Can High Temperature Steam Electrolysis Function With Geothermal Heat

International Journal of Hydrogen Energy 32 (2007) 1174–1182www.elsevier.com/locate/ijhydene

Can high temperature steam electrolysis function with geothermal heat?

J. Sigurvinssona, C. Mansillaa,∗, P. Loverab, F. Werkoffa

aCEA/DEN/DANS/DM2S CEA/Saclay (Bat. 470), 91191 Gif-sur-Yvette, Cedex, FrancebCEA/DEN/DANS/DPC CEA/Saclay (Bat. 450), 91191 Gif-sur-Yvette, Cedex, France

Available online 10 January 2007

Abstract

It is possible to improve the performance of electrolysis processes by operating at a high temperature. This leads to a reduction in electricityconsumption but requires a part of the energy necessary for the dissociation of water to be in the form of thermal energy.

Iceland produces low cost electricity and very low cost geothermal heat. However, the temperature of geothermal heat is considerably lowerthan the temperature required at the electrolyser’s inlet, making heat exchangers necessary to recuperate part of the heat contained in the gasesat the electrolyser’s outlet.

A techno-economic optimisation model devoted to a high-temperature electrolysis (HTE) process which includes electrolysers as well as ahigh temperature heat exchanger network was created. Concerning the heat exchangers, the unit costs used in the model are based on industrialdata. For the electrolyser cells, the unit cost scaling law and the physical sub-model we used were formulated using analogies with solid oxidefuel cells.

The method was implemented in a software tool, which performs the optimisation using genetic algorithms.The first application of the method is done by taking into account the prices of electricity and geothermal heat in the Icelandic context. It

appears that even with a geothermal temperature as low as 230 ◦C, the HTE could compete with alkaline electrolysis.� 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

Keywords: Techno-economic optimization; Hydrogen production; High temperature electrolysis; Genetic algorithms; Geothermics; Iceland

1. Introduction

High-temperature steam electrolysis (HTE) is an alternativeto the conventional electrolysis process. Some of the energyrequired to split the water molecule is provided as heat insteadof electricity, thus reducing the overall energy required andimproving the process efficiency. Because the conversion effi-ciency of heat to electricity is low compared to using heat di-rectly, the energy efficiency can be improved by supplying thesystem with energy in the form of heat rather than electricity.

Recent HTE research programs have profited from new fi-nancing, mainly within the Generation IV International Forumframework for developing long-term nuclear reactors [1]. Theforum considers the possibilities of using nuclear energy, partic-ularly high-temperature helium cooled reactors (HTR), whichinclude the possibility of producing hydrogen.

∗ Corresponding author. Fax: +33 1 69 08 29 77.E-mail address: [email protected] (C. Mansilla).

0360-3199/$ - see front matter � 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.ijhydene.2006.11.026

For HTRs the expected efficiency of electricity productionis 50%, hence we can assume that the cost of thermal energyfor HTR is 50% of the cost of electricity.

kWh(th−HTR) = 0.5 kWh(e−HTR). (1)

In Iceland the cost of extracting thermal energy from ageothermal source is only about 10% of the price of electricityproduced.

kWh(th−geo) = 0.1 kWh(e−geo). (2)

Thermal energy from a geothermal source is very inexpen-sive compared to thermal energy obtained from an HTR. Inthe Icelandic context, steam could be supplied at 200.230 ◦C.Only 3.8 kWh(e)/N m3 H2 are needed with a thermal inputof 200 ◦C, compared with about 4.5 kWh(e)/N m3 H2 in con-ventional electrolysers. Furthermore, the cost of electricity toindustry in Iceland is approximately ¥0.014/kWh comparedto ¥0.0284/kWh [2] for medium-term electricity produced by

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J. Sigurvinsson et al. / International Journal of Hydrogen Energy 32 (2007) 1174–1182 1175

Table 1Energy prices, geothermics/HTR

¥/kWh(e) Iceland 0.014¥/kWh(e) France 0.0284¥/kWh(th) Iceland 0.0014¥/kWh(th) France 0.0142

Cost of Geothermal and HTR supplied energy

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

010

015

025

035

045

055

065

075

085

0

Supplied thermal energy [°C]

Co

st

€/k

g [

H2]

Geothermal, Iceland HTR, France

Fig. 1. Cost of vaporising and heating water to the required temperature forthe electrolyser.

nuclear reactors in France. When this price difference, reportedin Table 1, is taken into account, the advantage of producinghydrogen by HTE in Iceland is evident, as demonstrated inFig. 1, only in terms of the cost of vaporising and heating waterto the operating temperature of the electrolyser.

