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Three-dimensional nonlinear vibration model and fatigue failure mechanism of deepwater test pipe

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Abstract

In deepwater test condition, the riser–test pipe (tubing string) system (RTS) is subject to the vortex-induced effect on riser, flow-induced effect on test pipe and longitudinal/transverse coupling effect, which is prone to buckling deformation, fatigue fracture and friction perforation. To resolve this, the three-dimensional (3D) nonlinear vibration model of deepwater RTS is established using the micro-finite method, energy method and Hamilton variational principle. Based on the elastic–plastic contact collision theory, the nonlinear contact load calculation method between riser and test pipe is proposed. Compared with experimental measurement results, calculation results using the proposed vibration model in this study and the single tubing vibration model in our recent work, the correctness and effectiveness of the proposed vibration model of the deepwater RTS are verified. Meanwhile, the cumulative damage theory is used to establish the fatigue life prediction method of test pipe. Based on that, the influences of outflow velocity, internal flow velocity, significant wave height, as well as top tension coefficient on the fatigue life of test pipe are systematically analyzed. The results demonstrate that, first, with the increase in outflow velocity, the maximum alternating stress and the annual fatigue damage rate increased. The location where fatigue failure of the test pipe is easy to occur at the upper “one third” and the bottom of test pipe are easy to occur fatigue failure. Second, with the increase in internal flow velocity, the “one third damage effect” of the test pipe will decrease, and the “bottom damage effect” of the test pipe increased that needs the attention of field operators. Third, during field operation, it is necessary to properly configure the top tension coefficient so that there can be a certain relaxation between the riser and the test pipe, so as to cause transverse vibration and consume some axial energy and load. The study led to a theoretical method for safety evaluation and a practical approach for effectively improving the fatigue life of deepwater test pipe.

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Data availability

The authors declare that the data supporting the findings of this study are available within the article.

Abbreviations

\(\upsilon_{i} ,i = x,y,z\) :

Displacement components of riser, m

\(\upsilon^{\prime\prime}_{i} ,i = x,y,z\) :

Second derivative of riser displacements versus z

\(E\) :

Elastic modulus of the RTS, Pa

\(I_{\upsilon }\) :

Polar moment of inertia of the riser, m4

\(\rho_{\upsilon }\) :

Density of the riser, kg/m3

\(F_{x} \left( {z,t} \right)\) :

Contact/impact force of riser–test pipe in x-directions, N

\(F_{L} \left( {z,t} \right)\) :

Lateral lift in the CF direction, N

\(\zeta\) :

Structural damping ratio

\(\omega_{\upsilon }\) :

Natural angular frequency of riser

\(L_{\upsilon }^{{}}\) :

Length of riser, m

\(D_{o}\) :

Riser outer diameter, m

\(m_{i}\) :

The mass of the gas per unit length (kg)

\(S_{i} ,i = x,y,z\) :

Displacement components of the test pipe, m

\(S^{\prime\prime}_{i} ,i = x,y,z\) :

Second derivative of test pipe displacements versus z

\(f_{x} \left( {z,t} \right)\) :

High-speed fluid impact load in test pipe in x-direction, N

\(f_{z} \left( {z,t} \right)\) :

High-speed fluid impact load in test pipe in z-direction, N

\(\omega_{s}\) :

Natural angular frequency of test pipe

\(w_{s} \left( { = m_{s} g} \right)\) :

Weight of test pipe per unit length, N

\(V_{{\text{r}}}\) :

Relative velocity between the fluid and the riser, m/s

\(U_{c}\) :

Outflow velocity of the riser, m/s

\(F_{D}^{\prime } ,C_{D}\) :

Component forces of the fluctuating drag force and corresponding coefficient

\(F_{L}^{\prime } ,C_{L}\) :

Fluctuating lift force and corresponding coefficient

\(S_{t}\) :

Strouhal number

\(R_{1}\) :

Radius of riser, m

\(f_{F}\) :

The friction of RTS, N

\(E\) :

Elastic modulus of the riser or test pipe material, Pa

\(\rho_{i}\) :

