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Dynamic response of platform-riser coupling system with hydro-pneumatic tensioner
Accepted Manuscript Dynamic Response of Platform-Riser Coupling System with Hydro-pneumatic Tensioner
Teng Wang, Yujie Liu PII:
S0029-8018(18)30712-1
DOI:
10.1016/j.oceaneng.2018.08.004
Reference:
OE 5409
To appear in:
Ocean Engineering
Received Date:
04 May 2018
Accepted Date:
06 August 2018
Please cite this article as: Teng Wang, Yujie Liu, Dynamic Response of Platform-Riser Coupling System with Hydro-pneumatic Tensioner, Ocean Engineering (2018), doi: 10.1016/j.oceaneng. 2018.08.004
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ACCEPTED MANUSCRIPT
1
Dynamic Response of Platform-Riser Coupling System with Hydro-
2
pneumatic Tensioner
3
Teng Wang, Yujie Liu
4
School of petroleum Engineering, China University of Petroleum (East China),
5
Qingdao 266580, P.R. China
6
ABSTRACT
7
A mathematical model of direct-acting tensioner system was developed to analyze the
8
effect of internal friction of tensioner cylinder on the tensioner performance. The platform-
9
tensioner-riser coupling system was established by implementing the tensioner model into
10
ANSYS-AQWA through user subroutines written in PYTHON scripts. The overall coupling
11
dynamic response under different wave conditions was investigated. The results from current
12
analyses considering the effect of internal friction of hydraulic cylinder show that the
13
relationship between tension and piston stroke of tensioner under the cyclic displacement is not
14
simple nonlinear relationship but hysteretic loop relationship. Based on the results of the
15
dynamic response under same wave conditions, it found that the variation of vertical relative
16
displacement between platform and riser obtained with the hysteretic tensioner model is similar
17
to that with the nonlinear tensioner model. Whereas the tension obtained with the hysteretic
18
tensioner model has greater scope when compared to that with the nonlinear tensioner model.
19
Moreover, the tension from the hysteretic tensioner model would change suddenly several times
20
in relatively short period under irregular waves, due to the existence of high-frequency
21 22 23
component, which resultantly exerts great impact on the fatigue life of the riser and tensioner. Keywords: tensioner system, riser, hysteretic tensioner model, tension variations, complete coupled analysis
24
0 INTRODUCTION
25
As the exploration of oil and gas in the ocean moves towards deep waters, the riser string
26
which connected the drilling unit and the wellhead, becomes longer and heavier. To prevent
27
buckling of the riser string due to its own weight and external environment load, the top-
28
tensioned risers(TTRs) is usually applied to deep-water operations. As TTRs is equipped with
29
the riser tensioners to maintain a nearly constant tension at the top of the riser, and to
30
compensate for the relative movements between the Semi-submersible platform and riser [1][2].
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For the performance analysis of tensioner, GrΓΈnevik. [3] used the beam elements to
32
simulate the tensioner, and analyze the tension variation due to the change of volume in the
33
nitrogen pressure vessels. However, Yang et al. [4] found that the tensioner performance
34
analysis cannot only consider the impact of the state variation of gas, it also need to take the
35
impact of the internal friction of the hydraulic cylinder into account. Yang et al. [4] and Zhang
36
et al. [5] regarded the internal friction of the hydraulic cylinder as coulomb friction, and the
37
coulomb friction on the tensioner piston by the cylinder was assumed to be related to the tension.
38
Andersson et al. [6] and Lee et al. [7] indicated that the internal friction of the hydraulic cylinder
39
can be regarded as a damping force in the cylinder and internal friction can be seen as the sum
40
of seal friction, coulomb friction and viscous friction. However, there is still a lack of studies
41
considering the impact of different friction on the performance of tensioner. Therefore, it is
42
necessary to conduct a deeper study on the effect of internal friction on the performance of
43
tensioner.
44
In addition to the performance of the tensioner, Chen et al. [8] and Gupta et al. [9] also
45
found that the coupling effect of the tensioner, the riser and the platform can not be ignored in
46
the simulation considering the large impact of the coupling effect on the global response. And
47
in the coupling dynamic response analysis, the results are largely influenced by the simulation
48
method of tensioner [10]. Kang [11] established the gas state model of the tensioner to analyze
49
the coupling dynamic response. Pestana et al. [12] used the nonlinear spring-damping element
50
in the software ORCAFLEX to simulate the tensioner, but the impact of the internal friction in
51
the tensioner cylinder on the overall response was not considered. Haziri [13] used the library
52
of Hydraulics & Pneumatics in SimulationX to simulate the tensioner, and established the whole
53
coupling model of platform-tensioner-riser by SimulationX, but it cannot be used to analyze
54
the effect of wave condition on the whole motion response.
55
Based on the existing work on tensioner performance from different scholars, it is found
56
that the internal friction is one of the key factors in the tensioner cylinder. But the simplified
57
friction model neglecting the effect of internal friction were mostly applied in these existing
58
work. Therefore, a reasonable tensioner simulation model taking account of the internal friction
59
of hydraulic cylinder is proposed specially for the current study. And based on this tensioner
60
model, a full platform-tensioner-riser coupling system is developed to study the effect of the
61
tensioner performance on the dynamic response of the platform and riser.
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1 Riser tensioner
63
There are two main types of tensioners currently used in deepwater drilling operations:
64
wire ropes tensioner (WRT) and direct-acting tensioner (DAT). However, due to the
65
complexity and limited payload ability of the WRT types, the DAT types with hydro-pneumatic
66
have become predominant in recent offshore field developments. The direct-acting tensioner
67
(DAT) eliminates the transmission devices such as pulleys and wire ropes. While the tension is
68
directly transmitted by the hydraulic cylinder piston rod, which brings advantages such as
69
strong stability and accurate compensation to DAT [14]. All analyses in the current work are
70
based on the direct-acting tensioner (DAT). A schematic diagram of the direct-acting tensioner
71
(DAT) is shown in Fig.1.
72 73
Fig.1 Schematic diagram of direct-acting tensioner (DAT)
74
The direct-acting tensioner (DAT) typically consists of hydro-pneumatic tensioner
75
cylinders, oil-gas accumulators, high-pressure gas vessels and low-pressure gas vessels. The
76
hydro-pneumatic tensioner cylinders provide almost constant tension to the riser in order to
77
counter the balance of the overall weight of the riser and tube-inside fluid. The internal piston
78
divides hydraulic cylinder into two parts: low-pressure pneumatic chamber and high-pressure
79
hydraulic chamber. The low-pressure chamber of the hydraulic cylinder is connected through a
80
pneumatic pressure line to the low-pressure gas vessels, which is mainly used to provide
81
damping effect and play the protective role of the riser tensioner system. The high-pressure
82
chamber of the hydraulic cylinder is connected through a hydraulic pressure line to the oil-gas
83
accumulators, which provides the tension for the riser. And the tension maintained by oil
84
pressure in this side of the hydraulic cylinder from the oil-gas accumulator is pressurized by
85
high-pressure gas vessels.
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2 The mathematical model of the riser tensioner system
87
The riser tensioner is a complicated structure composed of hydro-pneumatic and
88
mechanical subsystems. In order to simplify the analysis, principle hypothesizes of the current
89
work are as follows:
90
(1) Ignored the friction loss inside the oil/gas accumulator;
91
(2) Ignored the pressure loss inside the pressure line;
92
(3) Ignored the quality of the piston rod and the hydraulic fluid;
93
(4) Met the variation law of gas state and ignored the effect of the temperature.
94 95 96
2.1 Modelling of gas state variations Supposing that there is no heat transfer, the internal pressure variation of the high-pressure gas cylinder satisfies the following relation: π
97
ππ΄0ππ΄0 = ππ΄1ππ΄1
π
(1)
98
where, π is the adiabatic gas constant, which is 1.4 for nitrogen [3]; ππ΄0 is the initial pressure
99
in the high pressure gas vessels;ππ΄0 is the initial volume in the high pressure gas vessels; ππ΄1
100
is the pressure after considering the pressure variation in the high pressure gas vessels, and ππ΄1
101
is the volume after considering the volume variation in the high pressure gas vessels.
102
Considering that the hydraulic fluid is incompressible, it is thought that the gas volume
103
varies along with the motion of hydraulic cylinder piston. The volume variation in the high-
104
pressure gas vessels is expressed as follows:
105
(2)
βππ΄ = ππ΄1 β ππ΄0 = π΄π β π₯π
106
where, βππ΄ is the variation of gas volume in the system; π΄π is the cross sectional areas of the
107
piston at the rod-side, and π₯π is the displacement of the piston in the hydraulic cylinder.
108 109 110 111 112 113
Overall, the pressure variations βPA in a high-pressure cylinder due to the gas volume variation can be represented as:
(
βππ΄ = PA0 (1 β Ar * xp/VA0)
βπ
)
(3)
β1
Similarly, pressure variations βππ΅ in a low-pressure cylinder due to the gas volume variation can be represented as:
(
βππ΅ = ππ΅0 (1 β π΄π * π₯π/ππ΅0)
-π
)
β1
(4)
114
where, ππ΅0 is the initial pressure in the low pressure gas vessels, ππ΅0 is the initial volume in the
115
low pressure gas vessels, and π΄π is the cross sectional areas of the piston at the piston-side.
116
2.2 Modelling of internal friction in hydraulic cylinder
117
The hydraulic cylinder is an important part of tensioner, its internal friction performance
118
should not be ignored in the analysis process. In order to achieve the tensioner model, and to
119
ensure the condition in simulation is in conformity with the actual operating conditions, the
ACCEPTED MANUSCRIPT 120
friction model considering the "Stribeck effect" should be the preferred for such study. Based
121
on Xuan et al. [14]βs findings, the hydraulic cylinder has significant Stribeck effect when the
122
direction of piston movement changes. In hydraulic cylinder, the Stribeck effect occurs when
123
the hydraulic fluid contacts with the moving piston. When the piston velocity is smaller than
124
the Stribeck velocity (piston limit velocity), the friction decreases with the increase of the piston
125
velocity.
