Residence Time of Particles and its Distribution

Any process takes a certain amount of time and the length of the residence time often dictates the occasions when particular equipment or technology can be used. On the other hand, in almost all chemical unit processes the driving forces vary from time to time, and therefore time has the nature of non-equivalence, i.e., an equal time interval yields different, even greatly different, results for the early and later stages of a process. The result mentioned here means the processing amount accomplished, such as the increments of reaction conversion, absorption efficiency, moisture removal etc. Normally, these parameters vary as parabolic curves with time. Because of the nature of the non-equivalence of time, in addition to the mean residence time, the residence time distribution (RTD) affects the performance of equipment, and thus receives common attention. 

In nature, residence time distribution is an important behavior of particle crowds because of its complexity, it will be subject of focus in this chapter. 

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Baskaran and Santschi (1993) examined " Th from six shallow Texas estuaries. They found dissolved residence times ranged from 0.08 to 4.9 days and the total residence time ranged from 0.9 and 7.8 days. They found the Th dissolved and total water column residence times were much shorter in the summer. This was attributed to the more energetic particle resuspension rates during the summer sampling. They also observed an inverse relation between distribution coefficients and particle concentrations, implying that kinetic factors control Th distribution. Baskaran et al. (1993) and Baskaran and Santschi (2002) showed that the residence time of colloidal and particulate " Th residence time in the coastal waters are considerably lower (1.4 days) than those in the surface waters in the shelf and open ocean (9.1 days) of the Western Arctic Ocean (Baskaran et al. 2003). Based on the mass concentrations of colloidal and particulate matter, it was concluded that only a small portion of the colloidal " Th actively participates in Arctic Th cycling (Baskaran et al. 2003). 

The combustion process of wet wood chips and formation of pollutants in a biomass furnace have been investigated. Distributions of species CO, UHC, O2 where calculated numerically and compared to experimental data. It is shown that char, as flying particle, though in small amount has a significant influence on the CO emissions at the outlet. Numerical simulation indicates that half of the CO emission at the outlet is due to the combustion of flying char particles at the upper part of the furnace. Over-fire air staging has a significant influence on the residence time of panicles and gas species in the furnace, and thus the conversion of fuel and intermediate species to final products. 

Figure 2.1.6 shows the results of such a continuous synthesis process. It shows the variation of the mean particle size during the experiment. The error bars indicate the standard deviation of the particle size distribution of each sample based on the transmission electron micrographs (number distribution). The experiment was performed under the following conditions (A) ammonia, water, and TEOS concentrations were 0.8, 8.0, and 0.2 mol dm-3 7", = 273 K, T2 = 313 K total flow rate was 2.8 cm3 min-1 100 m reaction tube of 3 mm diameter residence time 4 h and (B) ammonia, water, and TEOS concentrations were 1.5,8.0, and 0.2 mol dm- 3 Tx = 273 K, T2 = 313 K total flow rate was 8 cm3 min-1 50 m reaction tube of 6 mm diameter, residence time 3 h. Further details and other examples are described elsewhere (38). Unger et al. (50) also described a slightly modified continuous reaction setup in another publication. 

After an iPP particle reached the FBR, co-polymerization of ethylene-propylene starts preferrably inside the porous PP matrix. Depending on the individual residence time, the particle will be filled with a certain amount of ethylene-propylene rubber, EPR, that improves the impact properties of the HIPP. It is important to keep the sticky EPR inside the preformed iPP matrix to avoid particle agglomeration that could lead to wall sheeting and termination of the reactor operation. Ideally a "two phase" structure, see Fig.5.4-3, is produced. Finally, a "super-high impact" PP results that contains up to 70% EPR. How much EPR is formed per particle depends on three factors catalyst activity in the FBR, individual particle porosity, and individual particle residence time in the FBR. All particle properties are therefore influenced by the residence time distribution, and finally, a mix of particles with different relative amounts of EPR is produced - a so called "chemical distribution" see, for example, [6]. 

Because of the importance of the residence time distribution in the impingement zone, the basic requirement when designing the experimental equipment is that it should be suitable for understanding the residence time and its distribution of particles in the impingement zone. For this purpose, the rest of the equipment should be as simple as possible. From the point of view of residence time distribution, this means shortening the residence times in the spaces other than the impingement zone as much as possible. 

Theoretical analysis gives some useful information on the characteristics of residence time and its distribution of particles although experimental evidence is always important. 

Only solid particles residence time and its distribution are discussed in the present chapter although, because of the similarities of movements of the dispersed phases in impinging streams, the results described above are also of referential significance for gas-liquid impinging streams. The differences between the properties of liquids and solids and their influences will be discussed in detail in the relevant chapters. 

In the previous chapters, the materials in the dispersed phases of impinging streams discussed are essentially solid particles, although a few aspects of liquid as dispersed phase were mentioned. Since liquids and solids have densities of the same order of magnitude, quite different from those of gases, the analysis and conclusions described in those chapters, including enhancing transfer between phases, the motion of particles, the residence time and its distribution, and the hydraulic resistance and the related problems, etc., are, in principle, also applicable for the occasions where, instead of solid, liquid is in the dispersed phase without significant deviation. 

Equation (4Ib) is valid when there are no polymer particles flowing into the reactor with all the particles nucleated within the reactor. It is assumed that density changes can be neglected and that particles follow the streamlines. These are reasonable assumptions in view of the small size of particles and the small density difference between particle and water. When two or more CSTRs are employed in series, however, one must remember that the total residence time of a polymer particle is made up of different times in each reactor in the train. The relative amounts of time spent in each reactor will not matter when the volumetric growth rate of a particle is the same in each. This would require that the temperature, monomer concentration, and average number of radicals per particle he the same for each reactor, an unlikely possibility. This idealization is useful, however, when illustrating the effect of increasing the number of CSTRs in series on the breadth of the particle size distribution. 

Physical interferences may arise from incomplete volatilization and occur especially in the case of strongly reducing flames. In steel analysis, the depression of the Cr and Mo signals as a result of an excess of Fe is well known. It can be reduced by adding NH4C1. Further interferences are related to nebulization effects and arise from the influence of the concentration of acids and salts on the viscosity, the density and the surface tension of the analyte solutions. Changes in physical properties from one sample solution to another influence the aerosol formation efficiencies and the aerosol droplet size distribution, as discussed earlier. However, related changes of the nebulizer gas flows also influence the residence time of the particles in the flame. 

Studies of the atmospheric input of chemicals to the open ocean have also been increasing lately. For many substances a relatively small fraction of the material delivered to estuaries and the coastal zone by rivers and streams makes its way through the near shore environment to open ocean regions. Most of this material is lost via flocculation and sedimentation to the sediments as it passes from the freshwater environment to open sea water. Since aerosol particles in the size range of a few micrometers or less have atmospheric residence times of one to several days, depending upon their size distribution and local precipitation patterns, and most substances of interest in the gas phase have similar or even longer atmospheric residence times, there is ample opportunity... 

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