#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""Pychemqt, Chemical Engineering Process simulator
Copyright (C) 2009-2025, Juan José Gómez Romera <jjgomera@gmail.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Module with neumatic conveying equipment library
"""
from scipy.constants import g, pi
from lib.unidades import Dimensionless, Speed
from lib.utilities import refDoc
__doi__ = {
1:
{"autor": "Rhodes, M.",
"title": "Introduction to Particle Technology 2Ed",
"ref": "(John Wiley & Sons) 2008",
"doi": "10.1002/9780470727102"},
2:
{"autor": "Rizk, F.",
"title": "Pneumatic conveying at optimal operation conditions and a "
"solution of Bath's equation",
"ref": "Proceedings of Pneumotransport 3, paper D4. BHRA Fluid "
"Engineering, Cranfield, England (1973)",
"doi": ""},
3:
{"autor": "Matsumoto, S., Hara, M., Saito, S., Maeda, S.",
"title": "Minimum Transport Velocity for Horizontal Pneumatic "
"Conveying",
"ref": "J. Chem. Eng. Japan 7(6) (1974) 425-430",
"doi": "10.1252/jcej.7.425"},
4:
{"autor": "Matsumoto, S., Harada, S., Saito, S., Maeda, S.",
"title": "Saltation Velocity for Horizontal Pneumatic Conveying",
"ref": "J. Chem. Eng. Japan 8(4) (1975) 331-333",
"doi": "10.1252/jcej.8.331"},
5:
{"autor": "Matsumoto, S., Kikuta, M., Maeda, S.",
"title": "Effect of Particle Size on the Minimum Transport Velocity "
"for Horizontal Pneumatic Conveying of Solids",
"ref": "J. Chem. Eng. Japan 10(4) (1977) 273-279",
"doi": "10.1252/jcej.10.273"},
6:
{"autor": "Ochi, M.",
"title": "Saltation Velocity of the Gas-Solid Two-Phase Flow in a "
"Horizontal Pipe",
"ref": "Trans. JSME B. 59(564) (1993) 2416-2421",
"doi": "10.1299/kikaib.59.2416"},
7:
{"autor": "Stemerding, S.",
"title": "The pneumatic transport of cracking catalyst in vertical "
"risers",
"ref": "Chem. Eng. Sci. 17(8) (1962) 599-608",
"doi": "10.1016/0009-2509(62)80053-0"},
8:
{"autor": "Reddy, K.V.S., Pei, D.C.T.",
"title": "Particle Dynamics in Solids-Gas Flow in a Vertical Pipe",
"ref": "Ind. Eng. Chem. Fundamen. 8(3) (1969) 490-497",
"doi": "10.1021/i160031a020"},
9:
{"autor": "van Swaaij, W.P.M., Buurman, C., van Breugel, J.W.",
"title": "Shear Stresses on the Wall of a Dense Gas-Solids Riser",
"ref": "Chem. Eng. Sci. 25(11) (1970) 1818-1820",
"doi": "10.1016/0009-2509(70)80072-0"},
10:
{"autor": "Capes, C.E., Nakamura, K.",
"title": "Vertical Pneumatic Conveying: An Experimental Study with "
"Particles in the Intermediate and Turbulent Flow Regimes",
"ref": "Can. J. Chem. Eng. 51(1) (1973) 31-38",
"doi": "10.1002/cjce.5450510106"},
11:
{"autor": "Konno, H., Saito, S.",
"title": "Pneumatic Conveying of Solids Through Straight Pipes",
"ref": "J. Chem. Eng. Japan 2(2) (1969) 211-217",
"doi": "10.1252/jcej.2.211"},
12:
{"autor": "Yang, W.-C.",
"title": "A Correlation for Solid Friction Factor in Vertical "
"Pneumatic Conveying Lines",
"ref": "AIChE J. 24(3) (1978) 548-552",
"doi": "10.1002/aic.690240326"},
13:
{"autor": "Yang, W.-C.",
"title": "Correlations for Solid Friction Factors in Vertical and "
"Horizontal Pneumatic Conveying",
"ref": "AIChE J. 20(3) (1974) 605-607",
"doi": "10.1002/aic.690200327"},
14:
{"autor": "",
