A large pond has a volume of 8 million gallons and the flow into is one milion g

Question

A large pond has a volume of 8 million gallons and the flow into is one milion gallons each day. A pollutant called BOD isin the inflow at 20 mg/L and it has a decay rate constant of 0.30/day. write a mass balance that describes BOD levels in this pond, what assumptions do you make in writing this? What order reaction is the destruction of BOD? What is the effluent concentration of BOD from this pond? What if the pond was split into two separate ponds, each of 4 million gallons? Calculate the effluent concentration in this case.

Explanation / Answer

1. Rate of BOD in=Rate of BOD out+ Rate of BOD accumulation.+ rate of loss of BOD due to Chemical Reaction

Assuming there is thorough mixing, i.e the river acts like a perfect CSTR

1 gallon = 3.78 L, 1 million gallon = 106 gallons = 3.78*106 L

Rate of BOD in = 3.78*106 L/day* 20 mg/L= 7.56*107 mg/day

since the rate of decay of BOD is 1st order,

assuming that the river operates under steady state, i.e accumulation =0

The mass balance equation becomes

Rate of mass in = Rate of mass out + rate of loss due to chemical reaction

7.56*107 = 3.78*106*C + 0.4*8*106*3.78 *C , C is concentration at the exit of river

20 = C+0.4*8C

20 = 4.2C, C= 20/4.2 = 4.76 mg/L

2. If the infllow enters the 1st tank and from there it goes to the second tank ( series arrangement)

7.56*107 = 3.78*106*C +0.4*4*106*3.78C

20 = 1.7C, C= 20/1.7= 11.76 mg/L

from this concentration it goes into the second pond,

writing mass balance for the second pond,

11.76*3.78*106 =3.78*106C+0.4*4*106*3.78C

11.76 = 1.7C

C= 11.76/1.7= 6.91 mg/L

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