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 to export the properties within the Reaction Engineering interface to physics interfaces solving for fluid flow, mass transport and heat transfer in a space-dependent geometry. Properties exported from Reaction Engineering are reaction kinetics, thermodynamics, and transport parameters. The reaction kinetics are replicated in a Chemistry interface added to the space-dependent component. The physicochemical properties in Chemistry can be coupled to mass, fluid and heat transfer interfaces.
To add the Generate Space-Dependent Model node, find the Reaction Engineering toolbar and 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
When using the Generate Space-Dependent Model feature, select which geometry and physics interfaces to create in the following manner:
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Select the component to use: 1D, 1D Axisymmetric, 2D, 2D Axisymmetric, 3D, or an existing component in the Model Builder.
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Select the physics interfaces to use in each category (chemical species transport, fluid flow and heat transfer).
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Select a study type.
Then click the Create/Refresh button at the top of the settings window (see Figure 2-6). A new Chemistry interface is generated by default when a new geometry or a new chemical species transport interface is selected. It is also possible to add a new Chemistry interface to an existing component, for example after changing the reaction mechanism, by using the Chemistry list and setting the other lists to None.
When possible, one or several multiphysics coupling features are automatically added under the Multiphysics node in the Model Builder window. The coupling node simplifies multiphysics models by synchronizing settings between interfaces. When for example a Transport of Diluted Species interface is created together with a Laminar Flow interface, a Reacting Flow, Diluted Species multiphysics coupling node is also added.
To add physics interfaces to an existing component, simply select the component from the Components to use list, use the Physics Interfaces section to select additional interfaces, and click the Create/Refresh button.
Figure 2-6: Using the Generate Space-Dependent Model node the, reaction mechanism in 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. The geometry selection affects the content of other interface lists. For example, the reacting flow interfaces are only available in 2D and 3D.
Physics Interfaces
Select the applicable physics interfaces to create from the Chemical species transport, Fluid flow, and Heat transfer lists. The interfaces available depends on the reaction system. When a solvent species is defined, a diluted solution is assumed and available interfaces for mass transport are based on the Transport of Diluted Species interface. When no solvent is defined, interfaces based on Transport of Concentrated Species are also available.
The Chemical species transport list contains two categories of mass transfer interfaces, as seen in Figure 2-7. The top of the list contains single physics interfaces, such as Transport of Diluted Species. These can be used together with other single physics interfaces, from the Fluid Flow or Heat Transfer lists, to create a manual multiphysics setup.
The Chemical species transport list also contains predefined multiphysics interfaces, like Reacting Flow or Reacting Flow in Porous Media. Selecting one of these automatically includes multiple interfaces, as well as dedicated coupling features. These multiphysics interfaces correspond to the ones available in the Chemical Species Transport branch of the Model Wizard or the Add Physics window. When different versions the interface exists, additional lists corresponding to sub-branches (in the Model Wizard) are enabled. An example of a multiphysics interface version is shown in Figure 2-8, where the Porous Catalyst, Transport of Concentrated Species version of the Reacting Flow in Porous Media has been selected.
Figure 2-7: The Chemical species transport list contains both single interface entries as well as multiphysics interfaces.
Figure 2-8: The Porous Catalyst, Transport of Concentrated Species version of the Reacting Flow in Porous Media interface is one example of a multiphysics interface that can be created from the Generate Space-Dependent Mode node.
The Chemistry Interface is always created and added when generating a new component or a new chemical species transfer interface. It generates global variables for the reaction kinetics, thermodynamics, and transport properties. The variables generated are available for all space-dependent interfaces. Figure 2-9 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 2-9: The Chemistry node generates global variables for rate variables and properties defined in the Reaction Engineering interfaces, and announces these to be used in relevant features of other space-dependent interfaces. The reaction rates within a Reaction Sources feature in a Transport of Concentrated 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.
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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.
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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 the Packed Bed feature.
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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 2-10, 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 2-10: A Packed Bed feature including surface species cab be automatically created, from a Reaction Engineering interface, using the Generate Space-Dependent Model feature.
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The Packed Bed Feature
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The Transport of Diluted Species Interface
Chemical Species Transport
The following single physics interfaces are available with the Chemical Reaction Engineering Module:
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The Transport of Diluted Species Interface
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The Transport of Diluted Species in Porous Media Interface
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The Transport of Concentrated Species Interface
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The Transport of Concentrated Species in Porous Media Interface
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The Nernst–Planck Equations Interface
The model generation automatically defines the dependent variables for all species. The interfaces based on transport of diluted species uses default variable names according to the syntax cspeciesname, referring to species concentrations in mole per volume. The interfaces based on transport of concentrated species 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 in the Reaction Engineering interface.
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:
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The Single-Phase Flow, Laminar Flow Interface
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The Darcy’s Law Interface (in the CFD Module User’s Guide)
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The Free and Porous Media Flow, Brinkman 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.
Transport Properties
NOx Reduction in a Monolithic Reactor: Application Library path Chemical_Reaction_Engineering_Module/Tutorials/monolith_reactor
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
In 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 Heat transfer:
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Heat Transfer in Fluids
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Heat Transfer in Porous Media
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:
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Liquid, if assuming the liquid to be ideal and incompressible. The liquid mixture density depends on the density of i number of pure species, ρi, and the species weight fraction, wi.
(2-93)
The volume fraction is given by the species concentration, ci, and the molar mass, Mi.
(2-94)
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Gas mixture density depends on the concentrations and molar masses of the mixture species.
(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 three options the Porous media type:
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Local thermal equilibrium
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Local thermal nonequilibrium
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Packed bed
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.