Although only approximately 200 ◦C of thermal input inthe HTE process coupled with a geothermal source is possi-ble today, this could change. Recent research carried out byLandsvirkjun on deep drilling in Iceland shows the possibil-ity of extracting 500.600 ◦C of steam at a depth of 4–5 km. Atpresent, deep drilling is purely experimental but it could be-come a possibility within the next 10 years.

There are three possible operating modes for HTE depend-ing on the energy balance at the level of the electrolyser: en-dothermal, isothermal and exothermal [3].

• Endothermal: The temperature of the steam decreases fromthe input of the electrolyser to the output. This correspondsto the best energy efficiency but the worst production costbecause an endothermal electrolyser is much more expensivethan an exothermal one.

• Isothermal: The temperature of the steam is the same at boththe input and output. The energy efficiency is better than inthe exothermal case but the electrolyser cost still outweighsthe increased efficiency.

• Exothermal: The temperature of the steam increases fromthe input of the electrolyser to the output. The exothermal

mode is best suited for the geothermal context because partof the heat required is provided by ohmic heating insidethe electrolyser. It is the only operating mode we will beconsidering.

The electrolyser’s inlet temperature could be between 700and 900 ◦C. To be effective from a thermodynamic point ofview, the HTE requires the heat contained at the electrolyser’soutlet to be recovered. Heat needs to be recovered both fromoxygen and from the hydrogen-steam mixture, in order to heatthe steam in contact with the geothermal source up to the desiredtemperature at the electrolyser’s inlet.

In the following sections we will present an flowsheet foran HTE process coupled with a geothermal source. This HTEprocess includes heat exchangers and an electrolyser based onsolid oxide fuel cell (SOFC) technology working in inverse,producing oxygen and hydrogen instead of consuming them.Using features related to the heat exchangers and the electrol-yser, a set of physical parameters will be calculated by using atechno-economic optimisation methodology.

2. A flowsheet for HTE coupled with a geothermal source

The usable temperature of the geothermal source at the Nes-javellir site, for example, is approximately 230 ◦C at 15 bar.This is relatively low and the vaporisation and heating of thewater for the electrolyser therefore needs to be carried out inseveral stages.

• The water input, which is in liquid state and at ambient tem-perature (that we will assume to be equal to 20 ◦C), will entera primary heat exchanger where the water will be heated andvaporised up to Tin_H2O = 230 ◦C with geothermal steam.The unit cost of thermal energy will be given.

• The water vapour at a temperature of Tin_H2O will be heatedin heat exchangers by the gases exiting the electrolyser upto a temperature of Tout_H2O.

• Eventually external electric heating can be used to heat thewater vapour from Tout_H2O to Tin_elec (Tout_H2O �Tin_elec).The unit cost of electric energy will be given. The investmentcost of this heating element is estimated to be negligible.

• In the electrolyser, the electric power is not only usedfor splitting the water molecules into hydrogen and oxy-gen but also for heating the gas from the inlet to theoutlet. The temperature of the oxygen (Tin_O2) and hy-drogen (Tin_H2) are the same at the outlet. Since we arelimiting ourselves to exothermal or isothermal conditions:Tin_O2 = Tin_H2 �Tin_elec.1

• Oxygen enters the heat exchangers at Tin_O2 and exits atTout_O2 , with Tout_O2 > Tin_H2O (and Tin_O2 > Tout_H2O).

• Hydrogen enters the heat exchangers at Tin_H2 and exits atTout_H2 , with Tout_H2 > Tin_H2O (and Tin_H2 > Tout_H2O).

