Sandwich pipes composed of two steel layers separated by a polypropylene annular can be used for deepwater oil&gas transportation. They combine high structural strength to resist external pressure with thermal insulation to prevent blockage by paraffin and hydrate.
In this work, experimental tests and numerical models were employed to verify the influence of the inter-layer adhesion on the ultimate strength under external pressure and longitudinal bending of a sandwich pipe prototype. The maximum shear stress obtained from sandwich pipe specimens bonded with a specific adhesive indicated the adhesion levels to be adopted in the numerical simulations. Two contact models were employed to simulate the bonding and slipping conditions between layers, one adopting a friction model and the other including non-linear springs between metal and polymer nodes. The latter is an adapted solution to simulate both tension and shear loads. As expected for a sandwich structure, the structural strength is strongly dependent on the interface stickiness. The analyzed geometry is able to withstand a water depth up to 3,000 meters with a bonding strength corresponding to only 10% of the idealized perfect adhesion condition.
INTRODUCTION
Sandwich Pipe (SP) is composed of two concentrically mounted steel pipes with polypropylene in the annular. Great structural strength combined with adequate flow assurance can be obtained because the sandwich structure is a particular kind of composite characterized by the combination of different materials bonded together, contributing with their single properties to the global structure performance. Usually, the sandwich structure is divided in three layers: two external thin and stiff and a central thick and flexible. The external layers are bonded to the core to allow the load transfer between the components. Numerical and experimental studies have been carried out to obtain data about the mechanical behavior of this type of structure not very well understood so far, as presented by Borselino et.al. [2] for sandwich structures employing
polymers and glass fiber and Sokolinsky et.al. [3], for panel buckling under compressive loading with completely or partially bonded central layer. Sandwich structures, i.e. light and stiff panels, have been employed in the naval industry mainly, searching the advantages associated with weight reduction, fuel economy, stability during navigation and corrosion resistance, as mentioned by Mouring [4]. Several multilayered applications are available for thermal insulation purposes including submarine pipelines and equipment in the offshore industry, but the benefit of the structural performance of sandwich structures has not been yet pursued for deepwater pipelines and risers, as it is the case of the present work.
Numerical and experimental studies carried out by Estefen et al. [5] for the ultimate strength under combined external pressure and bending indicated that SP are viable for application in water depths up to 3,000 meters. Inter-layer contact behavior, i.e. the degree of adhesion, was observed to have significant influence on the collapse pressure. Among the advantages compared with single wall pipe, it was noted a substantial higher bending capacity for equivalent external pressure with similar steel weight and less submerged weight. Structural strength is also strongly affected by the material of the annular layer. Polypropylene was adopted in the present work due to reasonable low cost, good mechanical properties and relatively low thermal conductivity. In fact, the choice of the annular material for the SP is a compromise between strength and thermal insulation.
External coating with low thermal conductivity materials, i.e. polyurethane foam, is widely employed in submarine pipelines. It can be applied in multilayer with different density polymers to combine single properties as thermal, mechanical, chemical and corrosion protection. However, the external pressure imposed by the water depth limits the application of polymeric foams to certain depth and the use of PIP systems become necessary if the thermal insulation is an essential requirement. SP insulation capacity is dependent on the polymer thickness and thermal conductivity. The solid polypropylene, employed in this study, has lower insulation capacity than other polymer foams, but it has relatively good mechanical strength. Glass bubbles can be added to the
polymer structure to lower the thermal conductivity without affecting significantly its mechanical properties, converting it to a syntactic polymer. Moreover, for applications that require higher insulation, active heating system using electrical wires, associated with passive insulation provided by the annular material can be adopted, as proposed by Su Jian et al. [6][7]. The study of the heat transfer in transient flow for a deepwater scenario indicates the need of certain amount of heating input to avoid line blockage in case of either production interruption or long distance tieback, specially for heavy oil (low API grade).
