This document provides an overview of modeling and simulation approaches for an alkaline water electrolyzer. It describes the electrolysis process and reaction equations. A thermodynamic model is presented that calculates the reversible voltage and thermoneutral potential from changes in Gibbs free energy and enthalpy with temperature. The document also discusses sources of cell overpotential including activation, ohmic resistance, and gas bubble formation that increase the actual operating voltage above the minimum reversible value. Flow rates of hydrogen and oxygen produced are calculated from Faraday's laws using current and Faraday efficiency.

1. Helwan University
Faculty of Engineering at El-Mataria
Department of Mechanical Power Engineering
Modelling and Simulation Approach of an
Alkaline Water Electrolyzer
1- Ahmed Saber Omar 2- Ahmed Sayed Abdelaziz
3- Ahmed Samir Ahmed 4- Ahmed Mohamed Mosallam
5- Adham Ahmed Mahmoud 6- Adham Ragab Mahmoud
7- Alhassan Osama Mahmoud 8- Ibrahim Mostafa Ibrahim
9- Osama Hussein Hussein 10- Nader Mohsen Mohamed
June , 2022

2. 1. Model Description
The process of water electrolysis described as the decomposition of water to its
elements Hydrogen and Oxygen. This process can be achieved by passing a DC
electric current in a based aquas solution of water. The reaction of water splitting is
𝐻𝐻2𝑂𝑂(𝑙𝑙) + 𝐸𝐸𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸
�⎯⎯⎯⎯⎯⎯⎯� 𝐻𝐻2(𝑔𝑔) +
1
2
𝑂𝑂2(𝑔𝑔) (1.1)
The process must be achieved at minimum potential applied on the electrodes. The
required minimum or Reversable Voltage can be calculated from Gibbs energy
equation of water splitting. In an Alkaline Electrolyzer its common to use KOH or
NaOH as an aquas solution. The ions of Na+ and K+ as used to increase the process
of electrolysis by increasing the conductivity and ions of OH- used to increase the
reaction on the anode. The rection on each electrode can be described as
Anode 𝑂𝑂𝑂𝑂−(𝑎𝑎𝑎𝑎)
……………
�⎯⎯⎯⎯�
1
2
𝑂𝑂2(𝑔𝑔) + 𝐻𝐻2𝑂𝑂(𝑙𝑙) + 2𝑒𝑒−
(1.2)
Cathode 2𝐻𝐻2𝑂𝑂(𝑙𝑙) + 2𝑒𝑒−
……………
�⎯⎯⎯⎯� 𝐻𝐻2(𝑔𝑔) + 2𝑂𝑂𝑂𝑂−
(𝑎𝑎𝑎𝑎) (1.3)
Due to that alkaline solution the electrodes must be corrosion resistive and have
good electric conductivity. This could be achieved by using materials like Nickel,
Cobalt and Iron, See [1]. This could be illustrated in other sections.
1.1 Thermodynamic Model
The process of water electrolysis is the converting of electrical energy into chemical
energy. As both Oxygen and Hydrogen are available in the atmosphere, the chemical
energy can be calculated from the difference of enthalpy of formation ∆𝑓𝑓𝐻𝐻. The
change in chemical energy results a change in entropy. And as the change of
chemical energy is the change of enthalpy, the energy required is described by Gibbs
Equation.
ΔG = ΔH − TΔS (1.4)
ΔG = −Δ𝑓𝑓𝐺𝐺𝐻𝐻2𝑂𝑂(𝑙𝑙)
◦
= 237.1 𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑚𝑚
ΔH = −Δ𝑓𝑓𝐻𝐻𝐻𝐻2𝑂𝑂(𝑙𝑙)
◦
= 285.8 𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑚𝑚
The enthalpy of formation of both Hydrogen and Oxygen is zero, but water at the
conditions in Table 1.1 has an enthalpy value.
As water splitting increase entropy through the formation of gas, the TΔS term is
positive and contributes towards making the reaction progress more easily as it

