As part of the analysis of the possibility of using the Ukrainian gas transportation system for transporting blends of natural gas and hydrogen, the peculiarities of the influence of hydrogen degradation of pipe steel on the brittle strength of girth welds and local corrosion metal losses were considered. For this, they were used the methods of finite-element modeling of the stress-strain state of structures during welding and subsequent operation loading along with advanced criteria of macroscopic fracture of a body with a crack. The results of predicting the safety factor for a typical welded part of a main gas pipeline with postulated surface cracks during the transportation of gas-hydrogen blends of various compositions showed that the most susceptible to brittle fracture are the weld metal and heat affected zone. But with regard to the fatigue strength of welded joints under the action of cyclic loading by internal pressure or bending moment, larger stress intensity factor ranges in the heat affected zone cause a more significant reduction of the residual safety factors. Local corrosion damage during the transportation of gas-hydrogen blends had a considerable negative impact on pipeline reliability, particularly when material properties experienced hydrogen degradation and a decrease in fracture toughness. However, this effect could be mitigated by adjusting the operating load accordingly.
Research Article
Numerical analysis of brittle strength of welded pipelines with corrosion metal loss in transportation of blends of natural gas with hydrogen
https://doi.org/10.21203/rs.3.rs-3303744/v1
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pipeline
blends of natural gas with hydrogen
girth weld
corrosion metal loss
safety factor
hydrogen degradation
brittle strength
reliability
To ensure the safe utilization of Ukrainian gas grids for transporting blends of fossil natural gas and green hydrogen, it is essential to substantiate their operational safety. This involves addressing potential hydrogen leaks and accumulation issues. During the technical evaluation of gas pipelines, factors related to hydrogen degradation of pipe steel must be taken into account [1, 2]. Assembly girth welds, subjected to residual stresses and strains from field welding, are particularly vulnerable. This makes them more susceptible to nucleation of defects such as non-welds, pitting corrosion, and stress-corrosion cracking, increasing the risk of structural damage under static or cyclic operational loading [3, 4]. Geometric anomalies of local corrosion wall thinning are another critical area prone to pipeline failure. These defects are common in older pipelines with damaged protective insulation. Standardized criteria for the allowability of such anomalies may not be fully applicable when significant hydrogen degradation of the metal occurs. This is due, in part, to the possibility of a change in the prevailing mechanism of damage from ductile to brittle-ductile or brittle behavior caused by hydrogen embrittlement.
While there is a wealth of literature on the hydrogen degradation of pipe steels, most studies focus on determining how mechanical properties deteriorate over extended exposure to hydrogen [5–7]. However, understanding how hydrogen degradation affects the load-bearing capacity and overall condition of a specific gas pipeline under design operation conditions remains a pertinent concern. Elevated concentrations of diffusible hydrogen in typical pipe steels of various strength classes can lead to decreased brittle strength and resistance to fatigue failure. Factors like assembly or repair welding can also introduce residual tensile stresses in the weld metal and the heat affected zone (HAZ), promoting crack initiation and propagation. Similar negative impacts occur due to local stress concentration in areas with surface corrosion metal loss anomalies. Despite these issues, comprehensive analyses of the reliability of welded pipeline systems during the transportation of gas-hydrogen blends are still lacking.
The main objective of this research is to conduct a numerical analysis of the brittle strength of welded gas pipelines with local corrosion metal losses during the transportation of hydrogen-natural gas blends to determine the impact of hydrogen degradation of pipe metal on pipeline reliability.
Investigation the impact of hydrogen embrittlement on welded elements of main pipelines with corrosion wall thinning anomalies is crucial to consider the intricate interaction between residual stress-strain states resulting from assembly welding and external loads. To achieve this, a numerical finite-element approach was employed for simulating assembly welding and operational loading of the pipeline while accounting for the presence of surface geometry anomalies of semielliptical shape (see Fig. 1a).
