A study on the behavior of CO₂ corrosion on pipeline using computational fluid dynamics, experimental and artificial neural network approach

The electrochemical corrosion of the steel surface is represented by one anodic and at least one cathodic reaction. The anodic reaction in carbon dioxide corrosion is represented by

$$\begin{eqnarray}&&{\rm{Fe}}\to {{\rm{Fe}}}^{2+}+2{{\rm{e}}}^{-}\end{eqnarray} \tag{ 4 }$$

Moreover, the presence of CO₂ increased the rate of corrosion of steel in aqueous solution by increasing the rate of hydrogen evolution as per,

$$\begin{eqnarray}&&2{{\rm{H}}}^{+}+2{{\rm{e}}}^{-}\to {{\rm{H}}}_{2}\end{eqnarray} \tag{ 5 }$$

Also, the direct reduction of H₂CO₃ could increase the corrosion rate,

$$\begin{eqnarray}&&2{{\rm{H}}}_{2}{{\rm{CO}}}_{3}+2{{\rm{e}}}^{-}\to {{\rm{H}}}_{2}+2{{\rm{HCO}}}_{3}^{-}\end{eqnarray} \tag{ 6 }$$

In addition, the direct reduction of the bicarbonate ion becomes significant at pH greater than 5

$$\begin{eqnarray}&&2{{\rm{HCO}}}_{3}^{-}+2{{\rm{e}}}^{-}\to {{\rm{H}}}_{2}+{{\rm{CO}}}_{3}^{2-}\end{eqnarray} \tag{ 7 }$$

CO₂ corrosion of the steel surface is the electrochemical corrosion, and oxidation of iron is the main anodic reaction. The overall corrosion behavior is dependent on H⁺ ions transported from the solution to the corroding metal interface. As per the Butler-Volmer equation, the electrochemical reaction rate depends on the temperature and exchange current density of the anodic and cathodic reactions [19].

The oxidation of iron at the corrosion potential is charge transfer control and corrosion potential for the anodic reaction represented as

$$\begin{eqnarray}&&{i}_{a(Fe)}={i}_{^\circ (Fe)}{10}^{\displaystyle \frac{{E}_{corr}-{E}_{rev(Fe)}}{{b}_{a(Fe)}}}\end{eqnarray} \tag{ 8 }$$

Where i_o is the exchange current density, b_a is Tafel slope, E_corr is corrosion potential and E_rev is the reversible potential of iron oxidation.

Similarly, H⁺ and carbonic acid reduction reaction is dependent on charge transfer and mass transfer (diffusion) control and can be represented as

$$\begin{eqnarray}&&\displaystyle \frac{1}{{i}_{c(R)}}=\displaystyle \frac{1}{{i}_{a(R)}}+\displaystyle \frac{1}{{i}_{\mathrm{lim}(R)}^{d}}\end{eqnarray} \tag{ 9 }$$

Where ${i}_{a}$ charge transfer current density and ${i}_{\mathrm{lim}}^{d}$ is the diffusion limit current density for the cathodic reaction

Also, the charge transfers the current density of the H⁺, H₂CO₃ reactants is calculated from Tafel's equation,

$$\begin{eqnarray}&&{i}_{a\left(R\right)}={i}_{o(R)}{10}^{\displaystyle \frac{{E}_{corr}-{E}_{rev(R)}}{{b}_{c(R)}}}\end{eqnarray} \tag{ 10 }$$

Where b_c is Tafel slope for the cathodic reaction

The reversible potential, E_rev(R) is used to calculate the exchange current density and is computed from pH and temperature, T

$$\begin{eqnarray}&&{E}_{rev\left(R\right)}=-\displaystyle \frac{2.303R\left(T+273.15\right)}{nF}pH\end{eqnarray} \tag{ 11 }$$

Where n is no. of electrons transferred and F is Faraday's constant

Moreover, the reduction mechanism of the species H⁺ and H₂CO₃ is mass transfer limited and diffusion limit charge current, i^d_lim(R) is determined from

$$\begin{eqnarray}&&{i}_{\mathrm{lim}\left(R\right)}^{d}=\,{k}_{m(R)}\,F{Y}_{(R)}\end{eqnarray} \tag{ 12 }$$

Where k_m is the diffusion coefficient and Y is the species concentration. In the present study, empirical correlations were used to calculate the mass transfer coefficients.

The corrosion potential will be solved from mixed potential theory, from which corrosion current is estimated and using Faraday's law corrosion rate is estimated.

