# -*- coding: utf-8 -*-
"""
This module contains methods and correlations to find aeration requirements
for bioreactors.
.. contents:: :local:
.. autofunction:: biosteam.units.design_tools.aeration.log_mean_driving_force
.. autofunction:: biosteam.units.design_tools.aeration.Henrys_law_constant
.. autofunction:: biosteam.units.design_tools.aeration.C_L
.. autofunction:: biosteam.units.design_tools.aeration.C_O2_L
.. autofunction:: biosteam.units.design_tools.aeration.kLa_stirred_Riet
.. autofunction:: biosteam.units.design_tools.aeration.kla_stirred_Labik
.. autofunction:: biosteam.units.design_tools.aeration.kLa_stirred_Galaction
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Deshpande
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_DeJesus
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Akita_Yoshida
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Posarac_Tekic
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Seno
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Suh
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Shah
.. autofunction:: biosteam.units.design_tools.aeration.kla_bubcol_Dewes
.. autofunction:: biosteam.units.design_tools.aeration.P_at_kLa_Riet
References
----------
.. [1] Van’t Riet, K. Review of Measuring Methods and Results in Nonviscous
Gas-Liquid Mass Transfer in Stirred Vessels. Ind. Eng. Chem. Proc. Des.
Dev. 1979, 18 (3), 357–364. https://doi.org/10.1021/i260071a001.
.. [2] Deshpande, S. S., Kar, K., Pressler, J., Tebeka, I., Martins, B., Rosenfeld, D., & Biggs, J. (2019).
Mass transfer estimation for bubble column scale up. Chemical Engineering Science, 205, 350–357.
https://doi.org/10.1016/j.ces.2019.05.011
.. [3] De Jesus, S. S., Moreira Neto, J., & Maciel Filho, R. (2017).
Hydrodynamics and mass transfer in bubble column, conventional airlift,
stirred airlift and stirred tank bioreactors, using viscous fluid: A comparative study.
Biochemical Engineering Journal, 118, 70–81. https://doi.org/10.1016/j.bej.2016.11.019
.. [4] Akita, K., & Yoshida, F. (1973).
Gas Holdup and Volumetric Mass Transfer Coefficient in Bubble Columns.
Effects of Liquid Properties. Industrial & Engineering Chemistry Process Design and Development, 12(1), 76–80.
https://doi.org/10.1021/i260045a015
.. [5] Pošarac, D., & Tekić, M. N. (1987).
Gas holdup and volumetric mass transfer coefficient in bubble columns with dilute alcohol solutions.
AIChE Journal, 33(3), 497–499. https://doi.org/10.1002/aic.690330316
.. [6] Seno, T., Uchida, S., & Tsuyutani, S. (1990).
Mass transfer in countercurrent and cocurrent bubble columns. Chemical Engineering & Technology, 13(1), 113–118.
https://doi.org/10.1002/ceat.270130115
.. [7] Suh, I. ‐S., Schumpe, A., Deckwer, W. ‐D., & Kulicke, W. ‐M. (1991).
Gas‐liquid mass transfer in the bubble column with viscoelastic liquid.
The Canadian Journal of Chemical Engineering, 69(2), 506–512. https://doi.org/10.1002/cjce.5450690215
.. [8] Shah, M., Kiss, A. A., Zondervan, E., Van Der Schaaf, J., & De Haan, A. B. (2012).
Gas Holdup, Axial Dispersion, and Mass Transfer Studies in Bubble Columns.
Industrial & Engineering Chemistry Research, 51(43), 14268–14278. https://doi.org/10.1021/ie301227t
.. [9] Labík, L., Moucha, T., Petříček, R., Rejl, J. F., Valenz, L., & Haidl, J. (2017).
Volumetric mass transfer coefficient in viscous liquid in mechanically agitated fermenters.
Measurement and correlation. Chemical Engineering Science, 170, 451–463. https://doi.org/10.1016/j.ces.2017.04.006
.. [10] Galaction, A.-I., Cascaval, D., Oniscu, C., & Turnea, M. (2004).
Prediction of oxygen mass transfer coefficients in stirred bioreactors for bacteria, yeasts and fungus broths.
