Modeling and energy demand analysis of a scalable green hydrogen production system

international journal of hydrogen energy xxx (xxxx) xxx

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Modeling and energy demand analysis of a scalable green hydrogen production system Petronilla Fragiacomo, Matteo Genovese* Department of Mechanical, Energy and Management Engineering, University of Calabria, Arcavacata di Rende, 87036, Cosenza, Italy

highlights
Mathematical model development for PEM and Alkaline Water electrolysis.
Energy flows, auxiliaries, electricity and heat demand are the core of the model.
Model validated with experimental data from literature.
Scaling up of the results to a “connector hydrogen infrastructure.
Comparison between PEM and Alkaline energy performance.

article info

abstract

Article history:

Models based on too many parameters are complex and burdensome, difficult to be

Received 29 May 2019

adopted as a tool for sizing these technologies, especially when the goal is not the

Received in revised form

improvement of electrochemical technology, but the study of the overall energy flows.

20 September 2019

The novelty of this work is to model an electrolysis hydrogen production process, with

Accepted 24 September 2019

analysis and prevision of its electrical and thermal energy expenditure, focusing on the

Available online xxx

energy flows of the whole system. The paper additionally includes investigation on auxiliary power consumption and on thermal capacity and resistance as functions of the

Keywords:

stack power. The electrolysis production phase is modeled, with a zero-dimensional,

Hydrogen production

multi-physics and dynamic approach, both with alkaline and polymer membrane

Water electrolysis

electrolyzers.

Hydrogen station

Models are validated with experimental data, showing a good match with a root-mean-

PEM electrolyzer

square percentage error under 0.10. Results are scaled-up for 180 kg/day of hydrogen,

Alkaline electrolyzer

performing a comparison with both technologies. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Context and background Climate changes are one of the most important phenomena which the scientific community is focusing on. It affects

temperature increase and it causes severe weather disasters, such as extreme storms, floods and droughts, which contribute to increase psychological stress and to overwhelm quality of life [1]. Among the various solutions that research has made available, renewable energies and hydrogen technology are among the most promising systems for the

* Corresponding author. E-mail addresses: [email protected], [email protected] (M. Genovese). https://doi.org/10.1016/j.ijhydene.2019.09.186 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Fragiacomo P, Genovese M, Modeling and energy demand analysis of a scalable green hydrogen production system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.186

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production of electricity [2]. In fact, in view of alternative solutions and the overcoming of fossil fuels, new plants for renewable energy generation are being installed all over the world, trying to create a decentralized structure for energy production. In this context, hydrogen storage technologies and power-to-gas (P2G) applications, incorporated into decentralized energy systems, can facilitate the temporal matching of energy supply and demand [3]. When an abundant amount of renewable energy is available, the surplus energy can be stored with high energy density as hydrogen by mean of water electrolysis, and it is an interesting a long-term storage alternative [4]. This technology is currently associated with high costs, as it needs a complex multi-component system, characterized by high costs due to expensive materials and manufacturing. In fact electrolyzers, compressor systems and hydrogen storage technologies are all required to facilitate hydrogen storage [3]. Despite its non-economic competitiveness, the electrolysis has several advantages, first of all its flexibility of operation and the high purity of the hydrogen produced, a very important requirement to avoid polluting the catalysts present on the electrodes of the fuel cell [2,5]. The hydrogen produced could be: used for a hydrogen fueling station and hydrogen vehicles, injected and mixed into natural gas pipelines, or used in a methanation process in order to produce synthetic methane, improving the energy production fluctuations and stabilization and reducing the transient limitations [6]. In this way, water electrolysis offers a more sustainable and costeffective option [7]. Several and different electrolysis technologies are present in the research environment or in the market, such as alkaline, proton exchange membrane (PEM) and solid oxide electrolysis cells (SOEC). Alkaline electrolysis is the most economically and technically mature, follows PEM technology that offers greater current density and quality of hydrogen [8,9]. SOEC technology combines the qualities of the other two types of electrolyzers but remains to this day the development stage [10e12]. For this reason, in this present paper the analysis focused on the modeling of alkaline and PEM electrolyzer. The low temperature technologies have already been integrated into numerous international projects, like in Germany at Munich Airport [13], Japan [14], Irvine (California) [15], Madrid [16], Birmingham (UK) [17], Los Angeles [18], Corsica (FR) [19]. More detailed reviews for international projects adopting water electrolysis can be found in Refs. [20,21]. Since on-site electrolysis can play a big role in P2G technologies and in the enhancement of the hydrogen economy, modelling is an essential tool for designing and sizing hydrogen infrastructures and their sustainability [22,23], saving on the costs of pre-planning, and in a remarkable way on the costs of monitoring and analysis, allowing to reduce time-consuming activities with early-stage experiments. Through modeling researchers and industries can focus on analyzing and solving complex problems (above all when several processes are involved and simultaneously they interact with each other), investigating the influence of main parameters or operating conditions through sensitive analysis and allowing the proposal of new design. The scientific community estimates more or less correctly the electrolyzer power consumption by modeling the

operating voltage as a function of current density and gradually introducing the parameters that affect its behavior. Most models analyze the operation of an electrolyzer, improve efficiency and reduce dissipative phenomena. However, they are very complex and burdensome, and infrastructures operators and companies may find it difficult to adopt them as a tool for the sizing of these technologies, especially when the goal is not the improvement of electrochemical technology, but the study of the overall energy flows. The aim of this work is to contribute to the spreading out of hydrogen infrastructures by formalizing and implementing a mathematical modeling for production processes, as a design tool to predict energy flows of the systems, not only those related to the electrochemical domain, but also to the auxiliaries and their energy consumption which cannot be neglected. The model enables also an overview of several energy-related parameters.

Modeling literature review Literature offers mathematical models describing the evolution of the electrolyzer with its characteristic curve (current, voltage), each with its own particular features. For PEM electrolyzer models, the research effort in modeling has increased in recent years, inspired by the strong progress in the field of PEM Fuel Cell Systems [19]. In the past years, M. Carmo et al. presented a review where PEM water electrolysis is comprehensively highlighted and discussed [24], and in recent years Abdol Rahim et al. performed another detailed literature review [8], classifying the analyzed models into different categories based on model assumptions and approach. Another exhaustive literature review on low temperature electrolysis was presented by Olivier et al. [9], where differences between all the modeling approaches have been compared. A brief summary of the papers with more correlation with this work is present below. In Ref. [25] the authors analyzed the electrolysis process by mean of a simple model based on equivalent electrical circuit analogy, showing good agreement with experimental testing. Gorgu¨n [26] developed through Matlab-Simulink® software a dynamic model for four main sectors of an electrolyzer (anode, cathode, membrane and voltage), with no experimental validation. Marangio et al. [27] presented a model whose final result was a theoretical polarization curve. Thanks to experimental results, experimental data fitting and employed statistical methods the authors obtained the estimated important parameter trends as a function of different temperature and pressure conditions. Awasthi et al. created a model to analyze and to investigate the effects of changing the temperature and pressure on the cell performance and polarization, coding with MatlabSimulink® and validating the model with experimental data [28]. Yigit et al. presented in Ref. [29] a dynamic model using the Matlab-Simulink® software, including some of the ancillaries, running simulations on several scenarios assuming a constant power and analyzing systems performance for different current density values. Other authors developed models based on EMR [30,31] for multi-physical phenomena. Shen et al. [32] have been the first to introduce simultaneously thermodynamic, kinetic and electrical resistance effects in a mathematical model. More dynamic modern models, based

