ANALYSIS AND DESIGN OF A LAZY-WAVE STEEL CATENARY RIZERS (LWSCR or LWR)By;

OLIYIDE, ABIODUN AREMU

&

ADEGBAYI, ADEOLA PHILIP

A Coursework in NM 958, Risers and Mooring Lines Submitted to; The Department of Naval Architecture, Ocean and Marine Engineering

UNIVERSITY OF STRATHCLYDEDecember, 2014

21.0EXECUTIVE SUMMARY

32.0INTRODUCTION

33.0OPTIMISATION METHOD

43.1Input Data

43.2Output Data

44.0CASE STUDY

55.0RESULTS AND DISCUSSION

55.1 Effect of Change in Buoyancy Ratio

95.2 Effect of Change in Hang-Off Angle

105.3 Effect of Change in Size of Riser Diameter

125.4: Effect of Change in Internal Fluid Density

145.4 Effect of Change in Water Depth

155.6 Effect of Change in Platform Offset

175.7 Effect of Change in Arch Bend & Sag Bend Height

185.8 Effect of Change in Catenary Lengths

181. Hang-off Catenary

192. Buoyancy Catenary

203.Touchdown Catenary

226.0CONCLUSION

227.0REFERENCES

1.0 EXECUTIVE SUMMARYA very good understanding of the structural configuration and characteristics of a Lazy-wave riser is very essential is very essential for the riser engineer to analyse effectively and do a design that will serve its intended purpose throughout the life of the riser without jeopardizing cost effectiveness and time constraints. In this coursework, an analysis code was designed for the optimisation of the configuration of a lazy-wave riser. Lazy-wave configuration has been proved adequate due to its structural dynamic behaviour when compared to other configurations [3] [4] [5]. Thereafter, a parametric study was carried out to better understand the structural behaviour and configuration of lazy-wave risers under the effect of change in different parameters like; water depth, riser diameter, arc length, hang-off angle, platform-offset and buoyancy ratio. Two options were considered according to the literature, Option 1 makes use of the length of the three catenaries while option 2 specifies the height of the sag bend and the arch bend above the seabed [1]. 2.0 INTRODUCTION

With the recent increase in the discoveries in the discoveries in the deep water oil fields and rapid development of deep-water floating production systems the design of dynamic risers to produce and export oil to and from these floating production systems has become more complex. The riser engineer is saddled with the responsibility to determine the best riser configuration to be used in a subsea development. Lazy-wave riser is gaining popularity because it has been considered as an adequate solution due to its structural dynamic behaviour when compared to other riser types [2].

Despite the suitability of a lazy-wave riser, the onus to choose the best lazy-wave configuration is quite demanding because any little change in the geometric properties of the riser has a significant effect on the static and dynamic behaviour of the riser [2].This coursework presents an optimised configuration of a lazy-wave riser, a tool with which the riser engineer can lay his hands upon in practice to determine the approximate lazy-wave configuration to be used for a particular subsea development [1]. 3.0 OPTIMISATION METHOD

A Mathcad program was designed for the optimisation process, the program takes the input data, process them, analyse the data statically and plot the configuration on a graph with report on the static properties and configuration of the Lazy-wave riser. Several buoyancy ratios were used for the optimization and the buoyancy ratio was fixed at 2 at hang-off angle of 40.82O, this forms the base or seed lazy wave riser that was used for the parametric analysis.3.1Input DataTwo options were considered differently for the input parameters, option one was for shallow water of 150m water depth while option two after being tested and confirmed that it worked for the same parameters in option 1 was used for parametric study in deep water with depth of 2000m. For option one, the input data that was used to plot the riser configuration are; hang-off catenary length Si, buoyancy catenary length Sj, touch-down catenary length Sk, and the water depth V. The analysis program was designed to iterate for optimum value of the of hang-off angle in degree for every parameter that was varied. The other geometric properties of the lazy-wave riser were generated from the analysis code.3.2Output Data

