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Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases
international journal of hydrogen energy xxx (xxxx) xxx
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Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases Mayken Espinoza-Andaluz a,*, Jordy Santana b, Martin Andersson c nica y Ciencias de La Produccion, Centro Escuela Superior Politecnica Del Litoral, ESPOL, Facultad de Ingenierı´a Meca de Energı´as Renovables y Alternativas, Campus Gustavo Galindo Km. 30.5 Vı´a Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador b nica y Ciencias de La Produccion, Escuela Superior Politecnica Del Litoral, ESPOL, Facultad de Ingenierı´a Meca Campus Gustavo Galindo Km. 30.5 Vı´a Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador c Lund University, Department of Energy Sciences, Lund, Sweden a
highlights An experimental study of a single PEFC with 25 cm2 of effective area is carried out. The impact of the relative humidity on the performance of a PEFC has been analyzed. Correlations for current and power density as a function of RHs have been proposed. Predictions for current, power and RH related to the temperature have been proposed.
article info
abstract
Article history:
The growing energy demand and the impact of polluting gases lead to the necessity of
Received 3 January 2019
alternative energy sources and conversion energy devices. Fuel cells (FCs) appears as a
Received in revised form
suitable solution for facing the mentioned issues. Predicting the behavior of a polymer
19 August 2019
electrolyte fuel cell (PEFC) under different conditions represents a proper initial step to
Accepted 12 September 2019
solve the several issues, e.g., aging water balance problems, which occur inside the cell
Available online xxx
during the energy conversion process. Understanding microstructural impacts of the diffusion media, water management issues of FCs or the impacts of the inlet reactant gases
Keywords:
to the cell represent some of the processes that have to be analyzed to improve the effi-
PEFC
ciency and behavior of FCs.
Relative humidity
The current study aims, based on experimentally collected data, to propose empirical
Membrane resistance
correlations that describe and predict the performance of a PEFC. The single cell considered
Power density
in this study corresponds to a single PEFC with a Nafion® 112 membrane as electrolyte and
Current density
with an effective area of 25 cm2. Relative humidity as a function of the reactive inlet gas temperature, as well as the power and the current density as a function of the cell/reactant gas temperature gradient are analyzed. In addition, correlations for power and current density as a function of the relative humidity (RH) have been proposed. Our correlations are obtained for an operating voltage of 0.6 V. It was shown a strong correlation between the power and current densities with the RH since the membrane conductivity depends mainly on the water content. The PEFC behavior was evaluated at different RHs. The results show
* Corresponding author. E-mail address: [email protected] (M. Espinoza-Andaluz). https://doi.org/10.1016/j.ijhydene.2019.09.098 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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big losses of operating power and current densities, as well as an increment of the resistance of the membrane when it operates at low RH. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The results of studies regarding atmospheric CO2 levels shows that the global temperature in 2100 will likely reach levels which would lead to severely damaging long-term impacts [1]. Due to this, the fuel cell (FC) technology emerges as a source of clean energy that supplies the required energy to different sectors [2]. A polymer electrolyte fuel cell (PEFC) is an electrochemical device that provides electrical energy from the chemical reactions that occurs in two catalytic regions due to the interaction of fuel flow (H2) and oxidant flow (O2), respectively. PEFC has been the most researched cell type in the last 7 years according to “The Fuel Cell Industry Review 2017”, at the same time they are also the most improved FC related to power delivery [3]. It offers a quick start-up time since it operates at a relatively low temperature (80 C) resulting in an increment of its durability. Currently, research are focused on increasing the efficiency and reducing costs of the fuel cell systems facing several issues, such as obtaining new materials to build up bipolar plates in order to reduce costs [4]. The hydrogen storage systems for transport applications is other area that has been extensively researched as presented by Refs. [5,6], the influence of the catalyst structure in PEFC cell is reviewed by Carcadea et al. [7], while Kongkanand et al. [8] considered the development of new catalytic materials for the membrane electrode assembly (MEA). From a modeling point of view, a study investigated transport parameters in the GDL under certain compression conditions [9]. To improve and understand the diffusion transport process of the reactant gases, several studies have been performed [10e13]. In addition, a detailed literature review about cell-scale multiphase flow modeling was presented by Andersson et al. [14]. Several studies show that one of the most important factors in the performance of a FC is the water management [15e19]. The water vapor produced in the cathode side can be condensed which causes flooding of the diffusion media giving a reduced efficiency during the energy conversion process. The water balance is a critical issue in water management for current PEFC technologies [16]. The lack of water management in PEFC systems can trigger dehydrations when working at elevated temperatures [17]. Therefore, the inlet fuel/oxidant gases commonly enter to the PEFC after a previous humidification stage. However, an excess of humidification in the inlet gases causes flooding producing a partial or total blockage of the diffusion media [18]. Recent studies have focused on the effects of the relative humidity (RH) on the MEA. A complete performance test has been considered in several studies [20e22], modeling the flooding channel during the energy conversion process has been analyzed by Machado et al. in Ref. [20], liquid water distributions using computational tools
have been studied Iranzo et al. in Ref. [21]. The effects of deterioration of the MEA have been considered by Wu et al. in Ref. [22], and Xie et al. [23] and the characterization was studied by Kim et al. in Ref. [24], showing the performance changes on the PEFC. In addition, a decrement of oxygen reduction kinetics and proton conduction losses which occur within the catalyst layers (CLs) Fig. 1 is especially important at low relative humidity. Results indicate that at low RH the ionic conductivity is decreased, while the proton exchange resistance of the membrane increases [26]. In addition, the kinetic reaction is also affected decreasing its rated, and the mass transfer in the MEA is increased. Most of the studies are only focused on the main variables versus the current density, but not on the relationship that exists between the other variables that influence the performance of a PEFC, such as RH, anode temperature, cathode temperature, power density and ohmic resistance. The aim of this paper, in addition of showing the traditional performance curves of a fuel cell PEFC, is to propose empirical correlations and to explain the behavior of a PEFC with a Nafion® 112 membrane based on experimental data. Correlations for current and power density at the operating voltage of a PEFC are also presented. The rest of the paper is divided as follows: Experimental set-up, physical characteristics, and properties of the single PEFC is given in Experimental. Obtained results considering the variables involved in the study as well as the proposed correlations are presented in Results and discussion. Finally, in Conclusions, conclusions and discussions are given.
Experimental The present study was carried out with a Fuel Cell Test System 850e from Scribner Inc., which is a complete test station for operation and measurement of the performance variables of a PEFC. Among the main components of the system can be mentioned: a mass flow controller, water humidifier tank, temperature controller in anode/cathode and in the cell, it also has a data acquisition card that displays the results in a peripheral device. The structure of the system is detailed in Fig. 2. The equipment is able to control the current load to evaluate the performance and obtain the polarization curves of PEFCs. The acquisition process depends on the parameters to be analyzed. Readers interested in more detailed information about the FC Test System are referred to Ref. [27]. A single PEFC was used for the experiments, and the electrolyte is a polymer membrane Nafion® 112. The external view of the FC stack is shown in Fig. 3. As usual, the membrane is sandwiched between the catalyst plates containing platinum nanoparticles, and in turn they are inside the gas diffusion layers,
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 1 e Scanning electron microscopy of a MEA. Adapted from Ref. [25].
all these elements forming the MEA. The bipolar plates have an effective area of 25 cm2, with a three channels design which contribute to distribute the reactants in the MEA. These channels have a serpentine shape with a width and depth of 1mm/1 mm, respectively. Those data are according to the manual of experimental methods and data analysis for a PEFC [28]. Once the FC equipment installation is stated and communications requirements have been reached, the cell is ready to start up. The gases used during the current experiment are H2 (anode side) and O2 (cathode side), where the anode and cathode pressure are kept at 55 psig. In addition, N2 was used to purge the waste in the ducts that transmit the main reactive gases, as a safety measure. The water used was ASTM Type I (with 18 MU/cm minimum resistivity). The MEA was tested at 80 C under ambient pressure conditions, i.e., 1 atm, and data were collected by varying the temperature of the H2/O2 reactive gases in the anode/cathode from 40 C to 80 C in steps of 10 C. The reactive gases entered with 100% humidification at the set temperature. The RHs were calculated as the ratio between the saturation pressure at the temperature of the inlet gases and the saturation pressure at the MEA temperature. The current study was done for symmetric RHs at the anode and cathode. The values of the flow rate of reactants were configured according to the study presented by Calle et al. [30].