Please cite this article as: Fragiacomo P, Genovese M, Modeling and energy demand analysis of a scalable green hydrogen production system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.186

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on Bond Graph Formalism, can be found in Refs. [33,34], taking into account also the balance of plant. Alkaline electrolyzers are the most used technology, thanks to their maturity [35]. A detailed literature review for alkaline and other low temperature technologies modeling can be found in Ref. [8]. Most of the models are based on the semi-experimental coefficients whose identification is performed by a fitting method for experimental polarization curves, related above all to solar-hydrogen demonstrations [36e38]. Some interesting and important works in this field have been reported by Ulleberg [39e41], whose models have been used also by other authors, for dynamic simulation of renewable energy systems. Ulleberg’s modeling approach presented a characterization of the electro-chemical polarization curve with parameters fitted empirically, and a lumped parameter approach to describe the thermal behavior of the stack. This mathematical approach to the problem includes the temperature as the operating parameter, neglecting the impact of other parameters variation such as pressure, electrolyte concentration or bubbling rate in the bulk electrolyte and on the electrode surface. Modifications to this model to include variables such as pressure, electrode/diaphragm distance, electrolyte concentration, flow rate or cell architecture have been reported in later works, to achieve a more detailed description of the over-potentials [42] and to describe the degradation of an electrolyzer [43]. The most recent one [44] improved and extended Ulleberg’s model, introducing parameters which are a function of several operating conditions, such as, temperature and pressure. Some authors adopted a physics approach focusing on modeling in a separated way the phenomena which occur in an electrolysis process, using electrical [45e48], transfer functions [49,50], but limiting the validity to a constant power working point. An Alkaline Electrolyzer Simulation Tool (AEST) developed with an electric analogy has been proposed also in Ref. [51], where the approach adopted is more general and takes into account the thermodynamic effects and electrochemical phenomena. In Ref. [52] authors investigated how different power supplies could influence the energy efficiency in alkaline electrolyzer systems. Haug et al. [53] proposed a complex model for the estimation of how operating conditions can affect the exhaust gas. A more enhanced one-dimensional model was proposed in Ref. [54], which includes also the materials properties and the configuration of components. The methodology adopted in the reviewed studies is based on a mathematical description of the stack polarization curve to calculate the efficiency of the electrochemical stack. Some of the investigated papers include also a thermal description of the electrolyzer in order to investigate the temperature impact on the steady-state stack electrochemical response, even if they are based on fixed values of thermal capacity and resistance which depend on the electrolyzer size. Because of their focus was different, most of the models do not include a description of all the energies involved in hydrogen production systems, not taking into account the whole physical state of the electrolyzer and the auxiliary system. Questions about how the auxiliary system could influence system performance remain. In the reviewed papers, when the authors included other ancillary components such as pumps, chillers, they combined their electrical

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consumption in a single term, constant during stack operation [55] or as a linear function of the stack power [9]. In the examined literature above, no model with a detailed characterization for auxiliary components was found with a description of their power consumption in function of the stack power. Moreover, thanks to their modularity, electrolyzer cells could be easily assembled in order to build stacks, and more stacks could be connected to achieve the required system size and a certain hydrogen production. As a consequence, all the equipment performance and the thermal parameters change, since their size and features strongly depend on the electrolyzer size. It remains not investigated how their values and their energy expenditure are related to the stack power. In fact, while analysis of polarization curve has been widely examined, less focus and attention have been given to others energy parameters, such as stack power, system power, auxiliary power, stack efficiency, system efficiency, maximum power required, average power, system energy required and heat-related parameters. Through the consideration of these parameters, it could be possible to estimate correctly the system energy consumption and hydrogen production capacities in transient regimes. In this train of thoughts, the novelty of the present work has been to formalize and implement a mathematical model which can lead to a deep analysis of the whole energy system, investigating several physical domains, following a rapid approach and enabling an easily scaling up of several energy parameters, of the auxiliaries and of the thermal capacity and thermal resistance values. As a novel consideration, these latter variable values were processed so as to bring out a dependence on the electric kilowatt size of the electrolyzer and therefore to be used later in the scaling-up phase. It is remarkable how this approach allowed to create a powerful energy model with the goal to minimize the risk for uniformed design features and decision, and then avoiding overpriced systems, poor performance or unpredictable operational cost. In fact, models based on too many parameters are very complex and burdensome, difficult to be adopted as a tool for the sizing of these technologies, especially when the goal is not the improvement of electrochemical technology, but the study of the overall energy flows. The electrolysis production phase was modeled, both with traditional technologies, such as alkaline electrolyzers (Alkaline), and more advanced technologies, such as polymer membrane electrolyzers (PEM). The model follows a zerodimensional, multi-physics and dynamic approach, useful for steady-state operation (typical of electrolyzer performance characterization) and transient operation (typical of hydrogen system coupled with renewable energy or of a hydrogen refueling station). It included the investigation on auxiliary power consumption on different stack sizes, as well as the main electrolyzer thermal parameters (thermal capacity and thermal resistance) as a function of the electrolyzer size. The model allowed also analysis on irreversibility, over-voltages, energy efficiencies, thermal energy management and system energy consumption, and furthermore, the possibility to scale up the models and investigating several hydrogen production system sizes.

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Electrolyzer models have been validated and then compared with electrolyzer experimental data. To make the models robust and reliable, the validation was carried out considering seven most relevant energy parameters, such as polarization curve, production curve, stack power trend, auxiliary power and system power, voltage efficiency curve and energy efficiency trends. As a case study of a potential application of the models, a “connector hydrogen infrastructure” has been considered, and the models have been scaled-up to obtain a 180 kg/day of hydrogen produced from renewable energy through water electrolysis. Finally, a comparison with both technologies has been performed.

Electrolyzer modeling and experimental validation The basic unit for water electrolysis consists of two electrodes and chambers (anode and cathode), an electrolyte, and it is powered by direct current. To represent in detail a power system, an energy balance and description are needed. Indeed, an electrolysis system requires also a mass balance (fluid-dynamic analysis) and an energy conservation balance. This analysis includes power demand, heat produced during electrochemical reactions, cooling power and heat losses [34]. The modeling performed in this paper concerned the following sub-models, related to different physical phenomena [9]:
Fluid-dynamic model, which represents mass flows in the electrolysis system;
Thermodynamic model, which represents the pressure at cathode and anode;
Electrochemical models, which allow describing the electrical behavior of the electrolytic stack;
Thermal models, to determine the transient thermal behavior of the stack. The approach used to model the several domains involved in the electrolysis process is based on four modules, describing: (a) fluid-dynamic domain for anode and cathode, (b) thermo-dynamic domain, (c) electro-chemical domain, and (d) thermal domain. Every module is represented by a complex box ad hoc developed in Simulink®, and every block communicates with each other basing on linked mathematical modules. The following main assumptions have been considered in order to develop the mathematical model:
Stack polarization curve has been modeled as a variable voltage, which depends on the input current, the temperature of the stack and other internal parameters (cell area and properties).
Pressure drop and pressure effects are neglected, and no high-pressure electrolyzer has been considered, where problems such as cross-permeation phenomena and corrosion take place more frequently.