Biochemical Engineering Journal, 20(1), 85–94. https://doi.org/10.1016/j.bej.2004.02.005
.. [11] Benz, G. T. Bioreactor Design for Chemical Engineers. AICHE CEP 2011, 21–26.
.. [12] Dewes, I., & Schumpe, A. (1997). Gas density effect on mass transfer in the slurry bubble column.
Chemical Engineering Science, 52(21–22), 4105–4109. https://doi.org/10.1016/S0009-2509(97)00252-2
"""
__all__ = (
'C_L',
'C_O2_L',
'kLa_stirred_Riet',
'P_at_kLa_Riet',
'log_mean_driving_force',
)
# from inspect import signature
from math import exp, log, sqrt
#: Henry's law coefficients. Data from NIST Standard Reference Database 69: NIST Chemistry WebBook:
#: https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782447&Mask=10#Notes
H_coefficients = { # k_H, A
'O2': (0.0013, 1500),
'CO2': (0.035, 2400),
'H2': (0.00078, 500),
}
[docs]
def Henrys_law_constant(T, k_H, A):
"""
Return Henry's law constant [mol / kg / bar] for a chemical given the temperature
[K] and the coefficients.
"""
dTinv = (1. / T - 1. / 298.15)
return k_H * exp(A * dTinv)
[docs]
def C_L(T, Py, chemical):
"""Chemical concentration [mol / kg] in the liquid given the temperature [K] and its
partial pressure in the gas [bar]."""
return Py * Henrys_law_constant(T, *H_coefficients[chemical])
[docs]
def C_O2_L(T, P_O2): # Commonly used, so here for convinience
"""O2 concentration [mol / kg] in the liquid given the temperature [K] and oxygen
partial pressure of O2 in the gas [bar]."""
return P_O2 * Henrys_law_constant(T, *H_coefficients['O2'])
kLa_methods = {}
kLa_method_names = {
'Bubble column': [],
'Stirred tank': []
}
def register(f):
# parameters = list(signature(f).parameters)
name = f.__name__
_, kind, *authors = name.split('_')
authors = ' & '.join(authors)
if kind == 'bubcol': kind = 'Bubble column'
elif kind == 'stirred': kind = 'Stirred tank'
else: raise ValueError(f"only 'bubcol' and 'stirred' are valid types; not {kind!r}")
kLa_methods[kind, authors] = f
kLa_method_names[kind].append(authors)
return f
_kLa_coefficients_Riet = {
# Garcia-Ochoa, F.; Gomez, E. Bioreactor Scale-up and Oxygen Transfer Rate
# in Microbial Processes: An Overview. Biotechnology Advances 2009, 27 (2),
# 153–176. https://doi.org/10.1016/j.biotechadv.2008.10.006.
# Name: (a, b, c) # kLa = a * (P/V) ** b * U**c
'Figueiredo & Calderbank': (0.026, 0.6, 0.8),
"Van't Riet": (0.026, 0.4, 0.5),
}
[docs]
@register
def kLa_stirred_Riet(P, V, U, coefficients=None):
"""
Return the lumped mass transfer coefficient and the
mean bubble specific interfacial area (k_L*a; 1/s) given the
gassed power input (P; W), the total volume (V; m3), and the
gas superficial velocity in the reactor (m/s).
Other Parameters
----------------
coefficients : Iterable[float]|str, optional
Name of author or an iterable in the form of a, b, c. The
Notes
-----
The correlation is kLa = a * (P/V) ** b * U ** c.
"""
if coefficients is None:
a, b, c = _kLa_coefficients_Riet['Figueiredo & Calderbank']
elif isinstance(coefficients, str):
a, b, c = _kLa_coefficients_Riet[coefficients]
else:
a, b, c = coefficients
return a * (P / V) ** b * U ** c
# TODO:
# def get_efficiency_factor():
# """
# Return the efficiency factor for mass transfer in
# bubble column reactors.
# Take present that the units of the efficiency factor are [m**-1].
# This values are
# - 0.016-0.028 m**-1 for coarse bubble diffusers
# - 0.07-0.1 m^-1 for fine bubble diffusers
# """
# K = None
# return K
[docs]
@register
def kla_bubcol_Deshpande(K, M_l, Rhat, T, rho_l, U_g, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on
the Deshpande et al. (2019) correlation [2]_.
