Simulations of the Irradiation and Temperature Dependence of the Efficiency of Tandem Photoelectrochemical Water-splitting Systems

Transcription

1 Simultions of the Irrdition nd Temperture Dependence of the Efficiency of Tndem Photoelectrochemicl Wter-splitting Systems Sophi Hussener 1,, Shu Hu 2, Chengxing Xing 2 Adm Z. Weber 3, nd Nthn S. Lewis 2 1 Institute of Mechnicl Engineering École Polytechnique Fédérle de Lusnne, 1015 Lusnne, Switzerlnd 2 Joint Center for Artificil Photosynthesis Cliforni Institute of Technology, Psden, CA 91125, USA 3 Joint Center for Artificil Photosynthesis Lwrence Berkeley Ntionl Lbortory, Berkeley, CA 94720, USA The efficiency of n operting photoelectrochemicl solr-fuelsgenertor system is determined by the system design, the properties nd morphology of the system s components, nd the opertionl conditions. We used previously developed model comprising of i) the detiled blnce limit to describe the currentpotentil performnce of the photobsorber component, nd ii) the detiled multi-physics device model solving for the governing conservtion equtions (mss, momentum, species nd chrge) sptilly resolved in the device, to quntify the performnce of photoelectrochemicl devices. The investigted the performnce nd its vritions s function of opertionl conditions, i.e. dily nd sesonl irrdition vritions, concentrtion fctor of irrdition, nd isotherml device temperture. Additionlly, the difference in performnce of n integrted photoelectrochemicl system nd photovoltic rry connected electriclly to stndlone electrolyzer system ws quntified. Introduction An opertionl solr-driven electrochemicl-fuel-generting rector tht electrolyzes wter or tht reduces CO 2 involves light bsorbers, chrge genertors, nd electroctlytic components embedded in or connected to conducting phses, whilst insuring product seprtion for efficiency nd sfety purposes. All of these components re closely coupled, nd their individul performnce gretly influences the performnce of the integrted genertor s system (1-4). A comprehensive model tht includes the detiled device rchitecture nd ccounts for the sptilly resolved governing physics is therefore required to evlute quntittively the overll efficiency of such system s function of the design, component properties nd morphologies, nd opertionl conditions. Equivlent circuit models hve been developed to support component choices of device, such s the choice of light bsorber combintions or electroctlysts (5-8). Recently, models tht solve for the governing coupled conservtion equtions hve been developed in 1D (9), 2D (10, 11), nd 3D (12), llowing for better understnding of the interctions between the properties of the components nd the design choices of the system.

2 This work is summry of the previously published detiled study on the simultion of the efficiency of photoelectrocehmicl device s function of operting conditions, design, nd component properties (11). We used the dvnced multi-physics model comprising of n nlyticl model for the semiconducting light bsorbers (detiled blnce limit (13)) in combintion with sptilly resolved multi-physics device model tht solved for the governing conservtion equtions in the vrious other prts of the system (10, 11). Governing Equtions Theoreticl Multi-physics Model nd Boundry Conditions. The engineering multi-physics PEC model hs been described previously (10, 11). The model solves for chrge trnsport nd conservtion in the liquid electrolyte phse s well s in the solid conducting phses, i.e. the semiconductor, ctlyst, nd/or trnsprent conducting oxide (TCO), if present. The electrochemicl rections were ssumed to be the electrolysis of wter in n cidic environment vi the nodic oxygen-evolution rection (OER), eq. [1], nd the cthodic hydrogen-evolution rection (HER), eq. [2]. 2H 2 O O 2 + 4H + + 4e - [1] 4H + + 4e - 2H 2 [2] The kinetics of the electrochemicl wter-splitting rection were modeled by use of Butler-Volmer expressions for the OER nd HER, respectively (14). Species trnsport ws given by n dvection/diffusion eqution, wheres trnsport for chrged species ws given by the Nernst-Plnk eqution (14, 15). The mss nd momentum conservtion equtions were solved to clculte the pressure nd velocity vector fields (16, 17). The model lso incorported recent extensions tht provide more complete description of the semiconductor prts of the system, including specificlly the detiled blnce limit (13), nd semi-empiricl dpttions thereof. The system ws ssumed to operte t isotherml conditions. The boundry condition for the light-bsorber tndem cell ws given by the solr irrdition, i.e. by the intensity nd spectrl distribution of the incident photon flux. The boundry conditions for the current conservtion equtions were given by the performnce of the dul-bsorber tndem cell, with the cthode-side electrode ssumed to be grounded. A best cse boundry conditions for species conservtion ws used, i.e. sturtion concentrtions of O 2 nd H 2 were ssumed in the nolyte nd ctholyte chmbers, resulting in the bsence of concentrtion grdients of the species. The permebility of the polymeric seprtors ws ssumed to be sufficiently low to withstnd the pressure differentils expected in the system during opertion, hence convective flows were neglected. Mtlb ws used to clculte the chrcteristics of the dul-bsorber tndem cell, with the output of the Mtlb code coupled to commercil finite-element solver, Comsol Multiphysics, to solve the coupled conservtion equtions with the previously described boundry conditions.

