1. Introducton Hgh-temperature steam electrolyss (HTE) s an alternatve to the conventonal electrolyss process. Some of the energy requred to splt the water molecule s provded as heat nstead of electrcty, thus reducng the electrc energy requred. Because the converson effcency of heat to electrcty s low compared to usng heat drectly, the energy effcency can be mproved by supplyng the system wth energy n the form of heat rather than electrcty. In the current Icelandc context, steam could be suppled at 00-30 C. Only 3.8 kwh (e) /Nm 3 H s needed wth a thermal nput of 00 C, compared wth about 4.5 kwh (e) /Nm 3 H n conventonal electrolysers. Furthermore, the cost of electrcty to ndustry n Iceland s approxmately 0.014/kWh compared to 0.084 /kwh [1], as expected for medum-term electrcty produced by next Generaton III nuclear reactors n France. In Iceland the cost of extractng thermal energy from a geothermal source s only about 10% of the cost of electrcty produced. kwh ( th geo ) =. 1kWh( e geo ) 0 (1) Gven these prces, reported n Table (1), the advantage of producng hydrogen by HTE n Iceland s evdent, as demonstrated n Fgure (1), only n terms of the cost of vaporsng and heatng water to the operatng temperature of the electrolyser. /kwh(e) Iceland 0.014 /kwh(th) Iceland 0.0014 Table 1. Energy prces, n Iceland Contrbuton to the producton cost /kg [H] n the current Icelandc context 0,15 0,1 0,05 0 0 100 150 50 350 450 550 650 750 850 Suppled thermal energy [ C] Fgure 1. Contrbuton to the producton cost of vaporsng and heatng steam to the requred temperature for the electrolyser (# 850 C), as a functon of the temperature of the geothermal source and wth the values 1 kwh th = 0.0014 and 1 kwh e = 0.014. Although only approxmately 00 C of thermal nput n the HTE process coupled wth a geothermal source s possble today, ths could change. Recent research carred out by Landsvrkjun on deep drllng n Iceland shows the possblty of extractng 500-600 C steam at a depth of 4-5 km. At present, deep drllng s purely expermental but t could become a possblty wthn the next 10 years. There are three possble operatng modes for HTE dependng on the energy balance at the level of the electrolyser: endothermal, sothermal and exothermal []. The exothermal mode s best suted for the geothermal context because part of the heat requred s provded by ohmc heatng nsde the electrolyser. The temperature of the steam ncreases from the nput of the electrolyser to the output. It s the only operatng mode we wll be consderng. 1/11
The electrolyser s nlet temperature could be between 700 C and 900 C. To be effectve from a thermodynamc pont of vew, the HTE requres the heat contaned at the electrolyser s outlet to be recovered. Heat needs to be recovered both from oxygen and from the hydrogen-steam mxture, n order to heat the steam n contact wth the geothermal source up to the desred temperature at the electrolyser s nlet. In the followng sectons we wll present a flowsheet for a HTE process coupled wth a geothermal source. Ths HTE process ncludes heat exchangers and an electrolyser based on Sold Oxde Fuel Cell (SOFC) technology workng n nverse, producng oxygen and hydrogen nstead of consumng. Usng features related to the heat exchangers and the electrolyser, a set of physcal parameters wll be calculated by usng a techno-economc optmsaton methodology.. A flowsheet for HTE coupled wth a geothermal source The usable temperature of the geothermal source at the Nesjavellr ste, for example, s approxmately 30 C at 15 bar. Ths s relatvely low and therefore the vaporsaton and heatng of the water for the electrolyser needs to be carred out n several stages. The water nput, whch s n lqud state and at ambent temperature (that we wll assume to be equal to 0 C) wll enter a prmary heat exchanger where the water wll be vaporsed and heated up to T n_ho = 00 C from geothermal steam at 30 C. The water vapour at the temperature of T n_ho wll be heated n heat exchangers by the gases extng the electrolyser up to a temperature of T out_ho. Eventually external electrc heatng can be used to heat the water