Tension and Expansion Analysis of Pipe-In-Pipe Risers: Part B, Finite Element Modeling

Bin Yue, Kevin C. Man, David Walters 2H Offshore Inc.

Houston, TX, USA

ABSTRACT We developed a mathematical model for accurately calculating the pipe-in-pipe riser tension and elongation in Part A of the paper. In this Part B, we focus on finite element modeling of the multi-string riser system. The simulations are performed using two widely used riser analysis finite element software, OrcaFlex and Flexcom. A tensioner supported pipe-in-pipe TTR system is studied. Special measures and considerations in modeling the pipe-in-pipe features are discussed. The finite element analysis solutions are benchmarked against theoretical results considering weight, temperature, pressure, and tensioner loads. Good agreements, including riser stroke and tension distributions between the inner and outer risers along the length of the riser, are observed. The riser dynamic analysis with environmental loads is subsequently performed with finite element software. KEY WORDS: Riser; Pipe-In-Pipe; Pre-tension; Tensioner; Thermal Expansion; Pressure Expansion. INTRODUCTION Pipe-in-pipe Top Tension Riser (TTR) systems are widely used in the offshore oil and gas industry. The main feature of a typical pipe-in-pipe TTR system is a concentric inner string (tubing) protected by one or more protective outer strings (casings). All strings are firmly connected at top ends. The bottom ends of casings are fixed to the subsea wellhead, whereas the bottom end of tubing is fixed to a mud line tubing hanger or downhole packer. Insulation materials, in the form of solid, liquid, or gas, exist in the annulus between strings. Generally, the wall temperature and annulus pressure are higher for the inner strings than the outer strings. If the strings were not connected, the free elongation of inner string will be larger than those of the outer strings. However, due to the existence of end constraints, pressure and temperature variations result in the redistribution of tensions amongst strings. The complexity of the problem is further enhanced by the tubing pretension and the riser external forces. The external forces include weight, environmental loads, and aircan or tensioner tensions. Due to the importance and complexity of the pipe-in-pipe TTR system, it is desirable to have a systematic and accurate methodology to model the static and dynamic responses of the TTRs.

In the offshore industry, the pipe-in-pipe interaction is of particular concern for pipelines and flowlines due to their likelihood of buckling. Comprehensive researches have been performed. Some of the examples include the study considering thermal expansion and soil resistance (Harrison, Kershenbaum, and Choi, 1997, and Bai, and Bai, 2005), as well as the bulkhead arrangements (Chen, Wang, Chia, and Ngiam, 2009). The studies for pipe-in-pipe risers are mainly concentrated on the bending moments generated by the centralizers. The concept of Bending Magnification Factor (BMF) is used in both the Steel Catenary Riser (SCR) assessment (Masson, Fang, Jordan, and Hays, 2006) and TTR assessment (Harrison and Helle, 2007). There is also Vortex Induced Vibration (VIV) study considering the fluid-structure interaction within the pipe-in-pipe riser (Yettou, Derradji-Aouat, and Williams, 2008). However, the detailed tension and expansion formulae and finite element modeling methodology of pipe-in-pipe risers is yet to be developed. In Part A of the paper, we have developed a mathematical model for accurately calculating the riser tension and elongation under static loads. In this Part B, we focus on finite element modeling of the multi-string TTR riser system. The primary goals for this paper are to:

Identify the special considerations that must be taken in modeling the pipe-in-pipe feature in a finite element software; and to

Benchmark the finite element analysis results against the theoretical solutions obtained from Part A of the paper.