For each of the variation in input parameter, several output data were generated which include the hang-off angle , maximum horizontal projection H, minimum bending radius a, Maximum Curvature, maximum bending stress, horizontal force acting on the riser N at the TDP and the top tension. All these output will help the riser design engineer to make his initial decision on what type of configuration he should choose.4.0 CASE STUDYThe case study used for this analysis is a rise with outer diameter of 150mm, wall thickness 45mm, weight in air of 37.86kg/m and catenary lengths Si, Sj, Sk equal 150, 60 and 130m respectively in a shallow water of 150m depth. On the attaining a lazy-wave configuration the plot, the buoyancy ratio was fixed at 2 and the following parameters were varied one after the other while holding the other parameters constant.1. Buoyancy ratio

2. Hang off angle

3. Pipe size diameter

4. Density of internal fluid

5. Catenary length Si, Sj, Sk

6. Water depth

7. Platform offset

The effect of variation in the above parameters were recorded and monitored against the following important features of the Lazy-wave riser which forms the basis for our discussion in the next section1. Hang off angle at the vessel

2. Maximum Horizontal projection H

3. Minimum bending radius, a4. Maximum Curvature, k5. Maximum bending moment, M6. Maximum bending stress

7. Horizontal force8. Top Tension 5.0 RESULTS AND DISCUSSION

Based on the optimisation, the following results were generated and the parametric analysis for each change in configuration are presented below.5.1 Effect of Change in Buoyancy RatioThe buoyancy catenary of a lazy-wave riser consist of a section of pipe where the upward buoyancy force in water is greater than its downward gravity force in water, this gives an equavalent negative force and is responsible for the upward curvature of the buoyancy section of the riser. A variation in the buoyancy ratio of the lazy-wave riser could give rise to a shaped Steel catenary riser or a degenerated Lazy-wave Riser with less buoyancy and no sag bend or arch bend [4]. In our optimisation, the bouyance ratio was varied from 1 to 3 on a step on 0.5 and its effect on the configuration of the riser properties are discussed below.Firstly at buoyancy ratio of 1, the properties of the risers were the same and the configuration was a shaped SCR as in the figure below.

Figure 5.1: Lazy-wave riser with buoyancy ratio of 1(Shaped SCR)The properties and parameters of the hang-off section and the buoyancy sections like the minimum bending radius, curvature, bending moment and bending stress were the same for a buoyancy ratio of 1. This implies that the whole length of the pipe was made of the same material.We started noticing a difference in the riser properties when the buoyancy ratio was greater than 1. Physically, as the buoyancy ratio increased, the arch heigh continued to increased and the shape of the riser metamophosized from a steel catenary shape through a low-water arch, to a mid-water arch and finally to a high-water arch with a buoyancy ratio of 3 as in the figure below.

Figure 5.2: Effect of change in buoyance on the shape of a lazy-wave riserFor the hang-off catenary, the minimum bending radius was decreasing with respect to an increase in the buoyancy ratio, this was because the MBR is a function of the inverse of the buoyancy ratio i.e (Qj/Qi). As the bouyancy ratio increased, the MBR was reducing. Conversely, there was an increase in the bending moment since bending moment is inversely propotional to the MBR. An increase in the bending moment also gave rise to the bending stress, this implies that As the buoyancy ratio increases, the bending moment and bending stress also increase.As the buoyancy ratio increases there was a decrease in the Top Tension, this was due to an increase in the net upward force, since sum of upward forces is equal to sum of downward forces there was a reduction in the top tension and subsequently the Horizontal force at the Touch Down Point. Finally, the hang-off angle at the vessel and the Horizontal disstance between the vessel and the TDP (Platform offset) also reduced with respect to an increase in the buoyancy ratio as shown in the graph below.

Figure 5.3: Effect of change in buoyance on the properties of lazy-wave riserAfter the optimisation, for the purpose of our research, the buoyancy ratio was fixed at 2, being our uptimum buoyancy ratio. It is important to note at this point that the buoyancy catenary is obtained in practice by adding a series of floaters to the riser. The effect of variation can be seen in the table below.Figure 5.1: Effect of change in buoyance on the properties of lazy-wave riserRiser ParametersBuoyancy Ratio

