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1
Chatter of Safety Valve
Hisao IZUCHI
PLE Technology Center
Chiyoda Advanced Solutions Corporation
April, 2008
@CHIYODA/ChAS All rights reserved 2007
2
Contents
1. Purpose of Study
2. Chatter Test at Test Facility
3. Dynamic Simulation
4. Stability Analysis
5. Future Plan
@CHIYODA/ChAS All rights reserved 2007
3
Purpose of StudySafety valve chatter would result in (1) Mechanical failure of the valve and related piping system (risk of failure would increase for large size of the safety valve)(2) Reliving flow rate reduction caused by insufficient valve opening due to chatterSince there is no publication which clearly explains the mechanism of chatter, Chiyoda executed to study safety valve chatter for the following purposes:(1) Investigate mechanism of chatter(2) How to prevent chatter
@CHIYODA/ChAS All rights reserved 2007
4
Study Program(1) Chatter test at a manufacturer test facility
(2) Dynamic simulation taking valve disc motion and fluid dynamics in the connected piping system into account (to simulate actual valve motion)
(3) Stability Analysis based on Professor Hayama’s theory recently published for pressure-open-type valve which is similar to safety valve (to investigate valve stable condition)
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5
Possible Cause of Chatter
(1) Excessive pressure drop of inlet or outlet pipe (well known characteristics)
(2) Interaction between valve disc motion and pressure wave propagation into piping system (acoustic phenomena)
(3) Effect of outlet area ratio to orifice area(Increase of valve body pressure in case of small outlet area ratio)
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6
Outlet Area Ratio to Orifice Area API A Manufacturer
1D2 27.7 22.31.5D3 62.2 50.11E2 15.5 10.8
1.5E3 34.9 24.31.5F2 9.9 8.11.5F3 22.3 18.22G3 13.6 11.52H3 8.7 7.42J3 5.3 4.63J4 9.5 8.23K4 6.6 5.73K6 14.9 12.93L4 4.3 3.74L6 9.6 8.34M6 7.6 6.64N6 6.3 5.44P6 4.3 3.76Q8 4.4 3.76R8 3.0 2.66R10 4.8 4.18T10 2.9 2.6
SizeOutlet Area / Orifice Area
Orifice area ratio tends to decrease as SV size becomes larger
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7
V = cW = ρ1A1cP = P1
V = cW = ρ2A2cP = P2
1
21
1
212 /
AAPPP =⋅=
ρρ
P2 becomes larger as area ratio, A2/A1 decrease.Increase of P2 affects to close the valve and might result in chatter except balance type safety valve. This instability is similar to the excessive inlet pipe pressure drop.
V : velocityc : sound speedW : weight flow rateρ : densityA : flow areaP : pressure suffix 1 : orifice (nozzle)suffix 2 : outlet
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8
Safety Valve Chatter Test
1st Day Lift Force Measurement (1)2nd Day Lift Force Measurement (2)3rd Day Chatter Test (1)4th Day Chatter Test (2)5th Day Chatter Test (3)@ a test bench of a manufacturer
No. of Tests135139506272
458Total
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9
Lift Force Measurement (to obtain basic characteristic of safety valve)
Compressor Vessel(0.5m3)
20barG
Lift Force was measured by load cell(Spring is removed and position of disc is adjusted)
Investigate effect of outlet area1. With no attachment2. With reducer and effuser 2” > 1-1/2” < 2”3. With reducer and effuser 2” > 1-1/4” < 2”4. With reducer and effuser 2” > 1” < 2”5. With reducer and effuser 2” > 3/4” < 2”
Ball Valve
P1
P2
P3
Pn Pressure Sensor
P4Minimum inletPipe length
(Corresponding to larger size of safety valves)
Test Valve1E2 & 1.5F2
