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1 Electronic Sulementary Material (ESI) or Energy & Environmental Science. Thi journal i The Royal Society o Chemitry 2016 Electronic Sulementary Inormation The Eect o the Ga-Solid Contacting Pattern in a High-Temerature Thermochemical Energy Storage on the Perormance o a Concentrated Solar Power Plant S. Ströhle, a A. Haelbacher, b,c Z. R. Jovanovic b and A. Steineld b a Solar Technology Laboratory, Paul Scherrer Intitute, 5232 Villigen, Switzerland b Deartment o Mechanical and Proce Engineering, ETH Zurich, 8092 Zurich, Switzerland c Correonding author: haelbac@ethz.ch Content Reaction Model and Material Proertie... 2 Eect o Packed Bed Reactor Length and Granule Size... 5 Fluidized Bed Model... 9 Reerence

2 Reaction Model and Material Proertie The theoretical equilibrium temerature o the manganee oxide redox ytem were calculated with HSC Chemitry ( a a unction o the oxygen artial reure. 1 Leat-quare itting o the reult gave ln ( ) O2, eq = + (1) T where i the equilibrium artial reure o oxygen in the O O 2, eq 2-N 2 ga mixture correonding to the equilibrium temerature T eq. The rm o the relative error i The emirical reaction kinetic model wa derived rom exerimental data obtained with a dierential acked bed at variou temerature and oxygen artial reure. 1,2 The bed conited o a mixture o commercial Mn3O 4 owder (Sigma Aldrich, Manganee (II,III) oxide, CAS: ) with a meaured mean article diameter o 5.5 m m and inert SiO 2 (Merck, Seeand reint, CAS: ) that wa ieved to article diameter o mm. The ratio o SiO2 to Mn3O4 by ma wa at leat 40. Each exeriment wa erormed at nearly contant temerature ( ± 5 K ) and oxygen artial reure ( O 2, / O2, in = 1± 0.05). The model i where dx E A a k0 ex = X 1 X 1 dt RT eq b O2 ( ) O2, eq X i the olid converion ( X = 0 and 1 correond to ully oxidized and reduced tate, reectively), t i time, k 0 i the rate contant, energy, R i the univeral ga contant, T i the temerature, o oxygen, E A i the aarent activation O 2 i the artial reure i the equilibrium oxygen artial reure at the given temerature (ee O 2, eq Eq. (1)), and a, b and are arameter. Note that thi model i baed on the aumtion that the manganee oxide can be comletely reduced/oxidized uing cycle-indeendent kinetic, i.e., both the degree o converion and the kinetic do not change with the number o cycle. The value o the itting arameter or oxidation and reduction are lited in Tab. 1. The ign o k 0 wa choen to make the converion rate negative or oxidation and oitive or reduction. The maximum converion rate occur at X = and or oxidation and reduction, reectively. Table 1: Fitted arameter or emirical kinetic model given by Eq. (2) Oxidation Reduction 12 k E A J / mol J / mol a b (2) 2

3 Figure 1 how the maximum converion rate obtained rom Eq. (1) and (2) a a unction o the temerature and oxygen artial reure. At a given oxygen artial reure, an increae in the temerature u to ab 1000 K lead to increaing oxidation rate becaue o the Arrheniu term in Eq. (2). By urther increaing the temerature, equilibrium i aroached, and the oxidation rate become lower becaue o the reure term in Eq. (2). To reduce the material, it need to be heated to a temerature igniicantly above the theoretical equilibrium temerature. An increae in O 2 lead to a higher equilibrium temerature T eq (ee Eq. (1)), and generally caue higher oxidation rate and lower reduction rate at a given temerature. Figure 1: Maximum converion rate a a unction o temerature and oxygen artial reure determined rom Eq. (1) and (2). The circle indicate the theoretical equilibrium temerature correonding to the our oxygen artial reure. The theoretical relative ma gain during the oxidation i w theor, ox = We aumed a article internal oroity o ε = 0.5 and an intrinic denity o 3 ρ Mn O = kg m. 3 The heat caacitie o the manganee oxide were conidered to 4 be temerature-deendent. 4 The reaction enthaly H rxn wa calculated a a temeraturedeendent unction uing Kirchho law 5 T 0 H rxn ( T ) = H rxn + 0 ( uc ) ( uc ) dt T roduct reactant where the uercrit 0 denote tandard condition and υ i the toichiometric coeicient. For the imulation o the luidized bed, the article ize (100 m m ) wa choen to rereent Geldart A tye article that are tyically ued in indutrial luidized bed. 6 The article were conidered to be mall enough o that the temerature and reaction rate (3) 3

