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# -*- coding: utf-8 -*- 

'''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.''' 

 

from __future__ import division 

from scipy.constants import g, pi 

from scipy.optimize import fsolve 

 

 

__all__ = ['voidage_experimental', 'specific_area_mesh', 

'Stichlmair_dry', 'Stichlmair_wet', 'Stichlmair_flood', 'Robbins', 

'dP_demister_dry_Setekleiv_Svendsen_lit', 

'dP_demister_dry_Setekleiv_Svendsen', 

'dP_demister_wet_ElDessouky', 'separation_demister_ElDessouky'] 

 

 

### Demister 

 

def dP_demister_dry_Setekleiv_Svendsen(S, voidage, vs, rho, mu, L=1): 

r'''Calculates dry pressure drop across a demister, using the 

correlation in [1]_. This model is for dry demisters with no holdup only. 

 

.. math:: 

\frac{\Delta P \epsilon^2}{\rho_f v^2} = 10.29 - \frac{565} 

{69.6SL - (SL)^2 - 779} - \frac{74.9}{160.9 - 4.85SL} + 45.33\left( 

\frac{\mu_f \epsilon S^2 L}{\rho_f v}\right)^{0.75} 

 

Parameters 

---------- 

S : float 

Specific area of the demister, normally ~250-1000 [m^2/m^3] 

voidage : float 

Voidage of bed of the demister material, normally ~0.98 [] 

vs : float 

Superficial velocity of fluid, Q/A [m/s] 

rho : float 

Density of fluid [kg/m^3] 

mu : float 

Viscosity of fluid [Pa*S] 

L : float, optional 

Length of the demister [m] 

 

Returns 

------- 

dP : float 

Pressure drop across a dry demister [Pa] 

 

Notes 

----- 

Useful at startup and in modeling. Dry pressure drop is normally neglible 

compared to wet pressure drop. Coefficients obtained by evolutionary 

programming and may not fit data outside of the limits of the variables. 

 

Examples 

-------- 

>>> dP_demister_dry_Setekleiv_Svendsen(S=250, voidage=.983, vs=1.2, rho=10, mu=3E-5, L=1) 

320.3280788941329 

 

References 

---------- 

.. [1] Setekleiv, A. Eddie, and Hallvard F. Svendsen. "Dry Pressure Drop in 

Spiral Wound Wire Mesh Pads at Low and Elevated Pressures." Chemical 

Engineering Research and Design 109 (May 2016): 141-149. 

doi:10.1016/j.cherd.2016.01.019. 

''' 

term = 10.29 - 565./(69.6*S*L - (S*L)**2 - 779) - 74.9/(160.9 - 4.85*S*L) 

right = term + 45.33*(mu*voidage*S**2*L/rho/vs)**0.75 

return right*rho*vs**2/voidage**2 

 

 

def dP_demister_dry_Setekleiv_Svendsen_lit(S, voidage, vs, rho, mu, L=1): 

r'''Calculates dry pressure drop across a demister, using the 

correlation in [1]_. This model is for dry demisters with no holdup only. 

Developed with literature data included as well as their own experimental 

data. 

 

.. math:: 

\frac{\Delta P \epsilon^2}{\rho_f v^2} = 7.3 - \frac{320} 

{69.6SL - (SL)^2 - 779} - \frac{52.4}{161 - 4.85SL} + 27.2\left( 

\frac{\mu_f \epsilon S^2 L}{\rho_f v}\right)^{0.75} 

 

Parameters 

---------- 

S : float 

Specific area of the demister, normally ~250-1000 [m^2/m^3] 

voidage : float 

Voidage of bed of the demister material, normally ~0.98 [] 

vs : float 

Superficial velocity of fluid, Q/A [m/s] 

rho : float 

Density of fluid [kg/m^3] 

mu : float 

Viscosity of fluid [Pa*S] 

L : float, optional 

Length of the demister [m] 

 

Returns 

------- 

dP : float 

Pressure drop across a dry demister [Pa] 

 

Notes 

----- 

Useful at startup and in modeling. Dry pressure drop is normally neglible 

compared to wet pressure drop. Coefficients obtained by evolutionary 

programming and may not fit data outside of the limits of the variables. 

