Laboratory Testing of Safety Relief Valves

Transcription

1 Laboratory Testing of Safety Relief Valves Thomas Kegel and William Johansen Colorado Engineering Experiment Station, Inc. (CEESI) 5443 WCR 37, Nunn, Colorado 8648 Proceedings of the ASME/USCG 217 4th Workshop on Marine Technology and Standards MTS217 October 16-17, 217, Washington, DC, USA MTS Introduction Industrial fluid handling and storage systems can experience excessive pressure resulting from process upsets. A catastrophic component failure can compromise personnel safety or damage property. A pressure relief valve (PRV) represents a common design element that allows material to be vented to reduce pressure and restore safe conditions. Obviously selecting the proper PRV requires specification of the relief pressure. Less obvious might be the requirement of confirming that the flowrate is adequate to vent the system volume. The relationship between discharge pressure and flowrate must ultimately be based on laboratory testing. In the absence of laboratory data the predicting the flowrate capacity will be higher. Common practices include testing one sample valve of a particular size and design or extrapolating to a similar design. Uncertainty is always introduced when a group of products is characterized based on a few samples. In the current application P the user needs to decide if the uncertainty in predicted flowrate, if available, is acceptable for the application. This paper describes several aspects of PRV testing. The discussion begins with design descriptions and operating equations for orifice and venturi meters. Next several PRV operating equations are presented along with a generic valve design. Flow meter and valve similarities and differences are noted. The third section consists of five case studies based on PRV calibration data. The case studies illustrate several types of tests and relate the data to laboratory experience with flow meter calibration. Flowmeter Equations The conservation equations of energy (Bernoulli) and mass (continuity) are applied to provide a simplified mathematical description of the flow through a converging-diverging channel. The differential producing flow element represents one common industrial application of the generalized analysis. The volume (q V ) and mass (q m ) flowrates of fluid through a differential producing flow element are given by: FLOW q v 2 π CdY d = 4 ρ 4 1 β 2 p [Eq. 1] Figure 1: Typical Venturi Meter P FLOW Free Jet Figure 2: Typical Orifice Meter 2 CdY d 4 π qm = 2ρ p 4 1 β Where: ρ = density p 1, p 2 = two pressure measurements p = p 1 -p 2 : differential pressure d = throat or bore diameter D = inlet or tube diameter β = d/d C d = discharge coefficient Y= gas expansion factor [Eq. 2] 57 Published with permission.

2 A typical Venturi meter is shown in Figure 1. The shape of the venturi provides complete guidance from a larger flow area (inlet) to a smaller flow area (throat). The p is the difference between inlet (p 1 ) and throat (p 2 ) pressures. A typical orifice meter, shown in Figure 2, consists of a sharp edged orifice installed within a 15D - 3D long meter tube. The flow forms a free jet downstream of the plate, the acceleration of the fluid into the jet produces the reduced pressure (p 2 ). The Reynolds Number (Re) is defined as: or 4q m 4ρq Re = = v π dµ π dµ 4q m 4ρq Re = = v π Dµ π Dµ where μ is the absolute viscosity. [Eq. 3a] [Eq. 3b] The Reynolds number is the ratio if inertial forces to viscous forces. The inertial forces quantify the tendency of the fluid to keep moving, the momentum; the viscous forces quantify the tendency of the fluid motion to be retarded. The Reynolds number allows for kinematic similarity between two systems; in flow measurement the two systems are the calibration laboratory and the field installation. The Reynolds number is calculated based on a characteristic length that is relevant to the particular application. With flow measurement either the inlet or throat diameter is used. The discharge coefficient accounts for Reynolds number effects that reduce the mass flowrate from the ideal case. In a Venturi, the dominant Re effect arises from a boundary layer that forms along the internal wall. The presence of a low velocity boundary layer reduces the flowrate and C d decreases in proportion. An example of Venturi calibration results is contained in Figure 3. The open symbols represent data points, the lines represent curve fits of the data. The equation formats match those that traditionally predict boundary layer thickness changes with Reynolds number. The laminar boundary layer is much more sensitive to Re. Most Venturi meters are designed to operate at high Re to reduce the sensitivity. The flow through an orifice plate is unguided, a free jet forms adjacent to the outlet pressure tap. The discharge coefficient accounts for jet contraction in response to the inlet velocity profile, which is in turn a function of Reynolds number. The orifice meter data contained in Figure 4 represent part of the database of on which Reference 1 is based. Like the Venturi the C d is nominally constant over the higher Re range. Unlike the venturi the C d rises at low Re, the result of very different underlying physical behavior. The random variations in the data of Figure 4 are quite a bit smaller in the low Reynolds number range. These data were obtained in a liquid calibration system while the higher Re data were obtained using compressed gas. These results are typical; gas calibration systems are more difficult to control because of larger variations in pressure and temperature. The gas expansion factor accounts for the change in density between the two pressure taps. Typically Y< 1, Discharge Coefficient Turbulent boundary layer Laminar boundary layer Discharge Coefficient Reynolds Number [thousands] Reynolds Number [millions] Figure 3: Typical Venturi Meter Data 58 Figure 4: Typical Orifice Meter Data

