Development of Computational Tools for Automatic ... - CiteSeerX

INTERNATIONAL JOURNAL OF MODELING AND SIMULATION FOR THE PETROLEUM INDUSTRY, VOL. 1, NO. 1, AUGUST 2007

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Development of Computational Tools for Automatic Modeling and FE Analysis of Corroded Pipelines Hélder L. D. Cabral1 , Ramiro B. Willmersdorf1 , Silvana M. B. Afonso2 , Paulo R. M. Lyra1 and Edmundo Q. de Andrade3 1 Mechanical

Engineering Department Federal University of Pernambuco, CEP: 50740-530, Recife, Brazil 2 Civil

Engineering Department Federal University of Pernambuco, CEP: 50741-500, Recife, Brazil 3 PETROBRAS

Research and Development Center(CENPES) Cidade Universitária Quadra 7-Ilha do Fundão-Rio de Janeiro, Brazil [email protected], [email protected], {smb, prmlyra}@ufpe.br, [email protected]

Abstract—Corrosion is one of the most common causes of accidents involving pipelines. The computational simulation through Finite Element Method (FEM) is one of the most efficient tools to quantify reliably the remaining strength of corroded pipes. However, the process of modeling demands intense manual labor from the engineer, and it is also slow and extremely repetitive; therefore it is very prone to errors. The main purpose of this work is to present the PIPEFLAW program which has tools for generating automatically FE pipe models with corrosion defects, ready to be analyzed with commercial FEM programs. PIPEFLAW has computational tools based on MSC.PATRAN pre and post-processing program, and were written with PCL (Patran Command Language). The program has a friendly and customized graphical user interface which allows the user to provide the main parameters of the pipe and defect (or a series of defects). These tools were validated by comparing the results of numerical simulations, done with the PIPEFLAW tools, with the numerical, experimental and semi-empiric results available in the literature. Index Terms—Automatic Modeling, Corrosion Defects, Finite Element Method, GUI, PATRAN, Pipelines.

I. INTRODUCTION The operational safety of hydrocarbon transport pipelines is a major concern of all oil companies, due to the enormous economic, social and public image damage that can arise from a major pipeline accident. These pipelines must be monitored continuously and potential problems must be evaluated reliably, to assess the structural integrity of the compromised pipe and to allow that repair be effected safely, before these defects cause an accident. Previous studies [1] showed that the major cause of failure for liquid and gas pipelines in the USA is ”outside force” (often termed ”third party damage” or ”external interference”) followed by corrosion. According to failure data obtained from CETESB-SP (Technology and Environmental Sanitation Company of São Paulo - Brazil [2]) during period of 1980-2002, among the causes of accidents which could be detected, the majority of accidents were due

Fig. 1. Causes of pipeline failures in state of São Paulo-Brazil between 1980-2002: Total of 149 cases registered by CETESB Company.[2]

to corrosion (32%) and third party damage (21%) as can be seen in Fig. 1. Fig. 2 shows a photography of an oil-pipeline failure which have been caused by deterioration due corrosion in the year of 1990 in city of Campinas (state of São Paulo-Brazil). There are many codified semi-empirical methods available for the assessment of the integrity of corroded pipelines such as BS 7910 [3] and DNV RP-F101 [4]. However, the use of these codes implies in a simplification of the actual geometry of the defect leading to a conservative prediction of the failure pressure of corroded pipes which causes the removal of pipelines prematurely. The Finite Element Method (FEM) is one of the most efficient tools to quantify reliably the remaining strength of corroded pipes. These tools allow the direct simulation of the physical phenomena involved in the failure of the pipe, providing more precise results than the ones found through

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Fig. 3. Example of a 1/4 FE pipe model containing a single rectangular defect: Pattern of mesh discretization adopted by PETROBRAS R & D Center. Fig. 2.

Pipeline failure due to corrosion damage in São Paulo-Brazil.[2]

semi-empirical methods and much faster and cheaper results than the ones obtained through experiments. A. Issues involving FE Modeling Although the FEM has proved to be a powerful tool to predict the failure pressure of corroded pipes, the generation of good computational models of pipe with corrosion defects can take several days. This makes difficult the use of computational simulation in practice once an engineer can not order the removal of a suspected pipe for several days while elaborates computational models. By doing this, it will certainly result in a waste of time and a lot of money. The modeling through FEM requires specific knowledge and training that are not characteristic of all pipeline engineers. The process of creating good computational models for a defect, which includes precise representation of the geometry of the defect and the generation of an appropriate mesh demands intense manual labor from the engineer, and it is also slow and extremely repetitive and it is very prone to errors. Normally, this process is repeated from the very beginning for each new defect to be analyzed, in a clear waste of time and qualified human resources. Particularly this situation becomes worse when we consider the generation of mesh using the procedure adopted by the PETROBRAS R. & D. Center. This procedure requires a higher level of difficulty and manual labor due to some rules which are applied to ensure a high mesh quality which means a mesh to be fine enough for good detail where information is needed (i.e. in the defect region), but not too fine, or the analysis will require considerable time and storage in the computer. A simple model containing a single defect as shown in Fig. 3 can take many hours or even days to be generated depending on the experience and ability of the engineer with the software of modeling. The larger the defect dimensions the more will be the necessary time demanded for generating the entire model. The same happens when the defect configuration becomes more complex (for example, a pipe with multiple defects Fig. 4). With the development of automatic tools for rapid generation of FE pipe models with corrosion defects, this time is drastically reduced (from days to minutes) allowing

