The authors have declared that no competing interests exist.

A planned experimental study on the production of green hydrogen by alkaline electrolysis is carried out by the Plan Composite Centered (PCC) method. The parameters studied are the concentration of the electrolyte, the distance between electrodes, the height of the electrodes, the total supply voltage of the electrolyser, temperature, and the electrolyte type. The results show that the effect of concentration, height, voltage and temperature are positive. However, the effect of the distance between the electrodes is negative. Electrolysis with potassium hydroxide (KOH) is more efficient than with sodium hydroxide (NaOH). The second-order interactions are weak, except for the voltage-temperature interaction which is significant. The results of the experimental study conducted in this work are in agreement with previous studies. Two a polynomial modeling (with KOH and with NaOH) suitable for predicting the flow of hydrogen produced are presented. Three optimizations of ascending constraints on the operating parameters to have a maximum hydrogen production and with a minimum of electrical energy and a minimum of concentration consumed are carried out.

Energy production across the world depends primarily on fossil fuels. This leads to contamination of the environment. An effective alternative to this serious danger is the rapid substitution of fossil fuels, carbon energy sources, by clean renewable energy sources that cause no emissions 1-3. The acceleration of the energy transition is necessary 4-7. It is the gradual transition from carbon-based, polluting energies to clean, renewable, and safe energies. These clean energies are solar, wind, geothermal, hydraulic energy, etc., which meet a series of complementary challenges: the reduction of greenhouse gas emissions; decentralization and redevelopment of infrastructure; reducing inequalities in access to energy and protecting the health of populations. But with all these advantages unfortunately renewable energies also have limitations such as the initial investment is very expensive and the intermittency. Hydrogen as an energy carrier presents itself as a promising solution. There are several sources of hydrogen production with different cleanliness and different colors. The electrolyte is one of the central factors in the electrolyser. This electrolyte must be carefully chosen to reduce the ohmic drops. For industries that need hydrogen in their production process, there is the possibility of producing hydrogen of renewable origin by electrolysis 8. The principle is to install an electrolyser on site, supplied with green electricity (solar and wind), as well as a storage unit. There are several methods and several types of hydrogen production by electrolysis. However, the yield of hydrogen production by electrolysis remains more or less low and further research on it should be carried out 9-11. The work of this article is articulated in this context.

The studies carried out on alkaline electrolysis are numerous but none of them are planned; each

author studies one parameter while keeping the others constant.

In this work a planned parametric study using the centered experimental design method is conducted. To predict the response, we have to do a model. To increase the efficiency of

hydrogen production by electrolysis, the optimal operating parameters must be identified; therefore, an optimization of these parameters is sought.

The design of experiments method consists in establishing an experimental plan comprising the minimum number of experiments taking into account the desired results. The main advantages of this method compared to traditional methods of experimentation are as follows: reduction in the number of tests, possibility of studying the effects of a very large number of factors, detection of possible interactions between factors, determination of the results with good precision, make a reduction of the answer with a modeling and the possibility of making an optimization 12-18. The response matrix of the design of experiments is the rate of hydrogen production.

The main purpose of the Plan Composite Centered (PCC) is to mathematically model the studied responses in the form of a 2nd order polynomial equation and to optimize them. This method is also called the Box-Wilson type design which uses the response surface methodology and is used for continuous variables. The Design-Expert software 18 is used.

The main purpose of the Plan Composite Centered (PCC) is to mathematically model the studied responses in the form of a 2nd order polynomial equation and to optimize them. This method is also called the Box-Wilson type design which uses the response surface methodology and is used for continuous variables. The Design-Expert software 18 is used.

Trials of the two-level full factorial design (coded ∓ 1). The number of experiments

𝑁_{1} = 2^{𝑛} (with n: number of factors)

Star trials (coded ∓𝛼 ) α is the distance from the axial points to the center. The number of experiments 𝑁_{2} = 2𝑛 ; the distance α is calculated by the statistical method:

Trials at the center of the domain (coded 0). The number of experiments 𝑁_{3} this number is used to assess the reproducibility of experiments.

In our study, the answer is the flow of hydrogen produced. The number of factors chosen is five: the concentration of the electrolyte in the electrolyser, the distance between the electrodes, the height of the electrode immersed in the solution, the total supply voltage, the temperature of the solution and the type of electrolytes. Therefore, the total number of experiments is Ntotal=50 experiences ((N1=32, N2=10 et N3=8). We repeated this test matrix twice, once with potassium hydroxide (KOH) electrolyte and once with sodium hydroxide (NaOH) electrolyte (50+50=100 experiences).

