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Production of Antibody–Drug Conjugates in a Stirred Tank Reactor
Introduction
In oncology, antibody–drug conjugates (ADCs) are engineered proteins that carry a cytotoxic drug. They mimic human antibodies by binding selectively to specific antigen in the body in order to target the delivery of the drug to the malignant cells.
In this example, the conjugation process to produce an ADC in an isothermal, semi-batch, stirred tank reactor is modeled. The monoclonal antibody (mAb) used in this example has two linker molecules that serve to attach two drug molecules in a site-directed conjugation reaction. At the start of the conjugation process, the tank contains a dilute solution of mAb. The drug is fed into the tank through a dip-tube with an outlet into the tank close to the stirrer. The drug is fed at a controlled rate over a specified feed duration and once the feeding step is done, the reactions continue until the desired conversion is reached.
The desired outcome of the conjugation process is a homogeneous and stable antibody–drug conjugate without aggregation. The product quality of the ADC is highly dependent on the conjugation process conditions such as the initial antibody concentration, antibody-to-drug ratio, and mixing time. This model can be used to study the influence of these conditions, as well as broader process factors such as stirrer speed, feed rate, and reactor design.
The simulation gives the fluid flow and the concentration fields in the reactor. The space-dependent results are compared with the concentrations in a perfectly mixed system, described by the Reaction Engineering interface. The current model can be extended to study the influence of temperature by adding a heat transfer interface.
Model Definition
This model describes the coupled reaction kinetics, fluid flow, and mass transfer in the semi-batch stirred tank reactor. The temperature is assumed to be constant at 25°C.
Model geometry
The tank is cylindrical with a cone-shaped bottom. A stirrer with four blades is located on the slanted cone surface. The geometry is not axisymmetric so a full 3D geometry is needed. Figure 1 shows the tank geometry where half of the tank wall has been hidden in order to show the stirrer inside. The subdomain surrounding the stirrer marks the rotating domain. The dip-tube outlet is located close to the rotating domain, however the tube is not explicitly modeled. The total volume of the tank is 25 dm3.
Figure 1: Model geometry. The edges around the stirrer show the rotating domain. The dip-tube is not included in the model.
Reactions
The modeled chemical system consists of two conjugation reactions to produce the ADC and one undesired side-reaction where the drug is consumed (Ref. 1):
•
Conjugation step one:
(1)
•
Conjugation step two:
(2)
•
Undesired side-reaction:
(3)
The reactions are irreversible and the reaction rates are modeled according to the mass-action law. Since the system is isothermal, constant values are used for the reaction rate constants at the operating temperature.
Fluid Flow
The Turbulent Flow, k–ε interface is used to describe the fluid flow. The flow is modeled as incompressible and the fluid material is water since the solution is dilute and the reactions are assumed to have little effect on the flow field. The rotational speed of the stirrer is 360 rpm and a flow continuity boundary condition is applied to the rotating domain boundaries which surround the stirrer.
Mass Transfer
The Transport of Diluted Species interface is used to describe the mass transfer in the fluid phase with water as the solvent. Initially, the tank contains a dilute concentration of the monoclonal antibody (mAb) reactant. A point mass source is used to feed the drug reactant into the tank since the dip tube outlet is not explicitly modeled. The feeding process is modeled using a step function which ramps up the feeding rate from zero during the first second, stays constant for two seconds, and then turns off. In an analogous manner to the fluid flow description, a continuity boundary condition for mass transfer is applied on the rotating domain boundaries that surround the stirrer.
Computation
The model contains four studies: one for the perfectly mixed system, and three for the space-dependent system.
1
A time-dependent study computes the concentration in a space-independent, ideal semi-batch reactor defined by the Reaction Engineering interface.
2
A stationary Frozen Rotor study solves only for the fluid flow in the tank. This study step uses an auxiliary sweep to increase the stirrer rate from 10 to 360 rpm.
3
A time-dependent study computes the flow field in the tank. The flow field solution from the previous stationary Frozen Rotor study step at 360 rpm is used as the initial flow field.
4
A time-dependent study solves all of the physics interfaces, including Chemistry, Transport of Diluted Species, Turbulent Flow, and the Reacting Flow multiphysics coupling. The flow field solution from the previous time-dependent study step is used as the initial flow field.
Results and Discussion
Figure 2 and Figure 3 compare the results from the perfectly mixed model and the space-dependent model. In Figure 2, the concentration of the monoclonal antibodies (mAb) as well as the conjugated antibodies (mAbDrug and mAb(Drug)2) are shown.
Figure 2: .The concentration of the nonconjugated antibody decreases as it reacts to form the conjugated species mAbDrug. This conjugated species is then converted into the final product.
Figure 3 shows the drug-to-antibody ratio (DAR) and the yield (Y) of the final product mAb(Drug)2.
Figure 3: Drug-to-antibody ratio (DAR) and yield of final product for the perfectly stirred tank as well as for the space-dependent tank.
Figure 2 and Figure 3 clearly show that the results from the 3D model are consistent with those of the perfectly mixed system. This indicates that despite the concentration gradients in the space-dependent tank (see Figure 4 through Figure 15), the reactions are not limited by mass transfer at this mixing speed.
Figure 4 through Figure 7 show the concentration of Drug at 2, 4, 8, and 16 s. At time zero, there is no drug in the reactor yet. The feeding rate of the drug is ramped up during one second and reaches the maximum feed rate at 1 s. At 2 s, the feeding stops. At this time, the concentration gradients of the drug throughout the reactor are still high. At 8 s, the concentration gradients have decrease due to stirring and the reaction. At 16 s, the drug concentration is homogeneous in the tank.
Figure 4: Concentration of Drug at 2 s.
Figure 5: Concentration of Drug at 4 s.
Figure 6: Concentration of Drug at 8 s.
Figure 7: Concentration of Drug at 16 s.
Figure 8 through Figure 11 show the concentration of the mono-conjugated species, mAbDrug, at 2, 4, 8, and 16 s. The concentration of mAbDrug reaches a maximum before the stirring enables further reaction with Drug.
Figure 8: Concentration of mAbDrug at 2 s.
Figure 9: Concentration of mAbDrug at 4 s.
Figure 10: Concentration of mAbDrug at 8 s.
Figure 11: Concentration of mAbDrug at 16 s.
