Corrosion
Introduction
Corrosion is a spontaneous and time dependant process of metals reducing to their respective oxides. Rusting refers to oxides of iron and iron based alloys which mainly consist of hydrous ferric oxides [1].
Corrosion results in direct and indirect losses. The direct losses of pipe replacement and repair in Gas and Liquid Transmission Pipelines accounts to about $7.0billion (approximately) in the United States Of America according to a study done involving NACE and DOT (USA)[2]. This cost can be reduced by repairing the pipe by determining the remaining the reaming strength of pipelines in service. The correct assessment of the remaining strength will help unnecessary replacement, over safe rapiers, more than necessary down time and pressure reductions.
The occurrence of corrosion can be attributed to two parameters which are (1)change in Gibbs Free Energy (2) Pilling-Bedworth Ratio. The rate of corrosion reaction depends on temperature, pH, surface area ratio of anodic area and cathodic area, flow/ turbulence etc.
Classification of corrosion defects
These metal loss by corrosion broadly classified into general corrosion, localised corrosion and stress assisted corrosion. General corrosion can be described as large surface areas of uniform corrosion whilst localised corrosion could be in the form of Pitting, Crevice, Erosion Galvanic, Cavitation, Fretting and Interganular. The stress assisted corrosion can be devided into Stress corrosion cracking (SCC), Corrosion Fatigue and Scaling[2].
In the Pipeline industry based on where the corrosion is happening it is distinguished as external corrosion and internal corrosion. External corrosion defects were responsible for 27% of line pipe incidents in the period of 1996- 1999 where as Internal Corrosion accounted for only 5%[12]. Even in the CONCAWE report published in 2006, out of the 11 reported pipelines spillage incidents associated with corrosion 7 were due to external corrosion, 3 internal corrosion and 1 from SCC [13, pp13 table 2].
Corrosion defects are divided into two major types based on their orientation – Longitudinally oriented defects and circumferentially oriented defects.
These corrosion defects can be further sub-divided into various types which are (1) Single defect, (2) Interacting defect and (3) Complex shaped defects according to the DNV RP-F-101[pp ].
What are Interacting defects?
Two defects that are lying close to each other are called as interacting defects when they result in a failure pressure which is less than the failure pressure when these defects are treated as individual defects. The interaction of defects minimises as the distance between them increases and failure will depend on the defect that is more severe.
The book “Piping and Pipeline Assessment Guide” says that there are 3 types of interacting corrosion defects
Type 1 circumferentially separated corrosion colonies
Type2 axially separated and
Type3 one or more deep pits within shallow pits
Assessment of corrosion defects
Considering the pipeline to be successive bands of hoops. These bands are stressed in the hoop direction when the pipe is under internal pressure.
During corrosion, the defect will reduce the wall thickness of the respective steel bands which they are affecting .This intern reduces the stress carrying capacity or the strength of that ring of hoop. This strength of the remaining steel is reinforced by the neighbouring hoops. Since the internal pressure is trying to split the hoop of steel, as the axial length and the depth of the corrosion defect increases the reaming strength of the pipeline reduced in that area. Thus making them the two most important parameters [11,pp5,].
Hoop stress;
Semi-empirical methods of corrosion assessment
The many pipeline failure incidents in the past resulted in regulators enforcing on substantial factor of safety during operation. This resulted in the evolution of many codes for determination of remaining strength of corroded pipelines like
ANSI/ASME B 31 G -Manual for Determining Reaming Strength of Corroded Pipelines,
DNV RP- F-101
BS7910 and
RSTRENG.
For circumferentially oriented corrosion defects the Kastner local collapse solution these codes are supposed to have a certain safety factor but the assessment method in B31 G code have been recognised to be over conservative in nature [3].
Work on the desired techniques for assessing metal loss in pipelines was started in the year 1960 which gave raise to the classic work of Jhon F. Kiefner and others by the year 1969 for the Battelle institute. All these works were based on burst tests that were conducted in the Battelle Memorial institute. Based on further refinements of Kiefner’s initial work for assessing flawed pipelines ANSI/ASME B 31 G -Manual for Determining Reaming Strength of Corroded Pipelines was drafted in the year 1984. This code gives us the relation between the dimensions of a metal loss defect and 100% SMYS in the form a chart, the chart is divided into the acceptable region and the unacceptable region which is fenced by a line representing 100% SMYS of the steel. This has been obtained by the plotting the results of about 47 burst tests of varying diameter from 16 inch to 30 inch with varying yield strengths. But the code does not give any guidelines on interacting defects.
