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Packed bed mean field model

Posted 21.05.2013, 12:25 GMT-4 Chemical Reaction Engineering Version 4.3b 6 Replies

brc
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Hi,

I am trying to solve the time-dependent concentration profile in a packed bed using the mean field theory rather than the whole CFD definition of the problem. The mass giving rise to the concentration in the bed comes from a source (diffusive flux coming out of spheres in the bed).

I have tried the convection-diffusion equation in the Mathematics library. My problem though is that I am not quite sure how to couple the diffusion out the spheres to the external flow.

Any help is greatly appreciated
6 Replies Last Post 19.05.2014, 07:56 GMT-4
Mayur
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Posted: 1 decade ago 06.06.2013, 11:04 GMT-4
Hi,
I may assist you if you can post your model file (you can modify the file if you don't want to share the original one). I have developed coupled 2d and 1d packed bed models. Have you tried using flux boundary conditions?
Hi, I may assist you if you can post your model file (you can modify the file if you don't want to share the original one). I have developed coupled 2d and 1d packed bed models. Have you tried using flux boundary conditions?
brc
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Posted: 1 decade ago 06.07.2013, 06:34 GMT-4
Hi,

Thanks for your response.

Yes, I have tried to use flux boundary conditions, but the problem I have is that that boundary is time dependent.

The flux would be given by a term involving a mass transfer coefficient and (C_bulk - C_sphere), being C_bulk the concentration in the porous space of the bed and C_sphere the concentration in the spheres at the boundary.

The problem I have is that C_sphere is obtained through the solution to Fick's second law and I do not know how to link both.

All I have is just solve convection-diffusion with a time-depedent source I made up.

Do you have any suggestion?

Hi, Thanks for your response. Yes, I have tried to use flux boundary conditions, but the problem I have is that that boundary is time dependent. The flux would be given by a term involving a mass transfer coefficient and (C_bulk - C_sphere), being C_bulk the concentration in the porous space of the bed and C_sphere the concentration in the spheres at the boundary. The problem I have is that C_sphere is obtained through the solution to Fick's second law and I do not know how to link both. All I have is just solve convection-diffusion with a time-depedent source I made up. Do you have any suggestion?
Mayur
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Posted: 1 decade ago 11.07.2013, 20:46 GMT-4
I think you need to define two different modules of convection and diffusion separately each for c_sphere and c_bulk; then define flux boundary conditions for both sides.

--
Mayur
I think you need to define two different modules of convection and diffusion separately each for c_sphere and c_bulk; then define flux boundary conditions for both sides. -- Mayur
brc
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Posted: 1 decade ago 23.07.2013, 05:25 GMT-4
Hi,


I have tried to do that and couple both phenomena through a flux boundary condition and extrusion coupling but it does not seem to work properly...


How did you do it?

Thanks in advance
Hi, I have tried to do that and couple both phenomena through a flux boundary condition and extrusion coupling but it does not seem to work properly... How did you do it? Thanks in advance
Mayur
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Posted: 1 decade ago 23.07.2013, 07:53 GMT-4
Hi,
if you could send me your model file I may look at it.
cheers

--
Mayur
Hi, if you could send me your model file I may look at it. cheers -- Mayur
Anifa Tamara
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Posted: 1 decade ago 19.05.2014, 07:56 GMT-4
Hi Mayur, brc and everyone,
I have same problem with brc, but my model is extraction with shrinking core model. I have tried to developed with transport diluted species (chds) with 2 models, there are 1D for gas phase, and 2D as solid phase. First of all, these are mathematical modelling in shrinking core:
Concentrate solute A in bulk: Cb: (∂Cb)/∂t + u*(∂Cb)/∂t =DL*(∂^2 Cb)/(∂z^2) - (3*kf/R)*((1-ε)/ε)*(Cb-Cp)
Concentrate solute A in Pore: Cp : εp*(∂Cp/∂t) = (De/r^2)*(∂/∂r (r^2*(∂Cp)/∂r)) + G
Concentrate A in solid: Cs : - G = (1-εp )*(∂Cs/∂t) ↔ (∂Cs/∂t) = -G/(1-εp)
Concentrate A in solid average: (Csbar) : (∂Csbar/∂t) = (3*kf/R)* ((1-ε)/ε)*(Cb-Cp)
Where, (Csbar/Cs0 =(rc/R)^3


This model run with time dependent. The question are:
1. How to input the mathematics formulas of shrinking core model in above in comsol?
2. How to coupling both of models (1D and 2D) or we usually calls as extruction?

Please reply my question, I really need a solutions of these problems. Thank you very much.

Best Regards,
Anifa
Hi Mayur, brc and everyone, I have same problem with brc, but my model is extraction with shrinking core model. I have tried to developed with transport diluted species (chds) with 2 models, there are 1D for gas phase, and 2D as solid phase. First of all, these are mathematical modelling in shrinking core: Concentrate solute A in bulk: Cb: (∂Cb)/∂t + u*(∂Cb)/∂t =DL*(∂^2 Cb)/(∂z^2) - (3*kf/R)*((1-ε)/ε)*(Cb-Cp) Concentrate solute A in Pore: Cp : εp*(∂Cp/∂t) = (De/r^2)*(∂/∂r (r^2*(∂Cp)/∂r)) + G Concentrate A in solid: Cs : - G = (1-εp )*(∂Cs/∂t) ↔ (∂Cs/∂t) = -G/(1-εp) Concentrate A in solid average: (Csbar) : (∂Csbar/∂t) = (3*kf/R)* ((1-ε)/ε)*(Cb-Cp) Where, (Csbar/Cs0 =(rc/R)^3 This model run with time dependent. The question are: 1. How to input the mathematics formulas of shrinking core model in above in comsol? 2. How to coupling both of models (1D and 2D) or we usually calls as extruction? Please reply my question, I really need a solutions of these problems. Thank you very much. Best Regards, Anifa

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