The Effect of Friction in Passive and ActiveHeave Compensation of Crown Block

Mounted Compensators

Jørgen Haaø ∗ Steffen Vangen ∗ Ilya Tyapin ∗ Martin Choux ∗

Geir Hovland ∗ Michael R. Hansen ∗

∗ University of Agder, Department of Engineering, Grimstad, Norway(e-mail: firstname.surname@uia.no).

Abstract: This paper studies the effects of friction model during passive and active heavecompensation of offshore drilling equipment. The main purpose of heave compensation whiledrilling from vessels or semi-submersible platforms is to maintain the drilling operationunaffected by the wave induced motion. The investigated system is of an existing crown mountedcompensator. A model of the system is developed which includes mechanics, hydraulics andpneumatics. The passive heave compensation scheme is described including force equalisinghydraulic cylinders. In this paper the detrimental effect of friction on the heave compensationperformance in both passive and active heave compensation is investigated and discussed.

Keywords: Friction, Active Compensation, Passive Compensation, Electro-Hydraulics Systems.

1. INTRODUCTION

In general, heave compensation is introduced in order tofacilitate offshore operations so that they may be per-formed in a safe, effective and controlled way as roughweather as possible. Today this type of heave compensa-tion is utilising large hydraulic-pneumatic cylinder-pistonarrangements that effectively suspend the drill-string orthe riser in a weak gas spring. The weakness of the springis designed so that the spring force is approximately con-stant independent of the heave motion induced by thesurrounding conditions. Active heave compensation is in-troduced by adding actively controlled hydraulic cylindersthat counteract non-linearities of the passive system andbased on position measurements attempt to maintain theposition or the tension in the upper part of the drill-stringat a constant level.

A major obstacle in advances within model based re-search and development of heave compensation equipment,in general, is the difficulties and costs associated withexperimental work and the more or less total absenceof prototypes. Despite this, several interesting researchwork has been carried out in the later years. On passiveheave compensation Skaare and Egeland (2006) as wellas Hatleskog and Dunnigan (2007) has investigated modelbased approach. Recently, Ottestad et al. (2010) has shownthat the friction in the main cylinder often has a strongdetrimental effect on the performance of passive heavecompensation systems. It has also been shown, Hansen andOttestad and Hansen (2011), that the ability to predict theCoulomb friction is the most important parameter whenemploying direct force compensation. It has, however, notbeen investigated whether the cylinder friction has the thesame importance on an active heave compensation systemusing a classical motion control scheme.

The approach that is taken to investigate this is byaddressing a worst case heave compensation scenario asseen from a passive heave compensation point of view.This corresponds to a situation with low weight-on-bit(WOB), short drillstring, and stiff formation. A modelof such a system is modeled with a typical active heavecompensation control and the best possible performanceregarding variations in WOB is determined for differentcombinations of friction and control valve bandwidth.

2. COMPENSATOR MODEL

The compensator model consists of several parts such asactive hydraulic, passive hydro-pneumatic and mechanicalsubsystems. In Fig. 1 and 2 a Drill String Compensatoris shown which is located on the top of the derrickand consists of the passive Crown Mounted Compensator(CMC) and the Active Heave Compensator (AHC). Themain compensator function is to compensate the platformheave motion while drilling or landing equipment on theseabed.

CMC consists of one plunger cylinder and two small forceequaliser cylinders, see Fig. 3. The passive compensatorworks as a hydro-pneumatic spring and the force in itdepends on its extension. The compensator uses two smallequaliser cylinders to reduce the effect of a force variationdue to the compressed air. AHC allows the rig to carry outoperations in an extended weather window and consists oftwo double acting cylinders positioned besides the plungercylinder on the CMC, see Fig. 4. AHC makes it possible tokeep the crown block position with respect to the seabedconstant typically within 0.01− 0.05 metres with a heavemotion amplitude up to 4 − 5 meters, Haaø and Vangen(2011). In purpose of the heave motion compensation thecrown block is moving while the drawworks is fixed onthe drilling deck. The wire line length variation is taken

Proceedings of the 2012 IFAC Workshop on AutomaticControl in Offshore Oil and Gas Production, NorwegianUniversity of Science and Technology, Trondheim,Norway, May 31 - June 1, 2012

FrBT2.4

Copyright held by the International Federation ofAutomatic Control

316

Fig. 1. The Drill String Compensator. The total height ofthe compensator equals 20 metres.

up by the rocker arm system. This design prevents thecompensator from adding any wear to the wire, Haaø andVangen (2011).

