Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method

Round 1

Reviewer 1 Report

This manuscript is concerned with the well-known problem of immiscible fluid displacement in porous media. Even though the paper is technically correct and I found no flaws in the methodology nor in the set-up of the test cases, the novelty of the content with respect to the previous literature and the physical insights provided appear to be too limited to justify publication.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

 Immiscible fluid displacement in a porous medium 2 using Lattice Boltzmann Model

 By

Magzhan Atykhan, Bagdagul Kabdenova (Dauyeshova), Ernesto Monaco and Luis R. Rojas- Solórzano

Minor changes in the references : doi to be added, homogeneity in the references according to the instruction for authors in the journal Fluids https://0-www-mdpi-com.brum.beds.ac.uk/journal/fluids/instructions.

Ref. 6 : Liu, H., Zhang, Y., & Valocchi, A. J. (2015). Lattice Boltzmann simulation of immiscible fluid displacement in porous media: Homogeneous versus heterogeneous pore network. Physics of Fluids, 27(5), 052103. doi:10.1063/1.4921611 

Ref. 4 : Saxena, R., Singh, V. K., & Kumar, E. A. (2014). Carbon Dioxide Capture and Sequestration by Adsorption on Activated Carbon. Energy Procedia, 54, 320–329. doi:10.1016/j.egypro.2014.07.275

Ref. 5 : Taghilou, M., & Rahimian, M. H. (2014). Investigation of two-phase flow in porous media using lattice Boltzmann method. Computers & Mathematics with Applications, 67(2), 424–436. doi:10.1016/j.camwa.2013.08.005 

Reference 10 : not published in 2011 but much earlier in 1991 :

Gunstensen, A. K., Rothman, D. H., Zaleski, S., & Zanetti, G. (1991). Lattice Boltzmann model of immiscible fluids. Physical Review A, 43(8), 4320–4327. doi:10.1103/physreva.43.4320 

Reference 12

Meakin, P., and A. M. Tartakovsky (2009), Modeling and simulation of pore-scale multiphase fluid flow and reactivetransport in fractured and porous media, Rev. Geophys.,47, RG3002, doi:10.1029/2008RG000263

Reference 18 : https://0-doi-org.brum.beds.ac.uk/10.1115/IMECE2019-10876 ASME meeting

Reference 21 : Lee, T., & Liu, L. (2010). Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces. Journal of Computational Physics, 229(20), 8045–8063. doi:10.1016/j.jcp.2010.07.007 

Reference 26 Liu, H., Valocchi, A. J., Kang, Q., & Werth, C. (2013). Pore-Scale Simulations of Gas Displacing Liquid in a Homogeneous Pore Network Using the Lattice Boltzmann Method. Transport in Porous Media, 99(3), 555–580. doi:10.1007/s11242-013-0200-8

Minor changes.

Line 50 : what standard CFD techniques  ? : reference 8 compares LBM and analytical results !, reference 9 contains only LBM results ! No other CFD techniques seem to appear in these references

Line 88-89 relaxation time τ is stated as dimensionless but in kinetic viscosity line 89 is it still true ? I do not think so !

Suggestions

Line 110 : Shan-Chen model could be added to the references

Shan, X., & Chen, H. (1993). Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47(3), 1815–1819. doi:10.1103/physreve.47.1815

Or

Shan, X., & Chen, H. (1994). Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Physical Review E, 49(4), 2941–2948. doi:10.1103/physreve.49.2941

Or

Luo, L.-S. (1998). Unified Theory of Lattice Boltzmann Models for Nonideal Gases. Physical Review Letters, 81(8), 1618–1621. doi:10.1103/physrevlett.81.1618 

Line 125 : Peng-Robinson EOS should be cited as reference

Peng, D. Y.; Robinson, D. B. (1976). "A New Two-Constant Equation of State". Industrial and Engineering Chemistry: Fundamentals. 15: 59–64. doi:10.1021/i160057a011

Line 147 : viscosity ratio is D not M right ? Same in table 2 line 238-239

Table 1 : fingering length T and not L same in table 2 & 3 right ?

