Multiphysical Models for Hydrogen Production Using NaOH and Stainless Steel Electrodes in Alkaline Electrolysis Cell

-e cell voltage in alkaline water electrolysis cells remains high despite the fact that water electrolysis is a cleaner and simpler method of hydrogen production. A multiphysical model for the cell voltage of a single cell electrolyzer was realized based on a combination of current-voltage models, simulation of electrolyzers in intermittent operation (SIMELINT), existing experimental data, and data from the experiment conducted in the course of this work.-e equipment used NaOH as supporting electrolyte and stainless steel as electrodes. Different electrolyte concentrations, interelectrode gaps, and electrolyte types were applied and the cell voltages recorded. Concentrations of 60wt% NaOH produced lowest range of cell voltage (1.15–2.67V); an interelectrode gap of 0.5 cm also presented the lowest cell voltage (1.14–2.71V). -e distilled water from air conditioning led to a minimum cell voltage (1.18–2.78V). -e water from a factory presented the highest flow rate (12.48×10cm/min). It was found that the cell voltage of the alkaline electrolyzer was reduced considerably by reducing the interelectrode gap to 0.5 cm and using electrolytes that produce less bubbles. A maximum error of 1.5% was found between the mathematical model and experimental model, indicating that the model is reliable.


Introduction
e continuous use of fossil fuels and biofuels due to high energy demands poses problems of pollution, feedstock, and quality challenges [1][2][3]. e production and application of hydrogen still remains expensive and the technology is still premature [4,5]. Furthermore, it is a high energy-consuming technology. In fact, 2393 Ah are required to produce 1 Nm 3 of hydrogen [6]. e transportation sector still encounters the problem of space and load for tanks and storage batteries for the FCEVs [7], therefore the need to produce on the spot for consumption, giving credit to the continuous research in alkaline water electrolysis (AWE).
Combustion of fossil fuels and their overuse lead to severe air pollution, global warming, acid rains, and ozone depletion in stratosphere [8][9][10]. e search for possible alternative sources of energy is a must. ere are a number of primary energy sources available, such as thermonuclear energy, solar energy, wind energy, hydropower, and geothermal energy. Unfortunately, they cannot be used directly like fossil fuels. In most cases, they need to be converted into fuels leading to a search for a new energy carrier [11]. Hydrogen fuel cells are two to three times more efficient than combustion engines [12]. ey are becoming more widely available and would reduce the dependency on fossil fuels. In a fuel cell, hydrogen and oxygen are combined in an electrochemical reaction that produces electricity and a byproduct: water. e production of hydrogen for fuel cell applications requires performance improvements. In spite of considerable achievement realized so far in the field of polymer electrolyte membrane fuel cells, one substantial question has not been answered yet; i.e., what combination of performance criteria brings the greatest benefits? [13,14].
Currently, the supply and use of energy from fossil fuels is unsustainable economically, environmentally, and socially. Without decisive action, energy-related emissions of carbon dioxide (CO 2 ) will be more than double by 2050 [6,12,15] and increased fossil energy demand will heighten concerns over the security of supply [3]. e current path can and must be changed [12].
is calls for an energy revolution and low-carbon energy technologies to play a crucial role [16]. Hydrogen technologies are already commercially available [17]. One of the technologies is thermo catalytic and gasification processes using natural gas as a starting material, and heavy oils and naphtha make up the next largest source, followed by coal. About half of the hydrogen produced is obtained through these technologies [1,2,8], which are neither renewable nor clean. ey involve carbon capture and storage, leading to their reduced efficiency. Autothermal processes suffer from high energy requirements and high startup time [18]. Biohydrogen production is