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Porous Catalytic Reactor with Injection Needle
Introduction
Heterogeneous catalytic reactors have been widely used in the chemical engineering industry. This type of gas-solid catalytic reactors, where gas phase reactions are catalyzed by a solid catalyst, have widespread applications in the areas such as catalytic oxidation and selective catalytic reduction. This example illustrates the modeling of a porous catalytic reactor for hydrogen oxidation on a noble metal Rh catalyst dispersed on an alumina support (Rh/Al2O3). The model investigates the kinetics of the heterogeneous catalytic reaction system, the species concentration distribution (both the species in the bulk gas phase and absorbed on the catalytic surface) and the velocity field in the pore volume.
First, the hydrogen oxidation rate and the rates of adsorption and desorption for all species are studied by using the Reaction Engineering interface, assuming that the chemical system is perfectly mixed. Then, in a space-dependent model of the porous catalytic reactor, the concentration and velocity fields are investigated by using the Transport of Diluted Species in Porous Catalysts interface, which is a combination of Transport of Diluted Species with Porous Catalyst feature and the Brinkman Equation interfaces. The thermodynamic and kinetic properties of the reaction system in the space-dependent model are provided using a Chemistry interface.
Model Definition
Heterogeneous Catalytic Reactions
For a gas-solid catalytic reaction, the reaction rate (Rs) can be expressed as
where nprod is the number of product moles; catalystunit is the measure unit of catalyst amount, which has following different unit bases:
•
Active surface area of catalyst (m2)
•
Unit mass of catalyst (kg)
•
Unit volume of catalyst (m3)
•
Active metal loading percentage
The reaction-rate unit depends on the measurement unit of the catalyst. In the Porous Catalyst feature in the Transport of Diluted Species and Transport of Concentrated Species interfaces, there are two measure units for the catalyst: one based on the surface area (m2) and another based on the mass amount (kg).
A general surface reaction can be written as
The reaction rate of this elemental reaction is
where kf and kr are the forward and backward reaction rate constants, respectively, and θA, θB, and θAB are the surface coverages of surface species A(ads), B(ads), and AB(ads). The coefficient kf has the form
where
•
 A is a pre-exponential factor
•
 T is the temperature (K)
•
 β is the temperature exponent
•
 E is the activation energy (J/mol)
•
 Rg is the gas constant (J/(mol·K))
The rate constant kr has the same form as that for kf. Alternatively, it can be obtained from the reaction equilibrium constant (K0):
The gas-solid catalytic reaction system of H2 + O2 + H2O on Rh/Al2O3 catalyst is investigated using the Reaction Engineering interface. The following reactions are considered:
•
Gaseous H2 being dissociatively adsorbed on two neighboring Rh sites:
•
Gaseous O2 being dissociatively absorbed on two neighboring Rh sites:
•
Gaseous H2O being absorbed on a Rh site:
•
The surface reactions of the adsorbed species H(ads), O(ads), OH(ads), and H2O(ads):
The thermodynamic and kinetic behaviors of all species and reactions can be simulated provided that the rate constants kf and kr are available for these six reactions.
After the initial analysis of the gas-solid reaction system in the Reaction Engineering interface, the reaction system will be exported to a Chemistry interface using the Generate Space-Dependent Model feature. The Chemistry interface will then be used to define the gas-solid reaction system in the space-dependent model.
Space-Dependent Model of Porous Catalytic Reactor
The reactor consists of a tubular structure, with an injection tube whose main axis is perpendicular to the reactor axis. The reactor geometry is shown in Figure 1. The incoming species in the main and injection tubes react in a fixed porous catalyst bed. The model couples the free fluid and porous media flow through the Brinkman equation interface. This physics interface includes two physics features for modeling the fluid flow, one being Porous Medium for porous domain, and the other being Fluid Properties for free flow domain. Because of symmetry, only one half of the reactor is modeled.
Figure 1: The species O2 and H2 enter the reactor from the main and injection tubes, respectively, and react in a fixed porous catalyst bed to produce H2O.
In the porous catalyst domain, the hydrogen oxidation on the Rh/Al2O3 catalyst takes place. The net reaction of the gas phase species is 2H2 + O2 → 2H2O.
Governing Equations
The Navier–Stokes equations describe the fluid flow in the free-flow regions. In the porous domain, the Brinkman equations for porous media apply.
As the modeled species are present in low concentrations, diffusion is assumed to take place according to Fick’s law. The mass transport for the three species H2, O2, and H2O can therefore be modeled with the following convection–diffusion equation
(1)
In this equation, ci denotes the concentration (SI unit: mol/m3), Di the diffusivity (SI unit: m2 /s), and Ri the reaction rate for species i (SI unit: mol/(m3·s)). Because the reaction takes place in the porous bed only, the reaction term is zero in the free-flow regions. The reaction rate Ri is contributed by the surface reaction, which takes place inside the porous catalyst material.
The bulk transport species H2, O2, and H2O adsorb onto the active sites on the Rh catalyst surface. The adsorption of H2, O2, and H2O is described using the Langmuir adsorption isotherm:
Here, for species i,
•
cP,e,i is the equilibrium amount adsorbed on the catalyst (mol/kg),
•
KL,i is the Langmuir constant (m3/mol),
•
cPmax,i is the maximum adsorbed amount (mol/kg), and
•
ci is the species molar concentration in the gas phase (mol/m3)
In the Langmuir isotherm, the equilibrium adsorbed amount is dependent both on the maximum possible amount adsorbed (cPmax,i), and the bulk concentration of species i (ci). If the bulk concentration is zero, the equilibrium concentration is also zero.
The equilibrium molar concentration (ceq,i, mol/m3) for adsorbed species i is given by
(2)
where ρb is the catalyst bulk density.
For the adsorbed species concentration cads,i (mol/m2), its corresponding volumetric concentration cvol,i (mol/m3) is
(3)
Using Equation 2 and Equation 3, the adsorption/desorption rate Rads,i (mol/(m3·s)) is defined as
where hLDF,i is the mass transfer coefficient (1/s), which is based on a linear driving force. The adsorption rate is a mass source term and contributes to the bulk reaction rate Ri in Equation 1. With this definition, a positive Rads,i corresponds to desorption of species i, that is, a positive source term of species i in Equation 1.
