Chatter of Safety Valve

Chatter of Safety Valve Hisao IZUCHI PLE Technology Center Chiyoda Advanced Solutions Corporation April, 2008 1 @CHIYODA/ChAS All rights reserved 200...
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Chatter of Safety Valve Hisao IZUCHI PLE Technology Center Chiyoda Advanced Solutions Corporation April, 2008

1 @CHIYODA/ChAS All rights reserved 2007

Contents 1. Purpose of Study 2. Chatter Test at Test Facility 3. Dynamic Simulation 4. Stability Analysis 5. Future Plan

2 @CHIYODA/ChAS All rights reserved 2007

Purpose of Study Safety 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 chatter Since 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

3

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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) 4 @CHIYODA/ChAS All rights reserved 2007

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) 5 @CHIYODA/ChAS All rights reserved 2007

Outlet Area Ratio to Orifice Area Size 1D2 1.5D3 1E2 1.5E3 1.5F2 1.5F3 2G3 2H3 2J3 3J4 3K4 3K6 3L4 4L6 4M6 4N6 4P6 6Q8 6R8 6R10 8T10

Outlet Area / Orifice Area API A Manufacturer 27.7 22.3 62.2 50.1 15.5 10.8 34.9 24.3 9.9 8.1 22.3 18.2 13.6 11.5 8.7 7.4 5.3 4.6 9.5 8.2 6.6 5.7 14.9 12.9 4.3 3.7 9.6 8.3 7.6 6.6 6.3 5.4 4.3 3.7 4.4 3.7 3.0 2.6 4.8 4.1 2.9 2.6

Orifice area ratio tends to decrease as SV size becomes larger

6 @CHIYODA/ChAS All rights reserved 2007

V=c W = ρ2A2c P = P2

V=c W = ρ1A1c P = P1

ρ2 A2 P2 = P1 ⋅ = P1 / ρ1 A1

V : velocity c : sound speed W : weight flow rate ρ : density A : flow area P : pressure suffix 1 : orifice (nozzle) suffix 2 : outlet

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.

7

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Safety Valve Chatter Test No. of Tests

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 Total

135 139 50 62 72 458

8 @CHIYODA/ChAS All rights reserved 2007

Lift Force Measurement (to obtain basic characteristic of safety valve) Test Valve 1E2 & 1.5F2

Lift Force was measured by load cell (Spring is removed and position of disc is adjusted) Minimum inlet Pipe length

P4 P1 P3 P2

20barG Ball Valve Compressor

Pn

Vessel (0.5m3) Pressure Sensor

Investigate effect of outlet area 1. With no attachment 2. 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) 9 @CHIYODA/ChAS All rights reserved 2007

Chatter Test Investigate effect of outlet pipe length 1. No pipe 3. 10m 2. 5m

Investigate effect of Inlet pipe length 1. 1m 4. 10m 2. 3m 5. 15m 3. 5m 6. 20m P4

P5

P1 P3 P2

Ball Valve

20barG Ball Valve コンプレッサ

Vessel (0.5m3) Pn

Pressure Sensor

Investigate effect of outlet area 1. With no reduce 2. 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) 10 @CHIYODA/ChAS All rights reserved 2007

Test Valve 1E2

Set Press. = 20 barg

1.5F2

Disk position was measured by non-contact displacement meter with laser sensor

11 @CHIYODA/ChAS All rights reserved 2007

Test Bench Displacement Meter

Safety Valve

Vessel

Inlet Piping (5m) 12 @CHIYODA/ChAS All rights reserved 2007

Test Bench No Inlet Pipe

Inlet Pipe Length is 1m

13

Lift Force Measurement Load Cell

14

Results of Lift Force Measurement

Lift Force < Spring Load with Reducer of 1”or 3/4” => Possibility of Unstable Characteristic

1.5F2

1E2 1200

1000 900

1000

800

800 Lift Force (N)

Lift Force (N)

700 600 500 400

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

300 200 100

600

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

400 Max Lift 3.8mm

200

Area Ratio = Outlet Area / Orifce Area

0

Area Ratio = Outlet Area / Orifce Area

0 0

1

2

3 Lift (mm)

Lift Force > Spring Load => Popping Action

4

5

0

1

2

3 Lift (mm)

4

5 Max Lift 4.4mm

Lift Force > Spring Load => Popping Action 15 @CHIYODA/ChAS All rights reserved 2007

Results of Test / Effect of Inlet Pipe Length Chatter occurs Inlet length < 5m

1E2

1"/0m -

1.5F2

1-1/2"/0m 74-92Hz

1E2

No Chatter Inlet Length >= 10m

Inlet Pipe Size / Inlet Pipe Length Chatter Frequency 1"/1m 1"/3m 1"/5m 1"/10m 1"/15m 55-68Hz 71-111Hz 79-104Hz 1-1/2"/1m 42-59Hz

1-1/2"/3m

-

1"/20m -

1-1/2"/5m 1-1/2"/10m

-

1-1/2"/1m

1-1/2"/5m

-, 43-52Hz

-

-

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

Longer line length means larger pressure drop of pipe. Therefore, chatter could not be caused by excessive pressure drop of pipe. 16 @CHIYODA/ChAS All rights reserved 2007

Time History in Case of Chatter Occurrence 1. Relatively Shortチャタリング試験 length of inlet pipe, 1E2, Inlet pipe length = 1m 圧力 (MPa) Press. (MPaG)

試験No.3-39 SVサイズ 1E2

上流ボール弁 全開

上流配管 管台+100cm

下流絞り ---

下流ボール弁 ---

下流配管 ---

2.50 2.5 1.5 1.50

Point 1 圧力① Point 2

圧力②

0.5 0.50

-0.5 -0.50

圧力 (MPa) Press. (MPaG)

0 0.00

弁リフト (mm) Lift (mm)

0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 -0.05 -0.05 0 0.00

3.003 2.002 1.001 0.000 -1 -1.00 0 0.00

1 1.00

2 2.00

3 3.00 Time (sec,) 経過時間 (sec)

4 4.00

5 5.00

6 6.00

圧力③ Point 3 Point 4 圧力④ Point 5 圧力⑤

1 1.00

2 2.00

3 3.00 Time (sec,) 経過時間 (sec)

4 4.00

5 5.00

6 6.00

弁リフト 1 1.00

2 2.00

3 3.00 Time (sec,) 経過時間 (sec)

4 4.00

5 5.00

6 6.00

17 @CHIYODA/ChAS All rights reserved 2007

Time History in Case of Normal Actuation チャタリング試験 2. Relatively Long length of 上流配管 inlet pipe, 1E2, Inlet pipe下流ボール弁 length = 10m下流配管 上流ボール弁 下流絞り 圧力 (MPa) Press. (MPaG)

試験No.3-45 SVサイズ 1E2

全開

管台+1000cm

---

---

---

2.50 2.5 1.50 1.5

Point 1 圧力① Point 2

圧力②

0.50 0.5

圧力 (MPa) Press. (MPaG)

-0.5 -0.50 0 0.00

1 1.00

2 2.00

3 3.00 Time (sec,) 経過時間 (sec)

4 4.00

5 5.00

6 6.00

0.10 0.15

圧力③

0.10 0.05

Point 3 Point 4 圧力④ Point 5

0.05

0.00

圧力⑤

0.00

1 1.00

2 2.00

3 3.00 経過時間 (sec) Time (sec,)

4 4.00

5 5.00

6 6.00

弁リフト (mm) Lift (mm)

-0.05 -0.05 0 0.00

3.003 2.002 1.001 0.000 -1.00 -1 0 0.00

弁リフト

1 1.00

2 2.00

3 3.00 経過時間 (sec) Time (sec,)

4 4.00

5 5.00

6 6.00

18 @CHIYODA/ChAS All rights reserved 2007

1. Relatively Short length of inlet pipe, 1E2, Inlet pipe length = 1m Vibration Occurs Lift (mm) 弁リフト (mm)

33 22 11 00 1.10 1.10

1.15 1.15

1.20 1.20

1.25 1.25

1.30 1.30

1.35 1.35

1.40 1.40

1.45 1.45

1.50 1.50

1.35 1.35

1.40 1.40

1.45 1.45

1.50 1.50

時間 (sec) Time (sec.)

