | ||||
0.88 @120 °C | 1.14 | @120 °C | |||||
0.3 wt% | 1.05 | @40 °C | |||||
1.20 | @75 °C | ||||||
1.65 | @120 °C | ||||||
0.5 wt% | 1.13 | @40 °C | |||||
1.30 | @75 °C | ||||||
1.49 | @120 °C | ||||||
49% Na2CO3 - 51% Li2CO3, wt% | 0.69 | MgO | - | - | 0.87 | [120] | |
MgO + graphene | 1.24 | ||||||
Cu + MgO | 1.34 | ||||||
Solar Salt | 0.41 @300 °C | MWCNT | l = 3-15 μm | 0.3 wt% | 1.62 | [121] | |
d = 12-15 nm | 0.4 wt% | 0.78 |
Table 8 Thermal conductivity of some composite PCMs embedded in porous media |
PCMs | Porous media | Thermal conductivity of form-stable composites W/mK | Refs | |||
---|---|---|---|---|---|---|
Material | k W/mK | Material | Amount | |||
NaNO3 | 0.50 | Expanded Perlite | 10 wt% | 0.84/1.14 | @25/300 °C | [124] |
20 wt% | 0.67/0.81 | @25/300 °C | ||||
40 wt% | 0.54/0.62 | @25/300 °C | ||||
60 wt% | 0.42/0.57 | @25/300 °C | ||||
58.1% LiNO3 - 41.9% KCl, wt% | 0.93 | Expanded graphite | 18.3 wt% | 5.59 | [125] | |
49% LiNO3 - 51% NaNO3, wt% | 0.84 | 18.2 wt% | 6.61 | |||
87% LiNO3 - 13% NaCl, wt% | 0.80 | 24.2 wt% | 4.71 | |||
Solar Salt | 2.27 | Expanded graphite | 0.5 wt% | 2.88 | [126] | |
1 wt% | 3.34 | |||||
1.5 wt% | 4.14 | |||||
2 wt% | 4.88 | |||||
40% LiNO3 - 60% KNO3, wt% | 1.03 @5 MPa | Expanded graphite | 5 wt% | 4.19 | @5 MPa | [127] |
1.10 @15 MPa | 5.34 | @15 MPa | ||||
1.30 @25 MPa | 5.53 | @25 MPa | ||||
15 wt% | 1.36 | @5 MPa | ||||
12.41 | @15 MPa | |||||
13.04 | @25 MPa | |||||
30 wt% | 15.42 | @5 MPa | ||||
16.29 | @15 MPa | |||||
16.73 | @25 MPa | |||||
53.4% NaCl - 15.0% CaCl2-31.6% MgCl2, mol% | 1.17 | Expanded graphite | 0.5 wt% | 1.58 | [128] | |
0.7 wt% | 1.64 | |||||
1 wt% | 1.64 | |||||
3 wt% | 1.68 | |||||
5 wt% | 2.08 | |||||
31.5% MgCl2 - 68.5% KCl, mol% | 0.41 | Expanded graphite | 15 wt% | 4.92 | [129] |
3.3.2 Component level
3.3.3 System level
3.4 Summary
4 Thermochemical energy storage
4.1 Classifications by temperature range
4.2 Various thermochemical heat storage systems
4.2.1 Metal hydrides
Table 9 Metal hydrides candidates for TCES [164] |
TCES systems | Temperature (°C) | Energy storage density (kJ/kg) | Energy storage density (MJ/m3) |
---|---|---|---|
NaH/NaMgH3 | 430-585 | 1463 | 2134.8 |
Mg/MgH2 | 300-400 | 2389 | 3463.2 |
Ti/TiH1.7 | 700-1000 | 851 | 3243.6 |
Ca/CaH2 | > 1000 | 4198 | 7016.4 |
Mg-Fe/Mg2FeH6 | 350-550 | 1776.5 | 4867.2 |
4.2.2 Metal hydroxides
Table 10 The kinetic models of $f(X) $ [187] |
Reaction model | Code | 𝑓(𝑋) |
---|---|---|
