albers tudelft introduction, heave compensation

Introduction to Power drives in Offshore applications Passive and Active heave Compensation

Heave Compensation System, Passive All kind of activities offshore are being done from moving vessels or platforms. These activities could be drilling, handling loads in cranes or pipe laying. The movements of the vessel or platform because of the see waves cause large load variations in the drill pipe, winch cable or in the pipes that are being installed. To compensate for these movements the so called Heave Compensator Systems are used. In drilling rigs these kinds of compensators are often used in the so called Travelling Block, see figure at the right. Drill String Compensators A hook mounted compensator on a drill rig / vessel is basically hanging in the draw works hook. The design depends on lots of interface details related to the derrick construction and also the way the drill string is driven either by a rotary table or a top drive. In modern rig / vessel design the derrick top mounted or crown block compensator is more popular, still for specific rig / vessels the hook mounted compensator is sed.

u

Drill String Compensator of Rexroth Hydraudyne

urved Sheave Compensators

g here

urns out to be unacceptable for obtaining the portant sensitive geo-technical data.

C The curved sheave compensator is a drill string compensators, which means that it compensates the relative movements of the drillship to the sea bottom. The curved sheave compensator is a passive hydro pneumatic spring system and most probably the most accurate passive compensator ever built. The curved sheave unit is a travelling block compensator. The computer designed curve compensates the adiabatic thermodynamics of the pneumatic sprinand enables rather small air pressure vessels. This is ideal for geo-technical surveys wnoise from the inaccurate compensator tim

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Example of Curved Compensator ( Rexroth Hydraudyne )

iser Tensioner Systems

ire Line Tensioners

e

of

rs, pressure vessels, hydraulic and pneumatic valving and wire line sheavers to run e wires.

irect riser tensioner

g

nd pulling

ving

ting under extreme

R W Wire line tensioners are, as theword says, used to keep wire lines tensioned. In the Offshoreindustries many wire lines are used to hold or hoist a specific load. Relative movements can cause a wire line to become slackand therefore causing dangerous shock loads. Wire line tensionersare used in drilling packages as well as in transport applications such as offshore cranes. The wirline tensioners as described arehydraulic / pneumatic springs built-up from a combinationhydraulic cylinders, piston accumulato

th D As the wire line riser tensioners are tensioning the marine riser via wire lines, the direct riser tensioner is directly mechanical connected to the riser tension rinby a shackle or similar connections. The direct riser cylinders are long stroke (15 m or more) atheir design is very slim. Options such as accumulators specific installation and safety valare project specified. The piston rod coating is critical, as the cylinder is acenvironmental conditions. Production riser tensioners are used for deep water

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production platforms such as Tension Leg Platforms (TLP’s), deepwater SEP’s and FPSO’s. On each platform a number of smaller production risers are to be tensioned to cope with the relatively small rig movements. Production riser tensioners are normally grouped in a cassframe carrying 4 tensioner or more cylinders with their related equipment. The system is redundant, woperation. Both tension, system stiffness, stroke, etc. are project specific as the rig specific movementduring normal workingp

ette

hich means that it can stay operational having one tensioner in a cassette out of

s conditions, storm, hundred years storm, hurricane, etc. will set the

roject specific limits.

rinciple of Operation

he most common used Heave Compensator System is the Passive version, see figure below.

mechanical

pring and absorbs high load peaks due to the vessel or platform movements.

ir is used in ombination with a non-explosive hydraulic fluid like Erifon or Houghtosafe.

lume. In simplified form the pressure in the gas system is given by the diabatic gas law:

