Residence time coefficient

Traditionally, distribution kinetics has been described in terms of volume of distribution parameters (V and K,s) and structure-specific distribution parameters, e.g., the k 2, 21 parameters of the two-compartment model. LSA offers a less-structured alternative that considers the net effect of the distribution kinetics based on the disposition decomposition analysis. For example, the partition/distribution properties of a drag may be expressed in terms of the affinity of the drag molecules to a kinetic space expressed as the MRT in the kinetic space. Accordingly, it is meaningful to consider ratios of MRTs for two kinetic spaces as a metric for the relative affinity. Thus, residence time coefficients (RTC) similar to a partition coefficient may be defined Residence Time Coefficient The residence time coefficient RTC for the distribution of a drug in two kinetic spaces is the ratio of the MRT of the drug in the two kinetic spaces. It is readily shown thaC ... 

Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

The dispersion coefficient is orders of magnitude larger than the molecular diffusion coefficient. Some rough correlations of the Peclet number are proposed by Wen (in Petho and Noble, eds.. Residence Time Distribution Theory in Chemical Tngineeiing, Verlag Chemie, 1982), including some for flmdized beds. Those for axial dispersion are ... 

Both reactors used 38.1 mm 0 tubes. The commercial reactor was 12 m long while the length of the laboratory reactor was 1.2 m. Except for the 10 1 difference in the lengths, everything else was the same. Both reactors were simulated at 100 atm operation and at GHSV of 10,000 h-1. This means that residence times were identical, and linear gas velocities were 10 times less in the lab than at the production unit. Consequently the Re number, and all that is a function of it, were different. Heat transfer coefficients were 631 and 206 in wattsWK units for the large and small reactors. 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

Some processes have large heat transfer requirements. This may result in large inventories of material within the heat transfer equipment. If the material is thermally unstable it would be inherently safer to reduce the residence time in the heat exchanger. Options to minimize heat exchanger inventory include the use of different types of heat exchangers. Inventories in shell and tube heat exchangers can be reduced by the use of turbulators in the tubes to enhance heat transfer coefficients, and by placing the more hazardous material on the tube side. 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

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). 

When the gas velocities are increased, both the Reynolds number and the Nusselt number would increase, while the ratio Nu/Re decreases with (Re) to the —0.4 to —0.6 power. An increase in gas velocities would improve on the heat and mass transfer coefficients from gas to wall, but would also increase the fraction of heat that is not given up to the wall and the fraction of benzene that never goes near the wall due to the reduction in residence time. 

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 results reported for beds of small particles (1 mm diameter and less) are in substantial agreement on the fact that the presence of solid particles tends to decrease the gas holdup and, as a consequence, the gas residencetime. This fact may also support the observations of gas absorption rate by Massimilla et al. (Section V,E,1) if it is assumed that a decrease of absorption rate caused by a decrease of residence time outweighs the increase of absorption rate caused by increase of mass-transfer coefficient arising from the increase in bubble Reynolds number. These results on gas holdup are in... 

This result can be useful for design purposes when the diffusivities, partition coefficients, feed-stream conditions, dispersed-system volume, gas-phase holdup (or average residence time), and the size distribution are known. When the size distribution is not known, but the Sauter-mean radius of the population is known, (293) can be approximated by... 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

The main limitation of HEX reactors is the short residence time, typically from a few seconds to a few minutes. Indeed, the apparatuses are smaller than the traditional ones and fast flow velocities are necessary in order to maintain good level of heat-transfer coefficients. However, as described in the previous paragraph, the highlighted transfer properties of HEX reactors allow us to operate in a few minutes, whereas it takes many hours in batch or semibatch mode. 

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

OS 63] ]R 27] ]P 46] Experimental results were compared with a kinetic model taking into account liquid/liquid mass transfer resistance [117]. Calculated and experimental conversions were plotted versus residence time the corresponding dependence of the mass-transfer coefficient k,a is also given as well (Figure 4.78). 

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