Smoothing of Slug Tests for Laboratory Scale Aquifer Assessment—A Comparison among Different Porous Media

Round 1

Reviewer 1 Report

This is an interesting paper dealing with interpretation of slug tests performed on a laboratory  model of an aquifer. 4 different layouts  were considered, as well as 4 different injected volumes. In order to remove noise and short time effects, several treatments of the data using FT or wavelets were carried out. The writing is essentialy clear.

I understand that there is no deterministic heterogeneity in each of the examples, is that correct? In addtion, the duraction of the injection is not given, only the overall volume. What is the importance of the injected volume in the linear case? 

Regarding the wavelets, I think that there is some mistake, the exponential functions must involve exp - t² areguments, the minus signs seem lacking.

As the storativity and permeability are determined, some investigation radius of the test can be estimated, did the authors have an idea about it?

An interesting question is that the slug test is essentially the derivative of the standard drawdown in the linear regime, so some effective "instantaneous apparent permeability " t times observed t can be deduced, did you try to introduce  that concept?

Feitosa, G. S., Chu, L., Thompson, L. G., & Reynolds, A. C. (1994). Determination of permeability distribution from well-test pressure data. Journal of Petroleum Technology, 46(07), 607-615.

Gautier, Y., & Nœtinger, B. (2004). Geostatistical parameters estimation using well test data. Oil Gas Sci. Technol, 59(2), 167-183.

In addition, the question of the "quantity of information" that may be obtained from a test is important, as highlighted in the following paper

Abellan, A., & Noetinger, B. (2010). Optimizing subsurface field data acquisition using information theory. Mathematical Geosciences, 42(6), 603-630.

So basically a well conducted and interesting work that can be easily improved

Author Response

This is an interesting paper dealing with interpretation of slug tests performed on a laboratory  model of an aquifer. 4 different layouts were considered, as well as 4 different injected volumes. In order to remove noise and short time effects, several treatments of the data using FT or wavelets were carried out. The writing is essentially clear.

We thank the Reviewer for his/her appreciation on our work and for his/her addressing suggestions. Please note that the sentences added or revised in the manuscript have been highlighted in red color. Below we provide a point-by-point reply to the reviewer questions/concerns.

Point 1: I understand that there is no deterministic heterogeneity in each of the examples, is that correct? In addition, the duration of the injection is not given, only the overall volume. What is the importance of the injected volume in the linear case? 

Response 1: It is correct to state that there is no deterministic heterogeneity occurring in the aquifer. As regards the duration of the injection, it is theoretically negligible, even if in the experiments a manual injection of the water volume was performed. Its duration is about 1 s, as specified in Section 2.3. However, only the maximum value and the decreasing part of the hydraulic head was studied in order to analyze the non-linear effects and for the calculation of the hydraulic conductivity.

Point 2: Regarding the wavelets, I think that there is some mistake, the exponential functions must involve exp - t2 areguments, the minus signs seem lacking.

Response 2: The minus signs are not lacking in the exponential functions of the wavelet. Please check in detail Eqs. (9) and (10).

Point 3: As the storativity and permeability are determined, some investigation radius of the test can be estimated, did the authors have an idea about it?

Response 3: The approach used in our study is experimental and, even if estimation methods of the radius of influence exist (U.S. Department of Navy, 1961; Barker and Black, 1993; Butler, 1997), the values of the radius of influence here considered were measured by the pressure transducers placed in the observation wells. In particular, the first well, in which the hydraulic head value resulted equal to zero, and the previous one, in which the hydraulic head value was again recorded, were taken into account. Considering the hydraulic head variation in this last range of linear type, it was possible to determine the radius of influence. Note also that the values of S and k were estimated by the method of Cooper et al. (1967), as specified in the text.

Point 4: An interesting question is that the slug test is essentially the derivative of the standard drawdown in the linear regime, so some effective "instantaneous apparent permeability " t times observed t can be deduced, did you try to introduce that concept?

Feitosa, G. S., Chu, L., Thompson, L. G., & Reynolds, A. C. (1994). Determination of permeability distribution from well-test pressure data. Journal of Petroleum Technology, 46(07), 607-615.

Gautier, Y., & Nœtinger, B. (2004). Geostatistical parameters estimation using well test data. Oil Gas Sci. Technol, 59(2), 167-183.

Response 4: Our manuscript, which originates from a series of measurements carried out in the context of experimental studies about the scaling analysis of hydraulic conductivity, is substantially based on the search for the most reliable smoothing methods of hydraulic head data sets. The papers mentioned (Feitosa et al., 1994; Gautier & Nœtinger, 2004), although very interesting, are beyond the scope of the present study. However, in the wider field of experimentation on scaling analysis, it will be of great interest to take these papers into account. Therefore, we thank the reviewer, who addressed us towards issues of great interest to be taken into account in our studies.

Point 5: In addition, the question of the "quantity of information" that may be obtained from a test is important, as highlighted in the following paper

Abellan, A., & Noetinger, B. (2010). Optimizing subsurface field data acquisition using information theory. Mathematical Geosciences, 42(6), 603-630.

Response 5: The Authors thank the reviewer for the suggestion of this interesting paper. Indeed, the topic related to the quantity of information is important to analyze the characteristics of an aquifer. This approach based on the information theory has been added in the Introduction of the manuscript.

Reviewer 2 Report

The manuscript is very interesting and important in the investigation of filtering analysis. The laboratory tests results presents and it comparing with results of 3D model.

This manuscript highlights that a careful smoothing analysis is certainly very useful when the data  sets obtained by slug tests are very large. Useful indications are given on the most appropriate smoothing method to be used.

Author Response

The manuscript is very interesting and important in the investigation of filtering analysis. The laboratory tests results presents and it comparing with results of 3D model.

This manuscript highlights that a careful smoothing analysis is certainly very useful when the data  sets obtained by slug tests are very large. Useful indications are given on the most appropriate smoothing method to be used.

We thank the Reviewer for his/her appreciation on our work.

Round 2

Reviewer 1 Report

The paper was well corrected. I still think that the minus signs of the exponentials defining the wavelets are not very visible, but that is a production issue