Distribution integral reactor

The total acidity deterioration and the acidity strength distribution of a catalyst prepared from a H-ZSM-5 zeolite has been studied in the MTG process carried out in catalytic chamber and in an isothermal fixed bed integral reactor. The acidity deterioration has been related to coke deposition. The evolution of the acidic structure and of coke deposition has been analysed in situ, by diffuse reflectance FTIR in a catalytic chamber. The effect of operating conditions (time on stream and temperature) on acidity deterioration, coke deposition and coke nature has been studied from experiments in a fixed integral reactor. The technique for studying acidity yields a reproducible measurement of total acidity and acidity strength distribution of the catalyst deactivated by coke. The NH3 adsorption-desorption is measured by combination of scanning differential calorimetry and the FTIR analysis of the products desorbed. 

Several interesting features of the above simple relationships are noteworthy. If an inert liquid phase is introduced into an all-gas-phase differential reactor, keeping the inlet gas-phase composition constant, the reaction rate would, in general, be distributed between gas and liquid phases thus reducing the overall effective concentration of the reactant. In the limiting case, if the feed liquid is saturated with the reactant, the reaction rate will be unaffected by the introduction of liquid, ln an integral reactor, the overall reaction rate (as a space time yield) would increase if the feed liquid is saturated with the reactant. The conversion is always decreased by the introduction of liquid because of the contribution of the term QL(rG/Bi5L) in the denominator of Eq. (4-19). 

Fig. 17 (a-e) Kinetic evaluation from the plug flow reactor distributions. Integration of the peak areas led to a total monomer consumptirai, i.e., an average polymerization rate, but determined at very short reaction times. See text for description of figure parts... 

In the study of dynamics, the integral reactor can be divided into two types — isothermal and adiabatic reactor. Because isothermal integral reactor is simple and cheap as well as the lower demand on the accuracy on analysis, it is always the preferred option. In order to overcome its difficulties to maintain the temperature uniform, there are several actions. The first one is to reduce the diameter to obtain uniform radial temperature as much as possible. When the inner diameter of reactor is 4-6 times bigger than the particle size of catalyst, the effect of reducing the diameter of tube on the distribution of temperature still is the main factor. The second is to use various mediums with high thermal conductivity, to provide heating indirectly through the whole piece of metal or sand bath, which is commonly used presently. The third is to dilute the catalyst bed with inert materials. 

The adiabatic integral reactor has the characteristics of uniform diameter, filling with homogeneous catalyst, and good insulation. The feeds preheated to a certain temperature infiood into the reactor, and measure axially the reaction heat and the corresponding temperature distribution of kinetic law. However, the data acquisition and mathematic explanation are difficult for the reactors. 

In Chapter 7 the effects of transport phenomena on the scale of the reactor are considered. We call these macro flow effects. These can be described in terms of macro-mixing. For continuous reactors macro>mixing causes residence time distribution. Combined with micro-mixing this will lead to backmixing. When two or more phases are present in the reactor, the way these are each introduced into and removed from the reactor are quite essential for the performance of the reactor. These various effects are considered in this chapter in order to arrive at an integral reactor model. As in Chapter 3, only isothermal reactor models are considered so far. 

Fig. 8 Laboratory integral reactor for the experimental determination of packing parameters (top left distribution of thermocouples, bottom left detail of probe crossection, right whole reactor...

Ho wever, certain advantages and disadvantages result from the different concentration and temperature distribution in both reactors. Because of the uniformi concentration and temperature inside the loop reactor, the concentration of the reactants could be measured only in the reactor inlet and outlet to determine the reaction rate. The steep concentration and temperature gradients inside the integral reactor require measurements at many spots along the tube. This becomes rather expensive in time if several components are to be analyzed as in the oxidation of xylene. 

Incipient fluidization. See Fluidization Interfacial heat and mass transport, 106 Integral reactor, 72 Internal age distribution, 423 Internal (intraphase) transport resistance, 106... 

Residence Time Distributions in Fiow Reactors 711 Integrating Equation 8-73 gives... 

For all likely operating conditions, (ie., for t < X), the appropriate values of the concentration and the polymerization rate constant are the values calculated at t = t ( 2). To prove this, the exit age distribution function for a backmix reactor was used to weight the functions for Cg and kj and the product was integrated over all exit ages (6). It is enlightening at this point to compare equation 18 with one that describes the yield attainable in a typical laboratory semibatch reactor at comparable conditions. ... 

Solution The numerical integration techniques require some care. The inlet to the reactor is usually assumed to have a flat viscosity profile and a parabolic velocity distribution. We would like the numerical integration to reproduce the paraboUc distribution exactly when q, is constant. Otherwise, there will be an initial, fictitious change in at the first axial increment. Define... 

Impulse Response and the Differential Distribution. Suppose a small amount of tracer is instantaneously injected at time 1 = 0 into the inlet of a reactor. All the tracer molecules enter together but leave at varying times. The tracer concentration at the outlet is measured and integrated with respect to time. The integral will be finite and proportional to the total quantity of tracer that was injected. The concentration measurement at the reactor outlet is normalized by this integral to obtain the impulse response function. ... 

The stagnant region can be detected if the mean residence time is known independently, i.e., from Equation (1.41). Suppose we know that f=lh for this reactor and that we truncate the integration of Equation (15.13) after 5h. If the tank were well mixed (i.e., if W t) had an exponential distribution), the integration of Equation (15.13) out to 5f would give an observed t of... 

Material flowing at a position less than r has a residence time less than t because the velocity will be higher closer to the centerline. Thus, F(r) = F t) gives the fraction of material leaving the reactor with a residence time less that t where Equation (15.31) relates to r to t. F i) satisfies the definition. Equation (15.3), of a cumulative distribution function. Integrate Equation (15.30) to get F r). Then solve Equation (15.31) for r and substitute the result to replace r with t. When the velocity profile is parabolic, the equations become... 

As described above, microchannel reactor scale-up requires integrated models, which include the reaction chemistry with heat transfer, pressure drop, flow distribution, and manufacturing tolerances. The culmination of scale-up models is their successful demonstration. 

The regression for integral kinetic analysis is generally non-linear. Differential equations may include unobservable variables, which may produce some additional problems. For instance, heterogeneous catalytic models include concentrations of species inside particles, while these are not measured. The concentration distributions, however, can affect the overall performance of the catalyst/reactor. 

There is a variety of ways in choosing r (5, 40-44). If r is set equal to t, i.e. the birth time of the polymer particles in the reactor vessel, then n(r,t) becomes n(t,t) and (n(t,t)dt) represents number of particles in the reactor at some time t which were born during the infinitesimal time interval dt. Integration of (n(t,t)dt) over the time period t will give the total number of particles in the reactor at time t. Since the particle phase space is now the t-axis, the analysis becomes an age or residence time distribution analysis, and equation (II-3) simplifies to ... 

The convenience of Eq. (6) is realizable only in the rather unrealistic situation where the charge distribution exhibits cylindrical or spherical symmetry. For storage silos, blenders, fluidized bed reactors, and other real vessel geometries, integral solutions are usually not possible, necessitating an alternate problem formulation. Poisson s equation serves this need, relating the volume charge distribution to the electrostatic potential. 

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