3 the exact value depends on the thermodynamic process as the fluid moves from between the taps. It is often characterized as a function of the measured pressure values, three examples are: or or Y = f( p/p 1 ) [Eq. 4a] Y = f( p/p 2 ) [Eq. 4b] Y = f(p 2 /p 1 ) [Eq. 4c] Liquids are considered incompressible and Y=1. In general the curves predicting C d and Y are unique for an individual meter. Calibration is always recommended for critical applications. Relief Valve Equations The flow through a pressure relief valve is governed by the same principles as a differential producing flowmeter. This section describes similarities and difference in the presentation and interpretation of laboratory data. One way to represent PRV data is to define an effective area (A e ): 2 CdY d 4 π Ae = β Applying Equations 1, 2 and 5 results in: qv = A p e ρ m e [Eq. 5] [Eq. 6] q = A ρ p [Eq. 7] The differential p is the difference between pressure vessel and barometric pressures. Selecting the proper density can be a challenge because it might be unknown during a process upset. The terms d and β are constant aside from minor thermal expansion while the terms C d and Y might be constant depending on valve design. The effective area is constant if all four variables are constant. Like a flowmeter C d, constant A e simplifies the task of predicting field performance by reducing the sensitivity to an independent variable like flowrate or Reynolds number. The control valve coefficient, C v, represents another way to represent valve data. Below is one of several equations given in Reference 2: where: C V W = NY xp ρ 1 1 C v = valve coefficient W = mass flowrate N = unit conversion coefficient Y = gas expansion factor P 1 = inlet pressure ρ 1 = inlet density x = P/P 1 [Eq. 8] The N coefficient varies in value depending on the engineering units. The values of Cv and Y are determined from laboratory test data. As noted Reference 2 contains several multiple equations to include the following conditions: gas or liquid low (laminar) or high (turbulent) Reynolds number installed fittings choked flow Several parameters appear in other equations. A Reynolds number factor (F R ) accounts for reduced flow at low Re. A factor (FP) accounts for the pipe and fittings installed adjacent to the PRV; either during testing or in the final installation. Choked flow is a special case where the pressure drop is sufficiently high enough so that the local velocity reaches the speed of sound. Operation at the speed of sound is outside the scope of this paper. Relief Valve Operation Figure 5 shows the conceptual sketch of a generic pressure relief valve in the open and closed position. It is bolted to the top a pressure vessel being protected. The spring holds the valve disc and seal against the seat. The housing is a rigid structure that supports the spring load as well as providing some protection from the ambient environment. The nut at the top of the housing represents a method to adjust the spring tension and change the valve characteristics. 59

