Page 135 - Modelling in Transport Phenomena A Conceptual Approach

4.6. FLOW IN PACKED BEDS 115

Solution

If the inside and outside pipe diameters are designated by Di and Do, respectively,
the supeTficia1 velocity, vo, is defined by
Q 5
uo=-- = 25.5 m/ min
xDz/4 - ~(0.5)~/4

The actual average velocity, (v),,t, in the annulus is
-
Q - 5 = 40 m/ min
= x (02 - DZ) /4 x [(0.5)2 - (0.3)2] /4
Comment: The superficial velocity is always less than the actual average velocity
by a factor of porosity, which is equal to [l - (Di/Do)2] in this example.

For packed beds, the Reynolds number is defined by

(4.6-2)

For laminar flow, the relationship between the friction factor and the Reynolds
number is given by
(4.6-3)

which is known as the Kozeny-Carman equation.
In the case of turbulent flow, Le., Rep6 > 1000, the relationship between Repb
and fpb is given by the Burke-Plummer equation in the form

(4.6-4)

The so-called Ergun equation (1952) is simply the summation of the Kozeny-
Carman and the Burke-Plummer equations

(4.6-5)

Example 4.20 A column of 0.8m2 cross-section nd 30m height is p eked with
spherical particles of diameter 6mm. A fluid with p = 1.2 kg/ m3 and p = 1.8 x
kg/ m. s flows through the bed at a mass flow rate of 0.65 kg/ s. If the pressure
drop is measured as 3200Pa, calculate the porosity of the bed:
a) Analytically,
b) By using Newton-Raphson method.