PRV Stability Project Overview PERF ... - mycommittees.api.org Document… · API 2011 Fall Meeting...

API 2011 Fall Meeting - November 14, 2011

Ron Darby, PhD, PE and Abdul Aldeeb, PhD

Presented to theAPI 2011 Fall Meeting

November 14, 2011Los Angeles, CA

PRV Stability Project OverviewPERF 99-05


Project Objective

To develop a method of predicting the instability or “chatter” of a relief valve that is based on sound fundamental scientific principles, to replace the API “3% Rule.”


API “3% Rule”

Assumption:valve will not re-close (or “chatter”) if the nozzle pressure does not fall more than 3% of PRV set pressure, due to non-recoverable friction loss in the inlet line.

Fact:This criterion is based on static conditions and does not account for other dynamic factors that affect valve stability. Thus, it is not sufficient to consider static conditions only for avoiding chatter.


Program Goals

Develop a mathematical model to predict stability characteristics (e.g., disc lift vs. time) of a PRV in vapor/gas service, accounting for effects that may contribute to instability.

Obtain experimental data on various PRV’s for the purpose of validating the predictive accuracy of the model.

Incorporate the model into an easily-used computer program.


Factors Influencing Disc Response

Valve disc dynamic response (damped spring-mass oscillatory system)

Pressure and fluid momentum forces on disc

Blow-down setting and backpressure effects

Dynamics of fluid response in inlet line (friction, capacitance, and acoustic coupling)

Dynamics of fluid response in outlet line

Lift-flow characteristics of the valve Geometry of flow path leaving the disc

d

Dc

Dd


Mathematical Model

The model consists of a number of coupled nonlinear differential and algebraic equations which are solved numerically in a spreadsheet. The output is displayed as the disc lift vs. time, on a millisecond time scale.


Mathematical Model

Factors considered in the model:

Forces on disc: Total fluid pressure on disc Fluid momentum force on disc Propagating acoustical pressure wave in inlet line Blowdown and backpressure effects

Dynamic response of disc vs. time: Spring-mass impulse response Capacitance of vessel and inlet line


Model Assumptions

Choked gas flow

Valve opens at set pressure (Psg)

Relief mass flow determined at 1.1 Psg=Po

Max lift when Acurtain = Anozzle (choke point shifts from annulus to nozzle)

Pressure on disc determined by mass flow rate and:

Friction loss in inlet line;

Capacity of vessel and inlet line;

Expansion shock – (speed of sound, Li, Di, opening time).

Update force (magnitude and phase) on disc determined by PN, AD, momentum transfer from fluid to disc (geometry of disc and exit chamber).

Valve closes when P < PBD


Governing Equations

5 coupled nonlinear equations for disc dynamic response:

x

N B

o N

x

x N B N

N o N

B o N

N N B

x= valve lift , F = force on disk , t=time

P ,P = pressure at nozzle , backpressure

m = relief mass rate , m =nozzle mass rate

x = fn F ,t,x,xF = fn P ,P ,mP = fn m ,m ,tP = fn m ,m ,t

m = fn x,P ,P


Model Input Parameters

1. Mass of moving parts

2. Spring constant

3. Damping of moving parts

4. Discharge coefficient (at full and partial lift)

5. Geometry of nozzle, disc, and fluid flow path

1. Inlet piping length and diameter

2. Outlet piping length and diameter

3. Friction loss in fittings

4. Capacity of vessel and inlet line

5. Inlet and outlet piping roughness factor

1. Set pressure and overpressure

2. Vessel pressure and temperature

3. Discharge pressure and temperature

4. Relief mass flow rate

5. Gas molecular weight and isentropic exponent

ValveParameters

DesignParameters

OperatingConditions


Stability Criterion

Valve is stable if x(t) is monotonic, or oscillatory with small decreasing amplitude

Stable

0.0

0.1

0.2

0.3

0.4

0.000 0.005 0.010 0.015Time (s)

Dis

k Li

ft

Flutter

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.000 0.005 0.010 0.015Time

Dis

k Li

ft

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0Time (s)

Val

ve L

ift (i

n.) Low frequency

oscillations

Is this stable lift?