3 Semiconductor Physics. The detiled blnce limit (13) describes the mount of incident solr irrdition tht is bsorbed nd produces n electron-hole pir, i.e. chrge or current, in the semiconductor, minus the current lost due to rditive recombintion: g ph rr ph,sol ph,b 0 0 g i i i q n ( x, )d q n (, T)d. [3] i ph describes the photocurrent density, i rr is the current density lost due to rditive recombintion, g is the bnd-gp energy of the semiconducting light bsorber, n ph,sol is the spectrl photon flux rriving t the erth surfce t loction x, nd n ph,b is the spectrl photon flux due to blckbody rdition t temperture T. In cse of dul-bsorber tndem cell, the irrdition is prtilly bsorbed by the top cell nd the remining bovebnd-gp rdition, > g,top, is bsorbed by the bottom cell. The resulting performnce curve of the dul cell cn be pproximted by fitted diode eqution of the form qv qirser V i iph i0 exp 1 kt, [4] Rsh where i 0 describes the drk sturtion current density nd R ser nd R sh re re-normlized series nd shunt resistnces (Ω m 2 ). For the detiled blnce limit, the quntity R ser is zero nd R sh goes to infinity. Non-zero vlues of R ser were dditionlly used in this study to ccount semi-empiriclly for the losses within the semiconductor mteril. Definitions The instntneous solr-to-hydrogen (STH) efficiency of PEC device is defined s iu F pc. [5] I i is the current density of the operting device, U is the equilibrium potentil of the electrochemicl rection under the specified conditions, ssumed 1.23 V. I is the solr irrdition (W m -2 ) t specific loction, dte nd time, integrted over 1.5 Air Mss spectrl distribution, F is the Frdic efficiency of the electrode rection, nd pc is the product collection efficiency, given by eq. describes the instntneous efficiency for I = 1 kw m -2. We neglected prsitic rections t the electrode ( F = 1). pc A/c ida nfn da Asep A/c ia d fuel, [6] i.e. the integrted current over the electrode surfce (: node, c: cthode) used for the electrochemicl rection minus the product lost due to crossover by diffusion or convection through the chmber-seprtor surfce to the other side of the system. For simplicity we ssumed pc = 1. The efficiency vries during dytime, the dytime verge efficiency is defined by: d t sunset tsunset 1. [7] t sunrise ttsunrise

4 Similrly, the nnul dytime verge efficiency is given by: nseson 1 d. [8] n The stndrd devition of the nnul dytime verge efficiency ws clculted by: seson s1 1 n t t n seson tsunset 2 ( ). [9] seson ( sunset sunrise) 1 s1 tsunrise Model Prmeters The temperture-dependent reference-cse mterils properties of the vrious components nd the correltions to clculte them re given in tble I. Tble I. Correltions nd prmeters used for the vrious mterils nd components in the system, s function of temperture. Prmeter Vlue Prm Vlue Prm Vlue Ref. E Correltion: i0,oer/her i0,oer/her, T exp ref RT red ox red,oer/her c F op c ox c,oer/her Fop ir,oer/her i0,oer/her exp exp c red,0 RT c ox RT 0 i 0,OER,Tref 4.62 A cm -2 E,OER 48.6 kj mol (18-20) i 0,HER,Tref A cm -2 E,HER 28.9 kj mol (21, 22) Correltion: exp E mem 0,mem RT 0,mem S m -1 E,mem 2 kj mol (23) Correltion: l l, =293K T T l,t=293k 40 S m -1 α K (24) A0 E Correltion: TCO exp R t kt s,0 R s,0 10 Ω/ A ΔE ev (25) 2 2T Correltion: E g E g,0 T E g,0,si ev α 2,Si ev K -1 Si 1108 K (26) E g,0,gas ev α 2,GAs ev K -1 GAs 572 K (26) c exp A B / ( T /100K) C ln( T /100K) / M 1000 Correltion: st, k k k k 2 A H B H C H (27) A O B O C O (27) The decrese in the equilibrium potentil for the one-step wter-electrolysis rection with incresing temperture is given by H O