11.522.53

Ya (m)76.7073.0477.3089.10116.34

Ys (m)53.0465.3576.7686.3689.93

(degrees)42.4441.9740.8237.8328.08

H (m)297.64297.55295.53287.29248.69

MBR (m)201.17170.90138.21100.9553.22

BM (N.m)22.2226.1632.3444.2883.99

Bending (kN/m2)88.25108.88128.46175.87333.61

Horizontal Force (kN)56.4747.9738.7928.3414.94

Top tension (kN)83.6871.7359.3546.2031.74

5.2 Effect of Change in Hang-Off Angle

Figure 5.4: Effect of Change in Hang-Off Angle

The motion of vessels to which risers and mooring lines are connected due to environmental forces such as waves and current or the disconnection of a turret can give rise to a change in the hang-off angle of the LWR. In addition flow induced motion resulting from under water current and/or slug flow in the riser itself may lead to larger displacement in the LWR profile consequently leading to variations the hang-off angle of the LWR. The knowledge of the possible variations in the hook-up angle is important to the riser engineer in the design of the LWR. To do this the possible hook-up angles corresponding to the likely environment scenarios need to be derived in order to design against the corresponding stresses that may arise in the life time of the well.

In order to determine the variation in the configuration of the LWR, the hang-off angle of the riser was varied from around the obtained hang-off angle of 40.82. the At a constant buoyancy ration, a 20 increase in the hang-off angle resulted in a 47.35m increase in the TDP/hang-off angle offset.

From the parametric study carried out, it was observed that increase in the hang-off angle resulted in an increase in the minimum bending radius (MBR) which led to a reduction in the bending stress and bending moment of the riser pipe as indicated in the table below. However, increase in LWR horizontal tension and top tension was observed as the hang-off angle was increased.Figure 5.2: Effect of Change in Hang-Off Angle

(degrees)30.8235.8240.8245.8250.82

Ya (m)98.7487.6177.3067.7058.71

Ys (m)97.9686.9676.7667.2358.33

H (m)266.78283.06295.53305.75314.13

MBRi (m)95.46115.48138.21164.65196.32

BM (N.m)46.8338.7132.3427.1522.77

(KN/m2)185.99153.73128.46107.8390.43

N (KN)26.7932.4138.7946.2255.11

T (KN)52.3055.3959.3564.4471.09

5.3 Effect of Change in Size of Riser DiameterIn order to compare the effect of change in riser diameter, the outer diameter was varies while the wall thickness was kept constant,

Figure 5.5: Effect of Change in Size of Riser Diameter

The chat above summarises the effect of change in the side of the riser pipe diameter. When the diameter of the riser pipe is increased, it mean the volume per unit length will increase which will increase the mass of internal fluid, but the equivalent mass of fluid displayed by a larger volume is more than the mass of internal fluid, this increase in mass of fluid displaced reduces the wet mass Q per unit length of the riser. Hence, an increase in the size of the riser pipe will lead to reduction in the minimum bending radius.Since the minimum bending radius is inversely proportional to the maximum bending moment, an increase in pipe side diameter will lead to an increase in the maximum bending moment.

A reduction was noticed in the maximum bending stress when the size of the riser pipe was increased, this was so because the bending stress depends on the second moment of inertia I of the cylindrical pipe which increases as the radius of the pipe increasesIt was also noticed that there was a reduction in top tension when the diameter of the riser pipe was increased, this reduction was due to the reduction in wet mass of the riser as explained above. Consequently, there was also a reduction in the Horizontal force at the touch down point which is constant throughout the height of the riser and is equal to the horizontal component of the top tension. To maintain the water depth, there was also a reduction in the hang-off angle at the vessel when there is an increase in the size of the riser pipe.Finally on the change in pipe size diameter, the offset of the platform H reduced slightly, while the arch height and the sag bend height also increased respectively. The analysis complete analysis is shown in the table belowFigure 5.3: Effect of Change in Size of Riser Diameter

Riser parametersPipe diameter

110mm130mm150mm170mm190mm

wet weight (N/m)309.109294.9280.69266.48252.27

MBR (m)158.71153.39147.43140.70133.06

BM (N.m)28.1629.1430.3231.7733.59

(kN/m2)245.46165.33120.4293.0775.50

Top tension (kN)73.8268.3162.7757.2251.64

N (kN)49.0645.2341.3837.4933.57

(degrees)41.6541.4741.2440.9440.54

Ys (m)69.8671.7473.7875.9778.33

Ya (m)73.8974.5575.4976.7778.51

H (m)297.13296.83296.41295.79294.98

5.4: Effect of Change in Internal Fluid Density

Figure 5.6: Effect of Change in Internal Fluid Density

It is possible that several fluids with different densities are passed through the riser during its service life, for example prior to installation the riser is flooded with seawater and later on, the riser is used for oil or gas production. To check the effect of different fluid densities, an investigation was done with an empty riser with fluid density of 1kg/m3, gas with density 200kg/m3, oil with density 800kg/m3 and seawater with density 1025kg/m3.