Best regards

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

The authors investigated the interpenetrating flow dynamics of a gas injected into a homogeneous porous media numerically by employing a modified version of DL_MESO LBM package. The interplay among different physical parameters is characterized, and kind of interesting results are obtained, which could provide some insights into related research area. Bu the manuscript is not well-written and somehow, it is very confusing. I would like to recommend the manuscript to be further polished  and then to consider its publication in your journal. Some are listed as follows:

• delete the period in the formula (1) in the row 86
• In the row 98, the sentence is very confusing: ``for i=0 weighting factor is 4/9…”, should that be ``for i=0,$ the weighting factor is 4/9?
• Necessary illustrations for formulas (3) and (4) need to be made.
• What is the formula (8) used for?
• In the formula (10), row 128, the bracket should be adjusted to cover the whole formula like the second parenthesis
• Row 133, adding ``as” after ``set” should be better.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

The manuscript presents Lattice Boltzmann simulations of immiscible flow through 2-D uniform porous media at the pore scale. The authors characterize the effects of capillary number, viscosity ratio and contact angle on flow structure and find those to be consistent with expectations from the literature. The value of the study lies in the application of LBM to a well-defined geometry and studying the effects of parameters. However, some improvements are needed as noted below before the manuscript can be accepted for publication. 

1. Provide a detailed and clear description of how the contact angle is implemented.
2. Provide a detailed and clear description of how the fluid-fluid interface is modeled and tracked in time.
3. In Figures 4, 6, and 7, show flow structure at the same physical times in all subfigures. The numerical time step used clearly does not result in the same physical time because the amounts of injected mass are different.
4. The study of only three parameters is too basic and does not go beyond what is known already. More cases are needed along with discussion on physical insights gained in order to make the study compelling.
5. How does the study go beyond what is already available in the literature for multiphase pore scale LBM, for example Liu et al. (2013)?
6. The writing is satisfactory overall but could benefit from a more careful review and editing.

Author Response

Please, see the attachment. Thanks and kindest regards

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I appreciate the author's efforts to improve the manuscript; however, my comments are the same as in my previous review.

While it is true that the Peng-Robinson EOS constitutes a (marginal) aspect of novelty, it does not appear to be the actual focus of the paper, and the authors provide no proof or arguments that its use leads to better results with respect to previous models.

Author Response

Please, see the attachment. Thanks and kindest regards

Author Response File: Author Response.docx

Reviewer 4 Report

The authors have provided a response but have not highlighted the text in the revised manuscript where they have made the changes. This needs to be done to judge whether the changes are satisfactory.

A further comment is that the labeling of Figure 6(a) and 6(b), 8(a) and 8(b), 9(a) and 9(b) is confusing because (a), (b) and (c) and are also used as sub-figure labels in these figures.     

The main problem with the manuscript is comment 3 in the previous review. The intent of the comment was not to suggest that the authors use a single time instant for all figures. What is needed is a consistent time unit for the sub-figures in each of these figures. For example, in Figure 6 the amount of injected mass in the three sub figures (a), (b) and (c) is different at the time step shown. This apparently motivates the authors to state in the abstract that “The results demonstrate that increasing the Capillary number and the surface wettability leads to an increase in the effective gas penetration rate” This statement is misleading because the increase in the capillary number has apparently been caused by an increase in inlet velocity, which would naturally lead to a larger injected mass and a greater penetration distance at any given dimensional time. This is obviously expected for an incompressible flow and is trivial. What would support the claim would be to show the effect of Ca for a dimensionless time that has been scaled with the injection velocity, which is the inlet boundary condition as shown in Figure 4.

Figures 8 and 9 are even more problematic. It is not possible for the injected mass to be so different in the respective sub figures (a), (b) and (c) at the same time step, when a fixed velocity is used as the inlet boundary condition and the flow is incompressible. Either the flow is being treated as compressible, which is physically inconsistent for these flow conditions, or mass is not being conserved, which is worse. It could also be that the inlet boundary condition is not constant velocity or that the stated t-step does not correspond to any physical time.

Author Response

Dear Reviewer,

Please, see the attachment.

Also, please find also in set of attachments, the document with tracked-changes as requested.

Thank you so much for your valuable and insightful comments and observations.

Best regards

Author Response File: Author Response.docx

Round 3

Reviewer 4 Report

The authors have revised the manuscript and it is now appropriate for publication.