Suspended spans in subsea pipelines are typically constructed in ways to mitigate the irregularities in seabed bathymetry. A subsea pipeline span may be subjected to motions due to currents that produce a phenomenon commonly referred to as vortex induced vibration (VIV). The motions could result in high cycle fatigue damage that may potentially reduce the effective life of the pipeline. Some pipelines operating in deep waters are not affected by surface wave effects but are affected by VIVs.
Reducing the length of a pipeline span may accomplish sufficient mitigation of the VIV effects provided that the natural frequency of the pipeline span is away from the shedding frequency of the VIV so that no resonant vibration can take place. Pipeline span length reduction may be accomplished by re-routing the line along a path associated with shorter spans or by supporting the span using various methods. These span length reduction attempts are in many cases very costly or practically unfeasible.
Helical strakes are widely used to mitigate VIV as they can generally accomplish significant pipeline response reductions with no requirements for pipeline span shortening. Due to the many uncertainties involved in VIV response prediction, the engineering methodologies currently available tend to be conservative and decisions for the provision of strakes over significant extensions of pipeline lengths are not unusual. However, use of helical strakes increases project costs for procurement, fabrication, inspection, transportation, and installation, as well as detrimentally affecting the associated project schedule and risk.
One important factor inherent in pipeline VIV response is the low amount of damping of the system. Typically, the pipelines have small amounts of damping because (a) the damping capacity of the pipeline itself (structural damping) is quite limited, (b) the pipeline is in contact with the soil only at the span ends which significantly limits the soil contribution to the damping of the system, and (c) under the effects of VIV, usually referred to as “lock-in,” there is no hydrodynamic damping available. Hence, the VIV response, which fundamentally is resonant-like, is not adequately mitigated by damping. This lack of damping is a major limitation, especially because resonant-like responses are very sensitive to and can be significantly reduced by increases in system damping.
This disclosure provides Pipeline Vibration Dampers (PVDs) configured to mitigate subsea pipeline VIV. The PVDs reduce the pipeline response by effectively increasing the damping of pipeline systems to which the PVDs are attached. This can be potentially useful since, as noted above, the availability of damping in a typical pipeline system can be quite limited. In some embodiments, utilization of PVDs reduces the pipeline VIV response and thereby avoids excessive fatigue damage to the pipeline. The PVDs may also be used in combination with strakes, thereby reducing the extents of pipeline lengths required and/or associated with straking. Furthermore, the PVDs can be attached to the pipeline before and/or after a pipeline offshore installation campaign, and the PVDs can be used to help suppress VIV for existing pipelines. Accordingly, the use of PVDs as disclosed herein provide a practical, flexible solution to mitigating pipeline VIV.
Numerous objects and advantages of the invention will become apparent as the following detailed description of the preferred embodiments is read in conjunction with the drawings, which illustrate such embodiments.
Some PVDs disclosed herein are substantially similar to the so-called tuned vibration absorber (TVA). TVAs often comprise a reaction mass and a spring element with appropriate damping and the TVAs may be effective for reducing vibrations. TVA design and selection may comprise considering constraints of weight, damping and physical dimensions needed for a particular application.
Many TVA design configurations have been developed, and different optimal tuning rules have been studied for tonal and broadband applications. TVAs are useful for more than simply the isolation of machinery at the frequency of a rotating unbalance. For example, TVAs are useful for controlling the modal and forced response of complex continuous systems such as civil engineering structures including above ground pipelines. TVAs may also be referred to as tuned mass dampers, dynamic vibration absorbers, and/or auxiliary mass dampers. TVAs have been utilized to control wind-induced oscillations of pipelines above the Arctic Circle. TVAs may be placed at mid-span locations on pipeline spans between adjacent vertical supports of a pipeline. Vibrations of the pipeline result from wind-induced vortices exciting its natural vibration modes. Depending upon the wind conditions and pipeline configuration, as many as ten vibration modes or more of a pipeline span can be excited, and potentially greater numbers in subsea applications. Although the amplitudes of vibration are relatively small, the accumulation of vibration cycles can cause fatigue at the pipeline joints and/or other pipeline components and/or features. In some cases, by adding a PVD to a pipeline system, pipeline system damping is increased ameliorates the motion of the pipeline.