{A} with V = gas volume en P = gas pressure and κ (kappa) = gas constant

P T

Gas bottles

Accumulator

Principle diagram of a Passive Heave Compensator System

A V1

ΔF

Δy

P1, ΔP ΔV

In this example the system is installed onto the wire of a winch. It consists of a hydrauliccylinder that is provided with a cable sheave on top. The weight of the load is now also carried by the hydraulic cylinder. The bottom end of the cylinder is connected via a mediumseparator= accumulator to a number of gas bottles. In fact this system acts as as The gas bottles are pre-charged with high pressure gas. The need for the back-up gas bottles depends on the stiffness of the system that is required. In most cases Nitrogen is used as gas. This is done of because the possibility of an ignition when mineral oil comes in contact with oxygen at temperatures above the ignition point. In some cases high pressure Ac The stiffness constant C of a Passive Heave Compensation System can be adjusted by changing the gas voa

ConstVP =⋅ κ

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Note: all units are in SI-units , i.e. m3, N/m2

º C the value of κ is 1,6 to 1,75. For pressures from 200-250 ar the value of κ is 1,5 to 1,6

y differentiating the equation of the gas law to the volume V we obtain:

The value of κ changes with temperature and pressure. For operating pressures from 250 to 300 bar and temperatures of 30b B

κ

κ⎟⎠⎞

⎜⎝⎛ −

⋅=

11

VConstdVdP

{B}

cylinder will move down with a displacement Δy. The stiffness C of the spring is efined by:

The gas spring can only be compressed if the external load ΔF increases. Because of this the piston of thed

yFCΔΔ

= {C} [N/m]

and also: and AVy Δ

=ΔPAF Δ⋅=Δ we get:

κκκ

κκ

κκκ⎟⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛ −

⋅=

⋅⋅=

⋅==

ΔΔ⋅=

ΔΔ⋅

=1

1

2

11

2

11

222 VPAVVPAVConstAdVdPA

VPA

AV

PAC {D} [N/m]

For higher loads (=pressure) and sing the same gasvolume the stiffness becomes higher.

ractical stiffness calculations:

uppose we have a passive system as shown below with the following parameters:

f l strok ] aximum system pressure : 250 [bar]

ified. In our case the minimum ylinder stroke becomes 2.5 [m] plus 2 x 0.25 [m] = 3 [m]

ith the specified stiffness of 120 [kN/m] the maximum cylinder force becomes

Note: This formula is only valid for small displacements of the medium separator as the adiabatic formula itself is not linear. What we may conclude from the formula is that the stiffness has a linear relation with the load to the system. u P S Maximum wire tension : 500 [kN] heave, top-top : 5 [m] Required stiffness cylinder, ul e : 120 [kN/mM If we neglect the friction of the sheaves the maximum cylinder force at 50 Ton wire tension becomes 1000 [kN]. The mechanical stroke of the cylinder shall be >50% of the maximum heave. In most cases an additional 25 cm is designed for the mechanical stroke. This spare stroke is often used to install mechanical damping inside the cylinder that can withstand the impact if the wire shows a larger heave movement than specc W

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1000 [kN] + 120 [kN/m] * 1.25 [m] = 1150 [kN]

e maximum specified system pressure the bore size of the cylinder can be alculated with:

To stay within thc

5

32

10*25010*1150

4≥cylDπ or Dcyl >= 0.242 [m]

ct Dcyl =260 [mm] he maximum operating pressure at the maximum load then becomes:

Cylinder tubes come in different standard diameters. In this case we seleT

52

3

101*

260.0*4

10*10001π

=P = 188 [bar]

aximum stroke of the cylinder ompletely retracted) becomes:

Due to the stiffness of the system the pressure at the m(c

52

3

101*

260.0*4

10*11502π

=P = 217 [bar]

The pressure ratio becomes :

154.1188217

12

==PP {E}

lume ΔV of the medium separator when the cylinder retracts due to the perating heave is:

The displacement voo

2

4**5.0 DheaveV π

=Δ = 66.3 [dm3]

he smaller gasvolume V2 becomes : V2 = V1 – ΔV {F}

T

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The movement of the vessel is in short period of 8-10 seconds. Therefore the compression of the gas is according to an adiabatic process. The pressure in the gas volume can be described with formula {A}, ConstVP =⋅ κ

This formula can be rewritten as:

( ) κ

κ

κ

κ

21

11

12

VV

VVV

PP

=Δ−

= , or with formula {E} : and with κ = 1.6

==⎟⎠⎞

⎜⎝⎛= 625.0

1

154.112

21 κ

PP

VV 1.094 {G}

Combining {F} and {G} results in: V1 = 708 [dm3]. This volume V1 includes the volume of the medium separator at half stroke Plus the volume of the gas piping plus the volume of the additional gas bottles.

