1. Randall's Seafood Processing Plant in southern Louisiana has
historically discharged their wastewater into the nearby lake
with a bayou flowing in and out of the lake. However, the
Louisiana Department of Environmental Quality has recently
fined the company for noncompliance of their NPDES
discharge permit. Randall's has argued that their discharges
do not impact the lake (or the bayou downstream of the lake).
Given the expertise of this class, you have been asked by the
seafood company to provide expert testimony on their behalf.
Before you can agree to this, you need to determine whether
the company's claim is correct. The specifics of the case are
below (55 points):
Bayou flowrate: 13 cfs
Seafood processing discharge flowrate: 4 cfs (ft³/s)
Bayou BOD, upstream of lake: 3 mg/L
Seafood processing discharge BOD$_5$: 545 mg/L
Background BOD$_5$ level in lake: 1.5 mg/L
Decay coefficient: 0.115/day
Volume of lake: 550,000 m³
a) LDEQ has set a maximum limit of 20 mg/L BOD$_5$ (at steady
state conditions) in the lake. Is the company's claim that it
does not impact the lake correct?
b) How long will it take the lake to reach steady state
conditions with the given conditions as listed above?
c) If the lake is above the 20 mg/l maximum level (at steady
state), what must the plant discharge BOD$_5$ concentration
be to reach the 20 mg/l lake concentration?