Hydro TLP.pdf

Ocean Engineering 30 (2003) 1269–1282www.elsevier.com/locate/oceaneng

Hydrodynamic design of a TLP type offloadingplatform

Muhittin Soylemeza,∗, Oguz Yılmazb

a Department of Ocean Engineering, Istanbul Technical University, Ayazaga Kampusu, 80626,Istanbul, Turkey

b Department of Mathematics, Abant Izzet Baysal University, Golkoy Kampusu, Bolu, 14280, Bolu,Turkey

Received 9 April 2002; accepted 24 July 2002

Abstract

The hydrodynamic aspects of a design study of a TLP type offloading platform, that willoperate in the north-east of Marmara Sea are presented in this paper. The main scope of thepaper is to discuss the general properties of the platform and environmental conditions prior tothe calculation of hydrodynamic forces based on Morison’s equation and the resultant motionresponses. The non-linear quasi-static effect is taken into account due to set-down phenomenonin the calculation of surge responses. Comparisons between the designs with two differentdrafts and the results of their spectral analysis are presented. With decrease in the draft of theplatform, surge responses increase in the low frequency region. Since the differences betweenthe surge responses of two different designs are not significant, the shorter platform has beenadopted for the location due to its low cost. The non-linear set-down effect is not foundto be significant because this platform has relatively short taut chains compared to those ofconventional type. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Offloading platform; Hydrodynamic design; Non-linear quasi-static effect

∗ Corresponding author. Fax:+90-212-285-6508.E-mail address: [email protected] (M. So¨ylemez).

0029-8018/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0029-8018(02)00107-5

1270 M. Soylemez, O. Yılmaz / Ocean Engineering 30 (2003) 1269–1282

1. Introduction

This paper presents some results of a hydrodynamic analysis of a TLP typeoffloading platform. This platform is designed to operate nearshore of Ambarı, whichis a suburb located west of the city of Istanbul. The platform is intended to servethe tankers in the severe sea conditions to offload their cargo to the storages on landwithout any trouble to manouvre to board to the pier.

Tension leg platforms (TLPs) are of great interest to offshore researchers in broadareas. One of the areas investigated in TLPs is their surge motion either induced bywave or current. Lee et al. (1999) studied the effect of material properties of strainedelastic tethers on the surge motion of the platform. Jain (1997) presented a motionanalysis method of TLPs non-linearly coupled in the restoring force matrix in sixdegrees-of-freedom. Paik et al. (1996) applied quadratic transfer functions to predictand compare responses of a TLP with those obtained with a linear transfer functionsonly. A wide range of different aspects of research studies on TLPs is widelypresented in a review paper by Adrezin et al. (1996).

In this paper, the platform is analysed for the conditions that are obtained for thenorth of Marmara Sea. The configuration of the platform is unique in its own oper-ational conditions. However, it is much like a TLP type of structure except the ten-dons are made of chains instead of cables. The main floating body of the structureis also longer than any conventional TLP configuration comparing to its lateraldimensions. This main body of the structure is shortened in the second phase of theproject in order to minimize the initial building cost. The fundamental purpose ofconstructing a floating offloading platform for the location having shallow watercharacteristics is to keep the construction and material cost of the platform low. Thereason for deciding on a TLP type of configuration is mainly due to almost noheave response during the offloading process and that TLPs have also better responsecharacteristics in surge and sway motions than other type of offshore platforms.

The motion of the platform is analyzed using both single-wave prediction andspectral methods. In storm conditions, surge motions could be quite large causingnon-linear effects in the motion responses of the platform. Therefore, the non-linearquasi-static effect is also included due to set-down occurring in the surge motion.Wave forces are calculated using Morison’s equation since the platform has all slen-der cylindrical members.

The motion characteristics of the platform are derived and found to be appropriatefor this type of structure to operate as an offloading platform. The motion responsesestimated by spectral analysis are more favorable than those by the single-waveprediction method. The emphasis is shown by including the set-down behavior dueto non-linear stiffness, which comes into effect during large surge motions.

The paper starts with defining the geometry of the platform and the environmentalconditions. General particulars of the platform are presented in Section 2. Naturalfrequencies and the mean displacement due to current are given in Section 3.Methods of calculating the hydrodynamic forces and motions are briefly introducedin Section 4. Results for the single-wave prediction method are presented in Section

1271M. Soylemez, O. Yılmaz / Ocean Engineering 30 (2003) 1269–1282

5. The non-linear quasi-static set-down effect is described in Section 6. Finally, Sec-tion 7 summarizes the results of spectral analysis.