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10
コンプレッサ Vessel(0.5m3)
20barG
Ball Valve
P1
P2
P3
Pn Pressure Sensor
Investigate effect of outlet pipe length1. No pipe 3. 10m2. 5m
Investigate effect of Inlet pipe length1. 1m 4. 10m2. 3m 5. 15m3. 5m 6. 20m
P4
Ball Valve
P5
Chatter Test
Investigate effect of outlet area1. With no reduce2. With reducer and effuser 2” > 1-1/2” < 2”3. With reducer and effuser 2” > 1-1/4” < 2”4. With reducer and effuser 2” > 1” < 2”5. With reducer and effuser 2” > 3/4” < 2”
(Corresponding to larger size of safety valves)
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11
Test Valve1E2 1.5F2
Set Press. = 20 barg
Disk positionwas measured by non-contact displacement
meter with laser sensor
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12
Test Bench
Vessel
Safety Valve
DisplacementMeter
Inlet Piping (5m)
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13
Test BenchNo Inlet Pipe Inlet Pipe Length is 1m
14
Lift Force Measurement
Load Cell
15
0
200
400
600
800
1000
1200
0 1 2 3 4 5Lift (mm)
Lift
Forc
e (N
)
Area Ratio = 8.3 (outlet = 2inch)Area Ratio = 5.6 (outlet = 1-1/2inch)Area Ratio = 4.1 (outlet = 1-1/4inch)Area Ratio = 2.5 (outlet = 1inch)Area Ratio = 1.5 (outlet = 0.75inch)Spring Load
Max Lift4.4mm
Area Ratio = Outlet Area / Orifce Area0
100
200
300
400
500
600
700
800
900
1000
0 1 2 3 4 5Lift (mm)
Lift
Forc
e (N
)
Area Ratio = 11.2 (outlet = 2inch)Area Ratio = 7.5 (outlet = 1-1/2inch)Area Ratio = 5.5 (outlet = 1-1/4inch)Area Ratio = 3.3 (outlet = 1inch)Area Ratio = 2.0 (outlet = 3/4inch)Spring Load
Max Lift3.8mm
Area Ratio = Outlet Area / Orifce Area
Results of Lift ForceMeasurement
1E2 1.5F2
Lift Force > Spring Load=> Popping Action
Lift Force < Spring Loadwith Reducer of 1”or 3/4”=> Possibility of Unstable Characteristic
Lift Force > Spring Load=> Popping Action
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16
1"/0m 1"/1m 1"/3m 1"/5m 1"/10m 1"/15m 1"/20m- 55-68Hz 71-111Hz 79-104Hz - - -
1-1/2"/0m 1-1/2"/1m 1-1/2"/3m 1-1/2"/5m 1-1/2"/10m74-92Hz 42-59Hz - - -
1-1/2"/5m-
Actual length is figure in table + 1.2m of safety valve stand Chatter occurs Both cases were observed with chatter and without chatter
Natural frequency of valve disc and spring is 75 Hz
1E2
1.5F2
1E2
Inlet Pipe Size / Inlet Pipe LengthChatter Frequency
1-1/2"/1m-, 43-52Hz
Results of Test / Effect of Inlet Pipe LengthChatter occurs
Inlet length < 5m No Chatter
Inlet Length >= 10m
Longer line length means larger pressure drop of pipe.Therefore, chatter could not be caused by excessive pressure drop of pipe.
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17
Time History in Case of Chatter Occurrence試験No.3-39 チャタリング試験
---SVサイズ 上流ボール弁
1E2 全開 管台+100cm ---上流配管 下流絞り 下流ボール弁 下流配管
---
-0.50
0.50
1.50
2.50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
圧力
(M
Pa)
圧力①
圧力②
-1.000.001.002.003.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
弁リ
フト
(m
m)
弁リフト
-0.050.000.050.100.15
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
圧力
(M
Pa)
圧力③
圧力④
圧力⑤
2.5
1.5
0.5
-0.5Pre
ss. (
MP
aG)
1. Relatively Short length of inlet pipe, 1E2, Inlet pipe length = 1m
0 1 2 3 4 5 6
Time (sec,)
Point 1Point 2
0 1 2 3 4 5 6
Time (sec,)
Point 3Point 4Point 5
0.150.10
0.00-0.05P
ress
. (M
PaG
)
0.05
0 1 2 3 4 5 6
Time (sec,)
32
0-1Li
ft (m
m)
1
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18
試験No.3-45 チャタリング試験
---SVサイズ 上流ボール弁
1E2 全開 管台+1000cm ---上流配管 下流絞り 下流ボール弁 下流配管
---
-0.50
0.50
1.50
2.50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