The Navier–Stokes equations of mass, momentum, energy, and species model were considered in CFD study. To capture the turbulent fluctuating components of fluid velocity, pressure and other species, a set of Reynolds-Averaged Navier–Stokes equations were assembled in the simulation. In the current work, a more reliable k-ω Shear-Stress Transport (SST) model had been applied to determine the near-wall viscous sub-layer established during a turbulent flow. The Shear Stress Transport (SST) $k-\omega$ model effectively blends the robust and accurate formulation of the $k-\omega$ model in the near-wall region with the free-stream independence of $k-{\epsilon }$ model in the far-field.

Species model

In the species model, reaction rates were determined by general finite-rate chemistry and the effects of turbulent fluctuations on kinetics rates were neglected. When no turbulence-chemistry interaction (TCI) model was used, the finite-rate kinetics was incorporated by computing the chemical source terms using general reaction-rate expressions. This approach is recommended for laminar flows, where the formulation is exact. However, for the turbulent flows, the turbulence time-scales were used in a relative to the chemistry time scales using complex chemistry.

The net source of chemical species due to reaction, R_i, is computed as the sum of the molar rate of creation or destruction of species in the reaction,

$$\begin{eqnarray}&&{R}_{i}={M}_{w,i}\displaystyle \sum _{R=1}^{{N}_{R}}{R}_{i,R}\end{eqnarray} \tag{ 13 }$$

Where M_w,i is the molecular weight of species; and R_i,R is the molar rate of creation/destruction of species, i, in reaction, R.

The molar rate of creation/destruction of species in reaction, R_i,R is given by

$$\begin{eqnarray}&&{R}_{i,R}={\rm{\Gamma }}\left({\nu }_{i,R}^{{\prime\prime} }-{\nu }_{i,R}^{{\prime} }\right)\left[{k}_{f,R}\displaystyle \prod _{N}^{j=1}\left({C}_{j,R}^{{\eta }_{j,R}^{{\prime} }}\right)-{k}_{b,R}\displaystyle \prod _{N}^{j=1}\left({C}_{j,R}^{{\eta }_{j,R}^{{\prime\prime} }}\right)\right]\end{eqnarray} \tag{ 14 }$$

Where, N is number of chemical species in the system; ${\nu }_{i,R}^{{\prime\prime} }$ and ${\nu }_{i,R}^{{\prime} }$ are the stoichiometric coefficient for product and reactant, i, in reaction R; ${k}_{f,r}$ and ${k}_{b,r}$ is forward and backward rate constants for reaction, R; C_j,R is molar concentration of species in reaction R; ${\eta }_{j,R}^{{\prime} }$ and ${\eta }_{j,R}^{{\prime\prime} }$ are rate exponent for reactant and product species in reaction R. Moreover, Γ represent the net effect of third bodies on the reaction rate and is not considered in the reaction rate calculation. Also, the forward rate constant for reactions, ${k}_{f,R}$ is computed using Arrhenius expression.

ANSYS - 18.1 software was used to simulate the pipeline corrosion rate when a fluid flows with a certain quantity of species. The simulations were performed to determine the corrosion rate from initializing the model with inlet boundary conditions for varying pH values of carbonic acid. Moreover, the in-built E-Chem reaction model of [20] was used to perform the simulations. In the analysis, Butler-Volmer parameters for anodic and cathodic reactions and species charge numbers were incorporated in the species model. Also, $k-\omega$ SST viscous model was used for the turbulence behavior of the flow which considered the near wall and far-off effects to model the wall-bounded flows and free-shear flows in the domain.

A second-order discretization scheme was used for pressure, momentum, turbulence, species and energy variables study. The simulation studies were carried out for steady and transient state conditions. Moreover, the effect of wall roughness and heat generated by the species interactions were not considered, since no details were available in the present experimental study.

Model geometry and grid details

In this study, a three-dimensional hexahedral meshing of the pipeline was created in ANSYS Workbench 18.1. The electrochemical reactions of anodic and cathodic reactions were solved numerically in ANSYS Fluent 18.1 to define the CO₂ corrosion rate. Also, independent grid elements were used to model the flow within the geometry and the accuracy of grid size was observed by performing a grid-independent convergence. Moreover, structured grid structures (hexahedral type elements) had been implemented along with the flow domain. A 30 cm length and 12.7 mm diameter carbon steel pipe was chosen to study the CO₂ corrosion. Figure 1 shows the model and meshed geometry of the pipeline domain.