vapour from T out_ho to T n_elec (T out_ho T n_elec ). The nvestment cost of ths heatng element s estmated to be neglgble. In the electrolyser, the electrc power s not only used for splttng the water molecules nto hydrogen and oxygen but also for heatng the gas from the nlet to the outlet. The temperature of the oxygen (T n_o ) and hydrogen-steam mxture (T n_h ) are the same at the outlet. Snce we are lmtng ourselves to exothermal or sothermal condtons T n_o = T n_h T n_elec. The oxygen enters the heat exchangers at T n_o and exts at T out_o, wth T out_o > T n_ho (and T n_o > T out_ HO ) The hydrogen-steam mxture enters the heat exchangers at T n_h and exts at T out_h, wth T out_h > T n_ho (and T n_h > T out_ HO ) Fgure () shows the dagram of the model and llustrates the constrants on the nput and output of both the electrolyser and heat exchangers. /11
Fgure. Heat exchanger networks coupled wth the electrolyser.1 The physcal model for the heat exchanger networks The heat exchangers n our model are counter-current heat exchangers. We consdered exchangers wth corrugated plates,.e. not smooth. The corrugated plates allow a better heat transfer. The physcal equatons of the heat exchangers are defned by Manslla et al. [3]. For HTE coupled wth a geothermal source the networks of heat exchangers need to span a large dfference n temperature. The temperature range n the geothermal case s from ~00 C to ~950 C. Ths temperature range cannot be covered by only one type of exchanger. The materals used, and thus the cost of the exchanger drectly depend on the temperature. The heat exchangers can be classfed nto 3 categores accordng to the ranges of temperatures [3]. The followng notatons wll be used for the exchanger modules: - LT for "low temperature" (up to 600 C), - MT for "medum temperature" (from 600 C to 850 C), - HT for "hgh temperature" (above 850 C). At low temperatures stanless steel domnates. Other steels come next, to be replaced by ceramcs at very hgh temperatures. The heat exchanger proposed for the medum temperature level s stll beng tested and further detals wll be avalable soon. Assumng that plate heat exchangers wth secondary surfaces are used to nsure a hgh level of effectveness, the overall heat transfer coeffcent can be derved as explaned by Sgurvnsson [4]. There are two exchanger networks, they are presented n [3]. For the frst one (H exchangers), the flud n the prmary s a steam-hydrogen mxture. For the second one (O exchangers), t s oxygen. Steam crculates nto the secondary of both networks. 3/11
The ntegraton of the exchangers studed n the HTE system mposes bonds between the varous flows va the recyclng rate r. Usng & as the total molar water flow through the two secondary n H O branches of the exchangers, the varous molar flows are: - (1-r) n& H O of hydrogen n the prmary H exchangers - r n& H O of water n the prmary H exchangers ( 1 r ) - n& H O of oxygen n the prmary O exchangers - x n& H O of water n the secondary H exchangers - (1-x) & H O of water n the secondary O exchangers n x s the dvson rate of the prncpal water flow. It s a number between 0 and 1. The detals of the mass flows n the prmary and secondary of all the exchangers are expressed n [3].. The electrolyser model To fnd the quantty of thermal and electrc energy needed for water decomposton, the Nernst equaton was used and adjusted for overvoltages. In the chemstry of fuel cells and electrolysers E s the potental of the cell n [V]: R RT P P ohm E E H O = 0 + ln + Ract j () F PH O P ref R con E o : Thermodynamc potental of steam decomposton at equlbrum [V] R ohm : Resstance due to ohmc losses n membrane [Ωm ] R act : Resstance due to reacton actvaton [Ωm ] R con : Resstance due to knetc problems, caused by nhomogenc concentraton of gases n the electrodes [Ωm ] R : The unversal gas constant [J/mol.K] T : The temperature [K] F : Faraday s constant [C/mol] P : Partal pressure [MPa] P ref : Pressure of reference =0.1 MPa j : Current densty [A/m ] The frst part of the equaton s the Nernst local equaton, whch expresses the exact electromotve force of a cell