12. Filtration

Mean velocity of flow in a filtration process can be calculated if resistance to filtration is known. Filtration resistance is due to cake and cloth.

Where V is volume of liquid flowing in time t, A is filtration area, l is thickness of filter cake, L is the thickness of filter cake offering same resistance as that of cloth, r is specific resistance of cake, μ is viscosity of fluid and -ΔP is total pressure drop. Replacing l by vV/A we can get

Where v is a ratio of volume of the deposited to the volume of filtrate.

For a period of constant rate filtration, dV/dt = V/t, and the following equation results

For a period of constant pressure filtration, -ΔP is constant, and the following equation results

Pressure difference is built up gradually and during this period filtration is conducted at constant filtration rate for time t₁, then.

Where V₁ is volume of liquid passing in time t₁.

The filter press: The filter press is made in two main forms, the plate and frame and the recessed or chamber press. If filtration is carried out entirely at constant pressure, then

Where B₁ and B₂ are constants given as

Example 12.1: A leaf filter having 0.05 m² of filtering surface is operated under an absolute pressure of 30 kN/m². The volume of filtrate collected in the first 300 seconds is 250 cm³ and, after further 300 seconds, an additional 150 cm³ are collected. Assume the cake is incompressible. If the operation is run for additional 120 seconds, how much filtrate will be collected?

Solution:

Pressure drop can found to be

Equation 12.6 can be written for two data points to obtain