1 The unit cost for electricity is evidently the same as for the electricreheater.

1176 J. Sigurvinsson et al. / International Journal of Hydrogen Energy 32 (2007) 1174–1182

Fig. 2. Heat exchanger networks coupled with the electrolyser.

Fig. 2 shows the diagram of the model and illustrates theconstraints on the input and output of both the electrolyser andheat exchangers.

2.1. The physical model for the heat exchanger networks

The heat exchangers in our model are counter-current heatexchangers.

We considered exchangers with corrugated plates, i.e. notsmooth. The corrugated plates allow a better heat transfer. Thecross sections, as well as the physical equations of the heatexchangers are defined by Mansilla et al. [4].

For HTE coupled with a geothermal source the networks ofheat exchangers need to span a large difference in temperature.The temperature range in the geothermal case is from ∼ 200 to∼ 950 ◦C. This temperature range cannot be covered by onlyone type of exchanger. The materials used, and thus the cost ofthe exchanger directly depend on the temperature.

The heat exchangers can be classified into three categoriesaccording to the ranges of temperatures [4]. The following no-tations will be used for the exchanger modules:

• LT for “low temperature” (up to 600 ◦C),• MT for “medium temperature” (from 600 to 850 ◦C),• HT for “high temperature” (above 850 ◦C).

• Low temperature “LT ”: T < 600 ◦C, stainless steel heat ex-changer capable of 7 MPa up to 300 ◦C.

• Medium temperature “MT ”: 650 ◦C < T < 850 ◦C, nickel-based heat exchanger capable of 1–2 MPa at 650 ◦C, cur-rently under testing.

• High temperature “HT ”: T > 850 ◦C, ceramic-based heat ex-changer capable of 10.50 MPa at 850 ◦C, further investiga-tion into what material and which heat exchanger to use forthis temperature level is required.

Tee_O2Tin_O2

T1_HT

T1_MT

Tout_O2

T2_HT

T2_MT

Tin_H2O

O2

HT

MT

LT

H2O

Fig. 3. Diagram of a heat exchanger network for the oxygen branch. Relatedto the notation of Fig. 2: Tout_H2O = xT ee_H2 + (1 − x)Tee_O2 .

At low temperatures stainless steel dominates. Othersteels come next, to be replaced by ceramics at very hightemperatures.

The heat exchanger proposed for the > 850 ◦C temperaturelevel is still being tested and further details will be availablesoon. Assuming that plate heat exchangers with primary sur-faces are used to insure a high level of effectiveness, the over-all heat transfer coefficient can be derived as explained bySigurvinsson [5].

The heat exchanger network for the oxygen branch can there-fore be shown in a diagram as in Fig. 3.

The same mass flow crosses the three modules. In addition,it is estimated that the temperature variation between two


exchangers is negligible. The definition of the exchanger mod-ules gives us orders of magnitude for these temperatures:T1_HT must be lower than 850 ◦C, and T1_MT must be lowerthan 600 ◦C.

For the first exchanger network, the fluid in the primary is asteam-hydrogen mixture. For the second, it is oxygen. Steamcirculates into the secondary of the two exchanger networks.

The integration of the exchangers studied in the HTE sys-tem imposes bonds between the various flows via the recyclingrate r. Using nH2O as the total molar water flow through thetwo secondary branches of the exchangers, the various molarflows are:

• (1 − r) nH2O of hydrogen in the primary H2 exchanger,

• r nH2O of water in the primary H2 exchanger,

• (1−r)2 nH2O of oxygen in the primary O2 exchanger,

• x nH2O of water in the secondary H2 exchanger,

• (1 − x) nH2O of water to the secondary O2 exchanger,

where nH2O is the total molar water flow (mol/s). x is the divi-sion rate of the principal water flow. It is a number between 0and 1.

The details of the mass flows in the primary and secondaryof all the exchangers are expressed in [4].