圧力 (MPa) Press (MPaG)

2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 1.10 1.10

弁箱内 SV Inlet SV Body SV上流

1.15 1.15

1.20 1.20

1.25 1.25

1.30 1.30

Time (sec.) 時間 (sec) 19 @CHIYODA/ChAS All rights reserved 2007

2. Relatively Long length of inlet pipe, 1E2, Inlet pipe length = 10m 71 msec = Duration pressure wave propagates from safety valve to vessel and return back to safety valve Lift (mm) 弁リフト (mm)

33

Nonlinear characteristics 22 11

Disc oscillating motion is attenuated 00 1.38 1.38

1.43 1.43

1.48 1.48

1.53 1.53

1.58 1.58

1.63 1.63

1.68 1.68

1.73 1.73

1.78 1.78

1.63 1.63

1.68 1.68

1.73 1.73

1.78 1.78

圧力 (MPa) Press (MPaG)

時間 (sec) Time (sec.)

2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 1.38 1.38

弁箱内 SV Inlet SV Body SV上流

1.43 1.43

1.48 1.48

1.53 1.53

1.58 1.58

Time (sec.) 時間 (sec)

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1.43 1.43

1.48 1.48

00 1.38 1.38

1.53 1.53

15m

22 11 1.15 1.15

1.20 1.20

1.25 1.25

1.30 1.35 1.30 1.35 時間 (sec) Time (sec.)

1.40 1.40

1.45 1.45

20m

22 11 1.24 1.18

1.29 1.18

1.34 1.23

1.39 1.44 1.28 1.33 時間 (sec) Time (sec.)

1.49 1.38

1.54 1.43

1.59 1.59

3 3

1.43 1.43

1.1.4848

1.53 1.53

95msec

1.58 1.63 1.58 1.63 時間 (sec) Time (sec.)

1.68 1.68

1.73 1.73

1.78 1.78

1.15 1.20 1.15 1.20 時間 (sec) Time (sec.)

1.25 1.25

1.30 1.30

1.35 1.35

1.24 1.29 1.24 1.29 時間 (sec) Time (sec.)

1.34 1.34

1.39 1.39

1.44 1.44

2 2 1 1

0 0 0.95 0.95

1.50 1.50

33

00 1.19 1.13

11

Lift (mm)

1.33 1.38 1.33 1.38 時間 (sec) Time (sec.)

71msec

22

弁リフト (mm)

1.28 1.28

33

Lift (mm)

Lift (mm) 弁リフト (mm)

Lift (mm) 弁リフト (mm)

1.1.2323

33

00 1.10 1.10

5m

1.18 1.18

Lift (mm)

11 00 1.13 1.13

1m

10m

22

弁リフト (mm)

33

弁リフト (mm)

弁リフト (mm)

0m

Lift (mm)

Time History of Valve Lift / Effect of Inlet Pipe Length

1.00 1.00

1.1.0505

1.10 1.10

123msec

3 3 2 2 1 1 0 0 1.04 1.04

1.09 1.09

1.1.1414

1.19 1.19

Duration of pressure wave propagation becomes longer as inlet pipe length increases

Inlet Pipe Length 1m - 5m : Chatter Inlet Pipe Length >= 10m : No Chatter 21 @CHIYODA/ChAS All rights reserved 2007

Results of Test / Effect of Outlet Area Ratio Reducer Size at Outlet 2" Chatter No 1E2 Press. at SV Body (MPag) 0.06 ( 11.2 ) Outlet Area Ratio Chatter No 1.5F2 Press. at SV Body (MPag) 0.10 ( 8.3 ) Outlet Area Ratio

1-1/4" No 0.11

1" Yes*1 -

3/4" -

( 7.5 )

( 5.5 )