126
In the Stribeck model, the total friction πΉππ is simulated as a function of relative velocity
127
and pressure, and is assumed to be the sum of Stribeck, Coulomb, and viscous components. The
128
friction can be defined by two parts: the velocity-dependent part, πΉππ,π£, and the pressure-
129
dependent part, πΉππ,π. The total friction force and the two parts are defined as [7, 14, 15]:
130
πΉππ = πΉππ,π£ + πΉππ,π ππ£
131
πΉππ,π£ = (πΉπ + (πΉπ β πΉπ)ππ₯π( β |π£π|/π£π))π πππ(π£π) + ππ£π£π
132
πΉππ,π = ππ|πππ| = πΉπ
133
where, πΉπΆ is the Coulomb friction force; πΉπ is the static friction force;π£π is the piston velocity;
134
π£π is the piston limit velocity (Stribeck velocity) (|π£π| β€ 0.05π/π ) [14]; πππ is the pressure
135
difference; ππ£ is the viscous friction coefficient;ππ£ is the friction exponent (0 < ππ£ β€ 1) ,and
136
ππ is the linear coefficient.
(5)
137
In the velocity-dependent part (πΉππ,π£), the first term represents the Coulomb friction (πΉπΆ),
138
which is usually defined as a constant. The second term represents the mixed friction (also
139
known as Stribeck effect friction), which is expressed by the exponential function relation
140
between Static friction πΉπ and Stribeck velocity π£π (piston limit velocity). The third term is the
141
fluid dynamic fricti on (viscous friction), which is related to the viscous properties of the
142
hydraulic fluid. The pressure-dependent part (πΉππ,π) of the friction force represents the static
143
friction force.
144
2.3 Modelling of tension variations
145
In the direct-acting tensioner system, the tension is applied to the top of the riser through
146
the piston rod of the hydraulic cylinder. The tension πΉπ can be expressed as the sum of the
147
hydraulic force produced by the pressure difference between both sides of the cylinder piston
148
and the internal friction of the hydraulic cylinder, which is shown as follows:
149 150 151
πΉπ = πΉβπ¦π + πΉππ
(6)
The hydraulic force produced by the pressure difference between both sides of tensioner piston in the hydraulic-pneumatic cylinder πΉβπ¦π can be represented as:
152
πΉβπ¦π = πππ΄π β πππ΄π
153
where ππ is the pressure of the piston at the rod-side, π΄π is the cross sectional areas of the piston
(7)
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at the rod-side, ππ is the pressure of the piston at the piston-side, and π΄π is the cross sectional
155
areas of the piston at the piston-side. Based on the gas state variations in section 2.1, the pressure
156
difference between both sides of tensioner piston in the hydraulic-pneumatic cylinder also can
157
be represented as:
158
ππ = π
159
ππ = π
π΄0
+ βππ΄
π΅0
(8)
+ βππ΅
160
For a comprehensive consideration of the internal friction of the hydraulic cylinder, the
161
equation of force equilibrium on both sides of tensioner piston πΉπ in the hydraulic-pneumatic
162
cylinder can be reformulated as:
163
πΉπ = ππ΄0(1 β Ar * π₯π/VA0)
-π
π΄π - ππ΅0(1 β π΄π * π₯π/ππ΅0)
-π
π΄π + πΉππ
(9)
164
The tensioner is an important connection between the platform and riser, and its
165
performance will be affected by the relative movement between the platform and riser. However,
166
in the traditional tensioner analysis process, Pestana et al. [12] and Mao et al. [17] normally
167
used the platform motions as the input signal of the tensioner piston, which is not in accordance
168
with the actual operation conditions. Unlike those studies, the real time responses of the
169
platform and riser at the connected location are inputted to the tensioner to simulate the coupling
170
dynamic response of the tensioner with the platform and riser system in this paper. Therefore,
171
the calculation formula of the tensioner model in the simulation process can be rewritten by the
172
parametric formulation:
173 174
πΉπ = ππ΄0(1 β Ar * (π₯ππππ‘ππππ β π₯πππ ππ)/VA0)
-π
- ππ΅0(1 β π΄π β (π₯ππππ‘ππππ β π₯πππ ππ)/VB0)
Ar
-π
π΄π
175
+ (πΉπ + (πΉπ β πΉπ)ππ₯π( β |π£ππππ‘ππππ β π£πππ ππ|/π£π))π πππ(π£ππππ‘ππππ β π£πππ ππ)
176
+ ππ£(π£ππππ‘ππππ β π£πππ ππ) + ππ|πππ|
ππ£
(10)
177
where π₯ππππ‘ππππ and π£ππππ‘ππππ are the real time displacement and velocity of the connection
178
point between the platform and tensioner along the tensioner cylinder, respectively; π₯πππ ππ and
179
π£πππ ππ are the real time displacement of the connection point between the riser and tensioner
180
along the tensioner cylinder, respectively. These parameters can be extracted dynamically by
181
user subroutines from ANSYS-AQWA result file. The schematic diagram of the tensioner
182
between the platform and riser is shown in Fig.2.
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183 184 185
Fig.2 The schematic diagram of the tensioner between the platform and riser
3 Performance of the tensioner system
186
Based on the mathematical model for each components of the tensioner system, the
187
tensioner performance can be simulated by using MATLAB program to study the effect of the
188
internal friction of the hydraulic cylinder on the tension variations. The direct-acting tensioner
189
used on the βHYSY-981β deepwater semi-submersible drilling platform was taken as an
190
example for the current study. The input piston stroke signal of the tensioner cylinder is
191
consisted of a cyclostationary sinusoidal signal. Assuming that the sinusoidal signal is with an
192
amplitude of 5 meters and time period of 10 seconds, while the piston is in the mid-stroke at
193 194
the initial time, the basic parameters of the tensioner system are shown in Table 1. Table.1 Hydro-pneumatic tensioner system data Parameter
Value
unit
Initial volume of high-pressure gas vessels ππ΄0
9380
L
Initial pressure of high-pressure gas vessels ππ΄0
11.2
MPa
Initial volume of low-pressure gas vessels ππ΅0
2250
L
Initial pressure of low-pressure gas vessels ππ΅0
0.1
MPa
Stroke-length of cylinders π₯π
Β± 7.62
m
Piston diameter π΄π
560
mm
ACCEPTED MANUSCRIPT
195
Piston rod diameter π΄π
230
mm
Density of hydraulic oil
850
kg/m3
Viscosity of hydraulic oil
84.2416
cSt(10-6 m2/s)
3.1 Analysis of internal friction effect in hydraulic cylinder
196
In the tensioner system, the internal friction of hydraulic cylinder is closely related to the
197
piston movement and frictional pressure drop. Based on eq.(5), we compiled the MATLAB
198
program to analyze the variation of internal friction in the hydraulic cylinder. The values of the
199
corresponding parameters are as follows: the limit velocity of the piston in the hydraulic
200
cylinder is 0.05m/s, the pressure drop due to friction is 2bar, the Coulomb friction coefficient
201
is 0.5, the viscous friction coefficient is 65818Ns/m and the viscous friction index is 1. The
202
calculation results are shown in Fig.3 and Fig.4.
203
Fig.3 shows the variation of the friction with the piston velocity. The total internal friction
204
of the hydraulic cylinder is mainly composed of three parts: the pressure-dependent friction,
205
the viscous friction and the Stribeck effect friction. As shown in Fig.3, the pressure-dependent
206
friction is a constant regardless of the piston velocity. The viscous friction increases linearly
207
with the increase of piston velocity. And the Stribeck effect friction is closely related to the
208
limit velocity of the piston. When the piston velocity is lower than a certain value (0.05m/s),
209
the total friction force increases with the decrease of the piston velocity due to the Stribeck
210
effect. When the piston velocity equals to 0, the velocity changes from a positive value to a
211
negative one, and the total friction also changes abruptly from a positive value to a negative
212
one.
213
Fig.4 shows the variation of Stribeck effect friction and piston velocity with time. As
214
shown in Fig.4, the Stribeck effect friction decreases with increasing piston velocity until piston
215
velocity goes beyond the limit, after which the Stribeck effect friction keeps as a constant. In
216
addition, the Stribeck effect friction reaches the maximum when the piston velocity is zero and
217
changes suddenly when the direction of velocity changes. 3
105
2
Friction[N]
1 0 -1
Total friction Viscous friction Pressure-dependent friction Stribeck friction
-2
218
-3 -4
-3
-2
-1 0 1 Piston velocity[m/s]
2
3
4
ACCEPTED MANUSCRIPT Fig.3 Relation between internal friction of the hydraulic cylinder and piston velocity 104
Stribeck effect friction[N]
5
Stribeck effect friction Piston velocity
0
-5
220 221 222
5
0
0
2
4
6
8
Piston velocity[m/s]
219
-5 10
Time [s]
Fig.4 The variation of Stribeck effect friction and piston velocity with time
3.2 Performance of the tensioner system under cyclic displacement
223
The reciprocating motion of the piston is regarded as cyclic displacement in the current
224
study. In the analysis of tensioner system, we take the down-stroke as positive and take the up-
225
stroke as negative, respectively. In order to analyze the influence of internal friction of hydraulic
226
cylinder, the tensioner models considering separately the state variation of gas and internal
227
friction of hydraulic cylinder are developed specially in the current work. The simulated
228
tension-stroke curve at the piston side chamber of a single cylinder in the tensioner system is
229
shown in Fig.5.
230
Firstly, when the tension is assumed to be related to the state variation of gas only, the
231
relation between the tension and the piston stroke is shown in Curve 1 (Fig.5). As shown by
232
Curve 1, the relationship between the tension and the piston stroke is nonlinear. So the tensioner
233
model considering only the state variation of gas is named as nonlinear tensioner model. When
234
the piston is displaced upward with respect to the cylinder housing, it will cause the hydraulic
235
fluid to flow from the accumulator to the hydraulic cylinder. Meantime, the pressure of the
236
high-pressure hydraulic chamber will be reduced and the tension will be reduced accordingly.
237
Otherwise, the pressure of the high-pressure hydraulic chamber will be increased and the
238
tension will be increased accordingly. In addition, calculation results show that the tension
239
ranges from 1.9MN to 2.68MN under a given piston dynamic stroke (from -5 m to 5 m).
240
Secondly, when the tension is assumed to be also related to the internal friction of the
241
hydraulic cylinder, the relation between the tension and the piston stroke is shown in Curve 2
242
(Fig.5). As shown by Curve 2, the relationship between them is similar to a hysteretic curve.
