Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
Dynamic Response of Deepwater LazyWave Catenary Riser Songcheng Li, 2H Offshore Inc. & Chau Nguyen, 2H Offshore Inc.
1 Abstract Lazy-wave catenary risers have gained popularity as a viable solution to improve fatigue and strength performance at the touchdown zone of a simple catenary riser. With the objective to provide technical reference for a lazy-wave shaped riser, this paper focuses on the study of lazy-wave configurations and dynamic responses when the riser is supported from high motion floating production platforms such as semi-submersibles and FPSOs. The study explores the behavior of lazy-wave risers with respect to a variety of input parameters, such as critical curvature radii, hang-off angle, top tension and buoyancy distribution. A systematic approach to pinpoint driving factors and critical locations is discussed. Equations are also presented to provide an analytic and deterministic approach to a desired lazy-wave shape for further numerical assessment of strength and fatigue responses.
2 Introduction The application of lazy-wave catenary riser (LWR) has been popular in deep water application due to its adjustable payload on vessel and its options to control dynamic strength and fatigue response along the riser [1]. With help of commercial software or self-developed optimization tools [2], current practices rely on numerical approaches using trial and error or iterative procedures to explore a lazy-wave riser configuration [3], which demands a huge effort for optimization. It is time consuming and not cost effective, especially during preliminary screening stage or riser study for a project. The challenge encountered in the optimization of lazy-wave configuration is associated with the lack of parameterized equations for the configurations.
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
In this work, configuration of lazy-wave riser is derived analytically with two design input options. The key factors for dynamic strength and fatigue responses are explored and expressed as equations of the lazy-wave configuration parameters, which provide insight and perspective in lazy-wave riser behavior. This work simplifies the riser optimization process and can be used as a framework for lazy-wave configuration design.
3 Static Configuration of SCR and LWR A simple steel catenary riser (SCR) is considered a cord of uniform density and cross-section area hanging on two ends under gravity and buoyancy force in water [4], although slight variation in density or cross-section may exist due to strakes, marine growth or special joints such as taper stress joint. A typical SCR is characterized by downward wet weight along its length.
A lazy-wave catenary riser (LWR) is a special SCR with a segment of its length equipped with external buoyancy modules, where its upward buoyancy force in water is greater than its downward gravity force and thus an equivalent negative “gravity” force. A typical LWR consists of three segments, each segment a catenary, namely the hang-off catenary (hanging and jumper sections), the buoyancy catenary (lift and drag sections) and the touchdown catenary, as illustrated in Figure 3.1. The buoyancy catenary lies between the hang-off catenary and the touchdown catenary. A typical LWR has a sag bend and an arch bend. The elevation difference between the top of the arch bend and the bottom of the sag bend is termed arch height.
As a general rule of thumb, the buoyancy force provided by the buoyancy modules is around twice the self-weight of the steel pipe with internal fluid. The variation of the net buoyancy buoya ncy force from the buoyancy modules produces p roduces high-arch, mid-arch or low-arch LWR configurations, or a shaped SCR[5]. A shaped SCR is defined as a degenerated LWR with no sag bend or arch bend. That is, its lowest elevation along the hang-off catenary coincides with the highest elevation along the buoyancy catenary at their connection point. A sag bend along the hang-off catenary and an arch bend along the buoyancy catenary distinguish a LWR from a shaped SCR. 2
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
The equations in the subsequent sections apply to SCR, LWR and shaped SCR. 8000
7000
Hangoff Catenary
6000
Hangoff Location
) t f ( d e b5000 a e S m4000 o r f n o i t 3000 a v e l E
Buoyancy Catenary
Touchdown Catenary
Hanging Section Arch Bend
Lift Section Lift Point
Drag Section Drag Point
Jumper Section
2000 Sag Bend 1000
Touchdown Point
0 0
1000
2000
3000
4000
5000
6000
7000
Horizontal Distance from Hangoff (ft)
Figure 3.1 – Example Configuration of Lazy-Wave Catenary Riser 3.1
General Characteristics of SCR
As a special SCR, the LWR shares some common characteristics of SCR such as correlations between curvature, riser mass density, arc length and hang-off angle. A catenary is governed by a hyperbolic cosine function [6] in Equation (1) as illustrated in Figure 3.2: y a (cosh
x a
x
a
1) (e e a
x a
2
2) ,
(1)
where a is the curvature radius of a catenary at its origin, since curvature k or 2
k
where
|
d y dx
2
|
1
,
(2)
dx ds cos , dy ds sin ,
(3)
dy 2 1 ( ) dx
3 2
a cosh
at origin x 0 gives 3
2
x a
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
k
1 a
.
