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Multiscale Packed Bed Reactor with Extra Dimension. An extra dimension approach to model the mass and reaction distribution along the 3D reactor and within each catalyst pellet along the reactor length. The pellet radial dimension constitutes the extra 4th dimension.

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multiscale packed bed reactor with extra dimension
Multiscale Packed Bed Reactor with Extra Dimension

An extra dimension approach to model the mass and reaction distribution along the 3D reactor and within each catalyst pellet along the reactor length. The pellet radial dimension constitutes the extra 4th dimension.

A is reactant and B is product.First order irreversible

catalytic reaction:

Macroscale

transport in reactor

Raction rates follow

moles/(m3·s)

Microscale

transport and reaction in pellet

Inflow

CA=1 mol/m3, CB=0 mol/m3

equations
Equations

In bed volume, transport by convection

and diffusion

In bed volume, velocity determined by Darcy’s law

In pellet, reaction and transport by diffusion, spherical formulation

At pellet boundary, flux continuity and concentration continuity is assured

results macroscale
Results, macroscale

Bed pressure distribution,

gauge pressure.

Concentration distribution of reactantA in the macro space. A is consumedby the pellet reactions along the flowpath.

results microscale
Results, microscale

Example plots of the pellet concentrations

at center of column, at 1 m height position

results microscale1
Results, microscale

Concetration distibution in one catlytic pellet:

The product B has higher concetrationat the center and diffues to the surfaceleaves to the fluid

3D representation of the product

concentrations

step by step instructions are available in model documentation
Step-by-step instructions are available in model documentation
  • Supporting slides follow, use only if needed.
slide7

Preferences Dialog Box. Click Model Builder, select the Enable technology preview functionality check box, and then click OK.

slide9

Add Extra Dimension and Attach Dimensions

Right Click to Component 1 to add

Extra dimension, choose 1D for pellet

Right Click Component1>Definitions

And choose Extra Dimensions>Attached Dimensions

slide11

SCreate geometry for extra dimension which is 1D, for normalized pellet radius

Note that x=0 represent the center of pellet and x=1 is the surface of the pellet

slide12

Meshing Extra dimension geometry

Mesh the extra dimension geometry

Using the above values for size

slide13

Meshing the reactor geometry

Use structured meshes by combining triangular with swept meshes

There are 5 elements in the swept direction

slide15

Define Physics

Darcy’s Law for fluid flow

Assign porosity and permeability

in matrix properties for packed bed

slide16

Add Transport of Diluted Species with number of dependent variable as 2 (A & B)

Assign Diffusion coefficient of A & B inside the packed bed column

slide19

Step 14: Within weak contribution

Select all domains in both Domain Selection and Extra Dimension 1

Make sure to choose “Attached Dimensions 1” in “Extra Dimension attachment”

4*pi*N*r_pe*r^2*(-DAp*pellet_CAr*test(pellet_CAr)-DBp*pellet_CBr*test(pellet_CBr)+r_pe^2*(react*test(pellet_CB)-react*test(pellet_CA)))

slide20

Make sure the first spatial coordinates is “r” for the Extra dimension this is because

The weak expression is has gradient term that is in r-direction

slide21

Define Auxiliary Variable, right click Weak Contribution 1

Field Variable name is “pellet_CA” this is the concentration of A inside the pellet

slide22

Define Auxiliary Variable, right click Weak Contribution 1

Field Variable name is “pellet_CB” this is the concentration of B inside the pellet

slide23

Add Inflow boundary condition, Only specie A comes in

A is converted to B from reaction inside the pellet

A ---> B

slide25

Results: Plotting concentration inside the pellet along the 3D reactor

Make a duplicate of solution 1

Under Data Sets

Change the Component to

Extra Dimension 1 in the setting

window

slide27

Add Line Plot and Type the following expression

“comp1.atxd3(0,0,0.1,pellet_CA)”

This gives concentration of A inside pellet at position z=0.1 in the column

Similar line plot is added for concentration of B

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