Drag Coefficients of Irregularly Shaped Particles in Newtonian Fluids

Round 1

Reviewer 1 Report

Authors have corrected the paper following remarks from the review,

Author Response

The reviewer did not demand any revision.

Reviewer 2 Report

The following errors need to be corrected.

1. Line 19: The meaning of the abbreviation should be explained when it is first mentioned in the text. So write „Computational fluid dynamics (CFD) analysis“ instead of „CFD analysis“.
2. Line 28/29: The underlined word “the bottom to” is missing in the sentence and should be added: „However, the transportation of these cuttings from the bottom to the surface during drilling can be a challenging task due to so many wellbore complexities.
3. Table 3: Density of water is 997 kg/m³ (3 should be written as superscript). Viscosity of water should be written as 0,001 Pa∙s (or 1 mPa∙s).
4. Table 4: Nre is used in the table header (Reynolds number – Re??). It is necessary to correct or add its meaning to the nomenclature.
5. Use the fluid viscosity unit Pa∙s instead of kg/m∙s.
6. Line 343: The title needs to be corrected. Write 4. The applicability and limitations of the proposed model instead of 4. Conclusions
7. Line 400/401: subscript  f  refers to fluid and subscript s to solids. Lines 400 and 401 need to be replaced.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Here are a few suggestions the authors should include in the reviewed paper.

L 6: "... Accurate ..." Write "Accurate" in small letters, i.e, "accurate".

L 12: "... a bow shape; using a ..." Replace "; using" with "with". The reviewed sentence will read: "... a bow shape with a ..."

L 37: "Many Experiment ..." Write "Experiment" in small letters, i.e, "experiment".

L 106: "... ANSYS FLUENT is established ...". Replace "established" with "proposed". The authors' claim to have "established" a solution has not been substantiated by the present study. The flaw was pointed out in the first review.

L 154: "... using the non-spherical ..."  Replace "using" with "with". The reviewed sentence will read: "... with the non-spherical ..."

The word "using" should be replaced elsewhere in the paper with "with".

L 343: The paper should have ONLY one conclusion as a subheading.

The authors should consider the following suggestion as a subheading for section 4.  "4. The applicability and limitations of the proposed model"

L 351: "... transportation.."  Replace "transportation" here and elsewhere in the paper with "transport". The reviewed sentence will read: "... transport ..."

Author Response

Please see the attachment

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The subject of the paper is quite intersting. The title and Abstract give hope to obtain interesting information about drag coefficient of certain shapes.

The results of numerical experiment are presented and lead to interesting conclusions.

But some remarks have to be written:

1. The algorithm of numerical experiment is not clear. This remark concerns point 4 in algorithm given on page 3 (line 117). It is pointed that the equations (8-10) are used. The equations consist of Reynolds. But where are used relations of Reynolds numer with Cd coefficient? It is written „Simulation of particle drag coefficient” - but the question is: how it is done?

2. What is u? Is it velocity of particle or the velcity of fluid?

3. The continuity equation (8) is not correct.

4. What is Viscosity ratio used in Boundary conditions?

5. The results show that the aim of the numerical experiment is to calculated drag coefficient. It is quite suprising. It is not given how it is obtained. From my point of view the movement of fluid depents on drag coefficient. The boundary value problem (BVP) is given, so the movement of fluid is not given. It should be calculated solving BVP. But it can not be solved, because drag coefficient is unknown. It is calculated as well. In my opinion there are to many unknown quantities to solve the problem. This remark is related to remark 1.

6. The title suggest that the drag coefficient will be calculated. But the results of experiment are presented in 3 figures (one of them is the comparision with other papers). It is difficult to get values of the drag coefficient. Authors cite mathematical functions describing drag coefficients. It could be useful to give table of calculated numbers of drag coefficient – reader can find mathematical approximation of the dependency of drag coefficient on Reynolds number. Otherwise, there is no information about dependency of drag coeficient on Reynolds number for particle shapes introduced by Authors (elliptic like shape).

7. There are some surprising graphs (Fig. 7). It i not written for which shape of particle it is done.

8. The results of numerical experiment are presented, but the presentation sholud be done more carrefully.

9. Density of water, given in Table 3, is very strange. Is the water less dense than air?

10. The notation should be corrected: all declared quantities should be written Italic or not Italic, but in consequence way, i. e. Page 4, lines 126, 127: u, v are written using italic; line 128: u, v are written non-Italic font.

11. There is incensequence of notation of high od particle: Figure 4 and Table 1. The high of particle is denoted as h and t.

12. The notation of numbers is text in not correct (for example line 210).

13. The paragraph Acknowledgements has no sense (in context of the paper).

Reviewer 2 Report

A brief summary 

In the paper, the authors investigated the transportation behavior of irregular particles in water by modeling these shapes as variants of a bow shape; using a numerical simulation approach for their drag coefficients. The drag coefficients of the particle (modified into sub-shapes) were modeled. In addition, the inlet velocity of the fluid was varied to see the effects on the shape drag coefficients. A sensitivity analysis was carried out to investigate the effects of fluid properties on the drag coefficient. It was observed that as the particles became less streamlined, their drag coefficient increased, and found that CFD analysis provides a reliable estimation of the drag coefficient, which will help optimize the transportation of drill cuttings during drilling operations.