In this work, numerical modeling of the ultimate strength for combined external pressure and longitudinal bending was performed for the sandwich pipe with geometric properties indicated in Table 1. Prototypes with similar geometries, at present under construction, will be used for laboratorial tests. The numerical models incorporate special contact features to simulate the adhesion effects. Experimental tests with sandwich pipe segments were conducted to evaluate the adhesive bonding capacity and to correlate the results with those from numerical simulations. The numerical results showed strong influence of the adhesion degree between polypropylene annular and steel outer pipe on the sandwich pipe ultimate strength. Reduction of the idealized perfect bonding condition to 10% of its full adhesion capacity resulted in a SP collapse pressure well beyond 3,000 meters of water depth.
NUMERICAL MODEL FOR COMBINED LOADING
Structural analyses were performed employing the finite element program ABAQUS [8], including initial ovality and both longitudinal and transversal symmetry conditions. Figure 1 shows the ring model used for the ultimate strength analyses, where one solid element is considered for each metal layer and two solid elements for the polymer annular through the sandwich pipe thickness. The element longitudinal size defines the model length. The symmetry conditions applied to the X-Y and Y-Z planes are the displacement node constraints in the respective normal directions.
Figure 1: Finite element mesh for the sandwich pipe
idealized as a ring model Table 1 presents the geometric properties of the analyzed
sandwich pipe, where Dn is the nominal diameter, t is the considered layer thickness and Ri and Re are inner and outer radius, respectively. The steel pipes were selected according to
API 5L standard. Geometry was determined based on pipe availability at the fabrication site and laboratory maximum pressure vessel capacity of 50 MPa, considering that the research program includes prototype experimental tests.
Table 1: Geometrical properties of the sandwich pipe
Dn (in) Ri (mm) Re (mm) t (mm) 6 5/8 77.75 84.15 6.4
Annular 84.15 103.15 19 8 5/8 103.15 109.55 6.4
Initial ovality ( 0∆ ) given by the expression below was
assumed as 1% for the mesh sensitivity analyses and 0.2% for the ultimate strength results, where and are maximum and minimum diameters, respectively.
maxD minD
minmax
minmax0 DD
DD+−
=∆ . (1)
Smaller diameter along the pipe length is coincident with the bending plane in order to generate lower bound results for the ultimate strength. For both external pressure and bending acting independently, Riks method and automatic increment control have been employed, respectively. Combined loading was initially implemented by fixed increments of external pressure followed by incremental rotations until buckling failure has been achieved. The external pressure is applied through surface load on the outer pipe. The bending was induced by the use of a reference node located at the neutral axis, where the angular displacement around z axis is applied. Automatically generated kinematic coupling equations are used to link the degrees of freedom of the nodes of the transverse plane to the reference node. It is assumed that this plane remains flat and normal to the neutral axis during loading. Additionally, the coupling of x degree of freedom induces a plane strain state for the SP section in order to simulate a long pipe configuration.
The applied curvature (K) is calculated by the following expression:
LK θ= , (2) where the rotation angle θ (in radians) is input for each
load step and L is the pipe length. The use of displacement control for the bending loads
allows extending the analysis beyond the ultimate load, thus generating the unloading moment-curvature relationship. The collapse curvature corresponds to the maximum moment reaction at the reference node.
In all models the mesh was generated using three-dimensional quadratic solid elements C3D27, with twenty-seven nodes and three degrees of freedom per node. As the polymer can be assumed as volumetric incompressible, elements with mixed formulation C3D27H were used for the annular layer.
The model employed in this work is similar to those of Estefen et al. [5], which were validated with small-scale experimental tests. In the current research program a correlation study between experimental and numerical results for a SP prototype is expected. A mesh sensivity study is performed again for the ring model, which differs from the previous works only in pipe thickness, radius and model length. The half ring presented in Figure 1 was modeled with 10, 16, 20 and 24
elements in the circumferential direction for 5, 6.4 and 10 mm longitudinal length. The results for collapse pressure (Pco) tend to converge for 20 elements with lengths (L) of 6.4 mm. The Pco for a long sandwich pipe (5200mm length) was also determined to obtain a more precise value, confirming the convergence of the ring model in 44.55 MPa.
