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samanjalilian / Pore-Network-Modeling-of-Porous-Media

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Calculating the Effective Diffusivity of Microparticles #5

Open samanjalilian opened 2 years ago

samanjalilian commented 2 years ago

It goes without saying that in many usual pore network model simulations, the pores are completely void spaces and a certain substance moves from one pore to another. In the current project, we are dealing with something different. Pores in this simulation are porous microparticles, and have their own internal porous (and optionally hierarchical) structure. Hence, instead of handing the bulk diffusivity to the microparticles' ['pore.diffusivity'] item, we have to calculate their effective diffusivity give it to the ['pore.diffusivity']. This effective diffusivity can be calculated by importing the total reaction rate, the average concentration of the second outer layer of each microparticle, and the average size of those throats that connect the boundary pores to the second layer. By doing this, for each microparticle, we are able to calculate the gradient of concentration on their surface. By using this gradient and also the total reaction rate and the Fick's first law, we can calculate the effective diffusivity of each microparticle. Again, we define a function that takes a microparticle's diameter, microporosity, and average Damkohler number, and returns its effective diffusivity. we give this function to the ['pore.diffusivity'].

samanjalilian commented 2 years ago

The second layer pores are shown as red pores in the pictures below: ddd daddad

samanjalilian commented 2 years ago

By following the mentioned procedure, a function for effective diffusivity is defined. The figure below shows how D_eff/D_bulk changes with microporosity. It shows that by increasing the microporosity the effective diffusivity increases, which is totally reasonable. Also, changing the Damkohler number and diameter do not change this trend either qualitatively, or quantitively, which is also seems reasonable.

image

samanjalilian commented 2 years ago

What do you think @masoodmoghaddam ? We had a long-term conversation about this parameter and whether in some circumstances it depends on reaction rate (Damkohler number) or not. But this function shows that there is no dependency on reaction. It gives the same trend for different Damkohler numbers.

masoodmoghaddam commented 2 years ago

This is the second step of upscaling procedure in our multiscale method. In the second step we should find the effective diffusivity of the particles with different microprosity, diameter and average pore Damkohler number.

masoodmoghaddam commented 2 years ago

The question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal is an interesting area of research. Linear or non linear reactions, tortuosity, Knudsen diffusion and reaction type (heterogeneous reaction or homogeneous reaction) are some of the different aspects that seen in this topics. This question is investigated in: https://www.sciencedirect.com/science/article/pii/S0009250906007780 https://www.sciencedirect.com/science/article/pii/S0009250910001880 and we should have a look at their assumptions and results.

samanjalilian commented 2 years ago

Yes definitely. We have to take a look into them.

masoodmoghaddam commented 2 years ago

Yes definitely. We have to take a look into them.

I think its better to open an issue for this purpose.

samanjalilian commented 2 years ago

Our method to calculate the effective diffusivity seems correct. So, I label this issue as an achievement, but still as "in progress" to double-check in the future.

samanjalilian commented 2 years ago

After double-checking, it is correct.