Adsorption-based processes are widely used to remove contaminants and odors in various everyday applications. These processes often rely on materials with large internal sub-micron surfaces, such as activated carbon or zeolites. For instance, in agriculture, these materials help protect against exposure to fertilizers and pesticides, while they are also vital for ensuring the safety of drinking water and the treatment of wastewater.

Use the Adsorption GeoApp to model those processes by simulating tracer particles moving through the structure and interacting with porous voxels. Within the porous active zone, the governing adsorption equations are solved based on the transported concentration and the equilibrium concentration. The GeoApp is tailored for applications in filtration and gas separation.

The results include breakthrough behavior of given species as well as the locally adsorbed load inside the porous active zones over time. These insights help determine optimal usage durations for adsorbent materials and guide design adjustments, such as geometry changes, to maximize the efficiency and sustainability of valuable materials.

Isotherm Models

Currently two isotherm models are implemented in the Adsorption GeoApp: Langmuir and Toth.

Both models assume monolayer adsorption, where solute species (solute in solvent) can bind to the surface of a solid (adsorbent) until no free adsorption sites are available. The adsorbed solute is called adsorbate. Due to the monolayer adsorption the amount of adsorption sites on the surface is finite with the adsorption of one species per adsorption site.

Already adsorbed species can detach from the surface and switch back to the solute phase. Thus, the process is reversible.

Additionally, the solute behaves like an ideal gas and no interaction between adsorbates is assumed.

The adsorption reaction can be formulated as such:

where is a solute species, is an adsorbent site, and is the adsorbent species.

Below a schematic representation of the adsorption process is shown. Here, (A) depicts the adsorbent surface, (B) indicates the adsorbate at the interface, and (C) shows the solvent containing the solute.

For the Langmuir model the equilibrium loading of the adsorption sites can be calculated by:

All parameters and their units are explained in the table below.

The Toth model is an extension of the Langmuir model that includes temperature dependency to the adsorption reaction. Here, the equilibrium loading of the adsorption sites is computed from:

is the solute partial pressure and can be calculated by:

, , and are Toth parameters and are calculated from these equations:

The calculation of the Toth parameters requires Toth coefficients (, , , , ) that are valid for given adsorbent/adsorbate pairs and can be derived from experiments or found in literature. See Coker and Knox (2014) for some exemplary Toth coefficients.

If you require different adsorption isotherm models to accurately simulate your reactions, please contact us to discuss the possibility of implementation.

Isotherm Models: Used Variables and their Units

In the Adsorption GeoApp, the adsorbent is always represented by a porous material with unresolved porosity. Adsorption then occurs on internal interfaces in this unresolved adsorption zone.

The amount of available adsorption sites is given as a maximum load under the defined equilibrium conditions. Inside the porous zone the tracer representing the solute can loose or gain concentration , while the porous voxel of the adsorbent gains or looses the corresponding adsorbate load . Here, the adsorption speed is defined by the solute concentration and the number of free adsorption sites on the adsorbent surface . The desorption speed is only determined by already occupied number of adsorption sites .

Together with the mass transfer coefficient the uptake rate inside the voxel can be calculated according to the Liner Driving Force model:

The mass transfer coefficient depends on the adsorption reaction that is simulated and must be provided by the user.

When the mass transfer coefficient for the adsorption reaction should differ from the mass transfer coefficient for the desorption reaction ,  the Dual Driving Force model can be employed: