Completely mixed reactor

An anaerobic digester is a no-recycle complete mix reactor. Thus, its performance is independent of organic loading but is controlled by hydraulic retention time (HRT). Based on kinetic theoiy and values of the pseudo constants for methane bac teria, a minimum HRT of 3 to 4 days is required. To provide a safety factor and compensate for load variation as indicated earlier, HRT is kept in the range 10 to 30 days. Thickening of feed sludge is used to reduce the tank volume required... 

Deactivating catalytic reaction with Langmuir-Hinshelwood kinetics in a completely mixed reactor. 

Substitute for the partial pressures in the rate equation in terms of x. For the plug flow case, values of 1/r are tabulated over a range of x at the three temperatures, as well as some values of the integrals. Some values of Wc/F0 also are shown for the mixed cases. Note that at high conversions, the completely mixed reactor is much larger than the plug flow. 

SMITH, M.P.W. and EVANS, M.R. (1982). The effects of low dissolved oxygen tension during the aerobic treatment of piggery slurry in completely mixed reactors. J. appl. Bact. 53,117-126... 

Thus far we have considered only two flow patterns the completely mixed reactor and the completely unmixed reactor. This is because only for these flow patterns can we completely ignore the fluid flow configurations in the reactor. In this chapter we will begin to see how reactors that have more complex flow patterns should be treated. We will not attempt to describe the fluid mechanics completely. Rather, we will hint at how one would go about solving more realistic chemical reactor problems and examine the errors we have been making by using the completely mixed and unmixed approximations. 

Human exposure limits through air exposure are to be applied at a plant that manufactures Heptachlor, C10H5CI7. Heptachlor is a chemical that is currently restricted in use to termite control, because of exposure concerns. These limits are given in ppm(v), but the release to the air is determined in g/s. Applying the volume flow with the current ventilation system and the volume of the plant in a complete mix reactor assumption resulted in a vapor phase concentration of 0.1 M-g/m. What is the vapor phase concentration in ppm(v) ... 

Complete Mix Reactor - The complete mix reactor is also labeled a completely stirred tank reactor. It is a container that has an inhnite diffusion coefficient, such that any chemical that enters the reactor is immediately mixed in with the solvent. In Example 2.8, we used the complete mix reactor assumption to estimate the concentration of three atmospheric pollutants that resulted from an oil spill. We will use a complete mix reactor (in this chapter) to simulate the development of high salt content in dead-end lakes. A series of complete mix reactors may be placed in series to simulate the overall mixing of a one-dimensional system, such as a river. In fact, most computational transport models are a series of complete mix reactors. 

Dead Zones - Dead zones in a complete mix reactor do not participate in the mixing process. They effectively reduce the reactor size, with no exchange between the dead zone and the reactor. An example might be a wetland at the edge of... 

Table 6.1 Systems that are most often simulated by complete mix reactors, plug flow reactors, etc.

Complete mix reactors Plug flow or complete mix reactors in series... 

The various systems that are modeled by complete mix reactors and plug flow reactors are given in Table 6.1. 

A complete mix reactor is one with a high level of turbulence, such that the fluid is immediately and completely mixed into the reactor. The outflow concentration and the reactor concentration are equal, and the diffusion term is zero due to the gradient being zero. Figure 6.1 shows an illustration of the concept. If we make the entire reactor into our control volume, then a mass balance on the reactor gives Rate of = Flux rate - Flux rate - - Source — sink... 

If the inflow and outflow are zero, our complete mix reactor becomes a batch reactor, as utilized in Example 6.1 to relate half-life to a first-order rate constant. 

A complete mix reactor can also be used to simulate a larger water body when the process under consideration has a larger time scale than the mixing processes in the lake, as the next example demonstrates. 

The Great Salt Lake can be considered as a complete mix reactor for this problem. This is a valid assumption because the time scale of the salinity changes that lead to a salty lake is on the order of tens of thousands of years. 

The current conditions regarding residence time and evaporation rate apply to the past. With no reaction utilizing sodium in the lake, the mass transport equation for the complete mixed reactor is... 

An estuary or river will not be completely mixed, but will have some mixing that goes with the convective transport velocity. Complete mix reactors-in-series respond to a first-order reaction in the manner given in Example 6.5. 

In the next example, we will compare a complete mixed reactor with a first-order degradation reaction at steady state for a plug flow reactor and a series of smaller complete mixed reactors. 

EXAMPLE 6.6 Degradation in various systems modeled by one complete mixed reactor, one plug flow reactor, and several complete mixed reactors-in-series... 

The compound formaldehyde is biodegrading in several systems simultaneously (1) a lake, modeled as a complete mix reactor (2) an estuary, modeled as three complete mixed reactors in series (3) a large river, modeled as 10 complete mixed reactors in series, and a small stream, modeled as a plug flow reactor. What is the nondimensional reaction/residence time, k p, that is required for each of these systems to reach a degradation of 50%, 90%, 99%, and 99.9% ... 

Table E6.6.1 tells us two things that are important to understanding these reactors. First, it takes significantly more residence time to achieve a given level of degradation in a complete mixed reactor than in a plug flow reactor. This is because the mixed reactor is continually mixing in compound that is not degraded, similar to a lake or reservoir. The plug flow reactor has no mixing of fresh compound...

The response of a single complete mix reactor to a pulse or front input is essential to our analysis. A pulse would be a Dirac delta in concentration, whereas a front would be a sharp step at a given time to a different concentration. Let us first develop the outflow equation for a front input, illustrated in Figure 6.3, with boundary conditions ... 

Figure 6.3. Response of a single complete mix reactor to a front in concentration.

For a single complete mix reactor, we found that there is little difference in the nondimensional response to a front versus a pulse. This will not be the case for a series of complete mix reactors. Let us assume that we have four complete mix reactors in series, each with a volume Yi and a residence time, tn, as illustrated in Figure 6.5. Then, for a pulse input, we have the boundary conditions ... 

The concept of a leaky dead zone is illustrated in Figure 6.9. A complete mix reactor is connected to a leaky dead zone through the inflow and outflow discharges to and from the dead zone, Qd. The dead zone is, in itself, a complete mix reactor, but it is not part of the main flow system with discharge Q. The independent parameters that can be ht to a tracer pulse or front are the volume of the primary complete mix reactor, Vi, the volume of the dead zone, Vd, and the discharge into and out of the dead zone, Qd. 

Figure 6.9. Illustration of a complete mix reactor with a leaky dead zone.

A reactor modeled as a complete mix reactor with a leaky dead zone will have a concentration front from Q =0to Q = Co applied. Develop an equation for the concentration in the outflow of the reactor. 

Figure E6.8.2. Solution of a complete mix reactor with a leaky dead zone to a step-down concentration front applied at f = 0 with ty = 1.2 hrs and h = 1 hr.

Boundary condition 1 occurs because the pulse is instantaneously mixed only into the primary reactor in the model. Boundary condition 2 indicates that, as the dead zone disappears, the reactor becomes a standard complete mix reactor. Applying boundary condition 1 gives... 

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