Tc 67/sc 4 n date: 2005-03-9 iso/wd XXXXXX ISO tc 67/sc 4/wg 6 Secretariat: Design of dynamic risers for offshore production systems Élément introductif — Élément central — Élément complémentaire  Warning



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Phase 1. The static deflection due to current drag is calculated for each riser in the array, neglecting any hydrodynamic interaction between them, i.e. assuming the inflow velocity for each riser to be equal to the current at the relevant level. Simple application of the ordinary drag formula results in the following maximum static deflection of each riser:

...(56)

where

= Surface current velocity,

= Length of riser,

= Mean effective tension averaged along the riser.

The constant k3 depends on the type of current profile and the ratio between riser top tension T1 and bottom tension Tb. Table 5 shows the value of k3 for different tension ratios Tt/Tb and different current profiles. The current profiles included in Table 5 are rectangular profile and different profiles decreasing linearly from the surface to depth h. The quantity H is water depth, see Figure 39. The k3 values shown in Table 5 are based on the top end riser fixture coinciding with the level of the free surface.

If the riser deflections as calculated above do not exceed significantly the average of top and bottom spacings in the riser array, one can safely conclude that there will be no collisions between the risers due to the current, and no further analysis is necessary. On the other hand, if the deflections as calculated are much larger than the spacings, more accurate analysis is recommended as described in the following phase.



Phase 2. This calculation procedure takes wake interaction into account. Being limited to unidirectional current, and by assuming ideal constant tensioning at the top end, a computer program can be quickly prepared. The procedure consists in calculating the deflection of each riser, starting with the far upstream riser, and continuing with each riser in the sequence of their position in downstream direction.96 The shape of each riser is calculated by choosing an inclination angle at the top end and calculating its curvature at many levels down the riser, based on local inflow velocity and tension. By numerical double integration of the curvature, one obtains the shape and lower end position. If this position deviates from the specified one, the deviation is used to correct the choice of top end angle and the process repeated in an iterative manner. The essential feature is that when calculating the local inflow velocity, the wakes generated by all upstream risers are taken into account by the formulae shown above, adding up the wakes by rms summation.

If the deflections determined by the Phase 2 calculations show that no collisions will occur, then no further analysis is necessary. However, if the direction of the current varies for different levels down the risers, or if the stiffness of the tensioning devices is such that it significantly reduces the deflection, there is still hope that collisions will not occur, even if the Phase 2 calculation showed that they would. In this situation it is recommended that one proceeds to the more complete analysis of Phase 3.



Phase 3. This more complete analysis accounts for variations of current direction for different levels down the riser and for the stiffness of the tensioning device of each riser. The calculations are now done by a stepwise increase of the current velocity. For each step of current, the drag force is calculated for each level in the two horizontal directions (x and y). The riser curvature and deflections in the two directions are determined accordingly. The drag force is calculated, correcting the inflow for the wakes generated by all the other risers, using the geometry of the other risers determined in the previous current step. Thus, the program will consist of four main loops. Starting with the innermost loop they are:

  • iterate top end angle until correct bottom end x and y coordinates are achieved;

  • adjust top end pretension according to actual length along deflected riser and specified tensioner stiffness;

  • continue with next riser in the array;

  • continue with next step of current.

If the deflections of the different risers according to this calculation procedure are such that they collide, the designer has two options;

  • change the spacings or other parameters of riser system in order to avoid collisions;

  • verify that mechanical contact between risers will be acceptable

If the second is chosen, one will have to evaluate possible damage due to two effects:

  1. Risers at different angles making continuous mechanical contact, producing additional bending moments at the position of contact;

  2. Risers vibrating due to VIV, producing dynamic impact forces at the points of collision, thus producing additional bending moments as well as possible damage to the surface of the risers. In this case a maximum possible impact velocity will be 2wA, where w and A are the frequency and amplitude of the VIV, respectively.


          1. Flexible risers of arbitrary geometry

The numerical procedures described above refer primarily to a vertical or nearly vertical riser. For this type of riser, the numerical procedures up to and including Phase 2 calculations have been verified by experiments.95 For conditions typically referring to Phase 3 calculations, there is so far no experimental verification available, and the reliability of the results of the calculations should be judged with this limitation in mind.