Results and discussion The effect of RH on the behavior of PEFCs, the computation of RH as a function of temperature and proposed correlations for power and voltage of a PEFC are also presented in this section.
Fig. 2 e Schematic of the FC test system used in the current study. Adapted from Ref. [27].
Effects of the RHs on fuel cell in the literature To maintain and improve performance in the operation of a FC, it is necessary to know the behavior of the variables that greatly affect the process of operating, one of which is the hydration of the proton exchange membrane. Hydration is an essential requirement for the membrane to work optimally, because the proton conductivity has a relationship directly proportional to its water content, in addition to being a key factor in the useful system life time. The membrane must work humidified throughout the operation time of the FCs; which is achieved by humidifying the H2/O2 reactive gases. The humidified reactive gases enter the anode/cathode channels respectively, encountering their respective catalytic layers, where a proton stream with water molecules passes through the membrane from the catalytic layer of the anode to the catalytic layer of the cathode. It is known as electro osmotic drag. On the other hand, in the catalyst layer of the cathode, the O2 molecules react with the H2 cations, producing water. The water formation in the cathode produces a gradient of concentration in the membrane, and therefore appears a transfer of water from the cathode to the anode, this process is known as back diffusion. Finally, the water that remains on the side of the cathode is drained outside of the
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 3 e Picture of the single PEFC used in this study (left), and exploded view of the analyzed cell (right). Adapted from Ref. [29].
system. In the absence of hydration of the membrane there is a low proton conductivity, i.e., correct water management is required to maintain the hydration of the membrane and to work with great performance. The concept of relative humidity (RH) is introduced which gives a numerical hydration of the membrane relative to the water content of the reactive gases. Due to the importance of a previous humidification of reactive gases, several studies have been carried out on the effects that RH produces on the performance of a FC, some results are presented in Table 1. As observed, the performance of a FC has a great dependence on the degree of RH. In a study presented by Xu et al. [31], the polarization curve was used to analyze the losses for the voltage and the ohmic resistance as a function of the current density. The single cell analyzed was of active are 5 cm2 and the electrolyte a Nafion 112. The operating temperature was established at 120 C, and the symmetric RH was decreased from 100% to 20%. As result, the ohmic resistance increased from 0.092 to 0.407 U cm2. In addition, for a current density of 600 mA/cm2, the cell voltage decreased from 0.617 V to 0.226 V. Zhang et al. [32] carried out a study using a Nafion 112 electrolyte with an active are of 4.4 cm2. In this study the testing of the performance of the FC was performed at exact values of 100% and 0% of symmetric RH at operating temperature of 80 C. Results showed a considerable reduction of the resistance cell. It was concluded that the lower performance is mainly caused by the low velocity of proton transfer within the catalyst layers. The last mentioned issue was analyzed using an impedance AC analysis. They also performed an study considering high temperatures [17]. The tests were carried out using and AC impedance method and measurements of cyclic voltammetry
for several conditions of symmetric RHs. Results showed a significant reduction of the kinetics of the electrode. The conductivity of the membrane was also affected producing too much losses in the performance. In the study performed by Yan et al. [33], an individual analysis of the anode and cathode was carried out. They configured different RHs at the anode/ cathode side varying the inlet temperature of the reactant gases until reaching the 100% of humidification at its corresponding saturation temperature. The analyzed cell had an effective area of 5 cm2. Results show that the humidification of the inlet gases in the cathode side has a significate impact on the performance of the FC. Experimental results show that the decrease in RH on the cathode side has a harmful effect on the FC stability and its dynamic performance. In addition, they showed that for medium and higher RHs at the cathode side is good enough to maintain the membrane hydrated without any additional humidification of the anode side reactant gases. This occurs due to a sufficient inverse diffusion from the cathode to the anode side. Similar to previous studies, Saleh et al. [34] performed experimental tests with symmetric and asymmetric RHs with an effective area of 25 cm2. They concluded that the performance of the cell increases with an increase of the RH at the anode side, however, it is possible to obtain an acceptable performance of the cell for with 100% RH at the anode. This indicates that the RH at the cathode side has a strong influence on the membrane hydration. Moreover, they conclude that to high temperatures higher RHs are required to obtain a proper membrane hydration while that at lower temperatures a limited diffusion of the reactant gases is observed at conditions of high RHs. On the other hand, Amirinejad et al. [35] found that the humidification at the
Table 1 e Results of experimental studies considering the relative humidity of reactant gases. Membrane Nafion Nafion Nafion Nafion Nafion Nafion
112 112 112 112 212 117
Active area (cm2)
Operating Temperature ( C)
Operating current density (A cm2)
Relative humidity (%)
Membrane resistance (U cm2)
Power density (W cm2)
Ref.
4.4 5 4.4 5 25 5
120 120 80 65e85 70e90 70
0e2.1 0.2 0.1e1.2 0e0.5 0.1e1.4 0.2
25e100 20e100 0e100 0e100 0e100 0e100
~0.15e0.75 0.092e0.407 ~0.1e0.5 ~0.15e0.65 ~0.1e1.75 e
0.1e0.6 e 0.25e0.62 e 0.05e0.4 ~0.075e0.13
[17] [31] [32] [33] [34] [35]
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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anode has a bigger impact on the performance of the cell in comparison with the humidification of the cathode which does not agree to previous studies. This discrepancy is mainly due the operating conditions and characteristics of the analyzed cells.