Figure 12 through Figure 15 show the concentration of the final product, mAb(Drug)2, at 2, 4, 8, and 16 s. By 16 s the concentration is homogeneous in the tank reactor.
Figure 12: Concentration of mAb(Drug)2 at 2 s.
Figure 13: Concentration of mAb(Drug)2 at 4 s.
Figure 14: Concentration of mAb(Drug)2 at 8 s.
Figure 15: Concentration of mAb(Drug)2 at 16 s.
Application Library path: Chemical_Reaction_Engineering_Module/Reactors_with_Mass_Transfer/stirred_tank_adc_production
Reference
1. J.T. Weggen, J. Seidel, R. Bean, M. Wendeler, and J. Hubbuch, “Kinetic studies and CFD-based reaction modeling for insights into the scalability of ADC conjugation reactions,” Front. Bioeng. Biotechnol., vol. 11, 2023; doi.org/10.3389/fbioe.2023.1123842.
Modeling Instructions
This space-dependent model describes a stirred semibatch tank reactor used for producing antibody-drug conjugates. When simulating a chemical reactor, it is often good practice to first study the reaction kinetics in an ideal tank reactor. The steps to set up such a space-independent system follows.
From the File menu, choose New.
New
In the New window, click  Blank Model.
Import the model parameters from a text file. The imported parameters are for both the space-independent and the space-dependent models.
Global Definitions
Parameters: Process Conditions
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file stirred_tank_adc_production_process_parameters.txt.
5
In the Label text field, type Parameters: Process Conditions.
While at it, also import the parameters related to the tank geometry.
Parameters: Geometry
1
In the Home toolbar, click  Parameters and choose Add > Parameters.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file stirred_tank_adc_production_geometry_parameters.txt.
5
In the Label text field, type Parameters: Geometry.
Add the component for the ideal tank reactor system and give it a descriptive name.
Add Component
In the Home toolbar, click  Add Component and choose 0D.
Ideal Semibatch Reactor
In the Settings window for Component, type Ideal Semibatch Reactor in the Label text field.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Chemical Species Transport > Reaction Engineering (re).
4
Click the Add to Ideal Semibatch Reactor button in the window toolbar.
5
In the Home toolbar, click  Add Physics to close the Add Physics window.
Reaction Engineering (re)
1
In the Settings window for Reaction Engineering, locate the Reactor section.
2
From the Reactor type list, choose Semibatch.
3
Locate the Energy Balance section. In the T text field, type T_iso.
4
Locate the Mixture Properties section. From the Phase list, choose Liquid.
Reaction 1
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type mAb + Drug => mAbDrug.
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type k1.
Species: mAb
1
In the Model Builder window, click Species: mAb.
2
In the Settings window for Species, locate the Chemical Formula section.
3
In the M text field, type M_mAb.
Species: Drug
1
In the Model Builder window, click Species: Drug.
2
In the Settings window for Species, locate the Chemical Formula section.
3
In the M text field, type M_Drug.
Species: mAbDrug
1
In the Model Builder window, click Species: mAbDrug.
2
In the Settings window for Species, locate the Chemical Formula section.
3
In the M text field, type M_mAb+M_Drug.
Reaction 2
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type mAbDrug + Drug => mAb(Drug)2.
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type k2.
Species: mAb(Drug)2
1
In the Model Builder window, click Species: mAb(Drug)2.
2
In the Settings window for Species, locate the Chemical Formula section.
3
In the M text field, type M_mAb+M_Drug*2.
Reaction 3
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type Drug => sink.
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type k3.
Species: sink
1
In the Model Builder window, click Species: sink.
2
In the Settings window for Species, locate the Chemical Formula section.
3
In the M text field, type M_Drug.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the General Parameters section.
3
In the Vr0 text field, type V_reactor.
4
Locate the Volumetric Species Initial Values section. In the table, enter the following settings:
Species
Concentration (mol/m^3)
mAb
c_init_mAb
Add an Analytic function to specify the varying volumetric feed rate to the tank. For convenience, use the built-in Step function in the feed rate expression.
Definitions
Step 1 (step1)
1
In the Definitions toolbar, click  More Functions and choose Step.
2
In the Settings window for Step, locate the Parameters section.
3
In the Location text field, type t_transitionZone/2.
4
Click to expand the Smoothing section. In the Size of transition zone text field, type t_transitionZone.
Click Plot if you want to see what the step function looks like.
Volumetric Feed Rate
1
In the Home toolbar, click  Functions and choose Local > Analytic.
2
In the Settings window for Analytic, type Volumetric Feed Rate in the Label text field.
3
In the Function name text field, type feedRate.
4
Locate the Definition section. In the Expression text field, type v_feed*(t<t_feed+t_transitionZone)*step1(t).
5
In the Arguments text field, type t.
6
Locate the Units section. In the Function text field, type m^3/s.
7
In the table, enter the following settings:
Argument
Unit
t
s
8
Locate the Plot Parameters section. In the table, enter the following settings:
Plot
Argument
Lower limit
Upper limit
Fixed value
Unit
√
t
0
t_run
0
s
Use the analytic function in a Feed Inlet feature.
Reaction Engineering (re)
Feed Inlet 1
1
In the Reaction Engineering toolbar, click  Feed Inlet.
2
In the Settings window for Feed Inlet, locate the Feed Inlet Properties section.
3
In the vf text field, type feedRate(t).
4
Locate the Feed Inlet Concentration section. In the table, enter the following settings:
Species
Concentration (mol/m^3)
Drug
c_feed_Drug
The perfectly mixed reactor system is now defined. Add a study to compute the solution.
Add Study
1
In the Study toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies > Time Dependent.
4
Click the Add Study button in the window toolbar.
5
In the Study toolbar, click  Add Study to close the Add Study window.
Study 1
Step 1: Time Dependent
1
In the Settings window for Time Dependent, locate the Study Settings section.
2
In the Output times text field, type range(0,0.1,t_run).
3
In the Model Builder window, click Study 1.
4
In the Settings window for Study, type Study 1: Ideal Semibatch Reactor in the Label text field.
5
In the Study toolbar, click  Compute.
The 1D Plot Group labeled Concentration shows the concentrations of the species in the ideal tank reactor.
In the next phase of this example, set up a space-dependent 3D model of the stirred tank reactor, including mass transport, reactions, and fluid flow.
