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ENVE-2110

ENVE-2110. Lecture#6. BATCH REACTOR. Radon 222 is a naturally occurring radioactive gas formed by the decay of radium-226, a trace element in soil and rock. The radioactive decay of radon can be described by the elementary reaction

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ENVE-2110

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  1. ENVE-2110 Lecture#6

  2. BATCH REACTOR • Radon 222 is a naturally occurring radioactive gas formed by the decay of radium-226, a trace element in soil and rock. The radioactive decay of radon can be described by the elementary reaction The rate constant for this reaction is k=2.1x10-6 s-1 independent of temperature. At time t=0 a batch reactor is filled with air containing radon at concentration C0. How does the radon concentration in the reactor change over time?

  3. For t>0 only one reaction influences the concentration of radon (CRn). The change in radon concentration is related to the reaction rate by expression b/c consumed

  4. Since radon decay is an elementary reaction, we expect the rate to be first-order (always true for radioactive compounds) Differential equation can be solved by direct integration and rearrangement (see notes from Thursday and today), we obtain The radon concentration decays exponentially towards zero.

  5. CSTR • Consider a 10 x 106 lake fed by a polluted stream having a flow rate of 5.0 m3/s and pollutant concentration of 10.0 mg/L. There is also a sewage outfall that discharges 0.5 m3/s of wastewater having a concentration of 100 mg pollutant/L. The stream and sewage wastes have a decay rate coefficient of 0.20/day. Assuming the pollutant is completely mixed in the lake and assuming no evaporation or other water losses or gains, find the steady state pollutant concentration in the lake.

  6. DRAW A SCHEMATIC Sewage outfall Qw = 0.5 m3/s Cw = 100 mg/L Incoming stream Outgoing stream Qout =? Cout= ? Qin = 5.0 m3/s Cin = 10.0 mg/L

  7. AT STEADY STATE Completely mixed Input rate –output rate –kCV = accumulation rate = 0

  8. Thus,

  9. Insert values

  10. PFR • Every year herons, seagulls, eagles, and other birds mass along a 4.75 km stretch of stream connecting to a lake and to the ocean to catch the fingerling salmon as they migrate downstream to the sea. The birds are efficient fishermen and will consume 10,000 fingerlings per km of stream each hour regardless of the number of salmon in the stream. In other words, there are enough salmon; the birds are only limited by how fast they can catch and eat the fish. The stream’s average cross-sectional area is 20 m2 and salmon move downstream with the stream’s flow rate of 700 m3/min. If there are 7 fingerlings per m3 in the water entering the stream, what is the concentration of salmon that reach the ocean when the birds are feeding?

  11. DRAW A SCHEMATIC LAKE Qin = 700 m3/min Cin=7 fish/m3 OCEAN STREAM L L = 4.75 km A = 20 m2 Qout=700 m3/min Cout=?

  12. Since the birds eat the salmon at a steady rate that is not dependent on the concentration of salmon in the stream, the rate of salmon consumption is zero-order. For a steady-state PFR

  13. Insert values Solve equation by inserting values:

  14. OTHER EXAMPLES • EXAMPLE 1: A pipe from municipal wastewater treatment plant discharges 1.0 m3/s poorly treated effluent containing 5.0 mg/L of phosphorous compounds reported as mg P/L into the river with an upstream flow rate of 25 m3/s and background phosphorous concentration of 0.010 mg P/L. What is the resulting concentration of phosphorous in mg P/L in the river just downstream of the plant flow?

  15. DRAW A SCHEMATIC River Qu, Cu Qd, Cd River Treatment plant With pipe discharge.

  16. Determine the phosphorous concentration downstream of the discharge pipe, Cd. To find Cd, use the standard mass balance equation with steady-state conditions and without chemical formation or decay:

  17. INPUT VALUES

  18. EXAMPLE 2: The CSTR shown below is used to treat industrial waste, using a reaction that destroy the pollutant according to first-order kinetics, with k=0.216/day. The reaction volume is 500 m3, the volumetric flow rate of the single inlet and exit is 50 m3/day, and the inlet pollutant concentration is 100 mg/L. [a] What is the outlet concentration after treatment? [b] Calculate the hydraulic retention time. Qin, Cin Qout, Cout

  19. SOLUTION • An obvious C.V. is the tank itself. The problem is asking for a single, constant outlet concentration, and all problem conditions are constant. Therefore, this is a steady-state problem. The mass balance equation with first-order decay term is Therefore, and

  20. SOLVE • Solve for Cout and assume Qin=Qout=Q [b] solve for hydraulic retention time:

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