Voidage fraction

The linear superficial flow velocity in the packing voids v is calculated from volumetric flow rate Lin, voidage fraction of the adsorbant bed e and column diameter d as... 

In a packed bed of unit volume, the volumes occupied by the voids and the solid particles are e and (1 — e) respectively where e is the voidage fraction or porosity of the bed. Let S0 be the surface area per unit volume of the solid material in the bed. Thus the total surface area in a packed bed of unit volume is (1 — e)S0. 

L = actual depth of methanator bed in ft plus 3 ft more added on to account for AP due to nozzles, distributor, and supports e = voidage (fractional free volume of packing) = 0.40 for this case h = exponent = a function of the Reynolds number = 2.0 for this case D = average catalyst particle diameter, ft = 0.0238 ft for this case gc = dimensional constant = 32.17 (lb mass) (ft)/(lb forceXs2) p = fluid density, lb/ft3, based on average temperature and entering pressure = 0.464 lb/ft3 for this case (j)s = shape factor for the solid catalyst particles = 1.0 for this case... 

Biesheuvel and Gorrisen (1990) have derived one-dimensional conservation equations for void fraction disturbances in a uniform bubbly fluid. They have studied the features of the propagation of void fraction disturbances and investigated the stability of uniform bubbly flows. They observed that the voidage fraction waves are unstable for void fractions above some critical value (>45%). Their method of approach was similar to that of Batchelor (1988) in many respects. 

A design will typically be required to meet specified rates pf gas-liquid mass transfer and heat transfer and achieve suitable mixing of the liquid and gas phase at a certain throughput (or batch size). The designer will need to know the power consumption, gas holdup (voidage) fraction, C( . and foam height associated with such duty. 

Lockett, M. J. and Harrison, D. The distribution of voidage fraction near bubbles rising in gas-fluidized beds. Proc. Int. Symp. on Fluidization, Drinkenberg. Netherland Univ. Press, Amsterdam, 1967. 

The reactor is quite tall. This is because the voidage fraction eg is very large. We can rework the design by increasing the reactor diameter. Let us take the reactor diameter to be 80 cm. 

Noting that power = volumetric flow rate x pressure drop, the overall power per unit mass of liquid is straightforward to calculate for single-phase systems given the friction factors and voidage fraction in the mixer as supplied by mixer manufacturers or measured in the laboratory. For gas-liquid systems the volume of fluid in the mixer must be multiplied by (1 — c )) to obtain the liquid volume, so the gas fraction 4) must be known (see Section 11-5). It has been found that the Lockhart-Martinelli (1944) correction for the effect of the gas phase on pressure drop in pipe flow can be applied to static mixers with reasonable accuracy ( 20%). 

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