5 U U T, [10] where U is the equilibrium potentil ssuming hydrogen reference electrode, nd α 3 is given by the temperture-dependence of the Gibbs free energy (ΔG=-nFU). The kinetic prmeters used in the study re for stte-of-the-rt ctlysts, i.e. Pt-bsed electrodes for the HER rection nd RuO 2 -bsed electrodes for the OER rection (28, 29). Intermittency nd Locl Vribility of Solr Irrdition. The irrdition intensity of Brstow in Southern Cliforni ws chosen for the investigtions. Brstow hs high solr irrdition nd is currently used s loction for lrge-scle concentrted-solr nd photovoltic power genertion. The solr irrdition (with hourly resolution) of Brstow for typicl meteorologicl spring, summer, utumn nd winter dy, respectively ws obtined from NREL s TMY3 dtsets. NREL s 1.5 AM dt were used for the spectrl rdition distribution, nd these spectrl dt were scled ccording to the solr irrdition using the reltionship I nph,sol( x, )d. Device Design 0 The sme bsic solr-fuels-genertor device designs s in our previous study were investigted herein (10, 11). The results presented herein focus on one of the designs, i.e. the design consists of one plnr dul-bsorber tndem cell or ctlyst-covered duljunction photovoltic cell immersed in n electrolyte-filled chnnel but seprted from ech other by n impermeble, ion-conducting seprtor. A conductive lyer ws dded on top of the bsorber, photovoltic device, or electrode, to model properly the conducting light bsorber or conducting ctlyst lyer, or trnsprent conductive oxide (TCO) lyer protecting ginst the cidic or lkline environment. For ll designs, no potentil loss ws ssumed in the conductive connection for electron trnsport between the two electrodes. Ech design ws chrcterized by n electrode length (l el ), n electrolyte height of thickness (t e ), nd seprtor of thickness (t s ), nd rtio of the electrode length to the device length (f = l el /l d ). Unless stted otherwise, t s = 10 µm nd f = 0.9 were used in the clcultions. 3 Figure 1. Schemtic of the top-to-bottom design used s model device, indicting the vrious dimensionl vribles. The red dotted box indictes the modeled unit cells. Results The detiled blnce limit for modeling the performnce of dul-bsorber tndem cell ws used in the first prt of the results. Results for Si/GAs system (with bnd gps of 1.12 ev nd 1.43 ev), which is not current-mtched dul bsorber tndem-cell, but which hs well-known temperture-dependent mterils properties, re discussed. The results re then expnded to more relist, mesured photobsorber performnces.

6 Dily nd Annul Vritions in Efficiency Figure 2 depicts the model results for the hourly vrition in instntneous efficiency for four chrcteristic dys of the yer. Almost no chnge in instntneous efficiency either hourly or for vrious dys in yer ws observed when the selected system dimensions resulted in smll ohmic electrolyte losses, i.e. t smll l el nd lrge t e vlues. Figure 2. () Efficiency vritions of the device for four typicl sesonl dys for Si/GAs multi-junction cell. (b) The i-v-performnce (solid blck lines) of the Si/GAs cell for every hour during the July dy (15 hours between 5m nd 8pm) nd the lod curve for l el = 50 mm nd t e = 1 mm (green dotted) nd for l el = 10 mm nd t e = 10 mm (green solid), respectively. For optimized design dimensions (e.g. with l el = 10 mm nd t e = 10 mm), d nd were both 15.3%. The instntneous efficiency ws lowest during the hours of the dy tht hd the highest solr irrdition. Similrly, the lowest d were observed for the dys tht hd the lrgest solr irrdition. For l el = 50 mm nd t e = 1 mm, ws 14.6%, with d = 15.2, 14.5, 14.1, 14.8% for typicl winter, spring, summer nd utumn dy, respectively. Effect of System Operting Temperture A vrition in the isotherml system temperture is expected to produce two competing chnges in the system performnce chrcteristics: reduction in the bsorber efficiency due to incresed rdition losses, nd n enhncement in the trnsport nd kinetics, leding to less efficiency losses ssocited with these fetures of the system. The modeling results demonstrted tht the specific integrted solr fuels genertor system evluted exhibited net decrese in mximl efficiency with incresing temperture, due to the reduction in photovoltge with incresing temperture more thn offsetting the reduction in losses produced by the incresed electrode kinetics nd incresed electrolyte conductivity t higher tempertures. For exmple, for l el = 50 mm, nd t e = 1 mm, when the temperture incresed from 300 to 353 K, decresed from 14.6% to 13.6% nd σ decresed from 0.90% to 0.49%. When the temperture ws incresed, the efficiency vritions during given dy decresed, but the system exhibited lower efficiencies t the beginning nd end of ech dy, i.e. exhibited less steep (i.e. less rpid) rmp-up nd rmp-down phses in response to sunrise or sunset, respectively.

