The manuscript presents numerical experiments of reactive transport in a homogeneous porous medium, where dissolution and precipitation leads to porosity and conductivity changes. The Lagrangian particle tracking approach is implemented. The analysis focuses on the self organization of the spatial distribution of concentration and the breakthrough curves, employing Shanon entropy as a measure of self organization. The main results are: (1) The characterization of the mean and variance of conductivity and global reaction rate variations with time as a function of the Peclet number, including a scaling relationship. (2) A surprising channel behavior of the transport as a result of the reactions is found and characterized with Shanon entropy, shown also to scale with the Peclet number. (3) A thermodynamic explanation if presented for the self organization behavior in the form of increased energy from hydraulic power. 

The manuscript is well written and clear. It offers novel physical insight and results which are of great interest to the hydrology community. I recommend acceptance following some minor revisions and questions as detailed below.

1) It would have been nice to see a comparison of a simple simulation without reaction to the analytical solution for validation of the numerical code. Perhaps a citation regarding validation can be provided?

2) A sentence for motivation can be added – for example, how self organization and Shanon entropy can be used for prediction.

3) In Figure 1 units are missing for the color bar values. 

4) Figures 1, 2c and 2d all show that the heterogeneity that develops is very minor and for most practical purposes the media could still be considered homogeneous. How would the results of this work change if there were more significant changes in conductivity?

5)  It was not clear to me how the concentration in Fig. 3 is defined. In line 556 it is stated that it is the number of particles visiting a cell. Shouldn't that be normalized by the total number of particles?

6) Line 712 states that a few paths carry the larger part of the injected particles. Does Figure 3 support this? What does a path with 0.2 value mean?  How many more particles (in terms of percentage) are in that path compared to the 0 value path?

In this paper the authors study the formation of heterogeneities of conductivities in an initially homogeneous porous media as it undergoes a precipitation/dissolution dynamic, during which some part of the media reduce their porosity and hence their permeability while other increase. To characterize the consequences of the heterogeneities of conductivity upon the transport, they choose to consider the entropy of transport quantities, namely (i) concentration of transported non-reactive particles undergoing advection and diffusion, (ii) arrival times of these particles.

Overall, the phenomena itself of emergence of heterogeneity during this process is of interest. The document is clearly written except for a few rare mistakes (see below), however the figures could be improoved and the global articulation of the concepts seems a bit tenuous despite each of them being well explained separately. At the end of the article, I am still left wondering why the entropy was chosen to characterize this interesting heterogeneity of conductivity. I propose a solution to the authors, which is to compare their results to reference situations, either hydrodynamical situations of thermodynamical situations for which the reader could build his intuition.

Global comments: figures could use some work, validity is good, english is excellent.

I think we can discuss essentially the figures, which follow the development of the argument.

Figure 1:

- set the aspect ratio of X and Y to 1? daspect([1, 1, 1])

- Plot, on the same plot, the Y averaged conductivity versus X, (++ within its standard deviation?)

It seems the reactive front has not gone through the whole media: could the authors show a map where this is the case, probably for t*>1?

Concerning the non dimensionalization of time, maybe the author could plainly state that "qualitatively, t is nondimensionalized so that for t* = 1, the reactive front has permeated through the whole media (cf figure 2 a)

Units of K are not specified here. Add them or maybe switch to (K-K0)/K0 to convince us that these changes are indeed minor as stated in the text? Maybe a check of tortuosity would be helpful to convince the readers that the flow remains truly along the x direction?

How come K-K0 is not 0 on the right-hand side of a and b?

If you decide to keep (d), get rid of the ticks of the coorbar and mark both colors as dissolving/precipitating areas.

Figure 2:

There are two regimes for the global reactivity and only one for the evolution of the conductivity: how come? The evolutions could be compared if (a) had its x axis in log scale, to compare with (c) and (d). Is there a prediction for the plateau of (a)? I find the scaling of the variance of conductivity following a reciprocal Péclet number very interesting and clean. Is there a formal reason for that? I think this important result  is a bit undersold: only briefly mentioned line 533. It deserves more.

Figure 3:

Aspect ratio of 1 would be nice as well.

Does the stripe feature correspond to the conductivity K(Y) when averaged over the X direction?

Figure 4: Snorm

Caption: Snorm= (S-Smax)/Smax. Please correct parenthesis.

The quantities presented are novel: please see further comments for figure 5.

Figure 5: Snorm BTC

• a) Please nondimensionalize breakthrough time.
• b) What is the tilde version of Sbtc_norm (unspecified in text)? How come they do not start at -1, but all at -0.875? At t*=0, S = 0 and Sbtc = (0-Smax)/Smax = -1.

Hydro comparison: (also for previous figure 4 concerning Snorm)

Compared to the previous plots, this quantity is very novel: could you plot it for a reference HYDRO situation for which the reader would have an intuition? For instance, and plug flow turning progressively into a Poiseuille flow: at t=0, the flow field is homogeneous, at t=0.5, the flow field is a Poiseuille flow from x=0 to x=0.5 x L and still homogeneous for x=0.5 x L to L, at t=1, the Poiseuille flow is fully developed along the X direction. (should have an analytical expression)

Thermodynamic comparison: (also for previous figure concerning Snorm)

This figure (and also the former) would also be a good place to link your results for this quantity to other entropic evolution of THERMODYNAMIC transformations of reference: a Joule expansion of a perfect/real gas maybe? If not this, what thermodynamic transformation is analogous to your problem?

• c) Without intuition on either the X axis and the Y axis, it is hard for me to comment. Indicate the time direction on the line plots with arrows please.

Corresponding text: Correct line 630: interpretation of values 0 and values -1 are the other way around concerning the arrival time of particles, (I think!).

Figure 6: Hydraulic power

• a) The quantity is also very novel: could you compare it to reference situation? You do it in the text, which is great: but it would really help to see it on the plots.
• b) Without intuition on either the X axis or the Y axis, it is hard for me to comment. Indicate the time direction on the line plots with arrows please.