Burst Pressure Estimation of CorrodedPipeline Using Damage Mechanics

Benzerga. D

Department of Mines and Metallurgy, LSCMI, Faculty of Mechanical, University of Science andTechnology of Oran Mohamed Boudiaf, B.P. 1505 El M’naouer 31000 Oran, Algeria

djeb_ben@yahoo.fr

Abstract. Pipelines are being widely employed worldwide as means of con-veyance of crude oil and its derivatives. Especially in the south and in the north ofAlgeria many pipelines connect oil fields to oil refineries. Nevertheless, a consid-erable distance is covered crossing hills, in which landslides could change not on-ly the pipelines alignment but also the stresses. Besides, landslides may causecracks in the pipes. Furthermore, both the close contact with soil and the action ofweather can provide the corrosion of the pipes, which will reduce the cross sectionarea, allowing the formation of disturbed flow areas, and also will develop stressconcentrated regions on the pipe wall. Generally, the main cause of high-pressuregas and oil pipeline ruptures is metal loss in a pipe wall from corrosion. Particular-ly, SONATRACH company data show that corroded defects (general corrosionand pitting corrosion) are the primary causes of accidents. Corrosion is one of themost common causes of accidents involving pipelines. To avoid these undesirablesituations, computational models are playing an important role, as they are able topredict the behaviour of pipelines in several ways. . The computational simulationthrough Finite Element Method (FEM) is one of the most efficient tools to quanti-fy reliably the remaining strength of corroded pipes.

This work presents a new method based on the concept of Continuum DamageMechanics (CDM) which currently has reached a stage of maturity enabling it tomodel any type of degradation. The value of the critical pressure, i.e., the allowa-ble operating pressure, of a corroded pipeline is obtained by using a post processorbased upon damage mechanics. This post processor allows the calculation of thecrack initiation conditions from the history of strain components taken as the out-put of the ANSYS Software. The ANSYS code is used for physical and geomet-rical non-linear analysis to obtain the critical point where at any time the damageequivalent stress is maximum. This method was validated by comparing the re-sults of numerical simulations with experimental and ASME/ B31G results availa-ble in the literature.

2 D. Benzerga

Keywords: Burst pressure, pipe, corrosion, damage mechanics, damage, finiteelement

1 Introduction

In most applications, the damage is very localized in such a way that the dam-aged material occupies a volume small in comparison to the macroscale of thestructural component and even to the mesoscale of the representative volume ele-ment RVE. This is due to the high sensitivity of damage to stress concentrations atthe macroscale and to defects at the microscale. This allows us to consider that theeffect of the damage on the state of stress and strain occurs only in very smalldamaged regions. In other words, the coupling between damage and strains maybe neglected everywhere in the structure except in the RVE(s) where the damagedevelops. This is the principle of the locally coupled analysis [Lemaitre andDoghri] where the procedure may be split into the following two steps as shown inFig. 1:

- a classical structure calculation in elasticity or elastoplasticity by the finite el-ement method (FEM) to obtain the fields of strain and stress;

- a local analysis at the critical point only dealing with the elasto-plastic consti-tutive equations coupled with the kinetic law of damage evolution, that is a set ofdifferential equations. This method is much simpler and saves a lot of computertime in comparison to the fully coupled analysis, which takes into account thecoupling between damage and strain in the whole structure. The fully coupledmethod must be used when the damage is not localized but diffused in a large re-gion [Lemaitre and Doghri]. Our main motivation in this study is to show that thismethod is a contribution to the rehabilitation of corroded pipes. The study andanalysis of the damage at critical point where at any time the damage equivalentstress is maximum in the vicinity of the corrosion defect of a steel pipe X65. Themethod developed here is to construct a numerical tool to determine the new max-imum pressure that could support a corroded pipe. The Modeling of the damagephenomenon is based upon Damage Mechanics, which currently has reached astage of maturity enabling it to model any type of degradation. Using the pro-grammable ANSYS, a subroutine was developed and implemented in the maincode for the determination of the critical point (M*) in the vicinity of corrosiondefect where potential crack may occurs. In a second step, a post-processor basedon the iterative Newton method was applied to this critical point (M*) for the de-termination of the maximum internal pressure that a corroded pipe could supportin the case of a longitudinal corrosion defect. The maximum pressure is the pres-sure value corresponding to the critical value of the DC damage (crack initiation).This method was validated by comparing the results of numerical simulations withexperimental and ASME/ B31G results available in the literature.