Reaction Engineering (re)
The Generate Space-Dependent Model feature creates a link between the space-independent model and the space-dependent model. It allows you to transfer reaction kinetics, thermodynamics, and transport properties from the Reaction Engineering interface to the corresponding physics interfaces in the space-dependent model. For this example, we need physics that describe turbulent flow and mass transfer.
Generate Space-Dependent Model 1
1
In the Reaction Engineering toolbar, click  Generate Space-Dependent Model.
2
In the Settings window for Generate Space-Dependent Model, locate the Physics Interfaces section.
3
Find the Chemical species transport subsection. From the list, choose Reacting Flow: New.
4
From the list, choose Turbulent Flow, Diluted Species.
5
Locate the Study Type section. From the Study type list, choose None.
6
Locate the Space-Dependent Model Generation section. Click Create/Refresh.
Space-Dependent Reactor
1
In the Model Builder window, click Component 2 (comp2).
2
In the Settings window for Component, type Space-Dependent Reactor in the Label text field.
Begin by loading the geometry from a file.
Geometry 1(3D)
1
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file stirred_tank_adc_production_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
Add Selections to the geometry. Selections are useful when setting up the physics interfaces, as well as the mesh and result nodes.
Explicit Selection 1: Symmetry Boundary (Physics)
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
Add a Clip Plane to see inside the domain.
2
In the Settings window for Explicit Selection, in the Graphics window toolbar, clicknext to  Clipping, then choose Add Clip Plane.
3
In the Label text field, type Explicit Selection 1: Symmetry Boundary (Physics).
4
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
5
On the object fin, select Boundaries 13, 14, 17, 18, 43, 45, 51, and 67 only.
Explicit Selection 2: Stirrer Edges (Results)
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, locate the Entities to Select section.
3
From the Geometric entity level list, choose Edge.
4
Click the  Select Box button in the Graphics toolbar.
5
On the object fin, select Edges 150–153, 155, 156, 158, 159, 161, 162, 170, 173, 175, 176, 178, 179, 181, 182, 184, 186, 188, 193, 195, 198, 199, 201, 206, 208, 210, 212, 236–240, 243–248, 251–255, 257–260, 265, 266, 269, 272, 276, 277, 279, 280, 282, and 283 only.
6
In the Label text field, type Explicit Selection 2: Stirrer Edges (Results).
Explicit Selection 3: Source (Mesh)
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Explicit Selection 3: Source (Mesh) in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 73–80, 109–112, 114, and 116–118 only.
Explicit Selection 4: Destination (Mesh)
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Explicit Selection 4: Destination (Mesh) in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 21–28, 55–58, 61, 63, 65, and 66 only.
Explicit Selection 5: Inside Glass Wall Boundary (Mesh)
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Explicit Selection 5: Inside Glass Wall Boundary (Mesh) in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 9–12, 31, 32, 41, 42, 48, 50, 53, 56, and 69 only.
The steps left before we have defined our system are 1) add a material for the fluid phase, 2) add a moving mesh node, 3) set up all the physics interfaces, 4) build the mesh, and 5) add probes to evaluate the fluid flow field. The material that we will add for the fluid domains is water. After these steps, add studies to compute the solutions. Now, continue by adding the material.
Add Material from Library
In the Home toolbar, click  Windows and choose Add Material from Library.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in > Water, liquid.
3
Click the Add to Component button in the window toolbar.
4
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Water, liquid (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Fluid Domains.
Now add the moving mesh node.
Space-Dependent Reactor (comp2)
Rotating Domain 1
1
In the Physics toolbar, click  Moving Mesh and choose Rotating Domain.
2
In the Settings window for Rotating Domain, locate the Domain Selection section.
3
From the Selection list, choose Rotating Domain.
4
Locate the Rotation section. From the Rotation type list, choose Specified rotational velocity.
5
From the Rotational velocity expression list, choose Constant revolutions per time.
6
In the f text field, type rpm.
Use the coordinated given by the Centroid Measurement nodes to define the rotational axis.
7
Locate the Axis section. Specify the rax vector as
geom1.cm1.x
X
geom1.cm1.y
Y
geom1.cm1.z
Z
8
Specify the urot vector as
(geom1.cm1.x-geom1.cm2.x)/sqrt((geom1.cm1.x-geom1.cm2.x)^2+(geom1.cm1.y-geom1.cm2.y)^2+(geom1.cm1.z-geom1.cm2.z)^2)
X
(geom1.cm1.y-geom1.cm2.y)/sqrt((geom1.cm1.x-geom1.cm2.x)^2+(geom1.cm1.y-geom1.cm2.y)^2+(geom1.cm1.z-geom1.cm2.z)^2)
Y
(geom1.cm1.z-geom1.cm2.z)/sqrt((geom1.cm1.x-geom1.cm2.x)^2+(geom1.cm1.y-geom1.cm2.y)^2+(geom1.cm1.z-geom1.cm2.z)^2)
Z
We have added the interfaces that we need. Now go through these and add the settings.
Transport of Diluted Species (tds)
Fluid 1
1
In the Model Builder window, expand the Space-Dependent Reactor (comp2) > Transport of Diluted Species (tds) node, then click Fluid 1.
2
In the Settings window for Fluid, locate the Diffusion section.
3
From the Material list, choose Water, liquid (mat1).
Inflow 1
In the Model Builder window, right-click Inflow 1 and choose Delete.
Outflow 1
Right-click Outflow 1 and choose Delete.
Point Mass Source 1
1
In the Physics toolbar, click  Points and choose Point Mass Source.
2
In the Settings window for Point Mass Source, locate the Point Selection section.
3
From the Selection list, choose Feed Point.
4
Locate the Species Source section. In the [[dot]]qp,cDrug text field, type comp1.feedRate(t)*c_feed_Drug.
Turbulent Flow, k-ε (spf)
1
In the Model Builder window, under Space-Dependent Reactor (comp2) click Turbulent Flow, k-ε (spf).
2
In the Settings window for Turbulent Flow, k-ε, locate the Domain Selection section.
3
From the Selection list, choose Fluid Domains.
4
In the Model Builder window, expand the Turbulent Flow, k-ε (spf) node.
Fluid Properties 1
1
In the Model Builder window, expand the Space-Dependent Reactor (comp2) > Turbulent Flow, k-ε (spf) > Fluid Properties 1 node, then click Fluid Properties 1.
2
In the Settings window for Fluid Properties, locate the Model Input section.
