Safety/relief valve sizing (fluids.safety_valve)

This module contains functions for sizing and rating pressure relief valves. At present, this consists of several functions from API 520.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.

Interfaces

fluids.safety_valve.API520_A_g(m, T, Z, MW, k, P1, P2=101325, Kd=0.975, Kb=1, Kc=1)

Calculates required relief valve area for an API 520 valve passing a gas or a vapor, at either critical or sub-critical flow.

For critical flow:

\[A = \frac{m}{CK_dP_1K_bK_c}\sqrt{\frac{TZ}{M}}\]

For sub-critical flow:

\[A = \frac{17.9m}{F_2K_dK_c}\sqrt{\frac{TZ}{MP_1(P_1-P_2)}}\]

Parameters:

mpython:float

Mass flow rate of vapor through the valve, [kg/s]

Tpython:float

Temperature of vapor entering the valve, [K]

Zpython:float

Compressibility factor of the vapor, [-]

MWpython:float

Molecular weight of the vapor, [g/mol]

kpython:float

Isentropic coefficient or ideal gas heat capacity ratio [-]

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

P2python:float, optional

Built-up backpressure; the increase in pressure during flow at the outlet of a pressure-relief device after it opens, [Pa]

Kdpython:float, optional

The effective coefficient of discharge, from the manufacturer or for preliminary sizing, using 0.975 normally or 0.62 when used with a rupture disc as described in [1], []

Kbpython:float, optional

Correction due to vapor backpressure [-]

Kcpython:float, optional

Combination correction factor for installation with a rupture disk upstream of the PRV; 1.0 when a rupture disk is not installed, and 0.9 if a rupture disk is present and the combination has not been certified, []

Returns:

Apython:float

Minimum area for relief valve according to [1], [m^2]

Notes

Units are interlally kg/hr, kPa, and mm^2 to match [1].

References

[1] (1,2,3,4,5)

API Standard 520, Part 1 - Sizing and Selection.

Examples

Example 1 from [1] for critical flow, matches:

>>> API520_A_g(m=24270/3600., T=348., Z=0.90, MW=51., k=1.11, P1=670E3, Kb=1, Kc=1)
0.0036990460646834414

Example 2 from [1] for sub-critical flow, matches:

>>> API520_A_g(m=24270/3600., T=348., Z=0.90, MW=51., k=1.11, P1=670E3, P2=532E3, Kd=0.975, Kb=1, Kc=1)
0.004248358775943481

The mass flux in (kg/(s*m^2)) can be found by dividing the specified mass flow by the calculated area:

>>> (24270/3600.)/API520_A_g(m=24270/3600., T=348., Z=0.90, MW=51., k=1.11, P1=670E3, Kb=1, Kc=1)
1822.541960488834

fluids.safety_valve.API520_A_steam(m, T, P1, Kd=0.975, Kb=1, Kc=1, edition='10E')

Calculates required relief valve area for an API 520 valve passing a steam, at either saturation or superheat but not partially condensed.

\[A = \frac{190.5m}{P_1 K_d K_b K_c K_N K_{SH}}\]

Parameters:

mpython:float

Mass flow rate of steam through the valve, [kg/s]

Tpython:float

Temperature of steam entering the valve, [K]

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

Kdpython:float, optional

The effective coefficient of discharge, from the manufacturer or for preliminary sizing, using 0.975 normally or 0.62 when used with a rupture disc as described in [1], []

Kbpython:float, optional

Correction due to backpressure, see API520_B [-]

Kcpython:float, optional

Combination correction factor for installation with a rupture disk upstream of the PRV; 1.0 when a rupture disk is not installed, and 0.9 if a rupture disk is present and the combination has not been certified, []

editionpython:str, optional

One of ‘10E’, ‘7E’, [-]

Returns:

Apython:float

Minimum area for relief valve according to [1], [m^2]

Notes

Units are interlally kg/hr, kPa, and mm^2 to match [1]. With the provided temperature and pressure, the KN coefficient is calculated with the function API520_N; as is the superheat correction KSH, with the function API520_SH.

