With the revised version of the paper that has been uploaded by the Author, most of the questions posed by the reviewers have been answered.
However, I think that the paper still needs a major revision, to improve its quality.
The paper requires a careful revision of the language, which is sometimes
In the introduction the discussion on multiple-domain models at lines 54ff. is partly repeated at lines 77ff. Furthermore the literature results recalled at lines 95 to 97 and 104 to 107 are largely similar and these sentences could be merged. Finally, lines 135 to 138 could be rewritten, as they seem to repeat the same concept with different words.
It could be useful to clearly state in the introduction the dimensionality (1D, 2D or 3D) of the flow considered both in the experiments and in the models.
Equations (1), (2), (3) and (5): I do not like to see the power of a vector. I suggest to use a different
The model should be described more clearly. I have some concerns about equation (14). If I understand correctly, the Authors consider a network of conduits, labelled with the index i=1,…,n, that connect two fracture intersections in parallel. Then 1/R is equal to the sum of 1/Ri. In this case equation (14) should read Qj = sum(Q)/[Rj sum (1/Ri)], which is different from equation (14). In fact, the two expression coincide only in the simplest case of two parallel conducts (R6 and R3+R4+R5). These are exactly the conditions of the paper. Therefore, I suggest to simplify the notation of the model.

The Authors answered most of the raised questions, as recognized by the Reviewers, and I sincerely appreciated their effort!
However, equation (14) was modified, but it is not yet correct. In fact a dimensional analysis easily shows that (14) can hold only if n=2: if [Qj]=[Q] and [Ri]=[R], then [Q]=[Q R^(n-2)].
I repeat my comment. If I understand correctly, the Authors consider a network of conduits, labelled with the index i=1,…,n, that connect two fracture intersections in parallel. Then 1/R is equal to the sum of 1/Ri. In this case equation (14) should read Qj = sum(Q)/[Rj sum (1/Ri)]. The equation is used in the paper only for the simplest case of two parallel conduits (R6 and R3+R4+R5). Therefore, I suggest again to simplify the notation of (14) to this case, as the wrong equation is not used in the paper.

I thank the Authors for the last correction, which is in agreement with my original suggestion.