Thermal and material transport in nonisothermal packed beds

Abstract

T e x a sThe turbulent transport of mass, energy, and momentum was studied in a 4 in. diameter cylindrical column packed with 0.3 in. diameter stoneware spheres. Helium was used as a tracer material, with air as the mainstream fluid. The concentration of tracer present, the temperature, and the velocity of the gas were measured a t several axial and radial increments.These data were analyzed numerically to obtain the radial component of the effective thermal conductivity and the radial component of the mass-dispersion coefficient as functions of radial position. Experimental conditions covered isothermal determinations a t room temperature and nonisothermal determinations in which a temperature gradient was established in the radial direction. Significant differences were found between the isothermal and strong13 nonisothermal results, primarily for the velocity profiles and thermal conductivities. Correlations were developed for the local values of the parameters.Heat and mass transfer in packed beds is important in many ways in the chemical industry. Some examples of the use of packed beds are catalytic reactors, chromatographic reactors, ion exchange columns, and contacting towers. The objective of this study was to obtain correlations of the point values of eddy thermal conductivity and mass dispersion coefficients in a nonisothermal system in terms of the physical properties of the packed bed and the fluid flowing through it.Considerable data has been reported in the literature concerning the prediction of temperatures and concentrations in packed bed reactors (1 through 9). Much of the effort has utilized the procedure of writing differential mass and energy balances on the reactor, assuming that the packed bed could be treated as a continuum, although alternate methods have also been used (I 0, 11 ) . The resulting differential equations were then simplified by various assumptions to yield equations that could be solved analytically. Results from computations of this type have been useful tools, but have not been completely successful in predicting the performance of actual reactors (1 ) . The next level of sophistication was to solve the partial differential equations by numerical methods using high speed computers. This allowed Richardson and Fahien ( 1 2 ) , for example, to use varying values for the bed properties in calculations of reactor behavior. However, they found that various assumptions utilizing mean value correlations for varying local values gave poor comparison with measured reactor data.Ideally, one would like the values of the mass and heat transfer dispersion coefficients to be as representative of the real case as possible. In other words, if these parameters are dependent upon temperature level, concentration, position, velocity, etc., knowledge of this dependence is desired so that the most accurate values may be used in design calculations. Yagi and Kunii ( 1 3 ) measured effective values of thermal conductivity, and also used values reported by other investigators (1 4 through 19) t...

Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects

“…It is relevant to nore that in the geothermal literature [64], the stagnant thermal conductivity of a saturated porous medium is evaluated from (24) which is the rust term in Eq. (22).…”

Internal Heat Transfer to Power-Law Fluid Flows Through Porous Media

“…Some salient aspects of porous ow are outlined in order to throw light on the present heat transfer results. The porosity from the wall along the normal direction varies in an exponentially decaying oscillatory manner, and causes channeling effect, i.e., the ow velocity is maximum near the wall, but not at the center [7,9,13]. Hence, steeper temperature gradients occur close to the wall.…”

“…Turning to heat transfer in porous ows, longitudinal and lateral thermal dispersion was examined theoretically and experimentally [11][12][13][14]. There are far fewer experimental than theoretical investigations of forced-convection ows in packed beds in the literature [15].…”

Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance

“…The solution of the variation al problem was obtained without difficulties and Figure 2 shows a typical calculated flow profile. To our sur prise the calculated profiles turned out to be quite different from the main body of published measurements (Figure 2), [5,6] which were taken some millimeters above the exit crossection of the fixed bed within the empty tube. Comparing a measured and caluculated pro file in Figure 2 we find that the calculated maximum flow velocity is much higher than the measured one and that also the calculated maximum lies closer to the wall.…”