References

[1] (1,2,3,4,5)

API Standard 520, Part 1 - Sizing and Selection.

Examples

Example 4 from [1] 7th edition, matches:

>>> API520_A_steam(m=69615/3600., T=592.5, P1=12236E3, Kd=0.975, Kb=1, Kc=1, edition='7E')
0.001103471242369

Example 4 from the 10th edition of [1]:

>>> API520_A_steam(m=69615/3600., T=707.0389, P1=12236E3, Kd=0.975, Kb=1, Kc=1, edition='10E')
0.00128518893191

fluids.safety_valve.API520_A_l(m, rho, P1, P2, overpressure, Kd=0.65, Kc=1.0, Kw=None, Kv=None, edition='10E', mu=None)

Calculates required relief valve area for an API 520 valve passing a liquid in sub-critical flow.

\[A = \frac{11.78Q}{K_d K_w K_c K_v}\left(\frac{G_1}{P1 - P2}\right)^{0.5}\]

Parameters:

mpython:float

Mass flow rate of liquid through the valve, [kg/s]

rhopython:float

Liquid density, [kg/m^3]

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

P2python:float

Built-up backpressure; the increase in pressure during flow at the outlet of a pressure-relief device after it opens, [Pa]

overpressurepython:float

The maximum fraction overpressure; used if Kw is not specified, [-]

Kdpython:float, optional

The effective coefficient of discharge, from the manufacturer or for preliminary sizing, using 0.65 normally or 0.62 when used with a rupture disc as described in [1], []

Kcpython:float, optional

Combination correction factor for installation with a rupture disk upstream of the PRV; 1.0 when a rupture disk is not installed, and 0.9 if a rupture disk is present and the combination has not been certified, []

Kwpython:float, optional

Correction due to liquid backpressure [-]

Kvpython:float, optional

Correction due to viscosity [-]

editionpython:str, optional

One of ‘10E’, ‘7E’, [-]

mupython:float, optional

If provided and Kv is None, Kv will be calculated automatically, [Pa*s]

Returns:

Apython:float

Minimum area for relief valve according to [1], [m^2]

Notes

Units are interlally kg/hr, kPa, and mm^2 to match [1].

This expression is essentially a form of the Loss coefficient K expression, with many factors and unit conversions. The raw expression in SI units, with K the true loss coefficient, is as follows:

\[A = \frac{\sqrt{2} m \sqrt{\frac{K}{\rho \left(P_{1} - P_{2}\right)}}}{2}\]

The constant 11.78 is the result of the following conversions:

• 60000, converting from m^3/s to L/min

• sqrt(2)/2 as a factor from algebra

• 1e6 converting from m^2 to mm^2

• sqrt(1e-3*(rho0)) converting from Pa to kPa and kg/m^3 to specific gravity

The full precise value is (depending on the reference density chosen)

>>> sqrt(1e-3*(999.0107539518483))/60000*sqrt(2)/2*1e6
11.779282389196

The K value from a relief valve sized with this method can be calculated as follows:

\[K = \frac{2 A^{2} \rho \left(P_{1} - P_{2}\right)}{m^{2}}\]

The K value can also be directly calculated from the coefficients Kd, Kc, Kw, and Kv. The calculation is as follows, making use of the correction above.

\[K = \left(\frac{1}{K_d K_w K_c K_v\cdot (11.779282389196/11.78)}\right)^2\]

References

[1] (1,2,3,4)

API Standard 520, Part 1 - Sizing and Selection.

Examples

Example 5 in [1], 10th edition. The calculation involves numerous steps, shown below and ending with a recalculation with a viscosity correction.