The temperature is supposed to be uniform in the electrolyzer stack.
Each cell has the same thermal behavior.
The stack model is based on cells with the identical electrical behavior connected in series. Therefore the total stack working voltage can be obtained, multiplying the cell voltage by the number of series-connected cells. We developed a dynamic zero-dimensional model of a complete electrolyzer cell using Simulink/MATLAB in this study. The developed PEM model is based on the classical relations for the dissipation, activation and ohmic phenomena, but focuses on the energetic aspects, introducing experimental correlations for Faraday efficiency and for the estimation of the energy request by the auxiliaries of the system. The model is based on analytical correlations, then tuned regarding the electrolyzer experimental data, from Ref. [56]. For Alkaline electrolyzer, multi-physic phenomena are more complex than PEM electrolyzer. Among the reviewed papers, most of them focused on very detailed models, taking into account concentration phenomena, diffusion, separator, electrode porosity, etc. For all these aspects, even steadystate electrochemical models are tough, and empirical correlations are needed. For the same reasons shown for PEM model, the Alkaline electrolyzer model performed in this paper will follow a simple approach, based on multiparameter equation, tuned and validated with experimental data from Ref. [56]. The model is based on empirical correlations, taken from Ulleberg’s models [39], introducing experimental correlations for Faraday efficiency and for the estimation of the energy request by the auxiliaries of the system.

Fluid-dynamic model It is largely known that hydrogen production truly depends on the operational current (I), which is the first input of the model. This equation follows the Faraday law to represent the hydrogen molar flow. It depends on the number of free electrons (z) moving in the reaction inherent to hydrogen and the constant of Faraday (F). To take into account that all the electrons are not involved during the electrolysis reaction (leakage currents, parasitic currents, etc.), the equation can be modified with the addition of Faraday’s efficiency hFaraday (Eq. (1)). n_pH2 ¼ hFaraday

I I Nc ¼ hFaraday Nc z$F 2$F

(1)

where Nc is the number of series-connected cells. Faraday’s efficiency is often considered equal or very close to 1 (in particular for the PEM electrolyzer). In this paper, it is calculated with empirical equations involving operating conditions such as temperature (T) and current (I). For oxygen the production is half than hydrogen one (Eq. (2)), while for water it is considered 25% more than hydrogen one to take in account water cross-over in the electrolyte, diffusion phenomena and water losses as steam (Eq. (3)).

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1 p p n_O2 ¼ n_H2 2

(2)

p n_H2 O ¼ 1:25n_pH2

(3)

The fluid-dynamic modeling regards in particular the molar flows to the cathode and the anode (Eq. (4) and Eq. (5)). out At the anode, oxygen has to be considered. n_O2 depends on anode nominal pressure: if anode nominal pressure is reached, all oxygen produced is vented and no oxygen is a out p accumulated (n_O2 ¼0 and n_O2 ¼ n_O2 Þ, while if anode pressure is less than anode nominal pressure, no oxygen goes out or vents and all oxygen produced is accumulated to make the anode chamber reach the nominal operation conditions p (n_aO2 ¼n_O2 and n_out O2 ¼ 0). p out a n_O2  n_O2 ¼ n_O2

(4)

No water is considered to be accumulated. p n_H2 O  n_out H2 O ¼ 0

(5)

At the cathode (Eq. (6)), hydrogen is involved. Hydrogen out outflow n_H2 depends on cathode nominal pressure: if cathode nominal pressure is reached, an ideal hydrogen compressor out comp starts to store gas into the tanks (n_H2 ¼ n_H2 Þ, while if cathode pressure is less than cathode nominal pressure, no hydrogen goes out and all hydrogen produced is accumulated to make the cathode chamber reach the nominal operation conditions _comp ¼ 0). (n_aH2 ¼n_pH2 and n_out H2 ¼ nH2 p out a n_H2  n_H2  n_H2 ¼ 0

(6)

Thermodynamic model Partial pressures are needed to calculate cell voltage with Nernst Equation. Under the assumption of a certain volume of cathodic and anodic chambers (Vca andVan ) and of the same temperature between anode chamber, cathode chamber and electrolyzer temperature (Tel ), the ideal gas equation has been used. First of all, hydrogen and oxygen moles are integrated from each molar flow accumulated (Eq. (7) and Eq. (8)). tZ 0 þDt

nH2 ¼

a n_H2 dt

(7)

a n_O2 dt

(8)

t0

tZ 0 þDt

nO2 ¼ t0

Then partial pressures are calculated in Eq. (9) and Eq. (10), with the assumption that gases are supposed to have an ideal behavior, and they can be modeled through the ideal equation of state, valid for the parameters (pressure and temperature) range used in the model. pH2 ¼

RTel nH Vca 2

(9)

pO2 ¼

RTel nO Van 2

(10)

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Electro-chemical model The conversion of electrical energy into hydrogen is the core activity of an electrolysis system. For this reason, electrochemical models are the heart of any modeling of an electrolysis system, establishing the link between the input (electric power) and the output (hydrogen flow). To characterize cell efficiency, it is necessary to connect the input of electricity with hydrogen production. Thus, Faraday’s law is not sufficient, as it correlates only the current with the flow of hydrogen, while the calculation of electrical energy also requires the knowledge of the cell voltage. The electrical response of the cell must therefore be analyzed, involving the mathematical description of the cell voltage (and by extension of the stack) with the polarization curves. Eq. (11) used to describe each term of the polarization concerns: the reversible potential (Erev ) and the over-voltages of various sources of irreversibility (activation over-voltages at the anode and cathode, ohmic over-voltage and diffusion over-voltage). VCELL ¼ Erev þ hact þ hohm þ hdiff

(11)

The reversible potential is related to the Gibbs free-energy change, through which the molar enthalpy of formation (hf Þ, and the molar entropy are connected, and their values vary with temperature. Literature offers several empiric correlations or thermodynamic tables extrapolations. To make the model more flexible, this paper extrapolates the molar entropy and enthalpy of formation values from Ref. [2], considering them a function of temperature. Over a range of temperatures, molar heat capacity cp of gases is not constant, and empirical equations have been used (with an accuracy of 0.6% in the range 300e3500 K) [58]. Hydrogen specific heat does not change significantly with the pressure, while oxygen and water ones have more variations [59e61]. Nevertheless, for the pressure range of the electrolyzer (between 1 and 30 bar), these variations are negligible. Once the ideal potential at a given temperature is known, the ideal voltage can be determined at other pressures through the use of these equations. According to the Nernst equation, the ideal cell potential decreases if the operating pressure of the reactant gets higher. The symbol Erev represents the equilibrium potential, ETrev the potential at a given temperature. In order to calculate the actual voltage, over-voltages have to be modeled. For PEM technology, the activation over-voltages at the anode and cathode come from the kinetics of the electronic charge transfer phenomena. They are modeled considering a charge transfer coefficient, whose value is often set equal to 0.5, with the assumption that there is symmetry in the charge distribution [25,62e65]. Other values can be found in the literature [30,62,63]. Since in this work the identification of this parameter resulted from empirical curves, its value has been extrapolated by means of non-linear regression method. At the cathode side these phenomena show to have a smaller magnitude compared to the anode side. Since kinetics associated with hydrogen reactions occur faster than the

