Uncertainty Propagation through a Point Model for Steady-State Two-Phase Pipe Flow

Round 1

Reviewer 1 Report

It was my pleasure to review the manuscript "Uncertainty propagation through a point model for steady-state two-phase pipe flow". It could be accepted even now in the current form, but I would like to propose some points where I can see posible space for improvements:

-Please avoid use of footnotes; I belive they are not allowed in MDPI's journals,

-Table 1 shows the parameters that you use for uncertainty analysis; Can you cover first three parameters (mass rate, viscosity and density) with the Reynolds number? In such case you can test the Reynolds number, hydraulic roughness and pipe diameter as basic parameters and in addition pipe inclination. These are input parameters for determination of one-phase pipe flow (hydraulic friction through Colebrook equation). I see also that the first three parameters need to be selected separately for liquid and for gas phase; please provide some detailed explanations (buble flow, or so...).

-From Figure 1 I can see that the relative roughness of inner pipe surface are not that sensitive parameter to have large influence to the final results. However, in my experience it is not easy to measure sand-grain roughness or inner pipe surface: Guo X, Wang T, Yang K, Fu H, Guo Y, Li J. Estimation of Equivalent Sand–Grain Roughness for Coated Water Supply Pipes. Journal of Pipeline Systems Engineering and Practice. 2020 Feb 1;11(1):04019054. https://0-doi-org.brum.beds.ac.uk/10.1061/(ASCE)PS.1949-1204.0000433

-In Section 2.2., you provide discussion about pressure drop. I am a petroleum engineer specialized in single-phase pipe flow, but in your case it could be of interest to discuss vertical versus horisontal flow. I hope that your parameter inclination are in Table 1 for this purpose. Vertical two-phase flow is of interest for oil and gas exploitation.

-I work for one large super-computing center and I feel that your Section 2.3. Computational cost can be of interest for such readers with similar backround as mine. Can you please further elaborate in more details how do you measure computational costs? Anyway, in you formula 11b, you have choosen Haaland approximation of the Colebrook turbulant flow friction, but recent studies showed that the most accurate and the most computationally efficient are formula by Brkić and Praks: Brkić, D.; Praks, P. Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function. Mathematics 2019, 7, 34., https://0-doi-org.brum.beds.ac.uk/10.3390/math7010034 (you don't need to change Haaland's formula from your computation, but simply mention the new facts in term of accuracy and speed). 

-Does your formula 11a deal with Darcy of Fanning friction factor?

Author Response

It was my pleasure to review the manuscript "Uncertainty propagation through a point model
for steady-state two-phase pipe flow". It could be accepted even now in the current form,
but I would like to propose some points where I can see posible space for improvements: -Please avoid use of footnotes; I belive they are not allowed in MDPI's journals, Answer: Thank you. We have removed footnotes and integrated them into the body text. -Table 1 shows the parameters that you use for uncertainty analysis; Can you cover first three
parameters (mass rate, viscosity and density) with the Reynolds number? In such case you can
test the Reynolds number, hydraulic roughness and pipe diameter as basic parameters and in
addition pipe inclination. These are input parameters for determination of one-phase pipe flow
(hydraulic friction through Colebrook equation). I see also that the first three parameters need
to be selected separately for liquid and for gas phase; please provide some detailed
explanations (buble flow, or so...). Answer: For one-phase flow, the Reynolds number can be computed directly from mass rate,
viscosity and diameter. From the uncertainty in measurements of mass rate, viscosity and
diameter we can compute the uncertainty in the Reynolds number and get a sensitivity index
from simulations. The situation is different for two-phase flow because the characteristic
dimension is the hydraulic diameter. The Reynolds number is separate for each phase and a
function of the holdup. Consequently we do not know the distribution of the Reynolds numbers
prior to simulations. The quantities that goes into the Reynolds number also appears separately
in some parts of the model. Thus, the Reynolds number is not sufficient for two-phase flow. -From Figure 1 I can see that the relative roughness of inner pipe surface are not that sensitive
parameter to have large influence to the final results. However, in my experience it is not easy
to measure sand-grain roughness or inner pipe surface: Guo X, Wang T, Yang K, Fu H, Guo Y, Li J.
Estimation of Equivalent Sand-Grain Roughness for Coated Water Supply Pipes. Journal of Pipeline
Systems Engineering and Practice. 2020 Feb 1;11(1):04019054.
https://0-doi-org.brum.beds.ac.uk/10.1061/(ASCE)PS.1949-1204.0000433 Answer: The roughness of the pipe is inferred from one-phase experiments to be 7 micrometers
with a standard deviation in measurements of 1 micrometer. This is a large uncertainty, yet
from simulations, we see that the effect of this uncertainty on holdup and pressure drop
predictions is small. -In Section 2.2., you provide discussion about pressure drop. I am a petroleum engineer
specialized in single-phase pipe flow, but in your case it could be of interest to discuss
vertical versus horisontal flow. I hope that your parameter inclination are in Table 1 for
this purpose. Vertical two-phase flow is of interest for oil and gas exploitation. Answer: Vertical two-phase flow is undoubtedly of great interest, but horizontal flow has so
far been the focus. Still, the model handles inclined pipes and this is essential to the analysis.
Several laboratory experts have expressed that a small deviation from horizontal when mounting
the pipe will have great impact on the holdup and pressure drop predictions. Thus, in the analysis
we consider zero inclination, but plus or minus some error. From Figure 1, we see that the
deviation from zero inclination make up about 5 percent of the uncertainty in the holdup
estimates. -I work for one large super-computing center and I feel that your Section 2.3. Computational cost
can be of interest for such readers with similar backround as mine. Can you please further
elaborate in more details how do you measure computational costs? Anyway, in you formula 11b, you
have choosen Haaland approximation of the Colebrook turbulant flow friction, but recent studies
showed that the most accurate and the most computationally efficient are formula by Brkic and
Praks: Brkic, D.; Praks, P. Accurate and Efficient Explicit Approximations of the Colebrook Flow
Friction Equation Based on the Wright-Function. Mathematics 2019, 7, 34.,
https://0-doi-org.brum.beds.ac.uk/10.3390/math7010034 (you don't need to change Haaland's formula from your
computation, but simply mention the new facts in term of accuracy and speed) Answer: Yes, we believe this work can be interesting for researchers within high-performance
computing. More details are added to Section 2.3. We have added a reference to Brkic and Praks
and an explanation for choosing the Haaland approximation. -Does your formula 11a deal with Darcy of Fanning friction factor? Answer: It approximates the Fanning friction factor.

