Study on a Mechanical Semi-Active Heave Compensation System of Drill String for Use on Floating Drilling Platform

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There are some disadvantages for existing heave compensation systems of drill string used for the Floating Drilling Platform (FDP), including high energy consumption, large and complex structure, and expensive manufacturing and maintenance costs. In view of the above, we present a streamlined mechanical semi-active heave compensation system (MSAHC) in this study. This system consists of active compensation part with the pinion and rack and passive compensation part. In order to evaluate system performance of the MSAHC, we establish its simulation model with AMEsim software. In the process of simulation, displacement of rotary hook and energy consumption is regarded as performance parameters of the system. And the change rule of two performance parameters are analyzed by changing these design parameters including gear radius of the pinion and rack, scale coefficient of PID, rotary hook load, heave height and heave period of the FDP, and accumulator volume. Then, based on the simulation results of the MSAHC system performance, we have selected out a best set of design parameters from them. Moreover, the feasibility of the design scheme of the MSAHC is effectively verified by comparison with the existing three heave compensation system. The result shows that the energy consumption of the MSAHC is lower than the active heave compensation system (AHC) and the semi-active heave compensation system (SAHC) when achieving a same compensation effect as well as the accumulator volume of MSAHC is half of the passive heave compensation system (PHC). Therefore, the new designed MSAHC not only ensure compensation effect but also lower energy consumption, and its structure is simplified by adopting the simple mechanical structure to decrease manufacturing cost, maintenance cost and floor space.

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Citation: Liu Q, Tang Y, Huang C, Xie C (2015) Study
on a Mechanical Semi-Active Heave Compensation
System of Drill String for Use on Floating Drilling
Platform. PLoS ONE 10(7): e0133026. doi:10.1371/
journal.pone.0133026

Editor: Xiaosong Hu, University of California
Berkeley, UNITED STATES

Received: February 9, 2015

Accepted: June 22, 2015

Published: July 17, 2015

Copyright: © 2015 Liu et al. This is an open access
[article distributed under the terms of the Creative](http://creativecommons.org/licenses/by/4.0/)
[Commons Attribution License, which permits](http://creativecommons.org/licenses/by/4.0/)
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.

Data Availability Statement: All relevant data are
within the paper and its Supporting Information files.

Funding: The work was supported by the Natural
Science Foundation of China (grant no. 51274171),
the Graduate Student Innovation Fund of School of
Mechatronic Engineering. Southwest Petroleum
University (CX2014BZ04), and the Graduate
Innovation Foundation of Southwest Petroleum
University, SGIFSWPU.

Competing Interests: The authors have declared
that no competing interests exist.

RESEARCH ARTICLE
# Study on a Mechanical Semi-Active Heave Compensation System of Drill String for Use on Floating Drilling Platform

Qingyou Liu 1,2,3, Yang Tang 1,2 *, Chongjun Huang 4, Chong Xie 1

1 School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, China, 2 State Key
Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu,
China, 3 Xi Hua University, Chengdu, China, 4 Drilling & Production Engineering Technology Research
Institute, Chuanqing Drilling Engineering Company Limited, CNPC, Guanghan, China

- tangyanggreat@126.com

## Abstract

There are some disadvantages for existing heave compensation systems of drill string

used for the Floating Drilling Platform (FDP), including high energy consumption, large and

complex structure, and expensive manufacturing and maintenance costs. In view of the

above, we present a streamlined mechanical semi-active heave compensation system

(MSAHC) in this study. This system consists of active compensation part with the pinion

and rack and passive compensation part. In order to evaluate system performance of the