Burst Pressure Estimation of Corroded Pipeline Using Damage Mechanics3

Fig. 1. Locally coupled analysis of crack initiation.

2 Modeling

To model the pipeline we used the ANSYS code with two scenarios, a modelwithout a cavity (no corrosion, Figure 2) and a model with cavity (corroded pipe-line, Figure 3). Taking into account the symmetry of the pipeline, we modeled on-ly one-fourth of cylinder. The dimensions of the structure are length, inner radiusand thickness. To do this, we have created a rectangular area, which has the samelength as the pipeline, and a width equivalent to the thickness of the pipeline. By a90° rotation of this surface around the axis X, a volume was obtained in the formof a quarter cylinder. For meshing the structure, we used volume elements with 20nodes Solid95. These elements have compatible displacement shapes and are wellsuited to model curved boundaries. The mesh of the volume is made to obtain aconcentration of elements around the side where the cavity is represented (Figure2). For boundary conditions, we have respected the conditions of symmetry andthe experience.

4 D. Benzerga

Fig. 2. Pipe without cavity (pipe not corroded)

On the corroded pipe (model with cavity), we kept the same data used in themodel without cavity, and created a cavity that represents the corrosion defects onthe pipeline. To do this we created a parabolic surface to the thickness of onequarter of the cylinder with a length equivalent to the defect length and widthequal to the depth of the defect. The volume of the cavity is obtained by a rotationof 90 ° around the upper line of the pipeline wall. This volume is subtracted fromthe volume of the non-corroded pipeline (Figure 2). The same meshing is usedwith a mesh filtering around the cavity. We varied the values of the depth and ex-tension of the cavity (corrosion defects, see Figure 2). The burst pressure is deter-mined according to the geometrical characteristics of each cavity. The criticalpressure or the maximum pressure that will support a corroded pipe is that corre-sponding to the critical value of the damage Dc (this value depends on the materialand temperature).

Burst Pressure Estimation of Corroded Pipeline Using Damage Mechanics5

Figure 3. Model with cavity

Using the programmable language ANSYS, a subroutine was developed and im-plemented in the main code for the determination of critical point (M *) in thezone of corrosion defect (see figure below) where microcracks may grow.

MEF Calculations Post-Processor

Dangerous area Critical point (M*)

6 D. Benzerga

Next, the constitutive law of the critical point (M, *) where the equivalentstress σ * is maximum, obtained using the ANSYS code, is implanted in the post-processor based on the iterative Newton method [Benallal et al, 1988.]:

2

σeq

σH2ν13ν13

2RV

21

Rvσeq*σwith

*σSupM*σ

(1)

(1)In most cases, this criterion is satisfied in areas of high stress concentration

with a high coefficient of triaxiality σH / σeq. The final step is to determine theevolution of damage in solving the following constitutive laws:

p0pSiPRv2ES

σ2eq

D

0ffSiPσeq

σ~ Dij

2

3E p

ij

δijD1

σkkE

υD1

σ ij

E

ν1Ee

ij

E pijEe

ijEij

(2)

Using a stepwise method simultaneously with the method (scheme) implicitNewton, which ensures good convergence [Benallal et al, 1988].

The method developed above gives versus of the internal pressure of the pipe,the value of the damage, the accumulated plastic strain and stress components ateach instant until a macroscopic crack initiation at the defect corrosion. This al-lows determining the new maximum pressure that will support a pipe with a cor-rosion defect.

