Completely segregated fluids

Calculate the mean conversion in the reactor we have characterized by RTD measurements in Examples 13-1 and 13-2 for a first-order, liquid-phase, irreversible reaction in a completely segregated fluid ... 

Complete segregation any fluid element is isolated from all other fluid elements and retains its identity throughout the entire vessel. No micromixing occurs, but macromixing may occur. 

The segregated-flow reactor model (SFM) represents the micromixing condition of complete segregation (no mixing) of fluid elements. As noted in Section 19.2, this is one extreme model of micromixing, the maximum-mixedness model being the other. 

For particles of glass ballotini with free falling velocities of 10 and 20 mm/s the index n has a value of 2.39. If a mixture of equal volumes of the two particles is fluidised, what is the relation between the voidage and fluid velocity if it is assumed that complete segregation is obtained ... 

In a mixing process where complete segregation occurs, the fraction of fluid elements with residence times (t, t + dt) is E(t)dt, and the average exit composition in the vessel is defined by ... 

Since the fluid flows in clumps and is completely segregated by age (i.e., each clump behaves like a batch reactor), it is possible to determine the reactant concentration in every clump for a constant density fluid as ... 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

In a reactor with a segregated fluid, mixing between particles of fluid does not occur until the fluid leaves the reactor. The reactor exit is, of course, the latest possible point that mixing can occur, and any effect of mixing is postponed until after all reaction has taken place. We can also think of completely segregated flow as being in a state of minimiun mixedness. We now want to consider the other extreme, that of maximum mixedness consistent with a given residence-time distribution. 

Conversion if fluid is completely segregated. Tlhe batch reactor equation for a second-order reaction of this type is... 

The calculations for this integration are carried out in Table E13-7.2. The numerical integration uses the simple hapezoid rule. The conversion for this system if the fluid were completely segregated is 0.61 or 61%. 

If the reaction is not first-order, the RTD can be used to place bounds on the conversion using concepts associated.with micromixing. One bound is obtained treating the reactor fluid as if it were completely segregated the other bound results from considering the fluid as being in a state of maximum mixedness. 

In the case of complete segregation, the volume dv of an element of fluid with age between a and a + da is... 

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