- Email: [email protected]
A coupled temperature–displacement model for predicting the long-term performance of offshore pipeline insulation systems
Journal of Materials Processing Technology 155–156 (2004) 1242–1246
A coupled temperature–displacement model for predicting the long-term performance of offshore pipeline insulation systems A.M. Harte a,∗ , D. Williams b , F. Grealish b a
Department of Civil Engineering, National University of Ireland, Galway, Ireland b MCS, Galway Technology Park, Parkmore, Galway, Ireland
Abstract Insulation systems for offshore oil and gas pipelines operate in aggressive environments over lifetimes of about 20 years. The effectiveness of the insulation over the entire lifetime is essential to provide flow assurance. Fluid temperatures must be kept high enough to ensure that waxes or hydrates do not form and result in pipeline blockages. The operating environment for offshore pipelines will become more severe with planned developments in 2000 m waters having well temperatures of up to 160 ◦ C. Insulation systems proposed for such deepwater wells are typically multilayered with foamed polymers providing most of the thermal resistance. The high hydrostatic pressures and well temperatures associated with deepwater wells can lead to a degradation of the thermal performance of foamed materials due to creep. The prediction of the long-term thermal behaviour is complex. The material characteristics of foams are dependent on the density, temperature and stress level, all of which change with time as the material creeps. This leads to a non-linear coupled thermal-structural response. This paper describes analytical models, which predict the system behaviour over time. These models have been implemented in a user-friendly design tool, named DISDANS. Good agreement is found between the model results and equivalent finite element models. © 2004 Elsevier B.V. All rights reserved. Keywords: Insulation; Foam; Pipeline; Creep
1. Introduction As oil and gas exploration moves into water depths of 2000 m and beyond, the flow assurance requirements become more stringent and thus the need for thermal insulation is increased. These deepwater developments usually consist of a number of wells with temperatures of up to 160 ◦ C, ‘tied back’ to the production platform by means of pipelines and risers. The pipelines associated with these deepwater developments can be up to 100 km in length. Control of the fluid temperature in these pipelines is essential for flow assurance purposes. When the temperature of the fluid drops below certain critical values, waxes or hydrates precipitate out the fluid. These solids can form a coating on the inside of the pipe that builds up over a period of time and causes an obstruction to the flow. Coated insulation systems have been used on existing pipelines in water depths of up to 1000 m. For wells at greater depths, new insulation products are required that are capa-
ble of withstanding the high water pressure together with the thermal gradient due to the difference in temperature between the production fluid and the external environment. In addition, the long-term behaviour of the system becomes increasingly important as creep rates increase significantly at higher stress levels. This can result in levels of densification of the insulation that reduce the thermal performance of the system. This paper describes an analytical design tool, which can be used to predict the short and long-term thermal and mechanical response of multi-layered insulation systems. The analytical models are implemented in a user-friendly software tool, called DISDANS [1]. This tool allows the user to vary layer materials and thicknesses to achieve an optimum configuration. The work described was carried out as part of the DeFRIS (Deep-water Flowline and Riser Insulation Systems) Joint Industry Project funded by the European Union.
2. Insulation system description ∗
Corresponding author. E-mail addresses: [email protected] (A.M. Harte), [email protected] (D. Williams). 0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.288
Multi-layered coating systems incorporating polymer foams have been found to provide a cost-effective solution
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246
Outer PP Shield Outer Foam Layer Solid PP Layer Inner Foam Layer Inner Solid PP Layer Adhesive and FBE Steel Pipe
Fig. 1. Typical 7-layer insulation system.
to the insulation of offshore pipelines. These systems have typically five or seven layers, depending on the water depth. A cross-section through a 7-layer system, incorporating polypropylene (PP) foam and solid layers is shown in Fig. 1. The foam layers provide the main thermal resistance of the system. These foam layers may have different densities and may incorporate reinforcement. The other layers have varied functions. The outer solid PP shield layer provides impact resistance and prevents water ingress to the foam layers. The internal solid PP layers are used as a thermal barrier to the inner foam layer and as a transition between the different foam layers. The inner fusion bonded epoxy layer, which forms a corrosion barrier for the steel pipe, and the adhesive layer are assumed to provide negligible contribution to the thermal and structural capacity of the system. Five-layer systems are used in shallower waters. These have a similar configuration to the 7-layer system but with one of the foam and solid PP layers removed. The design of these insulation systems for deepwater applications is complicated by the fact that the thermal and structural response is coupled. The material behaviour of the foam layer is a function of the current temperature, stress and density, which may change over time due to material creep. A complete understanding of the long-term behaviour of such materials is fundamental to the proper design of insulation systems for these critical applications.