Parameters
----------
K: float
Efficiency change per unit change in liquid height above sparger, [m^-1]
M_l: float
Molar mass, e.g. water = 0.018 kg/mol, [kg/mol]
Rhat: float
Ideal gas constant, [J/mol-K]
T: float
Temperature, [K]
rho_l: float
Mass density of the liquid, e.g. 1000 kg/m^3 for water [kg/m^3]
U_g: float
Superficial gas velocity, [m/s]
"""
H_at_T = Henrys_law_constant(T)
alpha = K * (H_at_T * M_l)/(Rhat * T * rho_l)
if coefficients is None: coefficients = (1,)
beta, = coefficients
return alpha * U_g ** beta
[docs]
@register
def kla_bubcol_DeJesus(Q, mu, k, n, system_like = None, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
De Jesus et al. (2017) correlation [3]_.
Parameters
----------
Q: float
Specific air flow rate, [vmm]
mu: float
Dynamic viscosity, [Pa.s]
k: float
Consistency index, [Pa.s^n]
n: float
Flow behavior index
system_like: str
Name of the system, e.g. "Glycerol" or "Xanthan"
"""
if system_like == "Glycerol":
if coefficients is None: coefficients = (1.27e-2, 0.51, -0.12)
a, c, d = coefficients
return a * Q ** c * mu ** d
elif system_like == "Xanthan":
if coefficients is None: coefficients = (5.80e-3, 0.66, -0.50, -0.80)
e, h, i, j = coefficients
return e * Q ** h * k ** i * n ** j
else:
if coefficients is None and system_like is None:
raise ValueError(
"To use the De Jesus et al. (2017) correlation without\n a "
"system_like, please provide the necessary coefficients"
)
else:
if system_like == 'Newtonian':
a, c, d = coefficients
return a * Q ** c * mu ** d
elif system_like == 'Non-Newtonian':
e, h, i, j = coefficients
return e * Q ** h * k ** i * n ** j
else:
raise ValueError(
"system_like must be either 'Newtonian' or 'Non-Newtonian'"
)
[docs]
@register
def kla_bubcol_Akita_Yoshida(D, mu_l, rho_l, D_l, g, sigma_l, epsilon_g, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
Akita & Yoshida (1973) correlation [4]_.
Parameters
----------
D: float
Diameter of the column, [m]
mu_l: float
Viscosity of the liquid, [Cp]
rho_l: float
Density of the liquid, [kg/m^3]
D_l: float
Diffusivity ofliquid, [m^2/s]
g: float
Gravitational acceleration, [m/s^2]
sigma_l: float
The surface tension ofliquid [N/m]
epsilon_g: float
Overall gashold-up
Notes
-----
This correlation is valid under the following range of values:
D = 0.15 m -> Diameter of the column
H = 4 m -> Liquid height in the column
V_g = 0 - 0.33 m/s -> Superficial gasvelocity [m/s]
And the conditions are for:
-> O2-Water, Aqueous Solutions of Glycerol, Glycol, Methanol, Sodium Sulphite
"""
kla = (D_l/(D**2)) * 0.6 *(mu_l/(rho_l * D_l))**(0.5) * ((g*rho_l*D**2)/sigma_l)**(0.62) * ((g * D**3 * rho_l**2)/mu_l)**(0.31) * epsilon_g**(1.1)
return kla
[docs]
@register
def kla_bubcol_Posarac_Tekic(D, mu_l, rho_l, D_l, g, sigma_l, epsilon_g, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
Pošarac & Tekić (1987) [5]_.