"title": "",
"ref": "",
"doi": ""},
}
# Saltation speed correlations
[docs]
@refDoc(__doi__, [1, 2])
def saltation_Rizk(M, dp, rhog, D):
r"""Calculates saltation velocity of gas for pneumatic conveying, using
the correlation of Rizk (1973) as described in [1]_
.. math::
\begin{array}[t]{c}
\frac{M}{\rho_g V_{salt} A} = \frac{1}{10^{\delta}}
\left(\frac{V_{salt}}{\sqrt{gD}}\right)^{\chi}\\
\delta = 1440d_p + 1.96\\
\chi = 1100d_p + 2.5\\
A = \frac{pi}{4} D^2\\
\end{array}
Rearanged saltation velocity
.. math::
V{salt} = \left(\frac{M 10^\delta (g D)^{0.5 \chi}}{\rho_g A}\right)^
{\frac{1}{\chi+1}}
Parameters
----------
M : float
Solid mass flow rate, [kg/s]
dp : float
Particle diameter, [m]
rhog : float
Gas density, [kg/m³]
D : float
Diameter of pipe, [m]
Returns
-------
Vs : float
Saltation velocity of gas, [m/s]
Examples
--------
Example 8.1 from [1]_, pag. 238
>>> "%0.2f" % (saltation_Rizk(M=0.25, dp=1e-4, rhog=1.2, D=0.078))
'9.88'
"""
# Using dp in mm
dp *= 1e3
delta = 1.44*dp + 1.96
Xi = 1.1*dp + 2.5
A = pi/4*D**2 # Cross section of pipe
# Solving saltation velocity
Vs = (M * 10**delta * (g*D)**(0.5*Xi) / rhog / A)**(1/(Xi+1))
return Speed(Vs)
[docs]
@refDoc(__doi__, [3, 4, 5])
def saltation_Matsumoto(M, rhop, dp, rhog, D, Vt, method="1977"):
r"""Calculates saltation velocity of the gas for pneumatic conveying,
according to any of method defined in Matsumoto papers.
* 1974 method, [3]_.
.. math::
\begin{array}[t]{c}
\frac{M}{\rho_g V_{salt} A} = 0.488 \left(\frac{\rho_p}{\rho_f}\right)
^{0.5} \left(\frac{Fr_t}{10}\right)^{-1.75}
\left(\frac{Fr_s}{10}\right)^{3}\\
Fr_s = \frac{V_{salt}}{\sqrt{g D}}\\
Fr_t = \frac{V_{t}}{\sqrt{g d_p}}\\
A = \frac{pi}{4} D^2\\
\end{array}
* 1975 method changing only the parameters of equation, [4]_.
.. math::
\frac{M}{\rho_g V_{salt} A} = 1.11 \left(\frac{\rho_p}{\rho_f}\right)
^{0.55} \left(\frac{Fr_t}{10}\right)^{-2.3}
\left(\frac{Fr_s}{10}\right)^{3}
* 1977, [5]_. In this case the correlations have two step formulation
definning a critical particle diameter
.. math::
\frac{d_c}{D} = 1.39\left(\frac{\rho_p}{\rho_g}\right)^{0.74}
For :math:`d_p < d_c`:
.. math::
\frac{M}{\rho_g V_{salt} A} = 5560 \left(\frac{d_p}{D}\right)^{1.43}
\left(\frac{Fr_s}{10}\right)^{4}
For :math:`d_p > d_c`:
.. math::
\frac{M}{\rho_g V_{salt} A} = 0.373 \left(\frac{\rho_p}{\rho_f}\right)
^{1.06} \left(\frac{Fr_t}{10}\right)^{-3.7}
\left(\frac{Fr_s}{10}\right)^{3.61}
Parameters
----------
M : float
Solid mass flow rate, [kg/s]
rhop : float
Particle density, [kg/m^3]
dp : float
Particle diameter, [m]
rhog : float
Gas density, [kg/m^3]
D : float
Diameter of pipe, [m]
Vt : float
Terminal velocity of particle settling in gas, [m/s]
method : str
Specified the method from the year of paper, 1974|1975|1977
Returns
-------
Vs : float
Saltation velocity of gas, [m/s]
Examples
--------
>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16, method="1974"))
'18.03'
>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16, method="1975"))
'16.49'
>>> "%0.2f" % (saltation_Matsumoto(M=0.25, rhop=2500, dp=4.7e-4, \
... rhog=1.2, D=0.0026, Vt=3.16))
'10.51'
"""
if method == "1977":