Fig. 4. Example of a 1/4 FE pipe model containing a single rectangular defect: Pattern of mesh discretization adopted by PETROBRAS R & D Center.

the engineer to use these tools in practice during the process of evaluation of the integrity of a corroded pipeline. The main purpose of this work was to develop a set of computational tools to produce automatically models of pipes with defects, ready to be analyzed with commercial FEM programs, starting from a few parameters that locate and provide the main dimensions of the defect or a series of defects. These tools were based on MSC.PATRAN pre and postprocessing program [5], and were written with PCL (Patran Command Language). The program for the automatic generation of models (PIPEFLAW) has a simplified and customized graphical interface, so that an engineer with basic notions of computational simulation with the FEM can generate rapidly models that result in precise and reliable simulations. The models generated automatically by the PIPEFLAW program have the same pattern of mesh discretization adopted by PETROBRAS R. & D. Center. B. Issues involving FE Analysis Most finite element commercial software has powerful tools to perform and control FE analysis. They allow the user to set the main parameters of an analysis including several solution

CABRAL et al.: DEVELOPMENT OF COMPUTATIONAL TOOLS FOR AUTOMATIC . . .

controls (for example: the type of analysis, the load step scheme, the type of solver, convergence criteria, etc.). Particularly, the ANSYS Software [6] provides some advanced load step options which allows the user to activate an internal automatic load step scheme which ensures that the load step variation is neither too aggressive (resulting in many bisection/cutbacks) nor too conservative (load step size is too small). At the end of a load step, the size of the next load step is predicted based on some factors pre-defined by the solver. Sometimes the user may need to apply different load increment during the non-linear analysis according to its specific load increment rules and convergence criteria that are not supported by the automatic load step scheme. This can be done in ANSYS by using the “save/restart” procedure in which the user has to enter manually its own convergence criteria and load increment at every new step of the non-linear analysis. In particular, the “restart” procedure was used by our research group PADMEC (High Performance Processing in Computational Mechanics) during some research projects and consulting works under the supervising of PETROBRAS R. & D. Center which had a special set of rules adopted to control the non-linear analysis [7]. However, this procedure requires the engineer to monitor constantly the entire non-linear analysis recovering and interpreting the results at each load step (approximately at each one hour) and making the changes to the input of the next load step according to its customized pre-defined convergence criteria and load increment rules. This process demands again manual labor, is very repetitive, slow and therefore it is very prone to errors. To overcome this difficult, the PADMEC Group developed another set of computational tools written in Python [8] to control automatically the procedure of non-linear analysis adopted by the PETROBRAS R. & D. Center. The development of this tool eliminates the need of an engineer to repeat a mechanical procedure at each load step. Instead, the engineer will be able to concentrate on evaluation of the reliability and validity of the results obtained from the FE analysis. C. Benefits The computational tools presented here were developed by the PADMEC Research Group in a project for PETROBRAS. As the FEM is nowadays one of the main tools for the evaluation of the integrity of corroded pipelines, there are several benefits obtained by the pipeline engineer when using these automatic tools. We can just mention some: reduction of time necessary to create FE models, reduction of errors during the process of modeling, efficient use of qualified human resources, saving of money and higher operational safety. II. PIPEFLAW PROGRAM A detailed description of the PIPEFLAW program has been published recently in a MSc. Dissertation [9]. Herein, only the main steps involving the automatic generation of pipe models with corrosion defects will be presented. PIPEFLAW program includes a set of functions and graphical interface classes implemented with PCL [5] to generate automatically FE pipe models with corrosion defects

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Fig. 5. Main window of PATRAN Software with the customized PIPEFLAW menu added.

of rectangular or elliptic shape located on the internal or external pipe surface. Defects generated by the PIPEFLAW can assume the configuration of isolated defect (single defect) or multiple defects aligned (longitudinally or circumferentially aligned). The final version of the program should include others capabilities such as multiple defects located at arbitrary position. Fig. 5 shows the customized graphical interface of the PIPEFLAW program integrated to the PATRAN software through a menu added on the main window which guides the user along the process of modeling. PCL classes were specifically designed to create graphical objects (widgets) and to manage events generated by the user. Each class contains a reserved set of PCL functions which are used to define, display and update the forms and all the widgets contained in the forms. The input data for the automatic generation of pipe models with corrosion defects is done entirely by graphical user interface (GUI) tools. PIPEFLAW interface has several widgets (such as window, menu, button, data box, switch, etc.) which are used by the user to interact with the program to provide the main input parameters related to the modeling process. Fig. 6 shows the main window of PIPEFLAW containing various widgets where the user is able to inform the defect configuration (single or multiple defects), number of defects, pipe dimensions (diameter, thickness and length), defect shape (rectangular or elliptic) and the defect location (internal or external to the pipe surface). If the user “clicks” on the “Defect Parameters” button, a new window appears inviting the user to provide the defect dimensions (depth “D”, circumferential length “LC”, longitudinal length “LL” and the fillet radius “RA” and “RC”) as indicated in the right window of Fig. 6. If the user “clicks” on the “Defect Position” button, another window appears and the user has to provide through data boxes the positions of each defect along the pipe. For the multiple longitudinally aligned defect case, the user has to enter the distance (in meters) of the centre of each defect. Similarly, for the case of multiple defects aligned in circumferential direction, the user should enter the angular position (in degrees) of the centre of each defect. For both cases, the respective window has customized icons illustrating how the user should enter the parameters. A. Automatic Mesh Generation The automatic process of modeling is executed by several implemented PCL functions that, together with the graphical user interface classes, compose the PIPEFLAW program.

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Fig. 7. Default mesh discretization generated by the PIPEFLAW including the defect region and six adjacent regions.

Fig. 6. Main window of PIPEFLAW (left) and window for input data of rectangular defect dimensions (right).

After the user have been entered all modeling parameters via graphical interface, the automatic generation of the model is initiated. The first step performed by the PIPEFLAW is the automatic generation of the geometry and mesh of the defect region (see Fig. 7). The program computes the element thickness inside the defect region by dividing the remaining wall thickness (TD) by four (defects generated by the PIPEFLAW has always four elements along the wall thickness in the defect region). The element thickness is used as a parameter to compute automatically the number of elements along all edges of the solids on the model. This produces an aspect ratio around unit for the elements inside the defect region. The solid FE models can be generated by PIPEFLAW using linear Hex8 elements or quadratic Hex20 elements available in MSC.PATRAN Library. The models presented here were constructed using tri-linear Hex8 elements. The second step of the automatic modeling procedure is the generation of six adjacent regions of the defect which are used to reduce the model size. As shown in Fig. 7, the modeling of adjacent regions includes: one region for mesh transition along the pipe thickness (from four elements reduces to two elements), three regions for mesh transition along the surface and two expansion regions (no mesh transition). This mesh density was selected based on a convergence study executed by the PETROBRS R. & D. Center in which nonlinear analyses were performed using an increasing degree of mesh refinement. The third and last step is the generation of the pipe model with single or multiple defects. For the single defect case, complementary solids and meshes of one quarter of the pipe are generated taking advantage of symmetry conditions.

Multiple defects are generated through translations (multiple defects longitudinally aligned) and rotations (multiple defects circumferentially aligned) of previously created defect and adjacent regions. To detect which regions will be moved to the specific defect location, the PIPEFLAW program has three levels of proximity between adjacent defects (Fig. 8): level 0 (moves only the defect region), level 1 (moves regions until the first surface transition), and level 3 (moves all adjacent regions). The level 0 represents the minimum distance between adjacent defects allowed by the PIPEFLAW. This level encompasses the box defect region which is defined by the corroded region and a small full thickness material around the defect. Due to this small distance around the corroded area, the program does not allow the generation of adjacent defects when they are too close approaching the situation of touching defects. To connect one adjacent defect to another, the program generates automatically new geometry and mesh in the remainder region between adjacent defects.


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Fig. 9. Flowchart containing the main tasks executed by the Python script during automatic control of the non-linear analysis.

Fig. 10. Input directory where the standard files are created and used by the script during the non-linear analysis.

Fig. 8. Example of a pipe model with four defects longitudinally aligned: Three levels of proximity allowed by the PIPEFLAW program.

III. AUTOMATIC CONTROL OF NON-LINEAR ANALYSIS During some research projects and consulting work which were supported and monitored by the PETROBRAS, it was used a special procedure developed by the PETROBRAS R. & D. Center [7]. This procedure is based on the “save/restart” command of ANSYS program and was developed to execute and control the non-linear analysis using the convergence criteria and load increment adopted by PETROBRAS. As discussed previously, this special procedure lead to a clear waste of time and requires intense manual labor from the engineer who has to manage manually the entire non-linear analysis by recovering and interpreting the results obtained at each load step of the analysis and has to reenter the new input values for the next load step. In order to eliminate the need of an engineer to repeat a mechanical procedure at each load step, it was developed a script written in Python [8] which manages all non-linear analysis though the execution of preprogrammed tasks. At each iteration of the non-linear analysis, the ANSYS solver is run by the script; following that, the results of that iteration are read and interpreted by the script, allowing that convergence criteria and load increments, predefined by the user (PETROBRAS R. & D. Center), be applied automatically, in contrast with the

usual procedure where automatic convergence criteria and load increments are determined by the solver. Fig. 9 shows a simple flowchart with the main tasks executed by the script during the process of automatic control of non-linear analysis. The program does not have graphical user interface and the input data still have to be entered manually by editing the main file of the program to provide the data related to the geometry, material, convergence criteria and termination criteria. After the input data process has been finished, the automatic pre-processing procedure is performed (Fig. 10). This procedure consists of generating six standard files necessary for the automatic control of non-linear analysis executed by the script. These files are generated automatically by the script using the main input file of the correspondent FE model (for example, IDTS3.prp) which was generated automatically by the PATRAN system. These files are saved automatically in the input directory from where the script accesses its contents and creates new files for each load step. At the end of the non-linear analysis, the script accesses the information stored in a file during the analysis and generates automatically a load step history in an Excel spreadsheet with the main results of each step. Fig. 11 shows an example of a partial spreadsheet (only the main steps are shown) containing the summary of the history of a non-linear analysis.

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Fig. 11. Example of a partial Excel spreadsheet generated automatically by the script containing the main results (history) of a non-linear analysis. Load step 2 (start yielding point), load step 17 (maximum plastic strain increment of 0.0025 was reached), load step 17a (failure criteria was reached).

IV. VALIDATION The ANSYS program [6] is a well known general-purpose finite element program which has been extensively validated and can be used to perform FE stress analysis. Here it is used to predict the failure pressure of an internally pressurized corroded pipe. However, a good accuracy of the above failure prediction relies on a good accuracy of the stress analysis which is obtained by using an appropriated mesh density and application of correct boundary conditions. This section presents the results of FE simulations executed previously [9] to validate the mesh discretization of the models generated automatically by the PIPEFLAW program. The validation consisted on simulating three of the six specimens which were previously investigated experimentally [10] and numerically [11]. Fig. 12 shows the configuration of the rectangular machined defects contained in the three specimens modeled using the PIPEFLAW program: IDTS2 (single defect), IDTS3 (two defects longitudinally aligned) and IDTS4 (two defects circumferentially aligned). The rectangular defects are located at the external surface of the pipe and the main dimensions are presented in Table I. PIPEFLAW program uses an angle φ (in degrees) as a distance parameter between defects circumferentially aligned. The angle φ equivalent to the actual distance of 9.9mm (specimen IDTS4) is 5.23. However, the angle used for the specimen IDTS4 was 5.45 (equivalent to a distance of SC* = 11.65mm) due the fact that the distance between defects exceeded the minimum value allowed by the PIPEFLAW program. Therefore, due to this small difference,the model IDTS4 used in the validation was named as IDTS4*. Appropriate boundary conditions were applied at the symmetry planes when applicable. Pressure was incrementally applied to the internal surfaces of the model and longitudinal force due to the internal pressure was simultaneously applied to the pipe wall at the cut-off boundary of the models. The ANSYS program [6] was employed to perform the

finite element analyses which accounted for geometrical and physical nonlinearities. The material properties used in the FE simulations, which was the same used in [11], assume a rate-independent plasticity model using the von Mises yield criterion and adopting an isotropic hardening rule. The values of Young modulus, yield stress and true ultimate tensile stress are, respectively: 200,000MPa, 534.1MPa and 718.2MPa. The true stress-true strain curve of the API 5L X80 steel was constructed based on the Ramberg-Osgood equation of the material determined experimentally in [10]. Table II presents the failure pressures measured in the laboratory tests in [10], the failure pressures predicted by FE simulations conducted in [11] (Pf1) and [9] (Pf2) and the failure pressures predicted through semi-empirical method BS7910 [3]. The failure criterion adopted in [9] was the same used in [11] and establishes that failure is reached when the von Mises stress along a radial direction (all points situated across the thickness), within the colony of defects, exceeds the true ultimate tensile stress. The errors of the predicted failure pressures are also presented in Table II. It should be noted that the errors obtained by FE simulations were quite similar and showed excellent agreement with the experimental results. Failure pressures were within -3.83% and +5.49% for [11] and within -2.31% and +5.98% for [9]. The failure pressures predicted by the BS7910 method presented more conservative values comparing with the ones obtained by FE simulations and were within -8.88% and -0.92% which confirms the conservative assessment embodied in these semiempirical methods. The photographs of the defects of the tubular specimens IDTS2, IDTS3 and IDTS4 obtained in laboratory tests [10] after failure are presented here in Fig. 13. In these photos the regions in which the failure took place are marked with a ellipse. Results provided by the FE non-linear analysis are presented in Fig. 14, Fig. 15, and Fig. 16. These figures present, respectively, the von Mises stress distribution in the region of the defects of the solid FE models IDTS2, IDTS3, and IDTS4*. These contour plots were drawn together with the deformed configuration of the model (applying a scale factor of 5 to the displacements) and were obtained at the last load step of the non-linear analysis where the failure criterion was reached. Comparing Fig. 14, and Fig. 16 with Fig. 13 (containing photos from laboratory tests) one can observe that the failure configuration of the specimens IDTS2 and IDTS4*, predicted through FE simulation, are very close to the actual failure configuration presented in laboratory tests. The FE models were able to represent precisely the deformed configuration of the defects and were able to detect accurately the place where the failure took place. The failure configuration of the solid FE model IDTS3 (Fig. 15 - with two defects aligned in the longitudinal pipe direction) presented a slight difference from the actual failure configuration presented in laboratory tests (Fig. 13). The solid FE model presented the highest stress level in the region between the defects (see Fig. 15) while the laboratory results indicated a failure inside the defect region (see ellipse


Fig. 12.

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Defect configurations of the tubular specimens investigated experimentally [10] and numerically [11] TABLE I ACTUAL D IMENSIONS OF THE T UBULAR S PECIMENS AND OF THE M ACHINED D EFECTS . [11] Specimen

LL[mm]

LC[mm]

D[mm]

RA[mm]

RC[mm]*

SL [mm]

SC [mm]

SC [mm]**

IDTS2

39.6

31.9

5.39

3.5

8.0

-

-

-

66.5%

IDTS3

39.6

31.9

5.32

3.5

8.0

20.5

-

-

65.7%

IDTS4

39.6

32.0

5.62

3.5

8.0

-

9.9

11.65

69.4%

D/T.100 [%]

DE = 458.8 mm (pipe outside diameter) T = 8.1 mm (pipe wall thickness) * Actual

SL e SC = Longitudinal and Circunferencial spacing, respectively.

value unknown. ** Minimum spacing used by the PIPEFLAW.

TABLE II ACTUAL AND P REDICTED FAILURE P RESSURES . Errora (%)

Failure Pressures [MPa] Experimental

Fig. 14.