MSAHC, we establish its simulation model with AMEsim software. In the process of simula
tion, displacement of rotary hook and energy consumption is regarded as performance

parameters of the system. And the change rule of two performance parameters are ana
lyzed by changing these design parameters including gear radius of the pinion and rack,

scale coefficient of PID, rotary hook load, heave height and heave period of the FDP, and

accumulator volume. Then, based on the simulation results of the MSAHC system perfor
mance, we have selected out a best set of design parameters from them. Moreover, the fea
sibility of the design scheme of the MSAHC is effectively verified by comparison with the

existing three heave compensation system. The result shows that the energy consumption

of the MSAHC is lower than the active heave compensation system (AHC) and the semi
active heave compensation system (SAHC) when achieving a same compensation effect

as well as the accumulator volume of MSAHC is half of the passive heave compensation

system (PHC). Therefore, the new designed MSAHC not only ensure compensation effect

but also lower energy consumption, and its structure is simplified by adopting the simple

mechanical structure to decrease manufacturing cost, maintenance cost and floor space.

Introduction

To meet the increasing market demand of industrial production and daily life, such as transportation sector and manufacturing industry, the development of oil and gas has turned from

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Mechanical Semi-Active Heave Compensation System

the shallow seas to the deepwater gradually [1–3]. In the exploration and development of deepwater oil and gas, the FDP will come up heave, roll, pitch and yaw influenced by the wind,
wave and ocean current [4]. The heave motion of the FDP can bring about the drill string in
the process of drilling to perform a reciprocating move up and down. That will lead to drilling
weight change on drill bit and even make the drill bit break away from bottom hole. And then
drilling efficiency is reduced, service life of the drill string and the drill bit is decreased, and
even drilling safety problems may be given rise [5] [6]. Therefore, it is necessary to add some
appropriate compensation measures to eliminate the reciprocating heave movement of drill
string in the offshore drilling process. By investigation found that the heave compensation system of drill string on the FDP is one common way to solve the problem above at present [7]

[8].

The existing heave compensation systems used on the FDP mainly have three different concepts, namely passive heave compensation; active heave compensation and semi-active heave
compensation [9]. Over the years, a lot of research works on three heave compensation systems
have been done, through a variety of measures including scheme design, theoretical analysis,
simulation and optimization, etc. Recent research on PHC systems include the work by Driscoll et al.[10] who found stiffness and damping characteristics of a passive cage-mounted heave
compensator, and by Jia et al. [11] [12] who proposed a PHC system with accumulators and
carried out a simulation and modeling research. Another work on AHC is that Hao and Liu
et al. [13] who presented a kind of AHC system design scheme which the control object was
variable pump and electro-hydraulic proportional directional valve, and Xu et al. [14] proposed
a principle and mathematical modeling of a new AHC system. Moreover, a new SHAC system
has been developed lately by Zhang et al. [15] and model and simulation of the system were
also done to ensure necessary design performance. In order to solve the conflict between compensation effect and power consumption of heave compensation system, a new type of drill
string heave compensation system is designed by H. Jiang et al. [16].

However, the previous research for the heave compensation systems had failed to consider
these problems associated with high energy consumption, large and complex structure, expensive manufacturing and maintenance cost and big floor space and so on. In order to achieve
energy conservation, cost reduction and environment protection, it is necessary to carry out an
improvement and optimization for the heave compensation system to make up for the above
deficiencies. Therefore, we designed a new heave compensation system of drill string——
MSAHC in this paper.

The remainder of this paper is organized as follows: Section Establishment of Design
Scheme, the active compensation part of the system was designed by combining the advantages
of mechanical structure, and passive compensation part was improved based on the existing
SAHC system. The Establishment of Simulation Model introduces the mathematical model of
main components and the simulation model of the MSAHC established based on the AMEsim
software. In Section Results and Discussion, the change rule of the system performances were
analyzed by setting different design parameters and a comparative analysis of the existing
heave compensation systems was performed. Finally, Section Conclusion summarizes our
work and future research avenues.