2.2. The electrolyser model

To find the quantity of thermal and electric energy neededfor water decomposition, the Nernst equation was used andadjusted for overvoltages. In the chemistry of fuel cells andelectrolysers E is the potential of the cell in (V):

E = E0 + RT

2Fln

(PH2

√PO2

PH2O√

Pref

)+⎛⎜⎝

RohmRactRcon

⎞⎟⎠ j , (3)

Where E0 is the thermodynamic potential of steam decompo-sition at equilibrium (V); Rohm the resistance due to ohmiclosses in membrane (� m2); Ract the resistance due to reactionactivation (� m2); Rcon the resistance due to kinetic problems,caused by inhomogenic concentration of gases in the electrodes(� m2); R the universal gas constant (J/mol. K); T the temper-ature (K); F the Faraday’s constant (C/mol); P the partial pres-sure (MPa), Pref the pressure of reference = 0.1 MPa and j thecurrent density (A/m2).

The first part of the equation is the Nernst local equation,which expresses the exact electromotive force of a cell in termsof the activities of the cell’s products and reactants. This is onlya function of temperature and pressure. The partial pressuresthroughout the electrolyser are not constant. They change withthe position, and the partial pressures of gases will affect theresulting energy needed for the electrolysis. This is dependenton how much of the incoming water is electrolysed. The lastterms in the equation represent unwanted losses due to ohmiclosses in membrane, reaction activation and kinetic problemscaused by inhomogenic concentration of gases in the electrodes.

The products Rj , linked to the unwanted losses are usuallycalled overpotentials.

There are many factors in the overpotential calculationswhich are very difficult to evaluate correctly. The evaluationdepends on actual test results for all three types of resistances.An analytical model was used for the simplifications based onthe work of Lovera [6].

The model is validated on results from experiments on SOFC.It is possible that the overpotentials are not exactly the samefor fuel cells and electrolysers but initial results show that theyare very similar.

In this simplified model the overpotentials are linearised,i.e. assumed to be proportional to the current density. Eq. (3)therefore becomes

E = E0 + RT

2F

{Ln

(√PO2√Pref

)− A + B�in

}

+ RT B

4F 2qmol

1

1 − e−(RT B/4F 2qmol)�/RsI , (4)

where � is the electrolyte surface (m2), I the current intensity(A), �in the portion of water electrolysed (input), A = 2.3843;B = 4.7685 the mathematical constants due to the linearisationof the logarithmic term in the Nernst equation, PO2 the partialpressure of oxygen (supposed to be constant in the model), qmolthe molar flow rate of hydrogen + steam (mol/s) and Rs thetotal area specific resistance (Rohm + Ract + Rcon) (� m2).

According to [6] the exothermal mode works when the op-erating cell potential is greater than 1.3V. If the potential ishigher, all of the extra energy will go into heating the gases andcompensating insulation losses. This will allow us to directlycalculate the temperature difference from the electrolyser’s in-let to the outlet, using the following simple relation:

(Uelectrolyser − Udiss)I = •m Cpelec,mix�Telectrolyser × 10−3, (5)

where m is the total mass flow (kg/s), Cpelec,mix the specific heatof the water/hydrogen/oxygen mixture (kJ/kg K), �Telectrolyserthe temperature difference from electrolyser inlet to outlet (K),Udiss the potential required for dissociation (V) and Uelectrolyserthe potential applied to the electrolyser (V).

3. A techno-economic optimisation method applied tothe HTE

3.1. Principles of the techno-economic optimisation

In the following section we will present a method for op-timising the HTE process including heat exchangers and anelectrolyser from a techno-economic point of view.

The techno-economic approach we selected presupposes aheat exchanger network, also called a flow sheet. The optimi-sation procedure consists in minimising an objective functionwhich takes into account operating as well as investment costs.In the current context of sustainable development, advancedsystems are being studied. These systems involve either highpressures, high temperatures, or corrosive products, and some-times several of these severe conditions. In all of these cases,


investment costs can increase by one or two orders of magni-tude when compared to classical alternative systems, leadingto a growing interest in the techno-economic approach.

In a previous study [4], TE optimisations were performedonly for heat exchanger networks (excluding the electrolyser).In that case the primary heat sources were HTR or Geothermics.We present an extension of this work of [4] by including anelectrolyser which is coupled with a geothermal source.

The low-temperature heat is very inexpensive from a geother-mal source. Further on, we do not consider heat exchangers forpre-heating the cold water entering the boiler.

