Simulation Analysis of Erosion–Corrosion Behaviors of Elbow under Gas-Solid Two-Phase Flow Conditions

Round 1

Reviewer 1 Report

My first observation is related to the SI units which need revision. For example, there should be a space between a number and its unit:

60 % but no 60%

250 ^oC but not 250^oC

 

My other comments are related to the electrochemical topic only because it is directly related to my expertise area.

188: "The ionization reactions of carbonic acid are formed into the hydrogen ion and bicarbonate ions, in the chem interface, and the distribution of the substance concentration is affected by diffusion and convection in the tds interface". I do not know what is the meaning of "chem interface" here. Perhaps the authors intended to refer to the metal/electrolyte interface. If so, they should say the "electrode interface".  However, it is important to consider that the ionization reaction of carbonic acid occurs also in the bulk of the solution (far from the metallic surface). 

196: I do not know the expression "siec"

197-198: "..hydrogen evolution reaction ....was occurred near the inner". It occurs ON the internal surface of the pipe and not NEAR

199: "electrode-electrolyte". An electrode is metal/electrolyte interface.

200-201: "The electrolyte conductivity is 2.5e-3 S/m." This value was obtained by measurement or was taken from a paper? The origin of this number should be explained.

201: "The initial potential of electrolyte and electrode is 0 V.". What does it mean? I do not agree that the initial potential of carbon steel in carbonate-containing solution is equal to zero. On the other hand, an electrode potential should be measured or cited against a reference electrode.

201-202: "The exchange current density and Tafel slope of iron dissolved reaction are 10^-3 A/m² and 100 mV, respectively". It is necessary to indicate from which reference (paper) these values were taken. A Tafel slope of      100 mV (the correct way is "mV per decade") is not a common value for the iron corrosion. Normally, anodic oxidation of iron presents a Tafel slope of less than 60 mV per decade.

Equation 13 is not fit to the situation described in the paper, in which the anodic reaction is the iron dissolution and the cathodic reaction is the hydrogen reduction reaction. In this case, the Wagner Traud equation should be used and thus i_o should be replaced by i_corr (corrosion current density which means that the rate of iron oxidation is equal to the rate of hydrogen reduction).

i_o should be used only for a single reaction at equilibrium, such as:

Fe²⁺+ 2 e^- ⇔ Fe        or         2H⁺ + 2e^- ⇔ H₂

 

the Butler-Volmer anodic reaction of iron corrosion is:

i_Fe→Fe²⁺ = i_{o(Fe → Fe²⁺+ 2e^-).} C_O.exp(αFη/(RT))

and the Butler-Volmer cathodic reaction of hydrogen is:

i_{H⁺ → H2} = i_{o(2H⁺+ 2 e^- → H2).} C_R.exp(-αFη/(RT))

 

Equation 14:

E = -0.44 + 2.303RT/(2F).log(10^-4)

The number 2.303 is missing.

It should be also explained the source of the 10^-4 mol/L which indicates the Fe²⁺ concentration.  Why did the authors use this concentration value?

 

The values of Table 2 are presented without a comprehensive explanation.

270 3.2.1. Species concentration distribution characteristic - In this item two three-dimensional diagram of carbonate concentration are presented: one was named as "carbonate  concentration distribution" and the other "carbonate ion concentration distribution". In chemical point of view, both can be interpreted as CO_3²⁺.

Later in the line 278, the authors referred to "carbonic acid concentration reaches 443.84 mol/m³." from which it can be concluded that Figure 7a should be named as "carbonic acid concentration". 

 

Author Response

1. My first observation is related to the SI units which need revision. For example, there should be a space between a number and its unit: 60 % but no 60%, 250 ^oC but not 250^o

Response: The authors are heartily grateful to the Editor and Reviewers’ comments and suggestions. Some errors in this manuscript have been found and corrected in details, for example, 60 %, 250 ^oC, and so on.

2. "The ionization reactions of carbonic acid are formed into the hydrogen ion and bicarbonate ions, in the cheminterface, and the distribution of the substance concentration is affected by diffusion and convection in the tdsinterface". I do not know what is the meaning of "chem interface" here. Perhaps the authors intended to refer to the metal/electrolyte interface. If so, they should say the "electrode interface".  However, it is important to consider that the ionization reaction of carbonic acid occurs also in the bulk of the solution (far from the metallic surface).

