^{a}Electromechanical Engineer erickdanielrc@ufps.edu.co https://orcid.org/0000-0002-2425-3833
Universidad Francisco de Paula Santander, San José de Cúcuta, Colombia.

^{b}Magister in Automation and Instrumentation josericardobs@ufps.edu.co
https://orcid.org/0000-0001-9265-0083 Universidad Francisco de Paula Santander, San José de Cúcuta, Colombia.

^{c} Magister in Thermal Engineering, Mention Thermofluidics, correo: luisemiliovd@ufps.edu.co, https://orcid.org/0000-0001-8756-7779 Universidad Francisco de Paula Santander, San José de Cúcuta, Colombia.

^{d} PhD in Mechanical Engineering jjgp@unifei.edu.br , https://orcid.org/0000-0002-1894-534X Universidade Federal de Itajubá, Itajubá, Brasil.

**Cómo cotar:**

E.D. Rincon-Castrillo, J.R. Bermudez-Santaella, L.E. Vera-Duarte, J.J. Garcia - Pabon “Modeling and simulation of an electrolyser for the production of HHO in Matlab-Simulink®”. Respuestas, vol. 24, no. 2, 6-15.

Recivido: Agosto 10, 2018; Aceptado: Noviembre 15, 2018

The electrolyzers work through an electrochemical process, their derivatives (H2, O2, and HHO) are used as enriching fuels due to the electrolysis of water, being cleaner than gasoline and diesel. This article presents the dynamic model of an alkaline electrolyzer that uses an electrolyte (KOH o NaHCO3) dissolved in distilled water to accelerate the production of oxyhydrogen (HHO). The model shows the phase change that occurs inside the electrolytic cell. The EES® software was used to determine the values of enthalpy, entropy, and free energy that vary during the electrochemical reaction; the equations were simulated in Matlab-Simulink® to observe their dynamic behavior. The Simulations presented varying every 5 g the electrolyte until reaching 20 g. The flow rate of HHO with potassium hydroxide (20 g) is higher than 0.02 L / s, and with sodium bicarbonate (20 g) it is above 0.0006 L / s, confirming what the literature of alkaline cells state, that the most efficient electrolyte for its energy conversion is KOH.

**Keywords:**Alkaline electrolyser, dynamic model, simulation, Matlab-Simulink®, EES.

Los electrolizadores funcionan mediante un proceso electroquímico, sus derivados (H2, O2, y HHO) debido a la electrólisis del agua son utilizados como combustibles enriquecedores, siendo más limpios que la gasolina y diesel. Este artículo presenta el modelo dinámico de un electrolizador alcalino que utiliza un electrolito (KOH o NaHCO3) disuelto en agua destilada para acelerar la producción de oxihidrógeno (HHO). El modelo muestra el cambio de fase que ocurre en el interior de la celda electrolítica. Se utilizó el software EES® para determinar los valores de entalpía, entropía, y energía libre que varían durante la reacción electroquímica, las ecuaciones fueron simuladas en Matlab-Simulink® para observar su comportamiento dinámico. Las simulaciones fueron realizadas variando cada 5 g el electrolito hasta llegar a 20 g. El caudal de HHO con hidróxido de potasio (20 g) es superior a 0.02 L/s, y con bicarbonato de sodio (20 g) está por encima de 0.0006 L/s, permitiendo confirmar lo que se enuncia en la literatura de celdas alcalinas, donde se establece que el electrolito más eficiente para su conversión energética es KOH.

**Keywords:**Electrolizador alcalino, modelo dinámico, simulación, Matlab-Simulink®, EES.

Voltaic cells and electrolytic cells are fuel cells that operate by means of an electrochemical process in which reagents and products are subjected to an energy imbalance due to the fact that the reaction can be exothermic (it gives off energy) or endothermic (it needs to be supplied with energy), from this perspective the spontaneity of these devices is studied [1].

Fuel cells are a cleaner choice compared to gasoline and diesel used in internal combustion engines [2]. The efficiency of the cells is another parameter that must be taken into account, being approximately twice as high as the thermal engines because the latter are affected by the following limitations established by Carnot’s Theorem [3].

There are several types of fuel cells, currently the classification that is made for these devices is taking into account the type of electrolyte they use, this way we have the AFC (Alkaline Fuel Cells), PEMFC (Proton Exchange Membrane Fuel Cells), DMFC (Direct Methanol Fuel Cells), PAFC (Phosphoric Acid Fuel Cells), MCFC (Fused Carbonate Fuel Cells) and SOFC (Solid Oxide Fuel Cells) [2]. The versatility of the cells has allowed them to have a field of application in the industry specifically in transportation, stationary power systems and portable systems, the last three sectors is where its impact has been most noticeable [1], [4].

The effect caused by fuel cells in industry is largely due to their efficiency in conversion and energy input, to understand the above is necessary to understand the principle of operation of these devices being necessary to identify the mathematical equations that model their dynamic behavior.