3 Validation of the methodology

In order to validate our model, we compared our results with ASME/B31Gstandard and experimental results obtained by TA Netto [Netto, 2005] [3] (see ta-ble 1). For the model without cavity, we took the analytical value P = 50.89 MPa.

Burst Pressure Estimation of Corroded Pipeline Using Damage Mechanics7

Figure 4 illustrates the results obtained by three methods, the experimental,ASME / B31G and our proposed method.

Table 1: Maximum predicted pressure

0.0 0.5 1.0 1.5 2.0 2.5

2830323436384042444648505254565860 Burst pressure versus

depth for L=21 mm

Bur

st p

ress

ure

MP

a

corrosion defect depth mm

Simulation ASME/B31G Expérimental

0.0 0.5 1.0 1.5 2.0 2.5

25

30

35

40

45

50

55

60

Burst pressure versusdepth for L=41 mm

Burs

t pre

ssure

MPa

Corrosion defect depth mm

Simulation ASME/B31G Experimental

Figure 4. Burst pressure depending on the depth of corrosion defects for twoextensions L = 21mm and L = 41 mm.

N° d(mm)

L(mm)

BurstPressure

tests(MPa)

Burst Pres-sure(MPa)ASME/B31G

PredictedBurst pres-sure(MPa)

Erreuren %

T1 - - 57.33 50.89 53.4 6.85T2 1.58 42 37.02 35.05 36 2.75

T3 1.59 21 44.65 42.53 44.7 0.11T4 1.87 42 32.47 30.85 32.5 0.09

9T5 1.91 21 41.28 38.93 42.5 2.95T6 2.13 42 26.76 24.50 29.5 10.2

3T7 2.14 21 34.55 34.86 36.8 6.51

8 D. Benzerga

4 Analysis and Interpretation of Results

We note that the numerical results are more realistic (experimental results).These numerical results do not exceed a 10% difference. Comparing simulationresults and ASME/B31G, we note that the average error is smaller in numericalcase. This is due to a factor of safety used by B31G standard. The ASME/B31Guses the projection of corrosion defect, while the numerically exact corrosion sur-face defect is used. The difference between the numerical and experimental resultsdepends on several factors:

It was considered a perfectly continuous material, while in reality thereare defects, discontinuities and micro-voids in the material, which can bepotential sources of damage.There are always residual stresses after machining that we have ignoredin the laws of behavior considered in this study.The shape of the cavity is not identical for all specimens.It was considered perfect symmetry, which is not the case in realityFor the boundary conditions, it was considered a locking surface, thereare small displacements, which cause deformations, and the structure ofthe material is changed.The mesh is not fine enough or sufficiently homogeneous.S values (damage coefficient) pD (plastic deformation damage threshold)and DC (critical damage) of X65 material taken approximately, true val-ues are determined by load-unload tests.The yield condition was considered without hardening. We consideredthat damage only occurs when strain hardening is saturated

5 Conclusion

In this paper, we presented a new method based upon damage mechanics,which is now in its stage of maturity. Our main motivation in this work was toshow that this method is a contribution to the rehabilitation of corroded pipes. Inspite of some differences between proposed method results and the experimentalresults, our method have had a good performance in predicting the failure pressureof a pipeline containing corrosion defects. The ASME/B31G results were moreconservative than proposed method; however, our method provided more preciseresults. Our models proved to be capable of simulating the corroded pipe bursttests adequately.

Burst Pressure Estimation of Corroded Pipeline Using Damage Mechanics9

References

Benallal. A., Billardon. R. and Doghri, I. (1988). An integration algorithm and thecoresponding consistent tangent operator for fully coupled elastoplastic and dam-age equations, Comm. Appl. Numer. Methods 4, 731-740.Lemaitre. J., Doghri. I. (1994). Damage 90: a post processor for crack initiation,Comput. Methods appl. Mech. Eng.115, 197-232.Netto T.A., Ferraz U.S. and Estefen S.F. (2005). The effect of corrosion defects onthe burst pressure of pipeline, J Constr Steel Res, 61, pp 1185-1204.