Modeling, design and simulation of intensified chromatography processes

In this thesis, methods and tools have been developed to aid the transition towards intensified multi-column chromatography processes through design, modeling and simulation.

A general shortcut Simulated Moving Bed (SMB) design method was developed, which supports the design of multi-component gradient SMBs, a promising process intensification strategy. The method was validated through numerous case studies and can provide good initial guesses for feasible flow rates in process optimizations. However, it was also shown that non-ideal phenomena such as axial dispersion and mass transfer must be taken into account to capture the dynamics of the SMB process. Consequently, the underlying partial differential equations must be solved numerically.

To solve the equations numerically, a combination of the discontinuous Galerkin spectral element method and the Galerkin spectral method for discretizing the equations was implemented in Julia. The developed code base was named CADET-Julia. In two different studies, the Julia implementation was compared to a C++ implementation using the same discretization methods and a finite volume method.

The first study benchmarked simulations of a single chromatography column. To reveal the performance difference due to different programming languages, baseline benchmarks were performed where the same time integrator was used in both the Julia and C++ implementation. The results showed that Julia implementation was faster for smaller systems but the C++ implementation scaled better. Using the best-performing settings
in Julia, the three implementations were benchmarked. Overall, the Julia implementation performed better than the C++ implementation, and the Galerkin methods were generally superior to the finite volume method.

In the second study, the implementations were compared for simulating multi-column chromatography processes, specifically SMBs, in two different benchmarks: The startup phase of a SMB and the simulation until cycling steady state. Furthermore, a one-column analog method was implemented in CADET-Julia as an alternative to simulating all the columns simultaneously for the cyclic steady state simulations. For the startup benchmarks, the Julia implementation performed slightly better than the C++ implementation, and both implementations outperformed the finite volume method, underscoring the advantages of using Galerkin methods for simulating multi-column chromatography processes. The C++ implementation scaled better than the Julia implementation, resulting in a computational advantage for large systems with many degrees of freedom. For the cycling steady state benchmarks, the one-column analog approach performed best for spatial resolutions above a certain threshold of states, otherwise simulating all columns simultaneously using the Julia implementation was slightly faster.

To investigate how hybrid models can be used to model adsorption in chromatography processes, various neural network-based hybrid models of adsorption were developed. Using CADET-Julia as the building block, a systematic screening of ten different hybrid model structures was conducted. The hybrid models were trained and tested on two different case studies of varying complexity, and compared to a validated mechanistic model. The first case study investigated a non-reactive binary component system whereas the second case study investigated a four-component reactive system. For both cases, increasing the size of the neural network in terms of the number of neurons and layers did not necessarily improve model performance. Adding more mechanistic knowledge into the hybrid model for adsorption generally resulted in better hybrid model performance. While many hybrid models performed well on interpolation data, most hybrid models struggled to predict extrapolation data accurately. The successful development and implementation of the hybrid models show that they could potentially be useful for predicting adsorption behavior for chromatography modes where the currently known mechanistic models do not match the complexity of the system. However, more testing of these hybrid models on various systems is needed.
Overall, CADET-Julia is a modular simulation tool capable of simulating arbitrary networks
of unit operations fast. The modular structure of the code base in CADET-Julia and the
high-level language of Julia makes implementing new models straightforward. Using Julia,
a homogeneous programming language, enables seamless combination of different
Julia code bases to evaluate sensitivities and gradients, generate neural networks, solve
differential equations and perform optimization.