The weld heating flux qw is modeled as being distributed according to the Gaussian law. It is assumed that the heat transfer within the welded structure occurs through conductive processes, which can be described by solving the nonstationary heat conduction equation. The dissipation of heat into the environment, including technological equipment and the atmosphere with a temperature of Te, is considered by applying appropriate boundary conditions along the surface Θ based on the laws of Newton-Richmann and Stefan-Boltzmann [8]:
$$c\rho \left( {r,\beta ,z,T} \right)\frac{{\partial T\left( {r,\beta ,z} \right)}}{{\partial \tau }}=\nabla \left[ {\lambda \left( {r,\beta ,z,T} \right)\nabla T\left( {r,\beta ,z} \right)} \right]$$
1
$$- \lambda \left( T \right){\left. {\frac{{\partial T}}{{\partial {{\varvec{n}}_{\varvec{p}}}}}} \right|_{\left( {r,\beta ,z \in \Theta } \right)}}= - {q_w}+{\alpha _T}\left( {T - {T_e}} \right)+{ ε _{SB}}{\sigma _{SB}}\left( {{T^4} - T_{e}^{4}} \right)$$
2
where Т, λ, cρ are temperature, thermal conductivity and heat capacity of the material at a given point, correspondingly, np is normal to the surface; αT is heat transfer coefficient; εSB is emissivity of the surface of the structure; σSB is the Stefan-Boltzmann constant. The initial temperature state of the structure is assumed to be uniform, designated as Te.
An appropriate finite-element approach is utilized to solve the combined problem of temperature field kinetics and the development of stresses and strains. This method involves eight nodal finite elements (FE) based on the WeldPrediction software complex [9], as shown in Fig. 1b. Within these specific FEs, the distribution of temperatures, stresses, and strains is assumed to be uniform. The growth of the strain tensor can be expressed using the following equation:
$$\text{d}{ ε _{ij}}=\text{d} ε _{{ij}}^{e}+\text{d} ε _{{ij}}^{p}+{\delta _{ij}}\left( {\text{d}{ ε _T}+φ } \right)$$
3
where \(\text{d} ε _{{ij}}^{e}\), \(\text{d} ε _{{ij}}^{p}\), \({\delta _{ij}}\text{d}{ ε _T}\), φ are components of the strain tensor growth caused by the elastic deformation mechanism, plastic deformations, kinetics of the nonuniform temperature field, volumetric changes of metal due to phase transportations, respectively, i, j = r, β, z (Fig. 1a).
The kinetics of the stress-strain state of the structure was evaluated by tracing the elastic-plastic deformations, utilizing the FE solution for the boundary value problem of non-stationary thermoplasticity. This analysis considered the temperature-dependent mechanical properties of the material. During each tracing step, the relationship between the components of stress tensors (σij) and strains (εij) was determined using the generalized Hooke's law and the associated plastic flow law [10]:
where δij is Kronecker symbol, K = (1–2ν)/E, G = 0.5E/(1 + ν), E is Young’s modulus, ν is Poison’s ratio, symbol "*" refers to the variable of the previous tracing step, Ψ is the state function of the material, which is determined by iteration algorithm according to the plastic flow surface σs and was considered as follows [10]:
$$\begin{gathered} \Psi =\frac{1}{{2G}},\;\text{i}\text{f}\;{\sigma _{eq}}<{\sigma _s}={\sigma _Y}\left( {T,\;{ ε _p}} \right); \hfill \\ \Psi >\frac{1}{{2G}},\;\text{i}\text{f}\;{\sigma _{eq}}={\sigma _s}; \hfill \\ \text{s}\text{t}\text{a}\text{t}\text{e}\;{\sigma _{eq}}>{\sigma _s}\;\text{i}\text{s} \text{n}\text{o}\text{n}\text{a}\text{l}\text{l}\text{o}\text{w}\text{a}\text{b}\text{l}\text{e}. \hfill \\ \end{gathered}$$
5
At each tracing step, conditions (5)–(7) are implemented through an iterative method, considering the temperature-dependent σS and the history of plastic deformation (strain hardening). Simultaneously, during each iteration on Ψ, the stresses σij are calculated as follows (summation occurs based on repeated indices):
$${\sigma _{ij}}=\frac{1}{\Psi }\left( {\Delta { ε _{ij}}+{\delta _{ij}}\frac{{\Psi - K}}{K}\Delta ε } \right)+{J_{ij}}$$
6
where \({J_{ij}}=\frac{1}{\Psi }\left[ {\left( {{b_{ij}} - {\delta _{ij}}b} \right)+{\delta _{ij}}\left( {K{\sigma ^ * } - \frac{{\Delta { ε _T}+φ }}{K}} \right)} \right]\), \(\Delta ε ={{\Delta { ε _{ii}}} \mathord{\left/ {\vphantom {{\Delta { ε _{ii}}} 3}} \right. \kern-0pt} 3}\), \(b={{{b_{ii}}} \mathord{\left/ {\vphantom {{{b_{ii}}} 3}} \right. \kern-0pt} 3}\).