(4)
Y
Y X
ds ds
T+dT
β
dy T
dx
Qds=mgds
X O Figure 3.2 – Coordinate System of Catenary
Curvature Equation (2) can be rewritten as 1
k
a cosh
2
x
a
( a y ) 2
,
a
which dontes the maximum curvature or the lowest curvature radius along a catenary occurs at the origin y=0. The catenary curve is symmetric about the Y-axis in Figure 3.2. Without loss of generality, the absolute values of X and Y are used for the equations in this paper. The arc length of a catenary from its origin can be obtained from 2
S ds
x dy 1 dx a sinh . a dx
(5)
The inclination angle β suffices tan
dy dx
sinh
x a
S a
.
From horizontal equilibrium
T cos (T dT ) cos 0 , one obtains d (T cos ) 0 ,
4
(6)
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
which implies a constant horizontal force along a catenary. By defining horizontal force N and wet weight per unit length Q: N T cos const , Q mg ,
(7)
where m is the wet mass per unit length and g the acceleration of gravity, the relationship between the horizontal force N and wet weight per unit length Q can be derived using vertical equilibrium equation:
T sin Qds (T dT ) sin 0 , d (T sin ) Qds ,
or or
d (T cos tan ) Qds .
(8)
Substituting (3) and (7) into (8) gives d ( N
dy dx
) Qdx 1 (
2
or
N
d y dx
2
Q 1 (
dy dx
dy dx
)2 ,
)2 .
(9)
Substituting Equation (1) to (9), the relationship between the horizontal force N and wet weight per unit length Q is obtained: N aQ const , or a
N Q
.
(10)
This implies that the curvature radius at origin can be adjusted by varying the horizontal force N or the wet weight per unit length Q. 3.2
General Characteristics of Lazy-Wave Riser
The static equilibrium of the LWR illustrated in Figure 3.3 (a) and (b) indicates that, the resultant forces at the sag bend B and the arch bend D are horizontal and both equal to the horizontal force N at the touchdown point. In the vertical direction, there are no shear forces at points B and D, which requires static equilibrium of the weight of the jumper section BC and net buoyancy force of the lift section CD, as well as the drag section DE and the touchdown catenary EF. In other words, the net buoyancy force of the lift section CD “lifts” the wet weight of the jumper section, and that of the drag section “drags” the wet weight of the touchdown section. 5
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
N
Lift Section
N
D
Drag Section
D
C
E
N Jumper Section
B
Touchdown Catenary (a)
N
(b)
F
Figure 3.3 – Static Equilibrium Analysis of the LWR
In local coordinate systems x-B-y, u-D-v and p-F-q, as shown in Figure 3.4, the hang-off catenary ABC, the buoyancy catenary CDE and the touchdown catenary EF can be expressed as the following equations: y ai (cosh
x ai
1) , v a j (cosh
u
1) , q ak (cosh
a j
p ak
1) .
where ai , a j and ak are the curvature radii at their corresponding origins B, D, and F. Hangoff Catenary (i) S1
Buoyancy Catenary (j) S2
Touchdown Catenary (k)
S4
S3
S5
A β θ
y1
y D
u V
y3 y2
v
C
B
y4
x
E
ya
ys
q
y5 F x1
x2
x3
x4
p
x5
H
Figure 3.4 – Local Coordinate Systems of Catenary Equations
6
(11)
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
Assuming mi , m j and mk the wet masses of steel pipes with internal fluid at unit length of the hang-off catenary, the buoyancy catenary and the touchdown catenaries, the wet weights of riser per unit length are Qi mi g , Q j F m j g , Qk mk g ,
(12)
where F is the net buoyancy force from the buoyancy modules pointing upward. Application of the dimensions in Figure 3.4 to Equation (5), the arc lengths of the jumper section and the lift section become S 2 ai sinh
x2 ai
, S 3 a j sinh
x3 a j
.
(13)
The vertical equilibrium in Figure 3.3 (a) requires S 2Qi S 3Q j , or
S 2 S 3
Q j
Qi
(14)
Equation (14) implies that the lengths of the jumper section and the lift section are proportional to their vertical weight at unit length. Further derivations using Equation (10) give S 2 S 3
x2 x3
y2 y3
Q j Qi
ai a j
.
(15)
Similarly, for the drag section and the touchdown catenary, the following is true: S 4 S 5
x4 x5
y4 y5
Qk Q j
a j ak
.
