Residence time factors

However, the laboratory data seem to indicate that a constant concentration in the reactor to maintain 63 percent sulfuric acid would be beneficial. Careful temperature control is also important. These two factors would suggest that a continuous well-mixed reactor is appropriate. There is a conflict. How can a well-defined residence time be maintained and simultaneously a constant concentration of sulfuric acid be maintained ... 

By contrast with ideal models, practical reactors must consider many factors other than variations in temperature, concentration, and residence time. Practical reactors deviate from the three idealized models but can be classified into a number of common types. 

The factors which govern the efficiency of waste destmction iaclude atomi2ation, ie, mean drop si2e, and si2e distribution temperature residence time O2 concentration and flow patterns. 

The classical experiment tracks the off-gas composition as a function of temperature at fixed residence time and oxidant level. Treating feed disappearance as first order, the pre-exponential factor and activation energy, E, in the Arrhenius expression (eq. 35) can be obtained. These studies tend to confirm large activation energies typical of the bond mpture mechanism assumed earlier. However, an accelerating effect of the oxidant is also evident in some results, so that the thermal mpture mechanism probably overestimates the time requirement by as much as several orders of magnitude (39). Measurements at several levels of oxidant concentration are useful for determining how important it is to maintain spatial uniformity of oxidant concentration in the incinerator. 

Factors Affecting Performance. There are many factors that affect both the choice of a particular thermal treatment and its performance. Chief among these are waste characteristics, temperature, residence time, mixing or turbulence, and air supply. 

More often than not the rate at which residual absorbed gas can be driven from the liqmd in a stripping tower is limited by the rate of a chemical reaction, in which case the liquid-phase residence time (and hence, the tower liquid holdup) becomes the most important design factor. Thus, many stripper-regenerators are designed on the basis of liquid holdup rather than on the basis of mass transfer rate. 

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

This method uses the separation factor given in the section titled Vapor Residence Time. The first three steps use equations and a graph (or alternate equation) in that section to get Kv and Uvapormax- Nomenclature is explained there. 

The intrinsic drawback of LIBS is a short duration (less than a few hundreds microseconds) and strongly non-stationary conditions of a laser plume. Much higher sensitivity has been realized by transport of the ablated material into secondary atomic reservoirs such as a microwave-induced plasma (MIP) or an inductively coupled plasma (ICP). Owing to the much longer residence time of ablated atoms and ions in a stationary MIP (typically several ms compared with at most a hundred microseconds in a laser plume) and because of additional excitation of the radiating upper levels in the low pressure plasma, the line intensities of atoms and ions are greatly enhanced. Because of these factors the DLs of LA-MIP have been improved by one to two orders of magnitude compared with LIBS. 

Chemical Factors. These involve mainly the kinetics of the reaction. The design must provide sufficient residence time for the desired reaction to proceed to the required degree of conversion. 

As with HjS, the distribution of sulfur among the other FCC products depends on several factors, which include feed, catalyst type, conversion, and operating conditions. Feed type and residence time are the most significant variables. Sulfur distribution in FCC products of several feedstocks is shown in Table 2-4. Figure 2-9 illustrates the sulfur distribution as a function of the unit conversion. 

Slip factor is defined as the ratio of catalyst residence time in the riser to the hydrocarbon vapor residence time. Some of the factors affecting the slip factor are circulation rate, riser diameter/geometry, and riser velocity. 

A high fractionator bottoms level, a low riser temperature, and a high residence time in the reactor dome/vapor line are additional operating factors that increase coke buildup. If the main column level rises above the vapor line inlet nozzle, donut shaped coke can form at the nozzle entrance. 

Slip Factor is the ratio of catalyst residence time to hydrocarbon vapors residence time in the riser. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

The results of Massimilla et al., 0stergaard, and Adlington and Thompson are in substantial agreement on the fact that gas-liquid fluidized beds are characterized by higher rates of bubble coalescence and, as a consequence, lower gas-liquid interfacial areas than those observed in equivalent gas-liquid systems with no solid particles present. This supports the observations of gas absorption rate by Massimilla et al. It may be assumed that the absorption rate depends upon the interfacial area, the gas residence-time, and a mass-transfer coefficient. The last of these factors is probably higher in a gas-liquid fluidized bed because the bubble Reynolds number is higher, but the interfacial area is lower and the gas residence-time is also lower, as will be further discussed in Section V,E,3. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

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