>>> Q = 6814*1.6666666666666667e-05 # L/min to m^3/s
>>> rho = 0.9*999 # specific gravity times density of water kg/m^3
>>> m = rho*Q # mass flow rate, kg/s
>>> overpressure = 0.1
>>> P_design_g = 1724E3 # design pressure, guage
>>> P1 = (1+overpressure)*P_design_g + 101325.0 # upstream relieving pressure, Pa
>>> backpressure = 0.2
>>> mu = 0.388 # viscosity, Pa*s, converted from 2000 Saybolt Universal Seconds
>>> P2 = backpressure*P_design_g + 101325.0 # backpressure, Pa

Do the first calculation, using the value of Kw=0.97 shown in [1]

>>> A0 = API520_A_l(m=m, rho=rho, P1=P1, P2=P2, overpressure=overpressure, Kd=0.65, Kw=0.97, Kc=1.0, Kv=1.0)
>>> A0
0.0030661356203

This value matches the 3066 mm^2 shown in the example calculation.

Do the same calculation but allow the calculation of Kw automatically:

>>> A0 = API520_A_l(m=m, rho=rho, P1=P1, P2=P2, overpressure=overpressure, Kd=0.65, Kc=1.0, Kv=1.0)
>>> A0
0.0030585022573

There is a slight deviation with a more precise Kw value.

Compute Reynolds number from this original area

>>> from math import pi
>>> D = (A0*4/pi)**0.5
>>> v = Q/A0
>>> Re = rho*v*D/mu
>>> Re
5369.4253339

The reynolds number shown in [1] is 4525; the difference comes from the less precise Saybolt Universal Seconds conversion.

Compute the viscosity correction:

>>> Kv = API520_Kv(Re, '10E')
>>> Kv
0.984535878488

Compute the final area

>>> A = API520_A_l(m=m, rho=rho, P1=P1, P2=P2, overpressure=overpressure, Kd=0.65, Kc=1.0, Kv=Kv)
>>> A
0.003106542203

The final answer given in API 520 example 5 is 3122 mm^2, a very similar value despite the small differences.

If is also possible to have Kv be calculated by this routine automatically, by setting Kv to None and providing the fluid’s viscosity.

>>> A = API520_A_l(m=m, rho=rho, P1=P1, P2=P2, overpressure=overpressure, Kd=0.65, Kc=1.0, Kv=None, mu=mu)
>>> A
0.003106542203

As described in the note, an overall K value can be calculated for the valve

>>> K = 2*A**2*rho*(P1 - P2)/m**2
>>> K
2.5825844233354602

We can check the calculation

>>> from fluids.core import dP_from_K
>>> v = Q/A
>>> dP_from_K(K=K, rho=rho, V=v), P1-P2
(1551600.000, 1551600.00)

fluids.safety_valve.API521_noise(m, P1, P2, c, r)

Calculate the the noise coming from a flare tip at a specified distance according to API 521. A graphical technique is used to get the noise at 30 m from the tip, and it is then adjusted for distance.

\[L_{30 \text{m}} = L - 10 \log_{10}(0.5 m c^2)\]

\[L_p = L_{30 \text{m}} - 20 \log_{10}(r/(30 \text{m}))\]

Parameters:

mpython:float

Mass flow rate of relieving fluid, [kg/s]

P1python:float

Upstream pressure at the source, before the relieving device [Pa]

P2python:float

Atmospheric pressure, [Pa]

cpython:float

Speed of sound of the fluid at the relieving device [m/s]

rpython:float

Distance from the flare stack, [m]

Returns:

Lpython:float

Sound pressure level at the specified distance from the stack tip [decibels]

References

[1]

API Standard 521.

Examples

Example as shown in [1]:

>>> API521_noise(m=14.6, P1=330E3, P2=101325, c=353.0, r=30)
113.6841057

Functions and Data

fluids.safety_valve.API520_round_size(A)

Rounds up the area from an API 520 calculation to an API526 standard valve area. The returned area is always larger or equal to the input area.

Parameters:

Apython:float

Minimum discharge area [m^2]

Returns:

areapython:float

Actual discharge area [m^2]

Notes

To obtain the letter designation of an input area, lookup the area with the following:

API526_letters[API526_A.index(area)]

An exception is raised if the required relief area is larger than any of the API 526 sizes.

