diff --git a/master/_sources/getting_started/installation.rst.txt b/master/_sources/getting_started/installation.rst.txt
index 3c05ffbb5..e775dd851 100644
--- a/master/_sources/getting_started/installation.rst.txt
+++ b/master/_sources/getting_started/installation.rst.txt
@@ -3,17 +3,17 @@
Installation
============
-A CADET installation consists of two parts: The CADET core simulator and a frontend.
+A CADET installation consists of two parts: The CADET-Core simulator and a frontend.
-Install CADET core simulator
+Install CADET-Core simulator
----------------------------
The core simulator can be compiled from source, or you can download pre-built binaries.
-If you want to extend or modify CADET (e.g., add a custom binding model), you will need to build CADET from source.
+If you want to extend or modify CADET-Core (e.g., add a custom binding model), you will need to build CADET-Core from source.
Install pre-built binaries
^^^^^^^^^^^^^^^^^^^^^^^^^^
-CADET can be installed via `conda `_ from the ``conda-forge channel``.
+CADET-Core can be installed via `conda `_ from the ``conda-forge channel``.
``conda install -c conda-forge cadet``
diff --git a/master/_sources/index.rst.txt b/master/_sources/index.rst.txt
index d54b536ac..a1e50400d 100644
--- a/master/_sources/index.rst.txt
+++ b/master/_sources/index.rst.txt
@@ -20,12 +20,13 @@
:target: https://www.fz-juelich.de/en/rse/community-initiatives/jurse-code-of-the-month/october-2024
|
-CADET
-=====
-CADET is developed at the Institute of Bio- and Geosciences 1 (IBG-1) of Forschungszentrum Jülich (FZJ) under supervision of Dr. Eric von Lieres.
-The heart of the CADET software is a fast and accurate solver for a comprehensive model family.
+CADET-Core
+==========
+
+CADET is developed at the Institute of Bio- and Geosciences 1 (IBG-1) of Forschungszentrum Jülich (FZJ) under supervision of Prof. Eric von Lieres.
+The heart of the CADET software is CADET-Core, a fast and accurate solver for a comprehensive model family.
Typical applications include (but are by far not limited to) chromatography, filtration, crystallization, and fermentation.
-CADET can handle arbitrary sequences and networks of unit operations, including reactors, tanks, tubes, pumps, valves, detectors, etc.
+CADET-Core can handle arbitrary sequences and networks of unit operations, including reactors, tanks, tubes, pumps, valves, detectors, etc.
The resulting models are solved with state-of-the-art mathematical algorithms and scientific computing techniques.
- **Forum:** https://forum.cadet-web.de
@@ -47,7 +48,8 @@ Features
Installation
------------
-CADET can be installed via conda from the ``conda-forge`` channel.
+
+CADET-Core can be installed via conda from the ``conda-forge`` channel.
``conda install -c conda-forge cadet``
@@ -63,7 +65,7 @@ Ongoing Development
-------------------
We do our best to provide you with a stable API.
-However, CADET is actively developed and breaking changes can sometimes be unavoidable.
+However, CADET-Core is actively developed and breaking changes can sometimes be unavoidable.
For non-developers, it is recommended to upgrade from release to release instead of always working with the most recent commit.
@@ -75,16 +77,16 @@ Please report any bugs that you find `here `_ for helping to host, maintain, and further develop the CADET project are highly appreciated.
+`Donations `_ for helping to host, maintain, and further develop the CADET-Core project are highly appreciated.
Citing
------
-The development of CADET has been a collaborative effort, with multiple dedicated individuals contributing their expertise to create a powerful and versatile open-source software tool.
+The development of CADET-Core has been a collaborative effort, with multiple dedicated individuals contributing their expertise to create a powerful and versatile open-source software tool.
Countless hours of hard work have been invested to provide the scientific community with a valuable resource.
-As an open-source project, CADET relies on the support and recognition from users and researchers to thrive.
-Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET acknowledge its creators and their contributions by citing an adequate selection of our publications.
+As an open-source project, CADET-Core relies on the support and recognition from users and researchers to thrive.
+Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET-Core acknowledge its creators and their contributions by citing an adequate selection of our publications.
**General:**
@@ -92,22 +94,22 @@ Therefore, we kindly ask that any publications or projects leveraging the capabi
- 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.
-**Numerics:**
+**Major extensions:**
- Breuer, J. M.; Leweke, S.; Schmölder, J.; Gassner, G.; von Lieres, E.: `Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET `_, Computers and Chemical Engineering **177** (2023), 108340.
-- Leweke, S.; von Lieres, E.: `Fast arbitrary order moments and arbitrary precision solution of the general rate model of column liquid chromatography with linear isotherm `_, Computers and Chemical Engineering **84** (2016), 350–362.
+- Zhang, W.; Przybycien T., Schmölder J. , Leweke S. , von Lieres E.: `Solving crystallization/precipitation population balance models in CADET, part I: Nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids `_, Computers and Chemical Engineering 183 (2024), 108612.
- 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** (2013), 46–57.
