"""Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
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 <https://github.com/CalebBell/fluids/>`_
or contact the author at Caleb.Andrew.Bell@gmail.com.
.. contents:: :local:
Interfaces
----------
.. autofunction:: API520_A_g
.. autofunction:: API520_A_steam
.. autofunction:: API520_A_l
.. autofunction:: API521_noise
Functions and Data
------------------
.. autofunction:: API520_round_size
.. autofunction:: API520_C
.. autofunction:: API520_F2
.. autofunction:: API520_Kv
.. autofunction:: API520_N
.. autofunction:: API520_SH
.. autofunction:: API520_B
.. autofunction:: API520_W
.. autofunction:: API521_noise_graph
.. autofunction:: VDI_3732_noise_ground_flare
.. autofunction:: VDI_3732_noise_elevated_flare
.. autodata:: API526_letters
.. autodata:: API526_A_sq_inch
.. autodata:: API526_A
"""
from math import log10, pi, sqrt
from fluids.compressible import is_critical_flow
from fluids.constants import atm, inch
from fluids.numerics import bisplev, interp, tck_interp2d_linear
__all__ = ['API526_A_sq_inch', 'API526_letters', 'API526_A',
'API520_round_size', 'API520_C', 'API520_F2', 'API520_Kv', 'API520_N',
'API520_SH', 'API520_B', 'API520_W', 'API520_A_g', 'API520_A_steam',
'API521_noise', 'API521_noise_graph', 'VDI_3732_noise_ground_flare',
'VDI_3732_noise_elevated_flare', 'API520_A_l']
API526_A_sq_inch = [0.110, 0.196, 0.307, 0.503, 0.785, 1.287, 1.838, 2.853, 3.60,
4.34, 6.38, 11.05, 16.00, 26.00] # square inches
"""list: Nominal relief area in for different valve sizes in API 520, [in^2]"""
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"""
inch2 = inch*inch
API526_A = [i*inch2 for i in API526_A_sq_inch]
"""list: Nominal relief area in for different valve sizes in API 520, [m^2]"""
del inch2
TENTH_EDITION = '10E'
SEVENTH_EDITION = '7E'
[docs]def API520_round_size(A):
r'''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
----------
A : float
Minimum discharge area [m^2]
Returns
-------
area : 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.
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'
References
----------
.. [1] API Standard 526.
'''
for area in API526_A:
if area >= A:
return area
raise ValueError('Required relief area is larger than can be provided with one valve')
[docs]def API520_C(k):
r'''Calculates coefficient C for use in API 520 critical flow relief valve
sizing.
.. math::
C = 0.03948\sqrt{k\left(\frac{2}{k+1}\right)^\frac{k+1}{k-1}}
Parameters
----------
k : float
Isentropic coefficient or ideal gas heat capacity ratio [-]
Returns
-------
C : 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.
.. math::
C = 0.03948\sqrt{\frac{1}{e}}
Examples
--------
From [1]_, checked with many points on Table 8.
>>> API520_C(1.35)
0.02669419967057233
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
if k != 1:
kp1 = k+1
return 0.03948*sqrt(k*(2./kp1)**(kp1/(k-1.)))
else:
return 0.023945830445454768
# return 0.03948*sqrt(1./exp(1))
[docs]def API520_F2(k, P1, P2):
r'''Calculates coefficient F2 for subcritical flow for use in API 520
subcritical flow relief valve sizing.
.. math::
F_2 = \sqrt{\left(\frac{k}{k-1}\right)r^\frac{2}{k}
\left[\frac{1-r^\frac{k-1}{k}}{1-r}\right]}
.. math::
r = \frac{P_2}{P_1}
Parameters
----------
k : float
Isentropic coefficient or ideal gas heat capacity ratio [-]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
P2 : float
Built-up backpressure; the increase in pressure during flow at the
outlet of a pressure-relief device after it opens, [Pa]
Returns
-------
F2 : float
Subcritical flow coefficient `F2` [-]
Notes
-----
F2 is completely dimensionless.
Examples
--------
From [1]_ example 2, matches.
>>> API520_F2(1.8, 1E6, 7E5)
0.8600724121105563
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
r = P2/P1
return sqrt(k/(k-1.0)*r**(2./k) * ((1-r**((k-1.)/k))/(1.-r)))
[docs]def API520_N(P1):
r'''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.
.. math::
K_N = \frac{0.02764P_1-1000}{0.03324P_1-1061}
Parameters
----------
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
Returns
-------
KN : 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.