圧力
(M
Pa)
圧力①
圧力②
-1.000.001.002.003.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
弁リ
フト
(m
m)
弁リフト
-0.05
0.00
0.05
0.10
0.00 1.00 2.00 3.00 4.00 5.00 6.00
経過時間 (sec)
圧力
(M
Pa)
圧力③
圧力④
圧力⑤
Time History in Case of Normal Actuation 2. Relatively Long length of inlet pipe, 1E2, Inlet pipe length = 10m
2.5
1.5
0.5
-0.5Pre
ss. (
MP
aG)
0 1 2 3 4 5 6
Time (sec,)
Point 1Point 2
0 1 2 3 4 5 6
Time (sec,)
Point 3Point 4Point 5
0.150.10
0.00-0.05P
ress
. (M
PaG
)
0.05
0 1 2 3 4 5 6
Time (sec,)
32
0-1Li
ft (m
m)
1
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19
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
時間 (sec)
圧力
(M
Pa)
弁箱内
SV上流
0
1
2
3
1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
時間 (sec)
弁リ
フト
(m
m)
Vibration Occurs
1. Relatively Short length of inlet pipe, 1E2, Inlet pipe length = 1m
SV InletSV Body
3
2
0
Lift
(mm
)
1
Time (sec.)1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Time (sec.)1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
2.5
Pre
ss (M
PaG
)
2.01.51.00.50.0
-0.51.10
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20
2. Relatively Long length of inlet pipe, 1E2, Inlet pipe length = 10m
0
1
2
3
1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78
時間 (sec)
弁リ
フト
(m
m)
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78
時間 (sec)
圧力
(M
Pa)
弁箱内
SV上流
3
2
0
Lift
(mm
)
1
Time (sec.)1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78
SV InletSV Body
Time (sec.)1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78
2.5
Pre
ss (M
PaG
)
2.01.51.00.50.0
-0.51.38
Disc oscillating motion is attenuated
71 msec = Duration pressure wave propagates from safety valve tovessel and return back to safety valve
Nonlinear characteristics
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21
0
1
2
3
1.19 1.24 1.29 1.34 1.39 1.44 1.49 1.54 1.59
時間 (sec)
弁リ
フト
(m
m)
0
1
2
3
1.13 1.18 1.23 1.28 1.33 1.38 1.43 1.48 1.53
時間 (sec)
弁リ
フト
(m
m)
0
1
2
3
1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
時間 (sec)
弁リ
フト
(m
m)
0
1
2
3
1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78
時間 (sec)
弁リ
フト
(m
m)
0
1
2
3
0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35
時間 (sec)
弁リ
フト
(m
m)
0
1
2
3
1.04 1.09 1.14 1.19 1.24 1.29 1.34 1.39 1.44
時間 (sec)
弁リ
フト
(m
m)
Time History of Valve Lift / Effect of Inlet Pipe Length
Duration of pressure wave propagation becomes longer as inlet pipe length increases
Inlet Pipe Length 1m - 5m : ChatterInlet Pipe Length >= 10m : No Chatter
30m2
1
0
Lift
(mm
)
1.13 1.18 1. 23 1.28 1.33 1.38 1.43 1.48 1.53Time (sec.)
3
2
1
0
Lift
(mm
)
1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
1m
Time (sec.)
3
2
1
0
Lift
(mm
)
1.13 1.18 1.18 1.23 1.28 1.33 1.38 1.43 1.59Time (sec.)
5m
3
2
1
0
Lift
(mm
)
1.38 1.43 1. 48 1.53 1.58 1.63 1.68 1.73 1.78
10m
Time (sec.)
71msec
95msec
123msec
3
2
1
0
Lift
(mm
)
0.95 1.00 1. 05 1.10 1.15 1.20 1.25 1.30 1.35Time (sec.)
3
2
1
0
Lift
(mm
)
1.04 1.09 1. 14 1.19 1.24 1.29 1.34 1.39 1.44Time (sec.)
15m
20m
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22
Results of Test / Effect of Outlet Area Ratio
Outlet Area Ratio to Orifice Area < 5.5There is possibility of chatter
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87
時間 (sec)
圧力
(M
Pa)
弁箱内
SV上流
0
1
2
1.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87
時間 (sec)
弁リ
フト
(m
m)
1E2Outlet 1”
2
Lift
(mm
)
1
01.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87
Time (sec.)
1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87Time (sec.)