The components of the stress tensor satisfy the statics equation for internal FEs and the boundary conditions for surface ones. Similarly, the components of the vector ΔUi=(ΔUi, ΔVi, ΔWi) adhere to their respective boundary conditions. To compose the system of algebraic equations for the vector of displacement increments at FE nodes during each tracing step and iterations along Ψ, the following functional (Lagrange's variational principle) is minimized [11]:
$${L_1}= - \frac{1}{2}\sum\limits_{V} {\left( {{\sigma _{ij}}+{J_{ij}}} \right)} \Delta { ε _{ij}}{V_{m,n,r}}+\sum\limits_{\Theta } {{F_i}\Delta {U_i}\Delta S_{P}^{{m,n,r}}}$$
7
where \(\sum\limits_{V} {}\) is the sum operator for internal FE; \(\sum\limits_{\Theta } {}\) is the sum operator on the surface FE, on which the components of the force vector Fi are specified, i.e. the following system of equations allows to obtain a solution in the components of the vector of displacement increment at each step of tracing and iterations on Ψ for a specific FE:
\(\frac{{\partial {L_1}}}{{\partial \Delta {U_{m,n,r}}}}=0\) , \(\frac{{\partial {L_1}}}{{\partial \Delta {V_{m,n,r}}}}=0\), \(\frac{{\partial {L_1}}}{{\partial \Delta {W_{m,n,r}}}}=0\). (8)
The FE description of equations (3)-(10) and its software implementation can be found in reference [12].
Assessment the actual reliability of the pipeline under varying degrees of hydrogen embrittlement of the material within a significantly heterogeneous stress field across the structure was carried out by the method of postulated defects. This method involves assuming the presence of small defects in specific locations and then evaluating their acceptability. For the evaluation of brittle strength in corroded welded pipelines with hydrogen-degraded metal, the implementation of the method of postulated defects entails assuming a crack (surface and embedded) of a particular size and orientation at each node of the FE mesh. For each postulated defect scenario, the safety factor n is calculated based on the corresponding limit state criterion for a body with a crack. The commonly used criterion is the R6 procedure [10], which relies on a two-parameter diagram of brittle-ductile fracture (Fig. 2) and can be mathematically described as:
\(n{K_r}\left( {{L_r}} \right)=\left\{ \begin{gathered} \left[ {1 - 0.14{{\left( {nL_{r}^{{}}} \right)}^2}} \right]\left\{ {0.3+0.7\exp \left[ { - 0.65{{\left( {nL_{r}^{{}}} \right)}^6}} \right]} \right\},\;\text{i}\text{f}\;n{L_r} \leqslant L_{{r\hbox{max} }}^{{}} \hfill \\ 0,\;\text{i}\text{f}\;n{L_r}>L_{{r\hbox{max} }}^{{}}. \hfill \\ \end{gathered} \right.\)
where Kr=KI/KIc, Lr = σref/σT, KI is stress intensity factor, KIc is fracture toughness, σref is reference stresses. The calculation of KI and σref is performed following the algorithms provided in [10].
Analyzing the safety factor distribution across the structure allows estimation the brittle strength of the welded pipeline with a corrosion anomaly, considering parameters like welding process, external force loading, and hydrogen degradation of the material. Proper implementation of this algorithm crucially depends on selecting an appropriate size for the postulated defect. On one hand, the crack's linear dimensions should not exceed the resolution of instrumental flaw detection tools, while on the other hand, they should be large enough to reveal the welded structure's susceptibility to brittle failure. A conservative approach could involve complying with regulatory requirements regarding the size of the postulated defect or correlating the safety factor of the cracked pipeline with design requirements.
In addition to accounting for hydrogen degradation of material properties, it is essential to consider the possibility of fatigue failure resulting from cyclic loading when evaluating the performance of a welded pipeline element. This type of failure can be assessed using classical approaches such as S-N diagrams for long-term strength analysis of welded structures or by evaluating the acceptability of postulated cracks using the algorithms mentioned earlier. Additionally, the growth rate of fatigue cracks (increase in their linear dimensions) over a certain period of operation must be taken into account. The growth rate can be calculated based on the number of load cycles N with cycle asymmetry R using Paris law [13]:
$$\frac{{da}}{{dN}}=\frac{{C \cdot \Delta {K^m}}}{{\left( {1 - R} \right) - \frac{{\Delta K}}{{{K_{Ic}}}}}},$$
9
where C, m are the Paris coefficients, ΔK is the range of the stress intensity coefficient.
