A new type of anti-heave semi-submersible drilling platform

PETROLEUM EXPLORATION AND DEVELOPMENT Volume 44, Issue 3, June 2017 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2017, 44(3): 487–494.

RESEARCH PAPER

A new type of anti-heave semi-submersible drilling platform CHEN Bo, YU Zhiyong*, LYU Yong, LI Xiaojian, LI Chunfang School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Abstract: A new type of semi-submersible drilling platform is designed. The numerical simulation software is used to analyze the heave response of the new platform in the frequency domain and time domain, and the semi-submersible drilling platforms with double-floating four-column structure and heave plate structure are compared with the new platform. This paper introduces the design principles of the new platform and the theoretical basis, mathematical model and boundary conditions during correlation analysis. The numerical simulation results show that the maximum and mean values of the heave response of the new platform are significantly reduced in the frequency domain analysis compared with the double-floating four-column and the heave-plate structure platform; and the new platform has a significant increase in the natural heaving period of the new platform, which can effectively prevent the occurrence of resonance. In the mooring time domain coupling analysis, the surge, sway and roll response of the new platform is small, and the heave response is greatly reduced. In the spectral analysis, the new platform has a smaller peak response and better wave frequency characteristics. The new platform has excellent anti-heave performance, reasonable structure and feasibility, and can provide reference for the design and selection of new generation semi-submersible drilling platform. Key words: drilling platform; semi-submersible drilling platform; heave prevention; frequency domain analysis; time domain analysis

Introduction A drilling platform is important equipment for offshore oil and gas exploitation, of which a semi-submersible drilling platform with unique advantages becomes one of the platforms with the most promising development prospect[13]. In the marine environment, forces applied on a platform are in various forms[45], so it is difficult to analyze the overall performance of the platform with mathematical model, but hydrodynamic simulation is able to solve this problem[6]. The motion of platform in waves is nonlinear, which is caused by the coupling of different forms of motion (such as roll and heave coupling), the platform large-amplitude rolling and complex hydrodynamic loads[7]. The platform has six degrees of freedom in the marine environment[8], due to the structural characteristics of the semi-submersible drilling platform, the roll and heave responses have strong impacts on the safety of the platform[9] under the towing, operation and storm survival conditions, but the increase of additional mass can inhibit the roll and heave responses[1011]. Non-linearity of roll motion can be simulated and studied by using chaos theory, differential dynamical system theory and bifurcation theory. There existing large safety hazard during normal drilling if the heave response is large, in order to reduce the impact of heave and ensure the constant contact of bit with well bottom, heave

compensation device must be installed on the platform, which used telescopic drill pipe in the early stage, and now uses traveling compensation, crane compensation and winch compensation etc.[12]. At present, semi-submersible drilling platform has already developed the sixth generation which combines with the chain and the dynamic positioning system, can reduce the heave motion to some extent, but can not adapt to harsh sea conditions[1314]. Therefore, a new type of semi-submersible drilling platform has been designed (referred to as the new platform), the performance of the new platform has been investigated with hydrodynamic numerical simulation, and compared with the original double floating four column structure platform (referred to as the original platform) and heave plate platform in this study.

1.

Design of the new platform

1.1.

Theoretical basis

When the ratio of the cross-sectional dimension of a structure to the wavelength is less than 0.2, the structure is called a small structure. Wave forces on it are dominated by inertial force and drag force, using a semi-theoretical and semi-empirical Morrison formula[1516], the simplified calculation formula is: F  V  I 3  C a  vw  0.5  C D vw vw e (1) When the ratio of cross-sectional dimension of a structure

Received date: 27 Apr. 2016; Revised date: 10 Mar. 2017. * Corresponding author. E-mail: [email protected] Copyright © 2017, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.

CHEN Bo et al. / Petroleum Exploration and Development, 2017, 44(3): 487–494

to the wavelength is greater than or equal to 0.2, three dimensional potential flow theory is taken[17] to do the analysis. The theory is an important basic theory for hydrodynamic analysis of structures, in which the velocity potential of fluid is particularly crucial. The total velocity potential includes the incident potential caused by the incident wave, the diffraction potential caused by the floating to the flow field, and the radiation potential caused by the perturbation of floating motion to the flow field, namely:

Φ  x, y , z , t   ΦI  x, y , z , t   ΦD  x, y , z , t   ΦR  x , y , z , t 

1.2.

