Packing & demister pressure drop (fluids.packed_tower)¶
This module contains correlations and functions for calculating pressure drop from packings and demisters; separation efficiency of demisters; demister pressure drop; and demister geometry.
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.
Packing Pressure Drop¶
- fluids.packed_tower.Robbins(L, G, rhol, rhog, mul, H=1.0, Fpd=24.0)[source]¶
Calculates pressure drop across a packed column, using the Robbins equation.
Pressure drop is given by:
\[\Delta P = C_3 G_f^2 10^{C_4L_f}+0.4[L_f/20000]^{0.1}[C_3G_f^210^{C_4L_f}]^4\]\[G_f=G[0.075/\rho_g]^{0.5}[F_{pd}/20]^{0.5}=986F_s[F_{pd}/20]^{0.5}\]\[L_f=L[62.4/\rho_L][F_{pd}/20]^{0.5}\mu^{0.1}\]\[F_s=V_s\rho_g^{0.5}\]- Parameters
- Lfloat
Specific liquid mass flow rate [kg/s/m^2]
- Gfloat
Specific gas mass flow rate [kg/s/m^2]
- rholfloat
Density of liquid [kg/m^3]
- rhogfloat
Density of gas [kg/m^3]
- mulfloat
Viscosity of liquid [Pa*s]
- Hfloat
Height of packing [m]
- Fpdfloat
Robbins packing factor (tabulated for packings) [1/ft]
- Returns
- dPfloat
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.
References
- 1
Robbins [Chem. Eng. Progr., p. 87 (May 1991) Improved Pressure Drop Prediction with a New Correlation.
Examples
>>> Robbins(L=12.2, G=2.03, rhol=1000., rhog=1.1853, mul=0.001, H=2.0, Fpd=24.0) 619.6624593438102
- fluids.packed_tower.Stichlmair_dry(Vg, rhog, mug, voidage, specific_area, C1, C2, C3, H=1.0)[source]¶
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:
\[\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} \rho_G \frac{H}{d_p}V_g^2\]\[f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3\]\[d_p = \frac{6(1-\epsilon)}{a}\]- Parameters
- Vgfloat
Superficial velocity of gas, Q/A [m/s]
- rhogfloat
Density of gas [kg/m^3]
- mugfloat
Viscosity of gas [Pa*s]
- voidagefloat
Voidage of bed of packing material []
- specific_areafloat
Specific area of the packing material [m^2/m^3]
- C1float
Packing-specific constant []
- C2float
Packing-specific constant []
- C3float
Packing-specific constant []
- Hfloat, optional
Height of packing [m]
- Returns
- dP_dryfloat
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.
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.
Examples
>>> Stichlmair_dry(Vg=0.4, rhog=5., mug=5E-5, voidage=0.68, ... specific_area=260., C1=32., C2=7.0, C3=1.0) 236.80904286559885
- fluids.packed_tower.Stichlmair_wet(Vg, Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1.0)[source]¶
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:
\[\frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac {1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3} \left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65}\]\[h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right]\]\[Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}}\]\[h_0 = 0.555 Fr_L^{1/3}\]\[c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0}\]\[\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} \rho_G \frac{H}{d_p}V_g^2\]\[f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3\]\[d_p = \frac{6(1-\epsilon)}{a}\]- Parameters
- Vgfloat
Superficial velocity of gas, Q/A [m/s]
- Vlfloat
Superficial velocity of liquid, Q/A [m/s]
- rhogfloat
Density of gas [kg/m^3]
- rholfloat
Density of liquid [kg/m^3]
- mugfloat
Viscosity of gas [Pa*s]
- voidagefloat
Voidage of bed of packing material []
- specific_areafloat
Specific area of the packing material [m^2/m^3]
- C1float
Packing-specific constant []
- C2float
Packing-specific constant []
- C3float
Packing-specific constant []
- Hfloat, optional
Height of packing [m]
- Returns
- dPfloat
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.
References
- 1(1,2,3)
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.