Stability Criterion

Valve is unstable if x(t) is oscillatory with a large or increasing amplitude

0 5 10 15-0.1

0

0.1

0.2

0.3

Time (secs)

Val

ve L

ift (i

n)


Factors Impacting Stability

Stability is affected by the following factors: damping of the moving parts stiffness of the spring opening time of the valve blowdown setting diameter of inlet piping diameter of discharge piping length of inlet piping length of outlet piping mass of moving parts geometry of valve/disc

Because the system is highly nonlinear, all of

these factors interact and cannot therefore be

considered separately or in isolation from all the others.

Thus it is not possible to generalize about the

effect of any one "parameter" in isolation

from the others.


Experimental Program

Three different size valves (1E2, 2J3, and 3L4) from three manufacturers were tested in gas service.

Disc lift vs. time data obtained at 50 and 250 psig set pressure for each valve.

More than 250 unique test runs were completed with: No inlet piping - determine opening time

characteristics.

Inlet piping - three different lengths.

Discharge piping – two different lengths.


Experimental Program


Experimental Program – Collected Data


Testing Observations – No Inlet Piping

3L4 @ 250 psig

80% Capacity

Valves were tested at flow rates ranging from 10 to 100% of their measured flowing capacities and all valves operated without signs of chattering (high frequency opening and closing)

1E2 @ 50 psig

100% Capacity



For the same valve, the transient disc lift response profiles were nearly identical for most of the tests, regardless of the pressure rise rate and the percentage of valve capacity



Mfg. F - 1E2 - 250 psig - No Inlet Piping

0.00

0.04

0.08

0.12

0.16

0.20

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14Time (s)

Val

ve L

ift (i

n)

10% Capacity_1.13 psi/sec








Mfg. F - 1E2 - 250 psig - No Inlet Piping

0.00

0.04

0.08

0.12

0.16

0.20

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14Time (s)

Val

ve L

ift (i

n)










Testing Observations – Inlet Piping

18 valves were tested at flow rates ranging from 30 to 100% of their measured flowing capacities.

The range of testing is not significant but results illustrate complexity of stability problem.

For the same valve at a specific inlet piping length, the transient disc lift responseprofiles were nearly identical for most of the tests.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

6.1 6.12 6.14 6.16 6.18 6.2 6.22 6.24Correlated Time (Secs)

Valv

e Li

ft (i

n)

Run 46 - 30% Capacity



Repeat Run 48*

* The repeat of Run 48 showed that theset pressure of the valve had changedto approximately 232 psig. Testing was then terminated with this valve.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

6.1 6.12 6.14 6.16 6.18 6.2 6.22 6.24Correlated Time (Secs)

Valv

e Li

ft (i

n)




Repeat Run 48*

* The repeat of Run 48 showed that theset pressure of the valve had changedto approximately 232 psig. Testing was then terminated with this valve.



44 valves tested valves at 100% capacity:

50 psig valves: 8 of 9 were stable at all “tested” lengths with inlet pressure drop ranging from 1.1 to 4.6% of set pressure (the only unstable case has pressure drop of 4.3%).

250 psig valves: 6 of 9 valves were not tested at 6 foot inlet lines (presumably because of damage during earlier testing).

4 valves became unstable at higher inlet piping lengths: 3 of the unstable PRVs had inlet pressure drops < 3% of set pressure (all were < 5%).



44 valves tested valves at 100% capacity:

10 of the 18 tested valves had measured blowdown less than 7% of set pressure.

5 valves had a difference between blowdown and inlet pressure drop (w/ 6 foot inlet length) that was < 2% (4 of the 5 valves became unstable).


Testing Observations – Inlet and Outlet Piping

J and L valves set only at 50 psig were tested due to damaged 250 psig valves.

Dynamic backpressure was ~8% of set pressure.

Stability was not impacted by adding outlet piping.