Ring meshes for collapse curvature (Kco) results were evaluated for the same three cases (5, 6.4 and 10 mm length with 20 elements in hoop direction) and compared with the Kco result for the long pipe. The same 6.4 mm ring model length that converged for Pco also yielded good approximation with the long pipe result of 1.12 m-1.
One element through the thickness for steel layers and two for the polymer layer were considered to yield good approximation results employing quadratic elements. A higher refinement would increase the elements aspect ratio which is not recommended.
MATERIAL MODELING
API X-60 steel was used for inner and outer pipes, with 481.46 MPa of yield stress. An experimental stress-strain tensile curve is used as input for the program as well as the derived elastic modulus equal to 206,863 MPa and Poisson ratio 0.3. The steel layers are modeled by plasticity theory with potential flow rule J2 associated with isotropic hardening and von Mises yield criteria for the combined loading models, Lubliner [9].
Solid polypropylene of the annular layer was modeled as non-linear elastic material (hyperelastic) and volumetrically incompressible. The stress-strain tensile curve of the polymer has a hard ductile shape with uniform extension, as described by Nielsen and Landel [10]. Compression tests were not conducted, however rigid polymers are common to have a ratio of 1.5:4 between tensile and compressive strength. So, assuming the same strength for both loadings is to underestimate the material strength under compression, which is acceptable at this stage of development. Rupture under tensile test of the analyzed solid polypropylene occurs at 39.3MPa maximum stress and 10% strain. The stress-strain curve is used by the program to automatically adjust an Ogden strain energy approximation model.
ADHESION BETWEEN STEEL PIPES AND POLYMER
The sandwich pipe prototype construction involves similar steps to those employed in the single wall pipe multilayered coating. In this process, the inner steel pipe is externally blast cleaned, pre-heated and one layer of Fusion Bonded Epoxy powder (FBE) is then applied. While the FBE is still in its gelled state an adhesive layer is laterally extruded onto the FBE, followed by a layer of extruded polypropylene until the desired thickness is obtained. This coating process assures a high level of adhesion between polymer and metal layer, so that the adhesion strength of this interface is assumed standard and will not be performed any additional analysis in the present research stage.
The set of inner pipe coated with polypropylene is slipped inside the outer pipe in the last step of fabrication of the sandwich pipe segment. During this process, the adhesion should be guaranteed by the application of a structural adhesive
in the remaining space between the polymer and outer pipe. The adhesive thickness is not under optimization now because the fabrication process needs to be initially implemented.
Shear loading on whole bonded area uses the joint to the best advantage, giving an economical joint that is most resistant to failure. Whenever possible, joints should be formed in such a way that most of the load is transmitted through the joint as a shear load. Pure tension also is comparable to shear in strength, but not always is possible to be sure that this is the only stress present, as described by Shields [11].
Peel and cleavage types of loading result in non-uniform stress and strain distribution over the bonded area. Load concentrates on the joint boundary line inducing failure and its propagation.
In most cases, the thicker the adhesive, the higher the stresses and strains, and thus the bending deformation. In the case of pure shear loading maximum stresses will occur at joint ends as demonstrated by Li et al. [12]. In the case of the sandwich pipe, the increase of section ovality caused by external pressure, bending or the combination of both, will induce shear in the circumferential direction. Additionally, tension and compression will occur between the layers, depending on the loading case. The mixing of these loadings will lower the adhesive strength, but it will be smoothly distributed and there are no joint borders for stress concentration.
The adhesive stress and strain behavior were not analyzed here. The intention is to obtain the sandwich pipe strength as a function of the adhesion level disregarding the influence of the adhesive thickness, bonding failure type or process. The level of adhesion of the bonded pipe is evaluated by the maximum shear stress obtained from the contact surfaces.
Adhesion tests were conducted using two specimen types. The simple shear specimen test was designed in order to compare different adhesives and the sandwich pipe specimens used to evaluate the effective adhesion level with two polypropylene surface conditions.