-Additionally, to ensure reproducibility of your work, we recommend citing the `zenodo doi `_ corresponding to the specific CADET release that you used.
+Additionally, to ensure reproducibility of your work, we recommend citing the `zenodo doi `_ corresponding to the specific CADET-Core release that you used.
-Selected applications that demonstrate the capabilities and use-cases of CADET are highlighted `here `_.
+For a comprehensive list and guidance on citing CADET-Core publications, please refer to the publications section of the `documentation `_.
Acknowledgments
---------------
-Please refer to the `list of contributors `_ who helped building and funding this project.
+Please refer to the `list of authors and contributors `_ who helped building and funding this project.
.. toctree::
@@ -119,9 +121,9 @@ Please refer to the `list of contributors
license
+ publications
zbibliography
Legal notice
diff --git a/master/_sources/interface/unit_operations/index.rst.txt b/master/_sources/interface/unit_operations/index.rst.txt
index 078802e29..3c1ac1736 100644
--- a/master/_sources/interface/unit_operations/index.rst.txt
+++ b/master/_sources/interface/unit_operations/index.rst.txt
@@ -15,5 +15,5 @@ Unit Operations
cstr
radial_flow_models
multi_channel_transport_model
- population_balance_model
+ ../population_balance_model
diff --git a/master/_sources/publications.md.txt b/master/_sources/publications.md.txt
deleted file mode 100644
index 22db96e46..000000000
--- a/master/_sources/publications.md.txt
+++ /dev/null
@@ -1,28 +0,0 @@
-
-**General CADET-Core:**
-
-- Leweke, S.; von Lieres, E.: `Chromatography Analysis and Design Toolkit (CADET) `_, Computers and Chemical Engineering **113** (2018), 274–294.
-
-- 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.
-
-**CADET-Core numerics:**
-
-- Breuer, J. M.; Leweke, S.; Schmölder, J.; Gassner, G.; von Lieres, E.: `Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET `_, Computers and Chemical Engineering **177** (2023), 108340.
-
-- Leweke, S.; von Lieres, E.: `Fast arbitrary order moments and arbitrary precision solution of the general rate model of column liquid chromatography with linear isotherm `_, Computers and Chemical Engineering **84** (2016), 350–362.
-
-- 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** (2013), 46–57.
-
-**Selected applications and use-cases of CADET-Core:**
-
-- Heymann, W.; Glaser, J.; Schlegel, F.; Johnson, W.; Rolandi, P.; von Lieres, E.: `Advanced score system and automated search strategies for parameter estimation in mechanistic chromatography modeling `_, Journal of Chromatography A **1661** (2022): 462693.
-
-- He, Q.-L.; Leweke, S.; von Lieres, E.: `Efficient numerical simulation of simulated moving bed chromatography with a single-column solver `_, Computers and Chemical Engineering **111** (2018), 183–198.
-
-- Freier, L.; von Lieres, E.: `Robust multi-objective global optimization of stochastic processes with a case study in gradient elution chromatography `_, Biotechnology Journal **13,1** (2018), 1700257.
-
-- Freier, L.; von Lieres, E.: [Multi-objective global optimization (MOGO): `Algorithm and case study in gradient elution chromatography `_, Biotechnology Journal **12,7** (2017), 1600613.
-
-- Diedrich, J.; Heymann, W.; Leweke, S.; Kunert, C.; Johnson, W.; Hunt, S.; Todd, B.; von Lieres, E.: `Multi-state steric mass-action model and case study on complex high loading behavior of mAb on ion exchange tentacle resin `_, Journal of Chromatography A **1525** (2017), 60–70.
-
-- Püttmann, A.; Schnittert, S.; Leweke, S.; von Lieres, E.: `Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities `_, Chemical Engineering Science, **139** (2016), 152–162.
diff --git a/master/_sources/publications.rst.txt b/master/_sources/publications.rst.txt
new file mode 100644
index 000000000..bb95dbc7e
--- /dev/null
+++ b/master/_sources/publications.rst.txt
@@ -0,0 +1,64 @@
+Publications
+============
+
+As an open-source project, CADET-Core relies on the support and recognition from users and researchers to thrive.
+Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET-Core acknowledge its creators and their contributions by citing an adequate selection of our publications.
+
+
+General CADET-Core publications
+-------------------------------
+
+**Publication of CADET-Core with its current C++ architecture**
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ Leweke2018CADET
+
+**Original Publication of chromatography models and their FV discretization in CADET**
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ VonLieres2010a
+
+
+CADET-Core Numerics and Modeling
+--------------------------------
+
+**Publication on DG discretization of axial transport models (GRM, LRMP, LRM) in CADET-Core**
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ Breuer2023
+
+**Publications on Crystallization models and their entropy-preserving FV discretization in CADET-Core**
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ ZHANG2025solving
+ zhang2024solving
+
+**Publications on Parameter sensitivites and (compressed) algorithmic differentiation**
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ Puttmann2016
+ Puttmann2013
+
+
+CADET-Core SELECTED APPLICATIONS AND USE-CASES
+----------------------------------------------
+
+.. bibliography:: literature.bib
+ :filter: False
+
+ Lanzrath2024
+ Heymann2022advanced
+ Jaepel2022
+ Schmoelder2020
+ He2018
+ Diedrich2017
diff --git a/master/developer_guide/build_options.html b/master/developer_guide/build_options.html
index 6f85b8d00..988038382 100644
--- a/master/developer_guide/build_options.html
+++ b/master/developer_guide/build_options.html
@@ -62,6 +62,7 @@
The core simulator can be compiled from source, or you can download pre-built binaries.