243
The tensioner model of considering internal friction of hydraulic cylinder is thus named as
244
hysteretic tensioner model. And the time-history curve of tension and piston displacement under
245
the single cylinder of hysteretic tensioner model are shown in Fig.6. When the piston is
246
displaced upward with respect to the cylinder housing, the tension will be reduced with the
ACCEPTED MANUSCRIPT 247
internal friction of the hydraulic cylinder. Otherwise, the tension will be increased when the
248
piston is displaced downward with respect to the cylinder housing. In addition, when the piston
249
stroke reaching stop positon, the tension will have the sudden change due to the viscous friction
250
of tensioner cylinder. And the tension has opposite change with piston movement when the
251
piston velocity is lower than the limit value. This result was caused by the impact of the Stribeck
252
effect friction of the tensioner cylinder. 106 2.8
Tension[N]
2.6 2.4 2.2 2 1.8 1.6
253
5
Fig.5 Simulation of tension-stroke curve in piston-side chamber for single tensioner cylinder 106
Tension[N]
6
2.7
4
2.5
2
2.3
0
2.1
-2
1.9
Tension -4 Piston displacement Piston velocity -6 30 35 40
1.7
256
0
Pistion Stoke[m]
2.9
255
-5
0
5
10
15
20 Time[s]
25
Piston velocity[m/s] Piston displacement[m]
254
1 Nonlinear tensioner model 2 Hysteresis tensioner model
Fig.6 The variation trend of tension and piston displacement under single tensioner cylinder 15% Total friction Stribeck friction Viscous friction Pressure-dependent friction
Tension loss/Tension
10% 5% 0 -5% -10% -15%
257 258
0
2
4
6
8
10
Time[s]
Fig.7 Variation of tension loss due to internal friction of hydraulic cylinder
259
The internal friction of hydraulic cylinder contributes to the tension loss. The friction
260
caused tension loss expressed as a percentage of the total tension is shown in Fig.7. It shows
261
that the tension loss due to the internal friction of hydraulic cylinder is up to 13.6% of the total
ACCEPTED MANUSCRIPT 262
tension. Among this 13.6% tension loss, 10.4% is due to the viscous friction, while the
263
contribution of the Stribeck effect friction and pressure-dependent friction is similar with a
264
proportion of 2.1% and 2.2%, respectively. Based on the current results, it can be concluded
265
that the internal friction can not be omitted in the performance analysis of tensioner.
266
4 Response analysis of platform-tensioner-riser coupling system
267
Based on the tensioner mathematical model established in the previous section 2, the
268
platform-tensioner-riser coupling system was established by implementing the tensioner system
269
model into commercial software ANSYS-AQWA through user subroutines written in
270
PYTHON scripts. In the ANSYS-AQWA module, the platform geometry model can be created
271
in Workbench using Design Modeler, the riser string is modeled by the Tethers Connections,
272
and the tensioner can be joined between the platform and the riser string by the external force
273
calculation program. A full platform-tensioner-riser coupling system is thus developed and the
274
effect of the performance of the tensioner on platform and riser dynamic response is simulated.
275
4.1 Model dimensions and wave conditions
276
The current study takes the βHYSY-981β deepwater semi-submersible drilling platform as
277
an example to analyze the dynamic response of the platform-tensioner-riser coupling system.
278
In accordance with the demands of actual drilling operation, the normal operating wave
279
conditions which is extensively applied in South China Sea is chosen for the study. Meanwhile,
280
in order to check the applicability of the tensioner used in the coupling system, the overall
281
dynamic response under different regular waves and irregular waves is analyzed. The
282
corresponding wave condition parameters are shown in Table.2. The overall model of the
283
platform and the riser system has been established in the hydrodynamic analysis software
284
ANSYS-AQWA. In ANSYS-AQWA hydrodynamic analysis, the Schematic of drilling
285
platform model is shown in Fig.8. And the principal dimensions of drilling platform and riser
286
system are shown in Table.3 and Table.4 Here the catenary mooring are adopted and the
287
parameters of mooring system are shown in Table.5 and Table.6.
288
ACCEPTED MANUSCRIPT 289 290
Fig.8 Schematic of drilling platform model Table.2 Wave conditions parameters Case
Wave Type
Wave amplitude
Wave period
Wave direction
Regular waves1
Stokes Wave
5m
10s
0ΒΊ
Regular waves2
Stokes Wave
5m
15s
0ΒΊ
Irregular waves 291
P-M spectrum 5m 10s Table.3 Boundary conditions for semisubmersible Parameter
Value
unit
Operation depth
1500
m
Length
114.07
m
Breadth
78.68
m
Deep
38.6
m
0ΒΊ
Draft 19 m Table.4 Riser system data
292
Parameter
Value
unit
Length of the riser
1500
m
Internal diameter of the riser
0.508
m
External diameter of the riser
0.5334
m
Density of the riser
7850
kg/m3
293
Table.5 Mooring cable material properties Cable type
Diameter
Mass/Unit Length
Maximum Tension
Stiffness, EA
Steel cable
140 mm
97 kg/m
1.693e10 N
1.74e9 N
Polyester cable
175 mm
294
23 kg/m 1.0e10 N Table.6 Length of mooring cable
3.0e8 N
Angle
Length of upper steel cable
Length of polyester cable
Length of lower steel cable
45Β°
90 m
1944.7 m
90 m
295
By the coupling dynamic response analysis, the vertical movement between the platform
296
and the riser, and the tension on the top of the riser, are analyzed to investigate the performance
297
of the hysteretic tensioner model under regular waves1. Fig.9 and Fig.10 present the vertical
298
relative movement of the platform and the riser, and the tension on the top of the riser under
299
regular waves1, respectively. The results show that the tension does change with the relative
300
movement in real time. When the platform moves upward relative to the riser, the riser tension
301
increases with the relative displacements. In addition, Fig.10 shows that the tension increases
302
with decreasing relative velocity value when the velocity is close to 0 and has a sudden change
ACCEPTED MANUSCRIPT 303
when the relative velocity is 0. This is similar to the variation trend shown in Fig.6. And the
304
main difference between the two graphs (Fig.10 and Fig.6) is that the scope of the suddenly
305
changed tension in Fig.10 takes a larger proportion of the total tension variation when compared
306
to that shown in Fig.6. The reason of this difference is that the range of relative displacement
307
and relative velocity are smaller than the range of piston stroke and piston velocity in Fig.6. 6
Tension Relative displacement
Tension[N]
6.6
7
6.2
6.5
6
6 5.5
5.6 800
820
840
860
880
900
920
940
960
980
5 1000
Time[s]
Fig.9 The variation trend of tension with relative displacement under regular waves1 6.8
106 Tension Relative velocity
Tension[N]
6.65
0.8 0.6
6.5
0.4
6.35
0.2
6.2
0
6.05
-0.2
5.9
-0.4
5.75
-0.6
5.6 800
820
840
860
880
900
920
940
960
980
Relative velocity[m/s]
309
7.5
6.4
5.8
308
8
Relative displacement[m]
10
6.8
-0.8 1000
310
Time[s]
311
Fig.10 The variation trend of tension with relative velocity under regular waves1
312
Based on the traditional nonlinear tensioner model, the overall dynamic response of the
313
two different tensioner models are compared and analyzed. Fig.11a shows the vertical relative
314
displacement variation based on the two different tensioner models. As shown in Fig.11a, the
315
time-history curves of the relative displacement from different tensioner models are similar.
316
And the scope of vertical relative displacement from the nonlinear tensioner model is slightly
317
smaller than that from the hysteretic tensioner model. It can be concluded that the hysteretic
318
tensioner also can compensate the relative movement between the platform and the riser as the
319
nonlinear tensioner. Unlike the variation of vertical relative displacement, the tension variation
320
from the two tensioner models has a great difference. As shown in Fig.11b, the tension provided
321
by the hysteretic tensioner model and the nonlinear tensioner model varied from 5.728MN to
322
6.605MN and from 5.948 MN to 6.397MN under the regular waves1, respectively. It shows
323
that the variation range of the tension from the hysteretic tensioner model is larger than that
ACCEPTED MANUSCRIPT 324
from the nonlinear tensioner model. And Fig.11b also shows that the tension will has a sudden
325
change for the hysteretic tensioner model due to the internal friction of the tensioner cylinder,
326
which has an impact on the fatigue life of the riser. In addition, Fig.11c shows the relation
327
between tension and relative displacement based on different tensioner models. As shown in
328
Fig.11c, the variation curves of tension with the relative displacement for both the nonlinear
329
tensioner model and the hysteretic tensioner model are identical with the original curves shown
330
in Fig.5. 8
Relative displacement[m]
7.5 7 6.5 6 5.5
331 332
Hysteresis tensioner model Nonlinear tensioner model
5 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.11a Relative displacement variation under different tensioner models 106
6.7
Hysteresis tensioner model Nonlinear tensioner model
6.6 6.5
Tension[N]
6.4 6.3 6.2 6.1 6 5.9 5.8
333 334
5.7 800
820
840
860
880
900
920
940
960
980
1000
Time[s]
Fig.11b Tension variation under different tensioner models 6
10
6.8
Tension[N]
6.6 6.4 6.2 6 Hysteresis tensioner model Nonlinear tensioner model
5.8 5.6
335 336
5
5.5
6
6.5
7
7.5
8
Relative displacement[m]
Fig.11c Variation of tension with relative displacement under different tensioner models
337
In order to confirm the applicability of the hysteretic tensioner model under different wave
338
conditions. The overall coupled dynamic response under different wave periods is analyzed.
ACCEPTED MANUSCRIPT 339
Fig.12a and Fig.12b present the vertical relative movement variation of the platform and the
340
riser, and the tension variation under different regular waves, respectively. It turned out that the
341
variation scope of the relative displacement and the tension under regular waves1 are larger
342
than that under regular waves2. Under the regular waves2, the relative displacement varied
343
from 2m to 10.5m and the tension varied from 5.19MN to 7.15MN, and the tension does change
344
with the relative movement in real time. In addition, compared with the stroke range of the
345
tensioner piston, it can also be found that the relative displacement variation under regular
346
waves2 is in a reasonable scope. These results indicated that the hysteretic tensioner model can
347
effectively compensate the relative movement between the platform and the riser under the
348
regular waves2.