Another difference from coupling with an HTR is that we willconsider the possibility of an electric reheater for increasingthe temperature of the steam at the inlet of the electrolyser.

The heat exchanger networks and the electrolyser arethen optimised by minimising the production cost per kgof hydrogen. The optimisation was achieved using geneticalgorithms.

3.2. The objective function

The objective function is the function that we want to min-imise. The objective is to minimise the cost of producing hy-drogen. CTA is the notation for the total cost (¥/kg H2).

The numerator has two main groups of factors, the first beingthe investment cost for the electrolyser and heat exchangersand the second, the operating cost of the electrolyser and heatexchangers.

The investment costs are firstly the capital costs for the heatexchangers (Ci,exch) and electrolyser (Ci,elec). The operatingcosts in the numerator are the thermal consumption cost (Co,th)

and the electric energy consumption cost (Co,elec).The denominator of the objective function is the hydrogen

production per year (Ht (kg H2/year)). It depends on the cur-rent intensity, flow rate and recycling ratio in the electrolysercell. The objective function is expressed with the followingformula:

CTA =∑Ti+Te

t=1

[((Ci,exch)t + (Ci,elec)t + (Co,th)t + (Co,elec)t

)(1 + �)−t

]∑Ti+Te

t=1 [Ht(1 + �)−t ] , (6)

where CTA is the total cost (¥/kg H2)2 , Ci,exch the heat ex-changers investment cost (¥), Ci,elec the electrolyser invest-ment cost (¥), Co,th the thermal consumption operating cost(¥), Co,elec the electric consumption operating cost (¥), Ht thehydrogen production (kg of H2/year), � the discount rate, Tethe number of years in use (years), Ti the number of years ofinvestment (years), and t the year considered.

This equation is based upon a similar equation used to calcu-late the future electricity cost from nuclear reactors [1]. In thefollowing section we will define each cost contribution factorand explain the calculations where necessary.

2 ¥ has been chosen, however, it can be replaced by the Icelandic krónaor by any other currency.

3.3. Investment cost of heat exchangers

Ci,exch is obtained by summing the investment costs of allthe heat exchangers:

Ci,exch =N∑

j=1

Cj , (7)

with

Cj = Cj × Sj , (8)

where N is the number of heat exchangers, Cj the cost of capitalfor the j th exchanger (¥), Cj the unit investment cost for thej th exchanger (¥/m2) and Sj the heat exchangers surface ofthe j th exchanger (m2).

Cj is defined according to the type of exchanger, materialand the operating conditions [4]:400¥/m2: for the low-temperature exchangers;800¥/m2: for the medium-temperature exchangers;4000¥/m2: for the high-temperature exchangers.

3.4. Investment cost, of the electrolyser

The definition of the contribution of the electrolyser(Ci,elec) to the total investment cost is obtained by assumingthat:

• The cost is proportional to the surface of the electrolyser.• The operation life duration of the electrolyser is expected to

be constant for large ranges of temperatures, voltages andcurrent densities. It has been estimated to be 5 years.

• Based on the target objective for SOFC [7], a 2000 ¥/kWunit cost for cells with a surface power density of 0.5 W/cm2

has been retained.

These assumptions take into account improvements expectedat the 2030’s horizon, due to the current world research anddevelopment works, related to the SOFC. The investment costis then expressed by:

Ci,elec = Ptot,useful2000

[0.5

j × Uelectrolyser

](¥), (9)

where j is the current density in cell (A/cm2), Uelectrolyser theoperating voltage of the electrolyser (V), Ptot,useful the electricpower required for the dissociation of water (kW).

Although there are strong uncertainties related to these as-sumptions and that the final production cost of hydrogen de-pends greatly on them, it is reasonable to consider that, in the


frame of the present preliminary techno-economic study, theyallow to assess the long-term potentiality of the HTE.