-If you want to extend or modify CADET (e.g., add a custom binding model), you will need to build CADET from source.
+If you want to extend or modify CADET-Core (e.g., add a custom binding model), you will need to build CADET-Core from source.
CADET is developed at the Institute of Bio- and Geosciences 1 (IBG-1) of Forschungszentrum Jülich (FZJ) under supervision of Dr. Eric von Lieres.
-The heart of the CADET software is a fast and accurate solver for a comprehensive model family.
+
+
CADET is developed at the Institute of Bio- and Geosciences 1 (IBG-1) of Forschungszentrum Jülich (FZJ) under supervision of Prof. Eric von Lieres.
+The heart of the CADET software is CADET-Core, a fast and accurate solver for a comprehensive model family.
Typical applications include (but are by far not limited to) chromatography, filtration, crystallization, and fermentation.
-CADET can handle arbitrary sequences and networks of unit operations, including reactors, tanks, tubes, pumps, valves, detectors, etc.
+CADET-Core can handle arbitrary sequences and networks of unit operations, including reactors, tanks, tubes, pumps, valves, detectors, etc.
The resulting models are solved with state-of-the-art mathematical algorithms and scientific computing techniques.
We do our best to provide you with a stable API.
-However, CADET is actively developed and breaking changes can sometimes be unavoidable.
+However, CADET-Core is actively developed and breaking changes can sometimes be unavoidable.
For non-developers, it is recommended to upgrade from release to release instead of always working with the most recent commit.
The development of CADET has been a collaborative effort, with multiple dedicated individuals contributing their expertise to create a powerful and versatile open-source software tool.
+
The development of CADET-Core has been a collaborative effort, with multiple dedicated individuals contributing their expertise to create a powerful and versatile open-source software tool.
Countless hours of hard work have been invested to provide the scientific community with a valuable resource.
-As an open-source project, CADET relies on the support and recognition from users and researchers to thrive.
-Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET acknowledge its creators and their contributions by citing an adequate selection of our publications.
+As an open-source project, CADET-Core relies on the support and recognition from users and researchers to thrive.
+Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET-Core acknowledge its creators and their contributions by citing an adequate selection of our publications.
Additionally, to ensure reproducibility of your work, we recommend citing the zenodo doi corresponding to the specific CADET release that you used.
-
Selected applications that demonstrate the capabilities and use-cases of CADET are highlighted here.
+
Additionally, to ensure reproducibility of your work, we recommend citing the zenodo doi corresponding to the specific CADET-Core release that you used.
+
For a comprehensive list and guidance on citing CADET-Core publications, please refer to the publications section of the documentation.
Unlike the multi component Langmuir model and the multi component Bi-Langmuir model that presume a fixed number of discrete binding sites, the affinity energy distribution (AED) model considers a continuous distribution of binding site types on a heterogeneous surface on the energy space \(\ln(K_{eq}) \in \mathbb{R}^{>0}\) (see e.g. [3]).
-Assuming a single component system, the AED isotherm reads [3]:
+
Unlike the multi component Langmuir model and the multi component Bi-Langmuir model that presume a fixed number of discrete binding sites, the affinity energy distribution (AED) model considers a continuous distribution of binding site types on a heterogeneous surface on the energy space \(\ln(K_{eq}) \in \mathbb{R}^{>0}\) (see e.g. [3]).
+Assuming a single component system, the AED isotherm reads [3]:
The Freundlich isotherm model is an empirical model that considers changes in the equilibrium constant of the binding process due to the heterogeneity of the surface and the variation of the interaction strength [11, 12].
+
The Freundlich isotherm model is an empirical model that considers changes in the equilibrium constant of the binding process due to the heterogeneity of the surface and the variation of the interaction strength [11, 12].
This variant of the model is based on the linear driving force approximation (see section Linear Driving Force (LDF)) and is given as
The generalized ion exchange model is based on the steric mass action model [13, 14].
+
The generalized ion exchange model is based on the steric mass action model [13, 14].
In addition to the first component \(c_{p,0}\), which represents salt, the second component \(c_{p,1}\) represents another non-binding modifier (e.g., pH).
In comparison to the SMA model, the characteristic charge \(\nu\) and the adsorption and desorption rate constants are modified:
This model implements a slightly modified version of the HIC isotherm by Wang et al. based on their 2016 paper [16].
+
This model implements a slightly modified version of the HIC isotherm by Wang et al. based on their 2016 paper [16].
A naive multicomponent version was added that reduces to the original formulation if only 1 binding species is present.
This model is a modified Langmuir model (see Section Multi Component Langmuir) which can be used to describe hydrophobic interaction chromatography [17, 18].