The research focused on investigating the specific impact of hydrogen in the blend transported through the pipeline on the strength of assembly welded joints. A typical straight section of the pipeline with a diameter of D = 1420 mm and wall thickness of t = 20 mm was used as a case study, as pipe material it was considered X80 pipe steel. The analysis considered two types of external load: internal pressure of the transported blend (maximum value P = 7.5 MPa) and additional bending moment M in the plane of the pipe axis. Both static and cyclic loading up to 10,000 cycles were examined. A bending moment of 8.4·109 N·mm was chosen, resulting in additional axial stresses comparable to those caused by the maximum internal pressure. Such bending moments can arise from various factors, depending on the pipeline's location and operating conditions. For instance, in sections passing through obstacles, additional bending may occur due to wind loads or the passage of intra-tube diagnostic projectiles, while underwater areas might experience this effect due to distributed ballasting integrity issues and cyclic underwater currents.
In the considered pipeline element, the mechanical properties of the metal depend on the concentration of hydrogen (vH) in the transported blend and the corresponding level of hydrogen degradation. According to available data [14], hydrogen has the most significant negative impact on pipe steel's resistance to fatigue failure, quantitatively described by changes in the Paris coefficients C and m (see Table 1). However, concentrations of hydrogen up to 50% in the atmosphere do not lead to significant reductions in the ultimate and yield strength [15].
As mentioned earlier, the size of the postulated crack is an important parameter when calculating the brittle strength of welded pipe elements. For the case under consideration, a preliminary calculation showed that with a crack size of 2.5×0.4 mm, the safety factor for the pipe at the periphery of the welded joint and local corrosion metal loss is approximately 1.81, which conservatively meets the design requirements for the pipeline (1.79). For accurate taking into account the three-dimensional state of stresses and strains when calculating brittle strength, cracks of different orientations relative to the pipe axis (longitudinal, circumferential) were considered, and the minimum safety factor n was chosen.
The first part of the research focuses on assessing the influence of hydrogen degradation on the pipeline's reliability in the area of girth welds under static and cyclic loading conditions for various hydrogen concentrations in the transported blend. By conducting finite element (FE) analysis of the residual stresses and strains in the area of girth welds, the technological aspect of assembly welding was taken into consideration to ensure the pipeline's reliability and operability during the transportation of natural gas and hydrogen blends.
The interaction between operational and post-welding stresses has a nonlinear nature in both characteristic directions relative to the pipeline's axis, namely circumferential and axial directions (as depicted in Figs. 3 and 4). The stress field's inhomogeneity at different stages of cyclic loading in the welded pipe leads to a corresponding spatial distribution of stress intensity coefficient ranges (ΔK), resulting in varying susceptibility to brittle failure of different parts of the structure during long-term operation. Among them, the areas of the weld and HAZ are particularly susceptible to brittle fracture under static loading (Fig. 5).
|
vH. % |
σU, MPa |
σY, MPa |
С 108 |
m |
|---|---|---|---|---|
|
0 |
656.39 |
523.90 |
2.25 |
2.592 |
|
5 |
666.00 |
518.56 |
25.7 |
2.582 |
|
10 |
657.81 |
525.52 |
29.8 |
2.580 |
|
20 |
656.06 |
524.83 |
35.1 |
2.574 |
|
50 |
661.54 |
523.67 |
99.3 |
2.389 |
Concerning the fatigue strength of the girth weld under cyclic internal pressure or bending moment, larger stress intensity factor ranges in HAZ result in a notable reduction in the residual safety factor n. As shown in Fig. 5, hydrogen degradation has the most significant impact on the residual safety factor of HAZ metal during cyclic loading by internal pressure. The overall decrease in n exceeds 25% compared to the scenario of pure natural gas transportation. However, it should be noted that the cyclic bending moment's influence does not significantly affect the pipeline's reliability.
Quantitative evaluations of the fatigue growth rate of postulated cracks hold practical significance. For cyclic variations in internal pressure, depending on the concentration of hydrogen in the blend, the maximum increase in the defect's linear dimensions over 10,000 load cycles ranges from 0.13 mm (at vH = 0%) to 4.7 mm (at vH = 50%). For cyclic loading with a bending moment M, the respective range is from 0.013 mm to 0.31 mm.