Traditionally pipe-in-pipe risers are typically analyzed using the so called composite models. This is mainly due to software limitations. For riser analysis finite element software like Flexcom and OrcaFlex, there was not a true pipe in pipe feature. For general purpose finite element software like ABAQUS and ANSYS, the effort of modeling true pipe in pipe riser and the computational cost associated with it are both significant. In a composite model, the multi-string sections are modeled using one equivalent string with section properties equal to the summation of all strings. The interactions between strings cannot be captured by the model. Oftentimes post-processing’s accounting for pressure and

temperature changes are performed. This method can have acceptable engineering accuracy if cautions are used during finite element modeling (FEM) and post-processing. However, some true interactions within the system are hard to capture. In addition, the procedure of pre-processing and post-processing are time consuming and mistake prone. The recent versions of riser analysis software, OrcaFlex (version 9.6b) and Flexcom (version 7.9.7), have incorporated the pipe-in-pipe feature. The analyses of pipe-in-pipe risers are thus significantly simplified. However, the pipe-in-pipe interactions established by Part A of the paper need to be well understood to correctly and accurately model the PIP risers. This is demonstrated in the latter part of this paper. Moreover, neither of the software is fully equipped for modeling all aspects of the true pipe in pipe feature. Some special but simple measures must be taken. The rest of the paper is organized as follows. Firstly, a tensioner supported pipe-in-pipe TTR system is introduced with key components and design parameters. Selected loading conditions, including temperature, pressure, and environments, are also introduced. Secondly, the finite element modeling consideration and procedure for both OrcaFlex and Flexcom are given. This is followed by the FEM results with static loads and comparison with the theoretical solutions obtained using the method introduced in Part A of the paper. The dynamic finite element analysis solutions are subsequently provided. The paper is concluded with key considerations and recommendations for modeling pipe-in-pipe risers. TTR SYSTEM UNDER CONSIDERATION The following generic TTR system is used as an example to aid the demonstration of FEM modeling of a multi-string riser system. The parameters are hypothetic and not specific to a particular project. System Description The key components and their arrangements for a production TTR system in 1000m water depth are shown in Fig. 1. The inner string is fixed to the surface wellhead and tree from the top, and fixed to the Mud Line Tubing Hanger (MLTH) at 150m below mud line. There are three sections considered for the outer string: the tension joint, the standard outer riser joint, and the lower Taper Stress Joint (LTSJ). This is a simplified version of a realistic outer string which also includes splash zone joints and pup joint (a joint of pipe of non-standard length, to make up a string to an exact required length) and considers marine growths at different water depth. The outer string is fixed to the surface wellhead and tree from the top, and fixed to the subsea wellhead just above the mud line. A four rod pull-up tensioner is considered in this example. The actual tensioner is not shown in the figure for clarity. Key Parameters of the TTR System Key parameters of the TTR system, including geometries and physical properties of different components, are summarized in Table 1. The pre-tension forces are the tensions applied on the outer and inner strings, respectively, during lock-off when the two strings are firmly connected on the top. The pre-tension is applied on the outer string for keeping it steady during installation. The pre-tension is applied on the inner string for reducing the compression resulted from the pressure and temperature increase during operation. For this example the inner string pre-tension is relatively large due to its high operating temperature and pressure.

Fig. 1 Riser Stack-up Overview (Normal Operating) Table 1 Key Parameters of the TTR System

Parameter Value Inner String Outer Diameter (mm, in) 228.6, 9 Inner Diameter (mm, in) 203.2, 8 Wt. Increase Due to Couplings etc. 3% Outer String Standard Outer Diameter (mm, in) 304.8, 12 Standard Inner Diameter (mm, in) 330.2, 13 Wt. Increase Due to Couplings etc. 10% Tension Joint OD (mm, in) 355.6, 14 TSJ Thick End OD (mm, in) 355.6, 14 Physical Properties Young’s Modulus (GPa) 207 Poisson’s Ratio 0.3 Steel Density (kg/m3) 7850 Thermal Expansion Coefficient (1/°C) 13E-6 Other Gravity Acceleration (m/s2) 9.81 Mass of Tree (kg) 10000 Tensioner Nominal Vertical Tension (kN, kips) 2035, 457 Outer Riser Pre-tension (kN, kips) 133, 30 Inner Riser Pre-tension (kN, kips) 1779, 400

Loading Conditions Five loading conditions are to be analyzed for the TTR system as given in Table 2. They cover some most typical extreme conditions that a production TTR sees in the life time. The scenarios where the riser is used for well work-over and completion are not considered. Note that the temperatures given in the table are the average temperature increases above the initial (ambient) temperature when the riser is installed. The load case of normal operating is the specified nominal condition. Dynamic analysis uses wave Hmax=20m and T=12s.

