Tension Loss of Hydro-Pneumatic Riser Tensioners · 2018-04-18 · As an example, a drilling riser...

1 Copyright © 2013 by ASME

TENSION LOSS OF HYDRO-PNEUMATIC RISER TENSIONERS

Songcheng Li 2H Offshore Inc.

Houston, TX, USA

Mike Campbell 2H Offshore Inc.

Houston, TX, USA

Hugh Howells 2H Offshore Ltd.

London, UK

John Orsak 2H Offshore Inc.

Houston, TX, USA ABSTRACT

With drilling exploration extending to deeper water, the total top tension to lift a drilling riser increases accordingly. Tensioners with higher tension capacity are preferred to minimize the total number of tensioners due to space limitation on a drilling vessel. Higher tension capacity requires more advanced recoil control for emergency events. Hydro-pneumatic tensioners are widely used for risers with anti-recoil control in deep water, and are commonly simulated as an equivalent linear or nonlinear spring or a pneumatic system. The discrepancy between simulation and measurement calls for a model with rate dependent stiffness considering the compressibility of hydraulic oil, the interference of valve control and friction loss along piping or hose.

In this paper, the hydro-pneumatic tensioner system with anti-recoil valve control is simulated in 2HRecoil, a customized version of ANSYS Mechanical APDL, and benchmarked with commercial software DeepRiser. The tension loss due to hydraulic oil friction, mass inertia, piston-cylinder friction is evaluated with coupled riser motion. The conventional approach in simulating the hydro-pneumatic tensioner system as an equivalent pneumatic system is found inaccurate. The sensitivity of the pressure difference between the cylinder chamber and the high pressure accumulator on the gas constant is discussed. The scatter in predicting gas constant, friction and damping coefficients from measured data is explained using hydro-pneumatic approach.

Keywords: Recoil, Tensioners, Friction, Losses

INTRODUCTION Hydro-pneumatic riser tensioners are commonly

categorized into tension-style and ram-style tensioners [1]. The widely used tension-style tensioners are the direct acting tensioners and wire line tensioners. The fundamental mechanism of all the hydro-pneumatic systems for a riser is similar to a cylinder-piston system: the tension or compression force of the piston rod is provided by the pressure difference in the cylinder between two sides of the piston, each side is connected directly or indirectly with pressurized air or nitrogen bottles. For example, the high pressure of the cylinder-piston

system in Figure 1 is indirectly supplied by the air pressure vessels (APV) via the hydraulic piping or hoses between the high pressure accumulator (HP) and the cylinder, while the low pressure in the cylinder chamber comes directly from the low pressure bottle (LP), which may be shared by other tensioners.

The riser is lifted directly at the bottom of the piston rod of a direct acting tensioner, or indirectly at the top of the piston rod via the reeving system of a wire line tensioner. The vessel and riser motions drive the piston up and down, changing the pressures and volumes of the gas and oil in the system. The pressure and volume relationship inside the HP and the LP is assumed following polytropic process of ideal gas. The difference in the gas laws is associated with quantitative choice of the polytropic index or gas constant, which is often selected between 1.0 for isothermal process and 1.4 for reversible adiabatic process.

Figure 1 – Direct Acting Tensioner System Schematic An important feature of a hydro-pneumatic system is the

anti-recoil valve, which controls the flow rate of its hydraulic oil and position of the piston. A valve can be widely open, 100% closed or at any other closure state, where the tensioner stiffness of the hydro-pneumatic system can be anywhere between nearly pneumatic and completely hydraulic, owing to bottle neck effect of the flow lines and the valve closure. Even if the valve is widely open with its maximum flow capacity,

Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013

June 9-14, 2013, Nantes, France

Learn more at www.2hoffshore.com


pressure difference between the oil in cylinder and the gas in APV can be induced in any sea states. Generally, the tensioner stiffness varies with piston stroke, stroke rate and acceleration, though most simulations consider tensioner stiffness as a function of piston positions regardless of rod speed and valve closure.

