PRV Stability Project Overview PERF 99-05

Transcription

1 PRV Stability Project Overview PERF Ron Darby, PhD, PE and Abdul Aldeeb, PhD Presented to the API 2011 Fall Meeting November 14, 2011 Los Angeles, CA

2 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.

3 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 nonrecoverable 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.

4 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.

5 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 d D c d

6 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.

7 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

8 Model Assumptions Choked gas flow Valve opens at set pressure (P sg ) Relief mass flow determined at 1.1 P sg =P o Max lift when A curtain = A nozzle (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, L i, D i, opening time). Update force (magnitude and phase) on disc determined by P N, A D, momentum transfer from fluid to disc (geometry of disc and exit chamber). Valve closes when P < P BD

9 Governing Equations 5 coupled nonlinear equations for disc dynamic response: N o B x=fn F,t,x,x F =fn P,P,m x x N B N P =fn m,m,t N o N P =fn m,m,t B o N m =fn x,p,p x N N B x= valve lift, F = force on disk, t=time P,P = pressure at nozzle, backpressure m=relief massrate,m =nozzlemassrate N

10 Model Input Parameters Valve Parameters Design Parameters Operating Conditions 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

11 Stability Criterion Valve is stable if x(t) is monotonic, or oscillatory with small decreasing amplitude Disk Lift Stable 0.5 Is this stable lift? Time (s) Disk Lift Flutter Time Valve Lift (in.) Low frequency oscillations Time (s)

12 Stability Criterion Valve is unstable if x(t) is oscillatory with a large or increasing amplitude 0.3 Valve Lift (in) Time (secs)

13 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.

14 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.

15 Experimental Program

16 Experimental Program Collected Data

17 Testing Observations No Inlet Piping 50 psig 100% 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) 250 psig 80% Capacity

18 Testing Observations No Inlet Piping 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

19 Testing Observations No Inlet Piping Mfg. F - 1E2-250 psig - No Inlet Piping Valve Lift (in) % Capacity_1.13 psi/sec 24% Capacity_3.20 psi/sec 48% Capacity_6.26 psi/sec 72% Capacity_9.66 psi/sec 96% Capacity_12.46 psi/sec 96% Capacity_0.96 psi/sec 72% Capacity_0.72 psi/sec 48% Capacity_0.46 psi/sec Time (s)

20 Testing Observations Inlet Piping 18 valves were tested at flow rates ranging from 30 to 100% of their measured flowing capacities Run 46-30% Capacit y Run 47-50% Capacit y Run % Capacity Repeat Run 48* 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 response profiles were nearly identical for most of the tests. Valve Lift (in) * The repeat of Run 48 showed that the set pressure of the valve had changed to approximately 232 psig. Testing was then terminated with this valve Correlated Time (Secs)

21 Testing Observations Inlet Piping 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%).

22 Testing Observations Inlet Piping 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).

23 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 No Exit Pipe w/ Exit Pipe No Exit Pipe w/ Exit Pipe 0.14 Lift (in) psig 2-foot Inlet Piping Lift (in) Correlated Time (secs) Correlated Time (secs)

24 Testing Program Results Inlet Piping Length and Pressure Drop Inlet Pressure Inlet Pressure Valve Size 2 Feet 4 Feet 6 Feet Valve Inlet Pressure Drop Drop Measured & Valve Initial Valve Initial Valve Initial Number Drop % of Set % of Set Blowdown Set Pressure Lift Lift Lift % of Set Pressure Pressure Pressure (Test) (Test) (Test) 1 1E2-50 psig Stable 1.2 Stable 2.0 Stable* E2-250 psig Stable 1.0 Unstable 1.7 Unstable J3-50 psig Stable 2.2 Stable 3.2 Unstable J3-250 psig Stable 2.0 Test Failed 3.0 Not Tested L4-50 psig Stable 2.3 Stable 3.3 Stable L4-250 psig Stable 1.8 Stable 2.7 Not Tested E2-50 psig Stable 1.1 Stable 1.9 Stable E2-250 psig Stable 1.0 Unstable 1.7 Unstable J3-50 psig Stable 2.3 Stable 3.5 Stable J3-250 psig Stable 1.9 Not Tested 2.8 Not Tested L4-50 psig Stable 2.3 Stable 3.3 Stable L4-250 psig Stable 1.8 Not Tested 2.7 Not Tested E2-50 psig Stable 1.1 Stable 1.9 Stable E2-250 psig Stable 1.0 Stable 1.7 Stable J3-50 psig Stable 2.3 Stable 3.4 Stable J3-250 psig Stable 1.9 Not Tested 2.8 Not Tested L4-50 psig Stable 2.5 Stable 3.5 Stable L4-250 psig Stable 1.8 Unstable 2.7 Not Tested

25 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 d D c d

26 Model Prediction - Examples 1.1 Mfg. E - 3L4-50 psig - Large Tank psi/s - 100% of Capacity - 0 ft Inlet Piping Valve lift (in) Model Prediction Test Run - Cycle 1 Test Run - Cycle Time (s)

27 Model Prediction - Examples Mfg. D - 3L4-50 psig - Large Tank psi/s - 100% of Capacity - 0 ft Inlet Piping Model Prediction Test Data Valve Lift (in) Time (s)

28 Model Prediction - Examples Mfg. F - 2J3-50 psig - Large Tank psi/s - 100% of Capacity - 6 ft Inlet Piping Valve Lift (in.) Model Prediction Test Data Time (s)

29 Model Prediction - Examples Mfg. D - 2J3-50 psig - Large Tank psi/s - 100% of Capacity - 6 ft Inlet Piping Model Prediction Test Data Valve Lift (in) Time (s)

30 Model Prediction - Examples Mfg. D - 1E2-250 psig - Small Tank psi/s - 74% of Capacity - 6 ft Inlet Piping Valve Lift (in) Model Prediction Test Data Time (s)

31 Model Prediction - Examples Mfg. D - 3L4-250 psig - Large Tank psi/s - 76% of Capacity - 0 ft Inlet Piping Model Prediction Test Data Valve Lift (in) Time (s)

32 Model Prediction - Examples Mfg. D - 2J3-250 psig - Large Tank psi/s - 100% of Capacity - 2 ft Inlet Piping Valve Lift (in) Model Prediction Test Data Time (s)

33 Model Prediction - Examples Mfg. E - 1E2-50 psig - Small Tank psi/s - 100% of Capacity Mfg. E - 1E2-50 psig - Small Tank psi/s - 100% of Capacity Valve Lift (in) Test Data - 0 ft Inlet Piping Test Data - 2 ft Inlet Piping Test Data - 4 ft Inlet Piping Test Data - 6 ft Inlet Piping Valve Lift (in) Model Prediction - 0 ft Inlet Piping Model Prediction - 2 ft Inlet Piping Model Prediction - 4 ft Inlet Piping Model Prediction - 6 ft Inlet Piping Time (s) Time (s)

34 Model Prediction - Examples 2J3-50 psig - Large Tank psi/s - 100% of Capacity - 4 ft Inlet Piping & No Outlet Piping 2J3-50 psig - Large Tank psi/s - 100% of Capacity - 4 ft Inlet Piping & ft Oulet Piping Model Prediction 0.5 Valve Lift (in.) Test Data Valve Lift (in.) Model Prediction Test Data Time (s) Time (s)

35 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.

36 Questions Thank you for your attention!