.

1000 m

Surface Wellhead and Tree

Tension Joint

Tensioner Rod

Outer Riser

Inner Riser

Taper Stress Joint 12.2 m

Conductor and Casing

Mud Line Tubing Hanger

0 m

-150 m

1030 m

1040 m

1050 m

Subsea Wellhead

Tensioner Ring

Table 2 TTR Loading Conditions

Load Case Parameter Inner String

Outer String

1. Normal Operating

Fluid Density (kg/m3) 350 70 Pressure (MPa) 21 7 Temperature Inc. (°C) 75 6

2. Shut-in Hot

Fluid Density (kg/m3) 350 70 Pressure (MPa) 35 7 Temperature Inc. (°C) 75 6

3. Shut-in Cold

Fluid Density (kg/m3) 300 80 Pressure (MPa) 28 7 Temperature Inc. (°C) 0 0

4. Shut-in Hot, Inner String Leak

Fluid Density (kg/m3) 350 70 Pressure (MPa) 35 35 Temperature Inc. (°C) 75 6

5. Shut-in Cold, Outer String Leak

Fluid Density (kg/m3) 300 1025 Pressure (MPa) 28 0 Temperature Inc. (°C) 0 0

The TTR geometry and tension variations are not only dependent on the current loads applied on the riser, but also dependent on the load history starting from installation. So the study must start from installation. As load conditions change, the TTR stack-up also evolves. The geometry shown in Fig. 1 is only valid for one chosen load condition. As the normal operating load condition is what the riser experiences in most of the life time, we choose it to be the nominal condition whose geometry meets Fig. 1. If the load condition changes, e.g., the well is shut-in and becomes cold (Case 3), the tension ring will move to a different elevation from 1040m. Following is a brief description of the load cases. Normal operating is the chosen nominal condition whose geometry matches Fig. 1. It has high pressure in the inner string and high temperatures that are 75°C above ambient. The inner string product is gas and the annulus uses nitrogen as insulation. If the well is shut-in, initially the inner string remains hot and the pressure is even higher. After an extended period of time, the temperature drops to ambient temperature with the pressure remains relatively high. Those are the two conditions covered by cases 2 and 3. Case 4 and Case 5 study two accidental conditions of Case 2 and Case 3, respectively. Case 4 considers the high pressure seen by the annulus if the inner string leaks. Case 5 considers the annulus flooded by sea water if the outer string leaks. The latter is not typically a design case as the outer string connectors are usually water proof. However, it will be interesting to observe the tension distribution changes among the two strings in that scenario. FINITE ELEMENT MODELING String Original Length and Apparent Length The most important consideration for modeling the pipe-in-pipe TTR is the original lengths of the strings. Original length is defined as the string length without any load that stretches it. A dry pipe lying horizontally on the deck is a good example, wherein the pipe has no axial elongation/contraction although gravity exists. Consider the inner string shown in Fig. 1, in this normal operating condition its apparent length is 1200m between the two end connections (MLTH and surface wellhead). However, that is not the original length as it is the resulting apparent length under a variety of loads. To achieve the apparent length of 1200m, the original length of this section should be 1198.41m, with 1.59m stretched by the loads. Similarly, the original length of the outer string is 1049.58m and not 1050m from mud line to surface wellhead. When 1200m and 1050m are used in the model, the resultant tension

ring elevation is found to be 1040.74m, or 0.74m higher than nominal. The consequences are much larger riser stroke and wrong tension distribution between the two strings. The original lengths of the two strings cannot be determined by the above finite element modeling result. On the contrary, they are the input of the model. If the finite element modeling predicts that the elongation will be 0.74m if 1200m and 1050m are used for the two strings, subtracting this elongation from the apparent lengths won’t give the correct original lengths. This is because the elongations of the two strings are different during the procedure from installation to the nominal condition. There are two variables to solve for (differences between original and apparent lengths for inner and outer strings) but we have only one equation (the combined elongation). The other equation is obtained from installation. The original lengths of the strings can be determined by using the formulae given in Part A of this paper (equations 12-14). In addition, the installation procedure has to be known. This is because the string length evolves from the start of installation. A simplified procedure for the purpose of the original length determination is as follows:

