Question

Design a CSTR to provide pretreatment for an industrial wastewater that flows at a rate of 1,000 fpm with a phenol concentration of 200 mg/L. Phenol undergoes a first-order decay reaction in the CSTR with a rate constant, k=0.50 hr^(-1). The current industrial pretreatment permit limitation for phenol is 20 mg/L. The permit limitation may be changed, either higher or lower, in the future.

1. Determine the required CSTR volume, V (in gallons), and hydraulic residence time, in V/Q (hours), to comply with the current industrial pretreatment permit limitation for phenol.

2. Plot a graph with CSTR effluent phenol concentration in mg/L along the vertical axis as a function of CSTR hydraulic residence time in hours, on the horizontal axis for assessing the impact of changes in the permit limitation. Use a spreadsheet to perform the repetitive calculations and then use the spreadsheet's graphing tools to plot the graph. Comment on a type of "Law of Diminishing Returns" on effluent phenol concentration versus the V/Q that applies to CSTR design for first-order decay reactions.

Answer 1

For a CSTR and 1^st order reaction, space time T= (CO-C1)/KC1

Where C0= initial concentration = 200mg/L, C1= 20 mg/L

K= 0.5/hr

T= (200-20)/0.5*20 = 18 hrs

Flow rate= 1000 ft3/min =1000/60 ft3/hr=16.67 ft3/hr

Volume of tank, V= Vo*T= 16.67*18 ft3=300 ft3=300*7.48 Us gallon =2214 Gallon

KT= (CO-C1)/C1

KT= CO/C1-1

CO/C1= (1+KT)

C1= CO/(1+KT)

C1 is determined by varying T and Calculating C1.

The calculations and the graph are shown below

T (hr)	C1(mg/L)
1	133.3333
3	80
5	57.14286
7	44.44444
9	36.36364
11	30.76923
13	26.66667
15	23.52941
17	21.05263
19	19.04762