For the adsorbed species, the governing equation is
and for other surface species (without mass transfer between the bulk and the catalyst surface)
where Rs,ads,i and Rs,surf,i are the surface reaction rates for adsorbed and surface species, respectively.
Boundary Conditions
In the Brinkman Equations interface, a constant velocity profile is assumed at the inlet boundaries:
For the outlet, a zero pressure condition is applied.
In the Transport of Diluted Species in Porous Catalysts interface, the concentrations at the inflows are fixed:
At the outflow, the convection is assumed to dominate the mass transport:
This implies that the gradient of ci in the direction perpendicular to the outlet boundary is negligible. This is a common assumption for tubular reactors with a high degree of transport by convection in the direction of the main reactor axis. The condition eliminates the need for specifying a concentration or a fixed value for the flux at the outlet boundary. At all other boundaries, no flux conditions apply:
Results and Discussion
Figure 2 shows the velocity magnitude. The flow is almost homogeneous in the porous part of the reactor.
Figure 2: Magnitude of the velocity field in the free and porous reactor domains.
Figure 3 shows the pressure drop, which occurs mainly across the porous bed.
Figure 3: The pressure drop across the reactor.
Figure 4 and Figure 5 show the concentrations of species H2 and O2, respectively.
Figure 4: Isoconcentration surfaces for species H2.
Figure 5: Isoconcentration surfaces for species O2.
Figure 4 shows that the concentration of the injected species H2 decreases very rapidly with distance from the injection point due to quick mixing with the main flow. It also shows that hydrogen is consumed in the porous catalyst domain. The rate of hydrogen oxidation is significantly lower after about half the bed length, meaning that half the bed is poorly utilized. This indicates an opportunity for optimizing the reactor design by, for example, using a thinner catalyst bed. Figure 5 shows the isoconcentration surfaces of species O2, which is introduced in the main channel of the reactor. Similar to the species H2, its concentration also decreases across the porous domain. The injection of H2 results in a reduction in O2 concentration at the injection point.
Figure 6 show the concentration distributions of surface and bulk species along the centerline of the porous catalyst bed. There is a surplus of oxygen in the gas phase. The net effect is that, after about half the bed length, the empty Rh surface sites are successively covered by oxygen adatoms, and at the end of the bed, the majority of surface sites are covered by oxygen atoms.
Figure 6: Concentration distribution along the centerline of catalyst.
Application Library path: Chemical_Reaction_Engineering_Module/Reactors_with_Porous_Catalysts/porous_reactor
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  0D.
2
In the Select Physics tree, select Chemical Species Transport > Reaction Engineering (re).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Time Dependent.
6
Click  Done.
Load reaction parameters (general) from a text file.
Global Definitions
Parameters 1, reaction
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Parameters 1, reaction in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file porous_reactor_reaction_parameters.txt.
Variables 1
1
In the Model Builder window, right-click Global Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
In the table, enter the following settings:
Name
Expression
Unit
Description
c0N2
minput.pA/R_const/minput.T - c0H2_inflow - c0O2_inflow
mol/m³
 
Reaction Engineering (re)
1
In the Model Builder window, under Component 1 (comp1) click Reaction Engineering (re).
2
In the Settings window for Reaction Engineering, locate the Energy Balance section.
3
In the T text field, type T_iso.
Create the H2+O2 reaction system over the Rh/Al2O3 catalyst.
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 H2+2Rh(ads)<=>2H(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf1.
6
In the kr text field, type kr1.
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 O2+2Rh(ads)<=>2O(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf2.
6
In the kr text field, type kr2.
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 H2O+Rh(ads)<=>H2O(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf3.
6
In the kr text field, type kr3.
Reaction 4
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 O(ads)+H(ads)<=>OH(ads)+Rh(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf4.
6
In the kr text field, type kr4.
Reaction 5
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 OH(ads)+H(ads)<=>H2O(ads)+Rh(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf5.
6
In the kr text field, type kr5.
Reaction 6
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 OH(ads)+OH(ads)<=>O(ads)+H2O(ads).
4
Click Apply.
5
Locate the Rate Constants section. In the kf text field, type kf6.
6
In the kr text field, type kr6.
Species 1
1
In the Reaction Engineering toolbar, click  Species.
Add a solvent (N2). It is not involved in any reaction but it will later be exported to a space-dependent model.
2
In the Settings window for Species, locate the Name section.
3
In the text field, type N2.
4
Locate the Type section. From the list, choose Solvent.
Enter the reactive specific surface for the surface reactions.
5
In the Model Builder window, click Reaction Engineering (re).
6
In the Settings window for Reaction Engineering, locate the Reactor section.
7
Find the Surface reaction area subsection. Click the Surface area to volume ratio button.
8
In the as text field, type cat_area.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Volumetric Species Initial Values section.
3
In the table, enter the following settings:
Species
Concentration (mol/m^3)
H2
c0H2_inflow
N2
c0N2
O2
c0O2_inflow
4
Locate the Surface Species Initial Values section. In the Γs text field, type 2.72E-5.
5
In the table, enter the following settings:
Species
Surface concentration (mol/m^2)
Site occupancy number (1)
H(ads)
c0H_surf
1
H2O(ads)
c0H2O_surf
1
O(ads)
c0O_surf
1
OH(ads)
c0OH_surf
1
Rh(ads)
c0Rh_surf
1
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,0.01,0.2).
4
In the Study toolbar, click  Compute.
Results
Concentration (re), bulk species
1
Right-click Results > Concentration (re) and choose Rename.
2
In the Rename 1D Plot Group dialog, type Concentration (re), bulk species in the New label text field.
3
Click OK.
Plot the bulk species concentrations.
Global 1
1
In the Model Builder window, expand the Concentration (re), bulk species node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
Click  Clear Table.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.c_H2 - Concentration - mol/m³.
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.c_H2O - Concentration - mol/m³.
6
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.c_O2 - Concentration - mol/m³.
7
In the Concentration (re), bulk species toolbar, click  Plot.
8
Click the  Zoom Extents button in the Graphics toolbar.
