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Question about the equation for 'Species Transport in Porous Media'

Posted Jul 9, 2012, 8:28 a.m. EDT Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.2a 3 Replies

Raymond Ruigbaard
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Dear colleagues,

I have a question about the Species transport in porous media equation. The porosity term epsilon is only present in front of the dC/dt term. However, I do not see it anywhere near the convective term. I think I have seen papers where they did put the porosity also in front of the convective term.

Why is the porosity not in the convective term?

I included the equations from COMSOL and I included my equations, written as a mass balance (for more clarity). They should be the same, currently without the porosity in the convective term.

I hope anyone can answer this. Thanks a lot and kind regards,

Ray

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3 Replies Last Post Jul 10, 2012, 8:31 a.m. EDT
Raymond Ruigbaard
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Posted: 1 decade ago Jul 10, 2012, 3:42 a.m. EDT
Anyone have an idea? Thanks.
Anyone have an idea? Thanks.
Juergen Hansmann
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Posted: 1 decade ago Jul 10, 2012, 7:12 a.m. EDT
Hi Raymond,

maybe this helps, you can find the following text in the documentation of the "Theory for the Solute Transport Interface".

Hope this explanation is what you were looking for,
Juergen



Advection
Advection describes the movement of a solute, such as a pollutant, with the bulk fluid velocity. In this interface the velocities, u, are provided, which correspond to superficial volume averages over a unit volume of the medium, including both pores and matrix. These velocities are sometimes called Darcy velocities, and defined as volume flow rates per unit cross section of the medium. This definition makes the velocity field continuous across the boundaries between porous regions and regions with free flow. The velocity field to be used in the Model Inputs section can for example be prescribed using the velocity field from a Darcy’s Law or a Brinkman Equations interface.
The average linear fluid velocities u_a, provides an estimate of the fluid velocity within the pores:

u_a = u/θ_s (Saturated)

u_a = u/θ (Unsaturated)

where θ_s is the pore volume fraction and θ the liquid volume fraction. For saturated porous media, θ_s is typically in the range of 0.1 to 0.5.
Hi Raymond, maybe this helps, you can find the following text in the documentation of the "Theory for the Solute Transport Interface". Hope this explanation is what you were looking for, Juergen Advection Advection describes the movement of a solute, such as a pollutant, with the bulk fluid velocity. In this interface the velocities, u, are provided, which correspond to superficial volume averages over a unit volume of the medium, including both pores and matrix. These velocities are sometimes called Darcy velocities, and defined as volume flow rates per unit cross section of the medium. This definition makes the velocity field continuous across the boundaries between porous regions and regions with free flow. The velocity field to be used in the Model Inputs section can for example be prescribed using the velocity field from a Darcy’s Law or a Brinkman Equations interface. The average linear fluid velocities u_a, provides an estimate of the fluid velocity within the pores: u_a = u/θ_s (Saturated) u_a = u/θ (Unsaturated) where θ_s is the pore volume fraction and θ the liquid volume fraction. For saturated porous media, θ_s is typically in the range of 0.1 to 0.5.
Raymond Ruigbaard
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Posted: 1 decade ago Jul 10, 2012, 8:31 a.m. EDT

Dear Juergen,

thanks for your help :) . I am however not entirely sure this is about the same thing. From what I can tell, the text you found explains how to calculate the Darcy velocity into the interstitial velocity. But I don't really see how this connects to the question if the porosity should be in the convective part of the differential equation.
I do appreciate the help though ;)

I wonder where COMSOL has based their equations on, isn't there a reference list somewhere?

Greetings,

Ray
Dear Juergen, thanks for your help :) . I am however not entirely sure this is about the same thing. From what I can tell, the text you found explains how to calculate the Darcy velocity into the interstitial velocity. But I don't really see how this connects to the question if the porosity should be in the convective part of the differential equation. I do appreciate the help though ;) I wonder where COMSOL has based their equations on, isn't there a reference list somewhere? Greetings, Ray

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