Please cite this article as: Fragiacomo P, Genovese M, Modeling and energy demand analysis of a scalable green hydrogen production system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.186

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reactions related to the oxygen at anode, activation overvoltages are negligible at cathode [19,64e66]. There are a lot of possible equations in the literature. In this paper, they are described by Tafel correlation (Eq. (12)), whose main parameters are the charge transfer coefficient a and exchange current densityi0 . Current density is defined in Eq. (13).   R$T i $ln hact ¼ a$z$F i0 i¼

(12)

I Acell

(13)

For their values, many authors proposed values depending on catalyst materials, or using correlations such as Arrhenius’s one. Since the catalyst materials were unknown, in this paper its value has been extrapolated from experimental data through non-linear regression fitting [56]. The ohmic overvoltage hohm is caused by the non-infinite conductivity of the cell. The different sources of ohmic overvoltage are electrolytes, electrodes, bipolar plates and contact resistors. Since the most important contribution derives from the electrolyte and membrane and its value is about 10 times bigger than other resistances, it has been considered the ohmic overvoltage due to the membrane alone, using empirical correlations to determine its conductivity. This assumption is proposed and used also in as [19]. Among the several empirical correlations present in the literature (Kopitzke [67], Bernardi [68], Springer [69]), our model considers the one proposed by Springer (Eq. (14) and Eq. (15)), used in many PEM electrolysis models. The empirical correlation used makes it possible to determine the membrane conductivity sm of protonic exchange as a function of temperature (T) and of the average water content of the membrane (l).  sm ¼ ð0:005139 $ lm  0:00326Þ$exp tm $i hohm ¼ sm



1268$

 1 1 303T

  R$T i $ln 1 þ b$z$F ilim

  Vcell ¼ Erev þ ðr1 þ r2 $ TÞ $ i þ s1 þ s2 $ T þ s3 $ T2 $log10   t2 t3 t1 þ þ 2 $ i þ 1 T T

(17)

The decision to choose this model derives from the vastness of its use in the literature, as highlighted in the first part. And because of its accuracy and adaptability to different electrolyzers. The diffusion overvoltage occurs when the mass transfer becomes preponderant with respect to the other phenomena, and therefore for high values of current density. In alkaline electrolyzers, high current density values are almost never achieved, as this technology has larger volumes than PEMs [39]. For this reason, in the modeling of the alkaline electrolyzers, the diffusion over-voltages were not considered, since high values of current density are not achieved during their operation. The Alkaline modeled cell potential is based on 8 parameters, whose r1 and r2 representing Ohmic and the others are related to Activation phenomena. The identification of these parameters resulted from empirical curves [56] adopting a non-linear regression method performed through the “lsqcurvefit” function, which can be found in the Optimization Toolbox of Matlab Software [70]. Operating conditions of experimental data and the validation process are described in the following sections. Once cell potential is calculated, the potential of the entire stack can be derived by multiplying the voltage for the number of cells (Eq. (18)). Vstack ¼ Ncell Vcell

(18)

Thermal model (14)

(15)

with tm representing the thickness of the polymeric membrane. PEM water management system usually assures a good level of hydration. Indeed, the membrane is considered as being completely saturated with water; therefore, its conductivity is only a function of temperature. Its value is assumed to be 17 representing good hydration [22]. Mass transfer processes affect the reaction and the polarization curve when higher current densities are applied. Diffusion over-voltages, hdiff , take into account the contribution of these phenomena, and they are described by means of Eq. (16). hdiff ¼

technologies. Because of this complexity, an empirical correlation (Eq. (17)) has been used in order to calculate cell potential, based on Ulleberg’s model [39].

(16)

b is an empirical coefficient and ilim is called limit current density. Their values have been extrapolated from experimental data through non-linear regression fitting [56]. From a phenomenological point of view, an alkaline electrolysis system is a more complex system than PEM

The temperature of the electrolyzer heavily affects the relationship between the voltage V and the current I. To represent the behavior of the temperature and build a thermal model, it is necessary to identify all the induced heat sources. Mathematical modeling of the system thermal behavior is based on a lumped thermal capacitance approach, proposed in Ref. [39] and adopted both for PEM and Alkaline technology [57]. With this approach, to build the thermal model, the principle of conservation of thermal energy has been used, assuming a negligible Joule Effect, a constant external temperature (Ta) and the same temperature for all electrolyzer components (Telec Þ. In other words, temperature gradients within the electrolyzer components are neglected. Hence the thermal model can be written as the continuous dynamic equation (Eq. (19)). Ct

dTelec ¼ Q_ gen  Q_ loss  Q_ cooling dt

(19)

where:
Ct is the total thermal capacity of the electrolyzer;

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Q_ gen is the heat transfer rate generated by the chemical reaction (caused by the entropy energy, Eq. (20));
Q_ loss is the heat transfer rate caused by the external temperature and fluid movement (Eq. (21));
Rt is the total thermal resistance of the electrolyzer;
Q_ cooling is the amount of energy required to cool down the system and it assures a constant target temperature operation (Eq. (22)).

Q_ gen ¼ Nc ðVcell  Utn ÞI

(20)

1 Q_ loss ¼ ðTelec  Ta Þ Rt Q_ cooling ¼



To enable a fast evaluation and scaling up, and at the same time to take into account the thermal phenomena, it was deemed appropriate to estimate the values of these parameters from experimental data found in the literature [19,39,40,62,72e75], shown in Table 1 and Table 2. In particular, these values were found and processed so as to bring out a dependence on the electric size of the electrolyzer and therefore to be used later in the scaling-up phase. The values found in the literature for PEMs are quite close to each other, so the average values have been considered (Eq. (25) and Eq. (26)). Specific thermal capacity ¼

(21)

¼ 0 if Telec < Ttarget s0 if Telec  Ttarget

(23)

During the electrolyzer start-up phase, the magnitude of Q_ cooling is null until temperature approaches the setpoint value and the system controller begins to start thermal management system operation, regulated by a proportional valve [71]. When the thermal management system starts its operation, all the electrolyzer overheating must be compensated and disposed of throughQ_ cooling . After these considerations, the solutions of the first-order differential equation are shown in Eq. (24). Ttarget if Telec  Ttarget  Telec ¼ > Tin  b ½expða$tÞ þ b if Telec < Ttarget : a a 

(26)

The values found in the literature for the Alkalines show considerable deviations: this is due to the progress that this type of electrolyzers has experienced in recent years, with the use of new materials and reduced thickness. The values associated with the most recent literature have therefore been considered (Eq. (27) and Eq. (28)).

The equation can be written and solved with a linear dynamic model of the first order [39], in Eq. (23).

8 > <

(25)

 C Rt ¼ 0:09 W

(22)

dTelec þ aTelec ¼ b dt

 Ct kJ ¼ 3:0  kW C kW

Specific thermal capacity ¼

 Ct kJ ¼ 11  kW C kW

(27)

 C Rt ¼ 0:167 W

(28)

PEM experimental validation PEM model results have been compared with experimental data from Wind-to-Hydrogen Project from National Renewable Energy Laboratory (NREL) in their Technical Report NREL/ TP-550-44082 (March 2009) [56]. The electrolyzer system is the model HOGEN S40 RE from Proton Energy Systems, whose nominal parameters are listed in Table 3. The same values have been used as input parameters in the model for the experimental validation. The root-mean-square error (RMSE) has been used as a metric in order to measure the differences between the model predicted values and the values actually belonged to

(24)

Some of these parameters are difficult to estimate, especially thermal resistance and thermal capacity (Rt and Ct). They depend essentially on the size of the electrolyzer, on the chosen materials and on the thicknesses used. Sometimes their magnitude can also be estimated experimentally from heating curves, insulating thermally the stack and turning off the auxiliary cooling system [72].