Create a figure for the surface species concentrations.
Concentration (re), surface species
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Concentration (re), surface species in the Label text field.
3
Locate the Legend section. From the Position list, choose Lower right.
Global 1
1
Right-click Concentration (re), surface species and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
Click  Clear Table.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.csurf_H_surf - Surface concentration - mol/m².
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.csurf_O_surf - Surface concentration - mol/m².
6
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.csurf_OH_surf - Surface concentration - mol/m².
7
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.csurf_H2O_surf - Surface concentration - mol/m².
8
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Reaction Engineering > re.csurf_Rh_surf - Surface concentration - mol/m².
9
Click the  x-Axis Log Scale button in the Graphics toolbar.
10
Click the  y-Axis Log Scale button in the Graphics toolbar.
11
In the Concentration (re), surface species toolbar, click  Plot.
12
Click the  Zoom Extents button in the Graphics toolbar.
Export the catalytic oxidation of hydrogen over Rh/Al2O3 to a space-dependent model.
Reaction Engineering (re)
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 in Porous Media: New.
4
From the list, choose Porous Catalyst.
5
Locate the Study Type section. From the Study type list, choose Time dependent.
6
Locate the Space-Dependent Model Generation section. Click Create/Refresh.
Load catalyst parameters from a text file.
Global Definitions
Parameters 2, catalyst
1
In the Home toolbar, click  Parameters and choose Add > Parameters.
2
In the Settings window for Parameters, type Parameters 2, catalyst in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file porous_reactor_catalyst_parameters.txt.
Component 2 (comp2)
Build the geometry for the catalytic reactor.
1
In the Model Builder window, expand the Component 2 (comp2) node.
Geometry 1(3D)
1
In the Model Builder window, expand the Component 2 (comp2) > Geometry 1(3D) node, then click Geometry 1(3D).
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type do_reac/2.
4
In the Height text field, type 5*do_reac.
5
Locate the Axis section. From the Axis type list, choose Cartesian.
6
In the x text field, type 1.
7
In the z text field, type 0.
8
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
wt_reac
Cylinder 2 (cyl2)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type do_reac/2-wt_reac.
4
In the Height text field, type 0.7*do_reac.
5
Locate the Position section. In the x text field, type 3*do_reac.
6
Locate the Axis section. From the Axis type list, choose Cartesian.
7
In the x text field, type 1.
8
In the z text field, type 0.
Cylinder 3 (cyl3)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type do_needle/2.
4
In the Height text field, type do_reac.
5
Locate the Position section. In the x text field, type 2.7*do_reac/2.
6
Locate the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
wt_needle
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object cyl1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object cyl3 only.
6
Select the Keep objects to subtract checkbox.
Union 1 (uni1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Select the objects cyl3 and dif1 only.
3
In the Settings window for Union, locate the Union section.
4
Click the  Paste Selection button for Input objects.
5
In the Paste Selection dialog, type cyl2 in the Selection text field.
6
Click OK.
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 5*do_reac.
4
In the Depth text field, type 2*do_reac.
5
In the Height text field, type 3*do_reac.
6
Locate the Position section. In the y text field, type -2*do_reac.
7
In the z text field, type -1.5*do_reac.
Difference 2 (dif2)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object uni1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object blk1 only.
Form Union (fin)
In the Geometry toolbar, click  Build All.
Add a Mesh Control Faces feature to control the mesh in the vertical injection needle.
Mesh Control Faces 1 (mcf1)
1
In the Geometry toolbar, click  Virtual Operations and choose Mesh Control Faces.
Select the faces corresponding to the symmetry plane and the outlet into the reactor.
2
On the object fin, select Boundaries 19 and 20 only.
Ignore Faces 1 (igf1)
1
In the Geometry toolbar, click  Virtual Operations and choose Ignore Faces.
2
In the Settings window for Ignore Faces, locate the Input section.
3
Click the  Paste Selection button for Faces to ignore.
4
In the Paste Selection dialog, type 11,20 in the Selection text field.
5
Click OK.
6
In the Geometry toolbar, click  Build All.
Definitions (comp2)
Create a geometry selection list for model entities.
Catalyst Bed
1
In the Model Builder window, expand the Component 2 (comp2) > Definitions node.
2
Right-click Component 2 (comp2) > Definitions and choose Selections > Explicit.
3
In the Settings window for Explicit, type Catalyst Bed in the Label text field.
4
Select Domain 4 only.
Symmetry plane
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Symmetry plane in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundaries 5, 19, and 22 only.
Inlet species O2
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Inlet species O2 in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 4 only.
Inlet species H2
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Inlet species H2 in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 15 only.
Outlet
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Outlet in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 25 only.
First Free-Porous Interface
1
In the Definitions toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type First Free-Porous Interface in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Size and Shape section. In the Top distance text field, type 0.5*do_reac.
5
In the Bottom distance text field, type 0.
6
Locate the Position section. In the x text field, type 2.5*do_reac.
7
In the y text field, type 0.25*do_reac.
8
Locate the Axis section. From the Axis type list, choose x-axis.
Free Flow Domains
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Free Flow Domains in the Label text field.
3
Select Domains 2 and 5 only.
Free and Porous Media Domains
1
In the Definitions toolbar, click  Union.
2
In the Settings window for Union, type Free and Porous Media Domains in the Label text field.
3
Locate the Input Entities section. Under Selections to add, click  Add.
4
In the Add dialog, in the Selections to add list, choose Catalyst Bed and Free Flow Domains.
5
Click OK.
Solid Domains
1
In the Definitions toolbar, click  Adjacent.
2
In the Settings window for Adjacent, type Solid Domains in the Label text field.
3
Locate the Input Entities section. Under Input selections, click  Add.
4
In the Add dialog, select Free and Porous Media Domains in the Input selections list.
5
Click OK.
6
In the Settings window for Adjacent, locate the Output Entities section.
7
From the Geometric entity level list, choose Adjacent domains.
Solid Bnds
1
In the Definitions toolbar, click  Adjacent.
2
In the Settings window for Adjacent, type Solid Bnds in the Label text field.