4 within each article could be aumed to be uniorm. Thereore, Eq. (2) wa ued to calculate the reaction rate. The ize o granule ued or the imulation o the acked bed TCS ( 5 mm ) i tyical or acking in large-cale indutrial acked bed. 7 Granule o uch a diameter reult in mall to moderate reure dro or tyical acked-bed length. Eq. (2) wa evaluated in each cell o a granule a a unction o the local value o T,, and X. The eective thermal conductivity o Mn3O4 owder wa meaured a kg, e = 0.59 W / mk. 8 Simulation indicated that varying the eective intragranule thermal conductivity within the range o W / mk did not lead to igniicant intragranule temerature gradient. However, varying k g, e in the given range wa ound to aect the eective axial bed conductivity and thereore the axial ga and olid hae temerature roile. In rincile, the lattening o the axial temerature roile through increaing k g, e could lead to an increae in T, c,, and thereore to a reduction in the eective gravimetric torage denity e tot. However, or the range o W / mk the maximum dierence in T, c, wa ab 1 K, and the correonding relative change in e tot wa le than 1%. 5 2 The eective ma diuion coeicient wa et to Dg, e = 10 m / ollowing imulation that howed variation in the range o m / to have a negligible inluence on the reaction rate. The denity o air wa calculated rom the ideal ga law. The variation o the heat caacity c, air with the temerature wa baed on tabulated value o ure nitrogen and oxygen at 1bar. 9 O 2 4

5 Eect o Packed Bed Reactor Length and Granule Size The reaon or chooing a length o Lbed = 1.5 m or the acked bed may not be clear at irt ight. In act, one may exect a horter bed to be advantageou becaue almot no energy i tored in the granule near the cold end o the bed (ee 1.0 m< z < 1.5 m in Fig. 9 in the manucrit). However, a reduction in the bed length not only aect the gravimetric energy torage denity ( e tot ) but alo the maximum HTF low temerature during charging ( T, c,,max ). From the reult o additional imulation or dierent bed length, rovided in Tab. 2, it can be een that a reduction in the bed length would lead to an increae in e tot at the exene o increaed T, c,,max. A tated in Section 3 o the manucrit, in a arallel coniguration a deviation o T, c, rom T PB, lead to exergy loe due to mixing o the HTF tream leaving the TCS and the ower block. Thi i why we have choen the bed length and oerating condition uch that T, c, TPB, during the entire charging eriod. For eciic CSP lant coniguration, a limited deviation o T, c, rom T PB, may be accetable becaue the increaed e tot and the aociated reduced cot o the TCS material and reactor houing may weigh the increaed exergy loe. Thereore, the condition reulting in T, c, TPB, lead to conervative reult that are more generally alicable. Table 2: Simulated imact o bed length on the maximum HTF low temerature during charging c,max ) and the gravimetric energy torage denity ( e tot ). Note that the remaining arameter were unchanged. T (,, Lbed [ m ] T, c,,max [ K ] e tot [ MJ / kgmn2o ] To invetigate the enitivity o our reult to the ize o the granule, we erormed additional imulation or granule o d = 2 mm while keeing the other arameter unchanged. The erormance o thi acked bed i comared with the erormance o the bed acked with d = 5 mm granule in Fig. 2 to 5. The conequence o reducing the granule ize can be ummarized a ollow: 1. The HTF low temerature i not aected igniicantly, ee Fig. 2. The dro in T, d, at the end o dicharging i lightly teeer or the maller granule but thi could be mitigated by a light decreae in the HTF ma lux during dicharging. 2. A hown by Fig. 3 and 4, the axial temerature gradient are teeer or the maller granule during both charging and dicharging. The main reaon or the teeer temerature gradient i the increaed eciic urace area o the granule, which reult in enhanced interhae heat traner. A a reult o the 5

