SIMPLE NUMERICAL MODELS FOR PIPELINE WALKING ACCOUNTING FOR MITIGATION AND COMPLEX SOIL RESPONSE

Proceedings of the ASME 211 3th International Conference on Ocean, Offshore and Arctic Engineering OMAE211 June 19-24, 211, Rotterdam, The Netherlands OMAE211-49 SIMPLE NUMERICAL MODELS FOR PIPELINE WALKING ACCOUNTING FOR MITIGATION AND COMPLEX SOIL RESPONSE Daniel Carneiro* BUREAU VERITAS Rio de Janeiro Technical Center Rio de Janeiro, Brazil David Murphy INTECSEA WorleyParsons Group Houston, USA ABSTRACT Non-buried subsea pipelines subjected to high internal pressures and high operational temperatures (HP/HT) may experience significant axial. Asymmetries in the loading and unloading in startups and shutdowns (e.g. due to seabed slope, temperature transients or riser tension) may cause the axial displacements to accumulate over operational cycles, in a ratcheting process often called pipeline walking. Despite the complexity of the pipe-soil interaction governing this behavior, several analytical and simple numerical models have been used for estimating the total accumulated pipeline axial displacement. These simple models are powerful tools in preliminary phases of a pipeline design, although their use is limited due to the simplifications. This paper presents results of a simple numerical model able to account for additional features in the preliminary walking assessment, such as loads on mitigation systems. The models were originally prepared to assess walking mitigation for some rigid flowlines in a recently installed subsea system, and remarkable agreement with complex three-dimensional finite element models was observed. The effect of different types of mitigation systems on the global behavior of the pipelines is presented and discussed. The influence of the pipesoil interaction model employed is also investigated. INTRODUCTION When a pipeline is first exposed to operational pressure and temperature, it will expand axially. The soil friction will convert part of this into mechanical axial strain. If it is shut down for a sufficient time to cool back to its original temperature, it will contract. However, due to the frictional slipping in the pipe-soil interface (along with other effects), it will not contract back to the original position. The axial soil resistance may act in an unsymmetrical manner while heating-up and cooling-down: seabed slope will impose an axial component of weight, acting always in the same direction (downwards); heat-up will occur gradually from the upstream end, while cool-down occurs roughly uniformly. Those effects might induce a net axial shift after each cycle. Although small if compared to the thermal, this global displacement will accumulate over the pipeline life, possibly leading to significant axial movement after several heat-up/cool-down cycles. Konuk (1998) tried to model the cyclic end of what would later be termed a long pipeline. The axial ratcheting due to the temperature transient was first studied by Tørnes et al. (2). The categorization of short and long pipelines depending on its behavior is also introduced in this work. Carr et al. (26) presented a comprehensive description of, and formulated analytical models for what they called pipeline walking due either to seabed slope, thermal transient or sustained end tension (associated with a steel catenary riser). A review of these models including a new * Corresponding author dcarneiro@gmail.com 1 Copyright 211 by ASME

driving mechanism (multiphase content) is presented by Bruton et al. (21). Short and long pipelines A long pipeline is one in which the axial compressive force built up from its ends by the axial soil resistance during, achieves a maximum value for which the compressive mechanical strain has the same magnitude as the thermal. In the (central) region where it occurs, no apparent is observed, and the compressive force corresponds to that which would occur if the pipeline was fully restrained. In a short pipeline, on the other hand, the compression build up from both ends intercept, and the maximum compression is not achieved. Long pipelines are not prone to walk, as the region with no apparent does not move, holding back the expanding ends. As explained, the term long refers not to the pipeline length itself, but to a correlation between length, soil resistance and loading (maximum temperature and internal pressure). Global buckling, if observed, will interfere in the way the pipeline moves in, and can (in regard to the walking behavior) divide a long pipeline into a series of interacting short pipeline sections (the buckles being the boundary between the short sections). All the examples in the present work are short pipelines. There is no apparent reason why the proposed model would not be able to deal with long pipelines, but the results would not be valuable. Global buckling, however, cannot be addressed by the model, so it is not considered hereafter. Walking mitigation Pipeline walking itself is not a limit state, but if not carefully addressed can lead to overstressing of connections or increased loading within a lateral buckle. This phenomenon has been observed in a number of pipelines, in one case leading to system failure when the end connection ruptured (Bruton et al. 21). The most common method of mitigation, which has now been used in a few projects, is to limit the pipeline end displacement using anchor piles. For example, some flowlines in the Greater Plutonio field had their second