Examples
--------
>>> API520_N(10500e3)
0.9969100255
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
P1 = P1*1e-3 # Pa to kPa
if P1 <= 10339.0:
KN = 1.0
else:
KN = (0.02764*P1 - 1000.)/(0.03324*P1 - 1061.0)
return KN
# Values from API 520 7th edition through 9th edition
_KSH_psigs_7E = [15, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260,
280, 300, 350, 400, 500, 600, 800, 1000, 1250, 1500, 1750, 2000,
2500, 3000]
_KSH_tempFs_7E = [300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]
# _KSH_psigs_7E converted from psig to Pa
_KSH_Pa_7E = [204746.3593975254, 239220.14586336722, 377115.29172673443,
515010.4375901016, 652905.5834534689, 790800.7293168361,
928695.8751802032, 1066591.0210435705, 1204486.1669069377,
1342381.312770305, 1480276.4586336722, 1618171.6044970395,
1756066.7503604065, 1893961.8962237737, 2031857.042087141,
2169752.187950508, 2514490.0526089263, 2859227.9172673444,
3548703.64658418, 4238179.375901016, 5617130.834534689,
6996082.29316836, 8719771.616460452, 10443460.939752541,
12167150.263044631, 13890839.58633672, 17338218.232920904,
20785596.879505083]
# _KSH_tempFs_7E converted from F to K
_KSH_tempKs_7E = [422.03888888888889, 477.59444444444443, 533.14999999999998,
588.70555555555552, 644.26111111111106, 699.81666666666661,
755.37222222222226, 810.92777777777769, 866.48333333333335,
922.03888888888889]
_KSH_factors_7E = [[1, 0.98, 0.93, 0.88, 0.84, 0.8, 0.77, 0.74, 0.72, 0.7],
[1, 0.98, 0.93, 0.88, 0.84, 0.8, 0.77, 0.74, 0.72, 0.7],
[1, 0.99, 0.93, 0.88, 0.84, 0.81, 0.77, 0.74, 0.72, 0.7],
[1, 0.99, 0.93, 0.88, 0.84, 0.81, 0.77, 0.75, 0.72, 0.7],
[1, 0.99, 0.93, 0.88, 0.84, 0.81, 0.77, 0.75, 0.72, 0.7],
[1, 0.99, 0.94, 0.89, 0.84, 0.81, 0.77, 0.75, 0.72, 0.7],
[1, 0.99, 0.94, 0.89, 0.84, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 0.99, 0.94, 0.89, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 0.99, 0.94, 0.89, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 0.99, 0.94, 0.89, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 0.99, 0.95, 0.89, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 0.99, 0.95, 0.89, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.95, 0.9, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.95, 0.9, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.96, 0.9, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.96, 0.9, 0.85, 0.81, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.96, 0.9, 0.86, 0.82, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.96, 0.91, 0.86, 0.82, 0.78, 0.75, 0.72, 0.7],
[1, 1, 0.96, 0.92, 0.86, 0.82, 0.78, 0.75, 0.73, 0.7],
[1, 1, 0.97, 0.92, 0.87, 0.82, 0.79, 0.75, 0.73, 0.7],
[1, 1, 1, 0.95, 0.88, 0.83, 0.79, 0.76, 0.73, 0.7],
[1, 1, 1, 0.96, 0.89, 0.84, 0.78, 0.76, 0.73, 0.71],
[1, 1, 1, 0.97, 0.91, 0.85, 0.8, 0.77, 0.74, 0.71],
[1, 1, 1, 1, 0.93, 0.86, 0.81, 0.77, 0.74, 0.71],
[1, 1, 1, 1, 0.94, 0.86, 0.81, 0.77, 0.73, 0.7],
[1, 1, 1, 1, 0.95, 0.86, 0.8, 0.76, 0.72, 0.69],
[1, 1, 1, 1, 0.95, 0.85, 0.78, 0.73, 0.69, 0.66],
[1, 1, 1, 1, 1, 0.82, 0.74, 0.69, 0.65, 0.62]]
_KSH_Pa_10E = [500000.0, 750000.0, 1000000.0, 1250000.0, 1500000.0, 1750000.0,
2000000.0, 2250000.0, 2500000.0, 2750000.0, 3000000.0, 3250000.0,
3500000.0, 3750000.0, 4000000.0, 4250000.0, 4500000.0, 4750000.0,
5000000.0, 5250000.0, 5500000.0, 5750000.0, 6000000.0, 6250000.0,
6500000.0, 6750000.0, 7000000.0, 7250000.0, 7500000.0, 7750000.0,
8000000.0, 8250000.0, 8500000.0, 8750000.0, 9000000.0, 9250000.0,
9500000.0, 9750000.0, 10000000.0, 10250000.0, 10500000.0,
