Linear + Langmuir isotherm in CADET-Process

Chromatography Modeling
1

Hi everyone

I would like to use a Linear + Langmuir binding model in CADET-Process. Something like:

q_i = m_i C_i + \dfrac{Q b_i C_i}{1 + b_1 C_1 + b_2 C_2}

I see Langmuir and Bi-Langmuir models in CADET already, but if I’m understanding correctly, Linear + Langmuir version is not possible at the moment. What would be my options?

Do I have to implement the Linear+Langmuir model following instructions from Registration, Implementation and Testing of New Binding Model in CADET?

Following this, I still have to implemented it in CADET-Process right? Or will I be able to use it in CADET-Process or only in CADET?

Any tips on how to do this?

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It seems like you have a two-component system (i=2). I don’t think combinations of different isotherms are supported now, but as you mentioned, you can always implement customized isotherm in CADET core, but it will take some efforts. I would instead think about some numerical treatment to configure the available isotherms to your ones. For instance, a two-component Bi-Langmuir isotherm is:

q_1 = \frac{Q_{11} b_{11} C_1}{1 + b_{11} C_1 + b_{12} C_2} + \frac{Q_{21} b_{21} C_1}{1 + b_{21} C_1 + b_{22} C_2}

and

q_2 = \frac{Q_{12} b_{12} C_2}{1 + b_{11} C_1 + b_{12} C_2} + \frac{Q_{22} b_{22} C_2}{1 + b_{21} C_1 + b_{22} C_2}

This is already available in CADET. You can set b_{11} and b_{12} to a small number such that the denominator (b_{11} C_1 + b_{12} C_2) is approximately 1. And further set Q_{11} and Q_{12} to large numbers such that Q_{11} b_{11} = m_1 and Q_{12} b_{12} = m_2. This would make the first term the same as the linear isotherm.

2 Likes
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I agree with Flynn, the Bi-Langmuir (or in CADET, the N-Langmuir) can already be considered a superset of Linear and Langmuir isotherms. There are even further extensions that we would love to implement eventually, e.g. as reported in Lars Aumann’s PhD thesis.

Edit: I just remembered, we do have the Extended Mobile Phase Modulator model where you can set flags for Linear vs (modulated) Langmuir for each component. So this one should work out of the box.

1 Like
4

Thanks to both.

Hacking the Bi-Langmuir model to fall back to Linear+Langmuir was on my mind but I was wondering if I it would play nice since b_i is in both the denominator and numerator. I will try it.

I was not aware of the Extended Mobile Phase Modulator model, I will look into it.