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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.23 no.1 São Paulo Jan./Mar. 2006 



Theoretical and experimental study of the effects of scale-up on mixing time for a stirred-tank bioreactor



P. Bonvillani; M. P. Ferrari; E. M. Ducrós*; J. A. Orejas

Universidad Nacional de Río Cuarto, Facultad de Ingeniería, Dpto. de Tecnología Química, Grupo de Ingeniería de las Reacciones (G.I.R.). Ruta Nacional 36, Km. 601, 5800, Río Cuarto - Argentina. Phone: +(54) 358-4676, 581/586, Fax: +(54) 358-4676, 246. E-mail:




Mixing time is one of the criteria most widely used to characterize mixing intensity in bioprocesses. In bioreactors, mixing mainly depends on amount of energy consumed, reactor and stirrer shapes, airing speed and the rheology of the medium. In this work we experimentally determined the mixing times for a lab-scale bioreactor equipped with a stirrer propelled by two Rushton turbines. From these experiments we could obtain expressions to evaluate the effects of stirring speed, superficial gas velocity, specific power consumption and system geometry on mixing times under various flow regimes. The resulting correlations were employed to analyze the effect of scale-up on mixing times for the production of Staphylococcus aureus Smith.

Keywords: Stirred-tank bioreactor; Mixing time; Scale-up; Staphylococcus aureus.




Mixing efficiency is one of the most significant factors, affecting both performance and scale-up in a bioreactor. Stirring is frequently decisive for the yield of fermentative processes and it is associated with many fermentator scaling problems. The effect of scale-up on a system's mixing efficiency affects its transfer processes. Therefore, concentration and temperature gradients as well as oscillations of pH, which cause substantial damage to the microorganisms, may occur. One of the parameters most widely used to characterize stirring in a bioreactor is mixing time, which is defined as the time a liquid needs to be stirred to obtain a specific degree of homogeneity after adding a pulse signal of a tracer.

There is information in the literature on how to predict mixing times for two-phase systems (liquid-gas) (Einsele and Finn, 1980; Van't Riet and Tramper, 1991; Vasconcelos et al., 1995). Most of the proposed correlations have been determined for turbulent-flow regimes (NRe >10000).

In this work the mixing time of a lab-scale stirred-tank bioreactor was experimentally determined, and the ways it was affected by operating conditions, such as stirring speed, superficial gas velocity and specific power consumption, were quantified. The resulting expressions, together with the results of previous work (Ducrós, 2003; Ducrós et al., 2001), were used to analyze the effect of scale-up on mixing times for the production of Staphylococcus aureus Smith. This strain is used in the formulation of vaccines developed to fight bovine mastitis, an illness that affects dairy bovine cattle (Calzolari et al., 1997).



Installations and Equipment

The experiments were performed in a stirred-tank bioreactor (Applikon Instruments) with a 2.5 l capacity, equipped with a six-blade stirrer propelled by two Rushton turbines with a diameter of 45 mm, and three baffles at 120º angles. The pH was measured with an autoclave-sterilizable Phoenix sensor with a Cole Palmer controller 29041-02. Air was introduced into the system through a distributor located under the stirrer. The details and dimensions of the fermenter are shown in Figure 1. The data were registered by means of a Linear 1200 recorder.



Experimental Conditions

The medium employed for all the experiments was distilled water. The effect of stirring speed in the range between 0.1667 and 13.33 r.p.s., which corresponds to a variation in Reynolds number of 0.337 to 27x103, was studied. Stirring speed was controlled by means of an ADI 1012 controller (Applikon Instruments) that had an output signal in mA, which was proportional to the torque. This signal had been previously calibrated so as to evaluate the power of the stirring system.

The effect of airing speed was assessed using the following values for volumetric air flow per volume of medium: 0, 0.5, 1, 1.5, 2 v.v.m. Air flowrate was registered by means of a mass flow meter AALBORG GFM17.

Experimental Determination of Mixing Times

Mixing time was experimentally determined using the pH-response technique (Van't Riet and Tramper, 1991). The tracer was a solution of hydrochloric acid (1 ml 3.9 M). It was introduced in pulses 10 mm from the liquid surface, and the variations in pH were registered as a function of time. Mixing time was determined using the homogeneity criterion based on the time required for the pH to reach ± 5% of the final value. A typical experimental profile for the acid-pulse response obtained in this work is shown in Figure 2.




