Estimation of the volumetric oxygen tranfer coefficient (KLa) from the gas balance and using a neural network technique

Estimation of the volumetric oxygen tranfer coefficient (K_La) from the gas balance and using a neural network technique

A. J. G. CRUZ¹, A. S. SILVA², M. L. G. C. ARAUJO³, R. C. GIORDANO¹ and C. O. HOKKA1

1Departamento de Engenharia Química, Universidade Federal de São Carlos,Via W. Luiz, km 235 C.P. Box 676, 13565-905, São Carlos - SP, Brazil, Phone: [phone],FAX: [phone]Programa de Pós-Graduação em Engenharia Química, Universidade Federal de São Carlos, Via W. Luiz, km 235, C.P. Box 676, 13565-905, São Carlos - SP, Brazil ³Departamento de Tecnologia, Instituto de Química, UNESP, Campus de Araraquara, C.P. Box 355, 14801-970, Araraquara - SP, Brazil, Phone: [phone] E-mail: [e-mail]

(Received: January 19, 1999; Accepted: April 13, 1999)

Abstract -This paper reports on the use of the gas balance and dynamic methods to obtain an estimate of the volumetric oxygen transfer coefficient (k_La) in a conventional reactor during the growth phase of the microorganism Cephalosporium acremonium. A new way of calculating k_La by the dynamic method employing an electrode with a slow response, is proposed. The calculated values of k_La were used in the training of a feedforward neural network, for which the inputs were the parameter measurements of the related variables. The neural network technique proved effective, predicting values of k_La accurately from input data not used during the training phase. In contrast, the gas balance method was shown to be less useful. This could be attributed to the poor data obtained with the apparatus used to measure the oxygen in the exhaust gas, explained by the low rate of oxygen consumption by the microorganism.

Keywords: neural network technique, dynamic methods, volumetric oxygen transfer coefficient.

INTRODUCTION

During the aerobic fermentation that is used in the production of cephalosporin C by the microorganism C. acremonium, it is necessary to maintain the oxygen concentration at an appropriate level to allow optimal conditions in the growth phase and during product formation. In the agitated and aerated stirred-tank fermenters widely employed for this process, the rate of oxygen transfer is often a limiting factor and in turn is dependent on the volumetric oxygen transfer coefficient (k_La) and the driving force, C_L* - C_L (where C_L is the concentration of dissolved oxygen and C_L* that of saturated oxygen in the liquid under given conditions). The volumetric transfer coefficient (k_La) itself depends on the operating conditions (rates of stirring and air flow), the rheological properties of the fluid (apparent viscosity, density and surface tension) and the system geometry.

Owing to the important role played by k_La, much work has been published on methods for its estimation. Several empirical formulae are available in the literature. Cooper et al. (1944) use a relation involving power per unit volume (P_g/V) and surface gas velocity (v_s) to calculate k_La in broths exhibiting Newtonian dynamics. So as to widen the scope of this formula to include fermenting broths with non-Newtonian behavior, several authors have developed relations that take account of the physical properties of these broths (Ryu & Humphrey, 1972; Yagi & Yoshida, 1975; Zlokarnik, 1978). The use of these more comprehensive equations implies the introduction of further formulae, for example to predict variations in the apparent viscosity and surface tension of the broth, which may vary considerably throughout the growth cycle.

Another approach to the estimation of k_La makes use of an overall mass balance for oxygen, applied to a control volume (Zabriskie in Moo-Young; Badino Jr, 1997). For this technique, a wide variety of experimental data has to be obtained: concentration of dissolved oxygen in the broth, volume of broth, pressure in the fermenter, air flow rate, and concentration of oxygen and other gases (CO₂, N₂, NH₃) in the input and output streams. Variations in the concentrations of carbohydrates and salts during the fermentation run must also be taken into consideration. This approach, used together with a data-acquisition system and a data-processing routine, could enable on-line estimation of k_La.

In the work described here, an alternative way of finding the volumetric oxygen transfer coefficient, consisting of applying the neural network technique to the determination of this parameter, has been developed. The values of key variables used in estimating the coefficient are spread across the inputs of the network, whose output then predicts values of k_La.

The values of k_La used in the work were calculated from data obtained by the method known as "dynamic" or "gas out-gas in," first proposed by Taguchi and Humphrey (1966), but assuming that the oxygen electrode has second-order dynamics and a dead time (initial lag). These values were also compared with those calculated using the classic analysis (without delay) and that proposed by Tribe et al. (1995). The latter suggests first-order dynamics for the electrode and introduces its time constant into the balance equations for oxygen dissolved in the liquid phase.