Effects on the performance of the single cell studied In the current study, to analyze the performance of the single FC, typical ‘curves’ were obtained at different symmetric RHs. The cell was established to be working at a constant temperature Tcell ¼ 80 C, while the inlet temperature of the reactant gases was changed between 40 C and 80 C with steps of 10 C. The minimum RH considered in this study, i.e., 16%, was obtained when the inlet temperature of the reactant gases is 40 C while the maximum RH was 100% which occurs when the inlet temperature of the reactant gases reached 80 C. The performance of the cell voltage as a function of the current density is presented in Fig. 4. Considering the RH variations, it is also observed a strong influence of the humidification of the reactant gases. Maximum and minimum current density of 1887.2 mA/cm2 and 219.7 mA/cm2 were obtained for 100% and 16% of RH, respectively, i.e., a reduction of the RH produces a wide reduction of the operating range. In addition, the voltage loss in the activation zone is reported as 80 mV varying between 0.88 V and 0.80 V. It is clear that at low RH the losses for proton transfer are noticeable due to the low water content of the membrane and therefore the resistance of the membrane increases. The opposite situation occurs at high RH; the proton conductivity has a great improvement. The obtained results show a good agreement with that was reported in previous studies [17,28,30e36]. Fig. 5 shows the behavior of the power density as a function of the current density considering different RHs. For 100% and 16% of RH the obtained power densities are 561.1 mW/cm2 and 68.6 mW/cm2, respectively. According to the obtained results
5
a reduction of 493.1 mW/cm2 when the RH varies in the analyzed range was observed. Similar to the voltage-current behavior, the power density reaches bigger values when RH increases. It is important to mention that the power density curve increases until a maximum value is obtained and then it has a decreasing behavior. This trend is due to the mass transport losses which normally occur when the FC is working at high current densities and temperatures. The ohmic resistance of the membrane was also analyzed for different RHs. Fig. 6 shows the behavior of the resistance as a function of the current density, considering the different RHs of the reactant gases respect to the cell. At high RHs the membrane absorbs a greater quantity of water compared to at low RHs, i.e., the ionic channels in the catalyst layer are filled in a bigger proportion improving the protonic transfer. This phenomenon gives a decreased protonic resistance when the RHs increase. This implies that the kinetic reactions inside a FC at low RHs are considerable lower than for higher RHs, which agrees with published studies [37,38]. It was found that for a RH 60% the resistance of the membrane is around 125 mU cm2, and it has a constant trend, i.e., the cell can operate in stable conditions independently of the power demand. However, this behavior does not occur at lower RHs when, for example at RH 16%, average membrane resistance of 600 mU cm2 is observed. The curves at lower RHs present a parabolic trend, which occur due to at low RH the produced water at the cathode side increases from zero to a certain value when the operating time increase. As result of the inverse diffusion, the catalyst layer at the anode side is humidified and the conductivity of the membrane is improved. However, when the cell starts to operate at high current and power densities, the diffusion through the membrane is not enough and pore obstructions at the catalyst layer appears. This yields an increase in the membrane resistance, which can explain the increase at the end of the curve.
Fig. 4 e Performance curve for cell voltage as function of current density for different RHs. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 5 e Performance curve for power density as a function of the current density for different relative humidity.
Fig. 6 e Performance curve for resistance membrane as a function of current density for different RHs.
Predicted relative humidity (RH) correlations for a single PEFC As showed in Table 1, the RH between the reactant gases and membrane has a large effect on the behavior of the cell, i.e., it is necessary to quantify or have an estimation of the RH. Most of the FC test systems have humidification tanks for which the reactant gases pass before they enter into the anode and cathode channels. The temperature and humidity sensors allow to humidify the reactant gases according to the requirements. As the inlet temperature of the reactant gases can be different to the temperature of the cell, the humidification degree changes as the temperature changes. One way to obtain an approximation of the RH, is
by means of thermodynamic tables. It is made dividing the saturation pressure of the inlet temperature of the reactive gases (considering symmetric RH) to the saturation pressure at the cell temperature. However, the mentioned procedure is cumbersome. Considering the difficulty, three possible correlations are proposed to calculate the RH in Table 2. These correlations are functions of the H2/O2 reactive gas temperature with respect to a cell temperature set to 80 C. This cell temperature was considered because it obtains maximum electrical efficiency according to Ref. [39]. All the proposed correlations in this study are constructed considering the collected data under the specified conditions and with the help of fitting tools provided by Matlab® toolbox.
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Table 2 e Proposed correlations to compute the RH as a function of inlet temperature of fuel/oxidant gases. Type
Correlation
R-square
Polynomial
RHðTÞ ¼ 0:0381T2 2:538T þ 58:24
0.9986
NRMSD (%) 1.50
Exponential
RHðTÞ ¼ 3:214e0:04308T
0.9986
1.25
Power
RHðTÞ ¼ ð5:329 104 ÞT2:766
0.9965
2.17
Fig. 7 e Correlation better adjusted to the experimental data for RH as a function of the inlet temperature of fuel/oxidant gases.
The behavior of the RH is best explained with an exponential correlation. Because it has a R-square value of 0.9986 with a normalized root mean square deviation (NRMSD) of 1.25%, which estimates the percentage of the associated error with the predicted model. Note that when the inlet temperature of the reactant gases is higher than the ambient temperature, the RH increases rapidly. In addition, it is also observed that an equal temperature of the reactant gases and the cell gives a 100% humidification of the membrane. In Fig. 7, the correlation best fitted to the experimental data is depicted. The errors between the experimental data and the values computed with the empirical correlation are presented in Appendix.
Predicted performance correlations for a single PEFC To understand how the RH impact the behavior of a PEFC inoperando, empirical correlations are suggested based on our experimental data. The selected data are according to the average voltage that a FC delivers in working operation, i.e.,
0.6 V [40]. In the same way three possible empirical correlations to evaluate the power as a function of temperature difference, i.e., cell temperature minus the temperature of the inlet gases anode/cathode are presented in Table 3. According to the obtained results, the correlation that best fit the collected data is the polynomial type. The selection was carried out based on the R-square and the NRMSE. For the first statistic parameter, i.e., R-square, the polynomial and rational have similar value, and therefore the decision is made considering the NRMSE which is better for the polynomial correlation. Note how the Power Density is greater when the Temperature Difference tends to zero, that is, the maximum power density is obtained when the temperature of the reactive gases is equal to the cell temperature, this case is met for 80 C, Equivalent to a relative humidity of 100%. Fig. 8 shows the selected correlation together with the experimental data. The empirical correlations to evaluate the current density as a function of the temperature difference between the gas inlet and the cell, are presented in Table 4. Similar to the
Table 3 e Proposed correlations for power density as a function of the temperature difference at 0.6 V. Type
Correlation
R-square
NRMSD (%)
Polynomial
PðDTÞ ¼ 0:1246DT 11:87DT þ 301:2
0.989
5.16
Exponential
PðDTÞ ¼ 308:1e0:05015DT
0.970
7.42
0.989
5.91
Rational
2
PðDTÞ ¼
4:4E4DT2 ð4:152E6ÞDT þ ð1:048E8Þ DT þ ð3:473E5Þ
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 8 e Correlation better adjusted to the experimental data for power density in function delta temperature.
Table 4 e Proposed correlations for current density as a function of the temperature difference at 0.6 V. Type
Correlation
R-square
NRMSD (%)
Polynomial
JðDTÞ ¼ 0:2083DT 19:81DT þ 502:5
0.987
5.11
Exponential
JðDTÞ ¼ 513:8e0:05017DT
0.970
7.40
0.986
5.93
Rational
2
JðDTÞ ¼
9:091E4DT2 ð8:409E6ÞDT þ ð2:095E8Þ DT þ ð4:152E5Þ
previous analysis, the three best correlations have been grouped to select one based on the statistic parameters. As shown in the previous table, the R-square values are similar for the polynomial and rational curve, the selection is
made based on the NRMSD, according to this value, the correlation that best describe the current density as a function of temperature difference is the polynomial type. Fig. 9 shows the selected correlations together with the experimental data,
Fig. 9 e Correlation better adjusted to the experimental data for current density in function delta temperature. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 10 e Correlation better adjusted to the experimental data for power density and current density in function RH.