( 3.3 )

-

Yes*2 0.12

Yes*2 0.16

Yes 0.27

Yes 0.32

( 5.6 )

( 4.1 )

( 2.5 )

( 1.5 )

Outlet Area Ratio to Orifice Area < 5.5 There is possibility of chatter

22

Small Area Ratio

11

00 1.47 1.47

1.52 1.52

1.57 1.57

1.62 1.62

1.67 1.67

1.72 1.72

1.77 1.77

1.82 1.82

1.87 1.87

時間 (sec)

Time (sec.) 圧力 (MPa) Press. (MPaG)

1E2 Outlet 1”

Lift (mm) 弁リフト (mm)

*1 : Repeated popping action is observed *2 : Chatter occus before closure of SV

1-1/2" No 0.09

Press at SV Body Increase

2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0

SV Inlet 弁箱内 SV Body SV上流

Chatter

0.5 0.5 0.0 0.0

-0.5 -0.5 1.47 1.47

1.52 1.52

1.57 1.57

1.62 1.62

1.67 1.67

1.72 1.72

時間 (sec) Time (sec.)

1.77 1.77

1.82 1.82

1.87 1.87

22 @CHIYODA/ChAS All rights reserved 2007

Results of Test / Effect of Outlet Area Ratio SV Size 1E2

(1) Orifice Area 1.82 cm2 Chatter

1.5F2

2.43 cm2 Chatter

4P6

47.80 cm2

Outlet Size 2" 1-1/2" 1-1/4" 1" 2" 1-1/2" 1-1/4" 1" 6"

(2) Outlet Area 20.3 cm2 13.6 cm2 10.0 cm2 6.0 cm2 20.3 cm2 13.6 cm2 10.0 cm2 6.0 cm2 182.4 cm2

Ratio (2) / (1) 11.2 7.5 5.5 3.3 8.3 5.6 4.1 2.5 3.8

Almost Equivalent

For larger size of safety valve such as 4P6, relatively small outlet area ratio would cause chatter Safety valve size including outlet area is specified in API526 23 @CHIYODA/ChAS All rights reserved 2007

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. (the ratio is specified by API526) 24 @CHIYODA/ChAS All rights reserved 2007

Simulation Model Safety Valve Equation of Motion for Valve Disc Orifice Flow Equation at Nozzle Flow Equation at Outlet Mass Conservation in Valve Body

Inlet / Outlet Piping Equation of Mass Conservation Equation of Motion for Gas Flow Equation for Energy Conservation Equation of State for Gas 25 @CHIYODA/ChAS All rights reserved 2007

Simulation Model / Safety Valve 1 Lift Force Equation of Motion for Valve Disc 2 ⎧ ⎫ ψ ⎛ ⎞ & & & M S Z + CS Z + KZ = (PV − PB )AH ⎨1 + f ( Z )⎜ ⎟ ⎬ − KZ s ψ c⎠ ⎝ ⎩ ⎭ Ms : Mass of Moving Part (kg) PU : Upstream Pressure (Pa) Cs : Damping Constant (Ns/m) PD : Downstream Pressure (Pa) K : Spring Constant (N/m) PC : Critical Pressure (Pa) κ : Specific κHeat Ratio Z : Valve Lift (m) ⎛ 2 ⎞ κ −1 PV : Inlet Pressure of SV (Pa) Pc = PU ⎜ ⎟ κ 1 + ⎝ ⎠ PB : Pressure at SV Body (Pa) PD ≤ Pc κ +1 AH : Area of SV disc holder (m2) ⎛ 2 ⎞ κ −1 = κ ψ ⎜ ⎟ c f : Lift Force Function (-) ⎝ κ +1⎠ ψ : Flow Coefficient of Orifice (-) PD > Pc 2 κ +1 ⎡ ⎤ ψc : ψ at Critical Flow Condition (-) 2κ ⎢⎛ PD ⎞ κ ⎛ PD ⎞ κ ⎥ ⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ψ=   Zs : Initial Displacement of Spring (m) ⎢ ⎥ κ − 1 ⎝ PU ⎠ ⎝ PU ⎠ ⎢⎣ ⎥⎦ t : Time (sec.) 26