SHEAR TEST
A specimen composed of two metal pieces bonded to a polypropylene square plate in between was employed to evaluate the shear stress at the union of the two different materials. Specimen dimensions are shown in Figure 2. The intention was to compare the adhesive strengths employed in the small scale sandwich pipes manufactured with PANG adhesives, Estefen et al. [5], with the adhesive 3M-DP8005 to be applied in the prototype. The comparative results are presented in Figure 3 for the two adhesives.
The test specimen was tensioned until failure of the adhesive at 1 mm/min of loading speed using an Instron (type 8892) machine.
The pure shear stress is calculated by the total force applied to the specimen divided by overlapping area, assuming equally distributed stress on the entire bonded area, as done by Lanting and Spelt [13] for the primary shear of linear-elastic adhesive behavior. The overlapping area considered here is only one polypropylene-steel interface. The failure of one interface means the sandwich specimen failure.
Figure 3: Tensile test results for PANG and 3M adhesives
A value of 3.3 MPa for the shear stress was obtained for
the 3M adhesive test, which is 68% higher than the PANG adhesive. The displacement at failure was also significantly different. It was noted that the PANG adhesive, which is recommended for elastomeric union by vulcanization, presented higher elasticity than the 3M, normally employed for structural joints.
SANDWICH PIPE SPECIMENS
Attempting to evaluate a more realistic adhesion condition, four sections of 100 mm length of prototype sandwich pipes prior to final stage of fabrication were tested in two different polypropylene surface preparations, two specimens with smooth surfaces and two with rough surfaces. The bonded interface between outer pipe and polypropylene layer was prepared manually, applying the adhesive while sliding the inner pipe with polymer coating inside the outer pipe.
Average radial gap between outer pipe and polymer layer is 2 mm. Total available volumes for the adhesive in the gap of the sandwich pipe segments was filled only 60%. The inner surface of outer steel pipes was blasted to increase roughness, in all cases. Figure 4 shows a sandwich pipe specimen before and after bonding failure. Hydraulic actuator connected to both load cell and LVDT was employed in the tests. The experiment consisted in shearing the interface through reverse
axial forces over the inner and outer pipes, with the help of two steel rings. Shear stress is calculated as the ratio between applied force and total area of bonding surface, i.e. the outer surface of the polypropylene layer. Test results for the four specimens are shown in Figure 5.
Figure 5: Test results for sandwich pipe with 3M adhesive
The results show a maximum shear stress of about 1.9 MPa
for the specimens with rough polypropylene surfaces. Values between 1.2 and 1.5 MPa were obtained for the specimens with smooth surfaces. These results indicate the adhesion levels that should be used as input to evaluate numerically the structural strength of the sandwich pipe.
COULOMB FRICTION MODEL
The isotropic Coulomb friction model was adopted to simulate the stick-slip conditions representing bonded and failure situations in the interface between outer pipe and polypropylene layer. The model uses element contact surfaces defined for both polymer and metal layers to allow shear stress and contact pressure to be calculated. For the stick condition, i.e. no relative motion between contacting layers, the equivalent frictional stress ( eqτ ) calculated by the program for the surface
must be lower then the critical shear stress ( critτ ). The equivalent stress is calculated as a function of both tangential stresses ( 1τ and 2τ ):
The critical stress is proportional to the contact pressure, , and depends on the friction coefficient, p µ . It can also be
limited by the maximum shear stress, maxτ , which is more useful for the desired purpose:
( maxmin ,crit pτ µ τ= ) . (4)
For the slip condition, the equivalent stress should be at least equal to the critical stress.
For the isotropic friction, the directions of slip and frictional stresses coincide. If the critical slip critγ is not specified, as in fact it is not, a default value of 0.5% of the average element length is adopted, which means a very small value (0.08 mm) for the mesh employed in the sandwich pipe model. In the elastic stick formulation, the shear stress in the slip direction i, iτ , is related to the elastic tangential slip, el
iγ : el
i s ikτ γ= , (5)
where sk is the current stiffness for stick condition, which is defined by:
crits
crit
kτγ
= . (6)
The behavior is assumed in the elastic stick as long as the equivalent shear stress does not exceed the critical stress. Then, it is possible to simulate the adhesive behavior considering that the slipping would only occur for the bonding failure, when the critical stress at the interface is reached.
