# How to solve a single volume averaged transport equation of a porous domain

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 June 20, 2012, 11:45 How to solve a single volume averaged transport equation of a porous domain #1 New Member   Naf Join Date: Apr 2010 Posts: 4 Rep Power: 8 Hi, I need to define and solve a modified transport equation of additional variable (AV). The equation obtained from volume averaging of the transport equations (PDEs) in the gas phase and in solid phase of the porous domain is as shown below a(dC/dt) + del(UC) = del(D)del(C) + R where, a is a constant.

 June 20, 2012, 18:31 #2 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,725 Rep Power: 99 You mean you want to add the "a" term in front of the transient term, but otherwise a normal transport equation? Why would you want to do this? What physical process does this model? I would use a normal transport equation and put the modification to the transient term in a source term.

June 20, 2012, 20:25
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Naf
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Quote:
 Originally Posted by ghorrocks You mean you want to add the "a" term in front of the transient term, but otherwise a normal transport equation? Why would you want to do this? What physical process does this model? I would use a normal transport equation and put the modification to the transient term in a source term.

Dear ghorrocks, thanks for your interest. Ya, its a normal transport equation. Its to model gas diffusion and adsorption in porous media. The equation arises after adding and simplifying the transport equations for the fluid phase and for the solid phase of the porous media.

What do you mean by putting the modification to the transient term in a source term? how do you do it? what happen to the convective and diffusive terms?

 June 21, 2012, 06:10 #4 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,725 Rep Power: 99 Recast your equation in the form (dC/dt) + del(UC) = del(D)del(C) + (R-(a-1)(dC/dt)) And you can now use the normal transport equation AV, and the term (R-(a-1)(dC/dt)) becomes your source term.

 June 21, 2012, 10:30 #5 New Member   Naf Join Date: Apr 2010 Posts: 4 Rep Power: 8 Thanks so much! this looks promising...then I plan to approximate the dC/dt term in the source as CEL expression given as C.Time Derivative, what do you think?

 June 21, 2012, 11:48 #6 New Member   Naf Join Date: Apr 2010 Posts: 4 Rep Power: 8 Look the error message I got, Error detected by routine PSHDIR CDRNAM = TIMEDERIV CRESLT = NONE may be not proper to try to simultaneously evaluate both the variable and its derivative

 June 21, 2012, 18:48 #7 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,725 Rep Power: 99 No, I do not think CEL can access time derivatives. So you need to work out how to access time derivatives. There has been some posts about this on the forum, do a search for them.

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