FE Simulations

BS7910

FE Simulations

BS7910

Specimen

Pf (EXP )

Pf 1

Pf 2

Pf 3

E1

E2

E3

IDTS2

22.679

22.710

22.791

21.253

+0.14

+0.49

-6.29

IDTS3

20.314

19.535

19.810

18.511

-3.83

-2.48

-8.88

IDTS4

21.138

22.298

22.403*

20.944

+5.49

+5.98*

-0.92

meanb

-

-

-

-

3.15

*

Values associated with the model IDTS4* used in [9].

a

Error (%) = ( ( Pf i - Pf (EXP ) ) / (Pf (EXP ) )) × 100% ( i = 1, 2 and 3 )

Von Mises stresses for the model with single defect (IDTS2).

Fig. 15.

b

2.98

P

Mean =

5.36

kErrork ÷ 3

Von Mises stresses for the model with single defect (IDTS3).

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Fig. 13.

Photographs of the defects of the tubular specimens after failure.[10]

Fig. 16.

Von Mises stresses for the model with single defect (IDTS4). Fig. 17.

in Fig. 13). However, the contour plots of the model IDTS3 indicates that the region where the actual fracture took place is also under high stress level (see the second most stressed region of the defect indicated in Fig. 15). In addition, the FE model was able to represent accurately the actual shape of the deformed configuration. Fig. 17 presents the results of von Mises stress variations against pressure values for the correspondent FE models IDTS2, IDTS3 and IDTS4*. The stress values were obtained at a point located at the most stressed region on the internal pipe surface of the FE model. As suggested in the BS7910, appendix G [3], stress variations with increased pressure load (for all models) showed three distinct stages. The first is a linear response progressing to a point when the elastic limit is reached (σy = 534.1MPa). On the second stage, the maximum von Mises stress remains approximately constant or increase slowly (plasticity spreads through the remaining ligament). The third stage is dominated by material hardening progressing to the point where failure occurs.

Von Mises stress variations with increased pressure load.

V. PARAMETRIC STUDY This section summarizes the results of parametric studies performed previously to investigate the behavior of pipelines subjected to multiple defects aligned in the longitudinal and circumferential directions. The main objective of these studies was to evaluate the effect of interaction between defects in the failure pressure of corroded pipes using the PIPEFLAW tools. A detailed description of these parametric studies has been published recently [12], [13] and therefore, only the main results will be shown. The models analyzed in the parametric studies adopted the same material, boundary conditions and failure criterion of the validation models described previously. The methodology of the parametric study was done by varying the distance between defects and the number of interacting defects. Three groups of pipe models were analyzed containing two, three and four identical defects aligned in the


longitudinal and circumferential direction of the pipe. In order to investigate the effect of interaction between defects, for each group of pipe models it was generated a series of models with defects equally spaced (seven models for the longitudinal case and five models for the circumferential case). The FE models are identified by a name indicating the status of the model (MD - multiple defects or SD - single defect), the number of defects (2, 3 or 4) followed by the letter of the correspondent defect configuration (L - longitudinally or C - circumferentially aligned) and the distance between defects as a function of the pipe wall thickness (2T, 3T, etc.). For example, the model named MD 2L 3T means a pipe model with two defects longitudinally aligned and equally separated by three wall thicknesses. Table III presents the pipe dimensions (outside diameter DE, wall thickness - T, length - LD) and the dimensions of the investigated defects. Numerical simulations considering isolated (or single) defects were also executed in order to compare with the results of longitudinally and circumferentially aligned defect cases. Four FE models with single defects were analyzed for each case (longitudinal and circumferential) as shown in Table III. The defect dimensions are the same, except the longitudinal length (LL) and circumferential length (LC) which are variables. For example, the model SD LL1 represents the isolated defect with longitudinal length equal to 40.0 mm (the same value used for the models with longitudinally aligned defects). The other three FE models with single defects (SD LL2, SD LL3 and SD LL4) were analyzed to investigate the effect of longitudinal defect length in the failure pressure of pipes. These three FE models with single defect represent the limit situation where the multiple defects of each group are touching (spacing SL between defects is null). For these situations, the touching defects are expected to behave as a unique composed longer defect with longitudinal length equal to two, three and four times the longitudinal length of the single defect of model SD LL1. The same procedure is applied to the other four single defect models where the parameter which varied was the circumferential length of the defect (LC). A. Circumferentially Aligned Corrosion Defect Results of predicted failure pressure of the FE pipe models are presented in Table IV for the study of circumferentially aligned corrosion defects. One can observe that there is no influence of the circumferential length of the defect on the failure pressure of pipes. A variation of 400% in the value of LC (between models SD LC1 and SD LC4) caused a small difference of -0.45% on the predicted failure pressure. Therefore, the semi-empirical methods appear to adopt a reasonable consideration when they neglect the circumferential dimension of the defect on the computation of the predicted failure pressure of corroded pipes. It is also observed that the predicted failure pressures are not significantly influenced neither by the number of circumferentially aligned defects nor by the distance between

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Fig. 18.

Von Mises stresses for the model MD 2C 2T.

