Mixing behavior

Process engineering characteristics of reactors deal with the mixing conditions of the main reaction phase, the L phase. The degree of segregation (Danckwerts, 1958) can be used as an example. The two extreme conditions are referred to as maximal mixing, mm, and total segregation, ts (see Fig. 3.1). 

Consider a particular reactor space, for example a tube in which there is a flow of velocity in the direction z. The entering fluid stream is thought of as separate layers, and the fate of these layers is observed as they pass through the reactor space. In the case of mm, there is complete mixing of the layers over the cross section of the tube. In the case of ts, the layers leave the reactor unchanged. These extreme conditions are realizable in the reactor conformations shown in Fig. 3.1c (Zwietering, 1959). 

In practice, in the case of stirred reactors, the mixing time is used for characterizing mixing its experimental measurement is described in Sect. 3.3.2. That this one-dimensional quantity can represent the actual three-dimensional time course of mixing is due to the condition of mm, which occurs at the same rate in all three directions ( lumped parameters in a stirred vessel). The state of mixing in reactors with concentration profiles (tubular reactors or reactors with internal and external circulation) is experimentally more difficult to observe (Hartung and Hiby, 1973 Hiby, 1972). 

The same model of inhomogeneity has also been used to model conversion in various combinations of reactors (Tsai et al., 1969,1971 Wen and Fan, 1975 see Chap. 6). Finally, a systematic picture of the various types of bioreactors on the basis of the criteria discussed is shown in Fig. 3.3. Of course, in practice a strict classification is not possible since the intermediate states (especially with regard to micro and macromixing) are often dominant. 

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Bubble columns in series have been used to establish the same effective mix of plug-flow and back-mixing behavior required for Hquid-phase oxidation of cyclohexane, as obtained with staged reactors in series. WeU-mixed behavior has been established with both Hquid and air recycle. The choice of one bubble column reactor was motivated by the need to minimize sticky by-products that accumulated on the walls (93). Here, high air rate also increased conversion by eliminating reaction water from the reactor, thus illustrating that the choice of a reactor system need not always be based on compromise, and solutions to production and maintenance problems are complementary. Unlike the Hquid in most bubble columns, Hquid in this reactor was intentionally weU mixed. 

The RTD is a distinctive characteristic of mixing behavior. In Fig. 7-2>e, the CSTR has an RTD that varies as the negative exponential of the time and the PFR is represented by a vertical line at = 1. Multistage units and many packed beds have beU-shaped RTDs, like that of... 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

The tracer is completely conserved within the system and is identical to the process fluid in its flow and mixing behavior. 

Despite their popularity, these methods normally have an inherent limitation—the fluid dynamics information they generate is usually described in global parametric form. Such information conceals local turbulence and mixing behavior that can significantly affect vessel performance. And because the parameters of these models are necessarily obtained and fine-tuned from a given set of experimental data, the validity of the models tends to extend over only the range studied in that experimental program. 

Near room temperature most gases become less soluble in water as the temperature is raised. The lower solubility of gases in warm water is responsible for the tiny bubbles that appear when cool water from the faucet is left to stand in a warm room. The bubbles consist of air that dissolved when the water was cooler it comes out of solution as the temperature rises. In contrast, most ionic and molecular solids are more soluble in warm water than in cold (Fig. 8.22). We make use of this characteristic in the laboratory to dissolve a substance and to grow crystals by letting a saturated solution cool slowly. However, a few solids containing ions that are extensively hydrated in water, such as lithium carbonate, are less soluble at high temperatures than at low. A small number of compounds show a mixed behavior. For example, the solubility of sodium sulfate decahydrate increases up to 32°C but then decreases as the temperature is raised further. 

The effect of the mixing behavior on the rheological properties of styrene-butadiene mbber (SBR) compounds has been reported by Leblanc. ... 

So far, some researchers have analyzed particle fluidization behaviors in a RFB, however, they have not well studied yet, since particle fluidization behaviors are very complicated. In this study, fundamental particle fluidization behaviors of Geldart s group B particle in a RFB were numerically analyzed by using a Discrete Element Method (DEM)- Computational Fluid Dynamics (CFD) coupling model [3]. First of all, visualization of particle fluidization behaviors in a RFB was conducted. Relationship between bed pressure drop and gas velocity was also investigated by the numerical simulation. In addition, fluctuations of bed pressure drop and particle mixing behaviors of radial direction were numerically analyzed. 

A stirred-tank model has been proposed, (Daly, 1980), to model the mixing behavior of an air-solid, spouted, fluidised-bed reactor. The central spout is modelled as two tanks in series, the top fountain as a further tank and the down flowing annular region of the bed as 6 equal tanks in series. It is assumed that a constant fraction of the total solids returns from each stage of the annular region into the central two tank region, as depicted below. 

In this example, we have a stirred-tank with a volume Vj of 4 m3 being operated with an inlet flow rate Q of 0.02 m3/s and which contains an inert species at a concentration Cm of 1 gmol/m3. To test the mixing behavior, we purposely turn the knob which doses in the tracer and jack up its concentration to 6 gmol/m3 (without increasing the total flow rate) for a duration of 10 s. The effect is a rectangular pulse input (Fig. 2.7). 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Figure 2. Mixing behavior of the reactor cell gas phase response to a step increase in inlet CO concentration.

Ideal flow models contain inherent assumptions about mixing behavior. In BMF, it is assumed that all fluid elements interact and mix completely at both the macroscopic and microscopic levels. In PF, microscopic interactions occur completely in any plane perpendicular to the direction of flow, but not at all in the axial direction. Fluid elements at different axial positions retain their identities as they progress through the vessel, such that a fluid element at one axial position never interacts with a fluid element at another position. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

Reactors sometimes conform to some sort of ideal mixing behavior, or their performance may be simulated by appropriate combinations of ideal models. The commonest ideal elements are stated following, together with their tracer material balances. Initial values, boundary conditions and solutions of the equations depend on the kinds of inputs and are stated with individual solved problems. 

Figure 5.41 G-X diagram illustrating application of Darken s Quadratic Formalism to a binary join. Although mixing behavior of components 1 and 2 in phases a and ]8 is nonideal (heavy lines), in each of the simple regions it is modeled by an ideal mixing model (light lines) by means of an appropriate choice of the Active standard state potential /x. From Will and Powell (1992). Reprinted with permission of The Mineralogical Society of America.

The first term in parentheses on the right side of equation 5.213 is the distribution coefficient (K ), and the second groups activity coefficients related to the mixing behavior of components in the two phases. The equilibrium constant is thus related to the interaction parameters of the two phases at equilibrium. For example, the equilibrium between two regular mixtures is defined as... 

Stormer s (1975) model is based on the assumption that the potassic end-member has no influence on the mixing behavior of the plagioclase series and that the calcic component does not affect the mixing behavior of the K-feldspar series to any extent. With these assumptions, the problem of equilibrium between two ternary feldspars, normally represented by the equalities... 

We have already seen (section 6.5) that the mixing behavior of melt components with identical amounts of silica is essentially ideal. Ideal mixing implies that extensive properties of the melt, such as heat capacity at constant pressure Cp, is a linear function of the molar properties of the end-members—i.e.. 

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