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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 

from math import log, pi 

 

__all__ = ['adjust_homogeneity', 'agitator_time_homogeneous', 

'Kp_helical_ribbon_Rieger', 'time_helical_ribbon_Grenville', 'size_tee', 

'COV_motionless_mixer', 'K_motionless_mixer'] 

 

max_Fo_for_turbulent = 1/1225. 

min_regime_constant_for_turbulent = 6370. 

 

def adjust_homogeneity(fraction): 

'''Base: 95% homogeneity''' 

multiplier = log(1-fraction)/log(0.05) 

return multiplier 

 

 

def agitator_time_homogeneous(D=None, N=None, P=None, T=None, H=None, mu=None, rho=None, homogeneity=.95): 

r'''Calculates time for a fluid mizing in a tank with an impeller to 

reach a specified level of homogeneity, according to [1]_. 

 

.. math:: 

N_p = \frac{Pg}{\rho N^3 D^5} 

 

Re_{imp} = \frac{\rho D^2 N}{\mu} 

 

\text{constant} = N_p^{1/3} Re_{imp} 

 

Fo = 5.2/\text{constant} \text{for turbulent regime} 

 

Fo = (183/\text{constant})^2 \text{for transition regime} 

 

Parameters 

---------- 

D : float 

Impeller diameter (optional) [m] 

N : float: 

Speed of impeller, [r/s] 

P : float 

Actual power required to mix, ignoring mechanical inefficiencies [W] 

T : float 

Tank diameter, [m] 

H : float 

Tank height, [m] 

mu : float 

Mixture viscosity, [Pa*s] 

rho : float 

Mixture density, [kg/m^3] 

homogeneity : float 

Fraction completion of mixing, optional, [] 

 

Returns 

------- 

t : float 

Time for specified degree of homogeneity [s] 

 

Notes 

----- 

If impeller diameter is not specified, assumed to be 0.5 tank diameters. 

 

The first example is solved forward rather than backwards here. A rather 

different result is obtained, but is accurate. 

 

No check to see if the mixture if laminar is currently implemented. 

This would underpredict the required time. 

 

Examples 

-------- 

>>> agitator_time_homogeneous(D=36*.0254, N=56/60., P=957., T=1.83, H=1.83, mu=0.018, rho=1020, homogeneity=.995) 

15.143198226374668 

 

>>> agitator_time_homogeneous(D=1, N=125/60., P=298., T=3, H=2.5, mu=.5, rho=980, homogeneity=.95) 

67.7575069865228 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

''' 

if not D: 

D = T*0.5 

Np = P*g/rho/N**3/D**5 

Re_imp = rho/mu*D**2*N 

regime_constant = Np**(1/3.)*Re_imp 

if regime_constant >= min_regime_constant_for_turbulent: 

Fo = (5.2/regime_constant) 

else: 

Fo = (183./regime_constant)**2 

time = rho*T**1.5*H**0.5/mu*Fo 

multiplier = adjust_homogeneity(homogeneity) 

time = time*multiplier 

return time 

 

#print [agitator_time_homogeneous(D=1, N=125/60., P=298., T=3, H=2.5, mu=.5, rho=980, homogeneity=.95)] 

#print 'example 2:' 

#print [agitator_time_homogeneous(D=36*.0254, N=56/60., P=957., T=1.83, H=1.83, mu=0.018, rho=1020, homogeneity=.995)] 

 

def Kp_helical_ribbon_Rieger(D=None, h=None, nb=None, pitch=None, width=None, T=None): 

r'''Calculates product of power number and reynolds number for a 

specified geometry for a heilical ribbon mixer in the laminar regime. 

One of several correlations listed in [1]_, it used more data than other 

listed correlations and was recommended. 

 

.. math:: 

K_p = 82.8\frac{h}{D}\left(\frac{c}{D}\right)^{-0.38} \left(\frac{p}{D}\right)^{-0.35} 

\left(\frac{w}{D}\right)^{0.20} n_b^{0.78} 

 

Parameters 

---------- 

D : float 

Impeller diameter (optional) [m] 

h : float 

Ribbon mixer height, [m] 

nb : float: 

Number of blades, [-] 

pitch : float 

Height of one turn around a helix [m] 

width : float 

Width of one blade [m] 

T : float 

Tank diameter, [m] 

 

Returns 

------- 

Kp : float 

Product of power number and reynolds number for laminar regime [] 

 

Notes 

----- 

Example is from example 9-6 in [1]_. Confirmed. 