Parameters
----------
D: float
Diameter of the column, [m]
mu_l: float
Viscosity of the liquid, [Cp]
rho_l: float
Density of the liquid, [kg/m^3]
D_l: float
Diffusivity ofliquid, [m^2/s]
g: float
Gravitational acceleration, [m/s^2]
sigma_l: float
The surface tension ofliquid [N/m]
epsilon_g: float
Overall gashold-up
Notes
-----
This correlation is valid under the following range of values:
D = 0.1 m -> Diameter of the column
H = 2.5 m -> Liquid height in the column
V_g = 0.008 - 0.08 m/s -> Superficial gas velocity [m/s]
And the conditions are:
-> Air-Water, Aqueous Solution of Methanol, Ethanol, i-Propanol, nButanol
"""
kla = (D_l/(D**2)) * 0.961 *(mu_l/(rho_l * D_l))**(0.5) * ((g*rho_l*D**2)/sigma_l)**(0.62) * ((g * D**3 * rho_l**2)/mu_l**2)**(0.31) * epsilon_g**(1.1)
return kla
[docs]
@register
def kla_bubcol_Seno(D, mu_l, rho_l, D_l, g, sigma_l, epsilon_g, V_g, V_l, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
Seno et al. (1990) correlation [6]_.
Parameters
----------
D: float
Diameter of the column, [m]
mu_l: float
Viscosity of the liquid, [Cp]
rho_l: float
Density of the liquid, [kg/m^3]
D_l: float
Diffusivity ofliquid, [m^2/s]
g: float
Gravitational acceleration, [m/s^2]
sigma_l: float
The surface tension ofliquid [N/m]
epsilon_g: float
Overall gashold-up
V_g: float
Superficial gas velocity, [m/s]
V_l: float
Superficial liquid velocity, [m/s]
Notes
-----
This correlation is valid under the following range of values:
D = 0.0464 m -> Diameter of the column
H = 1.36 m -> Liquid height in the column
V_g = 0.005 - 0.04 m/s -> Superficial gas velocity [m/s]
V_l = 0.005 - 0.1 m/s -> Superficial liquid velocity [m/s]
rho_l = 995 - 1043 kg/m^3 -> Density of the liquid [kg/m^3]
mu_l = 0.653- 1.31 Cp -> Viscosity of the liquid [Cp]
sigma_l = 0.0348-0.0728 N/m -> The surface tension ofliquid [N/m]
D_l = 1.68-3.24 × 10^-9 m^2/s
Conditions:
O2- Water, Aqueous Solution of Butanol, Polyoxyethylene sorbitan monolaurate with silicone oil
"""
kla = (D_l/(D**2)) * 0.6 * (V_g/(V_g+V_l))**-0.39 *(mu_l/(rho_l * D_l))**(0.5) * ((g * rho_l**2 * D**2)/sigma_l)**(0.62) * ((g * D**3 * rho_l**2)/mu_l**2)**(0.31) * epsilon_g**(1.1)
return kla
[docs]
@register
def kla_bubcol_Suh(D, mu_l, rho_l, D_l, g, sigma_l, epsilon_g, V_g, V_l, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
Suh et al. (1991) correlation [7]_.
Parameters
----------
D: float
Diameter of the column, [m]
mu_l: float
Viscosity of the liquid, [Cp]
rho_l: float
Density of the liquid, [kg/m^3]
D_l: float
Diffusivity ofliquid, [m^2/s]
g: float
Gravitational acceleration, [m/s^2]
sigma_l: float
The surface tension ofliquid [N/m]
epsilon_g: float
Overall gashold-up
V_g: float
Superficial gas velocity, [m/s]
V_l: float
Superficial liquid velocity, [m/s]
Notes
-----
This correlation is valid under the following range of values:
D: 0.15 m -> Diameter of the column [m]
H: 2.9 m -> Liquid height in the column [m]
V_g: 0.005 - 0.04 m/s -> Superficial gas velocity [m/s]
rho_l: 1001 - 1264 kg/m^3 -> Density of the liquid [kg/m^3]
sigma_l: 0.0656-0.0746 N/m -> The surface tension of the liquid [N/m]
D_l: 0.318-2.5 * 10^-9 m^2/s -> Diffusivity of liquid [m^2/s]
And the conditions are:
Air-Aqueous Sucrose Solution
"""
kla = (D_l/(D**2)) * 0.018 * (mu_l/(rho_l * D_l))**(0.5) * ((g*rho_l*D**2)/sigma_l)**(0.75) * (g*D**3*rho_l**2/(mu_l**2))**(0.39)*(V_g/(sqrt(g*D)))**0.51
return kla
[docs]
@register
def kla_bubcol_Dewes(V_g, mu_l, rho_g):
"""
Returns the KLa coefficient for a bubble column reactor based on the Dewes & Schumpe (1997) correlation [12]_.