n terms of the actvtes of the cell s products and reactants. Ths s only a functon of temperature and pressure. The partal pressures throughout the electrolyser are not constant. They change wth the poston, and the partal pressures of gases wll affect the resultng energy needed for electrolyss. Ths s dependent on how much of the ncomng water s electrolysed. The last terms n the equaton represent unwanted losses due to ohmc losses n membrane, reacton actvaton and knetc problems caused by nhomogenc concentraton of gases n the electrodes. The products R j, lnked to the unwanted losses, are usually called overpotentals. There are many factors n the overpotental calculatons whch are very dffcult to evaluate correctly. The evaluaton depends on actual test results for all three types of resstances. An analytcal model was used for the smplfcatons based on the work of Lovera [5]. The overpotentals are lnearsed,.e. assumed to be proportonal to the current densty: 4/11
The equaton () therefore becomes: R T P O E E Ln = 0 + A + F P ref R T B 1 B ξ n + I (3) R T B 4 F q Σ mol 4 F qmol Rs 1 e Σ : Electrolyte surface [m ] I : Current ntensty [A] ξ n : The porton of water electrolysed (nput) A =.3843 and B = 4.7685 : mathematcal constants P : Partal pressure of oxygen (supposed to be constant n the model) O q mol : Molar flow rate of hydrogen + steam [mol/s] R s : Total area specfc resstance (R ohm +R act +R con ) [Ω.m ] Accordng to [5] the exothermal mode works when the operatng cell potental s greater than 1.3V. If the potental s hgher, all of the extra energy wll go nto heatng the gases. Ths wll allow us to drectly calculate the temperature dfference from the electrolyser s nlet temperature to the outlet, usng the followng smple relaton: 3 U electrolyser U dss ) I = m C p elec T 10, mx electrolyser (4) ( m& : Total mass flow [kg/s] C : Specfc heat of the water/hydrogen/oxygen mxture [kj/kg/k], p elec mx T electrolyser : Temperature dfference from electrolyser nlet to outlet [K] U dss : Potental requred for dssocaton [V] U : Potental appled to the electrolyser [V] electrolyser 3. A Techno-Economc optmsaton method appled to the HTE 3.1 Prncples of the Techno-Economc optmsaton In the followng secton we wll present a method for optmsng the HTE process ncludng heat exchangers and an electrolyser from a techno-economc pont of vew. The techno-economc approach we selected presupposes a flow sheet. The optmsaton procedure conssts n mnmsng an objectve functon whch takes nto account operatng as well as nvestment costs. In the current context of sustanable development, advanced systems are beng studed. These systems nvolve ether hgh pressures, hgh temperatures, or corrosve products, and sometmes several of these severe condtons. In all of these cases, nvestment costs can ncrease by one or two orders of magntude when compared to classcal alternatve systems, leadng to a growng nterest n the techno-economc approach. In a prevous study [3], TE optmsatons were performed only for the heat exchanger networks (excludng the electrolyser). In that case the prmary heat sources were HTR or Geothermcs. We wll present an extenson of ths work by ncludng an electrolyser whch s coupled wth a geothermal source. The low-temperature heat s very nexpensve from a geothermal source. Further on, we do not consder heat exchangers for pre-heatng the cold water enterng the boler. Another dfference from the couplng wth a HTR s that we wll consder the possblty of an electrc reheater to ncrease the temperature of the steam at the nlet of the electrolyser. 5/11
