Dispersion parameter

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

The Sherwood number, Sh, is estimated from Table 16-9, and the dispersion parameters Yi and Jo ffom Table 16-10 for well-packed columns. Typical values are a 1-4 and b 0.5-1. Since HETP -2HTU, Fig. 16-13 can also be used for approximate calculations. 

The concentration x resulting at a receptor at x, y, z) from a point source located at (0, 0, H) is given by one of the three following equations. (Methods for obtaining values for the dispersion parameters (Xy and cr, in the following equations are discussed later in this chapter.)... 

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. 

Pasquill s dispersion parameters were restated in terms of a-y and Cj by Gifford (14, 15) to allow their use in the Gaussian plume equations. The... 

As an example of the use of the Gaussian plume equations using the Pasquill-Gifford dispersion parameters, assume that a source releases 0.37 g s of a pollutant at an effective height of 40 m into the atmosphere with the wind blowing at 2 m s . What is the approximate distance of the maximum concentration, and what is the concentration at this point if the atmosphere is appropriately represented by Pasquill stability class B ... 

Urban Dispersion Parameters by Briggs (for Distances between 100 and 10000 m)... 

Methods of estimating gaseous effluent concentrations have undergone many revisions. For a number of years, estimates of concentrations were calculated from the equations of Sutton, with the atmospheric dispersion parameters C, C, and n, or from the equations of Bosanquet with the dispersion parameters p and Q. More common approaches are based on experimental observation that the vertical distribution of spreading particles from an elevated point is... 

O2 = vertical dispersion parameter (m) Z, = receptor height above ground (m)... 

Plume height is based on the assumed F stability and 2.5 m/s wind speed, and the dispersion parameter (o, ) incorporates the effects of buoyancy induced dispersion. If x , is less than 200 m, then no shoreline fumigation calculation is made, since the plume may still be influenced by transitional rise and its interaction with the TIBL is more difficult to model. 

Three commonly used dispersion calculation methods for the prediction of ground level concentrations are based on the above expression. The variance in each method is the calculation of plume rise, Ah, and the horizontal and vertical plume dispersion parameters. These methods are ... 

The ASME plume rise equations and the ASME dispersion parameters. 

The Pasquill-Gifford dispersion parameters and Brigg s plume rise equations. 

The ASME Dispersion Parameters. The horizonal and vertical dispersion parameters are represented by the following empirical power law equation... 

The Pasquill-Gifford dispersion parameters are functions of downwind distance and meteorological conditions. The parameters, and Oy may be obtained from Figure 6(a) and 6(b) respectively. The user must know the atmospheric stabihty as well as downwind distance from the somce to select the appropriate dispersion 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... 

Here q is tlie source strengtli per unit distance (e.g., g/s-in). Note tliat tlie horizontal dispersion parameter Oy does not appear in tliis equation, since it is assumed tliat lateral dispersion from one segment of the line is compensated by dispersion in tlie opposite direction from adjacent segments. Also, y does not appear, since tlie concentration at a given x is tlie same for any value of y. Concentrations from infinite line sources, when tlie wind is not perpendicular to Uie line, can also be approximated. If tlie angle between the wind direction and line source is (f), we may write... 

TABLE 12.7.1 Estimation of Dispersion Parameters for Quasi Instantaneous Sources... 

Quality, magnitude, and duraUon of the release Dispersion parameters -Wind speed -Wind direction -Weather stability... 

Three ranges of values of n were considered, >1, 0.7—1.0 and <0.7. When n> 1, and particularly when 3 < n < 4, the Weibull distribution readily reduces to a normal distribution if the Erofe ev function is symmetrical about a = 0.5. [The Weibull distribution is symmetrical for n = 3.26, i.e. (1 — In 2)-1, and the inflection point varies only slowly with n.] Thus, under these conditions (3 < n < 4 and symmetry about a = 0.5), we may derive the parameters of the corresponding normal distribution (where p defines the half-life of the reaction and the dispersion parameter, a, is a measure of the lack of homogeneity of the surface centres), viz. 

FIGURE 6.9 Dependence of viscoelastic parameters on solvent quality. The (A) static force, (B) drag coefficient at 10 kHz, (C) dynamic spring constant, and (D) dispersion parameter are shown as a function of the surface-sphere distance. The results for water, propanol, and a 50/50 water/propanol mixture are given. Reprinted with permission from Benmouna and Johannsmann (2004). 

Dispersion parameter for the distribution of measured values, sy, or analytical results, sx, for a given sample or the population, oy and ox. The SD is the square root of the variance. 

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. 

For small values of the dispersion parameter one may take advantage of the fact that equation 11.1.37 takes the shape of a normal error curve. This implies that for a step function input a plot of (C — Cq)/(Cq — Co) or F(t)... 

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