Parameters
----------
V_g: float
Superficial gas velocity, [m/s]
mu_l: float
Viscosity of the liquid, [mPa.s]
rho_g: float
Density of the gas, [kg/m^3]
Notes
-----
This correlation is valid under the following range of values:
D_c: 0.115 m -> Diameter of the column [m]
H_l: 1.37 m -> Liquid height in the column [m]
V_g: 0.01 - 0.08 m/s -> Superficial gas velocity [m/s]
mu_l: 1.35 - 583 mPa.s -> Viscosity of the liquid [mPa.s]
rho_g: 0.4 - 18.8 kg/m^3 -> Density of the gas [kg/m^3]
"""
kla = V_g**0.90 * mu_l**(-0.55) * rho_g**0.46
return kla
[docs]
@register
def kla_bubcol_Shah(D, V_l, g, V_g, rho_l, mu_l, coefficients=None):
"""
Returns the KLa coefficient for a bubble column reactor based on the
Shah et al. (2012) correlation [8]_.
Parameters
----------
D: float
Diameter of the column, [m]
V_l:
Superficial liquid velocity, [m/s]
g:
Gravitational acceleration, [m/s^2]
V_g:
Superficial gas velocity, [m/s]
rho_l:
Density of the liquid, [kg/m^3]
mu_l:
Viscosity of the liquid, [Cp]
Notes
-----
This correlation is valid under the following range of values:
D: 0.29 m -> Diameter of the column [m]
H: 0.2 m -> Liquid height in the column [m]
V_g: 0.021 - 0.105 m/s -> Superficial gas velocity [m/s]
V_l: 0.0005 - 0.002 m/s -> Superficial liquid velocity [m/s]
mu_l: 1 - 50 Cp -> Viscosity of the liquid [Cp]
"""
kla = (V_l/D) * 0.0029 * (V_g**2 / (g * D))**0.301 * (V_l**2/(g * D))**-0.511 * (g*rho_l**3 * D**3 / (mu_l**2))**0.12
return kla
[docs]
@register
def kla_stirred_Labik(N, D, v_s, P0, coefficients=None):
"""
Returns the KLa coefficient for a stirred tank reactor based on the
Labik et al. (2017) correlation [9]_.
Parameters
----------
N: float
impeller frequency [s^-1]
D: float
impeller diameter [m]
v_s: float
gas superficial velocity [m/s]
P0: float
impeller power number (P_u/rhh N^3 D^5) [-]
"""
kla = 0.295 * (N * D)**2.083 * v_s**0.461 * P0 ** 0.737
return kla
def _kLa_submerged(alpha, beta, gamma, delta, C_x, P_a, V, v_s):
"""
Auxiliary function to calculate kla for submerged aeration.
"""
return alpha * C_x ** beta * (P_a / V) ** gamma * v_s ** delta
def _kLa_surface(alpha, beta, P, V):
"""
Auxiliary function to calculate kla for surface aeration.
"""
return 1/exp(alpha) * (P/V) ** beta
[docs]
@register
def kLa_stirred_Galaction(
aeration_type: str, V, C_x, v_s, P_a=None, P=None,
organism_type=None, coefficients=None,
):
"""
Return the kLa for a stirred tank reactor based on the
Galaction et al. (2004) correlation [10]_.