In the case of subsea VIV, the dynamic motions induced by VIV can be significantly larger than those above ground due to wind-induced vibration. Accordingly, this disclosure contemplates providing PVDs, TVAs, tuned mass dampers, dynamic vibration absorbers, and/or auxiliary mass dampers configured to increase damping of a subsea pipeline to reduce subsea current induced VIV. The deep-water subsea pipeline environment is considered to be more challenging than the above ground pipeline environment because of various factors, including accessibility to deep-water pipeline locations and the fact that water is denser than air with the associated implications on VIV and PVD performance. For example, in some embodiments disclosed herein, PVDs are disposed within inside a small pressure vessel to avoid fluid-structure interaction between the PVD and the water and ensure PVD performance. In some embodiments, an adjustable location or tunable mass and a torsional elastomeric spring may be disposed within the pressure vessel so that the PVD contents within the pressure vessel may apply a dynamic force that mitigates the VIV induced motion of the subsea pipeline to which the pressure vessel is attached.
The pipeline fatigue-producing stress range for cross-flow VIV is given by
Scf=2Acf(Az/D)Rkγs Equation 1
where Acf is the unit-diameter modal stress amplitude, Az/D is the reference normalized pipeline cross-flow VIV response which is a function of the reduced velocity, D is the pipeline outside diameter including any external coating, γs is a safety factor, and the amplification reduction factor Rk is given by
in which Ks, referred to as the stability parameter, is defined by
where me is the effective mass, ζT is the total modal damping ratio, and ρ is the mass density of the sea water.
It is important to note that because the main effect of the PVDs is to increase damping, as will be demonstrated in the following section, the influence of the PVDs on the stress range Scf is captured through the damping parameter ζT involved in Ks in Equation 3 and in turn in Rk in Equations 1 and 2. Potential reductions in Scf due to increases in the damping parameter ζT are displayed in
The PVD is a mass-spring system in which viscous-type damping is integrated with the spring element resulting in a complex-valued stiffness k*pd as shown in the simplified model below. As previously indicated, the PVD is attached to the pipeline system which is also represented in
The quantity k*pd may be referred to as the complex-valued stiffness of the PVD because it accounts for both the resistance of the spring element and its inherent viscous damping. The complex-valued stiffness is given by
k*pd=kpd(1+i2ζpd) Equation 4:
where kpd is the spring element stiffness and ζpd is the associated viscous damping ratio.
The transmissibility T of the PVD, which is the ratio of the response of the PVD mass given a unit amplitude displacement at its base with varying frequency ω, can be expressed as
T=k*pd/(k*pd−mpdω2) Equation 5:
where mpd is the mass of the PVD, ω is the frequency of oscillation when the PVD is excited by a displacement at its attachment point to the primary structure (in this case the pipeline). The force applied by the PVD on the pipeline is given by,
Fpd=−mpdω2T x′ Equation 6:
where x′ is the displacement of the pipeline at the point of attachment of the PVD, and the PVD can move to damp the response at frequency ω. At the undamped resonance of the PVD, ωpd, the PVD forcing on the pipeline is found using Equations 4-6, (with the undamped PVD natural frequency
and has the expression
Fpd=mpdωpd2(1+2iζpd)/(2iζpd)x′ Equation 7:
with small values of ζpd (such as less than 0.2), Equation 7 can be approximated by
Fpd=−i mpdωpd2/(2ζpd)x′ Equation 8:
In Equation 8, when the PVD is operating close to its resonance, that the forcing fpd on the pipeline is in quadrature with the displacement x′, which means that it acts as an ideal dashpot where the damping of PVD is given by
cpd=mpdωpd/(2ζpd)=2πmpdfpd/(2ζpd) Equation 9:
where fpd is the natural frequency in cycles per second for the PVD. The PVD effective damping on the pipeline structure PVD is inversely proportional to the damping ζpd in the PVD. Additionally, when the pipeline is excited by VIV near the resonance of the PVD, the model shown above takes on the form of the model shown in
The damping of the PVD near its resonance is also proportional to the mass mpd and its resonant frequency ωpd. A PVD favorably tuned with natural frequency ωpd has a viscous damping ratio given by
ζpd-O=(3μ/[8(1+μ)])1/2 Equation 10:
where ζpd-O is the “optimal damping” and μ is the mass ratio of the PVD mass m to the pipeline effective mass me given by
μ=mpd/me,me=m+ma Equation 11:
The mass ratio only includes the mass of the pipeline and internals. Equation 11 shows that the PVD mass ratio is dependent on the pipeline mass m and the hydrodynamic mass ma. Using Equations 10 and 11, the above tuning provides what is called the “equal-peak method”, and when the PVD is tuned at the 1/(1+μ) times the resonance of the pipeline, however, for VIV the hydrodynamic mass term ma is included.