Table 1 e PEM technology thermal parameters. Nm3/h

Type MYRTE (2018) [19] Hydrogen Office building (2016) [74] Fuel Cells Lab (2013) [73] Genport srl (2011) [75] Ecole des Mines de Douai (2008) [62]

Acell [m2]

10.00 4.0 2 e e

0.029 e 0.02 0.05 e

kW

Rt [ C/W]

Ct [kJ/ C]

Ct/kW [kJ/ C kW]

46.00 5.00 2.5 0.300 e

0.0688 e 0.111 e 0.0934

162.116 11.005 e 0.978 68.544

3.52 2.20 e 3.26 e

Table 2 e Alkaline technology thermal parameters. Type HyStat (2008) [72] PHOEBUS (2003) [39,40] ERRE DUE (2016) [74]

Nm3/h

Acell [m2]

kW

Rt [ C/W]

Ct [kJ/ C]

Ct/kW [kJ/ C kW]

1.00 1.45 2.66

0.030 0.250 0.060

5.00 26.00 15.00

0.164 0.167 0.200

174.00 625.00 168.24

34.800 24.038 11.216

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Table 3 e PEM electrolyzer nominal parameters. Number of series-connected cells Operating Temperature [K] Stack Rated Power [kW] Operating Current [A] Hydrogen Nominal Flow [Nm3/h] Hydrogen Purity [] Cathode Nominal Pressure [bar] Anode Nominal Pressure [bar]

20 328 7 135 1.05 99.999% 13.10 2

experimental data [56]. However, RMSEs are not dimensional quantities, but take the unit of measure of the considered parameter. Therefore, they are not absolute indices of the reliability of the estimate made, but they depend on the variation range of the data acquired (and estimated). The corresponding absolute indices are indicated with the RMSE Percent (RMSEP). It can be calculated by substituting the RMSE numerator with the normalization of the error [76]. The identification of the model parameters resulted from an empirical approach using the lsqcurvefit function [70], and in Table 4 their values are shown. From experimental data, Faraday Efficiency has been modeled with a third-degree polynomial interpolation as a function of stack current I (Eq. (29)). hFaraday ¼  0:0922 þ 0:0091$I þ 0:00003$I2  0:0000003$I3

(29)

Hydrogen flow model data follows almost perfectly the experimental ones (Fig. 1), thanks to Faraday Efficiency interpolation. In the range between 18 A and 138 A the RMSE is about 0.022 Nm3/h and the RMSEP is about 0.1372. In the range between 35 A and 138 A, the model is more accurate, with a RMSEP value of 0.0532. The polarization stack curve has a maximum percentage error of 3.75%, and the voltage model results find a good approximation with experimental data, as shown in Fig. 2. Stack power, shown in Fig. 3, in the range between 18 A and 135 A is almost accurate, with a RMSE value of 0.057 kW and a RMSE of 0.0224. The power of the ancillary system (cooling fan, security instrument, etc.) has to be calculated in order to calculate the overall system power. From stack power experimental data and system power, a fitting curve for ancillary power has been proposed (Eq. (30)). Wancillary ¼ %ancillary $Wstack

(30)

where Wstack is the stack power, Wancillary is the ancillary power and %ancillary is function of Wstack (Eq. (31)). Coefficient values of this correlation are respectively a ¼ 79.153 and b ¼ 0.975. The trend of the percentage of the ancillary power is represented in function of the stack power in Fig. 4. Table 4 e PEM Model parameters. A [cm2], Cell, Active Area a [], Charge transfer coefficient i0 [A/cm2], Exchange current density lm , Membrane Water Content tm [cm], Membrane Thickness b [], Empirical Coefficient ilim [A/cm2], Limit current density

100 0.5316 4.576e-07 17 0.03306 0.315 1.401

Fig. 1 e PEM hydrogen production trend.

%ancillary ¼ a$Wbstack ½

(31)

System Power is the sum of stack power and ancillary power. As shown in Fig. 5, there is a good match between model and experimental data, with an RMSE value of 0.0744 kW and a RMSE of 0.0159 in the range between 18 A and 135 A. The Appendix presents the validation of other energy parameters, such as the voltage efficiency for the stack and the energy efficiency of the system.

Alkaline experimental validation As for PEM electrolyzer, experimental data have been extrapolated from Wind-to-Hydrogen Project from National Renewable Energy Laboratory (NREL) in their Technical Report NREL/TP-550-44082 (March 2009) [56]. The alkaline electrolyzer model was HMXT-100 from Teledyne Technologies. The identification of the r, s, t parameters has been performed in Matlab [70]. Table 5 shows the value of the input parameters used in the model, while Table 6 illustrates the non-linear regression parameters. From experimental data, Faraday Efficiency has been modeled with a fourth degree polynomial interpolation (Eq. (32)) as function of stack current I. hFaraday ¼  0:9059 þ 0:0389$I  0:00037$I2 þ 0:0000016$I3  0:0000000024433$I4

(32a)

Hydrogen flow model data shows (Fig. 6) a very good match with experimental data, thanks to Faraday Efficiency interpolation. In the range between 41 A and 220 A the RMSE is about 0.045 Nm3/h and the RMSEP is about 0.0632. In the range between 50 A and 220 A, the model is more accurate, with an RMSEP value of 0.0222. The polarization stack curve has a maximum percentage error of 3.2%, and the voltage model results find a good approximation with experimental data, as shown in Fig. 7. Stack power, shown in Fig. 8, in the range between 50 A and 220 A is almost accurate, with a RMSE value of 0.536 kW and a RMSE of 0.0226.

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Fig. 2 e PEM polarization curve.

Fig. 3 e PEM stack power trend.

Fig. 5 e PEM system power trend.

160

Table 5 e Alkaline nominal parameters.

Percentage % [-]

140 120

Number of series-connected cells Operating Temperature [K] Stack Rated Power [kW] Operating Current [A] Hydrogen Nominal Flow [Nm3/h] Hydrogen Purity [] Cathode Nominal Pressure [bar] Anode Nominal Pressure [bar]

y = 79.153x-0.975

100 80 60 40 20 0 0

1

2

3

4

5

75 345 40 58 5.6 99.999% 9.44 9.44

6

Stack Power [kW] Ancillary Power

Model

Fig. 4 e PEM ancillary power percentage trend.