References

[1]

API Standard 526.

Examples

From [1], checked with many points on Table 8.

>>> API520_round_size(1E-4)
0.00012645136
>>> API526_letters[API526_A.index(API520_round_size(1E-4))]
'E'

fluids.safety_valve.API520_C(k)

Calculates coefficient C for use in API 520 critical flow relief valve sizing.

\[C = 0.03948\sqrt{k\left(\frac{2}{k+1}\right)^\frac{k+1}{k-1}}\]

Parameters:

kpython:float

Isentropic coefficient or ideal gas heat capacity ratio [-]

Returns:

Cpython:float

Coefficient C [-]

Notes

If C cannot be established, assume a coefficient of 0.0239, the highest value possible for C.

Although not dimensional, C varies with the units used.

If k is exactly equal to 1, the expression is undefined, and the formula must be simplified as follows from an application of L’Hopital’s rule.

\[C = 0.03948\sqrt{\frac{1}{e}}\]

References

[1]

API Standard 520, Part 1 - Sizing and Selection.

Examples

From [1], checked with many points on Table 8.

>>> API520_C(1.35)
0.02669419967057233

fluids.safety_valve.API520_F2(k, P1, P2)

Calculates coefficient F2 for subcritical flow for use in API 520 subcritical flow relief valve sizing.

\[F_2 = \sqrt{\left(\frac{k}{k-1}\right)r^\frac{2}{k} \left[\frac{1-r^\frac{k-1}{k}}{1-r}\right]}\]

\[r = \frac{P_2}{P_1}\]

Parameters:

kpython:float

Isentropic coefficient or ideal gas heat capacity ratio [-]

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

P2python:float

Built-up backpressure; the increase in pressure during flow at the outlet of a pressure-relief device after it opens, [Pa]

Returns:

F2python:float

Subcritical flow coefficient F2 [-]

Notes

F2 is completely dimensionless.

References

[1]

API Standard 520, Part 1 - Sizing and Selection.

Examples

From [1] example 2, matches.

>>> API520_F2(1.8, 1E6, 7E5)
0.8600724121105563

fluids.safety_valve.API520_Kv(Re, edition='10E')

Calculates correction due to viscosity for liquid flow for use in API 520 relief valve sizing.

From the 7th to 9th editions, the formula for this calculation is as follows:

\[K_v = \left(0.9935 + \frac{2.878}{Re^{0.5}} + \frac{342.75} {Re^{1.5}}\right)^{-1}\]

Startign in the 10th edition, the formula is

\[K_v = \left(1 + \frac{170}{Re}\right)^{-0.5}\]

In the 10th edition, the formula is applicable for Re > 80. It is also recommended there that if the viscosity is < 0.1 Pa*s, this correction should be set to 1.

Parameters:

Repython:float

Reynolds number for flow out the valve [-]

editionpython:str, optional

One of ‘10E’, ‘7E’, [-]

Returns:

Kvpython:float

Correction due to viscosity [-]

Notes

Reynolds number in the standard is defined as follows, with Q in L/min, G1 as specific gravity, mu in centipoise, and area in mm^2:

\[Re = \frac{Q(18800G_1)}{\mu \sqrt{A}}\]

The constant 18800 is derived as follows, combining multiple unit conversions and the formula from diameter from area together. The precise value is shown below.

>>> from scipy.constants import *
>>> liter/minute*1000./(0.001*(milli**2)**0.5)*sqrt(4/pi)
18806.319451591

Note that 4 formulas are provided in API 520 part 1; two metric and two imperial. One pair of formulas uses viscosity in conventional units; the other uses it in Saybolt Universal Seconds. A conversion is essentially embedded in the the Saybolt Universal Seconds formula. A more precise conversion can be obtained from chemicals.viscosity.viscosity_converter.