The variation interval of each factor is deduced on the one hand from the bibliographical study and on the other hand from the experimental constraints. The five factors and their ranges of variation are listed in

Factor level | Factor level | |||

- α | -1 | 0 | 1 | |

A: Concentration (mol/l) | 0.31 | 1 | 1.5 | 2 |

B: Distance between electrodes (cm) | 3.24 | 6 | 8 | 10 |

C: Electrode height (cm) | 1.62 | 3 | 4 | 5 |

D: Tension (V) | 3.62 | 5 | 6 | 7 |

E: Temperature (°C) | 39.66 | 50 | 57.5 | 65 |

After we fixed the factors and the necessary experimental plan, we carried out the experimental tests to fill the two matrices (with KOH and with NaOH).

To carry out the necessary experiments, we first prepared a tank with the five distances between the electrodes (- α, -1, 0, +1 et + α) where we placed crocodile clips. Then we prepared the solutions with the requested concentrations. We heated the solution to the required temperatures. We carried out the experiments following an order where there is the minimum of the chemicals used.

The experimental results found of the volume flow of hydrogen produced are grouped in

Number of experience | Flow rate (ml/min) | |

with KOH | with NaOH | |

1 | 0.184706 | 0.09696 |

2 | 0,207318 | 0,105009 |

3 | 0,143133 | 0,090897 |

4 | 0,185099 | 0,095343 |

5 | 0,230176 | 0,066979 |

6 | 0,249283 | 0,105197 |

7 | 0,167715 | 0,088113 |

8 | 0,170097 | 0,101885 |

9 | 0,378215 | 0,199641 |

10 | 0,424809 | 0,219925 |

11 | 0,318674 | 0,168563 |

12 | 0,378 | 0,237727 |

13 | 0,433557 | 0,236798 |

14 | 0,449035 | 0,290276 |

15 | 0,338983 | 0,174474 |

16 | 0,350324 | 0,206058 |

17 | 0,188324 | 0,129803 |

18 | 0,239378 | 0,168919 |

19 | 0,179953 | 0,090897 |

20 | 0,200844 | 0,167827 |

21 | 0,254162 | 0,1344 |

22 | 0,319693 | 0,195599 |

23 | 0,167715 | 0,096656 |

24 | 0,343761 | 0,130736 |

25 | 0,402982 | 0,282765 |

The mathematical model is a polynomial model according to the coded factors and applicable to the defined experimental domain. To choose the suggested model, the R² value must be on the one hand close to 1 and on the other hand it is necessary that R² and R² adjusted do not differ considerably; if not then there is a strong chance that there are insignificant terms in the model.

Source | Sequential P-value | lack of adjustment P-value | R2 | Adjusted R2 | predicted R2 | |

Linear | < 0.0001 | 0.0029 | 0.7772 | 0.7519 | 0.7183 | |

2FI | 0.9856 | 0.0014 | 0.7931 | 0.7018 | 0.6042 | |

Quadratic | 0.0018 | 0.0061 | 0.8899 | 0.8139 | 0.5395 | Suggested |

Cubic | 0.9661 | 0.0008 | 0.9213 | 0.7245 | -9.0284 |

Source | Sequential P-value | lack of adjustment P-value | R2 | Adjusted R2 | predicted R2 | |

Linear | < 0.0001 | 0.0004 | 0.8689 | 0.854 | 0.8273 | |

2FI | 0.728 | 0.0003 | 0.8909 | 0.8428 | 0.8167 | |

Quadratic | <0.0001 | 0.0028 | 0.9547 | 0.9235 | 0.8161 | Suggested |

Cubic | 0.2259 | 0.003 | 0.9827 | 0.9393 | -0.7385 |

Source | Sum of squares | Freedom degree | Mean of Square | Ratio-F | Valeur-p Prob > F | Statistical significance |