From stack power experimental data and system power, a fitting curve for ancillary power has been proposed with a polynomial interpolation, as for PEM Technology. %ancillary is function of Wstack , adopting Eq. (31). Coefficient values of this correlation are respectively a ¼ 192.76 and b ¼ 0.751. The trend of the percentage of the ancillary power is represented in function of the stack power in Fig. 9. System Power is the sum of stack power and ancillary power. As shown in Fig. 10, model results appear to have a good match with experimental data, with a RMSE value of

Table 6 e Alkaline model parameters. A [cm2], Cell, Active Area, r1 [Ohm m2], Empirical Coefficient r2 [Ohm m2/K], Empirical Coefficient s1 [V], Empirical Coefficient s2 [V/K], Empirical Coefficient s3 [V/K2], Empirical Coefficient t1 [m2/A], Empirical Coefficient t2 [m2/A K], Empirical Coefficient t3 [m2/A K2], Empirical Coefficient

2082 0.0004296 4.153e-07 0.1803 0 0 0.05171 2.415 8134

0.7188 kW and a RMSE of 0.0322 in the range between 50 A and 220 A. Appendix describes a further validation for the Alkaline electrolyzer, based on the voltage efficiency for the stack and the energy efficiency of the system.

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Fig. 8 e Alkaline stack power trend.

Fig. 6 e Alkaline hydrogen production trend. After the validation, it results that the Faraday efficiency of the analyzed alkaline electrolyzer is relatively low (about 70%). More modern and compact electrolyzers allow reaching almost unitary Faraday efficiency values. To make the model as flexible as possible, a further Faraday efficiency curve was introduced for better performance, experimentally validated through PHOEBUS electrolyzer (26 kW, 7 bar, 80  C) literature data [39,40], and the fitting equation used is defined in Eq. (32). Its parameter values are listed in Table 7, while its trend is shown in Fig. 11. 1

0

C Ba B I2 þ a32 C A @A hFaraday ¼ a1 $exp

I A

(32b)

Compared to Wind-to-Hydrogen Project electrolyzer [56], PHOEBUS higher values could be related to a new design development associated with on-going technical improvements for Alkaline technologies.

Electrolyzer model scaling-up and simulation results As many authors have highlighted in many states of the world [77], as in Japan [78], in Europe [79,80], or in California [81],

building a network of hydrogen infrastructures is a key step to help the hydrogen economy spreading out, and many governments and energy departments are already promoting projects of integration between hydrogen stations and renewable energies [82]. As reported in the last “Retail Hydrogen Fueling Station Network Update”, February 15, 2018, by members of the California Fuel Cell Partnership [83], a “connector station” size is about 180 kg/day, while “main stations” size is about 360 kg/ day. Fuel cell electric vehicles are already on the road, but since hydrogen stations in many countries are still at an early stage, it could be important to investigate connector stations with on-site production and their performance, helping the scientific community in the definition of lowcarbon hydrogen based supply chain. For this reason, in this paper, a “connector hydrogen infrastructure” has been considered, and the results obtained through the models have been scaled-up to obtain a 180 kg/day of hydrogen produced from renewable energy through water electrolysis. Fig. 12 summarizes the algorithm and the logic of the model. The developed mathematical model is based on the external “Function Optimization Box” by Matlab. By means of

Fig. 7 e Alkaline polarization curve. Please cite this article as: Fragiacomo P, Genovese M, Modeling and energy demand analysis of a scalable green hydrogen production system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.186

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60

Percentage % [-]

50

y = 192.76x-0.751

40 30 20 10 0

0

5

10

15

20

25

30

35

40

Stack Power [kW] Ancillary Power

Model

Fig. 9 e Alkaline ancillary power percentage trend.

Fig. 10 e Alkaline system power trend.

Table 7 e Alkaline faraday efficiency, coefficients. a1 [], Empirical Coefficient  2 cm , Empirical Coefficient A  4 cm , Empirical Coefficient a2 A2 a2

100:1 6.567

this tool, the model can receive as input experimental curves from real datasheets, tuning the semi-empirical parameters according to different brands of electrolyzer. The overall structure of the model is the same, both for alkaline technology and for PEM electrolyzers. The main difference can be found in the electrochemical domain, as described in Electro-chemical model. The main inputs of the model are the electrolyzer geometry (volumes of the anodic and cathodic chambers, active area of the cells), electrolyzer nominal parameters (nominal temperature and pressures), electrolyzer initial condition (temperature and pressure), external weather condition (temperature), working point for the stack current. As additional required inputs, there are the simulation time and station size chosen as a target, in terms of hydrogen production. Both values allow the model to calculate the hydrogen net production in the analyzed range of time. This process is iterative: the model analyzes the required number of cells in order to achieve the daily production target. In the fluid domain block, hydrogen and oxygen start to be produced and pressure increases in the chambers. Stack voltage fluctuates because of the pressure variations, and meanwhile, the chemical reaction generates a heat transfer rate, which together with the heat transfer rate caused by the external temperature and fluid movement, has to be disposed of by

4703

Fig. 11 e Alkaline new faraday efficiency trend. Please cite this article as: Fragiacomo P, Genovese M, Modeling and energy demand analysis of a scalable green hydrogen production system, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.186

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Fig. 12 e Synthetic summary scheme of the model.

mean of the thermal domain block, in order to assure the achievement of the target temperature. Once the pressure reaches its target point, as well as the stack temperature, the electrolyzer works at nominal conditions, and the algorithm extrapolates the nominal electrical power (kWe). Since the thermal capacity and the thermal resistance are a function of this nominal electric power, the algorithm re-iterates the calculations, including thermal inertia phenomena with thermal capacity and resistance. Temperature trend is very important, not only for thermal phenomena and cooling system, but also for voltage: Gibbs energy and enthalpy values are strongly influenced by temperature effect, as well as over-voltages rates and pressure values on the anodic and cathodic chambers. Indeed the model calculates and uses temperature simultaneously with pressure and voltage calculations. As a final result, the model calculates electrolyzer stack power and ancillaries influence, in addition to flow-related parameters (water consumption, oxygen and hydrogen production) and several energy design specification, such as maximum power, specific energy consumption and energy efficiencies.

The alkaline electrolyzer model resulted to have a good match with experimental data in the range between 75 A and 220 A for every parameter analyzed. For this reason, the scaling up and the interpreted results will focus on trying to maximize energy production in this range of current. Therefore the operating current has been set to almost the upper limit of the range. For PEM electrolyzer, the model had as outcomes power trends which are accurate in the range of 18 A and 135 A, while efficiency curves resulted to better match experimental data in the range between 63 A and 135 A. As for the alkaline technology, the operating current has been set to upper limit of the range with the goal to maximize energy production.

Scaling-up and simulation As discussed above, a “connector hydrogen infrastructure” is characterized by a 180 kg/day capacity. In order to produce 180 kg/day of hydrogen, PEM electrolyzer has been scaled up to a stack with 1600 series-connected cells working with a nominal current of 135 A, in the range where the model matches with good approximation the experimental data.

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Alkaline electrolyzer has been scaled up to a stack with 9000 series-connected cells working with a nominal current of 200 A, in the range where the model matches with good approximation the experimental data. In the scaling-up process, pressures in the anodic and cathodic chambers have been set to same values used for the experimental validation. PEM electrolyzer has different nominal pressures in anode and cathode, since the electrolytic membrane usually designed to resist pressure delta, while alkaline electrolyzers are characterized by a liquid electrolyte, and therefore the chambers are considered to have the same pressure. Nominal temperature value has been increased to 353 K, which is usually the nominal operating point for electrolyzers commercially available. In fact, a higher temperature reduces the over-potential rates and then it increases the overall efficiency of the system. Operating points and parameters are shown in Table 8 for both technologies. Simulations have been carried out with a daily-basis as a range of time, considering thermal phenomena, startup, nominal points reaching and operation. Table 9 shows the main output parameters of the model, which describe the performance and the daily energy required by the electrolyzer system.

