Modeling and Simulation related to Column Liquid Chromatography

1. Extending the Model Library and Improving
Numerical Aspects of the Chromatography
Model Solver CADET-CS
SAURABH SINGH

2. CHROMATOGRAPHIC MODEL SOLVER CADET-CS
1SAURABH SINGH
OVERVIEW
15/10/2013
1. MOTIVATION
2. THEORY
3. TASKS & RESULTS
3.1. RADIAL DISCRETIZATIONS
3.2. SURFACE DIFFUSION MODEL
3.3. SELF ASSOCIATION ISOTHERM (SAI) MODEL
3.4. SENSITIVITY ANALYSIS
3.5. EXPERIMENTAL DESIGN STUDY
4. CONCLUSION

3. 2SAURABH SINGH
1. MOTIVATION
15/10/2013
- Column Liquid Chromatography (CLC)
- Applications in separation sciences e.g. protein separation
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
Packed Bed
[Tallarek et al]

4. 2SAURABH SINGH
1. MOTIVATION
15/10/2013
- Column Liquid Chromatography (CLC)
- Applications in separation sciences e.g. protein separation
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
© Metrohm AG

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2. THEORY: MODEL
15/10/2013
- The General Rate Model
COLUMN MODEL
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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- The General Rate Model
COLUMN MODEL
PARTICLE MODEL
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
2. THEORY: MODEL

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- The General Rate Model
COLUMN MODEL
PARTICLE MODEL
SORPTION MODEL
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
2. THEORY: MODEL

8. 3SAURABH SINGH15/10/2013
- The General Rate Model
COLUMN MODEL
PARTICLE MODEL
SORPTION MODEL
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
2. THEORY: MODEL

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2. THEORY: APPROACH
15/10/2013
- Finite Volume Method (FVM)
Mass Conservation
- BDF Scheme
Stiff Equations
- WENO Scheme
Godunov’s Order Barrier Theorem
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
Exact
Solution
2 Points
FD
4 Points
FD
WENO

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2. THEORY: DISCRETE MODEL
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
Components
Column
Particle
Boundary
STATE VECTOR

11. 5SAURABH SINGH
2. THEORY: DISCRETE MODEL
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
Components
Column
Particle
Boundary
STATE VECTOR

12. 5SAURABH SINGH
2. THEORY: DISCRETE MODEL
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
Components
Column
Particle
Boundary
STATE VECTORJACOBIAN MATRIX
How is the sparsity of the Jacobian?

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3.1. RADIAL DISCRETIZATIONS
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- What is Radial Discretization?

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3.1. RADIAL DISCRETIZATIONS
15/10/2013
- Depends on the Number and Distribution of nodes
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

15. 8SAURABH SINGH
3.1. RADIAL DISCRETIZATIONS (Results)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Residual is estimated by comparing coarse grid with finer grid

16. 9SAURABH SINGH
3.1. RADIAL DISCRETIZATIONS (Results)
15/10/2013
- Residual is estimated by comparing coarse grid with finer grid
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

17. 10SAURABH SINGH
3.1. RADIAL DISCRETIZATIONS (Results)
15/10/2013
- Residual decreases linearly & achieves a second order convergence
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

18. 11SAURABH SINGH
3.1. RADIAL DISCRETIZATIONS (Results)
15/10/2013
- Benchmarked on a single core of JuRoPA
- Computational endeavour is directly proportional to the grid size
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.2. SURFACE DIFFUSION MODEL
15/10/2013
- What is Surface Diffusion?
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.2. SURFACE DIFFUSION MODEL
15/10/2013
- Pore Diffusion Model + Surface Diffusion Model
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.2. SURFACE DIFFUSION MODEL
15/10/2013
- Pore Diffusion Model + Surface Diffusion Model
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
PORE DIFFUSION SURFACE DIFFUSION

22. 13SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
- Bandwidth of Jacobian increased due to coupling
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
PARTICLE JACOBIAN (PORE)
PORE DIFFUSION ISOTHERM

23. 13SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
- Bandwidth of Jacobian increased due to coupling
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
PARTICLE JACOBIAN (PORE) PARTICLE JACOBIAN (PORE + SURFACE)
PORE DIFFUSION SURFACE DIFFUSIONISOTHERM

24. 13SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
- Bandwidth of Jacobian increased due to coupling
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
PARTICLE JACOBIAN (PORE) PARTICLE JACOBIAN (PORE + SURFACE)
PORE DIFFUSION SURFACE DIFFUSIONISOTHERM

25. 14SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
- Validation of Surface Diffusion Model was challenging!
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
- Validation of Surface Diffusion Model was challenging!
- Literature suggested the following:
1.) Surface Diffusion Model is a form of Pore Diffusion
2.) Surface Diffusion Coefficient is 2-3 orders of magnitude
lower than Pore Diffusion Coefficient
- The Surface Diffusion Model was then validated by formulating
a parameter estimation problem
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