3
From the T list, choose User defined. In the associated text field, type T_iso.
Inlet 1
In the Model Builder window, right-click Inlet 1 and choose Delete.
Outlet 1
Right-click Outlet 1 and choose Delete.
Pressure Point Constraint 1
1
In the Physics toolbar, click  Points and choose Pressure Point Constraint.
2
Select Point 63 only.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, locate the Boundary Selection section.
3
From the Selection list, choose Explicit Selection 1: Symmetry Boundary (Physics).
Time to build the mesh.
Mesh 1
1
In the Model Builder window, under Space-Dependent Reactor (comp2) click Mesh 1.
2
In the Settings window for Mesh, locate the Sequence Type section.
3
From the list, choose User-controlled mesh.
Size
1
In the Model Builder window, under Space-Dependent Reactor (comp2) > Mesh 1 click Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Calibrate for list, choose Fluid dynamics.
4
Click the Custom button.
5
Locate the Element Size Parameters section. In the Maximum element size text field, type 0.0206.
6
In the Minimum element size text field, type 0.00289.
Size 1
1
In the Model Builder window, click Size 1.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Selection list, choose Rotating Domain.
4
Locate the Element Size section. Click the Custom button.
5
Locate the Element Size Parameters section.
6
Select the Maximum element size checkbox. In the associated text field, type 2e-2.
7
Select the Minimum element size checkbox. In the associated text field, type 1e-3.
Size 2
1
In the Model Builder window, click Size 2.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Selection list, choose Explicit Selection 1: Symmetry Boundary (Physics).
4
Locate the Element Size section. Click the Custom button.
5
Locate the Element Size Parameters section.
6
Select the Minimum element size checkbox. In the associated text field, type 0.00108.
7
Select the Maximum element size checkbox. In the associated text field, type 0.0206.
8
Select the Maximum element growth rate checkbox. In the associated text field, type 1.15.
9
Select the Curvature factor checkbox. In the associated text field, type 0.6.
10
Select the Resolution of narrow regions checkbox. In the associated text field, type 0.7.
Size 3
1
In the Model Builder window, right-click Mesh 1 and choose Size.
2
Drag and drop Size 3 below Size 2.
3
In the Settings window for Size, locate the Geometric Entity Selection section.
4
From the Geometric entity level list, choose Boundary.
5
From the Selection list, choose Explicit Selection 5: Inside Glass Wall Boundary (Mesh).
6
Locate the Element Size section. From the Calibrate for list, choose Fluid dynamics.
7
Click the Custom button.
8
Locate the Element Size Parameters section.
9
Select the Maximum element size checkbox. In the associated text field, type 0.0114.
10
Select the Minimum element size checkbox. In the associated text field, type 0.00108.
11
Select the Maximum element growth rate checkbox. In the associated text field, type 1.1.
12
Select the Curvature factor checkbox. In the associated text field, type 0.4.
13
Select the Resolution of narrow regions checkbox. In the associated text field, type 0.9.
Size 4
1
Right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Explicit Selection 3: Source (Mesh).
5
Locate the Element Size section. From the Calibrate for list, choose Fluid dynamics.
6
Click the Custom button.
7
Locate the Element Size Parameters section.
8
Select the Maximum element size checkbox. In the associated text field, type 0.004.
9
Select the Minimum element size checkbox. In the associated text field, type 4.62E-4.
10
Select the Maximum element growth rate checkbox. In the associated text field, type 1.08.
11
Select the Curvature factor checkbox. In the associated text field, type 0.3.
12
Select the Resolution of narrow regions checkbox. In the associated text field, type 0.95.
Size 5
1
Right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Stirrer Blade Short Surfaces (Straight Blade Bottom Fitted Impeller 1).
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section.
7
Select the Maximum element size checkbox. In the associated text field, type 0.001.
Identical Mesh 1
1
In the Model Builder window, click Identical Mesh 1.
2
In the Settings window for Identical Mesh, locate the First Entity Group section.
3
From the Selection list, choose Explicit Selection 3: Source (Mesh).
4
Locate the Second Entity Group section. From the Selection list, choose Explicit Selection 4: Destination (Mesh).
Corner Refinement 1
1
In the Model Builder window, click Corner Refinement 1.
2
In the Settings window for Corner Refinement, locate the Boundary Selection section.
3
In the list box, select 33.
4
Click to select the  Activate Selection toggle button.
5
Select Boundaries 9–12, 31, 32, 41, 42, 48, 50, 53, and 69 only.
Free Tetrahedral 1
1
In the Model Builder window, click Free Tetrahedral 1.
2
In the Settings window for Free Tetrahedral, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Fluid Domains.
5
Click  Build Selected.
Free Tetrahedral 2
In the Mesh toolbar, click  Free Tetrahedral.
Boundary Layer Properties 1
1
In the Model Builder window, expand the Boundary Layers 1 node, then click Boundary Layer Properties 1.
2
Select Boundaries 9–12, 31–34, 41, 42, 48, 50, 53, 59, 62, 64, 69, 81–108, 113, 115, and 119–129 only.
3
In the Settings window for Boundary Layer Properties, click  Build All.
The mesh is finished. Now add probes. The probes will be used to monitor the fluid flow field in the tank at three points.
Definitions (comp2)
Probe 1: Feed Point
1
In the Definitions toolbar, click  Probes and choose Point Probe.
2
In the Settings window for Point Probe, locate the Source Selection section.
3
Click  Clear Selection.
4
From the Selection list, choose Feed Point.
5
In the Label text field, type Probe 1: Feed Point.
6
Locate the Expression section. In the Expression text field, type spf.U.
Probe 2: Top of Tank Opposite Stirrer
1
Right-click Probe 1: Feed Point and choose Duplicate.
2
In the Settings window for Point Probe, type Probe 2: Top of Tank Opposite Stirrer in the Label text field.
3
Locate the Source Selection section. Click  Clear Selection.
4
Select Point 23 only.
Probe 3: Center of Tank Near Cone
1
In the Definitions toolbar, click  Probes and choose Domain Point Probe.
2
In the Settings window for Domain Point Probe, locate the Point Selection section.
3
From the Line entry method list, choose None.
4
In the Label text field, type Probe 3: Center of Tank Near Cone.
Point Probe Expression 1 (ppb1)
1
In the Model Builder window, expand the Probe 3: Center of Tank Near Cone node, then click Point Probe Expression 1 (ppb1).