Relative displacement[m]
12
8 6 4 2 0 800
349 350
Regular waves1 Regular waves2
10
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.12a Relative displacement variation under different regular waves 7.5
106 Regular waves1 Regular waves2
Tension[N]
7 6.5 6 5.5
351 352 353
5 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.12b Tension variation under different regular waves
4.3 Coupled dynamic response analysis under irregular waves
354
Aimed at the random characteristics of the wave conditions in the actual operation process.
355
The coupling dynamic response such as the vertical movement between the platform and the
356
riser, and the tension on the top of the riser are analyzed for the hysteretic tensioner model under
357
the irregular waves. The selected irregular waves type in this paper is Pierson-Moskowitz
358
spectrum. The corresponding wave parameters of Pierson-Moskowitz spectrum is shown in
359
Table.2 and the wave spectrum curve of the Pierson-Moskowitz spectrum is shown in Fig.13.
ACCEPTED MANUSCRIPT 360
The results of the coupled dynamic response analysis are shown in Fig.14 and Fig.15. The
361
results also show that the tension does change with the relative movement in real time. As
362
shown in Fig.14, the tension reaches maximum when the value of vertical relative displacement
363
between the platform and the riser reaches maximum. The corresponding tension and relative
364
displacement varied from5.635MN to 6.579MN and from 4.85m to 7.3m, respectively. Fig.15
365
shows the variation trend of tension and relative velocity under irregular waves. In addition,
366
comparing the result with the regular waves, it shows that the variation law of Fig.15 is
367
identical to the Fig.10. 35
Spectral density (m 2/Hz)
30 25 20 15 10 5 0
368
0.1
0.15
0.2
0.25
0.3
0.35
Fig.13 The wave spectrum curve of Pierson-Moskowitz spectrum
6.4
7
6.1
6
5.8
5
5.5 800
820
840
860
880
900
920
940
960
4 1000
980
Time[s]
Fig.14 The variation trend of tension and relative displacement under irregular waves
Tension[N]
106
0.8
6.55
0.6
6.4
0.4
6.25
0.2
6.1
0
5.95
-0.2
5.8
-0.4 Tension Relative velocity
5.65
373
8
Tension Relative displacement
Relative displacement[m]
Tension[N]
106
6.7
372
0.4
Frequency(Hz)
6.7
370 371
0.05
5.5 800
820
840
860
880
900 920 Time[s]
940
960
980
Relative velocity[m/s]
369
0
-0.6
-0.8 1000
Fig.15 The variation trend of tension and relative velocity under irregular waves
374
Based on the overall dynamic response analysis under the irregular waves, the calculation
375
results based on the two different tensioner models under irregular waves are compared. Fig.16a
ACCEPTED MANUSCRIPT 376
and Fig.16b show the relative displacement variation and the tension variation from analyses
377
using the two different tensioner models, respectively. It can be found that the time-history
378
curves of the relative displacement for the two different tensioner models under irregular waves
379
are similar to those results under regular waves. This result shows that the hysteretic tensioner
380
model can be applied in different wave conditions. Similarly, under the irregular waves, the
381
hysteretic tensioner model also has a great scope of tension variation than the nonlinear
382
tensioner model. As shown in Fig.16b, the tension provided by the hysteretic tensioner model
383
and the nonlinear tensioner model varied from 5.635MN to 6.579MN and from 5.826 MN to
384
6.356MN under the irregular waves, respectively. Fig.16c shows the variation trend of the
385
vertical relative displacement with tension from analyses using the two different tensioner
386
models. And the relations between tension and relative displacement for the different tensioner
387
models are identical to that shown in Fig.11c. In addition, compared with the periodic dynamic
388
response under regular waves1, the tension variation under the irregular waves is random
389
variation. Due to the existence of the high-frequency component under the irregular waves, the
390
tension would change suddenly several times in a relatively short period, which put forward
391
higher requirement for the fatigue life of the tensioner and riser. 7.5
Relative displacement[m]
7 6.5 6 5.5 5 4.5 4 800
392 393
Hysteresis tensioner model Nonlinear tensioner model 820
840
860
880
900
920
940
960
980
1000
Time[s]
Fig.16a Relative displacement variation under different tensioner models 6.6
106
Tension[N]
6.4
6.2
6
5.8 Hysteresis tensioner model Nonlinear tensioner model
394 395
5.6 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.16b Tension variation under different tensioner models
ACCEPTED MANUSCRIPT 106
6.6
Tension[N]
6.4
6.2
6
5.8
5.6
396 397 398
Hysteresis tensioner model Nonlinear tensioner model 4
4.5
5
5.5 6 Relative displacement[m]
6.5
7
7.5
Fig.16c Relation between tension and relative displacement under different tensioner models
5 Conclusions and future studies
399
In this paper, the mathematical model of the direct acting riser tensioner system was
400
developed to analyze the impact of internal friction of hydraulic cylinder on the tensioner
401
performance. The platform-tensioner-riser coupling system was established by implementing
402
the tensioner system model into commercial software ANSYS-AQWA through user
403
subroutines written in PYTHON scripts. The overall coupling dynamic response of the system
404
under different wave conditions was investigate. As a result of the analysis, some significant
405
conclusions can be drawn as follows:
406
(1) For the tensioner considering the internal friction of the hydraulic cylinder, the
407
relationship between tension and piston stroke is not a simple nonlinear relationship
408
but a hysteretic loop relationship. Moreover, when the piston stroke reaching stop
409
positon, the tension will have the sudden change due to the viscous friction of
410
tensioner cylinder. And due to the Stribeck effect friction, the tension will have
411
opposite change with piston movement when the piston velocity is lower than the limit
412
value.
413
(2) By comparing the calculation results from different tensioner models, the scope of
414
vertical relative displacement under the nonlinear tensioner model is slightly smaller
415
than that for the hysteretic tensioner model. The scope of the tension under the
416
hysteretic tensioner model is larger than that for the nonlinear tensioner. And the
417
tension also has a sudden change under the hysteretic tensioner model due to the
418
internal friction of the tensioner cylinder. In addition, due to the existence of the high-
419
frequency component under the irregular waves, the tension of the hysteretic tensioner
420
model will complete more sudden changes in a relatively short period, which has an
421
impact on the fatigue life of the riser and tensioner.
422
In this study, a tensioner model considering internal friction of hydraulic cylinder is
ACCEPTED MANUSCRIPT 423
established, which is more consistent with the working condition. And by using the ANSYS-
424
AQWA, the overall coupling dynamic response can be really simulate under the normal
425
operating conditions. In the future work, the emergency disconnection of the riser under
426
dangerous conditions will be analyzed. The model is further verified by analyzing the overall
427
dynamic response during the emergency disconnection of the riser.
ACCEPTED MANUSCRIPT 428
References
429
[1] Chakrabarti, S., 2005. Handbook of Offshore Engineering.
430
[2] Von, D. O.C.B., Ankargren, D.B.J., 2015. Riser tensioner.
431
[3] GrΓΈnevik, A., 2013. Simulation of drilling riser disconnection - Recoil analysis. Institutt
432
for Marin Teknikk.
433
[4] Yang, C.K., Kim, M., 2010. Linear and Nonlinear Approach of Hydropneumatic Tensioner
434
Modeling for Spar Global Performance. Journal of Offshore Mechanics and Arctic
435
Engineering 132 (1), 011601.
436 437 438 439
[5] Zhang, L., Chang, Y., Liu, X., Liu, K., Yang, H., 2013. AMESim-based Modeling and Simulation of Platform Riser Tensioner. China Petroleum Machinery. [6] Andersson, S., SΓΆderberg, A., BjΓΆrklund, S., 2007. Friction models for sliding dry, boundary and mixed lubricated contacts. Tribology International 40 (4), 580-587.
440
[7] Lee, H., Roh, M.I., Ham, S.H., Ha, S., 2015. Dynamic simulation of the wireline riser
441
tensioner system for a mobile offshore drilling unit based on multibody system dynamics.
442
Ocean Engineering 106, 485-495.
443
[8] Chen, B., Yu, J., Yu, Y., Xu, L., Wu, H., Li, Z., 2018. Modeling Approach of
444
Hydropneumatic Tensioner for Top-Tensioned Riser. Journal of Offshore Mechanics and
445
Arctic Engineering 140 (5), 051706.
446
[9] Gupta, H., Nava, V., Banon, H., Gkaras, V., Spanos, P., 2008. Determination of Riser
447
Tensioner Properties From Full-Scale Data, ASME 2008 International Conference on
448
Offshore Mechanics and Arctic Engineering, pp. 389-396.
449
[10]Wang, K.P., Xue, H.X., Tang, W.Y., 2012. Numerical simulation of hydropneumatic
450
tensioner for coupled deepwater platform system. Journal of Shanghai Jiaotong University
451
46 (10), 1652-1657.
452
[11]Kang, H.S., Kim, M.H., Aramanadka, S.S.B., 2017. Tension variations of hydro-pneumatic
453
riser tensioner and implications for dry-tree interface in semisubmersible. 7 (1), 21-38.
454
[12]Pestana, R.G., Roveri, F.E., Franciss, R., Ellwanger, G.B., 2016. Marine riser emergency
455
disconnection analysis using scalar elements for tensioner modelling. Applied Ocean
456
Research 59, 83-92.
457 458 459 460 461
[13]Haziri, S., Dyngvold, Γ., 2011. Development of simulation model for virtual testing and design of a riser tensioner system. [14]Xuan, B.T., Hafizah, N., Yanada, H., 2012. Modeling of dynamic friction behaviors of hydraulic cylinders. Mechatronics 22 (1), 65-75. [15]Marton, L., Lantos, B., 2007. Modeling, Identification, and Compensation of Stick-Slip
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Friction. IEEE Transactions on Industrial Electronics 54 (1), 511-521.
463
[16]Mao, L., Liu, Q., Zhou, S., Wang, G., Fu, Q., 2016. Deep water drilling riser mechanical
464
behavior analysis considering actual riser string configuration. Journal of Natural Gas
465
Science & Engineering 33, 240-254.
ACCEPTED MANUSCRIPT Highlights ο¬ Development of a hysteretic tensioner model with the Stribeck effect. ο¬ Development of mathematical equations for tensioner model based on the real time movement of platform and riser. ο¬ Investigation on the dynamic response of the platform-tensioner-riser coupling system by implementing the hysteretic tensioner model into ANSYS-AQWA. ο¬ Study on the performance of the tensioner under different wave conditions.
