Study on the Design Method of the Jack-up’s X-Type Cantilever Allowable Load Nephogram

Yazhou Zhu, Chengmeng Sun, Hongde Qin, Bin Jiang and Yansong Fan

1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

2.Offshore Engineering Equipment Research Institute, Bohai Equipment Manufacturing Co., Ltd., China National Petroleum Corporation(CNPC), Panjin 124010, China

1 Introduction1

The Jack-up dominates the floating offshore drilling units market with its advantages of mobility, convenient operation and low manufacturing cost. By May of 2013,Jack-up units totaled up to 563 worldwide according to the statistics collected by RIGZONE. The Jack-up’s drilling floor has developed from a primitive rabbet type to the current cantilever type with the side beams for the load. The design and construction of the Jack-up with the cantilever greatly enhance the operation function, reduce the load carrying capacity and lower the design cost of the well jacket platform, which has caused it to become prevalent in the oil and gas exploitation in the continental shelf seas where the water depth is lower than 150 m. The cantilever type has been adopted by almost all the newly-built Jack-ups and the soon to-be-built ones (Chen and Li, 2004).

The Jack-up consists of four parts: mail hull, braced legs,spud can and cantilever. The spud can and legs are the main bearing structures that are affected by the atmosphere,seawater and seabed. Many studies have been focused on the assessment of the bearing capacity and structure strength of the spud can and legs (Karunakaranet al., 1998;Karunakaran and Spidsoe, 1997). Karunakaran and Spidsoe from Norway have researched the Jack-up in several areas,including the method of dynamic response analysis,nonlinear stochastic response characteristics, environment loads and foundation models. Cassidy (Cassidy, 2011;Vlahoset al., 2011; Cassidyet al., 2004, 2006, 2010;Bienen and Cassidy, 2009) from the Centre for Offshore Foundation Systems of UWA have conducted research into the Jack-up’s foundation safety performance through the combination analysis method of theory and tests. Cassidy(1999) also studied the non-linear effects on the Jack-up structures subjected to random waves for his PhD thesis.Zhanget al. (2013) obtained the response characteristic by using the fifth-order stokes regular wave theory to simulate water particle motion regularity, and probed the effects of variable environment loads on the results of the numerical simulation. Lu(2005) and Wanget al.(2009) researched the Jack-up dynamic responses under wave and current loads.Li and Li (2011) have done some basic studies on the static and dynamic response of the Jack-up unit and seabed strength.

The drilling zone and drilling capacity have become important parameters for the value of the advancement of an ocean platform. The application of the cantilever for the Jack-up expands the drilling zone and raises the operation efficiency, which has caused the cantilever Jack-up to become the major design type. At present, the common types of cantilever construction include the XY-type and the X-type: the XY-type of cantilever can move longitudinally and laterally to cover a larger drilling zone than the other types, and its patent protection is registered by MSC (Qian and Bo, 2009). The X-type, widely used now, can only do longitudinal movement, and its lateral drill zone depends on the drill floor’s lateral movement.

The present studies mainly stress the comparative analysis of the different cantilever types. Renet al.(2011),from Harbin Engineering University, presents his type-selection guideline for cantilever design by comparing the X-type cantilever, XY-type cantilever and rotating cantilever. Fanet al. (2011) performed analysis on cantilever dimensions, the stress conditions with the drilling operation and the assessment method for structure strength.Wanget al. (2009) also gave the cantilever selection guideline by making a comparative analysis of the characteristics of the various structures of the cantilever beam. A conclusion can be drawn from the studies mentioned above that there are few studies focused on the bearing capacity and structure strength assessment of the cantilever. The allowable loading nephogram in this paper aims at the X-type cantilever and it is designed with a comprehensive consideration for all the combination loads with the different conditions of the cantilever extending and drilling floor traversing.

2 Design method of the allowable loading nephogram

The allowable loading nephogram describes the interrelations between the stand set-back area load, wind load, derrick and drilling floor self weight, drilling load including hook load, rotary table load,pensioner load, and the cantilever and stockyard self weight, in different conditions of the cantilever extending and drilling floor traversing. The basis of the designing nephogram is the strength of the cantilever satisfying the rules (SNAME,2002). This paper explores the interrelationships among the cantilever position, drilling floor and the loads through analyzing the structures and loads characteristics of the “X”type cantilever and simplified mechanics model with the restriction of the maximum moment capacity of the cantilever single side beam. By referring to several of the typical positions’ design load values, the cantilever allowable load nephogram can be obtained by using the suitable interpolation method. This paper mainly studies the influences of the various cantilever loads on the nephogram and the corresponding processing methods.

