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Stirred Tanks: a Physical Explanation for the Exponents of Classical Empirical Mass Transfer Equations

Mariano Martín, Francisco J. Montes, and Miguel A. Galán. Departamento de Ingeniería Química, Universidad de Salamanca, Plz. de los Caídos 1 - 5, Salamanca, 37008, Spain

Aerated stirred tank reactors are one of the most typical equipment in biochemical industry. The base for its design has traditionally been the empirical correlations obtained for different scales, often lower than the industrial scale. Scale up has become the major problem due to the wide variety of results obtained.


In order to illuminate the effect of the scale on the oxygen transfer a combined study of the hydrodynamics and the mass transfer has been carried out.


The study of the hydrodynamics inside the tank provides prime knowledge of the contact between phases and the flow in the tank, responsible for the concentration gradient. The characteristics studied for the liquid phase were its scales of flow, macro and micromixing. In the case of the gas phase, the parameters studied were the bubbles, their generation, the bubble mean diameter of the dispersion for different impellers and dispersion devices and the effect of the relative position of the impeller in the tank.


The study of the hydrodynamics of the system allows developing a theoretical equation based on Higbie's penetration theory to explain the traditional empirical equations of mass transfer in stirred tanks



The exponent related to the power input per unit volume (α) turned out to depend on the break up of the bubbles as well as on the quality of the dispersion, the specific area available.

The exponent related to the superficial gas velocity (β) depended on the effect of the gas on the impeller and on the specific area available of the dispersion.

Neither α nor β depended on the scale of the tank. However, the constant k gathered the influence of the physical properties of the liquid, the influence of the transport properties and what is more important, the influence of the predominant flow scale in the tank.


With the appropriate hydrodynamic data obtained recording the bubble dispersions, the proposed theoretical equation predicted the empiric values of the volumetric mass transfer correlation.

  <>Acknowledgment: The support of the Ministerio de Educación y Ciencia of Spain providing a F.P.U. fellowship to M. Martín is greatly welcomed. The funds from the project reference PPQ2000-0097-P4-02 are also appreciated.