Density of gas in the test pipe, kg/m3

\(\alpha \left( t \right)\) :

Deflection angles of test pipe in x-direction, rad

\(\alpha \left( s \right)\) :

Inclination angle, rad

\(K_{U}\) :

Rotational stiffness of the upper flexible joint

\(u_{{{\text{boat}}}} \left( t \right)\) :

Heave displacement of the platform, m

\(m_{{\text{p}}}\) :

Mass of platform, kg

\(\eta \left( t \right)\) :

Surface displacement of random wave, m

\(\hat{\omega }_{i}\) :

Circular frequency of the \(i\)th harmonic, Hz

\(a_{i}\) :

Amplitude of the \(i\)th harmonic component, m

\(S\left( \omega \right)\) :

Random wave spectrum

\(\omega\) :

Circular frequency, Hz

\(T_{1/3}\) :

Significant period of the wave, s

\(T_{p}\) :

Peak period of the wave, s

\(\sigma\) :

Peak shape coefficient

\(F_{p} \left( t \right)\) :

Exciting force of the random wave on the heave plate, N

\(J_{1} \left( \cdot \right)\) :

First-order Bessel function of first kind

\(z_{{{\text{plate}}}}\) :

Depth of heave plate, m

\({\mathbf{d}}\) :

Displacement vector of riser unit

\({\mathbf{\varphi }}_{i} ,i = x,y,z\) :

Vibration shape function of riser and test pipe unit

\({\mathbf{F}}\left( t \right)\) :

Load column vector

\({\mathbf{M}}\left( t \right)\) :

Matrices of the overall mass

\(\rho_{p}\) :

Density of the actual RTS, kg/m3

\(\rho_{m}\) :

Density of the RTS in the simulation experiment

\(\lambda\) :

Radial similarity ratio

\(C_{L}\) :

Load-type correction factor

\(K_{f}\) :

Stress concentration correction factor

\(C_{{\text{S}}}\) :

Surface quality correction factor

\(S_{e}\) :

Corrected stress, Pa

\(\upsilon^{\prime}_{i} ,i = x,y,z\) :

First-order derivative of riser displacements versus z

\(\dot{\upsilon }_{i} ,i = x,y,z\) :

First-order derivative of riser displacements versus time

\(A_{\upsilon }\) :

Cross-sectional area of the riser, m2

\(F_{z} \left( {z,t} \right)\) :

Friction force of riser–test pipe in z-directions, N

\(m_{\upsilon }\) :

Mass of the per unit length riser, kg

\(F_{y} \left( {z,t} \right)\) :

Contact/impact force of riser–test pipe in y-directions, N

\(F_{D} \left( {z,t} \right)\) :

Drag force in the IL direction, N

\(c_{\upsilon } \left( {{ = }2m_{\upsilon } \omega_{\upsilon } \zeta } \right)\) :

Structural damping coefficient of riser

\(w_{g}\) :

Buoyant weight of riser per unit length, N

\(\rho_{w}\) :

Density of the seawater, kg/m3

\(A_{s}\) :

Cross-sectional area of the test pipe, m2

\(m_{s}\) :

Mass of the per unit length test pipe, kg

\(S^{\prime}_{i} ,i = x,y,z\) :

First-order derivative of test pipe displacements versus z

\(\dot{S}_{i} ,i = x,y,z\) :

First-order derivative of test pipe displacements versus time

\(f_{y} \left( {z,t} \right)\) :

High-speed fluid impact load in test pipe in y-direction, N

\(c_{s} \left( {{ = }2m_{s} \omega_{s} \zeta } \right)\) :

Structural damping coefficient of test pipe

\(v_{i} ,i = x,y,z\) :

Absolute velocities of the internal high-speed fluid (m/s)

\(V\) :

Fluid flow velocity in the test pipe, m/s

\(\overline{C}_{d}\) :

Coefficient of steady-state drag force

\(\overline{C}_{l}\) :

Coefficient of steady lift force

\(q_{i} ,i = x,y\) :