end anchored to pre-installed suction piles (Jayson et al. 28). The use of chain anchoring allows free of the pipeline in operation, restraining only the accumulated displacement during shutdown by tensioning the aft end. Two flowlines in the Golfinho field were chain anchored to post-installed torpedo piles (Carneiro et al. 29). The disadvantage of post installation is the absence of initial tension, with the result that a few walking cycles will occur before the mitigation is effective. Rigid connection to suction piles, combined with a sliding end structure, was employed for example in the Tahiti Development (Thompson et al. 29). The sliding mechanism allows limited range, without which high compressive loads would be imposed to the system (mitigation apparatus and flowline, for this last possibly inducing buckling) when in operation. Expansion can, however, be restricted, and a balance of compressive loads on pipeline and displacements imposed to jumpers, for example, can be studied for each specific project. Early design stage The anchoring load might be high. In the mentioned examples it ranged between 7kN and 18kN. Means for permanently holding loads of this magnitude are not trivial, and the cost and schedule impact of identifying this need late in a project is often significant. Models to estimate mitigation loads in early design stages are crucial. According to Carr et al. (23) the mitigation load should be calculated by the unit soil axial resistance multiplied by the entire pipeline length. This corresponds to the load necessary to displace the entire pipeline, which might be huge. Complex finite element models, accounting for some flexibility in the mitigation apparatus and for the mobilization displacement in the soil axial resistance, yield lower values (although usually of the same order of this simple calculation result). Although possibly conservative, the load calculated in this simple way can be thought of as an upper bound value (provided that the uncertainty in the soil resistance itself is adequately addressed). This paper presents results of a simple one-dimensional finite element model used to quickly assess walking behavior and mitigation loads. Only the walking driven by seabed slope was analyzed. End tension could be included straightforwardly; temperature transient and multiphase product could also be included with a few more steps in the model algorithm. ONE-DIMENSIONAL NUMERICAL MODEL The present model was first proposed to roughly estimate loads on a walking mitigation system being designed. After a few unsuccessful attempts to derive analytical models, based on those by Carr et al. (26) accounting for the mitigation, it was decided to reproduce these models numerically. Considering the same simplifying assumptions as the analytical model should yield rapid (immediate) computational run times, while the versatility of the numerical approach would permit the inclusion of additional components. The simplified model was built using ANSYS Mechanical ADPL Release 12..1. Being one-dimensional, every node in it is described by its single coordinate X and has one single degree-of-freedom UX. The pipeline was modeled using PIPE16 Elastic Straight Pipe elements provided with its nominal steel cross section. The only relevant material properties are the Young s modulus, the Poisson coefficient and the longitudinal thermal coefficient (for all the analyses herein presented, the typical values E = 27GPa, ν =.3 and α = 1.165 1-5 C -1, respectively, were assumed). Pipe-soil interaction is simulated using COMBIN39 Nonlinear Spring elements attached to all pipeline nodes. A typical number of 1 pipeline elements connecting 11 nodes equally spaced from X = to X = L (where L is the original length of the pipeline) was used for all the analyses, 2 Copyright 211 by ASME

although a mesh convergence study could be performed to optimize this number. The effect of the average (constant) seabed slope is accounted for by a uniformly distributed longitudinal load equivalent to the corresponding component of the pipeline weight (given by its submerged unit weight times the sine of the slope angle). No additional load is considered (i.e., pipeline elements have zero strain) in the initial condition. After that, pairs of temperature increment and internal pressure increment are imposed uniformly to the pipeline elements. After each load step is run, the results of effective axial force and displaced position for each of the pipeline nodes are outputted to a spreadsheet for post processing. Comparison with analytical model The results of the proposed numerical model for typical case were compared to the results given by equation (1) of Carr et al. (26), hereafter termed analytical model. Soil axial resistance in the analytical model is perfectly plastic, for which a pipe section will not move before the interaction force reaches a limit value; and after that it will move with no increase in resistance. This infinite stiffness in the first stage cannot be employed in the numerical model. A bilinear response, with an initial elastic range defined by a mobilization displacement was used. Mobilization displacements of 5mm, 1mm, 2mm and 5mm were used in the numerical analyses. Results in Figure 1 show that the numerical model gives lower values of walking rate (accumulated axial displacement per cycle). Longer mobilization displacements yield lower rates, and for some extreme cases, the walking rate goes