Discrepancy between simulation and measurements is induced if the pressure monitored in the cylinder is directly applied to the gas law. Considerable error can occur at riser disconnect events where reduced valve closure, increased stroke rate and sharp tension fluctuation are expected. The accuracy in predicting tension and stroke plays a critical role in analyzing riser fatigue during normal operation and avoiding a hazardous recoil incident at riser emergency disconnect.

As an example, a drilling riser in 1933 m of water depth is studied to demonstrate the significance of the tension loss in the simulation of hydro-pneumatic tensioners. The tension losses are expressed as a percentage of the top tension, which does not necessarily imply that they are proportional to the top tension, for example, the ratio of seal and Coulomb friction to the top tension may become higher in shallower water.

PRESSURE DROP ACROSS ANTI-RECOIL VALVE The flow rate Q of the valve is a function of pressure drop,

ΔP, across the valve or

)(*||

PsignS

PCQ

oV

(1)

where S0 is the specific weight of the hydraulic oil and CV is the flow coefficient, which is a known value in gallon per minute under pressure drop of one pound per square inch for a given valve closure, and is provided by manufacturers or valve suppliers. The pressure drop ΔP relies on the history of pressure build-up on both sides of the valve, which can be tracked to its initial equilibrium state where there is no pressure drop across the valve.

The pressure difference varies with rod speed and valve closure. During normal operation, the anti-recoil valve is widely open. For a vessel motion with heave amplitude of 0.7m (peak to peak 1.4m) and period of 7 sec at the riser hang-off location, the maximum pressure difference across the anti-recoil valve is less than 1% of the APV pressure, as shown in Figure 2 with time t<35 sec, where the rod speed is up to 0.6 m/s. In hurricane events the maximal rod speed exceeds 1.2 m/s.

At events of planned or emergency riser disconnect, the riser is unlatched between the lower marine riser package (LMRP) and the blow-out preventer (BOP). The anti-recoil valve in this study is closed steadily from 30% closure to 85% closure as a function of the piston stroke, which gives a rod speed up to 1.6 m/s (upward) within 1.8 sec from the moment the riser is disconnected. With limited valve flow rate and delayed valve response, fast upward movement of the piston causes rapid expansion of the hydraulic oil in the cylinder with sharp decrease of its local pressure, as shown in Figure 2. The APV pressure remains relatively stable after riser disconnect at

time t=35 sec. The maximum pressure difference across the valve reaches about 96% of the APV pressure within 3.0 sec. In conjunction with closure of the anti-recoil valve, the tensioner stiffness is shifted from largely pneumatic (softer) to mainly hydraulic (stiffer).

Figure 2 – Oil Pressures across the Anti-Recoil Valve

FRICTION OF HYDRAULIC OIL LINES Hydraulic oil friction along piping (including hoses)

depends on oil viscosity that varies with oil rheology and temperature. Water based hydraulic fluids, which is fire and explosion resistant with high compression ignition ratio of 50:1 [2], are preferred for riser tensioners. For example, the water glycol fluids contain 35% to 45% of water with typical Newtonian rheology [3]. Other hydraulic fluids may demonstrate Herschel-Bulkley, Cross, Carreau or Power-Law rheology [4].

The flow of hydraulic fluid in tensioner piping system is largely laminar or transitional during normal operation, while turbulent in storm condition or after riser disconnect. A rod speed of 1 m/s is translated into a volumetric oil speed of 6~11 m/s inside 6~8 inch piping, assuming a cylinder bore size of 22 inches in diameter with a rod outer diameter of 9 inches. Shear rate of the oil is calculated from mass continuity or controlled volume depending on rheological type of the oil. For Newtonian rheology with a constant viscosity of 220 cSt, the friction force as a percentage of the nominal tension is shown in Figure 3. The oil friction is less than 1.3% of the top tension during normal operation and up to 3.5% after the riser is disconnected.

