^{1}

^{2}

^{2}

^{2}

^{2}

^{1}

^{2}

Deepwater surface BOP (surface blowout prevention, SBOP) drilling differs from conventional riser drilling system. To analyze the dynamic response of this system, the riser-conductor was considered as a beam with varied cross-sections subjected to loads throughout its length; then an equation of motion and free vibration of the riser-conductor string for SBOP was developed. The finite difference method was used to solve the equation of motion in time domain and a semianalytical approach based on the concept of section division and continuation was proposed to analyze free vibration. Case simulation results show that the method established for SBOP system natural frequency analysis is reasonable. The mode shapes of the riser-conductor are different between coupled and decoupled methods. The soil types surrounding the conductor under mudline have tiny effect on the natural frequency. Given that some papers have discussed the response of the SBOP riser, this work focused on the comparison of the dynamic responses on the wellhead and conductor with variable conditions. The dynamic lateral displacement, the bending moment, and the parameters’ sensitivity of the wellhead and the conductor were analyzed.

Several operators have developed surface BOP (surface blowout prevention, SBOP) drilling technology for deepwater drilling. SBOP drilling differs from a conventional riser drilling system: the BOP stack is located at the surface below the drill floor of the platform, not at the seabed. Another key difference is that the riser of the SBOP drilling system is designed to contain wellbore pressure, whereas a conventional drilling riser does not contain pressure. The SBOP drilling system can use smaller 2nd- or 3rd-generation semisubmersible rigs for operation. Moreover, it has illustrated a considerable amount of day rate saving over traditional drilling methods using subsea BOP [

Surface BOP is not a new concept, but it was extended into deepwater only a few years ago. Based on successful drilling campaigns in Asia, Shell extended its SBOP technology to the more demanding offshore operations in Brazil with the implementation of a SID. Unocal and Transocean pioneered the application of the SBOP from floating drilling units, which began in early 1996 in the relatively benign environment of Southeast Asia (Kozicz, 2006) [

Typical configurations of the casing riser include diameters of 273.1 mm, 339.7 mm, and 406.4 mm. At the top and bottom of the casing riser, heavy walled transition joints are required to distribute stresses [

Specialized computer programs are generally used to predict conventional riser’s behavior under the designed conditions [

For the SBOP drilling system, the design loads include bending loads, coming from the riser, stress joint and wellhead above the mudline, and soil reaction below the mudline. IADC identified that the casing riser and conductor analysis should be conducted in a coupled manner [

However, the casing riser analysis for the SBOP drilling system is conducted in accordance with API RP 16Q for the conventional riser. Some literatures discussed the dynamic behavior of the SBOP drilling riser. Morooka et al. (2008) presented a numerical simulation to estimate the riser behavior for a drilling system with surface BOP, but the research did not consider the coupling effect between the wellhead and conductor [

In this paper, a coupled time-domain dynamic FDM method for the riser-conductor of the SBOP system is derived, and a semianalytic method is developed for the free vibration of riser-conductor. These methods are more convenient for the analysis coupled with the riser, SID, wellhead, and conductor of the deepwater SBOP drilling system.

As the transition joints connect to the surface BOP and SID, there is no rotary joint on the riser-conductor for the SBOP system. Thus, the riser-conductor can be considered as a beam with varied cross-sections subjected to loads. The riser-conductor of the SBOP system is modeled as a variable section Euler-Bernoulli beam undergoing transverse vibration under axial force, as is shown in Figure

Forces diagram of SBOP system.

By assuming (1) the riser-conductor is a Euler-Bernoulli beam, (2) the riser and casing string are both linear elastic, (3) the drilling string has no effect on its bending rigidity, and (4) the vessel, wave, current, and riser all move in a plane, then the riser can be modeled as a beam subjected to loads throughout its length with boundary conditions at the top and bottom ends.

According to the Euler-Bernoulli theory [^{2}; ^{4};

The external forces on the riser, SID, and wellhead can be computed using the Morison equation (American Petroleum Institute, 2001) [

The bending stiffness of the riser can be calculated easily; however, the strings under the mudline are much more complicated containing the conductor, cement, and surface casing. Su et al. (2008) described a method to obtain the equivalent bending rigidity [

The riser mass per unit length should include the mass of the riser itself and the internal drilling mud [^{3}; ^{3}; ^{3}; ^{3}; ^{3}; ^{3}; ^{2};

The stiffness of the conductor and casing string can be derived from

As (

The initial condition of the equation of motion is^{2};

It is difficult to solve the equations analytically; therefore, numerical simulation with the finite difference method was adopted in this paper.

The riser-conductor string is divided into

According to the difference scheme, the differential equations of the upper boundary condition are expressed as in (

When

Starting from the initial conditions, the responses at a series of discrete time instants can be obtained through direct integration. MATLAB was employed to solve the model by time step. Through iterative calculation, the displacement, offset angle, bending moment, shear force, and soil reaction force at each node and any time were calculated.

For the free vibration of the riser-conductor system, (

Assuming that the system is a uniform beam, (

The solution of (

The riser-conductor of the deepwater SBOP system consists of several sections of different diameters shown in Figure

The segmental diagram of SBOP riser-conductor.

For the segment

Let

Then (

Therefore, the

Since the deflection, slope, moment, and shear force of the

By substituting (

As (

Assuming

Solving (

Then, (

A case study with the parameters given in Table

Basic parameters.