The outer string is installed and pre-tensioned (30kips); The inner string is installed and pre-tensioned (400kips); The two strings are connected at the top; The riser is operating with the design fluid, pressure, and

temperature, and nominal tension provided by the tensioner. The calculation of original lengths is as follows. Firstly, assume that the original lengths are equal to the apparent lengths. In this example, they are 1200m and 1050m for the inner string and outer string, respectively. Secondly, use the pipe-in-pipe expansion formulae given in Part A of this paper wherein all loads including weight, pressure, thermal, internal fluid weight, tension applied by tensioner, as well as the interaction between the two pipes are taken into account, and consider the above installation procedure, the elongations of each pipe can be obtained. They are 1.59m and 0.42m for the inner string and outer string, respectively, for this example. The details of calculating the pipe elongations are covered in Part A of this paper and are not repeated here. Finally, those elongations are subtracted from the apparent lengths to obtain the original lengths. As the subtracted lengths are small fractions of the apparent length, the second order effect is small and no iteration is needed. Model PIP Riser Using OrcaFlex The current version of OrcaFlex has the feature of modeling pipe-in-pipe risers. This is done by simply specifying string A is inside of string B. The locations of centralizers and associated stiffnesses can also be defined. Modeling pipe-in-pipe in OrcaFlex is convenient since it defines the component by its section length. The section length is defined as, from the OrcaFlex manual, “The un-stretched length of the section. This is the unstressed length (i.e. zero wall tension) at atmospheric pressure inside and out”. This is the same as the string original length concept that we discussed. Modeling pipe-in-pipe in the current version of OrcaFlex does need some extra effort because it does not consider the axial thermal expansion. However, this can be overcome by incorporating the thermal expansion length into the original length. For the example that we study, the thermal expansion lengths for the inner string and outer string are 1.17m and 0.08m if their temperatures increase 75°C and 6°C

above ambient temperature, respectively. The section lengths for the two strings are thus input into OrcaFlex as given in either of the last two rows of Table 3 depending on the cold or hot condition. Table 3 Section Length Inputs into OrcaFlex

Parameter Inner String Outer String

Original Length (m) 1198.41 1049.58 Temperature Increase Hot (°C) 75 6 Thermal Expansion Hot (m) 1.16 0.08 Input Section Length Cold (m) 1198.41 1049.58 Input Section Length Hot (m) 1199.57 1049.66

Model PIP Riser Using Flexcom Flexcom also has the feature of modeling pipe-in-pipe risers. This is done by simply specifying string A is inside of string B. The locations of centralizers and associated stiffnesses can also be defined. Flexcom allows the user to directly specify temperature variations and pipe thermal expansion coefficients. The software will calculate the axial thermal expansion automatically. There are two approaches to specify the string length in Flexcom, both of which define the original length. The first approach is to define the string as a cable of given length between two finite element nodes. Intermediate nodes can be defined as arc length distance from the start of the cable. This is similar to the way that OrcaFlex defines its components. The other approach is to directly define the coordinates of the finite element nodes. The distance between two nodes is taken as the element length and the original length. If this approach is taken caution must be used. This is because usually the coordinates of the nodes are defined according to the apparent locations when the string is already expanded. If this is the case, the original length can be achieved by converting the apparent length to original length using the thermal expansion/contraction correction. For the example that we study, inner string temperature is corrected for -102°C for 1200m to contract to 1198.41m. The temperature variations for the two strings are thus input into Flexcom as given in either of the last two rows of Table 4 depending on the cold or hot condition. Table 4 Temperature Inputs into Flexcom

Parameter Inner String Outer String

Temperature Increase Hot (°C) 75 6 Original Length (m) 1198.41 1049.58 Apparent Length (m) 1200.0 1050.0 Temperature Correction (°C) -102 -31 Input Temperature Cold (°C) -102 -31 Input Temperature Hot (°C) -27 -25

RESULTS WITH STATIC LOADS Results Comparison The static tension and expansion results for the pipe-in-pipe TTR are summarized in Table 5 for the five load cases defined in Table 2. The table compares the results obtained from three sources: theoretical solutions based on the pipe-in-pipe formulae developed in Part A of this paper, FEM results from OrcaFlex, and FEM results from Flexcom. The key parameter for the riser expansion is the riser stroke at tension ring. Effective tension forces are reported at control locations (MLTH, Mud Line, and Top at tension ring) and for separate strings and the combined riser (at Mud Line and Top at tension ring).