2.1 Wind load

The transverse moving structures of the drill floor and derrick are bearing wind loads which can be transferred to the cantilever through transverse tracks. The wind load calculation of the drill floor and derrick can refer to the relative rules of the classification society.present the wind forces of the drill floor and derrick, wind bending moment, and the angle of wind direction.Ffcan be neglected because of its minimal force on the cantilever since the wind direction is parallel to the cantilever surface .Mfcan transfer to the bearing reactions ofM,N,PandQwhich are the connecting points between the cantilever and drill floor. The above definitions are shown in Fig.1.

Mfbreaks downMfxandMfy, as shown in equation 1.

where,Mfx-wind bending moment in the x-axis direction,Mfy- wind bending moment in the y-axis direction,q-wind angle.

The reaction force of points M,N,P and Q caused byMfxandMfyare shown in equation 2.

where，RMfx，RNfx，RPfx，RQfxare the reaction forces of pointsM,N,PandQcaused byMfx,RMfy，RNfy，RPfy，RQfywhich are the reaction forces of pointsM,N,PandQcaused byMfy.

Fig. 1 Diagram of the cantilever overhang operation

It can obtain the reaction force of pointsM,N,PandQby the principle of the forces equilibrium, as shown in equation (3).

where,RMf-PointMreaction by wind load,RNf-Point N reaction by wind load,RPf-PointPreaction by wind load,RQf-PointQreaction by wind load,d1-Half the width of the drilling floor through theydirection,d2-Half the width of the drilling floor through thexdirection.

The foundation beams between pointAandCapproximate the simple beams, based on which the pointAreaction can be obtained under the effects ofRMfandRPf,as shown in equation (4). The pointBreaction can be obtained in the same way.

where,RAf-PointAreaction by wind load,RBf-PointBreaction by wind load.

The cantilever single side beam between pointAand pointEis approximated to the clamped beam, based on which the pointEbending moment can be obtained under the effects ofRAfandRBf, as shown in equation 5.

where,MEf-point E moment by wind load,x-extended distance of the drilling floor,y-transverses the distance of the drilling floor,b-Half the width of the cantilever.

2.2 Stand set-back area

The weight of the stand set-back area isGs, the center of gravity isand the reaction forces of pointsM,N,PandQare caused by the beading moment running around the x-axis and y-axis as shown in equation 6.

It can obtain the points’ reaction force of points M,N,P andQthrough the stand set-back area weight by the principle of forces equilibrium, as shown in equation 7.

It can obtain the points’ reaction of pointsAandBthrough use of the simple mechanics model between theACbeam and BD beam, as shown in equation (8).

where,RAs,RBs-pointsAandBreaction by the stand set-back area weight.

Whereas, the bending moment of point E of the cantilever single side by the stand set-back area load can be calculated by equation 9.

where,MEs-point E moment by the stand set-back area weight.

2.3 Self weight of the drill floor and derrick

The equipment weight of the drill floor and derrick isGd, and the center of gravity is(x+ Dxd,y+ Dyd), the equation (10) can be obtained as follows,

where,MEd,RAd,RBd-pointsE,AandBmoment by self weight of the drill floor and derrick.

2.4 Drilling loads

The drilling load ishG, including the hook load, rotary table load and pensioner load, and the load acts on well bore(x,y) , the equation 11 can be obtained as,

where,RMh,RNh,RPh,RQh-reaction forces at pointsM,N,PandQcaused by the drilling load, and reaction forces at pointsAandBcan be obtained by the principle of forces equilibrium, as shown in equation (12).

The pointEbeading moment is calculated by the principle of force equilibrium of reaction forces at pointsAandB. The beading moment is shown in equation (13).

where,MEh-point E moment by drilling loads.

2.5 Self weight of the cantilever

The self weight of the cantilever isbG, excluding the weight of the drill floor and derrick, which distributes unevenly along the cantilever’s lengthbL. The pointEbending moment is calculated by equation (14).

where,MEb-pointEmoment by self weight of the cantilever.

2.6 Pipe stockyard load

The weight of the drill pipe and drill tool in the cantilever stockyard isGp,xis the length from the well bore to the transom,xais the length from the aft of the pipe stockyard to the well bore, andxfis the length from the fore of the pipe stockyard to the well bore. The length is shown in Fig.2. The length area of the stockyard isand the breadth isBp. The pointEbending moment is calculated by equation (15) assuming that the weight distributes evenly in the area.