As the density of internal fluid increases, there is an increase in in-water weight of the riser which increases the minimum bending radius (MBR). Since MBR is inversely proportional to the maximum bending moment, a reduction was noticed in the maximum bending moment and the maximum bending stress as it can be noticed in the graph above.With an increase in fluid density, the downward wet weight of the pipe also increases which gave rise to an increase in the Top tension and subsequently the Horizontal force at the touch down point of the riser which is the horizontal component of the top tension and is constant throughout the height of the riser.From the analysis carried out, it was also noticed that the touch down point of the riser increases with the increase in internal fluid density while the arch and sag bend of the riser reduces respectively. A progressive increase was also noticed in the hang-off angle when the internal fluid density is increased. The results of the parametric analysis for change in internal fluid densities are presented in the table below.

Table 5.4: Effect of change in density of internal fluid

Riser parametersInternal Fluid Densities

1kg/m3200kg/m3800kg/m31025kg/m3

Wet weight (N/m)193.73210.633261.582280.688

MBR(m)83.75102.29138.21147.43

BM (N.m)53.3743.7032.3430.32

(kN/m2)211.99173.56128.46120.42

Top tension28.0335.0055.3162.77

Horizontal16.2221.5536.1541.38

(degrees)35.3738.0040.8241.24

H (m)279.00287.79295.53296.41

Ys (m)89.0486.0876.7673.78

Ya (m)97.1588.5477.3075.49

5.4 Effect of Change in Water Depth In this parametric study, the effect of increased water depth on the LWR configuration investigated. With exploration moving further offshore into deeper waters, the conditions in which the operations take place becomes more difficult as the pay zone more is harder to reach due to the environmental conditions and the increase distance between the platform and the seabed. With the advent of subsea separation, the need for vessels in deeper waters can be reduced. However for region with no pipeline infrastructure such as in West Africa, floating production, storage and offloading (FPSO) vessels moored to the seabed can be employed at different water depths resulting in flexible riser at different water depth. The heave motion of the platform leads to a corresponding change in the hang-off location this change in the vertical height of the riser is small compared to the change in water depth.

Figure 5.7: Effect of Change in Water Depth

Having determined an optimum buoyancy ratio R, varying the water depth of the LWR flooded with seawater at a constant buoyancy ratio, culminated in changes to the arch & sag bend, hang-off angle, hang-off/TDP offset, Top & horizontal tensions, and the minimum bending radius (MBR), bending and shear stresses for both the hang-off and the buoyancy section. A 40m increase in water depth from 130m resulted in rise in the sag and arch bend heights: this was observed to be the case as the height of the touchdown catenary is a function of the water depth, V. The observed reduction in the hang-off angle as the water depth was increased, is a function of the accompanied reduction in the offset of the hang-off point from the touchdown (TDP). Furthermore, as the water depth was increased, the minimum bending radius, the top tension and the horizontal force was observed to reduce whilst increment was observed in the values of the bending moment and bending stresses of the LWR. The chart above depicts the variations in the riser configuration presented in the table below.

Table 5.5: Effect of Change in Water Depth

Water depth(m)130m140m150m160m170m

Ya (m)66.5271.8877.3082.7588.25

Ys (m)66.0871.3976.7682.1587.59

(degrees)46.4643.6040.8238.1335.52

H (m)306.91301.46295.53289.13282.23

MBRi (m)168.37152.37138.21125.59114.21

BM (N.m)26.5529.3432.3435.5939.14

(KN/m2)105.44116.52128.46141.36155.44

N (KN)47.2642.7738.7935.2532.06

Top tension (KN)65.2062.0259.3557.0955.18

5.6 Effect of Change in Platform OffsetFrom the second option, the offset of the platform from the TDP was also varied. As the platform offset increases, the minimum bending radius also increases, the increase was obvious as a result of the constant length S of the riser. Since the bending moment is inversely proportional to the minimum bending radius, an increase in the platform offset will resulted in a decrease in the maximum bending moment of the curvatures.