Power law | P4 | $4 X^{\frac{3}{4}} $ |
Power law | P3 | $3 X^{\frac{2}{3}}$ |
Power law | P2 | $2 X^{\frac{1}{2}} $ |
Power law | P2/3 | $\frac{2}{3} X^{-\frac{1}{2}}$ |
One-dimensional diffusion | D1 | $ \frac{1}{2} X^{-1}$ |
Mampel (first order) | F1 | $1-X $ |
Avrami-Erofeev | A4 | $4(1-X)[-\ln (1-\mathrm{X})]^{\frac{3}{4}} $ |
Avrami-Erofeev | A3 | $3(1-X)[-\ln (1-\mathrm{X})]^{\frac{2}{3}}$ |
Avrami-Erofeev | A2 | $ 2(1-X)[-\ln (1-\mathrm{X})]^{\frac{1}{2}} $ |
Three-dimensional diffusion | D3 | $\frac{3}{2}(1-X)^{\frac{2}{3}}\left[1-\ln (1-X)^{\frac{1}{3}}\right]^{-1} $ |
Contracting sphere | R3 | $ 3(1-X)^{\frac{2}{3}} $ |
Contracting cylinder | R2 | $ 2(1-X)^{\frac{1}{2}}$ |
Two-dimensional diffusion | D2 | $ {[-\ln (1-X)]^{-1}}$ |
Table 11 The whole kinetic models of Ca(OH)2 dehydration and CaO hydration |
𝐴(𝑠−1) | 𝐸(𝑘𝐽/𝑚𝑜𝑙) | ℎ(𝑝,𝑝𝑒𝑞,𝑇,𝑇𝑒𝑞) | 𝑓(𝑋) | Reaction stage | Ref |
---|---|---|---|---|---|
15 | 0 | $\frac{T_{e q}-T}{T_{e q}} $ | $1-X $ | CaO hydration | [184] |
$\frac{3.5 \times 10^{-4}}{d_p[\mu m]}$ | -59.4 | $\frac{p_{H_2 O}-p_{e q}}{p_{\text {total }}} $ | $3(1-X)^{\frac{2}{3}} $ | CaO hydration | [188] |
390.827 | 87.46 | ${\left[\max \left(\frac{1}{p_{H_2 O} / p_{e q}}\right)-1\right]^{3.43}}$ | $1-X $ | CaO hydration | [189, 190] |
13,945 | 89.486 | $\left(\frac{p_{H_2 O}}{p_{e q}}-1\right)^{0.83} $ | $3(1-X)[-\ln (1-X)]^{\frac{2}{3}} $ | CaO hydration | [149] |
1.0004·10-34 | -443.427 | $\left(\frac{p}{10^5 P q}\right)^6 $ | $1-X $ | CaO hydration | [149] |
449,974 | 91.282 | ${\left[1-\min \left(\frac{1}{p_{H_2 O} / p_{e q}}\right)\right]^{3.47}} $ | $X$ | Ca(OH)2 dehydration | [189] |
1.9425·1012 | 187.88 | $ \left(1-\frac{p}{p_{e q}}\right)^3 $ | $1-X$ | Ca(OH)2 dehydration (X < 0.2) | [149] |
8.9588·109 | 162.62 | $\left(1-\frac{p}{p_{e q}}\right)^3$ | $2(1-X)^{\frac{1}{2}}$ | Ca(OH)2 dehydration (X > 0.2) | [149] |
Fig. 9 The novel reactor concept based on a plow share mixer for fluidization of CaO/Ca(OH)2 system [206] |
4.2.3 Metallic carbonates
Fig. 10 The sintering mechanism of CaO materials during TCES process [213] |
Fig. 11 The CO2 capacity of Al2O3 doped CaCO3 materials at long cycles [217] |
Fig. 12 An operation scheme of a chemical heat pump (heat storage mode) utilizing the MgO-CO2 working pair [207] |
Fig. 13 CSP-CaL integration conceptual scheme and representation of energy storage and release processes [209] |
4.2.4 Metal oxides
Table 12 Candidate materials for the TCS system based on the redox reaction [241] |
