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NO 976 802 357 MVA · BANK 9494 05 00103
PAGE 1
Vibration Analysis of Gas Lift Compressor
Foundation Table of contents
1. INTRODUCTION........................................................................................................ 2
1.1. Scope of work ..................................................................................................... 2
2. DESIGN BASIS ........................................................................................................... 3
2.1. Design Loads....................................................................................................... 3
2.2. Analysis Combinations........................................................................................ 4
3. STRENGTH ANALYSIS............................................................................................. 7
3.1. Analysis tool ....................................................................................................... 7
3.1.1. SOLID187 ............................................................................................... 7
3.2. Geometry ............................................................................................................ 7
3.3. Boundary conditions............................................................................................ 8
3.3.1. Single degree of freedom.......................................................................... 9
3.3.2. Two degree of freedom ...........................................................................11
4. RESULTS ...................................................................................................................13
4.1. Combination 101 ................................................................................................13
4.2. Combination 102 ................................................................................................15
4.3. Combination 103 ................................................................................................17
4.4. Combination 104 ................................................................................................20
5. DISCUSSION OF RESULTS......................................................................................23
5.1. Displacements analsysis .....................................................................................23
5.2. Natural frequency ...............................................................................................23
5.3. Furthe.................................................................................................... r work: 23
6. REFERENCES............................................................................................................24
1. APPENDIX 1: NATURAL FREQUENCY PLOTS.....................................................25
1.1. Load Combination 103 .......................................................................................25
1.2. Load Combination 104 .......................................................................................30
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1. INTRODUCTION
On the FPSO Petrojarl 1 the Gas Lift Compressor Skid has shown weaknesses in its foundation,
causing excess loads in the axle between the El-Motor and the Compressor Unit
1.1. SCOPE OF WORK
The scope of work as given by Petrojarl is as follows /ref 10/
Item Description Comment
1 Static deflection of compressor skid in
operating mode with the old el-motor
fitted.
The objective of representing real-life
deflections by the analysis model should
be reversed. The real-life deflection
measurement should rather be used to
calibrate the analysis model
2 Static deflection of compressor support
frame
The support frame will be modeled
according to ref. /4/
3 Static deflection of compressor skid
without and with spring supports on el-
motor
The objective is to determine the
behavior of the structure
4 Harmonic response analysis for the third
condition
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2. DESIGN BASIS
The compressor skid is located in the process area of the vessel and the geometry analyzed is
based on drawing refs./1/,/2/,/3/,/4/ and /5/
2.1. DESIGN LOADS
Magnitude Reference Comment
1. Self weight of
skid
19.642.00 kg Ansys model
2. Self weight of
skid motor
4.484 kg Ansys model
3. Self weight of the
foundations
18.823 kg Ansys model
4. New el-motor 11.112 kg Ref. /6/ Applied as point mass on
the el-motor foundation
5. New el-motor
with springs
11.112 kg Ref. /6/ Defined as structural
element connected to the el-
motor foundation by means
of springs supports
6. Compressor 17.576 kg Ref. /6/ Applied as point mass on
compressor foundation
7. Tank V-4 3.820 kg Ref. /6/ Applied as point mass
directly on the skid
8. Tank V-1 4.400 kg Ref. /6/ Applied as point mass on
the skid
9. Precooler 2.097 kg Ref. /6/ Applied as point mass on
the support frame in ref. /5/
10. I.C. 1 2.000 kg Ref. /6/ Applied as point mass on
the support frame in ref. /5//
11. Aftercooler 2.426 kg Ref. /6/ Applied as point mass on
the support frame in ref. /5/
12. Heat Exchanger 4.316 kg Ref. /6/ Applied as point mass
directly on the skid
13. El.motor reaction
on operating
mode
+/- 16,8 kN Ref. /6/ Applied as reactions force
on the el-motor foundation
14. El.motor velocity ≈15 Hz (94,2 rad/s) For calculation of the
stiffness of the springs
supports
The point mass coordinates are defined in terms of the centroid coordinate of the element. In the
case of the load 5, the el-motor is defined by a box with 1,51m x 3,66m x 2 m.
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2.2. ANALYSIS COMBINATIONS
The load combinations are based on the scope of work and are as follows:
Combination Load
101 102 103 104
1. Self weight of skid x x x x
2. Self weight of skid motor x x x x
3. Self weight of the foundations x x
4. New el-motor x x
5. New el-motor with springs x x
6. Compressor x x x x
7. Tank V-4 x x x x
8. Tank V-1 x x x x
9. Precooler x x x x
10. I.C. 1 x x x x
11. Aftercooler x x x x
12. Heat Exchanger x x x x
13. El-motor velocity x x x x
For each combination, the static and modal analyses were performed. For the modal analysis, the
frequency range to check was set between 0 and 20 Hz, as the el-motor operates approximately
at 15 Hz. The analysis was set to check the 10 first modes.
