Generate Space-Dependent Model
It is often relevant to perform an extended analysis of the reaction model. For example, to study how a reacting system’s detailed geometry impacts the concentration and temperature distributions. Use the Generate Space-Dependent Model feature tool to export the properties within the Reaction Engineering interface to other physics interfaces using a space-dependent geometry. Properties that are exported are reaction kinetics, thermodynamics, and transport parameters.
To add this feature, on the Reaction Engineering toolbar click Generate Space-Dependent Model () or right-click the Reaction Engineering node to add it from the context menu. Note that only a single Generate Space-Dependent Model node can be added.
Selecting the Geometry and Physics Interfaces
To utilize the Generate Space-Dependent Model feature, select which geometry and physics interfaces to create in the following manner:
1
2
3
Then click the Create/refresh button to create the space-dependent model and the selected physics interfaces (see Figure 2-6).
If more interfaces are needed in a component after the initial model generation, select the appropriate component and the new interface(s) and click Create/Refresh to introduce the interface into it.
Figure 2-6: Using the Generate Space-Dependent Model node the properties of a Reaction Engineering interface is transferred to physics interfaces in a space-dependent component (1D, 1D Axisymmetric, 2D, 2D Axisymmetric, or 3D).
Component Settings
Select a Component to use. Either specify the space dimension of a new component — 1D, 1Daxi, 2D, 2Daxi, or 3D — or select a component already present in the Model Builder.
Physics Interfaces
Select the applicable physics interfaces to create from the Chemical species transport, Fluid flow, and Heat transfer lists. The physics interfaces available are based on the specific modules installed. These include the Chemical Reaction Engineering Module, the MEMS Module, the Heat Transfer Module, and the Subsurface Flow Module. Note that a mass balance physics interface must always be selected when generating a space-dependent model.
If desired, physics interfaces for fluid flow, heat transfer, or other features affecting the reacting system can be added later separately from the physics interfaces created by the Generate Space-Dependent Model feature.
The Chemistry Interface is always created and added when generating a space-dependent model. It generates and announces global variables for the reaction kinetics, thermodynamics, and transport properties. The variables generated are available for all space-dependent interfaces. Figure 2-7 displays an application where a Reactions feature uses reaction rates defined by a Chemistry interface. The syntax chem points to the default Name of the Chemistry node.
Figure 2-7: The Chemistry node generates global variables from rate variables and properties defined in the Reaction Engineering interfaces, and announces these to be used in relevant sections of other generated space-dependent interfaces. The Reaction Rates within a Reactions feature in a Transport of Dilute Species interface illustrate this.
Surface Reactions
When surface species are present (that is, when the Type is set to Surface species for at least one species in the reactor), the surface reactions can be implemented in the space-dependent model in three different ways.
When Transport of Diluted Species in Porous Catalysts or Transport of Concentrated Species in Porous Catalysts is selected, the surface reactions will be modeled using a Surface Reaction node under the Porous Catalyst feature.
When Transport of Diluted Species in Packed Beds or Transport of Concentrated Species in Packed Beds is selected, the surface reactions will be modeled using a Reactions node under the subnode Pellets of Packed Bed feature.
When any other chemical species transport interface (except these mentioned above) is selected, the surface reactions will be modeled using a separate Surface Reaction interface defined on the boundaries of the geometry. The surface reaction rates of species will be represented by a Flux feature in the created chemical species transport interface.
A feature for volumetric reactions is also added and set up, in accordance with the reaction kinetics defined in the Reaction Engineering interface, when clicking the Create/Refresh button in the Space-Dependent Model Generation section.
In Figure 2-8, the surface reaction kinetics in a Reacting Engineering interface has been implemented in a Packed Bed feature using a Reactions subfeature. Note that the surface reaction rates are defined by the Chemistry interface with the Define variables for porous pellets being checked under Pellet Chemistry section.
Figure 2-8: A Packed Bed feature with a Reactions subfeature can be automatically created, from a Reaction Engineering interface including surface species, using the Generate Space-Dependent Model feature.