(16)
Usually same materials and same geometric properties are utilized for both the hang-off catenary and the touchdown catenary, that is Qi Qk or ai ak .
(17)
Combination of Equations (15) through (18) obtains S 2 S 3 3.3
S 5 S 4
Q j Qi
, or
S 2 S 5 S 3 S 4
Q j Qi
.
(18)
Configurations of Lazy-Wave Riser
For a lazy-wave configuration, there are usually two design input options. One option give the lengths of the three catenaries, and the other the elevations of the sag bend and the arch bend. 7
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
For design input option 1, given the lengths of the hang-off catenary S i , the buoyancy catenary S j , either the water depth V at the hang-off location A or the touchdown catenary length S k , the configuration of the LWR is determined. Without loss of generality, the touchdown catenary length S k is assumed provided herein, as presented in Equations (19) through (21). S i S 1 S 2
(19)
S j S 3 S 4
(20)
S k S 5
The total length of the LWR is therefore S S i S j S k
(21)
Combination of Equations (19) through (21) provides the arc length of the hanging section: S 1 S (1
Q j Qi
) S j .
(22)
On the other hand, application of Equation (6) to the hang-off location gives S 1 ai tan ai cot ,
(23)
where is the given top hang-off angle, and 900 is the inclination angle at the hang-off location, as shown in Figure 3.4. Substituting Equation (22) into Equation (23) obtains the curvature radius of the sag bend or the touchdown point:
Q j
Qi
ai S (1
) S j tan .
(24)
Substituting Equations (23) and (24) into Equations (5), (10) and (11), one obtains the spread and height of the hanging section: x1 ai arcsin h(cot ) , y1 ai (cosh
x1 ai
1) .
Equations (11), (13) and (19) give the spread and height of the jumper section: x2 ai arcsin h(
S i S 1 ai
x ) , y2 ai [cosh( 2 ) 1] . ai
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
Equation (15) gives the spread and the height of the lift section: x3
x2Qi Q j
, y3
y2Qi Q j
.
Equations (16) and (21) provide the length of the drag section: Qi
S 4
Q j
( S S i S j ) .
Subsequently, the curvature radius at arch bend is a j
Qi Q j
ai ,
the spread and height of the drag section are x4 a j arcsin h(
S 4
x ) , y4 a j [cosh( 4 ) 1] , a j a j
and the spread and height of the touchdown catenary are x5 ai arcsin h(
S S i S j ai
) , y5
y4Q j Qi
.
With all the dimensions calculated above, the sag bend height is determined by: y s y 4 y5 y 2 y 3 ,
and the arch bend height becomes y a y 4 y 5 .
The water depth V at the hang-off location can be checked by V y1 y 4 y5 y 2 y3 .
For design input option 2, the LWR configuration can also be uniquely determined if the sag bend height ys , the arch bend height ya and the water depth V at the hang-off location A are provided. Starting with the height of the hanging section y1 V ys ,
Equations (6) and (11) give the curvature radius at the sag bend as ai
y1
cosh[arcsin h(cot )] 1
.
The curvature radius at the arch bend is given by Equations (15) and (25) as 9
(25)
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
a j
Qi
y1
Q j cosh[arcsin h(cot )] 1
.
(26)
The spread of the hanging section is calculated from Equation (25) as x1 ai arcsin h(cot ) .
Given the arch height, or the vertical distance between the arch bend and the sag bend, y2 y3 ya ys .
(27)
Equations (15) and (27) produce the heights of the jumper section and the lift section: y2
Q j ( ya ys ) Qi Q j
, y3
Qi ( ya y s ) Qi Q j
.
Subsequently, the spreads of the jumper section and the lift section are thus x2 ai arccos h(
y2 ai
1) , x3 a j arccos h(
y3 a j
1) .
The same derivations apply to the drag section and the touchdown catenary. Given the arch bend elevation y4 y5 ya ,
(28)
Equations (16) and (28) yield the heights of the drag section and the touchdown catenary: y 4
Qi y a Qi Q j
, y5
Q j ya Qi Q j
.
Hence their spreads can be expressed as x4 a j arccos h(
y4 a j
1) , x5 ai arccos h(
y5 ai
1) .
As a result, the arc length of each catenary can be calculated using Equation (5) as follows: S i ai (sinh
x1 ai
sinh
x2 ai
) , S j a j (sinh
x3 a j
sinh
x4 a j
) , S k S 5 ai sinh
x5 ai
.