Table 9 e Simulation results. Parameter Faraday Efficiency Hydrogen Produced Hydrogen Flow Ideal Water Consumption Real Water Consumption Water Flow Rate LHV Stack Efficiency HHV Stack Efficiency Reversible Voltage Thermo-neutral Voltage Cell Voltage Electrolyzer Maximum DC Power Electrolyzer Required Energy Auxiliary Power Percentage Electrolyzer Maximum Ancillary Power Electrolyzer Ancillary Energy Electrolyzer Maximum Cooling Power Electrolyzer Needed Cooling Energy Electrolyzer LHV Efficiency without ancillary Electrolyzer LHV Efficiency Electrolyzer Specific Energy Consumption Heat Power/Electric Power

PEM Alkaline 0.945 182.46 85.2 1645 2048 0.001 0.620 0.774 1.182 1.486 1.979 427.48 10.26 0.220 0.921

0.986 180.04 84.1 1620 2018 0.001 0.486 0.621 1.189 1.485 2.198 448.4 10.76 1.97 8.82

[] [kg] [Nm3/h] [l] [l] [l/h] [] [] [V] [V] [V] [kW] [MWh] [%] [kW]

0.0221 0.106

0.212 0.145

[MWh] [MW]

2.539 0.6

3.482 0.56

[MWh] []

0.59 56.93

0.54 61.96

[] kWh/kg

0.24

0.31

kWt/kWe

Technologies comparison and result discussions As shown in Table 9, there are several energy parameters as model output. It is the aim of this paper also to compare these parameters considering the application of modern technology (PEM Electrolyzer) and more mature technologies (Alkaline Electrolyzers). The comparison has been done scaling up the electrolyzers to produce the same amount of hydrogen (180 kg) in 24 h, in order to simulate a daily operation of hydrogen connector infrastructure. Concerning hydrogen production parameters, for the input values chosen in model simulation, in this case, Alkaline is producing hydrogen with fewer losses associated with leakage currents and parasitic currents. The parameter which takes into account these phenomena is the Faraday Efficiency, which is a couple of percentage points higher for Alkaline than for PEM one. As a consequence, with almost the same amount of hydrogen produced, the alkaline electrolyzer is requiring a little less water to be fed (about 30 liters less than PEM real water consumption). From this point of view, the hydrogen

Table 8 e Model simulation parameters. Parameter Number of series-connected cells Membrane Cross Section Area Nominal Temperature Anode Nominal Pressure Cathode Nominal Pressure Anode Volume Cathode Volume Simulation Time Operating Current Electrolyzer Initial Temperature

PEM

Alkaline

1600 100.00 353 2.00 13.44 0.001 0.001 24 135 353

1020 2082.00 353 9.44 9.44 0.001 0.001 24 200 353

[] [cm2] [K] [bar] [bar] [m3] [m3] [h] [A] [K]

production process appears more mature for alkaline technology. Considering the process irreversibility associated with the ohmic, activation and diffusion losses, it is possible to notice how the point of operation of the PEM electrolyzer is more advantageous, since the cell voltage is closer to its reversible voltage than the Alkaline result, indicating the presence of fewer losses associated with over-voltages and consequently less energy used to cope with such phenomena. Other parameters that allow analyzing the influence of the irreversibility are the LHV Stack efficiency and the HHV Stack efficiency, which confirm the PEM electrolyzer better voltage efficiency. In fact, the values of LHV and HHV stack efficiencies for a PEM are about 13e15 percentage points higher than the Alkaline. Indeed, from an energy point of view, very interesting parameters are the electrolyzer maximum DC power (important for power electronics to be installed, as inverters and transformers, and for coupling with any renewable energy system), and the electrolyzer required energy (which is the most important rate of energy demand of a hydrogen infrastructure). Between PEM and Alkaline electrolysis, the first one seems more energy efficient, requiring 500 kWh less than the other electrolyzer, with also 30 kW less of installed power. Auxiliary system seems to play a more important role for Alkaline than for PEM electrolyzer: it requires about 22 kWh for PEM and about 10 times for Alkaline, corresponding to about 2% of the installed electrolyzer power. According to Eq. (31), this percentage is an exponential function, decreasing with the installed power. This trend represents realistically the whole of the auxiliary system associated with an

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electrolyzer. In fact, part of this system always works with the same installed power (such as emergency lights, alarms, sensors, and gas detectors), and partly that is variable with the operation of the electrolyzer (in particular those of the circulation pump, and those associated with system cooling, such as the external circulation pump, the chiller or the cooling fan). As an alkaline system has a more complex cooling and circulation management system, it is understandable to justify a greater influence of the auxiliaries in its energy consumption. In fact, analyzing the terms associated with cooling and thermal management, it is possible to notice that, while a PEM system requires about 2.5 MWh of needed cooling energy with a maximum power of 106 kW, an Alkaline system requires more effort, with about 3.5 MWh of needed energy and 145 kW maximum power. These larger thermal aliquots of an alkaline electrolyzer, are also associated with the larger dimensions that this electrolyzer presents, which make the heat dissipation slower. On the other side, it could be possible to improve the energy efficiency of the system, trying to exploit this heat, which must be disposed of, using it for example for the production of domestic hot water. In these cogeneration applications, a fundamental parameter for the design is the relationship between thermal power and electric power, presented in this paper as a ratio between the two quantities. For Alkaline electrolyzer, this ratio shows a value of 0.31 kWt/kWe, while for PEM one it has a value of 0.24. Overall energy system parameters are the total electrolyzer LHV efficiency, which considers the overall electrical energy demand, and the specific energy consumption, which is an intensive property easy to understand and that reveals how much energy the electrolyzer system needs to produce one kg of hydrogen. Comparing the two technologies, Alkaline presents a 56% of overall efficiency with 65 kWh/kg of energy consumption, while PEM electrolyzer shows a higher efficiency value, about 60%, which is a consistent value compared also to other power to gas technologies, and a lower specific energy consumption of about 57 kWh/kg. The higher energy performance of PEM technology versus Alkaline is one of the key reason for the dissemination and focus of this technology by the entire international scientific community.

For this reason, in this paper models with a simple approach have been implemented, considering multi-physical phenomena (fluid-dynamic model, thermodynamic model, electrochemical model and thermal model, too, to determine the transient thermal behavior of the stack). Part of the main parameters has been extrapolated with regression technique from existing polarization curve. Then, the model results have been validated using experimental data extrapolated from Ref. [56]. PEM and Alkaline models showed a good match with experimental data, with RMSEP values under 0.10. Nowadays, model-based design is becoming a very powerful tool also in new technologies, allowing a deep understanding of components integration and facilitating the forecasting of energy performance, saving on the costs of early-stage experiments. For this reason, a scaling-up of the model results has been performed, in order to investigate a 180 kg/day hydrogen infrastructure with on-site production through water electrolysis. As a result of the analysis carried out in this paper, PEM technology appears very efficient in terms of energy consumption. Through all parameters investigated, three main interesting areas can be outlined:

Conclusions

The approach used in this work allows the development of an intuitive and fast model. Its potential applications could be as a tool for designing, sizing or investigating hydrogen infrastructures with on-site production systems, predicting the overall energy demand. The model is also based on real physical domains, a key feature that could facilitate phenomena understanding, diagnostic of new control strategies, as well as THE development of new techniques of energy management.