3. decreases the Gibbs free energy. Therefore, the cost in energy supplied as work
required to drive the reaction is less than the energy available by combustion of
hydrogen. This enables water electrolysis to operate at electrical efficiencies above
100%.
Although rarely feasible in practice for alkaline systems due to kinetics, it is
practically possible at high temperatures with free heat energy available. That a fuel
cell or combustion process cannot convert back all the energy available in hydrogen
into work or electrical energy is a different aspect.
Fuel cells suffer the same entropy-driven energy penalty and is also kinetically
limited, whereas combustion processes are limited by the Carnot efficiency, See[2].
Table 1.1.1 Thermodynamic quantities at standard temperature and pressure
(STP), T = 298.15 K, p = 1 bar.
𝚫𝚫𝒇𝒇𝑯𝑯°
𝒌𝒌𝒌𝒌/𝒎𝒎𝒎𝒎𝒎𝒎
𝚫𝚫𝒇𝒇𝑮𝑮°
𝒌𝒌𝒌𝒌/𝒎𝒎𝒎𝒎𝒎𝒎
𝑺𝑺°
𝑱𝑱/𝒎𝒎𝒎𝒎𝒎𝒎. 𝒌𝒌
𝑪𝑪𝒑𝒑
°
𝑱𝑱/𝒎𝒎𝒎𝒎𝒎𝒎. 𝒌𝒌
𝑯𝑯𝟐𝟐 0 0 130.7 28.8
𝑶𝑶𝟐𝟐 0 0 205.2 29.4
𝑯𝑯𝟐𝟐𝑶𝑶(𝒍𝒍) -285.8 -237.1 70 75.3
𝑯𝑯𝟐𝟐𝑶𝑶(𝒈𝒈) -241.8 -228.6 188.8 33.6
1.1.1 Temperature dependence
Increasing the temperature effects on the chemical equilibrium of the system. That
equilibrium is calculated by Gibbs equation. The change in enthalpy and molar
change in entropy is a function of both temperature and heat capacity. At operating
temperature below 100 𝐶𝐶 the variation of heat capacity can be assumed to be
constant. That temperature dependance can be described as
H(T) = 𝐻𝐻◦
+ ∫ 𝐶𝐶𝑝𝑝(𝑇𝑇)𝑑𝑑𝑑𝑑 ≈
𝑇𝑇
𝑇𝑇° 𝐻𝐻◦
+ 𝐶𝐶𝑝𝑝∆𝑇𝑇 (1.5)
S(T) = 𝑆𝑆◦
+ ∫
𝐶𝐶𝑝𝑝(𝑇𝑇)
𝑇𝑇
𝑑𝑑𝑑𝑑 ≈
𝑇𝑇
𝑇𝑇° 𝑆𝑆◦
+ 𝐶𝐶𝑝𝑝 ln
𝑇𝑇
𝑇𝑇°
(1.6)
1.2 Electromechanical Model
1.2.1 Reversible Potential
The electromechanical reversible potential which is the minimum applied potential
to split water is calculated by the equation
𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 =
ΔG
𝑛𝑛𝑛𝑛
(1.7)

4. Where ΔG is Gibbs change in energy from equation (1.4), n is the number of
electrons of the covalent bond of water typically equals 2 and F is Faraday constant.
The reversible value is an ideal value considering no change in entropy (Reversible
process). But for more accurate values at temperatures lower than 100 degrees
Celsius we can consider the process is Isothermal and thus that potential the
thermoneutral potential can be calculated from the change in enthalpy by
𝑉𝑉𝑡𝑡𝑡𝑡 =
ΔH
𝑛𝑛𝑛𝑛
(1.8)
𝑛𝑛 = 2
𝐹𝐹 = 96485 𝐶𝐶/𝑚𝑚𝑚𝑚𝑚𝑚
The values of both 𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 and 𝑉𝑉𝑡𝑡𝑡𝑡 varies with temperature as both enthalpy and
entropy of the system are a function of time functions (1.5 and 1.6). That variation
is illustrated in Table 1.2.
Table 1.2 Variation of 𝑽𝑽𝒓𝒓𝒓𝒓𝒓𝒓 and 𝑽𝑽𝒕𝒕𝒕𝒕 with temperature
Temperature (C) 20 25 40 60 80
𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 (Volt) 1.233 1.229 1.216 1.12 1.183
𝑉𝑉𝑡𝑡𝑡𝑡 (Volt) 1.482 1.481 1.479 1.475 1.472
In conclusion, 𝑉𝑉𝑡𝑡𝑡𝑡 seems to be more accurate as it more practical, but the system
cannot be fully isolated and the conversion of electric energy into heat is
inevitable. So, neither 𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 nor 𝑉𝑉𝑡𝑡ℎ is practical to be used in the cell calculations.
Commonly this lies in the range 1.54-1.74 V for alkaline and PEM systems, See
Figure 1.1. A deeper discussion of this is beyond the scope of this project, and the
reader is referred to the reference.

