Theorem of Corresponding Hydrodynamic States for Estimation of Transport Properties:  Case Study of Mass Transfer Coefficient in Stirred Tank Fitted with Helical Coil

Abstract

Application of concepts similar to those used in thermodynamics provides an alternate, simple, and scale-independent approach to predict hydrodynamics-dependent transport properties in multiphase systems. A theorem of corresponding hydrodynamic states analogous to the theorem of corresponding states in thermodynamics is proposed. According to the former, systems in the same corresponding hydrodynamic state exhibit identical mass transfer coefficients. A posteriori proofs from experimental measurements bear testimony to the validity of this physical postulate. It is shown that this approach unifies data from widely different and distributed sources in terms of time as well as methodology and results in simple and adequately accurate correlations for mass transfer coefficients in stirred reactors, the most complex yet widely used process equipment. For this a posteriori proof based on literature data as well as new data on solid−liquid mass transfer coefficient ( K SL ) in a widely differing system, stirred tanks fitted with helical coils are used. It is concluded that K SL in a two-/three-phase stirred tank reactor (STR) can be correlated reliably over a wide range of system configurations, scales, and operating conditions by a two-parameter equation involving a reduced hydrodynamic state similar to the reduced thermodynamic state in thermodynamics.