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Simulation Model / Safety Valve 2 Lift Force Function f(z)

Lift Force

1.6

1000

2 ⎧ ⎫ ψ ⎞ ⎛ F = (PV − PD )AH ⎨1 + f ( Z )⎜ ⎟ ⎬ ⎝ ψc ⎠ ⎭ ⎩

900

1.4

800 1.2 700 Lift Force F(N)

1+f

1.0 0.8 0.6

600 500 22 barg 400

21 barg 20 barg

300

19 barg

0.4 Max Lift 3.8mm

0.2

18 barg

200 100

0.0 0.00

1.00

2.00

3.00

4.00

0 0.00

5.00

1.00

2.00

3.00

4.00

5.00

Lift z ( mm)

Lift z(mm)

Outlet Area Ratio =11.2 (Outlet = 2inch)

Outlet Area Ratio = 3.3 (Outlet = 1inch)

1000

1000

900

900

800

800

700

700 Lift Force (N)

Lift Force (N)

Max Lift 3.8mm

Spring Load

600 Measured Calculated by Lift Force Function Spring Load

500 400 300

600

Max Lift 3.8mm

400 Measured Calculated by Lift Force Function

200

100

Comparison with measured data

500

300

200

Safety valve characteristic can be expressed by lift force function

Max Lift 3.8mm

Spring Load

100

0

0 0

1

2

3 Lift (mm)

4

5

0

1

2

3 Lift (mm)

4

5

27 @CHIYODA/ChAS All rights reserved 2007

Safety Valve Characteristic API520 Part1

28 @CHIYODA/ChAS All rights reserved 2007

Simulation Model / Safety Valve 3 Orifice Flow Equation

AS CdψPV WS = , AS = min (πd H Z , AO ) zRT0 / M w

AD CdDψPB Flow Equation at Outlet WD = zRT0 / M w Equation of Mass ρ B zRTB dM B MB = Ws − WD , ρ B = , PB = Conservation at VB Mw dt Valve Body Ws WD As AO Cd CdD z Mw

: Inflow Rate (kg/s) : Outflow Rate (kg/s) : Effective Orifice Area (m2) : Orifice Area (m2) : Orifice Flow Coefficient (-) : Flow Coefficient at Outlet (-) : Compressibility Factor (-) : Molecular Weight (kg/kmol)

R T0 dH MB PB

ρB

TB VB

: Gas Constant (8314 J : Total temperature (K)

kg/kmol/K)

: Diameter of disc holder (m) : Mass of gas in valve body (kg) : Pressure of gas in valve body (Pa) : Density of gas in valve body (Pa) : Temperature of gas in valve body (K) : Volume of valve body (m3) 29 @CHIYODA/ChAS All rights reserved 2007

Simulation Model / Pipe 1 Equation of Mass Conservation dM = Win − Wout dt M ρzRT ρ= , P= AΔx Mw

Win

P, T

Wout

Δx

M : Mass of Gas (kg) Win : Inflow Rate (kg/s) Wout : Outflow Rate (kg/s) Equation of Energy Conservation ρ : Density of Gas (kg/m3) A : Flow Area in Pipe (m2) 2 U ⊿x : Divided Length (m) T+ = T0 = const . 2C p P : Pressure of Gas (Pa) T : Temperature of Gas (K) U : Velocity of Gas (m/s) Cp : Specific Heat at Constant 30 Pressure (J/kg/K)

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Simulation Model / Pipe 2 Equation of Motion Uu U 1 ρU U ∂P ∂U ⎞ ⎛ ∂U −f ⋅ +U ρ⎜ ⎟=− Pu , ρu t x x D 2 ∂ ∂ ∂ ⎠ ⎝ Δx dU = F1 + F 2 + F 3 dt Pd − Pu 1 ∂P 1 UU F1 = − =− , F3 = − f ⋅ ρ ∂x ρΔx D 2 U −Uu Ud −U ∂U = −U u F 2 = −U or F 2 = −U ∂x Δx Δx

f D

Friction Factor of Pipe (-) : Pipe Internal Diameter (m) :

