Instantaneous dispersion models

The dispersion model is typically used to determine the downwind concentrations of released materials and the total area affected. Two models are available the plume and the puff. The plume describes continuous releases the puff describes instantaneous releases. 

AFTOX is a Gaussian dispersion model that is used by the Air Force to calculate tu accidental releases. Limited to non-dense gases, it calculates the evaporation rate from liquid spills. It treats instantaneous or continuous releases from any elevatic ... 

If it is assumed that the equilibrium between the two phases is instantaneous and, at the same time, that axial dispersion is negligible, the column efficiency is infinite. This set of assumptions defines the ideal model of chromatography, which was first described by Wicke [3] and Wilson [4], then abundantly studied [5-7,32-39] and solved in a number of cases [7,33,36,40,41]. In Section 2.2.2, which deals with the equilibrium-dispersive model, it is shown how small deviations from equilibrium can be handled while retaining the simplicity of Eq. 2.4 and of the ideal model. 

The Pasquill - Gifford model PUFF is suited for dispersion modeling in instantaneous outflow conditions. It is a dispersion model with normal (Gauss) distribution of concentrations and Lagrange approach, which consists in gas element move monitoring in wind field. The gas cloud spreads in the wind direction. At first the cloud grows and the gas concentration sinks. Later the cloud volume decreases, because more and more gas disperses in insignificant concentrations outside the cloud. 

Two types of dispersion models are used to describe these releases when the puff or plumes are neutrally or positively buoyant. When there is an instantaneous release or a burst of material, we make use of a puff model. In this model the puff disperses in the downwind, cross wind, and vertical directions simultaneously. Computer codes written for puff models usually have the capability of tracking multiple puff releases over a period of time. When the release rate is constant with time, the puff model can be mathematically integrated into a continuous model. In this case, dispersion takes place in the cross wind and vertical directions only. The mathematical expressions are those discussed in Section III. The dispersion coefflcients used, however, may differ from those described in Section IV. Plume rise equations from Section V for positively buoyant plumes may be used in conjunction with these dispersion models. The equations of current models indicate that they are well formulated, but the application of the models suffers from poor meteorological irrformation and from poorly defined source conditions that accompany accidental releases. Thus, performance of these models is not adequate to justify their use as the sole basis for emergency response planning, for example. 

Instantaneous versus time-average dispersion models... 

The Gaussian dispersion model has several strengths. The methodology is well defined and well validated. It is suitable for manual calculation, is readily computerized on a personal computer, or is available as standard software packages. Its main weaknesses are that it does not accurately simulate dense gas discharges, validation is limited from 0.1 to 10 km, and puff models are less well estabUshed than plume models. The predictions relate to 10 min averages (equivalent to 10 min sampling times). While this may be adequate for most emissions of chronic toxicity, it can underestimate distances to the lower flammable limit where instantaneous concentrations are of interest. More discussion will follow. 

In RANS-based simulations, the focus is on the average fluid flow as the complete spectrum of turbulent eddies is modeled and remains unresolved. When nevertheless the turbulent motion of the particles is of interest, this can only be estimated by invoking a stochastic tracking method mimicking the instantaneous turbulent velocity fluctuations. Various particle dispersion models are available, such as discrete random walk models (among which the eddy lifetime or eddy interaction model) and continuous random walk models usually based on the Langevin equation (see, e.g.. Decker and... 

PasquiU Atmo.spheric Diffusion, Van Nostrand, 1962) recast Eq, (26-60) in terms of the dispersion coefficients and developed a number of useful solutions based on either continuous (plume) or instantaneous (puff) releases, Gifford Nuclear Safety, vol, 2, no, 4, 1961, p, 47) developed a set of correlations for the dispersion coefficients based on available data (see Table 26-29 and Figs, 26-54 to 26-57), The resulting model has become known as the Pasquill-Gifford model. 

The Britter and McQiiaid model was developed by performing a dimensional analysis and correlating existing data on dense cloud dispersion. The model is best suited for instantaneous or continuous ground-level area or volume source releases of dense gases. Atmospheric stability was found to have little effect on the results and is not a part of the model. Most of the data came from dispersion tests in remote, rural areas, on mostly flat terrain. Thus, the results would not be apphcable to urban areas or highly mountainous areas. 

This model was later expanded upon by Lifshitz [33], who cast the problem of dispersive forces in terms of the generation of an electromagnetic wave by an instantaneous dipole in one material being absorbed by a neighboring material. In effect, Lifshitz gave the theory of van der Waals interactions an atomic basis. A detailed description of the Lifshitz model is given by Krupp [34]. 

EMGRESP is overly conservative for passive gas dispersion applications. No time-varying releases may be modeled. Dense gas dispersion may be computed for only "instantaneous" releases conditions. 

This brief discussion of some of the many effects and interrelations involved in changing only one of the operating variables points up quite clearly the reasons why no exact analysis of the dispersion of gases in a liquid phase has been possible. However, some of the interrelationships can be estimated by using mathematical models for example, the effects of bubble-size distribution, gas holdup, and contact times on the instantaneous and average mass-transfer fluxes have recently been reported elsewhere (G5, G9). 

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