+
This model is a modified Langmuir model (see Section Multi Component Langmuir) which can be used to describe hydrophobic interaction chromatography [17, 18].
A modulator component (termed “saltâ€, \(c_{p,0}\) and \(q_0\)) influences ad- and desorption processes:
The multi component Bi-Langmuir model [3] adds \(M - 1\) additional types of binding sites \(q_{i,j}\) (\(0 \leq j \leq M - 1\)) to the Langmuir model (see Section Multi Component Langmuir) without allowing an exchange between the different sites \(q_{i,j}\) and \(q_{i,k}\) (\(k \neq j\)).
+
The multi component Bi-Langmuir model [3] adds \(M - 1\) additional types of binding sites \(q_{i,j}\) (\(0 \leq j \leq M - 1\)) to the Langmuir model (see Section Multi Component Langmuir) without allowing an exchange between the different sites \(q_{i,j}\) and \(q_{i,k}\) (\(k \neq j\)).
Therefore, there are no competitivity effects between the different types of binding sites and they have independent capacities.
The colloidal isotherm assumes that adsorbed protein molecules are evenly distributed in a hexagonal arrangement at equilibrium, with the coverage varying via adjustment of the lattice size [19].
+
The colloidal isotherm assumes that adsorbed protein molecules are evenly distributed in a hexagonal arrangement at equilibrium, with the coverage varying via adjustment of the lattice size [19].
Protein-surface interactions are captured in a parameter \(K_{e}\).
The surface coverage is modulated at higher coverage, described by a Yukawa potential.
The Yukawa constant \(b_{pp}\) characterizes protein-protein interactions.
diff --git a/master/modelling/binding/multi_component_langmuir.html b/master/modelling/binding/multi_component_langmuir.html
index 75a67b509..ebd4de02b 100644
--- a/master/modelling/binding/multi_component_langmuir.html
+++ b/master/modelling/binding/multi_component_langmuir.html
@@ -64,6 +64,7 @@
The Langmuir binding model includes a saturation term and takes into account the capacity of the resin [3, 20].
+
The Langmuir binding model includes a saturation term and takes into account the capacity of the resin [3, 20].
All components compete for the same binding sites.
In this binding model an additional quadratic term is added to the linear model [21].
+
In this binding model an additional quadratic term is added to the linear model [21].
The quadratic term allows to take interactions of liquid phase components into account.
This binding model is similar to the steric mass action model (see Section Steric Mass Action) but is also capable of describing dimerization [14, 22].
+
This binding model is similar to the steric mass action model (see Section Steric Mass Action) but is also capable of describing dimerization [14, 22].
The dimerization, which is the immobilization of protein at some already bound protein, is also termed “self-associationâ€.
It is modeled by adding a quadratic (in \(c_{p,i}\)) term to the adsorption part of the equation.
The steric mass action model takes charges of the molecules into account [23] and is, thus, often used in ion-exchange chromatography.
+
The steric mass action model takes charges of the molecules into account [23] and is, thus, often used in ion-exchange chromatography.
Each component has a characteristic charge \(\nu\) that determines the number of available binding sites \(\Lambda\) (ionic capacity) used up by a molecule.
Due to the molecule’s shape, some additional binding sites (steric shielding factor \(\sigma\)) may be shielded from other molecules and are not available for binding.
In CADET, we chose particle size and axial coordinate as the internal and external coodinate respectively.
The PBM in CADET is implemented so that it can be used in any unit operation that supports reactions.
Typical applications consider crystallization in a CSTR or, to model continuous processes, in a Dispersive Plug-Flow Reactor (DPFR), which is described by the LRM without solid phase.
-
In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to [24].
+
In the following, we give a brief overview on the modelling equations, for more information on the PBM as implemented in CADET, please refer to [24].
The general rate model is the most comprehensive model of mass transfer in column liquid chromatography, when only the axial coordinate in the column and the radial coordinate in the beads are considered [1, 2, 3, 4].
+
The general rate model is the most comprehensive model of mass transfer in column liquid chromatography, when only the axial coordinate in the column and the radial coordinate in the beads are considered [1, 2, 3, 4].
The main assumptions are:
The cross sections of the column are homogenous in terms of interstitial volume, fluid flow, and distribution of components.
@@ -190,7 +191,7 @@
The GRM describes transport of solute molecules through the interstitial column volume by convective flow, band broadening caused by axial dispersion, mass transfer resistance through a stagnant film around the beads, pore (and surface) diffusion in the porous beads [5, 6, 7], and adsorption to the inner bead surfaces.
+
The GRM describes transport of solute molecules through the interstitial column volume by convective flow, band broadening caused by axial dispersion, mass transfer resistance through a stagnant film around the beads, pore (and surface) diffusion in the porous beads [5, 6, 7], and adsorption to the inner bead surfaces.