2. Geometry of the structure and environmental data

The general configuration and the coordinate system with the geometrical drawingdetails are depicted in Fig. 1 and Fig. 2, respectively. Structure consists of fairlyslender cylindrical members with 1/20 column diameter and length ratio. The plat-form is moored with taut vertical chains to restrict the vertical heave motions. Mainparticulars of the platform is given in Table 1. The environmental data are listed foroperational and 50-year storm conditions in Tables 2 and 3, respectively.

As seen in Fig. 2, x and z axes are placed on the free surface of the sea while yaxes is taken vertically upward. Motions in x direction is defined as surge; in zdirection as sway and in y direction as heave.

Fig. 1. General configuration of TLP.


Fig. 2. Definition of the coordinate system.

Table 1Main particulars of the platform

Properties Values

Column Diameter (D, R = D/2) 1.016 mColumn Length (L) 20 m and 24 mWater Depth (h) 40 mDistance between the centres of columns (xc = zc) 7 mChain length (l) 20 m and 16 mChain diameter (d) 0.06 mProof load for chain 1383 kNBreaking load for chain 1942 kNMinimum weight 0.801 kN/mCross sectional area (Ac) pd2/4Initial tension (T0) 71 kN

3. Natural frequencies and mean displacements

Hydrodynamic analysis consists of two parts; in the first part natural frequenciesand mean displacements due to current are calculated and given in this section. Inthe second part, oscillations about the mean displacements are predicted using afrequency-domain analysis, which is presented in Section 5.


Table 2Operational conditions for the Marmara Sea

Properties Values

Maximum wave height (Hmax) 1 mWave period (Tz) 4 sCurrent speed (Vc) 0.5 m/s

Table 350-year storm conditions for the Marmara Sea

Properties Values

Maximum wave height (Hmax) 8.7 mWave period (T-Z) 8 sCurrent speed (Vc) 1 m/s

Natural circular frequencies and periods are calculated using the following equa-tions, respectively:

wni � �ki

Ai

and Tni �2pwni

(1)

where i = x stands for the surge motion; i = y for the heave motion and i = z forthe sway motion. The stiffness in surge direction is calculated as 14.23 kN/m usingthe formula kx = 4 (To/l). The stiffness in heave direction is calculated as 113130kN/m using the formula ky = 4 (ρgp R2 + AcE/l) where E is the Young’s Modulus.The total of mass and added mass in surge direction is 1196.8 kN using the formulaAx = 4ρ (πR2L + πR2L). The total of mass and added mass in heave direction is539.55 kN using the formula Ay = 4r (pR2L + 4/3R3). Undamped heave naturalperiod (Tny) and the frequency (wny) is calculated as 0.138 seconds and 45.36 rad/s,respectively. The natural surge period (Tnx) and the frequency (wnx) is calculated as18.41 seconds and 0.34 rad/s, respectively. Considering the environmental data, itis easily seen that resonance is not possible in the operational site and this will bemore clear when we consider the wave spectrum and the spectral response of theplatform in Section 7.

Using the static calculations due to the mean current velocity, mean horizontaldisplacement is calculated as 0.42 m for the operational conditions based on thecurrent force given by Fc = 4 (1/2 ρ Cd D L V2

c). Similarly, Fc and the mean displace-ment for the 50-year storm condition are calculated as 24 kN and 1.69 m, respectivelyand seems to be quite reasonable for the operational site. Since the wind exposedarea of the superstructure is quite small, the wind forces and the mean displacementdue to wind are ignored.


4. Hydrodynamic forces and motions

4.1. Wave forces

Since the structure consists of slender cylindrical members, Morison’s equation(Morison et al., 1950) is suitable to calculate the wave forces acting on the structure.The added mass (Cm) and the drag (Cd) coefficients are chosen to be 1.5 and 0.6,respectively. These values of Cm and Cd are also suitable for the storm conditions(Sarpkaya et al., 1981).

The horizontal and vertical velocities and the accelerations and the pressure aregiven by the following formulas:

u �∂j∂x

,v �∂j∂y

,u �∂u∂t

,v �∂v∂t

,p � �r∂j∂t

(2)

where ϕ is the velocity potential is defined as follows:

j �g�a

wcosh[k(y � h)]

cosh[kh]sin(kx�wt) (3)

where g stands for the gravitational constant; �a for the wave amplitude; ω for thecircular wave frequency; k for the wave number; h for the water depth and t for thetime. Using the above equations, total heave and surge forces on the structure caneasily be calculated by summing the forces acting on the individual members of theplatform. There will be some cancellations due to phasing. The total heave force iswritten in the following form:

Fy � Asinwt � Bcoswt (4)

in which B = 4(Apy + Aay) cos (kxc/2) and A = 0 and where

Apy � rg�a

cosh[k(h�L)]coshkh

pR2 and Aay �43rR3��aw2

sinh[k(h�L)]sinhkh � (5)