Methods

Establishment of Design Scheme

Design for Active Compensation Part of the MSAHC. The whole design scheme of the
MSAHC consists of active compensation part and passive compensation part. In order to simplify the system structure to reduce the manufacturing and maintenance cost, the active

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Mechanical Semi-Active Heave Compensation System

compensation part was considered using a simpler mechanical structure. The dominating function of the mechanism is to drive piston rod of the MSAHC to move up and down along a
straight line [17]. Through massive information acquisition of conventional mechanism, the
drive mechanisms used to achieve linear motion were listed as shown in Table 1[18].

According to the comparative analysis of characteristics of every mechanism, the pinion
and rack possesses higher performance including simple structure, convenient processing, precision transmission and wear-resisting. So we deemed that the pinion and rack type meet better
the design requirements of the system. And we chose the pinion and rack as the active transmission mechanism of the active compensation part.

Besides, the active compensation part adopted a motor to drive the pinion and rack, and
then the system implemented an active compensation by controlling the motor to ensure
movement of a piston rod of the system. Based on the pinion and rack, we proposed two design
schemes for the active compensation part as shown in Fig 1:

Design scheme 1. One Rack is fixed on Upper frame of traveling block and two Pinions
are connected to a support plate fixed on two piston rods. When the system starts running, the
two Pinions are driven by the motor. Then the two Pinions and the support plate move up
and down along direction of the Rack. Finally, a compensation of heave motion is performed
without moving the drilling string through the movement of the piston rod with the support
plate.

Design scheme 2. One Rack is fixed on Lower frame of traveling block. The bottom of
the rack is connected to one Rotary hook, and two Pinions are installed respectively on the
bottom of two Compensation cylinders [19]. The working principle of the Design scheme 2 is
just like Design scheme 1 except that the Rack is driving to move up and down by two Pinions.

The comparison analysis on the advantages and disadvantages of these two schemes were
analyzed as follows.

Design scheme 1. As the pinion and rack is installed on the upper frame of traveling
block, it comes true a multiplicative path in running process. Then the displacement of the
rack in vertical direction is only half of compensative displacement that the drill string needs.
And the whole system structure in the Design scheme 1 is very compact and simple, as shown
in the Fig 1A;

Design scheme 2. In the Fig 1B, the pinion and rack is installed the lower frame of traveling block, so the displacement of the pinion is equal to the compensation distance. For the
Design scheme 2, by contrast, its whole structure is bigger and operating space is also larger.
Moreover, the stability of the system is not ensured.

Table 1. Conventional mechanism structure of linear motion.

Institutions Work characteristics

CAM mechanism It is high speed movement, compact structure and high reliability. But it is easy
to wear and difficult to machine, and its strokemm is small.

Slider-crank mechanism It is less wear, big transmission power and low cost. But it is restricted by
space so that crank diameter can't be too big

Belt drive It is simple structure, stable transmission and has buffer load and safety
protection. But it is low efficiency, short service life and can't turn-back.

Chain drive It is high efficiency, strong applicability, big transmission power and low cost.
But it is easy to wear and has big noise.

Leadscrew and nut
mechanism

It is stable transmission, high precision, but machining precision of its long
leadscrew is difficult to guarantee and has limited movement distance.

Pinion and rack It is high performance, simple structure, convenient processing, and high
transmission precision and wear-resisting.

doi:10.1371/journal.pone.0133026.t001

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Mechanical Semi-Active Heave Compensation System

Fig 1. The design of active compensation system with the pinion and rack. (a) Design scheme 1 and (b)
Design scheme 2.

doi:10.1371/journal.pone.0133026.g001

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Mechanical Semi-Active Heave Compensation System

Fig 2. The diagram of passive compensation system.

doi:10.1371/journal.pone.0133026.g002

On comprehensive analysis, it was decided that the Design scheme 1 was a more suitable
design scheme of the active compensation part.