For both design input options, the total horizontal distance from the hang-off location to the touchdown point is H x1 x2 x3 x4 x5 ,
the horizontal force at any point along the LWR and at touchdown point is N ai Qi a j Q j ak Qk ,
10
(29)
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
and the top tension at hang-off location is T N / sin .
(30)
Combination of Equations (29) and (30) gives ai
T sin Qi
, a j
T sin Q j
, or ak
T sin Qk
.
(31)
4 Dynamic Response of Lazy-Wave Riser 4.1
Wave and Drift Motion Response of Lazy-Wave Riser
The first order motions in heave, surge and sway directions at the hang-off point A are mainly translated into heave motions at the sag bend B due to the constraint of the length of the hangoff catenary and the drag of the buoyancy modules at lift point C, as shown in Figure 4.1. For example, the horizontal surface motion ∆x as a function of time at point A becomes a heave dominated motion ∆y at sag bend B due to the motion difference in amplitude and phase between A and C. Y P
∆x A
R
C
Q ∆y
X
B
Figure 4.1 – Heave Motion at Sag Bend due to Horizontal Motion at Hang-Off Point
As opposed to the first order motion, the relatively long period of the second order motion gives the more time for the LWR to respond globally, especially along the buoyancy catenary. The second order motions at the hang-off point A turn into both horizontal motion and heave motion at the sag bend, as shown in Figure 4.2. For example, a horizontal second order motion at the hang-off point A is followed by dominant horizontal motions at the lift point C and the drag point E. This generates open and close movements of the sag bend or the arch bend, 11
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
fluctuating curvature radii along LWR, especially at such critical locations as the sag bend B, the arch bend D and touchdown point F. Hangoff Catenary ∆x A
Buoyancy Catenary
Touchdown Catenary
A β θ
D
∆uD
∆uC
V
B
C E
∆uB
∆uE
F x1
x2
x3
x4
∆uF
x5
Figure 4.2 – Illustration of Second Order Motion along LWR
Techically, the critical locations for curvature radius refer to critical zones. The local top point D may travel along the buoyancy catenary, such that the points near the arch bend D on the riser take turns to become the local top elevation to account for tension variations and section length adjustment during dynamic motions. In this sense, the arch bend is actually a zone in length instead of a fixed point, so are the sag bend and the touchdown point.
The length of these critical zones varies with dynamic motions as well as vessel offsets, as shown in Figure 4.3. At a far offset of 10% water depth, a LWR shape with a decent arch height at near offset may degenerate into a low arch LWR, or even a shaped SCR if failed to optimize the buoyancy catenary for large offsets. Extreme far and near offset positions should be checked for a LWR configuration to avoid undesired buckling problem of a low-arch configuration, and to avoid local high stress at the arch bend at near offset.
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
Critical curvatures along LWR are associated with extreme vessel positions under driving load conditions and are functions of the horizontal force N or top tension T and hang-off angle θ as indicated in Equation (31). A configuration with higher top tension T or greater hang-off angle θ gives larger critical curvature radii and generally provides a better dynamic strength response. Restricted by vessel payload, sag bend can also be adjusted for a given top tension cap. The density, length and thickness of the buoyancy modules are among other key parameters for optimization of LWR configuration.