Fig. 19.


them. This confirms the results reported earlier [14] in which the authors showed that defects aligned in the circumferential direction do not interact even when the defects are touching. Contour plots of the von Mises stresses for the models with defects circumferentially separated by the smallest distance of 2T are presented in Fig. 18 to Fig. 20 together with the correspondent contour plots for the isolated defect model (Fig. 21). These plots were drawn together with the deformed configuration of the corroded region applying a scale factor of 5 to the displacements. All contours plots correspond to the last load step where failure criteria was reached. These figures show a high stress level in the remaining ligament of the outer defects, which confirms the tendency of the outer defect in a group of circumferentially aligned defects to fail first. For all single defect FE models, the highest von Mises stress occurs near the region of the frontal fillet radius of the defect along the longitudinal direction of the pipe, as indicated in the plots by the longitudinal strips of the model SD LC1. As can be seen, the stress states within the outer defect for the models with multiple defects (MD 2C 2T, MD 3C 2T, MD 4C 2T) were quite similar to that of single defect, suggesting that no interaction occurred.

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TABLE III D IMENSIONS OF THE FE P IPE M ODELS WITH R ECTANGULAR D EFECTS USED IN THE PARAMETRIC S TUDIES . Pipe Dimensions

Rectangular Defect Dimensions

DE[mm]

T[mm]

LD[mm]

LL[mm]

LC[mm]

D[mm]

RA[mm]

RC[mm]

(D/T).100%

480.0

9.0

2500.0

40.0

30.0

5.4

2.0

8.0

60%

54.0 (6T)

90.0 (10T)

135.0 (15T)

—

Multiple Defects Distance (SL or SC) [mm]

18.0 (2T)

27.0 (3T)

36.0 (4T)

45.0 (5T)

Single Defects SD LL2

Models

SD LL1

LL[mm]

40.0

80.0

120.0

160.0

Models

SD LC1

SD LC2

SD LC3

SD LC4

LC[mm]

30.0

60.0

90.0

120.0

FAILURE P RESSURE P REDICTED VIA FEM FOR

SD LL3

SD LL4

TABLE IV C IRCUMFERENTIAL S TUDY: N O I NTERACTION O CURRED .

THE

Single Defects SD LC2 SD LC3 24.601 24.592 Group of 2 Defects

Model P fM EF [M P a]

SD LC1 24.630

Model

MD 2C 2T

MD 2C 3T

P fM EF [M P a]

24.583

24.583

SD LC4 24.515

-

MD 2C 4T

MD 2C 5T

MD 2C 6T

24.508

24.508

24.486

Group of 3 Defects Model

MD 3C 2T

MD 3C 3T

MD 3C 4T

MD 3C 5T

MD 3C 6T

P fM EF [M P a]

24.458

24.458

24.421

24.421

24.421

Group of 4 Defects

Fig. 20.

Model

MD 4C 2T

MD 4C 3T

MD 4C 4T

MD 4C 5T

MD 4C 6T

P fM EF [M P a]

24.458

24.421

24.396

24.377

24.377


B. Longitudinally Aligned Corrosion Defects Table V presents the results of predicted failure pressure of the FE pipe models for the study of longitudinally aligned corrosion defects. The correspondent failure pressures predicted through semi-empirical method BS7910 are also presented. All predicted failure pressures using BS7910 method presented more conservative results when compared with the FE predictions, especially for longer defects. The failure pressure predicted via BS7910 method for the model SD LL4 (with the longest single defect) was -12.15% less than the one predicted

Fig. 21.

Von Mises stresses for the model SD LC1.

via the FEM while for the model SD LL1 (the shorter single defect) the semi-empirical value differed -4.74% from the FEM result. Fig. 22 shows the predicted FE failure pressures plotted as a function of the distance between defects for the three groups analyzed with two (MD 2L), three (MD 3L) and four (MD 4L) defects. The correspondent values for the single defect cases are also indicated by four different lines. As indicated in Fig. 22, the failure pressures appear to be more influenced by the number of defects rather than their separation especially for the cases where the defects are separated by


FAILURE P RESSURE P REDICTED VIA FEM

Model P fM EF [M P a] P fBS [M P a]

19

TABLE V BS7910 M ETHOD FOR THE L ONGITUDINAL S TUDY.

AND VIA

Single Defects SD LL2 22.182 20.088

SD LL1 24.583 23.418

SD LL3 19.790 17.455

SD LL4 17.876 15.705

Group of 2 Defects (MD-2L) Model

MD 2L 2T

MD 2L 3T

MD 2L 4T

MD 2L 5T

MD 2L 6T

MD 2L 10T

MD 2L 15T

P fM EF [M P a]

22.315

22.782

23.07

23.24

23.42

23.915

24.315

P fBS [M P a]

20.695

20.876

21.021

21.145

21.255

21.621

23.418

Group of 3 Defects (MD-3L) Model

MD 3L 2T

MD 3L 3T

MD 3L 4T

MD 3L 5T

MD 3L 6T

MD 3L 10T

MD 3L 15T

P fM EF [M P a]

20.640

21.315

21.731

22.115

22.470

23.440

24.070

P fBS [M P a]

18.864

19.301

19.658

19.964

20.232

21.061

23.418

Group of 4 Defects (MD-3L)

Fig. 22. defects.

