Re: [DuMuX] A fundamental question concerning diffusion in Dumux

[Georg.Futter]

Hallo Rainer,

Let's meet next week any day is fine for me.

Best regards
Georg

Von: Dumux [mailto:dumux-boun...@listserv.uni-stuttgart.de] Im Auftrag von 
Rainer Helmig
Gesendet: Freitag, 4. Dezember 2015 15:56
An: DuMuX User Forum
Betreff: Re: [DuMuX] A fundamental question concerning diffusion in Dumux

HI Georg,

thank you very much for your explanations.  We agree with the second part of 
your e-mail. What do you, would we like to meeting us to try to clarify the 
open questions?  We are still working on similar problems and we can try to 
optimize it.

Have a  nice weekend,
best wishes,
Rainer
Am 04.12.2015 um 10:29 schrieb georg.fut...@dlr.de:
Here is a Mickey Mouse example that shows the what the Dumux diffusion 
formulation can produce:

[cid:image001.png@01D12EAF.1632D680]

I just plotted an imaginary molfraction gradient and 2 gradient of molar 
density over some spatial domain. For an ideal gas, the molar density is 
propotional to the gas pressure (ideal gas law).
So the molar density gradient corresponds to a pressure gradient which is again 
proportional to 1/K (the permeability).
I also plotted the molar concentration which is rho*x.
If only a gradient of the molfraction drives the diffusion, transport will be 
from right to left. However, it is obvious that for case 2 (high pressure 
gradient), the concentration has its maximum not at the right boundary but 
inside the domain. I think this illustrates that Fickian diffusion breaks down 
even for a binary system in porous media if the permeability is low.
A better approach would probably be the dusty gas model (Stefan-Maxwell + 
Knudsen diffusion) but I need to check how it is derived. Maybe the same 
problem can occur when the dusty gas model is used.

Best regards
Georg

Von: Dumux [mailto:dumux-boun...@listserv.uni-stuttgart.de] Im Auftrag von 
Alexander Kissinger
Gesendet: Donnerstag, 3. Dezember 2015 16:06
An: DuMuX User Forum
Betreff: Re: [DuMuX] A fundamental question concerning diffusion in Dumux

sorry one more clarification to the last post:

I wrote:



Mass or molar gradients are only valid if


I meant:

Mass or molar concentration gradients [mol_comp/m3] are only valid if



On 12/03/2015 03:56 PM, Alexander Kissinger wrote:
Dear Dumux,

one clarification to the last post:

The driving force for Fickian diffusion is a gradient in the mole fractions x 
[mol_comp/mol_total] as implemented in the Dumux models:
Diffusive flux: J_D = -rho_molar [mol_total/m3] * D * grad x

Mass or molar gradients are only valid if
- the volume of the solute is much smaller than the total concentration or 
molar density [mol_total/m3] and
- isothermal conditions prevail, i.e. no volume change due to changes in 
temperature

A detailed explanation can be found in:
Taylor, Ross, and Rajamani Krishna. Multicomponent mass transfer. Vol. 2. John 
Wiley & Sons, 1993.

Chapter 3.1 and 3.1.1


Best regards
Alex



On 12/03/2015 01:40 PM, Bernd Flemisch wrote:
Hi,

I discussed this a bit here with Alex, Holger and Rainer. The main point is 
that Fickian diffusion is described by _molar_ concentrations [mol/m3], not 
_mass_ concentrations [kg/m3],
https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion

The multiplication by molar/mass density comes then from the fact that we 
balance moles/mass. But it happens outside of the gradient.

This indeed allows diffusion to occur against the mass concentration gradient, 
if that differs from the molar concentration gradient like in the setup that 
you prescribe.

Kind regards
Bernd

On 12/02/2015 10:45 AM, georg.fut...@dlr.de wrote:
I forgot the attached file...

Von: Dumux [mailto:dumux-boun...@listserv.uni-stuttgart.de] Im Auftrag von 
georg.fut...@dlr.de
Gesendet: Mittwoch, 2. Dezember 2015 10:44
An: dumux@listserv.uni-stuttgart.de
Betreff: Re: [DuMuX] A fundamental question concerning diffusion in Dumux

Hello Dumux,

I am back with the same question and some more infos. The modeling approach for 
diffusion in Dumux is (in my opinion) wrong and gives unphysical results. This 
is most pronounced for diffusion in a gas phase and when the intrinsic 
permeability is low.

Consider the model setup depicted in Figure1.jpg. In this setup the only 
transport mechanism for H2O from the right boundary is diffusion because the 
sink of N2 is high and the advective flow is from left to right. In this setup, 
the pressure will drop to the right while the gradient of x_g^H2O is vice 
versa. However, the concentration of H2O will be lower at the right boundary 
and diffusion will occur from a lower to a higher concentration!
This is completely unphysical. There is no reason why the component should flow 
against its concentration gradient. The reason for this lies in the formulation 
of the diffusive fluxes:


[cid:image002.png@01D12EAF.1632D680]

Re: [DuMuX] A fundamental question concerning diffusion in Dumux

[Rainer Helmig]

HI Georg,

thank you very much for your explanations.  We agree with the second 
part of your e-mail. What do you, would we like to meeting us to try to 
clarify the open questions?  We are still working on similar problems 
and we can try to optimize it.