Zoom In Zoom Out Reset image size

The wall-bounded turbulent flows were meshed using inflation layer meshing to accurately capture the boundary layer region. Table 1 highlights the mesh details of the studied pipe.

Table 1.  Mesh details for the studied pipeline.

No. of nodes	209 760
No. of Faces	616 041
No. of Cells	203 196
Type of elements	Hexahedral element
Maximum aspect ratio	206
Minimum orthogonal quality	0.572

Boundary conditions

Artificial neural networks are computing systems based on artificial neurons, which can transmit the signal from one neuron to another. In the current work, the Multilayer Perceptron Neural Network method was used to predict the CO₂ corrosion in the pipeline. The selection process of several data points for training, testing and validation will be carried out automatically in MATLAB-NNTOOL.

Multilayer perceptron neural network (MLPNN)

Multi-layer perceptron's are the most useful type of neural network and the analytical capability of neural networks comes from the multi-layered structure of the networks. The data structure can learn to represent features at different resolutions and combine them into higher-order features.

MLPNN consists of four neurons in the input layer corresponding to four input parameters (pH, pCO₂, velocity, and temperature) in this study. The output layer consists of a single neuron, which is corrosion rate as an output parameter. A single hidden layer with N_h (number of hidden neurons) was used in this work which will hold weights and biases in the hidden layer (W_ij, b_ij) and an output layer (W_jk, b_jk) as shown in figure 2. Sigmoidal activation function was selected to link between inputs and output. For training purposes, the back-propagation (BP) algorithm was used in MLPNN. Gradient descent with momentum and adaptive learning rate back-propagation (gdx) was used due to its ability to update weights and biases. Also, other factors like learning rate (γ) and momentum rate (μ) were chosen and the performance of MLPNN was validated through MSE (Mean Square Error). The learning rate parameter was used during the adjustment of weights and biases to control the speed of learning algorithm and activation functions (hyperbolic tangent sigmoid and log-sigmoid).

$$\begin{eqnarray}&&MSE=\displaystyle \frac{sum{(y-targets)}^{2}}{length(y)}\end{eqnarray} \tag{ 15 }$$

where y is the net of input values and targets expected output value.

Zoom In Zoom Out Reset image size

The structure of the MLPNN is shown in figure 2.

Simplest method to predict the corrosion wear. In this method, the weight of the pipe is determined at the end of an experiment and the loss in weight signifies the corrosion wear.

In the current work, the Scanning Electron Microscope study on the samples was carried out at the Central Analytical and Applied Research Unit (CAARU), Sultan Qaboos University, Sultanate of Oman. The engaged SEM setup had high power optics irradiation system with an integration of a gentle beam that enables top-surface imaging of a specimen at very low energies and possible to obtain high-resolution images of samples. The model name of the employed SEM unit is JSM-7600F Schottky Field Emission Scanning Electron Microscope, Jeol Company, Japan.

The flow behavior in a pipe specimen was studied using CFD for varying the velocities from 0.5 m s⁻¹ to 1.5 m s⁻¹. Figure 4(a) explains the velocity contour plots for the 0.9 m s⁻¹ velocity and pH 4. The study results revealed that fully developed turbulence is encountered in the bulk fluid and as the fluid approached the solid wall, turbulent fluctuations were dampened and negligible velocity was noticed at the wall. Also, a Schmidt number value of 504 was noticed for the flow, and it showed that the mass transfer boundary layer is very small in the flow.

Zoom In Zoom Out Reset image size

In addition, shear stress exerted at the wall is highlighted in figure 4(b) and in the CFD simulation, a maximum shear stress value of 1.73 Pa was noticed at the wall surface for 0.9 m s⁻¹. However, analytical calculations showed a stress value of 2.45 Pa for 0.9 m s⁻¹. The variation in stress values could be due to in CFD simulation CO₂ corrosion species densities were considered as against the carbonic acid density in the analytical calculation. Furthermore, the analytical study results also indicated that with increase in velocity the wall shear stress augmented because of the rise in the velocity head across the flow path and also it enhanced the friction at the wall surfaces as highlighted in figure 5. The analytically calculated shear stress values for change in the velocity curve indicated the R² value of 0.99 and the observed shear stress values lies within 20% range from the best-fitted curve.