Chemical Species Transport
The following Chemical Species Transport interfaces are available with the Chemical Reaction Engineering Module:
The model generation automatically defines the dependent variables for all species. The Transport of Diluted Species, Transport of Diluted Species in Porous Media, Transport of Diluted Species in Porous Catalysts, Transport of Diluted Species in Packed Beds, and Nernst-Planck Equations interfaces use the default variable names according to the syntax cspeciesname, referring to species concentrations in mole per volume. The Transport of Concentrated Species, Transport of Concentrated Species in Porous Media, Transport of Concentrated Species in Porous Catalysts, and Transport of Concentrated Species in Packed Beds interfaces use the syntax wspeciesname for default variable names, referring to the species weight fraction. The initial values for the dependent species variables in the space-dependent model are based on the initial species values collected in the Reaction Engineering interface.
The parallel set of dependent variables on extra dimension are created for both the Transport of Diluted Species in Packed Beds and Transport of Concentrated Species in Packed Beds. For the Transport of Concentrated Species in Packed Beds, a pressure dependent variable on extra dimension is also created.
For surface species, dependent variables are defined on extra dimension (Transport of Diluted Species in Packed Beds and Transport of Concentrated Species in Packed Beds) or base geometry (all other chemical species interfaces).
Binary diffusion coefficients can be computed and transferred to a space-dependent model. The available diffusion models for the mass balance physics interfaces sometimes require the binary diffusion coefficients of the mixture, describing all pairwise diffusion interactions between species. Under the assumption of an ideal gas the mass transfer interface for Transport of Concentrated Species can utilize the binary diffusion coefficient. The Transport of Diluted Species and Nernst-Planck Equations interfaces assumes that the chemical species being transported are present in small amounts and are diluted in a solvent. The binary diffusion coefficient in these cases (in the presence of a solvent species) become the diffusion coefficient of the bulk species.
Fluid Flow
The model generation process can be selected to generate a Fluid Flow interface.
There are these separate momentum balance physics interfaces:
The Darcy’s Law Interface (in the CFD Module User’s Guide)
The Free and Porous Media Flow Interface (in the CFD Module User’s Guide)
Species density (see Equation 2-93, Equation 2-94, and Equation 2-95) and dynamic viscosity can for some mixture options be transferred from the Reaction Engineering interface to the Fluid Flow interfaces.
NOx Reduction in a Monolithic Reactor: Application Library path Chemical_Reaction_Engineering_Module/Tutorials/monolith_3d
Hydrocarbon Dehalogenation in a Tortuous Microreactor: Application Library path Chemical_Reaction_Engineering_Module/Reactors_with_Mass_Transfer/tortuous_reactor
Protein Adsorption: Application Library path Chemical_Reaction_Engineering_Module/Mixing_and_Separation/protein_adsorption
Heat Transfer
Base on the Reaction Engineering interface, time- and space-dependent energy balance equations can also be set up. In the model generation process the physics interface generates expressions used by the Heat Transfer interface, such as the heat generated by a chemical reaction. It also generates expressions for physical transport properties.
There are two heat transfer interfaces under the Heat transfer:
Several expressions for the species density, heat capacity, and thermal conductivity are available and can be transferred from the Reaction Engineering interface.
The densities are available from the Calculate Transport Properties section in the interface, where the fluid mixture properties are selected. The density depends on the Species settings and is computed as follows for:
(2-93)
The volume fraction is given by the species concentration, ci, and the molar mass, Mi.
(2-94)
(2-95)
For mixtures with solvent all values are taken from the species set as solvent.
The heat capacity, cp (SI unit: J/(mol·kg)), of the mixture is calculated by the species’ molar heat capacity, Cp (SI unit: J/(mol·kg)) according to
(2-96)
where M is the molar mass (SI unit: kg/mol) and wi the weight fraction.
Porous media type
The Porous media type is available when Transport of Diluted Species in Packed Beds or Transport of Concentrated Species in Packed Beds is selected for Chemical species transport and the Heat Transfer in Porous Media is selected for Heat transfer. There are tree options the Porous media type:
These options are the same as that for Porous Medium feature under Heat Transfer in Porous Media interface. The heat balance equation is set up inside pellets when the Packed bed is selected.
Study Type
Select a Study Type, either Stationary or Time Dependent. It is also possible to edit this choice after the space-dependent model has been generated.