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 80

0.05

0.1

0.15

0.2

0.25

Correlated Time (secs)

Lift

(in)

No Exit Pipew/ Exit Pipe

7.6 7.62 7.64 7.66 7.68 7.7 7.72 7.74 7.76 7.780

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Correlated Time (secs)

Lift

(in)

No Exit Pipew/ Exit Pipe

2J3 @ 50 psig

2-foot Inlet Piping


Testing Program Results

Valve Number

Valve Size&

Set Pressure

Inlet Piping Length and Pressure Drop

Measured Blowdown

2 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

4 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

6 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

1 1E2 - 50 psig Stable 1.2 Stable 2.0 Stable* 2.7 5.32 1E2 - 250 psig Stable 1.0 Unstable 1.7 Unstable 2.2 5.63 2J3 - 50 psig Stable 2.2 Stable 3.2 Unstable 4.3 8.04 2J3 - 250 psig Stable 2.0 Test Failed 3.0 Not Tested 4.0 7.65 3L4 - 50 psig Stable 2.3 Stable 3.3 Stable 4.5 4.36 3L4 - 250 psig Stable 1.8 Stable 2.7 Not Tested 3.5 11.97 1E2 - 50 psig Stable 1.1 Stable 1.9 Stable 2.6 7.18 1E2 - 250 psig Stable 1.0 Unstable 1.7 Unstable 2.3 2.59 2J3 - 50 psig Stable 2.3 Stable 3.5 Stable 4.6 9.110 2J3 - 250 psig Stable 1.9 Not Tested 2.8 Not Tested 3.8 6.411 3L4 - 50 psig Stable 2.3 Stable 3.3 Stable 4.6 5.612 3L4 - 250 psig Stable 1.8 Not Tested 2.7 Not Tested 3.6 5.713 1E2 - 50 psig Stable 1.1 Stable 1.9 Stable 2.7 9.914 1E2 - 250 psig Stable 1.0 Stable 1.7 Stable 2.2 6.415 2J3 - 50 psig Stable 2.3 Stable 3.4 Stable 4.5 11.816 2J3 - 250 psig Stable 1.9 Not Tested 2.8 Not Tested 3.7 5.617 3L4 - 50 psig Stable 2.5 Stable 3.5 Stable 4.6 10.618 3L4 - 250 psig Stable 1.8 Unstable 2.7 Not Tested 3.5 4.4

Valve Number

Valve Size&

Set Pressure

Inlet Piping Length and Pressure Drop

Measured Blowdown

2 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

4 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

6 FeetValve Initial

Lift(Test)

Inlet Pressure Drop

% of Set Pressure

1 1E2 - 50 psig Stable 1.2 Stable 2.0 Stable* 2.7 5.32 1E2 - 250 psig Stable 1.0 Unstable 1.7 Unstable 2.2 5.63 2J3 - 50 psig Stable 2.2 Stable 3.2 Unstable 4.3 8.04 2J3 - 250 psig Stable 2.0 Test Failed 3.0 Not Tested 4.0 7.65 3L4 - 50 psig Stable 2.3 Stable 3.3 Stable 4.5 4.36 3L4 - 250 psig Stable 1.8 Stable 2.7 Not Tested 3.5 11.97 1E2 - 50 psig Stable 1.1 Stable 1.9 Stable 2.6 7.18 1E2 - 250 psig Stable 1.0 Unstable 1.7 Unstable 2.3 2.59 2J3 - 50 psig Stable 2.3 Stable 3.5 Stable 4.6 9.110 2J3 - 250 psig Stable 1.9 Not Tested 2.8 Not Tested 3.8 6.411 3L4 - 50 psig Stable 2.3 Stable 3.3 Stable 4.6 5.612 3L4 - 250 psig Stable 1.8 Not Tested 2.7 Not Tested 3.6 5.713 1E2 - 50 psig Stable 1.1 Stable 1.9 Stable 2.7 9.914 1E2 - 250 psig Stable 1.0 Stable 1.7 Stable 2.2 6.415 2J3 - 50 psig Stable 2.3 Stable 3.4 Stable 4.5 11.816 2J3 - 250 psig Stable 1.9 Not Tested 2.8 Not Tested 3.7 5.617 3L4 - 50 psig Stable 2.5 Stable 3.5 Stable 4.6 10.618 3L4 - 250 psig Stable 1.8 Unstable 2.7 Not Tested 3.5 4.4


Model Prediction

Valve parameters, design parameters, and test conditions were utilized as inputs to the mathematical model for valve stability modeling.