Model

MD 4L 2T

MD 4L 3T

MD 4L 4T

MD 4L 5T

MD 4L 6T

MD 4L 10T

MD 4L 15T

P fM EF [M P a]

19.315

20.261

21.070

21.600

22.070

23.315

24.040

P fBS [M P a]

17.793

18.438

18.959

19.395

19.769

20.866

23.418

Predicted FE failure pressure vs. longitudinal distance between

a small distance. However, this influence do not appear to continue indefinitely as indicated in the graph where the gap between curves MD-2L and MD-3L is greater than the gap between curves MD-3L and MD-4L. As expected, increasing the distance between defects, the predicted failure pressures tend to reach the superior value of 24.583MPa equivalent to the failure pressure of the single defect case (SD LL1) with an asymptotic behavior. Fig. 22 indicates also a very strong influence of the longitudinal length of the defects on the failure pressure of corroded pipelines. Fig. 23 to Fig. 26 present the contour plots of von Mises equivalent stress together with the deformed configuration of the corroded region for the FE models with single defect (these plots were drawn applying a scale factor of 5 to the displacements). In all single defect FE models, the highest von Mises stress occurs near the region of the frontal fillet radius of the defect along the longitudinal direction of the pipe, as indicated in the plots.

Fig. 23.

Von Mises stresses for the model SD LL1.

Fig. 24.


20

Fig. 25.

Fig. 26.


Von Mises stresses for the model SD LL3. Fig. 27.

Von Mises stresses for the model MD 2L 2T.

Fig. 28.


Fig. 29.



In contrast with the circumferential study, it was shown that for longitudinally aligned corrosion defects [15] by decreasing the distance between them they begin to interact reducing the remaining strength of the corroded pipe. Here this is confirmed in Fig. 27 to Fig. 32 which present the contour plots of the von Mises stress at the last load step for the models with defects separated by the smallest distance of 2T and separated by the distance of 15T (the longest distance between defects analyzed in this study). For the case where the distance of separation was 2T (Fig. 27, Fig. 28, and Fig. 29), the defects interacted as indicated by the two highest stress levels located at the central defect. These figures show a high stress level in the remaining ligament of the central defects, which confirms the tendency of the central defect in a group of longitudinally aligned defects to fail first. In addition, the highest stress level occurs through the full thickness pipe material between the central defects suggesting that in a limit situation, where adjacent defects are touching, defects will behave as single longer defect. The BS7910 interaction rules applied to the models with two, three and four defects separated by 15T treat the defects as isolated due to the fact that the axial spacing of 15T exceeds


21

the value of . This rule appears to be a good consideration as indicated by the contour plots of von Mises stress for the correspondent models (Fig. 30, Fig. 31, and Fig. 32). These stress contours are almost identical to those of the isolated defect (Fig. 23) suggesting that no effective interaction occurred (see also the similar values obtained for the models separated by 15T presented in Table V). VI. CONTRIBUTIONS This work described the application of computational tools developed by the PADMEC Research Group which can be used effectively for the automatic evaluation of the integrity of corroded pipelines. In the following we summarize some important contributions achieved with this work.

Fig. 30.

Fig. 31.



A. Automatic Modeling Tools The main contribution of this work was the development of a set of reliable and robust computational tools (PIPEFLAW) used for automatic FE modeling of pipelines with corrosion defects. The PIPEFLAW program was written with PCL (Patran Command Language) and was integrated to the MSC.PATRAN software through GUI tools. PIPEFLAW program allows the user to generate automatically FE pipe models with corrosion defects of rectangular or elliptical shape, located on the internal or external pipe surface. Defects generated by the PIPEFLAW can assume the configuration of isolated defect (single defect) or multiple defects aligned (longitudinally or circumferentially). The final version of the program will include others capabilities such as multiple defects located at arbitrary position. PIPEFLAW program generate automatically 3D hex meshes using Hex8 tri-linear elements or Hex20 tri-quadratic elements. An appropriated mesh density is used based on sensitivity and convergence studies performed by the PETROBRAS R. & D. Center. B. Graphical User Interface Tools PIPEFLAW program has simplified and customized graphical user interface containing several widgets (windows, menus, buttons, data boxes switches icons, etc.), which allows the user to provide intuitively the main input modeling parameters of the pipe and defect (such as: dimensions, number of defects, type of geometry of the defect, location of the defects, etc.). C. Tools for Automatic Control of Non-Linear Analysis

Fig. 32.


PADMEC Research Group developed another set of computational tools written in Python specially to control automatically the procedure of non-linear analysis adopted by the PETROBRAS R. & D. Center. The non-linear analyses are run by a Python “script”, which manages all analysis though the execution of preprogrammed tasks. This allows that convergence criteria and load increments, adopted by PETROBRAS R. & D. Center, be applied automatically using the “save/restart” procedure of the ANSYS program.

22


VII. CONCLUSIONS

ACKNOWLEDGMENT

From the results, the following conclusions are drawn according to each topic presented in this work.

The authors would like to thank PETROBRAS for permission to publish this paper, for supplying the experimental and numerical data used in the validation portion of this study and for giving financial support and guidance throughout the course of this research project. The authors also wish to thank FINEP-Brazil, CAPES and CNPq for the financial support of various research projects developed in this area by the PADMEC Research Group.