1.47Pre
ss. (
MP
aG)
2.52.01.51.00.50.0
-0.5
Small Area Ratio
Press at SV BodyIncrease
ChatterSV InletSV BodySV InletSV Body
2" 1-1/2" 1-1/4" 1" 3/4"Chatter No No No Yes*1 -
Press. at SV Body (MPag) 0.06 0.09 0.11 - -Outlet Area Ratio ( 11.2 ) ( 7.5 ) ( 5.5 ) ( 3.3 ) -
Chatter No Yes*2 Yes*2 Yes YesPress. at SV Body (MPag) 0.10 0.12 0.16 0.27 0.32
Outlet Area Ratio ( 8.3 ) ( 5.6 ) ( 4.1 ) ( 2.5 ) ( 1.5 )
*1 : Repeated popping action is observed*2 : Chatter occus before closure of SV
Reducer Size at Outlet
1E2
1.5F2
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23
SV Size (1) OrificeArea
OutletSize
(2) OutletArea
Ratio(2) / (1)
1E2 1.82 cm2 2" 20.3 cm2 11.21-1/2" 13.6 cm2 7.51-1/4" 10.0 cm2 5.5
1" 6.0 cm2 3.31.5F2 2.43 cm2 2" 20.3 cm2 8.3
1-1/2" 13.6 cm2 5.61-1/4" 10.0 cm2 4.1
1" 6.0 cm2 2.54P6 47.80 cm2 6" 182.4 cm2 3.8
Chatter
Chatter
For larger size of safety valve such as 4P6, relatively small outlet area ratio would cause chatter
AlmostEquivalent
Safety valve size including outlet area is specified in API526
Results of Test / Effect of Outlet Area Ratio
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24
Summary of Chatter Test
1. Safety valve chatter occurs under following conditions:- Excessive pressure drop of inlet or outlet piping- Inlet pipe length shorter than 5m (No chatter for inlet pipe length equal to or longer than 10m)
- Relatively small outlet area ratio
2. Chatter in case of inlet pipe length shorter than 5m is caused by interaction effect of valve disc motion and pressure wave propagation through inlet piping system.
3. For larger size of safety valves, chatter could occur because they have relatively small outlet area ratio. (theratio is specified by API526)
@CHIYODA/ChAS All rights reserved 2007
25
Simulation Model
Safety ValveEquation of Motion for Valve DiscOrifice Flow Equation at NozzleFlow Equation at OutletMass Conservation in Valve Body
Inlet / Outlet PipingEquation of Mass ConservationEquation of Motion for Gas FlowEquation for Energy ConservationEquation of State for Gas
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26
Simulation Model / Safety Valve 1
( ) sc
HBVSS KZZfAPPKZZCZM −⎭⎬⎫
⎩⎨⎧
⎟⎠⎞⎜
⎝⎛+−=++
2
)(1 ψψ&&&
Equation of Motion for Valve Disc
Ms : Mass of Moving Part (kg) Cs : Damping Constant (Ns/m)K : Spring Constant (N/m)Z : Valve Lift (m)PV : Inlet Pressure of SV (Pa)PB : Pressure at SV Body (Pa)AH : Area of SV disc holder (m2)f : Lift Force Function (-)ψ : Flow Coefficient of Orifice (-)ψc : ψ at Critical Flow Condition (-)Zs : Initial Displacement of Spring (m)t : Time (sec.)
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−
=
+κ
κκ
κκψ
12
12
U
D
U
D
PP
PP
11
12 −
+
⎟⎠⎞
⎜⎝⎛
+=
κκ
κκψ c
1
12 −
⎟⎠⎞
⎜⎝⎛
+=
κκ
κUc PP
cD PP ≤
cD PP >
PU : Upstream Pressure (Pa)PD : Downstream Pressure (Pa)PC : Critical Pressure (Pa)κ : Specific Heat Ratio
Lift Force
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270
100
200
300
400
500
600
700
800
900
1000
0 1 2 3 4 5Lift (mm)
Lift
Forc
e (N
)
MeasuredCalculated by Lift Force FunctionSpring Load Max Lift
3.8mm
0
100
200
300
400
500
600
700
800
900
1000
0 1 2 3 4 5Lift (mm)
Lift
Forc
e (N
)
MeasuredCalculated by Lift Force FunctionSpring Load
Max Lift3.8mm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.00 1.00 2.00 3.00 4.00 5.00Lift z(mm)
1+f
Max Lift3.8mm
Simulation Model / Safety Valve 2
0
100
200
300
400
500
600
700
800
900
1000
0.00 1.00 2.00 3.00 4.00 5.00Lift z(mm)
Lift
Forc
e F(
N)
22 barg21 barg20 barg19 barg18 bargSpring Load
Max Lift3.8mm
( )⎭⎬⎫
⎩⎨⎧
⎟⎠⎞⎜
⎝⎛+−=
2
)(1c
HDV ZfAPPF ψψLift ForceLift Force Function f(z)
Outlet Area Ratio =11.2 (Outlet = 2inch) Outlet Area Ratio = 3.3 (Outlet = 1inch)
Comparison with measured data
Safety valve characteristic can be expressed by lift force function