 

Examples 

-------- 

>>> Kp_helical_ribbon_Rieger(D=1.9, h=1.9, nb=2, pitch=1.9, width=.19, T=2) 

357.39749163259256 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

.. [2] Rieger, F., V. Novak, and D. Havelkov (1988). The influence of the 

geometrical shape on the power requirements of ribbon impellers, 

Int. Chem. Eng., 28, 376-383. 

''' 

c = (T-D)/2 

Kp = 82.8*h/D*(c/D)**-.38*(pitch/D)**-0.35*(width/D)**0.2*nb**0.78 

return Kp 

 

#print [Kp_helical_ribbon_Rieger(D=1.9, h=1.9, nb=2, pitch=1.9, width=.19, T=2)] 

 

def time_helical_ribbon_Grenville(Kp, N): 

r'''Calculates product of time required for mixing in a helical ribbon 

coil in the laminar regime according to the Grenville [2]_ method 

recommended in [1]_. 

 

.. math:: 

t = 896\times10^3K_p^{-1.69}/N 

 

Parameters 

---------- 

Kp : float 

Product of power number and reynolds number for laminar regime [] 

N : float: 

Speed of impeller, [r/s] 

 

Returns 

------- 

t : float 

Time for homogeneity [s] 

 

Notes 

----- 

Degree of homogeneity is not specified. 

Example is from example 9-6 in [1]_. Confirmed. 

 

Examples 

-------- 

>>> time_helical_ribbon_Grenville(357.4, 4/60.) 

650.980654028894 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

.. [2] Grenville, R. K., T. M. Hutchinson, and R. W. Higbee (2001). 

Optimisation of helical ribbon geometry for blending in the laminar 

regime, presented at MIXING XVIII, NAMF. 

''' 

t = 896E3*Kp**-1.69/N 

return t 

 

#print [time_helical_ribbon_Grenville(357.4, 4/60.)] 

 

 

### Tee mixer 

 

def size_tee(Q1=None, Q2=None, D=None, D2=None, n=1, pipe_diameters=5): 

r'''Calculates CoV of an optimal or specified tee for mixing at a tee 

according to [1]_. Assumes turbulent flow. 

The smaller stream in injected into the main pipe, which continues 

straight. 

COV calculation is according to [2]_. 

 

.. math:: 

TODO 

 

Parameters 

---------- 

Q1 : float 

Volumetric flow rate of larger stream [m^3/s] 

Q2 : float 

Volumetric flow rate of smaller stream [m^3/s] 

D : float 

Diameter of pipe after tee [m] 

D2 : float 

Diameter of mixing inlet, optional (optimally calculated if not 

specified) [m] 

n : float 

Number of jets, 1 to 4 [] 

pipe_diameters : float 

Number of diameters along tail pipe for CoV calculation, 0 to 5 [] 

 

Returns 

------- 

CoV : float 

Standard deviation of dimentionless concentration [-] 

 

Notes 

----- 

Not specified if this works for liquid also, though probably not. 

Example is from example Example 9-6 in [1]_. Low precision used in example. 

 

Examples 

-------- 

>>> size_tee(Q1=11.7, Q2=2.74, D=0.762, D2=None, n=1, pipe_diameters=5) 

0.2940930233038544 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

.. [2] Giorges, Aklilu T. G., Larry J. Forney, and Xiaodong Wang. 

"Numerical Study of Multi-Jet Mixing." Chemical Engineering Research and 

Design, Fluid Flow, 79, no. 5 (July 2001): 515-22. 

doi:10.1205/02638760152424280. 

''' 

V1 = Q1/(pi/4*D**2) 

# print 'V1', V1 

Cv = Q2/(Q1 + Q2) 

COV0 = ((1-Cv)/Cv)**0.5 

# print 'COV0', COV0 

if not D2: 

D2 = (Q2/Q1)**(2/3.)*D 

V2 = Q2/(pi/4*D2**2) 

# V2 = 45.67 

# print 'D2, V2', D2, V2 

B = n**2*(D2/D)**2*(V2/V1)**2 

# print 'B', B 

if not n == 1 and not n == 2 and not n == 3 and not n ==4: 

raise Exception('Only 1 or 4 side streams investigated') 

if n == 1: 

if B < 0.7: 

E = 1.33 

else: 

E = 1/33. + 0.95*log(B/0.7) 

elif n == 2: 

if B < 0.8: 

E = 1.44 

else: 

E = 1.44 + 0.95*log(B/0.8)**1.5 

elif n == 3: 

if B < 0.8: 

E = 1.75 

else: 

E = 1.75 + 0.95*log(B/0.8)**1.8 

else: 

if B < 2: 

E = 1.97 

else: 

E = 1.97 + 0.95*log(B/2.)**2 

COV = (0.32/B**0.86*(pipe_diameters)**-E )**0.5 

return COV 

 

### Commercial motionless mixers 

'''Data from: 

Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004.''' 