2
In the Settings window for Point Probe Expression, locate the Expression section.
3
In the Expression text field, type spf.U.
Probe 4: Between Wall and Rotary Domain
1
In the Model Builder window, right-click Probe 3: Center of Tank Near Cone and choose Duplicate.
2
In the Settings window for Domain Point Probe, type Probe 4: Between Wall and Rotary Domain in the Label text field.
3
Locate the Point Selection section. In row Coordinates, set y to 0.16.
Add a Frozen Rotor study to find the initial conditions to be used in the time dependent simulation of the flow field. Use the Auxiliary Sweep functionality to ramp up the stirring speed to the desired one. This helps with convergence.
Add Study
1
In the Study toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Some Physics Interfaces > Frozen Rotor.
4
Click the Add Study button in the window toolbar.
Study 2
Step 1: Frozen Rotor
1
In the Settings window for Frozen Rotor, locate the Physics and Variables Selection section.
2
In the Solve for column of the table, under Space-Dependent Reactor (comp2), clear the checkboxes for Chemistry (chem) and Transport of Diluted Species (tds).
3
In the Solve for column of the table, under Space-Dependent Reactor (comp2) > Multiphysics, clear the checkbox for Reacting Flow, Diluted Species 1 (rfd1).
4
Click to expand the Study Extensions section. Select the Auxiliary sweep checkbox.
5
Click  Add.
6
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
rpm (Revolutions per second)
10 50 100 200 360
1/min
7
In the Model Builder window, click Study 2.
8
In the Settings window for Study, type Study 2: Frozen Rotor in the Label text field.
9
In the Study toolbar, click  Compute.
Study and edit the default plots that were added.
Results
Pressure (spf), Velocity (spf), Wall Resolution (spf)
Right-click and choose Group.
Frozen Rotor
In the Settings window for Group, type Frozen Rotor in the Label text field.
Frozen Rotor: Velocity (spf)
1
In the Model Builder window, expand the Results > Frozen Rotor > Velocity (spf) node, then click Velocity (spf).
2
In the Settings window for 3D Plot Group, type Frozen Rotor: Velocity (spf) in the Label text field.
Multislice 1
1
In the Model Builder window, click Multislice 1.
2
In the Settings window for Multislice, locate the Coloring and Style section.
3
From the Color table list, choose Passiflora.
4
From the Color table type list, choose Discrete.
Frozen Rotor: Pressure (spf)
1
In the Model Builder window, expand the Results > Frozen Rotor > Pressure (spf) node, then click Pressure (spf).
2
In the Settings window for 3D Plot Group, type Frozen Rotor: Pressure (spf) in the Label text field.
Surface
1
In the Model Builder window, click Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Scale list, choose Linear symmetric.
4
From the Color table type list, choose Continuous.
Frozen Rotor: Wall Resolution (spf)
1
In the Model Builder window, expand the Results > Frozen Rotor > Wall Resolution (spf) node, then click Wall Resolution (spf).
2
In the Settings window for 3D Plot Group, type Frozen Rotor: Wall Resolution (spf) in the Label text field.
Surface 1
1
In the Model Builder window, click Surface 1.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Agama.
Now use the solution for the highest stirrer rate as the initial value for a time dependent simulation of the fluid flow. Simulate two seconds, that is, 12 rotations for the stirrer. This time period should be sufficiently long to see if the flow field is varying significantly or not. The results from the time dependent study will be used to initiate the simulation of the complete system.
Add Study
1
Go to the Add Study window.
2
Find the Studies subsection. In the Select Study tree, select General Studies > Time Dependent.
3
Click the Add Study button in the window toolbar.
4
In the Home toolbar, click  Add Study to close the Add Study window.
Study 3
Step 1: Time Dependent
1
In the Settings window for Time Dependent, locate the Study Settings section.
2
In the Output times text field, type range(0,0.05,2).
3
Locate the Physics and Variables Selection section. In the Solve for column of the table, clear the checkbox for Ideal Semibatch Reactor (comp1).
4
In the Solve for column of the table, under Space-Dependent Reactor (comp2), clear the checkboxes for Chemistry (chem) and Transport of Diluted Species (tds).
5
In the Solve for column of the table, under Space-Dependent Reactor (comp2) > Multiphysics, clear the checkbox for Reacting Flow, Diluted Species 1 (rfd1).
6
Click to expand the Values of Dependent Variables section. Find the Initial values of variables solved for subsection. From the Settings list, choose User controlled.
7
From the Method list, choose Solution.
8
From the Study list, choose Study 2: Frozen Rotor, Frozen Rotor.
9
From the Parameter value (rpm (1/min)) list, choose 360 1/min.
10
In the Model Builder window, click Study 3.
11
In the Settings window for Study, type Study 3: Time-Dependent Flow Field in the Label text field.
12
In the Study toolbar, click  Compute.
Study the results in the added default plots and edit them if needed. Also study the probe plot.
Results
Pressure (spf), Velocity (spf), Wall Resolution (spf)
Right-click and choose Group.
Time-Dependent Flow Field
In the Settings window for Group, type Time-Dependent Flow Field in the Label text field.
Multislice 1
1
In the Model Builder window, expand the Velocity (spf) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Coloring and Style section.
3
From the Color table list, choose Passiflora.
4
From the Color table type list, choose Discrete.
Surface
1
In the Model Builder window, expand the Results > Time-Dependent Flow Field > Pressure (spf) node, then click Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table type list, choose Continuous.
4
From the Scale list, choose Linear symmetric.
Surface 1
1
In the Model Builder window, expand the Wall Resolution (spf) node, then click Surface 1.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Agama.
Probe Plots
1
In the Model Builder window, under Results click Probe Plot Group 2.
2
In the Settings window for 1D Plot Group, type Probe Plots in the Label text field.
3
Locate the Legend section. From the Position list, choose Middle right.
4
Drag and drop on Time-Dependent Flow Field.
Probe Table 1: Time-Dependent Flow Field
1
In the Model Builder window, expand the Results > Tables node, then click Probe Table 1.
2
In the Settings window for Table, type Probe Table 1: Time-Dependent Flow Field in the Label text field.
Time-Dependent Flow Field
1
In the Model Builder window, expand the Probe Plots node, then click Probe Table Graph 1.
2
In the Settings window for Table Graph, type Time-Dependent Flow Field in the Label text field.
