The following data were obtained for a plate-and-frame filter of total area A=500 sq cm. operating under a constant pressuredrop of 0.1 atm: Time t (min): 50 75 100 Volume of filtrate V (liter): 9.7 12.3 14.0 The filtrate is essentially water. the volume of the cake is 1/10 the volume of the filtrate passed. The resistance of the filtrate medium may be neglected.
a) Estimate the permeability k (darcies) of the cake
b) At a certain time t after start-up, the filter is shut down. There follows a cleaning time t_c, in which the accumulated cake is removed, the cloth is cleaned, and the filter is reassembled. This cyclical pattern of productive operation, followed by cleaning, etc., is continued indefinitely. If t_c= 30 min, what value of t will maximize the average volume of filtrate produced per unit time? (Hint: Your goal is to maximize the volume filtered V over time. However, time becomes now the sum of the filtering time (t) and the cleaning time (t_c), giving you V/(t+t_c) that would be maximized. You should also have an expression for V from part a)
c) What is the value (liter/min) of this maximum average volumetric flow rate of filtrate?