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0 10 20 30 40 50 60

Time (sec)

Oil

Pre

ssu

re (

MP

a)

Cylinder Side Pressure APV Side Pressure

Riser Disconnected



Figure 3 – Oil Friction along Hydraulic Lines

The temperature was observed to have more influence than

the shear rate on viscosity. The natural logarithm of viscosity versus the reciprocal of temperature is approximately linear [5][6][7]. To simulate tensioner stiffness for a wide range of both temperatures and shear rates, Modified Cross and Carreau models are used [8].

INERTIA OF HYDRAULIC OIL AND PISTON MASS The inertia of the hydraulic oil also contributes to tension

loss. For a tensioner system with 25m long 8 inch hose, 8m long 8 inch hard piping on the cylinder side and 16.5m long 8 inch hard piping on the high pressure accumulator side, about 5 tons of hydraulic oil is stored in the hydraulic system with hard piping, flexible hoses, valves, diverters, bends, goosenecks, as well as the high pressure accumulator and the cylinder chamber. The oil is constantly mobilized by the piston motion by means of pressure waves propagating along the hydraulic system. With averaged fluid hammer effect, the inertia of 5 tons of hydraulic oil along with 8 tons of piston-rod mass is up to 1% of the top tension during normal operation, as shown in Figure 4. The peak inertia force increases with faster piston reversal and piston acceleration under irregular waves. Some inertia energy is converted into lost work due to local mechanical compliance of the oil bulk modulus with the container (cylinder and piping) stiffness.

Figure 4 – Inertia Force during Normal Operation

EFFECT OF PISTON FRICTION The tensioner stick-slip phenomenon is found in low sea

states [9][10]. For the pneumatic approach, piston Coulomb friction and viscous damping are usually assumed to represent the oil line friction and mass inertia of the hydraulic oil and piston-rod system. This method results in very scattered friction and damping coefficients [11]. In comparison, the hydro-pneumatic approach considers the oil/piston inertia and oil/piston friction independently.

For lubricated piston-cylinder contact, the piston friction is assumed the sum of seal friction, Coulomb friction and viscous friction, as illustrated in Figure 5. Piston friction in low rod speeds is also referred to as Stribeck friction [12][13]. The seal friction decreases exponentially with rod speed and can be expressed as

)(|/|1

2 vsignecf svvcs

where: c1 and c2 are constants, vs is the Stribeck velocity, and v is the rod velocity. Coulomb friction is a constant regardless of the rod speed. The combination of seal friction and Coulomb friction at static is termed breakaway friction. The viscous friction increases linearly with rod velocity as

vcf v 3

where: c3 is a constant. The total friction is:

cvs ffff

The coefficients for piston friction can be evaluated by experiments [14] or provided by manufacturers. A 10% friction factor provided by a seal supplier for a one inch seal height inside a 22 inch cylinder bore gives a breakaway friction of about 3% of total tension and a Coulomb friction of about 2% of total tension. Piston friction varies with tension level, load type, frequency, extending/retracting stroke, etc. The viscous friction is associated with the applied lubricant.

Figure 5 – Piston Friction Components

PREDICTION OF GAS CONSTANT The hydro-pneumatic tensioner system is commonly

simulated as a simple cylinder-piston system [1][11][15]. Reversible adiabatic process and ideal gas law are widely assumed with a constant polytropic index, or gas constant. The pressure in the cylinder as opposed to that in the high pressure accumulator or air pressure vessels is commonly applied directly to the pressure-volume relationship. This is essentially a pneumatic approach that defines the adiabatic process approximately as

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-1%

0%

1%

2%

0 10 20 30 40 50 60

Time (sec)

Oil

Fri

cti

on

/ N

om

inal

Ten

sio

n

Riser Disconnected

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

0 5 10 15 20 25 30 35

Time (sec)

Inert

ia F

orc

e /

No

min

al T

en

sio

n



n

zz

zpp )(

0

00

(2)

or

n

V

Vpp )( 0

0 (3)

where P and P0 are the instant and initial oil pressure values, respectively, in the cylinder, Z0 is the effective length of the gas column of the piston-cylinder system, Z is the stroke of the piston with respect to the cylinder, V and V0 are the instant and initial gas volumes, respectively. With measured P and P0 at each instant, the gas constant n is predicted from Equation (3), or

)ln(

ln

0

0

VVpp

nn p (4)

The equation above causes scatter and error in prediction of gas constant and other parameters.

