Tutorial Relief valve The Relief valve tutorial describes the theory and modeling process of a pressure relief valve or safety valve. It covers the algorithm BOSfluids uses to model the valve and a worked out example of how to include a relief valve in a system.
1. INTRODUCTION This tutorial describes the theory, modeling procedure and example of a pressure relief valve in BOSfluids. A pressure relief valve or safety valve is generally used to protect a vessel or piping system from over-pressure in emergency situations such as rapid valve closure. Typically the inlet nozzle of the relief valve is closed-off by a disk which is held down by a spring. The relief valve is designed or set to open at a certain Set Pressure. According to the upstream pressure the disk rises to attain a maximum lift at the Full Flow Pressure. At this point the effective flow area and hence the flow rate through the valve attains a maximum. As the fluid is discharged, the pressure drops and when the upstream pressure decreases below the Reseat Pressure the valve closes. Relief valves are classified as conventional or balanced, depending on the effect of back pressure on their performance. For conventional relief valves the back pressure acting on the disk is influenced by the upstream pressure, while for balanced type relief valves, the back pressure is isolated from the valve. Relief valves are used for both liquid and gas systems. Liquid relief valves rise more slowly as the pressure increases, while relief valves in a gas system (called safety valves), already attain maximum disk lift with little overpressure. The Full Flow Pressure, where the rated flow is established, depends on the manufacturers design, but typically for gases it is between 103% and 105% of the Set Pressure and for liquids it is around 110%. The Reseat Pressure is typically between 80% and 95% of the Set Pressure. 1.1. Choked Flow Capacity Theory For relief valves for gas services the flow rate through the valve reaches a constant value so that, under adiabatic flow conditions, the flow through a relief valve is directly proportional to the absolute upstream pressure (choked flow). The gas discharge is evaluated by the formula: ( ) ( ) Where Q = Flow rate through the valve. Cd = Discharge coefficient of the valve. A = Effective discharge area of the valve. Copyright Dynaflow Research Group. Page 1 of 11
Pu = Upstream absolute pressure. M = Molecular weight of the gas or vapor. Z = Compressibility factor. If not available (for a gas), a value of 1.0 is conservatively used. R = Universal gas constant. T = Absolute gas temperature at the inlet. γ = Specific heat ratio of the gas (cp/cv). This flow rate is valid for choked gas flow. When the downstream pressure exceeds the critical pressure P* the flow rate is restricted. The absolute critical pressure is found by the following perfect gas relationship: ( [ ] ) 1.2. BOSfluids Algorithm for s BOSfluids uses the following relation to determine the flow rate through valves: With Q the mass flow rate, A the cross-sectional area, g the gravitational acceleration and Δh the pressure loss in head. To account for the differential head loss during the opening or closing of a relief valve the model shown in Figure 1 is used. Figure 1 Schematic of a basic relief valve Page 2 of 11 Copyright Dynaflow Research Group.
The parameters as shown in Figure 1 are provided by the user, Where: m k = Valve bore = Mass of disk and moving parts = Spring stiffness = Dampening percentage The maximum lift, xr, the disk reaches is estimated as 27% of the valve bore. The displacement, x, of the valve disk is found from: where τ is opening percentage and em the valve closure exponent (a value of 1.0 will provide a linear opening curve). The critical damping, ζ0, and the actual damping, ζ, are calculated as: If the mass or spring stiffness is entered the pressure loss (in head) is found as: With Q the flow rate, ρ the density, g the gravitational constant, A the throat area of the valve and hset the set pressure in head. When the mass and spring stiffness are not entered the pressure loss is found as: ( ) If the user did not enter a value for the mass and stiffness, the valve response is based on the pressure rise. When the response time of the valve is important with respect to the response time of the event, (usually in the order of 10 to 20 ms or less), then the user is encouraged to enter the mass and stiffness associated with the valve. Copyright Dynaflow Research Group. Page 3 of 11
2. EXAMPLE-TANK FILL 2.1. Introduction Figure 2 Node description of model The following example will describe the process of filling a tank while a shutoff valve is closing, causing the flow to be diverted through the relief valve. The tank fluid elevation is 10 m which converts into a static pressure at node 25 of 1 barg. The quick closure shutoff valve between nodes 15 and 20 can be closed in one second. When the shutoff valve closes and the pressure builds up sufficiently, the relief valve will lift at 17 barg. Its rated opening pressure (full flow pressure) is 21 barg, and the reseat pressure on closing is 15.5 barg. Therefore the question is: When the Shutoff valve shuts, will the relief valve adequately redistribute the flow. A Long Pipe boundary condition will be used at node 5 with a rated flow of 0.1 m 3 /s = 360 m 3 /h. The Long Pipe boundary will prevent reflections and will support any pressure or flow presented to it downstream. This will represent a long incoming pipeline. 2.2. Building the model Start BOSfluids and create a new model using the information from Figure 2 and Table 1 to define all the elements leave the other parameters as default. The valve at 15-to-20 will be closed in one second (starting after 1 second and ending after 2 seconds) during the transient simulation, with a closure exponent of 0.23 (Click Configure Valve and specify the Closure Exponent). For the relief valve specify the Set Pressure at 17 barg, the Full Flow Pressure at 21 barg and the Reseat Pressure 15.5 barg. For this initial simulation no disk mass or spring stiffness will be defined. Leave all other parameters as default, see Figure 3. Page 4 of 11 Copyright Dynaflow Research Group.
