What kind of ideal reactor describes disinfection in a pipe. Please provide both

Question

What kind of ideal reactor describes disinfection in a pipe. Please provide both the type and the order of decay? (Batch, CSTR, Plug Flow) (zero order, first order)

What is the pipe volume? (ft3)

What is the first order rate constant, K?

What concentration of ozone (in mg/L) should be injected at the head of the pipe so that there will be an ozone concentration of 1.0 mg/L at the pipes exit into the plant?

M&E 1.14. Ozone is sometimes used as a disinfectant for drinking water. Ozone is highly reactive. It will react with many benign species found in water, as well as the pathogens it is intended to kill. It is found that ozone reaction in water nearly follow:s first-order kinetics in ozone concentration, such that its concentration decreases by 50% in 12 min (t1/2 12 min). A water supplier wants to inject ozone into a pipe bringing water to the water treatment plant to predisinfect the influent. The 3.0-ft diameter pipe is 3,400 ft long with a steady flow rate of 10,000 gal/min.

Explanation / Answer

1. The ideal reactors that describes the disinfection in a pipe are Batch reactors, Plug Flow reactors and Continuously Stirred Tank Reactor.

Batch Reactor: In a batch reactor, the reagents are added together and allowed to react for a given amount of time. The compositions change with time, but there is no flow through the process. Additional reagents may be added as the reaction proceeds, and changes in temperature may also be made. Products are removed from the reactor after the reaction has proceeded to completion. Batch processes are suitable for small scale production and for processes where several different products or grades are to be produced in the same equipment. When production volumes are relatively small and the chemistry is relatively complex, batch processing provides an important means of quality control.

Plug Flow Reactor: A Plug Flow Reactor with tubular geometry has perfect radial mixing but no axial mixing. All materials have the same residence time, t, and experience the same temperature and concentration profiles along the reactor. It follows the first order. Equation of Plug Flow Reactor depends on Molar flow rate (dM), incremental voume (dV) and the rate of the reaction per unit volume (R) is given by:

dM = R*dV

Continuously Stirred Tank Reactor: The stirred tank reactor models a large scale conventional laboratory flask and can be considered to be the basic chemical reactor. In a CSTR, there is no spatial variation- the entire vessel contents are at the same temperature, pressure, and concentration. Therefore the fluid leaving the reactor is at the same temperature and concentration as the fluid inside the reactor.

2. Diameter of the pipe (d) = 3.0 ft

Radius of the pipe (r) = d/2 = 1.5 ft

Length of the pipe (l) = 3400 ft

Volume of the pipe = ( * r2 * l) = 3.14 * 1.52 * 3400 = 24021 ft3

3. Ozone reaction in water nearly follows first order kinetics in ozone concentration. Concentration decreases by 50 % in 12 minutes. C = C0 e-kt

k is the first order rate constant. C is the normal concentration and C0 is the initial concentration and t is the time.

k = (ln (C0/C)) / t = ln (C0/0.5 C0) / 12 = ln2/12 = 0.05776 /min.

4. Flow rate = 10000 gal/min = 1336.806 ft3/min

Time taken to reach the exit of the pipe = 24021/1336.806 = 17.9689 min = 17.97 min

ozone concentration at the exit of the pipe (C) = 1.0 mg/l

Initial concentration (C0) = C/e-kt = 1/e-(0.05776 * 17.97) = 1/ 0.3542 = 2.82 mg/l

Concentration of ozone that should be injected at the head of the pipe is 2.82 mg/l

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