Materials and Reaction | Temperature (°C) | Reaction Enthalpy (kJ/mol) | Energy Density (kJ/kg) |
---|---|---|---|
2𝑃𝑏𝑂2→2𝑃𝑏𝑂+𝑂2 | 405 | 62.8 | 262 |
4𝑀𝑛𝑂2→2𝑀𝑛2𝑂3+𝑂2 | 530 | 41.8 | 481 |
2𝐵𝑎𝑂2→2𝐵𝑎𝑂+𝑂2 | 885 | 72.5 | 474 |
2𝐶𝑜3𝑂4→6𝐶𝑜𝑂+𝑂2 | 890 | 202.5 | 844 |
6𝑀𝑛2𝑂3→4𝑀𝑛3𝑂4+𝑂2 | 1000 | 31.9 | 202 |
4𝐶𝑢𝑂→2𝐶𝑢2𝑂+𝑂2 | 1120 | 64.5 | 811 |
6𝐹𝑒2𝑂3→4𝐹𝑒3𝑂4+𝑂2 | 1400 | 79.2 | 496 |
2𝑀𝑛3𝑂4→6𝑀𝑛𝑂+𝑂2 | 1700 | 194.6 | 850 |
Table 13 Reaction temperature region, enthalpy and heat capacity of metal oxides |
Temperature | Materials | Reaction Enthalpy (kJ/mol) | aHeat capacity J/(mol·K) | Refs |
---|---|---|---|---|
700 °C < T < 900 °C | Co3O4 | 202.5 | 56.04 ~ 57.63 | [242] |
BaO | 72.5 | 56.93 ~ 58.54 | [244] | |
900 °C < T < 1100 °C | Mn2O3 | 31.9 | 143.63 ~ 150.52 | [243] |
CuO | 64.5 | 56.75 ~ 58.39 | [245] | |
1100 °C < T | Fe2O3 | 79.2 | 141.28(1100 ℃) | [246] |
Mn3O4 | 194.6 | 212.37(1100 ℃) | [243] |
aAll heat capacity data correspond to the temperature in the first column |
Fig. 14 30 cycles experiment of $C{o}_{3}{O}_{4}$ powder in the TGA between 985 and 785 °C with a heat/cooling rate of 5℃/min. (Weight loss: 6.75% for the 1st cycle vs. 6.50% for the 30th cycle) [253] |
Table 14 Recent studies on reaction kinetics of metal oxide redox reactions |
Year | Oxides | Kineticsa | Refs |
---|---|---|---|
2015 | Co3O4 | Reduction (Avrami-Erofeyev nucleation model): an Avrami constant of 1.968 and apparent activation energy of 247.21 kJ/mol at 1113 K-1213 K Oxidation: apparent activation energy of 58.07 kJ/mol at 450 K-750 K | [268] |
2019 | MnFe2O4 | First by a diffusion-controlled reaction mechanism (Ea=192±2kJ/mol) with no phase change, followed by a nucleation-growth reaction mechanism (Ea =181.4±0.3kJ/mol) | [265] |
2019 | Mn + Fe oxide | For reaction in Ar between conversions 0.05<α<0.95 and reaction in air in the conversion range of 0.05<α<0.8: $ \frac{\mathrm{d}\alpha}{\mathrm{d}T}=\frac{(8.85\pm0.00)10^{15}}{\beta}\mathrm{exp}\left(-\frac{426.13\pm0.04}{RT}\right)\frac{3(1-\alpha)^{2/3}}{2\left[1-(1-\alpha)^{1/3}\right]}\left(1-\frac{P_{0_{2}}}{P_{0_{2},eq}}\right)^{25.01} $ | [260] |
