1

TABLE OF CONTENT

Nomenclature………………………………………………………………………2

Executive summary………………………………………………………………...3

Input Data…………………………………………………………………………..5

Results and Discussion……………………………………………………………..6

Conclusion…………………………………………………………………………18

Reference…………………………………………………………………………..19

2

NOMENCLATURE

Si……………………………………………………………………………….Length of hang-off catenary

Sj……………………………………………………………………………….Length of buoyancy catenary

Sk……………………………………………………………………………….Length of touchdown catenary

Ya……………………………………………………………………………….Arch bend height

Ys……………………………………………………………………………….Sag bend height

WD…………………………………………………………………………….Water depth

H……………………………………………………………………………….….Horizontal span of riser

TH………………………………………………………………………………...Horizontal force

T…………………………………………………………………………………....Top tension

EM……………………………………………………………………………..….Effective mass ratio

θ……………………………………………………………………………….…….Hang-off angle

δ…….……………………………………………………………………………….Bending stress

M…………………………………………………………………………………….Maximum Bending moment

SCR…………………………………………………… Steel catenary riser

FPSO………………………………………………….. Floating production storage and offloading

TDZ…………………………………………………… Touch down zones

LWSCR………………………………………………. Lazy wave steel catenary riser

LWR…………………………………..…………….... Lazy Wave riser

3

EXECUTIVE SUMMARY

Steel catenary risers (SCRs) have been popularly used because of their cost efficiency and structural

simplicity. However, for semi-submersibles and FPSOs (Floating Production Storage Offloading)

in deep water field, there is a need to carefully scrutinized and design conventional SCRs due to

the tendency of high structural stresses, global buckling, and fatigue failure induced by floater

motions. The sectional failure is also closely related to high internal and external pressures. Floating

platform makes large motions due to severe environmental loadings, this motion of the platform is

directly transferred to the attached mooring lines and risers which causes dynamic response of the

riser due to the force induced by the motion of the platform, also there are additional forces directly

applied to the riser which may induce fatigue of the riser. Additional forces may also result from

riser interactions with the seabed. Many researchers have question the suitability of conventional

SCRs for Deepwater FPSOs because of their highly amplified dynamic responses under severe

environmental conditions (Wu and Huang 2007; Yue et al., 2010; Yue et al., 2011; Yang and Li,

2011).

Due to the highly amplified dynamic response, the excessive structural stress may occur at hang

off and touchdown zones (TDZ). In addition, the frequently occurring large fluctuating stresses

significantly reduce fatigue life of deep-water SCRs. This then necessitates the design of lazy wave

steel catenary riser (LWSCR) as an alternative. LWSCR is well able to mitigate the dynamic

response motion induced on the riser by the vessel offset. The LWSCR configuration is design to

isolate the vessel motion from the riser motion through the sag and arch regions with buoyancy

modules added thereby minimising or avoiding the fatigue damage/ heavy dynamic behaviour

induced on the riser by motion of the floaters. (Jacob et al., 1999; Torres et al., 2002; Torres et al.,

2003; Li and Nguyen, 2010; Yue et al., 2011; Yang and Li, 2011).

Figure 1: Model of Lazy Wave Catenary Riser

4

This work deals with the development of a systematic iterative approach to the analysis and design

of LWR with the application of catenary theory. This could be useful in preliminary screening stage

of selecting the best LWR configurations.

To carry out the analysis and design, PTC Mathcad was used to develop the codes used to determine

and plot the LWR configurations and perform parametric investigation of several key parameters

(the effect of pipe size or diameter, effect of lengths (Si, Sj, Sk); effect of arch and/ or bend height;

effect of internal fluid, effect of hang-off angle; effect of water depth; effect of effective mass

ratio, effect of platform offset etc. Two design input options are considered with respect to fig.1

OPTION 1: The hang-off catenary length (Si), the buoyancy catenary length (Sj), the touchdown

catenary length (Sk) are specified whereas the hang-off angle (θ) is obtained iteratively by the

developed codes using the water depth as a check criteria.