Note that the greater operating range is obtained with a delta temperature of zero, that is, for 100% RH. It is important to notice that for power and current density the trends were similar, this is given due the relation of the analyzed data with the Ohm's law since the power is proportional to the voltage and the current. Additionally, the impact of the temperature is clear and it affects the cell performance. If the temperature difference is high, the current density and power density suffer big losses. The highest power and current density are obtained when the temperature difference is zero, i.e., RH equal to 100%. However, if the temperature difference is 20 C, i.e., the inlet reactants temperature is 60 C, and having a RH of 42% the power density and current density are around 100 mW cm-2 and 180 mA cm-2, respectively. The results obtained in the current study are acceptable if compared with the reported values in Table 1. A similar analysis was performed to correlate the power and current density as a function of the RH. The following correlations were selected to evaluate the mentioned variables: PðRHÞ ¼ 1:546RH1:148
(1)
JðRHÞ ¼ 2:572RH1:148
(2)
Eq. (1) and Eq. (2) were selected with at same R-square of 0.979, and NRMSD of 6.17 and 6.18 respectively. Fig. 10 shows both correlations together with the experimental data. Finally, in Table 5, a summary of the correlations proposed in this study is shown. This table includes the R-square and NRMSD in percentage, evaluated between the experimental data and adjusted by correlation. For all the correlations, the associated error is around maximum 6%. The NRMSD is used as it facilitates a comparison of different scales and provides
Table 5 e Summary of prediction models for the best correlations. Correlation
R-square
NRMSD (%)
RHðTÞ ¼ 3:214e0:04308T
0.999
1.25
PðDTÞ ¼ 0:1246DT2 11:87DTþ 301:2
0.989
5.16
JðDTÞ ¼ 0:2083DT2 19:81DTþ 502:5
0.987
5.11
PðRHÞ ¼ 1:546RH1:148
0.979
6.18
JðRHÞ ¼ 2:572RH1:148
0.979
6.17
information on the reliability of the proposed equation. The associated errors in the correlations obtained are relatively low, in addition a good fit can be observed in the graphs and the behavior of the adjusted curve has a single monotony, i.e., the selected models are suitable to obtain a good approximation.
Conclusions In the present study, the importance of the reactive gas humidification and their correlation with the phenomenon of inverse diffusion and electroosmotic drag in the water balance of a PEFC was analyzed, which determines the impact of relative humidity on the cell behavior. According to the obtained results, it was found that at low RHs the proton conductivity decreases due to the low mass diffusion velocities, due to the water content influences the proton conductivity of the membrane directly and at the same time the kinetics of the electrode is reduced. In addition, it was found that the ohmic resistance of the membrane appears to be affected at low RHs. The resistance curves have a non-stable behavior in comparison with at high RHs. This is explained for the inverse diffusion and the blockage of the pores of the catalyst layers when low currents and RHs appear. Considering the polarization curves, a maximum current density of 1887.2 mA/cm2 and 219.7 mA/ cm2 were found when the RH change from 100% to 16%. Changing the RH in the same range gives a reduction of the maximum power from 561 mW cm-2 to 60 mW cm-2. The ohmic resistance of the membrane also experience a significant variation, varying between 125 mU cm2 and about 600 mU cm2. Last but not least, several empirical correlations are proposed, a correlation based on experimental data has been proposed to describe the behavior of the RH as a function of the temperature of the reactive gases, and others for the current density and power density as a function of difference temperature and relative humidity. These last proposed correlations are obtained for an operating voltage of 0.6 V. The correlations show a strong dependence on the temperature difference between the reactive gases/cell, which is directly related to the relative humidity.
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Acknowledgements The authors kindly acknowledge the financial support from FIMCP-CERA-05-2017 project. Computational and physical resources provided by ESPOL are also very grateful. In addition, Aforsk project No 17-331 is gratefully acknowledged.
Appendix
Experimental and theoretical values for the RH correlation as a function of the inlet temperature of fuel/ oxidant gases. Tanode/cathode [ C] 40 45 50 55 60 65 70 75 80
RHexperimental
RHtheoretical
%Eabsolute
17 21 27 36 43 53 66 82 100
17.21 21.51 27.11 34.21 43.02 53.76 66.63 81.89 99.76
1.22 2.37 0.41 5.23 0.05 1.41 0.95 0.13 0.24
Nomenclature CL CO2 E FC H2O H2 J MEA P PEFC PEM R RH RMSE T
Catalyst layer Carbon dioxide Cell voltage, V Fuel cell Water Hydrogen Current density, mA/cm2 Membrane electrode assembly Power, W Polymer electrolyte fuel cell Polymer Electrolyte Membrane Ohmic Resistance, U Relative Humidity Root mean square error Temperature, C
references
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[6] Wilberforce T, Alaswad A, Palumbo A, Dassisti M, Olabi AG. Advances in stationary and portable fuel cell applications. Int J Hydrogen Energy 2016;41(37):16509e22. [7] Carcadea E, Varlam M, Marinoiu A, Raceanu M, Ismail MS, Ingham DB. “Influence of catalyst structure on PEM fuel cell performance e a numerical investigation. Int J Hydrogen Energy 2019;44(25):12829e41. [8] Kongkanand A, Subramanian NP, Yu Y, Liu Z, Igarashi H, Muller DA. Achieving high-power PEM fuel cell performance with an ultralow-Pt-content core-shell catalyst. ACS Catal 2016;6(3):1578e83. n B. “‘Compress [9] Espinoza M, Andersson M, Yuan I, Sunde effects on porosity, gas-phase tortuosity, and gas permeability in a simulated PEM gas diffusion layer. Int J energy Res 2015;31(August 2007):135e47. n B. Effects of gas diffusion layer deformation on [10] Li S, Sunde the transport phenomena and performance of PEM fuel cells with interdigitated flow fields. Int J Hydrogen Energy 2018;43(33):16279e92. n B. “‘Predicting transport [11] Espinoza M, Andersson M, Sunde parameters in PEFC gas diffusion layers considering microarchitectural variations using the Lattice Boltzmann method. Int J energy Res 2016;31(August 2007):135e47. n B, Andersson M. Impact on [12] Espinoza-Andaluz M, Sunde diffusion parameters computation in gas diffusion layers, considering the land/channel region, using the lattice Boltzmann method. ECS Trans 2016;75:14. [13] Zhao J, Shahgaldi S, Alaefour I, Yang S, Li X. Pore structure and effective diffusion coefficient of catalyzed electrodes in polymer electrolyte membrane fuel cells. Int J Hydrogen Energy 2018;43:2e11. [14] Andersson M, Beale SB, Espinoza M, Wu Z, Lehnert W. A review of cell-scale multiphase flow modeling, including water management, in polymer electrolyte fuel cells. Appl Energy 2016;180. [15] Li H, et al. A review of water flooding issues in the proton exchange membrane fuel cell. J Power Sources 2008;178(1):103e17. [16] Dai W, et al. A review on water balance in the membrane electrode assembly of proton exchange membrane fuel cells. Int J Hydrogen Energy 2009;34(23):9461e78. [17] Zhang J, et al. PEM fuel cell relative humidity (RH) and its effect on performance at high temperatures. Electrochim Acta 2008;53(16):5315e21. [18] Sahay N, Ierapetritou M. Drops, slugs, and flooding in polymer electrolyte membrane fuel cells. IFAC Proc 2009;7(Part 1):405e10. [19] Dokkar B, Settou NE, Imine O, Saifi N, Negrou B, Nemouchi Z. Simulation of species transport and water management in PEM fuel cells. Int J Hydrogen Energy 2011;36(6):4220e7. [20] Machado BS, Chakraborty N, Das PK. Influences of flow direction, temperature and relative humidity on the performance of a representative anion exchange membrane fuel cell: a computational analysis. Int J Hydrogen Energy 2017;42(9):6310e23. [21] Iranzo A, Boillat P, Biesdorf J, Salva A. Investigation of the liquid water distributions in a 50cm2 PEM fuel cell: effects of reactants relative humidity, current density, and cathode stoichiometry. Energy 2015;82:914e21. [22] Wu J, et al. A review of PEM fuel cell durability: degradation mechanisms and mitigation strategies. J Power Sources 2008;184(1):104e19. [23] Xie J, Wood DL, Wayne DM, Zawodzinski TA, Atanassov P, Borup RL. Durability of PEFCs at high humidity conditions. J Electrochem Soc 2005;152(1):104e13. [24] Kim YS, Lee KS. Fuel cell membrane characterizations. Polym Rev 2015;55(2):330e70.