As a result of the inherent conservatism in this code as it is assumed that flow stress is 1.1 times the yield strength, and that the corrosion flaw has a parabolic shape, this results in the 2/3 area factor.
Hence to have a more realistic representation of metal loss defect new criteria for evaluating corroded pipes were developed such as the RSTRENG which is known as the effective area method, DNV RP- F101 and BS7910.
“Piping and Pipeline Assessment Guide” also says that when the full wall thickness is less than 1 inch long these have to be considered as an elongated defect, L1 +L2 +L3 [4], which is based on the reference of Kiefner and Vieth, “PC program speeds new criterion for evaluating corroded pipe”, Oil Gas Journal, 1990-91. This paper was backed by experimental results.
The remaining strength of a pipe with multiple defects considering an equivalent corroded profile obtained by projection into a longitudinal projection line of all defects which are supposed to interact.
On the other hand the Det Norske VERITAS (DNV) recommends a norm in their Recommended Practice – F101 for corroded pipelines which takes into account the external diameter of the pipeline and the wall thickness for interaction of longitudinally arranged defects [5].
This same point of view is shared by the (British Standards)BS 7910 code, i.e. it refers to the same interaction rules for axially aligned defects.
In BS7910 the single flaw has been expansively validated with small scale testing, full-scale testing in also Finite Element Analysis. The document also states that the interaction rules for assessment of method have been checked against a limited assortment involving equally sized defects and that it may not be appropriate for multiple flaws of largely differing in their sizes.[10]
Rules of interaction are only applicable to corrosion defects and the equation which is used in the case of individual defect is not applicable.
The defects that are axially aligned as in this thesis the document states that the defects can be treated as individual defects i.e. they do not interact if the depth is less than 20% of the wall thickness in which they are contained. Also the axial spacing ‘S’ should be less than 2.0√(D.t) to consider interaction of the two defects.
How to check for interaction by DNV and BS7910
The DNV RP- F-101 says the interaction rules are exclusively for defects which are under internal pressure type loading.
The minimum details that are required for assessing interacting defects are
The angular position of each defect around the circumference on the pipe
The axial spacing between the defects
Length of each individual defect
Depth of each defect
The steps that are involved in assessment of corrosion defects are :
1)The minimum details required for assessing the corrosion colonies are found out i.e. Projected length of the defect and the depth as the minimum remaining ligament.
2)The corroded portion of the defect is divided into a number of divisions with a minimum length of 5.0(Dt)1/2.
3)The pipeline is divided into number of sections based on
Z= 360(t/D)1/2 degrees
4)The defects that lie within each section is then projected on to a line which is parallel to the longitudinal axis of the pipe at distances of +Z degrees.
5)When the defects are overlapping each other on the projected line then they are made into a composite defect which has its length as combined length and depth as the one of the deepest defect.
6)After following the steps from 1 to 5 then the failure pressure for the individual defects are calculated using the formula to calculate Pi
The defects are then checked for interaction according to the norm that if the axial distance between the two is ‘S’ then the failure pressure of the defects are calculated as individual defects then the defect is allowed to interact till a distance of S=2(Dot)1/2.
Then the length of the combined defect is calculated as Lmn = Lm + S + Ln
and the depth of the combined defect is got by
i=m, n, mn
where m is defect 1, n is defect2 and mn is the interacting defect with a spacing of S in between the two defects.
For interaction Pm or Pn > Pmn
This rules of defect analysis (DNV-RP-F101) is applicable to both internal, external corrosion defects in line-pipe and when these corrosion defects are subjected to internal pressure only.
There are a number of occasions for which these rules cannot be applied:- for material other than carbon steel, line-pipe above X80 grade, cyclic loading, sharp edged defects which induce stress concentrations, corrosion combined with cracking or mechanical damage, metal loss as a result of mechanical damage and defects with the ‘d/t’ ratio greater than 85%.
