Model Prediction of the Proximity Effect

To predict the proximity effect, I have applied the "Markov I" stochastic model of Nicas (2001) to characterize the dispersion of air pollution from a "puff" release in a room that has dimensions of 10.7 x 7 x 2.6 meters (L x W x H). The model treats the dispersion of emitted particles as a Markov Chain process, where each particle moves by a series of "random walks" due to turbulent diffusion. The value for the turbulent diffusion coefficient, D, was set at 0.04 m2/sec.

In applying the model, I used 6 receptor positions located 0.5, 1, 1.5, 2, 2.5, and 3 meters away from the source in the horizontal direction. The air exchange rate for the simulation was 0.5 ach, which is typical for a residential location.

Attached to this post are two plots showing the results of the simulation:

1. A "Concentration versus Time" plot showing the concentration time series at each of the receptor points (note the y axis is on a log scale) for a period of 15 minutes after the release.

2. A "Average Concentration versus Distance" plot showing the proximity effect of 1-minute average concentration as a function of distance from the source. The 1-min average was take during the minute just after the release occurred.

These plots are in broad agreement with prior work showing that (A) air pollution from a "puff" release generally mixes thoroughly in the room of release within 5 to 10 minutes after release, and (B) that the proximity effect is generally an f(x) = 1/x function of Concentration vs. Distance.

This modeling approach can be expanded to include advection (air currents), obstructions, inlet and outlet flows, particle deposition, and reflection.

Note: Also attached to this post is the R source code used to run the Nicas model.