# Defining critical diameter, Eq 1.
dc = 1.39*D*(rhop/rhog)**-0.74
if dp <= dc:
# Fine particles, Eq 2.
rhs = 5.56e3*(dp/D)**1.43 * (1/(g*D)**0.5/10)**4
A = pi/4*D**2
Vs = (M/rhog/A/rhs)**0.2
return Vs
# Coarse particles, Eq 3
alpha, a, b, c = 0.373, 1.06, -3.7, 3.61
elif method == "1974":
alpha, a, b, c = 0.488, 0.5, -1.75, 3
elif method == "1975":
alpha, a, b, c = 1.11, 0.55, -2.3, 3
A = pi/4*D**2
Frt = Vt/(g*dp)**0.5
rhs = alpha*(rhop/rhog)**a * (Frt/10.)**b * (1/(g*D)**0.5/10.)**c
Vs = (M/rhog/A / rhs)**(1/(c+1))
return Speed(Vs)
[docs]
@refDoc(__doi__, [6])
def saltation_Ochi(M, dp, rhog, D, Vt, fp=0.4):
r"""Calculates saltation velocity of the gas for pneumatic conveying,
according to Ochi correlation, [6]_.
.. math::
\begin{array}[t]{c}
Fr_s = 1.05 f_d^{0.47}Fr_t^{0.82} \mu_s^{0.25}\\
Fr_t = \frac{V_{t}}{\sqrt{g d_p}}\\
\mu_s = \frac{M}{\rho_g V_{salt} A}\\
A = \frac{pi}{4} D^2\\
\end{array}
Rearanged saltation velocity
.. math::
V_{salt} = \left(\frac{1.05 M^{0.25} f^{0.47} Fr_t^{0.82} \sqrt{g d_p}}
{\left(\rho_g A\right)^{0.25}}\right)^{0.8}
Parameters
----------
M : float
Solid mass flow rate, [kg/s]
dp : float
Particle diameter, [m]
rhog : float
Gas density, [kg/m^3]
D : float
Diameter of pipe, [m]
Vt : float
Terminal velocity of particle settling in gas, [m/s]
fp : float
Coefficient of friction between particles and surface, [-]
Returns
-------
Vs : float
Saltation velocity of gas, [m/s]
Examples
--------
>>> "%0.2f" % (saltation_Ochi(M=0.25, dp=4.7e-4, rhog=1.2, D=0.0026, Vt=3.16))
'8.82'
"""
A = pi/4*D**2
Frt = Vt/(g*dp)**0.5
Vs = (1.05*fp**0.47*Frt**0.82*M**0.25*(g*dp)**0.5/(rhog*A)**0.25)**0.8
return Speed(Vs)
[docs]
def V_saltation(method=0, *args):
"""List with all saltation velocity correlations availables
* 0 - Rizk (1973)
* 1 - Matsumoto (1977)
* 2 - Matsumoto (1975)
* 3 - Matsumoto (1974)
* 4 - Ochi (1991)
"""
if method == 0:
return saltation_Rizk(*args)
elif method == 1:
return saltation_Matsumoto(*args, method="1977")
elif method == 2:
return saltation_Matsumoto(*args, method="1975")
elif method == 3:
return saltation_Matsumoto(*args, method="1974")
elif method == 4:
return saltation_Ochi(*args)
# Solid friction factor correlations
[docs]
@refDoc(__doi__, [7])
def fs_Stemerding():
"""Calculate solid friction factor as define in [7]_.