Probe Plots
The probe plot suggests that although the field is not varying by orders of magnitude, it is not steady over time. In this system, neither the mass transfer or the addition of feed is assumed to influence the flow field, as the concentrations for the species are low, and the added total feed volume amounts to less than two percent of the total tank volume. Despite this, the probes indicate that the flow is not steady enough to be considered periodic. Therefore, add a time-dependent study step to perform the simulation of the complete system.
Definitions (comp2)
Probe 1: Feed Point (point1)
1
In the Model Builder window, under Space-Dependent Reactor (comp2) > Definitions click Probe 1: Feed Point (point1).
2
In the Settings window for Point Probe, click to expand the Table and Window Settings section.
3
Click  Add Table.
Probe 2: Top of Tank Opposite Stirrer (point2)
1
In the Model Builder window, click Probe 2: Top of Tank Opposite Stirrer (point2).
2
In the Settings window for Point Probe, locate the Table and Window Settings section.
3
From the Output table list, choose Table 2.
Point Probe Expression 1 (ppb1)
1
In the Model Builder window, under Space-Dependent Reactor (comp2) > Definitions > Probe 3: Center of Tank Near Cone click Point Probe Expression 1 (ppb1).
2
In the Settings window for Point Probe Expression, click to expand the Table and Window Settings section.
3
From the Output table list, choose Table 2.
Point Probe Expression 1 (ppb2)
1
In the Model Builder window, expand the Space-Dependent Reactor (comp2) > Definitions > Probe 4: Between Wall and Rotary Domain node, then click Point Probe Expression 1 (ppb2).
2
In the Settings window for Point Probe Expression, locate the Table and Window Settings section.
3
From the Output table list, choose Table 2.
Add the fourth study that will be used to simulate the complete system.
Add Study
1
In the Study toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies > Time Dependent.
4
Click the Add Study button in the window toolbar.
5
In the Study toolbar, click  Add Study to close the Add Study window.
Study 4
Step 1: Time Dependent
1
In the Settings window for Time Dependent, locate the Study Settings section.
2
In the Output times text field, type range(0,2,16).
3
Locate the Physics and Variables Selection section. In the Solve for column of the table, clear the checkbox for Ideal Semibatch Reactor (comp1).
4
Locate the Values of Dependent Variables section. Find the Initial values of variables solved for subsection. From the Settings list, choose User controlled.
5
From the Method list, choose Solution.
6
From the Study list, choose Study 3: Time-Dependent Flow Field, Time Dependent.
7
From the Time (s) list, choose Last.
Generate the solver nodes. This is needed since we want to edit them.
8
In the Model Builder window, click Study 4.
9
In the Settings window for Study, type Study 4: Space-Dependent Semibatch Reactor in the Label text field.
Solution 4 (sol4)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 4 (sol4) node.
3
In the Model Builder window, expand the Study 4: Space-Dependent Semibatch Reactor > Solver Configurations > Solution 4 (sol4) > Dependent Variables 1 node, then click Concentration (comp2.cDrug).
4
In the Settings window for Field, locate the Scaling section.
5
From the Method list, choose Manual.
6
In the Scale text field, type 1e-2.
7
In the Model Builder window, under Study 4: Space-Dependent Semibatch Reactor > Solver Configurations > Solution 4 (sol4) > Dependent Variables 1 click Concentration (comp2.cmAb).
8
In the Settings window for Field, locate the Scaling section.
9
From the Method list, choose Manual.
10
In the Scale text field, type c_init_mAb.
Study 4: Space-Dependent Semibatch Reactor
1
In the Model Builder window, collapse the Study 4: Space-Dependent Semibatch Reactor > Solver Configurations > Solution 4 (sol4) > Dependent Variables 1 node.
2
In the Model Builder window, under Study 4: Space-Dependent Semibatch Reactor > Solver Configurations > Solution 4 (sol4) click Time-Dependent Solver 1.
3
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
4
Select the Initial step checkbox. In the associated text field, type t_rev/500.
Compute the model. This will take something between one and three weeks, depending on your hardware.
5
In the Model Builder window, click Study 4: Space-Dependent Semibatch Reactor.
6
In the Settings window for Study, type Study 4: Space-Dependent Semibatch Reactor in the Label text field.
7
Locate the Study Settings section. Clear the Generate default plots checkbox.
8
In the Study toolbar, click  Compute.
Set up figures that illustrate how the concentrations of species vary.
Begin with the concentration of Drug.
Results
2s
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type 2s in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 4: Space-Dependent Semibatch Reactor/Solution 4 (8) (sol4).
4
From the Time (s) list, choose 2.
5
Click to expand the Selection section. From the Geometric entity level list, choose Domain.
6
From the Selection list, choose Fluid Domains.
7
Click to expand the Title section. From the Title type list, choose None.
8
Locate the Plot Settings section. From the View list, choose View 1.
9
Clear the Plot dataset edges checkbox.
10
Locate the Color Legend section. Select the Show titles checkbox.
11
Select the Show units checkbox.
12
From the Position list, choose Bottom.
13
Click to expand the Plot Array section. From the Array type list, choose Linear.
14
From the Array axis list, choose y.
15
In the Relative padding text field, type 0.1.
Slice 1
1
Right-click 2s and choose Slice.
2
In the Settings window for Slice, locate the Plane Data section.
3
From the Entry method list, choose Coordinates.
4
Locate the Coloring and Style section. From the Color table list, choose Excorticata.
5
In the Color legend title text field, type (a).
6
Click to expand the Plot Array section. Select the Manual indexing checkbox.
Surface 1: Tank
1
In the Model Builder window, right-click 2s and choose Surface.
2
In the Settings window for Surface, type Surface 1: Tank in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Click to expand the Plot Array section. Select the Manual indexing checkbox.
Material Appearance 1
1
Right-click Surface 1: Tank and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Glass.
Selection 1
1
In the Model Builder window, right-click Surface 1: Tank and choose Selection.
2
Select Boundaries 1–10, 29, 30, 38–40, 47, 49, 54, 59, 62, 70, 71, 83, 84, 86, 90–92, 96, 99, 104, 113, 115, 119, 120, 124, 125, and 127–129 only.
Surface 2: Stirrer
1
In the Model Builder window, right-click 2s and choose Surface.
2
In the Settings window for Surface, type Surface 2: Stirrer in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Locate the Plot Array section. Select the Manual indexing checkbox.