As a comparison, the hydro-pneumatic approach applies the gas pressure in the APV as opposed to the oil pressure in the cylinder. It simulates the pressure drop caused by the anti-recoil valve, the hydraulic oil lines, the end fittings, and the inertia and friction of all moving components. The adiabatic process and ideal gas law gives:

n

V

Vqq )( 0

0

where q and q0 are the instant and initial APV gas pressures, respectively. The gas constant n suffices:

)ln(

ln

0

0

V

Vqq

n (5)

Since the APV pressure q is not monitored or not available, back calculation from the oil pressure p is required to predict the gas constant, with the use of the pressure difference induced by the anti-recoil valve, as specified in Equation (1), and those due to friction and inertia of hydraulic oil and other moving components.

The error in predicting the gas constant with the pneumatic approach can be derived from the combination of Equations (4) and (5), or

0

ln

ln

qqq

pq

n

nnp

(6)

where the initial condition q0 = p0 is applied and the pressure difference ΔP=p-q. The equation above suggests the scatter in prediction of the gas constant increases with pressure

difference. Equation (6) can also be expressed in terms of the pressure p monitored in the cylinder:

0

ln

ln

ppppp

p

n

nnp

(7)

During normal operation, the anti-recoil valve is widely open with a constant flow coefficient CV. The pressure maximum difference ΔP across the valve in Figure 2 is less than 1% of the APV pressure when t<35 sec. This seemingly negligible pressure difference leads to considerable scatter in prediction of the gas constant, as shown in Figure 8. Given gas constant n=1.4 in Equation (7), the predicted gas constant using the pneumatic approach varies with time and fluctuates from 1.12 to 1.68 with a standard deviation of 0.12. Apart from the pressure difference across the anti-recoil valve, other pressure drops along the hydraulic system also contribute to the scatter in the predicted gas constant.

In hurricane events, the mean pressure in the APV may deviate from the pressure associated with the mean stroke due to nonlinear adiabatic process, as illustrated in Figure 6. Similarly, the nonlinear behavior of the pressure drop across the anti-recoil valve is demonstrated in Figure 7 as far as normal operation in Figure 2 is concerned. If the averaged pressure difference is non-zero, it is called biased. The average pressure difference can be more biased in hurricane events, with more deviation in predicting the gas constant according to Equation (6).

Figure 6 – Nonlinear Pressure-Volume Relationship

Figure 7 – Hysteresis Curve for Pressure Difference Biased and scattered gas constant is observed in

interpreting full-scale measured data in Holstein Spar

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6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3

Stroke (m)

Pre

ss

ure

Dif

fere

nc

e /

AP

V P

ress

ure

Start Point (7.5, 0.0%)

P

V

V2V1 Vm

? Pm

Pm



production facility during 2005 hurricane season [11], as shown in Figure 9. The pneumatic approach was used, and an average gas constant of 1.46 was reported, which looks biased and overestimated. In addition, the predicted gas constant is as scattered as that in Figure 8, despite of different significant wave heights.

The hydro-pneumatic approach is more accurate in predicting the gas constant as well as other parameters than the pneumatic approach. The latter assumes no pressure difference between the gas in the APV and the oil in the cylinder, while the former models the pressure difference with model parameters that can be calibrated by tests or experiments.