This following criteria is given in BS 7910 which is similar to the DNV-RP-F101 :
Finite Element Method in structural analysis[19]
All engineering problems in the real world have can be solved with the use of mathematics. When a system is divided into small components of finite number for enhanced understanding and their behaviour analysis it is called as Finite Element Method. These components are called as elements.
Available commercial FEM packages inclued ANSYS, NASTRAN, ABAQUS, Hyper Mesh(pre/ post processing), Dyna-3D (crash-testing/ impact analysis).
The Non-linear Finite Element Analysis (FEA) in this paper was carried out using ANSYS version 11.0 which is very versatile in giving an optimum and reliable simulation of real-world analysis problems. It is used in almost all industries like – automobiles, aeronautics, power generation, biomechanics etc for the purpose of mechanical, structural, electrical, electromagnetic, thermal and fluid dynamics.
In this paper the structural discipline of finite element analysis is used, under this the model is subjected to static analysis which determines displacements, strains and stresses under static loading conditions in a nonlinear material property.
Non-Linear Analysis
Almost all of the phenomena in the real-world exhibit nonlinear behaviour meaning that when the analysis is carried out in nonlinear fashion it gives suitable results.
Nonlinearity can be divided into many section-.
1) Geometric Nonlinearity – this of two types
Large deflection and rotation: large displacement compared to its smallest dimension or rotation from its original position. Example- fishing rod which will have large deflection, as the load at the end of the line is increases so does the geometry of the material which influences the analysis.
Stress stiffening: This refers to substances with little or no stiffness in compression while having considerable stiffness during tension. Example – Cables
2) Material Nonlinearity
When the material is analysed beyond the elastic limit it is called nonlinear analysis. For this purpose we use a true-stress vs. true-strain graph.
Nonlinear material behaviour in ansys is characterised as
Plasticity : Permanent, time – Independent deformation
Creep : Permanent, time –dependant deformation
Nonlinear Elastic : nonlinear stress–strain, where the material returns to its intial shape upon the removal of the load.
Hyper-elasticity: material which is rubber like.
3) Changing- status nonlinearity:
Some structures which exhibit nonlinear behaviour that is status dependant. In this case the stiffness of the material suddenly changes when the physical system changes. Example: a shrink fit behaviour modelling.[14 pp 18,19]
Numerical Modelling of longitudinally corroded pipe
The idea for creating a numerical model has been taken from a publications i.e. “Predicting failure pressure of internally corroded linepipe using the finite element method” by Bin Fu and Mike G Krikwood which gives the details about failure prediction and the failure criteria based on the Von-misses stress for Non-linear anlysis, but this paper does not give any details on shape and modelling of the corrosion defect[15pp-177, 178, 179]. The details regarding to the shape of the model has been taken from some more publications in this regard such as “ Integrity of non-crack like corroded pipelines subjected to internal pressure” by Saldanha. S and Bucherie. Cwhich was presented t the 3rd Seminar on Pipeline held in Rio de Janerio in November 2001 and “Full scale burst test and finite element analysis on corroded gas pipeline” by Woo-sik Kim et al, 4th International Pipeline Conference
September 29-October 3, 2002, Alberta, Canada in these publications the corrosion defect is shown as a flat bottomed defect with a stress concentration free defect i.e. it has been rounded at all the edges. The defect geometry of the defedct is very important with respect to the accuracy of the results obtained from the Finite Element Analysis (FEA) because if the defect have any sharp edges or corners these would behave as stress concentrations and the pipe would fail even before the remaining ligament of the pipe reached the Ultimate Tensile Strength (UTS). The stress concentration would reach failure stress even before the remaining ligament which would give us highly in-accurate results, therefore the idealised defect has a flat bottom with spherical ends at the back corners all the diameters of the spherical regions and the curvature of the edges is equal to the depth of the defect.
The software gives a lot of inconvenience during the modelling with the modelling tolerance which has to be adjusted i.e. reduced in order to get the necessary shapes to Boolean add or Boolean subtract.