Design for Passive Compensation Part of the MSAHC. As shown in Fig 2, the passive
compensation part of the MASHC was designed based on the heave compensation strategy of
displacement type of the existing SAHC [20]. In the process of the passive compensation of the
MASHC, the pressure in Working cylinder can be adjusted by making the force of Piston rod
reach a balance with change of the rotary hook load. In the meantime, the Piston rod is staid
in one intermediate position of Compensation cylinder body. When the rotary hook loads
increases, the system will add the work pressure by injecting a high pressure gas to the Working cylinder. When the rotary hook load decreases, the work pressure is also lowered by releasing the gas in the Working cylinder with exhaust valve. In addition to the conventional
function above, the passive compensation system of the MASHC can also be used to adjust the
drilling weight on drill bit in drilling process and deal with the accident of drill string broken,
etc.

Establishment of Simulation Model

Mathematical Model of the System Components. In the process of establishing the simulation model of the MSAHC with AMESim software, it is necessary to identify movement relationships, logical structures and transmission ways among every component. Through analysis
of every component in the MSAHC, we have obtained these mathematical models of main

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Mechanical Semi-Active Heave Compensation System

components, including rotary hook load, hydraulic cylinder, pinion and rack, hydraulic pipe,
accumulator and PID control system. These mathematical models are directly applicable to the
establishment of simulation model of the MSAHC, which given by.

(1) Dynamics model of the rotary hook load [12]

M d2x2

dt 2 ¼ �k2x2 þ c2

dx2

dt þ F1 þ dk2 � Mg ð1Þ

(2) Mathematical model of the hydraulic cylinder

a. flow continuity equation of the compensation cylinder [14]

qL ¼ K

ðApvL þ lcpL þ qLÞdt ð2Þ

a. equilibrium equation of movement of the piston rod

dx dt h � dx dt 1

ð3Þ

dx dt 1 ~~Þ~~ þ f1 � F1 � F2

d 2 xh

ddt 2 x 2 h ¼ k1ðxh � x1Þ þ c1ðdx dt h

(3) Mathematical model of the pinion and rack [9]

T � F2r ¼ mrð d dt 2x2h

d dt 2x2h � d dt 2x21

ð4Þ
dt 2x21 ~~Þ~~

(4) Mathematical model of hydraulic line.

The hydraulic line between the compensation hydraulic cylinder and the accumulator was
simplified a vessel. The pressure in it is given by [21–22]:

px ¼ K

Vc1

ðqx þ 2qLÞdt ð5Þ

(5) Mathematical model of accumulator

The ideal gas state equation is defined as follow [21]:

psbVsb n

sb n ¼ p 0 V 0 n

0 n ¼ p x V x n ¼ const ð6Þ

Because the speed of releasing energy is very fast in the process of heave compensation, the
hydraulic oil can be considered as an ideal gas working under adiabatic condition. And taking
n = 1.4. Volume change ΔVsb of accumulator is given by

DVsb ¼ xbAp ð7Þ

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Mechanical Semi-Active Heave Compensation System

Assuming that the gas is in the adiabatic condition and the compressibility of the hydraulic
oil is not considered, the accumulator pressure change Δpsb is given by

8
<

psb0Vsb0
Dpsb ¼ ð
Vsb0 þ xbAsb

xb ¼ ðx2 � x1Þ=2

1:4 � psb0

ð8Þ

(6) Movable pulley

Due to the multiplicative path effect of the movable pulley group, rotary hook displacement
x2 is computed as shown in the following equation:

x2 ¼ x1 � 2xb ð9Þ

(7) Mathematical model of PID

In the MSAHC, PID is used as the controller by which the motion of the pinion and rack is
controlled, and controlling the movement law of the piston in the compensated cylinder is
actually realized. The block diagram of control systems of MSAHC was defined as shown in
Fig 3, and the control model of PID controller is established as follow [23].

uðtÞ ¼ KpeðtÞ þ Ki

Z t

eðtÞdt þ Kd
0

deðtÞ

ð10Þ
dt

deðtÞ

Establishment of Simulation Model. According to the analysis on every unit of the
MSAHC, we established its simulation model of the overall system with the AMESim software,
as shown in Fig 4 [24]. The simulation model of the MSAHC runs as follows: When the FDP
occur a heave motion, the displacement sensor on the compensation cylinder will detect an
absolute speed between compensation cylinder and piston rod. And it will be converted into
displacement value of the rotary hook which is a relative displacement between the drill string
and the FDP. Then the displacement value is input to PID controller after calculation. Furthermore, the PID controller outputs a signal to control motion of the pinion and rack. Finally, the
rack pushes the piston in the compensation cylinder to move up or down so that the heave
compensate of the drilling platform is achieved.

