Design a CSTR to provide pre-treatment for an industrial wastewater that flows at a rate of 1000 gpm (gallons per minute) with a phenol concentration of 200 mg/l. Phenol undergoes a first-order decay reaction in the CSTR with rate constant, k = 0.50 hr^-1. The current industrial pre-treatment permit for Phenol is 20 mg/l. The permit limitation may be changed, either higher or lower, in the future.
Determine the required CSTR volume, V (gallons), and hydraulic residence time, t = V/Q (hours), to comply with the current industrial pre-treatment permit limitation for phenol.
Plot a graph with CSTR effluent phenol concentration (mg/l) along the vertical axis as a function of CSTR hydraulic residence time, t (hours), on the horizontal axis for assessing the impact of changes in the permit limitation. Comment on a type of "Law of Diminishing Returns" on effluent phenol concentration versus 't' that applies to CSTR design for first-order decay reactions.