3. Material characteristics of polymer foams The thermal conductivity of polymer foams increases with foam density. In order to optimise the insulation performance, therefore, the density of the foam should be minimised. The structural performance of foams, on the other hand, improves with increasing density. Compression of foam due to pressure loading results in an increase in foam density. This densification can be significant, particularly for low-density foams and at elevated temperatures. In addition to the short-term compression due to the pressure of immersion, polymer foams have a tendency to creep. The creep rate is influenced by the foam density, the stress level and the temperature. Lower creep rates are associated with
1243
higher foam densities. The creep rate increases significantly as the stress level and temperature increase. In order to characterise the short and long-term thermal and structural response of a foam-based insulation system, a significant programme of testing is required. Thermal conductivity tests must be carried out over a range of densities and temperatures. Short-term compression and creep testing must be performed for a range of densities over the range of temperatures and stresses, which will be experienced in service. For this project, thermal conductivity tests on foam specimens were carried out over a range of temperatures using the guarded hot plate method. The thermal conductivity was found to increase linearly with density at each temperature. Creep testing was carried out using a new triaxial compression test rig developed by Thermotite and SINTEF [2]. Specimens of polypropylene foam with densities varying from 650 to 760 kg/m3 were subjected to creep tests over a range of temperatures between 20 ◦ C and 60 ◦ C and at stress levels ranging from 8 to 12 MPa. In all cases, the creep response was found to follow Findley’s power law [3], which may be expressed as εcr = ktn
(1)
where εcr is the creep strain and t is the time interval over which the system is loaded. The exponent n is a material constant that depends on the temperature and the density of the material. The parameter k is a function of the stress level, the temperature and the foam density and may be expressed in the following power law form: k = Aσ m
(2)
where A and m are functions of temperature and density.
4. Description of design tool An empirical based software tool, DISDANS (Deepwater Insulation Systems-Design and Analysis), has been developed to facilitate the design and optimisation of layered insulation systems. Analytical models of the thermal, elastic and creep behaviour are implemented in the software. The tool predicts the system U-value, temperature distribution, short and long-term deformations and stresses. Other features of the model including water ingress and cool-down calculations and fluid exit temperatures calculations are described in [1,4]. Insulation system performance is usually described in terms of the overall heat transfer coefficient or U-value. Using a classical heat transfer approach [5], system U-values are found using Eq. (3) U=
(1/ hinner ) + r1
1 i=1 (1/ki ) ln(ri+1 /ri ) + (r1 /rn )(1/ houter ) (3)
n
1244
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246
where ki , ri and ri+1 are the thermal conductivity and inner and outer radii of layer i; hinner and houter are the convection heat transfer coefficients for the internal and external surfaces, respectively. The temperature distribution and density distribution of the system are required in order to determine the correct k value for each layer. This information is generated by the thermo-mechanical analysis, which provides the temperature distribution, radial displacement and stress distribution over the system lifetime. U-values are calculated prior to immersion (‘dry’ U-value), after installation (‘wet’ U-value) and after 20 years creep. The ‘dry’ U-value is calculated using the k values at 25 ◦ C and using the undeformed system dimensions. In order to determine the ‘wet’ U-value, a steady state temperature–displacement analysis is performed, which determines the temperature distribution and radial displacement due to the pressure of immersion and the temperature gradient between the production fluid and the surroundings. This is an iterative process whereby the steady-state temperature distribution is found and then the elastic system deformation is determined. The radial displacement u of a single layer of the system due to pressure and thermal loading is derived using the classical thick tube theory [6] and may be expressed as: 1+ν1 r A2 u= αTr dr + A1 r + (4) 1 − ν r ri r where T is the temperature distribution in the layer and α and ν are the thermal expansion coefficient and Poisson’s ratio for the material, respectively. A1 and A2 are constants, which are found by considering compatibility of radial displacement and stress at inter-layer boundaries. This radial displacement leads to a densification of the foam layers. The system material properties are updated to account for the densification and the analysis is repeated until convergence occurs. The procedure for determining the 20-year U-value is illustrated by the flow chart given in Fig. 2. The time span is subdivided into a number of time steps at each of which the equilibrium temperature–displacement distribution must be determined in a similar manner to that described above. In addition to the displacement due to the pressure loading and temperature gradient, the radial displacement increment due to creep of the foam layer is included.
