Residence time distribution INDEX

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

In industrial reactors, the full equilibration of the chain length distribution is prevented by incomplete mixing, as well as by the residence time distribution, thus resulting in considerable deviations from the equilibrium polydispersity index. These deviations are generally higher for continuous plants than for batch plants and increase with increasing plant capacity as demonstrated in Figure 2.2. 

Since the dimensionless time for a first-order reaction is the product of the reaction time t and a first-order rate constant k, there is no reason why k(x)t should not be interpreted as k(x)t(x), that is, the reaction time may be distributed over the index space as well as the rate constant. Alternatively, with two indices k might be distributed over one and t over the other as k x)t(y). We can thus consider a continuum of reactions in a reactor with specified residence time distribution and this is entirely equivalent to the single reaction with the apparent kinetics of the continuum under the segregation hypothesis of residence time distribution theory, a topic that is in the elementary texts. Three indices would be required to distribute the reaction time with a doubly-distributed continuous mixture. 

Figure 6.50 presents the cumulative residence time distribution for a tube with a Newtonian model and for a shear thinning fluid with power law indices of 0.5 and 0.1. Plug flow, which represents the worst mixing scenario, is also presented in the graph. A Bingham fluid, with a power law index of 0, would result in plug flow. 

The notion of an effectiveness factor introduced by Thiele, Amundson s exploitation of the phase plane (34), Gavalas use of the index theorem (41), the Steiner symmetrization principle used by Amundson and Luss (42) and the latter s exploitation of the formula for Gaussian quadrature (43)—perhaps the prettiest connection ever made in the chemical engineering literature—are theoretical counterparts, large and small, of the careful craft of the experimentalist. So perhaps also the very important insight that Danckwerts contributed in his formulation of the residence time distribution is a happy foil to his heroic ambition to trace a blast furnace (44). 

Continuous Stirred Tank Reactors. Biesenberger (8) solved for the MWD with condensation polymerization in a CSTR, analogous to the treatment Denbigh (14) provided for the other two mechanisms. In this case, the variable residence time distribution leads to an extremely broad MWD with even the maximum weight fraction at the lowest molecular weight (monomer). The dispersion index approaches infinity as the condensation is driven to completion in a stirred tank reactor. A sequential analytical solution of the algebraic equations was obtained with a numerical evaluation of the consecutive equations. 

Finally, we consider a preliminary approach for the optimal synthesis of reactor-separation systems. Here, we formulate a combined reaction-separation model by postulating a species-dependent residence time distribution. The optimization of this distribution function leads to a separation profile as a function of time along the reactor. The costs for maintaining a separation profile are handled through a separation index, which models the intensity of separation,... 

Polymerizations as part of liquid-phase organic reactions are also influenced by mass and heat transfer and residence time distribuhon [37, 48]. This was first shown with largely heat-releasing radical polymerizations such as for butyl acrylate (evident already at dilute concentration) [49]. Here, a clear influence of microreactor operation on the polydispersity index was determined. Issues of mass transfer and residence time distribution in particular come into play when the soluhon becomes much more viscous during the reachon. Polymerizahons change viscosities by orders of magnitude when carried out at high concentration or even in the bulk. The heat released is then even more of an issue, since tremendous hot spots may arise locally and lead to thermal runaway, known in polymer science as the Norrish-Tromsdorff effect. 

Figure 7.158 Residence time distribution curves for several power law index values...

Keywords peroxide, molar weight distribution (MWD), rheology, crystallization, extrusion, melt flow index (MFI), controlled rheology (CR), peroxide-degradation, residence time distribution (RTD), halflifetime of peroxides, melt elasticity, die swell, viscosity curve, shear rate, elongational viscosity, melt fracture, heterophasic PR... 

In the case of free radical polymerization (figure 13.2) the dispersion index D at low degrees of conversion appears to be 1.5. In a batch or plug flow reactor D increases as the degree of conversion goes up. The reason is that the propagationrinitiation ratio decreases as the monomer is consumed. For a segregated CSTR the effect is enhanced by the residence time distribution. For a well mixed CSTR D remains constant and low. This is explained by the fact that all polymer molecules are made under identical conditions. 

FIGURE 8.30 Cumulative residence time distribution function versus reduced time in an extender for fluids with various values of the power-law index and compared to values for plug flow and complete back-mixing continnons stirred tank reactor (Bigg and Middlemann, 1974). 

The rotational temperature obtained from a linear relation in the Boltzmann plot of the rotational energy distribution is an index of the lifetime in the intermediate excited state and decreases with decreasing lifetime. The rotational temperature of CO desorbed from Pt(l 1 1) is very low as compared with that of NO desorption, i.e. the lifetime of the excited CO is supposed to be much shorter than that of NO. In the case of CO desorption from Pt(l 11), however, the lifetime is not obtained from the rotational energy distribution, since desorbed molecules are detected by the (2 + 1 )REMPI method in the experiment [ 12] and then the single rotational states are not resolved. On the other hand, the rotational temperature of NO desorbed from Pt(l 1 1)-Ge surface alloy is lower than that from Pt(l 1 1). Then, it is speculated that the lifetime of the excited CO on the alloy is shorter than that on Pt( 111) and the residence time of the excited CO on the alloy is too short to be desorbed. As a consequence, the excited CO molecules are recaptured in the relaxation without desorption. However, it has not been understood why the lifetime of the excited CO molecule (or the excited CO-Pt complex) on Pt( 1 1 1) is shorter than that of the excited NO molecule (complex) on Pt(l 11), and further on the Pt-Ge alloy as compared with Pt(l 1 1). 

Kilkson (35) also treated stepwise addition in a CSTR, using Z-transforms and calculating the moments of the distribution. The dispersion index was shown to increase from the lower limit of 1 for a batch reactor at high conversions, and to approach 2 in the CSTR at high residence time. 

Judgment of steady state. The judgment of the time needed for the response to reach the steady state is generally referred to settling time 65, which is necessary in order to evaluate the required time for start-up operation. Attainment of the steady state was determined from the convergence of the < tal size distribution. This was done by the use of the performance index (e) which is defined as the change in the mass based crystal size distrunition in every 1 residence time. 

Company Reaction Phase Reactor Solvent Residence Time (h) Molecular Weight Distribution Isotactic Index (%)... 

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