In this article the modeling of an electrolyzer or alkaline electrolytic cell (AFC) with a single output will be carried out, for the study of the production of oxyhydrogen gas (HHO) as a clean energy, in this way it can be used as an enriching fuel or enhancer in the processes where combustion takes place. In this research, concepts of thermodynamics, chemistry, thermochemistry, and electrochemistry are taken into account for the approach of the equations, thus enunciating a thermodynamic model, electric model, chemical model, and thermal model. The EES software is used to determine the value of the variables of the thermodynamic model (enthalpy, entropy and free energy), the equations of the other models are simulated in Matlab-Simulink® because some do not present linearity, and others are empirical electrochemical relations.

The phase change (liquid to gaseous state) of the water that occurs in the alkaline electrolyser to be modelled, occurs when energy is supplied to the electrochemical reaction in the form of electrical work (non-spontaneous process) [5].

In order to know in detail what happens in the electrodes of the cell, the generation of gaseous oxygen in the anode is presented by means of (1), and the generation of gaseous hydrogen is shown in the cathode with (2).

Anode:

OH

O

H

e

Cathode:

H

H∆ : Change of enthalpy

S∆ : Change of entropy

G∆ : Free energy exchange

T : Temperature

z : Number of electrons ( 2e− )

F : Faraday Constant (96500 C)

The electric model is designed to determine the current (I) and voltage of the electrolyzer, the relationship between these two variables is modeled by means of (8) found in [11], [12].

r,s,t: Coefficients

A: Electrode area

Source:[11]

Source:[11]

Figure 3 shows a straight line (grade 1 polynomial), because a linear dependence on the temperature of the electrochemical reaction has been assumed in the least squares setting.

c

d

e

∆E= Q −P∆V

∆E: Energy shift

Q: Heat at the entrance.

Because the mathematical model focuses on the phase change of the solution (electrolyte dissolved in water) that by means of an electrochemical reaction at atmospheric pressure, the work (P∆V) is neglected in (17).

C

Electrolyte heat: In the literature of alkaline cells (AFC) when modeling is considered, the energy provided by the electrolyte in the reaction is not studied. Contrary to the previous thing in this investigation the energetic contri-bution of the conductor of second species for this process is analyzed.

The heat of the electrolyte models the calorific or energy potential provided by KOH or NaHCO during the elec-trolysis of water, for its calculation the speed constant (k) and the concentration (CA) must be taken into account by means of (21) [14].

E: Activation energy

R: Ideal gas constant(8.3144 J/mol°C)

For the calculation of the frequency factor (Ko) the mo-les of the reagents, and of the products must be conside-red, as well as it expresses it.

T

T

The thermal resistance is calculated on the acrylic sheets that are part of the electrolyzer as expressed in (26).

L : Thickness of acrylic sheet

K: Thermal conductivity of acrylic

A: Surface of acrylic sheet

With the above values of L, K and A, the thermal resis-tance of the acrylic film is calculated (R1= 6.66 k/W), this value takes great relevance in the simulation.

For the implementation of the mathematical model in Si-mulink, the previously defined equations are added and the respective connection is made. Figure 5 shows the subsystems of the process, where you can see the propo-sed models that simulate the behavior of the electrolytic cell, in which the input variables are the voltage (13.8 V) supplied by the DC source in the process, and the elec-trolyte mass (in kg) in the solution, in order to analyze the reaction temperature and HHO volumetric flow.

Figure 6 shows the behaviour of the electrolyser tempe-rature using, it was dosed every 5 g until reaching 20 g to perceive the increase in temperature at different concen-trations of the electrolyte, the simulated maximum value is above 45°C. On the other hand, the establishment time for the different quantities supplied coincides in 25 s.

Figure 8 and Figure 9 show the variation of the HHO flow rate in the electrolyser with KOH, and NaHCO3, accor-ding to the simulation a HHO flow rate above 0.02 L/s with potassium hydroxide (20 g) is recorded, in the case of sodium bicarbonate (20 g) a lower flow rate is produ-ced (above 0.0006 L/s).Figure 6.

The modeling was performed, and the simulation of an alkaline electrolytic cell that produces oxyhydrogen, in the thermal model the values of the thermal capacitance and thermal resistance influenced notably in the dynamic behavior of the temperature, because Ct adjusts its time of establishment and Rt can make vary its value.

The dynamic behavior in the simulation of the elec-trolyzer with potassium hydroxide was better in compa-rison of sodium bicarbonate, because in the flow (most significant variable) with (20 g) is higher than 0.02 L/s, and with (20 g) is above 0.0006 L/s, allowing to confirm what is stated in the literature of alkaline cells, where it is established that the electrolyte with the most efficient operates is.

The variables analyzed (temperature and flow) showed a behavior directly proportional to each other, ie, as the amount of electrolyte was increased (each 5 g to 20 g) both the temperature and flow increased, this behavior is presented because the current flow is gradually higher, thus happens experimentally in this type electrochemical processes.

In the simulation of the electric and chemical model, it was necessary to calculate some correcting coefficients of adjustment with the nominal operating conditions, and constructive parameters of the electrolyzer, the results were Alpha = 1.038, and Beta = 1.082, these values allow to establish the proximity or the existing closeness be-tween the simulated mathematical model, and the beha-vior of an electrolytic cell experimentally.

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