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28
Safety Valve Characteristic API520 Part1
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29
Simulation Model / Safety Valve 3Orifice Flow Equation ,
/0 w
VdSS MzRT
PCAW ψ=
Flow Equation at Outletw
BdDDD MzRT
PCAW/0
ψ=
Equation of MassConservation at Valve Body
,DsB WW
dtdM
−=w
BBB M
zRTP ρ=
( )OHS AZdA ,min π=
Ws : Inflow Rate (kg/s) WD : Outflow Rate (kg/s)As : Effective Orifice Area (m2)AO : Orifice Area (m2)Cd : Orifice Flow Coefficient (-) CdD : Flow Coefficient at Outlet (-)z : Compressibility Factor (-)Mw : Molecular Weight (kg/kmol)
R : Gas Constant (8314 J kg/kmol/K)T0 : Total temperature (K) dH : Diameter of disc holder (m) MB : Mass of gas in valve body (kg)PB : Pressure of gas in valve body (Pa)ρB : Density of gas in valve body (Pa) TB : Temperature of gas in valve body (K)VB : Volume of valve body (m3)
,B
BB V
M=ρ
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30
Simulation Model / Pipe 1
Equation of Mass Conservation
outin WWdt
dM−=
wMzRTP ρ
=,xA
MΔ
=ρ M : Mass of Gas (kg)Win : Inflow Rate (kg/s) Wout : Outflow Rate (kg/s)ρ : Density of Gas (kg/m3) A : Flow Area in Pipe (m2)⊿x : Divided Length (m)P : Pressure of Gas (Pa)T : Temperature of Gas (K)U : Velocity of Gas (m/s)Cp : Specific Heat at Constant
Pressure (J/kg/K)
Equation of Energy Conservation
.2 0
2
constTC
UTp
==+
P, T
Δx
Win Wout
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31
Simulation Model / Pipe 2
Equation of Motion
f : Friction Factor of Pipe (-)D : Pipe Internal Diameter (m)
21 UUD
fxP
xUU
tU ρ
ρ ⋅−∂∂
−=⎟⎠⎞
⎜⎝⎛
∂∂
+∂
∂
,11xPP
xPF ud
Δ−
−=∂∂
−=ρρ
xUUU
xUUF u
u Δ−
−=∂∂
−=2xUUUF d
Δ−
−=2or
U
Δx
Uu Ud
Pu , ρu Pd , ρd
321 FFFdt
dU++=
213
UUD
fF ⋅−=
Note : Loss of valves and fittings can be expressed by the following form
213
UUx
KD
fF ⋅⎟⎠⎞
⎜⎝⎛ +−=
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32
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Time(s)
Lift(
m)
SimulationExperiment
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Time(s)U
pstre
am P
ress
ure
(MP
aG)
SimulationExperiment
0.00
0.05
0.10
0.15
0.20
0.25
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
) SimulationExperiment
Simulation Results / Chatter Test 1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Lift(
m)
SimulationExperiment
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Ups
tream
Pre
ssur
e (M
PaG
)
SimulationExperiment
0.00
0.05
0.10
0.15
0.20
0.25
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
) SimulationExperiment
1E2, Inlet Pipe = 0mLi
ft (m
m)
Ups
tream
Pre
ssur
e(M
PaG
)
Val
ve B
ody
Pre
ssur
e(M
PaG
)SimulationExperiment
Simulation can reproduce chatter phenomena
1E2, Inlet Pipe = 1m
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Lift(
m)
SimulationExperiment
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)U
pstre
am P
ress
ure
(MPa
G)
SimulationExperiment
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
) SimulationExperiment
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Lift(
m)
SimulationExperiment
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Ups
tream
Pre
ssur
e (M
PaG
)
SimulationExperiment
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
) SimulationExperiment
Simulation Results / Chatter Test 2Li
ft (m
m)
Ups
tream
Pre
ssur
e(M
PaG
)
Val
ve B
ody
Pre
ssur
e(M
PaG
)SimulationExperiment
Simulation can reproduce pressure wave propagation in pipe
1E2, Inlet Pipe = 10m 1E2, Inlet Pipe = 20m
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34
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Lift(
m)
SimulationExperiment
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)U
pstre
am P
ress
ure
(MPa
G)
SimulationExperiment
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
)