Teng Wang, Yujie Liu PII:
S0029-8018(18)30712-1
DOI:
10.1016/j.oceaneng.2018.08.004
Reference:
OE 5409
To appear in:
Ocean Engineering
Received Date:
04 May 2018
Accepted Date:
06 August 2018
Please cite this article as: Teng Wang, Yujie Liu, Dynamic Response of Platform-Riser Coupling System with Hydro-pneumatic Tensioner, Ocean Engineering (2018), doi: 10.1016/j.oceaneng. 2018.08.004
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
1
Dynamic Response of Platform-Riser Coupling System with Hydro-
2
pneumatic Tensioner
3
Teng Wang, Yujie Liu
4
School of petroleum Engineering, China University of Petroleum (East China),
5
Qingdao 266580, P.R. China
6
ABSTRACT
7
A mathematical model of direct-acting tensioner system was developed to analyze the
8
effect of internal friction of tensioner cylinder on the tensioner performance. The platform-
9
tensioner-riser coupling system was established by implementing the tensioner model into
10
ANSYS-AQWA through user subroutines written in PYTHON scripts. The overall coupling
11
dynamic response under different wave conditions was investigated. The results from current
12
analyses considering the effect of internal friction of hydraulic cylinder show that the
13
relationship between tension and piston stroke of tensioner under the cyclic displacement is not
14
simple nonlinear relationship but hysteretic loop relationship. Based on the results of the
15
dynamic response under same wave conditions, it found that the variation of vertical relative
16
displacement between platform and riser obtained with the hysteretic tensioner model is similar
17
to that with the nonlinear tensioner model. Whereas the tension obtained with the hysteretic
18
tensioner model has greater scope when compared to that with the nonlinear tensioner model.
19
Moreover, the tension from the hysteretic tensioner model would change suddenly several times
20
in relatively short period under irregular waves, due to the existence of high-frequency
21 22 23
component, which resultantly exerts great impact on the fatigue life of the riser and tensioner. Keywords: tensioner system, riser, hysteretic tensioner model, tension variations, complete coupled analysis
24
0 INTRODUCTION
25
As the exploration of oil and gas in the ocean moves towards deep waters, the riser string
26
which connected the drilling unit and the wellhead, becomes longer and heavier. To prevent
27
buckling of the riser string due to its own weight and external environment load, the top-
28
tensioned risers(TTRs) is usually applied to deep-water operations. As TTRs is equipped with
29
the riser tensioners to maintain a nearly constant tension at the top of the riser, and to
30
compensate for the relative movements between the Semi-submersible platform and riser [1][2].
ACCEPTED MANUSCRIPT 31
For the performance analysis of tensioner, GrΓΈnevik. [3] used the beam elements to
32
simulate the tensioner, and analyze the tension variation due to the change of volume in the
33
nitrogen pressure vessels. However, Yang et al. [4] found that the tensioner performance
34
analysis cannot only consider the impact of the state variation of gas, it also need to take the
35
impact of the internal friction of the hydraulic cylinder into account. Yang et al. [4] and Zhang
36
et al. [5] regarded the internal friction of the hydraulic cylinder as coulomb friction, and the
37
coulomb friction on the tensioner piston by the cylinder was assumed to be related to the tension.
38
Andersson et al. [6] and Lee et al. [7] indicated that the internal friction of the hydraulic cylinder
39
can be regarded as a damping force in the cylinder and internal friction can be seen as the sum
40
of seal friction, coulomb friction and viscous friction. However, there is still a lack of studies
41
considering the impact of different friction on the performance of tensioner. Therefore, it is
42
necessary to conduct a deeper study on the effect of internal friction on the performance of
43
tensioner.
44
In addition to the performance of the tensioner, Chen et al. [8] and Gupta et al. [9] also
45
found that the coupling effect of the tensioner, the riser and the platform can not be ignored in
46
the simulation considering the large impact of the coupling effect on the global response. And
47
in the coupling dynamic response analysis, the results are largely influenced by the simulation
48
method of tensioner [10]. Kang [11] established the gas state model of the tensioner to analyze
49
the coupling dynamic response. Pestana et al. [12] used the nonlinear spring-damping element
50
in the software ORCAFLEX to simulate the tensioner, but the impact of the internal friction in
51
the tensioner cylinder on the overall response was not considered. Haziri [13] used the library
52
of Hydraulics & Pneumatics in SimulationX to simulate the tensioner, and established the whole
53
coupling model of platform-tensioner-riser by SimulationX, but it cannot be used to analyze
54
the effect of wave condition on the whole motion response.
55
Based on the existing work on tensioner performance from different scholars, it is found
56
that the internal friction is one of the key factors in the tensioner cylinder. But the simplified
57
friction model neglecting the effect of internal friction were mostly applied in these existing
58
work. Therefore, a reasonable tensioner simulation model taking account of the internal friction
59
of hydraulic cylinder is proposed specially for the current study. And based on this tensioner
60
model, a full platform-tensioner-riser coupling system is developed to study the effect of the
61
tensioner performance on the dynamic response of the platform and riser.
ACCEPTED MANUSCRIPT 62
1 Riser tensioner
63
There are two main types of tensioners currently used in deepwater drilling operations:
64
wire ropes tensioner (WRT) and direct-acting tensioner (DAT). However, due to the
65
complexity and limited payload ability of the WRT types, the DAT types with hydro-pneumatic
66
have become predominant in recent offshore field developments. The direct-acting tensioner
67
(DAT) eliminates the transmission devices such as pulleys and wire ropes. While the tension is
68
directly transmitted by the hydraulic cylinder piston rod, which brings advantages such as
69
strong stability and accurate compensation to DAT [14]. All analyses in the current work are
70
based on the direct-acting tensioner (DAT). A schematic diagram of the direct-acting tensioner
71
(DAT) is shown in Fig.1.
72 73
Fig.1 Schematic diagram of direct-acting tensioner (DAT)
74
The direct-acting tensioner (DAT) typically consists of hydro-pneumatic tensioner
75
cylinders, oil-gas accumulators, high-pressure gas vessels and low-pressure gas vessels. The
76
hydro-pneumatic tensioner cylinders provide almost constant tension to the riser in order to
77
counter the balance of the overall weight of the riser and tube-inside fluid. The internal piston
78
divides hydraulic cylinder into two parts: low-pressure pneumatic chamber and high-pressure
79
hydraulic chamber. The low-pressure chamber of the hydraulic cylinder is connected through a
80
pneumatic pressure line to the low-pressure gas vessels, which is mainly used to provide
81
damping effect and play the protective role of the riser tensioner system. The high-pressure
82
chamber of the hydraulic cylinder is connected through a hydraulic pressure line to the oil-gas
83
accumulators, which provides the tension for the riser. And the tension maintained by oil
84
pressure in this side of the hydraulic cylinder from the oil-gas accumulator is pressurized by
85
high-pressure gas vessels.
ACCEPTED MANUSCRIPT 86
2 The mathematical model of the riser tensioner system
87
The riser tensioner is a complicated structure composed of hydro-pneumatic and
88
mechanical subsystems. In order to simplify the analysis, principle hypothesizes of the current
89
work are as follows:
90
(1) Ignored the friction loss inside the oil/gas accumulator;
91
(2) Ignored the pressure loss inside the pressure line;
92
(3) Ignored the quality of the piston rod and the hydraulic fluid;
93
(4) Met the variation law of gas state and ignored the effect of the temperature.
94 95 96
2.1 Modelling of gas state variations Supposing that there is no heat transfer, the internal pressure variation of the high-pressure gas cylinder satisfies the following relation: π
97
ππ΄0ππ΄0 = ππ΄1ππ΄1
π
(1)
98
where, π is the adiabatic gas constant, which is 1.4 for nitrogen [3]; ππ΄0 is the initial pressure
99
in the high pressure gas vessels;ππ΄0 is the initial volume in the high pressure gas vessels; ππ΄1
100
is the pressure after considering the pressure variation in the high pressure gas vessels, and ππ΄1
101
is the volume after considering the volume variation in the high pressure gas vessels.
102
Considering that the hydraulic fluid is incompressible, it is thought that the gas volume
103
varies along with the motion of hydraulic cylinder piston. The volume variation in the high-
104
pressure gas vessels is expressed as follows:
105
(2)
βππ΄ = ππ΄1 β ππ΄0 = π΄π β π₯π
106
where, βππ΄ is the variation of gas volume in the system; π΄π is the cross sectional areas of the
107
piston at the rod-side, and π₯π is the displacement of the piston in the hydraulic cylinder.
108 109 110 111 112 113
Overall, the pressure variations βPA in a high-pressure cylinder due to the gas volume variation can be represented as:
(
βππ΄ = PA0 (1 β Ar * xp/VA0)
βπ
)
(3)
β1
Similarly, pressure variations βππ΅ in a low-pressure cylinder due to the gas volume variation can be represented as:
(
βππ΅ = ππ΅0 (1 β π΄π * π₯π/ππ΅0)
-π
)
β1
(4)
114
where, ππ΅0 is the initial pressure in the low pressure gas vessels, ππ΅0 is the initial volume in the
115
low pressure gas vessels, and π΄π is the cross sectional areas of the piston at the piston-side.
116
2.2 Modelling of internal friction in hydraulic cylinder
117
The hydraulic cylinder is an important part of tensioner, its internal friction performance
118
should not be ignored in the analysis process. In order to achieve the tensioner model, and to
119
ensure the condition in simulation is in conformity with the actual operating conditions, the
ACCEPTED MANUSCRIPT 120
friction model considering the "Stribeck effect" should be the preferred for such study. Based
121
on Xuan et al. [14]βs findings, the hydraulic cylinder has significant Stribeck effect when the
122
direction of piston movement changes. In hydraulic cylinder, the Stribeck effect occurs when
123
the hydraulic fluid contacts with the moving piston. When the piston velocity is smaller than
124
the Stribeck velocity (piston limit velocity), the friction decreases with the increase of the piston
125
velocity.