In order to verify usability, desirability and feasibility of the MSAHC, there should be a
comparison with other typical heave compensation system including PHC, AHC and SAHC.
Based on their working principle diagrams (see S1 Fig, S2 Fig, and S3 Fig), their simulation
model were also established by using the AMESim software, as shown in Figs 5, 6 and 7 [12]

[14] [15].

Fig 3. Block diagram of control systems of MSAHC.

doi:10.1371/journal.pone.0133026.g003

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Mechanical Semi-Active Heave Compensation System

Results and Discussion

Effects of design parameters on system

In this study, we evaluated the system performance of MSAHC based on the two targets: displacement of rotary hook (DRH) and energy consumption (EC). But they were affected by
these design parameters, including gear radius (GR), scale coefficient (SC) and accumulator
volume (AV), and environment parameters, including rotary hook load (RHL), heave height
(HH) and heave period (HP) of the drilling platform.

Effects of GR on system. By referring to Table 2, system parameters of the MSAHC were
set in the simulation model. Then we calculated respectively DRH and EC of the MASHC by
taking different gear radius of pinion and rack ranging from 90 mm to 150 mm. The system
change rule was obtained with increase of the gear radius and the simulation time in Fig 8. As
shown in the Fig 8, it illustrated that the DRH slightly decreased with an increase of gear radius,
which means that the compensation effect of the MASHC get more and more better. But there
is little change for the EC of the system with increase of the gear radius and the simulation
time.

Effects of SC on system. The system parameters of the MSAHC simulation model were
set as shown in Table 3. With the SC of PID controller ranging from 10 to 50, the change rules

Fig 4. Simulation model of the MSAHC system. Part A—The compensation cylinder models; Part B—The drill string model; Part C—Frequency control of
motor speed model; Part D–The energy consumption calculation model; Part E—The pinion and rack model.

doi:10.1371/journal.pone.0133026.g004

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Mechanical Semi-Active Heave Compensation System

Fig 5. Simulation model of the PHC system. Part A—The compensation cylinder model; Part B—The rotary hook displacement calculation model; Part C
—The signal control model; Part D–The drill string model;

doi:10.1371/journal.pone.0133026.g005

of DRH in 60 seconds were obtained in Fig 9. It can be seen from the Fig 9 that amplitude of
the DRH decreases gradually along with increasing value of the SC, namely the compensation
effect of the system became better. Moreover, the system lag is abated effectively because the
increase of the SC leads to an increase of output speed of motor. Furthermore, the pinion and
rack will be driven to run quickly so that the piston comes back the equilibrium position
rapidly.

Fig 10 shows a cure graph describing the variation trend of the EC with the change of the
SC. It is clear from the Fig 10 that the EC is quickly lower when the SC value changes from 10
to 20. But the changes will become obviously slow after reaching 20.

Effects of RHL on system. With increasing the RHL, a simulation for the MSAHC was
carried out by setting system parameters in Table 4. It was found that there wasn’t any change
on the compensation effect, but the EC of the system was affected. In Fig 11, the change rules
of the EC on different rotary hook load were obtained. From the change rule of the EC in the
Fig 11A, we can conclude that a higher rotary hook load will bring about a higher EC. And the
Fig 11B shows that the increase rule between the RHL and the EC is an approximate linear proportional relationship.

