Step-flow regime

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

The SHV flow regime has been studied systematically using the spin-echo and FLASH imaging sequences [39]. Figure 4.4.6 describes the steps for extracting... 

Especially for multiphase systems flow visualization (Wen-Jei Yang, 1989 Merzkirch, 1987) can provide valuable initial information on the prevailing flow patterns and should at least always be considered as a first step. Of course, in applications that involve extreme conditions such as high temperature and/or pressure it is very difficult if not impossible to apply flow visualization and other techniques should be considered. Here the use of cold flow models which permit visual observation might be considered as an alternative as an important first step to obtain (qualitative) information on the flow regime and associated flow pattern. Of course, multiphase flows exist such as dense gas-solid flows that do not permit visual observation and in such cases the application of idealized flow geometries should be considered. A well-known example in this respect is the application of so-called 2D gas fluidized beds to study gas bubble behavior (Rowe, 1971). 

The mass-transfer coefficient depends on the geometry of the solid surface, on the hydrodynamic conditions in the vicinity of the catalyst (which are a function, e.g., of the reactor type, geometry, operating conditions, flow regime), and it also depends on the dif-fusivity of the gas species. Correlations for the mass-transfer coefficient are a large topic and outside the scope of this section. For more details see Bird, Stewart, and Lightfoot, Transport Phenomena, 2d ed., John Wiley Sons, New York, 2002, and relevant sections in this handbook. For non-first-order kinetics a closed-form relationship such as the series of resistances cannot always be derived, but the steady-state assumption of the consecutive mass and reaction steps still applies. 

No simplification can be used for the problem of the backward facing penetrable step but the full Navier—Stokes equations. Therefore, no solution is available to validate the numerical algorithm. To be aware of it, the numerical algorithm shortly described in the previous section was tested over the whole range of the above-mentioned problems. In this case, the outlet boundary condition (3 = which is associated with the steady flow in an infinite duct, was used. The results of two numerical performances for the flow regime Re = 100 and EPR dimensions h = 0.3 and L x = 1, are shown in Fig. 3.16 the halves of flows in each case are symmetric. Let us analyze them. 

In the future, novel developments of liquid membranes for biochemical processes should arise. There are several opportunities in the area of fermentation or cell culture, for the in situ recovery of inhibitory products, for example. Another exciting research direction is the use of liquid membrane for enzyme encapsulation so that enzymatic reaction and separation can be combined in a single step. Chapter 6 by Simmons ial- (49) is devoted to this technique. The elucidation of fundamental mechanisms behind the liquid membrane stability is essential, and models should be developed for the leakage rate in various flow conditions. Such models will be useful to address the effect of parameters such as flow regime, agitation rate, and microdroplet volume... 

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