126
In the Stribeck model, the total friction πΉππ is simulated as a function of relative velocity
127
and pressure, and is assumed to be the sum of Stribeck, Coulomb, and viscous components. The
128
friction can be defined by two parts: the velocity-dependent part, πΉππ,π£, and the pressure-
129
dependent part, πΉππ,π. The total friction force and the two parts are defined as [7, 14, 15]:
130
πΉππ = πΉππ,π£ + πΉππ,π ππ£
131
πΉππ,π£ = (πΉπ + (πΉπ β πΉπ)ππ₯π( β |π£π|/π£π))π πππ(π£π) + ππ£π£π
132
πΉππ,π = ππ|πππ| = πΉπ
133
where, πΉπΆ is the Coulomb friction force; πΉπ is the static friction force;π£π is the piston velocity;
134
π£π is the piston limit velocity (Stribeck velocity) (|π£π| β€ 0.05π/π ) [14]; πππ is the pressure
135
difference; ππ£ is the viscous friction coefficient;ππ£ is the friction exponent (0 < ππ£ β€ 1) ,and
136
ππ is the linear coefficient.
(5)
137
In the velocity-dependent part (πΉππ,π£), the first term represents the Coulomb friction (πΉπΆ),
138
which is usually defined as a constant. The second term represents the mixed friction (also
139
known as Stribeck effect friction), which is expressed by the exponential function relation
140
between Static friction πΉπ and Stribeck velocity π£π (piston limit velocity). The third term is the
141
fluid dynamic fricti on (viscous friction), which is related to the viscous properties of the
142
hydraulic fluid. The pressure-dependent part (πΉππ,π) of the friction force represents the static
143
friction force.
144
2.3 Modelling of tension variations
145
In the direct-acting tensioner system, the tension is applied to the top of the riser through
146
the piston rod of the hydraulic cylinder. The tension πΉπ can be expressed as the sum of the
147
hydraulic force produced by the pressure difference between both sides of the cylinder piston
148
and the internal friction of the hydraulic cylinder, which is shown as follows:
149 150 151
πΉπ = πΉβπ¦π + πΉππ
(6)
The hydraulic force produced by the pressure difference between both sides of tensioner piston in the hydraulic-pneumatic cylinder πΉβπ¦π can be represented as:
152
πΉβπ¦π = πππ΄π β πππ΄π
153
where ππ is the pressure of the piston at the rod-side, π΄π is the cross sectional areas of the piston
(7)
ACCEPTED MANUSCRIPT 154
at the rod-side, ππ is the pressure of the piston at the piston-side, and π΄π is the cross sectional
155
areas of the piston at the piston-side. Based on the gas state variations in section 2.1, the pressure
156
difference between both sides of tensioner piston in the hydraulic-pneumatic cylinder also can
157
be represented as:
158
ππ = π
159
ππ = π
π΄0
+ βππ΄
π΅0
(8)
+ βππ΅
160
For a comprehensive consideration of the internal friction of the hydraulic cylinder, the
161
equation of force equilibrium on both sides of tensioner piston πΉπ in the hydraulic-pneumatic
162
cylinder can be reformulated as:
163
πΉπ = ππ΄0(1 β Ar * π₯π/VA0)
-π
π΄π - ππ΅0(1 β π΄π * π₯π/ππ΅0)
-π
π΄π + πΉππ
(9)
164
The tensioner is an important connection between the platform and riser, and its
165
performance will be affected by the relative movement between the platform and riser. However,
166
in the traditional tensioner analysis process, Pestana et al. [12] and Mao et al. [17] normally
167
used the platform motions as the input signal of the tensioner piston, which is not in accordance
168
with the actual operation conditions. Unlike those studies, the real time responses of the
169
platform and riser at the connected location are inputted to the tensioner to simulate the coupling
170
dynamic response of the tensioner with the platform and riser system in this paper. Therefore,
171
the calculation formula of the tensioner model in the simulation process can be rewritten by the
172
parametric formulation:
173 174
πΉπ = ππ΄0(1 β Ar * (π₯ππππ‘ππππ β π₯πππ ππ)/VA0)
-π
- ππ΅0(1 β π΄π β (π₯ππππ‘ππππ β π₯πππ ππ)/VB0)
Ar
-π
π΄π
175
+ (πΉπ + (πΉπ β πΉπ)ππ₯π( β |π£ππππ‘ππππ β π£πππ ππ|/π£π))π πππ(π£ππππ‘ππππ β π£πππ ππ)
176
+ ππ£(π£ππππ‘ππππ β π£πππ ππ) + ππ|πππ|
ππ£
(10)
177
where π₯ππππ‘ππππ and π£ππππ‘ππππ are the real time displacement and velocity of the connection
178
point between the platform and tensioner along the tensioner cylinder, respectively; π₯πππ ππ and
179
π£πππ ππ are the real time displacement of the connection point between the riser and tensioner
180
along the tensioner cylinder, respectively. These parameters can be extracted dynamically by
181
user subroutines from ANSYS-AQWA result file. The schematic diagram of the tensioner
182
between the platform and riser is shown in Fig.2.
ACCEPTED MANUSCRIPT
183 184 185
Fig.2 The schematic diagram of the tensioner between the platform and riser
3 Performance of the tensioner system
186
Based on the mathematical model for each components of the tensioner system, the
187
tensioner performance can be simulated by using MATLAB program to study the effect of the
188
internal friction of the hydraulic cylinder on the tension variations. The direct-acting tensioner
189
used on the βHYSY-981β deepwater semi-submersible drilling platform was taken as an
190
example for the current study. The input piston stroke signal of the tensioner cylinder is
191
consisted of a cyclostationary sinusoidal signal. Assuming that the sinusoidal signal is with an
192
amplitude of 5 meters and time period of 10 seconds, while the piston is in the mid-stroke at
193 194
the initial time, the basic parameters of the tensioner system are shown in Table 1. Table.1 Hydro-pneumatic tensioner system data Parameter
Value
unit
Initial volume of high-pressure gas vessels ππ΄0
9380
L
Initial pressure of high-pressure gas vessels ππ΄0
11.2
MPa
Initial volume of low-pressure gas vessels ππ΅0
2250
L
Initial pressure of low-pressure gas vessels ππ΅0
0.1
MPa
Stroke-length of cylinders π₯π
Β± 7.62
m
Piston diameter π΄π
560
mm
ACCEPTED MANUSCRIPT
195
Piston rod diameter π΄π
230
mm
Density of hydraulic oil
850
kg/m3
Viscosity of hydraulic oil
84.2416
cSt(10-6 m2/s)
3.1 Analysis of internal friction effect in hydraulic cylinder
196
In the tensioner system, the internal friction of hydraulic cylinder is closely related to the
197
piston movement and frictional pressure drop. Based on eq.(5), we compiled the MATLAB
198
program to analyze the variation of internal friction in the hydraulic cylinder. The values of the
199
corresponding parameters are as follows: the limit velocity of the piston in the hydraulic
200
cylinder is 0.05m/s, the pressure drop due to friction is 2bar, the Coulomb friction coefficient
201
is 0.5, the viscous friction coefficient is 65818Ns/m and the viscous friction index is 1. The
202
calculation results are shown in Fig.3 and Fig.4.
203
Fig.3 shows the variation of the friction with the piston velocity. The total internal friction
204
of the hydraulic cylinder is mainly composed of three parts: the pressure-dependent friction,
205
the viscous friction and the Stribeck effect friction. As shown in Fig.3, the pressure-dependent
206
friction is a constant regardless of the piston velocity. The viscous friction increases linearly
207
with the increase of piston velocity. And the Stribeck effect friction is closely related to the
208
limit velocity of the piston. When the piston velocity is lower than a certain value (0.05m/s),
209
the total friction force increases with the decrease of the piston velocity due to the Stribeck
210
effect. When the piston velocity equals to 0, the velocity changes from a positive value to a
211
negative one, and the total friction also changes abruptly from a positive value to a negative
212
one.
213
Fig.4 shows the variation of Stribeck effect friction and piston velocity with time. As
214
shown in Fig.4, the Stribeck effect friction decreases with increasing piston velocity until piston
215
velocity goes beyond the limit, after which the Stribeck effect friction keeps as a constant. In
216
addition, the Stribeck effect friction reaches the maximum when the piston velocity is zero and
217
changes suddenly when the direction of velocity changes. 3
105
2
Friction[N]
1 0 -1
Total friction Viscous friction Pressure-dependent friction Stribeck friction
-2
218
-3 -4
-3
-2
-1 0 1 Piston velocity[m/s]
2
3
4
ACCEPTED MANUSCRIPT Fig.3 Relation between internal friction of the hydraulic cylinder and piston velocity 104
Stribeck effect friction[N]
5
Stribeck effect friction Piston velocity
0
-5
220 221 222
5
0
0
2
4
6
8
Piston velocity[m/s]
219
-5 10
Time [s]
Fig.4 The variation of Stribeck effect friction and piston velocity with time
3.2 Performance of the tensioner system under cyclic displacement
223
The reciprocating motion of the piston is regarded as cyclic displacement in the current
224
study. In the analysis of tensioner system, we take the down-stroke as positive and take the up-
225
stroke as negative, respectively. In order to analyze the influence of internal friction of hydraulic
226
cylinder, the tensioner models considering separately the state variation of gas and internal
227
friction of hydraulic cylinder are developed specially in the current work. The simulated
228
tension-stroke curve at the piston side chamber of a single cylinder in the tensioner system is
229
shown in Fig.5.
230
Firstly, when the tension is assumed to be related to the state variation of gas only, the
231
relation between the tension and the piston stroke is shown in Curve 1 (Fig.5). As shown by
232
Curve 1, the relationship between the tension and the piston stroke is nonlinear. So the tensioner
233
model considering only the state variation of gas is named as nonlinear tensioner model. When
234
the piston is displaced upward with respect to the cylinder housing, it will cause the hydraulic
235
fluid to flow from the accumulator to the hydraulic cylinder. Meantime, the pressure of the
236
high-pressure hydraulic chamber will be reduced and the tension will be reduced accordingly.
237
Otherwise, the pressure of the high-pressure hydraulic chamber will be increased and the
238
tension will be increased accordingly. In addition, calculation results show that the tension
239
ranges from 1.9MN to 2.68MN under a given piston dynamic stroke (from -5 m to 5 m).
240
Secondly, when the tension is assumed to be also related to the internal friction of the
241
hydraulic cylinder, the relation between the tension and the piston stroke is shown in Curve 2
242
(Fig.5). As shown by Curve 2, the relationship between them is similar to a hysteretic curve.