3
Locate the Input Entities section. Under Input selections, click  Add.
4
In the Add dialog, select Solid Domains in the Input selections list.
5
Click OK.
Porous Bed Bnds
1
In the Definitions toolbar, click  Adjacent.
2
In the Settings window for Adjacent, type Porous Bed Bnds in the Label text field.
3
Locate the Input Entities section. Under Input selections, click  Add.
4
In the Add dialog, select Catalyst Bed in the Input selections list.
5
Click OK.
Outer Bnds
1
In the Definitions toolbar, click  Difference.
2
In the Settings window for Difference, type Outer Bnds in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Under Selections to add, click  Add.
5
In the Add dialog, select Solid Bnds in the Selections to add list.
6
Click OK.
7
In the Settings window for Difference, locate the Input Entities section.
8
Under Selections to subtract, click  Add.
9
In the Add dialog, select Porous Bed Bnds in the Selections to subtract list.
10
Click OK.
Bed Bnds
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Bed Bnds in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 18,20,21 in the Selection text field.
6
Click OK.
Component 2 (comp2)
Five model nodes are created by the Generate Space-Dependent Model feature, they are Porous Material, Chemistry, Transport of Diluted Species in Porous Catalysts, Brinkman Equations and Reacting Flow, Diluted Species.
Materials
Add a Material node for nitrogen.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Liquids and Gases > Gases > Nitrogen.
4
Click the Add to Component button in the window toolbar.
Materials
Nitrogen (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose All domains.
3
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Porosity
epsilon
0.3
1
Basic
Permeability
kappa_iso ; kappaii = kappa_iso, kappaij = 0
1e-9
m²
Basic
4
Right-click Component 2 (comp2) > Materials > Nitrogen (mat1) and choose Move Up.
set properties for Porous Material which is used for Porous Catalyst feature.
Porous Material 1 (pmat1)
1
In the Model Builder window, click Porous Material 1 (pmat1).
2
Select Domain 4 only.
Fluid 1 (pmat1.fluid1)
1
In the Model Builder window, expand the Porous Material 1 (pmat1) node, then click Fluid 1 (pmat1.fluid1).
2
In the Settings window for Fluid, locate the Fluid Properties section.
3
From the Material list, choose Nitrogen (mat1).
Solid 1 (pmat1.solid1)
1
In the Model Builder window, click Solid 1 (pmat1.solid1).
2
In the Settings window for Solid, locate the Solid Properties section.
3
In the θs text field, type 0.7.
Porous Material 1 (pmat1)
1
In the Model Builder window, click Porous Material 1 (pmat1).
2
In the Settings window for Porous Material, locate the Homogenized Properties section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Permeability
kappa_iso ; kappaii = kappa_iso, kappaij = 0
1e-9
m²
Basic
Transport of Diluted Species in Porous Catalysts (tds)
1
In the Model Builder window, under Component 2 (comp2) click Transport of Diluted Species in Porous Catalysts (tds).
2
In the Settings window for Transport of Diluted Species in Porous Catalysts, locate the Domain Selection section.
3
From the Selection list, choose Free and Porous Media Domains.
If the section Advanced Settings is not visible in the settings window, turn it on in Show More Options.
4
Click the  Show More Options button in the Model Builder toolbar.
5
In the Show More Options dialog, in the tree, select the checkbox for the node Physics > Advanced Physics Options.
6
Click OK.
Since the gas will be modeled as compressible, use the Conservative form of the material balance equation.
7
In the Settings window for Transport of Diluted Species in Porous Catalysts, click to expand the Advanced Settings section.
8
From the Material balance form list, choose Conservative.
Set all parameters for the Porous Catalyst feature and its subfeatures.
Porous Catalyst 1
The adsorption process is explicitly handled via chemical reactions. Therefore, disable the default adsorption mechanism.
1
In the Model Builder window, expand the Transport of Diluted Species in Porous Catalysts (tds) node, then click Porous Catalyst 1.
2
In the Settings window for Porous Catalyst, locate the Adsorbed Species section.
3
Clear the Adsorption/Desorption of bulk species checkbox.
Enter the initial molar concentrations for the surface species.
4
Locate the Surface Species section. In the table, enter the following settings:
Surface species
Initial values (mol/m^2)
H
c0H_surf
H2O
c0H2O_surf
O
c0O_surf
OH
c0OH_surf
Rh
c0Rh_surf
Fluid 1
Select the diffusion coefficients from Chemistry.
1
In the Model Builder window, expand the Porous Catalyst 1 node, then click Fluid 1.
2
In the Settings window for Fluid, locate the Diffusion section.
3
From the DcH2 list, choose Diffusion coefficient , H2 in N2 (solvent) (chem).
4
From the DcH2O list, choose Diffusion coefficient , H2O in N2 (solvent) (chem).
5
From the DcO2 list, choose Diffusion coefficient , O2 in N2 (solvent) (chem).
6
From the Effective diffusivity model list, choose Bruggeman model.
Definitions (comp2)
Variables 1, bulk concentration defined from surface concentration
1
In the Model Builder window, under Component 2 (comp2) right-click Definitions and choose Variables.
2
In the Settings window for Variables, type Variables 1, bulk concentration defined from surface concentration in the Label text field.
Load variable definitions from a text file.
3
Locate the Geometric Entity Selection section. From the Geometric entity level list, choose Domain.
4
Select Domain 4 only.
5
Locate the Variables section. Click  Load from File.
6
Browse to the model’s Application Libraries folder and double-click the file porous_reactor_variables.txt.
Transport of Diluted Species in Porous Catalysts (tds)
Initial Values 1
1
In the Model Builder window, under Component 2 (comp2) > Transport of Diluted Species in Porous Catalysts (tds) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the cH2 text field, type 0.
4
In the cO2 text field, type 0.
Add necessary features to the Transport of Diluted Species interface.
Fluid 1
1
In the Physics toolbar, click  Domains and choose Fluid.
2
Select Domains 2 and 5 only.
3
In the Settings window for Fluid, locate the Diffusion section.
4
From the Source list, choose Chemistry.
5
From the DcH2 list, choose Diffusion coefficient , H2 in N2 (solvent) (chem).