The graph of
In the following numerical example, a hybrid approach is utilized that adds a PVD to the pipeline, and compute the reduction Rk for a given mass and damping of the PVD (with resonance equal to 1/(1+μ) times the pipeline resonance). At that point, the frequency response is generated as shown in
For the numerical example, a simply supported pipe section of length 130 feet where only the first mode is participating in the response is considered. Table 1 below provides the physical properties of the example. The example includes the hydrodynamic loading of the sea water, but does not include wave effects as it is assume that the pipe is operating on the seabed in deep water. The example places a PVD along the center of the pipe section, where the first modal deflection is the largest. Only the first mode of the pipeline is considered, and hence with a PVD attached at mid-span, the coupled system can be represented by a two degree-of-freedom system.
Now, consider the maximum displacement amplitudes of the two new resonances utilizing the PVD on the pipeline as shown in
Since VIV is a lock-in type phenomenon, only a single resonant frequency is needed to drive the structural response. The maximum amplitude the response of the pipeline is driven by the damping in each of the resonances in the system. In order to estimate what the new system damping is utilizing the PVD, an “effective” viscous damping ζc for the coupled system that produces the equivalent maximum displacement is developed by estimating what viscous damping the original system needs to have in order to provide the same reduction in the amplitude of response provided by the PVD.
where ζe denotes the effective viscous damping extracted from
From
Table 2 shows the Amplification Reduction Factors Rk utilizing PVDs of various mass. For each PVD case, the effective viscous damping of the system is obtained from
While the above analysis and numerical example have focused on cross-flow VIV, it is recognized that in-line or longitudinal VIV can occur under certain conditions. In general, the in-line VIV stress range tends to be much smaller than that produced by the cross-flow VIV. However, in-line VIV may result from current velocities which can be lower than those that may produce cross-flow VIV. These lower current velocities tend to have a relatively high probability of occurrence. The concepts and methodologies involved in using PVD devices to mitigate cross-flow VIV as explained above also apply to the mitigation of in-line VIV by employing such devices.
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With regard to PVDs 400, 500, the housings 402, 502, respectively are configured to isolate the interior spaces 404, 504, respectively, and their contents from corrosion, effects of water dynamics and damping, and sealife encroachment. The housings 402, 502 may generally comprises spherical, rectangular, cylindrical, hemispherical, and/or any other suitable geometric shape and/or profile. In some embodiments, the air PVD 500 may require a relatively more structurally robust housing as compared to a housing for an oil PVD 400. In some embodiments, PVDs 400, 500 may be designed to be buoyancy neutral, positive, or negative, as desired. In some embodiments, the PVDs 400, 500 may comprise one or more of the vibration absorbers disclosed in U.S. Pat. No. 6,397,988 B1 issued to Keith R. Ptak on Jun. 4, 2002.
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Other embodiments of the current invention will be apparent to those skilled in the art from a consideration of this specification or practice of the invention disclosed herein. Thus, the foregoing specification is considered merely exemplary of the current invention with the true scope thereof being defined by the following claims.
The present application claims priority to U.S. Provisional Patent Application No. 61/861,189 filed on Aug. 1, 2013 by Mark A. Norris, et al., entitled “METHOD FOR SUPPRESSION OF RESONANT VIBRATIONS IN SUBSEA PIPELINES,” which is incorporated by reference herein as if reproduced in its entirety.
Filing Document | Filing Date | Country | Kind |
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PCT/US2014/049428 | 8/1/2014 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
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WO2015/017792 | 2/5/2015 | WO | A |
Number | Name | Date | Kind |
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3194355 | Jeromson, Jr. | Jul 1965 | A |
5915508 | Lai | Jun 1999 | A |
Number | Date | Country |
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103615494 | Mar 2014 | CN |
0 349 978 | Jan 1990 | EP |
1 278 330 | Jun 1972 | GB |
1278330 | Jun 1972 | GB |
1 725 003 | Apr 1992 | SU |
Number | Date | Country | |
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20170074423 A1 | Mar 2017 | US |
Number | Date | Country | |
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61861189 | Aug 2013 | US |