def fluids_is_critical_flow(P1, P2, k):
'''
Determines if a flow of a fluid driven by pressure gradient P1 - P2 is
critical, for a fluid with the given isentropic coefficient. This function
calculates critical flow pressure, and checks if this is larger than P2.
If so, the flow is critical and choked.
'''
return comp.is_critical_flow(P1, P2, k)
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 ruture disk
upstream of the PRV, []
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 / 1000., P2 / 1000. # 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) * (T * Z / MW)**0.5
else:
F2 = API520_F2(k, P1, P2)
A = 17.9 * m / (F2 * Kd * Kc) * (T * Z / (MW * P1 * (P1 - P2)))**0.5
return A * 0.001**2 # convert mm^2 to m^2
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 ruture disk
upstream of the PRV, []
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 [2]_ 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
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
P1, P2 = P1/1000., P2/1000. # 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)*(T*Z/MW)**0.5
else:
F2 = API520_F2(k, P1, P2)
A = 17.9*m/(F2*Kd*Kc)*(T*Z/(MW*P1*(P1-P2)))**0.5
A = A*0.001**2 # convert mm^2 to m^2
return A