Ref:
Full scale burst test and finite element analysis on corroded gas pipeline” by Woo-sik Kim et al
Ref;
Integrity of non-crack like corroded pipelines subjected to internal pressure
The specification for the line pipe used for this analysis has been taken from the publication “Ductile failure analysis of API X65 pipes with notch-type defects using a local fracture criterion” by Chang-Kyun Oh et al
Pipeline specification
API 5L X65
External Diameter (D) 762mm
Length of pipe (L) 3820mm
Wall-thickness of pipe(t) 17.5mm
Young’s Modulus(E) 210700MPa
Poisson’s Ratio(υ) 0.3
Yield Strength (YS) 464.5MPa
Ultimate Tensile Strength 563.8MPa
The length of the pipeline chosen for analysis is always more than five times the external diameter of the pipeline as stated in BS 7910 and the
The two longitudinal interacting defects are of different dimensions –
Idealised defect 1
Length of the defect Lm = 90.4mm
Depth of the defect dm = 10.5mm
d/t = 0.6
Idealised defect 2
Length of the defect Ln = 110.6mm
Depth of the defect Ln = 8.65mm
d/t = 0.5
First the two defects are treated individually as considering the other as non existent and the pipe’s burst strength is found and then the two defects are put on a single pipe with varying axial distance between the two defects. The two are analysed with varying distances in between them in terms of the wall thickness as 1t, 2t, 3t and so on.
Using ANSYS
The Finite element analysis using ANSYS is done as the following steps which makes the problem solving more organised and simpler. The three steps include
Pre-processing
This includes defining the problem that requires the solution. The focus is mainly on:
Modelling the problem which includes areas/volumes/lines/ keypoints.
The Nonlinear material property from true stress vs. true strain graph.
Define element type
Meshing the model
Loading and Solution
In this stage the required boundary conditions (constraints), symmetry on areas and load on areas (pressure) and necessary solution controls (Load steps/ termination of analysis/method of solution etc) are applied before solving the problem.
Post-processing
The procedures that are used for analyzing the results are classified under this heading which includes:
Animation of results
List of nodal solutions of displacements, stresses, strains
Strain contour diagrams
Stress contour diagrams
Plotting of graphs using time-history options or general post process[20]
Pre-processing
Preliminary setup
The various sections of the ANSYS window has been mentioned in the below figure which include 1)Utility Menu 2) Command Bar 3)Tool Bar 4)Main Menu 5)Graphics window.
Fig : Showing the details of the ANSYS window with all its menus/ options
The Utility menu contains options which are needed right through the usage of the program, command bar is where input commands can be used but most of the work has been done with the help of the Graphic User Interface. The main menu also contains most of the options needed through the session while the graphic window gives the visual representation of all the parameters entered.
Modelling
First and most important step is the type of discipline which were defined for the programme as “Structural” in the main menu> preferences, then the units for the whole problem is fixed through main menu>pre-processor>material library>select units
The model has been made by sweeping areas around the created axis. The axis is initially made by creating Keypoints, one at the origin and another at the a certain convenient distance from the origin.
A rectangle was made which matched the cross-section of the pipe by using the option
Main Menu>Modelling>Create>Areas> Rectangle. The rectangular area was then swept by 180° about the imaginary axis created by the two initial keypoints. This leads to the formation half section of the pipe.
The defect was then inscribed into the pipe as a solid volume by creating swept solids out of circular areas and a rectangle. Then the working plane was changed by pivoting on the y-axis by -90 degrees by choosing the Utility Menu>Work-plane>Local coordinate system>Create LCS> At working plane origin> cylinder. A new location is specified for the system through the utility menu Work-plane>Local co-ordinate system>Create LCS>At Specified location where the origin was specified in the Pick menu which lead to the “Create LCS at Specified location”.
Fig : pop-up menu of Create Local Coordinate system
The new co-ordinate system was activated using Utility Menu>Workplane>Change active CS to> Specified Co-ordinate. Then the working plane was aligned to the active co-ordinate system thought the Utility Menu >Workplane>Align Workplane, where in the popup menu the co-ordinate system number is entered for activation. Then the view was changed to match the new co-ordinate system by Utility Menu> Workplane>Change display CS to> Specified coordinate system.