Zoom In Zoom Out Reset image size

To understand the mass transfer behavior of the species at pH less than 5 were important in the CO₂ corrosion mechanisms study. In this regard, the mass transfer characterization of a chosen pipe was made using CFD and the structured mesh was used in the simulation. Moreover, nearly 15 boundary layers were used to resolve the viscous sub-layer for the description of species distribution across the pipe length. Also, for the entire CFD simulations only one type of computational mesh was exercised based on the flow conditions. In the simulations, aqueous solution temperature was maintained at 25 °C and solution pH concentrations were varied to understand the CO₂ corrosion on the pipeline. The study results highlighted that a large contribution of H⁺ reduction could be seen at pH 4 and this influence gets diminished at pH 5 and 6. Figure 6(a) explains the concentration of H⁺ ions and maximum mass fraction of 0.0003 is noticed at the boundary layer of the pipe wall surface for pH 4 and 0.9 m/s flow. However, with the diluted carbonic acid (as pH increased) the concentrations of H⁺ ions at the wall boundary is more and it led to lower the H⁺ reduction reaction as indicated in figure 6(b) for pH 6 and 0.9 m s⁻¹ velocity. Furthermore, the CO₂ corrosion study revealed that at pH 5 and 6, the dominant cathodic reaction at the corrosion potential will be H₂CO₃ reduction.

Zoom In Zoom Out Reset image size

Figure 7 explains corrosion behavior in the pipe at different pH concentrations for the 0.9 m s⁻¹ flow velocity. At pH 4 concentrations the observed corrosion rate value was 5.41 × 10⁻⁷ kg m⁻²-s and is equal to 2.05 mm year⁻¹. However, at pH 5, very negligible corrosion was noticed on the pipeline. This is because the concentration of the H⁺ and H₂CO₃ species at the wall surface for pH 5 is less as compared to pH 4. Similarly, the current density for iron oxidation is very negligible for pH 5 concentration.

Zoom In Zoom Out Reset image size

Furthermore, at pH 6, very low corrosion was noticed on the pipe surface, and it could be due to a completely diminishing H⁺ reduction reaction with an increase in pH concentrations. Overall, the study confirmed that H⁺ reduction and current densities were the dominant parameters in CO₂ corrosion for pH values less than 5. However, at pH6, negligible corrosion traces were noticed on the pipeline surface because of the reduction of the bicarbonate ion which forms a protective iron carbonate film on the surface and decreased the CO₂ corrosion on the pipeline.

In addition, simulation studies had been carried out with varying flow velocities from 0.5–2 m s⁻¹. In the simulation study, a pH 4 was used to understand the effect of fluid convection on the corrosion rate. The careful assessment of mesh at the entrance length in the pipe and boundary layer zone (wall) is important to understand the turbulence behavior for different flow velocities. Hence, in the current study to reduce the computational mesh generation for various flow conditions the structured grid with a y⁺ approximately 1 was used.

Figure 8 explains the corrosion rates plot for different velocities. As velocity was increased, the limiting current for H⁺reduction augmented and led to an increased overall cathodic reaction and enhanced the corrosion rate. At higher velocities, the flow-dependent H⁺ reduction was dominant as the concentration of H⁺ species was maximum. The study results confirmed that at 2 m s⁻¹ the maximum corrosion value of 6.30 × 10⁻⁷ kg m⁻²-s was observed and is equal to 2.53 mm year⁻¹. The plotted curve indicated the 0.999 R² value and the observed corrosion rate values lie within a 10% range from the best-fitted trend line. Moreover, study results highlighted that for the same velocity with an increase in pH concentrations negligible corrosion was noticed because of limited H⁺ ions in the solution and small contribution to raise in the cathodic current.

Zoom In Zoom Out Reset image size

The simulation was carried out under transient conditions to identify the significance of testing time on the corrosion rate. In the analysis, the fluid flow velocity of 0.9 m s⁻¹ and the pH 4 were considered. Figure 9 highlights the variation of corrosion rate with respect to time and the study results revealed that until 2500 s, the corrosion rate values were decreased from 8.97 × 10⁻⁶ kg m⁻²-s to 5.7 × 10⁻⁷ kg m⁻²-s. This could be due to the species diffusion through the boundary layer is more in the beginning and it enhanced the corrosion rate. However, at the later part of the simulation, almost stable corrosion of 2 × 10⁻⁷ kg m⁻²-s was observed for the 5-h run. This could be due to a decrease in species diffusion through the boundary layer, and also H⁺ reduction and limiting current for cathodic reactions were time-independent and will be the same throughout the simulation.