Gas bottles

Medium Separator

ΔF

P1, P2 ΔV

V1, V2 Δy A

Principle diagram of a Passive Heave Compensator System

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Example of installation:

Shown is a semi-submersible platform equipped with a new design of a drilling tower. The travelling block of the hoist gear carries the load of the drill pipe. The vessel moves up and down because of the sea waves. As the drill pipe is connected to the sea bottom the force on the drill bit changes because of these vessel movements. Inside of the drilling tower two passive heave compensator systems are installedin parallel toe ach other. This is done because of redundancy. If one compensator system fails the drilling process may still continue depending o

Travelling Block

Drill Pipe

n the ea state.

tem has been designed for a wire pull of 100 Tons and a maximum vessel heave of 4 meter.

s

This sys

Travelling Block

WINCH A WINCH B

Safety Manifold

Hydraulic Cylinder

or

High Pressure Supply Bottle

Gas Bottles

Accumulat

Gas valve

The compensator cylinders are now being used in a pulling mode. At a wire load of 100 Tonthe cylinder pulling force becomes 200 Tons. If both cylinders are in operat

s ion the cylinder

troke becomes 4 meter. The maximum stroke for the cylinders is 6 meter.

the system the bottles can be connected to the accumulator with 2” Gas valves ( ball valves ).

s The total gas volume reaches 4 bottles of 1200 dm3. Depending on the required stiffness of

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The central high pressure supply bottle is pre-charged with 200 bar gas. From this bottle the other gas bottles can be charged to the required gas load. The maximum oil flow in this system reaches a value of 1500 lpm.

View at the rod end of the cylinder with the Safety Manifold

The Safety manifold provides a very important function. In case of a wire break the cylinder will loose its external load and the gas pressure will move the cylinder piston down like a rocket. The amount of energy that is released is tremendous. Special sensors are used to sense such a wire break. If it occurs a large cartridge valve in the Safety manifold closes immediately and blocks the accumulator from the hydraulic cylinder. A Passive Compensator System is widely being used because of its simplicity and reliability. The fact that it is a Passive system without the need for a running Hydraulic Power Unit is very important. Nevertheless a passive system has also some disadvantages:

• In a hoisting application the load is lowered to the sea bottom. By lowering the load the length and thus the weight of the wire also increases. The wire weight has to be added to the weight of mass on the wire hook. The weight of a wire for 200 Ton reaches 40 kg.mtr. At a water depth of 2000 mtrs the total load increases with a mass of 80 Tons. In fact the capacity of the hoisting system is reduced to a net weight of 120 Tons.

• If the load is lowered the load will increase due to the wire weight. This means that the gas pressure has to be increased while the load is lowered. This can be done a central high pressure gas bottle, see diagram.

• The wire has e certain elasticity. Together with the mass and depending on the drag in the water this will cause that the mass/wire behaves like a mass spring system. The cable forces may reach then very high values. Although a Passive heave Compensation System reduces the “activation” of this mass-spring system, the remaining force variation may still cause unwanted load movements.