Figure 8 – Scatter of Predicted Gas Constant

Figure 9 – Predicted Gas Constant Assuming Pneumatic

Approach (Gupta et al, 2008)

COMPARISON OF RESULTS BETWEEN 2HRECOIL AND DEEPRISER

The anti-recoil analysis software 2HRecoil is developed in FORTRAN that can be integrated in ANSYS with full access to ANSYS functions for 3-D riser simulation. In order to validate the tensioner model developed for 2HRecoil, a benchmarking exercise is carried out with the commercially available DeepRiser [16]. The methodology used in 2HRecoil is very similar to that used by DeepRiser [17].

The benchmarking exercise considers a drilling riser in 1933 m of water with the stack-up given in Table 1. The bare

riser joints have an outer diameter of 21 inches and a wall thickness of 0.875 inches. All the buoyancy modules used have an outer diameter of 54 inches. The total wet weight of the riser and LMRP is 4063 kN (excludes BOP and components above telescopic joint). The model is fixed at the base of the BOP, and a drill string with 6 inch diameter is considered to be present inside the riser. Two internal fluids are used for the analysis – 1025 kg/m3 seawater and 1650 kg/m3 drilling mud. The riser top tension setting is 5338 kN for the case with seawater and 8096 kN for the case with drilling mud.

The tensioner system used consists of six direct acting tensioner cylinders as described in Table 2. The system parameters are representative of high capacity tensioner systems currently on the market. In order to simplify the comparison, the only tensioner loss considered for the exercise is the pressure drop across the anti-recoil valve described earlier in this paper.

The typical results of interest for a recoil event are tensioner stroke, riser top tension – defined as the tension at the tension ring – and lower marine riser package (LMRP) clearance from the BOP stack. Therefore, the comparison will focus on these key results. No vessel motion is considered for this comparison in order to eliminate outside sources of error.

Component Joint

Length (m)

Number of

Joints

Base Elevation

(m) Diverter 1.536 1 1962.76

Upper Flexjoint 0.1 1 1962.66 10ft Pup 3.048 1 1959.62

Inner Barrel 9.6 1 1949.1 Outer Barrel 10.515 1 1923.8 Termination

Joint 25.928 1 1920.15

15ftPup 4.572 1 1915.57 Slick Joint 22.86 7 18.19

Buoyancy Joint 2000ft Rating

22.86 6 1778.41


22.86 26 1184.05


22.86 27 566.83


22.86 4 475.39

Slick Joint 22.86 13 18.19 Lower

Flexjoint 0.1 1 18.09

LMRP 7.23 1 10.86 BOP 7.209 1 3.67

Table 1 – Drilling Riser Stack-up

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 5 10 15 20 25 30 35Time (sec)

Gas

Co

nst

an

t, n

Predicted Using Cylinder Pressure Given Gas Constant



Parameter Value Number of Tensioners 6 Maximum Stroke 15 m Gas Constant (Polytropic Index) 1.4

Clylinder Bore Diameter 0.56 m

Piston Rod Diameter 0.23 m

Air/Oil Accumulator Volume 4 m3 Air Pressure Vessel Volume per Tensioner

9 m3

Low Pressure Accumulator Volume 4 m3/6

Table 2 – Direct Acting Tensioner System Parameters The case with seawater filled riser is assessed first. The

riser disconnects from the BOP at 15 seconds, at which point the tensioner quickly strokes until the anti-recoil valve closes at around 4.5 m of absolute stroke, which is defined as 0 m when the tensioner rod is fully retracted and 15 m when the rod is fully extended. The anti-recoil valve does not completely close, so the tensioner is able to slowly continue stroking. The tensioner stroke responses from the two programs are very similar as shown in Figure 10. The average relative difference between the strokes generated from the two programs is only 3%. Because the internal fluid is seawater, drag effects of a discharging fluid are non-existent, so the similarity shows that the general tensioner models are very similar. The anti-recoil valve slows the stroke down at practically the same time for both programs, indicating that the valve theory is the same.