10750000.0, 11000000.0, 11250000.0, 11500000.0, 11750000.0,
12000000.0, 12250000.0, 12500000.0, 12750000.0, 13000000.0,
13250000.0, 13500000.0, 14000000.0, 14250000.0, 14500000.0,
14750000.0, 15000000.0, 15250000.0, 15500000.0, 15750000.0,
16000000.0, 16250000.0, 16500000.0, 16750000.0, 17000000.0,
17250000.0, 17500000.0, 17750000.0, 18000000.0, 18250000.0,
18500000.0, 18750000.0, 19000000.0, 19250000.0, 19500000.0,
19750000.0, 20000000.0, 20250000.0, 20500000.0, 20750000.0,
21000000.0, 21250000.0, 21500000.0, 21750000.0, 22000000.0, ]
_KSH_K_10E = [478.15, 498.15, 523.15, 548.15, 573.15, 598.15, 623.15, 648.15,
673.15, 698.15, 723.15, 748.15, 773.15, 798.15, 823.15, 848.15,
873.15, 898.15]
_KSH_factors_10E = [[0.991, 0.968, 0.942, 0.919, 0.896, 0.876, 0.857, 0.839, 0.823, 0.807, 0.792, 0.778, 0.765, 0.752, 0.74, 0.728, 0.717, 0.706],
[0.995, 0.972, 0.946, 0.922, 0.899, 0.878, 0.859, 0.841, 0.824, 0.808, 0.793, 0.779, 0.766, 0.753, 0.74, 0.729, 0.717, 0.707],
[0.985, 0.973, 0.95, 0.925, 0.902, 0.88, 0.861, 0.843, 0.825, 0.809, 0.794, 0.78, 0.766, 0.753, 0.741, 0.729, 0.718, 0.707],
[0.981, 0.976, 0.954, 0.928, 0.905, 0.883, 0.863, 0.844, 0.827, 0.81, 0.795, 0.781, 0.767, 0.754, 0.741, 0.729, 0.718, 0.707],
[1, 1, 0.957, 0.932, 0.907, 0.885, 0.865, 0.846, 0.828, 0.812, 0.796, 0.782, 0.768, 0.755, 0.742, 0.73, 0.718, 0.708],
[1, 1, 0.959, 0.935, 0.91, 0.887, 0.866, 0.847, 0.829, 0.813, 0.797, 0.782, 0.769, 0.756, 0.743, 0.731, 0.719, 0.708],
[1, 1, 0.96, 0.939, 0.913, 0.889, 0.868, 0.849, 0.831, 0.814, 0.798, 0.784, 0.769, 0.756, 0.744, 0.731, 0.72, 0.708],
[1, 1, 0.963, 0.943, 0.916, 0.892, 0.87, 0.85, 0.832, 0.815, 0.799, 0.785, 0.77, 0.757, 0.744, 0.732, 0.72, 0.709],
[1, 1, 1, 0.946, 0.919, 0.894, 0.872, 0.852, 0.834, 0.816, 0.8, 0.785, 0.771, 0.757, 0.744, 0.732, 0.72, 0.71],
[1, 1, 1, 0.948, 0.922, 0.897, 0.874, 0.854, 0.835, 0.817, 0.801, 0.786, 0.772, 0.758, 0.745, 0.733, 0.721, 0.71],
[1, 1, 1, 0.949, 0.925, 0.899, 0.876, 0.855, 0.837, 0.819, 0.802, 0.787, 0.772, 0.759, 0.746, 0.733, 0.722, 0.71],
[1, 1, 1, 0.951, 0.929, 0.902, 0.879, 0.857, 0.838, 0.82, 0.803, 0.788, 0.773, 0.759, 0.746, 0.734, 0.722, 0.711],
[1, 1, 1, 0.953, 0.933, 0.905, 0.881, 0.859, 0.84, 0.822, 0.804, 0.789, 0.774, 0.76, 0.747, 0.734, 0.722, 0.711],
[1, 1, 1, 0.956, 0.936, 0.908, 0.883, 0.861, 0.841, 0.823, 0.806, 0.79, 0.775, 0.761, 0.748, 0.735, 0.723, 0.711],
[1, 1, 1, 0.959, 0.94, 0.91, 0.885, 0.863, 0.842, 0.824, 0.807, 0.791, 0.776, 0.762, 0.748, 0.735, 0.723, 0.712],
[1, 1, 1, 0.961, 0.943, 0.913, 0.887, 0.864, 0.844, 0.825, 0.808, 0.792, 0.776, 0.762, 0.749, 0.736, 0.724, 0.713],
[1, 1, 1, 1, 0.944, 0.917, 0.89, 0.866, 0.845, 0.826, 0.809, 0.793, 0.777, 0.763, 0.749, 0.737, 0.725, 0.713],
[1, 1, 1, 1, 0.946, 0.919, 0.892, 0.868, 0.847, 0.828, 0.81, 0.793, 0.778, 0.764, 0.75, 0.737, 0.725, 0.713],
[1, 1, 1, 1, 0.947, 0.922, 0.894, 0.87, 0.848, 0.829, 0.811, 0.794, 0.779, 0.765, 0.751, 0.738, 0.725, 0.714],
[1, 1, 1, 1, 0.949, 0.926, 0.897, 0.872, 0.85, 0.83, 0.812, 0.795, 0.78, 0.765, 0.752, 0.738, 0.726, 0.714],
[1, 1, 1, 1, 0.952, 0.93, 0.899, 0.874, 0.851, 0.831, 0.813, 0.797, 0.78, 0.766, 0.752, 0.739, 0.727, 0.714],
[1, 1, 1, 1, 0.954, 0.933, 0.902, 0.876, 0.853, 0.833, 0.815, 0.798, 0.782, 0.767, 0.753, 0.739, 0.727, 0.715],
[1, 1, 1, 1, 0.957, 0.937, 0.904, 0.878, 0.855, 0.834, 0.816, 0.798, 0.783, 0.768, 0.753, 0.74, 0.727, 0.716],
[1, 1, 1, 1, 0.96, 0.94, 0.907, 0.88, 0.856, 0.836, 0.817, 0.799, 0.783, 0.768, 0.754, 0.74, 0.728, 0.716],
[1, 1, 1, 1, 0.964, 0.944, 0.91, 0.882, 0.859, 0.837, 0.818, 0.801, 0.784, 0.769, 0.754, 0.741, 0.729, 0.716],
[1, 1, 1, 1, 0.966, 0.946, 0.913, 0.885, 0.86, 0.839, 0.819, 0.802, 0.785, 0.769, 0.755, 0.742, 0.729, 0.717],
[1, 1, 1, 1, 1, 0.947, 0.916, 0.887, 0.862, 0.84, 0.82, 0.802, 0.786, 0.77, 0.756, 0.742, 0.729, 0.717],
[1, 1, 1, 1, 1, 0.949, 0.919, 0.889, 0.863, 0.842, 0.822, 0.803, 0.787, 0.771, 0.756, 0.743, 0.73, 0.717],
[1, 1, 1, 1, 1, 0.951, 0.922, 0.891, 0.865, 0.843, 0.823, 0.805, 0.788, 0.772, 0.757, 0.744, 0.73, 0.718],
[1, 1, 1, 1, 1, 0.953, 0.925, 0.893, 0.867, 0.844, 0.824, 0.806, 0.788, 0.772, 0.758, 0.744, 0.731, 0.719],
[1, 1, 1, 1, 1, 0.955, 0.928, 0.896, 0.869, 0.846, 0.825, 0.806, 0.789, 0.773, 0.758, 0.744, 0.732, 0.719],
[1, 1, 1, 1, 1, 0.957, 0.932, 0.898, 0.871, 0.847, 0.827, 0.807, 0.79, 0.774, 0.759, 0.745, 0.732, 0.719],
[1, 1, 1, 1, 1, 0.96, 0.935, 0.901, 0.873, 0.849, 0.828, 0.809, 0.791, 0.775, 0.76, 0.746, 0.732, 0.72],
[1, 1, 1, 1, 1, 0.963, 0.939, 0.903, 0.875, 0.85, 0.829, 0.81, 0.792, 0.776, 0.76, 0.746, 0.733, 0.721],
[1, 1, 1, 1, 1, 0.966, 0.943, 0.906, 0.877, 0.852, 0.83, 0.811, 0.793, 0.776, 0.761, 0.747, 0.734, 0.721],
[1, 1, 1, 1, 1, 0.97, 0.947, 0.909, 0.879, 0.853, 0.832, 0.812, 0.794, 0.777, 0.762, 0.747, 0.734, 0.721],
[1, 1, 1, 1, 1, 0.973, 0.95, 0.911, 0.881, 0.855, 0.833, 0.813, 0.795, 0.778, 0.763, 0.748, 0.734, 0.722],
[1, 1, 1, 1, 1, 0.977, 0.954, 0.914, 0.883, 0.857, 0.834, 0.814, 0.796, 0.779, 0.763, 0.749, 0.735, 0.722],
[1, 1, 1, 1, 1, 0.981, 0.957, 0.917, 0.885, 0.859, 0.836, 0.815, 0.797, 0.78, 0.764, 0.749, 0.735, 0.722],
[1, 1, 1, 1, 1, 0.984, 0.959, 0.92, 0.887, 0.86, 0.837, 0.816, 0.798, 0.78, 0.764, 0.75, 0.736, 0.723],
[1, 1, 1, 1, 1, 1, 0.961, 0.923, 0.889, 0.862, 0.838, 0.817, 0.799, 0.781, 0.765, 0.75, 0.737, 0.723],
[1, 1, 1, 1, 1, 1, 0.962, 0.925, 0.891, 0.863, 0.839, 0.818, 0.799, 0.782, 0.766, 0.751, 0.737, 0.724],
[1, 1, 1, 1, 1, 1, 0.963, 0.928, 0.893, 0.865, 0.84, 0.819, 0.8, 0.782, 0.766, 0.751, 0.737, 0.724],
[1, 1, 1, 1, 1, 1, 0.964, 0.93, 0.893, 0.865, 0.84, 0.819, 0.799, 0.781, 0.765, 0.75, 0.736, 0.723],
[1, 1, 1, 1, 1, 1, 0.964, 0.931, 0.894, 0.865, 0.84, 0.818, 0.798, 0.78, 0.764, 0.749, 0.735, 0.722],
[1, 1, 1, 1, 1, 1, 0.965, 0.932, 0.894, 0.865, 0.839, 0.817, 0.797, 0.78, 0.763, 0.748, 0.734, 0.721],
[1, 1, 1, 1, 1, 1, 0.966, 0.933, 0.894, 0.864, 0.839, 0.817, 0.797, 0.779, 0.762, 0.747, 0.733, 0.719],
[1, 1, 1, 1, 1, 1, 0.967, 0.935, 0.895, 0.864, 0.839, 0.816, 0.796, 0.778, 0.761, 0.746, 0.732, 0.718],
[1, 1, 1, 1, 1, 1, 0.967, 0.936, 0.896, 0.864, 0.838, 0.816, 0.796, 0.777, 0.76, 0.745, 0.731, 0.717],
[1, 1, 1, 1, 1, 1, 0.968, 0.937, 0.896, 0.864, 0.838, 0.815, 0.795, 0.776, 0.759, 0.744, 0.729, 0.716],
[1, 1, 1, 1, 1, 1, 0.969, 0.939, 0.896, 0.864, 0.837, 0.814, 0.794, 0.775, 0.758, 0.743, 0.728, 0.715],
[1, 1, 1, 1, 1, 1, 0.971, 0.94, 0.897, 0.864, 0.837, 0.813, 0.792, 0.774, 0.757, 0.741, 0.727, 0.713],
[1, 1, 1, 1, 1, 1, 0.972, 0.942, 0.897, 0.863, 0.837, 0.813, 0.792, 0.773, 0.756, 0.74, 0.725, 0.712],
[1, 1, 1, 1, 1, 1, 0.976, 0.946, 0.897, 0.863, 0.835, 0.811, 0.79, 0.771, 0.753, 0.737, 0.723, 0.709],
[1, 1, 1, 1, 1, 1, 0.978, 0.947, 0.898, 0.862, 0.834, 0.81, 0.789, 0.77, 0.752, 0.736, 0.721, 0.707],
[1, 1, 1, 1, 1, 1, 1, 0.948, 0.898, 0.862, 0.833, 0.809, 0.787, 0.768, 0.751, 0.734, 0.72, 0.706],
[1, 1, 1, 1, 1, 1, 1, 0.948, 0.898, 0.862, 0.832, 0.808, 0.786, 0.767, 0.749, 0.733, 0.719, 0.704],
[1, 1, 1, 1, 1, 1, 1, 0.948, 0.899, 0.861, 0.832, 0.807, 0.785, 0.766, 0.748, 0.732, 0.717, 0.703],