The phase angle for the heave force can be written as Jheave = tan-1 (A/B), thatequals to zero. The total surge force can be given in a similar manner as follows:

Fx � Csinwt � Ecoswt (6)

in which C = -4Apx cos (kxc/2) and E = 4Adx cos (kxc/2) where Apx and Adx aredenotated by the following equations:

Apx � rg�aCmpR2sinh(kh)�sinh[k(h�L)]

cosh(kh)(7)

Adx �12rCdD� �aw

sinh(kh)�2 83p

12�L �

sinh(2kh)�sinh([2k(h�L)]2k � (8)

From the above equation the phase angle for the surge force can be defined asJsurge = tan-1 (C/E).


4.2. Motion responses

Uncoupled heave motion and phase angle are predicted using the following equ-ation of motion in the frequency domain,

Ayy � cyy|y| � kyy � Fy (9)

in which Ay is the mass+added mass of the structure in heave mode; cy is the viscousdamping force coefficient and ky is the restoring force coefficient due to the geometryand the chains. The non-linear viscous damping term is linearized (see Chakrabarti,1987) as follows:

y|y|�8

3p(wyest)y (10)

Hence Eq. 9 can be rewritten as follows:

Ayy � clyy � kyy � Fy (11)

where cly is the linearized viscous damping coefficient defined as cly = cy 8/3π (wyest)and cy is given as cy � 4 1 /2 rCdpR2.

The standard solution of a second order differential equation with harmonic forcingfunction on the right hand side is written as follows:

y � y1sinwt � y2coswt (12)

where

y1 �A(ky�Ayw2) � Bclyw(ky�Ayw2)2 � (clyw)2 and y2 �

B(ky�Ayw2) � Aclyw(ky�Ayw2)2 � (clyw)2 (13)

The phase angle for the heave motion is defined as Jheave = tan-1 (y1/y2). In orderto obtain the solution an initial estimation of yest is used, and after few steps iterationgives the desired result.

The equation of motion for the surge motion is similar to the heave motion exceptthe restoring forces are due to the moorings only, namely:

Axx � cxx|x| � kx � Fx (14)

in which Ax is the mass+added mass in surge direction; cx is the viscous dampingforce coefficient and kx is the restoring force due to the mooring. Viscous dampingis linearised by the following formulation.

x|x|�8

3p(wxest)x (15)

Axx � clxx � kx � Fx (16)

where clx is the linearized viscous damping coefficient defined as clx = cx8/3π(wxest)

and cx is given by cx = 41/2rCdLD. The solution of Eq.16 can be written as follows:

x � x1sinwt � x2coswt (17)


where

x1 �C(kx�Axw2) � Eclxw(kx�Axw2)2 � (clxw)2 and y1 �

E(kx�Axw2) � Cclxw(kx�Axw2)2 � (clxw)2 (18)

The phase angle for the surge response can be written as Jsurge = tan-1 (x1/x2). Inorder to obtain the surge motion, two iterations have to be performed; first, theiteration for the linearized damping term as was done in the heave motion and,second, the iteration to take the non-linear quasi-static effects into account asexplained in Section 6.

5. Results for the single-wave prediction method

The heave response amplitudes of the platform are found to be negligible and arenot presented here. The surge response amplitude and the phase angle for the 50-year design wave conditions are presented in Figs. 3 and 4. The surge responseamplitude for the storm conditions is estimated as 2.7 m and seems to be quitereasonable. For this condition the total mooring force per chain is calculated as 85.8kN and it is well below the anchor holding power.

For the operational conditions the surge response is obtained as 0.06 m and themooring force per chain is 49 kN (Fig. 5). The surge response of the structure reachesto a peak of about 8 m amplitude in the very low region of the frequency of 0.2rad/s (Fig. 3).

In Fig. 6 comparison of surge amplitudes of the designs with two different drafts

Fig. 3. Surge response (50-Year Storm).


Fig. 4. Surge response phase.

Fig. 5. Surge Response (Operational Sea State).

are shown. Draft of the platform was shortened 4 meters in the second phase of theproject in order to keep the initial constructional cost low without a significant causeto the chain loads and changing the significant surge response characteristics of thestructure. As it is seen in Fig. 6, there is not any change in the surge response of


Fig. 6. Comparison of two different designs with two different drafts.

the platform above the frequency of 0.35 rad/s. However, below that frequency only,there is an increment reaching to 33% in the surge response due to 4 m decrease inthe draft of the platform. However, the frequency range where the surge responseincrement occurs does not effect the operation of the platform since the dominantwave frequency for the operational and storm conditions is well outside this rangeof frequencies.