6
From the DcH2O list, choose Diffusion coefficient , H2O in N2 (solvent) (chem).
7
From the DcO2 list, choose Diffusion coefficient , O2 in N2 (solvent) (chem).
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 Symmetry plane.
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Boundary Selection section.
3
From the Selection list, choose Inlet species O2.
4
Locate the Concentration section. In the c0,cO2 text field, type c0O2_inflow.
Inflow 2
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Boundary Selection section.
3
From the Selection list, choose Inlet species H2.
4
Locate the Concentration section. In the c0,cH2 text field, type c0H2_inflow.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
In the Settings window for Outflow, locate the Boundary Selection section.
3
From the Selection list, choose Outlet.
Brinkman Equations (br)
1
In the Model Builder window, under Component 2 (comp2) click Brinkman Equations (br).
2
In the Settings window for Brinkman Equations, locate the Domain Selection section.
3
From the Selection list, choose Free and Porous Media Domains.
4
Locate the Physical Model section. Clear the Neglect inertial term (Stokes flow) checkbox.
5
Click to expand the Discretization section. From the Discretization of fluids list, choose P1+P1.
Fluid Properties 1
1
In the Physics toolbar, click  Domains and choose Fluid Properties.
2
Select Domains 2 and 5 only.
Inlet 1
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
In the Settings window for Inlet, locate the Boundary Selection section.
3
From the Selection list, choose Inlet species O2.
4
Locate the Boundary Condition section. From the list, choose Fully developed flow.
5
Locate the Fully Developed Flow section. In the Uav text field, type v_inlet.
Inlet 2
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
In the Settings window for Inlet, locate the Boundary Selection section.
3
From the Selection list, choose Inlet species H2.
4
Locate the Boundary Condition section. From the list, choose Fully developed flow.
5
Locate the Fully Developed Flow section. In the Uav text field, type v_inlet.
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
In the Settings window for Outlet, locate the Boundary Selection section.
3
From the Selection list, choose Outlet.
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 Symmetry plane.
Mesh 1
Size 1
1
In the Model Builder window, under Component 2 (comp2) 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 Domain.
4
Click the  Zoom Extents button in the Graphics toolbar.
5
Select Domain 5 only.
6
Locate the Element Size section. From the Calibrate for list, choose Fluid dynamics.
7
From the Predefined list, choose Coarser.
Size
1
In the Model Builder window, click Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Calibrate for list, choose Fluid dynamics.
4
From the Predefined list, choose Coarse.
Size 2
1
In the Model Builder window, 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
Click  Paste Selection.
5
In the Paste Selection dialog, type 6,9,10,14,20,23 in the Selection text field.
6
Click OK.
7
In the Settings window for Size, locate the Element Size section.
8
From the Calibrate for list, choose Fluid dynamics.
9
From the Predefined list, choose Fine.
Free Triangular 1
1
In the Mesh toolbar, click  More Generators and choose Free Triangular.
2
In the Settings window for Free Triangular, locate the Boundary Selection section.
3
From the Selection list, choose First Free-Porous Interface.
Size 1
1
Right-click Free Triangular 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Calibrate for list, choose Fluid dynamics.
4
From the Predefined list, choose Fine.
Size 2
1
In the Model Builder window, right-click Free Triangular 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 Edge.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 31,32 in the Selection text field.
6
Click OK.
7
In the Settings window for Size, locate the Element Size section.
8
From the Calibrate for list, choose Fluid dynamics.
9
Click the Custom button.
10
Locate the Element Size Parameters section.
11
Select the Maximum element size checkbox. In the associated text field, type 0.5.
Swept 1
1
In the Mesh toolbar, click  Swept.
2
In the Settings window for Swept, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Catalyst Bed.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
From the Distribution type list, choose Predefined.
4
In the Number of elements text field, type 30.
Corner Refinement 1
1
In the Mesh toolbar, click  More Attributes and choose Corner Refinement.
2
In the Settings window for Corner Refinement, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Select Domains 2 and 4–6 only.
5
Locate the Boundary Selection section. Click  Paste Selection.
6
In the Paste Selection dialog, type 6,9,10,14,20,23 in the Selection text field.
7
Click OK.
Free Tetrahedral 1
In the Mesh toolbar, click  Free Tetrahedral.
Size 1
1
Right-click Free Tetrahedral 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
Click  Paste Selection.
5
In the Paste Selection dialog, type 26 in the Selection text field.
6
Click OK.
7
In the Settings window for Size, locate the Element Size section.
8
From the Calibrate for list, choose Fluid dynamics.
Size 2
1
In the Model Builder window, right-click Free Tetrahedral 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 Domain.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 2,6 in the Selection text field.
6
Click OK.
7
In the Settings window for Size, locate the Element Size section.
8
From the Calibrate for list, choose Fluid dynamics.
9
Click the Custom button.
10
Locate the Element Size Parameters section.
11
Select the Maximum element size checkbox. In the associated text field, type 0.9.
Boundary Layers 1
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Free Flow Domains.
5
Click to expand the Corner Settings section. From the Handling of sharp edges list, choose Trimming.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 6,9,10,14,18,21,23 in the Selection text field.
5
Click OK.
6
In the Settings window for Boundary Layer Properties, locate the Layers section.
7
In the Number of layers text field, type 2.
8
In the Stretching factor text field, type 1.75.
9
In the Thickness adjustment factor text field, type 4.5.
Boundary Layers 2
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Catalyst Bed.
5
Locate the Corner Settings section. From the Handling of sharp edges list, choose Trimming.
6
Click to expand the Transition section. Clear the Smooth transition to interior mesh checkbox.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 18,20,21 in the Selection text field.
5
Click OK.
6
In the Settings window for Boundary Layer Properties, locate the Layers section.
7
In the Number of layers text field, type 4.
8
In the Stretching factor text field, type 1.25.
9
In the Thickness adjustment factor text field, type 2.75.
10
Click  Build All.
Study 2
Step 2: Stationary
1
In the Study toolbar, click  Stationary.