[1, 1, 1, 1, 1, 1, 1, 0.947, 0.899, 0.861, 0.831, 0.806, 0.784, 0.764, 0.746, 0.73, 0.716, 0.702],
[1, 1, 1, 1, 1, 1, 1, 0.947, 0.899, 0.861, 0.83, 0.804, 0.782, 0.763, 0.745, 0.728, 0.714, 0.7],
[1, 1, 1, 1, 1, 1, 1, 0.946, 0.899, 0.86, 0.829, 0.803, 0.781, 0.761, 0.743, 0.727, 0.712, 0.698],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.9, 0.859, 0.828, 0.802, 0.779, 0.759, 0.741, 0.725, 0.71, 0.696],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.9, 0.859, 0.827, 0.801, 0.778, 0.757, 0.739, 0.723, 0.708, 0.694],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.9, 0.858, 0.826, 0.799, 0.776, 0.756, 0.738, 0.721, 0.706, 0.692],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.9, 0.857, 0.825, 0.797, 0.774, 0.754, 0.736, 0.719, 0.704, 0.69],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.9, 0.856, 0.823, 0.796, 0.773, 0.752, 0.734, 0.717, 0.702, 0.688],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.9, 0.855, 0.822, 0.794, 0.771, 0.75, 0.732, 0.715, 0.7, 0.686],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.9, 0.854, 0.82, 0.792, 0.769, 0.748, 0.73, 0.713, 0.698, 0.684],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.9, 0.853, 0.819, 0.791, 0.767, 0.746, 0.728, 0.711, 0.696, 0.681],
[1, 1, 1, 1, 1, 1, 1, 0.944, 0.901, 0.852, 0.817, 0.789, 0.765, 0.744, 0.725, 0.709, 0.694, 0.679],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.901, 0.851, 0.815, 0.787, 0.763, 0.742, 0.723, 0.706, 0.691, 0.677],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.901, 0.85, 0.814, 0.785, 0.761, 0.739, 0.72, 0.704, 0.689, 0.674],
[1, 1, 1, 1, 1, 1, 1, 0.945, 0.901, 0.849, 0.812, 0.783, 0.758, 0.737, 0.718, 0.701, 0.686, 0.671],
[1, 1, 1, 1, 1, 1, 1, 0.946, 0.901, 0.847, 0.81, 0.781, 0.756, 0.734, 0.715, 0.698, 0.683, 0.669],
[1, 1, 1, 1, 1, 1, 1, 0.948, 0.901, 0.846, 0.808, 0.778, 0.753, 0.732, 0.713, 0.696, 0.681, 0.666],
[1, 1, 1, 1, 1, 1, 1, 0.95, 0.9, 0.844, 0.806, 0.776, 0.75, 0.729, 0.71, 0.693, 0.677, 0.663],
[1, 1, 1, 1, 1, 1, 1, 0.952, 0.899, 0.842, 0.803, 0.773, 0.748, 0.726, 0.707, 0.69, 0.674, 0.66],
[1, 1, 1, 1, 1, 1, 1, 1, 0.899, 0.84, 0.801, 0.77, 0.745, 0.723, 0.704, 0.687, 0.671, 0.657],
[1, 1, 1, 1, 1, 1, 1, 1, 0.899, 0.839, 0.798, 0.767, 0.742, 0.72, 0.701, 0.683, 0.668, 0.654],
[1, 1, 1, 1, 1, 1, 1, 1, 0.899, 0.837, 0.795, 0.764, 0.738, 0.717, 0.697, 0.68, 0.665, 0.651],
[1, 1, 1, 1, 1, 1, 1, 1, 0.898, 0.834, 0.792, 0.761, 0.735, 0.713, 0.694, 0.677, 0.661, 0.647],
[1, 1, 1, 1, 1, 1, 1, 1, 0.896, 0.832, 0.79, 0.758, 0.732, 0.71, 0.691, 0.673, 0.658, 0.643],
[1, 1, 1, 1, 1, 1, 1, 1, 0.894, 0.829, 0.786, 0.754, 0.728, 0.706, 0.686, 0.669, 0.654, 0.64],
[1, 1, 1, 1, 1, 1, 1, 1, 0.892, 0.826, 0.783, 0.75, 0.724, 0.702, 0.682, 0.665, 0.65, 0.636],
[1, 1, 1, 1, 1, 1, 1, 1, 0.891, 0.823, 0.779, 0.746, 0.72, 0.698, 0.679, 0.661, 0.646, 0.631],
[1, 1, 1, 1, 1, 1, 1, 1, 0.887, 0.82, 0.776, 0.743, 0.716, 0.694, 0.674, 0.657, 0.641, 0.627]]
API520_KSH_tck_7E = tck_interp2d_linear(_KSH_tempKs_7E, _KSH_Pa_7E, _KSH_factors_7E)
API520_KSH_tck_10E = tck_interp2d_linear(_KSH_K_10E, _KSH_Pa_10E, _KSH_factors_10E)
[docs]def API520_SH(T1, P1, edition=TENTH_EDITION):
r'''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
----------
T1 : float
Temperature of the fluid entering the valve [K]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
edition : str, optional
One of '10E', '7E', [-]
Returns
-------
KSH : 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.
