Dispersion parameters determination

Use the dispersion parameter determined in Illustration 11.2 to predict the conversion that will be attained in the reactor of Illustration... 

Use the dispersion parameter determined in Illustration 11.2 to predict the conversion that will be attained in the reactor of Illustration 11.1. Assume that the value of the first-order rate constant is 3.33 x 10" s . ... 

Where specialized fluctuation data are not available, estimates of horizontal spreading can be approximated from convential wind direction traces. A method suggested by Smith (2) and Singer and Smith (10) uses classificahon of the wind direction trace to determine the turbulence characteristics of the atmosphere, which are then used to infer the dispersion. Five turbulence classes are determined from inspection of the analog record of wind direction over a period of 1 h. These classes are defined in Table 19-1. The atmosphere is classified as A, B2, Bj, C, or D. At Brookhaven National Laboratory, where the system was devised, the most unstable category. A, occurs infrequently enough that insufficient information is available to estimate its dispersion parameters. For the other four classes, the equations, coefficients, and exponents for the dispersion parameters are given in Table 19-2, where the source to receptor distance x is in meters. 

Recalling that a separation is achieved by moving the solute bands apart in the column and, at the same time, constraining their dispersion so that they are eluted discretely, it follows that the resolution of a pair of solutes is not successfully accomplished by merely selective retention. In addition, the column must be carefully designed to minimize solute band dispersion. Selective retention will be determined by the interactive nature of the two phases, but band dispersion is determined by the physical properties of the column and the manner in which it is constructed. It is, therefore, necessary to identify those properties that influence peak width and how they are related to other properties of the chromatographic system. This aspect of chromatography theory will be discussed in detail in Part 2 of this book. At this time, the theoretical development will be limited to obtaining a measure of the peak width, so that eventually the width can then be related both theoretically and experimentally to the pertinent column parameters. 

They further determined the ratio of the dispersion reaetor volume to the plug flow reaetor volume required to aeeomplish the same degree of eonversion for several values of the dimensionless dispersion parameter /uL. Figure 8-39 shows the results of Equation 8-147... 

Equations 11.1.33 and 11.1.39 provide the basis for several methods of estimating dispersion parameters. Tracer experiments are used in the absence of chemical reactions to determine the dispersion parameter )L this value is then employed in a material balance for a reactive component to predict the reactor effluent composition. We will now indicate some methods that can be used to estimate the dispersion parameter from tracer measurements. 

In principle any of the equations 11.1.40, 11.1.44,11.1.45,11.1.47, or 11.1.48 could be used to determine the dispersion parameter. However, both equations 11.1.40 and 11.1.44 require that one accurately determine a small difference in large numbers to evaluate QjJuL. Hence equations 11.1.45 and 11.1.47 are preferred for evaluation of SiJuL for open and closed vessels, respectively. For small Q)JuL, equation 11.1.48 is appropriate. 

In addition to the aforementioned slope and variance methods for estimating the dispersion parameter, it is possible to use transfer functions in the analysis of residence time distribution curves. This approach reduces the error in the variance approach that arises from the tails of the concentration versus time curves. These tails contribute significantly to the variance and can be responsible for significant errors in the determination of Q)L. 

In addition to the three methods described above, nonlinear regression methods or other transform approaches may be used to determine the dispersion parameter. For a more complete treatment of the use of transform methods, consult the articles by Hopkins et al. (15) and Ostergaard and Michelsen (14). 

ILLUSTRATION 11.2 DETERMINATION OF REACTOR DISPERSION PARAMETER FROM EXPERIMENTAL RESIDENCE TIME DATA... 

The F(t) curve corresponding to this value of the reactor dispersion parameter may be determined using equation 11.1.33. 