(2)

Mathematical model

The force of current on the platform structure is:

Fliu  0.5Cd  Avliu 2

(3)

where the vliu is the velocity of ocean current. The current velocity of the South China Sea is about 0.2m/s, so relative to wave force on the platform, the force of the ocean current on platform is negligible. The wave force and torque of platform are respectively:

π 2 r 2  HL Fwave  Cm 1  e kh  sin  T2  1  e  kh  π 2 r 2  HLh M  Cm sin  1   2 T kh  

(4)

 Fjpq B jpq   Re   v  jp 1.3. 1.3.1.

1.3.2.

(j=1, 2, …, N; p=1, 2, 3; q=1, 2, 3) (7) where the pjp is pressure vector at any point in flow field, determined by Bernoulli's equation[18]. The relation between radiation wave force and hydrodynamic parameters is: Fjpq   Ajpq vjp  B jpq v jp (8) With further analysis, the calculation formulas of hydrodynamic parameters are:

 Fjpq Ajpq   Re   v  jp

  

(9)

Mooring boundary conditions

v  l  0   vbot

(12)

② Dynamic boundary conditions. For the upper end of the mooring anchor:

v  l  La   vtop   v  l  La   vtop

(13)

For lower end of the mooring anchor:

v  l  0   vbot   v  l  0   vbot

(6)

Sj

Platform displacement boundary conditions

For lower end of the mooring anchor:

is:

Fjpq   p jp  n j ds

Boundary conditions

① Statics boundary conditions. For the upper end of the mooring anchor: v  l  La   vtop (11)

(5)

Determining the hydrodynamic parameter of the platform motion response in waves is the basis of the numerical calculation. When the platform is subjected to a slight oscillatory motion in a specific mode, an outward radiation flow field is generated in a stable flow field to form radiated waves[18]. Separating the velocity and acceleration of the corresponding structure from radiation wave load, we can get the parameters of the radiation wave load related to the velocity and acceleration, namely, additional damping parameter and additional quality parameter are collectively referred to as hydrodynamic parameters[18]. The radiation wave load force is:

(10)

To avoid rigid displacement of the model, displacement boundary conditions are required in the analytical model, that is to say, 3 non-collinear nodes with great strength far away from platform structure evaluation area should be chosen to fix the structure. Displacement boundary conditions are applied at the selected nodes: node 1 restricts z direction displacement; node 2 restricts y and z direction displacement; node 3 restricts x, y, and z direction displacement.

Motion balance equation of platform under the wave load

M m X   CX   D1 X   D2 f ( X )  KX  Fsum

  

1.3.3.

(14)

Flow field boundary conditions

① Free surface boundary conditions. At each point of the free surface:

 2Φ Φ g 0 z t 2

(15)

In the local coordinate system, column surface immersed in sea water should meet the requirements of:

 Φ  z  0   Φ  0  r

(16)

②Surface boundary conditions. Instantaneous normal acceleration of fluid particle is zero for the area where surface total force is zero:  2Φ  0 (17) ③ Seabed boundary conditions. Seabed as a rigid wall, normal velocity component of the fluid particle is zero. ④ Radiation conditions of infinite point. Wave forms spread from near to far, that is when r approaches infinity,  approaches zero. 1.4.

Design principle

Since the external excitation time cannot be controlled, in  488 

CHEN Bo et al. / Petroleum Exploration and Development, 2017, 44(3): 487–494

order to effectively reduce the vertical displacement of the platform, reducing the instantaneous acceleration is an effective way. According to Newton's second law of motion, the mass of the platform should be increased or the resultant force on the platform should be reduced to reduce the instantaneous acceleration of the platform. The resultant force of the platform is the difference of wave force and damping force. Therefore, in the design of the new platform, we have tried to reduce the heave response of platform by increasing the platform's overall quality and the damping force. Under normal conditions, when the water depth is more than 30 m, the sea water is stable, almost unaffected by the waves. Full water tank with a large cross-sectional area and quality, can provide large vertical damping force, and increase the quality of platform. In order to validate the rationality and feasibility of the new platform structure, the platform structure has been compared with double floating four-column structure semi-submersible drilling platform and heaving plate semi-submersible drilling platform. Main sizes of 3 kinds of platforms, simulation environment, platform (columns, floating) working depth and other parameters are the same (Table 1).

2.