Examples
--------
Custom example from table 9, 7th edition:
>>> API520_SH(593+273.15, 1066.325E3, '7E')
0.7201800000
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
if T1 > 922.15:
raise ValueError('Superheat cannot be above 649 degrees Celcius')
if edition == SEVENTH_EDITION:
if P1 > 20780325.0: # 20679E3+atm
raise ValueError('For P above 20679 kPag, use the gas flow model')
if T1 < 422.15:
return 1. # No superheat under 15 psig
return float(bisplev(T1, P1, API520_KSH_tck_7E))
elif edition == TENTH_EDITION:
if T1 < 478.15:
# Avoid extrapolating above 1.0
return 1.0
if P1 > 22063223.338138755:
raise ValueError('For P1 above 22.06 MPa, use the gas flow model')
return float(bisplev(T1, P1, API520_KSH_tck_10E))
else:
raise ValueError("Acceptable editions are '7E', '10E'")
# Kb Backpressure correction factor, for gases
Kb_16_over_x = [37.6478, 38.1735, 38.6991, 39.2904, 39.8817, 40.4731, 40.9987,
41.59, 42.1156, 42.707, 43.2326, 43.8239, 44.4152, 44.9409,
45.5322, 46.0578, 46.6491, 47.2405, 47.7661, 48.3574, 48.883,
49.4744, 50.0]
Kb_16_over_y = [0.998106, 0.994318, 0.99053, 0.985795, 0.982008, 0.97822,
0.973485, 0.96875, 0.964962, 0.961174, 0.956439, 0.951705,
0.947917, 0.943182, 0.939394, 0.935606, 0.930871, 0.926136,
0.921402, 0.918561, 0.913826, 0.910038, 0.90625]
Kb_10_over_x = [30.0263, 30.6176, 31.1432, 31.6689, 32.1945, 32.6544, 33.18,
33.7057, 34.1656, 34.6255, 35.0854, 35.5453, 36.0053, 36.4652,
36.9251, 37.385, 37.8449, 38.2392, 38.6334, 39.0276, 39.4875,
39.9474, 40.4074, 40.8016, 41.1958, 41.59, 42.0499, 42.4442,
42.8384, 43.2326, 43.6925, 44.0867, 44.4809, 44.8752, 45.2694,
45.6636, 46.0578, 46.452, 46.8463, 47.2405, 47.6347, 48.0289,
48.4231, 48.883, 49.2773, 49.6715]
Kb_10_over_y = [0.998106, 0.995265, 0.99053, 0.985795, 0.981061, 0.975379,
0.969697, 0.963068, 0.957386, 0.950758, 0.945076, 0.938447,
0.930871, 0.925189, 0.918561, 0.910985, 0.904356, 0.897727,
0.891098, 0.883523, 0.876894, 0.870265, 0.862689, 0.856061,
0.848485, 0.840909, 0.83428, 0.827652, 0.820076, 0.8125,
0.805871, 0.798295, 0.79072, 0.783144, 0.775568, 0.768939,
0.762311, 0.754735, 0.747159, 0.739583, 0.732008, 0.724432,
0.716856, 0.70928, 0.701705, 0.695076]
[docs]def API520_B(Pset, Pback, overpressure=0.1):
r'''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
----------
Pset : float
Set pressure for relief [Pa]
Pback : float
Backpressure, [Pa]
overpressure : float, optional
The maximum fraction overpressure; one of 0.1, 0.16, or 0.21, [-]
Returns
-------
Kb : 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%.
Examples
--------
Custom examples from figure 30:
>>> API520_B(1E6, 5E5)
0.7929945420944432
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
gauge_backpressure = (Pback-atm)/(Pset-atm)*100.0 # in percent
if overpressure not in (0.1, 0.16, 0.21):
raise ValueError('Only overpressure of 10%, 16%, or 21% are permitted')
if (overpressure == 0.1 and gauge_backpressure < 30.0) or (
overpressure == 0.16 and gauge_backpressure < 38.0) or (
overpressure == 0.21 and gauge_backpressure <= 50.0):
return 1.0
elif gauge_backpressure > 50.0:
raise ValueError('Gauge pressure must be < 50%')
if overpressure == 0.16:
Kb = interp(gauge_backpressure, Kb_16_over_x, Kb_16_over_y)
elif overpressure == 0.1:
Kb = interp(gauge_backpressure, Kb_10_over_x, Kb_10_over_y)
return Kb
[docs]def API520_A_g(m, T, Z, MW, k, P1, P2=101325, Kd=0.975, Kb=1, Kc=1):
r'''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:
.. math::
A = \frac{m}{CK_dP_1K_bK_c}\sqrt{\frac{TZ}{M}}
For sub-critical flow:
.. math::
A = \frac{17.9m}{F_2K_dK_c}\sqrt{\frac{TZ}{MP_1(P_1-P_2)}}
Parameters
----------
m : float
Mass flow rate of vapor through the valve, [kg/s]
T : float
Temperature of vapor entering the valve, [K]
Z : float
Compressibility factor of the vapor, [-]
MW : float
Molecular weight of the vapor, [g/mol]
k : float
Isentropic coefficient or ideal gas heat capacity ratio [-]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
P2 : float, optional
Built-up backpressure; the increase in pressure during flow at the
outlet of a pressure-relief device after it opens, [Pa]
Kd : 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]_, []
Kb : float, optional
Correction due to vapor backpressure [-]
Kc : 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
-------
A : float
Minimum area for relief valve according to [1]_, [m^2]
Notes
-----
Units are interlally kg/hr, kPa, and mm^2 to match [1]_.