OPTION 2: The sag bend height (Ys) and arch bend height (Ya) are specified whereas Si, Sj, and Sk

are unknown. The hang-off angle (θ) is obtained iteratively by the developed codes using the

horizontal span of the riser (H) as a check criteria.

In both options, the water depth (WD) is specified a priori.

5

INPUT PARAMETERS:

The following input parameters were considered for this study:

Flexible pipe 1: outside diameter =150mm, inner diameter = 105mm, weight in air = 37.86kg/m

(smaller pipe)

Flexible pipe 2: outside diameter = 341mm, inside diameter = 259mm, weight in air = 141.62kg/m

(larger pipe)

Geometric parameters used for option 1 are Si = 150m, Sj = 60m, Sk= 130m and WD =

150m.

Gas density of 200kg/m3

Oil density of 800kg/m3

Sea water with density of 1025kg/m3

Effective mass ratio (EM) of 1, 2, 2.5 and 3 were considered.

Bending stiffness, EI: Flexible pipe 1 = 4.47 kNm2

Flexible pipe 2 = 50.95 kNm2

6

RESULTS AND DISCUSSION

Effect of varying Si

Table 1: Results of Increasing Si

As Si increases the hangoff angle increases while Ys and Ya decrease. The radii of curvature

increases, as well as the horizontal span of the riser. The top tension and constant horizontal force

increase with increasing Si. The bending moment of the sag and arch bend as well as the the bending

stresses reduce with increasing Si. It is therefore important that the Si be large enough to reduce to

the minimal the bending stress on the riser.

Effect of varying Sj

Table 2: Results of Increasing Sj

Si 100m 150m 200m 250m

θ(deg) 40.37 40.81 42.94 45.85

Ys(m) 99.14 76.77 58.56 44.55

Ya(m) 99.94 77.31 58.94 44.83

ai=ak(m) 93.52 138.18 195.41 267.80

aj(m) 46.76 69.09 97.70 133.90

H(m) 237.43 295.51 350.26 403.54

Sj 30m 45m 60m 75m

θ(deg) 38.61 40.17 40.81 39.65

Ys(m) 44.15 61.74 76.77 88.90

Ya(m) 64.30 69.11 77.31 91.66

ai=ak(m) 175.70 160.37 138.18 107.74

aj(m) 87.85 80.19 69.09 53.87

H(m) 262.44 280.21 295.51 304.62

Figure 2: LWSCR plots of increasing Si

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Increase in Sj results in corresponding increases in H, Ya and Ys. At Sj= Sk/EM, Ya is equal to Ys.

This value of Sj i.e. Sj=Sk/EM, is important for correlation between design option 1 and design

option 2. If Sj<Sk/EM, the hang-off angle, Si, Sj, Sk, ai and aj obtained from option 2 would be

different from those of option 1 even if the input parameters (Ya, Ys, H, and WD) where gotten

from option 1. Thus to correlate between the two methods, Sj in option 1 should be greater or equal

to Sk/EM. In design option 1, if Sj is greater than or equal to Sk/EM, there would be only positive

values of the different horizontal spans of the riser i.e. x1 to x5.

At a value of Sj > or = Sj1 above Sk/EM for a specific internal fluid density, EM ratio, Sk and Si,

the LWR configuration is unattainable. Point ‘Sj1’ for this case of EM= 2, Si= 150m, Sk=130m is

103m. Above this value there is no possible plot. ‘Sj1’ is inversely proportional to EM. Thus for

EM=3, Sj1= 68m, for EM=10, Sj1=20m

It is therefore suggested that Sj should be less than (Sj1 + 2m) in order to obtain a plot of the LWR

for any EM if the value of Sj1 is known for one EM.

The top tension and constant horizontal force decrease with increasing Sj. The bending moment of

the sag and arch bend as well as the bending stresses increase with increasing Sj.

Figure 3: LWSCR plots of increasing Sj

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Figure 4: LWSCR plots of increasing Sk

Effect of varying Sk

Table 3: Results of Increasing of Sk

Increase in Sk results in increases in the hang-off angle, H, and all the radii of curvature. The top

tension and constant horizontal force increase with increasing Sk. The bending moment of the sag

and arch bend as well as the the bending stresses reduce with increasing Sk.