Ud Pd , ρd

Note : Loss of valves and fittings can be expressed by the following form ⎛ 1 K ⎞ UU F 3 = −⎜ f + ⎟⋅ ⎝ D Δx ⎠ 2

31

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Simulation Results / Chatter Test 1 1E2, Inlet Pipe = 0m

1E2, Inlet Pipe = 1m 4.0

4.0 Simulation Experiment

Experiment 3.0

2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.10

0.20

0.30

Simulation

3.5

3.0

Lift(m)

Lift(m)

Lift (mm)

3.5

0.0 0.00

0.40

0.0 0.00

0.50

0.05

0.10

0.15

0.20

Time(s)

Simulation Experiment

0.40

0.45

0.50

Experiment 3.50

2.30 2.20 2.10 2.00 1.90 1.80 1.70

3.00 2.50 2.00 1.50 1.00

1.60 0.10

0.20

0.30

0.40

0.50 0.00

0.50

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.40

0.45

0.50

Time(s)

0.25

Simulation can reproduce chatter phenomena

0.25

0.20

Simulation Experiment

0.20 Body Pressure (MPaG)

Body Pressure (MPaG)

0.35

Simulation

Time(s)

Valve Body Pressure (MPaG)

0.30

4.00

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

2.40

0.15

0.10

0.05

0.00 0.00

0.25 Time(s)

2.50

1.50 0.00

Simulation Experiment

Simulation Experiment

0.15

0.10

0.05

0.10

0.20

0.30 Time(s)

0.40

0.50

0.00 0.00

0.05

0.10

0.15

0.20

0.25 Time(s)

0.30

0.35

32

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Simulation Results / Chatter Test 2 1E2, Inlet Pipe = 10m

1E2, Inlet Pipe = 20m 4.0

4.0

3.5 Simulation Experiment

3.0

Simulation Experiment

3.0 2.5 Lift(m)

2.5 Lift(m)

Lift (mm)

3.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0 0.00

0.10

0.20

0.30

0.40

0.0 0.00

0.50

0.10

0.20

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

Simulation Experiment

2.00 1.95 1.90 1.85 1.80 1.75

2.30 2.20 2.10 2.00 1.90 1.80 1.70 1.60

0.10

0.20

0.30

0.40

1.50 0.00

0.50

0.10

0.20

0.30

0.40

0.50

Time(s)

Simulation can reproduce pressure wave propagation in pipe

0.20

0.10

0.18

0.08

Body Pressure (MPaG)

0.09 Body Pressure (MPaG)

0.50

Simulation Experiment

2.40

2.05

Time(s)

Valve Body Pressure (MPaG)

0.40

2.50

2.10

Simulation Experiment

0.07 0.06 0.05 0.04 0.03 0.02

0.16

Simulation Experiment

0.14 0.12 0.10 0.08 0.06 0.04 0.02

0.01 0.00 0.00

0.30 Time(s)

Time(s)

1.70 0.00

Simulation Experiment

0.10

0.20

0.30 Time(s)

0.40

0.50

0.00 0.00

0.10

0.20

0.30 Time(s)

0.40

0.50

33

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Simulation Results / Chatter Test 3 1E2, Outlet = 1-1/4inch

1E2, Outlet = 1 inch

4.0

4.0 3.5

Simulation Experiment

3.0

Simulation Experiment

3.0

2.5

2.5 Lift(m)

Lift(m)

Lift (mm)

3.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0 0.00

0.10

0.20

0.30

0.40

0.0 0.00

0.50

0.10

0.20

2.10

2.10

2.05

2.05

2.00 1.95 Simulation Experiment

1.90 1.85 1.80 1.75

0.10

0.20

0.30

0.40

1.95 Simulation Experiment

1.90 1.85 1.80 1.75 1.70 0.00

0.50

0.10

0.20

0.30

0.50

Simulation Experiment

0.45

0.40

0.50

Simulation Experiment

0.45

0.40

Body Pressure (MPaG)