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.) 539.876823725352
Packing Flooding¶
- fluids.packed_tower.Stichlmair_flood(Vl, rhog, rhol, mug, voidage, specific_area, C1, C2, C3, H=1.0)[source]¶
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:
\[\frac{\Delta P_{irr}}{H} = \frac{\Delta P_{dry}}{H}\left(\frac {1-\epsilon + h_T}{1-\epsilon}\right)^{(2+c)/3} \left(\frac{\epsilon}{\epsilon-h_T}\right)^{4.65}\]\[h_T = h_0\left[1 + 20\left(\frac{\Delta Pirr}{H\rho_L g}\right)^2\right]\]\[Fr_L = \frac{V_L^2 a}{g \epsilon^{4.65}}\]\[h_0 = 0.555 Fr_L^{1/3}\]\[c = \frac{-C_1/Re_g - C_2/(2Re_g^{0.5})}{f_0}\]\[\Delta P_{dry} = \frac{3}{4} f_0 \frac{1-\epsilon}{\epsilon^{4.65}} \rho_G \frac{H}{d_p}V_g^2\]\[f_0 = \frac{C_1}{Re_g} + \frac{C_2}{Re_g^{0.5}} + C_3\]\[d_p = \frac{6(1-\epsilon)}{a}\]- Parameters
- Vlfloat
Superficial velocity of liquid, Q/A [m/s]
- rhogfloat
Density of gas [kg/m^3]
- rholfloat
Density of liquid [kg/m^3]
- mugfloat
Viscosity of gas [Pa*s]
- voidagefloat
Voidage of bed of packing material []
- specific_areafloat
Specific area of the packing material [m^2/m^3]
- C1float
Packing-specific constant []
- C2float
Packing-specific constant []
- C3float
Packing-specific constant []
- Hfloat, optional
Height of packing [m]
- Returns
- Vgfloat
Superficial velocity of gas, Q/A [m/s]
Notes
A numerical solver is used to solve this model.
References
- 1(1,2)
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.
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
Demister Pressure Drop¶
- fluids.packed_tower.dP_demister_dry_Setekleiv_Svendsen(S, voidage, vs, rho, mu, L=1.0)[source]¶
Calculates dry pressure drop across a demister, using the correlation in [1]. This model is for dry demisters with no holdup only.
\[\frac{\Delta P \epsilon^2}{\rho_f v^2} = 10.29 - \frac{565} {69.6SL - (SL)^2 - 779} - \frac{74.9}{160.9 - 4.85SL} + 45.33\left( \frac{\mu_f \epsilon S^2 L}{\rho_f v}\right)^{0.75}\]- Parameters
- Sfloat
Specific area of the demister, normally ~250-1000 [m^2/m^3]
- voidagefloat
Voidage of bed of the demister material, normally ~0.98 []
- vsfloat
Superficial velocity of fluid, Q/A [m/s]
- rhofloat
Density of fluid [kg/m^3]
- mufloat
Viscosity of fluid [Pa*s]
- Lfloat, optional
Length of the demister [m]
- Returns
- dPfloat
Pressure drop across a dry demister [Pa]
Notes
Useful at startup and in modeling. Dry pressure drop is normally negligible compared to wet pressure drop. Coefficients obtained by evolutionary programming and may not fit data outside of the limits of the variables.
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.
Examples
>>> dP_demister_dry_Setekleiv_Svendsen(S=250, voidage=.983, vs=1.2, rho=10, mu=3E-5, L=1) 320.3280788941329
- fluids.packed_tower.dP_demister_dry_Setekleiv_Svendsen_lit(S, voidage, vs, rho, mu, L=1.0)[source]¶
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.
\[\frac{\Delta P \epsilon^2}{\rho_f v^2} = 7.3 - \frac{320} {69.6SL - (SL)^2 - 779} - \frac{52.4}{161 - 4.85SL} + 27.2\left( \frac{\mu_f \epsilon S^2 L}{\rho_f v}\right)^{0.75}\]- Parameters
- Sfloat
Specific area of the demister, normally ~250-1000 [m^2/m^3]
- voidagefloat
Voidage of bed of the demister material, normally ~0.98 []
- vsfloat
Superficial velocity of fluid, Q/A [m/s]
- rhofloat
Density of fluid [kg/m^3]
- mufloat
Viscosity of fluid [Pa*s]
- Lfloat, optional
Length of the demister [m]
- Returns
- dPfloat
Pressure drop across a dry demister [Pa]
Notes
Useful at startup and in modeling. Dry pressure drop is normally negligible compared to wet pressure drop. Coefficients obtained by evolutionary programming and may not fit data outside of the limits of the variables.