There are two study steps in Study 2. The first Stationary study step solves for the pressure and velocity (from the Brinkman Equations) which is supposed to reach stationary state quickly and is insignificantly affected by the concentration field. The second Time Dependent study step solves for the molar concentrations (from the Transport of Diluted Species interface) with the velocity field from the first study step.
2
In the Settings window for Stationary, locate the Physics and Variables Selection section.
3
In the Solve for column of the table, under Component 2 (comp2), clear the checkbox for Transport of Diluted Species in Porous Catalysts (tds).
4
In the Solve for column of the table, under Component 2 (comp2) > Multiphysics, clear the checkbox for Reacting Flow, Diluted Species 1 (rfd1).
5
Right-click Step 2: Stationary and choose Move Up.
Step 2: Time Dependent
1
In the Model Builder window, click Step 2: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,0.05,1).
4
Locate the Physics and Variables Selection section. In the Solve for column of the table, under Component 2 (comp2), clear the checkbox for Brinkman Equations (br).
Solution 2 (sol2)
In the Study toolbar, click  Show Default Solver.
Step 2: Time Dependent
1
In the Model Builder window, under Study 2 click Step 2: Time Dependent.
2
In the Settings window for Time Dependent, click to expand the Values of Dependent Variables section.
3
Find the Values of variables not solved for subsection. From the Settings list, choose User controlled.
Solution 2 (sol2)
1
In the Model Builder window, expand the Solution 2 (sol2) node.
Set the scaling factor to 1 for the bulk species dependent variables.
2
In the Model Builder window, expand the Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 node, then click Concentration (comp2.cH2).
3
In the Settings window for Field, locate the Scaling section.
4
From the Method list, choose Manual.
5
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Concentration (comp2.cH2O).
6
In the Settings window for Field, locate the Scaling section.
7
From the Method list, choose Manual.
8
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Concentration (comp2.cO2).
9
In the Settings window for Field, locate the Scaling section.
10
From the Method list, choose Manual.
Set the scaling factors for all surface species dependent variables.
11
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Surface Concentration (comp2.tds.csurf_H).
12
In the Settings window for Field, locate the Scaling section.
13
From the Method list, choose Manual.
14
In the Scale text field, type cH_surf_scale.
15
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Surface Concentration (comp2.tds.csurf_H2O).
16
In the Settings window for Field, locate the Scaling section.
17
From the Method list, choose Manual.
18
In the Scale text field, type cH2O_surf_scale.
19
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Surface Concentration (comp2.tds.csurf_O).
20
In the Settings window for Field, locate the Scaling section.
21
From the Method list, choose Manual.
22
In the Scale text field, type cO_surf_scale.
23
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Surface Concentration (comp2.tds.csurf_OH).
24
In the Settings window for Field, locate the Scaling section.
25
From the Method list, choose Manual.
26
In the Scale text field, type cOH_surf_scale.
27
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Dependent Variables 2 click Surface Concentration (comp2.tds.csurf_Rh).
28
In the Settings window for Field, locate the Scaling section.
29
From the Method list, choose Manual.
30
In the Scale text field, type cRh_surf_scale.
31
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) click Time-Dependent Solver 1.
32
In the Settings window for Time-Dependent Solver, click to expand the Absolute Tolerance section.
33
In the Tolerance factor text field, type 0.05.
34
Click to expand the Time Stepping section. Find the Algebraic variable settings subsection. From the Error estimation list, choose Exclude algebraic.
35
Right-click Study 2 > Solver Configurations > Solution 2 (sol2) > Time-Dependent Solver 1 and choose Segregated.
36
In the Settings window for Segregated, locate the General section.
37
From the Stabilization and acceleration list, choose Anderson acceleration.
38
In the Dimension of iteration space text field, type 5.
39
In the Mixing parameter text field, type 0.9.
40
In the Iteration delay text field, type 1.
41
Right-click Study 2 > Solver Configurations > Solution 2 (sol2) > Time-Dependent Solver 1 > Segregated 1 and choose Segregated Step.
42
In the Settings window for Segregated Step, type Concentrations in the Label text field.
43
Locate the General section. Under Variables, click  Add.
44
In the Add dialog, in the Variables list, choose Concentration (comp2.cH2), Concentration (comp2.cH2O), and Concentration (comp2.cO2).
45
Click OK.
46
In the Settings window for Segregated Step, click to expand the Method and Termination section.
47
In the Damping factor text field, type 0.8.
48
From the Jacobian update list, choose Once per time step.
49
Right-click Segregated 1 and choose Segregated Step.
50
In the Settings window for Segregated Step, type Surface concentrations in the Label text field.
51
Locate the General section. Under Variables, click  Add.
52
In the Add dialog, in the Variables list, choose Surface Concentration (comp2.tds.csurf_H), Surface Concentration (comp2.tds.csurf_H2O), Surface Concentration (comp2.tds.csurf_O), Surface Concentration (comp2.tds.csurf_OH), and Surface Concentration (comp2.tds.csurf_Rh).
53
Click OK.
54
In the Settings window for Segregated Step, locate the Method and Termination section.
55
In the Damping factor text field, type 0.7.
56
From the Jacobian update list, choose Once per time step.
57
In the Model Builder window, under Study 2 > Solver Configurations > Solution 2 (sol2) > Time-Dependent Solver 1 > Segregated 1 right-click Segregated Step and choose Delete.
Add a Lower Limit to the surface species dependent variables.
58
Right-click Study 2 > Solver Configurations > Solution 2 (sol2) > Time-Dependent Solver 1 > Segregated 1 and choose Lower Limit.
59
In the Settings window for Lower Limit, locate the Lower Limit section.
60
In the Lower limits (field variables) text field, type comp2.tds.csurf_Rh 1e-16 comp2.tds.csurf_H 1e-16 comp2.tds.csurf_H2O 1e-16 comp2.tds.csurf_O 1e-16 comp2.tds.csurf_OH 1e-16.
61
In the Study toolbar, click  Compute.
Results
Cut Plane 1
1
In the Results toolbar, click  Cut Plane.
2
In the Settings window for Cut Plane, locate the Data section.
3
From the Dataset list, choose Study 2/Solution Store 1 (5) (sol3).
4
Locate the Plane Data section. From the Plane list, choose xy-planes.