The following figures show how the loads have been applied in the different combinations
Figure 1 – Load Combination 101.
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Figure 2 – Load Combination 102.
Figure 3 – Load Combination 103.
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Figure 4 – Load Combination 104.
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3. STRENGTH ANALYSIS
3.1. ANALYSIS TOOL
The strength analysis will be performed using ANSYS finite element software
3.1.1. SOLID187
SOLID187 is a higher order 3-D, 10-node solid element that exhibits quadratic displacement
behavior and is well suited to modeling irregular meshes. The element is defined by ten nodes
having three degrees of freedom at each node, translations in the nodal x, y, and z directions. The
element supports plasticity, hyperelasticity, creep, stress stiffening, large deflection, and large
strain capabilities. It also has mixed formulation capability for simulating deformation of nearly
incompressible elastoplastic materials, and fully incompressible hyperelastic material.
Figure 5 Solid 187 element
3.2. GEOMETRY
The Gas Lift Compressor skid was modeled in Solidworks according to dwg Oil & Gas Supply
Company dwg 0100 rev 01 ref./1/. The foundation for the el-motor and the compressor was
modeled in Solidworks according to Oil & Gas Supply Company dwg 0101 rev 0 ref /2/. The
skid foundation was modeled in Solidworks according to ref. /3/ and /4/.
The spring support properties and areas have defined in agreement with the Stop-Chock model
SP656, as shown in and Figure 6 (see ref. /7/).
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Figure 6 – Stop-Chock SP656 model.
3.3. BOUNDARY CONDITIONS
To determine the stiffness coefficient of the spring, we assume two vibrations systems (see
Figure 7):
a) The isolations springs are locate only between the skid and the foundations (single degree
of freedom)
b) The are isolation spring between the El.motor and the skid (two degrees of freedom)
In all cases, it is assumed that the weight of the structure is uniformly distributed on the spring.
All damping effect has been neglected.
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Mtotal
Foundations
ksupport Springs supports
Mmotor
Foundations
Springs supports
ksupport
Kskid
mskid
a) b)
Figure 7 – Vibrations isolation systems: a) single degree of freedom; b) two degrees of freedom.
3.3.1. Single degree of freedom
The stiffness of the isolation system can be obtained as (ref. /8/):
ksupport
ω motor2
Mtotal⋅ T⋅
1 T+( )2.1 10
5×
N
mm==
where
• T 50%= is the fraction of the forcing excitation that is transmitted to the support structure
(foundation)
• Mtotal 71873 kg= is the total mass of the structure,
• ω motor 2 π⋅ fmotor⋅ 94.2rad
s⋅== and fmotor 15 Hz⋅= are respectively the angular frequency
and the natural frequency of the El.motor
Considering that we have 41 springs, each spring constant should be
ks
ksupport
415190
N
mm⋅==
and maximum static deflection is:
δs
Mtotal g⋅
ks 41⋅3.3 mm⋅== ;where g is the standard earth gravity
Therefore the frequency o the system is:
fn1
2 π⋅
ksupport
Mtotal
⋅ 8.7 Hz⋅==
However, the maximum frequency that the springs can support is fs 6Hz= , consequently, the
maximum transmissibility is defined as (ref. /8/):
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T1
1fmotor
fs
2
−
219 %⋅==
Therefore
ksupport
ω motor2
Mtotal⋅ T⋅
1 T+( )1 10
5×
N
mm⋅==
For each spring, the constant is
ks
ksupport
412491.4
N
mm⋅==
and maximum static deflection is:
δs
Mtotal g⋅
ks 41⋅6.9 mm⋅==
Figure 8 shows the plot of the transmissibility function:
Tf ω( )ksupport
ksupport Mtotal ω2
⋅−
=
A good isolation system is obtained when the transmissibility T is less than one,
0 5 10 15 200.1
1
10
100
Transmissibility Curve
Frequency (Hz)
Tra
nsm
issi
bil
ity
1
fmotor
Figure 8 – Transmissibility curve
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3.3.2. Two degree of freedom
In this analysis the El.motor is separated from the structure by an isolation system, while the skid
structure is assume as an inertial block (see Figure 7).