Model | 0.4711 | 20 | 0.0236 | 11.71 | < 0.0001 | Significant |

A concentration | 0.0185 | 1 | 0.0185 | 9.21 | 0.005 | Significant |

B Distance | 0.0164 | 1 | 0.0164 | 8.14 | 0.0079 | Significant |

C Height | 0.01 | 1 | 0.01 | 4.97 | 0.0337 | Significant |

D Voltage | 0.3569 | 1 | 0.3569 | 177.48 | < 0.0001 | Significant |

E Temperature | 0.0097 | 1 | 0.0097 | 4.83 | 0.0362 | Not significant |

AB | 0.0001 | 1 | 0.0001 | 0.0261 | 0.8727 | Not significant |

AC | 0 | 1 | 0 | 0.019 | 0.8912 | Not significant |

AD | 0.0006 | 1 | 0.0006 | 0.2832 | 0.5986 | Not significant |

AE | 0.0016 | 1 | 0.0016 | 0.7729 | 0.3866 | Not significant |

BC | 0.001 | 1 | 0.001 | 0.476 | 0.4957 | Not significant |

BD | 0.0013 | 1 | 0.0013 | 0.6405 | 0.4301 | Not significant |

BE | 0.001 | 1 | 0.001 | 0.476 | 0.4957 | Not significant |

CD | 0.0019 | 1 | 0.0019 | 0.9482 | 0.3382 | Not significant |

CE | 0.0008 | 1 | 0.0008 | 0.4129 | 0.5255 | Significant |

DE | 0.0003 | 1 | 0.0003 | 0.1344 | 0.7166 | Not significant |

A |
0.002 | 1 | 0.002 | 1 | 0.3252 | Significant |

B |
428 | 1 | 428 | 21.3 | <0.0001 | Not significant |

C |
0.0114 | 1 | 0.0114 | 0.9152 | 0.3467 | Significant |

D |
0.0018 | 1 | 0.0018 | 5.67 | 0.024 | Significant |

E |
0.0064 | 1 | 0.0064 | 3.17 | 0.0856 | Not significant |

Source | Sum of Squares | Freedom degree | Mean of squares | Ratio-F | Valeur-p Prob > F | Statastical Significance |

Model | 0.3493 | 20 | 0.0175 | 30.56 | < 0.0001 | Significant |

A concentration | 0.0245 | 1 | 0.0245 | 42.91 | < 0.0001 | Significant |

B Distance | 0.0114 | 1 | 0.0114 | 20 | 0.0001 | Significant |

C Height | 0.0003 | 1 | 0.0003 | 0.4439 | 0.5105 | Not significant |

D Voltage | 0.2479 | 1 | 0.2479 | 433.84 | < 0.0001 | Significant |

E Temperature | 0.0338 | 1 | 0.0338 | 59.07 | < 0.0001 | Significant |

AB | 0.0002 | 1 | 0.0002 | 0.3327 | 0.5685 | Not significant |

AC | 0.0001 | 1 | 0.0001 | 0.2102 | 0.65 | Not significant |

AD | 0.0007 | 1 | 0.0007 | 1.17 | 0.2892 | Not significant |

AE | 0.0015 | 1 | 0.0015 | 2.6 | 0.1178 | Not significant |

BC | 0.001 | 1 | 0.001 | 1.77 | 0.1935 | Not significant |

BD | 0.0008 | 1 | 0.0008 | 1.4 | 0.2463 | Not significant |

BE | 0.0005 | 1 | 0.0005 | 0.896 | 0.3517 | Not significant |

CD | 0.0004 | 1 | 0.0004 | 0.686 | 0.4143 | Not significant |

CE | 0.0001 | 1 | 0.0001 | 0.1479 | 0.7034 | Not significant |

DE | 0.0028 | 1 | 0.0028 | 4.92 | 0.0345 | Significant |

A |
0.0001 | 1 | 0.0001 | 0.1182 | 0.7335 | Not significant |

B |
0.0012 | 1 | 0.0012 | 2.01 | 0.1666 | Not significant |

C |
0.0001 | 1 | 0.0001 | 0.1379 | 0.7131 | Not significant |

D |
0.0154 | 1 | 0.0154 | 26.99 | < 0.0001 | Significant |

E |
0.0101 | 1 | 0.0101 | 17.66 | 0.0002 | Significant |

The two models (for KOH and for NaOH) are validated by the Fischer test.