Parameters
----------
aeration_type: str
Type of aireation, in this case either 'Surface' or 'Submerged'
P_a: float
power consumption for mixing of aerated broths, [W]
P: float
power consumption for mixing of non-aerated broths, [W]
V: float
volume of the medium, [m**3]
C_x: float
Biomass concentration, [g/l dry weight]
v_s: float
superficial air velocity, [m/s]
"""
if aeration_type == 'Submerged':
if organism_type == 'P.shermanii':
if coefficients is None: coefficients = (6.586, -0.282, 0.0286, 0.429)
alpha, beta, gamma, delta = coefficients
return _kLa_submerged(alpha, beta, gamma, delta, C_x, P_a, V, v_s)
elif organism_type == 'S.cerevisiae':
if coefficients is None: coefficients = (52.44, -0.702, -0.0762, 0.514)
alpha, beta, gamma, delta = coefficients
return _kLa_submerged(alpha, beta, gamma, delta, C_x, P_a, V, v_s)
elif organism_type == 'P.chrysogenum_pellet':
if coefficients is None: coefficients = (0.193, -0.269, 0.0288, 0.257)
alpha, beta, gamma, delta = coefficients
return _kLa_submerged(alpha, beta, gamma, delta, C_x, P_a, V, v_s)
elif organism_type == 'P.chrysogenum_mycelia':
if coefficients is None: coefficients = (33.59, -1.012, -0.0463, 0.94)
alpha, beta, gamma, delta = coefficients
return _kLa_submerged(alpha, beta, gamma, delta, C_x, P_a, V, v_s)
else:
raise ValueError("Please provide a valid organism_type (in this case 'P.shermanii', 'S.cerevisiae', 'P.chrysogenum_pellet' or 'P.chrysogenum_mycelia')")
elif aeration_type == 'Surface':
if organism_type == 'P.shermanii':
alpha = 10.35 + 0.63 *log(C_x)
beta = 0.694 - 0.069 * log(C_x)
return _kLa_surface(alpha, beta, P, V)
elif organism_type == 'S.cerevisiae':
alpha = 11.64 + 0.307 * log(C_x)
beta = 1.14 - 0.187 * log(C_x)
return _kLa_surface(alpha, beta, P, V)
elif organism_type == 'P.chrysogenum_pellet':
alpha = 12.77 + 0.227 * log(C_x)
beta = 0.62 - 0.109 * log(C_x)
return _kLa_surface(alpha, beta, P, V)
elif organism_type == 'P.chrysogenum_mycelia':
alpha = 11.46 + 0.729 * log(C_x)
beta = 0.093 + 0.057 * log(C_x)
return _kLa_surface(alpha, beta, P, V)
else:
raise ValueError("Please provide a valid organism_type (in this case 'P.shermanii', 'S.cerevisiae', 'P.chrysogenum_pellet' or 'P.chrysogenum_mycelia')")
else:
raise ValueError("Please provide a valid aeration_type (in this case 'Surface' or 'Submerged')")
[docs]
def P_at_kLa_Riet(kLa, V, U, coefficients=None):
"""
Return the gassed power input (P; W) given the lumped mass transfer
coefficient and the mean bubble specific interfacial area (k_L*a; 1/s),
the total volume (V; m3), and the gas superficial velocity in the reactor (m/s).
Other Parameters
----------------
coefficients : Iterable[float]|str, optional
Name of author or an iterable in the form of a, b, c.
Notes
------
The correlation is kLa = a * (P/V) ** b * U ** c from [1]_.
"""
if coefficients is None:
a, b, c = _kLa_coefficients_Riet['Figueiredo & Calderbank']
elif isinstance(coefficients, str):
a, b, c = _kLa_coefficients_Riet[coefficients]
else:
a, b, c = coefficients
return (kLa / (a * U ** c)) ** (1 / b) * V
[docs]
def log_mean_driving_force(C_sat_out, C_sat_in, C_out, C_in=None):
"""
Return the driving force for mass transfer. In small vessels (<1 m tall)
where both liquid concentration and saturation are almost constant, the simple
form is adequate [11]_. In tall vessels, the log-mean driving force should be
used for more accuracy, since both the local concentration and the saturation
concentration are different in the top and bottom of a bioreactor [11]_.
Parameters
----------
C_sat_out : float
Saturated concentration entering the bioreactor.
C_sat_out : float
Saturated concentration exiting the bioreactor.
C_out : float, optional
Outlet concentration.
C_in : float
Inlet concentration. Defaults to the outlet concentration, which
assumes perfect mixing and oxygen uptake rate is the same everywhere.