The riser top tensions are shown in Figure 11, and aside from minor noise, the results compare very well between the two programs (2% average relative difference). After disconnect, the tension drops significantly and then rebounds up to match the riser weight. The cause of the noise in the DeepRiser results is unknown, but it may be due to structural damping not being considered in the analysis. Regardless, the general trend of the top tension is consistent between the two programs.

The LMRP displacement is shown in Figure 12, and the response is within 5% for the duration of the analysis. The fact that the LMRP clearances match up well indicates that the finite element models used for the riser compare well between ANSYS and DeepRiser.

Figure 10 – Tensioner Stroke: Seawater Filled Riser

Figure 11 – Riser Tension at Tension Ring: Seawater Filled

Riser

Figure 12 – LMRP Clearance from BOP: Seawater Filled

Riser

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Ab

solu

te S

tro

ke (

m)

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DeepRiser 2HRecoil

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Additional comparisons are conducted considering 1650 kg/m3 drilling mud as the internal fluid. After disconnect, the mud discharges from the riser and applies friction forces until the mud column reaches hydrostatic equilibrium with the external seawater. The tensioner stroke is shown in Figure 13 with riser disconnected from the BOP at 15 seconds. The two programs output very similar results aside from a slightly different stroke rate from 25 to 160 seconds. Over the course of the analysis, the average relative difference is only 7%.

The riser top tension is shown in Figure 14, and the average relative difference is 7%. For the first 20 seconds after disconnect, which is the critical time period for dynamic recoil in terms of maximum upstroke, minimum tension and BOP clearance the results are practically identical.

The mud shedding velocity comes to nearly zero or static relative to the riser string at about 160 sec when the downward flow of the internal fluid starts to reverse as a result of overshoot from the hydrostatic equilibrium with the external seawater. After this point, the tension should vary with mud friction, which oscillates and attenuates until the mud column with bottom refilled with water and diluted mud becomes static and reaches hydrostatic equilibrium with the external seawater pressure. At about 160 sec, the tension should be stabilized at the same value for both programs. However, the tensions are different by approximately 470 kN. This is in contrast to the case with seawater where there is no practical difference in the stabilized tension.

The most likely explanation of the tension difference, that has not been confirmed, is the mud in the auxiliary lines. For this case, the valves for the auxiliary lines are assumed closed in 2HRecoil without mud loss in the choke and kill lines. Hence, the tension trends towards the riser wet weight with mud in the choke and kill lines. DeepRiser trends towards only the riser wet weight, as shown in Figure 15.

Whilst there is a difference in the final static tension, the critical dynamic recoil response immediately following disconnect is very similar. The results for the recoil phase of the analysis (15-40 seconds) compare very well, and the difference in the long term tension pose little concern.

The LMRP displacement is very similar for both programs as shown in Figure 16. The response is not quite as similar as the case with seawater, and the difference is likely caused by the slightly different stroke rate. Overall, the average relative difference is 5%.

Figure 13 - Tensioner Stroke: Drilling Mud Filled Riser

Figure 14 – Riser Top Tension: Drilling Mud Filled Riser

Figure 15 – Riser Top Tension: Stabilized Tension

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ion

(kN

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Time (sec)

DeepRiser Top Tension

2HRecol Top Tension

Riser Wet Weight

Riser Wet Weight + Aux Line Fluid Wet Weight



Figure 16 – LMRP Clearance from BOP: Drilling Mud

Filled Riser

CONCLUSIONS Hydro-pneumatic tensioner systems can be simulated

accurately with model parameters calibrated from test results or measured data. The model parameters include the polytropic process of all gas components, the inertia and friction of hydraulic oil and piston-rod system, the control of the anti-recoil valve, the pressure loss along the hydraulic oil lines and end-fittings. The tension loss stems from the bottleneck effect of the hydraulic system and the dynamic interaction between all components.

Hydro-pneumatic tensioner systems are widely simplified as pneumatic systems, but this simplification is found sensitive to the cylinder-APV pressure difference. For instance, a pressure difference of less than 1% of the APV pressure gives a standard deviation of 0.12 in gas constant. The gas constant and other parameters predicted by the pneumatic approach can be scattering and biased.