Reviewer 2 Report

Dear Editor,

The paper conducts an interesting subject on the field of uncertainty propagation steady-state two-phase pipe flow. However, there are many drawbacks in the present manuscript. The authors are suggested to resubmit the paper after careful and major modifications. In the following, the major revisions are mentioned:

There are some grammatical errors and typos throughout the paper. Please review the paper and modify these typos. Introduction is too brief and unprofessionally presented (motivation of the work and current state of the art of targeted problem is not well clarified). It can be improved by citing more relevant works. An example is as follow:

Convective Bubbly Flow of Water in an Annular Pipe: Role of Total Dissolved Solids on Heat Transfer Characteristics and Bubble Formation, Water 2019, 11(8), 1566

Most of the cited works in the introduction are very old and gives the impression that it is not an active field of research. In page 2, line 49, it is mentioned that “We have removed 7 cases from the analysis where the sensitivity estimation failed with PC”. Why these cases cannot be estimated by PC? Please clarify this issue. Many terms are not defined in the equations. I suggest to add a nomenclature to this paper consist of the whole terms and their units. I believe that it can be very helpful for improving the readability of this paper. In section 2, the discussion about the results are shallow. The results should be investigated and analyzed with more detail and more deeply. In page 13, lines 155-156, please clarify that why use choose those values for a and b. I suggest to show all the calculation procedure discussed in section 4.1 in a flowchart preferably in the end of this section. It will help the readers of your article to simply understand how to predict holdup or pressure drop from measured inputs. The section “Materials and Methods” should be placed before section “Results”. First, the problem and how it is treated should be defined and discussed and then, the results should be mentioned. There is no conclusion section in this paper. Please add a conclusion section in the end of this paper which first discusses the problem and the method you used to deal with this problem. Then, you should mention your important achievement in this study.