to zero. To confirm the apparent convergence to the analytical model when the elastic range is reduced, all the points in Figure 1 were normalized by dividing it by the analytical result for the corresponding slope. Figure 2 indicates that, for any slope, the normalized walking rate tends to 1. (i.e. the numerical model result tends to the analytical model result) as the mobilization displacement is reduced. Comparison with finite element models The results of the first application of the model were compared to the complete finite element analyses performed for some pipelines for which mitigation systems were being designed. These last analyses, prepared using ABAQUS, considered the detailed pipeline configuration from post laid surveys, accounting for the seabed bathymetry. Pipe-soil response was modeled by decoupled axial and lateral bilinear friction. After the setup for the initial configuration, the temperature and internal pressure along each pipeline were gradually incremented to the maximum design profiles, and then lowered back to the initial condition. The heat-up/cooldown cycle was then repeated several times. The five analyzed pipelines, arbitrarily labeled A to E, range from 1.25km to 4.53km, with average slopes between.9deg and 3.9deg. The steel cross section diameter to thickness Accum. disp. per cycle (m) Normalized walking.2.15.1.5 1 2 3 4 5 Figure 1: Accumulated axial displacement per heatup/cool-down cycle versus seabed slope for analytical model (Carr et al. 26) and proposed numerical model considering different mobilization displacements. 1.5 5 Analytical 5mm 1mm 2mm 5mm 1deg 2deg 3deg 4deg 5deg 4 3 Slope (deg) ratio is 15.7 and the apparent specific gravity is 1.53 for all the five pipelines. The average slope in each pipeline was inputted to the numerical model. The bilinear curve for soil axial resistance was reproduced considering a uniform contact force equal to the pipeline submerged unit weight. Instead of temperature and internal pressure profiles, uniform values equivalent to the average maximum value over the pipeline length were applied. First analyses were performed for free-ends condition. Table 1 presents the results for end (at both ends) in first heat-up, and accumulated axial displacement per cycle, obtained using both the proposed numerical model and the complete finite element analyses. Results show that the simple straight model, with all the described simplifications, gives results within a 1% margin (many of them with an even lower 2 Mobilization displacement (mm) Figure 2: Normalized walking rate versus mobilization displacement for different seabed slopes values. 1 3 Copyright 211 by ASME

1 st end Displacement results (m) Numerical model 2 nd end Complete finite element model 1 st end 2 nd end Difference 1 st end 2 nd end Pipeline Load on mitigation (kn) Numerical model Complete finite element model Difference A 529 27 +155.6% C 576 172 +234.9% D 911 276 +23.1% E 643 25 +157.2% Pipeline A B C D E -1.76 -.57 -.83-1.2-1.77 2.1.61 1. 1.63 2.2 Accum. per cycle -1.86.153 -.58.2 -.83.142-1.33.332-1.7.293 Accum. per cycle Accum. per cycle -5.2% 1.95 3.1%.16-4.4% -1.5%.58 5.4%.2-2.4% -.5%.94 6.6%.15-5.% -9.5% 1.64 -.4%.36-7.7% 4.2% 1.62 36.%.28 4.5% Table 2: Load on mitigation systems: comparison of results given by the proposed model and by complete finite element models. Pipeline Load on mitigation (kn) Numerical model Simple formula by Carr et al. (23) Difference A 529 1697-68.8% C 576 743-22.5% D 911 1289-29.3% E 643 1722-62.7% Table 3: Load on mitigation systems: comparison of results given by the proposed model and by the simple formula by Carr et al. (23). Table 1: End for first load condition and accumulated axial displacement per cycle: comparison of results given by the proposed model and by complete finite element models. difference) from the finite element model with the complex aslaid geometry. The exception is pipeline E. The main difference of line E from all others is that this line includes a route curve over almost half of its length. The other routes are straight, although significant out-of-straightness due to the bathymetry and lay process is accounted for in the finite element models. A second set of analyses that included the walking mitigation system was prepared. The anchoring system, with its initial slackness followed by an estimated stiffness, was modeled using additional non-linear spring elements at the pipeline end. The analyses were run in the same way, and the load on the spring along the simulation time was monitored up to a converging maximum force value. Results in Table 2 show that the proposed model overestimates the load (in regard to the complete finite element analyses) about twice, with results between 155% and 235% higher in the analyzed cases. The numerical model results were also compared to the simple formula by Carr et al. (23), in which the load on the mitigation should be given by the unit soil axial resistance multiplied by the entire pipeline length. It was expected that the result of this simple formula would correspond to an upper bound load. Table 3 shows that the results of the present numerical model are 22% to 69% lower than this upper bound. More complex soil resistance models The bilinear soil response model used up to this point is commonly used in pipeline walking numerical analyses, although the actual response curve is expected to be highly nonlinear. The following is an exercise to assess the effect of