Apply Temperature Loading Get Temperature Distribution in System Apply Structural Loading Get Resultant Deformation of System Get Resultant Temperature Distribution in System
No
Equilibrium conditions reached Yes
t = t @ end of life
No Increase time increment, t = t + ∆t ∆t=∆t/2
Calculate Creep Strain
No
Creep Strain εCr > 0.5% Yes
End
Fig. 2. Flowchart for thermo-mechanical analysis.
Results of the DISDANS analytical models are compared with those of equivalent finite element models generated using the ANSYS software package. A two-dimensional axisymmetric finite element model of the insulated pipe Table 1 Insulation system—material properties Material property
Steel
5. Software tool application The software tool is used to analyse a 7-layer insulation system for a 250 mm steel pipe in a water depth of 2500 m. The fluid temperature is 60 ◦ C while that of the surrounding seawater is 4 ◦ C. Details of the material characteristics of the different layers are given in Table 1. For the purpose of the analysis, the FBE and adhesive layers are ignored. The dimensions of the remaining five layers are given in Table 2.
Yes
Compressive modulus (MPa) Poisson’s ratio Density (kg/m3 ) Thermal expansion coefficient (×10−6 ◦ C−1 ) Thermal conductivity (W/m K)
Foamed PP
2.0E+5 600 0.27 7900 8.9
50
Syntactic PP
Solid PP
600
1200
0.35 750 150
0.45 800 150
0.18
0.17
0.4 900 100
0.22
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246 Table 2 Insulation system—layer dimensions
Table 3 System U-value
Layer
Thickness mm Material
1245
1
2
3
4
5
10
30
4
52
4
Solid PP
Syntactic PP
Solid PP
Foamed PP
Solid PP
Initial ‘dry’ U-value (W/m2 K)
Initial ‘wet’ U-value (W/m2 K)
U-value after 20 years (W/m2 K)
3.05
3.21
3.40
DISDANS analytical model and the FE models for both temperature and axial displacement. Results for the 20-year radial creep displacement are given in Fig. 5 and the elastic displacements are also shown. It was not possible to carry out finite element modelling of the creep process, as ANSYS does not have a compressible creep model to replicate the foam behaviour. The variation in system U-value over time is shown in Table 3. Prior to immersion, the ‘dry’ U-value is
was generated. The element type used was a coupled temperature–displacement element PLANE13. Plane strain conditions were assumed. Convection effects were applied to the inner and outer surfaces. Pressure loading was also applied to these surfaces. The results of the elastic thermo-structural analysis for this system are shown in Figs. 3 and 4. Excellent agreement is found between the
Radial Temperature Distribution - FE Results vs. Analytical Results 340 330
Temperature (K)
320
Analytical Results FE Results
310 300 290 280 270 0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.25
Radius (m)
Fig. 3. Radial temperature distribution—comparison of FE and analytical results. Radial Displacement - FE Results vs. Analytical Results 0.00E+00 0.11150
0.13150
0.15150
0.17150
0.19150
0.21150
0.23150
Deformation (m)
-5.00E-04
-1.00E-03
-1.50E-03
Analytical Results FE Results
-2.00E-03
-2.50E-03
Radius (m)
Fig. 4. Radial deformation—comparison of FE and analytical results.
0.25150
1246
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246 Elastic Deformation vs. Creep Deformation 5.00E-04
Deformation (m)
0.00E+00 0.11150 -5.00E-04
0.13150
0.15150
0.17150
0.19150
0.21150
0.23150
0.25150
-1.00E-03 -1.50E-03 -2.00E-03
Elastic Deformations Creep Deformations
-2.50E-03 -3.00E-03 -3.50E-03 -4.00E-03 -4.50E-03
Radius (m)
Fig. 5. Initial elastic radial deformation vs. 20 year creep deformation.
3.05 W/m2 K. After installation, the U-value increases to 3.21 W/m2 K due to the densification of the foam layers and increases further to 3.40 W/m2 K after 20 years creep. These values represent increases of 5 and 11%, respectively, on the ‘dry’ U-values. Full-scale laboratory tests on coated pipelines are being carried out as part of the DeFRIS project. The results of this test program will be used to validate both the short and long-term modelling of the insulation system.