Have a  nice weekend,
best wishes,
Rainer

Am 04.12.2015 um 10:29 schrieb georg.fut...@dlr.de:


Here is a Mickey Mouse example that shows the what the Dumux diffusion 
formulation can produce:


I just plotted an imaginary molfraction gradient and 2 gradient of 
molar density over some spatial domain. For an ideal gas, the molar 
density is propotional to the gas pressure (ideal gas law).


So the molar density gradient corresponds to a pressure gradient which 
is again proportional to 1/K (the permeability).


I also plotted the molar concentration which is rho*x.

If only a gradient of the molfraction drives the diffusion, transport 
will be from right to left. However, it is obvious that for case 2 
(high pressure gradient), the concentration has its maximum not at the 
right boundary but inside the domain. I think this illustrates that 
Fickian diffusion breaks down even for a binary system in porous media 
if the permeability is low.


A better approach would probably be the dusty gas model 
(Stefan-Maxwell + Knudsen diffusion) but I need to check how it is 
derived. Maybe the same problem can occur when the dusty gas model is 
used.


Best regards

Georg

*Von:*Dumux [mailto:dumux-boun...@listserv.uni-stuttgart.de] *Im 
Auftrag von *Alexander Kissinger

*Gesendet:* Donnerstag, 3. Dezember 2015 16:06
*An:* DuMuX User Forum
*Betreff:* Re: [DuMuX] A fundamental question concerning diffusion in 
Dumux


sorry one more clarification to the last post:

I wrote:


Mass or molar gradients are only valid if



I meant:

Mass or molar *concentration* gradients [mol_comp/m3] are only valid if



On 12/03/2015 03:56 PM, Alexander Kissinger wrote:

Dear Dumux,

one clarification to the last post:

The driving force for Fickian diffusion is a gradient in the mole
fractions x [mol_comp/mol_total] as implemented in the Dumux models:
Diffusive flux: J_D = -rho_molar [mol_total/m3] * D * grad x

Mass or molar gradients are only valid if
- the volume of the solute is much smaller than the total
concentration or molar density [mol_total/m3] and
- isothermal conditions prevail, i.e. no volume change due to
changes in temperature

A detailed explanation can be found in:
Taylor, Ross, and Rajamani Krishna. /Multicomponent mass
transfer/. Vol. 2. John Wiley & Sons, 1993.

Chapter 3.1 and 3.1.1


Best regards
Alex



On 12/03/2015 01:40 PM, Bernd Flemisch wrote:

Hi,

I discussed this a bit here with Alex, Holger and Rainer. The
main point is that Fickian diffusion is described by _molar_
concentrations [mol/m3], not _mass_ concentrations [kg/m3],
https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion


The multiplication by molar/mass density comes then from the
fact that we balance moles/mass. But it happens outside of the
gradient.

This indeed allows diffusion to occur against the mass
concentration gradient, if that differs from the molar
concentration gradient like in the setup that you prescribe.

Kind regards
Bernd

On 12/02/2015 10:45 AM, georg.fut...@dlr.de
 wrote:

I forgot the attached file…

*Von:*Dumux
[mailto:dumux-boun...@listserv.uni-stuttgart.de] *Im
Auftrag von *georg.fut...@dlr.de 
*Gesendet:* Mittwoch, 2. Dezember 2015 10:44
*An:* dumux@listserv.uni-stuttgart.de

*Betreff:* Re: [DuMuX] A fundamental question concerning
diffusion in Dumux

Hello Dumux,

I am back with the same question and some more infos. The
modeling approach for diffusion in Dumux is (in my
opinion) wrong and gives unphysical results. This is most
pronounced for diffusion in a gas phase and when the
intrinsic permeability is low.

Consider the model setup depicted in Figure1.jpg. In this
setup the only transport mechanism for H2O from the right
boundary is diffusion because the sink of N2 is high and
the advective flow is from left to right. In this setup,
the pressure will drop to the right while the gradient of
x_g^H2O is vice versa. However, the concentration of H2O
will be lower at the right boundary and *diffusion will
occur from a lower to a higher concentration!*

This is completely unphysical. There is no reason why the
component 

Re: [DuMuX] A fundamental question concerning diffusion in Dumux

[Bernd Flemisch]

Hi,

I think that we agree that Fickian diffusion is implemented correctly in Dumux. 
And, like any modelling assumption, that it has its validity range which 
Georg's scenario maybe doesn't fit into.

For me, that means that there is a need for extending the Dumux compositional 
models such that they allow for plugging in other diffusion models like the 
ones mentioned by Georg.

We can set up a Flyspray task to discuss this further and implement a solution.

Kind regards 
Bernd 



 georg.fut...@dlr.de schrieb 

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