Therefore, to determine the stiffness of the spring under the El.motor, first we have to determine
the maximum transmissibility of the motor as:
Tmotor1
1fmotor
fs
2
−
219 %⋅==
where fs 6Hz= is the maximum frequency that the springs can support and fmotor 15 Hz⋅= is
the frequency of the motor. Consequently, the stiffness of the isolation spring of system
El.motor-skid is:
Kskid
ω motor2
Mmotor⋅ Tmotor⋅
1 Tmotor+15792.6
N
mm⋅==
Considering that there are 4 spring beneath the El.motor, each spring constant should be
kskid
Kskid
43948
N
mm⋅==
and maximum static deflection is
δmotor
Mmotor g⋅
kskid 4⋅6.9 mm⋅==
Considering that the mass of the flexible system is mflexible Mtotal Mmotor− 60761 kg== ,
the transmissibility ratio of force transmitted to the foundation is (ref. /8/):
Tflexible
ksupport− Kskid⋅
Kskid Mmotor ω2
⋅−
Kskid ksupport+ mflexibleω
2⋅−
⋅ Kskid
2−
4.6 %⋅==
Figure 9 shows the comparison between the single and two degrees of freedom. As can be
observed, the presence of the second isolation system provides better vibration isolation
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0 5 10 15 200.01
0.1
1
10
100
1 103
×
Single degree system
Two degree system
Frequency (Hz)
Tra
nsm
issi
bil
ity
1
fmotor
Figure 9 – Transmissibility for the El.motor
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4. RESULTS
4.1. COMBINATION 101
The following pictures shows the displacement plot of the structure
Figure 10 – Displacement for combination 101
The maximum reaction force found in the springs is 6.25 kN and are locate beneath the tank
position. Figure 11 shows the plot of the force on the springs, (the positive axis y correspond to
the positive axi z in the Figure 10)
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Spring Force (kN)
3.52 4.33 5.21 5.89 6.25 6.02 5.07 3.89 3.64 3.43 3.00 2.42 1.68 0.88
3.39 5.79 4.97 3.06 0.76
3.27 5.67 5.88 5.02 3.33 0.95
3.22 4.02 4.90 5.59 6.00 5.85 5.02 4.04 4.04 4.01 3.69 3.14 2.37 1.46
5.93
5.91
-2000
-1500
-1000
-500
0
500
1000
1500
2000
-20000 -15000 -10000 -5000 0
Figure 11 – Spring reaction on combination 101.
The table below shows the frequency of the first modes
Table 1 – Frequency results combination 101
Mode Frequency
Hz
mode 1 8.28
mode 2 9.11
mode 3 10.34
mode 4 11.05
mode 5 14.88
mode 6 16.02
mode 7 17.95
mode 8 18.98
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4.2. COMBINATION 102
The following pictures shows the displacement plot of the structure
Figure 12 Displacement for combination 102
The maximum reaction force found in the springs is 10.79 kN and are locate beneath the tank
position. Figure 13 shows the plot of the force on the springs, (the positive axis y correspond to
the positive axi z in the Figure 12)
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Spring Force (kN)
2.40 3.72 4.99 5.91 6.40 6.23 5.31 4.20 3.96 3.70 3.19 2.54 1.74 0.88
2.12 6.44 7.00 4.24 0.64
2.19 7.13 9.37 9.23 5.75 0.72
2.70 4.43 6.27 7.97 9.41 10.49 10.74 10.49 10.02 9.06 7.55 5.90 3.93 1.74
8.51
7.62
-2000
-1500
-1000
-500
0
500
1000
1500
2000
-20000 -15000 -10000 -5000 0
Figure 13 – spring reaction on combination 102.
The table below shows the frequency of the first modes
Table 2 – Frequency results combination 102
Mode Frequency
mode 1 0.00
mode 2 0.00
mode 3 0.60
mode 4 4.99
mode 5 5.65
mode 6 5.84
mode 7 6.96
mode 8 9.15
mode 9 10.37
mode 10 12.57
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4.3. COMBINATION 103
The following pictures shows the displacement plot of the structure
Figure 14 – Deformation of the skid on combination 103.
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Figure 15 – Deformation of the frame support on combination 103.
The maximum reaction force found in the springs is 11.89 kN and are locate beneath the tank
position. Figure 16 shows the plot of the force on the springs, (the positive axis y correspond to
the positive axi z in the Figure 15)
Spring Force (kN)
4.38 4.72 7.28 9.72 11.22 11.89 7.66 2.55 1.35 2.02 3.15 3.00 2.08 1.27
5.48 9.18 3.87 1.57 -0.36
4.64 8.20 10.23 4.23 2.26 0.01
3.63 4.08 6.30 8.25 9.23 9.61 7.47 3.41 2.56 3.41 4.53 4.17 2.91 1.90
10.88
11.53
-2000
-1500
-1000
-500
0
500
1000
1500
2000
-20000 -15000 -10000 -5000 0
Figure 16 – spring reaction on combination 103.
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The table below shows the frequency of the first modes.
Table 3 – Frequency results for combination 103
Mode Frequency
mode 1 4.62
mode 2 6.50
mode 3 7.76
mode 4 7.90
mode 5 9.66
mode 6 12.38
mode 7 13.16
mode 8 15.99
mode 9 18.75
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4.4. COMBINATION 104
The following pictures shows the displacement plot of the structure
Figure 17 – Deformation of the skid on combination 104.