Response: This is mentioned section 2.4 in the revised manuscript. There are five physical field interfaces and two multi-physics interfaces in the model: Turbulent Flow (spf), Particle Tracking For Fluid Flow (fpt), Chemistry (chem), Secondary Current Distribution (siec), Transport of Diluted Species (tds), Fluid-Particle Interaction (fpi) and Flow Coupling (fc). The chem interface is a physical field interface in the numerical simulation software, and the siec interface as same.

3."..hydrogen evolution reaction ....was occurred near the inner". It occurs ON the internal surface of the pipe and not NEAR.

Response: The authors has been changed this sentence: hydrogen evolution reaction was occurred on the inner surface of the tube.

4. "electrode-electrolyte". An electrode is metal/electrolyte interface.

Response: The interface of metal/electrolyte is considered to be an electrode-electrolyte coupled wall to complete charge transfer and charge conservation between ions and electrons.

5. "The electrolyte conductivity is 2.5e-3 S/m." This value was obtained by measurement or was taken from a paper? The origin of this number should be explained.

Response: Thank you for your comments. This value of 2.5e-3 S/m is measured and provided by coal chemical companies of the authors’ research partnership.

6. The initial potential of electrolyte and electrode is 0 V. What does it mean? I do not agree that the initial potential of carbon steel in carbonate-containing solution is equal to zero. On the other hand, an electrode potential should be measured or cited against a reference electrode.

Response: Thank you for your comments. The initial potential of electrolyte and electrode in carbonate-containing solution is -0.52 V.

7. The exchange current density and Tafel slope of iron dissolved reaction are 10^-3A/m²and 100 mV, respectively. It is necessary to indicate from which reference (paper) these values were taken. A Tafel slope of 100 mV (the correct way is "mV per decade") is not a common value for the iron corrosion. Normally, anodic oxidation of iron presents a Tafel slope of less than 60 mV per decade.

Response: According to the reviewer’s comments and reference, the current density and Tafel slope of iron dissolved reaction are 10^-3 A/m² and 40 mV/decade ^[1].

[1] Nesic S , Postlethwaite J , Olsen S . An electrochemical model for prediction of corrosion of mild steel in aqueous carbon dioxide solutions[J]. Corrosion, 1996, 52(4): 280-294.

8. Equation 13is not fit to the situation described in the paper, in which the anodic reaction is the iron dissolution and the cathodic reaction is the hydrogen reduction reaction. In this case, the Wagner Traud equation should be used and thus i_oshould be replaced by i_corr (corrosion current density which means that the rate of iron oxidation is equal to the rate of hydrogen reduction). i_o should be used only for a single reaction at equilibrium, such as: Fe²⁺+ 2 e^- ⇔ Fe or 2H⁺ + 2e^- ⇔ H₂ the Butler-Volmer anodic reaction of iron corrosion is: i_Fe→Fe²⁺ = i_{o(Fe → Fe}²⁺+ 2e^-). C_O.exp(αFη/(RT)) and the Butler-Volmer cathodic reaction of hydrogen is: i_H⁺ _{→ H2} = i_o(2H⁺+ 2 e^- → H2). C_R.exp(-αFη/(RT))

Response: As reviewers said, Equation 13 is not fit to the situation. And the Wagner Traud equation is listed as following. The i_o is used only for a single reaction at equilibrium, the Butler-Volmer anodic reaction of iron corrosion is: i_Fe→Fe²⁺ = i_{o(Fe → Fe}²⁺+ 2e^-). C_O.exp(αFη/(RT)) and the Butler-Volmer cathodic reaction of hydrogen is: i_H⁺ _{→ H2} = i_o(2H⁺+ 2 e^- → H₂). C_R.exp(-αFη/(RT))

Wagber Traud equation:

                (13)

Equation 14: E = -0.44 + 303RT/(2F).log(10^-4). The number 2.303 is missing. It should be also explained the source of the 10^-4mol/L which indicates the Fe²⁺concentration.  Why did the authors use this concentration value?