Consider a column of length \(L>0\) filled with spherical beads of (possibly) multiple types with radius \(r_{p,j} \ll L\) (see Fig. 2), where \(j\) is the particle type index. The mass balance in the interstitial column volume is described by
Here, \(c^\ell_i\colon \left[0, T_{\text{end}}\right] \times [0, L] \rightarrow \mathbb{R}^{\geq 0}\) denotes the concentration in the interstitial column volume, \(c^p_{j,i}\colon \left[0, T_{\text{end}}\right] \times [0, L] \times [r_{c,j}, r_{p,j}] \rightarrow \mathbb{R}^{\geq 0}\) the liquid phase concentration in the beads, \(k_{f,j,i}\geq 0\) the film diffusion coefficient, \(D_{\text{ax},i}\geq 0\) the dispersion coefficient, \(u\in\mathbb{R}\) the interstitial velocity, \(d_j > 0\) the volume fraction of particle type \(j\), and \(\frac{1}{\beta_c} = (1 - \varepsilon_c) / \varepsilon_c\) the column phase ratio, where \(\varepsilon_c\in (0,1]\) is the column porosity (ratio of interstitial volume to total column volume).
If reactions are considered, the term \(f_{\text{react},i}^\ell\left(c^\ell\right)\) represents the net change of concentration \(c_i\) due to reactions involving component \(i\).
-
Danckwerts boundary conditions [8] are applied to inlet and outlet of the column:
+
Danckwerts boundary conditions [8] are applied to inlet and outlet of the column:
(2)¶\[\begin{aligned}
u c_{\text{in},i}(t) &= u c^\ell_i(t,0) - D_{\text{ax},i} \frac{\partial c^\ell_i}{\partial z}(t, 0) & \forall t > 0,
@@ -302,7 +303,7 @@
The general rate model can be used to simulate size exclusion chromatography (SEC) [2].
+
The general rate model can be used to simulate size exclusion chromatography (SEC) [2].
The particle porosity \(\varepsilon_{p,j}\) on the mobile phase side of the transport equations is replaced by a component-dependent accessible porosity
The radial flow GRM describes transport of solute molecules through the interstitial column volume by radial convective flow, band broadening caused by radial dispersion, mass transfer resistance through a stagnant film around the beads, pore (and surface) diffusion in the porous beads [5, 6, 7], and adsorption to the inner bead surfaces.
+
The radial flow GRM describes transport of solute molecules through the interstitial column volume by radial convective flow, band broadening caused by radial dispersion, mass transfer resistance through a stagnant film around the beads, pore (and surface) diffusion in the porous beads [5, 6, 7], and adsorption to the inner bead surfaces.
The main assumptions are:
The cylindrical shells of the column are homogenous in terms of interstitial volume, fluid flow, and distribution of components.
@@ -364,7 +365,7 @@
Branches
\end{aligned}\end{split}\]
Here, \(c^\ell_i\colon \left[0, T_{\text{end}}\right] \times [\mathrm{P}_c, \mathrm{P}] \rightarrow \mathbb{R}^{\geq 0}\) denotes the concentration in the interstitial column volume, \(c^p_{j,i}\colon \left[0, T_{\text{end}}\right] \times [P_c, P] \times [r_{c,j}, r_{p,j}] \rightarrow \mathbb{R}^{\geq 0}\) the liquid phase concentration in the beads, \(k_{f,j,i}\geq 0\) the film diffusion coefficient, \(D_{\text{rad},i}\geq 0\) the dispersion coefficient, \(u>0\) the interstitial velocity, \(d_j>0\) the volume fraction of particle type \(j\), and \(\beta_c = \varepsilon_c / (1 - \varepsilon_c)\) the column phase ratio, where \(\varepsilon_c\in(0,1)\) is the column porosity (ratio of interstitial volume to total column volume).
If reactions are considered, the term \(f_{\text{react},i}^\ell\left(c^\ell\right)\) represents the net change of concentration \(c_i\) due to reactions involving component \(i\).
-
Danckwerts boundary conditions [8] are applied to inlet and outlet of the column:
+
Danckwerts boundary conditions [8] are applied to inlet and outlet of the column:
(11)¶\[\begin{aligned}
u c_{\text{in},i}(t) &= u c^\ell_i(t,0) - D_{\text{rad},i} \frac{\partial c^\ell_i}{\partial \rho}(t, 0) & \forall t > 0,
diff --git a/master/modelling/unit_operations/index.html b/master/modelling/unit_operations/index.html
index 9faf4f9b6..ad02d93d2 100644
--- a/master/modelling/unit_operations/index.html
+++ b/master/modelling/unit_operations/index.html
@@ -67,6 +67,7 @@
The lumped rate model with pores [3, 4] deviates from the general rate model (see Section General rate model (GRM)) by neglecting pore diffusion.
+
The lumped rate model with pores [3, 4] deviates from the general rate model (see Section General rate model (GRM)) by neglecting pore diffusion.
The particle phase \(c^p_j\) is still there, but no mass transfer happens except for binding and film diffusion.
Hence, the model equations are given by
The lumped rate model without pores [3, 4] deviates from the lumped rate model with pores (see Section Lumped rate model with pores (LRMP)) by neglecting pores completely.
+
The lumped rate model without pores [3, 4] deviates from the lumped rate model with pores (see Section Lumped rate model with pores (LRMP)) by neglecting pores completely.