Effects of drilling platform heave on system. Through a calculation based on system
parameters in Table 5, we obtained the change rules of the DRH with the change of the HH
and the HP, as shown in Fig 12. It can be concluded from the Fig 12 that the DRH increases
gradually with an increase of the HH so that the compensation effect of the system goes down.
But with an increase of the HP of drilling platform, the DRH decreases gradually to make the
compensation effect better.

Moreover, the change rules of the EC were also obtained on different drilling platform
heave in Fig 13. It is observed that, for the same HP, the EC of the system increases with an

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Mechanical Semi-Active Heave Compensation System

Fig 6. Simulation model of AHC system. Part A—The compensation cylinder model; Part B—The rotary hook displacement calculation model; Part C—
The drill string model; Part D—The Systems energy supply model; Part E—The energy consumption calculation model.

doi:10.1371/journal.pone.0133026.g006

increase of the HH of the drilling platform. And for the same HH, the compensation effect of
the system goes down and the EC decreases with a decrease of the HP in a single period.

Effect of AV on system. By setting the system simulation parameters in Table 6, we
obtained Fig 14 which shows change rule of the EC of the system on different AV in 60 seconds. In the Fig 14, the EC continuously decreases with an increase of the AV in the case of
other parameters no change. But the change amplitude of the EC is a trend from fast to slow.

Comparative Analysis of the Four Systems

Based on the simulation models of four systems (PHC, AHC, SAHC and MSAHC) in the Figs
4, 5, 6 and 7, the simulation parameter values were set based on Table 7. And then a lot of simulation analyses on their compensation effect and energy consumption were performed respectively. Finally, their system performances were contrasted in each other to verify usability,
desirability and feasibility of the MSAHC.

Through the simulation calculations, the compensation effects of the four heave compensation systems were shown in Fig 15. From the diagram, we can see that the compensation effect
of MSAHC, SAHC and AHC system is little difference, and the displacement fluctuation of the

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Mechanical Semi-Active Heave Compensation System

Fig 7. Simulation model of SAHC system. Part A—The compensation cylinder models; Part B—The drill string model; Part C–The compensation system
model; Part D–The Energy consumption calculation model.

doi:10.1371/journal.pone.0133026.g007

rotary hook using these three systems is within ±75 mm. But the PHC system is poor results
about 1.3m deviation.

Because there is no energy consumption about the PHC system, we made an analysis on the
EC of the AHC, the SAHC and the MSAHC, as shown in Fig 16. Compared with the SAHC
and the MSAHC, the EC of the AHC is quite high, which reaches 25000 kJ in the 60 second in
the Fig 16. But the EC of the SAHC is about 3572 kJ that is 14.2% of the AHC system. And the
MSAHC is 2864 kJ which is lower about 700KJ than the SAHC system. In addition, the accumulator volume of the MSAHC is only equivalent to 50% of the PHC.

In order to ensure drilling operations safety, improve drilling efficiency, and decrease drilling cost, the heave compensation system of drill string is widely adopted on the FDP. For the
existing heave compensation system of drill string, there are some problems associated with
high energy consumption, large and complex structure, expensive manufacturing and

Table 2. System parameter settings on different GR.

tParameter SC AV RHL HH HP

Value 50 10 m 3 230t 4.5 m 12 s

doi:10.1371/journal.pone.0133026.t002

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Mechanical Semi-Active Heave Compensation System

Fig 8. The system performance on different GR. (a) Change rule of the DRH under different GR in 60 seconds, (b) Change rule of total DRH in 60
seconds, (c) Change rule of the EC in 60 seconds,(d) Change rule of total EC in 60 seconds.

doi:10.1371/journal.pone.0133026.g008

maintenance cost and big floor space. But the previous research on heave compensation system
failed to take them into account. So the improvement and optimization for the heave compensation system should be carried out to make up for the above deficiencies. According to structure design and simulation modeling for the MSAHC, we have accomplished the analysis on its
design parameters and comparison with three typical heave compensation systems.