Effect of varying Effective Mass Ratio

Table 4: Results of Increasing the Effective mass ratio

Sk 90m 110m 130m 150m

θ(deg) 21.57 33.84 40.81 45.591

Ys(m) 68.41 75.31 76.77 76.53

Ya(m) 81.44 76.11 77.31 80.18

ai=ak(m) 47.45 93.87 138.18 183.75

aj(m) 23.72 46.93 69.09 91.88

H(m) 220.50 267.17 295.51 319.93

EM 1 2 2.5 3

θ(deg) 42.43 40.814 37.83 28.02

Ys(m) 53.05 76.77 86.36 89.94

Ya(m) 76.71 77.31 89.10 116.34

ai=ak(m) 201.13 138.18 100.95 53.21

aj(m) 201.13 69.09 40.38 17.74

H(m) 297.63 295.51 287.30 248.69

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Figure 5: LWSCR plots of Effective mass ratios 1, 2, 2.5 and 3

As EM increases the hangoff angle decreases while Ys and Ya increase. The radii of curvature

decreases, as well as the horizontal span of the riser. The top tension and constant horizontal force

decrease with increasing EM. The bending moment of the sag and arch bend as well as the the

bending stresses increase with increasing EM.

Effect of varying Ya

Table 5: Results of Varying Ya while Ys is kept constant at 25m

Ya(m) 27.5 55 82.5 110

θ(deg) 32.98 20.91 17.22 15.19

Si(m) 217.54 225.96 238.85 256.04

Sj(m) 47.69 77.73 99.23 121.26

Sk(m) 85.88 93.66 112.92 134.26

ai=ak(m) 135.02 62.73 47.51 40.13

aj(m) 67.51 31.36 23.75 20.07

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Figure 6: LWSCR of Ya=27.5m, 55m, 82.5m and 110m

As Ya is increased and Ys kept constant, the hangoff angle decreases while Si, Sj and Sk increases.

The radii of curvature decreases. The top tension and constant horizontal force decrease with

increasing Ya. The bending moment of the sag and arch bend as well as the the bending stresses

increase with increasing Ya due to reduction in the curvature radii.

Effect of varying Ys

Table 6: Results of Varying Ys while Ya is kept

constant at 100m

Ys(m) 25 50 75 100

θ(deg) 16.14 20.94 28.72 46.18

Si(m) 251.79 214.73 177.53 124.32

Sj(m) 94.85 89.15 83.97 73.69

Sk(m) 104.21 108.89 117.03 147.38

ai=ak(m) 48.11 55.60 69.39 129.56

aj(m) 24.05 27.80 34.70 64.78

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Figure 7: LWSCR plots of Ys= 25m, 50m, 75m, 100m

As Ys is increased and Ya kept constant, the hangoff angle increases while Si, Sj decreases and Sk

increases. The radii of curvature decreases. The top tension and constant horizontal force increase

with increasing Ys. The bending moment of the sag and arch bend as well as the the bending stresses

decrease with increasing Ys.

Effect of varying Ya and Ys: low, mid and high arch.

Table 7: Results of Varying Ya and Ys together

Ya(m)

Ys(m)

30

20

60

50

90

80

120

110

θ(deg) 26.23 28.40 33.61 43.56

Si(m) 246.60 203.17 165.24 128.27

Sj(m) 52.43 64.76 76.52 89.25

Sk(m) 67.21 94.11 118.38 143.48

ai=ak(m) 102.93 90.71 86.78 88.672

aj(m) 51.47 45.36 43.39 44.34

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Figure 8: LWSCR plot of varying Ya and Ys together

When choosing an LWR configuration, it is important to take into account the large displacement

on the riser buoyancy modules by the high current velocities dominant in mid water region. It is

therefore crucial to have a configuration with an arch bend in low current velocity region and a sag

bend that is considerably above the seabed when the riser is full of fluid. The need to ensure the

sag bend is above the seabed is further emphasised by Bai and Bai (2005), when there is oscillatory

motion of the part of the riser in contact with the seabed, the riser is forced into the soil, thereby

increasing the soil resistance. To ensure there is no seabed interaction or trenching, Sj should be

less than (1.5 x Sk/EM).