SimulationExperiment
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Lift(
m)
SimulationExperiment
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Ups
tream
Pre
ssur
e (M
PaG
)
SimulationExperiment
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.00 0.10 0.20 0.30 0.40 0.50
Time(s)
Body
Pre
ssur
e (M
PaG
)
SimulationExperiment
Simulation Results / Chatter Test 3Li
ft (m
m)
Ups
tream
Pre
ssur
e(M
PaG
)
Val
ve B
ody
Pre
ssur
e(M
PaG
)SimulationExperiment
Simulation can reproduce chatter caused by relatively small outlet area ratio
1E2, Outlet = 1-1/4inch 1E2, Outlet = 1 inch
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35
Simulation Results / Chatter Test 4
75.8 Hz-1.5F2 / 3m (+1.2m)74.8 Hz-1.5F2 / 5m+(1.2m)
76.9 Hz59.0 Hz1.5F2 / 1m (+1.2 m)91.8 Hz104.3 Hz1.5F2 / 0m (+1.2 m)80.3 Hz78.8 Hz1E2 / 5m (+1.2m)77.1 Hz76.5 Hz1E2 / 3m (+1.2m)79.2 Hz68.7 Hz1E2 / 1m (+1.2m)
SimulationChatter TestSV Size / Inlet Pipe Length
Natural Frequency of valve disc and body = 75Hz
(+1.2m) is length of flow pass in safety valve stand
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36
Summery of Simulation Results 1. Simulation results have good agreement with test results on chatter caused by the following phenomena:
- Interaction between valve disc motion and pressure wave propagation through inlet piping system
- Relatively small outlet area ratio of safety valve
2. Damping Problem (Mechanical Friction at Moving Part)- Nonlinear characteristics are observed in measured data- Possibility of difference in mechanical damping due to
manufacturing accuracy for guide and disc holder of safety valve
==> Additional tests with other parts of guide and disc holder show similar results on the effect of inlet pipe length
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37
Professor Hayama published “stability analysis of a piping system equipped with a pressure-open-type valve at the exit”As “Pressure-open-type valve ” is similar to safety valve, the stability of safety valve is investigated based on Hayama’s Theory.Professor Hayama mentioned that conventional method cannot succeed to obtain stability condition for this type of the valve because of complexity of the stability equation. He could succeed to investigate the stability condition by introducing additional virtual negative damping to the valve motion and assuming a neutral stability condition.
Stability Analysis 1
Model for Hayama Theory
Pipe
Pressure-open-type valve
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38
Stability Analysis 2Consider small disturbance from stable state
,~ZZZ += ,~PPP += ,~WWW +=
( ) ZdZdfAPfAPZKZCCZM HHSVSS
~1~~~)(~ ++=+++ &&&Equation of motion for valve disc
ZdZdfffff ~~
+=+=
Change of variables, etc.,ηω =tn ,/2
sn MK=ω,2/)( nsSVSSVS MCC ωζζζ +=+=
PPK
ZZ
dZdf
ZZ
ZZ ~~
1~
2~
1=⎟⎠⎞
⎜⎝⎛ −++ βζ
&&&
,KAP H=β
ZZZ
K f+=1
CSV : virtual damping coefficient to satisfy neutral stability condition (Ns/m)
df/dz affects to decrease natural frequency
(Choke flow is assumed at orifice : )cψψ =
Equation of motion can be transformed using above relations
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39
Stability Analysis 3Flow Rate Equation
,PZW ∝ZZ
PP
WW ~~~
+= Substitute into equation of motion
Appling Laplace transformation
PPK
dZdf
PP
PP
WW
dZdf
WW
WW ~
1~
2~~
1~
2~
1 ⎟⎠⎞
⎜⎝⎛ +−++=⎟
⎠⎞
⎜⎝⎛ −++ βζβζ
&&&&&&
PsPK
dZdfss
WsW
dZdfss )(12)(12 1
22⎥⎦
⎤⎢⎣
⎡+⎟
⎠⎞
⎜⎝⎛ −++=⎥
⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −++ βζβζ
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40
Stability Analysis 4General solution for wave equation at pipe (constant pressure at x=0 with length of L)
)()(),( πφξηπφξηηξ +−−= FFP
Laplace Transformation
[ ])()(),( πφξηπφξηηξ ++−= FFcAW
,/ Lx=ξ ,2/2/
cL
Lcff nn
p
n
πωπωφ ===
