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# ps_4 - DOWNSTREAM PROCESSING Problem Set#4 Problem 1...

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D OWNSTREAM P ROCESSING Problem Set #4 Problem 1 Streptomycin is an antibiotic used in combination with other drugs to treat tuberculosis (TB), which is a chronic bacterial infection. Suppose that you are running a fungal fermentation to produce this antibiotic and that the biomass titer at harvest is 20 g/L. To separate the biomass from the streptomycin product, you will harvest the fermentation broth, add filter aid to a concentration of 150 g/L, and proceed to perform the primary separation using a rotary vacuum filter. In pilot studies using a filter having 1.5 m 2 area, the pressure drop across the filter is 12 psi and the data shown in Table 1 are collected. Table 1: Filtration Time and Volume of Filtrate Collected Filtration Time (min) Total Volume Collected (L) 3 5.0 28 20.0 293 65.0 375 75.0 512 85.0 The viscosity of the filtrate is 2.69 x 10 -4 lb/ft-s and the cake is compressible with a resistance (R c ) that can be expressed as follows: c o V R A = αρ where α = specific cake resistance (length/mass) ρ o = mass of cake solids per volume of filtrate V = filtrate volume A = filter area 1

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a) Derive an equation that relates area (A), time (t), and volume (V) to area and volume in the following functional form (f means function of): At V f V A = b) Use your answer from part a to determine the value of α (in units of ft/lb) and the filter resistance R m
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