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 feature tool to export the properties within the Reaction Engineering interface to other COMSOL Multiphysics interfaces where a space-dependent model is set up. Properties that are exported are reaction kinetics, thermodynamics, and transport parameters.

To add this feature, on the toolbar click (

) or right-click the node to add it from the context menu. Only one node can be added per model file.

Selecting the Model Generation Settings

To utilize the feature, make selections in the following order:

Select the component to use: 1D Axisymmetric, 1D, 2D, 2D Axisymmetric, 3D, or an existing component within the model builder.

Select the physics interfaces.

Select a study type.

Then click the button to create the space-dependent model (Figure 2-6).

Figure 2-6: The Generate Space-Dependent Model transfers the properties from the Reaction Engineering interface to physics interfaces in a1D Axisymmetric, 1D, 2D, 2D Axisymmetric, or 3D component.

If more interfaces are needed in a component after the initial model generation, select the component and the new interface(s) and click to introduce the interface into it.

Component Settings

Select a . Either specify the space dimension of a new component — , , , , and — or select a component already defined in the Model Builder.

Physics Interfaces

Select the applicable physics interfaces to create or update from the , , and 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 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 from the Reaction Engineering interface. The global 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 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.

If necessary, variables and properties in the Chemistry node can be accessed with the Chemistry node (default Chem). An arbitrary reaction rate expression, R, is thus written as comp2.chem.R in the corresponding text fields of the generated interface (see Figure 2-7).

When surface species are present (that is, when the Species Type is set to for at least one species in the reactor), specify how to include surface reactions in the space-dependent model.

From the list, select or .

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When is selected, the surface reactions will be modeled using a interface defined on the boundaries of the geometry.

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When is selected, the surface reactions will be modeled using a feature added to a interface or a interface. In this case the content of the list is restricted to these interfaces.

A corresponding reaction feature is added and set up, in accordance with the reaction kinetics defined in the interface, when clicking the button in the section. In Figure 2-8, the surface reaction kinetics in a interface has been implemented in a feature using a subfeature. Note that the surface reaction rates are defined by the interface.

Figure 2-8: A Reactive Pellet Bed feature with a Reactions subfeature can be automatically created, using a Generate Space-Dependent Model feature, from a Reaction Engineering interface containing surface species.

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Theory for the Reactive Pellet Bed

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The Transport of Diluted Species Interface

Chemical Species Transport

The following Chemical Species Transport 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 Nernst–Planck Equations Interface

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The Transport of Concentrated Species Interface

The model generation automatically defines the dependent variables for all species. The Transport of Diluted Species, Nernst-Planck Equations, and Transport of Diluted Species in Porous Media interfaces use the default variable names according to the syntax cspeciesname, referring to species concentrations in mole per volume. The Transport of Concentrated Species interface uses 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. Note that only the Transport of Diluted interface is available for systems with equilibrium reactions.

Binary diffusion coefficients of different kinds 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 Transport of Concentrated Species interface 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.

Heat Transfer

The Reaction Engineering interface can also be set up with time- and space-dependent energy balance equations. 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 Energy balance:

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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 Equilibrium Species Vector 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.

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 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_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

Study Type

Select a , either or . It is also possible to edit this choice after the space-dependent model has been generated.