 

Examples 

-------- 

>>> dP_demister_dry_Setekleiv_Svendsen_lit(S=250, voidage=.983, vs=1.2, rho=10, mu=3E-5, L=1) 

209.083848658307 

 

References 

---------- 

.. [1] Setekleiv, A. Eddie, and Hallvard F. Svendsen. "Dry Pressure Drop in 

Spiral Wound Wire Mesh Pads at Low and Elevated Pressures." Chemical 

Engineering Research and Design 109 (May 2016): 141-149. 

doi:10.1016/j.cherd.2016.01.019. 

''' 

term = 7.3 - 320./(69.6*S*L - (S*L)**2 - 779) - 52.4/(161 - 4.85*S*L) 

right = term + 27.2*(mu*voidage*S**2*L/rho/vs)**0.75 

return right*rho*vs**2/voidage**2 

 

 

def dP_demister_wet_ElDessouky(vs, voidage, d_wire, L=1): 

r'''Calculates wet pressure drop across a demister, using the 

correlation in [1]_. Uses only their own experimental data. 

 

.. math:: 

\frac{\Delta P}{L} = 0.002357(1-\epsilon)^{0.375798}(V)^{0.81317} 

(d_w)^{-1.56114147} 

 

Parameters 

---------- 

vs : float 

Superficial velocity of fluid, Q/A [m/s] 

voidage : float 

Voidage of bed of the demister material, normally ~0.98 [] 

d_wire : float 

Diameter of mesh wire,[m] 

L : float, optional 

Length of the demister [m] 

 

Returns 

------- 

dP : float 

Pressure drop across a dry demister [Pa] 

 

Notes 

----- 

No dependency on the liquid properties is included here. Because of the 

exponential nature of the correlation, the limiting pressure drop as V 

is lowered is 0 Pa. A dry pressure drop correlation should be compared with 

results from this at low velocities, and the larger of the 

two pressure drops used. 

 

The correlation in [1]_ was presented as follows, with wire diameter in 

units of mm, density in kg/m^3, V in m/s, and dP in Pa/m. 

 

.. math:: 

\Delta P = 3.88178(\rho_{mesh})^{0.375798}(V)^{0.81317} 

(d_w)^{-1.56114147} 

 

Here, the correlation is converted to base SI units and to use voidage; 

not all demisters are stainless steel as in [1]_. A density of 7999 kg/m^3  

was used in the conversion. 

 

In [1]_, V ranged from 0.98-7.5 m/s, rho from 80.317-208.16 kg/m^3, depth  

from 100 to 200 mm, wire diameter of 0.2mm to 0.32 mm, and particle  

diameter from 1 to 5 mm. 

 

 

Examples 

-------- 

>>> dP_demister_wet_ElDessouky(6, 0.978, 0.00032) 

688.9216420105029 

 

References 

---------- 

.. [1] El-Dessouky, Hisham T, Imad M Alatiqi, Hisham M Ettouney, and Noura  

S Al-Deffeeri. "Performance of Wire Mesh Mist Eliminator." Chemical  

Engineering and Processing: Process Intensification 39, no. 2 (March  

2000): 129-39. doi:10.1016/S0255-2701(99)00033-1. 

''' 

return L*0.002356999643727531*(1-voidage)**0.375798*vs**0.81317*d_wire**-1.56114147 

 

 

def separation_demister_ElDessouky(vs, voidage, d_wire, d_drop): 

r'''Calculates droplet removal by a demister as a fraction from 0 to 1, 

using the correlation in [1]_. Uses only their own experimental data. 

 

.. math:: 

\eta = 0.85835(d_w)^{-0.28264}(1-\epsilon)^{0.099625}(V)^{0.106878} 

(d_p)^{0.383197} 

 

Parameters 

---------- 

vs : float 

Superficial velocity of fluid, Q/A [m/s] 

voidage : float 

Voidage of bed of the demister material, normally ~0.98 [] 

d_wire : float 

Diameter of mesh wire,[m] 

d_drop : float 

Drop diameter, [m] 

 

Returns 

------- 

eta : float 

Fraction droplets removed by mass [-] 

 

Notes 

----- 

No dependency on the liquid properties is included here. Because of the 

exponential nature of the correlation, for smaller diameters separation 

quickly lowers. This correlation can predict a separation larger than 1 

for higher velocities, lower voidages, lower wire diameters, and large  

droplet sizes. This function truncates these larger values to 1. 

