aeration

This module contains methods and correlations to find aeration requirements for bioreactors.

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 – 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.

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.

C_L(T, Py, chemical)

Chemical concentration [mol / kg] in the liquid given the temperature [K] and its partial pressure in the gas [bar].

C_O2_L(T, P_O2)

O2 concentration [mol / kg] in the liquid given the temperature [K] and oxygen partial pressure of O2 in the gas [bar].

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).

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.

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]

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”

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_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_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_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_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_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_stirred_Galaction(aeration_type, 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]

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).

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].

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] (1,2)

Benz, G. T. Bioreactor Design for Chemical Engineers. AICHE CEP 2011, 21–26.