1981 OTC 4067 Palmer [PDF]

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OTC 4067 MOVEMENTS OF SUBMARINE PIPELINES CLOSE TO PLATFORMS



by Andrew C. Palmer, University of Manchester; Michael T.S. Ling, Total Oil Marine Limited



©Copyrlght 1981 Offshore Technology Conference This paper was presented at the 13th Annual OTC in Houston, TX, May 4-7, 1981. The material is subject to correction by the author. Permission to copy Is restricted to an abstract of not more than 300 words.



ABSTRACT



and move towards the piatform:



An analytical model of expansion movements at the ends of pipelines is developed. A comparison with measurements on two North Sea pipelines shows that the analysis is consistent with observed behaviour, and can be used to assess the results of corrective action. An alternative mechanism, that of creep deformation in corrosion coating, is analysed briefly.



Alterations of pressure also cause movements. Close to the elbow, in the horizontal leg, the longitudinal stress is tensile, am the combination of circumferential and longitudinal stress induces a longitudinal tensile strain, and therefore a longitudinal movement. Far from the platform, on the other hand, longitudinal movement is prevented by friction on the bottom: there the strain is zero and the longitudinal stress is not the same as it is close to the elbow.



INTRODUCTION Expansion due to changes in temperature and internal pressure can produce substantial movements at the ends of submarine pipelines l • At platforms, these movements are important beca~se they can overstress risers and elbows, and bring the pipe into contact with the platform itself. The paper begins by describing the mechanisms that give rise to expansion movements, and goes on to an analysis that predicts how much movement is to be expected. The results are compared with measurements on two North Sea pipelines. In a few instances, another mechanism may occur, and the movement may be due to creep deformation in the corrosi9n coating : this will be analysed briefly. MOVEMENTS AT THE END OFA PIPELINE Consider a straight submarine pipeline connected to a platform riser (Fig.la). The riser passes through clamps on the platform, and then has a 900 elbow. At a short distance from the platform, the pipeline reaches the bottom, and from then on is continuously in contact with it. It is helpful to begin by considering why the pipeline should tend to move. The operating temperature and pressure are higher than the temperature and pressure when the pipe was tied in. Because the temperature is higher, the pipeline tends to expand. Far from the platform, the expansion is constrained by friction between the pipeline and the sea bottom, am longitudinal expansion stresses are set up. At the platform, however, the pipeline is only slightly constrained (by the vertical leg of the riser, which is relatively flexible) , and there it can expand freely References and illustrations at end of paper 17



It follows that both temperature and pressure changes induce movements. At a distance from the pJ.atform, friction prevents these movements, but it does not do so close to the platform. The movements occur within a transition region whose length depends on the limiting frictional force between the bottom and the pipeline: if friction is large, the transitior region is short and the movements are small, but if friction is small the movements are larger. If the operating temperature and pressure are reduced, the movement towards the platform is reversed. only part of the original movement returns, and there remains a residual movement towards the platform, even if the pressure and temperature are returned to their tie-in values. This is because friction always opposes motion, so that when the temperature is reduced the frictional forces do not return to zero, but partially reverse, holding the pipeline in its extended position and preventing it from slipping back. ANALYSIS The idealizations used in the analysis are those customary in pipeline engineering, and the errors they introduce will almost always be negligible in practice. They are : (1) that the pipe remains elastic, am that its material properties are described by Young 1 s modulus E, Poisson's ratio v and linear thermal expansion coefficient ll. (2) that the pipe can be treated as a straight thinwalled circular tube of thickness t and mean radius R (defined as ~ (outside diameter - t».



(3) that the limiting longitudinal force f per unit length, between the pipeline and the bottom, is uniform along the length, independent of the distance moved, and the same for either direction of motion.



The length Z over which movanent occurs can be found .. f.rom the condition that cr L is continuous at z, and so, by equating the values of crL in equations (5) and (7), z is the solution of



(4) that when the line was tied in, its temperature was the same as that of the sea water during subsequent operation, that its internal pressure was negligible, and there was no cold spring.



