The filter of Prob. 29.7 is operated at a constant rate of 0.6 gal/ft²-min from the start of the run until the pressure drop reaches 70 lb_ƒ/in.² and then at a constant pressure drop of 70 lb_ƒ/in.² until a total of 1,400 gal of filtrate is obtained. The operating temperature is 70°F. What is the total filtration time required.

Prob. 29.7

The following relation between α and Δp for superlight CaCO₃ has been determined to be 

a = 8.8 x 10¹⁰ [1 + 3.36 x 10^-4 (Δp)^0.86]

where Δp is in pounds force per square foot. This relation is followed over a pressure range from 0 to 1,000 lb_ƒ/in.². A slurry of this material giving 3.0 lb of cake solid per cubic foot of filtrate is to be filtered at a constant pressure drop of 70 lb_ƒ/in.² and a temperature of 70°F. Experiments on this sludge and the filter cloth to be used gave a value of R_∞ = 1.2 x 10¹⁰ ft^-1. A pressure filter of the tank type is to be used. How many square feet of filter surface are needed to give 1,400 gal of filtrate in a 1-h filtration? The viscosity is that of water at 70°F.