 

Response: I’m Sorry for such a simple error, the number 2.303 has been added. This value of 10^-4 mol/L is measured and provided by coal chemical companies.

                                  (14)

10. The values of Table 2 are presented without a comprehensive explanation.

Response: The values of Table 2 represent the Reaction equilibrium constant, positive reaction rate and diffusion coefficient.

11. 2.1. Species concentration distribution characteristic - In this item two three-dimensional diagram of carbonate concentration are presented: one was named as "carbonate  concentration distribution" and the other "carbonate ion concentration distribution". In chemical point of view, both can be interpreted as CO₃²⁺.Later in the line 278, the authors referred to "carbonic acid concentration reaches 443.84 mol/m³." from which it can be concluded that Figure 7a should be named as "carbonic acid concentration".

Response: Wrongly write carbonate ion concentration as carbonate concentration, have corrected.

Reviewer 2 Report

1. The aim of the work presented in this paper should be explained more clearly, i.e. simulation of the erosion-corrosion behaviors of elbows. At present the to many tasks are presented as aim, as example hydrogen evolution, turbulence and chemical reactions of carbonic acid ionization simultaneously.
2. In the Table 1 is presented the mesh dependence to max fluid velocity. However, is not explained what model was selected to analysis. Also in my opinion, it is important to compare the results received by FE analysis and calculated using empirical formulas.
3. The geometrical FE model prepared for analysis is explained clearly, however a boundary condition, loads used in erosion analysis, chemical reaction and electrochemical corrosion analysis presented poorly. It should be explained more clearly.
4. It should be explained how was modelled electromechanical corrosion behavior using FEM, how was estimated chemical reaction of steel and fluid.
5. It should be explained how was modelled particles in erosion analysis, how was evaluated interaction of the particles and pipe.
6. As results of the erosion analysis, it was presented the variation of mass loss per unit area caused by the erosion. In my opinion, it more clearly to present reduce of pipe wall thickness due to erosion process.
7. The parameters presented in lines 128 and 129 are not explained. The physical meaning should be presented.

Author Response

1. The aim of the work presented in this paper should be explained more clearly, i.e. simulation of the erosion-corrosion behaviors of elbows. At present the to many tasks are presented as aim, as example hydrogen evolution, turbulence and chemical reactions of carbonic acid ionization simultaneously.

Response: The aim is to simulate the erosion-corrosion behaviors of elbow involving the erosion of particles, electrochemical corrosions of the dissolved iron and hydrogen evolution, turbulence and chemical reactions of carbonic acid ionization simultaneously in the present paper. The complex situations in tube are simplified to gas-solid two-phase flow with the chemical reactions and electrochemical reactions, and the gas is a mixture of syngas and carbon dioxide. The Finnie’s erosion model is proposed to analyze the erosion of sulfur particles, the quantities of particles striking the wall and mass loss per unit area. The turbulent characteristics of gas in elbow and the erosion failure process of particles hitting the elbow wall are simulated under turbulence condition. The effect of turbulence on the substance concentration distribution and the substance concentration distribution on the electrochemical corrosion process of hydrogen evolution reaction and iron dissolution reaction are investigated systemically. Finally, the mechanism of different physical and chemical fields on the key parts of high temperature and pressure pipeline during operation is investigated, and the simulation model of the corrosion under the multi-field coupling actions is built. The stress, temperature and corrosion cracks of the key parts of the pipeline between corrosion development and status are achieved, and the corrosion leakage prediction model is establish and the corrosion development trend and prediction method of leakage occurrence location is predicted.

2. In the Table 1 is presented the mesh dependence to max fluid velocity. However, is not explained what model was selected to analysis. Also in my opinion, it is important to compare the results received by FE analysis and calculated using empirical formulas.

Response: The authors have compared the results received by FE analysis. It is found that the differences of the calculated maximum of fluid velocity among the three meshes are very small. Thus, the first mesh method is used in this manuscript to reduce the calculation time.

3. The geometrical FE model prepared for analysis is explained clearly, however a boundary condition, loads used in erosion analysis, chemical reaction and electrochemical corrosion analysis presented poorly. It should be explained more clearly.