A. PIPEFLAW Tools The PIPEFLAW tools for generating automatically FE pipe models with corrosion defects were successfully applied and validated in this work. These tools showed a rapid way of generating reliable FE models making easy the process of model generation. The use of PIPEFLAW automatic tools reduced drastically (from days to minutes) the time consuming for generation of FE pipe models with corrosion defects. This allows the capability of analyzing real problems by using computational tools helping engineers in the process of decision about the structural integrity of a corroded pipeline. With the automatic generator, the errors involved in the process of modeling are also decreased once there are less manual interventions. The customized graphical user interface developed especially for this kind of problem made the process of modeling very easy. This allows that an engineer with basic notion of computational simulation with the FEM generates rapidly models that result in precise and reliable simulations. B. Tools for Automatic Control of Non-Linear Analysis The automatic tools to control non-linear analysis through a Python script were applied successfully and has been used extensively during some consulting work executed for PETROBRAS R. & D. Center. These tools eliminated the need to have an engineer repeating a mechanical procedure at almost every hour (every load step). Instead, the pipeline engineers must be concentrated on the evaluation of the reliability and validity of the results obtained from the FE analysis. C. Parametric Studies The use of PIPEFLAW program has proved to be an excellent tool to create rapidly reliable FE models. With the use of PIPEFLAW tools one can accelerate the process of modeling and make easy the execution of parametric studies. The results obtained by the circumferential parametric study confirmed that multiple defects aligned in the circumferential direction do not interact. In addition, in a line of closely spaced circumferentially aligned defects, the outer defects are subjected to high stress level and will have the tendency to fail first. Similarly, results obtained by the longitudinal parametric study confirmed that multiple defects aligned in the longitudinal direction interact reducing the remaining strength of the corroded pipe. In addition, in a group of defects longitudinally aligned, the central defect will have the tendency to fail first. Finally, the longitudinal length of the defect showed a strong influence on the failure pressure while the circumferential length showed no influence.

R EFERENCES [1] P. HOPKINS, Training Engineers in Pipeline Integrity, Western Regional Gas Conference, Arizona, EUA, pp.1-9, 2002. [2] http://www.cetesb.sp.gov.br(in Portuguese) [3] BS7910, Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures- Annex G: The Assessment of Corrosion in Pipes and Pressure Vessels, British Standard, 1999. [4] DNV, Recommended Practice DNV RP-F101 Corroded Pipelines, Det Norske Veritas, Norway, 1999. [5] MSC. PATRAN, Help system: MSC.Patran Library (PCL Manuals) and MSC.Acumen Library (Develop Manuals). Patran Software Release 2005. http://www.mscsoftware.com [6] ANSYS, Ansys Release 9.0 Documentation: Operations Guide(Chapter 3) and Structural Guide (Chapter 8). http://www.ansys.com, 2004. [7] A. C. BENJAMIN and E. Q. de ANDRADE, Projeto 601295: Avaliaća˜ o de Dutos Corro´ıdos com Defeitos Curtos, Especificaça˜ o 13 (Revisão 2): Procedimento para Definiça˜ o da Estratégia de Aplicaça˜ o do Carregamento em Análises de Ruptura de Espécimes Tubulares com Defeitos Curtos de Corrosão usando Elementos Finitos,(in Portuguese), 2005. [8] PYTHON, Python Documentation Release 2.4.1: Tutorial and Library Reference Manual, http://www.python.org/doc/, 2005. [9] H. L. D. CABRAL, Desenvolvimento de Ferramentas Computacionais para Modelagem e Análise Automática de Defeitos de Corrosão em Dutos. Programa de Pós-Graduaça˜ o em Engenharia Mecânica, UFPE, Recife, Dissertaça˜ o de Mestrado(in Portuguese), 140p, 2007. [10] A. C. BENJAMIN, J. L. F. FREIRE, R. D. VIEIRA, J. L. C. DINIZ, E. Q. de ANDRADE, Burst Tests on Pipeline Containing Interacting Corrosion Defects. In: Proc. 24th Int. Conf. on Offshore Mechanics and Arctic Engineering (OMAE2005), Halkidiki, Greece, 2005. [11] E. Q. de ANDRADE, A. C. BENJAMIN, P. R. S. MACHADO Jr., L. C. PEREIRA, B. P. JACOB, E. G. CAMEIRO, J. N. C. GUERREIRO, R. C. C. SILVA, D. B. NORONHA Jr., Finite Element Modeling of the Behavior of Pipelines Containing Interacting Corrosion Defects. In: 25th Int. Conf. on Offshore Mechanics and Arctic Engineering (OMAE200692600), Hamburg, Germany, 2006. [12] H. L. D. CABRAL, R. B. WILLMERSDORF, S. M. B. AFONSO, P. R. M. LYRA, E. Q. de ANDRADE, Modelagem e Análise Automática de Dutos com Múltiplos Defeitos de Corrosão Alinhados Circunferencialmente. CMNE/CILAMCE2007(in Portuguese), in CD-ROM, ID 1108, Porto, Portugal, 2007. [13] H. L. D. CABRAL, R. B. WILLMERSDORF, S. M. B. AFONSO, P. R. M. LYRA, E. Q. de ANDRADE, Finite Element Analyses of the Behaviour of Pipelines with Multiple Longitudinally Aligned Corrosion Defects. In:19th International Congress of Mechanical Engineering COBEM2007, ID 1493 (accepted for publication), Brasilia, Brasil, 2007. [14] B. A. CHOUCHAOUI and R. J. PICK, Behaviour of Circumferentially Aligned Corrosion Pits, International Journal of Pressure Vessels and Piping, v.57, pp.187-200, 1994. [15] B. A. CHOUCHAOUI and R. J. PICK, Behaviour of Longitudinally Aligned Corrosion Pits, International Journal of Pressure Vessels and Piping, v.67, pp.17-35, 1996.