microsoft word - vibration analysis of gas lift compressor foundation

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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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Doc. No: HF112499-0217-ANL Revision: 01 Date: 27 Oct 2008 File no.: 2008-TD-8262 Page: 2 OF 34

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







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.







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.







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/).







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.







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/):







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







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







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







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)







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









Figure 12 Displacement for combination 102










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


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









Figure 14 – Deformation of the skid on combination 103.







Figure 15 – Deformation of the frame support on combination 103.




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








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









Figure 17 – Deformation of the skid on combination 104.







Figure 18 – Deformation of the frame support on combination 104.




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








The table below shows the frequency of the first modes.


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







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.







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.







1. APPENDIX 1: NATURAL FREQUENCY PLOTS

1.1. LOAD COMBINATION 103







1.2. LOAD COMBINATION 104

microsoft word - vibration analysis of gas lift compressor foundation

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