6 teeer axial temerature roile, however, a hown by Fig. 5, the local gravimetric energy torage denity change lightly: in the bed o 2 mm granule more enible heat i tored in the reaction zone and le enible heat i tored in the cooling zone. Figure 3-5 urther indicate that the length o the bed o 2 mm granule could be reduced, reulting in increaed overall gravimetric energy torage denity. 3. A decreae in the granule ize lead to an increae in the overall bed reure dro rom mbar ( d = 5 mm ) to mbar ( d = 2 mm ). The correonding increae in the required uming work tranlate to an increae in the araitic loe rom 0.2 % to 1.1% o the energy tored during charging. From thee reult it can be concluded that a change in the granule ize doe not aect any o our key concluion in Section 3 to 5. Figure 2: Air low temerature during dicharging or granule ize o 5 mm (black line) and 2 mm (red line). 6

7 Figure 3: Air temerature in the acked bed a a unction o the axial oition during charging or granule ize o 5 mm (black line) and 2 mm (red line). Figure 4: Air temerature in the acked bed a a unction o the axial oition during dicharging or granule ize o 5 mm (black line) and 2 mm (red line). 7

8 Figure 5: Local gravimetric energy torage denity in the acked bed, calculated rom the dierence in the energy content o the manganee oxide granule between the charged and dicharged tate or granule ize o 5 mm (black line) and 2 mm (red line). 8

9 Fluidized Bed Model The imulation o the luidized bed were baed on the aumtion that the ga reache the temerature o the olid beore leaving the bed. Thi rereent the ideal oerating condition or a luidized-bed TCS that i integrated in a erial coniguration. I T > T during charging, le thermal energy i tored and the attainable dicharging, c, duration i reduced. I T, d, < T during dicharging, the thermal eiciency in the ower block i decreaed. In the ollowing, the condition under which T, T can be conidered to be mall will be dicued. I the olid hae i aumed to be erectly mixed, it temerature can be taken to be atially uniorm. I in addition the temerature o the olid hae i contant in time and lug-low condition exit, the energy balance reduce to 6 L dt bed = α (4) h T T dz where L bed i the bed height, T and T are the temerature o the olid and ga hae, reectively, z i the axial coordinate, and α h i the ratio o interhae heat traner to the convective heat tranort in the bed, 61 ( ebed ) hbed Lbed αh = (5) ρuc, d where e bed i the bed void raction, φ i the hericity o the article, h bed i the aarent heat traner coeicient between the ga and the bed o olid baed on the total urace area o the article, ρ, u and c, are the denity, uericial velocity, and heat caacity o the ga, reectively, and d i the article diameter. The eect o byaing, i.e., ga riing within bubble and thu not exchanging heat with the olid hae, can be modeled by a raction 0 β 1 o the ma low o the ga aing through the bed and retaining it inlow temerature. Auming the remaining ma low to a through the bed at lug-low condition, and that α h and β are contant, the ga low temerature i given by T, T = ( 1 β) ex( αh ) + β (6) T, in T Deviation rom lug low, or examle through backmixing o the ga hae, lead to increaed dierence between the temerature o the ga hae at the let and the temerature o the olid hae 6,10,11 and hould thereore be avoided. In the limit o a erectly mixed ga hae, T, T 1 = (7) T T 1+ α, in h 9