Figure 5.8: Effect of Change in Platform OffsetA decrease in the maximum bending moment will also lead to a decrease in the stresses in the members, this implies an increase in platform offset will lead to a decrease in the bending stress in the members as it can be seen in the graph above. As the distance from the touch down point increases, there was also an increase in the top tension, which was due to a reduction in the height of the arch bend as a result of a constant riser length. The horizontal component of the Top Tension which is constant throughout the height of the riser and equal to the horizontal force at the TDP also increases as a result of the increase in platform offset. The table below shows the effect of change in platform offset on the riser configuration and properties.Table 5.6: Effect of Change in Platform OffsetRiser ParametersHANG-OFF OFFSET FROM TOUCH DOWN POINT

228m238m248m258m268m

Si (m)142.59146.29150.00153.81157.62

Sj (m)57.3658.6860.0061.3662.72

Sk (m)125.04127.51130.00132.57135.16

(degrees)25.6926.8728.0229.1630.27

MBRi (m)49.9649.5453.2257.0861.05

BM (kNm)92.2590.2383.9978.3173.22

(kN/m2)386.24358.38333.59311.03290.78

N (kN)12.9013.9014.9416.0217.14

Top tension (kN)29.7630.7531.8032.88

5.7 Effect of Change in Arch Bend & Sag Bend HeightThe hang-off catenary, the buoyancy catenary and the touchdown catenary both make up the lazy-wave riser. For simplification, this parametric study on the varying arch height Ya, and sag bend height Ys was carried out with one parameter constant as the other tends towards the constant value.

From the parametric study carried out on the arch and sag bend heights of the LWR, it was observed that the variations in the arch and sag bend heights produced high, mid-arch and low-arch LWR configurations. The effect of the sag bend and arch bend height seemed to be similar to the effect of the buoyancy ratio on the LWR configuration.

Figure 5.9: Effect of Change in Height Arch Bend and Sag Bend HeightThe investigation of sag bend height on the LWR configuration showed the same relationship and the arch bend as illustrated in the chart above from the tabulated data. From the reduced arch bend height, increments were observed for the top tension, the horizontal force at the TDP, the hang-off angle and the minimum bending radius is change is associated with the . On the other hand, the bending moments and bending stress in the hang-off catenary was observed to reduce as the arch bend height reduced to towards the value of the sag bend height. At this point where the arch bend height and sag bend height are at the same, a configuration having no sag or arch bend is produced.Table 5.7: Effect of Change in Height Arch Bend and Sag Height

Ya (m)116.34m107.54m98.74m89.94m

(degree)28.0229.7332.1138.04

MBRi (m)53.2259.0668.1696.45

BM (N.m)83.9975.6965.5846.35

(KN/m2)333.59300.60260.46184.07

N (KN)14.9416.5819.1327.07

T (KN)31.8033.4335.9943.93

5.8 Effect of Change in Catenary Lengths1. Hang-off Catenary

The hang-off catenary, the buoyancy catenary and the touchdown catenary both make up the lazy-wave riser. With varying water depths, the LWR configuration will have different catenary lengths. For simplification of this parametric study, the lengths of the two catenaries were kept constant as the catenary length of the third catenary was varied.

Figure 5.10: Effect of Change in Hang-off Catenary

To investigate the effect of the length of the hang-off catenary on the LWR configuration, the lengths of the buoyancy catenary Sj and the touchdown catenary Sk was kept constant while the length of the hang-off catenary Si was varied in 10m increments. The parametric analysis, it was observed that the sag bend height, the arch bend height, the minimum bending radius, bending stress, the horizontal force and top tension are largely dependent on the length of the hang-off catenary on the other hand the hang-off angle increased by just over 4 for a 40m increase in length of the hang-off catenary.Table 5.8: Effect of Length of Hang-off Catenary