From the analysis results of the MSAHC related parameters in the previous section, including gear radius of the pinion and rack, scale coefficient of PID controller, rotary hook load,
heave height and heave period of the FDP and accumulator volume, we can draw the following
summary:

a. Changing the GR of the pinion and rack is only a small effect on the compensation effect

and energy consumption of the MSAHC. Therefore, when choosing the gear radius in the
design process, we can just consider whether it meet the structural strength and spatial distribution of the pinion and rack.

b. To magnify the SC value within allowable scope of the PID controller can significantly

improve the compensation effect of the MSAHC and reduce the EC.

Table 3. System parameter settings on different SC

Parameter GR AV RHL HH HP

Value 120 mm 10 m 3 230t 4.5 m 12 s

doi:10.1371/journal.pone.0133026.t003

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Mechanical Semi-Active Heave Compensation System

Fig 9. Change rule of the DRH on different SC in 60 seconds.

doi:10.1371/journal.pone.0133026.g009

Fig 10. Change rule of total EC in 60 seconds.

doi:10.1371/journal.pone.0133026.g010

c. During the drilling process, the EC of the MSAHC has a great relationship with the real
time RHL, and it is an similar proportional growth between them.

d. When the drilling platform is a same heave height, the compensation effect of the MSAHC

becomes better and the EC is lower with an increase of its heave period. When the drilling
platform is same heave period and with enlargement of the heave height, the compensation
effect decreases and the EC increases.

e. With increasing the accumulator volume, the compensation effect has few change, but the

EC quickly lowers and then tends to vary gently.

Based on the comparison with three typical heave compensation systems, the following conclusions were obtained. The compensation effects of the AHC, the SAHC and the MSAHC are
much the same in the same working conditions. But the EC of the MSAHC is lower than both
the AHC and the SAHC. The MSAHC adopts a simpler mechanical structure to substitute the

Table 4. System parameter settings on different RHL.

Parameter GR SC AV HH HP

Value 120 mm 50 10 m 3 4.5 m 12 s

doi:10.1371/journal.pone.0133026.t004

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Mechanical Semi-Active Heave Compensation System

Fig 11. Change rule of the EC on different RHL. (a) Change rule of the EC in 60 seconds, (b) Change rule of total EC in 60 seconds.

doi:10.1371/journal.pone.0133026.g011

complex hydraulic structure. So its overall structure become more compact as well as its
manufacturing and maintenance cost of the MSAHC are reduced. In addition, the accumulator
volume of the MSAHC is only equivalent to 50% of the PHC. So its floor space will can be
decreased by almost half.

Table 5. System parameter settings on different HH and HP.

Parameter GR SC AV RHL

Value 120 mm 50 10 m 3 230t

doi:10.1371/journal.pone.0133026.t005

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Fig 12. Change rule of the DRH on different HH and HP.

doi:10.1371/journal.pone.0133026.g012

Fig 13. Change rule the EC on different HH and HP.

doi:10.1371/journal.pone.0133026.g013

Conclusion

In this paper, we have presented a MSAHC of drill string used for the FDP. With the purpose
of achieving energy conservation, cost reduction and environment protection, we put forward a new design scheme on its active compensation part. It adopted a simple mechanical
structure——the pinion and rack to substituted the existing complex hydraulic structure.
And the passive compensation part was improved based on the existing SAHC system. Then
the mathematical models of main components and the system simulation model of the
MSAHC were established to go to analyze its energy consumption and compensation effect.
The change rules of system performances were gained with the change of GR, SC, RHL, HH,
HP and AV. Moreover, the contrast results of the four heave compensation systems indicated
that the energy consumption of the MSAHC is lower than the AHC and SAHC, and the accumulator volume is half of the PHC. So that it has been basically achieved to lower energy consumption, optimize whole structure, reduce manufacturing and maintenance cost, and

Table 6. System parameter settings on different AV.