The second part of the research focuses on numerically assessing the pipeline's reliability when transporting blends of natural gas and hydrogen with various compositions, considering local corrosion metal loss. The developed numerical approach for determining the safety factor's accuracy is demonstrated using an example of a characteristic defect of local corrosion wall thinning in a semi-elliptical shape (2s = 100 mm, a = 4–12 mm). A comparison was made with standardized algorithms used to assess the acceptability of such anomalies according to the Ukrainian standard DSTU-Н B V.2.3–21:2008 [16]. This code is based on analyzing the residual safety factor for pressurized pipes with local corrosion metal loss, making the comparison with the proposed FE calculations reasonable. As shown in Fig. 6, the correlation between the proposed FE calculations and regulatory requirements is satisfactory.
The primary limitation of using standardized criteria is the potential shift in the nature of material failure during hydrogen degradation, transitioning from ductile to brittle behavior. This shift can be quantified by examining the change in the fracture toughness of the material at the region of minimum wall thickness in the corroded pipeline. Figure 7 illustrates the corrective relationships used to determine the residual safety factor of pipelines based on the degree of metal degradation and the depth of corrosion.
The correlation between the internal operating pressure P in the pipeline and the degree of hydrogen-induced property degradation is depicted, considering the depth of local wall thinning. The study has highlighted a considerable safety margin for corroded gas pipelines during the transportation of gas-hydrogen blends under static load (Fig. 8). In the realistic operation pressure ranges of 5.5–7.5 MPa, a notable reduction in fracture toughness remains acceptable. Consequently, the safety of a corroded main gas pipeline with significant hydrogen-induced property degradation can be balanced by making appropriate adjustments to operational parameters.
-
A numerical procedure has been developed to analyze the brittle strength of welded parts of main gas pipelines in transporting blends of natural gas and hydrogen. The methodology is based on FE analysis, considering the stress-strain state during welding and operational loading. It also involves calculating the residual safety factor assuming the presence of a postulated surface and embedded cracks of a specific size. The procedure accounts for predicting brittle strength under both static and cyclic loading, with the fatigue growth rate of the defect size determined using the Paris law.
-
The investigation focused on the impact of hydrogen-induced metal degradation on the pipeline's reliability using a characteristic case study of a straight part of the main gas pipeline (D×t = 1420×20 mm, X80). Internal pressure (up to Р=7.5 MPa) and bending moment in the axis plane (up to 8.4·109 N mm) were considered as external loads. The areas of the weld and HAZ were found to be particularly susceptible to brittle fracture, experiencing high total tensile stresses from the interaction of operational and post-weld stress-strain states. Under cyclic loading by internal pressure or bending moment, larger stress intensity factor ranges in the HAZ caused a more significant reduction in the residual safety factors when predicting long-term brittle strength.
-
The study showed that hydrogen degradation has the most significant effect on the brittle strength of the welded pipeline under cyclic internal pressure loading. After 10,000 load cycles, the overall reduction of the residual safety factor in the HAZ exceeds 25% compared to the case of pure natural gas transportation. On the other hand, cyclic bending moments do not significantly affect the pipeline's reliability.
-
The developed numerical approach for determining the residual safety factor demonstrated high accuracy, as showcased by the analysis of a characteristic defect of local corrosion thinning with a semi-elliptical shape. The approach was compared to standardized algorithms for assessing the admissibility of such anomalies (Ukrainian standard DSTU-Н B V.2.3–21:2008).
-
Corrective relationships for determining the residual safety factor of pipelines based on the degree of metal degradation have been proposed, with the fracture toughness as the main parameter of material degradation. The study also revealed the correlation between the internal operating pressure in the pipeline and the degree of hydrogen-induced property degradation, depending on the depth of local wall thinning. The research demonstrated a significant margin of brittleness for corroded gas pipelines during the transportation of gas-hydrogen blends under static load. Within real operation pressure ranges of 5.5–7.5 MPa, a notable decrease in fracture toughness remains acceptable.
Acknowledgements
The authors of this work are grateful to the Ukrainian armed forces and the world community, which is now helping Ukraine in the struggle for freedom and independence. Thanks to the unity and unbroken spirit of the Ukrainian nation during this period of our history, it is possible carrying out scientific researches for our peaceful and successful future.
Conflict of Interest
The authors declare that they have no conflict of interest.
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