For flexible risers of arbitrary, wave-type geometry the basic wake formulation is still applicable. Again there is no experimental verification available, and practical experience from this type of calculations is still very limited.



Table 12‑1 - Values of k3 for different velocity profiles and different riser top tension to bottom tension ratios

Tt/Tb Profile

12.0

5.5

3.3

1.6

1.0

Rectangular

1.14

1.07

1.03

1.00

1.00

h/H = 1.0

0.274

0.282

0.291

0.316

0.342

h/H = 0.8

0.193

0.196

0.212

0.237

0.262

h/H = 0.6

0.121

0.128

0.136

0.157

0.178

h/H = 0.4

0.0622

0.0663

0.0717

0.0852

0.0991

h/H = 0.3

0.0392

0.0423

0.0460

0.0555

0.0653

h/H = 0.2

0.0213

0.0231

0.0252

0.0307

0.0369

h/H = 0.1

0.00893

0.00967

0.0106

0.0131

0.0160


      1. Hydrostatic collapse



        1. Collapse of metal pipe


The formulas given below may be used to analyze collapse resistance. These formulas should be used with the criteria given in 5.4.1.

The collapse pressure for round pipe, Po, is given by:

Po = PePy (Pe2 + Py2)-1/2 ...(57)



The minimum collapse pressure for imperfect pipe, Pc, including the effect of bending strain, is given by:

Pc = Po (g - s/so) ...(58)



where

D,t = Nominal pipe outside diameter and wall thickness less any corrosion allowance,

Dmax = Maximum outside diameter of pipe,

Dmin = Minimum outside diameter of pipe,

E, u = Modulus of elasticity and Poisson's ratio,

sy = Specified minimum yield stress,

A = Cross sectional area of pipe = p(D2)/4,

a = Cross sectional area of wall = p [D2 - (D - 2t)2]/4

Te = Effective tension on tubular,

G = Unit weight of water,

H = Water depth,

Pi = Internal pressure,

P = Net external pressure = GH - Pi,

Sa = Mean axial stress = (Te - PA)/a-Pi,

Yr = Reduced yield stress = sy {[1 - 3(Sa/2sy)2]1/2 - (Sa/2sy)},

Py = Yield pressure with simultaneous tension = 2Yrt/D,

Pe = Elastic buckling pressure = [2E/(1-n2)] (t/D)3,

p = Plastic to elastic collapse ratio = Py/Pe,

Oi = Initial ovality = (Dmax - Dmin)/(Dmax + Dmin),

f = Out-of-roundness function = [1+(OiD/t)2]1/2 - OiD/t,

g = Imperfection function= (1 + p2)1/2/(p2 + f--2)1/2,

b = Strain reduction factor = 1.5 for API pipe,

so = Critical bending strain = t/2bD,

s = Bending strain experienced by tubular.



Langner92 provides more detailed information on the analysis methods suggested in this section.

        1. Collapse propagation


An acceptable method of calculating the net external pressure under which a pipe buckle can propagate Pp is to use the following formula:

Pp = 24sy(t/D)2.4 ...(59)



This formula should be used with the criteria in 5.4.

        1. Commentary


The following points have been considered in developing the criteria in 5.4 and 6.6.2.1:

  1. unless more accurate methods are used, the analysis procedures given in this section and the criteria provided in 5.4 should be applied to demonstrate that metal tubulars used in FPS risers will not collapse under external hydrostatic pressure. While based on a substantial amount of test data, these criteria may benefit from further refinement as additional tests are performed. For example, additional data may be beneficial to define the performance of DSAW pipe and the effects of pipe eccentricity and residual stress. Sections 5.4 and 6.6.2 are intended to apply to metal tubulars of steel, aluminum or titanium;

  2. little data exists to allow comparison of the results of this approach with experimental results for titanium. An alternative approach using the equations derived by Timoshenko and considering ovality may be used to verify predictions for this material but may require higher safety factors to yield the same degree of conservatism.




  1. the design factor is introduced to allow for variation in the criteria based on factors such as the following:

  • manufacturing methods, type of pipe;

  • consequences of failure;

  • service conditions.