5
In the z-coordinate text field, type -0.5.
Cut Line 3D 1
1
In the Results toolbar, click  Cut Line 3D.
2
In the Settings window for Cut Line 3D, locate the Line Data section.
3
In row Point 1, set x to 3*do_reac.
4
In row Point 2, set x to 3.7*do_reac.
Velocity (br)
1
In the Model Builder window, under Results click Velocity (br).
2
In the Settings window for 3D Plot Group, locate the Color Legend section.
3
Select the Show units checkbox.
The following steps reproduce, in turn, the plots shown in Figure 2, Figure 3, Figure 4, and Figure 5.
Multislice 1
1
In the Model Builder window, expand the Velocity (br) node, then click Multislice 1.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the x-planes subsection. In the Planes text field, type 9.
4
Find the y-planes subsection. In the Planes text field, type 0.
5
Find the z-planes subsection. In the Planes text field, type 0.
6
Locate the Coloring and Style section. From the Color table list, choose Iodinea.
Velocity, Surface
1
In the Model Builder window, under Results click Velocity (br).
2
In the Settings window for 3D Plot Group, type Velocity, Surface in the Label text field.
3
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
Surface 1
1
Right-click Velocity, Surface and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Gray.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Outer Bnds.
Surface 2
In the Model Builder window, under Results > Velocity, Surface right-click Surface 1 and choose Duplicate.
Selection 1
1
In the Model Builder window, expand the Surface 2 node, then click Selection 1.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Bed Bnds.
Arrow Surface 1
1
In the Model Builder window, right-click Velocity, Surface and choose Arrow Surface.
2
In the Settings window for Arrow Surface, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
Locate the Expression section. In the x-component text field, type u.
5
In the y-component text field, type v.
6
In the z-component text field, type w.
7
Locate the Arrow Positioning section. In the Number of arrows text field, type 300.
8
Locate the Coloring and Style section. From the Color list, choose Black.
9
In the Velocity, Surface toolbar, click  Plot.
10
Click the  Zoom Extents button in the Graphics toolbar.
Surface
1
In the Model Builder window, expand the Pressure (br) node, then click Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose HelfrichiZero.
4
In the Pressure (br) toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Concentration, H2, Surface (tds)
1
In the Model Builder window, under Results click Concentration, H2, Surface (tds).
2
In the Settings window for 3D Plot Group, click to expand the Title section.
3
From the Title type list, choose Automatic.
4
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
Surface: pipe
1
In the Model Builder window, expand the Concentration, H2, Surface (tds) node, then click Surface 1.
2
In the Settings window for Surface, type Surface: pipe in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Click to expand the Title section. From the Title type list, choose None.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Gray.
Selection 1
1
Right-click Surface: pipe and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Outer Bnds.
Surface: Catalyst
1
In the Model Builder window, right-click Concentration, H2, Surface (tds) and choose Surface.
2
In the Settings window for Surface, type Surface: Catalyst in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Gray.
Selection 1
1
Right-click Surface: Catalyst and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Bed Bnds.
Material Appearance 1
1
In the Model Builder window, right-click Surface: Catalyst 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 Rock.
Streamline 1
1
In the Model Builder window, right-click Concentration, H2, Surface (tds) and choose Streamline.
2
In the Settings window for Streamline, locate the Streamline Positioning section.
3
In the Number text field, type 10.
4
Locate the Selection section. Click  Paste Selection.
5
In the Paste Selection dialog, type 18 in the Selection text field.
6
Click OK.
7
In the Settings window for Streamline, locate the Coloring and Style section.
8
Find the Line style subsection. From the Type list, choose Ribbon.
9
In the Width expression text field, type br.U*1[s].
10
Find the Point style subsection. From the Color list, choose White.
Concentration, cH2, Isosurface
1
Right-click Concentration, H2, Surface (tds) and choose Isosurface.
2
In the Settings window for Isosurface, type Concentration, cH2, Isosurface in the Label text field.
3
Locate the Levels section. From the Entry method list, choose Levels.
4
In the Levels text field, type range(0.1,0.1,2).
5
Locate the Coloring and Style section. From the Color table list, choose RanaDraytonii.
Transparency 1
1
Right-click Concentration, cH2, Isosurface and choose Transparency.
2
In the Concentration, H2, Surface (tds) toolbar, click  Plot.
3
Click the  Zoom Extents button in the Graphics toolbar.
Surface 1
1
In the Model Builder window, expand the Results > Concentration, H2O, Surface (tds) 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 Kyanite.
Concentration, O2, Surface (tds)
1
In the Model Builder window, under Results click Concentration, O2, Surface (tds).
2
In the Settings window for 3D Plot Group, locate the Title section.
3
From the Title type list, choose Automatic.
4
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
Surface: Pipe
1
In the Model Builder window, expand the Concentration, O2, Surface (tds) node, then click Surface 1.
2
In the Settings window for Surface, type Surface: Pipe in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Gray.
Selection 1
1
Right-click Surface: Pipe and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Outer Bnds.
Surface: Catalyst
1
In the Model Builder window, right-click Concentration, O2, Surface (tds) and choose Surface.
2
In the Settings window for Surface, type Surface: Catalyst in the Label text field.
3
Locate the Expression section. In the Expression text field, type 1.
4
Locate the Title section. From the Title type list, choose None.
Selection 1
1
Right-click Surface: Catalyst and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Bed Bnds.
Material Appearance 1
1
In the Model Builder window, right-click Surface: Catalyst 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 Rock.
Streamline 1
1
In the Model Builder window, right-click Concentration, O2, Surface (tds) and choose Streamline.
2
In the Settings window for Streamline, locate the Expression section.
3
In the x-component text field, type tds.tflux_cO2x.
4
In the y-component text field, type tds.tflux_cO2y.
5
In the z-component text field, type tds.tflux_cO2z.
6
Locate the Streamline Positioning section. In the Number text field, type 10.
7
Locate the Selection section. Click  Paste Selection.
8
In the Paste Selection dialog, type 18 in the Selection text field.
9
Click OK.
10
In the Settings window for Streamline, locate the Coloring and Style section.
11
Find the Line style subsection. From the Type list, choose Ribbon.