5. Figure 1.1 The relation between reversible potential 𝑼𝑼𝒓𝒓𝒓𝒓𝒓𝒓 and thermoneutral
potential 𝑼𝑼𝒕𝒕𝒕𝒕.
The thermodynamic temperature behavior of the reaction at standard pressure is
summarized in Figure 1.2.
Figure 1.2 Thermodynamic entities; Gibbs free energy 𝜟𝜟𝒇𝒇𝑮𝑮, enthalpy of formation
𝜟𝜟𝒇𝒇𝑯𝑯 and thermal energy TΔS, and their temperature dependence assuming liquid
water at T < 100◦C.

6. 1.2.2 Cell overpotential
The reversible voltage and thermoneutral are the minimum value of potential
required for splitting water. But in practical, the value required potential is much
higher due to the energy loss of electrodes, foam formed, gas separation on surface,
and electrolyte. The sum of each potential is totally called the cell over potential and
described as shown in Figure 1.3.
As shown in the polarization curve the cell overpotential can be calculated as
𝑉𝑉𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = 𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 + 𝑉𝑉𝑜𝑜ℎ𝑚𝑚 + 𝑉𝑉𝐶𝐶𝐶𝐶𝐶𝐶 (1.9)
Where, 𝑉𝑉
𝑟𝑟𝑟𝑟𝑟𝑟 is the reversible voltage. 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 is the activation voltage used to transfer
charge from the electrodes to electrolyte. 𝑉𝑉𝑜𝑜ℎ𝑚𝑚 is the potential to over come the
resistance of the electrodes and electrolyte, depend on the space between electrodes.
𝑉𝑉
𝑐𝑐𝑐𝑐𝑐𝑐 is the concentration voltage. At concentration of 30% of KOH that value is
very low and can be neglected.
Figure 1.3 Polarization curve of cell over potential.
But in actual cell voltage calculations another two terms are added to the cell voltage
calculations.

7. 𝑉𝑉𝐼𝐼𝐼𝐼 =
𝑖𝑖𝑖𝑖
𝑘𝑘
(1.9)
Where 𝑉𝑉𝐼𝐼𝐼𝐼 the overpotential of cell gap. 𝑖𝑖 is the current per unit area. 𝑙𝑙 the distance
between the electrodes. 𝑘𝑘 the conductivity of electrolyte.
Another parameter effecting the cell overpotential is the bubbles formation which
will be illustrated later.
𝑉𝑉𝑜𝑜ℎ𝑚𝑚 =
𝑟𝑟1+𝑟𝑟2𝑇𝑇
𝐴𝐴
𝐼𝐼 (1.10)
𝑉𝑉
𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑠𝑠 log(
𝑡𝑡1+
𝑡𝑡2
𝑇𝑇
+
𝑡𝑡3
𝑇𝑇2
𝐴𝐴
𝐼𝐼 + 1) (1.11)
Where 𝑡𝑡1, 𝑡𝑡2, 𝑡𝑡3, 𝑟𝑟1, 𝑟𝑟2 and 𝑠𝑠 are the coefficients of overpotential. I is the current
between cell electrodes. T is the operating temperature. A is the active area of
electrodes.
1.3 Flow calculation and faraday efficiency
Faraday efficiency for electrolysis is the ratio between actual amount of hydrogen
produced to the maximum amount of hydrogen can be produced by the system.
Faraday efficiency can be calculated by
𝜂𝜂𝐹𝐹 =
(𝐼𝐼
𝐴𝐴
� )2
𝑓𝑓1+(𝐼𝐼
𝐴𝐴
� )2 𝑓𝑓2 (1.12)
From Faraday efficiency the number of moles of hydrogen produced per unit of
time can be calculated by
𝑛𝑛̇𝐻𝐻2
= 𝑛𝑛̇𝑂𝑂2
= 𝜂𝜂𝑓𝑓
𝑛𝑛𝑐𝑐𝐼𝐼
𝑛𝑛𝑛𝑛
(1.13)
Where 𝑓𝑓1 and 𝑓𝑓2 are faraday efficiency parameters. 𝑛𝑛𝑐𝑐 the number of cells per
stake.
If we assumed both hydrogen and oxygen are ideal gases, the volume flowrate of
hydrogen and oxygen can be calculated by
𝑉𝑉̇ =
𝑛𝑛̇𝐻𝐻2𝑅𝑅𝑅𝑅
𝑝𝑝
(1.14)
Where R is the universal gas constant and p is the pressure at standard conditions.
2 Bubbles formation