MATERIALS AND METHODS

Microorganism

Cephalosporium acremonium ATCC 48272 (C-10) was used; this was kindly donated by Fundação Tropical André Tosello (Campinas - SP, Brazil).

Culture Media

The synthetic media used for germination and preparation of the inoculum contained glucose (30 g/L) as the principal source of carbon and of energy (Araujo et al., 1996), while for the fermentation runs, a synthetic medium with glucose (27 g/L) and sucrose (36 g/L) was used (Araujo et al., 1996).

Experimental Apparatus

A New Brunswick Bioflo III fermenter with a working capacity of 5.0 L was employed. The set-up used to obtain and record the experimental data used to calculate k_La is sketched in Figure ¹.

Figure 1: Sketch of aparatus used to perform measurements of k_La. (1 mass flowmeter; 2 pressure gauge; 3 motor; 4 Bioflo III signal processor; 5 condenser; 6 impeller; 7 air sparger; 8 dissolved O₂ electrode; 9 signal converter; 10 chart recorder; 11 exhaust gas drying column; 12 CO₂ analyser; 13 O₂ analyser).

Dissolved Oxygen Electrode

An amperometric electrode with a slow response (Metler Toledo model 12/220 T) was used with a teflon-silicone-teflon membrane.

Experimental Trials

Two experiments were performed, during which several values of k_La were calculated under different operating conditions. Samples were taken at regular intervals and sugar concentrations and dry cell masses measured (sugar was analyzed by GOD-PAP, sucrose had been hydrolyzed beforehand).

RESULTS AND DISCUSSION

Calculation of the Volumetric Oxygen Transfer Coefficient (k_La)

In the standard "gas out-gas in" method (Taguchi & Humphrey, 1966), during the reaeration period the concentration of dissolved oxygen at time t, C(t), responds to a step change in air supply as follows:

where

C₀ is the initial dissolved oxygen value, when the air supply is reconnected and C^¥ is the dissolved oxygen value at steady state when the air supply is reconnected.

Thus, after measuring C(t) over a period of time, the oxygen transfer coefficient, k_La, was obtained from Equation 1. Non-linear regression (Marquardt, 1963) was used in this and subsequent calculations.

For convenience, and to simplify the derivations, the expressions in the equations were represented by their Laplace transforms. Hence, Equation 1 became

So as to reduce the errors caused by the finite response time of the oxygen electrode, further values of k_La were calculated, adopting two models for its behavior - first-order, and second-order with a "lag time." In each case, values were determined experimentally for the parameters: t (time constant), z (decay factor) and t_d (dead time).

Assuming first-order dynamics, the electrode response (in Laplace space) is

where

C_e,o is the value of C_e at the time the air is reconnected and C_e is the value of the electrode signal.

Hence, by substituting C(s) from Equation [2] into Equation [3] and inverting the Laplace transform, the concentration of oxygen can be derived as a function of time from the electrode signal, C_e (Tribe et al., 1995), thus calculating k_La.

When the second model is adopted for the probe, with second-order dynamics and a "lag time," the transformed response is

as was verified by the experiment.

By substituting C(s) from Equation [3] into Equation [4] and obtaining the inverse Laplace transform, the electrode signal could be derived as a function of time.

The Gas Balance Method

Values for k_La were also calculated from results obtained with this technique, which consists of achieving a molar balance between the input and output gas streams of the fermenter. The procedures and equations involved are described in detail by Badino Jr (1997).

The Neural Network Method

A feedforward neural network, whose single hidden layer contained six neurons with a sigmoidal activation function, was used to estimate k_La values. The following variable data were employed as the network inputs: impeller speed, dissolved oxygen concentration in the broth, fraction of CO₂ in the exhaust gas, flow rate of the air supply and volume of the medium. The network output provided the value of k_La. The data base consisted of experimental results from the two trials performed. Four of these results were chosen at random for validation of the trained network. The rest were used in the training phase, for which the standard algorithm of back propagation was employed.

Table ¹ illustrates values of the volumetric oxygen transfer coefficient (k_La) obtained from Equations 1, 3 and 4 and the gas balance under different operating conditions. Consistent values were obtained with the new approach (Equation 4).