Power Consumption

Experimental data obtained for power consumption as a function of Reynolds number, taking airing speed as a parameter, are shown in Figure 3. It can be noticed that, for laminar flow, the power number decreases as the Reynolds number increases, and the air flowrate does not affect the amount of power consumed. In contrast, in the case of turbulent regimes, the power number remains constant for systems without airing, and it decreases as airing increases.



Mixing Times

Experimental values for mixing times are plotted in Figure 4 as functions of stirring speed, taking volumetric air flow (expressed in v.v.m.) as a parameter.



It can be observed that the effect of airing on mixing time depends on the reactor's operating regime. For low stirring speeds, which correspond to Reynolds numbers under 4000, the mixing time decreases as airing increases, while at high stirring speeds the effect is reversed with mixing time either increasing or remaining constant as the volumetric air flow increases. These results agree with those reported by Pandit and Joshi (1983) and Vasconcelos et al. (1995). These authors state that this phenomenon is produced by the opposing effects of the pneumatic and mechanical mixing mechanisms, respectively generated by the air distributor and the stirrer. For high stirring speeds (above 6.67 r.p.s), the stirrer controls the flow regime so that any increase in superficial gas velocity negatively affects the mechanical stirring, without enough pneumatic stirring available to compensate for it. For low stirring speeds (below 2.08 r.p.s.), gas controls the regime, and the opposite effect prevails. In the range between 2.08 and 6.67 r.p.s., intermediate conditions can be observed with the negative effects of airing on stirring compensated for fairly well.

Mixing-Time Correlations

Laminar Flow

The experimental data were adjusted by means of a regression method in order to describe the mixing time as a function of stirring and airing speeds for laminar flow. The proposed fitting model is shown in Equation (1).

the following values were found for the parameters:

Finally, the resulting correlation for laminar flow may be expressed as given in Equation (5).

This equation holds for Reynolds numbers lower than 4000. In Figure 5 the model given by Equation (5) is represented in three dimensions. It can be observed that mixing time strongly depends on stirring speed. Besides, it is also clear that gas controls the regime because an increase in gas velocity causes a decrease in mixing time.



The correspondence between the theoretical mixing-time values estimated with Equation (5) and the experimental data is shown in Figure 6, where it can be observed that the percentage of deviation never exceeds 20%.



For Reynolds numbers above 10000 and for aired systems, several equations to describe the dependence of mixing time on operating conditions, fluid properties and bioreactor properties have been proposed in the literature. One of the most frequently used is the equation proposed by Van't Riet (1991), whose general expression is

where a = 216 and b = 0.33.

The experimental results were analyzed by means of a MATLAB implementation of a nonlinear fitting method in order to set the values for coefficients a and b. The resulting expression is shown in Equation (7).

In Figure 7, the theoretical mixing-time values obtained with Equation (7) are compared with the experimental values. Besides, the upper and lower bounds for a 20% error are shown.



Effects of Scale-Up on Mixing Times

Scaling up is a standard procedure for the design and construction of a large-scale system from experimental results gathered with small-scale equipment.

Analysis of scale-up for the production of strains of Staphylococcus aureus Smith and its capsular polysaccharide reported in a previous article (Ducrós, 2003; Ducrós et al., 2001) was taken as a basis to assess the effect of scale-up on mixing time. The same bioreactor and an identical geometric configuration were employed on that occasion. The analysis of production scale-up was developed following one of the criteria proposed by Hubbard (1987). According to this researcher, besides considering the geometric resemblance, the scale-up may be carried out by regarding the simultaneous constancy of both the kLa value and the volumetric air flow expressed in v.v.m. as additional criteria. The scale-up was performed for the following operating conditions: a stirring speed of 8.33 r.p.s. and a volumetric air flow of 1 v.v.m. The latter as well as the volumetric oxygen-transfer coefficient kLa=0.0012 sec-1 was kept constant.

Whenever a change of scale of one or two magnitudes is carried out, as in the case under study, it is necessary to analyze how other important features of the bioreactor are modified (Humphrey, 1998). One of these characteristics is mixing time.

The variations in specific power and stirring speed with bioreactor size obtained by Ducrós (2003) are shown in Figure 8. Taking those results as the basis for the calculations and applying Equation (7), as obtained in this work, Figure 9, which shows the evolution of mixing time with bioreactor diameter, was plotted. From this picture it is possible to evaluate the effect of scale-up on mixing times.