The compensator model used in this paper was consideredin Ottestad et al. (2010). The loads used in the modelare summarised in table 1. A pressure source used forthe active hydraulic system actuation is 345 bar. TheAHC consists of two electro-hydraulically actuated 4/3-way directional control valves in parallel, see Fig. 4. Forsimplicity they are modeled as a single large valve. Eachvalve has a rated flow of Qr = 460 L/min at a ratedpressure drop of ∆p = 35 bar per metering edge. Theactive heave cylinders are symmetrical actuators with apiston diameter of dp = 200 mm and a rod diameter ofdr = 170 mm. Like the valves they are modelled as a singlelarger cylinder.

The two active heave cylinders have a stroke length of7650 mm. The passive system consists of one oil filledplunger cylinder connected to a piston accumulator whichintermediates the pneumatic and the hydraulic system,see Fig.3. The hydro-pneumatic system is modeled as aspring to keep WOB around 3g kN. The plunger cylinderis modeled as a gas spring with stiffness 42 kN/m anddamping 52 kNs/m. These numbers are adopted fromOttestad and Hansen (2011), where a detailed model ofthe entire passive system all major flow resistances andcapacitances in both the pneumatic and hydraulic systemswere included. Two force equaliser cylinders (Fig. 3) areused to compensate for the force variations caused by thegas spring. The cylinders pull the Crown Block downwardswhen the plunger cylinder is under mid-stroke and up-wards when the plunger cylinder is above mid-stroke.

Table 1. The loads supported by the compen-sator.

Cylinder 10[t] Crown Block 20[t] Drill bit 3[t]

Travel. Block 20[t] Drill String 80[t] DDM 30[t]

Fig. 2. Main arrangement of CMC drilling equipment.

Fig. 3. The hydro-pneumatic system with a plunger cylin-der and two force equaliser cylinders.

In this paper the platform motion is modeled as a singlesine wave, see (1). The amplitude of the wave is 0.5 metresand the time period is 12 seconds. Clearly, this is a simpli-fication as compared to actual wave patterns. However, thetwo main parameters when designing heave compensationequipment are the maximum travel and maximum velocity,

Copyright held by the International Federation ofAutomatic Control

317

Fig. 4. The hydraulic system with active heave cylinders,two proportional valves and the bypass valve

Fig. 5. 20-Sim based model of the drill string compensatorwithout a control loop.

hence the simple sine wave is considered as adequate torepresent these parameters satisfactory.

Zh(t) = ∆Zh sin

(2πt

T

)(1)

where ∆Zh is the amplitude and T is a time period ofthe wave. The force from the force equalisers is basedon the geometry, see Fig. 3, and the pressure level inthe main cylinder. The active and passive compensatorsadjust the distance between the platform and the crownblock. The crown block holds payloads of different partsof the structure, as shown in Fig. 2. The parameters ofthe mechanical part such as the mass and the stiffnessare summarised in Ottestad et al. (2010) and some aregiven below. The total wire stiffness is kw = 4000 kN/m.Both the Drill String and wire stiffness vary with respectof their lengths but are considered constant in this paper.

The Drillstring spring stiffness is kDS = 298 kN/m. Thecontact stiffness with the formation is kF = 1000 kN/m.

The complete model is implemented in 20− Sim softwareand is shown in Fig. 5. The model has four outputs,wave position, wave velocity, WOB and cylinder position.The valve signal is an input which controls the valveopening. The active heave compensator is modeled bythe AHC cylinder and the hydraulic system on the right-hand side of Fig. 5, while the crown block, Drillstringand the spring dynamics are on the left-hand side. Theplatform is modeled as a position actuator with a sinewave input, representing the platform lateral motion. Thepassive compensator, CMC, along with the friction forceand force equalising cylinder is placed between the crownblock and platform in parallel with the AHC. The on/offbypass valve determines wether the heave compensation ispassive or active.

3. FRICTION MODEL

The friction in the hydraulic cylinders is caused by thepresence of elastomeric seals between piston rod andcylinder bore interfaces required to prevent leaks. Thepressure loss in the hydraulic lines and in the pistonaccumulator of the hydro-pneumatic system is caused byfriction forces. In general, there is a wide range of differentresistance models used to compute the effective dampingof the passive system. They include nozzles, leakage paths,pipes, hoses and orifices. As an example, the pressure dropin a hydraulic line is calculated as follows:

∆p = λL

DlρV 2l

2(2)

where λ is a dimensionless friction factor that depends onthe flow regime (laminar or turbulent), L is the lengthof the hydraulic line, Dl and Vl are the line diameterand velocity respectively and ρ is the oil density. Whenconsidering the friction in the main cylinder it is oftenconsidered as a sum of a constant force such as Coulombfriction, a force proportional to the pressure level, aforce proportional to the relative motion velocity (viscousfriction) and Stribeck friction at low velocity. Steady-statemodels provide an expression of the friction force for aconstant relative velocity as shown below.