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Figure 18 – Deformation of the frame support on combination 104.
The maximum reaction force found in the springs is 11.61 kN and are locate beneath the tank
position. Figure 19 shows the plot of the force on the springs, (the positive axis y correspond to
the positive axi z in the Figure 18)
Spring Force (kN)
3.71 4.43 7.01 9.41 10.91 11.61 7.46 2.43 1.26 1.95 3.10 2.97 2.07 1.27
4.54 8.80 3.79 1.58 -0.32
3.94 7.80 9.99 4.18 2.34 0.10
3.28 3.93 6.12 7.99 8.95 9.40 7.37 3.49 2.69 3.52 4.64 4.30 3.08 2.08
10.62
11.26
-2000
-1500
-1000
-500
0
500
1000
1500
2000
-20000 -15000 -10000 -5000 0
Figure 19 – spring reaction on combination 104.
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The table below shows the frequency of the first modes.
Table 4 – Frequency results combination 104
Mode Frequency
mode 1 0.00
mode 2 0.00
mode 3 0.60
mode 4 4.97
mode 5 5.07
mode 6 5.51
mode 7 5.93
mode 8 6.98
mode 9 8.31
mode 10 8.93
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5. DISCUSSION OF RESULTS
5.1. DISPLACEMENTS ANALSYSIS
All forces obtained in the springs are lesser than the maximum allowable in the spring
specification 40 kN (ref. /7/). Due to the boundary conditions, the maximum displacement of the
results of the combination 101 and 102 (figures 9 and 11) are located in different positions. This
is caused by the fact that the reaction force of the El.motor is applied as moment force in the
combination 102, which results in an different deformation reaction. However, in both cases, the
maximum forces on the springs are located in the same position. (see figures 10 and 12)
Comparing the results of the combinations 103 and 104, we can notice that the deformation in
the first case, combination 103, is higher than the deformation in the combination 104,
consequently, the forces in the spring are higher in combination 103 than combination 104. In
both cases, the maximum forces on the springs are locate beneath the tank positions, which is
similar to the positions where the broken springs have been found by the client.
5.2. NATURAL FREQUENCY
The number of the nodes obtained within the range of the El.motor operating revolutions.
However, it can be observed that in the case where the El.motor is assumed to be supported by
springs, combination 102 and 104, the natural frequency obtained are lesser than the operating
frequency of the El. Motor.
The most critical natural frequency deflections are the ones that cause the skid to twist about the
longitudinal axis, in the case of the combination 103, these forms are found in the mode 2 and 6,
while in the combination 104 , these forms are found in the mode 8 and 10 (see appendix).
This analysis is very sensitive to boundary conditions such as the stiffness of the springs and any
in-planar support of the skid, but with the boundary conditions and loading as described
combinations 101 and 103 in this report, there is a significant risk for occurrence of resonance as
a result of the el-motor revolutions. The center of the axle of the el-motor is located at about
300mm above its foundation and would under these conditions experience high loads. However,
using the boundary conditions of the combinations 102 and 104, this risk of resonance reduces,
which is an indicative that this option should be used.
5.3. FURTHER WORK:
As this analysis shows a risk for resonance the matter should be investigated further. The skid
static and operating loads as well as the boundary conditions should be verified with actual
conditions to ensure the quality of the input in the analysis.
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Actual modifications to the skid on the vessel should focus on altering the natural frequency of
the most critical modes. This could be done by changing the stiffness of the springs or the skid,
or adding supports that would constrain the most critical modes, as presented in the combinations
102 an 104.
Additionally, it should be realized an analysis to determine the behavior of the structure under
the acceleration of the inertial forces (sway and wave bending) on the FPSO.
6. REFERENCES
/1/ Oil & Gas Supply Company “Skid Substructure” dwg. No. 0100, rev 1
/2/ Oil & Gas Supply Company. “Motor and Compressor Base” dwg. No. 0101, rev 0
/3/ Lloyd Werft “Gas Lift Compressor Layout of Shock Absorbers” dwg. No. M-S-5346-
000-081, rev C
/4/ Lloyd Werft “Foundation for Gas Lift Compressor” dwg. No. S-S-0324-701-003
/5/ Oil & Gas Supply Company “Exchanger Support Detail” dwg. No. 0100A, rev 0
/6/ GGT document “Deflection analysis of Gas Lift Compressor Foundation” doc. No
HF112499-0095-ANL , rev 01
/7/ Stop-Choc Federisolator SP656
/8/ De Silva, C.W., Vibration Fundamentals and Practice, Taylor-Francis, CRC Press, Boca
Raton, FL, 2000.
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1. APPENDIX 1: NATURAL FREQUENCY PLOTS
1.1. LOAD COMBINATION 103
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1.2. LOAD COMBINATION 104
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