Axial diffusion of liquids in packed beds and end effects

Abstract

Experimental data were obtained on the effect of bed length of packed spheres on axial diffusion coefficients with the frequency response technique used. Lengths of packed section of 6 to 174 cm. were used. The end effects were eliminated by using a novel experimental technique for analyses of the inlet and outlet streams. No effects of length on DL were found.When the end effects were artificially introduced by using void analytical sections a t the two ends, then large effects of length on DL were found. These void sections were the cause of length effects found by other experimenters. The DL drops as the length of bed is increased. Above about 65 cm. length the DL remains constant with increase in length. The over-all results are in general agreement with the data of others.An understanding of the behavior of fluids in empty tubes and packed beds is very important in the study of heat, mass, and momentum transfer. Much experimental data exist on radial mass transfer or diffusion coefficients perpendicular to the axial flow of the liquid or gas. Recently Ebach and White ( 3 ) , Carberry and Bretton ( l ) , and Strang and Geankoplis (7) presented experimental correlations for packed beds of spheres for the effect of liquid velocity, particle diameter, and viscosity on the axial diffusion coefficient.However no comprehensive experimental study has been made of the elimination of end effects and the effect of column length on DL for liquids. McHenry and Wilhelm ( 5 ) obtained data on gases for different lengths and eliminated end effects by calculation. Carberry and Bretton (1) presented experimental points obtained at five different bed lengths and different velocities using liquids.To investigate the axial difhsion of a flowing system experimentally the outlet response resulting from an inlet disturbance is measured. This disturbance can be a step or pulse function or a continuous sine-wave function. The sine wave is used in the frequency response experiments. Ebach and White ( 3 ) discuss these methods in detail.In the present work DL values were obtained for glass spheres in packed beds with water used. End effects were experimentally eliminated which removed the column length effect on D,. The effect of length was also determined by introducing end effects artificially and varying the length. It is assumed that C is a function of Z and t only, that there are no radial gradients, and that U is constant. Carberry and Bretton (1) discuss in detail the assumptions implied in this model. Their data and that of others ( 3 ) suggest that Equation ( 1 ) does not apply owing to the fact the amplitude does not dampen as the square root of time or bed length. However in the present work it will be shown that it does apply under the carefully designed conditions of experimentation.Two boundary conditions are imposed at the inlet and the outlet of the bed respectively: UThis can be compared to the phase shift measured experimentally. Deisler and Wilhelm (2) discuss in detail the addition of nr radians to the .fHixp.. Eq...

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