The particle phase \(c^p\) is removed and the porosity \(\varepsilon_t\) is taken as total porosity
The Multichannel Transport (MCT) model in CADET is based on a class of compartment models introduced by Jonas Bühler et al. [9], which was originally developed in the field of plant sciences.
+
The Multichannel Transport (MCT) model in CADET is based on a class of compartment models introduced by Jonas Bühler et al. [9], which was originally developed in the field of plant sciences.
There it is used to determine transport and storage parameters of radioactive labelled tracer molecules from positron emission tomography (PET) or magnetic resonance imaging (MRI) based experimental data.
The model represents main functions of vascular transport pathways: axial transport of the tracer, diffusion in axial direction, lateral exchange between compartments and storage of tracer in compartments. Here, the axial direction represents the length of the stem of the plant and the lateral dimension its cross section. In the MCT context, the compartments of the model class are also referred to as channels.
-
The same model equations arise in describing other biological and technical processes outside of the field of plant sciences, where solutes are transported and exchanged between spatially separated compartments, for example liquid-liquid chromatography (LLC). Here, components in a mixture are separated based on their interactions with two immiscible phases of a biphasic solvent system [10]. The MCT model represents these phases by channels with respective transport and exchange properties. While the current implementation only covers linear driving forces for the exchange processes, the reaction module in CADET allows to add non-linear driving forces for the exchange processes and other chemical reactions in the channels.
+
The same model equations arise in describing other biological and technical processes outside of the field of plant sciences, where solutes are transported and exchanged between spatially separated compartments, for example liquid-liquid chromatography (LLC). Here, components in a mixture are separated based on their interactions with two immiscible phases of a biphasic solvent system [10]. The MCT model represents these phases by channels with respective transport and exchange properties. While the current implementation only covers linear driving forces for the exchange processes, the reaction module in CADET allows to add non-linear driving forces for the exchange processes and other chemical reactions in the channels.
The MCT model equations are given for all channels \(l \in \{1, \dots, N_k\}\) and components \(i \in \{1, \dots, N_c\}\) by
where \(e^i_{lk}\) denotes the exchange rate of component \(i\) from channel \(l\) to channel \(k\), and \(A_l\) denotes the cross section area of channel \(l\).
-The equations are complemented by Danckwerts boundary conditions [8]
+The equations are complemented by Danckwerts boundary conditions [8]
The cross-section area \(A_N\) is individually specified for each channel (see Fig. 7). The MCT is agnostic to the shape of these cross sections, while their ratio determines the distribution of the volumetric flow.
The MCT can be used to model tracer transport in plants, following Jonas Bühler et al. [9].
+
The MCT can be used to model tracer transport in plants, following Jonas Bühler et al. [9].
There, the model class is defined by a system of partial differential equations:
Leweke, S.; von Lieres, E.: ChromatographyAnalysisandDesignToolkit(CADET)<https://doi.org/10.1016/j.compchemeng.2018.02.025>_, Computers and Chemical Engineering 113 (2018), 274?294.
-
von Lieres, E.; Andersson, J.: Afastandaccuratesolverforthegeneralratemodelofcolumnliquidchromatography<https://doi.org/10.1016/j.compchemeng.2010.03.008>_, Computers and Chemical Engineering 34,8 (2010), 1180?1191.
-
-
CADET-Core numerics:
-
-
Breuer, J. M.; Leweke, S.; Schm?lder, J.; Gassner, G.; von Lieres, E.: SpatialdiscontinuousGalerkinspectralelementmethodforafamilyofchromatographymodelsinCADET<https://doi.org/10.1016/j.compchemeng.2023.108340>_, Computers and Chemical Engineering 177 (2023), 108340.
-
Leweke, S.; von Lieres, E.: Fastarbitraryordermomentsandarbitraryprecisionsolutionofthegeneralratemodelofcolumnliquidchromatographywithlinearisotherm<http://dx.doi.org/10.1016/j.compchemeng.2015.09.009>_, Computers and Chemical Engineering 84 (2016), 350?362.
-
P?ttmann, A.; Schnittert, S.; Naumann, U.; von Lieres, E.: Fastandaccurateparametersensitivitiesforthegeneralratemodelofcolumnliquidchromatography<http://dx.doi.org/10.1016/j.compchemeng.2013.04.021>_, Computers and Chemical Engineering 56 (2013), 46?57.
-
-
Selected applications and use-cases of CADET-Core:
-
-
Heymann, W.; Glaser, J.; Schlegel, F.; Johnson, W.; Rolandi, P.; von Lieres, E.: Advancedscoresystemandautomatedsearchstrategiesforparameterestimationinmechanisticchromatographymodeling<https://doi.org/10.1016/j.chroma.2021.462693>_, Journal of Chromatography A 1661 (2022): 462693.
-
He, Q.-L.; Leweke, S.; von Lieres, E.: Efficientnumericalsimulationofsimulatedmovingbedchromatographywithasingle-columnsolver<http://doi.org/10.1016/j.compchemeng.2017.12.022>_, Computers and Chemical Engineering 111 (2018), 183?198.
