Electrochemistry modeling in electrolysis devices or a hydrogen pump is very similar to that in the fuel cell add-on module described in Electrochemistry Modeling in the Fluent Theory Guide. The major difference is that in the fuel cell model, the electrical potential is fixed at zero on the anode side, while in the electrolysis and H2 pump model, it is fixed at zero on the cathode side.

In the Butler-Volmer equations (Equation 20–5 and Equation 20–6), the concentration dependence of species is modeled in different electrolysis devices as follows:

Typically, the electrolysis of water produces gaseous hydrogen and oxygen in electrolysis devices, which makes them multiphase fluid systems. The Ansys Fluent mixture multiphase model (see Mixture Model Theory in the Fluent Theory Guide) is used in electrolysis and hydrogen pump modeling where the gaseous phase is treated as the primary phase, while liquid water is treated as the secondary phase. The volume fraction of liquid water is obtained based on [586]:

(18–17)

where

= volume fraction of liquid water

= porosity

= liquid water density

= velocity of mixture

= osmotic drag coefficient

= ionic current density calculated as , where and are the electrolyte conductivity and electrolyte potential of the membrane, respectively

= Faraday constant (9.65x107 C/kmol)

= molecular weight of liquid water

= absolute permeability

= relative permeability

= liquid dynamic viscosity

= capillary pressure

= source term for liquid water due to electrochemistry reactions, which depends on electrochemistry reactions and is calculated based on transfer currents

= rate of the mass change between water vapor and liquid water

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Note:  The first term on the right-hand side in Equation 18–17 models the capillary pressure effects. In porous media, the liquid water velocity based on liquid water pressure gradient can be estimated from Darcy’s law as:

where is the liquid water pressure. Therefore, the first term can be derived as:

Note that this treatment is only an approximation.

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The third term on the left-hand side of Equation 18–17 represents the effect of electro-osmotic drag, which considers the movement of water through the membrane under the influence of a current carried by ions. Since the flow of membrane zone is not solved, the osmotic drag is treated as a source term in the catalyst layers. In the PEM electrolysis and alkaline electrolysis models, the liquid water is moved due to the movement of ions, while in the H2 pump, the water vapor is moved due to the movement of ions. The osmotic drag coefficient is defined as:

(18–18)

where is the water content, and is the modified osmotic drag coefficient that is used to generalize the osmotic drag coefficient. In the PEM electrolysis and alkaline electrolysis models, since liquid water is always abundant, the membrane is assumed to be fully hydrated, that is =22. In the hydrogen pump, the water content is estimated using an empirical relation as a function of relative humidity [214]:

(18–19)

In electrolysis devices, especially in an H2 pump, sometimes the membrane is not fully hydrated. The membrane hydration level affects electrolyte conductivity. To obtain the membrane hydration level, the transport equation of the water content is solved across the membrane. To account for the effect of the membrane hydration level on the electrolyte conductivity, user-defined functions can be used in Ansys Fluent. To model the water content across the membrane, Ansys Fluent uses the so-called equilibrium approach, which is summarized as follows:

The transport equations of species are solved for the primary phase. The volumetric source terms (kg/m³-s) for liquid water, hydrogen, and oxygen due to electrochemistry reactions are calculated at the adjacent cells of the interface. The source terms due to electrochemistry reactions are shown in Table 18.1: Source Terms for Species and Liquid Water due to Electrochemistry Reactions.

In the above table, , , and are the molecular mass of water, oxygen, and hydrogen, respectively. and are calculated using Equation 20–5 and Equation 20–6.

For alkaline electrolysis and a hydrogen pump, the method to calculate these sources terms is the same, although the formulations are different due to the difference in electrochemical reactions.

The mass transfer rate between water vapor and liquid water is computed based on the diffusion theory:

(18–22)

where

= porosity

= condensation rate coefficient

= evaporation rate coefficient

= water vapor partial pressure

= water saturation pressure

= liquid water saturation

= universal gas constant

= temperature

In an electrolysis device, both the catalyst and the porous layers are often porous media. Therefore, the effects of capillary pressure are also considered in electrolysis simulation. In Ansys Fluent, you can use either the default Leverett function (see Equation 20–35 - Equation 20–37) or user-defined functions to calculate capillary pressure. In Ansys Fluent, capillary pressure is treated as a diffusion term for the liquid volume fraction as shown the first term on the right-hand side of Equation 18–17 [586].

For pressurized water electrolysis, typically, the cathode side has higher pressure. As a result, the gas species or liquid water can cross membrane from the higher pressure side to the lower pressure side. To consider such species or liquid water crossover (or permeation), Fick’s law is used to estimate the species flux cross the membrane:

(18–23)

where is the species permeation rate [kg/(m² s)], is the pressure difference between the cathode and anode side, is the thickness of membrane cell zone, and is the permeation coefficient calculated by:

(18–24)

where [kg/(m² s)] is the permeation rate constant, and [J/kmol] is the permeation activation energy. In Ansys Fluent, the volume-averaged pressures on the catalyst layers are used to determine the pressure difference. Since the flow is not solved in the membrane zone, the species permeation is treated as source terms in the first layer of computational cells near the interface between the catalyst layers and membrane.

Additional volumetric sources in the thermal energy equation are present because not all electrical work can be converted into chemical energy when producing hydrogen and oxygen. Thermal energy is generated during electrolysis due to electrochemical reactions and irreversibilities of the processes. Volumetric heat source terms in various zones are listed in Table 18.2: Volumetric Heat Source Terms.

In this table:

= solid phase current density

= membrane phase current density

= conductivity of the solid phase

= surface overpotential given by Equation 20–11

= surface overpotential given by Equation 20–12

= temperature

= number of electrons involved in the electrochemistry reactions

and = entropy change in Equation 20–13 and Equation 20–14, respectively