7 Figure 3. of PEC device for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K), for the Si/GAs dul-bsorber tndem cells, l el = 50 mm, t e = 1 mm. Integrted System Versus Conventionl Photovoltic Module/electrolyzer System, d,, σ, nd the yerly mount of fuel produced by n integrted solr fuels genertor system were compred to the behvior of system insted comprised of conventionl photovoltic (PV) module-bsed stnd-lone system coupled electriclly to stnd-lone electrolysis unit. The efficiency of the system comprised of the discrete components cn be described s PV/electrolyzer PV DC-DC-converter electrolyzer, [11] where PV is the energy-conversion efficiency of the PV-bsed system, DC-DC-converter is the efficiency of DC-DC-converter, nd electrolyzer is the efficiency of the electrolyzer, mesured by dividing the electricl energy input into the electrolyzer into the vlue of the free energy of the H 2 (g) produced by the electrolyzer. An electrolyzer efficiency of 75% nd DC-DC-converter efficiency of 85% were used in the clcultions. Figure 4 shows the performnce of the stnd-lone PV system (Si/GAs) in combintion with the stnd-lone electrolyzer system. Si/GAs does not represent the mximum chievble efficiency of tndem-cell PV but ws chosen to fcilitte strightforwrd comprison. The stnd-lone PV plus stnd-lone electrolyzer system displyed its highest during mid-dy nd its highest d t mid-yer. Increses in the temperture from 300 K to 353 K of the light bsorber components of the discrete system decresed of the stnd-lone system combintion from 13.3% to 10.6%, with slight increse in σ (from 0.53% to 0.57%). The mss of H 2 produced nnully,, ws m tot,h 2,T0 7.5, 7.9, nd 8.6 kg m- 2 yer -1 for the stnd-lone PV nd stnd-lone electrolyzer combintion, integrted system, nd optimized integrted system, respectively t n bsorber operting temperture of 300 K in ll cses. Hence for these designs, stndlone PV nd stnd-lone electrolyzer combintion system would require 13% more re for the production of the sme mss of hydrogen per yer compred to n integrted system with smll totl overpotentil t T = 300 K. At higher tempertures, the stndlone system combintion exhibited lrger decrese in H 2 (g) production thn did the integrted system, requiring 23% more re for the sme production of hydrogen per yer.

8 Figure 4. of conventionl stnd-lone PV system with Si/GAs dul bsorber tndem-cell, electriclly connected to stnd-lone electrolyzer, for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K). Efficiency Clculted bsed on Experimentlly Mesured Single Absorber Cells The mesured performnce dt for single-bsorber cells mde of GAs nd Si, s detiled in Tble II, hve been used to ssess the performnce of systems tht re constructed using more relistic, currently vilble, single solr-bsorber cells. Tble II. Mesured short-current density, open-circuit voltge, fill fctor, nd temperture coefficients of commercil GAs (Alt devices * ) or Si (Schott,( 30 ) ) solr cells. GAs cell Si cell i sc, ma cm ma cm -2 V oc, V V FF α bs % K % K -1 bs or bs % K -1 2 mv K -1 The intensity dependence nd temperture dependence of the performnce cn be pproximted s: i i 1 T 298 I I, [12] sc sc,0 bs 0 sc sc,0 bs V V 1 T 298, [13] V V T. [14] oc oc,0 bs 298 The performnce of the tndem configurtion ws clculted by using the Si nd GAs cells in series. The resulting performnce of the integrted system nd stndlone tndem PV plus stnd-lone electrolyzer system (electrolyzer efficiency of 75% nd DC-DC-converter efficiency of 85%) using Si/GAs-bsed dul bsorber tndemcell bsed on mesured single cell performnce re depicted in Figure 5. The relistic stnd-lone PV plus stnd-lone electrolyzer system displyed its highest during mid-dy nd its highest d t mid-yer. Increses in the temperture from 300 K to 353 K of the photobsorber components of the discrete system decresed *

