Primer on dispersion modelling
When a material (e.g. a pollutant or chemical) is released to the atmosphere – there are two main physical processes that govern its transport/movement away from the source:
- Advection (bulk movement of the material)
- Spreading (due to diffusion/dispersion driven by atmospheric turbulence and mixing). Spreading can also occur due to gravity (for heavy/dense clouds)
Advection typically occurs alongwind (i.e. in the x or release direction to reflect the momentum vector) as this is momentum driven. Dispersion/diffusion occurs in the alongwind (x), crosswind (y) and vertical directions (z).
With regards to directions, the following applies (see Figure 1):
Figure 1: Plume showing conformity to Gaussian/normal profile (click to enlarge)
- Downwind (along wind) – along the x direction. Along wind refers to motion in the +/- direction that the wind is blowing.
Diffusion in this axis is called “Along wind diffusion” or AWD. - Crosswind – along the y direction. Cross wind refers to motion in the direction at right angles.
- Vertical – along the z direction.
Figure 2. Example of Gaussian or “normal” distribution (click to enlarge)
Cloud dispersion profiles (in the far field) have been observed to conform to a normal (i.e. gaussian profile). Imagine releases from stacks (see figure 1). Sigma x, y and z (σx, σy, σz) respectively represent the standard deviation of the distribution from the centreline concentration (the mean of the distribution) and are known as dispersion coefficients. See Figure 2.
Release types and lack of along wind diffussion
Broadly speaking, release types can be categorised as follows:
- Continuous releases (steady state or unsteady state i.e. time varying)
- Puff releases (i.e. instantaneous/catastrophic)
- Short duration releases
For continuous steady state releases, diffusion in the x direction is typically far less than the amount of advection; hence, often ignored. This is a reasonable assumption and the lack of AWD for this type of release is not significant. In Phast, the calculations for continuous releases assume that the duration is sufficient for the release to reach a steady state in which air is entrained only through the sides of the cloud, and entrainment in front of and behind the cloud can be neglected. In other words, advection forces in the x direction are strong and will dominate.
For puff (i.e. instantaneous releases), dispersion occurs in all directions. The effects of AWD are inherently accounted for.
However, for short duration releases the impact of AWD can be significant, particularly because advection forces in the along wind direction are weak.
Similar issues arise for time varying releases, including (especially volatile) rainout cases.
Key consequences associated with the lack of AWD are:
- Stable conditions can produce clouds too short and too wide
- Far-field concentrations can be very significantly over-estimated
Along wind diffusion (AWD) modeling capability coming to Phast/Safeti Version 8
We have established that dispersion in the AWD direction (or the lack of it) can be important, particularly for short duration releases . Therefore, short duration releases require special treatment.
In the current versions of Phast, approaches to handle this are limited. We have “Quasi-Instantaneous transition (QI)” and “Finite Duration Correction (FDC)”. Whilst these go some way to addressing the problem, they still offer a limited solution. More details on these approaches can be found in the Phast product documentation supplied with the program.
The upshot is that for short releases which do not reach a steady state, the modelling must be modified/updated to address this current limitation.
An updated version of the dispersion model in Phast/Safeti (called the “Unified Dispersion Model (UDM)” that accounts for the effects of AWD has been developed and will be available from version 8 onwards. This is called UDM Version 3. Current versions of Phast/Safeti (7.x) include version 2 of the UDM.
UDM 3 with AWD includes the following key features:
- Additional modelling which simulates the effect of clouds spreading in the along-wind direction, reducing maximum concentrations and elongating clouds. This includes spreading by both atmospheric turbulence and dense cloud gravity spreading. Gravity Spreading is a phenomenon whereby heavy clouds can also spread in the along-wind direction due to the ‘slumping’. The process is analogous to atmospheric mixing, but a different mechanism. It also only applies to the near-field rather than far-field. Only crosswind spreading modelled in Phast 7.x.
Figure 3: Illustration of gravity spreading mechanism associated with heavy clouds (click to enlarge)
In addition, the following benefits will be offered:
Figure 4: Illustration of time varying dispersion footprint – with and without AWD (click to enlarge)
- Improving the way the dispersing cloud interacts with evaporating pools, and improvements to the pool model
- Getting rid of the concept of continuous segments and permitting a more natural description of time-varying clouds. Plots of the cloud will show single continuous lines rather than clusters of segments.
- An improved model for the early stages of pressurized instantaneous releases (catastrophic ruptures)
The inclusion of Along-wind diffusion capability will be a revolution in the way dispersion calculations are performed and presented in Phast/Safeti.
It will provide more accurate results for far-field, short duration or time-varying releases including those which rain out – generally reducing concentrations and extended passage time. More generally the presentation of such clouds in the graphs will appear more realistic, doing away with multiple discrete segments and the more implausibly shaped clouds we see now.
The new model has undergone extensive verification and validation that involved comparison of the results versus other analytical solutions and large scale experiments with very good results.
This will be major benefit to users of Phast/Safeti and will help to provide more realistic and accurate results. Some specific benefits of UDM 3 in Phast/Safeti are:
- In general reduced concentrations in the medium and far field
- Reduced toxic effects where N values > 1
- More realistic near-field and far-field dispersion
- Mitigation of the ‘too short, too wide’ cloud problem
- Better modelling of time-varying releases
- Releases represented as continuous clouds rather than a collection of individual segments. (See Figure 4)
Phast/Safeti 8.0 is anticipated for release towards the end of 2017. Exciting times ahead!
Authors: Kenny Shaba and Colin Hickey