Question

Derive expressions for constant rate filtration and constant pressure difference filtration and explain clearly the difference between these filtration techniques.

Answer 1

Filteration :

In class of mechanical separations, placing a screen in the flow through which they cannot pass imposes virtually total restraint on the particles above a given size. The fluid in this case is subject to a force that moves it past the retained particles. This is called filtration.The analysis of filtration is largely a question of studying the flow system. The fluid passes through the filter medium, which offers resistance to its passage, under the influence of a force which is the pressure differential across the filter. Thus, we can write the familiar equation:

Rate of filteration = driving force / resistance

Rate flow in general is given as:

Where A is filter area, deltaP is pressure drop across filter.

As the total resistance is proportional to the viscosity of the fluid, we can write:

Where, R is resistance to flow, mu is vicsocity of fluid and r is specific resistance, L_c is thickness of fliter cake and L is fictious equivlanet thickness,

If the rate of flow of the liquid and its solid content are known and assuming that all solids are retained on the filter, the thickness of the filter cake can be expressed by:

                  L_c = wV/A

where w is the fractional solid content per unit volume of liquid, V is the volume of fluid that has passed through the filter and A is the area of filter surface on which the cake forms.

So, resistance can be written as,

And the equation for flow through the filter, under the driving force of the pressure drop is then:

Constant rate filteration

In the early stages of a filtration cycle, it frequently happens that the filter resistance is large relative to the resistance of the filter cake because the cake is thin. Under these circumstances, the resistance offered to the flow is virtually constant and so filtration proceeds at a more or less constant rate.

  

Constant pressure filteration

Once the initial cake has been built up, and this is true of the greater part of many practical filtration operations, flow occurs under a constant-pressure differential.

  t / (V/A) =   [mrw/2DP] x (V/A) + mrL/DP