  1. the reduced yield stress is calculated based on von Mises' failure theory to allow the incorporation of tension into the analysis. The reduced yield stress is introduced in place of the yield stress in the hoop pressure formula to give the yield pressure with simultaneously acting tension. This approach is conservative and results in predictions that agree well with experimental results;

  2. an alternative is to normalize the axial stress with the ultimate stress in the reduced yield stress formula. This approach offers even closer agreement between predictions and experiments performed to date but is not necessarily conservative;

  3. the strain reduction factor, b, has been taken as 1.5 for API grade pipe. Given a measured stress strain curve that is always increasing, a smaller value may be appropriate. Likewise, for non-API pipe with high yield stress or large wall thickness tolerances, a larger value of b may be warranted.


      1. Vortex-induced vibrations


For long cylindrical structures such as risers, the following basic model typifies an analysis for VIV:

  1. natural frequencies and mode shapes for bending are determined as accurately as possible;

  2. vortex shedding frequencies are determined (along the riser span) from the Strouhal relationship fs = VSt/D (where V is the local free stream velocity);

  3. vortex shedding frequencies are compared with the fundamental natural frequencies to see if VIV is possible and to estimate the highest mode in the response (if VIV is not possible, then no further analysis is necessary);

  4. if VIV is possible, then the VIV responses are determined from an appropriate model;

  5. VIV responses are used to compute the stress amplitudes and corresponding fatigue damage;

  6. if required, estimates of the mean drag coefficient for the vibrating riser are obtained.

For highly-tensioned risers, a tensioned cable approximation is usually sufficient and conservative for completion of Step a). Otherwise, bending rigidity of a riser must be taken into consideration. Both steps a) and b) can be performed for both the in-line (in-line with the flow) and transverse (normal to the flow) directions, however the transverse direction usually experiences somewhat higher bending stresses. Note that St is a function of several variables, including Re, surface roughness and the level of free stream turbulence.

Step c) requires the comparison of the highest vortex shedding frequency, Fs ,with the lowest natural frequency in bending, fn1. If Fs/fn1 > 0.2, then in-line VIV is possible. If Fs/fn1 > 0.6, then transverse VIV is possible. For transverse VIV of a long tensioned riser, the Fs/fn1 ratio may be rounded upwards (to the nearest whole number) to estimate the highest transverse bending mode in the response. Note however, that higher harmonics have been observed in some experiments with test cylinders, but none to date are known to have been observed for a marine riser experiencing VIV.

Step d) is the most difficult step in a VIV analysis. The VIV response depends upon numerous parameters, including Re, mass ratio, structural and hydrodynamic damping, the shape of the current profile, the specific modes responding, the riser roughness, etc. Numerous models exist for VIV amplitude prediction of risers experiencing VIV in uniform flows (uniform along the span) and for which the highest response mode is less than about 5. The best of these models are summarized by Blevins40, who notes that the predicted amplitudes of the various models differ by only about 15 percent. For low mode response, the response frequency may be conservatively assumed to be equal to the natural frequency of the highest mode excited. For higher mode response, and for situations in which the current is nonuniform or sheared along the riser span, the low mode models are usually overly conservative and accurate prediction of the response is complex. While there is not an accepted way of modeling high mode or sheared flow VIV, several conceptual models have been proposed, including those by Wang and Dalton50 and Vandiver. 41,42,45 These models account for the possibility of multiple bending modes being excited by a sheared current but require calibration with substantial model or field data before they can be used to confidently make responsible predictions. These models also attempt to properly account for hydrodynamic damping; however, the user must also include the correct structural damping which, for flexible pipe, can sometimes be substantial. The effects of adjacent tubulars should also be considered.

Once the VIV response is known, the bending stresses can be easily and accurately determined using common formulas for stress and strain. The bending stresses can then be combined with additional structural information, such as weld types and locations to produce fatigue life estimates. Analysis of wear may also be required for flexible pipe.



The predicted VIV amplitudes and frequencies can be used to obtain estimates of the local mean drag coefficients by use of an empirical formula. Blevins reports some of the more common formulas used to estimate these drag coefficients.40 All of the formulas are in effect an empirical coefficient (which accounts for the vibration) that is multiplied by the local steady drag coefficient for a stationary riser.


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