3.5. Thermal consumption operating cost

The definition of the contribution of thermal consumption(Co,th) to the total capital operating costs is as follows:

Co,th = ckWhth te•mH2O(Cp,H2O�Tgeothermal + Cv,H2O), (10)

where Co,th is the thermal consumption operating cost (¥/year),ckWhth the unit thermal energy cost (¥/kWhth), te the length ofoperation (h/year), mH2O the mass flow of water (kg/s), Cp,H2O

the specific heat of water (kJ/kg K), Cv,H2O the specific latentheat of water vaporisation (kJ/kg) and �Tgeothermal the temper-ature difference in the geothermal heat exchanger (K) and

�Tgeothermal = Tin_H2O − Text_H2O, (11)

where Tin_H2O is the temperature of steam at the geothermalheat exchanger outlet (K) and Text_H2O the temperature of waterat the geothermal heat exchanger inlet (K).

3.6. Electric consumption cost

The definition of the electric consumption’s contribution(Co,elec) to the total operating costs is the sum of the consump-tion of the electrolyser, the pump and the extra heating.

The cost of the electricity consumption = cost of the kWhe×Consumptions: by the electrolyser (on the basis of 5 kW) + forpumping + for the reheater.

Co,elec = ckWhe(ECelectrolyser + ECpump + ECreheater), (12)

where Co,elec is the electricity consumption operating cost(¥/year), ckWhe the unit cost of electricity (¥/kWhe),ECelectrolyser the electric consumption by the electrolyser(kWhe/year), ECpump the electric consumption by the pump(kWhe/year) and ECreheater the electric consumption by thereheater (kWhe/year).

This requires the precise definition of each component’s con-sumption: the electrolyser, the pump and the reheater.

3.6.1. The pumpThe electric consumption of the pump is due to pressure

losses in the two exchanger networks.

ECpump = m�P te

��pump, (13)

where ECpump is the electric consumption of the pump(kWhe/year), �pump the mechanical efficiency of the pump,m the mass flow (kg/s), � the specific mass (kg/m3), �P thepressure losses (Pa) and te the length of operation (h/year).

The pressure losses are proportional to the square of theflow. They depend on the length of the exchanger, the hydraulicdiameter, the cross section and the density of the fluid. This cost

must be taken into account for each branch of the exchanger.

�Pi = 4fi

Li

Dhi

1

2�i

(mi

Ai

)2

, (14)

where �Pi is the pressure loss (Pa), fi the friction factor, mi

the mass flow (kg/s), Ai the cross section in exchanger i (m2),Dhi the hydraulic diameter (m), and Li the heat exchangerlength (m).

The friction factor depends on the Reynolds number. Theexpression we used is valid for 50 < Re < 15000.

Since we assume that there is equal distribution of the fluid,the flow per channel is equal to the ratio of the total flowper number of channels. Moreover, the total cross sectionof the exchanger is equal to the product of the cross sectionof a channel per number of channels. Consequently, thecost of pumping can be calculated using the total size insteadof the size relating to one channel.

3.6.2. The electrolyserTo calculate the total electric consumption we need to mul-

tiply the power dissipated in the electrolyser by the annualoperation duration:

ECelectrolyser = UelectrolyserI ten × 10−3, (15)

where ECelectrolyser is the electric consumption of the elec-trolyser (kWhe/year), I the current in each electrolyser cell(A), te the length of operation (h/year), Uelectrolyser the operat-ing voltage of each electrolyser cell (V) and n the number ofelectrolyser cells.

3.6.3. The electric reheaterThe electric consumption of the reheater is evaluated by cal-

culating how much energy is needed to increase the tempera-ture by a specific amount.

ECreheater = •mH2O · Cp,H2O · te(Tin_elec − Tout_H2O), (16)

where ECreheater is the electric consumption of the reheater(kWhe/year), te the length of operation (h/year), mH2O the massflow of water (kg/s), Cp,H2O the specific heat of water (kJ/kg K),Tout_H2O the temperature at the outlet of the heat exchangernetwork and before the reheater (K) and Tin_elec temperature atthe electrolyser inlet (K).

3.7. Decision variables

There are 14 decision variables. They are the temperatures,expressed in ◦C, at the different places of the process exceptfor Tin_H2 and Tin_O2 which are calculated (exothermal mode)and Tin_H2O which is fixed. The temperature of the steam at thereheater’s inlet Tout_H2O is calculated from Tee_H2 and Tee_O2

(see Fig. 3).The division rate x of the principal water flow is also a

decision variable.The values of the decision variables will evolve throughout

the iterations to obtain optimised results. When an optimal pointhas been reached, the model has results for each of the decisionvariables.