Ffric = Fc + (Fs − Fc)e−(

|v|vs

)ns

+ σ2v + kpp (3)

where Fc is Coulomb friction, Fs is the maximum staticfriction (stiction) force, vs is Stribeck velocity, v is a veloc-ity between the contact surfaces, ns = 2 is an appropriateexponent, kp represents the pressure dependant frictionterm and σ2 is the viscous friction coefficient. The frictionmodel that has been implemented in 20− Sim is presentedin (4). The different parameters are summarised in table2.

Ffric = Fc + (Fs| tanh(ξ ∗ v)| − Fc)e−(

|v|vs

)2(sign(v))

+σ2v + pkp

where ξ represents the steepness of the Coulomb frictioncurve and p is the pressure level in the main cylinder.

Copyright held by the International Federation ofAutomatic Control

318

Table 2. Coulomb and Stribeck Friction modeland hydraulics parameters

Fc 12 [kN] σ2 10 [kNs/m]

Fs 22.8 [kN] vs 100 [mm/s]

ξ 1000 [s/m] kp 42 [kN/m]

dr 170 [mm] dp 200 [mm]

Qr 460 [L/min] ∆p 35 [bar]

Fig. 6. Force on the Drill Bit where the passive compen-sation is used.

4. FRICTION EFFECT

In order to evaluate the effect of friction in the maincylinder it is necessary to distinguish between passive andactive heave compensation. In the passive case previouswork has indicated that friction plays a significant rolein the compensation performance. This is especially pro-nounced when a force equalising system as the one used onthe considered system is present. This is verified with themodel used in this work, as maybe seen in Fig. 6 where thevariation in WOB is shown with and without friction. Thedifference in WOB is substantial and with a nominal WOBof 3000g we have had to reduce the original wave amplitudeof 1.75 meter to 0.5 meter to avoid slamming, i.e., the drillbit losing contact with the formation. In the following,we maintain an amplitude of 0.5 meter and employ theAHC system to increase the safety against slamming. Inthis work a simplified standard motion control scheme isused to investigate combinations of control valve band-width and friction in the main cylinder. The task of thecontrol system is obviously to minimize the variations inWOB, however, this is often translated into maintainingthe crown block position constant with respect to theseabed. The wave data is collected by a Motion ReferenceUnit (MRU) which measures effective heave motion of therig at the drillcenter. The controller is presented in Fig. 7and it uses a velocity feed-forward loop with a fixed gainKv. It also has the position feedback loop to counteractdeviation in position. The quality index φ is used to findtwo gains Kp, Kv and given below.

φ = 0.5

√√√√∫ T

0z2cbdt∫ T

0z∗2cb dt

+

√√√√∫ T

0z2cbdt∫ T

0z∗2cb dt

(4)

where zcb is the position and zcb is the velocity of thecrown block, the asterisk ∗ indicates the reference passivecompensation. The two gains Kv and Kp are found byusing a built-in parameter sweep tool in 20− Sim. Firstly,Kp is set to zero and 20− Sim runs the simulationswhere Kv is adjusted for each iteration. The value ofKv that gives the best result as compared to the passivecompensated system is saved as the optimal gain forvelocity compensation. Secondly, the parameter sweep

Fig. 7. Typical motion control.

Fig. 8. Force on the Drill Bit where the active compen-sation is used. Both frictionless and the simulationswith friction are shown.

tool is used to find Kp with multiple iterations. In thispaper several different control valves with a wide varietyof bandwidths have been considered and the optimalcontroller gains has been tuned in for each valve. Forexample, Kp = 3.02 [1/m] and Kv = 0.55 [s/m] whenvalve natural frequency equals 0.75 [Hz] and friction inthe main cylinder is considered. However, the controllergains are Kp = 6.15 [1/m] and Kv = 0.55 [s/m] for thesame valve but without friction.