2021 | Si doped Mn2O3 | Reduction:$ \frac{d\alpha_{\mathrm{red}}}{dt}=3.8\cdot10^{15}\cdot e^{\left(-\frac{341.72}{RT}\right)}\alpha^{0.1}\cdot\left(1-\alpha_{\mathrm{red}}\right)^{1.15}\cdot\left[-\ln\left(1-\alpha_{\mathrm{red}}\right)\right]^{0.05}\cdot\left(1-\frac{P_{O_{2}}}{8\cdot10^{7}\cdot e^{\cdot23.13}\left(\frac{1000}{T}\right)}\right)^{7.05} $ (Sestak-Berggren reaction model) Oxidation:$ \frac{d\alpha_{ox}}{dt}=1.7\cdot10^7\cdot e^{\left(-\frac{-120.42+156.88\frac{P_{\mathrm{O2eq}}}{P_{\mathrm{O2eq}}-P_{\mathrm{O2}}}}{RT}\right)}\cdot\alpha^{2.7}{}_{ox}\cdot\left(1-\alpha_{ox}\right)^{0.5}\cdot\left[-\ln\left(1-\alpha_{ox}\right)\right]^{-1.85} $ | [269] |
a$ \frac{d \alpha}{d t}=k(T) \times f(\alpha) \times h\left(p_{\mathrm{O}_{2}}\right), k(T)=A e^{-\frac{E_{a}}{R T}} $, where α(t) is the mass change with time, Ea is the activation energy, A is the pre-exponential factor, f(α) is the reaction model, and h($P_{\mathrm{O}_{2}}$) is a pressure-related term |
Fig. 16 The air-fed fluidized bed integrated with a solar receiver [264] |
4.3 Summary
5 Comparison and analysis
5.1 Comparison and analysis
Table 15 Comparison of some typical heat storage methods |
Materials | T °C | cp (kJ/kg∙K) | Δh (kJ/kg) | Cost (¥/kW·h) | Maturity | Refs | |
---|---|---|---|---|---|---|---|
SHS | Water | 0-100 | 4.183 | - | 0.07 | CA | [48] |
Mineral oil | 200-300 | 2.6 | - | 26.8 | [19] | ||
Synthetic oil | 250-350 | 2.3 | - | 274 | [19] | ||
Reinforced concrete | 200-400 | 0.85 | - | 6.4 | [19] | ||
Solar salt | 220-565 | 1.5 | - | 37 | [49] | ||
Carbonate salts | 450-850 | 1.8 | - | 70 | [19] | ||
LHS | n-Hexadecane | 18 | - | 237 | 577 | CA; PT | [54,55,56] |
Acetic acid | 16.7 | - | 184 | 156 | [54,55,56] | ||
Lauric acid | 44 | - | 218 | 248 | [54,55,56] | ||
Catechol | 104.3 | - | 207 | 1200 | [54,55,56] | ||
CaCl2·6H2O | 27.45-30 | - | 161.15-192 | 40-47 | [56, 64] | ||
Na(CH3COO)·3H2O | 58-58.4 | - | 226-264 | 72-85 | [54, 66] | ||
Ba(OH)2·8H2O | 78 | - | 265.7-301 | 72-81 | [65] | ||
MgCl2·6H2O | 115-117 | - | 195-172 | 31-37 | [65] | ||
88% Al-12% Si | 576 | - | 560 | 193 | [66, 73] | ||
LiNO3 | 250-254 | - | 360-373 | 1880-1950 | [56, 73] | ||
NaNO3 | 306-310 | - | 172-199 | 90-105 | [63] | ||
NaCl | 800-802 | - | 466.7-492 | 6.2-6.5 | [63, 73] | ||
NaCO3 | 854-858 | - | 165-275.7 | 52-87 | [73, 77] | ||
TCES | Mg/MgH2 | 279 | - | 2811 /(MgH2) | 90 | PT; LA | [164] |
CaO/Ca(OH)2 | 440 | - | 1409 /(Ca(OH)2) | 1.9 | [200] | ||
MgO/Mg(OH)2 | 325 | - | 1389 /(Mg(OH)2) | 4.5 | [171] | ||
CaO/CaCO3 | 890 | - | 1778 /(CaCO3) | 1.2 | [210] | ||
MgO/MgCO3 | 397 | - | 1381 /(MgCO3) | 3 | [207] | ||
CoO/Co3O4 | 905 | - | 841 /(Co3O4) | 2890 | [241, 242] | ||
Mn2O3/Mn3O4 | 928 | - | 265 /(Mn2O3) | 85 | [241, 243] | ||
Cu2O/CuO | 1025 | - | 811 /(CuO) | 277 | [241, 245] |