A calculation method for multicomponent mass transfer coefficient correlations

Mass transfer coefficients are usually based on measurements from binary mixtures. This leads to scalar correlation equation for mass transfer coefficient. These equations are usually obtained from dimensional analysis, and they include fractional powers of the system parameters, like the Reynolds number and the Schmidt number. Generalization according to the linearized Maxwell–Stefan theory (∇ c t and ∇[ D ] are assumed zero along the diffusion path) is then made by replacing the scalar values by corresponding matrix values. This leads to the problem of calculating the matrix fractional powers. This can be done by the similarity transform or by the Sylvester’s expansion, but it is quite a tedious procedure. Krishna and Standart (1976) American Institute of Chemical Engineers Journal 22 , 383–9 proposed that the binary mass transfer correlations could be used for each component pair in multicomponent systems. In this paper, another approximate approach is chosen for the simplification of the calculations. In the Maxwell–Stefan diffusion coefficient matrix, the off-diagonal elements describe diffusional interactions. These elements may be significant, but are usually smaller in magnitude than the diagonal elements. The method presented in this paper is based on that fact. The method gives more accurate results than the practice of using binary mass transfer coefficients. It is applicable to all mass transfer models, such as the film model, penetration model, and models resulting from boundary layer analyses.