i would like to hear your thoughts about your preferred complexity level for chromatography simulation, especially your preferences about when to use the General Rate Model in contrast to the Transport Dispersive Model (Lumped Rate Model with Pores). I am so far using the TDM for simulation of preparative protein chromatography and the accuracy of the simulation seems fine. Moreover, most related literature also uses this model, but some choose the GRM instead.
I view the additional complexity added by the GRM somewhat critical, as the additional pore diffusion parameter can hardly be measured directly. This leads to more fitting parameters, which on the one hand increases the flexibility of the model, but on the other hand could lead to more ambiguity within parameter sets.
What is your preferred approach and do you have certain standards, when to use which model?
Let me expand the scope a little. First of all, the units of some state variables and model parameters are somewhat different and more realistic in the GRM as compared to the TDM (without pores). In the GRM, the mobile and stationary phase concentrations in the porous particles refer to the respective mobile and stationary phase volumes, while in the TDM (without pores), the mobile phase concentration in the particles is neglected and the stionary phase concentration refers to the total particle volume. Even for non-rate-limiting pore diffusion, this is a conceptual difference which can lead to problems when interpreting and comparing model parameters and simulation results.
I would hence recommend using the lumped rate model with pores (LRMP) aka POR model, which brings me back to your original question. The LRMP concides with the GRM when the particles are discretized with just one volume element. In contrast to the TDM, the LRMP and GRM models also account for film diffusion aka external mass transfer.
Even when rate limititing, it can be challenging to independently quantify the contributions of film and pore diffusion but at least one should be accounted for. You can of course use correlations for one of them and use the other to fit your model to the data. Distinguishing between them can be worth the effort when the model is used for advanced predictions. For instance, the film diffusion coefficient is a function of the flow rate while the pore diffusion coefficient is not. Further, pore (and surface) diffusion coefficients can depend on local mobile and stationary phase concentrations in the porous particles while the film diffusion coefficient does not. If you lump film and pore diffusion together, the model cannot predict certain effects.
In the end, I would always recommend using a model that is consistent with the physical dimensions and as simple as possible for answering the question at hand.
I try to use the most capable model given the data that I have available. If I follow a stepwise parameter estimation process with the GRM and find that pore diffusion is not identifiable for a given molecule I either need to have more experiments run to identify it or I remove pore diffusion and step down to the Lumped Rate Model with Pores. If film diffusion and particle porosity can’t be identified I would further step down to the Lumped Rate Model without Pores.
In the end it is not different than other types of fitting. If you fit with a 3rd degree polynomial and you find one of the terms doesn’t matter then you remove that variable and refit without it and see if it makes the other terms better defined without degrading the fit.
Also remember when you are stepping down in models you are not saying that the parameters removed are unimportant. What you are saying is that you don’t have the data to support a model using with that parameter.
CADET-Match generates graphs that can be used to assess if a parameter is identifiable. We also cover that topic briefly in the workshop but during break out sessions I could elaborate on it if you have more questions.
Thank you for sharing your pracitcal experience! I have not yet looked into the identifiability-graphs of CADET-Match, but that seems to be a good approach to select the appropriate model.
Best regards,
Thomas
Hello Eric,
thank you for your insights on this topic. I think the flowrate dependency is a very good point, which benefits the GRM espescially for the prediction at varying flowrates. On the other hand, the dependency of the pore diffusion coefficient on local concentrations makes the determination of this parameter even more problematic. For my current simulations with constant flowrates, I think the GRM is not necessary, but if i want to investigate the effects of different flowrates, i probably should reconsider the appropiate model.
Thanks again for your answer, best regards,
Thomas