Experimental study of the supercritical CO2 diffusion coefficient in porous media under reservoir conditions

Reliable measurement of the CO2 diffusion coefficient in consolidated oil-saturated porous media is critical for the design and performance of CO2-enhanced oil recovery (EOR) and carbon capture and storage (CCS) projects. A thorough experimental investigation of the supercritical CO2 diffusion in n-decane-saturated Berea cores with permeabilities of 50 and 100 mD was conducted in this study at elevated pressure (10–25 MPa) and temperature (333.15–373.15 K), which simulated actual reservoir conditions. The supercritical CO2 diffusion coefficients in the Berea cores were calculated by a model appropriate for diffusion in porous media based on Fick's Law. The results show that the supercritical CO2 diffusion coefficient increases as the pressure, temperature and permeability increase. The supercritical CO2 diffusion coefficient first increases slowly at 10 MPa and then grows significantly with increasing pressure. The impact of the pressure decreases at elevated temperature. The effect of permeability remains steady despite the temperature change during the experiments. The effect of gas state and porous media on the supercritical CO2 diffusion coefficient was further discussed by comparing the results of this study with previous study. Based on the experimental results, an empirical correlation for supercritical CO2 diffusion coefficient in n-decane-saturated porous media was developed. The experimental results contribute to the study of supercritical CO2 diffusion in compact porous media.

The paper is written in a very straight-forward manner; "this is what we did, and this is what we measured." However, there are numerous grammatical and style problems, which could be fixed in revision. I list a few of them here: line 42 (abstract): "...then grow...". Change to " then grows significantly with increasing pressure": page 10. line 4: change to "has recently attracted much attention". line 23: Change "researches" to "studies". (apply this throughout the paper). line 31: need citation after "Renner" line 35: change "were 5.86...." to "were determined for conditions of 5.86..."

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? Yes

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
Studying in the real reservoir conditions is helpful to carry out the field work. I think that some major improvement can be made.
(1)In page 13, line 20. The first assumption is that the Berea cores used in these experiments are isotropic. But to the best of my knowledge, there are still some anisotropic Berea sandstones. So please give some pictures of the cores and setup.
(2)In page 13, line 30-31. Please explain the reason about which model is adapted in these experiments.
(3)In page 17, line 40. There are 23 groups of data in the table 1, but there are only 20 data points in figure 5. It should be pointed out that this is applicable to sandstone with a permeability of 100 mD.
(4)The conclusion in this manuscript is too simple. The effects of temperature and permeability on CO2 diffusion coefficient are well-known. I think the authors need to facet something new with comparison to previous work done.

11-Mar-2019
Dear Mr Lv, The editors assigned to your paper ("Experimental study of supercritical CO<sub>2</sub> diffusion coefficient in porous media under reservoir conditions") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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Comments to Author:
Reviewers' Comments to Author: Reviewer: 1 Comments to the Author(s) This paper presents experimental results measuring diffusion coefficients for supercritical CO2 under a variety of pressure, temperature, and permeability conditions of Berea sandstone. These results add important data to other studies of supercritical CO2 diffusion coefficients because the experiments were carried out under conditions relevant for CO2 sequestration. The authors compile their results with very useful empirical relationship between the diffusion coefficient and pressure, temperature, and hydrocarbon viscosity. Such a laboratory-based relationship could prove very useful for numerical modeling studies of CO2 sequestration, and therefore I recommend that these results be published.
The paper is written in a very straight-forward manner; "this is what we did, and this is what we measured." However, there are numerous grammatical and style problems, which could be fixed in revision. I list a few of them here: line 42 (abstract): "...then grow...". Change to " then grows significantly with increasing pressure": page 10. line 4: change to "has recently attracted much attention". line 23: Change "researches" to "studies". (apply this throughout the paper). Comments to the Author(s) Studying in the real reservoir conditions is helpful to carry out the field work. I think that some major improvement can be made.
(1)In page 13, line 20. The first assumption is that the Berea cores used in these experiments are isotropic. But to the best of my knowledge, there are still some anisotropic Berea sandstones. So please give some pictures of the cores and setup.
(2)In page 13, line 30-31. Please explain the reason about which model is adapted in these experiments.
(3)In page 17, line 40. There are 23 groups of data in the table 1, but there are only 20 data points in figure 5. It should be pointed out that this is applicable to sandstone with a permeability of 100 mD.
(4)The conclusion in this manuscript is too simple. The effects of temperature and permeability on CO2 diffusion coefficient are well-known. I think the authors need to facet something new with comparison to previous work done.

Author's Response to Decision Letter for (RSOS-181902.R0)
See Appendix A.

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation? Accept as is
Comments to the Author(s) Well revised.

