Friction factor

The frictional force can be expressed in terms of a friction factor. This leads to equations describing the flow of a fluid past a collection of particles. There are several approaches to treating fluid flow through packed beds. The most successful of these is the Ergun Equation, which describes flow in both the laminar and turbulent regimes. This method treats the packed column as a compact irregular bundle of tubes. Modifying the theory for straight tubes not only takes into account the irregularity of the tubes, but yields relationships similar to those derived for straight tubes as well. This analysis assumes several conditions. First, we assume that the particles are packed in random; there is no channeling in the packed bed. Channeling occurs when the fluid flowing through the packed bed finds a preferred path through the bed. We also assume that the diameter of the packing is much smaller than the diameter of the column as well. The maximum recommended particle diameter is one-fifth of the column diameter. We assume that velocity, particle diameter and void fraction behaves as a bulk behavior and hence we can use an average values. The pressure drop used in both the Blake-Kozeny equation and the Burke-Plummer equation is directly proportional to the friction factor (fp). Equations 7, 8, and 9 express the Blake-Kozeny, Burke-Plummer, and Ergun Equation respectively in terms of the friction factor:

= (7) = (8) = The experimental friction factors can be calculated using equation 10.

= (10)Using this equation and the Reynolds number equation a comparison can be established with the Ergun Equations friction factors. Although the Ergun Equation is valid for a wide range of Reynolds numbers, During experiment it is observed that friction factor decreases with increasing the gas velocity at the constant liquid flow rate. Experiment data can be predicted by Ergun correlation which are shown in equation (7).