Frequency domain analysis

In this study, the platform model was established by ANSYS software, and the hydrodynamic analysis was carried out by classical hydrodynamic analysis software AQWA. AQWA software is the software has the loosest restriction on the number of nodes among various hydrodynamic analysis software, so the grid unit can be smaller and the accuracy of calculation and analysis can be improved. Fig. 1 shows the frequency domain analysis model for the platform. 2.1.

Heave response under unit wave

Fig. 2 shows the heave response of the platform under unit regular waves of different wave directions, and the statistics are shown in Table 2. Table 2 shows that at the wave angles of 0°, 30°, 60°, 90°, compared with the original platform, the maximum values of unit wave of the new platform heave response decrease by 1.790 m, 1.880 m, 2.031 m, 2.094 m respectively, all by more than 49%; compared with the platform of heave plate, the maximum values of unit wave of the new platform heave response decrease by 1.041 m, 1.173 m, 1.428

Fig. 1.

m, 1.552 m respectively, all by more than 36%. At wave angles of 0°, 30°, 60°, 90°, compared with the original platform, the mean values of unit wave of the new platform heave response decrease by 0.283 1 m, 0.253 1 m, 0.239 5 m, 0.269 6 m respectively, all by more than 48%; compared with the heave plate platform, the mean values of unit wave of the new platform heave response decrease by 0.241 5 m, 0.231 9 m, 0.243 3 m, 0.277 4 m respectively, all by more than 47%. Therefore, under the action of unit regular waves, the new platform has a good anti-heave characteristic. From Table 2, it can be seen that with the increase of wave angle from 0° to 90°, the maximum values of platform heave increase, and the average values first decrease and then increase. 2.2.

Natural period of heave

Analysis shows that the natural periods of the original platform, heave plate platform and the new platform are 18.92, 16.31 and 39.81 s respectively. The waves in the ocean have uneven periods, but the waves with periods of 130 s occupy more than half of the total energy of the ocean waves, and the corresponding energy peak period is about 10 s. In the selection and design of platform, the heave natural period should be kept away from 10 s, the new platform has a maximal Table 1.

Main dimensions and draft of the platform model

Parameter Floating body length

Parameter Parameter value/m 101.23

Heave plate width Connecting column diameter Connecting column length

Parameter value/m 20.00

Floating body width

18.60

Floating body height

10.72

Column length

18.51

Full tank length

101.00

Column width

18.51

Full tank width

40.00

2.15

Full tank height

20.00

Transverse brace diameter Transverse brace length Platform main body draft

60.31

Heave plate length

40.00

20.00

Frequency domain analysis model of the platform.

 489 

Tank transverse brace diameter Tank transverse brace length Heave plate and tank draft

1.50 40.00

2.00 20.00 60.00

CHEN Bo et al. / Petroleum Exploration and Development, 2017, 44(3): 487–494

Fig. 2. Table 2.

Platform heave response under the action of unit regular wave at different wave angles.

Statistics of platform heave response under the action

of unit regular waves Wave angle/(°)

Platform type Original platform

0

30

Heave plate platform

Minimum Maximum Average value/103 m value/m value/m 4.662 3.637 0.549 8 6.700

2.888

0.508 2

New platform

1.430

1.847

0.266 7

Original platform

16.580

3.731

0.512 0

Heave plate platform New platform

9.348 2.097

3.024 1.851

0.490 8 0.258 9

Original platform

7.998

3.890

0.490 4

Heave plate platform

9.400

3.287

0.494 2

New platform

1.555

1.859

0.250 9

ertia force to the acceleration of the platform is the additional mass of the platform, and the larger the value is, the larger the resistance of the accelerated motion of the platform will be. Due to space limitation, only the additional mass components curves of heaving and rolling are shown (Fig. 3), it can be seen that vertical and rolling additional mass of the new platform increase significantly compared with the original platform and heave plate platform, so the new platform can effectively inhibit heave and roll.

3.

Time domain coupling analysis

heave natural period of 39.81 s, far longer than the heave natural periods of original platform and heave plate platform, so the new platform can prevent the occurrence of resonance effectively.

In the time domain coupling analysis, JONSWAP spectrum, which is similar to South China Sea spectrum was used, taking 0.026 2 and 1.520 0 Hz as the lower limit and upper limit of frequency, significant wave height was 3 m, peak frequency was 0.698 1 Hz, and peak factor was 4; The platform was fixed with 12 mooring anchor chains, and the angle between two adjacent anchor chains is 30° (Fig. 4). Considering the key factors affecting platform motion response, surge, sway, heave and roll are selected to be main responses for analysis, especially for the heave response.