)()sinh(2),( sFssP πφξξ −=
)()cosh(2),( sFscAsW πφξξ =
c : sound speed (m/s)
at X=L (ξ=1), i.e. condition at pipe end = safety valve inlet
)coth()()( s
cA
sPsW πφ−=
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41
Stability Analysis 5Using equations for safety valve and pressure wave in pipe
Under neutral stability condition, since root of s shall be purely imaginary number, the relation of s =iν can be introduced. And both of real and imaginary parts in above equation shall be zero simultaneously. Thus ν and ζ can be obtained as follows:
H
H
AA
cWAP
cWAP
==μ
0)coth(1212 21
2 =⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −+++⎥
⎦
⎤⎢⎣
⎡+⎟
⎠⎞
⎜⎝⎛ −++ s
dZdfssK
dZdfss πφβζμβζ
)(cot11 22
1
πφνμβν
++⎟
⎠⎞
⎜⎝⎛ −=
KdZdf
))(cot1(2)cot(
221
πφνμνπφνμζ
+−=
K
Here,
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42
Stability Analysis 6The following two functions Y1 and Y2 are assumed:
)(cot11)( 22
12 πφνμ
βν+
+⎟⎠⎞
⎜⎝⎛ −=
KdZdfY,)(1 νν =Y
)()( 21 νν YY =
Safety Valve Data for 1E2Z 0.0006 0.001 0.002 0.003
K 1 10.8 6.9 3.9 3.0P 1.90E+06 1.95E+06 2.10E+06 2.30E+06
df/dZ 180 100 50 25β 5.56E-03 5.71E-03 6.15E-03 6.73E-03W 0.16 0.28 0.60 0.98μ 19.5 11.7 5.9 3.9
1- β df/dz 0 0.43 0.69 0.83
(m)
(Pa)(1/m)(m)(kg/s)
At neutral stability condition, Point of intersection for Y1 and Y2 shows neutral stability condition
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43
Stability Analysis 7
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ν
Y1,
Y2
Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m
1E2, L=1m (φ=0.429)
ζ<0, stable ζ<0, stableζ>0, unstable
ζ>0, Unstable
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44
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ν
Y1,
Y2
Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m
Stability Analysis 81E2, L=5m (φ=2.15)
ζ>0, Unstable
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45
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ν
Y1,
Y2
Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m
Stability Analysis 91E2, L=5m (φ=2.15), Comparison between inlet pipe size of 2inch and 4inch
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ν
Y1,
Y2
Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m
No apparent difference is observed on stability
Inlet Pipe = 2inch
Inlet Pipe = 4inch
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46
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ν
Y1,
Y2
Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m
Stability Analysis 101E2, L=0.355m (φ=0.152)
No unstable point
12 KcL
nωπ
<Stable Condition :
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47
Stability Analysis 11
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5 6 7
φ
ν
1st
2nd
3rd
4th
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 1 2 3 4 5 6 7
φ
ζ
1st
2nd
3rd
4th
Non
-dim
ensi
onal
Freq
uenc
y
Lift 1mm
Dam
ping
Rat
io
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48
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5 6
φ
ν
1st
2nd
3rd
4th
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 1 2 3 4 5 6
φ
ζ
1st
2nd
3rd
4th
Stability Analysis 12Lift 2mm
Non
-dim
ensi
onal
Freq
uenc
yD
ampi
ng R
atio
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49
Test Results, 1E2, L=1m(inlet pipe length)
-0.50
0.50
1.50
2.50
0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000
経過時間 (sec)
圧力
(M
Pa)
圧力①
圧力②
0.0E+00
5.0E-02
1.0E-01
1.5E-01
2.0E-01
2.5E-01
0 20 40 60 80 100 120 140 160 180 200
周波数 (Hz)
0.0E+00
1.0E-01
2.0E-01
3.0E-01
4.0E-01
0 20 40 60 80 100 120 140 160 180 200
周波数 (Hz)
0.0E+00
5.0E-02
1.0E-01
1.5E-01
2.0E-01
2.5E-01
3.0E-01
3.5E-01
0 20 40 60 80 100 120 140 160 180 200
周波数 (Hz)
1.25 secLift 1.73 mm
2.68 secLift 1.16 mm
4.11 secLift 0.88 mm
Time History of Valve Inlet Press.
Spectrum
Pre
ss.
