"""Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell 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 `_ 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' 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') 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)) 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))) 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) 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] 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 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 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 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] 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 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 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 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 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) 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)