For each diameter value shown on the horizontal axes in Figures 8 and 9, the real dimensions of the bioreactor were obtained by employing the geometric resemblance criterion and the dimensions of the experimental bioreactor already shown in Figure 1.

It can be observed that mixing time is a variable that would not cause problems in production scale-up because this parameter never exceeds 30 seconds, even for large diameters.



In this work we have presented an experimental study of mixing times in a stirred-tank bioreactor equipped with two Rushton turbines. The experiments were carried out for a wide range of stirring and airing speeds. This study enabled the determination of expressions to estimate mixing times for various flow regimes. Through analysis of the experimental data it was possible to observe that, for low stirring speeds (laminar flow), increases in airing speed resulted in decreases in mixing times, while at high stirring speeds (turbulent flow), the opposite effect prevailed. The expressions obtained in this work, together with the results from a previous article (Ducrós, 2003), allowed us to evaluate the effects of scale-up on mixing times for the production of Staphylococcus aureus Smith and its capsular polysaccharide. It can be concluded that this parameter would not cause problems in the scale-up process because it never exceeds 30 seconds for a bioreactor with a four-meter diameter.



The authors wish to acknowledge the support given by the Secretary of Science and Technology (SECYT) of the National University of Río Cuarto (UNRC) and the Córdoba Ciencia Agency S.E. (ACC). Pablo Bonvillani, undergraduate student in Chemical Engineering at the UNRC, wishes to thank SECYT-UNRC for having awarded him a scholarship to work as a research assistant.



da Stirrer diameter, m
D Reactor diameter, m
Npot Power number

Reynolds number

PG Power under airing conditions, W

Volumetric air flowrate, m3/s

N Stirring speed, r.p.s.
tm Mixing time, s

Greek Letters

r Medium density, kg/m3



Calzolari, A., Giraudo, J., Rampone, H., Odierno, L., Giraudo, A., Frigerio, C., Bettera, S., Raspanti, C., Hernández, J., Wehbe, M., Mattea, M., Ferrari, M., Larriestra, A. and Nagel, R., Field Trials of a Vaccine Against Bovine Mastitis. 2. Evaluation in Two Commercial Dairy Herds, J. Dairy Science, 80, 854-858 (1997).        [ Links ]

Ducrós, E. M., Transferencia de Oxígeno en un Biorreactor de Tanque Agitado: Aplicación a la Producción de Staphylococcus aureus Smith, Master's thesis in Chemical Engineering, Universidad Nacional de Río Cuarto, Argentina (2003).        [ Links ]

Ducrós, E.M., Ferrari, M.P. and Orejas, J.A., Staphylococcus aureus Smith Production in a Stirred-Tank Bioreactor: Design and Scale-up Parameters, "3rd Mercosur Congress on Process Systems Engineering & 1er Mercosur Congress on Chemical Engineering – ENPROMER 2001" (ISSN 1666-1621), Vol. III, pp. 1813-1819, Santa Fe (Argentina), September 16-20 (2001).        [ Links ]

Einsele, A. and Finn, R., Influence of Gas Rates and Gas Holdup on Blending Efficiency, Ind. Eng. Chem. Process Des. Dev. 19, Nº 4, 600-603 (1980).        [ Links ]

Hubbard, D.W., Scale-up Strategies for Bioreactors, Biotechnology Processes, 6, 168-184 (1987).        [ Links ]

Humphrey, A., Shake Flask to Fermentor: What Have We Learned, Biotechnol. Prog. 14, 3-7, (1998).        [ Links ]

Pandit A.B and Joshi J.B., Mixing in Mechanically Agitated Contactors, Bubble Columns and Modified Bubble Columns, Chem. Eng. Sci., 38, 1189 (1983).        [ Links ]

Van't Riet, K. and Tramper, J., Basic Bioreactor Design. Marcel Dekker, N. Y. (1991).        [ Links ]

Vasconcelos, J., Alves, S. and Barata, J., Mixing in Gas-Liquid Contactors Agitated by Multiple Turbines, Chem. Eng. Sci., 50, Nº 14, 2343-2354 (1995).        [ Links ]



Received: October 20, 2004
Accepted: August 10, 2005



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