4 Adjust Housing Spring Seal Disc Seat P Flow Figure 5: Generic Valve in Closed (left) and Open (right) Positions The vessel pressure acting over the disc area increases until sufficient to overcomes spring force and the valve opens. The arrows represent the flow path of the vented material; the housing is perforated to allow venting. As shown in Figure 1 a Venturi is characterized by a gradual change in area along the flow path. In contrast an orifice is characterized by a single abrupt change in area. The area variation of the flow path in Figure 5 does not resemble that of either meter. The effect of a complex flow path is difficult to predict, another characteristic that can be determined from laboratory testing. One common feature not shown in Figure 5 is a physical stop that limits spring compression. The stop helps maintain a constant open flow area at higher flowrates. Test Data Examples This section describes examples of data from five tests. The cases illustrate a variety of PRV tests, based on both liquid and gas, as well as a variety of data presentations. The discussion compares and contrasts test results with flow meter calibrations. Case Reynolds Number [millions] Reynolds Number [millions] Figures 6a (upper) and 6b (lower) : Case 1 Test Results 6 Data from the first valve test are contained in Figures 6a and 6b. In each graph the abscissa is Reynolds Number with nominal valve diameter as the characteristic length. The ordinate is effective area as defined by Equation 5. Figure 6b shows a limited range of the same data as Figure 6a. The engineering units of effective area can vary depending on the units selected or the variables in Equation 5. The data presented as case studies is focused on how A e varies as opposed to the absolute value. When laboratory data are applied to the field it is important that consistent engineering units are applied when calculating A e. The Figure 6 data define very different curves above and below Re =.4 million. Much of the lower Re range data define a curve similar to the Venturi curve of Figure 3 suggesting a similar boundary layer based behavior.

5 Valve Coefficient, Cv Figure 7: Case 2 Test Results Flowrate [sc, thousands] Two observations are noted: First, the change in curvature for Re <.2 million is not generally observed with venturi meters. Second, the variation in A e is much larger than the typical range of Venturi C d values. Both observations are attributed to an assumed gradual change in valve disc position with increasing pressure. Laboratory data such as those in Figure 6 are applied to the installed conditions to predict flowrate based on differential pressure and density. The values of A e are nominally constant for Re >.4 million meaning that small variations in pressure or density will not affect the flowrate capacity. The region of constant A e likely represents valve operation where an increase in pressure does not result in movement of the valve disc. Ideally test data are obtained over the range of anticipated field operating conditions (pressure, temperature composition). Generally the valve cannot be tested using actual fluid and the laboratory uses a surrogate fluid that exhibits similar behavior. The Reynolds number is the most common parameter applied to achieve similarity. Sometimes the vented fluid composition is unknown because the fluid system operating in an upset condition. In this case calculating a Re value can be difficult. Figure 6b includes a pair of dashed lines that form a statistical interval that contains 95% of the data; within this interval it can be stated that A e = 6.26 ±1%. The PRV user can decide if the uncertainty is adequate to assume a constant A e in the application. Common laboratory practice is to average instrument readings over a time interval and process the averaged values to form a single data point. Each symbol in Figure 6 represents an individual sample. Analysis of individual readings data can often yield additional information about the test stability as well as supporting an uncertainty analysis. The data of Figure 4, for example, quantify the random variations in liquid and gas calibrations. Case 2 Data from the second valve test are contained in Figure 7. The abscissa is flowrate and the ordinate is C v as defined by Equation 8. As stated above in reference to A e, the engineering units for C v vary depending on the units of Equation 8. In the present discussion the shape of the curve is more important than the absolute value. These data were obtained over a very narrow range of conditions which is typical of many valve tests. While the data range is narrow, a trend is noted is the data; a 1% change in C v results from a 5% change in flowrate. The data are only applicable over the narrow range, operation outside the range requires extrapolation. A first impression might suggest that the observed trend represents operation where the valve disc position changes with pressure. This behavior would result in a positive slope that is not present in Figure 7. Another explanation would be a valve flow geometry that resembles an orifice meter, the low Re data of Figure 4 shows a negative slope. Confirming evidence can generally be obtained based on calibration over a broader flowrate range. One parameter that has not been discussed is the gas expansion factor. In general Y decreases with increasing flowrate which corresponds to increasing P/P. The slope of the data of Figure 7 could be the result of a decrease in Y. The gas expansion factor is a measure of Mach number which is important to understanding choked flow. As noted above, choked flow is beyond the scope of the present paper. Case 3 The first two cases are based on data obtained over steady state conditions. Case 3 is based on observing how instrument reading change under dynamic conditions. The data are contained in Figure 8; the abscissa is 61