6. Non-linear quasi-static effect

Since the surge motion of the platform will be quite large in storm conditions,the non-linear effects arising due to the stiffness in the horizontal direction shouldbe taken into account. The draft of the platform will increase with large surgemotions and this will result in increased tension in the chains (Fylling and Larsen,1989). Also due to the increase in the angle between the chains and the vertical axis,the restoring force in the horizontal direction will be non-linear. According to themoment equilibrium for the chain the non-linear stiffness will be as follows,

H(x) � 4Tx�

12wl0x

l0cosq(19)

in which T = T0 + �yKwp and �y = l0 (1 - cos θ) and Kwp = ρgpR2, where H(x)stands for the non-linear restoring force; T for the tension in the vertical directionin the displaced position of the platform; T0 for the initial tension; �y for the set-


down due to surge motion; w for the weight of chain per meter; l0 for the initiallength of the chain and q for the angle that the chains make with the vertical.

Relation between the surge motion x and the set down �y is not linear and canbe given as follows (Fylling and Larsen, 1989):

x2 � � �y(T0 � Kwpl0)EAl0

(l0��y)�(T0 � Kwp�y)� l0�

2

�(l0��y)2 (20)

In order to include this non-linear effect into the frequency-domain calculations,the Newton-Raphson and bisection iteration methods are used (Press et al., 1992).

The effect of set-down phenomena due to quasi-static non-linear stiffness is shownin Fig. 7. The non-linear set-down phenomenon comes into effect around the lowfrequency range that is smaller than 0.2 rad/s. The difference between the linear andthe non-linear modelling is quite significant in the lower range of frequencies asseen in the figure. The difference reaches to its maximum about 0.1 rad/s. There isan almost 50% reduction in the surge response estimation by employing the non-linear set-down modelling in the calculations. This nonlinear behavior is not soimportant for the operational conditions since the dominant wave frequencies forboth environmental conditions are well outside this region.

Fig. 7. Comparison of the nonlinear quasi-static effect with the linear model.


7. Spectral analysis

The spectral analysis is only performed for the 50-year storm conditions. Theshort-term wave characteristics are represented by a JonSwap spectrum with 4.4meters significant wave height Hs and 8 seconds zero crossing period Tz (Fig. 8).

The surge response spectrum is shown in Fig. 9 and the significant surge responseis calculated using the following equation

SS � 2��

0

Sxx(w)dw (21)

and is estimated as 1.74 meters. It is seen that spectral analysis gives more favorableresults than the single-wave prediction method. When looking at the natural surgefrequency of the structure (wnx = 0.34 rad/s) and its surge response spectrum in Fig.9, it is easy to conclude that the platform’s natural surge frequency is well outsidethe frequency of 0.6 rad/s at which the energy of the wave spectrum is concentrated.Hence, the platform has safe surge response characteristics for the operational site.

8. Conclusions

Hydrodynamic analysis of a TLP type of offloading platform, that will operate inthe north-east of Marmara Sea are carried out in a design study. The design study

Fig. 8. JonSwap wave spectrum (50-Year Storm for Hs = 4.7 m, Tz = 8s).


Fig. 9. Surge Response Spectrum (50-Year storm condition).

consists of two phases: The draft of the platform was chosen 24 m in the first phase.Having the hydrodynamic analysis performed for the preliminary design configur-ation, the draft of the platform was reduced to 20 m in order to lower the construc-tional cost of the platform. Therefore, all hydrodynamic calculations were repeatedfor the shorter form of the platform in the second phase of the design and the follow-ing results are obtained for the second design of 20 m draft.

Under operational conditions, the motion of the platform is negligible particularlyfor the heave mode. The surge response is 2.7 m according to the single-wave predic-tion method, and the significant surge response is found to be 1.74 m using theJonSwap wave spectrum for the 50-year storm conditions with Hs = 4.4 m and Tz

= 8 s. The maximum mooring force is calculated as 83.78 kN per chain under thestorm conditions. Thus, there is no danger that anchors will move.

The motion characteristics of two designs only differ in the very low frequencyrange which is outside the frequency range of the waves. Hence, there is no expec-tation for any unsafe surge motion response for the proposed configuration. More-over, the surge motion calculations are repeated for both linear and the non-linearmodelling in order to take into account the set-down effect. The non-linear modelgives more favorable results than the linear one does. However, the non-linear set-down phenomenon only comes into effect in the very low region of the frequenciesthat is outside the frequency range of the waves.

We can finally conclude that TLP type offloading platform designed for the Marm-ara Sea gives quite good response values and it should be preferred to a fixed plat-form.


Acknowledgements

The authors would like to gratefully acknowledge Professor A. Yucel Odabasi forhis kind interest and encouragement for this study, and the financial support providedby Aygaz A.S.

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