Neutrally Buoyant Dispersion Models

Neutrally buoyant dispersion models are used to estimate the concentrations downwind of a release in which the gas is mixed with fresh air to the point that the resulting mixture is neutrally buoyant. Thus these models apply to gases at low concentrations, typically in the parts per million range. 

Two types of neutrally buoyant vapor cloud dispersion models are commonly used the plume and the puff models. The plume model describes the steady-state concentration of material released from a continuous source. The puff model describes the temporal concentration of material from a single release of a fixed amount of material. The distinction between the two... 

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. 

The EPA lookup tables for dense gases are based on the SLAB dense gas model, developed by Lawrence Livermore National Laboratories (as of 1998). The EPA lookup tables for neutrally buoyant gases are based on a Gaussian model using Beals dispersion coefficients (documentation in U.S. Air Force, 1971). The facility may use other appropriate models such as ALOHA instead of the EPA lookup tables. 

The concentrations predicted by several popular gas dispersion models at the same distances downwind are presented in Table 17.3. The popular gas dispersion models selected were (1) neutrally buoyant Gaussian dispersion, (2) dense gas model SLAB, and (3) ALOHA version 5.2. When the model called for a concentration-averaging time, a one-minute average... 

The well-known Gaussian models describe the behavior of neutrally buoyant gas released in the wind direction at the wind speed. Dense gas releases will mix and be diluted with fresh air as the gas travels downwind and eventually behave as a neutrally buoyant cloud. Thus, neutrally buoyant models approximate the behavior of any vapor cloud at some distance downwind from its release. Neutrally or positively buoyant plumes and puffs have been studied for many years using Gaussian models. These studies have included especially the dispersion modeling of power station emissions and other air contaminants used for air pollution studies. Gaussian plumes are discussed in more detail in Section 2.3.1. 

Figure 5-19 shows an example of the dispersion of a chemical tracer in a stirred tank. A standard pitched blade turbine is used to mix two waterlike materials. The neutrally buoyant tracer is injected at time zero as a blob above the impeller, as shown on the top left in the figure. The flow field is calculated using the sliding mesh and LES models, and the dispersion of the tracer is derived from the flow field. The blob is stretched and the chemical is mixed with the rest of the fluid over time. It is interesting to see that despite the fact that there are four impeller blades and four baffles, the concentration field is not symmetric because of the off-axis injection. The consequence is that the full tank needs to be modeled instead of a 90° section. Bakker and Fasano (1993b) presented a successful comparison between blend time predicted by CFD and calculated from experimental correlations. 

All models possess empirical features and can be of questionable reliability under some release conditions. The Gaussian models are simple and valid for releases of neutrally or positively buoyant materials in a uniform flow field with no downwind obstacles. The box models represent a macroscopic approach to heavy-gas dispersion. 

Purpose. Neutral and positively buoyant plume or puff models are used to predict average concentration and time profiles of flammable or toxic materials downwind of a source based on the concept of Gaussian dispersion. Plumes refer to continuous emissions, and puffs to emissions that are short in duration compared with the travel time (time for cloud to reach location of interest) or sampling (or averaging) time (normally 10 min). 

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