Under the absorption conditions it is possible to find physical systems for which the mass-transfer resistance is concentrated mostly in one of the phases enabling the measurement of the individual volumetric mass-transfer coefficients, k_La and k_Ga of packings. Unfortunatelly no such systems are avaliable for corresponding distillation conditions which for a long tome limited the description of the packing mass-transfer performance to the overall mass-transfer efficiency characterized by HETP only.

To improve this situation the profile method has been developed in our research group for the evaluation of the volumetric mass transfer coefficient from concentration profiles measured along the distillation column.

Linek, V.; Moucha, T.; Prokopova, E.; Rejl, J.F., 2005. Simultaneous determination of vapour- and liquid-side volumetric mass transfer coefficients in distillation column. Chem. Eng. Res. Des. 83(A8), 979-986.Rejl, F.J.; Valenz, L.; Linek, V., 2010. Profile Method for the Measurement of kLa and kVa in Distillation Columns. Validation of Rate-Based Distillation Models Using Concentration Profiles Measured along the Column. Ind. Eng. Chem. Res. 49(9), 4383-4398.

The method is based on the rate-based model of the distillation column. The overall volumetric mass-transfer coefficient, K_Ga, can be used in this model as a parameter relating the local intensity of the mass transfer and the mass-transfer driving force.

with m₁=dy₁/dx₁ representing the slope of the vapor-liquid equilibrium line of the light component and c_L, c_G total molar concentration of liquid and vapor phase, respectively. Particular terms on the right side ofthe equation can be understood as contributions of the liquid and vapor phase to the total mass-transfer resistance.

For systems in which m₁ varies with the system composition (and therefore it also varies along the distillation column) the value of K_Ga, i.e. the local intensity of the mass transfer, also varies along the column. As a result, the hypothetical concentration profiles, obtained by the integration of the column rate-based model, differ mutually, when calculated as providing the resistance against the interfacial mass transfer, which is concentrated in the vapor or in the liquid phase, although both such profiles give the same overall separation efficiency – for example the same HETP.

The profile method leverages the fact that the relative resistance of the individual phases varies along the column for the separate determination of the volumetric mass-transfer coefficients in the vapor and liquid phases. It is an optimization procedure which adjusts values of the mass-transfer coefficients, or the relations for their calculations, until the best fit of experimental profile by the rate-based model of the column is achieved. The optimized values of k_La and k_Ga represent the most probable values of the mass-transfer coefficients for the given conditions. In the following figure the principle of the profile method is demonstrated on a hypothetical concentration profile measured along the packed bed. The red line represents the profile calculated for negligible mass-transfer resistance in the liquid phase, i.e., high k_La values. Similarly the blue profile was calculated for negligible mass-transfer resistance in the vapor phase (the concentration profiles calculated for negligible mass-transfer resistance in one of phases will be further denoted as critical profiles). The purple line represents the optimized profile which gives the best fit of experimental data. All three calculated profiles provide the same overall mass-transfer efficiency, i.e. HETP as the experimental profile.

In practical application the values of k_La and k_Ga are assumed to be a function of many variables – phase physical properties, flow rates, packing parameters, process conditions – therefore the correlations for their predictions, i.e. the mass-transfer models, are usually corrected with parameters b_L, b_G and the correcting parameters are optimized instead of the direct evaluation of the mass-transfer coefficients.

The ability of the profile method to evaluate the individual volumetric mass-transfer coefficient depends strongly on the relative mass-transfer resistance of the particular phase. For systems or conditions for which the mass-transfer resistance is concentrated in one phase only, the shape of the concentration profile is insensitive to the value of the mass-transfer coefficient in the other phase. For evaluation of both mass-transfer coefficients the profile method requires the particular mass-transfer resistances to vary significantly along the column. Thus, suitable distillation systems and conditions have to be chosen to satisfy this requirement.