The heat exchanger networks and the electrolyser are then optmsed by mnmsng the producton cost per kg of hydrogen. The optmsaton was acheved usng genetc algorthms. 3. The objectve functon The objectve functon s the functon that we want to mnmse. The objectve s to mnmse the cost of producng hydrogen. CTA s the notaton for Total cost [ /kgh ]. The numerator has two man groups of factors, the frst one beng the nvestment cost for the electrolyser and heat exchangers and the second one the operatng cost of the electrolyser and heat exchangers. The denomnator of the objectve functon s the hydrogen producton per year (H t [kgh /year]). It depends on the current ntensty, flow rate and recyclng rato n the electrolyser cell. The objectve functon s expressed wth the followng formula: CTA = + Te N ( C, exch ) + ( C elec ) + ( Co th ) + ( Co elec ) ( + ) n, t, t, t, 1 τ t T t= 1 n= 1 T + T e t= 1 H t t [ ( 1+ τ ) ] t (5) CTA : Total cost [ /kgh ] 1 C,exch : Heat exchangers nvestment cost durng the consdered year [ ] C,elec : Electrolyser nvestment cost durng the consdered year [ ] C o,th : Thermal consumpton operatng cost durng the consdered year [ ] C o,elec : Electrc consumpton operatng cost durng the consdered year [ ] H t : Hydrogen producton durng the consdered year [kg of H ] τ : Dscount rate T e : Number of years n use [years] T : Number of years of nvestment [years] N : Total number of heat exchangers t : Year consdered n : Heat exchanger consdered In the followng secton we wll defne each cost contrbuton factor and explan the calculatons where necessary. 3.3 Investment cost of heat exchangers C,exch s obtaned by summng the nvestment costs of all the heat exchangers: wth N C,exch = = j 1 C j (6) C j = C j S j (7) N : Number of heat exchangers C j : Cost of captal for the j th exchanger [ ] C j : Unt nvestment cost for the j th exchanger [ /m ] S j : Heat exchange surface of the j th exchanger [m ] C j s defned accordng to the type of exchanger, materal and the operatng condtons: 400 /m : for the low-temperature exchangers 800 /m : for the medum-temperature exchangers 4000 /m : for the hgh-temperature exchangers. 1 has been chosen, however, t can be replaced by the Icelandc króna or by any other currency. 6/11
3.4 Investment cost of the electrolyser The defnton of the contrbuton of the electrolyser (C,elec ) to the total nvestment costs s obtaned by assumng that the purchase cost of the electrolyser s n accordance wth the assumptons of [6]. The operaton lfe duraton of the electrolyser s estmated to be 5 years. The total nvestment cost for the electrolyser s calculated by multplyng the unt cost of the electrolysers per kw by the nstalled power. C,elec = P tot,useful 000 [ 0.5 j U electrolyser ] [ ] (8) j : Current densty n cell [A/cm ] U electrolyser : The operatng voltage of the electrolyser [V] : Electrc power requred for the dssocaton of water [kw] P tot,useful In ths formula t s assumed that the cost s proportonal to the surface of the electrolyser and 0.5 has a dmenson of kw.a/cm. 3.5 Thermal consumpton operatng cost The defnton of the contrbuton of the thermal consumpton (C o,th ) to the total operatng costs s as follows: and C ( C T C ) o, th = ckwh te m H O th p, H O geothermal + v, H O C o,th : Thermal consumpton operatng cost [ /year] c : Unt thermal energy cost [ /kwh th ] kwh th t e mh O C p H O Cv H O : Length of operaton [h/year] & : Mass flow of water [kg/s], : Specfc heat of water [kj/kg/k], : Specfc latent heat of water vaporsaton [kj/kg] T geothermal : Temperature dfference n the geothermal heat exchanger [K] = (10) Tgeothermal Tn _ H O T ext _ H O (9) T n _ H O : Temperature of steam at the geothermal heat exchanger outlet [K] Text H O _ : Temperature of water at the geothermal heat exchanger nlet [K] 3.6 Electrc consumpton cost The defnton of the electrc consumpton s contrbuton (C o,elec ) to the total operatng costs s the sum of the consumpton of the electrolyser, the pump and the extra heatng: The cost of the electrcty consumpton (Ce) = operatng lfe cost of the kwh e Consumptons: by the electrolyser + for pumpng + for the reheater. C o, elec = ckwhe ( ECelectrolyser + EC pump + ECreheater ) (11) C o,elec : Electrcty consumpton operatng cost [ /year] c : Unt cost of electrcty [ /kwh e ] kwhe EC electrolyser EC pump EC reheater : Electrc consumpton by the electrolyser [kwh e /year] : Electrc consumpton by the pump [kwh e /year] : Electrc consumpton by the reheater [kwh e /year] Ths requres the precse defnton of each component s consumpton: the electrolyser, the pump and the reheater. 7/11
