## Selecting coordinate for packed bed with spheres

General discussions about how to formulate a script for FlexPDE.

### Selecting coordinate for packed bed with spheres

Dear forum members,
I am looking for help on selecting the right coordinate system for equations 1 to 16 as attached. Accurately, equations 1 and 10 are the two main formulas defining the behaviors of spherical adsorbents in packed fixed-beds. I have had successful experiences on compiling scripts on equation 10 along using a spherical coordinate. But for equations 1 and 10 coexisting together, what kind of coordinate system should I take?

I know the Cartesian system works for spherical shape, but it won't work for both equations 1 and 10. Can someone kindly give any suggestions on it?

Thanks a lot!
Attachments
Modeling packed bed mass transfer1.pdf
enviexpress

Posts: 14
Joined: Fri Nov 07, 2014 3:23 am

### Re: Selecting coordinate for packed bed with spheres

I am not sure you have given us enough detail to say for sure, but assuming you are modeling a cylinder packed with the substrate, and that the spherical particles are not going to be modeled directly but rather by using parameters in your equation that reflect the behavior, you could use YCYLINDER coordinate system. Thus would give you R and Z as your modeled coordinates.
moderator

Posts: 827
Joined: Tue Jan 11, 2011 1:45 pm

### Re: Selecting coordinate for packed bed with spheres

Dear Moderator,
Thanks for your kind reply. I am afraid that the YCYLINDER coordinate system is not enough to model the problem, and I may not clearly explain what I am looking for help and the processes of the problem.

1)What I am looking for help?
A right coordinate system for directly modeling all equations 1, 9 and 10.

2) The processes of the problem
The problem describe pollutants in solution pass through column and also transfer into packed spheres. There are three consecutive processes defining the problem.
i) axial convection-diffusion transfer of pollutants through the packed area inside a column. In a differential section, Adz, as defined by equation 1, corresponding to this process with a constant DL,
ii) pollutants diffuse from bulk solution to the film around the spheres, and then migrate into the outer surface of spheres, which is called film diffusion and defined by equation 9 with a constant kf.
iii) pollutants transfer from their outer surface into the intra-pores inside, called intra-pore diffusion and defined by equation 10 with a constant Dp.

I expect to directly model all the three equations 1, 9 and 10 together and look for help on pointing out the right coordinate system.

Restricted by the allowed size of the attachment, I can not upload a clear version describing the problem. Can I post a webpage URL here, which links to a clear PDF version and clearly defines the problem?

http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
Last edited by enviexpress on Tue Mar 03, 2020 10:11 pm, edited 11 times in total.
enviexpress

Posts: 14
Joined: Fri Nov 07, 2014 3:23 am

### Re: Selecting coordinate for packed bed with spheres

Dear moderator,
YCYLINDER places the rotation axis of the cylinder, the Z coordinate, along the ordinate (or "y" axis) of the plot, with radial position along the abscissa. But the radius of the cylinder is different from the radius of sphere. So, I need more help from you and other experts.

Sincerely,
Enviexpres
enviexpress

Posts: 14
Joined: Fri Nov 07, 2014 3:23 am

### Re: Selecting coordinate for packed bed with spheres

Dear All,
Can I compile the scripts for the cylindrical column and the spherical particle separately and make them dependent, and then run them in a command-line terminal?
enviexpress

Posts: 14
Joined: Fri Nov 07, 2014 3:23 am