However it can be seen here that the gas balance method failed to produce compatible estimates of kLa in these trials. This may be explained by taking into account the slow respiration of this microorganism; its maximum specific rate of respiration is ca. 1.055 mmol O₂ (g cell)^-1h^-1 (Araujo et al., 1996). The low rate may have introduced instrumental errors into the readings of the fraction of oxygen (Y_O2) present in the exhaust gases. By analysis of the gas balance equations, it was shown that a 1 % error in the Y_O2 readings produces alterations of between 20 % and 70 % in the estimates of k_La.

Neural network estimates for k_La are presented in Table ². These results show that the technique of neural networks satisfactorily predicted k_La values for unseen conditions.

CONCLUSIONS

The methods proposed enabled readings from a slow-response electrode to be used in the calculation of the volumetric oxygen transfer coefficient (k_La) and achieved consistent results for this process. Values of k_La derived from gas balance measurements were unsatisfactory, whereas the neural network technique was shown to be capable of predicting this parameter well. The latter technique could be utilized to estimate kLa, for example in conjunction with a phenomenological model.

NOMENCLATURE

C₀ dissolved oxygen concentration at the time when the air supply is reconnected

C^¥ dissolved oxygen concentration at steady state when the air supply is reconnected

C_e electrode signal

C_e,0 electrode signal at the time when the air supply is reconnected

k_La volumetric oxygen transfer coefficient [T^-1]

t_d dead time [T^-1]

t time constant [T^-1]

z decay factor

ACKNOWLEDGMENTS

A.J.G.C. and M.L.G.C.A. are grateful to FAPESP and A.S.S. to CNPq for financial assistance received throughout the conduction of this research.

REFERENCES

Araujo, M.L.G.C. Oliveira, R.P. Giordano, R.C. and Hokka, C.O., Comparative Studies on Cephalosporin C Production Process with Free and Immobilized Cells of Cephalosporium acremonium ATCC 48272, Chem. Eng. Science, 14th ISCRE, 51(11), 2835-2840, 1996.

Badino Jr., A.C., Reologia, Consumo de Potência e Transferência de Oxigênio em Cultivos Descontínuos de Aspergillus Awamori NRRL 3112, Ph.D. diss., Universidade de São Paulo, Brazil, 1997, 182p.

Cooper, C.M. Fernstrom, G.A. And Miller, S.A., Performance of Agitated Gas-Liquid Contactors, Ind. Eng. Chem., 36(6), 504-509, 1944.

Koizumi, J. And Aiba, S., Reassessment of the Dynamic k_La Method, Biotechnology and Bioengineering, 26, 1131-1133, 1984.

Marquardt, D.M., An Algorithm for Least-Square Estimation of Non-Linear Parameters, J. Soc. Indust. Appl. Math., 11(2): 431-441, 1963.

Ryu, D.Y. And Humphrey, A.E., A Reassessment of Oxygen Transfer Rates in Antibiotics Fermentations, J. Ferm. Technol., 50, 424-431, 1972.

Taguchi, H. And Humphrey, A.E., Dynamic Measurement of the Volumetric Oxygen Transfer Coefficient in Fermentation Systems, J. Ferment. Technol., 44, 881-889, 1966.

Tribe, L.A. Briens, C.L. And Margaritis, A., Determination of the Volumetric Mass Transfer Coefficient (kLa) Using the Dynamic "Gas Out-Gas In" Method: Analysis of Errors Caused by Dissolved Oxygen Probes, Biotechnology and Bioengineering, 46(4), 388-392, 1995.

Yagi, H. And Yoshida, F., Gas Absorption by Newtonian and Non-Newtonian Fluids in Sparged Agitated Vessels, Ind. Eng. Chem. Proc. Des. Dev., 14(4), 488-493, 1975.

Zabriskie, D.W., in: Moo-Young, M., Comprehensive Biotechnology: The Principles, Applications and Regulation of Biotecnology in Industry, Agriculture and Medicine, vol. 3, cap. 10, Ontário, Pergamon Press Canada Ltd, 1985.

Zlokarnik, M., Sorption Characteristics for Gas-Liquid Contacting in Mixing Vessels, Adv. Biochem. Eng., 8, 133-151, 1978.

Table 1: Comparison of the values of k_La measured in cultures of C. acremonium.

Table 2: Comparison of k_La values obtained by Neural Network (RN) and Equation 4.

Publication Dates

• Publication in this collection
  15 Sept 1999
• Date of issue
  June 1999

History

• Received
  19 Jan 1999
• Accepted
  13 Apr 1999