6 [psi] Figure 9b shows an earlier test of the same PRV. The clearly defined hysteresis loop at 25 < P < 3 psi is missing; instead the A e value are unstable. Each test includes a buffer tank as described in Case 3; the first (9b) contains 48 cubic feet, the second (9a) contains 7 cubic feet. The larger volume likely results in more re- 62 elapsed time and the ordinates show flowrate and pressure. As the test begins the flowrate curve does not indicate zero flow; this behavior is a result of the test design. First, the flow standard is selected to best measure flowrate at nominal valve operating conditions; at lower flowrates it is operating below the best measurement range. Second, a buffer tank is installed between a control valve and the PRV under test to ensure an adequate supply of compressed air to maintain steady flow at high pressure Decreasing P 1 P Elapsed Tme [sec] Figure 8: Case 3 Test Results Flowrate [psi] P 3 P 4 Increasing Flowrate [lb/s] The initial flowrate data represent the process of charging the buffer tank. Returning to the graph, flowrate begins at the start to discharge pressure point at t = 146 sec. This is the first data point (P 1 ) of four that are reported to the customer. The interval 146 < t < 16 sec. characterizes the disc beginning to move way from the seat as the pressure force compresses the spring. The pressure decreases with flowrate while the laboratory control valve is moving to increase pressure; interaction between the valves causes the small instability observed in Figure 8. As noted earlier the instabilities are more common with compressible flow. The size of a buffer tank can affect the amplitude of instabilities. The pressure and flowrate curves each reach maximum values at t = 21 sec.; the peak values represent an overshoot condition that allows the target pressure to be approached from a higher value. The conditions are well controlled resulting in the steady pressure and flowrate data observed for 23 < t < 28 sec. Averaged data are reported at t = 23 and 28 sec. (P 2, Q and P, Q ); the two sets of data bracket the requested pressure (85 psia). For 28 < t < 3 sec. the control valve is closing with accompanying decreases in pressure and flowrate. At t = 311 sec. the pressure rises slightly as a result of the closed valve being bubble tight (P 4 ). Case 4 Two tests of the same valve illustrate valve dynamics and how they are potentially distorted by the test setup. Figure 9a shows a hysteresis loop exhibited by a PRV; the abscissa is pressure and the ordinate is effective area. Each symbol represents an instrument reading; blue and red represent increasing and decreasing pressure Decreasing [psi] Increasing Figure 9a (upper) and 9b (lower): Case 4 Test Results is seen to be gradually building up to 29 psi with no flow (A e = ). Once the valve begins to open, the flowrate increases rapidly, recorded as A e, settling to a steady value that is stable over a pressure range. As noted above, steady A e is beneficial for the user.

7 2 References Turns 12 Turns 9 Turns 6 Turns 3 Turns Flowrate [gpm] 1. API 14.3, Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids Concentric, Square-edged Orifice Meters, ANSI/ISA , Flow Equations for Sizing Control Valves, 22. Figure 1: Case 5 Test Results alistic PRV performance data. The lesson learned from these tests is to properly design the test setup. Case 5 The previous case illustrates that the PRV spring contributes two flow characteristics not present in traditional flowmeters: First, the physical flow area increases with pressure as the spring is compressed. Second, instability can complicate testing and data interpretation. One laboratory solution is to replace the spring with a mechanism that holds the disc in a fixed position and allows the flow characteristics to be documented. Data from such a test are shown in Figure 1. Disc position is proportional to a number of turns; the graph shows five disc positions. Each curve exhibits a linear region where A e does not vary with flowrate. As expected both A e and the linear range flowrate increase with the number of turns. Each curve exhibits an increase in A e at low flowrate, much like the orifice data of Figure 4. Summary and Conclusions This paper discussed laboratory testing of gas and liquid pressure relief valves. The first section described the operation and equations of two differential producing flowmeters. The next section compared and contrasted the valves and flowmeter equations. The paper concludes with five case studies. The important lesson is that the operation of a pressure relief valve can only be fully characterized based laboratory testing. 63