"""
if C_in is None: C_in = C_out # Assume perfect mixing and oxygen uptake rate is the same everywhere.
dC_out = C_sat_out - C_out
dC_in = C_sat_in - C_in
if dC_out < 1e-9: # This is not theoretically possible, but may be an assumption
dC_out = 1e-9 # Assume it near zero
return (dC_out - dC_in) / log(dC_out / dC_in)
if __name__ == "__main__":
print('hola')
repeated_names = [
('U_g', ('U_G', 'V_G')),
]
fermentation_variables_bub_col = {
'Dashpande': {
'epsilon_g': (0.5, 1.2),
'K': (0.016, 0.028), # for coarse bubble diffusers 'K': (0.07, 0.1), # for fine bubble diffusers
'M_l': 0.018, # kg/mol
'Rhat': 8.314, # J/mol-K
'T': 298.15, # K
'rho_l': 1000, # kg/m^3
'U_g': (0.01,0.1), # m/s
},
'DeJesus': {
'Q':(0, 1.6), # vvm
'mu': (0.001, 0.1), # Pa.s
'k': (0.1, 100), # Pa.s^n
'n': (0, 2) # Flow behavior index <1 for pseudoplastic, >1 for dilatant, 1 for Newtonian
},
'Akita_Yoshida': {
'D': 0.15, # m
'H': 4, # m
'V_g': (0, 0.33), # m/s
'mu_l': (0.5, 100), # Cp 1 water, 100 xanthan
'rho_l': (995, 1043), # kg/m^3
'D_l': (1.68 * 10**-9, 3.24 * 10**-9) , # m^2/s
'g': 9.81, # m/s^2
'sigma_l': (0.0348,0.0728), # N/m
'epsilon_g': (0.01, 1) # m/s
},
'Posarac_Tekic': {
'D': 0.1, # m
'H': 2.5, # m
'V_g': (0.008, 0.08), # m/s
'mu_l': (0.5, 100), # Cp 1 water, 100 xanthan
'rho_l': (995, 1043), # kg/m^3
'D_l': (1.68 * 10**-9, 3.24 * 10**-9), # m^2/s
'sigma_l': (0.0348,0.0728), # N/m
'epsilon_g': (0.01, 1) # m/s
},
'Seno': {
'D': 0.0464, # m
'H': 1.36, # m
'V_g': (0.005, 0.04), # m/s
'V_l': (0.005, 0.1), # m/s
'rho_l': (995, 1043), # kg/m^3
'mu_l': (0.653, 1.31), # Cp 1 water, 100 xanthan
'D_l': (1.68 * 10**-9, 3.24 * 10**-9), # m^2/s
'g': 9.81, # m/s^2
'sigma_l': (0.0348,0.0728), # N/m
'epsilon_g': (0.01, 1) # m/s
},
'Suh': {
'D': 0.15, # m
'H': 2.9, # m
'V_g': (0.005, 0.04), # m/s
'rho_l': (1001, 1264), # kg/m^3
'mu_l': (0.653, 1.31), # Cp 1 water, 100 xanthan
'D_l': (0.318 * 10**-9, 2.5 * 10**-9) , # m^2/s
'g': 9.81, # m/s^2
'sigma_l': (0.0656,0.0746), # N/m
'epsilon_g': (0.01, 1) # m/s
},
'Shah': {
'D': 0.29, # m
'H': 0.2, # m
'V_g': (0.021, 0.105), # m/s
'V_l': (0.0005, 0.002), # m/s
'rho_l': (1, 50), # kg/m^3
'mu_l': (1, 50), # Cp 1 water, 100 xanthan
},
}
fermentation_variables_stirred = {
'Labik':{
'N': (4.17, 14.17), # s^-1
'D':(0.1, 0.2), # m
'v_s': (2.12 * 1e-3, 8.48 * 1e-3) , # m/s
'P0': (100, 10000),
},
'Galaction':{ # look into what is better for the P_a/V and P/V
'P_a/V' : (30,120), # W/m^3
'v_s': (0.8 * 1e-3, 5 * 1e-3), # m/s
'C_x': (5, 150), # g/l dry weight
'P/V': (10, 1900), # W/m^3
}
}