Body Pressure (MPaG)

0.50

Time(s)

0.50

Valve Body Pressure (MPaG)

0.40

2.00

Time(s)

0.35 0.30 0.25 0.20 0.15 0.10

Simulation can reproduce chatter caused by relatively small outlet area ratio

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05

0.05 0.00 0.00

0.30 Time(s)

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

Upstream Pressure (MPaG)

Time(s)

1.70 0.00

Simulation Experiment

0.10

0.20

0.30 Time(s)

0.40

0.50

0.00 0.00

0.10

0.20

0.30 Time(s)

0.40

0.50

34

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Simulation Results / Chatter Test 4 SV Size / Inlet Pipe Length

Chatter Test Simulation

1E2 / 1m (+1.2m)

68.7 Hz

79.2 Hz

1E2 / 3m (+1.2m)

76.5 Hz

77.1 Hz

1E2 / 5m (+1.2m)

78.8 Hz

80.3 Hz

1.5F2 / 0m (+1.2 m)

104.3 Hz

91.8 Hz

1.5F2 / 1m (+1.2 m)

59.0 Hz

76.9 Hz

1.5F2 / 3m (+1.2m)

-

75.8 Hz

1.5F2 / 5m+(1.2m)

-

74.8 Hz

(+1.2m) is length of flow pass in safety valve stand

Natural Frequency of valve disc and body = 75Hz

35

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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 36 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 1 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. Pressure-open-type valve

Pipe

Model for Hayama Theory

37 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 2 Consider small disturbance from stable state ~ df ~ ~ ~ ~ Z = Z + Z , P = P + P, W = W + W , f = f + f = f + Z dZ (Choke flow is assumed at orifice : ψ = ψ c ) Equation of motion for valve disc df ~ ~ ~& ~ ~ && M S Z + (CS + CSV ) Z + KZ = P AH (1 + f ) + P AH Z dZ CSV : virtual damping coefficient to satisfy neutral stability condition (Ns/m) Change of variables, etc. Z +Zf P AH 2 ωnt = η , ωn = K / M s , β = , K1 = Z K ζ = ζ S + ζ SV = (CS + CSV ) / 2M sωn , Equation of motion can be transformed using above relations ~ ~& ~ ~ && df/dz affects to decrease Z Z ⎛ df ⎞ Z P + 2ζ + ⎜1 − β ⎟ = K1 natural frequency 38 Z Z ⎝ dZ ⎠ Z P @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 3 Flow Rate Equation ~ ~ ~ W P Z W ∝ PZ , = + Substitute into equation of motion W P Z ~ ~& ~ ~ ~& ~ && && W W ⎛ df ⎞ W P P ⎛ df P ⎞ K = + + − + + 2ζ + ⎜1 − β 2 ζ 1 β ⎟ ⎜ 1⎟ W W ⎝ dZ ⎠ W P P ⎝ dZ ⎠P Appling Laplace transformation

⎤ P( s) ⎡ 2 df ⎞⎤ W ( s ) ⎡ 2 df ⎞ ⎛ ⎛ ⎢ s + 2ζs + ⎜1 − β dZ ⎟⎥ W = ⎢ s + 2ζs + ⎜1 − β dZ ⎟ + K1 ⎥ P ⎝ ⎠ ⎝ ⎠⎦ ⎣ ⎣ ⎦

39 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 4 General solution for wave equation at pipe (constant pressure at x=0 with length of L) P(ξ ,η ) = F (η − πφξ ) − F (η + πφξ ) A W (ξ ,η ) = [F (η − πφξ ) + F (η + πφξ )] c f ωn / 2π ωn L n = = , c : sound speed (m/s) ξ = x / L, φ = πc fp c / 2L Laplace Transformation P(ξ , s ) = −2 sinh(πφξs ) F ( s ) A W (ξ , s ) = 2 cosh(πφξs ) F ( s ) c at X=L (ξ=1), i.e. condition at pipe end = safety valve inlet

