Macrofluid

Micromixing Mixing among molecules of different ages (i.e., mixing between macrofluid clumps). Mixing on a scale smaller tlian tlie minimum eddy size or minimum striation diickness by molecular diffusion. 

Segregration The tendency of the contents of a reactor to behave as a macrofluid. 

Segregrated flow model The fluid in a flow reactor is assumed to behave as a macrofluid. Each clump functions as a miniature batch reactor. Mixing of molecules of different ages occurs as late as possible. 

Equation 9-15 gives the conversion expression for the second order reaction of a macrofluid in a mixed flow. An exponential integral, ei(a), which is a function of a, and its value can be found from tables of integrals. However, the conversion from Equation 9-15 is different from that of a perfectly mixed reactor without reference to RTD. An earlier analysis in Chapter 5 gives... 

Flowing material is in some particular state of aggregation, depending on its nature. In the extremes these states can be called microfluids and macrofluids, as sketched in Fig. 11.2. 

Two-Phase Systems. A stream of solids always behaves as a macrofluid, but for gas reacting with liquid, either phase can be a macro- or microfluid depending on the contacting scheme being used. The sketches of Fig. 11.3 show completely opposite behavior. We treat these two phase reactors in later chapters. 

For macrofluids, imagine little clumps of fluid staying for different lengths of time in the reactor (given by the E function). Each clump reacts away as a little... 

These are terms to be introduced into the performance equation, Eq. 13. Also, further on in this chapter we will show that for first-order reactions, the macrofluid equation is identical to the batch or to the microfluid equation. 

For the real reactor the fraction unconverted, given by Eq. 13 for macrofluids, is found in Table El 1.4. Hence the fraction of reactant unconverted in the real reactor... 

Note that since this is a first-order reaction we can treat it as a microfluid, or a macrofluid, whatever we wish. In this problem we solved the plug flow case as a microfluid, and we solved the nonideal case as a macrofluid. ... 

A liquid macrofluid reacts according to A -> R as it flows through a vessel. Find the conversion of A for the flow patterns of Figs. PI 1.7 to PI 1.11 and kinetics as shown. 

These equations apply to both micro- and macrofluids. 

There is rare use for macrofluid equations for homogeneous reactions. However, if you do need them combine Eq. 11.3 with Eq. 3 for N tanks in series, to give... 

In the pure convection regime (negligible molecular diffusion) each element of fluid follows its own streamline with no intermixing with neighboring elements. In essence this gives macrofluid behavior. From Chapter 11 the conversion expression is then... 

The normally accepted state of a liquid or gas is that of a microfluid, and all previous discussions on homogeneous reactions have been based on the assumption. Let us now consider a single reacting macrofluid being processed in turn in batch, plug flow, and mixed flow reactors, and let us see how this state of aggregation can result in behavior different from that of a microfluid. 

Batch Reactor. Let the batch reactor be filled with a macrofluid containing reactant A. Since each aggregate or packet of macrofluid acts as its own little batch reactor, conversion is the same in all aggregates and is in fact identical to what would be obtained with a microfluid. Thus for batch operations the degree of segregation does not affect conversion or product distribution. 

Figure 16.1 Difference in behavior of microfluids and macrofluids in mixed flow reactors.

Mixed Flow Reactor-Macrofluid. When a macrofluid enters a mixed flow reactor, the reactant concentration in an aggregate does not drop immediately to a low value but decreases in the same way as it would in a batch reactor. Thus a molecule in a macrofluid does not lose its identity, its past history is not unknown, and its age can be estimated by examining its neighboring molecules. 

The performance equation for a macrofluid in a mixed flow reactor is given by Eq. 11.13 as... 

This is the general equation for determining conversion of macrofluids in mixed flow reactors, and it may be solved once the kinetics of the reaction is given. Consider various reaction orders. 

This is the conversion expression for second-order reaction of a macrofluid in a mixed flow reactor. The integral, represented by ei(a) is called an exponential integral. It is a function alone of a, and its value is tabulated in a number of tables of integrals. Table 16.1 presents a very abbreviated set of values for both ei(jc) and Ei(jc). We will refer to this table later in the book. 

Insertion into Eq. 4 gives the conversion for an nth-order reaction of a macrofluid. 

Figure 16.2 illustrates the difference in performance of macrofluids and microfluids in mixed flow reactors, and they show clearly that a rise in segregation improves reactor performance for reaction orders greater than unity but lowers performance for reaction orders smaller than unity. Table 16.2 was used in preparing these charts. 

Idealized Pulse RTD. Reflection shows that the only pattern of flow consistent with this RTD is one with no intermixing of fluid of different ages, hence, that of plug flow. Consequently it is immaterial whether we have a micro- or macrofluid. In addition the question of early or late mixing of fluid is of no concern since there is no mixing of fluid of different ages. 

Figure 16.2 Comparison of performance of mixed flow reactors treating micro- and macrofluids for zero- and second-order reactions with 8 = 0.

Table 16.2 Conversion Equations for Macrofluids and Microfluids with 8 = 0 in Ideal Reactors...

Figure E16.1 a) Microfluid, early mixing at molecular level b) Microfluid, fairly late mixing at molecular level (c) Microfluid, late mixing at molecular level d) Macrofluid, early mixing of elements (e) Macrofluid, late mixing of elements.

The results of this example confirm the statements made above that macrofluids and late mixing microfluids give higher conversions than early mixing microfluids for reaction orders greater than unity. The difference is small here because the conversion levels are low however, this difference becomes more important as conversion approaches unity. 

The concept of micro- and macrofluids is of particular importance in heterogeneous systems because one of the two phases of such systems usually approximates a macrofluid. For example, the solid phase of fluid-solid systems can be treated exactly as a macrofluid because each particle of solid is a distinct aggregate of molecules. For such systems, then, Eq. 2 with the appropriate kinetic expression is the starting point for design. 

In the chapters to follow we apply these concepts of micro- and macrofluids to heterogeneous systems of various kinds. 

To help understand what occurs, imagine that we have A and B available, each first as a microfluid, and then as a macrofluid. In one beaker mix micro A with micro B, and in another beaker mix macro A with macro B and let them react. What do we find Micro A and B behave in the expected manner, and reaction occurs. However, on mixing the macrofluids no reaction takes place because molecules of A cannot contact molecules of B. These two situations are illustrated in Fig. 16.4. So much for the treatment of the two extremes in behavior. 

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