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.
Examples
>>> dP_demister_dry_Setekleiv_Svendsen_lit(S=250, voidage=.983, vs=1.2, rho=10, mu=3E-5, L=1.0) 209.083848658307
- fluids.packed_tower.dP_demister_wet_ElDessouky(vs, voidage, d_wire, L=1.0)[source]¶
Calculates wet pressure drop across a demister, using the correlation in [1]. Uses only their own experimental data.
\[\frac{\Delta P}{L} = 0.002357(1-\epsilon)^{0.375798}(V)^{0.81317} (d_w)^{-1.56114147}\]- Parameters
- vsfloat
Superficial velocity of fluid, Q/A [m/s]
- voidagefloat
Voidage of bed of the demister material, normally ~0.98 []
- d_wirefloat
Diameter of mesh wire,[m]
- Lfloat, optional
Length of the demister [m]
- Returns
- dPfloat
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.
\[\Delta P = 3.88178(\rho_{mesh})^{0.375798}(V)^{0.81317} (d_w)^{-1.56114147}\]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.
References
- 1(1,2,3,4)
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.
Examples
>>> dP_demister_wet_ElDessouky(6, 0.978, 0.00032) 688.9216420105029
Demister Separation Efficiency¶
- fluids.packed_tower.separation_demister_ElDessouky(vs, voidage, d_wire, d_drop)[source]¶
Calculates droplet removal by a demister as a fraction from 0 to 1, using the correlation in [1]. Uses only their own experimental data.
\[\eta = 0.85835(d_w)^{-0.28264}(1-\epsilon)^{0.099625}(V)^{0.106878} (d_p)^{0.383197}\]- Parameters
- vsfloat
Superficial velocity of fluid, Q/A [m/s]
- voidagefloat
Voidage of bed of the demister material, normally ~0.98 []
- d_wirefloat
Diameter of mesh wire,[m]
- d_dropfloat
Drop diameter, [m]
- Returns
- etafloat
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.
\[\eta = 17.5047(d_w)^{-0.28264}(\rho_{mesh})^{0.099625}(V)^{0.106878} (d_p)^{0.383197}\]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 0.2 mm to 0.32 mm, and particle diameter from 1 to 5 mm.
References
- 1(1,2,3,4)
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.
Examples
>>> separation_demister_ElDessouky(1.35, 0.974, 0.0002, 0.005) 0.8982892997640582
Demister Geometry¶
- fluids.packed_tower.voidage_experimental(m, rho, D, H)[source]¶
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.
\[\epsilon = 1 - \frac{\frac{m_{mesh}}{\frac{\pi}{4}d_{column}^2 L_{mesh}}}{\rho_{material}}\]- Parameters
- mfloat
Mass of mesh or bed particles weighted, [kg]
- rhofloat
Density of solid particles or mesh [kg/m^3]
- Dfloat
Diameter of the cylindrical bed [m]
- Hfloat
Height of the demister or bed [m]
- Returns
- voidagefloat
Voidage of bed of the material []
Notes
Should be trusted over manufacturer data.
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.
Examples
>>> voidage_experimental(m=126, rho=8000, D=1, H=1) 0.9799464771704212
- fluids.packed_tower.specific_area_mesh(voidage, d)[source]¶
Calculates the specific area of a wire mesh, as used in demisters or filters. Shown in [1], and also self-evident and non-empirical. Makes the ideal assumption that wires never touch.
\[S = \frac{4(1-\epsilon)}{d_{wire}}\]- Parameters
- voidagefloat
Voidage of the mesh []
- dfloat
Diameter of the wires making the mesh, [m]
- Returns
- Sfloat
Specific area of the mesh [m^2/m^3]
Notes
Should be preferred over manufacturer data. Can also be used to show that manufacturer’s data is inconsistent with their claimed voidage and wire diameter.
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.
Examples
>>> specific_area_mesh(voidage=.934, d=3e-4) 879.9999999999994