Table 5 Static Result Summary

Results Theoretical OrcaFlex Flexcom

Load Case 1 Riser Stroke (m) 0.000 0.001 0.001 To at Mud Line (kN) 660.0 668.3 668.8 To at Top (kN) 984.7 992.9 990.0 Ti at MLTH (kN) 11.3 1.6 3.3 Ti at Mud Line (kN) 126.2 116.4 118.0 Ti at Top (kN) 923.0 912.9 914.7 T at Mud Line (kN) 786.2 784.7 786.8 T at Top (kN) 1907.6 1905.8 1904.7

Load Case 2 Riser Stroke (m) 0.038 0.039 0.040 To at Mud Line (kN) 757.3 766.1 768.3 To at Top (kN) 1082.0 1090.7 1087 Ti at MLTH (kN) -113.0 -122.6 -119.1 Ti at Mud Line (kN) 1.9 -7.7 -4.4 Ti at Top (kN) 798.7 788.8 789.5 T at Mud Line (kN) 759.3 758.4 763.9 T at Top (kN) 1880.7 1879.5 1876.5

Load Case 3 Riser Stroke (m) -0.380 -0.380 -0.380 To at Mud Line (kN) -105.1 -97.9 -103.8 To at Top (kN) 227.0 233.7 227.4 Ti at MLTH (kN) 1106.5 1086.0 1098.0 Ti at Mud Line (kN) 1218.5 1198.0 1210.0 Ti at Top (kN) 1994.5 1972.8 1981.0 T at Mud Line (kN) 1113.4 1100.1 1106.2 T at Top (kN) 2221.6 2206.5 2208.4

Load Case 4 Riser Stroke (m) 0.114 0.115 0.115 To at Mud Line (kN) 132.9 141.4 143.1 To at Top (kN) 457.6 466.0 464.4 Ti at MLTH (kN) 460.2 450.2 453.1 Ti at Mud Line (kN) 575.1 565.1 567.9 Ti at Top (kN) 1371.9 1361.6 1364.0 T at Mud Line (kN) 708.0 706.5 711.0 T at Top (kN) 1829.5 1827.6 1828.4

Load Case 5 Riser Stroke (m) -0.413 -0.412 -0.413 To at Mud Line (kN) -463.3 -455.7 -459.6 To at Top (kN) 542.7 549.9 537.3 Ti at MLTH (kN) 1240.7 1234.2 1243.0 Ti at Mud Line (kN) 1300.1 1289.1 1300.0 Ti at Top (kN) 1711.5 1685.3 1699.0 T at Mud Line (kN) 836.7 833.4 840.4 T at Top (kN) 2254.2 2235.2 2236.3 Positive riser stroke defined as tension ring moves upward Ti: Effective Tension of Inner String To: Effective Tension of Outer String T: Combined Inner and Outer Effective Tension

It can be observed from Table 5 that both the riser tension and expansion results among the three sources are very close. The differences in expansion are typically within 1 millimeter with the maximum of 2 millimeters. The differences in effective tensions are typically within 10kN with the maximum of 26kN (1.5%). The following conclusions can be made based on the comparison between theoretical and finite element results:

The formulae developed in Part A of this paper can accurately predict the pipe-in-pipe TTR tension and expansion behavior in static conditions;

Both OrcaFlex and Flexcom are benchmarked against the theoretical solutions;

The original string lengths must be correctly input into the FEM software to obtain the real string behaviors.