StatixMixers = {} 

StatixMixers['KMS'] = {'Name': 'KMS', 'Vendor': 'Chemineer', 'Description': 'Twisted ribbon. Alternating left and right twists.', 'KL': 6.9, 'KiL': 0.87, 'KT': 150, 'KiT': 0.5} 

StatixMixers['SMX'] = {'Name': 'SMX', 'Vendor': 'Koch-Glitsch', 'Description': 'Guide vanes 45 degrees to pipe axis. Adjacent elements rotated 90 degrees.', 'KL': 37.5, 'KiL': 0.63, 'KT': 500, 'KiT': 0.46} 

StatixMixers['SMXL'] = {'Name': 'SMXL', 'Vendor': 'Koch-Glitsch', 'Description': 'Similar to SMX, but intersection bars at 30 degrees to pipe axis.', 'KL': 7.8, 'KiL': 0.85, 'KT': 100, 'KiT': 0.87} 

StatixMixers['SMF'] = {'Name': 'SMF', 'Vendor': 'Koch-Glitsch', 'Description': 'Three guide vanes projecting from the tube wall in a way as to not contact. Designed for applications subject to plugging.', 'KL': 5.6, 'KiL': 0.83, 'KT': 130, 'KiT': 0.4} 

 

 

def COV_motionless_mixer(Ki=None, Q1=None, Q2=None, pipe_diameters=None): 

r'''Calculates CoV of a motionless mixer with a regression parameter in 

[1]_ and originally in [2]_. 

 

.. math:: 

\frac{CoV}{CoV_0} = K_i^{L/D} 

 

Parameters 

---------- 

Ki : float 

Correlation parameter specific to a mixer's design, [-] 

Q1 : float 

Volumetric flow rate of larger stream [m^3/s] 

Q2 : float 

Volumetric flow rate of smaller stream [m^3/s] 

pipe_diameters : float 

Number of diameters along tail pipe for CoV calculation, 0 to 5 [] 

 

Returns 

------- 

CoV : float 

Standard deviation of dimentionless concentration [-] 

 

Notes 

----- 

Example 7-8.3.2 in [1]_, solved backwards. 

 

Examples 

-------- 

>>> COV_motionless_mixer(Ki=.33, Q1=11.7, Q2=2.74, pipe_diameters=4.74/.762) 

0.0020900028665727685 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

.. [2] Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and 

application of motionless mixer technology, Proc. ISMIP3, Osaka, 

pp. 107-114. 

''' 

Cv = Q2/(Q1 + Q2) 

COV0 = ((1-Cv)/Cv)**0.5 

COVr = Ki**(pipe_diameters) 

COV = COV0*COVr 

return COV 

 

 

def K_motionless_mixer(K=None, L=None, D=None, fd=None): 

r'''Calculates loss ciefficient of a motionless mixer with a regression 

parameter in [1]_ and originally in [2]_. 

 

.. math:: 

K = K_{L/T}f\frac{L}{D} 

 

Parameters 

---------- 

K : float 

Correlation parameter specific to a mixer's design, [-] 

Also specific to laminar or turbulent regime. 

L : float 

Length of the motionless mixer [m] 

D : float 

Diameter of pipe [m] 

fd : float 

Darcy friction factor [-] 

 

Returns 

------- 

K : float 

Loss coefficient of mixer [-] 

 

Notes 

----- 

Related to example 7-8.3.2 in [1]_. 

 

Examples 

-------- 

>>> K_motionless_mixer(K=150, L=.762*5, D=.762, fd=.01) 

7.5 

 

References 

---------- 

.. [1] Paul, Edward L, Victor A Atiemo-Obeng, and Suzanne M Kresta. 

Handbook of Industrial Mixing: Science and Practice. 

Hoboken, N.J.: Wiley-Interscience, 2004. 

.. [2] Streiff, F. A., S. Jaffer, and G. Schneider (1999). Design and 

application of motionless mixer technology, Proc. ISMIP3, Osaka, 

pp. 107-114. 

''' 

K = L/D*fd*K 

return K 

 

#print K_motionless_mixer(K=150, L=.762*5, D=.762, fd=.01)