6. Conclusions An analytical design tool for the design of multi-layered insulation systems based on polymer foams has been developed. This tool incorporates material models, which allow for the variation in material properties with density, temperature and stress level. This tool allows the designer to predict both the short and long-term coupled thermal structural response of the insulation system. A range of different design configurations can be quickly generated in order to determine the optimum design. Significant savings in analysis time may be achieved compared to finite element based models. Comparison of the model results with equivalent finite element models has shown excellent agreement. Further validation of the model will take place when the current full-scale laboratory test results become available.
Acknowledgements This work was carried out as part of a Joint Industry Project funded by the EU. The contributions of the DeFRIS JIP members (Borealis, MCS, MERL, Technip-Coflexip and Thermotite) to the development of the software tool are acknowledged. References [1] D. Williams, An analytical tool for the design and analysis of thermal insulation systems for risers and subsea flowlines, M.Eng.Sc. Thesis, National University of Ireland, Galway, 2002. [2] A.B. Hansen, R. Friberg, Thermal insulation of non-jacketed deepwater flowlines and risers based on mobile manufacturing units, in: Proceedings of the Rio Oil and Gas Expo and Conference, IBP41900, Brazil, October 2000. [3] W.N. Findley, Combined stress creep of non-linear viscoelastic material, in: A.I. Smith, A.M. Nicolson (Eds.), Advances in Creep Design, The A.E. Johnson Memorial Volume, Applied Science Publishers Ltd., London, 1971. [4] A. Harte, D. Williams, F. Grealish, Short and long-term performance of polymer foam insulation systems in deepwater offshore applications, in: K. Drechsler (Ed.), Advanced Composites: The Balance between Performance and Cost, Proceedings of the 24th International SAMPE Europe Conference of the Society for the Advancement of Materials and Process Engineering, Paris, 2003, pp. 515–523. [5] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, 4th ed., Wiley, 1996. [6] S. Timoshenko, Strength of Materials, Part II, 3rd ed., Van Nostrand Reinhold, New Jersey, 1956.
A coupled temperature–displacement model for predicting the long-term performance of offshore pipeline insulation systems A.M. Harte a,∗ , D. Williams b , F. Grealish b a
Department of Civil Engineering, National University of Ireland, Galway, Ireland b MCS, Galway Technology Park, Parkmore, Galway, Ireland
Abstract Insulation systems for offshore oil and gas pipelines operate in aggressive environments over lifetimes of about 20 years. The effectiveness of the insulation over the entire lifetime is essential to provide flow assurance. Fluid temperatures must be kept high enough to ensure that waxes or hydrates do not form and result in pipeline blockages. The operating environment for offshore pipelines will become more severe with planned developments in 2000 m waters having well temperatures of up to 160 ◦ C. Insulation systems proposed for such deepwater wells are typically multilayered with foamed polymers providing most of the thermal resistance. The high hydrostatic pressures and well temperatures associated with deepwater wells can lead to a degradation of the thermal performance of foamed materials due to creep. The prediction of the long-term thermal behaviour is complex. The material characteristics of foams are dependent on the density, temperature and stress level, all of which change with time as the material creeps. This leads to a non-linear coupled thermal-structural response. This paper describes analytical models, which predict the system behaviour over time. These models have been implemented in a user-friendly design tool, named DISDANS. Good agreement is found between the model results and equivalent finite element models. © 2004 Elsevier B.V. All rights reserved. Keywords: Insulation; Foam; Pipeline; Creep
1. Introduction As oil and gas exploration moves into water depths of 2000 m and beyond, the flow assurance requirements become more stringent and thus the need for thermal insulation is increased. These deepwater developments usually consist of a number of wells with temperatures of up to 160 ◦ C, ‘tied back’ to the production platform by means of pipelines and risers. The pipelines associated with these deepwater developments can be up to 100 km in length. Control of the fluid temperature in these pipelines is essential for flow assurance purposes. When the temperature of the fluid drops below certain critical values, waxes or hydrates precipitate out the fluid. These solids can form a coating on the inside of the pipe that builds up over a period of time and causes an obstruction to the flow. Coated insulation systems have been used on existing pipelines in water depths of up to 1000 m. For wells at greater depths, new insulation products are required that are capa-
ble of withstanding the high water pressure together with the thermal gradient due to the difference in temperature between the production fluid and the external environment. In addition, the long-term behaviour of the system becomes increasingly important as creep rates increase significantly at higher stress levels. This can result in levels of densification of the insulation that reduce the thermal performance of the system. This paper describes an analytical design tool, which can be used to predict the short and long-term thermal and mechanical response of multi-layered insulation systems. The analytical models are implemented in a user-friendly software tool, called DISDANS [1]. This tool allows the user to vary layer materials and thicknesses to achieve an optimum configuration. The work described was carried out as part of the DeFRIS (Deep-water Flowline and Riser Insulation Systems) Joint Industry Project funded by the European Union.