8. During the operation of electrolyzer, bubbles of gas forms on the electrode surface.
Those bubbles effects the current and thus the reversible voltage. The bubbles
effect on the electrodes can be expressed by the relation
𝜃𝜃 = 0.365𝑖𝑖0.3
(1.15)
𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =
𝑖𝑖
1−𝜃𝜃
(1.16)
It was found that at fractional bubbles value higher than 0.3, the corrected value
increases significantly, See figure 1.4.
At 𝜃𝜃 = 0.3 the maximum obtained current density 𝑖𝑖 = 1000 𝐴𝐴/𝑚𝑚2
. So according
to the relation 1.15 and 1.16 its recommended to operate at current density lower
than 1000 𝐴𝐴/𝑚𝑚2
.
2.1 Gap analysis
As shown in Figure 2.1 demonstrate a lab experiment to clarify the relation between
cell overpotential and gap between electrodes. The optimum gap between electrodes
is 0.5 mm. This only can be achieved by zero gap cell design. The zero-gap alkaline
electrolyzers are the optimum design to its cost, it’s even more efficient than PEM
electrolyzer. The main reason for the high efficiency of this design is because of the
small gab reduces the effect of the bubbles. Zero gab is achieved by reducing the
gab to be lower than 2 mm and operates on current density higher than 5000 𝐴𝐴/𝑚𝑚2
,

9. See [3,4,5]. This high current density at conventional designs is not efficient. Zero
gab design is out of scope for this project.
Figure 2.1 A plot of cell voltage against the gap between electrodes.
3 Simulation and results
For the system we designed we take consideration of the effect increasing of current
density and bubbles formation. So, our system operates on 800 𝐴𝐴/𝑚𝑚2
.
The coefficients of over potential are lab experimental parameters. There are many
models of those parameters, but the model demonstrated in Table 3.1 and Table 3.2
is more common used.
Table 3.1 Polarization curve parameters.
I-V Curve Parameters Value Unite
𝑟𝑟1 4.45153 𝑒𝑒 − 5 Ω𝑚𝑚2
𝑟𝑟2 6.88874 𝑒𝑒 − 9 Ω𝑚𝑚2
/𝐶𝐶
𝑠𝑠 0.33824 V
𝑡𝑡1 −0.01539 𝑚𝑚2
/𝐴𝐴
𝑡𝑡2 2.00181 𝑚𝑚2
𝐶𝐶/𝐴𝐴
𝑡𝑡3 15.24178 𝑚𝑚2
𝐶𝐶2
/𝐴𝐴

10. Table 3.2 Faraday parameters.
Table 3.2 Electrolyzer design parameters.
Parameter Value Unite
l 0.006 𝑚𝑚
A 0.01 𝑚𝑚2
R 8.314 𝐽𝐽/𝑚𝑚𝑚𝑚𝑚𝑚. 𝐾𝐾
T 40 C
k 290 S/𝑚𝑚2
3.1 Results
3.1.1 System Polarization curve
Parameter Value Unite
𝒇𝒇𝟏𝟏 1500 𝐴𝐴2
/𝑚𝑚2
𝒇𝒇𝟐𝟐 0.99 -
F 96485 𝐶𝐶𝐶𝐶𝐶𝐶/𝑚𝑚𝑚𝑚𝑚𝑚

11. 3.1.2 System Power Consumption
4 References
[1] Ulleberg O., (2003), “Modeling of advanced alkaline electrolyzers: a system
simulation approach”, Institute for Energy Technology.
[2] Kraglund M. R., (2017), “Alkaline membrane water electrolysis with non-
noble catalysts”, Department of Energy Conversion and Storage, Technical
University of Denmark.
[3] Phillips R., Dunnil C., (2016), “Zero gap alkaline electrolysis cell design
for renewable energy storage as hydrogen gas”, The Royal Society of
Chemistry.
[4] Vogt H., (2012), “The actual current density of gas-evolving electrodes—
Notes on the bubble coverage”, Electrochemical Acta.
[5] Nagai N., (2003), “Existence of optimum space between electrodes on
hydrogen production by water electrolysis”, International Journal of
Hydrogen Energy.