Dimensionless wake oscillator variables in IL and CF directions

\(\delta\) :

The relative deformation between riser and test pipe, m

\(\omega^{\prime}_{s}\) :

Vortex shedding frequency

\(R_{2}\) :

Radius of test pipe, m

\(F\) :

Contact load of riser–test pipe, N

\(\xi\) :

Friction coefficient between the riser and test pipe

\(A_{i}\) :

Cross-sectional area of the wellbore, m2

\(\varphi \left( t \right)\) :

Deflection angles of test pipe in y-direction, rad

\(\varphi \left( s \right)\) :

Azimuth, rad

\(K_{L}\) :

Rotation stiffness of the BOP

\(B_{i} ,i = 1,\;2\) :

Heave radiation and heave viscous damping

\(A_{w}\) :

Area of the platform at sea level, m2

\(\overline{F}_{z}\) :

Random heave wave exciting force on platform, N

\(\varepsilon_{i}\) :

Initial phase of the \(i\)th harmonic component, rad

\(\Delta \omega\) :

Frequency step

\(f\) :

Frequency, Hz

\(H_{1/3}\) :

Significant wave height, m

\(f_{p}\) :

Peak frequency of the wave, Hz

\(\gamma\) :

Peak parameter

\(R\) :

Platform radius, m

\(F_{s} \left( t \right)\) :

Exciting force of the random wave on the platform body, N

\(d\) :

Draft of platform, m

\(B_{{{\text{plate}}}}\) :

Width of heave plate, m

\({\overline{\mathbf{d}}}\) :

Displacement vector of test pipe unit

\({\mathbf{D}}\) :

Matrix of overall displacement

\({\mathbf{K}}\left( t \right)\) :

Matrices of the overall stiffness

\({\mathbf{C}}\left( t \right)\) :

Matrices of the overall damping

\(E_{p}\) :

Elastic modulus of the actual RTS, Pa

\(E_{{\text{m}}}\) :

Elastic modulus of the RTS in the simulation experiment

\(T_{f}\) :

Service life of test pipe, year

\(C_{D}\) :

Test specimen size correction factor

\(R_{a}\) :

Surface roughness of the specimen, μm

\(S_{be}\) :

Standard stress, Pa

\(D^{\prime}\) :

Total fatigue damage

RTS:

Riser–test pipe system

VIV:

Vortex-induced vibration

CF:

Cross-flow

BOP:

Blowout preventer

LMRP:

Lower marine riser packing

3D:

Three-dimensional

CFD:

Computational fluid dynamics

IL:

Inline

RMS:

Root mean square

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 52105125 and No. 51875489), the China Postdoctoral Science Foundation (Grant No. 2021TQ0273) and Sichuan Province Youth Science and Technology Innovation Team (Grant No. 2019JDTD0017).

Funding

The funding was provided by National Natural Science Foundation of China (Grant Nos. 52105125, 51875489), Postdoctoral Research Foundation of China (Grant No. 2021TQ0273) and Sichuan Province Youth Science and Technology Innovation Team (Grant No. 2019JDTD0017).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, 610500, China

    Xiaoqiang Guo, Yuxin Nie, Jun Liu & Guorong Wang

  2. School of Mechanical Engineering, Hebei University of Technology, Tianjin, 300401, China

    Xiaoqiang Guo

  3. Energy Equipment Institute, Southwest Petroleum University, Chengdu, 610500, China

    Yufa He, Liangjie Mao & Guorong Wang

  4. CNOOC Research Institute Co., Ltd., Beijing, 100028, China

    Yufa He

  5. Industrial Systems Engineering, University of Regina, Regina, SK, S4S 0A2, Canada

    Xiaoqiang Guo & Liming Dai

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  1. Xiaoqiang Guo
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Guo, X., Nie, Y., Liu, J. et al. Three-dimensional nonlinear vibration model and fatigue failure mechanism of deepwater test pipe. Nonlinear Dyn 108, 1101–1132 (2022). https://doi.org/10.1007/s11071-022-07260-6

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