The hang-off angle increases as Ys and Ya are increased together. Furthermore the curvature radii

decreases with increasing Ya and Ys up till Ya=95m and Ys= 85m (aj=ai/EM), after this point the

radii start increasing.

Effect of varying Water Depth

Table 8: Results of Varying water depth; 150m, 500m, 850m, 1200m

WD(m) 150 500 850 1200

θ(deg) 23.6 5.87 3.09 2.04

Si(m) 231.49 560.82 903.21 1249

Sj(m) 64.22 54.23 51.37 49.85

Sk(m) 80.33 68.40 65.01 63.20

ai=ak(m) 80.12 53.50 46.73 43.25

aj(m) 40.06 26.75 23.37 21.63

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Figure 9: LWSCR plots of WD= 150m, 500m, 850m 1nd 1200m

With deeper water, Ya and Ya kept constant, the hangoff angle decreases while Si increase. Sj and

Sk decreases with increasing water depth. The radii of curvature decreases. The top tension and

constant horizontal forces increases while the bending moment of the sag and arch bend as well as

the the bending stresses decrease.

Comparing configurations of Flexible Pipe 1

EM=3, when: empty, filled with gas, filled with oil, filled with sea water.

Table 9: Results of Varying riser internal fluid density

Internal

content

Empty Gas OIL SEAWATER

θ(deg) 28.02 35.71 40.95 41.49

Ys(m) 89.94 88.80 75.93 71.42

Ya(m) 116.34 96.09 76.74 74.44

ai=ak(m) 53.21 85.79 140.84 154.30

aj(m) 17.74 32.04 71.81 87.69

H(m) 248.69 280.21 295.8 296.88

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Figure 10: LWSCR plot when riser is empty, filled with gas, filled with oil and filled with seawater

As the density of the riser internal fluid increases i.e. from an empty riser to riser filled with gas, to

riser filled with oil and riser filled with seawater, the hang-off angle increases along with H, and

all the radii of curvature. Ya and Ys also decrease as the riser become heavier. The top tension and

constant horizontal force increase with increasing internal fluid density. The bending moment of

the sag and arch bend as well as the the bending stresses reduce with increasing riser internal fluid

density.

Since the buoyancy force F is dependent on the wet weight of the riser with internal fluid, (Qj = F-

mjg) it is therefore important to specify the effective mass ratio based on the wet weight of the riser

with an adequate value of internal fluid density that would suffice for all the fluid that would be

transported by the riser to avoid low sag bend when the riser is filled with a heavy fluid.

Comparing flexible pipe 1 and flexible pipe 2:

Table 10: Results of flexible pipe 1 Vs Flexible pipe 2

PIPE 1 PIPE 2

θ(deg) 40.814 40.814

Ys(m) 76.77 76.77

Ya(m) 77.31 77.31

ai=ak(m) 138.18 138.18

aj(m) 69.09 69.09

H(m) 295.51 295.51

TH(kN) 26.76 65.06

T(kN) 40.94 99.53

15

As the diameter and weight of the pipe increases, the configuration of the riser remains the same

while the top tension, horizontal force, bending moment and bending stress are increased.

Effect of Vessel Offset

Table 11: Results of Far, Mean and Near vessel offsets

Figure 11: LWSCR plots when the vessel is at Far, mean, or near offset

Mmax(Nm) 64.7 737.47

δmax(kPa) 256.97 283.94

VESSEL

OFFSET

FAR

( H+10%WD)

MEAN

(H=275m)

NEAR

(H– 10%WD)

θ(deg) 38.73 34.28 30.55

Ys(m) 84.62 89.66 90.29

Ya(m) 85.84 100.36 110.31

ai=ak(m) 109.25 77.82 61.71

aj(m) 45.60 28.15 21.11

H(m) 290 275 260

TH(kN) 21.16 15.07 11.95

T(kN) 33.82 26.75 23.51

M(Nm) 98.04 158.77 211.80

δ(kPa) 389.37 630.59 841.18

16

As the vessel moves far from the mean position i.e. increased horizontal span, the hang off angle,

radii of curvature, horizontal force and top tension are increased. Ya, Ys, bending moment and

bending stress on the riser reduces. In near position, the hang off angle, radii of curvature,

horizontal force and top tension are reduced. Ya, Ys, bending moment and bending stress on the

riser increases.