The following comments need to be addressed to the authors:

Broad comments 

1. The authors found that CFD analysis provides a reliable estimation of the drag coefficient, which will help optimize the transportation of drill cuttings during drilling operations. However, the authors did not explain well enough the actual application of the results of their research to practice as well as the limitations.
2. It should be clearly stated whether the results are applicable to the removal of cuttings during drilling of oil and gas wells or some other type of wells (shallow or deep, vertical, directional, horizontal).
3. Hole cleaning (the transport of drill cuttings through annulus, from the bottom to the surface) of oil and gas wells is carried out exclusively by using drilling muds that are non-Newtonian fluids, and not by water that is a Newtonian fluid. It depends much more on parameters such as flow rate, hole inclination, drilling fluid properties (density, viscosity and yield point), drill pipe rotational velocity and eccentricity, solid particles size and density, than on the shape of the cuttings.

Specific comments 

1. Line 8: Use „the settling velocity“ instead of „the settlement velocity“
2. Line 18: Computational fluid dynamics (CFD) analysis instead of CFD analysis.
3. Line 28: The transportation of these cuttings from to the surface during drilling....- „from the bottom to the surface“.
4. Table : Density of water – 0.997 kg/m3 – not correct. Density of water is 997 kg/m³ at 25 ⁰C. Viscosity of water is 0,001 Pa∙s.
5. Line 210: Reynolds number from 50 to 2.0 x104 – correct number (50 to 2.0 x10⁴).
6. Equations (1) - (10) are taken from the literature so the source should be cited.
7. Line 224: A sensitivity analysis was also carried out to study the effect of fluid density and fluid viscosity on the drag coefficient as shown in Figure 7. It is not clear which drilling fluids are involved or whether the measured or assumed values ​​of drilling fluid density and viscosity were used. The density values ​​shown in Figure 7 suggest that gaseous muds and heavy-weight muds were taken into account.

Reviewer 3 Report

The paper presents a "2D numerical study that discusses the effect of irregular shapes on the drag coefficient and settling velocity of non-spherical particles in a Newtonian fluid. An elliptic cylinder is considered the base case.

I have attached the reviewed manuscript where some suggestions and changes are highlighted. Kindly ignore missing line numbers and changes in the equations due to conversion from pdf to MS Word.

The following is the review summary.

1)  The authors should be consistent with tenses and language style.  While both spellings of "modeling" and "modelling" are correct, the authors must decide whether to write in American or British English.

2) Besides the comparative study and sensitivity analysis presented in the paper, it is not clear what new contributions the authors made to existing models for calculating the drag coefficients and settling velocities of non-spherical particles. According to the authors, the non-spherical particles were modeled with ANSYS FLUENT, a commercial fluid simulation software ( see L 111).

L 111: "In this study, particles were modelled using ANSYS FLUENT."

L 94-96: "In this study, a numerical model is established to investigate the settling of planar and bow-shaped particles in a Newtonian fluid"

Consider the expression above (L 94-96), the authors seem to claim they have developed a numerical model. The claim is at variance with the information and results presented in the paper.

If the authors have added new contributions to ANSYS FLUENT, they should include the changes in the paper.

3) The figures and equations are not properly arranged. The authors should insert a blank space before and after all the figures, equations, and tables. Also, figure captions should end with a period/ full stop.

Comments for author File: Comments.pdf

Reviewer 4 Report

The paper deals with the determination of settling coefficients of non spherical particles. It is correctly written. The authors should check the dimensions of the presented equations which are not consistent : equation 1 gives Cd homogeneous to m  (1N = 1 kgms^-2), in equation 2 I don't see what is the role of  gravitationnal acceleration, but gives Cd dimensionless as it should, consistent with equation 4. There is a very basic problem with that set of equations that must be corrected.

Then the authors use a numerical model to solve the Navier Stokes equations around the body assumed to have some simplified cylindrical shape. The drag coefficient are plotted versus the Reynolds number constructed with the particle diameter.  The author should be carefull using the numerical model at small Reynolds numbers (check standard references  about Stokes paradox corrected by Oseen).  Be careful when using a black box commercial code for research purposes !

The numerical model itself is not clear :  why using a turbulence model? I understand that the imposed flow may be turbulent by considering Reynolds numbers constructed on another macroscopic lengthscale not equal to the particle size. The authors should clear that point. To get Reynolds numbers of 10⁶  at the particle scale does not seem very realistic. What is that viscosity ratio of 10% that is tabulated?

Regarding the cutting transport aspects, the following paper could be useful for the authors.