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page9/17

Typical Design Values: Pressure: Maximum 3000 psi or 210 bar , reasons for this limited value are: the oil business is very conservative and the 3000 psi limit has always been the maximum state of the art, compressors for high pressure air or nitrogen are more or less standard for pressures up to 200 bar. Accumulator: Most commonly used are piston type accumulators. This because of the need for high ( = low stiffness ) volumes. For applications with low loads and or reduced heave motions bladder type accumulators may be possible. Volumes for the accumulator vary from 200 to 1200 dm3. It is not possible to install accumulators in parallel to each other as the position of the individual pistons can not be controlled. The position of the accumulator piston must be in “accordance” with the position of the main cylinder as the accumulator piston in other situations may slam its end covers. In some cases the accumulator is provided with piston position sensors ( an ultrasonic sensor in the liquid phase and a wire type sensor in the gas phase ). The ultrasonic sensor is reliable but less accurate whereas the wire type sensor is very accurate but sensitive to failure. Gas bottles: The required size of the gas bottles depends on the required stiffness for the system. The volume can be obtained by a few high volume bottles or by many standard 50 dm3 bottles with intermediate piping. From experience it may be concluded that the large sized bottle have long delivery times ( 5-6 months ) and that the overall investment costs for large or small bottles is nearly the same. Design Rules: Mostly used is LROS, DNV or ABS ( ABS if the vessel or platform is under American flag). Experience showed also that ABS rules require larger tube thickness. In a particular case the end user could be convinced that the application of Deutsche AD-Merkblatter rules instead of ABS could save 30% of weight and therefore also costs. Deutsche AD-Merkblatter rules where then allowed.


Heave Compensation System, Active Disadvantage of a Passive heave Compensation System is that the wire tension always varies because of the pressure variations in the gas system and also because of friction in the cable sheaves. These tension variations reach 15-20% which is too much to lower the loads to the seabed. Another problem might be that with a passive system the natural frequency of the mass/wire system becomes equal to the frequency of the vessels movements. In the system as shown below an additional hydraulic system has been added. The system is called an Active Heave Compensation System.

Description of the system The Passive part of the system has been described before. Two additional smaller cylinders have been added to the main cylinder. These smaller cylinders can be controlled into position by means of a variable closed loop hydraulic pump. The control system for the Active system receives information from a so called Motion reference Unit (MRU). This sensor provides information on the vertical acceleration, velocity and heave of the vessel or platform. The active cylinders are now being controlled in an exact opposite direction and position of the vessels actual vertical heave (position). If this position control system acts alright the position of the wire-hook will be neutral. Instead of the closed loop pump also a proportional valve or servovalve can be used. The Active Valve set is necessary to enable or disable the use of the Active part of the system. For instance, if there is a power failure the Active Valve set must immediately cross connect the both cylinder ports of the active cylinders. The Active Valve set is also used to gradually take the active part of the system into operation.

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Dynamic behaviour of an active system In the figure below some velocity responses are presented of a hydraulic system that is controlled by a proportional directional control valve. In these examples the behavior of the system is very much depending on the stiffness of the oil hydraulic system. A hydraulic cylinder that is connected with a mass shows the behavior of a second order mass-spring system. in the examples 3 different input signal are being applied.

page11/17


Quasi static behavior In an active heave compensating system the active cylinders are being controlled in a position feedback system. If we observe the signals in the block diagram below we have the hydraulic valve that provides a flow to the cylinder with the control signal as input signal. The cylinder moves out with a velocity. After some time the cylinder obtains a new position. The position of the cylinder is measured with a position transducer. Its signal is used as feedback signal and compared with the set point signal from the MRU.

Calculating the different signal within the block diagram :

dtdyA

tyAQ

yAVtQ

..

..

=ΔΔ

=

Δ=Δ=Δ

The new position of the cylinder is obtained by integration of the velocity of the cylinder. In a block diagram this can be described with

+

-

r Cylinder, are A

Δy

valveamplifier

K1 K2

Q

pos transducer

K4

y

1 A

⌠ dt Q y y

. Piston area Integration

1 A

Q y

Hydraulic cylinder

⌠ dt

page12/17


De differential operator dtdy may also be described with the Laplace-operator s

The integral operator ∫ dt may then be described with s1

The former simplified block diagram can be rewritten in an even more simplified form with K3 = 1/A

If we replace the hydraulic cylinder by this block diagram we get:

This block diagram may be rewritten as a one-to-one feedback system.