 

The correlation in [1]_ was presented as follows, with wire diameter in 

units of mm, density in kg/m^3, V in m/s, separation in %, and particle 

diameter in mm. 

 

.. math:: 

\eta = 17.5047(d_w)^{-0.28264}(\rho_{mesh})^{0.099625}(V)^{0.106878} 

(d_p)^{0.383197} 

 

Here, the correlation is converted to base SI units and to use voidage; 

not all demisters are stainless steel as in [1]_. A density of 7999 kg/m^3  

was used in the conversion. 

 

In [1]_, V ranged from 0.98-7.5 m/s, rho from 80.317-208.16 kg/m^3, depth  

from 100 to 200 mm, wire diameter of 0.2mm to 0.32 mm, and particle  

diameter from 1 to 5 mm. 

 

Examples 

-------- 

>>> separation_demister_ElDessouky(1.35, 0.974, 0.0002, 0.005) 

0.8982892997640582 

 

References 

---------- 

.. [1] El-Dessouky, Hisham T, Imad M Alatiqi, Hisham M Ettouney, and Noura  

S Al-Deffeeri. "Performance of Wire Mesh Mist Eliminator." Chemical  

Engineering and Processing: Process Intensification 39, no. 2 (March  

2000): 129-39. doi:10.1016/S0255-2701(99)00033-1. 

''' 

eta = 0.858352355761947*d_wire**-0.28264*(1-voidage)**0.099625*vs**0.106878*d_drop**0.383197 

return min(eta, 1.0) 

 

 

def voidage_experimental(m, rho, D, H): 

r'''Calculates voidage of a bed or mesh given an experimental weight and 

fixed density, diameter, and height, as shown in [1]_. The formula is also 

self-evident. 

 

.. math:: 

\epsilon = 1 - \frac{\frac{m_{mesh}}{\frac{\pi}{4}d_{column}^2 

L_{mesh}}}{\rho_{material}} 

 

Parameters 

---------- 

m : float 

Mass of mesh or bed particles weighted, [kg] 

rho : float 

Density of solid particles or mesh [kg/m^3] 

D : float 

Diameter of the cylindrical bed [m] 

L : float 

Length of the demister or bed [m] 

 

Returns 

------- 

voidage : float 

Voidage of bed of the material [] 

 

Notes 

----- 

Should be trusted over manufacturer data. 

 

Examples 

-------- 

>>> voidage_experimental(m=126, rho=8000, D=1, H=1) 

0.9799464771704212 

 

References 

---------- 

.. [1] Helsør, T., and H. Svendsen. "Experimental Characterization of 

Pressure Drop in Dry Demisters at Low and Elevated Pressures." Chemical 

Engineering Research and Design 85, no. 3 (2007): 377-85. 

doi:10.1205/cherd06048. 

''' 

return 1 - m/(pi/4*D**2*H)/rho 

 

 

def specific_area_mesh(voidage, d): 

r'''Calculates the specific area of a wire mesh, as used in demisters or 

filters. Shown in [1]_, and also self-evident and non-emperical. 

Makes the ideal assumption that wires never touch. 

 

.. math:: 

S = \frac{4(1-\epsilon)}{d_{wire}} 

 

Parameters 

---------- 

voidage : float 

Voidage of the mesh [] 

d : float 

Diameter of the wires making the mesh, [m] 

 

Returns 

------- 

S : float 

Specific area of the mesh [m^2/m^3] 

 

Notes 

----- 

Should be prefered over manufacturer data. Can also be used to show that 

manufacturer's data is inconsistent with their claimed voidage and wire 

diameter. 

 

Examples 

-------- 

>>> specific_area_mesh(voidage=.934, d=3e-4) 

879.9999999999994 

 

References 

---------- 

.. [1] Helsør, T., and H. Svendsen. "Experimental Characterization of 

Pressure Drop in Dry Demisters at Low and Elevated Pressures." Chemical 

Engineering Research and Design 85, no. 3 (2007): 377-85. 

doi:10.1205/cherd06048. 