Parameter GR SC RHL HH HP

Value 120 mm 50 230t 4.5 m 12 s

doi:10.1371/journal.pone.0133026.t006

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Mechanical Semi-Active Heave Compensation System

Fig 14. Change of the EC rule on different AV.

doi:10.1371/journal.pone.0133026.g014

Table 7. Simulation parameters values.

System Heave period Heave height Accumulator volume Rotary hook load Scale coefficient Pump output Gear radius

PHC 12 s 4.5 m 20 m 3 230 t - -

AHC 12 s 4.5 m 230 t 8 12 L / rev
SAHC 12 s 4.5 m 10 m 3 230 t 2 3 L / rev
MSAHC 12 s 4.5 m 10 m 3 230 t 50 - 120 mm

doi:10.1371/journal.pone.0133026.t007

Fig 15. Contrast of heave compensation systems on compensation effect.

doi:10.1371/journal.pone.0133026.g015

decrease floor space. Thus, the feasibility and practicality of the design scheme of the
MSAHC is effectively verified. This system is not only that its overall structure is simpler
than the existing hydraulic structure to cost savings, but also that its energy consumption is
reduced with the precondition of high compensation effect. While these results and data of
this study can guide a further detailed design and optimization for the heave compensation
system and serve as a reference for subsequent related system research. It should be noted

PLOS ONE | DOI:10 1371/journal pone 0133026 July 17 2015 16 / 19

Mechanical Semi-Active Heave Compensation System

Fig 16. Contrast of heave compensation systems on the EC.

doi:10.1371/journal.pone.0133026.g016

that we do not carry out a prototype machining and some experimental studies of the
MSAHC, but these will be our next research work.

Supporting Information

[S1 Fig. Working principle diagram of PHC.](http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0133026.s001)
(TIF)

[S2 Fig. Working principle diagram of AHC.](http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0133026.s002)
(TIF)

[S3 Fig. Working principle diagram of SAHC.](http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0133026.s003)
(TIF)

Nomenclature

Ap —Compensation cylinder’s head port area, m 2

c1 —Piston resistance coefficient
c2 —Drag coefficient of drill string
f1 —Liquid damping force, N
F1 —Rotary hook suffered pull, N
F2 —Rack driving force onto piston, N
k1 —Liquid gas stiffness coefficient
k2 —Rigid coefficient of drill string, N/m
K —Oil bulk modulus, MPa
Kp —Scale coefficient
Ki —Integration time constant
Kd —Derivative time constant
m —Quality of the gear, kg
M —Quality of rotary hook and drill string, kg

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Mechanical Semi-Active Heave Compensation System

Mh —Quality of piston and pulley block, kg
qx —Rate of flow of flowing into the accumulator, L/s
qL —Rate of flow of flowing into rodless cavity, L/s
pL —Liquid pressure of rodless cavity, MPa
psb —Accumulator charging pressure, MPa
p0 —Initial pressure accumulator, MPa
psb 0 —Accumulator stress at the equilibrium position, MPa
r —Gear radius, m
T —Motor electromagnetic torque, N·m
Vc1 —Volume of the line vessel, L
Vsb —Accumulator aeration volume, m 3

V0 —Initial volume of accumulator, m 3

Vsb 0 —Volume of accumulator at equilibrium position, m 3

x1 —Drilling platform heave displacement, m
x2 —Rotary hook displacement, m
xh —Piston displacement, m
xb —Relative displacement between hydraulic cylinder and piston, m
vL —Relative speed of piston motion, m/s
λc —Leakage coefficient.

Acknowledgments

The work was supported by the Natural Science Foundation of China (grant no. 51274171),
the Graduate Student Innovation Fund of School of Mechatronic Engineering. Southwest
Petroleum University (CX2014BZ04).

Author Contributions

Conceived and designed the experiments: QYL YT. Performed the experiments: CJH YT. Analyzed the data: YT CJH. Contributed reagents/materials/analysis tools: CX QYL YT CJH.
Wrote the paper: YT CJH QYL.

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