3.6.1. The pump: The electrc consumpton of the pump s due to pressure losses n the two exchanger networks. m P te EC = & (1) pump ρ η pump EC pump : Electrc consumpton of the pump [kwh e /year] η : Mechancal effcency of the pump pump m& : Mass flow [kg/s] ρ : Specfc mass [kg/m 3 ] P : Pressure losses [Pa] : Length of operaton [h/year] t e The pressure losses are proportonal to the square of the flow. They depend on the length of the exchanger, the hydraulc dameter, the cross secton and the densty of the flud. Ths cost must be taken nto account for each branch of the exchanger. P = 4 f L Dh 1 ρ m& A (13) : Pressure loss [Pa] f m& P : Frcton factor : Mass flow [kg/s] A : Cross secton [m ] Dh : Hydraulc dameter [m] L : Heat exchange length [m] The frcton factor depends on the Reynolds number [3]. Snce we assume that there s equal dstrbuton of the flud, the flow per channel s equal to the rato of the total flow per number of channels. Moreover, the total cross secton of the exchanger s equal to the product of the cross secton of a channel per number of channels. Consequently, the cost of pumpng can be calculated usng the total sze nstead of the sze relatng to one channel. 3.6.. The electrolyser: To calculate the total electrc consumpton we need to multply the power dsspated n the electrolyser by the annual operaton duraton: EC = U I t n 10 3 electrolys er electrolyser e (14) : Electrc consumpton of the electrolysers [kwh e /year] : The current n each electrolyser cell [A] : Length of operaton [h/year] : The operatng voltage of each electrolyser cell [V] : Number of electrolyser cells EC electrolyser I t e U electrolyser n 3.6.3 The electrc reheater: The electrc consumpton of the reheater s evaluated by calculatng how much energy s needed to ncrease the temperature by a specfc amount. EC reheater ( T T ) = m (15) C p H O t H O, e n _ elec out _ H O : Electrc consumpton of the reheater [kwh e /year] : Length of operaton [h/year] & : Mass flow of water [kg/s] EC reheater t e mh O C p H O, : Specfc heat of water [kj/kg/k] 8/11
T out _ H O : Temperature at the outlet of the heat exchanger networks and before the reheater [K] T _ : Temperature at the electrolyser nlet [K] n elec 3.7 Decson varables The values of the decson varables wll be changed throughout the teratons to obtan optmsed results. When an optmal pont has been reached, the model has results for each of the decson varables. Alongsde CTA (the total cost [ /kgh ]), there are fourteen decson varables. They are temperatures expressed n C whch correspond to the expected re sults of the optmsaton procedure, for each heat exchanger network, devoted to oxygen as well as hydrogen flows. The dvson rate x of the prncpal water flow s also a decson varable. 3.8 Constrants Several constrants apply to the system. The electrolyser s operatng n exothermal mode so output gases are always hotter than nput ones. Other physcal constrants lnk the temperatures of each end of the heat exchangers: The temperatures of the prmary flow are hgher than those of the secondary flow throughout each heat exchanger. Inlet temperatures are hgher than outlet temperatures for the prmary flow, but lower for the secondary flow. 4. Implementaton of the TE optmsaton 4.1 Specfcaton of data for mplementng the TE optmsaton model 4.1.1 Economc data t e : Length of operaton: 7008 hours/year (80% avalablty) η pump : Mechancal effcency of the pumpng: 80% τ : Dscount rate: 6% number of years of constructon: 3 years; dstrbuton of captal expendtures: 10% frst year, 35% the second and 55% the thrd number of years of operaton: 30 years electrolyser operaton lfe duraton: 5 years c : 0.014/kWh e ( 1.4. 10-5 /Wh e ) kwh e c kwh th : 0.0014/kWh th. The frst parameters are selected n agreement wth [6]. 4.1. Physcal data These data have been defned for a 5 kw e prototype, n celand. Tn_H O = 473 [K] ( # 00 C) P tot, useful = 5. [kw], Useful power requrements for the electrolyser ξ out = 0.67 Porton of water electrolysed at the outlet r = 0.33 Recyclng rato ε =1.39 10-4 [m], Electrolyte membrane thckness, [5] Σ = 0.985 10 - [m ], Electrolyte surface for 1 cell, [5] P O = 1.5*10 6 [Pa] Steam pressure at the electrolyser s nlet H P = 5*10 5 O U electrolyser = 1.4 [Pa] Partal pressure of oxygen n the electrolyser [V] Cell potental, exothermal operatng mode The partal pressure of oxygen s not constant throughout the electrolyser. In our study we do, however, assume constant pressure at the anode. 9/11