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[25] Obermaier M, Bandarenka AS, Lohri-Tymozhynsky C. A comprehensive physical impedance model of polymer electrolyte fuel cell cathodes in oxygen-free atmosphere. Sci Rep 2018;8(1):1e9. [26] Ozen DN, Timurkutluk B, Altinisik K. Effects of operation temperature and reactant gas humidity levels on performance of PEM fuel cells. Renew Sustain Energy Rev 2016;59:1298e306. [27] Scribner Associates Inc.. Fuel cell test system scribner associates model 850e operating manual. 2010. p. 66. [28] Cooper KR, Ramani V, Fenton JM, Kunz HR. Experimental methods and data analyses for polymer electrolyte fuel cells. 2005. p. 122. [29] Penn State Department of Energy and Mineral Engineering, “Zero emission vehicles,” Technol Sustain Syst. [Online]. Available: https://www.e-education.psu.edu/eme807/node/ 671. [Accessed: 18-Aug-2019]. [30] Calle K, Parrales J. Estudio del Comportamiento y Estabilidad de las Propiedades fuel cell test system. ” ESPOL Polytechnic; 2013. [31] Xu H, Kunz HR, Fenton JM. Analysis of proton exchange membrane fuel cell polarization losses at elevated temperature 120 C and reduced relative humidity. Electrochim Acta 2007;52(11):3525e33. [32] Zhang J, Tang Y, Song C, Cheng X, Zhang J, Wang H. “PEM fuel cells operated at 0% relative humidity in the temperature range of 23e120 C. Electrochim Acta 2007;52(15):5095e101.
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[33] Yan Q, Toghiani H, Causey H. Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes. J Power Sources 2006;161(1):492e502. [34] Saleh MM, Okajima T, Hayase M, Kitamura F, Ohsaka T. Exploring the effects of symmetrical and asymmetrical relative humidity on the performance of H2/air PEM fuel cell at different temperatures. J Power Sources 2007;164(2):503e9. [35] Amirinejad M, Rowshanzamir S, Eikani MH. Effects of operating parameters on performance of a proton exchange membrane fuel cell. J Power Sources 2006;161(2):872e5. [36] Kahveci EE, Taymaz I. Effect of humidification of the reactant gases in the proton exchange membrane fuel cell. J. Clean Energy Technol. 2015;3(5):356e9. [37] Esfeh HK, Hamid MKA. Temperature effect on proton exchange membrane fuel cell performance Part II: parametric study. Energy Procedia 2014;61:2617e20. rez-Page M, Pe rez-Herranz V. Effect of the operation and [38] Pe humidification temperatures on the performance of a PEM fuel cell stack. Int J Electrochem Sci 2009;25(1):733e45. [39] Ou K, Yuan WW, Choi M, Yang S, Kim YB. Performance increase for an open-cathode PEM fuel cell with humidity and temperature control. Int J Hydrogen Energy 2017;42(50):29852e62. [40] Kuo JK, Chen CK. A novel Nylon-6-S316L fiber compound material for injection molded PEM fuel cell bipolar plates. J Power Sources 2006;162(1):207e14.
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Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases Mayken Espinoza-Andaluz a,*, Jordy Santana b, Martin Andersson c nica y Ciencias de La Produccion, Centro Escuela Superior Politecnica Del Litoral, ESPOL, Facultad de Ingenierı´a Meca de Energı´as Renovables y Alternativas, Campus Gustavo Galindo Km. 30.5 Vı´a Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador b nica y Ciencias de La Produccion, Escuela Superior Politecnica Del Litoral, ESPOL, Facultad de Ingenierı´a Meca Campus Gustavo Galindo Km. 30.5 Vı´a Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador c Lund University, Department of Energy Sciences, Lund, Sweden a
highlights An experimental study of a single PEFC with 25 cm2 of effective area is carried out. The impact of the relative humidity on the performance of a PEFC has been analyzed. Correlations for current and power density as a function of RHs have been proposed. Predictions for current, power and RH related to the temperature have been proposed.
article info
abstract
Article history:
The growing energy demand and the impact of polluting gases lead to the necessity of
Received 3 January 2019
alternative energy sources and conversion energy devices. Fuel cells (FCs) appears as a
Received in revised form
suitable solution for facing the mentioned issues. Predicting the behavior of a polymer
19 August 2019
electrolyte fuel cell (PEFC) under different conditions represents a proper initial step to
Accepted 12 September 2019
solve the several issues, e.g., aging water balance problems, which occur inside the cell
Available online xxx
during the energy conversion process. Understanding microstructural impacts of the diffusion media, water management issues of FCs or the impacts of the inlet reactant gases
Keywords:
to the cell represent some of the processes that have to be analyzed to improve the effi-
PEFC
ciency and behavior of FCs.
Relative humidity
The current study aims, based on experimentally collected data, to propose empirical
Membrane resistance
correlations that describe and predict the performance of a PEFC. The single cell considered
Power density
in this study corresponds to a single PEFC with a Nafion® 112 membrane as electrolyte and
Current density
with an effective area of 25 cm2. Relative humidity as a function of the reactive inlet gas temperature, as well as the power and the current density as a function of the cell/reactant gas temperature gradient are analyzed. In addition, correlations for power and current density as a function of the relative humidity (RH) have been proposed. Our correlations are obtained for an operating voltage of 0.6 V. It was shown a strong correlation between the power and current densities with the RH since the membrane conductivity depends mainly on the water content. The PEFC behavior was evaluated at different RHs. The results show
* Corresponding author. E-mail address: [email protected] (M. Espinoza-Andaluz). https://doi.org/10.1016/j.ijhydene.2019.09.098 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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big losses of operating power and current densities, as well as an increment of the resistance of the membrane when it operates at low RH. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The results of studies regarding atmospheric CO2 levels shows that the global temperature in 2100 will likely reach levels which would lead to severely damaging long-term impacts [1]. Due to this, the fuel cell (FC) technology emerges as a source of clean energy that supplies the required energy to different sectors [2]. A polymer electrolyte fuel cell (PEFC) is an electrochemical device that provides electrical energy from the chemical reactions that occurs in two catalytic regions due to the interaction of fuel flow (H2) and oxidant flow (O2), respectively. PEFC has been the most researched cell type in the last 7 years according to “The Fuel Cell Industry Review 2017”, at the same time they are also the most improved FC related to power delivery [3]. It offers a quick start-up time since it operates at a relatively low temperature (80 C) resulting in an increment of its durability. Currently, research are focused on increasing the efficiency and reducing costs of the fuel cell systems facing several issues, such as obtaining new materials to build up bipolar plates in order to reduce costs [4]. The hydrogen storage systems for transport applications is other area that has been extensively researched as presented by Refs. [5,6], the influence of the catalyst structure in PEFC cell is reviewed by Carcadea et al. [7], while Kongkanand et al. [8] considered the development of new catalytic materials for the membrane electrode assembly (MEA). From a modeling point of view, a study investigated transport parameters in the GDL under certain compression conditions [9]. To improve and understand the diffusion transport process of the reactant gases, several studies have been performed [10e13]. In addition, a detailed literature review about cell-scale multiphase flow modeling was presented by Andersson et al. [14]. Several studies show that one of the most important factors in the performance of a FC is the water management [15e19]. The water vapor produced in the cathode side can be condensed which causes flooding of the diffusion media giving a reduced efficiency during the energy conversion process. The water balance is a critical issue in water management for current PEFC technologies [16]. The lack of water management in PEFC systems can trigger dehydrations when working at elevated temperatures [17]. Therefore, the inlet fuel/oxidant gases commonly enter to the PEFC after a previous humidification stage. However, an excess of humidification in the inlet gases causes flooding producing a partial or total blockage of the diffusion media [18]. Recent studies have focused on the effects of the relative humidity (RH) on the MEA. A complete performance test has been considered in several studies [20e22], modeling the flooding channel during the energy conversion process has been analyzed by Machado et al. in Ref. [20], liquid water distributions using computational tools
have been studied Iranzo et al. in Ref. [21]. The effects of deterioration of the MEA have been considered by Wu et al. in Ref. [22], and Xie et al. [23] and the characterization was studied by Kim et al. in Ref. [24], showing the performance changes on the PEFC. In addition, a decrement of oxygen reduction kinetics and proton conduction losses which occur within the catalyst layers (CLs) Fig. 1 is especially important at low relative humidity. Results indicate that at low RH the ionic conductivity is decreased, while the proton exchange resistance of the membrane increases [26]. In addition, the kinetic reaction is also affected decreasing its rated, and the mass transfer in the MEA is increased. Most of the studies are only focused on the main variables versus the current density, but not on the relationship that exists between the other variables that influence the performance of a PEFC, such as RH, anode temperature, cathode temperature, power density and ohmic resistance. The aim of this paper, in addition of showing the traditional performance curves of a fuel cell PEFC, is to propose empirical correlations and to explain the behavior of a PEFC with a Nafion® 112 membrane based on experimental data. Correlations for current and power density at the operating voltage of a PEFC are also presented. The rest of the paper is divided as follows: Experimental set-up, physical characteristics, and properties of the single PEFC is given in Experimental. Obtained results considering the variables involved in the study as well as the proposed correlations are presented in Results and discussion. Finally, in Conclusions, conclusions and discussions are given.