As an open-source project, CADET-Core relies on the support and recognition from users and researchers to thrive.
+Therefore, we kindly ask that any publications or projects leveraging the capabilities of CADET-Core acknowledge its creators and their contributions by citing an adequate selection of our publications.
Publication of CADET-Core with its current C++ architecture
+
+
+
+[LvL18]
+
Samuel Leweke and Eric von Lieres. Chromatography analysis and design toolkit (cadet). Computers & Chemical Engineering, 113:274–294, 2018. doi:10.1016/j.compchemeng.2018.02.025.
+
+
+
+
Original Publication of chromatography models and their FV discretization in CADET
+
+
+
+[vLA10]
+
Eric von Lieres and Joel Andersson. A fast and accurate solver for the general rate model of column liquid chromatography. Computers & Chemical Engineering, 34(8):1180–1191, August 2010. doi:10.1016/j.compchemeng.2010.03.008.
Publication on DG discretization of axial transport models (GRM, LRMP, LRM) in CADET-Core
+
+
+
+[BLS+23]
+
Jan Michael Breuer, Samuel Leweke, Johannes Schmölder, Gregor Gassner, and Eric von Lieres. Spatial discontinuous galerkin spectral element method for a family of chromatography models in cadet. Computers & Chemical Engineering, 177:108340, 2023. doi:10.1016/j.compchemeng.2023.108340.
+
+
+
+
Publications on Crystallization models and their entropy-preserving FV discretization in CADET-Core
+
+
+
+[ZPBvL25]
+
Wendi Zhang, Todd Przybycien, Jan Michael Breuer, and Eric von Lieres. Solving crystallization/precipitation population balance models in cadet, part ii: size-based smoluchowski coagulation and fragmentation equations in batch and continuous modes. Computers & Chemical Engineering, 192:108860, 2025. doi:10.1016/j.compchemeng.2024.108860.
+
+
+[ZPS+24]
+
Wendi Zhang, Todd Przybycien, Johannes Schmölder, Samuel Leweke, and Eric von Lieres. Solving crystallization/precipitation population balance models in cadet, part i: nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids. Computers & Chemical Engineering, pages 108612, 2024. doi:10.1016/j.compchemeng.2024.108612.
+
+
+
+
Publications on Parameter sensitivites and (compressed) algorithmic differentiation
+
+
+
+[PSLvL16]
+
Andreas Püttmann, Sebastian Schnittert, Samuel Leweke, and Eric von Lieres. Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities. Chemical Engineering Science, 139:152–162, January 2016. doi:10.1016/j.ces.2015.08.050.
+
+
+[PSNvL13]
+
Andreas Püttmann, Sebastian Schnittert, Uwe Naumann, and Eric von Lieres. Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography. Computers & Chemical Engineering, 56:46–57, September 2013. doi:10.1016/j.compchemeng.2013.04.021.
Juliane Diedrich, William Heymann, Samuel Leweke, Stephen Hunt, Robert Todd, Christian Kunert, Will Johnson, and Eric von Lieres. Multi-state steric mass action model and case study on complex high loading behavior of mab on ion exchange tentacle resin. Journal of Chromatography A, 1525:60–70, 2017. doi:10.1016/j.chroma.2017.09.039.
+
+
+[HLvonLieres18]
+
Qiao-Le He, Samuel Leweke, and Eric von Lieres. Efficient numerical simulation of simulated moving bed chromatography with a single-column solver. Computers & Chemical Engineering, 111:183–198, 2018. doi:https://doi.org/10.1016/j.compchemeng.2017.12.022.
+
+
+[HGS+22]
+
William Heymann, Juliane Glaser, Fabrice Schlegel, Will Johnson, Pablo Rolandi, and Eric von Lieres. Advanced score system and automated search strategies for parameter estimation in mechanistic chromatography modeling. Journal of Chromatography A, 1661:462693, 2022. doi:https://doi.org/10.1016/j.chroma.2021.462693.
+
+
+[JB22]
+
Ronald Colin Jäpel and Johannes Felix Buyel. Bayesian optimization using multiple directional objective functions allows the rapid inverse fitting of parameters for chromatography simulations. Journal of Chromatography A, 1679:463408, 2022. doi:10.1016/j.chroma.2022.463408.
+
+
+[LvLMH24]
+
Hannah Lanzrath, Eric von Lieres, Ralf Metzner, and Gregor Johannes Huber. Analyzing Time Activity Curves from Spatio-Temporal Tracer Data to Determine Tracer Transport Velocity in Plants. September 2024. doi:10.2139/ssrn.4957804.
+
+
+[SK20]
+
Johannes Schmölder and Malte Kaspereit. A Modular Framework for the Modelling and Optimization of Advanced Chromatographic Processes. Processes, 8(1):65, 2020. doi:10.3390/pr8010065.
This chapter gives an overview of the simulation process and the different steps involved.
-
CADET uses a backward-differentiation-formula (BDF) time discretization as implemented by the IDAS solver from SUNDIALS [25].
+
CADET uses a backward-differentiation-formula (BDF) time discretization as implemented by the IDAS solver from SUNDIALS [25].