27. 15SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Numerical studies with SCL and LWE benchmark examples
confirmed the result
SCL Benchmark Example

28. 15SAURABH SINGH
3.2. SURFACE DIFFUSION MODEL (Results)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Numerical studies with SCL and LWE benchmark examples
confirmed the result

29. 16SAURABH SINGH
3.3. SELF ASSOCIATION ISOTHERM
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- What is Self Association Isotherm Model?
- A Isotherm Model describes the behavior of how macromolecules
bind or adsorb to the particle surfaces
- Self Association Isotherm (SAI) Model attempts to model the case
where a protein molecule associates with an adsorbed molecule
- Simplifying by reparametrizing, led to

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3.3. SELF ASSOCIATION ISOTHERM
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Understanding the process of dimerization

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3.3. SELF ASSOCIATION ISOTHERM
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Understanding the process of dimerization

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3.3. SELF ASSOCIATION ISOTHERM
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Understanding the process of dimerization

33. - Validation of SAI Model was another challenging task!
18SAURABH SINGH
3.3. SELF ASSOCIATION ISOTHERM (Result)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

34. - Validation of SAI Model was another challenging task!
- Comparison of SAI Model was carried out with SMA Model
- SAI essentially differs from SMA by a single non-linear term
18SAURABH SINGH15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
3.3. SELF ASSOCIATION ISOTHERM (Result)

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CHROMATOGRAPHIC MODEL SOLVER CADET-CS
3.3. SELF ASSOCIATION ISOTHERM (Result)

36. 19SAURABH SINGH15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
3.3. SELF ASSOCIATION ISOTHERM (Result)

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3.4. SENSITIVITY ANALYSIS
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Sensitivities are partial derivatives of time-dependent state vector y
with respect to specific model parameters pi

38. 20SAURABH SINGH
3.4. SENSITIVITY ANALYSIS
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Sensitivities are partial derivatives of time-dependent state vector y
with respect to specific model parameters pi

39. 21SAURABH SINGH
3.4. SENSITIVITY ANALYSIS
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- How to compute sensitivities?
Δp = 10-1
Δp = 10-6
ALGORITHMIC DIFFERENTIATION (AD)FINITE DIFFERENCES (FD)

40. 21SAURABH SINGH
3.4. SENSITIVITY ANALYSIS
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- How to compute sensitivities?
ALGORITHMIC DIFFERENTIATION (AD)FINITE DIFFERENCES (FD)
Δp = 10-1
Δp = 10-6
Why is FD not good?

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3.4. SENSITIVITY ANALYSIS (Results)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.5. EXPERIMENTAL DESIGN STUDY
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- Often, the measured results/data have noise or error associated
with them
- Task is to examine how error propagates through the model
QUESTIONS
1.) What is the optimal design of an experiment from which only one isotherm
parameter (qm or keq) can be estimated most accurately?
2.) What is the optimal design of an experiment from which both isotherm
parameters (qm and keq) can be (simultaneously) estimated most accurately?
- Used Monte Carlo Method
- Idea is repeated calculations of input parameter(s), each time
perturbing the input data with specific statistical distribution

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3.5. EXPERIMENTAL DESIGN STUDY (Result)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.5. EXPERIMENTAL DESIGN STUDY (Result)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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3.5. EXPERIMENTAL DESIGN STUDY (Result)
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS

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4. CONCLUSION
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- CADET-CS is a fast and accurate solver for the General Rate Model of
Column Liquid Chromatography
- The thesis aimed at extending several aspects of the solver
- Future work and further extensions possible:
 Incorporate the contribution of temperature (Energy Transport)
 Chemical Reaction can also be incorporated (Chemical Transport)
 From application viewpoint, be able to model a complex network
or configuration of chromatographic columns in series or parallel

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REFERENCES
15/10/2013
CHROMATOGRAPHIC MODEL SOLVER CADET-CS
- von Lieres, E.; Andersson, J.: A fast and accurate solver for the general
rate model of column liquid chromatography, Computers and Chemical
Engineering 34,8 (2010), 1180–1191.
- Saurabh Singh: Extending the Model Library and Improving Numerical
Aspects of the Chromatography Model Solver CADET-CS, Master's
Thesis, Juelich Forschungzentrum & Technische Universitaet Muenchen, June
2012.
- Püttmann, A.; Schnittert, S.; Naumann, U.; von Lieres, E.: Fast and
accurate parameter sensitivities for the general rate model of column
liquid chromatography, Computers and Chemical Engineering 56,13
(2013), 46-57.

48. THANK YOU
QUESTIONS?