3.8. Constraints

Several constraints apply to the system. The electrolyser isoperating in exothermal mode so output gases are always hotterthan input ones.

Other physical constraints link the temperatures of each endof the heat exchangers. The temperatures of the primary floware higher than those of the secondary flow throughout eachheat exchanger.

Inlet temperatures are higher than outlet temperatures for theprimary flow, but lower for the secondary flow.

Constraints on heat exchangers’ efficiencies and effective-nesses are eventually added to obtain meaningful results.

4. The TE optimisation applied to geothermics

4.1. Specification of data for implementing the TEoptimisation model

4.1.1. Economic datate: length of operation: 7008 hours/year (80% availability),�pump: mechanical efficiency of the pumping: 80%,�: discount rate : 6%Number of years of construction: 3 yearsDistribution of capital expenditures: 10% the first year, 35%the second and 55% the thirdNumber of years of operation: 30 yearsElectrolyser operation life duration: 5 yearsckWhe : ¥0.014/kWhe (¥1.4. × 10−5/Whe)ckWhth : ¥0.0014/kWhth.

The first parameters are selected in agreement with [7].

4.1.2. Physical dataThese data will not change throughout the optimisation iter-

ations. They have been fixed.Tin_H2O = 503 K or 230 ◦C,Ptot,useful = 5 kW: useful power requirements for the electrol-yser,�out = 0.67: portion of water electrolysed at the outlet,r = 0.33: recycling ratio,ε = 1.39 × 10−4 m: electrolyte membrane thickness [6],� = 0.985 × 10−2m2: electrolyte surface for 1 cell [6],PH2O = 1.5 × 106 Pa: steam pressure at the electrolyser’s inlet,PO2 =5×105 Pa: partial pressure of oxygen in the electrolyserandUelectrolyser =1.4 V: cell potential, exothermal operating mode.

The partial pressure of oxygen is not constant throughoutthe electrolyser. In our study we do, however, assume constantpressure at the anode.

4.2. Demonstration results of the HTE optimisation

The results of our optimisation show that two factors domi-nate the cost of hydrogen production: the electrolyser’s electricconsumption and the electrolyser’s investment cost. We foundthat the final cost of producing hydrogen was ¥1.7/kg H2. Thecost breakdown can be found in Table 2.

Table 2Cost breakdown of the hydrogen production cost

Thermal consumption cost 1.0%Pumping cost ∼0.0%Reheater consumption cost 0.8%Electrolyser consumption cost 31%Heat exchangers investment cost 0.1%Electrolyser investment cost 67%

This value shows that, at least in the Icelandic context, HTEcould compete with alkaline electrolysis [5]. For given electric-ity price and production capacity, the production cost of hydro-gen by alkaline electrolysis has been assessed in [5–8]. In theIcelandic context, an alkaline electrolysis plant with a capac-ity of 11.500 tH2/year (0.4 kg H2/s) can provide hydrogen ata cost of ¥1.6/kg.

For a given primary energy source, HTE must be compet-itive with the alkaline electrolysis fed by electricity producedby the same primary energy source [8]. HTE will have to reachan economy in terms of consumption cost. Fig. 4 shows thatabout 16 MJ/kg of H2 are needed for breaking water moleculesin the liquid state (as it is done with the alkaline electrolysis),while less than 14 MJ/kg of H2 are needed for breaking watermolecules in the liquid state. Besides in this last case, a partof the energy can be brought in the form of heat which is lessexpensive than electricity. At first glance, relatively low tem-perature geothermal sources (#230 ◦C) appear less favourablethan alternative high temperature energy sources, such as hightemperature nuclear reactors [8], but—at least in the Icelandiccontext—the very low cost of heat, as reported in Table 1, leadsto an appreciable economy in terms of energy consumption cost.

Our programme found that the investment cost of the elec-trolyser is the dominating one. Since the electric consumptiondecreases when the operating temperature of the electrolyserincreases and since the highest possible operating temperaturedefined in our scenario is 950 ◦C, the program provides resultsin this range.