Figure 4.3 – Variation of LWR Configuration with Large Offsets 4.2
Strength Response of Lazy-Wave Riser
Taper stress joint or flex joint is widely used for stress relief at the hang-off location, while other critical locations along LWR have to rely on the optimization of the buoyancy catenary. The horizontal motion and the heave motion at the hang-off location lead to an open and close movement of the sag bend, the arch bend and the touchdown zone as illustrated in Figure 4.2. The lowest curvature radii at these critical locations governs their stress response since stress and bending moment are proportional to curvature, as shown in Figure 4.4. The highest stress frequently occurs at the arch bend where the most critical curvature is more likely when the 13
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
lift point and the drag point move out of phase with the vessel at near offset position. On the other hand, the preference of high net buoyancy force for arch height optimization also results in lower curvature at the arch bend. Other critical curvatures occur at the touchdown point and the sag bend. For an optimized LWR, the stress at the touchdown point and the sag bend is normally not driving in strength response, which is another feature of the LWR. 0.8
7000
0.7
6000
o i t 0.6 a R s s 0.5 e r t S d l e0.4 i Y / s e0.3 s i M n o V0.2
) 5000 t f
( d e b a 4000 e S m o r f 3000 n o i t a v e l 2000 E
1000
0.1 0.0
0 0
1000
2000
3000
4000
5000
6000
7000
Horizontal Distance from Hangoff (ft)
Figure 4.4 – Strength Response of High Arch Lazy-Wave Riser
Riser mass density is another factor for LWR optimization. A lighter riser or smaller Qi including internal fluid improves the strength response at the sag bend and the touchdown point as suggested in Equation (12). As equivalent negative mass along the buoyancy catenary where Q j F m j g , lower net buoyancy force F favors a greater curvature radius, but may result in an undesirable low-arch configuration at vessel far offset. For instance, the stress response of a low-arch lazy-wave configuration with sag bend and arch bend elevations of 2900 ft and 3100 ft, respectively, is shown in Figure 4.5. Heave motion at the sag bend becomes whipping and buckling wave motion between sag bend and the arch bend, which results in local curvature and stress much higher than those otherwise at the sag bend or the arch bend. The structural and hydrodynamic damping effect is significantly compromised in this case. 14
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
o i t a R h t g n e r t S d l e i Y / s s e r t S s e s i M n o V
0.8
7000
0.7
6000
0.6
5000 ) t
0.3
f ( d e b 4000 a e S m o r f 3000 n o i t a v e l 2000 E
0.2
1000
0.5
0.4
0.1
0 0
1000
2000
3000
4000
5000
6000
Horizontal Distance from Hangoff (ft)
Figure 4.5 – Strength Response of Low Arch Lazy-Wave Riser 4.3
Motion Fatigue Response of Lazy-Wave Riser
Strength response is driven by extreme curvature at critical locations, while fatigue response is controlled by curvature fluctuation range associated with higher stress range. The highest curvature fluctuation occurs at the sag bend, the arch bend or the touchdown point. The low fatigue lives occur at these high curvature fluctuation zones, as shown in Figure 4.6. Critical fatigue damage is observed at the touchdown point and at the riser hang-off location. The fatigue damage at the touchdown zone is driven by soil-structure interaction under more frequent occurrence of small stress cycles from low seastates, while at the top hang-off section it is driven by combination of tension and bending moment from less frequent but high stress range from high seastates.
Three case studies are presented in this section for sensitivity of the fatigue response of LWR attached to an internally turret-moored FPSO.
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The first case explores the first order fatigue sensitivity to arch heights. Three configurations with different arch heights – namely high arch, mid arch and low arch – are developed by varying the length of the buoyancy catenary. The vessel payload remains the same in all configurations with a constant hang-off angle and sag bend elevation. It is observed that fatigue life at the touchdown point (TDP) improves with arch height. With the same buoyancy thickness, a higher arch configuration requires a longer buoyancy catenary that provides more damping to motions. The buoyancy lengths of the three arch heights are compared in Figure 4.7, and their first order motion fatigue lives are presented in Table 4.1. The fatigue life of the mid-arch configuration at the TDP improves slightly from the low-arch configurations, but that of the high-arch configuration doubled. A higher arch diverts and damps cable wave motion in more favorable directions. This also indicates nonlinear redistribution of structural damping and hydrodynamic damping between different configurations. 1.E+12
7000
1.E+11 6000
1.E+10 ) 1.E+09 s r a e 1.E+08 y ( e f i 1.E+07 L e u 1.E+06 g i t a F 1.E+05 m u 1.E+04 m i n i 1.E+03 M
)
t 5000 f ( d e b a e 4000 S e v o b 3000 a n o i t a v e 2000 l E
1.E+02
1000
1.E+01 1.E+00
0 0
1000
2000
3000
4000
5000
6000
7000
Horizontal Distance From Hangoff (ft) Fatigue Life
Slick Section
Buoyancy Section
Figure 4.6 – Example of Fatigue Response along Lazy-Wave Riser
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
7000
6000
Sag Bend Height: 2400ft Arch Be nd Hei ghts: Low Arch 2600ft Mid Arch 3100ft High Arch 3600ft
) t 5000 f ( d e b a e 4000 S m o r f 3000 n o i t a v e 2000 l E
Archbend
Sagbend
1000
0 0
1000
2000
3000
4000
5000
6000
7000
Horizontal Distance From Hangoff (ft) Low Arch
Mid Arch
High Arch
Buoyancy 1742 ft
Buoyancy 2261 ft
Buoyancy 2722 ft
Figure 4.7 – Buoyancy Lengths Variation with Arch Heights Riser Configuration Arch Type Arch Height (ft) High Arch 1200 Mid Arch 700 Low Arch 200
Minimum Fatigue Life at TDP (years) 1,500 750 670
Table 4.1 – First Order Motion Fatigue Life Variation with Arch Configurations
The second case compares the first order fatigue responses to sag bend elevations. Two configurations with different sag bend elevations are developed as shown in Figure 4.8. The hang-off angle and arch height are kept constant. The lower sag bend configuration improves the TDP fatigue life by 80%, however decreases the fatigue response at top of the riser by 13%, as compared in Table 4.2. The fatigue life increase at the TDP can be justified from Equation (31). The lower sag bend configuration has longer hang-off catenary length hence greater hang-off tension and smaller TDP curvature and bending stress range. The higher dynamic tension fluctuation near the hang-off location adversely contributes to the fatigue performance at top of the riser.