(MP
aG)
2.5
1.5
0.5
Time (sec.)0
-0.51 2 3 4 5 6
Point 1Point 2
0
Frequency (Hz)
20 40 60 80 100 120 140 160 180 200
0
Frequency (Hz)
20 40 60 80 100 120 140 160 180 200
0
Frequency (Hz)
20 40 60 80 100 120 140 160 180 200
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50
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Lift (mm)
νTheory, 1st ModeTheory, 2nd ModeExperiment
L=2.17m
Comparison between stability theory and measured data, L=1m (2.17m)
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51
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Lift (mm)
νTheory, 1st ModeTheory, 2nd ModeTheory, 3rd ModeTheory, 4th ModeExperiment
L=4.17m
Comparison between stability theory and measured data, L=3m (4.17m)
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52
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Lift (mm)
νTheory, 2nd ModeTheory, 3rd ModeTheory, 4th ModeTheory, 5th ModeTheory, 6th ModeExperiment
L=6.17m
Comparison between stability theory and measured data, L=5m (6.17m)
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53
Summary of Stability Analysis
1. Stable condition is
2. Frequency obtained by stability analysis agrees well to those obtained by chatter test
3. Size of inlet pipe size has no effect on stability
4. In case of relatively long length of inlet pipe, chatter cannot be excited since oscillating motion of the valve disc can be attenuated before the arrival of reflecting pressure wave as shown from the results of chatter test. These phenomena could not be solved by stability analysis because the steady amplitude of disc motion is assumed in the stability analysis though it decreased transiently by the damping effect.
12 KcL
nωπ
<
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54
Case StudyOutlet Area Ratio >= 6 SV Size : 1E2, 2J4, 4P8 Inlet Pipe Size
1E2 :1-2 inch2J4 : 2-4 inch4P8 : 4-10 inch
Gas : Air, Methane, HydrogenSet Pressure : 2barg, 20barg, 60barg, 100bargDamping Ratio : 20% (Mechanical Friction)
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55
Non-dimensional Parameters
( ) ZZZK f /1 +=
H
H
AA
cWAP
cWAP
==μ
cUM ach /0=
[ ] achMKDLfF += )/(
KMC
s
s
2=ζ
Mach Number, less than 0.5
Pressure Term / Momentum Force (Effect of Inlet Pipe Size)
cLfff npn /2/ ==φ SV Natural frequency / Acoustic natural frequency for 1st mode
Pressure drop of pipe and fitting
Damping ratio (20%)
Constant on SV Characteristic
κ Specific heat ratio of gas
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56
2 - 502 – 25
2.2 - 2.62.3 - 2.8
0.01 - 0.340.3 - 0.5
Case StudyRange in Design
cUM ach /0=
WcPA
=μ
max
max1 Z
ZZK f+
=
Range of Parameters
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57
cLfff npn /2/ ==φ
φ : Duration pressure wave propagate and return / Natural period of disc and spring
Pipe length increases => φ increasesSet pressure increases => Spring constant increases
=> fn increases => φ increasesMw increases => c decreases => φ increases
Longer pipe length tends to be stable= Large φ tends to be stable= Higher set pressure tends to be stable= larger Mw tends to be stable
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58
Safety Valve Stability Characteristics
0
2
4
6
8
10
12
0 0.5 1 1.5 2F = {f(L/D)+K)}Mach
φ =
2fnL
/c
Pulsation Rateless than 1%1% - 2%2% - 5%5% - 10%larger than 10%
Stable
Unstable
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Non
-Dim
ensi
onal
Inle
t Pip
e Le
ngth
Non-Dimensional Pressure Drop of Inlet Piping System
59
Conclusion and Future Plan / Approach 1
As the results of the study, the instability of the safety valve can be classified into the following three types:
(1) Excessive pressure drop of inlet/outlet piping system (well known phenomena)
(2) Interaction between disc motion and pressure wave propagation of inlet piping
(3) Relatively small out let area of safety valve
The safety valve chatter can be predicted by the dynamic simulation which is verified throughout the comparison to the test data for the small safety valves.
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60
Conclusion and Future Plan / Approach 2
Further investigation including the chatter test for larger sizes of the safety valves shall be required so as to confirm the cause of chatter more quantitatively and establish a reliable design method to prevent the chatter occurrence.
API is requested to execute the further study as a public organization. In this study the effects of inlet pipe length and outlet area ratio shall be confirmed for the safety valves made by several manufacturers. After the study, the method to prevent chatter will be discussed and determined on API committee.
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