Zoom In Zoom Out Reset image size

In the present work, CO₂ corrosion experiments on the pipeline were carried out for different pH concentrations of carbonic acid varying from 4 to 6. In the experimental study, fluid temperature and flow velocity were maintained as 25 °C and 0.9 m s⁻¹ respectively. For each case, experiments were carried out for 200 h and the corrosion rate was determined from the weight loss method. Refer table 3 for the calculated corrosion rate values for different pH values and at pH 4 about 2.08 mm\year corrosion was noticed.

In addition, at pH 5 and 6, the observed corrosion rate was very negligible. This could be due to a decrease in H⁺ species in the carbonic acid which reduced the tendency of Fe²⁺ to diffuse from the surface and finally diminished the corrosion on the wall surface.

Moreover, the SEM image of the cross-section of a specimen before the start of the experiment is indicated in figure 10 and the smooth surface was witnessed.

Zoom In Zoom Out Reset image size

Also, figure 11 represents the x-ray spectroscopy plot of a specimen before the start of the experiment. The study indicated small peaks of Fe, C and O compound in the specimen and no oxide formation on the surface.

Zoom In Zoom Out Reset image size

Figure 12(a) highlights the SEM image of the tested sample for 200 h at pH 4 and 25 °C and flow velocity of 0.9 m s⁻¹. The image results revealed that corrosion films on the surface were dense and the film witnessed laminated and fractured corroded surface and it confirmed that the presence of diffusion-controlled processes in the corrosion mechanism of the steel pipe surface. The image represented the corrosion products in dark color, while the steel pipe base metal appearing as white color.

Zoom In Zoom Out Reset image size

Moreover, SEM images for pH 5 and 6 are indicated in figures 12(b) and (c). For the pipe specimens corresponding to pH 5 and 6, and evenly attacked surface and very small thin films could be seen on the surfaces. However, at pH 5 case slightly more corrosion was noticed on the surface as compared to pH 6. The decrease in CO₂ corrosion on the pipeline with pH 6 is due to an increase in the formation of a protective iron carbonate film as compared to pH 5 cases. Thus, the SEM study confirmed that the CO₂ corrosion process on the pipeline was mass transfer controlled at lower temperatures and low flow velocity. Furthermore, at low pH values, the surface films were porous and allowed the species to diffuse in the film, and enhanced the corrosion of the surface.

Moreover, the x-ray spectroscopy plot of a corroded pipe for pH 4 is highlighted in figure 13. The study results revealed that high peaks of Fe, C, and O on the corroded specimen. The C peak is mainly associated with an iron carbide matrix filled with iron carbonate on the corrosion area. Thus, an x-ray spectroscopy plot confirmed that high concentration of Fe oxidation in the wall surface for pH 4.

Zoom In Zoom Out Reset image size

As mentioned earlier, MATLAB-NNTOOL was used to predict the corrosion rate using a neural network approach. The study results indicated that gradient, validation check, and learning rate values were 0.033 887, 10 and 0.022 92 respectively at epoch 17 for the training data of MLPNN. Additionally, mean square error results highlighted the best validation performance of 0.000 906 59 at epoch 7 and a small error value between training, validation and testing data.

Figure 14 shows the linear regression between training, validation, and testing of the MLPNN model. From the figure, it is confirmed that the target line ratio of the MLPNN model almost matched the experimental results and demonstrated that the predicted values were close to experimentally measured value under the same operating conditions. Also, ANN results confirmed that there was an excellent linear relationship between the output value and experimentally observed value. The optimal MLPNN configuration obtained was 4-5-1 (five neurons in N_h) with learning rate and momentum rate values of 0.022 92 and 0.0025 respectively.

Zoom In Zoom Out Reset image size

Experimental results of corrosion rate were compared with CFD and ANN analysis and close agreement were observed for flow velocity of 0.9 m s⁻¹ as indicated in table 4. An error of 1.44% was observed between CFD and experimental results for pH 4 conditions. Moreover, for pH 5 and 6 cases, the experimentally observed corrosion values were very less and the same trend was observed with CFD simulation. Furthermore, a close agreement was observed between experimentally observed values and the MLPNN approach for the case of pH 5 and 6. On the whole, from this study, it is confirmed that boundary conditions adopted in CFD analysis, and also ANN training, validation and testing approaches were accurate to predict the CO₂ corrosion in the pipeline for different conditions.