W (s) A = − coth(πφs ) P( s) c

40 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 5 Using equations for safety valve and pressure wave in pipe ⎡ 2 ⎤ ⎡ 2 df ⎞ df ⎞⎤ ⎛ ⎛ ⎢ s + 2ζs + ⎜1 − β dZ ⎟ + K1 ⎥ + μ ⎢ s + 2ζs + ⎜1 − β dZ ⎟⎥ coth(πφs ) = 0 ⎠⎦ ⎝ ⎠ ⎝ ⎣ ⎣ ⎦ P A P AH A = = μ Here, W c W c AH 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:

df ⎞ K1 ⎛ ν = ⎜1 − β ⎟+ dZ ⎠ 1 + μ 2 cot 2 (πφν ) ⎝ K1μ cot(πφν ) ζ =− 2ν (1 + μ 2 cot 2 (πφν ))

41 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 6 The following two functions Y1 and Y2 are assumed: df ⎞ K1 Y1 (ν ) = ν , Y2 (ν ) = ⎛⎜1 − β ⎟+ 2 2 dZ 1 + μ cot (πφν ) ⎝ ⎠ At neutral stability condition, Y1 (ν ) = Y2 (ν ) Point of intersection for Y1 and Y2 shows neutral stability condition Safety Valve Data for 1E2 Z K1 P df/dZ

β

W

μ

1- β df/dz

0.0006 0.001 0.002 0.003 (m) 10.8 6.9 3.9 3.0 1.90E+06 1.95E+06 2.10E+06 2.30E+06 (Pa) (1/m) 180 100 50 25 5.56E-03 5.71E-03 6.15E-03 6.73E-03 (m) (kg/s) 0.16 0.28 0.60 0.98 19.5 11.7 5.9 3.9 0 0.43 0.69 0.83

42

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Stability Analysis 7 1E2, L=1m (φ=0.429) 5

ζ0, unstable

ζ0, Unstable

3

Y2, Z=.0006m Y2, Z=.001m Y2, Z=.002m

2

Y2, Z=.003m 1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

ν

43 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 8 1E2, L=5m (φ=2.15) 5

ζ>0, Unstable 4

Y1,Y2

Y1 3

Y2, Z=.0006m Y2, Z=.001m Y2, Z=.002m

2

Y2, Z=.003m 1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

ν

44 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 9 1E2, L=5m (φ=2.15), Comparison between inlet pipe size of 2inch and 4inch 5

Inlet Pipe = 2inch

4

Y1,Y2

Y1 3

Y2, Z=.0006m Y2, Z=.001m

2

Y2, Z=.002m Y2, Z=.003m

1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

No apparent difference is observed on stability

4.0

ν

5

Inlet Pipe = 4inch

4

Y1,Y2

Y1 3

Y2, Z=.0006m Y2, Z=.001m Y2, Z=.002m

2

Y2, Z=.003m 1 0 0.0

0.5

1.0

1.5

2.0 ν

2.5

3.0

3.5

4.0

45 @CHIYODA/ChAS All rights reserved 2007

Stability Analysis 10 1E2, L=0.355m (φ=0.152) 5

No unstable point 4

Y1,Y2

Y1 3

Y2, Z=.0006m Y2, Z=.001m Y2, Z=.002m

2

Y2, Z=.003m 1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

ν

Stable Condition : L
φ increases Set pressure increases => Spring constant increases => fn increases => φ increases Mw 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 57 @CHIYODA/ChAS All rights reserved 2007

Safety Valve Stability Characteristics Pulsation Rate less than 1%

Stable

10

1% - 2% 2% - 5%

8 φ = 2fnL/c

Non-Dimensional Inlet Pipe Length

12

5% - 10% larger than 10% 6

Unstable

4

2

0 0

0.5

1

1.5

2

F = {f(L/D)+K)}Mach

Non-Dimensional Pressure Drop of Inlet Piping System 58 @CHIYODA/ChAS All rights reserved 2007

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.

59 @CHIYODA/ChAS All rights reserved 2007

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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