The significant parameters if the electrolyte is KOH are A, B, C, D, E, 𝐵

The significant parameters if the electrolyte is NaOH are A, B, D, E, DE, 𝐷

The effects and interactions on the response are grouped in Table 5a and

Effects | Interactions | Quadratic effects | |||

x_{0} |
0.2249 | x_{12} |
0.0013 | x_{11} |
0.006 |

x_{1} |
0.0207 | x_{13} |
-0.0011 | x_{22} |
0.0278 |

x_{2} |
-0.0194 | x_{14} |
-0.0042 | x_{33} |
0.0058 |

x_{3} |
0.0152 | x_{15} |
0.007 | x_{44} |
0.0143 |

x_{4} |
0.0908 | x_{23} |
-0.0055 | x_{55} |
0.0107 |

x_{5} |
0.015 | x_{24} |
-0.0063 | ||

x_{25} |
0.0055 | ||||

x_{34} |
-0.0077 | ||||

x_{35} |
0.0051 | ||||

x_{45} |
-0.0029 |

Effects | Interactions | Quadratic effects | |||

x_{0} |
0.1556 | x_{12} |
0.0024 | x_{11} |
0.0011 |

x_{1} |
0.0238 | x_{13} |
0.0019 | x_{22} |
0.0045 |

x_{2} |
-0.0162 | x_{14} |
0.0046 | x_{33} |
0.0012 |

x_{3} |
0.0024 | x_{15} |
0.0068 | x_{44} |
0.0167 |

x_{4} |
0.0757 | x_{23} |
-0.0056 | x_{55} |
0.0135 |

x_{5} |
0.0279 | x_{24} |
-0.005 | ||

x_{25} |
-0.004 | ||||

x_{34} |
0.0035 | ||||

x_{35} |
-0.0016 | ||||

x_{45} |
0.0094 |

The histograms of

From the ANOVA analysis, we can note that:

Concentration has a positive and significant effect regardless of the electrolyte used. This shows that if the concentration of the electrolyte increases the flow rate increases. This is explained by the fact that if the concentration increases then the charge transfer increases. These results are in agreement with the results of Fatima ezzahra Chakik et al

The distance between the electrodes has a negative and significant effect for both types of electrolytes. That is, if the distance between the electrodes increases then the hydrogen production rate decreases. Indeed, increasing the distance between the electrodes increases the path traveled by the charges, so it limits the production speed. N. Nagai et al

The supply voltage has a positive effect and is the most important parameter regardless of the electrolyte used (which is noticeable in Figures 4-a and 4-b). Dayana D'arc of Fatima Palhares et al 21 found that if the tension increases the production also increases. The same result is found by Kenji Kikuchi et al

The operating temperature has a positive and significant effect whatever the electrolyte used. Yangyang Li et al

The height of the electrodes has a positive and significant effect if the electrolyte is KOH. If the electrolyte is NaOH, the effect of the height of the electrodes is also positive but not significant.

From our results, we can notice very clearly that electrolysis with KOH is more efficient than electrolysis with NaOH. As long as the diameter of the electrolyte is large as long as the transfer is faster. These results are in good agreement with the results of M. Hassen sellami et al ^{30-31}; will no longer be the case, especially if wastewater is used in the electrolyser

According to the ANOVA analysis, we notice that no interaction of order 2 is significant with the KOH electrolyte. The only significant interaction found is DE (voltage-temperature) with the electrolyte NaOH.

The equation in terms of coded factors can be used to make predictions about rethink for given levels of each factor. By default, higher levels of factors are coded as +1 and lower levels are coded as -1. The coded equation is useful for determining the relative impact of factors by comparing factor coefficients.

The quadratic complete model used is given by the following equation:

𝑞 = 𝑥_{0} + 𝑥_{1} 𝐴 + 𝑥_{2} 𝐵 + 𝑥_{3} 𝐶 + 𝑥_{4} 𝐷 + 𝑥_{5} 𝐸 + 𝑥_{12} 𝐴𝐵 + 𝑥_{13} 𝐴𝐶 + 𝑥_{14} 𝐴𝐷 + 𝑥_{15} 𝐴𝐸

+ 𝑥_{23} 𝐵𝐶 + 𝑥_{24} 𝐵𝐷 + 𝑥_{25} 𝐵𝐸 + 𝑥_{34} 𝐶𝐷 + 𝑥_{35} 𝐶𝐸 + 𝑥_{45} 𝐷𝐸 + 𝑥_{11} 𝐴^{2}

+ 𝑥_{22} 𝐵_{33} 𝐶_{44} 𝐷^{55} 𝐸^{2}

with:

𝑥_{0}, 𝑥_{1}, 𝑥_{2}, 𝑥_{3}, 𝑥_{4}, 𝑥_{5} : average effects of variables respectively A, B, C, D, E.