Results Interpretation The normal operating load case (Case 1) is the riser nominal condition. All load variations will cause the stroke and tensions to change from the nominal condition. The stroke is 0 in this condition. The tension distributions of inner and outer strings are shown in Fig. 2. It is observed that the bottom of the inner string is close to zero tension despite the large pre-tension (1779kN, 400kips) applied to it during installation. This is because the high pressure and temperature cause the inner string to stretch, whereas this trend is constrained by the two ends at top and MLTH. On the other hand, the outer string has increased tension due to the stretch of the inner string. It is also interesting to observe that the weight per unit length of the inner string is heavier than that of the outer string. This is due to the low density of the annulus content which provides the inner string some low buoyancy and in the meantime low outer string weight. The inner string pressure increases from 21MPa to 35MPa (Case 2) when the well is shut-in. This causes the inner string to stretch and the riser to stroke. The riser strokes 0.038m from the nominal elevation. Again, the stretch of inner string is limited by the end constrains, which results in a decrease of inner string tension and an increase of outer string tension. The tension distributions are shown in Fig. 3. Compared with the normal operating tensions, it is observed that the inner string tension curve shifts to the left (decreasing) and the outer string tension curve shifts slightly to the right (increasing) by approximately 100kN in both cases. After the well is shut-in for an extended period of time, the temperature drops to ambient (Case 3). The control factor in this case is the thermal contraction of the inner string. In a free shrinkage scenario, the inner string would contract 1.16m due to its temperature drop. Due to the constraints of the outer string and tensioner (as well as the pressure change and outer string temperature drop), the inner string only expands 0.38m, as indicated by the calculated stroke. The contraction tendency of the inner string has the opposite effect compared with its elongation tendency. The inner string effective tension increases (approximately 1100kN) while the outer string tension decreases (approximately 750kN). This can be observed from Fig. 4. The combined tension increase is due to the effect of tensioner stiffness. Case 4 is an accidental scenario based on Case 2. The increased pressure leaking from the inner string to the annulus will stretch the outer string while contracting the inner string. The overall effect results in an increase in riser stroke of 0.114m. Due to the interaction between the inner and outer strings, as well as the constraint from the tensioner, the outer string tension decreases and the inner riser increases compared with the no-leak condition. The tension distributions are shown in Fig. 5.

Fig. 2 Tension Distribution (Normal Operating, Case 1)

Fig. 3 Tension Distribution (Shut-in, Hot, Case 2)

Fig. 4 Tension Distribution (Shut-in, Cold, Case 3) Case 5 is an accidental scenario based on Case 3. The heavy sea water leaking from the environment into the annulus causes the riser to stroke down 0.41m and the total tension from the tensioner increases. The tension distribution curves of the two strings are shown in Fig. 6 from

which two observations can be made. The changes in slopes of the curve indicate that the wet weights of the strings have changed. The wet weight of the inner string is lower as the heavier sea water replaces nitrogen in the annulus and provides more buoyancy. The wet weight of outer string is higher as sea water replaces the internal nitrogen. As a result of these weight changes, the inner string tends to contract and the outer string tends to elongate. These trends result in an increase in tension for the inner string and a reduction in outer string tension due to their constraints on each other. This phenomenon explains the second observation from Fig. 6 wherein approximately 450m (40%) of the outer riser is in compression.

Fig. 5 Tension Distribution (Shut-in, Hot, Inner String Leak, Case 4)

Fig. 6 Tension Distribution (Shut-in, Cold, Outer String Leak, Case 5) Despite the fact that either the inner string or the outer string is in compression in some of those load cases, the combined riser tension force is always positive, as given in Table 5, and shown in Fig. 2 through Fig. 6. This indicates that global buckling is not a concern for the riser. However, intervals of centralizers need to be calculated using the criteria of global and local buckling of individual strings and based on compressions and pressures. This calculation is outside of the scope of this paper. This paper focuses solely on the tension responses of the riser strings, with the riser centralized at each node along the strings. The responses of the tension rods are examined in terms of the relationship between length and tension force. The response of the

tensioner is examined in terms of the relationship between riser stroke and vertical tension force. These responses in all load conditions are captured in the curves depicted by Fig. 7 and Fig. 8.