inexpensive and favors waste management but employs expensive raw materials in some cases. Furthermore, low rates and yields of hydrogen formation are achieved and the technology is at the experimental level in the laboratory. Alkaline electrolyzers are currently the most mature technology, and investment costs are considerably lower than for others [12,[19][20][21][22]. Production of hydrogen by water electrolysis is very low (<4%) [23]. However, water electrolysis yields clean hydrogen in small amounts. Unexpectedly, at a larger scale, production of hydrogen is expensive. Recent research studies for hydrogen production improvement employed pressurized water electrolysis, others use plasma technology, and today natural hydrogen sources do exist. Pressurized water electrolysis presents high rate of gas crossover [24]. With the plasma technology, more hydrogen is produced at lower concentrations of NH 3 but under high temperatures, increased energy cost, and unwanted cooking and soot [17]. Concerning natural hydrogen, little is known about its generation, migration, consumption, and potential accumulation [5,25].
Electrolyzer models are generally formulated with Faraday's law [4,26]. Empirical models describing the electrolysis process developed by Ulleberg [27] and modified by Hug et al. [28] are widely used to evaluate the characteristics of cell performance. Electrodes made of different materials were used as well as different electrolyte concentrations, membranes of different materials, different types of electrolytes, and a variety of cell geometrical, and physicochemical parameters [29]. Models from first principles have been developed with theoretical considerations made on the basis of the theories of Laplace, Newton-Raphson, and Dirichlet to express the most significant parameters influencing the operation of monopolar or bipolar electrochemical reactors (current-potential distribution) [30,31]. Algorithms capable of helping designers develop more efficient electrochemical reactors were derived enabling the calculation of current-potential distributions [30]. Slama [32] and Rashed and Elmaihy [33] found that there is a significant increase of hydrogen production flow by the use of additives such as NaCl, KOH, and NaOH. KOH has a higher ionic conductivity compared to NaOH [34]. KOH is highly corrosive, limiting the type of materials to be used in the AWEs. Nickel is relatively cheaper and less corrosive, so it is suitable to be used with KOH [34][35][36]. Tijani et al. [4] and Martinez and Zamora [37], using MATLAB, simulated a mathematical model for the cell voltage with limited facts as compared to the model of Diaz [38] who used MATLAB/ Simulink. e model of Tijani et al. [4] does not take into account the effects of pressure, concentration, bubbles, and volumetric vacuum which are considered in the model of Camilo [38]. Baseline experiments using platinum electrodes and KOH as electrolyte additive have been carried out indicating that interelectrode gap, electrolyte concentrations, and electrolyte type are the most significant parameters affecting cell performance [39].
In this paper, the ideas of Opu [39], Tijani et al. [4], and Diaz [38] have been combined to come out with multiphysical models using NaOH as supporting electrolyte instead of KOH and stainless steel electrodes instead of noble metals like platinum. In the quest of reducing the energy consumed per Nm 3 of hydrogen produced and improving the flow rate in order to produce cost effective hydrogen, the cell performances for different levels of three independent variables were experimented. e above mentioned variables included (i) electrolyte concentration, (ii) electrolyte type, and (iii) interelectrode gap. Investigations on the flow rate for different electrolyte types were done by recording the time to 1000 ppm and calculating the hydrogen flow rate. ese were done by performing experiments, executing in MATLAB, and in combination with existing models and existing parameters in the literature, a multiphysical model was established for the cell voltage of an electrolyzer. is paper aims to investigate the interelectrode gap, the electrolyte concentration, and the types of electrolyte that can affect the production of hydrogen.