2.3.

3.1.

60

90

Original platform

30.610

3.956

0.524 6

Heave plate platform

14.010

3.414

0.532 4

New platform

4.837

1.862

0.255 0

Additional mass

The reaction force of the drilling platform is called the additional inertia force, which is opposite to the acceleration of the platform. In accelerated motion of platform, additional inertia force acts as a resistance, but it acts as a dynamic force in decelerated motion of platform. The ratio of additional in-

Time course of surge, sway and roll

From Figs. 5 and 6, it can be seen that the new platform has much smaller surge and sway response compared with original platform and platform of heave plate, so the possibility of fatigue failure due to excessive longitudinal and lateral motion is reduced; the new platform also has much smaller roll

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CHEN Bo et al. / Petroleum Exploration and Development, 2017, 44(3): 487–494

Fig. 3.

Fig. 4.

Platform additional mass.

Time domain coupling analysis model of the platform.

Fig. 5.

Surge and sway response time course curves.

response, lowering the possibility of ship water on deck due to excessive rolling, so the new platform meets the requirements of safe operation in harsh sea conditions. 3.2.

Time course of heave

Fig. 7 shows that, compared with the original platform and heave plate platform, the new platform has much smaller time domain coupling heave response, indicating that the new platform has excellent anti-heave performance. 3.3.

Time domain coupled heave response spectrum

The wave spectrum density function is used to express the distribution of the wave energy to the platform relative to

frequency in the irregular wave, also called energy spectrum. The response spectrum is equal to the product of wave spectral density function and transfer function RAO squared. Time domain coupling heaving response spectrum curve of platform is shown in Fig. 8. It can be seen that, the responses concentrate in the range of 0.30.4 Hz for original platform, with peak of 6.50 m2s, showing wave frequency response; for platform of heave plate, the responses concentrate in the range of 0.30.7 Hz, with peak of 0.85 m2s, presenting wave frequency response; for the new platform, the responses concentrate in the range of 0.30.6 Hz, with peak of 0.13 m2s, presenting wave frequency response mainly with some low frequency responses. Compared with the original platform and

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Fig. 6.

Fig. 7.

Roll response time course curves.

Fig. 8.

Time domain coupling heave response spectrum curves of platforms.

the heave plate platform, the new platform has smaller peak of response spectrum and better characteristics of heave wave frequency.

4.

Heave response time course curve.

Conclusions

In the frequency domain, compared with the original platform and heave plate platform, the new platform has much smaller maximum and mean values of heave response, indicating that the new platform has excellent anti-heave performance. Natural period of heave is an important parameter for platform performance evaluation, natural heave period of the new platform is about two times of the original platform and heave plate platform, can effectively prevent the occurrence of heave resonance, and improve the security of the platform. Additional mass value reflects how difficult it is to change the platform motion state, the heaving additional mass of the new platform is much larger than that of the original platform and heave plate platform, and thus can reduce the

instantaneous vertical effective excitation of platform. In waters of less than 1 500 m deep, the semi-submersible drilling platform is positioned mainly by mooring, the new platform has much smaller surge, sway, and roll in time domain coupling analysis of mooring, and the heave response is much smaller than that of the original platform and heave plate platform, so it has much better anti-heave performance in the same conditions, better operation ability, better adaptability and stability. Compared with the original platform and heave plate platform, the new platform has smaller peak value of response spectrum and better wave frequency characteristics.

Nomenclature A—projection area of structure in the direction perpendicular to the current, m2;

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Ajpq—additional mass parameter, kg;

CHEN Bo et al. / Petroleum Exploration and Development, 2017, 44(3): 487–494

Bjpq—additional damping parameter, kg/s;

θ—wave angle, (°);

C—damping matrix, kg/s;

ρ—sea water density, kg/m3;

Ca—3 × 3 order additional mass coefficient diagonal matrix;

Φ—total velocity potential;

Cd—drag coefficients obtained from experience and experiment;

ΦD—diffraction potential;

CD—3 × 3 order drag force coefficient matrix;

ΦI—incident potential;

Cm—inertial force coefficient;

ΦR—radiation potential.

D1—linear damping matrix, kg/s;

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