In both editions, if the formula is used below the recommended Re range and into the very low Re region this correction tends towards 0.

In the 10th edition, the formula tends to 1 exactly as Re increases. In the 7th edition, the formula can actually produce corrections above 1; this is handled by truncating the factor to 1.

References

[1]

API Standard 520, Part 1 - Sizing and Selection, 7E

[2]

API Standard 520, Part 1 - Sizing and Selection, 10E

[3]

CCPS. Guidelines for Pressure Relief and Effluent Handling Systems. 2nd edition. New York, NY: Wiley-AIChE, 2017.

Examples

From [1] 7E, checked with example 5.

>>> API520_Kv(100, edition='7E')
0.615744589

From [2] 10E, checked with example 5:

>>> API520_Kv(4525, edition='10E')
0.9817287137013179

Example in [3], using the 7th edition formula:

>>> API520_Kv(2110, edition='7E')
0.943671807

fluids.safety_valve.API520_N(P1)

Calculates correction due to steam pressure for steam flow for use in API 520 relief valve sizing.

For pressures below 10339 kPa, the correction factor is 1.

\[K_N = \frac{0.02764P_1-1000}{0.03324P_1-1061}\]

Parameters:

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

Returns:

KNpython:float

Correction due to steam temperature [-]

Notes

Although not dimensional, KN varies with the units used.

For temperatures above 922 K or pressures above 22057 kPa, KN is not defined.

Internally, units of kPa are used to match the equation in the standard.

References

[1]

API Standard 520, Part 1 - Sizing and Selection.

Examples

>>> API520_N(10500e3)
0.9969100255

fluids.safety_valve.API520_SH(T1, P1, edition='10E')

Calculates correction due to steam superheat for steam flow for use in API 520 relief valve sizing. 2D interpolation among a table with 28 pressures and 10 temperatures is performed.

Parameters:

T1python:float

Temperature of the fluid entering the valve [K]

P1python:float

Upstream relieving pressure; the set pressure plus the allowable overpressure, plus atmospheric pressure, [Pa]

editionpython:str, optional

One of ‘10E’, ‘7E’, [-]

Returns:

KSHpython:float

Correction due to steam superheat [-]

Notes

For P above 20679 kPag, use the critical flow model. Superheat cannot be above 649 degrees Celsius. If T1 is above 149 degrees Celsius, returns 1.

References

[1]

API Standard 520, Part 1 - Sizing and Selection.

Examples

Custom example from table 9, 7th edition:

>>> API520_SH(593+273.15, 1066.325E3, '7E')
0.7201800000

fluids.safety_valve.API520_B(Pset, Pback, overpressure=0.1)

Calculates capacity correction due to backpressure on balanced spring-loaded PRVs in vapor service. For pilot operated valves, this is always 1. Applicable up to 50% of the percent gauge backpressure, For use in API 520 relief valve sizing. 1D interpolation among a table with 53 backpressures is performed.

Parameters:

Psetpython:float

Set pressure for relief [Pa]

Pbackpython:float

Backpressure, [Pa]

overpressurepython:float, optional

The maximum fraction overpressure; one of 0.1, 0.16, or 0.21, [-]

Returns:

Kbpython:float

Correction due to vapor backpressure [-]

Notes

If the calculated gauge backpressure is less than 30%, 38%, or 50% for overpressures of 0.1, 0.16, or 0.21, a value of 1 is returned.

Percent gauge backpressure must be under 50%.

References

[1]

API Standard 520, Part 1 - Sizing and Selection.

Examples

Custom examples from figure 30:

>>> API520_B(1E6, 5E5)
0.7929945420944432

fluids.safety_valve.API520_W(Pset, Pback)

Calculates capacity correction due to backpressure on balanced spring-loaded PRVs in liquid service. For pilot operated valves, this is always 1. Applicable up to 50% of the percent gauge backpressure, For use in API 520 relief valve sizing. 1D interpolation among a table with 53 backpressures is performed.

