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Wastewater/manure production from a cattle operation is treated in a well-mixed

ID: 1711654 • Letter: W

Question

Wastewater/manure production from a cattle operation is treated in a well-mixed lagoon. The wastewater is produced for 18 hours per day, at a constant flow rate of 6.2 m^3/min. Of particular interest in the wastewater is pollutant MMM, which has a concentration that varies throughout the day, as given by the expression: C_ln = C_0 + C_1 t - C_2 exp(C_3 t) with C_0 = 250 mg/L, C_1 = 0.3 mg/L-min, C_2 = 0.3 mg/L and C_3 = 0.0065 min^-1. The value of t is 0 at 4 A.M. The lagoon volume is 660 m^3, where a biochemical treatment process reduces the MMM concentration via a first order reaction, with k = 0.02 mim^-1 at 12 degree C.middotThe lagoon output flow is constant at 6.2 m^3/min, so volume in the reactor does not change. 1. Plot C_ln as a function of time from 4 A.M. to 10 P.M. (0 to 18 hours). 2. Develop a mathematical expression for the mass balance for this treatment lagoon. It will be a differential equation in terms of C_0-3, C_Out, t, and constants. Do not plug in numbers yet. 3. The solution to the mass balance equation is in the form: C = A exp(-Bt) + D exp(-Et) + Ft + G with A, B, D, E, F, and G as constants. The values of the constants can be determined by substitution of this equation into the mass balance and solving for like terms. The initial condition is C = C* at t = 0. Determine the equation for C in terms of the reactor/reaction parameters. 4. Plot the lagoon discharge concentration, C, as a function of time from 0 to 18 hours on the same plot as #1. The initial concentration in the reactor at 0 hours, C* is 92 mg/L. 5. Find the maximum value of MMM leaving the treatment lagoon and the time it occurs. 6. During a cold winter, the treatment first order constant decreases to 0.01 min^-1 at 2 degree C: in this case, C* = 2 mg/L. a. Plot the lagoon discharge concentration, C, as a function of time from 0 to 18 hours on the same plot as #1. b. Find the maximum value of MMM leaving the treatment reactor and the time that it occurs. 7. Discuss your results.

Explanation / Answer

1. Plot Cln -

Calculate Cln and tabulate the values -

238.364      

t (hr) t(secs) Cln 0 0 249.7 1 60 267.5569 2 120 285.3456 3 180 303.0334 4 240 320.5724 5 300 337.8914 6 360 354.8856 7 420 371.4001 8 480 387.2061 9 540 401.9655 10 600 415.1793 11 660 426.1101 12 720 433.669 13 780 436.2477 14 840 431.4708 15 900 415.8297 16 960 384.1424 17 1020 328.7553 18 1080

238.364