Proportional valve , K2

Amplifier

K1

Position Transducer, K4

+

-

measured position Volt

valve signal in Volt Volume fow

m3/s

r

e

K3

S

y, position [m]

+ Proportional valve , K2

Amplifier

K1 K4

-

r*

e

K3

S 1 K4

r

K3 s

Q y

Hydraulic cylinder

page13/17


The transformation y/r* may be written as:

With ε××××= 4321 KS

KKKy and yr −= *ε

We get: yKS

KKKrKS

KKKy ××××−××××= 4321*4321

Or: 1

1

1143211

4321

* 0

0

+=

+=

+=

+=

⎟⎠⎞

⎜⎝⎛ ×××+

×××=

SKSK

SK

SK

H

H

KS

KKK

KS

KKK

ry

V

V

V

V

τ

With this formula we have proven something very important: A position feedback cylinder shows the behavior of a first order system. All individual gain parameters may be combined into one single “gain” Kv.

Step response: In the previous section we have showed that a position feedback controlled cylinder may be written as a first order system

With the consent that the Laplace operator s may be rewritten as dy/dt, we get the simple differential equation:

( )

rydtdyor

rySor

Kwith

SKSK

SK

SK

ry

VV

V

V

V

=+

=+

=+

=+

=+

=

.:

.1:

1:,1

1

1

τ

τ

ττ

KV

S r

y

e + -

y KV

τS+1r y

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The step response of a first order system can simply be found by first having a look at the velocity of the system at the condition at time t=0 and y=0

τ

τ

τ

rdtdyitystartvelocof

rdtdy

ywithrydtdy

=

=

==+

:

.

0:,.

We may also have a look at the static condition where the velocity dy/dt=0

rydtdywithry

dtdy

=

==+ 0:,.τ

With these simple results we may draw the graphic response of a hydraulic cylinder with a step-input signal as follows. The output signal (y) obtains a level of 63% after a time equal to t= τ.

r

The description of the hydraulic cylinder has to be extended with a part that describes the behavior of a second order mass-spring system. The real dynamic behavior of a hydraulic linear drive may again easy be deducted with block diagrams. The external forces that have influence on the position of the cylinder are mainly to be described with (= m x S2) acceleration forces and with (= w x S) friction forces. In the model we also have defined the parameter Co = oil stiffness. The oil stiffness Co defines the displacement of the cylinder piston under influence of all external and internal forces.

time

y

1τ 2τ 3τ

time y 1 1τ 0,63 2τ 0,86 3τ 0,95

page15/17


This block diagram can be transformed with simple rules into:

12

1

1

1

1

1*

020

2

0

2

00

2

++=

++=

++

=

ωβ

ωsss

Cws

Cm

Cwsmsy

y

with mC0

0 =ω [rad/s] (natural frequency) en 02 mC

w=β (damping coefficient)

The damping coefficient ß is a parameter for all friction in the system. For complete friction less cylinders with hydrostatic bearings β = 0,10 . For most practical systems ß has a value of 0,15 – 0,35. With the parameters ω and β we may look again at the previous block diagram:

K1 +

-

r

e

K3

s

y

w0 2b

s s2

w0 2 + +

1

1

K1 +

-

r

e

K3

s +

-

1 Co

ms2 + ws

y* y

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page17/17

The dynamic behavior of a hydraulic driven mass can be written as a first order system and a second order system in series. Te stability of a feedback system can be observed with the help of a so called Polar diagram of the open loop structure, see figure below.

For low frequencies the polar diagram of an open loop system shows a phase lag of -90°. For higher frequencies the phase lag increases with the frequency. For a frequency equal to ωo the phase lag is equal to -180° and the polar figure crosses the negative real axes. For sufficient stability of a closed loop system this crossing should be on the right hand side of the minus -1 point and for even more stability have a certain minimum distance of the minus -1 point. A good result is obtained if the polar curve stays out of the dashed M=1.3 circle. This stability criterium may also be written in a requirement for the total gain Kv of the system:

5,02

≤o

vKβω

or ovK βω≤

albers tudelft introduction, heave compensation

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