Each time step requires the solution of a nonlinear algebraic system of equations is performed by a Newton method.
Since chromatographic systems can exhibit strong nonlinearity and stiff systems, the Jacobian of the equation system is always updated (i.e., an “exact†Newton method is used).
@@ -256,7 +257,7 @@
Branches
&= \frac{\partial F}{\partial y}(t, y, \dot{y}, p) s + \frac{\partial F}{\partial \dot{y}}(t, y, \dot{y}, p) \dot{s} + \frac{\partial F}{\partial p}(t, y, \dot{y}, p).
\end{aligned}\end{split}\]
These linear DAEs depend on the solution \(y\), \(\dot{y}\) of the original DAE system.
-Consequently, the sensitivity systems are solved together with the original DAE system in a staggered approach [26].
+Consequently, the sensitivity systems are solved together with the original DAE system in a staggered approach [26].
After the nonlinear Eq. 29 has been successfully solved using Newton iteration (i.e., it has passed the convergence test), each sensitivity is solved using the same Newton iteration.
If direct linear solvers were used, this iteration would convergence with a single iteration as there is no nonlinearity.
The Newton method for the sensitivities performs at most MAX_NEWTON_ITER_SENS (see Table Group /solver/time_integrator) iterations.
@@ -264,7 +265,7 @@
Branches
The sensitivities can be excluded from the local truncation error test by setting ERRORTEST_SENS appropriately.
Note that time integration step size is always affected by sensitivities due to possible convergence test failures.
While the Jacobians \(\partial F / \partial y\) and \(\partial F / \partial \dot{y}\) can be computed either analytically or via AD, the last term \(\partial F / \partial p\) is always computed by AD.
-In fact, the terms \(\partial F / \partial y\) and \(\partial F / \partial p\) can be computed by one AD-enabled evaluation of \(F\) using the vector mode with appropriate seed vectors [27].
+In fact, the terms \(\partial F / \partial y\) and \(\partial F / \partial p\) can be computed by one AD-enabled evaluation of \(F\) using the vector mode with appropriate seed vectors [27].
A parameter sensitivity is specified by identifying the involved parameters, which can be more than one (see below).
Parameters are identified by name and multiple indices, which may not all be used (see Tab. Group /input/sensitivity/param_XXX). Indices that are not used for identification (e.g., flow rate is independent of bound phase or component) are set to \(-1\). All other indices are zero-based.
Note that the sensitivity systems need to be consistently initialized, too.
diff --git a/master/zbibliography.html b/master/zbibliography.html
index 5ae67d18a..6830efbfe 100644
--- a/master/zbibliography.html
+++ b/master/zbibliography.html
@@ -15,7 +15,7 @@
-
+
@@ -48,6 +48,7 @@
Georges Guiochon, Attila Felinger, Dean G. Shirazi, and Anita M. Katti. Fundamentals of Preparative and Nonlinear Chromatography. Elsevier Academic Press, Amsterdam, 2nd edition, 2006. ISBN 978-0-12-370537-2.
Thiemo C. Huuk, Tobias Hahn, Katharina Doninger, Jan Griesbach, Stefan Hepbildikler, and Jürgen Hubbuch. Modeling of complex antibody elution behavior under high protein load densities in ion exchange chromatography using an asymmetric activity coefficient. Biotechnology Journal, 12(3):1600336, March 2017. URL: http://doi.wiley.com/10.1002/biot.201600336, doi:10.1002/biot.201600336.
Ronald Colin Jäpel and Johannes Felix Buyel. Bayesian optimization using multiple directional objective functions allows the rapid inverse fitting of parameters for chromatography simulations. Journal of Chromatography A, 1679:463408, 2022. doi:10.1016/j.chroma.2022.463408.
Wendi Zhang, Todd Przybycien, Johannes Schmölder, Samuel Leweke, and Eric von Lieres. Solving crystallization/precipitation population balance models in cadet, part i: nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids. Computers & Chemical Engineering, pages 108612, 2024. doi:https://doi.org/10.1016/j.compchemeng.2024.108612.
+
Wendi Zhang, Todd Przybycien, Johannes Schmölder, Samuel Leweke, and Eric von Lieres. Solving crystallization/precipitation population balance models in cadet, part i: nucleation growth and growth rate dispersion in batch and continuous modes on nonuniform grids. Computers & Chemical Engineering, pages 108612, 2024. doi:10.1016/j.compchemeng.2024.108612.
-
+
[25]
Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dan E. Shumaker, and Carol S. Woodward. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31(3):363–396, September 2005. URL: http://portal.acm.org/citation.cfm?doid=1089014.1089020, doi:10.1145/1089014.1089020.
Andreas Püttmann, Sebastian Schnittert, Samuel Leweke, and Eric von Lieres. Utilizing algorithmic differentiation to efficiently compute chromatograms and parameter sensitivities. Chemical Engineering Science, 139:152–162, January 2016. doi:10.1016/j.ces.2015.08.050.
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# This file records the configuration used when building these files. When it is not found, a full rebuild will be done.
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