Experimental The present study was carried out with a Fuel Cell Test System 850e from Scribner Inc., which is a complete test station for operation and measurement of the performance variables of a PEFC. Among the main components of the system can be mentioned: a mass flow controller, water humidifier tank, temperature controller in anode/cathode and in the cell, it also has a data acquisition card that displays the results in a peripheral device. The structure of the system is detailed in Fig. 2. The equipment is able to control the current load to evaluate the performance and obtain the polarization curves of PEFCs. The acquisition process depends on the parameters to be analyzed. Readers interested in more detailed information about the FC Test System are referred to Ref. [27]. A single PEFC was used for the experiments, and the electrolyte is a polymer membrane Nafion® 112. The external view of the FC stack is shown in Fig. 3. As usual, the membrane is sandwiched between the catalyst plates containing platinum nanoparticles, and in turn they are inside the gas diffusion layers,
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 1 e Scanning electron microscopy of a MEA. Adapted from Ref. [25].
all these elements forming the MEA. The bipolar plates have an effective area of 25 cm2, with a three channels design which contribute to distribute the reactants in the MEA. These channels have a serpentine shape with a width and depth of 1mm/1 mm, respectively. Those data are according to the manual of experimental methods and data analysis for a PEFC [28]. Once the FC equipment installation is stated and communications requirements have been reached, the cell is ready to start up. The gases used during the current experiment are H2 (anode side) and O2 (cathode side), where the anode and cathode pressure are kept at 55 psig. In addition, N2 was used to purge the waste in the ducts that transmit the main reactive gases, as a safety measure. The water used was ASTM Type I (with 18 MU/cm minimum resistivity). The MEA was tested at 80 C under ambient pressure conditions, i.e., 1 atm, and data were collected by varying the temperature of the H2/O2 reactive gases in the anode/cathode from 40 C to 80 C in steps of 10 C. The reactive gases entered with 100% humidification at the set temperature. The RHs were calculated as the ratio between the saturation pressure at the temperature of the inlet gases and the saturation pressure at the MEA temperature. The current study was done for symmetric RHs at the anode and cathode. The values of the flow rate of reactants were configured according to the study presented by Calle et al. [30].
Results and discussion The effect of RH on the behavior of PEFCs, the computation of RH as a function of temperature and proposed correlations for power and voltage of a PEFC are also presented in this section.
Fig. 2 e Schematic of the FC test system used in the current study. Adapted from Ref. [27].
Effects of the RHs on fuel cell in the literature To maintain and improve performance in the operation of a FC, it is necessary to know the behavior of the variables that greatly affect the process of operating, one of which is the hydration of the proton exchange membrane. Hydration is an essential requirement for the membrane to work optimally, because the proton conductivity has a relationship directly proportional to its water content, in addition to being a key factor in the useful system life time. The membrane must work humidified throughout the operation time of the FCs; which is achieved by humidifying the H2/O2 reactive gases. The humidified reactive gases enter the anode/cathode channels respectively, encountering their respective catalytic layers, where a proton stream with water molecules passes through the membrane from the catalytic layer of the anode to the catalytic layer of the cathode. It is known as electro osmotic drag. On the other hand, in the catalyst layer of the cathode, the O2 molecules react with the H2 cations, producing water. The water formation in the cathode produces a gradient of concentration in the membrane, and therefore appears a transfer of water from the cathode to the anode, this process is known as back diffusion. Finally, the water that remains on the side of the cathode is drained outside of the
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 3 e Picture of the single PEFC used in this study (left), and exploded view of the analyzed cell (right). Adapted from Ref. [29].
system. In the absence of hydration of the membrane there is a low proton conductivity, i.e., correct water management is required to maintain the hydration of the membrane and to work with great performance. The concept of relative humidity (RH) is introduced which gives a numerical hydration of the membrane relative to the water content of the reactive gases. Due to the importance of a previous humidification of reactive gases, several studies have been carried out on the effects that RH produces on the performance of a FC, some results are presented in Table 1. As observed, the performance of a FC has a great dependence on the degree of RH. In a study presented by Xu et al. [31], the polarization curve was used to analyze the losses for the voltage and the ohmic resistance as a function of the current density. The single cell analyzed was of active are 5 cm2 and the electrolyte a Nafion 112. The operating temperature was established at 120 C, and the symmetric RH was decreased from 100% to 20%. As result, the ohmic resistance increased from 0.092 to 0.407 U cm2. In addition, for a current density of 600 mA/cm2, the cell voltage decreased from 0.617 V to 0.226 V. Zhang et al. [32] carried out a study using a Nafion 112 electrolyte with an active are of 4.4 cm2. In this study the testing of the performance of the FC was performed at exact values of 100% and 0% of symmetric RH at operating temperature of 80 C. Results showed a considerable reduction of the resistance cell. It was concluded that the lower performance is mainly caused by the low velocity of proton transfer within the catalyst layers. The last mentioned issue was analyzed using an impedance AC analysis. They also performed an study considering high temperatures [17]. The tests were carried out using and AC impedance method and measurements of cyclic voltammetry
for several conditions of symmetric RHs. Results showed a significant reduction of the kinetics of the electrode. The conductivity of the membrane was also affected producing too much losses in the performance. In the study performed by Yan et al. [33], an individual analysis of the anode and cathode was carried out. They configured different RHs at the anode/ cathode side varying the inlet temperature of the reactant gases until reaching the 100% of humidification at its corresponding saturation temperature. The analyzed cell had an effective area of 5 cm2. Results show that the humidification of the inlet gases in the cathode side has a significate impact on the performance of the FC. Experimental results show that the decrease in RH on the cathode side has a harmful effect on the FC stability and its dynamic performance. In addition, they showed that for medium and higher RHs at the cathode side is good enough to maintain the membrane hydrated without any additional humidification of the anode side reactant gases. This occurs due to a sufficient inverse diffusion from the cathode to the anode side. Similar to previous studies, Saleh et al. [34] performed experimental tests with symmetric and asymmetric RHs with an effective area of 25 cm2. They concluded that the performance of the cell increases with an increase of the RH at the anode side, however, it is possible to obtain an acceptable performance of the cell for with 100% RH at the anode. This indicates that the RH at the cathode side has a strong influence on the membrane hydration. Moreover, they conclude that to high temperatures higher RHs are required to obtain a proper membrane hydration while that at lower temperatures a limited diffusion of the reactant gases is observed at conditions of high RHs. On the other hand, Amirinejad et al. [35] found that the humidification at the
Table 1 e Results of experimental studies considering the relative humidity of reactant gases. Membrane Nafion Nafion Nafion Nafion Nafion Nafion
112 112 112 112 212 117
Active area (cm2)
Operating Temperature ( C)
Operating current density (A cm2)
Relative humidity (%)
Membrane resistance (U cm2)
Power density (W cm2)
Ref.
