Mixing factor in dual porosity model

[Olasz Tamas]

Hi,

I am trying to model a dual porosity medium, conceptualised as a fractured bedrock (concrete). I have the mobile cells (the fracture) and 5 associated immobile cells, which are rectangular. Calculating the mixing factor between the immobile cells is clear according to the equation presented in the manuals.

However, I am confused by how to calculate the mixf factor between the mobile cell and the first immobile cell (say, 1 and 22, since I have 20 mobile cells right now). Looking at example 13, the mixing factor from cell 1 to 22, the calculation is not detailed as surface, distance between midpoint of cells (h(ij)) and boundary condition factor values are omitted from the table 36.

Secondly, the mixing factor from cell 22 to 1. Here for the (h(ij))  0.002 is used. This assumes that the mobile cell width is the same as the immobile cell width. Is this specified somewhere? In my model, I would, by my intepretation, use the value of (h(ij)) of the mobile cell and the first immobile cell (1 and 22). Which would be a smaller value as the widht for the immobile cells is smaller, would that be correct?

An article suggests (Using PHREEQC to Simulate Solute Transport in Fractured Bedrock, by David S. Lipson, John E.McCray, and Geoffrey D. Thyne) that these two are calculated by the same formula, except that the volumes of the cells differ for the two, which makes sense. But, the (h(ij)) value for the distance between two immobile cells is used for both. This would have to be incorrect, since the diffusion is happening between the mobile and the immobile cells. So this value would have to be smaller, since the mobile cell width is smaller.

So to summarize, and I know this reads confusing, but I cannot put it clearer. I would like to know how to calculate the mixf factor from cell 1 to 22, and from cell 22 to 1, especially to what h(ij) to use. Thank you.