Response: The boundary conditions are the concentration of ions, temperature and pressure, and load used in analysis is current density. And all parameters are listed in the manuscript.

4. It should be explained how was modeled electromechanical corrosion behavior using FEM, how was estimated chemical reaction of steel and fluid.

Response: The FEM model is built in COMSOL Multiphysics software, and then boundary conditions are selected. The chemical reaction of steel and fluid is simulated by chemical corrosion module, which allows us to simulate all electrochemical corrosion processes. The transfer process of corrosive substances and corrosive materials is studied to simulate the changes in the corroded surface and the changes in the electrolyte nearby. A large amount of information can be obtained through the corrosion module, including electrochemical reactions, potentials in electrolytes and metal structures, homogeneous chemical reactions, and unique phenomena in the corrosion process.

5. It should be explained how was modeled particles in erosion analysis, how was evaluated interaction of the particles and pipe.

Response: Particles model: the sulfur particles are considered as the discrete phases in the fpt interface during simulation. The movement of particles under the framework of Lagrange is governed by Newton's second law (6) and affected by the drag force, gravity and brown force. The drag force (7) is generated by the speed difference between gas and particles and controlled by stokes’ law (8). In addition, the body force (9) formed by the effect of accelerated or decelerated particles on the movement of gas is obtained through gas-particles interaction in the fpi interface, and then the gas velocity in the spf interface and particles velocity in the fpt interface are coupled by gas-particles interaction. Through sampling and analysis of the pipe ash ,and in order to simplify the particle model, all sulfur particles, releasing 500 particles each 0.08 seconds at the boundary of inlet, are introduced into tube by high-speed gas and have the same physical properties of density (2360 kg/m³), diameter (50 μm) and shape (sphere). Assess the interaction between particles and pipes: Finnie erosion model is used to explain the rule of particle erosion of plastic materials at low impact angles, thus the classical Finnie erosion model (10) is used to describe the impact of particles and the count method is used to count the quantities of particles hitting the wall considering the shape of the pipeline model.

6. As results of the erosion analysis, it was presented the variation of mass loss per unit area caused by the erosion. In my opinion, it more clearly to present reduce of pipe wall thickness due to erosion process.

Response: The mass loss per unit area vs. exposure time is chosen to evaluate the erosion rate of steel in the manuscript. The particle bombardments are mostly occurred around the elbow and the erosion may be seriously, and it is relatively difficulty to measure the pipe wall thickness.

7. The parameters presented in lines 128 and 129 are not explained. The physical meaning should be presented.

Response: All parameters are RANS k-ε model constants.

Reviewer 3 Report

In this paper, erosion-corrosion behaviors of elbow are simulated and the model containing erosion, corrosion, turbulence and chemistry is built to describe the complicated failure phenomena. However, authors should take note of the following:

• Author should subject the manuscript to grammar check using grammarly. The English is not okay and it makes the paper uninteresting.
• Line 99-102, sentence needs restructuring.
• Line 248-253 makes mention of Figures 5c and 5d but the figures are not shown in the manuscript.
• Line 355-356, Compared to the straight section, the quality loss at the elbow is greatly high. State the increase in percentage.
• Figure 12: Mass loss (not lose) per unit (not unite) area
• Not enough citations are made. The discussion section should relate findings with literature in the field of study.

Author Response

1. Line 99-102, sentence needs restructuring.

Response: In thin film flow, the shell interface is used to solve the Reynolds equation for flow in narrow structures and the mass and momentum balances are used to formulate with a function across the thickness of the thin structure, which implies that the thickness does not have to be meshed.

2. Line 248-253 makes mention of Figures 5c and 5d but the figures are not shown in the manuscript.

Response: The authors have provided Figures 5c and 5d in the revised manuscript.

Fig.5 A three-dimensional diagram of fluid velocity distribution (Speed in color)

3. Line 355-356, Compared to the straight section, the quality loss at the elbow is greatly high. State the increase in percentage.

Response: As shown in Fig.12, the numbers of solid particle collisions is around 0.2e4 of the maximum value at the straight section, however, for example, the numbers of solid particle collisions is around 1.255e4 of the maximum value at the elbow. It is greatly high, and the percentage of the straight section is 16% of the elbow.