2. Insulation system description ∗
Corresponding author. E-mail addresses: [email protected] (A.M. Harte), [email protected] (D. Williams). 0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.288
Multi-layered coating systems incorporating polymer foams have been found to provide a cost-effective solution
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246
Outer PP Shield Outer Foam Layer Solid PP Layer Inner Foam Layer Inner Solid PP Layer Adhesive and FBE Steel Pipe
Fig. 1. Typical 7-layer insulation system.
to the insulation of offshore pipelines. These systems have typically five or seven layers, depending on the water depth. A cross-section through a 7-layer system, incorporating polypropylene (PP) foam and solid layers is shown in Fig. 1. The foam layers provide the main thermal resistance of the system. These foam layers may have different densities and may incorporate reinforcement. The other layers have varied functions. The outer solid PP shield layer provides impact resistance and prevents water ingress to the foam layers. The internal solid PP layers are used as a thermal barrier to the inner foam layer and as a transition between the different foam layers. The inner fusion bonded epoxy layer, which forms a corrosion barrier for the steel pipe, and the adhesive layer are assumed to provide negligible contribution to the thermal and structural capacity of the system. Five-layer systems are used in shallower waters. These have a similar configuration to the 7-layer system but with one of the foam and solid PP layers removed. The design of these insulation systems for deepwater applications is complicated by the fact that the thermal and structural response is coupled. The material behaviour of the foam layer is a function of the current temperature, stress and density, which may change over time due to material creep. A complete understanding of the long-term behaviour of such materials is fundamental to the proper design of insulation systems for these critical applications.
3. Material characteristics of polymer foams The thermal conductivity of polymer foams increases with foam density. In order to optimise the insulation performance, therefore, the density of the foam should be minimised. The structural performance of foams, on the other hand, improves with increasing density. Compression of foam due to pressure loading results in an increase in foam density. This densification can be significant, particularly for low-density foams and at elevated temperatures. In addition to the short-term compression due to the pressure of immersion, polymer foams have a tendency to creep. The creep rate is influenced by the foam density, the stress level and the temperature. Lower creep rates are associated with
1243
higher foam densities. The creep rate increases significantly as the stress level and temperature increase. In order to characterise the short and long-term thermal and structural response of a foam-based insulation system, a significant programme of testing is required. Thermal conductivity tests must be carried out over a range of densities and temperatures. Short-term compression and creep testing must be performed for a range of densities over the range of temperatures and stresses, which will be experienced in service. For this project, thermal conductivity tests on foam specimens were carried out over a range of temperatures using the guarded hot plate method. The thermal conductivity was found to increase linearly with density at each temperature. Creep testing was carried out using a new triaxial compression test rig developed by Thermotite and SINTEF [2]. Specimens of polypropylene foam with densities varying from 650 to 760 kg/m3 were subjected to creep tests over a range of temperatures between 20 ◦ C and 60 ◦ C and at stress levels ranging from 8 to 12 MPa. In all cases, the creep response was found to follow Findley’s power law [3], which may be expressed as εcr = ktn
(1)
where εcr is the creep strain and t is the time interval over which the system is loaded. The exponent n is a material constant that depends on the temperature and the density of the material. The parameter k is a function of the stress level, the temperature and the foam density and may be expressed in the following power law form: k = Aσ m
(2)
where A and m are functions of temperature and density.