Materials and Methods
Self-working temperatures as a result of the addition of NaOH are considered constant as we took measurements each time the temperatures were around 80°C. e experiment was designed such that each experiment considered a single independent variable with three levels each and the results are compared to the baseline experiment. Since the design considered one independent variable per experiment, 10 trials per level were done and the means calculated.

Existing Models.
Polarization curves were produced to characterize the process. Existing current-voltage (I-V) models have been used for the simulations as formulated by Tijani et al. [4] and Ulleberg [27]: where V cell is the cell voltage, V rev is the reversible voltage, V ohm is the ohmic voltage, and V act is the activation voltage.
where T is the temperature of the cell, A is the area of the electrodes, and r 1 and r 2 are the ohmic overvoltage parameters.

Journal of Combustion
where t 1 , t 2 , t 3 , and s are the activation overvoltage parameters. e reversible voltage (V rev ) is the minimum electric voltage that must be applied to both electrodes to enable the electrochemical reaction. It is a constant value of approximately 1.229 V obtained from the Gibbs relation [4]: where ΔG is the Gibbs energy, Z is the number of electrons, and F is the Faraday constant. e ohmic overvoltage (V ohm ) is as a result of electrochemical resistance due to the presence of bubbles in the electrolyte, ionic resistivity of the electrolyte, interelectrode gap, membrane (diaphragm) resistivity, electrolyte concentration, temperature effects, type of electrolyte, and other phenomena. e activation voltage is as a result of resistance from the electrode material type, electrode dimension, electrode shape, electrode operating temperature, and other aspects related to the electrodes. V ohm and V act are temperature dependent and take into account the ohmic resistance parameter, r, and the overpotential coefficients s and t, as suggested by Ulleberg [27]. e data used in the above modelling is shown in Table 1; constant parameters used for simulation calculations are given.
Hug et al. [28] have developed a model to analyse the performance of an electrolyzer, which expressed the cell voltage as follows: where E rev is the theoretical voltage, A 1 is the ohmic loss, and A 2 log(i) is the activation overpotential. Diaz [38] used KOH as the electrolyte and came out with the following model: where E th(T,P,C) is the theoretical voltage and is a constant (−1.229 V); b c and b a are Tafel's coefficients for the cathode and anode, respectively; J eff−c and J eff−a are the effective current densities of the cathode and anode, respectively; J o−c and J o−a are the exchange current densities of the cathode and anode, respectively; R T is the total resistance; i is the electrolyzer's current;R cat is the resistance of the cathode; R ano is the resistance of the anode; R mem is the resistance of the membrane; and R KOH−ε is the resistance of the electrolyte with bubbles considered [34].
On the basis of the high sensitivity of the gas detector used in this work, the hydrogen gas detector was used to determine the flow rate, by setting the detector and recording the time taken to attain 1000 ppm and this time is used to calculate the flow rate. From the physical relation below, the concentration is converted to a volume fraction of hydrogen developed by Never [40], Godish [41], and Cohen and Taylor [42].
where V m is the standard molar volume of ideal gas (22.71108 L/mol) and M is the molar weight of gas. e current or Faraday efficiency is an important tool to determine the specific energy consumption of an electrolyzer, particularly at partial load [28]. It is obtained from the following relationships, established by Tijani et al. [4], Rashid et al. [21], Schalenbach et al. [24], and Chisholm and Cronin [43]: where η c is the current efficiency, η cell is the cell efficiency, and η u is the voltage efficiency.

Experimental Setup.
Various instruments were used in the experiment (Figure 1). e diagram brings more insight on the functioning of the cell ( Figure 2).

Constituents of the Experimental Setup.
e baseline experimental electrolyzer was constructed with 200 ml 40 w % sodium hydroxide (NaOH) electrolyte. Each electrode was made up of a 10 cm long, 4 mm diameter straight stainless steel rod, with a 3 cm length submerged in NaOH solution. e electrodes were kept 1 cm apart for the baseline. e electrodes were connected to a DC power supply (Model PS-305D) manufactured by Guangzhou Xinyue Electronic Technology Co., Ltd., Guangzhou, China (Table 2). e effective surface area of the electrode in the electrolyte was calculated to be about 0.38957 cm 2 .
During the testing, a digital thermometer was used to monitor the temperature of the electrolyte. A hydrogen detector (S311) manufactured by Zhongan Electronic Detection Technology Co., Ltd., Zhengzhou, China (Table 3) was used to detect the presence of hydrogen during the experiments and also permitted the calculation of the flow rate.
e detector was set at the outlet of the cathode to record the time taken to attend 1000 ppm. is information was then used to calculate the flow rate for the different liquids used.
e measuring set for cell performance was made up of three multimeters and a 12-volt bulb represented by R, connected to enable us to read the supply voltage, cell current, and cell voltages of the circuit.

Characteristics of the Electrolyte Constituents.
e electrolytes used were from industrial waste (water from an air conditioning system, waste water from a dress making factory, and waste water from a dress washing machine). e physicochemical analysis of the samples was done in the HYDRAC laboratory using the standards ISO 7888 and NF T90-008 (Table 4).

Multiphysical Modelling.
e model considers the major aspects affecting cell performance including the following: (i) Hydrogen bubbles around the electrodes (ii) Ionic resistivity of the electrolyte (iii) Oxygen bubbles (iv) Interelectrode gap (v) Membrane (diaphragm) resistivity (vi) Electrode resistance (vii) Electrolyte concentration e model in equation (6) formulated by Diaz [38] was modified to take into account the logarithmic behaviour of cell voltages and tested with experimental parameters of KOH and NaOH, constituting the bases to the development of the multiphysical model. In fact, equation (6) where V rev is the reversible overpotential and is a constant (1.229). A generalized model for the cell performance of an alkaline electrolyzer was realized on the bases of published models and of the observations from the current experiments as well. erefore, where R NaOH is the resistance of sodium hydroxide and ε is the gas void fraction due to the presence of bubbles in a solution (gas void fraction or bubble coefficient).
where σ NaOH is the electrical conductivity of sodium hydroxide, d am is the distance between the anode and the membrane, d cm is the distance between the cathode and the membrane, and A is the area of the electrodes.  Values in bold italics are the characteristics after addition of 40 wt% NaOH.

Journal of Combustion
is a constant which depends on the parameters considered (separation distance, electrolyte concentration, and type of electrolyte values); it is a negative voltage due to the reactivity between the hydrogen ions and the electrode [44]. K is a correction factor, obtained from numerical trials. e other parameters are obtained from tables in literature.