The total cost of the heat exchangers is very low. In our set-up we do not include changing out the heat exchangers, buteven multiplying the cost of the heat exchangers by a factor of10 would not have a great effect on the final results.

The optimisation results for that system show that it hasenough energy to supply water at 888 ◦C, which is then heatedby the reheater up to 949 ◦C. Fig. 5 shows the final temperaturesfrom our optimisation. Other values of Ht, I, ncells, mH2 andmH2O are provided in Table 3.

5. Conclusion

It appeared from the results of the TE optimisation that HTEcan function with geothermal heat, even with a geothermal tem-perature as low as 230 ◦C. The power required for the electricreheater is very low when compared with the electric powerrequired for the electrolyser.

Although there are still many uncertainties on theaptness of the economic data and the physical models


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y D

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ΔGR, Electrical Energy Demand

TΔSR, Heat Demand

Fig. 4. Thermal and electricity supply to the electrolyser.

Fig. 5. Main operating temperatures of the system.

Table 3Optimisation results

Ht (kg/year) 1.01 × 103 H2 branch O2 branchI (A) 54.2 T1_HT (◦C) 680 807ncells 71 T1_MT (◦C) 442 468mH2 (kg/s) 4.0 × 10−5 T2_HT (◦C) 613 767mH2O (kg/s) 5.5 × 10−4 T2_MT (◦C) 324 283x 0.82 Tee (◦C) 789 937

(mainly at the level of the electrolyser: its operation life du-ration, its unit cost and the influence of temperature on thelatter), the first optimised results show that if the HTE iseconomical one day, then it can also be economical witha thermal source characterised by a low temperature and alow cost.

Acknowledgement

We would like to thank Alain Maréchal and AndréBontemps for their help in defining the heat exchanger fea-tures, and Michel Dumas and Gilles Arnaud for their help inimplementing genetic algorithms.


References

[1] Generation IV Nuclear Energy Systems Roadmap—Economics CrosscutGroup—R&D Scope Report. Draft authored by the members of theGeneration IV Economics Crosscut Group, August 6, 2002.

[2] Coûts de référence de la production électrique. Rapport du Ministère del’Economie, des Finances et de l’Industrie, Paris, December 2003.

[3] Rodriguez G, Pinteaux T. Studies and design of several scenarios forlarge production of hydrogen by coupling a high-temperature reactorwith steam electrolysers. CD-Proceedings of the first European hydrogenenergy conference, Grenoble, France, 2–5 September 2003, paper CO1/6.

[4] Mansilla C, et al. Heat management for producing hydrogen by high-temperature electrolysis. Proceedings of the 18th international conferenceon efficiency, cost, optimization (ECOS), Trondheim, Norway, June 2005.p. 1159–66. Energy, 2006, doi:10.1016/j.energy.2006.07.033.

[5] Sigurvinsson J. The production of hydrogen by high-temperatureelectrolysis and alkaline electrolysis in a context of sustainable

development. Diplôme de Recherche Technologique — Université JosephFourier, Grenoble, France, 21 October 2005. (See also: Sigurvinsson J,Werkoff F. On the cost of the hydrogen produced by alkaline electrolysis.CD-Proceedings of the international hydrogen energy congress (IHEC),Istanbul, Turkey, 13–15 July 2005, paper 1.2HPT221.)

[6] Lovera P, Blein F, Vuillet J. Operational modelling of high-temperatureelectrolysis. CD-Proceedings of the 16th world hydrogen energyconference, Lyon, France, 13–16 June 2006, paper SO5-017.

[7] Werkoff F, Maréchal A, Pra F. Techno Economic study on the productionof hydrogen by high temperature steam electrolysis. CD-Proceedingsof the first european hydrogen energy conference, Grenoble, France,2–5 September 2003, paper CO5/16.

[8] Werkoff F, et al. Processes of hydrogen production, coupled withnuclear reactors: economic perspectives. Proceedings of the europeannuclear conference (ENC), Versailles, France, 11–14 December 2005,paper no. 227.

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Can High Temperature Steam Electrolysis Function With Geothermal Heat

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