Parameters:

Psetpython:float

Set pressure for relief [Pa]

Pbackpython:float

Backpressure, [Pa]

Returns:

KWpython:float

Correction due to liquid backpressure [-]

Notes

If the calculated gauge backpressure is less than 15%, a value of 1 is returned.

References

[1]

API Standard 520, Part 1 - Sizing and Selection. 7E

[2]

API Standard 520, Part 1 - Sizing and Selection. 10E

Examples

Custom example from figure 31 in [1]:

>>> API520_W(1E6, 3E5) # 22% overpressure
0.95114718480085

Example 5 from [2], set pressure 250 psig and backpressure up to 50 psig:

>>> API520_W(Pset=1825014, Pback=446062)
0.97242133397677

fluids.safety_valve.API521_noise_graph(P_ratio)

Calculate the L parameter used in the API 521 noise calculation, from their Figure 18, Sound Pressure Level at 30 m from the stack tip.

Parameters:

P_ratiopython:float

The ratio of relieving pressure to atmospheric pressure [-]

Returns:

Lpython:float

Sound pressure level at 30 m from the stack tip [decibels]

Notes

Two logarithmic linear polynomials are used. The function is continious throughout. The pressure ratio should be more than 1 for physical reasons; the value is checked for this case.

References

[1]

API Standard 521.

fluids.safety_valve.VDI_3732_noise_ground_flare(m)

Calculate the the noise at the flare tip of a ground flare [1], [2].

\[L = 100 + 15\log_{10}\left(\frac{m}{\text{tonne/hour}}\right)\]

Parameters:

mpython:float

Mass flow rate of relieving fluid, [kg/s]

Returns:

noisepython:float

Sound pressure level at the relieving flare stack [decibels]

References

[1]

VDI 3732 - Standard Noise Levels of Technical Sound Sources - Flares, 1999. https://www.vdi.de/en/home/vdi-standards/details/vdi-3732-standard-noise-levels-of-technical-sound-sources-flares.

[2]

AdminFlare Noise Calculator. WKC Group (blog). https://www.wkcgroup.com/tools-room/flare-noise-calculator/.

Examples

>>> VDI_3732_noise_ground_flare(3.0)
145.501356332

fluids.safety_valve.VDI_3732_noise_elevated_flare(m)

Calculate the the noise at the flare tip of an elevated flare stack [1], [2].

\[L = 112 + 17\log_{10}\left(\frac{m}{\text{tonne/hour}}\right)\]

Parameters:

mpython:float

Mass flow rate of relieving fluid, [kg/s]

Returns:

noisepython:float

Sound pressure level at the relieving flare stack [decibels]

References

[1]

VDI 3732 - Standard Noise Levels of Technical Sound Sources - Flares, 1999. https://www.vdi.de/en/home/vdi-standards/details/vdi-3732-standard-noise-levels-of-technical-sound-sources-flares.

[2]

AdminFlare Noise Calculator. WKC Group (blog). https://www.wkcgroup.com/tools-room/flare-noise-calculator/.

Examples

>>> VDI_3732_noise_elevated_flare(3.0)
163.56820384

fluids.safety_valve.API526_letters = ['D', 'E', 'F', 'G', 'H', 'J', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'T']

list: Letter size designations for different valve sizes in API 520

fluids.safety_valve.API526_A_sq_inch = [0.11, 0.196, 0.307, 0.503, 0.785, 1.287, 1.838, 2.853, 3.6, 4.34, 6.38, 11.05, 16.0, 26.0]

list: Nominal relief area in for different valve sizes in API 520, [in^2]

fluids.safety_valve.API526_A = [7.09676e-05, 0.00012645136, 0.00019806412, 0.00032451547999999997, 0.0005064506, 0.00083032092, 0.00118580408, 0.00184064148, 0.002322576, 0.0027999944, 0.004116120799999999, 0.007129018, 0.01032256, 0.01677416]

list: Nominal relief area in for different valve sizes in API 520, [m^2]