Aws WJ Esp 201701
Aws WJ Esp 201701
Aws WJ Esp 201701
MTS2017-0408
Laboratory Testing of Safety Relief Valves
Thomas Kegel (tkegel@ceesi.com) and William Johansen (bjohansen@ceesi.com)
Colorado Engineering Experiment Station, Inc. (CEESI)
54043 WCR 37, Nunn, Colorado 80648
2
π C d Y
Figure 1: Typical Venturi Meter qm = d 2ρ∆p [Eq. 2]
4 1 − β4
Where:
∆P ρ = density
p1, p2= two pressure measurements
∆p = p1-p2: differential pressure
d = throat or bore diameter
FLOW Free Jet
D = inlet or tube diameter
β = d/D
Cd = discharge coefficient
Y= gas expansion factor
Figure 2: Typical Orifice Meter
57 Published with permission.
1.02 0.625
1.01
1.00 0.620
Discharge Coefficient
Discharge Coefficient
0.99
0.615
0.98 Turbulent boundary layer
0.97 0.610
Laminar boundary layer
0.96
0.605
0.95
0.94 0.600
0 20 40 60 80 100 120 140 0.0 0.5 1.0 1.5 2.0 2.5
Reynolds Number [thousands] Reynolds Number [millions]
Figure 3: Typical Venturi Meter Data Figure 4: Typical Orifice Meter Data
58
59
Spring
Housing
Seal Disc ∆P
Seat
Flow
The vessel pressure acting over the disc area increases flow path is difficult to predict, another characteristic
until sufficient to overcomes spring force and the valve that can be determined from laboratory testing.
opens. The arrows represent the flow path of the vented
material; the housing is perforated to allow venting. As One common feature not shown in Figure 5 is a physi-
shown in Figure 1 a Venturi is characterized by a gradu- cal stop that limits spring compression. The stop helps
al change in area along the flow path. In contrast an ori- maintain a constant open flow area at higher flowrates.
fice is characterized by a single abrupt change in area.
The area variation of the flow path in Figure 5 does not Test Data Examples
resemble that of either meter. The effect of a complex
This section describes examples of data from five tests.
7.0
The cases illustrate a variety of PRV tests, based on both
liquid and gas, as well as a variety of data presentations.
6.0 The discussion compares and contrasts test results with
flow meter calibrations.
Effecve Area
5.0
4.0 Case 1
3.0
Data from the first valve test are contained in Figures
2.0 6a and 6b. In each graph the abscissa is Reynolds Num-
0.0 0.2 0.4 0.6 0.8 1.0
Reynolds Number [millions]
ber with nominal valve diameter as the characteristic
length. The ordinate is effective area as defined by Equa-
6.6 tion 5. Figure 6b shows a limited range of the same data
as Figure 6a. The engineering units of effective area
6.4
can vary depending on the units selected or the vari-
ables in Equation 5. The data presented as case studies
Effecve Area
6.2
is focused on how Ae varies as opposed to the absolute
6.0
value. When laboratory data are applied to the field it is
5.8 important that consistent engineering units are applied
when calculating Ae.
5.6
0.2 0.4 0.6 0.8 1.0
Reynolds Number [millions] The Figure 6 data define very different curves above and
below Re = 0.4 million. Much of the lower Re range data
define a curve similar to the Venturi curve of Figure 3
Figures 6a (upper) and 6b (lower) : Case 1 Test Re-
suggesting a similar boundary layer based behavior.
sults
60
766
mation about the test stability as well as supporting an
764
uncertainty analysis. The data of Figure 4, for example,
762
quantify the random variations in liquid and gas cali-
760
brations.
758
756 Case 2
295 300 305 310 315 320
Flowrate [sc, thousands]
Data from the second valve test are contained in Fig-
ure 7. The abscissa is flowrate and the ordinate is Cv as
Figure 7: Case 2 Test Results defined by Equation 8. As stated above in reference to
Ae, the engineering units for Cv vary depending on the
units of Equation 8. In the present discussion the shape
Two observations are noted: First, the change in curva-
of the curve is more important than the absolute value.
ture for Re < 0.2 million is not generally observed with
These data were obtained over a very narrow range of
venturi meters. Second, the variation in Ae is much larg-
conditions which is typical of many valve tests. While
er than the typical range of Venturi Cd values. Both ob-
the data range is narrow, a trend is noted is the data; a
servations are attributed to an assumed gradual change
1% change in Cv results from a 5% change in flowrate.
in valve disc position with increasing pressure.
The data are only applicable over the narrow range, op-
eration outside the range requires extrapolation.