10 Figure 6: Eect o the ga low attern on the luid let temerature in a luidized bed, auming that the erectly mixed olid are ket at a contant temerature. Equation (6) and (7) are lotted in Fig. 6, rom which the ollowing concluion are drawn. Firt, or a given value o α h, lug low with ga byaing i the ideal low attern in a luidized bed TCS a it lead to the mallet temerature dierence between the olid and the ga at the let. Any ga byaing i detrimental to the heat exchange. For examle, or T, = 100 C and T = 900 C, 10 % ga byaing lead to in T T, 80 C. Second, to reduce the temerature dierence at the let, the bed hould be deigned and oerated uch that α h i uiciently large, or examle by chooing mall article and large bed height. Thereore, oerating regime with bubble cauing igniicant ga byaing hould be avoided or TCS in luidized bed. 11 In the imulation reented in thi aer, it wa aumed that lug low condition exit, ga byaing i avoided, and α h i large enough uch that T, = T i an accurate aroximation. With thee aumtion and conidering the olid to be at a atially uniorm temerature, the energy equation o the olid hae become: dt ( 1 ebed )( 1 e ) rc = Q rxn Q (8) dt where ε i the article internal oroity, ρ and c are the intrinic material denity and heat caacity o the olid hae, reectively, Q rxn i the heat releaed by the timedeendent ga-olid reaction, and Q i the heat tranerred between the olid and ga hae. The denity and heat caacity are evaluated or the mixture o Mn2O 3 and Mn3O 4 baed on the degree o converion. Equation (8) i imilar to the equation ued by other author, 12 excet or the additional term Q rxn that act a a ource term accounting or the heat involved in the chemical reaction. The heat tranerred between the olid and the air i calculated rom 10

11 m u Q c dt c dt (9) =, in T,, in T,, in, V = ρ T, in T, in bed L bed where m, in i the ma low rate o the air at the reactor inlet and V bed i the total volume o the bed. Note that Q i negative when heat i tranerred rom the air to the olid during charging. The heat releaed during the oxidation or aborbed during the reduction i obtained rom H rxn dx Q rxn = ( 1 ebed )( 1 e ) r,mn3o w 4 theor, ox (10) M dt where ρ,mn3o i the intrinic material denity o Mn 4 3O 4, w theor, ox i the theoretical relative weight gain during oxidation, H rxn i the heat o reaction er mole o oxygen, M O 2 i the molar weight o oxygen, and dx dt i the converion rate given by Eq. (2). The reult obtained with the luidized bed model are indeendent o the cro-ectional area o the reactor ince Eq. (8) i ormulated a a volumetric conervation equation and the reactor wall are aumed to be adiabatic. Furthermore, the reult are indeendent o the article ize, but it hould be ket in mind that the article mut be mall enough or the aumtion T, = T to hold, ee Eq. (5) and Fig. 6. Equation (8)-(10) are olved conecutively with the imlicit Euler method at each time te to a convergence tolerance 8 o 10. O2 11

12 Reerence 1 L. Geibühler, Mater Thei, ETH Zürich, F. Petalozzi, Mater Thei, ETH Zürich, C. Bouquet-Berthelin and D. Stuerga, J. Mater. Sci., 2005, 40, K. T. Jacob, A. Kumar, G. Rajitha and Y. Waeda, High Tem. Mater. Procee, 2011, 30, P. W. Atkin and J. De Paula, Atkin Phyical Chemitry, Oxord Univerity Pre, Oxord; New York, 10th edn., D. Kunii and O. Leveniel, Fluidization Engineering, Butterworth-Heinemann Boton, 2nd edn., H. F. Rae, Fixed-bed reactor deign and diagnotic: ga-hae reaction, Butterworth-Heinemann Boton, J. González-Aguilar, Peronal Communication, E. W. Lemmon, M. O. McLinden and D. G. Friend, in NIST Chemitry WebBook, NIST Standard Reerence Databae Number 69, ed. P. J. Lintrom and W. G. Mallard, National Intitute o Standard and Technology, Gaitherburg MD, W. Yang, Handbook o Fluidization and Fluid-Particle Sytem, CRC Pre, K. M. Wagialla, A. H. Fakeeha, S. S. E. H. Elnahaie and A. Y. Almaktary, Energy Source, 1991, 13, O. Leveniel, Engineering Flow and Heat Exchange, Sringer US, 3rd edn.,