The two ponds in the figure below can be modeled as completely-stirred tank reactors (CSTRs) in series. The first-order decay rates for each pond are different but the inflow and outflow rates and volumes for the two ponds are the same.

Question

a. Write a mass-balance (differential) equation describing dC2/dt.
b. Solve your mass balance to develop an expression for C2(t). Assume a spill results in an instantaneous input of mass M into the first pond. Assume the upstream concentration C(0)=0 and the initial concentration of the second pond, C2(t=0)=0.
c. For parameter values k1=0.1/day, k2=0.15/day, Q=10 m3/day, V=1000 m3, and M=1 kg, prepare a figure showing C2 as a function of time for 0<=t(days)<=50.
d. What is the maximum concentration in the second pond and when does it occur?

Q, C(0) Q, C1
------>Pond 1: V, C1, k1------>

Q, C2
Pond 2: V, C2, k2------>

Answer 1

To clarify the 'figure':
Q, C(0) are the inflow parameters into the first pond.

Q, C1 are parameters from pond 1 as it is about to enter pond 2.

Q, C2 are outflow parameters from the second pond.

Pond 1 has parameters V, C1, k1.
Pond 2 has parameters V, C2, k2.

Thanks, Christine