Both direct acting and wireline tensioner types are simulated in 2HRecoil, which produces similar riser responses to DeepRiser with regards to tensioner stroke, riser top tension, and LMRP displacement. The differences in the results are relatively minor and would not result in drastically different conclusions in an analysis report. The comparison shows that the tensioner model used in 2HRecoil is very similar to the model available in the commercial software, DeepRiser.

REFERENCES [1] Yu, A., Cheng, Y., and Bhat, S., “Evaluation of Key

Hydraulic Tensioner Performance Parameters for Ultra Deep Water Applications”, Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering, Portugal, June, OMAE 2008-57465

[2] MIL-H-22072 Rev C (1984), Military specification: hydraulic fluid, catapult, NATO code number H-579 (05 MAR).

[3] Philip Rakoff, G. John Colucci, Robert K. Smith, (1965) “Development of fire resistant water based hydraulic fluids”, E.F. Houghton & Company, Philadelphia, PA, USA

[4] W.B. Wan Nika, F.N. Anib, H.H. Masjukic, S.G. Eng Giapa, (2005) “Rheology of bio-edible oils according to several rheological models and its potential as hydraulic fluid”, Industrial Crops and Products, Volume 22, Issue 3, November, pp 249–255

[5] Stanciu, I., (2011), “Rheological properties of rapeseed oil and hydraulic oil”, U.P.B. Sci. Bull., Series B, Vol. 73, Iss. 3 ISSN 1454-2331

[6] H. Noureddini, B.C. Teoh, D.L.Clements, (1992), “Viscosities of vegetable oils and fatty acids”, Journal of American Oil Chemists’ Society, JAOCS, vol. 69, pp. 1189-1191

[7] Viswanath, D.S.,and Natarajan, G. (1989), Data Book on the Viscosity of Liquids, Hemisphere Publ. Corp., New York.

[8] Helleloid, G.T. “On the computation of viscosity-shear rate temperature master curves for polymeric liquids”, Morehead Electronic Journal of Applicable Mathematics, Issue 1, CHEM-2000-01

[9] H. Gupta, L. Finn, and J. Halkyard, “Spar Riser Alternatives for 10,000 ft Water Depth”, OTC paper 14298, 2002

[10] H. Gupta, F. Botros, Y. Cheng, and A. Yu, “Design Challenges for Ultra Deepwater Riser with Hydraulic Tensioners,” MCE Deepwater Development 2007, Wood Green, London, March 27-29, 2007

[11] Gupta, H., Nava, V., Banon.H, Gkara,V. and Spanos, P., “ Determination of Riser Tensioner Properties from Full-Scale Data”, Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering, Portugal, June, OMAE2008-57791

[12] B. Armstrong, C. de Wit. Canudas, ”Friction Modeling and Compensation”, the Control Handbook, CRC Press, 1995

[13] L. Marton and B. Lantos, “Modeling, Identification and Compensation of Stick-Slip Friction”, IEEE Transactions on Industrial Electronics, Vol 54, No.1, Feb 2007

[14] Tran, X.B, Hafizah, N., Yanada, H., “Modeling of dynamic friction behaviors of hydraulic cylinders”, Mechatronics, Vol 22, Issue 1, Feb 2012, pp 65-75

[15] Zhang, H., Song, R., “Theoretical Prediction of Tension-Stroke Relationship of Hydr-Pneumatic Tension Systems”, Proceedings of the ASME 31st International Conference on Offshore Mechanics and Arctic Engineering, Rio de Janeiro, July, OMAE2012-84071

[16] MCS, “DeepRiser Users Manual”, Version 2.5, June 2008 [17] Lang, D.W., Real, J., Lane, M., “Recent Development in

Drilling Riser Disconnect and Recoil Analysis for DeepWater Applications”, Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI, June, OMAE2009-79427

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