243
The tensioner model of considering internal friction of hydraulic cylinder is thus named as
244
hysteretic tensioner model. And the time-history curve of tension and piston displacement under
245
the single cylinder of hysteretic tensioner model are shown in Fig.6. When the piston is
246
displaced upward with respect to the cylinder housing, the tension will be reduced with the
ACCEPTED MANUSCRIPT 247
internal friction of the hydraulic cylinder. Otherwise, the tension will be increased when the
248
piston is displaced downward with respect to the cylinder housing. In addition, when the piston
249
stroke reaching stop positon, the tension will have the sudden change due to the viscous friction
250
of tensioner cylinder. And the tension has opposite change with piston movement when the
251
piston velocity is lower than the limit value. This result was caused by the impact of the Stribeck
252
effect friction of the tensioner cylinder. 106 2.8
Tension[N]
2.6 2.4 2.2 2 1.8 1.6
253
5
Fig.5 Simulation of tension-stroke curve in piston-side chamber for single tensioner cylinder 106
Tension[N]
6
2.7
4
2.5
2
2.3
0
2.1
-2
1.9
Tension -4 Piston displacement Piston velocity -6 30 35 40
1.7
256
0
Pistion Stoke[m]
2.9
255
-5
0
5
10
15
20 Time[s]
25
Piston velocity[m/s] Piston displacement[m]
254
1 Nonlinear tensioner model 2 Hysteresis tensioner model
Fig.6 The variation trend of tension and piston displacement under single tensioner cylinder 15% Total friction Stribeck friction Viscous friction Pressure-dependent friction
Tension loss/Tension
10% 5% 0 -5% -10% -15%
257 258
0
2
4
6
8
10
Time[s]
Fig.7 Variation of tension loss due to internal friction of hydraulic cylinder
259
The internal friction of hydraulic cylinder contributes to the tension loss. The friction
260
caused tension loss expressed as a percentage of the total tension is shown in Fig.7. It shows
261
that the tension loss due to the internal friction of hydraulic cylinder is up to 13.6% of the total
ACCEPTED MANUSCRIPT 262
tension. Among this 13.6% tension loss, 10.4% is due to the viscous friction, while the
263
contribution of the Stribeck effect friction and pressure-dependent friction is similar with a
264
proportion of 2.1% and 2.2%, respectively. Based on the current results, it can be concluded
265
that the internal friction can not be omitted in the performance analysis of tensioner.
266
4 Response analysis of platform-tensioner-riser coupling system
267
Based on the tensioner mathematical model established in the previous section 2, the
268
platform-tensioner-riser coupling system was established by implementing the tensioner system
269
model into commercial software ANSYS-AQWA through user subroutines written in
270
PYTHON scripts. In the ANSYS-AQWA module, the platform geometry model can be created
271
in Workbench using Design Modeler, the riser string is modeled by the Tethers Connections,
272
and the tensioner can be joined between the platform and the riser string by the external force
273
calculation program. A full platform-tensioner-riser coupling system is thus developed and the
274
effect of the performance of the tensioner on platform and riser dynamic response is simulated.
275
4.1 Model dimensions and wave conditions
276
The current study takes the βHYSY-981β deepwater semi-submersible drilling platform as
277
an example to analyze the dynamic response of the platform-tensioner-riser coupling system.
278
In accordance with the demands of actual drilling operation, the normal operating wave
279
conditions which is extensively applied in South China Sea is chosen for the study. Meanwhile,
280
in order to check the applicability of the tensioner used in the coupling system, the overall
281
dynamic response under different regular waves and irregular waves is analyzed. The
282
corresponding wave condition parameters are shown in Table.2. The overall model of the
283
platform and the riser system has been established in the hydrodynamic analysis software
284
ANSYS-AQWA. In ANSYS-AQWA hydrodynamic analysis, the Schematic of drilling
285
platform model is shown in Fig.8. And the principal dimensions of drilling platform and riser
286
system are shown in Table.3 and Table.4 Here the catenary mooring are adopted and the
287
parameters of mooring system are shown in Table.5 and Table.6.
288
ACCEPTED MANUSCRIPT 289 290
Fig.8 Schematic of drilling platform model Table.2 Wave conditions parameters Case
Wave Type
Wave amplitude
Wave period
Wave direction
Regular waves1
Stokes Wave
5m
10s
0ΒΊ
Regular waves2
Stokes Wave
5m
15s
0ΒΊ
Irregular waves 291
P-M spectrum 5m 10s Table.3 Boundary conditions for semisubmersible Parameter
Value
unit
Operation depth
1500
m
Length
114.07
m
Breadth
78.68
m
Deep
38.6
m
0ΒΊ
Draft 19 m Table.4 Riser system data
292
Parameter
Value
unit
Length of the riser
1500
m
Internal diameter of the riser
0.508
m
External diameter of the riser
0.5334
m
Density of the riser
7850
kg/m3
293
Table.5 Mooring cable material properties Cable type
Diameter
Mass/Unit Length
Maximum Tension
Stiffness, EA
Steel cable
140 mm
97 kg/m
1.693e10 N
1.74e9 N
Polyester cable
175 mm
294
23 kg/m 1.0e10 N Table.6 Length of mooring cable
3.0e8 N
Angle
Length of upper steel cable
Length of polyester cable
Length of lower steel cable
45Β°
90 m
1944.7 m
90 m
295
By the coupling dynamic response analysis, the vertical movement between the platform
296
and the riser, and the tension on the top of the riser, are analyzed to investigate the performance
297
of the hysteretic tensioner model under regular waves1. Fig.9 and Fig.10 present the vertical
298
relative movement of the platform and the riser, and the tension on the top of the riser under
299
regular waves1, respectively. The results show that the tension does change with the relative
300
movement in real time. When the platform moves upward relative to the riser, the riser tension
301
increases with the relative displacements. In addition, Fig.10 shows that the tension increases
302
with decreasing relative velocity value when the velocity is close to 0 and has a sudden change
ACCEPTED MANUSCRIPT 303
when the relative velocity is 0. This is similar to the variation trend shown in Fig.6. And the
304
main difference between the two graphs (Fig.10 and Fig.6) is that the scope of the suddenly
305
changed tension in Fig.10 takes a larger proportion of the total tension variation when compared
306
to that shown in Fig.6. The reason of this difference is that the range of relative displacement
307
and relative velocity are smaller than the range of piston stroke and piston velocity in Fig.6. 6
Tension Relative displacement
Tension[N]
6.6
7
6.2
6.5
6
6 5.5
5.6 800
820
840
860
880
900
920
940
960
980
5 1000
Time[s]
Fig.9 The variation trend of tension with relative displacement under regular waves1 6.8
106 Tension Relative velocity
Tension[N]
6.65
0.8 0.6
6.5
0.4
6.35
0.2
6.2
0
6.05
-0.2
5.9
-0.4
5.75
-0.6
5.6 800
820
840
860
880
900
920
940
960
980
Relative velocity[m/s]
309
7.5
6.4
5.8
308
8
Relative displacement[m]
10
6.8
-0.8 1000
310
Time[s]
311
Fig.10 The variation trend of tension with relative velocity under regular waves1
312
Based on the traditional nonlinear tensioner model, the overall dynamic response of the
313
two different tensioner models are compared and analyzed. Fig.11a shows the vertical relative
314
displacement variation based on the two different tensioner models. As shown in Fig.11a, the
315
time-history curves of the relative displacement from different tensioner models are similar.
316
And the scope of vertical relative displacement from the nonlinear tensioner model is slightly
317
smaller than that from the hysteretic tensioner model. It can be concluded that the hysteretic
318
tensioner also can compensate the relative movement between the platform and the riser as the
319
nonlinear tensioner. Unlike the variation of vertical relative displacement, the tension variation
320
from the two tensioner models has a great difference. As shown in Fig.11b, the tension provided
321
by the hysteretic tensioner model and the nonlinear tensioner model varied from 5.728MN to
322
6.605MN and from 5.948 MN to 6.397MN under the regular waves1, respectively. It shows
323
that the variation range of the tension from the hysteretic tensioner model is larger than that
ACCEPTED MANUSCRIPT 324
from the nonlinear tensioner model. And Fig.11b also shows that the tension will has a sudden
325
change for the hysteretic tensioner model due to the internal friction of the tensioner cylinder,
326
which has an impact on the fatigue life of the riser. In addition, Fig.11c shows the relation
327
between tension and relative displacement based on different tensioner models. As shown in
328
Fig.11c, the variation curves of tension with the relative displacement for both the nonlinear
329
tensioner model and the hysteretic tensioner model are identical with the original curves shown
330
in Fig.5. 8
Relative displacement[m]
7.5 7 6.5 6 5.5
331 332
Hysteresis tensioner model Nonlinear tensioner model
5 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.11a Relative displacement variation under different tensioner models 106
6.7
Hysteresis tensioner model Nonlinear tensioner model
6.6 6.5
Tension[N]
6.4 6.3 6.2 6.1 6 5.9 5.8
333 334
5.7 800
820
840
860
880
900
920
940
960
980
1000
Time[s]
Fig.11b Tension variation under different tensioner models 6
10
6.8
Tension[N]
6.6 6.4 6.2 6 Hysteresis tensioner model Nonlinear tensioner model
5.8 5.6
335 336
5
5.5
6
6.5
7
7.5
8
Relative displacement[m]
Fig.11c Variation of tension with relative displacement under different tensioner models
337
In order to confirm the applicability of the hysteretic tensioner model under different wave
338
conditions. The overall coupled dynamic response under different wave periods is analyzed.
ACCEPTED MANUSCRIPT 339
Fig.12a and Fig.12b present the vertical relative movement variation of the platform and the
340
riser, and the tension variation under different regular waves, respectively. It turned out that the
341
variation scope of the relative displacement and the tension under regular waves1 are larger
342
than that under regular waves2. Under the regular waves2, the relative displacement varied
343
from 2m to 10.5m and the tension varied from 5.19MN to 7.15MN, and the tension does change
344
with the relative movement in real time. In addition, compared with the stroke range of the
345
tensioner piston, it can also be found that the relative displacement variation under regular
346
waves2 is in a reasonable scope. These results indicated that the hysteretic tensioner model can
347
effectively compensate the relative movement between the platform and the riser under the
348
regular waves2.