Fig. 2 Schematic diagram of the pipe stockyard

where,MEp-point E moment caused by the pipe stockyard load.

2.7 Interpolation method

The moment of cantilever’s pointEis calculated by equation (16).

where,MEis the beading moment of cantilever’s pointE.

Generally, a series of allowable combination loading values in different positions of the cantilever extending and drill floor traversing are given at the preliminary design period of the Jack-up. Based on these given values, this paper obtains a series of values of the pointEbending moment, such asThe maximum bending momentis chosen to be the basis for designing the allowable load nephogram. The nephogram’s values need to match the load values.

where,Mmax-the maximum bending moment of pointEwhen the cantilever extends.

3 Allowable load nephogram calculation examples of cantilever for 300ft Jack-up

The method mentioned above is verified by the 300 ft Jack-up as an example.

The parameters are shown below,

The length of cantilever is 39.4 m, the half breadth is 9.15 m, the breadth of drilling floor is 10.668 m and half breadth is 5.334 m, the length of drilling floor is 12.192 m and half length is 6.096 m, the weight of the stand set-back area is 81 t, the gravity center of stand set-back inxdirection is the same as the center of drilling floor and the gravity center deviation in y direction is 2.95 m, the weight of the drill pipe and drill tool in the cantilever stockyard is 204 t, the length of cantilever stockyard area in x direction is from 9.9 m to 27.3 m, the equipment weight of the drill floor and derrick is 670 t, the gravity center of the drill floor and derrick deviation in x direction is ?0.06 m and the same as the center of drilling floor in y direction, the self weight of the cantilever is 600 t.

The maximum extending length of the cantilever is 15.24 m, and the maximum transverse length is 4.57 m. The values of the allowable combination drilling loads including the weight of the stand set-back area in several typical design positions are shown in Table 1.

Table 1 Allowable design drilling load

The cantilever allowable load nephogram is obtained in the working condition by the above method and the given values that are shown in Fig.3.

Fig. 3 Allowable drilling load nephogram (t)

The maximum capacity of the cantilever is 919 t, when it extends from 0 to 8.53 m in the x direction and the drilling floor makes transverse movement arbitrarily. The cantilever’s capacity decreases in a saddle shape when it extends more than 8.53 m. The cantilever’s capacity is 690 t when it extends to 15.24 m and the drilling floor is in the middle area. But the cantilever’s capacity reduces to 189 t when the drilling floor traverses to the limit position, just at the max. transverse position.

From the load nephogram, the designers can get that when the drilling floor moves less than 8.53 m inxdirection,the drilling load can reach the maximun capacity, and when the drilling floor moving out of the above area, the drilling load will decrease in saddle sharp.

Compared with the table of allowable design drilling load shown in Table 1, all the values obtained from the above calculations are smaller than the allowable load values. The above analysis indicates that this nephogram is a direct guideline for designing the cantilever structure.

4 Conclusions

Taking the X-type cantilever as the object, this paper provides the design and calculation methods. The validity and rationality of the adopted theory and method are verified in this paper through analyzing the practical examples. To each a conclusion, there are several points we can take from this paper:

1) The allowable drilling load can reach the maximum value when the cantilever extends in the defined zone and the allowable load at the well bore decreases with the extending of the cantilever.

2) The allowable load at the well bore is in a decreasing trend as the drilling floor moves from the central axis of the cantilever to the limit position in the traverse direction,when the cantilever extends to the maximum position.

3) The allowable drilling load reduces from 919 tons to 690 tons when the drilling floor is at the central axis of the cantilever without the transverse motion, and the cantilever extends from 8.53 m to 15.24 m, the limit position of the well bore in which the condition of the drilling capacity reduction factor is 0.25. The allowable drilling load reduces from 690 tons to 189 tons when the drilling floor is at the ±4.57 m offset position in the transverse direction, and the cantilever extends to the maximum position, and in this condition the drilling capacity reduction factor reaches 0.73. The calculation examples in this paper indicate that the allowable drilling load reduction factor in the transverse motion of the drilling floor is more sensible than in the extending motion of the cantilever and also highlights the validity and rationality of the adopted theory and method.

Attention should be paid to the fact that the method in this paper is only suitable for speed-estimates of allowable loads at the preliminary period of the cantilever design.

The authors convey their appreciation to the China National Petroleum Corporation, Bohai Equipment manufacturing Co., Ltd. Offshore Engineering Equipment Research Institute for their technical discussions and rig data during the course of this work. The corresponding author also thanks his dear wife Minghui Jin for her help during this work.

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