Fig.12 The number of solid particles hitting the wall at t=12 s.

4. Figure 12: Mass loss (not lose) per unit (not unite) area.

Response: Fig.12 shows that the variation of quantities of particles hitting the wall but Fig.13 reveals that the variation of mass loss per unit area caused by the erosion.

5. Not enough citations are made. The discussion section should relate findings with literature in the field of study.

Response: Pipeline is an important part of equipments, which is widely used in petrochemical, aerospace and other industrial applications, and occupies an extremely important in safe production. There are unavoidable erosion and corrosion during applications, which maybe lead to leakage of the pipeline due to harsh working environments ^[2-6]. The main reasons of leakage are erosion, electrochemical corrosion, turbulent and chemistry, and their interactions. It is well known that, due to the synergistic effect, the possibilities of leakage is generally much higher than the sum of pure electrochemical corrosion and pure mechanical erosion. Moreover, elbows are the weak parts of gathering and transferring pipelines. This study focuses on the following aspects: numerical study on the fluid flow, erosion, and corrosion along the axial direction of the pipeline for the real field cases and the related phenomenon of erosion-corrosion expecting to provide detailed and reasonable analysis of the failure incurred by the erosion-corrosion. In studies of erosion–corrosion there are no models available which attempt to combine the effects of particle erosion, corrosion and fluid flow ^[7]. Although the problems caused by the synergistic effect of erosion–corrosion are serious, the erosion–corrosion mechanism of the elbow, as influenced by the velocity and pressure, is still not thoroughly understood because of its complexity. Numerical simulations are often used in erosion–corrosion research ^[8].  

[1] Xu Y, Tan M. Probing the initiation and propagation processes of flow accelerated corrosion and erosion corrosion under simulated turbulent flow conditions [J]. Corrosion Science, 2019, 151: 163-174.

[2] Zhao J, Gu Y, Zeng Q, et al. A comparative study on the corrosion behaviors of X100 steel in simulated oilfield brines under the static and dynamic conditions [J]. Journal of Petroleum Science and Engineering, 2019, 173: 1109-1120.

[3] Islam M, Farhat Z, Ahmed E, et al. Erosion enhanced corrosion and corrosion enhanced erosion of API X-70 pipeline steel [J]. Wear, 2013, 302(1-2): 1592-1601.

[4] Wood R J K, Wharton J A, Speyer A J, et al. Investigation of erosion–corrosion processes using electrochemical noise measurements [J]. Tribology International, 2002, 35(10): 631-641.

[5] Zeng L, Chen G, Chen H. Comparative study on flow-accelerated corrosion and erosion–corrosion at a 90 carbon steel bend [J]. Materials, 2020, 13(7): 1780.

[6] Stack M, Abdelrahman S, Jana B. A new methodology for modelling erosion–corrosion regimes on real surfaces: gliding down the galvanic series for a range of metal-corrosion systems [J]. Wear, 2010, 268(3-4): 533-542.

[7] Liu J, BaKeDaShi W, Li Z, et al. Effect of flow velocity on erosion–corrosion of 90-degree horizontal elbow [J]. Wear, 2017, 376: 516-525.

[8] Zhang J, Jiang A, Xin Y, et al. Numerical investigation on multiphase erosion-corrosion problem of steel of apparatus at a well outlet in natural gas production [J]. Journal of Fluids Engineering, 2018, 140(12).

Round 2

Reviewer 1 Report

There are still some conceptual doubts

Comments for author File: Comments.pdf

Author Response

Review 1:

1. The interface of metal/electrolyte is considered to be an electrode-electrolyte coupled wall to complete charge transfer and charge conservation between ions and electrons. The electrolyte conductivity is 2.5e-3 S/m. The initial potential of electrolyte and electrode is -0.52 V.

I suppose that the authors are referring to the equilibrium potential of iron. If so, the value should be 0.56 against

 Nernst equation

 V vs SHE (Standard Hydrogen Electrode)

I guess it is miscalculation. Again, I suggest to mention the reference electrode. If the value is indeed calculate using the Nenrst Equation, the potential should refer to SHE.