''' 

return 4*(1-voidage)/d 

 

### Packing 

 

 

def Stichlmair_dry(Vg, rhog, mug, voidage, specific_area, C1, C2, C3, H=1.): 

r'''Calculates dry pressure drop across 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:: 

\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} 

\rho_G \frac{H}{d_p}V_g^2 

 

f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3 

 

d_p = \frac{6(1-\epsilon)}{a} 

 

Parameters 

---------- 

Vg : float 

Superficial velocity of gas, Q/A [m/s] 

rhog : float 

Density of gas [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 

------- 

dP_dry : float 

Pressure drop across dry packing [Pa] 

 

Notes 

----- 

This model is used by most process simulation tools. If H is not provided, 

it defaults to 1. If Z is not provided, it defaults to 1. 

 

Examples 

-------- 

>>> Stichlmair_dry(Vg=0.4, rhog=5., mug=5E-5, voidage=0.68, 

... specific_area=260., C1=32., C2=7, C3=1) 

236.80904286559885 

 

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. 

''' 

dp = 6*(1-voidage)/specific_area 

Re = Vg*rhog*dp/mug 

f0 = C1/Re + C2/Re**0.5 + C3 

return 3/4.*f0*(1-voidage)/voidage**4.65*rhog*H/dp*Vg**2 

 

 

def Stichlmair_wet(Vg, Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1): 

r'''Calculates dry pressure drop across a packed column, using the 

Stichlmair [1]_ correlation. Uses three regressed constants for each 

type of packing, and voidage and specific area. This model is for irrigated 

columns only. 

 

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} 

 

h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right] 

 

Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}} 

 

h_0 = 0.555 Fr_L^{1/3} 

 

c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0} 

 

\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} 

\rho_G \frac{H}{d_p}V_g^2 

 

f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3 

 

d_p = \frac{6(1-\epsilon)}{a} 

 

Parameters 

---------- 

Vg : float 

Superficial velocity of gas, Q/A [m/s] 

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 

------- 

dP : float 

Pressure drop across irrigated packing [Pa] 

 

Notes 

----- 

This model is used by most process simulation tools. If H is not provided, 

it defaults to 1. If Z is not provided, it defaults to 1. 

A numerical solver is used and needed by this model. Its initial guess 

is the dry pressure drop. Convergence problems may occur. 

The model as described in [1]_ appears to have a typo, and could not match 

the example. As described in [2]_, however, the model works. 

 

Examples 

-------- 

Example is from [1]_, matches. 

 

>>> Stichlmair_wet(Vg=0.4, Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5, 

... voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.) 

539.8768237253518 

 

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. 

.. [2] Piche, Simon R., Faical Larachi, and Bernard P. A. Grandjean. 

"Improving the Prediction of Irrigated Pressure Drop in Packed 

Absorption Towers." The Canadian Journal of Chemical Engineering 79, 

no. 4 (August 1, 2001): 584-94. doi:10.1002/cjce.5450790417. 

''' 

dp = 6*(1-voidage)/specific_area 

Re = Vg*rhog*dp/mug 

f0 = C1/Re + C2/Re**0.5 + C3 

dP_dry = 3/4.*f0*(1-voidage)/voidage**4.65*rhog*H/dp*Vg**2 

c = (-C1/Re - C2/(2*Re**0.5))/f0 

Frl = Vl**2*specific_area/(g*voidage**4.65) 

h0 = 0.555*Frl**(1/3.) 

def to_zero(dP_irr): 

hT = h0*(1 + 20*(dP_irr/H/rhol/g)**2) 

err = dP_dry/H*((1-voidage+hT)/(1-voidage))**((2+c)/3.)*(voidage/(voidage-hT))**4.65 -dP_irr/H 

return err 

return float(fsolve(to_zero, dP_dry)) 

 

 

def Stichlmair_flood(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1): 

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} 

 

h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right] 

 

Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}} 

 

h_0 = 0.555 Fr_L^{1/3} 

 

c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0} 

 

\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} 

\rho_G \frac{H}{d_p}V_g^2 

 

f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3 

 

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.) 

0.6394323542687361 

 

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. 