10-May-2019
Dear Mr Lv, I am pleased to inform you that your manuscript entitled "Experimental study of the supercritical CO 2 diffusion coefficient in porous media under reservoir conditions" is now accepted for publication in Royal Society Open Science.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org and openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight schedule, if comments are not received, your paper may experience a delay in publication.
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Dear Editor and Reviewers
Thank you for your comments concerning our manuscript entitled "Experimental study of supercritical CO2 diffusion coefficient in porous media under reservoir conditions". The comments are all valuable and helpful for improving our paper and our research. We provide this response letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers' comments as follows.
In order to make the changes easily traceable for you and reviewers, all the revisions were in red font both in this letter and the word file of manuscript we submitted. We also used language polishing service provided by American Journal Expert recommended by editor to improve the written English. The certification verification key is 0BD9-7416-C394-725D-5FEC.
We hope the revised manuscript would meet your and reviewers' requirements.

Dalian University of Technology
In page 13, line 20. The first assumption is that the Berea cores used in these experiments are isotropic. But to the best of my knowledge, there are still some anisotropic Berea sandstones. So please give some pictures of the cores and setup.
Responses to comments: Thanks for the reviewer's suggestion. We took some photos of the Berea cores and the experimental setup, as shown in Figure 1. The merchant who provided Berea cores confirmed that these cores were made isotropic. Those cores marked with 50 are cores with permeability of 50 mD. The other three marked with 100 are cores with permeability of 100 mD.  In the left of Figure 2, it's the experiment system we build to measure the supercritical CO2 diffusion coefficients. From left to right, there are computer which collects the pressure data in real time, temperature and pressure processor box, Julabo oil bath and pump. In the right of Figure 2, it's the customized diffusion cell made of stainless steel and can sustain pressure up to 30 MPa and temperature up to 150 ℃. On the side of the cell, there is an inlet which connected to the pressure and temperature transducer. The second inlet on the top is the one we used to inject and eject the supercritical CO2.
In page 13, line 30-31. Please explain the reason about which model is adapted in these experiments.
Responses to comments: Thanks for the reviewer's suggestion. The model we used in this study is adopted from Li's work which we referred in the manuscript. The reason that we used this model is that the cores were sealed on the top and bottom sides in both his and our study. So the diffusion process became a natural convection mass transfer induced by the diffusion CO2 into a decane-saturated vertical porous column. Equation 2 is a simplified version after a series of derivation from equation 1 and it is really convenient for calculation in practical application. We followed the reviewer's comments and make corresponding changes. The paragraph has been changed to "Based on the treatments to the cores mentioned previously, the diffusion process in this study became a natural convection mass transfer process induced by the diffusion of CO2 into a liquid-saturated vertical porous column. The effective CO2 diffusion coefficient under non-swelling conditions can be obtained from Fick's first law and the continuity equation, as shown in Eq. (1)."
In page 17, line 40. There are 23 groups of data in the table 1, but there are only 20 data points in figure 5. It should be pointed out that this is applicable to sandstone with a permeability of 100 mD.
Responses to comments: Thanks for the reviewer's suggestion. The correlation proposed is based on the data acquired with Berea cores with permeability of 100 mD. That's the reason why there are only 20 data points in figure 5. We followed the reviewer's comments and make corresponding changes. The sentence has been rephrased to "The correlation for Berea cores with a permeability of 100 mD is shown as Equation 3." The conclusion in this manuscript is too simple. The effects of temperature and permeability on CO2 diffusion coefficient are well-known. I think the authors need to facet something new with comparison to previous work done Responses to comments: Thanks for the reviewer's suggestion. The major novelty of this study focus on supercritical CO2 diffusion characteristics in oil-saturated porous media under reservoir conditions. There are few studies of CO2 diffusion process under high pressure and temperatures with the presence of porous media. Also, we are aiming at finding out whether the effects of temperature, pressure and permeability would still be the same when it comes to reservoir condition. We rephrased the conclusion part to emphasize the novelty of this study and add more comparison with previous work regarding with the presence of porous media. The paragraph has been rephrased to "These results demonstrated that under reservoir conditions the supercritical CO2 diffusion coefficient in oil-saturated porous media increased with increasing pressure and temperature, respectively. However, the effect of pressure on the diffusion process decreased at elevated temperature condition. Also, the supercritical CO2 diffusion coefficient first increases slowly at 10 MPa and then grows significantly with increasing pressure. The increase in the core permeability increased the diffusion coefficient and the growth trend was steady throughout the whole temperature range in the experiments. The supercritical state of the CO2 and the presence of porous media significantly impeded the diffusion process, compared with the results from pure gas CO2 diffusion in bulk alkanes in previous study. The pressuretemperature-viscosity based empirical equation developed in this paper successfully predicted the supercritical CO2 diffusion coefficients in porous media under reservoir conditions. Moreover, all the experimental data contributed to the theoretical study of supercritical CO2 diffusion in porous media at elevated temperatures and pressures."