This method give a constant value withoud dependent variables based in
experiment in vertical neumatic conveying
Returns
-------
fs : float
Solid friction factor, [-]
"""
# 0.012/4
return Dimensionless(0.003)
[docs]
@refDoc(__doi__, [8])
def fs_Reddy(Vs):
"""Calculate solid friction factor as define in [8]_.
Parameters
----------
Vs : float
Solid velocity of particle, [m/s]
Returns
-------
fs : float
Solid friction factor, [-]
"""
return Dimensionless(0.045/Vs)
[docs]
@refDoc(__doi__, [9])
def fs_Swaaij(Vs):
"""Calculate solid friction factor as define in [9]_.
Parameters
----------
Vs : float
Solid velocity of particle, [m/s]
Returns
-------
fs : float
Solid friction factor, [-]
"""
# Using the graphical slope in Fig. 1
return Dimensionless(0.08/Vs)
[docs]
@refDoc(__doi__, [10])
def fs_Capes(Vs):
"""Calculate solid friction factor as define in [10]_.
Parameters
----------
Vs : float
Solid velocity of particle, [m/s]
Returns
-------
fs : float
Solid friction factor, [-]
"""
# Converting parameter to Si units
# >>> 0.206*k.foot**1.22
# 0.04834654849325329
return Dimensionless(0.0483/Vs)
[docs]
@refDoc(__doi__, [11])
def fs_Konno(Vs, D):
"""Calculate solid friction factor as define in [11]_.
Parameters
----------
Vs : float
Solid velocity of particle, [m/s]
D : float
Diameter of pipe, [m]
Returns
-------
fs : float
Solid friction factor, [-]
"""
return Dimensionless(0.0285/Vs*(g*D)**0.5)
[docs]
@refDoc(__doi__, [12])
def fs_Yang(Vs, eps, Vt, V):
"""Calculate solid friction factor as define in [12]_.
Parameters
----------
Vs : float
Solid velocity of particle, [m/s]
eps : float
Voidage in transporting line, [-]
Vt : float
Terminal velocity of faling particle, [m/s]
V: float
Fluid velocity, [m/s]
Returns
-------
fs : float
Solid friction factor, [-]
"""
# Eq 15
# Converting factor /4 to fanning friction factor
return Dimensionless(0.00315*(1-eps)/eps**3*((1-eps)*Vt/(V-Vs))**-0.979)
[docs]
def f_solid(method=0, *args):
"""List with all solid friction factor correlations availables for vertical
conveying
* 0 - Stemerding (1962)
* 1 - Reddy-Pei (1969)
* 2 - Swaaij-Buurman-Breugel (1970)
* 3 - Capes-Nakamura (1973)
* 4 - Konno-Saito (1969)
* 5 - Yang (1978)
"""
if method == 0:
return fs_Stemerding()
elif method == 1:
return fs_Reddy(*args)
elif method == 2:
return fs_Swaaij(*args)
elif method == 3:
return fs_Capes(*args)
elif method == 4:
return fs_Konno(*args)
else:
return fs_Yang(*args)
[docs]
@refDoc(__doi__, [13])
def fs_Yang_Horizontal(eps, V, D):
"""Calculate solid friction factor as define in [13]_.
Parameters
----------
eps : float
Voidage in transporting line, [-]
V: float
Fluid velocity, [m/s]
D : float
Diameter of pipe, [m]
Returns
-------
fs : float
Solid friction factor, [-]
"""
# Eq 5
# Converting factor /4 to fanning friction factor
return Dimensionless(0.02925*(1-eps)/eps**3*((1-eps)*V/(g*D)**0.5)**-1.15)