 

Response: The authors are heartily grateful to the Editor and Reviewers’ comments and suggestions. The authors have calculated the initial potential of electrolyte and electrode again. As we known that the temperature in the pipeline is 250^oC, not 25^oC. And the concentration of Fe²⁺ is 1e-9 mol/L. So, the authors have calculated the concentration of H⁺ by the Nernst equation, the H⁺ concentration value is 1e-6 mol/L. Therefore, the initial potentials are calculated as follows.

According to calculation, the initial potential of electrolyte is V, and the initial potential of electrode is 0 V. The exchange current density and tafel slope of iron dissolved reaction are 10^-3 A/m² and 40 mV per decade, respectively. And the equilibrium potential depends on equation (14) in the revised manuscript. The exchange current density of hydrogen evolution reaction is 1.1e-2 A/m². The equilibrium potential is -0.3112 V.

 

2. The equilibrium potential is -1.03 V. How this value was obtained and which is the pH of the solution? The hydrogen equilibrium potential is obtained (or 1 atm of hydrogen pressure) using the following equation and the result is given in reference to SHE.

To obtain a value of -1.03 V, SHE the pH should be almost 17!

 

Response: The equilibrium potential depends on equation (14). The exchange current density of hydrogen evolution reaction is 1.1e-2 A/m². The equilibrium potential is -0.3112 V.

 

3. Wagber Traud equation:

Where, i_loc denotes the local charge transfer current density, i_corr is the corrosion current density, C_R and C_O are dimensionless expressions, describing the dependence on the reduced and oxidized species in the reaction.

- I_loc does not appear in the equation!

-It is important to know that, in the case of Wagner and Traud equation, η represent the difference between the applied potential and the corrosion potential both for cathodic and anodic reactions.

-In the case of the Butler-Volmer equation η represent the difference between the applied potential and the equilibrium potential of each reactions and we will have to equations one for the iron and other for the hydrogen.

Based on the above-mentioned issues, which equation did authors use? It is not clear because they referred to the equilibrium potential of hydrogen as being -1.03 V (which seems wrong as pointed in Comment 2) and to the potential of electrolyte and electrode as being -0.52 V?

 

Response: Based on the calculation, the equation of Concentration Dependent Kinetics in the origin manuscript is used.   

Where, i_loc denotes the local charge transfer current density, i₀ is the exchange current density, C_R and C_O are dimensionless expressions, describing the dependence on the reduced and oxidized species in the reaction.

As shown in the following figures from COMSOL software, the electrode kinetic expression type uses the concentration-dependent kinetic formula. The Wagner Traud equation is not mentioned in the formula embedded in COMSOL. The authors think it is the same as the Wagner Traud equation the reviewer mentioned in the first review. It is just expressed in a different way in the numerical simulation software. It is not clear because they referred to the equilibrium potential of hydrogen as being -0.3112 V.

    

Author Response File: Author Response.doc

Round 3

Reviewer 1 Report

Comments to the second review of the authors

Reviewer 1. The interface of metal/electrolyte is considered to be an electrode-electrolyte coupled wall to complete charge transfer and charge conservation between ions and electrons. The electrolyte conductivity is 2.5e-3 S/m. The initial potential of electrolyte and electrode is -0.52 V. I suppose that the authors are referring to the equilibrium potential of iron. If so, the value should be 0.56 against

 

Reviewer comments

I am very sorry that I did not realize that the simulation is being performed at 250 ^oC. As I focused my review on item 2.4.3, I did not realize that the simulation temperature is so high. I do not really know whether the Nernst equation can be applied to high temperatures. I do not even know that in the simulated condition there is an aqueous phase. Therefore, I think I am not able to accept these calculations.

 

 

Regarding this sentence:

“According to calculation, the initial potential of electrolyte is E 0.9068 eq Fe , = - V, and the initial potential of electrode is 0 V.”

I really do not know the meaning of “potential of electrolyte”. Nernst equation refers to the metal/ electrolyte interphase for a given reaction (in equilibrium) occurring at the interphase.

Comments for author File: Comments.pdf