The simulation results of the 20− Sim model have revealedwhen the valve bandwidth reaches a certain level, hence nomore improvement is obtained in the variations in WOB.This is the case for the both systems where the frictionin the main cylinder has been omitted and for systemswhere the full friction model as described in (4) is included.As an example, the WOB variation obtained with a valvebandwidth of 0.75 [Hz] is shown in Fig. 8. Clearly, frictionincreases the WOB variation, however, not dramatically.In table 3 some results have been assembled, and thetrend is quite clear that whether friction is present or notthe improvement in WOB variation is more or less non-existent from valves with [0.75..1] [Hz] and up. This is,in fact, in quite good accordance with on the basic rulesof thumb regarding valve bandwidth which states that thevalve bandwidth should be approximately 3..4 times largerthan the bandwidth of the hydro-mechanical system tobe manipulated. In this case, we have an eigenfrequencyof approximately 0.23 [Hz] of the mass-spring system in20− Sim which seems to correspond well with the rule ofthumb and the observations in table 3, where ∗ indicatesthe simulations without friction in the main cylinder,∆FWOB represent the force variation in both negative andpositive directions from the baseline of 30 [KN].

There is no doubt, that the valves used in heave com-pensation equipment as the one presented here has muchhigher bandwidth and there may be other good reasonsfor this. However, this study seems to indicate that low-response valves, width bandwidth below 4..5 [Hz] must bedisqualified as AHC valves based on other load cases thanthose investigated here.

Copyright held by the International Federation ofAutomatic Control

319

Table 3. Valve bandwidth and WOB varia-tions.

V alvefreq., [Hz] 0.25 0.5 0.75 1.0 2.5

∆FWOB , [kN ] 15 6.2 2.1 2 1.9

∆F ∗WOB , [kN ] 15 7.1 1.1 1 1

5. DISCUSSIONS AND CONCLUSIONS

The Drillstring compensator model in 20− Sim consists ofactive and passive parts, where the active compensatoris a hydraulic system connected to the controller andthe passive hydro-pneumatic compensator is modeled asa spring with friction components. The controller is usedto compensate the heave motion of the platform, wherethe crown block is fixed with a respect to the seabed. TheAHC system is able to reduce the motion to 2 cm witha wave amplitude of 0.5 meter and period of 12 secondswhile keeping the contact force between the drill bit andthe formation within the limitations ±1.1 [kN]. The forcevariation becomes higher (2.5 [kN]) than a wave amplitudeis increased to 1.75 meters, however the use of the passivecompensator only will increase the force variation to 10[kN] in this case.

The model presented in this paper has been used toverify the usefulness of force equalisers during the passivecompensation and to identify the impact of the frictionin the main cylinder on the AHC. The performance ofheave compensation equipment in practice depends on thevariation in WOB. The worst scenario might be a short andstiff Drillstring with very small tolerance on WOB. Thefriction in the main cylinder has a significant impact on theheave compensation performance when the passive heavecompensation and force equalizers are used. However, itwas proved in this paper that the friction in the maincylinder seems to have much smaller impact on the heavecompensation performance when active compensation isimplemented.

In additional, the ratio between valve bandwidth andhydro-mechanical system bandwidth is more importantthan friction. Generally, the valve bandwidth should bethree times higher than the mechanical system bandwidth.The threshold values for the valve bandwidths are sur-prisingly low as compared to what is usually used in Oiland Gas industry but they are in good accordance withrule of thumb. However the results maybe different thanmore/other load cases are considered. In fact, the marketprice for the valves with lower bandwidths is smaller andone of the further directions of this research is an investi-gation of the performance changes than more specific loadcases are applied.

ACKNOWLEDGEMENTS

This work has been partially funded by NORCOWE undergrant 193821/S60 from the Research Council of Norway.NORCOWE is a consortium with partners from industryand science, hosted by Christian Michelsen Research.

REFERENCES

Haaø, J. and Vangen, S. (2011). Implementation of a hardreal-time system for hardware-in-the-loop testing. InMasters Thesis. University of Agder, Norway.

Hatleskog, J. and Dunnigan, M. (2007). Passivecompensator load variation for deep-water drilling.IEEE Journal of Oceanic Engineering, 32(3), 593–602,doi:10.1109/JOE.2007.895276.

Ottestad, M., Haland, K., and Hansen, M. (2010). A modelbased approach to design of passive and active heavecompensation of crown mounted drilling equipment. InProc. 29th IASTED Intl. Conf. Modeling, Identificationand Control. Innsbruck, Austria.

Ottestad, M. and Hansen, M. (2011). A method forfriction control in hydraulic cylinders. In Proc. 24th Intl.Cong. Condition Monitoring and Diagnostics Engineer-ing Management, COMADEM2011. Stavanger, Norway.

Skaare, B. and Egeland, O. (2006). Parallelforce/position crane control in marine operations.IEEE Journal of Oceanic Engineering, 31(3), 599–613,doi:10.1109/JOE.2006.880394.

Copyright held by the International Federation ofAutomatic Control

320