different response curves to the walking rate. The curve considered in this exercise is composed of three linear segments, as shown in Figure 3. In a first linear section, the soil resistance increases from zero to a peak value F P at a relative displacement D P. It then decays linearly down to a final value F R at D R. Further displacements will occur with no change in soil reaction. When the movement is reversed, the model follows a reversed curve. The base case for the analyses was the case used for the comparison with the analytical model for 2deg slope with D P = 1mm. The same final resistance was used, while the peak resistance was increased from 1. F R to 2. F R. Three values of D R were considered: 2mm, 4mm and 8mm. The observed walking rate for each case, normalized by the result for the base case, is plotted in Figure 4. For D R = 2mm, the walking rate increases for increasing F P, up to F P /F R = 1.8. For further increase in peak resistance, the walking rate starts to decay. As D R increases, the highest walking rate moves closer to its initial value, while the resistance reduction for increasing peak reaction is still observed. 4 Copyright 211 by ASME

F F P 1.6 1.4 1.2 F R D P D R Unload along line parallel to slope at origin D Normalized walking 1.8.6.4 2mm.2 4mm 8mm Figure 3: Force Displacement model curve considered in last analyses. 1 1.2 1.4 1.6 1.8 2 FP / FR CONCLUSIONS The use of a simple one-dimensional finite element model to address walking (and eventually its mitigation) was proposed, with particular interest in early design stage where not all information is available and quick results to support decision making is crucial. Currently, the seabed slope is the only implemented driving source, but the other known ones are thought to be of easy implementation. The versatility of the finite element scaffold allows the easy inclusion of addition features, such as a mitigation system, into the analyses. Outstanding agreement with the analytical model by Carr et al. (26) is observed. The exact match is not possible as the infinite first stage stiffness of the rigid-plastic soil response considered in the analytical model cannot be used in the model. Bilinear response with short mobilization displacements yields good agreement. Very good agreement is also observed with regard to complex finite element models. Out-of-straightness due to the seabed bathymetry and to the pipe lay process does not compromise the quality of the results, and differences below 1% were observed. Poor quality results, however, were experienced for the end of routes with relevant curves (although for the analyzed case, the result of walking rate was still good). The results of load on mitigation obtained by the proposed model were significantly higher than (about twice) those from the complete finite element model, while 22% to 69% below the estimation according to Carr et al. (23). The proposed model was shown also capable with dealing with more complex pipe-soil interaction models. An exercise was presented, in which the effect of a peak before reaching the final soil resistance might for some particular cases increase the walking rate (although reduction is more often observed). The proposed model could then be used, in design stage, to quickly determine a worst case soil resistance curve to be employed in the three-dimensional finite element models. Figure 4: Normalized walking rate versus normalized peak resistance different values of residual displacement. REFERENCES Bruton, D. A. S., Sinclair, F., Carr, M., 21. Lessons Learned From Observing Walking of Pipelines with Lateral Buckles, Including New Driving Mechanisms and Updated Analysis Models. In: Proceedings of the Forty-second Offshore Technology Conference (OTC 21), Houston, OTC275. Carneiro, D., Gouveia, J., Parrilha, R., Cardoso, C. O., 29. Buckle Initiation and Walking Mitigation for HP/HT Pipelines. In: Proceedings of the Deep Offshore Technology Conference (DOT 29), Monte Carlo. Carr, M., Bruton, D., Leslie, D., 23. Lateral Buckling and Pipeline Walking, a Challenge for Hot Pipelines, In: Proceedings of the Twenty-sixth Offshore Pipeline Technology Conference (OPT 23), Amsterdam. Carr, M., Sinclair, F., Bruton, D. A. S., 26. Pipeline Walking Understanding the Field Layout Challenges, and Analytical Solutions Developed for the Safebuck JIP. In: Proceedings of the Thirty-eighth Offshore Technology Conference (OTC 26), Houston, OTC17945. Jayson, D., Delaporte, P., Albert, J. -P., Prevost, M. -E., Bruton, D., Sinclair, F., 28. Greater Plutonio Project Subsea Flowline Design and Performance. In: Proceedings of the Thirty-first Offshore Pipeline Technology Conference (OPT 28), Amsterdam. Konuk, I., 1998. Expansion of Pipelines Under Cyclic Operational Conditions: Formulation of Problem and Development of Solution Algorithm. In: Proceedings of the Seventeenth International Conference on Offshore Mechanics and Arctic Engineering (OMAE 1998), Lisbon, OMAE98-113. 5 Copyright 211 by ASME

Thompson, H., Shang, M., Brunner, M., DeLack, K., Qi, X., Noel, C., 29. Tahiti Flowline Expansion Control System. In: Proceedings of the Forty-first Offshore Technology Conference (OTC 29), Houston, OTC19858. Tørnes, K., Ose, B. A., Jury, J., Thomson, P., 2. Axial Creeping of High Temperature Flowlines Caused by Soil Ratcheting. In: Proceedings of the Ninth International Offshore Mechanics and Arctic Engineering (OMAE 2), New Orleans, OMAE2/PIPE-555. 6 Copyright 211 by ASME