4. Demonstraton results of the HTE optmsaton The results of our optmsaton show that two factors domnate the cost of hydrogen producton: the electrolyser s electrc consumpton and the electrolyser s nvestment cost. We found that the fnal cost of producng hydrogen was 1.7/kgH. Ths value shows that, at least n the Icelandc context, the HTE could compete wth alkalne electrolyss [4]. The cost breakdown can be found n Table (). Thermal consumpton cost 1% Pumpng cost ~0.0% Reheater consumpton cost 0.8% Electrolyser consumpton cost 31% Heat exchangers nvestment cost 0.1% Electrolyser nvestment cost 67% Table. Cost breakdown of hydrogen producton cost Our programme found that the nvestment cost of the electrolyser s the domnatng one. Snce the electrc consumpton decreases when the operatng temperature of the electrolyser ncreases and snce the hghest possble operatng temperature defned n our scenaro s 950 C, the program provdes results n ths range (cf. Fgure 3). The contrbuton of the total cost of the heat exchangers s very low. In our set-up we do not nclude changng out the heat exchangers, but even multplyng the cost of the heat exchangers by a factor of 10 would not have a great effect on the fnal results. The optmsaton results for that system show that t has enough energy to supply water at 888 C, whch s then heated by the reheater up to 949 C. F gure (3) shows the fnal temperatures from our optmsaton. Other values of H t, I, n cells, m& H and m& H O are provded n Table (3). H t (kg/year) 1.01 10 3 I (A) 54. n cells 71 m& (kg/s) 4.0 10-5 H & (kg/s) 5.5 10-4 mh O x 0.8 Table 3. Optmsaton results 10/11
949 C 954 C 888 C 30 C 84 C 38 C Fgure 3. Man operatng temperatures of the system 5. Concluson It appeared from the results of the TE optmsaton that the HTE can functon wth geothermal heat, even wth a geothermal temperature as low as 30 C. The power requred for the electrc reheater s very low when compared wth the electrc power requred for the electrolyser. Although there are stll many uncertantes on the aptness of the economc data and the physcal models (manly at the level of the electrolyser: ts operaton lfe duraton, ts unt cost and the nfluence of temperature on the latter), the frst optmsed results show that f the HTE s economcal one day, then t can also be economcal wth a geothermal source. References 1. Coûts de référence de la producton électrque, Rapport du Mnstère de l'économe des fnances et de l'ndustre. Pars, December 003.. Rodrguez G. and Pnteaux T. Studes and desgn of several scenaros for large producton of hydrogen by couplng a hgh-temperature reactor wth steam electrolysers, CD-Proceedngs of the Frst European Hydrogen Energy Conference, Grenoble, France, -5 September 003, paper CO1/6. 3. Manslla C. et al. Heat management for producng hydrogen by hgh-temperature electrolyss. Proceedngs of the 18 th nternatonal Conference on Effcency, Cost, Optmzaton, ECOS, June, 005, pp. 1159-1166. 4. Sgurvnsson J. The producton of hydrogen by hgh-temperature electrolyss and alkalne electrolyss n a context of sustanable development. Dplôme de Recherche Technologque Unversté Joseph Fourer, Grenoble-France, 1 October 005. See also: Sgurvnsson J. and Werkoff F. On the cost of the hydrogen produced by alkalne electrolyss. CD-Proceedngs of the Internatonal Hydrogen Energy Congress (IHEC), Istanbul, 13-15 July 005, paper 1.HPT1. 5. Lovera P. Blen F and Vullet Operatonal modellng of hgh-temperature electrolyss (HTE). 16 th World Hydrogen Energy Conference, paper n 356, Lyo n France 13-16 June 006. 6. Werkoff F. Maréchal A. and Pra F., Techno Economc study on the producton of hydrogen by hgh temperature steam electrolyss, CD-Proceedngs of the Frst European Hydrogen Energy Conference, Grenoble, France, -5 September 003, paper CO5/16. 11/11