4. Description of design tool An empirical based software tool, DISDANS (Deepwater Insulation Systems-Design and Analysis), has been developed to facilitate the design and optimisation of layered insulation systems. Analytical models of the thermal, elastic and creep behaviour are implemented in the software. The tool predicts the system U-value, temperature distribution, short and long-term deformations and stresses. Other features of the model including water ingress and cool-down calculations and fluid exit temperatures calculations are described in [1,4]. Insulation system performance is usually described in terms of the overall heat transfer coefficient or U-value. Using a classical heat transfer approach [5], system U-values are found using Eq. (3) U=
(1/ hinner ) + r1
1 i=1 (1/ki ) ln(ri+1 /ri ) + (r1 /rn )(1/ houter ) (3)
n
1244
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246
where ki , ri and ri+1 are the thermal conductivity and inner and outer radii of layer i; hinner and houter are the convection heat transfer coefficients for the internal and external surfaces, respectively. The temperature distribution and density distribution of the system are required in order to determine the correct k value for each layer. This information is generated by the thermo-mechanical analysis, which provides the temperature distribution, radial displacement and stress distribution over the system lifetime. U-values are calculated prior to immersion (‘dry’ U-value), after installation (‘wet’ U-value) and after 20 years creep. The ‘dry’ U-value is calculated using the k values at 25 ◦ C and using the undeformed system dimensions. In order to determine the ‘wet’ U-value, a steady state temperature–displacement analysis is performed, which determines the temperature distribution and radial displacement due to the pressure of immersion and the temperature gradient between the production fluid and the surroundings. This is an iterative process whereby the steady-state temperature distribution is found and then the elastic system deformation is determined. The radial displacement u of a single layer of the system due to pressure and thermal loading is derived using the classical thick tube theory [6] and may be expressed as: 1+ν1 r A2 u= αTr dr + A1 r + (4) 1 − ν r ri r where T is the temperature distribution in the layer and α and ν are the thermal expansion coefficient and Poisson’s ratio for the material, respectively. A1 and A2 are constants, which are found by considering compatibility of radial displacement and stress at inter-layer boundaries. This radial displacement leads to a densification of the foam layers. The system material properties are updated to account for the densification and the analysis is repeated until convergence occurs. The procedure for determining the 20-year U-value is illustrated by the flow chart given in Fig. 2. The time span is subdivided into a number of time steps at each of which the equilibrium temperature–displacement distribution must be determined in a similar manner to that described above. In addition to the displacement due to the pressure loading and temperature gradient, the radial displacement increment due to creep of the foam layer is included.
Apply Temperature Loading Get Temperature Distribution in System Apply Structural Loading Get Resultant Deformation of System Get Resultant Temperature Distribution in System
No
Equilibrium conditions reached Yes
t = t @ end of life
No Increase time increment, t = t + ∆t ∆t=∆t/2
Calculate Creep Strain
No
Creep Strain εCr > 0.5% Yes
End
Fig. 2. Flowchart for thermo-mechanical analysis.
Results of the DISDANS analytical models are compared with those of equivalent finite element models generated using the ANSYS software package. A two-dimensional axisymmetric finite element model of the insulated pipe Table 1 Insulation system—material properties Material property
Steel
5. Software tool application The software tool is used to analyse a 7-layer insulation system for a 250 mm steel pipe in a water depth of 2500 m. The fluid temperature is 60 ◦ C while that of the surrounding seawater is 4 ◦ C. Details of the material characteristics of the different layers are given in Table 1. For the purpose of the analysis, the FBE and adhesive layers are ignored. The dimensions of the remaining five layers are given in Table 2.