LWSCR vs SCR

Table 12: SCR vs LWSCR

Figure 12: SCR vs LWSCR

SCR LWSCR

θ(deg) 42.39 42.43

Ys(m) 0 53.05

Ya(m) 3.5x10^-15 76.71

ai=ak(m) 310.33 201.13

aj(m) -310.33 201.13

H(m) 294.00 297.63

TH(kN) 60.10 38.948

T(kN) 89.14 57.72

M (Nm) 14.40 22.23

δ (kPa) 57.21 88.27

17

One key difference between the SCR and LWSCR is the absence of an arch and sag bend in SCR

configuration. Although the SCR has larger top tension and horizontal force, it has a smaller

bending moment and bending stress when compared to the LWSCR. This is due to its bigger

curvature radius when compared to that of LWSCR.

Effect of Hang-off angle

Table 13: Results of Varying hang-off angle

Figure 13: LWSCR plot of hang-off angle = 8deg, 16deg, 24deg and 32deg

As the hang-off angle is increased, the radii of curvature increases thereby causing a reduction of

the bending moment and bending stress of the riser. The top tension and horizontal force increases

with increasing hang-off angle.

Hang-off

angle(deg)

8 16 24 32

ai=ak(m) 22.49 45.88 71.24 99.98

aj(m) 11.24 45.88 35.62 49.99

TH(kN) 4.36 8.88 13.80 19.36

T(kN) 31.29 32.23 33.92 36.54

M (Nm) 397.57 194.86 125.50 89.42

δ (kPa) 1579 734 498 355

18

CONCLUSION AND REMARK

This work was focussed on a systematic iterative approach to the analysis and design of LWR. A

key aspect in the design of LWR is having an LWR configuration with minimal bending curvature

and pipe stresses. From the analysis and parametric studies carried out, the following would lead

to minimal bending curvature and pipe bending stress and better riser fairing:

Increase in the hang-off angle

Increased length of the hang-off catenary

Far vessel offset

Reduced buoyancy catenary length ( less than 1.5* Sk/EM)

Low water arch

Achieving low water arch to avoid large displacement on the buoyancy modules by large current

velocities in the mid water region is possible by increasing Si to about 67% of the total length of

the riser while Sj should not be greater than 1.5 x Sk/EM.

Furthermore the densities of the fluids that would be transported by the riser should be taken into

account when designing the riser buoyancy module and choosing the riser configuration to avoid

seabed interaction when the riser is filled with a heavy fluid.

It should be noted that the method used for this work is iterative. The development of equations

that could give the hang-off angle is an area for possible investigation.

19

REFERENCES

* Dr. Shrini Narakorn – Risers and Mooring Lines Class notes and slides

* Jacob et al., 1999; Torres et al., 2002; Torres et al., 2003; Li and Nguyen, 2010; Yue et al., 2011;

Yang and Li, 2011

* Wu and Huang 2007; Yue et al., 2010; Yue et al., 2011; Yang and Li, 2011

* Keprate Arvind – Appraisal of riser concepts for FPSO in Deepwater

* Subsea7 – Deepwater installation of steel catenary risers subsea asia. 3rd October, 2012 Kuala

Lumpur, Malaysia. Grant

* Structural Performance of Deepwater Lazy-Wave Catenary Risers for FPSOs Seungjun Kim,

Moo-Hyun Kim, Sanghoon Shim, Sungwoo Imz

* Dynamic Response of Deepwater Lazy-Wave Catenary Riser – Songcheng Li, 2H offshore Inc

& Chau Nguyen, 2H 0ffshore Inc