# Determine the pore accessibility factor

Hello everybody,

first we implemented a GRM to simulate breakthrough curves of our chromatographic system.

In a next step, we wanted to extend our model with the ‘accessible pore porosity’, but we are not sure how to implement it correctly:

• What is the best way to describe the fact, that not the whole pore volume is accessible by a target molecule/particle (Determination of pore accessibility factor)?
• How does the the pore accessibility factor impact the determination of the maximal load (Qmax) related to the mass balance (eq 2.6, p.10 CADET 4.0.2. Manual)?

Thank you in advance and have a nice weekend everybody!

The pore accessibility factor has been implementet for modeling size exclusion chromatography. It effectively elevates the pore size concentration by reducing the available pore volume. However, I don’t think this formula makes sense in the presence of binding as the available solid phase volume remains unaffected.

I expected pore accessibility to impact retention but in my simulations it has no impact. Is this a coding error or is my assumption about retention incorrect?

I would also expect that, but I cannot see that in the equations.

@s.leweke, do you recall where you found these equations?

I think, it’s in the book of Gu: Mathematical Modeling and Scale-Up of Liquid Chromatography.
There’s a chapter on size-exclusion chromatography.

Another alternative is to use multiple particle types with the same binding model (if any) and the same radius (i.e., the particle types are actually identical). Then, you’d set the film diffusion for the some types and some components to `0`. Thus, some components can enter more particles (i.e., have access to more intra-particle volume) than others. This should yield the same effect.

I have double checked the equations. The CADET documentation is somewhat misleading, as the pore accessibility factor appears in the terms for the time derivative of the bound phase concentration, for the surface diffusion and for reactions in the bound phase. However, these terms are never applied as the pore accessibility factor must be one in the presence of binding, as thoroughly explained by Tingyue Gu, who invented this model. This considered, the equations greatly simplify and the pore accessibility factor only remains in the boundary condition between the bulk and pore phases. This makes sense, as less mass is transferred to the particle pores.

We should add a note and explain this in the documentation.

@s.leweke has successfully reproduced the expected beahvior under these conditions. Can you post the example here?

This is a pulse injection with a general rate model. It has two components, where component `0` has a `PORE_ACCESSIBILITY` of `0.1` and component `1` has `1.0`.

Here’s the model as JSON (call `cadet-cli sec.json sec.h5` for storing the result in `sec.h5`):
sec.json (4.5 KB)

I’ve updated the manual to reflect that SEC should not be modelled with binding.
I also added a note in the interface specifications for all relevant units.

I’m not sure this alternative approach will work, though. Competitive effects between the components would be lost.

Moreover, larger molecules might even just see a ‘core shell’ particle and will never even be able to enter the particle completely. But maybe this could be an approach to model these effects: Consider particle shells which all have the same volumetric saturation capacity while the transport between the shells is limited for some of the components.