Fig. 7 Tensioner Rod Responses for Static Load Conditions

Fig. 8 Tensioner Responses for Static Load Conditions RESULTS WITH DYNAMIC LOADS After the finite element model is correctly established by choosing accurate original lengths, the dynamic analyses of the riser can be carried out. These typically include extreme strength, vessel motion fatigue, and interference. This paper uses OrcaFlex to apply a harmonic wave of Hmax=20m and T=12s to the normal operation model to assess the tension and expansion responses of the strings. Vessel offset of 100m and set-down of 5m is assumed. The effective tension envelopes for the two strings are shown in Fig. 9. The variation range of the inner string is approximately 100kN and 180kN for the outer string. The difference between the two variations is due to the different stiffnesses of the two strings. As the strokes of the two strings are same and are solely caused by external tension from the tensioner, the tension variation is proportional to EA/L of the individual strings. The stroke responses are reported for different tensioner rods. Due to the directionality of wave load and vessel offset, the strokes of different

tensioner rods vary. The rod downstream of the wave elongates the most whereas the one upstream of the wave elongates the least. The elongation time histories of the four tensioner rods are shown in Fig. 10. The positive elongation indicates a riser down stroke. It is observed that the range of variation is the same for all the rods. The downstream rod has a maximum down stroke of 0.3m within which 0.12m is due to the vessel offset and set-down.

Fig. 9 Dynamic Tension Envelopes of the Two Strings

Fig. 10 Dynamic Tensioner Rod Stretch Time History

CONCLUSIONS This paper discusses some of the key considerations for modeling pipe-in-pipe risers using riser analysis finite element software OrcaFlex and Flexcom. The focus is capturing the tension and expansion responses for a tensioner supported TTR system. It is concluded that the riser original lengths are the most important factor for accurate riser tension and expansion analysis. These parameters can be determined by theoretical formulae developed in Part A of this paper. The two finite element models created using these parameters demonstrate very close agreement with each other and with the theoretical solution. In a pipe-in-pipe riser design including TTR, it is recommended that the theoretical formulae be used to 1), evaluate the tension distributions of all static loading conditions to optimize the pre-tensions; and 2), calculate the original lengths of all strings for correct FEM modeling. Note that the formulae and FEM modeling technique are applicable not only to pipe-in-pipe TTRs, but also to other pipe-in-pipe risers such as drilling riser, Free Standing Hybrid Riser (FSHR) and SCR. REFERENCES Bai, Y., and Bai, Q., (2005). Subsea Pipelines and Risers, Elsevier Chen, Q., Wang, L.Q., Chia, H.K., and Ngiam, A., (2009). “Thermal

Expansion Analysis of Pipe-In-Pipe System Having Multiple Bulkheads”, Proc ASME 28th Int Conf Ocean, Offshore and Arctic Eng., Honolulu, OMAE2009-80156.

Harrison, G., Kershenbaum, N., and Choi, H., (1997). “Expansion Analysis of Subsea Pipe-In-Pipe Flowline”, Proc 7th Int Offshore and Polar Eng Conf, Honolulu, ISOPE, Vol II, pp 293–298.

Harrison, R., and Helle, Y., (2007). “Understanding the Response of Pipe-In-Pipe Deepwater Riser Systems”, Proc 17th Int Offshore and Polar Eng Conf, Lisbon, ISOPE, pp 926–930.

Man, C.K., Yue, B., Szucs, A., and Thethi, R., (2013). “Tension and Expansion Analysis of Pipe-In-Pipe Risers: Part A, Theoretical Formulation”, Proc 23rd Int Offshore and Polar Eng Conf, Anchorage, ISOPE2013-TPC0839.

Masson, C., Fang, J., Jordan, D., and Hays, P.R., (2006). “Dynamic Analysis of Pipe-In-Pipe Steel Catenary Risers with Direct Modeling of Structure Interaction”, Offshore Technology Conf, Houston, OTC2006-18202.

Yettou, E., Derradji-Aouat, A., and Williams, C.D., (2008). “Fluid-Structure Interactions Modelling of Pipe-In-Pipe Riser Systems Operating in Ocean Environments”, National Research Council Canada, Institute for Ocean Technology, St. John's, NL, Canada