Constant Parameters Used in Implementing the Models.
ey are the physicochemical parameters obtained from previous works for the three parameters investigated (Tables 5-7): electrolyte concentration, interelectrode gap, and electrolyte type [4,27,38,[45][46][47][48]. ese constant parameters enabled us to come out with the models for each I-V characteristic.

Results and Discussion
To investigate the multiphysical effect on the energy consumed and flow rate in the production of hydrogen, experiments were designed and run. Results were expressed in the form of polarization curves and bar chart. e curves present cell performance by plotting current versus voltage. e cell voltage is an indicator of the energy consumed.

Implementation and Validation of the Multiphysical
Models. e characteristic equation for the linearized curves is as follows: where V i is the cell voltage, i is the current, and a and b are constants.

Cell Performance for Different Electrolyte
Concentrations. ree concentrations of NaOH were experimented, that is, 30 wt%, 50 wt%, and 60 wt%. e baseline was 40 wt% NaOH. e general way to express the performance is plot of voltage versus current. e plot showed very little variation between 30 wt% and 40 wt% NaOH and likewise 50 wt% and 60 wt% (Figure 3). e greater the concentration, the better the cell performance. In fact, a lower range of cell voltage (1.16-2.67 V) was obtained from 60 wt%, and a larger range (1.24-3.01 V) from 30 wt% NaOH. It can rightly be said that the cell performance was proportional to the electrolyte concentration. Diaz [38] found using a 24 cell electrolyzer with nickel electrodes and experimented with 15 wt%, 30 wt%, and 45 wt% KOH that 45 wt% gave an optimal result. Furthermore, Slama [32] working with 0.4 M, 0.2 M, and 0.1 M KOH had a minimum cell voltage (3.3 V) for 0.4 M concentration. is behaviour could be attributed to an increase in the electrical conductivity of the solution due to the relative high concentration of NaOH. By increasing the electrical conductivity, the electrical current flowing through the solution augmented proportionately requiring low voltage for the same current density. e ohmic resistance of water electrolysis cell is strongly dependent on the concentration of the electrolyte. High concentrations mean higher available reactant at the electrode surface area for reaction which led to an increase in hydrogen production efficiency. It was found that the conductivity and the rate of bubble build-up of solutions were concentrations-dependent. e errors calculated showed that the mathematical model and the experimental model were compatible with each other with a maximum error of 1.5% recorded at 60 wt% NaOH.

Cell Performance for Different Interelectrode Gaps.
ree interelectrode gaps were experimented including 0.5 cm, 0.75 cm, and 2 cm. e baseline was an interelectrode gap of 1 cm. Cell voltages ranged from 1.14-2.71 V for the interelectrode gap of 0.5 cm to 1.11-3.45 V for the interelectrode gap of 2 cm (Figure 4), indicating that the closer the electrodes are, the better cell performance will be. is implied that cell performance is inversely proportional to interelectrode gap. Opu [39] using platinum electrodes and KOH as supporting electrolyte obtained cell voltages (1.25-3.12 V) and (1.25-3.75 V) for 0.5 cm and 2 cm interelectrode gaps, respectively. One of the factors affecting the resistance in the electrolysis cell is the interelectrode gap. e wider the gap, the more difficult it becomes for ions to move from one electrode to another, resulting in low performance. When the interelectrode gap is small, there is less resistance in the cell which in turn leads to an increase in the flow of electrical current and therefore improves the cell performance. e results from the experimental model are close to those of the mathematical model (maximum error equal to 0.81% for the 0.75 cm interelectrode gap).

Cell Performance for Different Types of Electrolyte.
e three types of electrolyte included AC water, pressing water, and factory water. e tap water was the baseline for control. Cell voltage varied from 1.19-2.78 V for A.C water to 1.28-3.04 V for the control (tap water) ( Figure 5). Tijani et al. [4] investigated at 80°C and 350 mA/cm 2 and found a cell voltage of 2.359 V.
e voltage obtained at the same condition in this work was 2.45 V. e difference might have resulted from the parameters considered which were different from those used in the study of Tijani et al. [4]. Slama [32] using NaCl as supporting electrolyte ranked first ammonia water and urine, using the hydrogen flow rate as the cell performance indicator. It was noticed that at low current densities the cell voltage was inversely proportional to the salinity values.
is could be explained by the physicochemical parameters. Furthermore, low formation of bubbles was observed. AC water presented the lowest peak (at 500 mA/cm 2 ) value of cell voltage 2.78 V probably due to its low propagation of bubbles. is indicated the depressive effect of bubbles in the performance of an electrolyzer. With less bubbles, the ohmic resistance is decreased resulting in a low cell voltage. Tap water presented the maximum average error of 0.77%. e clustered nature of the curves at high pH Correction factor for 40 wt% NaOH at 80°C 0.034 k 2 Correction factor for 30 wt% NaOH at 70°C 0.034 k 3 Correction factor for 50 wt% NaOH at 80°C 0.03 k 4 Correction factor for 60 wt% NaOH at 90°C 0.03 l c , * Length of the cathode 0.1 m l a , * Length of the anode 0.1 m ρ c , * Resistivity of the cathode 6.9 × 10 −7 Ωm ρ a , * Resistivity of the anode 6.9 × 10 −7 Ωm R mem * Resistance of the membrane 0.007 × 10 −4 Ωm 2 * Parameters common to the various experiments: electrolyte concentration, interelectrode gap, and types of electrolyte. Correction factor for 1 cm at 80°C 0.0294 k 2 Correction factor for 0.75 cm at 80°C 0.035 k 3 Correction factor for 0.5 cm at 80°C 0.0304 k 4 Correction factor for 2 cm at 80°C 0.035 -Journal of Combustion 7 values showed that the alkalinity reduced cell voltage. Increasing the alkalinity led to an increase in electrical conductivity which in turn led to an increase in the electrical current passing through the solution and consequently to a decrease of cell voltage.

