Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET

Breuer, Johannes; Leweke, Samuel; Schmölder, Johannes; Gassner, Gregor J.; Lieres, Eric von

doi:10.1016/j.compchemeng.2023.108340

Cited by 12 publications

(5 citation statements)

References 32 publications

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“…Therefore, numerical methods were used for their solution. For equations involving spatial variables (e.g., the DPF model), spatial discretization was achieved using the discontinuous Galerkin finite element method (Breuer et al, 2023;Meyer et al, 2020). Its semidiscrete form, along with the CST model, can be efficiently solved by SciPy (Virtanen et al, 2020) using Python 3.10.…”

Section: Numerical Solution and Softwarementioning

confidence: 99%

Residence time distribution in continuous virus filtration

Chen,

Recanati,

De Mathia

et al. 2024

Biotech & Bioengineering

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Regulatory authorities recommend using residence time distribution (RTD) to address material traceability in continuous manufacturing. Continuous virus filtration is an essential but poorly understood step in biologics manufacturing in respect to fluid dynamics and scale‐up. Here we describe a model that considers nonideal mixing and film resistance for RTD prediction in continuous virus filtration, and its experimental validation using the inert tracer NaNO3. The model was successfully calibrated through pulse injection experiments, yielding good agreement between model prediction and experiment ( 0.90). The model enabled the prediction of RTD with variations—for example, in injection volumes, flow rates, tracer concentrations, and filter surface areas—and was validated using stepwise experiments and combined stepwise and pulse injection experiments. All validation experiments achieved 0.97. Notably, if the process includes a porous material—such as a porous chromatography material, ultrafilter, or virus filter—it must be considered whether the molecule size affects the RTD, as tracers with different sizes may penetrate the pore space differently. Calibration of the model with NaNO3 enabled extrapolation to RTD of recombinant antibodies, which will promote significant savings in antibody consumption. This RTD model is ready for further application in end‐to‐end integrated continuous downstream processes, such as addressing material traceability during continuous virus filtration processes.

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Section: Numerical Solution and Softwarementioning

confidence: 99%

Residence time distribution in continuous virus filtration

Chen,

Recanati,

De Mathia

et al. 2024

Biotech & Bioengineering

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“…Discontinuous Galerkin finite element method has demonstrated outstanding accuracy and fast computational speed in solving stiff problems such as these chromatography PDEs. [ 26–28 ]…”

Section: Introductionmentioning

confidence: 99%

“…Galerkin finite element method has demonstrated outstanding accuracy and fast computational speed in solving stiff problems such as these chromatography PDEs. [26][27][28] ( iments, the inverse method (IM) and the Yamamoto method [29,30] can be adopted. However, applying them to practical industrial applications has certain limitations.…”

Section: Introductionmentioning

confidence: 99%

Standardized approach for accurate and reliable model development of ion‐exchange chromatography based on parameter‐by‐parameter method and consideration of extra‐column effects

Chen,

Lu,

Wang

et al. 2024

Biotechnology Journal

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Developing an accurate and reliable model for chromatographic separation that meets regulatory requirements and ensures consistency in model development remains challenging. In order to address this challenge, a standardized approach was proposed in this study with ion‐exchange chromatography (IEC). The approach includes the following steps: liquid flow identification, system and column‐specific parameters determination and validation, multi‐component system identification, protein amount validation, steric mass action parameters determination and evaluation, and validation of the calibrated model's generalization ability. The parameter‐by‐parameter (PbP) calibration method and the consideration of extra‐column effects were integrated to enhance the accuracy of the developed models. The experiments designed for implementing the PbP method (five gradient experiments for model calibration and one stepwise experiment for model validation) not only streamline the experimental workload but also ensure the extrapolation abilities of the model. The effectiveness of the standardized approach is successfully validated through an application about the IEC separation of industrial antibody variants, and satisfactory results were observed with R2 ≈ 0.9 for the majority of calibration and validation experiments. The standardized approach proposed in this work contributes significantly to improve the accuracy and reliability of the developed IEC models. Models developed using this standardized approach are ready to be applied to a broader range of industrial separation systems, and are likely find further applications in model‐assisted decision‐making of process development.

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“…In arbitrary order, DG schemes usually offer higher accuracy for general chromatography settings as demonstrated in previous studies. However, it has been shown recently that there are chromatography settings where unstabilized arbitrary order methods may struggle in chromatography settings with strong gradients . Nonoscillatory schemes can be more efficient and prevent negative values, which can have considerable amplitude for the standard DG methods .…”

Section: Introductionmentioning

confidence: 99%

“…However, it has been shown recently that there are chromatography settings where unstabilized arbitrary order methods may struggle in chromatography settings with strong gradients. 43 Nonoscillatory schemes can be more efficient and prevent negative values, which can have considerable amplitude for the standard DG methods. 35 Hence, we choose a stabilized/TVD DG scheme that is limited to second-order but retains stability for such settings.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Fixed-Bed Chromatographic Processes Considering the Nonlinear Adsorption Isotherms

Khan,

Qamar

2023

ACS Omega

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This paper presents the numerical approximation of a nonlinear equilibrium-dispersive (ED) model of multicomponent mixtures for simulating single-column chromatographic processes. Using Danckwerts boundary conditions (DBCs), the ED is studied for both generalized and standard bi-Langmuir adsorption isotherms. Advection–diffusion partial differential equations are used to represent fixed-bed chromatographic processes. As the diffusion term is significantly weaker than the advection term, sophisticated numerical techniques must be applied for solving such model equations. In this study, the model equations are numerically solved by using the Runge–Kutta discontinuous Galerkin (RKDG) finite element method. The technique is designed to handle sudden changes (sharp discontinuities) in solutions and to produce highly accurate results. The method is tested with several case studies considering different parameters, and its results are compared with the high-resolution finite volume scheme. One-, two-, and three-component liquid chromatography elutions on fixed beds are among the case studies being considered. The dynamic model and its accompanying numerical case studies provide the initial step toward continuous monitoring, troubleshooting, and effectively controlling the chromatographic processes.

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Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET

Cited by 12 publications

References 32 publications

Residence time distribution in continuous virus filtration

Residence time distribution in continuous virus filtration

Standardized approach for accurate and reliable model development of ion‐exchange chromatography based on parameter‐by‐parameter method and consideration of extra‐column effects

Simulation of Fixed-Bed Chromatographic Processes Considering the Nonlinear Adsorption Isotherms

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