Material Appearance 1
1
Right-click Surface 2: Stirrer and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Car paint.
Selection 1
1
In the Model Builder window, right-click Surface 2: Stirrer and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Stirrer with Socket.
(a)
1
In the Model Builder window, right-click 2s and choose Annotation.
2
In the Settings window for Annotation, type (a) in the Label text field.
3
Locate the Annotation section. In the Text text field, type (a).
4
Locate the Position section. In the y text field, type -d_tank/2.
5
In the z text field, type h_cyl*1.1.
6
Locate the Coloring and Style section. Clear the Show point checkbox.
7
From the Anchor point list, choose Lower middle.
8
Click to expand the Plot Array section. Select the Manual indexing checkbox.
Isosurface 1
1
Right-click 2s and choose Isosurface.
2
In the Settings window for Isosurface, locate the Levels section.
3
In the Total levels text field, type 10.
4
Locate the Coloring and Style section. From the Color table list, choose Excorticata.
5
In the Color legend title text field, type (b).
6
Click to expand the Plot Array section. Select the Manual indexing checkbox.
7
In the Index text field, type 1.
Transparency 1
1
Right-click Isosurface 1 and choose Transparency.
2
In the Settings window for Transparency, locate the Transparency section.
3
Find the Transparency subsection. Set the Transparency value to 0.7.
(a), Surface 1: Tank, Surface 2: Stirrer
1
In the Model Builder window, under Results > 2s, Ctrl-click to select Surface 1: Tank, Surface 2: Stirrer, and (a).
2
Right-click and choose Duplicate.
Surface 1: Tank 1
1
In the Settings window for Surface, locate the Plot Array section.
2
In the Index text field, type 1.
Surface 2: Stirrer 1
1
In the Model Builder window, click Surface 2: Stirrer 1.
2
In the Settings window for Surface, locate the Plot Array section.
3
In the Index text field, type 1.
(b)
1
In the Model Builder window, under Results > 2s click (a) 1.
2
In the Settings window for Annotation, type (b) in the Label text field.
3
Locate the Annotation section. In the Text text field, type (b).
4
Locate the Plot Array section. In the Index text field, type 1.
2s
1
In the Model Builder window, click 2s.
2
Click the Zoom Box button on the Graphics toolbar and then use the mouse to zoom in. Adjust the view according to your preferences.
Duplicate this plot group and edit the time for which the results are shown.
4s
1
Right-click 2s and choose Duplicate.
2
In the Settings window for 3D Plot Group, type 4s in the Label text field.
3
Locate the Data section. From the Time (s) list, choose 4.
8s
1
Right-click 4s and choose Duplicate.
2
In the Settings window for 3D Plot Group, type 8s in the Label text field.
3
Locate the Data section. From the Time (s) list, choose 8.
Slice 1
1
In the Model Builder window, expand the 8s node, then click Slice 1.
2
In the Settings window for Slice, click to expand the Range section.
3
Select the Manual color range checkbox.
4
In the Minimum text field, type 0.00183.
5
In the Maximum text field, type 0.24919.
16s
1
In the Model Builder window, right-click 8s and choose Duplicate.
2
In the Settings window for 3D Plot Group, type 16s in the Label text field.
3
Locate the Data section. From the Time (s) list, choose 16.
16s, 2s, 4s, 8s
1
In the Model Builder window, under Results, Ctrl-click to select 2s, 4s, 8s, and 16s.
2
Right-click and choose Group.
Concentration Drug
In the Settings window for Group, type Concentration Drug in the Label text field.
Set up similar plots for mAbDrug and mAbDrug2.
Concentration mAbDrug
1
Right-click Concentration Drug and choose Duplicate.
2
In the Model Builder window, click Concentration Drug 1.
3
In the Settings window for Group, type Concentration mAbDrug in the Label text field.
Slice 1
1
In the Model Builder window, expand the Results > Concentration mAbDrug > 2s 1 node, then click Slice 1.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Isosurface 1
1
In the Model Builder window, click Isosurface 1.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Slice 1
1
In the Model Builder window, expand the Results > Concentration mAbDrug > 4s 1 node, then click Slice 1.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Isosurface 1
1
In the Model Builder window, click Isosurface 1.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Slice 1
1
In the Model Builder window, expand the Results > Concentration mAbDrug > 8s 1 node, then click Slice 1.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Range section. In the Minimum text field, type 4.59966e-5.
5
In the Maximum text field, type 0.00209.
6
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Isosurface 1
1
In the Model Builder window, click Isosurface 1.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Slice 1
1
In the Model Builder window, expand the Results > Concentration mAbDrug > 16s 1 node, then click Slice 1.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Range section. In the Minimum text field, type 4.59966e-5.
5
In the Maximum text field, type 0.00209.
6
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Isosurface 1
1
In the Model Builder window, click Isosurface 1.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type cmAbDrug.
4
Locate the Coloring and Style section. From the Color table list, choose Baptisia.
Perform the same steps for mAbDrug2. The steps are not shown in this modeling instruction.
Now look at the fluid flow in the model by setting up a velocity streamline plot.
Result Templates
1
In the Home toolbar, click  Result Templates to open the Result Templates window.
2
Go to the Result Templates window.
3
In the tree, select Study 4: Space-Dependent Semibatch Reactor/Solution 4 (8) (sol4) > Turbulent Flow, k-ε > Velocity Streamlines (spf).
4
Click the Add Result Template button in the window toolbar.
Results
Streamline 1
1
In the Model Builder window, expand the Velocity Streamlines (spf) node, then click Streamline 1.
2
In the Settings window for Streamline, locate the Streamline Positioning section.
3
From the Positioning list, choose Magnitude controlled.
4
In the Minimum density level text field, type 0.
5
In the Maximum density level text field, type 13.4.
6
Locate the Coloring and Style section. Find the Line style subsection. From the Type list, choose Tube.
7
Find the Point style subsection. From the Type list, choose Arrow.
8
Select the Number of arrows checkbox. In the associated text field, type 80.
9
From the Arrow type list, choose Cone.
10
Select the Scale factor checkbox. In the associated text field, type 0.1.
Color Expression 1
1
In the Model Builder window, expand the Streamline 1 node, then click Color Expression 1.
2
In the Settings window for Color Expression, locate the Coloring and Style section.
3
From the Color table list, choose ConopiformisZero.