12
In the Width expression text field, type br.U*1[s].
13
Find the Point style subsection. From the Color list, choose White.
Concentration, cO2, Isosurface
1
Right-click Concentration, O2, Surface (tds) and choose Isosurface.
2
In the Settings window for Isosurface, locate the Expression section.
3
In the Expression text field, type cO2.
4
In the Label text field, type Concentration, cO2, Isosurface.
5
Locate the Levels section. From the Entry method list, choose Levels.
6
In the Levels text field, type range(0.5,0.025,0.9).
7
Locate the Coloring and Style section. From the Color table list, choose Bryophyta.
Transparency 1
1
Right-click Concentration, cO2, Isosurface and choose Transparency.
2
In the Concentration, O2, Surface (tds) toolbar, click  Plot.
3
Click the  Zoom Extents button in the Graphics toolbar.
Plot the bulk species concentrations (mol/m^3) in the porous domain.
Graph Plot Style 1
1
In the Results toolbar, click  Configurations and choose Graph Plot Style.
2
In the Settings window for Graph Plot Style, locate the Coloring and Style section.
3
Find the Line style subsection. From the Line list, choose Cycle.
4
From the Color list, choose Cycle.
5
From the Color cycle list, choose Long.
6
From the Width list, choose 2.
7
Locate the Legends section. Find the Include in automatic mode subsection. Clear the Point checkbox.
8
Clear the Solution checkbox.
9
Select the Expression checkbox.
10
Clear the Headers checkbox.
Porous domain: bulk species
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Porous domain: bulk species in the Label text field.
3
Locate the Data section. From the Dataset list, choose Cut Line 3D 1.
4
From the Time selection list, choose From list.
5
In the Times (s) list box, select 1.
6
Click to expand the Title section. From the Title type list, choose None.
7
Locate the Plot Settings section.
8
Select the y-axis label checkbox. In the associated text field, type Concentration (mol/m<sup>3</sup>).
9
Click to expand the Style Configuration section. From the Configuration list, choose Graph Plot Style 1.
Line Graph 1
1
Right-click Porous domain: bulk species and choose Line Graph.
2
In the Settings window for Line Graph, click to expand the Title section.
3
Click to expand the Legends section. Select the Show legends checkbox.
Line Graph 2
1
Right-click Line Graph 1 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cO2.
Line Graph 3
1
Right-click Line Graph 2 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cH2O.
4
Locate the Title section. From the Title type list, choose None.
5
In the Porous domain: bulk species toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Plot the species concentrations (mol/m^3) being converted from surface species in the porous domain.
Porous domain: surface species
1
In the Model Builder window, right-click Porous domain: bulk species and choose Duplicate.
2
In the Model Builder window, click Porous domain: bulk species 1.
3
In the Settings window for 1D Plot Group, type Porous domain: surface species in the Label text field.
Line Graph 1
1
In the Model Builder window, click Line Graph 1.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cs_Rh.
Line Graph 2
1
In the Model Builder window, click Line Graph 2.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cs_H.
Line Graph 3
1
In the Model Builder window, click Line Graph 3.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cs_O.
Line Graph 4
1
Right-click Results > Porous domain: surface species > Line Graph 3 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cs_OH.
4
In the Porous domain: surface species toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
6
Click the  Zoom Extents button in the Graphics toolbar.
Plot the species concentrations (mol/m^3) being converted from adsorbed species in the porous domain.
Porous domain: all species
1
In the Model Builder window, right-click Porous domain: bulk species and choose Duplicate.
2
In the Model Builder window, click Porous domain: bulk species 1.
3
In the Settings window for 1D Plot Group, type Porous domain: all species in the Label text field.
4
Locate the Axis section. Select the y-axis log scale checkbox.
5
Locate the Grid section. Clear the Show grid checkbox.
6
Locate the Legend section. From the Layout list, choose Outside graph axis area.
Bulk: cH2
1
In the Model Builder window, under Results > Porous domain: all species click Line Graph 1.
2
In the Settings window for Line Graph, type Bulk: cH2 in the Label text field.
Bulk: cO2
1
In the Model Builder window, under Results > Porous domain: all species click Line Graph 2.
2
In the Settings window for Line Graph, type Bulk: cO2 in the Label text field.
Bulk: cH2O
1
In the Model Builder window, under Results > Porous domain: all species click Line Graph 3.
2
In the Settings window for Line Graph, type Bulk: cH2O in the Label text field.
Bulk: cH2O, Bulk: cO2
1
In the Model Builder window, under Results > Porous domain: all species, Ctrl-click to select Bulk: cO2 and Bulk: cH2O.
2
Right-click and choose Duplicate.
Surface: cs_Rh
1
In the Settings window for Line Graph, type Surface: cs_Rh in the Label text field.
2
Locate the y-Axis Data section. In the Expression text field, type cs_Rh.
Surface: cs_H
1
In the Model Builder window, under Results > Porous domain: all species click Bulk: cH2O 1.
2
In the Settings window for Line Graph, type Surface: cs_H in the Label text field.
3
Locate the y-Axis Data section. In the Expression text field, type cs_H.
Surface: cs_H, Surface: cs_Rh
1
In the Model Builder window, under Results > Porous domain: all species, Ctrl-click to select Surface: cs_Rh and Surface: cs_H.
2
Right-click and choose Duplicate.
Surface: cs_O
1
In the Settings window for Line Graph, type Surface: cs_O in the Label text field.
2
Locate the y-Axis Data section. In the Expression text field, type cs_O.
Surface: cs_OH
1
In the Model Builder window, under Results > Porous domain: all species click Surface: cs_H 1.
2
In the Settings window for Line Graph, type Surface: cs_OH in the Label text field.
3
Locate the y-Axis Data section. In the Expression text field, type cs_OH.
Surface: cs_H2O
1
Right-click Surface: cs_OH and choose Duplicate.
2
In the Settings window for Line Graph, type Surface: cs_H2O in the Label text field.
3
Locate the y-Axis Data section. In the Expression text field, type cs_H2O.
4
In the Porous domain: all species toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
6
Click the  Zoom Extents button in the Graphics toolbar.