The model yielded good results under pure external pressure, where the steel pipes and the polymer are always subjected to positive contact pressure during the increase of pipe ovality until collapse. Under bending loading the outer pipe has a different ovality shape than the inner pipe and, consequently, the initially contacted surfaces tend to separate in some regions before the ultimate curvature occurs. The contact pressure then disappears and the friction model does not work. A second model was prepared to deal with this problem in order to allow the ultimate strength analysis to be performed under bending loading. Although the friction model was effective under pressure only it was used to validate the second model.
NON-LINEAR SPRING MODEL
Non-linear axial spring elements (SPRINGA) have been employed to simulate the adhesion between layers. Each spring connects two nodes between polymer on one side and metal on the other side, as indicated in Figure 6.
Spring stiffness is modeled by a non-linear force related to displacement, in which the maximum force is proportional to the shear stress multiplied by the node influence area. In Figure 7, the nodes positions are represented by the dots. The dashed lines inside the element indicate the proportional area for each node, which are named as a, b, c and d. The nodal spring forces are represented in terms of a unit force F.
In Table 2 the symmetry condition and area are used to obtain the force F, or a fraction of F, that will result in a constant shear stress on the entire element surface. The side nodes, located on the hachured border Figure 7, use half of the force F because of symmetry condition at one side and the
section border at the loading side. Several tests have been performed until this observed relation was confirmed by the smoothness of strain distribution on the element surface. Also, a comparison study between friction and spring models was performed to increase the model confidence.
Figure 6: Spring connection between steel and polymer
nodes in the sandwich pipe ring model
Figure 7: Nodal forces and positions for the element face
Table 2: Nodal forces for each position on the element
Position Si e Area Force de Noda No A F b No A/2 F/2 c Yes A/2 F/4 d Yes A/4 F/8
The spring lengths are a small fraction of the millimeter to
allo work only in tension in all directions, considering that
ELATION BETWEEN MODELS
behavior, collapse dels (friction and
spri
w it to the spring axis can rotate over the nodes, thus allowing the
shear displacement. Therefore, the simulated bonding has the same strength in tension as in shear, which is an acceptable simplification. Additionally, the contact surface model was also incorporated to prevent the layers to superimpose on each other.
CORR
In order to evaluate the spring modelpressure results were obtained with both mo
ng) for different maximum shear stress values. The adhesive strength based on the maximum shear stress was varied from 1.5 to 14 MPa. The results are shown in Figure 8, where it can be observed that the collapse pressure converge for the perfect adhesion value obtained from previous work by Castello and Estefen [14] for the same geometry and initial ovality of 0.2%. A maximum shear stress of 14 MPa was obtained as the correspondent value of perfect adhesion.
Figure 8: Collapse pressure rsus maximum shear st ss
is observed that both models yielded very close results,
indi
RISER CURVATURE
tudinal strain reached on the sandwich pipe
rved that the curvature and longitudinal strain valu
able 3: Maximum curvature and longitudinal strain values
Depth (m ain (%)
ve refor the numerical models
Itcating that the spring model can be utilized adequately to
simulate the adhesion between layers. During the numerical simulation it was observed that the collapse, either under external pressure or bending, occurs just after the relative displacement of the layers initiates in the friction model. In the case of the spring model, the collapse occurs always after one or more springs reach its maximum strength value, or, in other words, when the spring stiffness decreases allowing the extension to increase. In both cases, the intention is to simulate the adhesive failure after reaching the maximum shear stress at the interface.
The maximum longi during installation when suspended in a catenary shape
was obtained for a quasi-static condition. The sandwich pipe was initially compared with a single wall pipe with the same bending stiffness and outer diameter. The bending stiffness was obtained by the linear portion of the moment versus curvature curves resulting from the bending simulation analysis. Table 3 shows the curvature and longitudinal strain results for different water depths.