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
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
P1, P2 = P1*1e-3, P2*1e-3 # Pa to Kpa in the standard
m = m*3600. # kg/s to kg/hr
if is_critical_flow(P1, P2, k):
C = API520_C(k)
A = m/(C*Kd*Kb*Kc*P1)*sqrt(T*Z/MW)
else:
F2 = API520_F2(k, P1, P2)
A = 17.9*m/(F2*Kd*Kc)*sqrt(T*Z/(MW*P1*(P1-P2)))
return A*1e-6# convert mm^2 to m^2
[docs]def API520_A_steam(m, T, P1, Kd=0.975, Kb=1, Kc=1, edition=TENTH_EDITION):
r'''Calculates required relief valve area for an API 520 valve passing
a steam, at either saturation or superheat but not partially condensed.
.. math::
A = \frac{190.5m}{P_1 K_d K_b K_c K_N K_{SH}}
Parameters
----------
m : float
Mass flow rate of steam through the valve, [kg/s]
T : float
Temperature of steam entering the valve, [K]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
Kd : 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]_, []
Kb : float, optional
Correction due to backpressure, see :obj:`API520_B` [-]
Kc : 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, []
edition : str, optional
One of '10E', '7E', [-]
Returns
-------
A : 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.
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
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
KN = API520_N(P1)
KSH = API520_SH(T, P1, edition)
P1 = P1*1e-3 # Pa to kPa
m = m*3600. # kg/s to kg/hr
A = 190.5*m/(P1*Kd*Kb*Kc*KN*KSH)
return A*1e-6# convert mm^2 to m^2
### Liquids
[docs]def API520_Kv(Re, edition=TENTH_EDITION):
r'''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:
.. math::
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
.. math::
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
----------
Re : float
Reynolds number for flow out the valve [-]
edition : str, optional
One of '10E', '7E', [-]
Returns
-------
Kv : 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:
.. math::
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
:obj:`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.
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
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.
'''
if edition == SEVENTH_EDITION:
factor = 1.0/(0.9935 + 2.878/sqrt(Re) + 342.75/(Re*sqrt(Re)))
if factor > 1.0:
factor = 1.0
return factor
elif edition == TENTH_EDITION:
return 1.0/sqrt(170.0/Re + 1.0)
else:
raise ValueError("Acceptable editions are '7E', '10E'")
# Kw, for liquids. Applicable for all overpressures.
Kw_x = [15., 16.5493, 17.3367, 18.124, 18.8235, 19.5231, 20.1351, 20.8344,
21.4463, 22.0581, 22.9321, 23.5439, 24.1556, 24.7674, 25.0296, 25.6414,
26.2533, 26.8651, 27.7393, 28.3511, 28.9629, 29.6623, 29.9245, 30.5363,
31.2357, 31.8475, 32.7217, 33.3336, 34.0329, 34.6448, 34.8196, 35.4315,
36.1308, 36.7428, 37.7042, 38.3162, 39.0154, 39.7148, 40.3266, 40.9384,
41.6378, 42.7742, 43.386, 43.9978, 44.6098, 45.2216, 45.921, 46.5329,
47.7567, 48.3685, 49.0679, 49.6797, 50.]
Kw_y = [1, 0.996283, 0.992565, 0.987918, 0.982342, 0.976766, 0.97119, 0.964684,
0.958178, 0.951673, 0.942379, 0.935874, 0.928439, 0.921933, 0.919145,
0.912639, 0.906134, 0.899628, 0.891264, 0.884758, 0.878253, 0.871747,
0.868959, 0.862454, 0.855948, 0.849442, 0.841078, 0.834572, 0.828067,
0.821561, 0.819703, 0.814126, 0.806691, 0.801115, 0.790892, 0.785316,
0.777881, 0.771375, 0.76487, 0.758364, 0.751859, 0.740706, 0.734201,
0.727695, 0.722119, 0.715613, 0.709108, 0.702602, 0.69052, 0.684015,
0.677509, 0.671004, 0.666357]
[docs]def API520_W(Pset, Pback):
r'''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
----------
Pset : float
Set pressure for relief [Pa]
Pback : float
Backpressure, [Pa]
Returns
-------
KW : float
Correction due to liquid backpressure [-]
Notes
-----
If the calculated gauge backpressure is less than 15%, a value of 1 is
returned.
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
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection. 7E
.. [2] API Standard 520, Part 1 - Sizing and Selection. 10E
'''
gauge_backpressure = (Pback-atm)/(Pset-atm)*100.0 # in percent
if gauge_backpressure < 15.0:
return 1.0
return interp(gauge_backpressure, Kw_x, Kw_y)
rho0 = 999.0107539518483
[docs]def API520_A_l(m, rho, P1, P2, overpressure, Kd=0.65, Kc=1.0,
Kw=None, Kv=None, edition=TENTH_EDITION, mu=None):
r'''Calculates required relief valve area for an API 520 valve passing
a liquid in sub-critical flow.
