def Stichlmair_flood(Vl,
rhog,
rhol,
mug,
voidage,
specific_area,
C1,
C2,
C3,
H=1.0):
r'''Calculates gas rate for flooding of a packed column, using the
Stichlmair [1]_ correlation. Uses three regressed constants for each
type of packing, and voidage and specific area.
Pressure drop is given by:
.. math::
\frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac
{1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3}
\left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65}
.. math::
h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right]
.. math::
Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}}
.. math::
h_0 = 0.555 Fr_L^{1/3}
.. math::
c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0}
.. math::
\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}}
\rho_G \frac{H}{d_p}V_g^2
.. math::
f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3
.. math::
d_p = \frac{6(1-\epsilon)}{a}
Parameters
----------
Vl : float
Superficial velocity of liquid, Q/A [m/s]
rhog : float
Density of gas [kg/m^3]
rhol : float
Density of liquid [kg/m^3]
mug : float
Viscosity of gas [Pa*s]
voidage : float
Voidage of bed of packing material []
specific_area : float
Specific area of the packing material [m^2/m^3]
C1 : float
Packing-specific constant []
C2 : float
Packing-specific constant []
C3 : float
Packing-specific constant []
H : float, optional
Height of packing [m]
Returns
-------
Vg : float
Superficial velocity of gas, Q/A [m/s]
Notes
-----
A numerical solver is used to solve this model.
Examples
--------
Example is from [1]_, matches.
>>> Stichlmair_flood(Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5,
... voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.)
0.6394323542746928
References
----------
.. [1] Stichlmair, J., J. L. Bravo, and J. R. Fair. "General Model for
Prediction of Pressure Drop and Capacity of Countercurrent Gas/liquid
Packed Columns." Gas Separation & Purification 3, no. 1 (March 1989):
19-28. doi:10.1016/0950-4214(89)80016-7.
'''
guess = [Vl * 100., 1000.0]
return newton_system(_Stichlmair_flood_f_and_jac,
x0=guess,
jac=True,
args=(Vl, rhog, rhol, mug, voidage, specific_area, C1,
C2, C3, H),
ytol=1e-11)[0][0]
def Stichlmair_flood(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3,
H=1.0):
r'''Calculates gas rate for flooding of a packed column, using the
Stichlmair [1]_ correlation. Uses three regressed constants for each
type of packing, and voidage and specific area.
Pressure drop is given by:
.. math::
\frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac
{1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3}
\left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65}
.. math::
h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right]
.. math::
Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}}
.. math::
h_0 = 0.555 Fr_L^{1/3}
.. math::
c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0}
.. math::
\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}}
\rho_G \frac{H}{d_p}V_g^2
.. math::
f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3
.. math::
d_p = \frac{6(1-\epsilon)}{a}
Parameters
----------
Vl : float
Superficial velocity of liquid, Q/A [m/s]
rhog : float
Density of gas [kg/m^3]
rhol : float
Density of liquid [kg/m^3]
mug : float
Viscosity of gas [Pa*s]
voidage : float
Voidage of bed of packing material []
specific_area : float
Specific area of the packing material [m^2/m^3]
C1 : float
Packing-specific constant []
C2 : float
Packing-specific constant []
C3 : float
Packing-specific constant []
H : float, optional
Height of packing [m]
Returns
-------
Vg : float
Superficial velocity of gas, Q/A [m/s]
Notes
-----
A numerical solver is used to solve this model.
Examples
--------
Example is from [1]_, matches.
>>> Stichlmair_flood(Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5,
... voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.)
0.6394323542746928
References
----------
.. [1] Stichlmair, J., J. L. Bravo, and J. R. Fair. "General Model for
Prediction of Pressure Drop and Capacity of Countercurrent Gas/liquid
Packed Columns." Gas Separation & Purification 3, no. 1 (March 1989):
19-28. doi:10.1016/0950-4214(89)80016-7.
'''
guess = [Vl*100., 1000.0]
return newton_system(_Stichlmair_flood_f_and_jac, x0=guess, jac=True,
args=(Vl, rhog, rhol, mug, voidage, specific_area, C1,
C2, C3, H), ytol=1e-11)[0][0]