It is obsees are higher for lower depths and that the strains are lower
than the API yield strain of 0.5%. Using the maximum curvature calculated for 3,000 meters, it is possible to find an approximate design point to be indicated in the ultimate strength curve, Figure 9. For design purposes this point should be inside the strength envelope curve for the sandwich pipe proposed for operation in such depth.
T
for different water depths ) Curvature (1/m) Str
3,000 0.00127 14 0.02,000 0.00191 0.021
0 0.00381 2 1,00 0.04
ULTIMATE STRENGTH
s for maximum shear stress values of 1
Ultimate strength curve.5, 3.0, 6.6, and 14 MPa are presented in Figure 9. The
estimated design point (Pd) assumed a safety factor for collapse pressure of 1.33 associated with the curvature obtained for the riser configuration at 3,000 meters of water depth.
Maximum Shear14 MPa6.6 MPa3 MPa1.5 MPaPd
0
10
20
30
40
50
P
60
ress
ure
(MP
a)
0 0.2 0.4 0.6 0.8 1 1.2Curvature (1/m)
Figure 9: Ultimate strength under combined pressure and
he ultimate strength obtained with maximum shear stress
of 1
degree on t
CONCLUSIONS
suitable for 3,000 meters water depth app
ilure was emp
bending for different adhesion degrees
T4 MPa (outer curve in Figure 9) corresponds to the assumed
perfect adhesion condition obtained in previous work [14]. The results show that even reducing the maximum shear strength to about 10% (1.5 MPa) of its assumed perfectly bonded condition, the design point still attends the design depth.
It is also noted a higher influence of the adhesion he ultimate curvature than on the collapse pressure. This is
because the failure under pure bending presents ovality more than twice the ovality caused by external pressure only. It was observed that the increase of ovality is the main failure inducer of the adhesive and that the relative displacement always occurs in the circumferential direction. The shear stresses in the longitudinal direction are, in most cases, irrelevant in relation to the circumferential direction, because in free bending the pipe maintain plane sections perpendicular to the neutral axis.
Sandwich pipelication was analyzed for ultimate strength under combined
external pressure and bending for several degrees of adhesion between the polymer annular and the outer steel pipe.
An efficient numerical model of the adhesion faloyed, where the bonding strength of the outer steel pipe
and polypropylene interface is simulated by the maximum shear stress supported by the union. Non-linear springs associated with contact surfaces were used.
The main conclusions are outlined below: ural adhesive
• rease
• ar stress supported
• gth curve it was possible to
Alth far achieved have attended the initi
ACKNOWLEDGMENTS
acknowledge the Petroleum Nat
REFERENCES
h, F.and Roddy, I. State-of-the-art on deep wate
Valenza, A. Exp
• Experimental tests indicate that 3M structhas higher adhesion capacity than previous adhesive PANG employed in small-scale sandwich pipes; The rough surface of the polypropylene incsignificantly the adhesion strength; The reduction of the maximum sheby the union affected mostly the bending strength than the external pressure capacity due to higher ovality of the pipe under bending; Based on the limit strenestimate for the proposed geometry a 3,000 m water depth application considering a realistic initial ovality of 0.2%, 1.33 safety factor for the external pressure, maximum longitudinal strain due to the catenary riser curvature and only 10% of the idealized perfect adhesion condition. ough the results so
al expectations, further experimental and numerical studies for full scale prototypes have been planned to build up the necessary confidence for the use of sandwich pipes in ultra-deepwaters.
The authors would like to ional Agency / ANP for the financial support to the first
author. Special thanks to TENARISCONFAB for the collaborative project with COPPE/UFRJ on sandwich pipe prototypes and to 3M for providing the adhesives. The support from the Submarine Technology Laboratory is recognized, in particular from Dr. Ilson P. Pasqualino and Dr. Theodoro A. Netto.
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