Author Response

Dear Editor, The paper conducts an interesting subject on the field of uncertainty
propagation steady-state two-phase pipe flow. However, there are many
drawbacks in the present manuscript. The authors are suggested to resubmit
the paper after careful and major modifications. In the following, the
major revisions are mentioned: There are some grammatical errors and typos throughout the paper. Please
review the paper and modify these typos. Answer: We have fixed several typos. Introduction is too brief and unprofessionally presented (motivation of
the work and current state of the art of targeted problem is not well
clarified). It can be improved by citing more relevant works. An example
is as follow: Convective Bubbly Flow of Water in an Annular Pipe: Role of Total
Dissolved Solids on Heat Transfer Characteristics and Bubble Formation,
Water 2019, 11(8), 1566. Most of the cited works in the introduction are very old and gives the
impression that it is not an active field of research. Answer: Yes, the introduction is extended substantially including
references to more recent work. In page 2, line 49, it is mentioned that “We have removed 7 cases from
the analysis where the sensitivity estimation failed with PC”. Why
these cases cannot be estimated by PC? Please clarify this issue. Answer: We have explained this issue in more detail and added Table 3. Many terms are not defined in the equations. I suggest to add a
nomenclature to this paper consist of the whole terms and their units.
I believe that it can be very helpful for improving the readability of
this paper. Answer: We chose not to include nomenclature, but we have added further
explanation of some variables and cleared up the description of bubbly
flow. In section 2, the discussion about the results are shallow. The results
should be investigated and analyzed with more detail and more deeply. Answer: Yes, we have extended each paragraph of the discussion with
more detail. In page 13, lines 155-156, please clarify that why use choose those
values for a and b. Answer: The choice of the values for a and b are not a part of this paper.
Those values were chosen by Smith et al, and we simply choose to study
their proposed model. We have emphasized this distinction better in the
beginning of Section 2. Talking to Smith, he explained that the choice is
done as the transition from laminar to turbulent flow is not a sharp
limit, but that there can be a transitional region. The values for the
parameters a and b were chosen as they seemed to give good results for
the presented dataset. Natural interpolation was chosen over other
interpolation methods for simplicity as the interpolation in the
transitional region is somewhat uncertain anyways. I suggest to show all the calculation procedure discussed in section 4.1
in a flowchart preferably in the end of this section. It will help the
readers of your article to simply understand how to predict holdup or
pressure drop from measured inputs. Answer: Yes, that is a good suggestion. A flowchart is added. The section “Materials and Methods” should be placed before section
“Results”. First, the problem and how it is treated should be defined
and discussed and then, the results should be mentioned. Answer: Yes, the order is changed. There is no conclusion section in this paper. Please add a conclusion
section in the end of this paper which first discusses the problem and
the method you used to deal with this problem. Then, you should mention
your important achievement in this study. Answer: Yes, it was necessary to make a clear conclusion. We
chose to add this as a paragraph in the end of the discussion.

Reviewer 3 Report

Review of the article " Uncertainty propagation through a point model for steady-state two-phase pipe flow " by Strand et al.

The article is well written and within the journal scope. However several minor issues must be corrected before the text can be accepted for publication.

In my opinion, the abstract must be rewritten. It should contain the most important things such as: what has been done, how and the most important conclusions.

A literature review is too poor according to me. The authors should provide more information about state of the art in the introduction by referring to the literature.

The order of the paper should be modified. Authors should start with the Introduction, then present the Material sand Models, then Results, then the Discussion and finally Future Research.

In section 4.1 authors wrote: “The model predictions are based on the measured input variables listed in Table 1.” As Model structure determination is one of the key issues for a field of knowledge known as system identification authors should at least refer their model to this approach. This can be easily done e.g. by adding. “In contrast to the presented approach System Identification with backward elimination method [R1, R2], forward selection [R3] or stepwise regression [R4] can be used for the same purpose. This would raise the model quality, but also increase the experiment costs and computational time significantly. Thus we did not used the following approach.

 

[R1] Lichota P., Szulczyk J., Tischler M. B.., Berger T. Frequency Responses Identification from Multi-Axis Maneuver with Simultaneous Multisine Inputs, Journal of Guidance, Control and Dynamics, 2019, 42, pp. 2550-2556

[R2] Lichota P., Noreña D. A., A Priori Model Inclusion in the Multisine Maneuver Design, 17th International Carpathian Control Conference, Tatranska Lomnica, Slovakia, may 2016, pp. 440-445.

[R3] Chen S., Wang X. X. and Harris C. J. NARX-Based Nonlinear System Identification Using Orthogonal Least Squares Basis Hunting, IEEE Transactions on Control Systems Technology, 2008, 16, pp. 78-84

[R4] Efremov, A. System Identification Based on Stepwise Regression for  Dynamic  Market  Representation.  International  Conference  on Data Mining and Knowledge Engineering, Rome, Italy, 28–30 April 2010,  132-137.

 

In section 4.1.5. the authors should clarify why they used natural interpolation instead of other methods

In section 4.2 authors clarify that they will use uncertainties to denote standard deviations in measurements. As uncertainty is a much broader term (especially when the parameters influence one another) this should not be done. Please correct the text.

In some parts of the text authors use phrases that are meaningless e.g. “which makes us more confident in the results”. The authors should be confident in their results, because they know the methodology, they conducted the research according to the state of the art etc. In other case the results should not be presented. Please delete meaningless phrases from the text.