All parameters are known or measured except for fluid deflection angel and damping factor. These were estimated.

Generally, the mathematical model was found to predict the actual test data reasonably well.

d

Dc

Dd


Model Prediction - Examples

Mfg. E - 3L4 - 50 psig - Large Tank - 3.52 psi/s - 100% of Capacity - 0 ft Inlet Piping

0.0

0.1

0.2

0.4

0.5

0.6

0.7

0.8

1.0

1.1

0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve li

ft (in

)

Model Prediction

Test Run - Cycle 1

Test Run - Cycle 2

Mfg. E - 3L4 - 50 psig - Large Tank - 3.52 psi/s - 100% of Capacity - 0 ft Inlet Piping

0.0

0.1

0.2

0.4

0.5

0.6

0.7

0.8

1.0

1.1

0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve li

ft (in

)

Model Prediction

Test Run - Cycle 1

Test Run - Cycle 2



Mfg. D - 3L4 - 50 psig - Large Tank - 3.53 psi/s - 100% of Capacity - 0 ft Inlet Piping

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data



Mfg. F - 2J3 - 50 psig - Large Tank - 1.57 psi/s - 100% of Capacity - 6 ft Inlet Piping

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.1 0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve L

ift (i

n.)

Model Prediction

Test Data

Mfg. F - 2J3 - 50 psig - Large Tank - 1.57 psi/s - 100% of Capacity - 6 ft Inlet Piping

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.1 0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve L

ift (i

n.)

Model Prediction

Test Data



Mfg. D - 2J3 - 50 psig - Large Tank - 1.57 psi/s - 100% of Capacity - 6 ft Inlet Piping

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0

Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0

Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data



Mfg. D - 1E2 - 250 psig - Small Tank - 12.29 psi/s - 74% of Capacity - 6 ft Inlet Piping

-0.05

0.00

0.05

0.10

0.15

-0.5 0.0 0.5 1.0 1.5 2.0Time (s)

Val

ve L

ift (i

n) Model Prediction

Test Data

Mfg. D - 1E2 - 250 psig - Small Tank - 12.29 psi/s - 74% of Capacity - 6 ft Inlet Piping

-0.05

0.00

0.05

0.10

0.15

-0.5 0.0 0.5 1.0 1.5 2.0Time (s)

Val

ve L

ift (i

n) Model Prediction

Test Data




0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.0 0.1 0.2 0.3 0.4 0.5Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data




0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data


0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)

Model Prediction

Test Data



Mfg. E - 1E2 - 50 psig - Small Tank - 3.02 psi/s - 100% of Capacity

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)

Test Data - 0 ft Inlet Piping





0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)

Model Prediction - 0 ft Inlet Piping





0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)






0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.1 0.2 0.3 0.4 0.5

Time (s)

Val

ve L

ift (i

n)







2J3 - 50 psig - Large Tank - 1.57 psi/s - 100% of Capacity - 4 ft Inlet Piping & 31.42 ft Oulet Piping

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6Time (s)

Valv

e Li

ft (in

.)

Model Prediction

Test Data

2J3 - 50 psig - Large Tank - 1.57 psi/s - 100% of Capacity - 4 ft Inlet Piping & No Outlet Piping

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5

Time (s)

Val

ve L

ift (i

n.)

Model Prediction

Test Data


Conclusions & Path Forward

PRV stability appears to be affected by several parameters including valve specifications, system design, and operating conditions.

Based on the tested valves, mathematical modeling of valve lift response was possible.

Additional work to test valves of different sizes from other manufacturers will be required to establish reliable methods to estimate the unknown parameters outside the range of sizes and conditions of those tested.


Questions

Thank you for your attention!

PRV Stability Project Overview PERF ... - mycommittees.api.org Document… · API 2011 Fall Meeting...

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