Overall residence time distribution

In the impinging stream contactor shown in Fig. 3.1 the particles pass through the four sub-spaccs in series described above, and the overall residence time distribution... 

This is the model for the overall residence time distribution of the particles in the impinging stream contactor under consideration. The model contains several parameters related to equipment structure and operating conditions, i.e. the mean residence times in the four sub-spaces, 7ac, 7im, 7fai and cs. Among the four parameters, the mean residence time in the impingement zone, t m, and that in the collision-slipping region, fcs, are symmetrical parameters, which have the same influence on the overall residence time distribution. It can be seen from Eq. (3.27) or... 

It is noted that the right-hand side of Eq. (10.20) is just the series expansion of an exponential function. Therefore the overall residence time distribution probability density function in the SCISR is obtained to be... 

The influence of channels, i.e. flow-guiding internal structures, also accounts for the overall residence time distribution in the square. This will be demonstrated by the observation of particles emitted at the structure inlet. The path of such an... 

The residence time of such a well is again best visible at the exit. The parabolic profile this time is much wider than for the structured case. The maximum relative deviation amounts to 233%, which is 6.5 times larger than for the structured well. This is important because it demonstrates that micro structures are indeed a means to obtain a narrow overall residence time distribution. The error introduced by manufacturing tolerances (estimated 5 pm absolute tolerance in a 320 pm wide channel) is 1.6% in width, a value which does not influence this evaluation. 

Tmeit (a.k.a. product or exit temperature) Overall residence time distribution (RTD, a.k.a. exit age distribution = E(t)) Standard release tests (e.g., assay, content uniformity, dissolution profile, d rada-tion products)... 

The combination of reac tor elements is facihtated by the concept of transfer functions. By this means the Laplace transform can be found for the overall model, and the residence time distribution can be found after inversion. Finally, the chemical conversion in the model can be developed with the segregation and maximum mixed models. 

The term macromixing refers to the overall mixing performance in a reactor. It is usually described by the residence time distribution (RTD). Originally introduced by Danckwerts (1958), this concept is based on a macroscopic lumped population balance. A fluid element is followed from the time at which it enters the reactor (Lagrangian viewpoint - observer moves with the fluid). The probability that the fluid element will leave the reactor after a residence time t is expressed as the RTD function. This function characterises the scale of mixedness in a reactor. 

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. 

The Level II calculations at pH 5.1 include the reaction half-lives of 550 h in air, 550 h in water, 1700 h in soil and 5500 h in sediment. No reaction is included for suspended sediment or fish. The steady-state input of 1000 kg/h results in an overall fugacity of 3.43 x 1(H Pa, which is about 24 times the Level I value. The concentrations and amounts in each medium are thus about 24 times the Level I values. The relative mass distribution is identical to Level I. The primary loss mechanism is reaction in soil, which accounts for 936 kg/h, or 94% of the input. Most of the remainder is lost by reaction and advection in water. The air and sediment loss processes are unimportant largely because so little of the PCP is present in these media. The overall residence time is 2373 h thus, there is an inventory of PCP in the system of 2373 x 1000 or 2,373,000 kg. 

Evaluate the conversion for first-order reaction from a tracer pulse response curve using the method in example CSTRPULSE. Show that although the residence time distributions may be the same in the two cases, the overall chemical conversion is not, excepting for the case of first-order reaction. 

In a commercial unit, catalyst is added continuously resulting in an age distribution of the catalyst in the unit. Therefore, the overall ZSM-5 activity is a distribution of the ZSM-5 activities and is related to their relative ages. To calculate the average ZSM-5 activity, the residence time distribution and rate expression are integrated over time. The steady state example is given in the following equation ... 

Figure 6.52 compares the cumulative residence time distributions of a perfect mixer to Poiseuille flow. Disregarding the fact that the stirring tank s output starts at t = 0, we can see that the overall shape of the curve with the prefect mixer is much broader, pointing to a more homogeneous output, or simply, a better mixer. 

The computed residence time distribution of the Sy elements is closely approximated by a delta distribution, and that is what is assumed here. Further, the reactant mole ratio in the Sy elements is taken to be the same as in the overall feed. 

Aside from the requirement of a sharp residence time distribution, the ideal fixed-bed reactor should also allow all parts of the catalyst bed to fully participate in the overall conversion, i.e., all catalyst particles must be contacted by the reactant fluid. With a single fluid phase, this condition is generally met when the plug flow criterion is obeyed since in this case there is a uniform flow through the bed. However, in two... 

In conventional fixed-bed reactors, catalyst particles of various sizes are often randomly distributed, which may lead to inhomogeneous flow patterns. Near the reactor walls, the packing density is lower than the mean value, and faster flow of the fluid near the wall is unavoidable. As a result, reactants may bypass the catalyst particles, and the residence time distribution (RTD) will be broadened. Moreover, the nonuniform access of reactants to the catalytic surface diminishes the overall reactor performance and can lead to unexpected hot spots and even to reactor runaway in the case of exothermic reactions. 

Problem. Think about the overall strategy that must be implemented to account for the effect of interpellet axial dispersion on ihe outlet concentration of reactant A when Langmuir-Hinshelwood kinetics and Hougen-Watson models are operative in a packed catalytic tubular reactor. Residence-time distribution effects are important at small mass transfer Peclet numbers. 

This relation is identical to that obtained for the first reactor configuration. This illnstration provides an example of the general principle that for irreversible first-order reactions carried out isothermally, all reactor combinations having the same residence-time distribution function lead to the same overall conversion. 

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