𝑥_{12}, 𝑥_{13}, 𝑥_{14}, 𝑥_{15}, 𝑥_{23}, 𝑥_{24}, 𝑥_{25}, 𝑥_{34}, 𝑥_{35}, 𝑥_{45} : effect of variable interactions.

𝑥_{11}, 𝑥_{22}, 𝑥_{33}, 𝑥_{44}, 𝑥_{55} : quadratic effects of variables.

We can improve the complete model by eliminating insignificant factors from the complete model and we obtain a so-called reduced model.

if the electrolyte is KOH the reduced model is:

𝑞 = 0.2249 + 0.0207 𝐴 − 0.0194 𝐵 + 0.0152 𝐶 + 0.0908 𝐷 + 0.0150 𝐸 + 0.0278 𝐵

+ 0.0143 𝐷^{2}

𝑞 = 0.1556 + 0.0238 𝐴 − 0.0162 𝐵 + 0.0757 𝐷 + 0.0279 𝐸 + 0.0094 𝐷𝐸 + 0.0167 𝐷

+ 0.0107 𝐸^{2}

To study the adequacy of the found model, we draw the curve which represents the values given by the model according to the experimental values. Figure 5-a and Figure 5-b respectively show the adequacy of the model if the electrolyte is KOH and if the electrolyte is NaOH.

Optimization seeks a combination of factor levels that simultaneously meet the established criteria for a best desired response.

2603500142240000 | Objective | Importance | Results | |

Optimization 1 | A : Concentration (mol/l) | - | - | 2 |

B : Distance between electrodes | - | - | 6 | |

(cm) | ||||

C : Height (cm) | - | - | 5 | |

D : Voltage (V) | - | - | 7 | |

E : Temperature (°C) | - | - | 65 | |

Hydrogen flow rate (ml/min) | Maximize | 5 | 0.372 | |

Optimization 2 | A : Concentration (mol/l) | - | - | 2 |

B : Distance between electrodes | - | - | 6 | |

(cm) | ||||

C : Height (cm) | - | - | 4.99 | |

D : Voltage (V) | Minimize | 2 | 6.167 | |

E : Temperature (°C) | - | - | 65 | |

Hydrogen flow rate (ml/min) | Maximize | 5 | 0.274 | |

Optimization 3 | A : Concentration (mol/l) | Minimize | 2 | 1 |

B : Distance between electrodes | - | - | 6 | |

(cm) | ||||

C : Height (cm) | - | - | 5 | |

D : Voltage (V) | Minimize | 2 | 6.262 | |

E : Temperature (°C) | - | - | 65 | |

Hydrogen flow rate (ml/min) | Maximize | 5 | 0.229 |

In this study three optimizations are carried out:

Optimization 1: The objective in this optimization is to maximize hydrogen production independently of other parameters. That is, to maximize the hydrogen production rate and the other parameters are random.

Optimization 2: In this optimization we will keep the same objective as the first optimization, and we add the condition to minimize the supply voltage of the electrolyser.

Optimization 3: n this optimization we will keep the same objective as the first optimization, and we add the condition to minimize the supply voltage of the electrolyzer and the condition to also minimize the concentration of the electrolyte.

Three optimizations of ascending constraints on the operating parameters to have a maximum hydrogen production are carried out. We notice that if we increase the constraints on the optimized parameters the value of the response (Hydrogen flow rate) decreases.

A planned experimental study on the production of green hydrogen by alkaline electrolysis is carried out by the Centered Composite Plan (PCC) method. The parameters studied are the concentration, the distance between electrodes, the height, the voltage, the temperature, and the type of electrolytes. The results show that the effect of the concentration, the height of the electrodes, the total voltage and the temperature are positive whatever the type of electrolyte. So, increasing these parameters increases hydrogen production. However, the effect of the distance between the electrodes is negative, so an increase in this distance leads to a decrease in the production of hydrogen. The interactions between the different parameters are weak and the only significant interaction is the voltage-temperature interaction. The experimental study conducted in this work gives a good agreement with previous studies. Two models (with KOH and with NaOH) suitable for predicting the flow of hydrogen produced are presented. Three optimizations of ascending constraints on the operating parameters to have a maximum hydrogen production are carried out.

Conflicts of Interest: no conflict of interest