Surface 1: Tank, Surface 2: Stirrer
1
In the Model Builder window, under Results > Concentration mAbDrug2 > 16s 1.1, Ctrl-click to select Surface 1: Tank and Surface 2: Stirrer.
2
Right-click and choose Copy.
Velocity Streamlines (spf)
1
In the Model Builder window, under Results > Concentration mAbDrug2 right-click Velocity Streamlines (spf) and choose Paste Multiple Items.
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges checkbox.
4
Right-click Velocity Streamlines (spf) and choose Move Out.
Compare the results from the space-dependent model with those from the perfectly stirred tank model.
Evaluation Group 1
1
In the Results toolbar, click  Evaluation Group.
2
In the Settings window for Evaluation Group, locate the Data section.
3
From the Dataset list, choose Study 4: Space-Dependent Semibatch Reactor/Solution 4 (7) (sol4).
Volume Integration 1
1
Right-click Evaluation Group 1 and choose Integration > Volume Integration.
2
In the Settings window for Volume Integration, locate the Data section.
3
From the Dataset list, choose Study 4: Space-Dependent Semibatch Reactor/Solution 4 (8) (sol4).
4
Locate the Selection section. From the Selection list, choose Fluid Domains.
5
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
cmAbDrug
mol
Molar concentration, cmAbDrug
cmAb
mol
Molar concentration, cmAb
cmAbDrug2
mol
Molar concentration, cmAbDrug2
6
In the Evaluation Group 1 toolbar, click  Evaluate.
Evaluation Group 1
1
Go to the Evaluation Group 1 window.
2
Click the Table Graph button in the window toolbar.
Results
Table Graph 1
1
In the Settings window for Table Graph, locate the Coloring and Style section.
2
Find the Line style subsection. From the Line list, choose None.
3
From the Color list, choose Black.
4
Find the Line markers subsection. From the Marker list, choose Cycle.
5
Click to expand the Legends section. Select the Show legends checkbox.
6
From the Legends list, choose Manual.
7
In the table, enter the following settings:
Legends
3D
3D
3D
Global 1
1
In the Model Builder window, right-click 1D Plot Group 22 and choose Global.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 1: Ideal Semibatch Reactor/Solution 1 (sol1).
4
Locate the y-Axis Data section. Click  Clear Table.
5
In the table, enter the following settings:
Expression
Unit
Description
comp1.re.c_mAbDrug*V_reactor
mol
 
comp1.re.c_mAb*V_reactor
mol
 
comp1.re.c_mAbDrug2*V_reactor
mol
 
6
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose Cycle.
7
From the Color list, choose Black.
8
Click to expand the Legends section. From the Legends list, choose Manual.
9
In the table, enter the following settings:
Legends
mAbDrug, 0D
mAb, 0D
mAbDrug2, 0D
Amount (mol)
1
In the Model Builder window, under Results click 1D Plot Group 22.
2
In the Settings window for 1D Plot Group, type Amount (mol) in the Label text field.
3
Locate the Plot Settings section.
4
Select the y-axis label checkbox. In the associated text field, type Amount (mol).
5
Locate the Legend section. From the Position list, choose Middle right.
6
In the Number of columns text field, type 2.
Global 1
1
In the Model Builder window, click Global 1.
2
Drag and drop above Table Graph 1.
3
In the Amount (mol) toolbar, click  Plot.
The final results to investigate in this model example is the drug-to- antibody ratio, and the product yield.
Volume Average 1
1
In the Results toolbar, click  More Derived Values and choose Average > Volume Average.
2
In the Settings window for Volume Average, locate the Data section.
3
From the Dataset list, choose Study 4: Space-Dependent Semibatch Reactor/Solution 4 (8) (sol4).
4
Locate the Selection section. From the Selection list, choose Fluid Domains.
5
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
(cmAbDrug+2*cmAbDrug2)/c_init_mAb
1
DAR
cmAbDrug2/c_init_mAb
1
Yield
6
Clicknext to  Evaluate, then choose New Table.
Drug-to-Antibody Ratio and Yield
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Drug-to-Antibody Ratio and Yield in the Label text field.
DAR, 0D
1
Right-click Drug-to-Antibody Ratio and Yield and choose Global.
2
In the Settings window for Global, type DAR, 0D in the Label text field.
3
Locate the y-Axis Data section. Click  Clear Table.
4
In the table, enter the following settings:
Expression
Unit
Description
(re.c_mAbDrug+2*re.c_mAbDrug2)/c_init_mAb
1
Drug-to-Antibody ratio
5
Locate the Coloring and Style section. From the Color list, choose Black.
6
Locate the Legends section. Find the Include subsection. Select the Label checkbox.
7
Clear the Solution checkbox.
8
Clear the Expression checkbox.
Yield, 0D
1
Right-click DAR, 0D and choose Duplicate.
2
In the Settings window for Global, type Yield, 0D in the Label text field.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
re.c_mAbDrug2/c_init_mAb
1
Yield of mAbDrug2
4
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dashed.
DAR, 3D
1
In the Model Builder window, right-click Drug-to-Antibody Ratio and Yield and choose Table Graph.
2
In the Settings window for Table Graph, type DAR, 3D in the Label text field.
3
Locate the Data section. From the Table list, choose Table 3.
4
From the Plot columns list, choose Manual.
5
In the Columns list box, select DAR (1).
6
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
7
From the Color list, choose Black.
8
Find the Line markers subsection. From the Marker list, choose Circle.
9
Locate the Legends section. Select the Show legends checkbox.
10
From the Legends list, choose Automatic.
11
Find the Include subsection. Select the Label checkbox.
12
Clear the Headers checkbox.
Yield, 3D
1
Right-click DAR, 3D and choose Duplicate.
2
In the Settings window for Table Graph, type Yield, 3D in the Label text field.
3
Locate the Data section. In the Columns list box, select Yield (1).
4
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Square.
Drug-to-Antibody Ratio and Yield
1
In the Model Builder window, click Drug-to-Antibody Ratio and Yield.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the Two y-axes checkbox.
4
In the table, select the Plot on secondary y-axis checkboxes for Yield, 0D and Yield, 3D.
5
Select the y-axis label checkbox. In the associated text field, type Drug-to-Antibody Ratio (1).
6
Select the Secondary y-axis label checkbox.
7
Click to expand the Title section. From the Title type list, choose None.