(S) that the force differences associated with the longitudinal pressure gradient are negligible over the length of pipeline that takes part in the movement



8 (x) = 8 exp (-x/A) • • • • • • • • • • (1) 1 where 8 (x) is the temperature difference between the pipeline and the water, at a distance x from the platform, 8 is the difference at the platform, and A is a decay length over which the temperature difference falls to lie (0.369) of its initial value. This assumed distribution corresponds to the steady state reached if fluid flows along the pipeline away from the platform at a uniform rate, and the overall heat transfer coefficient is independent of time and temperature. A negative value of A represents flow towards the platform, and a zero value represents uniform temperature. (7) that the shear force in the vertical riser leg is negligible by comparison with other forces in the system.



and the change in circumferential stress to the pressure p·.bY (3)



vpR/t



Ea8



vpR/t



Eet8 l exp(-x/A)



~



Z



E:L '" du/dx



• • • • • • • • • • • • • • • • (1.0)



and can be determined by substituting (7) into (2) and then integrating (10)'. At the platform, the movement !::. is !::. =



~:E:L(X)



dx



a8 l A{l-exp (-z/A) )+~{ {~-V)pRz/t - f z 2/41TRt} (11)



and if the temperature is uniform !::. = 1TRE (a8 l )2t / f { 1 + E:8l



r'~-V)}2



•• (12)



It should be noted that the temperature effect and the pressure effect interact in a nonlinear manner the total expansion movement is not the sum of the movement that would be induced by pressure alone and the movement that would be induced by temperature alone.



lI sd =



(4) in x



• (9)



I



t{



Longitudinal movements are confined to a length z, the distance from the platform to the (imaginary) 'anchor point' beyond which no movement occurs. Beyond this, EL is zero, and so cr L



If the temperature is uniform, this reduces to Z = (1TR2 p/f)(I - 2v + 2Ea8 l t/pR)



(8)



If the temperature and pressure are reduced, a segment of the pipeline moves away from the platform, and on that segment the frictional force acts towards the platform. If the temperature is uniform both before and after a temperature reduction fran a 1. to a 2 and the pressure is simultaneous1.y raiuced from PI to P2, analysis by the method described above shows that reversed movement occurs over a distance y, 1.ess than z, given by y = (~-v) (Pl-P2)1TR2 + Eet1TRt(8 l -8 2 )} (13) that at the platform em the reverse movement !::.sd is



The longitudinal strain E: and stress cr , the circumferential stress cr H and Lthe temperatu~e rise 8 are related by the stress-strain-temperature relation 1. "'L = E(O"L - VO"H) + eta •••• • • • (2)



• • • • •



•



The displacement u, positive away from the platform, is related to the longitudinal strain by



(6) that the temperature of the line is not necessarily uniform, but can be represented by an exponential function of distance from the platform, so that



cr H = pR/t



2 Z = (1TR p/f){1- 2v+ 2E:lt exp(-Z!A)}



~y



2



f/1TRtE



• • • • • • • • • •



(14)



and that the longitudinal stress is ~P2R/t



(5)



The longitudinal stress between the platform and the anchor point is statical1.y determinate. Fig. 1.b shows the forces that act on a segment of the pipeline and its contents between section across the riser just above the elbow and a vertical section at a distance x from the platform; x is less than z. At the right-hand end, 21TRtcr L is the longitudinal force in the pipe wall, and 1TR2p the longitudinal force on the contents. At the section above the e1.bow, the only horizontal force is the shear force S, which is negligible. OVer the length x, the pipeline is moving towards the platform, and so the bottom exerts on the pipe a force f per unit length, directed away from the platform. Since the segment and its contents are in equilibrium, the resultant horizontal force on it must be zero, and so o = fx + 21TRtcr L - 1TR 2p (6) (7) crL = ~R/t - fx/21TRt in x < Z



18



cr L =



+ fx/21TRt



in x < Y



~lR/t



- v (PrP2)R/t + Ea{8 r 8 2 ) - fx/21TRt iny



::2 y



z DISTANCE FROM PLATFORM



Fig. 2 - STRESS, STRAIN AND MOVEMENT AT THE END OF A PIPELINE Solid lines represent condition after a reduction in temperature and pressure, dashed lines condition before; numbers refer to equations in text.



Fig. 3 - RELATION BETWEEN CALCULATED MOVEMENT AND TEMPERATURE DECAY LENGTH.



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