 

Author Response

Review of the article " Uncertainty propagation through a point model for
steady-state two-phase pipe flow " by Strand et al. The article is well written and within the journal scope. However several
minor issues must be corrected before the text can be accepted for
publication. In my opinion, the abstract must be rewritten. It should contain the most
important things such as: what has been done, how and the most important
conclusions. Answer: We have made several changes to clarify the work and results. A literature review is too poor according to me. The authors should
provide more information about state of the art in the introduction by
referring to the literature. Answer: We have added much more information about the state of the art
including references to recent work. The order of the paper should be modified. Authors should start with the
Introduction, then present the Material sand Models, then Results, then
the Discussion and finally Future Research. Answer: Yes, the order is changed. In section 4.1 authors wrote: "The model predictions are based on the
measured input variables listed in Table 1." As Model structure
determination is one of the key issues for a field of knowledge known as
system identification authors should at least refer their model to this
approach. This can be easily done e.g. by adding. "In contrast to the
presented approach System Identification with backward elimination method
[R1, R2], forward selection [R3] or stepwise regression [R4] can be used
for the same purpose. This would raise the model quality, but also
increase the experiment costs and computational time significantly. Thus
we did not used the following approach." [R1] Lichota P., Szulczyk J., Tischler M. B.., Berger T. Frequency
Responses Identification from Multi-Axis Maneuver with Simultaneous
Multisine Inputs, Journal of Guidance, Control and Dynamics, 2019, 42,
pp. 2550-2556 [R2] Lichota P., Noreña D. A., A Priori Model Inclusion in the Multisine
Maneuver Design, 17th International Carpathian Control Conference,
Tatranska Lomnica, Slovakia, may 2016, pp. 440-445. [R3] Chen S., Wang X. X. and Harris C. J. NARX-Based Nonlinear System
Identification Using Orthogonal Least Squares Basis Hunting, IEEE
Transactions on Control Systems Technology, 2008, 16, pp. 78-84 [R4] Efremov, A. System Identification Based on Stepwise Regression for
Dynamic Market Representation. International Conference on Data
Mining and Knowledge Engineering, Rome, Italy, 28-30 April 2010,
132-137. Answer: This is a good point and we have made changes accordingly to the
first part of Section 2. In section 4.1.5. the authors should clarify why they used natural
interpolation instead of other methods Answer: The choice of the values for a and b are not really a part of
this paper. Those values were chosen by Smith et al, and we simply choose
to study their proposed model. We have emphasized this distinction better
in the beginning of Section 2. Talking to Smith, he explained that the
choice is done as the transition from laminar to turbulent flow is not a
sharp limit, but that there can be a transitional region. The values for
the parameters a and b were chosen as they seemed to give good results
for the presented dataset. Natural interpolation was chosen over other
interpolation methods for simplicity as the interpolation in the
transitional region is somewhat uncertain anyways. In section 4.2 authors clarify that they will use uncertainties to denote
standard deviations in measurements. As uncertainty is a much broader
term (especially when the parameters influence one another) this should
not be done. Please correct the text. Answer: This is a valid point, especially from the point of view of a
statistician. However, physicists will in our experience often use the
term uncertainty. We have explained the distinction better including a
reference to the Guide to the expression of uncertainty in measurement. In some parts of the text authors use phrases that are meaningless e.g.
"which makes us more confident in the results". The authors should be
confident in their results, because they know the methodology, they
conducted the research according to the state of the art etc. In other
case the results should not be presented. Please delete meaningless
phrases from the text. Answer: We have rewritten several parts.

Round 2

Reviewer 1 Report

Thank you for taking carefull care about my suggestions.

I would like to propose to change slightly:

"The comparative study in Brkić and Praks [27] suggests a more accurate and computationally efficient approximation than (11b) for the Colebrook turbulent friction factor. However, model tuning is not the main objective for this work. Instead, we use the Haaland approximation to allow for comparison to Smith et al. [13]. The friction factor is a small part of the computational cost of the point model. Thus, it is not essential to find the most efficient approximation."

to be, for example:

"The comparative study in Brkić and Praks [27] suggests a more accurate and computationally efficient approximation than (11b) for the Colebrook turbulent friction factor. However, we use the Haaland approximation to allow for comparison to Smith et al. [13]."

Please provide citation to your Norwegian colleague Haaland: 

Haaland, S.E., 1983. Simple and explicit formulas for the friction factor in turbulent pipe flow. J. Fluids Eng., 105(1): 89-90. https://0-doi-org.brum.beds.ac.uk/10.1115/1.3240948

Also, when you discuss OLGA, your also Norwegian colleague Biberg made contribution:

Biberg, D., 2017. Fast and accurate approximations for the Colebrook equation. Journal of Fluids Engineering, 139(3). J. Fluids Eng., 139(3): 031401. https://0-doi-org.brum.beds.ac.uk/10.1115/1.4034950

Your software codes are available [39], which is usefull.

I do not have further suggestions.

Reviewer 3 Report

In my opinion the improved manuscript looks better. The authors have made an effort to use my comments. I think I can definitely recommend this article for publication in its current form.