Ya116.34m109.27m102.72m96.57m90.83m

Ys (m)89.9385.7881.6477.5573.55

(degrees)28.0229.4630.6731.7532.73

H (m)248.69266.96283.57299.01313.52

MBRi (m)53.2262.1371.1780.4589.98

BM (N.m)83.9971.9562.8155.5649.68

(KN/m2)105.44285.73249.46220.68197.30

N (KN)14.9417.4419.9822.5825.26

T (KN)31.8035.4639.1642.9146.71

2. Buoyancy Catenary

Further investigation into the effect off buoyancy catenary length on the LWR required was conducted with the lengths of the hang-off and touchdown catenary keep constant at a buoyancy ratio of 3.0.

Figure 5.11: Effect of Change in Buoyancy CatenaryThe study showed that the arch bend height, sag bend height, bending moment of the buoyancy section and the bending stress of the buoyancy section reduces with the reduction in the length of the buoyancy whilst the hang-off angle, minimum bending radius of buoyancy section, horizontal force at the TDP and the top tension increased. The offset distance was observed to increase as the buoyancy catenary length increased: this can be associated with the upward movement of the TDP.Table 5.9: Effect of Change in Length of Hang-off Catenary

Ya (m)116.3498.7287.2779.1673.11

Ys (m)89.9388.6384.5379.0172.59

(degrees)28.0233.4836.5537.8438.37

H (m)248.69269.95275.62275.39272.40

MBRj (m)17.3425.7032.1237.5242.43

BM (N.m)257.79173.92139.17119.14105.35

(KN/m2)1001.00690.77552.65472.85420.43

N (KN)4.877.219.0210.5311.91

T (KN)10.3613.0815.1417.1719.19

3.Touchdown Catenary

Table 5.12: Effect of Change in Length of Touch down Catenary

In the third study of the effect of catenary, the touchdown catenary length of the LWR was increased. Increments were observed in the sag bend height, the hang-off angle, the offset, the horizontal force, the top tension and the minimum bending moment of the hang-off catenary as the touchdown catenary length increased. From the parametric study, the increase in offset distance, this was as a result of increase in the MBR of the hang-off section which in itself resulted from the increased hang-off angle as the touchdown catenary length increase as depicted in the table and chart below.

Table 5.10: Effect of Change in Length of Touch down Catenary

Sk (m)130m140m150m160m170m

Ya (m)116.34107.06102.7299.4097.85

Ys (m)89.9394.7396.7297.4297.44

(degrees)28.0236.6742.1345.9648.85

H (m)248.69284.44306.23322.87337.14

MBRi (m)53.2281.90108.54134.43160.20

BM (N.m)83.9954.5841.1833.2527.90

(KN/m2)333.61216.76163.46133.06110.82

N (KN)14.9422.9930.4737.7344.97

T (KN)31.8038.4945.4252.4959.72

6.0 CONCLUSION

Based on the optimisation and parametric analysis, the following conclusions were made;

1. Any little change in the geometric properties of the riser or environmental conditions has a significant effect on the static configuration and dynamic behaviour of the riser for example a 2O change in hang-off handle increased the bending stress at the hang off catenary by 30%.

2. For a constant water depth, the best way to reduce the Top tension is to reduce the hang-off angle, reduce the platform offset from the TDP, increase the buoyancy ratio or increase the diameter of the riser pipe.

3. The effective ways to reduce the Maximum bending moment is to reduce the buoyancy ratio, Increase the platform offset, and Increase the hang off-angle at the platform.

It is very important to note that most of the things we do to reduce the Top tension requires the opposite action to reduce the bending moment. This present a dilemma. Hence the riser engineer has to be careful to place a balance between these two important parameters lazy-wave parameters. 7.0 REFERENCES[1]Songchen Li et al (2010) Dynamic Response of Deepwater Lazy-wave Catenary Riser, DOT[2]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]

[3]Jacob B.P et al (1999) Alternative Configurations for Steel Catenary Risers for Turret Moored FPSO ISOPE[4]Silva R.M.C et all (1999) Feasibility Study and Preliminary Design of SCR attached to FPSO OMAE

[5]Torres A.L.F.L et all (2002) Lazy wave Steel Rigid Riser for Moored FPSO OFT-2P124