Table 1 Element parameters Element Length Type Parameters 5 10 X-dim : 60.0m Pipe Diameter = 273.1mm, Thickness = 9.27mm 10 15 X-dim : 1.5m Pipe Diameter = 273.1mm, Thickness = 9.27mm 15 20 X-dim : 0.5m Valve Diameter = 273.1mm, Valve Bore = 211.5mm, Discharge Coefficient = 0.5 20 25 X-dim : 0.5m Pipe Diameter = 273.1mm, Thickness = 9.27mm 10 30 Y-dim : 1.2m Pipe Diameter = 219.1mm, Thickness = 8.18mm 30 35 X-dim : -0.3m, Y-dim : 0.3m Relief Valve Diameter = 219.1mm, Valve Bore = 107.0mm, Discharge Coefficient = 0.632 35 40 X-dim : -4.7m Pipe Diameter = 273.1mm, Thickness = 9.27mm 40 45 Y-dim : -1.2m Pipe Diameter = 273.1mm, Thickness = 9.27mm Figure 3 Set element parameters in Elements sub-tab Copyright Dynaflow Research Group. Page 5 of 11
Continue to the Scenarios tab and specify the boundary conditions in the Nodes & BCs subtab, see Table 2. Table 2 Element parameters Node Type Parameters 5 Long Pipe Flow rate = 360 m 3 /h 25 Fixed Pressure Pressure = 1.0 barg 45 Fixed Pressure Pressure = 0.0 barg In the sub tab Analysis choose a Transient analysis. Specify the fluid as Water and the Simulation Time to be 4.0 seconds, see Figure 4. Figure 4 Specify the Boundary Conditions and Analysis parameters Proceed to the Run tab and run the simulation. Page 6 of 11 Copyright Dynaflow Research Group.
2.3. Results and Discussion 2.3.1. Initial Scenario First we take a look at the pressure over the relief valve. In the 2-D output section, select Element. Then double click or select the relief valve and plot the Pressure Drop, see Figure 5. Figure 5 Transient Pressure Drop over the In Figure 5, it can be seen that the pressure rises after 1 second due to the closing of the shutdown valve. Once the pressure reaches the set pressure of 17 bar at 1.84 seconds, the opens and the flow is diverted through the relief valve. The pressure only slightly increases between the 1.84 seconds and 2.0 seconds which causes the relief valve to open to 12% and support a flow rate of 140 m 3 /h, see Figure 6. Figure 6 The Opening of the and the Flow Rate through the Copyright Dynaflow Research Group. Page 7 of 11
After the shutdown valve is completely closed (after 2 seconds) the flow rate at the inlet marginally recovers. The information of the closing valve never reaches the source of the flow because of the Long Pipe boundary condition; hence there are no reflecting pressure waves. Depending on the type boundary at the source of the flow, the returning pressure wave will either be an expansion wave with an accompanying drop in pressure, or a compression wave, with an accompanying increase in pressure. At a pressure let-down station, the boundary condition would be more accurately simulated by a fixed flow. 2.3.2. Fixed Flow Boundary Condition Create a new scenario to simulate a fixed flow boundary at node 25. Go to the Nodes &BCs sub-tab and specify a Fixed Flow boundary condition at node 5 with a flow rate of 360 m 3 /h, see Figure 7. Figure 7 Create a new scenario in the scenarios tab and modify the boundary condition for node 5 Proceed to the Run tab and run the simulation for the new scenario. Page 8 of 11 Copyright Dynaflow Research Group.
The pressure reflections with a Fix Flow boundary condition at node 25 are shown in Figure 8. Figure 8 Transient Pressure Drop over the for a Fixed Flow boundary condition The Fix Flow boundary condition acts like a closed end that imparts a velocity onto the flow. This will send a compression wave through the system further increasing the pressure to a point that the full flow rate of 360 m 3 /h is diverted through the relief valve, see Figure 9. The pressure drop over the relief valve is still not large enough to completely open the valve. Figure 9 The Opening of the and the Flow Rate through the for a Fixed Flow boundary condition 2.3.3. Fast Closing Shutdown Valve A fast closing shutdown valve would create a much larger surge pressure and a high frequency response. Return to the Scenarios tab and create a new scenario based on the Fixed Flow BC scenario, by opening the scenarios menu and copying the second scenario. Copyright Dynaflow Research Group. Page 9 of 11
For the new scenario, open the Valve Actions dialog for the shutdown valve and modify the closure of the valve to close in 0.1 seconds, see Figure 10. Figure 10 Valve Actions for the shutdown valve to close in 0.1 second Run the simulation for the new scenario and examine the results. The fast closure of the shutdown valve causes a larger pressure peak and more fluctuations of the inlet pressure of the relief valve. Since the pressure drop over the relief valve determines the opening and the flow through the valve, for the relief valve will also see rapid fluctuations in its opening, see Figure 11. Figure 11 Opening of the due to the pressure peaks of the fast closing shutdown valve For this case, the relief valve is modeled without any mass and spring stiffness. This means the relief valve shows undamped behavior. For fast acting relief valves, such as in this latest scenario, adding a spring stiffness and assembly mass to the model dampens the disk travel and hence the valve opening. This could help make the system act more realistically. Page 10 of 11 Copyright Dynaflow Research Group.
2.3.4. Damped Create a fourth scenario based on the third scenario. To provide sufficient damping, specify a Disk Mass of 25 kg and a Spring Stiffness of 50000 N/m. Increase the Damping Percentage to 100%. Run the simulation for the new scenario. As shown in Figure 12 the opening behavior of the relief valve is more damped than for the case in Figure 11. Beware that specifying a low mass or spring stiffness could lead to unwanted flutter. Figure 12 Opening of the including damping Copyright Dynaflow Research Group. Page 11 of 11