Yes
Compressive modulus (MPa) Poisson’s ratio Density (kg/m3 ) Thermal expansion coefficient (×10−6 ◦ C−1 ) Thermal conductivity (W/m K)
Foamed PP
2.0E+5 600 0.27 7900 8.9
50
Syntactic PP
Solid PP
600
1200
0.35 750 150
0.45 800 150
0.18
0.17
0.4 900 100
0.22
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246 Table 2 Insulation system—layer dimensions
Table 3 System U-value
Layer
Thickness mm Material
1245
1
2
3
4
5
10
30
4
52
4
Solid PP
Syntactic PP
Solid PP
Foamed PP
Solid PP
Initial ‘dry’ U-value (W/m2 K)
Initial ‘wet’ U-value (W/m2 K)
U-value after 20 years (W/m2 K)
3.05
3.21
3.40
DISDANS analytical model and the FE models for both temperature and axial displacement. Results for the 20-year radial creep displacement are given in Fig. 5 and the elastic displacements are also shown. It was not possible to carry out finite element modelling of the creep process, as ANSYS does not have a compressible creep model to replicate the foam behaviour. The variation in system U-value over time is shown in Table 3. Prior to immersion, the ‘dry’ U-value is
was generated. The element type used was a coupled temperature–displacement element PLANE13. Plane strain conditions were assumed. Convection effects were applied to the inner and outer surfaces. Pressure loading was also applied to these surfaces. The results of the elastic thermo-structural analysis for this system are shown in Figs. 3 and 4. Excellent agreement is found between the
Radial Temperature Distribution - FE Results vs. Analytical Results 340 330
Temperature (K)
320
Analytical Results FE Results
310 300 290 280 270 0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.25
Radius (m)
Fig. 3. Radial temperature distribution—comparison of FE and analytical results. Radial Displacement - FE Results vs. Analytical Results 0.00E+00 0.11150
0.13150
0.15150
0.17150
0.19150
0.21150
0.23150
Deformation (m)
-5.00E-04
-1.00E-03
-1.50E-03
Analytical Results FE Results
-2.00E-03
-2.50E-03
Radius (m)
Fig. 4. Radial deformation—comparison of FE and analytical results.
0.25150
1246
A.M. Harte et al. / Journal of Materials Processing Technology 155–156 (2004) 1242–1246 Elastic Deformation vs. Creep Deformation 5.00E-04
Deformation (m)
0.00E+00 0.11150 -5.00E-04
0.13150
0.15150
0.17150
0.19150
0.21150
0.23150
0.25150
-1.00E-03 -1.50E-03 -2.00E-03
Elastic Deformations Creep Deformations
-2.50E-03 -3.00E-03 -3.50E-03 -4.00E-03 -4.50E-03
Radius (m)
Fig. 5. Initial elastic radial deformation vs. 20 year creep deformation.
3.05 W/m2 K. After installation, the U-value increases to 3.21 W/m2 K due to the densification of the foam layers and increases further to 3.40 W/m2 K after 20 years creep. These values represent increases of 5 and 11%, respectively, on the ‘dry’ U-values. Full-scale laboratory tests on coated pipelines are being carried out as part of the DeFRIS project. The results of this test program will be used to validate both the short and long-term modelling of the insulation system.
6. Conclusions An analytical design tool for the design of multi-layered insulation systems based on polymer foams has been developed. This tool incorporates material models, which allow for the variation in material properties with density, temperature and stress level. This tool allows the designer to predict both the short and long-term coupled thermal structural response of the insulation system. A range of different design configurations can be quickly generated in order to determine the optimum design. Significant savings in analysis time may be achieved compared to finite element based models. Comparison of the model results with equivalent finite element models has shown excellent agreement. Further validation of the model will take place when the current full-scale laboratory test results become available.
Acknowledgements This work was carried out as part of a Joint Industry Project funded by the EU. The contributions of the DeFRIS JIP members (Borealis, MCS, MERL, Technip-Coflexip and Thermotite) to the development of the software tool are acknowledged. References [1] D. Williams, An analytical tool for the design and analysis of thermal insulation systems for risers and subsea flowlines, M.Eng.Sc. Thesis, National University of Ireland, Galway, 2002. [2] A.B. Hansen, R. Friberg, Thermal insulation of non-jacketed deepwater flowlines and risers based on mobile manufacturing units, in: Proceedings of the Rio Oil and Gas Expo and Conference, IBP41900, Brazil, October 2000. [3] W.N. Findley, Combined stress creep of non-linear viscoelastic material, in: A.I. Smith, A.M. Nicolson (Eds.), Advances in Creep Design, The A.E. Johnson Memorial Volume, Applied Science Publishers Ltd., London, 1971. [4] A. Harte, D. Williams, F. Grealish, Short and long-term performance of polymer foam insulation systems in deepwater offshore applications, in: K. Drechsler (Ed.), Advanced Composites: The Balance between Performance and Cost, Proceedings of the 24th International SAMPE Europe Conference of the Society for the Advancement of Materials and Process Engineering, Paris, 2003, pp. 515–523. [5] F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, 4th ed., Wiley, 1996. [6] S. Timoshenko, Strength of Materials, Part II, 3rd ed., Van Nostrand Reinhold, New Jersey, 1956.