Laboratory data such as those in Figure 6 are applied
to the installed conditions to predict flowrate based on
A first impression might suggest that the observed
differential pressure and density. The values of Ae are
trend represents operation where the valve disc posi-
nominally constant for Re > 0.4 million meaning that
tion changes with pressure. This behavior would result
small variations in pressure or density will not affect the
in a positive slope that is not present in Figure 7. An-
flowrate capacity. The region of constant Ae likely rep-
other explanation would be a valve flow geometry that
resents valve operation where an increase in pressure
resembles an orifice meter, the low Re data of Figure 4
does not result in movement of the valve disc.
shows a negative slope. Confirming evidence can gen-
erally be obtained based on calibration over a broader
Ideally test data are obtained over the range of antici-
flowrate range.
pated field operating conditions (pressure, temperature
composition). Generally the valve cannot be tested us-
One parameter that has not been discussed is the gas
ing actual fluid and the laboratory uses a “surrogate”
expansion factor. In general Y decreases with increas-
fluid that exhibits similar behavior. The Reynolds num-
ing flowrate which corresponds to increasing ∆P/P.
ber is the most common parameter applied to achieve
The slope of the data of Figure 7 could be the result of
similarity. Sometimes the vented fluid composition is
a decrease in Y. The gas expansion factor is a measure
unknown because the fluid system operating in an up-
of Mach number which is important to understanding
set condition. In this case calculating a Re value can be
choked flow. As noted above, choked flow is beyond the
difficult.
scope of the present paper.
Figure 6b includes a pair of dashed lines that form a
Case 3
statistical interval that contains 95% of the data; within
this interval it can be stated that Ae = 6.26 ±1%. The
The first two cases are based on data obtained over
PRV user can decide if the uncertainty is adequate to
steady state conditions. Case 3 is based on observing
assume a constant Ae in the application.
how instrument reading change under dynamic condi-
tions. The data are contained in Figure 8; the abscissa is
Common laboratory practice is to average instrument
readings over a time interval and process the averaged
61
Flowrate [lb/s]
Pressure [psi]
Pressure
20
60 P4 discharge pressure” point at t = 146 sec. This is the first
15
40 data point (P1) of four that are reported to the customer.
10
The interval 146 < t < 160 sec. characterizes the disc be-
20 Flowrate 5
ginning to move way from the seat as the pressure force
0 0 compresses the spring. The pressure decreases with
50 100 150 200 250 300 350
Elapsed Tme [sec] 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 ear-
Figure 8: Case 3 Test Results lier the instabilities are more common with compress-
ible flow. The size of a buffer tank can affect the ampli-
tude of instabilities.
elapsed time and the ordinates show flowrate and pres-
sure.
The pressure and flowrate curves each reach maximum
values at t = 210 sec.; the peak values represent an over-
As the test begins the flowrate curve does not indicate
shoot condition that allows the target pressure to be ap-
zero flow; this behavior is a result of the test design. First,
proached from a higher value. The conditions are well
the flow standard is selected to best measure flowrate at
controlled resulting in the steady pressure and flowrate
nominal valve operating conditions; at lower flowrates
data observed for 230 < t < 280 sec. Averaged data are
it is operating below the best measurement range. Sec-
reported at t = 230 and 280 sec. (P2, Q2 and P3, Q3); the
ond, a buffer tank is installed between a control valve
two sets of data bracket the requested pressure (85 psia).
and the PRV under test to ensure an adequate supply of
For 280 < t < 300 sec. the control valve is closing with
compressed air to maintain steady flow at high pressure.
accompanying decreases in pressure and flowrate. At t
= 311 sec. the pressure rises slightly as a result of the
20
closed valve being bubble tight (P4).
15
Decreasing
Case 4
Effecve Area
Pressure
10
Two tests of the same valve illustrate valve dynamics
Increasing and how they are potentially distorted by the test setup.
5 Pressure
Figure 9a shows a hysteresis loop exhibited by a PRV;
the abscissa is pressure and the ordinate is effective area.
0
220 240 260 280 300 320 Each symbol represents an instrument reading; blue
Pressure [psi] and red represent increasing and decreasing pressure.
Decreasing
Pressure to a steady value that is stable over a pressure range. As
10
Pressure noted above, steady Ae is beneficial for the user.
5
Figure 9b shows an earlier test of the same PRV. The
clearly defined hysteresis loop at 250 < P < 300 psi is
0
220 240 260 280 300 320 missing; instead the Ae value are unstable. Each test in-
Pressure [psi] cludes a buffer tank as described in Case 3; the first (9b)
contains 480 cubic feet, the second (9a) contains 700
Figure 9a (upper) and 9b (lower): Case 4 Test Results cubic feet. The larger volume likely results in more re-
62
150
15 Turns
1. API 14.3, “Orifice Metering of Natural Gas and
Effecve Area
100
12 Turns
Other Related Hydrocarbon Fluids—Concentric,
9 Turns Square-edged Orifice Meters,” 2016.
50
6 Turns 2. ANSI/ISA–75.01.01, “Flow Equations for Sizing
3 Turns Control Valves,” 2002.
0
0 500 1000 1500 2000 2500
Flowrate [gpm]
Case 5
63