Parameters | Value |
---|---|

Water depth/m | 1361.0 |

Length of casing riser/m | 1350.0 |

OD of casing riser/m | 0.3397 |

ID of casing riser/m | 0.3112 |

Platform offset/% water depth | 3.0 |

Tension ratio of riser (TTR) | 1.2 |

Velocity of surface wind/m⋅s^{−1} |
1.0 |

Tide velocity/m⋅s^{−1} |
0.5 |

Current velocity/m⋅s^{−1} |
1.0 |

Significant wave height/m | 12 |

Significant wave period/s | 8 |

Platform slow drift amplitude/m | 9.3 |

Platform slow drift period/s | 259.8 |

Elastic modulus of steel/GPa | 210.0 |

Density of steel/kg⋅m^{−3} |
7850.0 |

Density of seawater/kg⋅m^{−3} |
1030.0 |

Density of drilling mud/kg⋅m^{−3} |
1200.0 |

Wellhead above the mudline/m | 3.0 |

Height of SID/m | 8.0 |

Equivalent outer diameter of SID/m | 0.8 |

Length of transition joint/m | 10.0 |

Equivalent OD of transition joint/m | 0.3683 |

Equivalent WT of transition joint/m | 0.0508 |

Length of conductor/m | 60.0 |

OD of conductor/mm | 0.762 |

WT of conductor/mm | 0.0254 |

Elastic modulus of cement sheath/GPa | 18.0 |

Length of surface casing/m | 500.0 |

Seabed soil conditions vary substantially around the world. However, to simplify the calculation process and compare the results, the soil type below the mudline 0–60 m is assumed as all clay or sand layer. The six soil type properties are listed in Table

Soil parameters.

Clay 1 | Clay 2 | Clay 3 | Sand 1 | Sand 2 | Sand 3 | ||
---|---|---|---|---|---|---|---|

Undrained shear strength/kPa | 20.0 | 60.0 | 60.0 | Angle of internal friction/degree | 30.0 | 39.5 | 39.5 |

Submerged unit weight/(kN/m^{3}) |
7.0 | 7.0 | 8.0 | Submerged unit weight/(kN/m^{3}) |
8.5 | 8.5 | 10.0 |

The natural frequencies with the data given in Tables

First six-order natural frequencies.

Mode #1 | Mode #2 | Mode #3 | Mode #4 | Mode #5 | Mode #6 | |
---|---|---|---|---|---|---|

Natural frequencies/Hz | 0.04895 | 0.08687 | 0.14998 | 0.18547 | 0.21846 | 0.27866 |

First five natural mode shapes for SBOP riser-conductor.

The mode shape comparison results for 4 situations (

First four natural mode shapes for 4 situations.

Although the TTR has little effect on the mode shape, its effect on the natural frequencies for the modes is obvious as shown in Figure

Mode shapes and natural frequency with variable TTR and soil type.

To analyze the dynamic response of the riser-conductor for the SBOP drilling system, lateral displacement, bending moment, and soil reactions at the different positions of the riser-conductor string are compared. Given that some papers have discussed the response of the SBOP riser, this work focuses on the comparison of the dynamic responses on the wellhead and the conductor with variable conditions.

The P-M spectrum has been employed to calculate the motion of the platform and the simulation results are shown in Figure

Dynamic response of the platform.

For the SBOP drilling system, some key joint points are critical to the drilling operation. This work focuses on 4 positions on the riser, namely, the bottom of the upper transition joint (USJ), the elevation 300 m under the mean water level (MWL), the elevation 800 m under the mean water level (MWL), and the top of the lower transition (stress) joint (LSJ), and 4 positions on the conductor, including the subsea wellhead (WH), the mudline (ML), −5 m under the ML, and −10 m under the ML.

The first four pictures in Figure

Lateral displacement at different positions.

In Figure

Dynamic bending moment on the riser, wellhead, and conductor.

Comparing the bending moment and the lateral displacement in the same position simultaneously in Figure

Moment-displacement curves.

It is also found that the displacement varies more at the bottom of the USJ than at the top of the LSJ. The displacement-moment curves change on the negative

The deformation and stress of the casing string below the mudline and the soil reaction force around the casing string are analyzed in a slow-drift period of a drilling platform. When the vibration reaches the steady state, 8 time points (

Deformation and stresses of the conductor in a drift period.

It can be seen from Figure

Effect of the platform offset and conductor size on wellhead and conductor.

Effect of the platform surge amplitude and riser size on wellhead and conductor.

Effect of the soil properties at wellhead, mudline, and −5 m on conductor.

For the SBOP drilling system, the riser-conductor is considered as combination sections with different cross-sections subjected to loads throughout its length, and a FDM solution is derived in time domain. Results show that the displacement amplitude at the wellhead is more than in other places of the conductor under mudline. The largest bending moment of the riser focuses on the LSJ, and the moment becomes smaller at the place of the conductor under the ML −5 m. The deformation, stress, and surrounding soil reaction of the casing string change with time in the slow-drift period.

Based on the concept of section division and continuation, a semianalytical approach for analyzing free vibration of the SBOP riser-conductor with variable cross-section is proposed, which can actually be applied to any variable cross-section. And this method established for SBOP system natural frequency analysis is reasonable. Results show that the mode shapes have some difference between the coupled and decoupled method. The natural frequencies at diverse modes have little variation with variable TTR. The soil types surrounding the conductor under mudline have very tiny effect on the natural frequency of the riser-conductor system.

The authors declare that there are no conflicts of interest regarding the publication of this article.

This work was done at the Drilling Technology Laboratory (DTL) at the Memorial University of Newfoundland, Canada. This work was supported by the National Natural Science Foundation of China (Grant no. 51004119), the Chongqing Research Program of Basic Research and Frontier Technology (Grant no. CSTC2015jcyjA90021), and the Academician Led Special Project of Chongqing Science and Technology Commission (Grant no. cstc2017zdcy-yszxX0009).