In order to proceed from this point to a determination of the reactor dispersion parameter one must know something about the experimental setup. If we consider an open vessel, equation 11.1.45 indicates that... 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

Levenspiel and Smith Chem. Eng. Sci., 6 (227), 1957] have reported the data below for a residence time experiment involving a length of 2.85 cm diameter pyrex tubing. A volume of KMn04 solution that would fill 2.54 cm of the tube was rapidly injected into a water stream with a linear velocity of 35.7 cm/sec. A photoelectric cell 2.74 m downstream from the injection point is used to monitor the local KMn04 concentration. Use slope, variance, and maximum concentration approaches to determine the dispersion parameter. What is the mean residence time of the fluid ... 

The ideal situation would be a combined and simultaneous experiment in which an electrolyte/insulator/semiconductor device is used to monitor if>o while a colloid dispersion of the same oxide is titrated to measure parameter determination that could result from such an experiment would be the set as, Kno+ an[Pg.96]

However, we must keep in mind the limitations of this approach, especially the transfer of consistent sets of dispersion parameters to the propagation of air pollution in the vicinity of a source. The Gaussian plume formula should be used only for those downwind distances for which the empirical diffusion coefficients have been determined by standard diffusion experiments. Because we are interested in emissions near ground level and immissions nearby the source, we use those diffusion parameters which are based on the classification of Klug /12/ and Turner /13/. The parameters are expressible as power functions,... 

The results just obtained for < y) are, however, rarely used in applications because (v ) and T are generally not known. The Gaussian dispersion parameters aj and al are, in a sense, generalizations of (Cj) and particle displacement variances o-y and a-] are not calculated by Eq. (8.8). Rather, they are treated as empirical dispersion coefficients the functional forms of which are determined by matching the Gaussian solution to data. In that way, the empirically determined a-y and deviations from stationary, homogeneous conditions which are inherent in the assumed Gaussian distribution. 

For USPIO particles containing only one nanomagnet per particle, the main parameters determining the relaxivity are the crystal radius, the specific magnetization and the anisotropy energy. Indeed, the high field dispersion is determined by the translational correlation time t. ... 

We used the dielectric function e of bulk MgO calculated from oscillator parameters determined by Jasperse et al. (1966), together with the dielectric function em of the KBr matrix given by Stephens et al. (1953) (corrected by June, 1972), to calculate the absorption spectrum (12.37) of a dilute suspension of randomly oriented MgO cubes. These theoretical calculations are compared with measurements on well-dispersed MgO smoke in Fig. 12.16c. Superimposed on a more or less uniform background between about 400 and 700 cm-1, similar to the CDE spectrum, are two peaks near 500 and 530 cm- , the frequencies of the two strongest cube modes. It appears that for the first time these two modes have been resolved experimentally. If this is indeed so we conclude that the widths of individual cube modes are not much greater than the width of the dominant bulk absorption band. Genzel and Martin (1972)... 

Models for the dyeing of polyester fibers with disperse dyes have been developed [8], When the dye is applied from aqueous medium, it is adsorbed from the molecularly dispersed aqueous solution onto the fiber surface and then diffuses into the interior of the fiber. The following parameters determine the rate of dyeing and, to some extent, the leveling properties (1) the dissolution rate during the transition from the dispersed crystalline state of the dye into the molecularly dispersed phase, and (2) the diffusion rate at the fiber surface and, especially, in the interior of the fiber. The rates of both processes vary with temperature. 

Liquid-liquid mixing has been widely used in chemical industries. The state of dispersion is determined by the balance of the break-up and coalescence of droplets. In the case of liquid-liquid mixing, the breakup of the droplet is accelerated in the impeller region. Although the droplet size distribution in the operation has been expressed by various PSD functions, the PSD function that is utilized the most is the normal PSD function. However, there is no physical background to apply the normal PSD function to the droplet size distribution. Additionally, when the droplet size distribution is expressed by various PSD functions, it becomes difficult to discuss the relationship between the parameters in PSD and operation conditions. This is one of the obstacles for developing particle technology. 

---