Deepwater Flexible Risers and Pipelines. Yong Bai

Чтение книги онлайн.

Figure 2.1 Schematic representation reference systems, initial radial displacements and initial diameters.

where and are the initial maximum and minimum diameters, respectively, which account for initial displacement as it can be seen in Figure 2.3.

By replacing Eq. (2.2) into Eq. (2.1), it is possible to get

      (2.5)

      for which the solution results in

(2.6)

      where pcr is the critical buckling pressure for a perfect ring.

The ovality is computed considering it as function of the maximum displacement uRmax. It is expressed in absolute value for cos(2) = 1; thus Eq. (2.6) assumes the following form:

(2.7)

      Ovality shows the variation of the minor and major axes. It is computed step by step for each load increment by adding and subtracting, respectively, the magnitude of the displacements for the corresponding step from the diameters. Limit value is considered, conservatively, as 20 times the initial one and it is equal to L = 0.04. Besides this value, the pipe can be considered not suitable anymore for its purpose, being rough liner crucial elements and easily affected by turbulence due to internal flow. As it will be shown for both theoretical and numerical simulation, the pipe can be considered collapsed at L, it already exhibits large development of ovalization for almost stable pressure value.

      If the pressure armor layer is not taken into account in the pipe configuration, as discussed in [1], the critical load for a perfect ring can be expressed as

(2.8)

where, EIeq is the equivalent ring bending stiffness of each layer per unit length of the pipe. For the interlocked carcass it is equal to

(2.9)

for which, n is the number of tendons in the layer, Lp is the pitch length, K is a factor that is function of the lay angle and of the moment of inertia of the section (for massive cross-section as carcass K = 1) and I_2’ is the smallest moment of inertia of the cross- section which can be computed, referring to Figure 2.2, as follows:

(2.10)

      To better control the model and to compare results, the actual load is normalized with respect to the theoretical buckling load that accounts for imperfections at its threshold L, it is equal to

(2.11)

      Finally, the need of a reliable theoretical model suitable for practical application is used in this work, in order to evaluate the need of the interlocked carcass. As it was demonstrated in Bai et al. [3] through experimental and numerical simulations, the critical buckling load is estimated by summing up the contribution of each layer. Thus, the collapse loads for both the cross-section geometries of SSRTP considered here are computed by using the following formulation: