Mixing residence time space

Figure 5.21 Geometric interpretation of mixing in residence time space. Mixtures also lie on a straight line when residence time is used since residence time also obeys a linear mixing law.

Other variations in the different zones of cascade reactors, which have not been reported, include residence time (space velocity), acid/hydrocarbon ratio, and character of the dispersions. The decreases in RON for alkylates in the latter zones are also partly due to degradation reactions. It has been shown (16,17) that TMPs degrade in the presence of sulfuric acid. It has also been indicated (14) that both the quality and quantity of allgrlates are reduced by such degradations the quality was estimated to reduce by perhaps 0.11 RON in cascade units. In Stratco units, the decrease was perhaps 0.07 RON this lower value is because of lower residence times. Degradation reactions of TMPs are also thought to be more pronounced in cascade reactors because of increased amounts of mixing of TMPs with olefins. 

There are a number of commercial operations where the objecl is to make useful produces with solid reactions. Design and practice, however, do not appear to rely generally on sophisticated kinetics, and they are rarely divulged completely. The desirable information is about temperatures, configuration, quahty of mixing, and residence times or space velocities. Most of the information about current practice of reaclions of solids is proprietary. Some of the sparse published data can... 

Little or no maintenance requirements Small space requirements Available m many construction materials No power requirements other than pumping Mixing achieved m short conduit lengths Minimal chance of material hangup or plugging Short residence times NaiTow residence time distribution Enhanced heat transfer Cost effective... 

Consider the flow mixing through three identical ideal CSTRs in series. Each tank has a space time, r, or mean residence time, Mj, of 2 min. An idealised impulse of tracer is made in the inlet to the first tank what tracer response will be observed from the third tank ... 

Let us illustrate the use of this method by considering three mixed flow reactors in series with volumes, feed rates, concentrations, space-times (equal to residence times because e = 0), and volumetric flow rates as shown in Fig. 6.7. Now from Eq. 5.11, noting that e = 0, we may write for component A in the first reactor... 

We take the heat transfer coefficient a to be independent of the jet velocity and of the residence time in the vessel. Physically, this assumption together with the assumption of complete mixing of the substance in the reaction vessel and of a constant mean temperature throughout the vessel corresponds to the idea that for heat transfer the governing factor is the thermal resistance from the internal wall of the vessel to the outside space in which the temperature is kept at T0. In other words, our assumption corresponds to the concept of a vessel which is thermally insulated from outside. 

Figure 5- Models, a, general case. Fluid flows from left to right at constant velocity and is transferred from the E.E. (unshaded tubes, Min. Mix.) to the L.E. (shaded area, Max. Mix.). In the s(, a) space, a particle having a given residence time tg describes a trajectory between the plane a = 0 and the plane X = 0 b, a model of Spencer et stl. (68). Each particle stays in the E.E. for a duration proportional to its residence time c,r p model of Spencer et al. (68), which is also the series model of Weinstein and Adler (69) Each particle stays for a constant time in the E.E., provided tg> d, parallel model of Weinstein and Adler...

Based on the above relation, for most practical operations, this reactor behaves much hke the plug-flow reactor, where ReF = pdtL/pOT, ReM = pdiNjp. Here, 0T is the average residence time. The relationship between power consumption and mixing time reveals the similarity of this vessel to the double helical-ribbon mixer. The fraction of dead space in this apparatus appears to be small. The relationships described above are valid for the fluids in the viscosity range of 50-5000 poises. 

The extent of gas dispersion can usually be computed from experimentally measured gas residence time distribution. The dual probe detection method followed by least square regression of data in the time domain is effective in eliminating error introduced from the usual pulse technique which could not produce an ideal Delta function input (Wu, 1988). By this method, tracer is injected at a point in the fast bed, and tracer concentration is monitored downstream of the injection point by two sampling probes spaced a given distance apart, which are connected to two individual thermal conductivity cells. The response signal produced by the first probe is taken as the input to the second probe. The difference between the concentration-versus-time curves is used to describe gas mixing. 

The age of a fluid element is defined as the time it has resided within the reactor. The concept of a fluid element being a small volume relative to the size of the reactor yet sufficiently large to exhibit continuous properties such as density and concentration was first put forth by Danckwerts in 1953. Consider the following experiment a tracer (could be a particular chemical or radioactive species) is injected into a reactor, and the outlet stream is monitored as a function of time. The results of these experiments for an ideal PFR and CSTR are illustrated in Figure 8.2.1. If an impulse is injected into a PFR, an impulse will appear in the outlet because there is no fluid mixing. The pulse will appear at a time ti = to + t, where t is the space time (r = V/v). However, with the CSTR, the pulse emerges as an exponential decay in tracer concentration, since there is an exponential distribution in residence times [see Equation (3.3.11)]. For all nonideal reactors, the results must lie between these two limiting cases. 

The space velocity in cocurrent upflow, e.g., in the froth reactor, can be controlled within large areas by the pumping rate. There is an upper velocity limit for formation of small bubbles in the glass frit, and the very high back-mixing in the monolith indicates that draining of the monolith down to the inlet area can be a problem at low velocities. The residence-time distribution in the monolith froth reactor has been studied by Patrick et al. [36] and Thulasidas et al. [37]. 

In addition, no mixing was predicted in the solution, so cold-shot cooling was not used at all. However, this decision is directly influenced by the ratio of the raw material to energy costs. For small ratios, even if mixing is not optimal in concentration space, the energy costs may drive the use of cold shots in order to reduce utility consumption. Within the constraints on the residence time... 

---