Relative displacement[m]
12
8 6 4 2 0 800
349 350
Regular waves1 Regular waves2
10
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.12a Relative displacement variation under different regular waves 7.5
106 Regular waves1 Regular waves2
Tension[N]
7 6.5 6 5.5
351 352 353
5 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.12b Tension variation under different regular waves
4.3 Coupled dynamic response analysis under irregular waves
354
Aimed at the random characteristics of the wave conditions in the actual operation process.
355
The coupling dynamic response such as the vertical movement between the platform and the
356
riser, and the tension on the top of the riser are analyzed for the hysteretic tensioner model under
357
the irregular waves. The selected irregular waves type in this paper is Pierson-Moskowitz
358
spectrum. The corresponding wave parameters of Pierson-Moskowitz spectrum is shown in
359
Table.2 and the wave spectrum curve of the Pierson-Moskowitz spectrum is shown in Fig.13.
ACCEPTED MANUSCRIPT 360
The results of the coupled dynamic response analysis are shown in Fig.14 and Fig.15. The
361
results also show that the tension does change with the relative movement in real time. As
362
shown in Fig.14, the tension reaches maximum when the value of vertical relative displacement
363
between the platform and the riser reaches maximum. The corresponding tension and relative
364
displacement varied from5.635MN to 6.579MN and from 4.85m to 7.3m, respectively. Fig.15
365
shows the variation trend of tension and relative velocity under irregular waves. In addition,
366
comparing the result with the regular waves, it shows that the variation law of Fig.15 is
367
identical to the Fig.10. 35
Spectral density (m 2/Hz)
30 25 20 15 10 5 0
368
0.1
0.15
0.2
0.25
0.3
0.35
Fig.13 The wave spectrum curve of Pierson-Moskowitz spectrum
6.4
7
6.1
6
5.8
5
5.5 800
820
840
860
880
900
920
940
960
4 1000
980
Time[s]
Fig.14 The variation trend of tension and relative displacement under irregular waves
Tension[N]
106
0.8
6.55
0.6
6.4
0.4
6.25
0.2
6.1
0
5.95
-0.2
5.8
-0.4 Tension Relative velocity
5.65
373
8
Tension Relative displacement
Relative displacement[m]
Tension[N]
106
6.7
372
0.4
Frequency(Hz)
6.7
370 371
0.05
5.5 800
820
840
860
880
900 920 Time[s]
940
960
980
Relative velocity[m/s]
369
0
-0.6
-0.8 1000
Fig.15 The variation trend of tension and relative velocity under irregular waves
374
Based on the overall dynamic response analysis under the irregular waves, the calculation
375
results based on the two different tensioner models under irregular waves are compared. Fig.16a
ACCEPTED MANUSCRIPT 376
and Fig.16b show the relative displacement variation and the tension variation from analyses
377
using the two different tensioner models, respectively. It can be found that the time-history
378
curves of the relative displacement for the two different tensioner models under irregular waves
379
are similar to those results under regular waves. This result shows that the hysteretic tensioner
380
model can be applied in different wave conditions. Similarly, under the irregular waves, the
381
hysteretic tensioner model also has a great scope of tension variation than the nonlinear
382
tensioner model. As shown in Fig.16b, the tension provided by the hysteretic tensioner model
383
and the nonlinear tensioner model varied from 5.635MN to 6.579MN and from 5.826 MN to
384
6.356MN under the irregular waves, respectively. Fig.16c shows the variation trend of the
385
vertical relative displacement with tension from analyses using the two different tensioner
386
models. And the relations between tension and relative displacement for the different tensioner
387
models are identical to that shown in Fig.11c. In addition, compared with the periodic dynamic
388
response under regular waves1, the tension variation under the irregular waves is random
389
variation. Due to the existence of the high-frequency component under the irregular waves, the
390
tension would change suddenly several times in a relatively short period, which put forward
391
higher requirement for the fatigue life of the tensioner and riser. 7.5
Relative displacement[m]
7 6.5 6 5.5 5 4.5 4 800
392 393
Hysteresis tensioner model Nonlinear tensioner model 820
840
860
880
900
920
940
960
980
1000
Time[s]
Fig.16a Relative displacement variation under different tensioner models 6.6
106
Tension[N]
6.4
6.2
6
5.8 Hysteresis tensioner model Nonlinear tensioner model
394 395
5.6 800
820
840
860
880
900 Time[s]
920
940
960
980
1000
Fig.16b Tension variation under different tensioner models
ACCEPTED MANUSCRIPT 106
6.6
Tension[N]
6.4
6.2
6
5.8
5.6
396 397 398
Hysteresis tensioner model Nonlinear tensioner model 4
4.5
5
5.5 6 Relative displacement[m]
6.5
7
7.5
Fig.16c Relation between tension and relative displacement under different tensioner models
5 Conclusions and future studies
399
In this paper, the mathematical model of the direct acting riser tensioner system was
400
developed to analyze the impact of internal friction of hydraulic cylinder on the tensioner
401
performance. The platform-tensioner-riser coupling system was established by implementing
402
the tensioner system model into commercial software ANSYS-AQWA through user
403
subroutines written in PYTHON scripts. The overall coupling dynamic response of the system
404
under different wave conditions was investigate. As a result of the analysis, some significant
405
conclusions can be drawn as follows:
406
(1) For the tensioner considering the internal friction of the hydraulic cylinder, the
407
relationship between tension and piston stroke is not a simple nonlinear relationship
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but a hysteretic loop relationship. Moreover, when the piston stroke reaching stop
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positon, the tension will have the sudden change due to the viscous friction of
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tensioner cylinder. And due to the Stribeck effect friction, the tension will have
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opposite change with piston movement when the piston velocity is lower than the limit
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value.
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(2) By comparing the calculation results from different tensioner models, the scope of
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vertical relative displacement under the nonlinear tensioner model is slightly smaller
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than that for the hysteretic tensioner model. The scope of the tension under the
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hysteretic tensioner model is larger than that for the nonlinear tensioner. And the
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tension also has a sudden change under the hysteretic tensioner model due to the
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internal friction of the tensioner cylinder. In addition, due to the existence of the high-
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frequency component under the irregular waves, the tension of the hysteretic tensioner
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model will complete more sudden changes in a relatively short period, which has an
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impact on the fatigue life of the riser and tensioner.
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In this study, a tensioner model considering internal friction of hydraulic cylinder is
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established, which is more consistent with the working condition. And by using the ANSYS-
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AQWA, the overall coupling dynamic response can be really simulate under the normal
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operating conditions. In the future work, the emergency disconnection of the riser under
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dangerous conditions will be analyzed. The model is further verified by analyzing the overall
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dynamic response during the emergency disconnection of the riser.
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References
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[1] Chakrabarti, S., 2005. Handbook of Offshore Engineering.
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[2] Von, D. O.C.B., Ankargren, D.B.J., 2015. Riser tensioner.
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[3] GrΓΈnevik, A., 2013. Simulation of drilling riser disconnection - Recoil analysis. Institutt
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for Marin Teknikk.
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[4] Yang, C.K., Kim, M., 2010. Linear and Nonlinear Approach of Hydropneumatic Tensioner
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Modeling for Spar Global Performance. Journal of Offshore Mechanics and Arctic
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Engineering 132 (1), 011601.
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[5] Zhang, L., Chang, Y., Liu, X., Liu, K., Yang, H., 2013. AMESim-based Modeling and Simulation of Platform Riser Tensioner. China Petroleum Machinery. [6] Andersson, S., SΓΆderberg, A., BjΓΆrklund, S., 2007. Friction models for sliding dry, boundary and mixed lubricated contacts. Tribology International 40 (4), 580-587.
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[7] Lee, H., Roh, M.I., Ham, S.H., Ha, S., 2015. Dynamic simulation of the wireline riser
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tensioner system for a mobile offshore drilling unit based on multibody system dynamics.
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Ocean Engineering 106, 485-495.
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[8] Chen, B., Yu, J., Yu, Y., Xu, L., Wu, H., Li, Z., 2018. Modeling Approach of
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Hydropneumatic Tensioner for Top-Tensioned Riser. Journal of Offshore Mechanics and
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Arctic Engineering 140 (5), 051706.
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[9] Gupta, H., Nava, V., Banon, H., Gkaras, V., Spanos, P., 2008. Determination of Riser
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Tensioner Properties From Full-Scale Data, ASME 2008 International Conference on
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Offshore Mechanics and Arctic Engineering, pp. 389-396.
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[10]Wang, K.P., Xue, H.X., Tang, W.Y., 2012. Numerical simulation of hydropneumatic
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tensioner for coupled deepwater platform system. Journal of Shanghai Jiaotong University
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46 (10), 1652-1657.
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[11]Kang, H.S., Kim, M.H., Aramanadka, S.S.B., 2017. Tension variations of hydro-pneumatic
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riser tensioner and implications for dry-tree interface in semisubmersible. 7 (1), 21-38.
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[12]Pestana, R.G., Roveri, F.E., Franciss, R., Ellwanger, G.B., 2016. Marine riser emergency
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disconnection analysis using scalar elements for tensioner modelling. Applied Ocean
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Research 59, 83-92.
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[13]Haziri, S., Dyngvold, Γ., 2011. Development of simulation model for virtual testing and design of a riser tensioner system. [14]Xuan, B.T., Hafizah, N., Yanada, H., 2012. Modeling of dynamic friction behaviors of hydraulic cylinders. Mechatronics 22 (1), 65-75. [15]Marton, L., Lantos, B., 2007. Modeling, Identification, and Compensation of Stick-Slip
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Friction. IEEE Transactions on Industrial Electronics 54 (1), 511-521.
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[16]Mao, L., Liu, Q., Zhou, S., Wang, G., Fu, Q., 2016. Deep water drilling riser mechanical
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behavior analysis considering actual riser string configuration. Journal of Natural Gas
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ACCEPTED MANUSCRIPT Highlights ο¬ Development of a hysteretic tensioner model with the Stribeck effect. ο¬ Development of mathematical equations for tensioner model based on the real time movement of platform and riser. ο¬ Investigation on the dynamic response of the platform-tensioner-riser coupling system by implementing the hysteretic tensioner model into ANSYS-AQWA. ο¬ Study on the performance of the tensioner under different wave conditions.