.. math::
A = \frac{11.78Q}{K_d K_w K_c K_v}\left(\frac{G_1}{P1 - P2}\right)^{0.5}
Parameters
----------
m : float
Mass flow rate of liquid through the valve, [kg/s]
rho : float
Liquid density, [kg/m^3]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
P2 : float
Built-up backpressure; the increase in pressure during flow at the
outlet of a pressure-relief device after it opens, [Pa]
overpressure : float
The maximum fraction overpressure; used if `Kw` is not specified, [-]
Kd : 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]_, []
Kc : 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, []
Kw : float, optional
Correction due to liquid backpressure [-]
Kv : float, optional
Correction due to viscosity [-]
edition : str, optional
One of '10E', '7E', [-]
mu : float, optional
If provided and `Kv` is None, `Kv` will be calculated automatically,
[Pa*s]
Returns
-------
A : 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:
.. math::
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:
.. math::
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.
.. math::
K = \left(\frac{1}{K_d K_w K_c K_v\cdot (11.779282389196/11.78)}\right)^2
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)
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
G1 = rho/rho0
Q = m/rho # m^3/s
Q *= 60000.0 # m^3/s to L/min in the original equation
P_set_guage = (P1 - atm)/(1.0 + overpressure)
P_set = P_set_guage + atm
if Kw is None:
Kw = API520_W(P_set, P2)
if Kv is None and mu is not None:
A0 = API520_A_l(m=m, rho=rho, P1=P1, P2=P2, overpressure=overpressure, Kd=Kd, Kc=Kc, Kv=1.0, Kw=Kw)
D = sqrt(A0*4.0/pi)
v = (Q/60000.0)/A0
Re = rho*v*D/mu
Kv = API520_Kv(Re, edition)
P1 = P1*1e-3 # Pa to kPa
P2 = P2*1e-3 # Pa to kPa
A = 11.78*Q*sqrt(G1/(P1-P2))/(Kd*Kw*Kc*Kv)
A = A*1e-6# convert mm^2 to m^2
return A
[docs]def API521_noise_graph(P_ratio):
r'''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_ratio : float
The ratio of relieving pressure to atmospheric pressure [-]
Returns
-------
L : 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.
'''
if P_ratio < 1.0:
P_ratio = 1.0
lgX = log10(P_ratio)
# Small curve fit
lower_value = 87.9084*lgX + 12.7647
higher_value = 4.8239*lgX + 51.6217
if P_ratio < 2.92:
value = lower_value
elif P_ratio < 2.93:
# interpolate between the two curves to keep the function continuous
value = interp(P_ratio, [2.92, 2.93], [lower_value, higher_value])
else:
value = higher_value
return value
[docs]def API521_noise(m, P1, P2, c, r):
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.
.. math::
L_{30 \text{m}} = L - 10 \log_{10}(0.5 m c^2)
.. math::
L_p = L_{30 \text{m}} - 20 \log_{10}(r/(30 \text{m}))
Parameters
----------
m : float
Mass flow rate of relieving fluid, [kg/s]
P1 : float
Upstream pressure at the source, before the relieving
device [Pa]
P2 : float
Atmospheric pressure, [Pa]
c : float
Speed of sound of the fluid at the relieving device [m/s]
r : float
Distance from the flare stack, [m]
Returns
-------
L : float
Sound pressure level at the specified distance from the
stack tip [decibels]
Notes
-----
Examples
--------
Example as shown in [1]_:
>>> API521_noise(m=14.6, P1=330E3, P2=101325, c=353.0, r=30)
113.6841057
References
----------
.. [1] API Standard 521.
'''
P_ratio = P1/P2
L = API521_noise_graph(P_ratio) # from chart, hardcoded for now
L30 = L + 10.0*log10(0.5*m*c*c)
Lp = L30 - 20.0*log10(r*(1.0/30.0))
return Lp
[docs]def VDI_3732_noise_ground_flare(m):
r'''Calculate the the noise at the flare tip of a ground flare
[1]_, [2]_.
.. math::
L = 100 + 15\log_{10}\left(\frac{m}{\text{tonne/hour}}\right)
Parameters
----------
m : float
Mass flow rate of relieving fluid, [kg/s]
Returns
-------
noise : float
Sound pressure level at the relieving flare stack [decibels]
Notes
-----
Examples
--------
>>> VDI_3732_noise_ground_flare(3.0)
145.501356332
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/.
'''
m *= 360.0
return 100.0 + 15.0*log10(m)
[docs]def VDI_3732_noise_elevated_flare(m):
r'''Calculate the the noise at the flare tip of an elevated flare stack
[1]_, [2]_.
.. math::
L = 112 + 17\log_{10}\left(\frac{m}{\text{tonne/hour}}\right)
Parameters
----------
m : float
Mass flow rate of relieving fluid, [kg/s]
Returns
-------
noise : float
Sound pressure level at the relieving flare stack [decibels]
Notes
-----
Examples
--------
>>> VDI_3732_noise_elevated_flare(3.0)
163.56820384
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/.
'''
m *= 360.0
return 112.0 + 17.0*log10(m)