4.4 5 4.4 5 25 5
120 120 80 65e85 70e90 70
0e2.1 0.2 0.1e1.2 0e0.5 0.1e1.4 0.2
25e100 20e100 0e100 0e100 0e100 0e100
~0.15e0.75 0.092e0.407 ~0.1e0.5 ~0.15e0.65 ~0.1e1.75 e
0.1e0.6 e 0.25e0.62 e 0.05e0.4 ~0.075e0.13
[17] [31] [32] [33] [34] [35]
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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anode has a bigger impact on the performance of the cell in comparison with the humidification of the cathode which does not agree to previous studies. This discrepancy is mainly due the operating conditions and characteristics of the analyzed cells.
Effects on the performance of the single cell studied In the current study, to analyze the performance of the single FC, typical ‘curves’ were obtained at different symmetric RHs. The cell was established to be working at a constant temperature Tcell ¼ 80 C, while the inlet temperature of the reactant gases was changed between 40 C and 80 C with steps of 10 C. The minimum RH considered in this study, i.e., 16%, was obtained when the inlet temperature of the reactant gases is 40 C while the maximum RH was 100% which occurs when the inlet temperature of the reactant gases reached 80 C. The performance of the cell voltage as a function of the current density is presented in Fig. 4. Considering the RH variations, it is also observed a strong influence of the humidification of the reactant gases. Maximum and minimum current density of 1887.2 mA/cm2 and 219.7 mA/cm2 were obtained for 100% and 16% of RH, respectively, i.e., a reduction of the RH produces a wide reduction of the operating range. In addition, the voltage loss in the activation zone is reported as 80 mV varying between 0.88 V and 0.80 V. It is clear that at low RH the losses for proton transfer are noticeable due to the low water content of the membrane and therefore the resistance of the membrane increases. The opposite situation occurs at high RH; the proton conductivity has a great improvement. The obtained results show a good agreement with that was reported in previous studies [17,28,30e36]. Fig. 5 shows the behavior of the power density as a function of the current density considering different RHs. For 100% and 16% of RH the obtained power densities are 561.1 mW/cm2 and 68.6 mW/cm2, respectively. According to the obtained results
5
a reduction of 493.1 mW/cm2 when the RH varies in the analyzed range was observed. Similar to the voltage-current behavior, the power density reaches bigger values when RH increases. It is important to mention that the power density curve increases until a maximum value is obtained and then it has a decreasing behavior. This trend is due to the mass transport losses which normally occur when the FC is working at high current densities and temperatures. The ohmic resistance of the membrane was also analyzed for different RHs. Fig. 6 shows the behavior of the resistance as a function of the current density, considering the different RHs of the reactant gases respect to the cell. At high RHs the membrane absorbs a greater quantity of water compared to at low RHs, i.e., the ionic channels in the catalyst layer are filled in a bigger proportion improving the protonic transfer. This phenomenon gives a decreased protonic resistance when the RHs increase. This implies that the kinetic reactions inside a FC at low RHs are considerable lower than for higher RHs, which agrees with published studies [37,38]. It was found that for a RH 60% the resistance of the membrane is around 125 mU cm2, and it has a constant trend, i.e., the cell can operate in stable conditions independently of the power demand. However, this behavior does not occur at lower RHs when, for example at RH 16%, average membrane resistance of 600 mU cm2 is observed. The curves at lower RHs present a parabolic trend, which occur due to at low RH the produced water at the cathode side increases from zero to a certain value when the operating time increase. As result of the inverse diffusion, the catalyst layer at the anode side is humidified and the conductivity of the membrane is improved. However, when the cell starts to operate at high current and power densities, the diffusion through the membrane is not enough and pore obstructions at the catalyst layer appears. This yields an increase in the membrane resistance, which can explain the increase at the end of the curve.
Fig. 4 e Performance curve for cell voltage as function of current density for different RHs. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 5 e Performance curve for power density as a function of the current density for different relative humidity.
Fig. 6 e Performance curve for resistance membrane as a function of current density for different RHs.
Predicted relative humidity (RH) correlations for a single PEFC As showed in Table 1, the RH between the reactant gases and membrane has a large effect on the behavior of the cell, i.e., it is necessary to quantify or have an estimation of the RH. Most of the FC test systems have humidification tanks for which the reactant gases pass before they enter into the anode and cathode channels. The temperature and humidity sensors allow to humidify the reactant gases according to the requirements. As the inlet temperature of the reactant gases can be different to the temperature of the cell, the humidification degree changes as the temperature changes. One way to obtain an approximation of the RH, is
by means of thermodynamic tables. It is made dividing the saturation pressure of the inlet temperature of the reactive gases (considering symmetric RH) to the saturation pressure at the cell temperature. However, the mentioned procedure is cumbersome. Considering the difficulty, three possible correlations are proposed to calculate the RH in Table 2. These correlations are functions of the H2/O2 reactive gas temperature with respect to a cell temperature set to 80 C. This cell temperature was considered because it obtains maximum electrical efficiency according to Ref. [39]. All the proposed correlations in this study are constructed considering the collected data under the specified conditions and with the help of fitting tools provided by Matlab® toolbox.
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Table 2 e Proposed correlations to compute the RH as a function of inlet temperature of fuel/oxidant gases. Type
Correlation
R-square
Polynomial
RHðTÞ ¼ 0:0381T2 2:538T þ 58:24
0.9986
NRMSD (%) 1.50
Exponential
RHðTÞ ¼ 3:214e0:04308T
0.9986
1.25
Power
RHðTÞ ¼ ð5:329 104 ÞT2:766
0.9965
2.17
Fig. 7 e Correlation better adjusted to the experimental data for RH as a function of the inlet temperature of fuel/oxidant gases.
The behavior of the RH is best explained with an exponential correlation. Because it has a R-square value of 0.9986 with a normalized root mean square deviation (NRMSD) of 1.25%, which estimates the percentage of the associated error with the predicted model. Note that when the inlet temperature of the reactant gases is higher than the ambient temperature, the RH increases rapidly. In addition, it is also observed that an equal temperature of the reactant gases and the cell gives a 100% humidification of the membrane. In Fig. 7, the correlation best fitted to the experimental data is depicted. The errors between the experimental data and the values computed with the empirical correlation are presented in Appendix.