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
7000 6000 ) t f ( 5000 d e b a e 4000 S m o r f 3000 n o i t a v 2000 e l E
Buoyancy 2722 ft
High Sagbend Buoyancy 2189 ft Low Sagbend
1000 0 0
1000
2000
3000
4000
5000
6000
7000
8000
Horizontal Distance From Hangoff (ft) Lazy Wave Sagbend 2400ft
Buoyancy 10inch Thickness
Lazy Wave Sagbend 600ft
Buoyancy 10inch Thickness
Figure 4.8 – Lazy-Wave Configuration with Varying Sag Bend Elevations Location
Touchdown Point Top Taper Stress Joint
Minimum Motion Fatigue Life (years) Sag Bend 2400 ft Sag Bend 600 ft 1,500 2,700 2,400 2,100
Table 4.2 – Motion Fatigue Life Sensitivity to Sag Bend Elevations
The third case study is about fatigue response to current loading. Background current interferences riser motion and helps dissipating cable wave energy in an addition to hydrodynamic damping. As shown in Figure 4.9, the TDP fatigue life improves with increased background current speed. Background current profile should be used with caution to reduce conservativeness. Generally, application of background profile with 50% occurrence increases TDP fatigue life 2~3 times from without background current depending on variation of current directions and speeds.
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Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
14,000
12,000 ) s r a10,000 e y ( e f i L 8,000 e u g i t a F 6,000 m u m i n 4,000 i M
2,000 Base Case (no background current) 0 0
0.1
0.2
0.3
0.4
0.5
Surface Speed of Background Current Profile (knots)
Figure 4.9 – Effect of Background Current on Motion Fatigue Life at Touchdown Point
5 Summary Consisting of three catenaries, namely the hang-off catenary, the buoyancy catenary and the touchdown catenary, a lazy-wave riser has better strength and fatigue responses than SCR. The buoyancy catenary produces effective hydrodynamic and structural damping to attenuate cables waves from vessel motions propagating along lazy-wave riser. The critical locations for strength and fatigue responses are at the top hang-off location, the sag bend, the arch bend and the touchdown point. This work provides parameterized equations for configuration optimization and strategic analysis.
The damping efficiency of the buoyancy catenary and the variation of the curvature radii at the critical locations in conjunction with the top tension and hang-off angle are the driving factors for lazy-wave riser strength and motion fatigue responses. The horizontal force along the riser is a constant and a function of net riser wet weight at the hanging section and the top hang-off angle. The curvature at the critical locations is a function of horizontal force and submerged weight of riser section, which drives dynamic response. Dynamic response is sensitive to arch height, sag bend elevation, top hang-off angle and background current loading. 19
Deep Offshore Technology International, Amsterdam, Netherlands, Dec 2010
6 References [1]
Torres, A.L.F.L. et al (2002), “Lazy-wave steel rigid risers for turret-moored FPSO”, OMAE’02/OFT-28124
[2]
Jaco, B.P. et al (2008), “Synthesis and optimization of steel catenary risers th configurtations through evolutionary computation,” 5 Report for Petrobras, COPPE/UFRJ
[3]
Edmundo Queiroz de Andrade et al (2010) “Optimization Procedure of Steel Lazy Wave Riser Configuration for Spread Moored FPSOs in Deepwater Offshore Brazil”, OTC 20777
[4]
Hugh Howells, (1995). “Advances in Steel Catenary Riser Design: Advances in Steel Catenary Riser design”, DEEPTEC '95, Aberdeen, February 1995
[5]
Bin Yue et al, (2010) “Improved SCR Design for Dynamic Vessel Applications”, OMAE2010-20406, Beijing, June 2010
[6]
Lockwood, E.H. (1961) “A Book of Curves”, Cambridge University Press.
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