''' 

def to_zero(inputs): 

Vg, dP_irr = inputs 

dp = 6*(1-voidage)/specific_area 

Re = Vg*rhog*dp/mug 

f0 = C1/Re + C2/Re**0.5 + C3 

dP_dry = 3/4.*f0*(1-voidage)/voidage**4.65*rhog*H/dp*Vg**2 

c = (-C1/Re - C2/(2*Re**0.5))/f0 

Frl = Vl**2*specific_area/(g*voidage**4.65) 

h0 = 0.555*Frl**(1/3.) 

hT = h0*(1 + 20*(dP_irr/H/rhol/g)**2) 

err1 = dP_dry/H*((1-voidage+hT)/(1-voidage))**((2+c)/3.)*(voidage/(voidage-hT))**4.65 -dP_irr/H 

term = (dP_irr/(rhol*g*H))**2 

err2 = (1./term - 40*((2+c)/3.)*h0/(1 - voidage + h0*(1 + 20*term)) 

- 186*h0/(voidage - h0*(1 + 20*term))) 

return err1, err2 

return float(fsolve(to_zero, [Vl*100., 1000])[0]) 

 

#print [Stichlmair_flood(Vl = 5E-3, rhog=5., rhol=1200., mug=5E-5, voidage=0.68, specific_area=260., C1=32., C2=7., C3=1.)] 

 

 

 

def Robbins(Fpd=24, L=None, G=None, rhol=None, rhog=None, mul=None, H=1, A=None): 

r'''Calculates pressure drop across a packed column, using the Robbins 

equation. 

 

Pressure drop is given by: 

 

.. math:: 

\Delta P = C_3 G_f^2 10^{C_4L_f}+0.4[L_f/20000]^{0.1}[C_3G_f^210^{C_4L_f}]^4 

 

G_f=G[0.075/\rho_g]^{0.5}[F_{pd}/20]^{0.5}=986F_s[F_{pd}/20]^{0.5} 

 

L_f=L[62.4/\rho_L][F_{pd}/20]^{0.5}\mu^{0.1} 

 

F_s=V_s\rho_g^{0.5} 

 

Parameters 

---------- 

Fpd : float 

Robbins packing factor (tabulated for packings) [1/ft] 

L : float 

Specific liquid mass flow rate [kg/s/m^2] 

G : float 

Specific gas mass flow rate [kg/s/m^2] 

rhol : float 

Density of liquid [kg/m^3] 

rhog : float 

Density of gas [kg/m^3] 

mul : float 

Viscosity of liquid [Pa*S] 

H : float 

Height of packing [m] 

A : float, optional 

Area of packing; Provide if G and L are in kg/s [m^2] 

 

Returns 

------- 

dP : float 

Pressure drop across packing [Pa] 

 

Notes 

----- 

Perry's displayed equation has a typo in a superscript. 

This model is based on the example in Perry's. 

 

Examples 

-------- 

>>> Robbins(Fpd=24, L=12.2, G=2.03, rhol=1000., rhog=1.1853, mul=0.001, H=2) 

619.6624593438099 

 

References 

---------- 

.. [1] Robbins [Chem. Eng. Progr., p. 87 (May 1991) Improved Pressure Drop 

Prediction with a New Correlation. 

''' 

if A: 

L, G = L/A, G/A 

# Convert SI units to imperial for use in correlation 

L = L*737.33812 # kg/s/m^2 to lb/hr/ft^2 

G = G*737.33812 # kg/s/m^2 to lb/hr/ft^2 

rhol = rhol*0.062427961 # kg/m^3 to lb/ft^3 

rhog = rhog*0.062427961 # kg/m^3 to lb/ft^3 

mul = mul*1000 # Pa*s to cP 

 

C3 = 7.4E-8 

C4 = 2.7E-5 

Lf = L *(62.4/rhol)*(Fpd/20.)**0.5*mul**0.1 

Gf = G*(0.075/rhog)**0.5*(Fpd/20.)**0.5 

dP = C3*Gf**2*10**(C4*Lf) + 0.4*(Lf/20000.)**0.1*(C3*Gf**2*10**(C4*Lf))**4 

return dP*817.22083*H # in. H2O to Pa/m