Predicted performance correlations for a single PEFC To understand how the RH impact the behavior of a PEFC inoperando, empirical correlations are suggested based on our experimental data. The selected data are according to the average voltage that a FC delivers in working operation, i.e.,
0.6 V [40]. In the same way three possible empirical correlations to evaluate the power as a function of temperature difference, i.e., cell temperature minus the temperature of the inlet gases anode/cathode are presented in Table 3. According to the obtained results, the correlation that best fit the collected data is the polynomial type. The selection was carried out based on the R-square and the NRMSE. For the first statistic parameter, i.e., R-square, the polynomial and rational have similar value, and therefore the decision is made considering the NRMSE which is better for the polynomial correlation. Note how the Power Density is greater when the Temperature Difference tends to zero, that is, the maximum power density is obtained when the temperature of the reactive gases is equal to the cell temperature, this case is met for 80 C, Equivalent to a relative humidity of 100%. Fig. 8 shows the selected correlation together with the experimental data. The empirical correlations to evaluate the current density as a function of the temperature difference between the gas inlet and the cell, are presented in Table 4. Similar to the
Table 3 e Proposed correlations for power density as a function of the temperature difference at 0.6 V. Type
Correlation
R-square
NRMSD (%)
Polynomial
PðDTÞ ¼ 0:1246DT 11:87DT þ 301:2
0.989
5.16
Exponential
PðDTÞ ¼ 308:1e0:05015DT
0.970
7.42
0.989
5.91
Rational
2
PðDTÞ ¼
4:4E4DT2 ð4:152E6ÞDT þ ð1:048E8Þ DT þ ð3:473E5Þ
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Fig. 8 e Correlation better adjusted to the experimental data for power density in function delta temperature.
Table 4 e Proposed correlations for current density as a function of the temperature difference at 0.6 V. Type
Correlation
R-square
NRMSD (%)
Polynomial
JðDTÞ ¼ 0:2083DT 19:81DT þ 502:5
0.987
5.11
Exponential
JðDTÞ ¼ 513:8e0:05017DT
0.970
7.40
0.986
5.93
Rational
2
JðDTÞ ¼
9:091E4DT2 ð8:409E6ÞDT þ ð2:095E8Þ DT þ ð4:152E5Þ
previous analysis, the three best correlations have been grouped to select one based on the statistic parameters. As shown in the previous table, the R-square values are similar for the polynomial and rational curve, the selection is
made based on the NRMSD, according to this value, the correlation that best describe the current density as a function of temperature difference is the polynomial type. Fig. 9 shows the selected correlations together with the experimental data,
Fig. 9 e Correlation better adjusted to the experimental data for current density in function delta temperature. Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
international journal of hydrogen energy xxx (xxxx) xxx
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Fig. 10 e Correlation better adjusted to the experimental data for power density and current density in function RH.
Note that the greater operating range is obtained with a delta temperature of zero, that is, for 100% RH. It is important to notice that for power and current density the trends were similar, this is given due the relation of the analyzed data with the Ohm's law since the power is proportional to the voltage and the current. Additionally, the impact of the temperature is clear and it affects the cell performance. If the temperature difference is high, the current density and power density suffer big losses. The highest power and current density are obtained when the temperature difference is zero, i.e., RH equal to 100%. However, if the temperature difference is 20 C, i.e., the inlet reactants temperature is 60 C, and having a RH of 42% the power density and current density are around 100 mW cm-2 and 180 mA cm-2, respectively. The results obtained in the current study are acceptable if compared with the reported values in Table 1. A similar analysis was performed to correlate the power and current density as a function of the RH. The following correlations were selected to evaluate the mentioned variables: PðRHÞ ¼ 1:546RH1:148
(1)
JðRHÞ ¼ 2:572RH1:148
(2)
Eq. (1) and Eq. (2) were selected with at same R-square of 0.979, and NRMSD of 6.17 and 6.18 respectively. Fig. 10 shows both correlations together with the experimental data. Finally, in Table 5, a summary of the correlations proposed in this study is shown. This table includes the R-square and NRMSD in percentage, evaluated between the experimental data and adjusted by correlation. For all the correlations, the associated error is around maximum 6%. The NRMSD is used as it facilitates a comparison of different scales and provides
Table 5 e Summary of prediction models for the best correlations. Correlation
R-square
NRMSD (%)
RHðTÞ ¼ 3:214e0:04308T
0.999
1.25
PðDTÞ ¼ 0:1246DT2 11:87DTþ 301:2
0.989
5.16
JðDTÞ ¼ 0:2083DT2 19:81DTþ 502:5
0.987
5.11
PðRHÞ ¼ 1:546RH1:148
0.979
6.18
JðRHÞ ¼ 2:572RH1:148
0.979
6.17
information on the reliability of the proposed equation. The associated errors in the correlations obtained are relatively low, in addition a good fit can be observed in the graphs and the behavior of the adjusted curve has a single monotony, i.e., the selected models are suitable to obtain a good approximation.
Conclusions In the present study, the importance of the reactive gas humidification and their correlation with the phenomenon of inverse diffusion and electroosmotic drag in the water balance of a PEFC was analyzed, which determines the impact of relative humidity on the cell behavior. According to the obtained results, it was found that at low RHs the proton conductivity decreases due to the low mass diffusion velocities, due to the water content influences the proton conductivity of the membrane directly and at the same time the kinetics of the electrode is reduced. In addition, it was found that the ohmic resistance of the membrane appears to be affected at low RHs. The resistance curves have a non-stable behavior in comparison with at high RHs. This is explained for the inverse diffusion and the blockage of the pores of the catalyst layers when low currents and RHs appear. Considering the polarization curves, a maximum current density of 1887.2 mA/cm2 and 219.7 mA/ cm2 were found when the RH change from 100% to 16%. Changing the RH in the same range gives a reduction of the maximum power from 561 mW cm-2 to 60 mW cm-2. The ohmic resistance of the membrane also experience a significant variation, varying between 125 mU cm2 and about 600 mU cm2. Last but not least, several empirical correlations are proposed, a correlation based on experimental data has been proposed to describe the behavior of the RH as a function of the temperature of the reactive gases, and others for the current density and power density as a function of difference temperature and relative humidity. These last proposed correlations are obtained for an operating voltage of 0.6 V. The correlations show a strong dependence on the temperature difference between the reactive gases/cell, which is directly related to the relative humidity.
Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098
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Acknowledgements The authors kindly acknowledge the financial support from FIMCP-CERA-05-2017 project. Computational and physical resources provided by ESPOL are also very grateful. In addition, Aforsk project No 17-331 is gratefully acknowledged.
Appendix
Experimental and theoretical values for the RH correlation as a function of the inlet temperature of fuel/ oxidant gases. Tanode/cathode [ C] 40 45 50 55 60 65 70 75 80
RHexperimental
RHtheoretical
%Eabsolute
17 21 27 36 43 53 66 82 100
17.21 21.51 27.11 34.21 43.02 53.76 66.63 81.89 99.76
1.22 2.37 0.41 5.23 0.05 1.41 0.95 0.13 0.24
Nomenclature CL CO2 E FC H2O H2 J MEA P PEFC PEM R RH RMSE T
Catalyst layer Carbon dioxide Cell voltage, V Fuel cell Water Hydrogen Current density, mA/cm2 Membrane electrode assembly Power, W Polymer electrolyte fuel cell Polymer Electrolyte Membrane Ohmic Resistance, U Relative Humidity Root mean square error Temperature, C
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Please cite this article as: Espinoza-Andaluz M et al., Empirical correlations for the performance of a PEFC considering relative humidity of fuel and oxidant gases, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.098