9 of the stnd-lone system combintion from 11.2% to 8.7%, with slight increse in σ (from 0.24% to 0.27%). The integrted system with l el = 50 mm, nd t e = 1 mm, showed = 11.3% nd 6.4% for T = 300 K nd 353 K, respectively, with slight increse in σ (from 0.02% to 0.03%). Chnging the dimensions of the system to l el = 10 mm, nd t e = 10 mm resulted in n increse in to vlues of 14.3% nd 10.6% for T = 300 K nd 353 K, respectively, with decrese in σ (from 0.34% to 0.28%). The integrted system only outperformed the stnd-lone PV system coupled electriclly to stnd-lone electrolysis unit when the integrted system ws designed to hve significntly reduced overpotentil. The nnully produced hydrogen mss decresed from 7.5, 7.9, nd 8.6 kg m- 2 yer -1 to 6.5, 5.9, 8.3 kg m -2 yer -1 for the stnd lone PV nd stnd-lone electrolyzer system, the integrted system, nd the optimized integrted system, respectively, when using dul bsorber tndem-cells tht exhibited relistic, mesured performnce insted of operting t the idel, detiled-blnce performnce limits, t T = 300 K. ) b) c) d) Figure 5. () of PV+electrolyzer system with Si/GAs dul bsorber tndem structure bsed on the mesured individul cell performnce for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K), nd (b,c) of PEC device with Si/GAs dul bsorber tndem-cell bsed on mesured individul cell performnce for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K) for (b) l el = 50 mm, nd t e = 1 mm, nd (c) l el = 10 mm, nd t e = 10 mm, nd (d) the normlized nnully integrted fuel production with m tot,h 2,T = 6.6, 5.9, nd 8.3 kg m -2 yer -1 for detiled 0 blnce limit (solid) nd the relistic cse (dotted).

10 Summry nd Conclusion The lrgest vrition in efficiency during the dy nd yer were observed t the locl or globl irrdition mxim. These vritions in efficiency were especilly pronounced for systems tht hd reltively lrge totl overpotentil, i.e. for devices with lrger electrode length, smller electrolyte height, lower electrolyte conductivity, nd/or smller bnd gp combintions of light bsorbers. A system designed to produce constnt efficiency throughout the yer therefore should be designed to operte t mximum efficiency under the mximl solr irrdition t the plnned loction. Incresed isotherml device tempertures led to reduction in mximl device efficiency nd less steep rmp up nd rmp down t the beginning nd end of the dy, due to decresed performnce of the dul-bsorber tndem cell with incresed temperture. Nevertheless, the middy nd midyer vritions in efficiency decresed, due to reduction in the totl overpotentil, i.e. reduced trnsport nd kinetic losses, with incresing device tempertures. The competition between decresed light bsorber performnce nd incresed trnsport performnce with incresing temperture leds to n interesting conclusion, in tht PEC device with limiting overpotentil cn gin in nnully verged efficiency if it is not driven t constnt lower system temperture but insted is dynmiclly dpted to higher operting tempertures s the solr irrdition increses, which will occur nturlly throughout dy. For device with low, nonlimiting overpotentils, i.e. σ =0, the incresed trnsport performnce with incresed temperture will not led to dditionl gins in efficiency nd, consequently, such device will show the best nnul performnce t low tempertures. The modeling lso llowed for comprison of integrted systems nd conventionl stnd-lone PV plus stnd-lone electrolyzer system. The simultions showed tht integrted systems cn benefit from the smll current densities by significntly incresing the internl electrolyzer efficiency. A conventionl PV plus electrolyzer system (with electrolyzer efficiency of 75% nd DC-DC-converter efficiency of 85%) mde from exemplry Si nd GAs tndem light bsorbers required 13% more re to produce the sme nnul mount of hydrogen s would be produced by n integrted system with comprble solr bsorbers. Additionlly, the discrete component PV plus electrolyzer system did not benefit from enhnced kinetics nd trnsport due to enhnced tempertures, dditionlly enlrging the performnce difference, i.e. 23% more re ws needed for discrete component system with the light bsorbers t 353 K versus n integrted system t n isotherml operting temperture of T = 353 K. This work provides predictive modeling nd simultion frmework for evlution of the performnce of such systems under vrying temperture nd irrdition conditions. Acknowledgements We cknowledge the Joint Center for Artificil Photosynthesis, DOE Energy Innovtion Hub, supported through the Office of Science of the U.S. Deprtment of Energy under Awrd Number DE-SC We thnk Hrry Atwter for fruitful discussions on temperture-dependent nlysis of relistic systems.

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