Presentation on theme: "Multiscale Packed Bed Reactor with Extra Dimension"— Presentation transcript:
1Multiscale 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 𝑘 𝐵𝑅 𝐴 =−𝑘∙ 𝐶 𝐴𝑅 𝐵 =𝑘∙ 𝐶 𝐵A is reactant and B is product. First order irreversiblecatalytic reaction:Raction rates followmoles/(m3·s)Macroscaletransport in reactorMicroscaletransport and reaction in pelletInflowCA=1 mol/m3, CB=0 mol/m3
2Equations In bed volume, transport by convection and diffusion In bed volume, velocity determined by Darcy’s lawIn pellet, reaction and transport by diffusion, spherical formulationAt pellet boundary, flux continuity and concentration continuity is assured
3Results, macroscale Bed pressure distribution, gauge pressure. Concentration distribution of reactant A in the macro space. A is consumed by the pellet reactions along the flow path.
4Results, microscale Example plots of the pellet concentrations at center of column, at 1 m height position
5Results, microscale Concetration distibution in one catlytic pellet: The product B has higher concetration at the center and diffues to the surface leaves to the fluid3D representation of the productconcentrations
6Step-by-step instructions are available in model documentation Supporting slides follow, use only if needed.
7Preferences Dialog Box Preferences Dialog Box. Click Model Builder, select the Enable technology preview functionality check box, and then click OK.
18Right Click chds interface and choose weak contribution
19Step 14: Within weak contribution Select all domains in both Domain Selection and Extra Dimension 1Make 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)))
20Make 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
21Define Auxiliary Variable, right click Weak Contribution 1 Field Variable name is “pellet_CA” this is the concentration of A inside the pellet
22Define Auxiliary Variable, right click Weak Contribution 1 Field Variable name is “pellet_CB” this is the concentration of B inside the pellet
23Add Inflow boundary condition, Only specie A comes in A is converted to B from reaction inside the pelletA > B
25Results: Plotting concentration inside the pellet along the 3D reactor Make a duplicate of solution 1Under Data SetsChange the Component toExtra Dimension 1 in the settingwindow
26Add 1d Plot group and make sure the Data set is selected as Solution 3
27Add 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 columnSimilar line plot is added for concentration of B
28Results: Volume plot of concentration of A in the entire reactor