From a phenomenological point of view, an electrolysis system is a complex system in that it involves many components and multi-physical phenomena. The main goal of this paper was to estimate the energy demand of a water electrolysis system, in order to understand how much energy can be stored from renewable energy and in order to introduce hydrogen as energy storage and buffer to face to fluctuations and intermittency in renewable energy-based plants. Models based on too many parameters are very complex and burdensome, and infrastructures operators and companies may find it difficult to adopt them as a tool for the sizing of these technologies, especially when the goal is not the improvement of electrochemical technology, but the study of the overall energy flows.

1. Hydrogen production area and their parameters; in this area Alkaline electrolyzer seems to be more performancecentered thanks to its greater maturity; 2. Irreversibility, over-voltages, and their related parameters. In this area, PEM operating point makes the values stack efficiencies about 13e15 percentage points higher than the Alkaline; 3. Energy Consumption, auxiliary influence and overall system efficiency. Through this analysis, in order to produce 180 kg/day of hydrogen, PEM electrolyzer appears the best solution from an energy point of view: it requires about 10 MWh per day, with a System Efficiency around 60%. In terms of thermal energy management, the PEM modeled system requires about 2.5 MWh of needed cooling energy with a maximum power of 106 kW, while the alkaline one requires more effort. This also related to auxiliary system influence, which for the PEM electrolyzer are playing a less important role. As overall conclusion, PEM system shows a specific energy consumption of about 57 kWh/kg, compared to the alkaline value, which is about 65 kWh/kg.

Acknowledgments The research was supported by the grant PON RI 2014e2020 for Innovative Industrial PhD (CUP H25D18000120006 and Code

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DOT1305040), funded by the European Union and the Italian Ministry of Education, University and Research (MIUR).

Nomenclature % a1

Percentage [] Faraday Efficiency Coefficient

a2

Faraday Efficiency Coefficient

a3 ACell Ct Erev F i

½   cm2 A



cm4 Faraday Efficiency Coefficient 2 A Active Cell Area [cm2 ] Total thermal capacity of the electrolyzer ½kJ = K Reversible Voltage [V] Faraday constant, 96485000 [Coulomb/kmol]  A Current Density cm 2

r1 r2 R Rt s1 s2 s3 t t1 t2 t3 tm T Utn V VCELL W z

Exchange current density [A/cm2] Limit current density [A/cm2] Direct Current [A] Mole [kmol] Molar flow rate [kmol/sec] Number of cells [] Pressure [Pa] Heat transfer rate required to cool down the system [W] Heat transfer rate generated by the chemical reaction [W] Heat transfer rate caused by the external temperature [W] Empirical Coefficient [Ohm m2] Empirical Coefficient [Ohm m2/K] Universal gas constant, 8314:3 ½J =ðkmol $KÞ Total thermal resistance of the electrolyzer ½K =W Empirical Coefficient [V] Empirical Coefficient [V/K] Empirical Coefficient [V/K2] Time [sec] Empirical Coefficient [m2/A] Empirical Coefficient [V/K] Empirical Coefficient [m2/A K2] Membrane Thickness [cm] Temperature [K] Thermo-neutral Voltage [V] Volume [m3 ] Cell Voltage [V] Power ½W Number of free electrons []

Greek a b DG DH hFaraday lm

Charge transfer coefficient [] Empirical Coefficient [] Free Gibbs energy of formation variation [W] Enthalpy of formation variation [W] Faraday Efficiency [] Membrane Water Content []

i0 ilim I n n_ Nc p Q_ cooling Q_ gen Q_ loss

Subscript a Parameter related to ambient conditions act Parameter related to activation phenomena an Parameter related to anode chamber

ancillary cell diff elec H2 H2 O2 ohm system stack target

15

Parameter related to the ancillary system Parameter related to electrolyte cell Parameter related to diffusion phenomena Parameter related to electrolyzer Parameter related to hydrogen O Parameter related to hydrogen Parameter related to oxygen Parameter related to ohmic phenomena Parameter related to the cell system Parameter related to the cell stack Value to achieve

Superscript a Parameter accumulated comp Parameter taken away through a compressor out Parameter in output from the system p Parameter related to production T Parameter calculated with a certain value of temperature

Appendix This appendix is an integration of the work with further validation of the developed mathematical model based on the voltage efficiency for the stack and the energy efficiency of the system. Model results have been compared with experimental data from Wind-to-Hydrogen Project from National Renewable Energy Laboratory (NREL) in their Technical Report NREL/ TP-550-44082 (March 2009) [56]. In order to determine stack voltage efficiency (Eq. (A.1)), thermo-neutral voltage Etn has been used, accounting also for the whole energy involved in the process, compared with the stack operating voltage. The voltage efficiency allows to understand how much the actual voltage is departing from a stack voltage ideal condition. Stack Efficency ¼

Ideal Voltage Etn ¼ Actual Voltage Vcell

(A.1)

with the goal to represent the overall system efficiency, both thermal and electric energies have to be considered as the whole energy demand to operate water dissociation. The minimum and ideal amount required is the higher heating value, which is the total (thermal and electrical) amount of energy required to dissociate water (higher heating value, HHV). A real system requires more energy. Indeed, the system efficiencies are defined in Eq. (A.2) and Eq. (A.3). DH Wsystem

(A.2)

DG Wsystem

(A.3)

System EfficencyðHHVÞ ¼

System EfficencyðLHVÞ ¼

where Wsystem is the system power. Another way to describe system efficiency is to define it with the free Gibbs energy of formation, which represents the lower heating value (LHV). Fig. A.1 shows model stack efficiency vs experimental stack efficiency for PEM technology.

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Fig. A.1 e PEM stack efficiency trend.

Fig. A.3 e PEM system efficiency LHV trend.

Model stack efficiency shows a RMS of 1.886 and a RMSEP of 0.02 in the range between 18 A and 135 A. It results more accurate in the range between 63 A and 135 A, with a RMSEs of 0.65 and a RMSEP of 0.00855. Figs A.2 and A.3 show both PEM system efficiencies and their comparison between model results and experimental data. Both efficiencies show a better correlation and match with experimental data in the range between 63 A and 135 A, with RMSEs under 0.018 and RMESPs under 0.043.

Considering Alkaline technology, Figure A4 shows model stack efficiency vs experimental stack efficiency. Model stack efficiency shows an RMS of 1.986 and an RMSEP of 0.02382 in the range between 50 A and 220 A. The outputs of the models are more accurate in the range between 75 A and 220 A, with an RMSEs of 1.375 and an RMSEP of 0.017.

Fig. A.2 e PEM system efficiency HHV trend.

Fig. A.4 e Alkaline stack efficiency trend.

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Figs A.5 and A.6 show both alkaline system efficiencies for model and experimental data. Both efficiencies show a better correlation and match with experimental data in the range between 50 A and 220 A, with RMSEs under 1.8 and RMESPs under 0.048.

Fig. A.5 e Alkaline system efficiency HHV trend.

Fig. A.6 e Alkaline system efficiency LHV trend.

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