Once this was done the whole axis of the model rotated by ‘-90°’ and then by plotting lines and listing details of the keypoints the solid cylinder and two solid sphere volumes are introduced by moving them from the origin in which they were formed. All these solids had a radius which is equals the depth of the defect.
Fig : The two patches of metal loss defect with reduced stress concentration bottom edges, corners and faces.
Finally all the solid volumes were Boolean Subtracted(Main menu>Operate> Boolean>Subtract)from the main pipe section which gives the defect with smoothened edges and corners. During the modelling of the pipe only half of the pipe has been modelled as the pipe is symmetrical about its axis only, using this option of symmetry the calculation for the rest of the pipe is done this reduces the computation time for the whole model by half.
Meshing
The element used for meshing was 10-Node Tetrahedral Structural solid. This element has three degrees of freedom in all its nodes in the translational directions. It can provide for any plasticity, creep, large deflection and strains. As shown below the node being a solid does not require any real constant parameter. Although a higher order node of 20 node is ideal but due to computational difficulties of processor time the 10 node element has been chosen. The impact it had on the result is not all that dominant.
Fig : The solid 92 geometry – ANSYS 11.0[18]
Fig : Free meshing with higher density of elements in the defected areas.
The complete model could have been mapped meshed but it is not possible in ANSYS due to geometric complexity of the defected area however it can be mapped using meshing softwares like Hyper-mesh, hence the model was free meshed.
The model could be free meshed in different volumes or in a single volume with size control option by picking suitable areas and lines which needs smaller mesh size to get higher density of mesh in and around the defect area which is the main subject of concern. This gave a smoother nodal solution distribution of results near the area of concern. Both methods of meshing yielded the same result. The number of elements should be kept at an optimum minimum in order to minimise the computation time and still get quality results.
Boundary conditions/Constraints and Loading
For the boundary conditions of the models the two ends are constrained by giving zero degrees of freedom for all three axis (DOF = 0)and the bottom line of the bottom section surface is constrained in the Y- axis direction. This mimics the long pipeline which is lying on the ground without any loading on top. The 5 times diameter length of the pipeline also helps in removing any influence of the boundary conditions on the results over the area of concern.
Fig : The ends have DOF=0,
Bottom line DY=0 and internal area pressure.
The application of load i.e. internal pressure which is applied on the inner surface areas of the pipe model which is higher than the failure pressure of the pipe taking its ultimate tensile stress in the hoop direction as that is the main stress on the pipe. This higher pressure helps in tracking the stress and strain patterns beyond the yielding to the UTS.
Non- linear material property
The material Nonlinearity is defined by the true-stress vs. true-strain graph as there is large deflection on static loading and it gives the full and actual response of the material to the forces. The true stress strain vs. true strain can be obtained from the Engineering stress-strain or vice versa.
Ref: Andre cosham Newcastle university
The True stress is defined as the ratio of applied load to cross section at that instant of loading, this results into the fact that the stress in a material continuously raises till it fractures. The true strain is also change in length to its previous length. The two graphs are related to each other with a number of relations :
True-Stress = Engineering Stress(1+ Engineering strain)
True-Strain = ln (1+ Engineering strain)
These relations are valid till the necking region which is Ultimate tensile strength or tensile stress. The paper by Bin-Fu and M.G. Krikwood[3] in 1995 has used the Von-Misses stress criterion for the nonlinear analysis. The defected area i.e. the area with the remaining ligament experiences higher equivalent stress than the other regions , this lead to its plastic deformation. The plastic deformation of the material weakens it which finally snaps, when the stress in the remaining ligament of the material is greater than the critical level the pipe will fail in some mechanism either by leaking or by bursting. The true stress-strain relationship is obtained from the paper on X65 written by C-K Oh et al [3] in 2006, material details have been specified in the earlier section.
Fig : Shows the relation of true stress-strain with Engineering stress.
UTS = 563.8
(MPa)
True UTS = 637.09 (MPa)
the figure above shows the relation of true- stress vs. true strain and engg stress.
The stress exists in all three principle axis(σ1, σ2, σ3) and the resultant of all these three are commonly called as the von-Misses equivalent stress. For a linepipe under internal pressure loading the
Entering the nonlinear material data was done by choosing the option under
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