Flow Rates for the Different Fluids.
Waste water from an AC source, waste water from a pressing, and water from a factory were used and the results were compared with that of a baseline experiment. Values of the hydrogen flow rate were obtained from the experiment with a baseline concentration of 40 wt% NaOH in the various types of liquids. e baseline experiment was that of tap water which is considered neutral. e flow rate was proportional to the salinity but for the water from pressing which presented an exceptionally low flow rate. It was noticed from simulations performed that water from a pressing had a higher void fraction which meant higher bubbles. is could be the reason for the low flow rate. e water from a factory with a high pH value (11.21) presented the highest flow rate of 12.48 × 10 −1 cm 3 / min ( Figure 6). Slama [32] ranked first ammonia water and urine, with hydrogen flow rates of 11.2 cm 3 /min and 11.5 cm 3 /min, respectively. e flow rate of urine is about 10 times more than that of the factory water, which could be explained by the large salinity of urine 33.5 g/l [32]  Void fraction of NaOH + AC water at 80°C 0.12 ε 3 Void fraction of NaOH + pressing water at 90°C 0.35 ε 4 Void fraction of NaOH + factory water at 90°C 0.29 -C 1 Voltage drop for NaOH + tap water at 80°C −1.7087 V C 2 Voltage drop for NaOH + AC water at 80°C −1.5259 V C 3 Voltage drop for NaOH + pressing water at 90°C −2.0872 V C 4 Voltage drop for NaOH + factory water at 90°C −1.8505 V k 1 Correction factor for NaOH + tap water at 80°C 0.034 k 2 Correction factor for NaOH + AC water at 80°C 0.032 k 3 Correction factor for NaOH + pressing water at 90°C 0.033 k 4 Correction factor for NaOH + factory water at 90°C 0.033 -  compared to that of water from a factory with a salinity of 1.015 g/kg (Table 4). e trend in improving the hydrogen production rate clearly indicated that electrolysis depends not only on the number of ions present in solution but also on their mobility in the solution. Gradual increase in bubbles surely decreased the ion mobility due to hindrance. e current efficiencies from the above flow rates were calculated and the values showed that the water from the factory had the highest efficiency of about 77.5%, followed by the AC water with 58.7%, and 53.6% for the water from pressing, in absolute terms. e baseline current efficiency for the tap water is 53.4%. Differences in the efficiency could be a result of the variation in current densities due to parasitic losses within the cell. e result of the water from a pressing was slightly higher than that of the tap water, in absolute terms. is could be explained by the fact that the current density is lower in the case of the tap water. Even though the flow rate of tap water was slightly higher than that of the water from a pressing, the current efficiency of water from pressing was relatively higher; this could be due to gas crossover and the bubble effects.

Conclusion
is study aimed to determine the electrolyte concentration, interelectrode gap, and the type of electrolyte that can improve the production efficiency of hydrogen through water electrolysis. A multiphysical model was obtained and tested and showed conformity with the mathematical model. In fact, the maximum error is below 2%. Results confirmed that reducing interelectrode gap to 0.5 cm, increasing electrolyte concentration to 60 wt% NaOH, and using electrolytes that provoke less bubbles improved cell performance considerably. Furthermore, the flow rate was greater using the factory water. Water from the dress making factory could be recommended as a suitable electrolyte. In addition, it required moderate cell voltage. Combined effects for the three parameters used in this work should be studied using a factorial design.

Data Availability
e experimental data used to support the findings of this study are provided in Supplementary Materials.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.