X1T- Dual porosity model-

[Mojo]

Hi, 

 

I am building  a dual porosity model in XT1. Could you please tell me:

1. How the the cumulative surface area of the stagnant zones affect a mineral reaction rate? I have my custom rate and need to know how to revise it to capture this. I have set the surface area of each mineral based on cm2/gr and I call "Surface" in my costume rate law. But certainly this is wrong as the minerals surface areas should be affected by the  cumulative surface area of the stagnant zones. 

2. Are the minerals equally distributed between the cubes representing the stagnant zones? 

3. What is the half-width of the cubes? Is it half of the width of the cube? And what is it for slab? What is the slab thickness? 

4. Can we set any arbitrary number for half-width of the cube as long as it is smaller than Node dimensions? For example, if my node cross sectional area is 10*10 cm2, how is it possible to have cubes with half-width of 2 cm while the volume fraction of stagnant zone is 0.9? How the cube can fit the node cross section while honouring their defined sizes and also the volume fraction of stagnant zones? In the manual's example, half-width of spheres defining stagnant zone was much higher than domain surface area, how is that possible? Can you show me the concept in a graphic please? I attached the common concept of dual porosity model to this text. The Spheeris or Cubes should fit the domain. 

5. Should not the porosity of fracture considered to be equal to one for the dual porosity model and matrix or stagnant zones have its own porosity? The Node/grid porosity should be calculated from these two values. In the Medium section, does the Porosity refer to overall Node porosity? 

 

Many thanks and kind regards

Mojo

[Jia Wang]

Hello Mojo,

When a volume fraction of the nodal block is specified as a stagnant zone, only the process of diffusion takes place in that volume. The diffusion profile into the spheres, cubes, or half-slabs are calculated based on the parameters provided in the Dual Porosity dialog under the Config menu in X1t. Please note that chemical reactions do not take place within stagnant zones. The mineral volume fraction specified operates in the free flowing zone, where chemical reactions (equilibrium, kinetic) takes place.

The half width is half the width of the cube or fractures. The radius or half widths should not be set arbitrarily. This is because the value set affects the cumulative surface area of the stagnant zones in contact of the free flowing zone, which is the most important quantity for controlling diffusion into and out of the stagnant zone. The geometry of your stagnant zones on the other hand has little effect on the simulation results. The parameters provided for the geometry is used to calculate the contact surface area. The contact area for the spherical geometry is calculated as the 3*X_stag*V_b/radius, where X_stag is the fraction of your nodal block specified as stagnant and V_b is the nodal bulk volume. The corresponding equation for cubic and fracture geometry are 3*X_stag*V_b/half_width and X_stag*V_b/half_width. If you decrease the radius or half-widths, then the contact area effectively increases. If you would like more details regarding this calculation, please see section 25.2.1 Contact Area of the Geochemical and Biogeochemical Reaction Modeling textbook 3rd edition.

The porosity value in the Medium pane is applied in both the stagnant and free-flowing zone. If you wish to set a different porosity for within the stagnant zone in your calculation, you can do so within the Dual Porosity dialog under the Config menu.

In the future, please post your queries on the Forum front page. Our team members do not receive notifications when a new post is added to the GWB post archive.

Hope this helps,
Jia Wang
Aqueous Solutions LLC