ISCST3 Tech Guide

Gaussian Plume Air Dispersion Model

6.2.4 The Short-Term Open Pit Source Model

The ISC open pit source model is used to estimate impacts for particulate emissions originating from a below-grade open pit, such as a surface coal mine or a stone quarry. The ISC models allow the open pit source to be characterized by a rectangular shape with an aspect ratio (length/width) of up to 10 to 1. The rectangular pit may also be rotated relative to a north-south and east-west orientation. Since the open pit model does not apply to receptors located within the boundary of the pit, the concentration at those receptors will be set to zero by the ISC models.

The model accounts for partial retention of emissions within the pit by calculating an escape fraction for each particle size category. The variations in escape fractions across particle sizes result in a modified distribution of mass escaping from the pit. Fluid modeling has shown that within-pit emissions have a tendency to escape from the upwind side of the pit. The open pit algorithm simulates the escaping pit emissions by using an effective rectangular area source using the ISC area source algorithm described in Section 1.2.3. The shape, size and location of the effective area source varies with the wind direction and the relative depth of the pit. Because the shape and location of the effective area source varies with wind direction, a single open pit source should not be subdivided into multiple pit sources.

The escape fraction for each particle size category, gi, is calculated as follows:

Formula

where:

vg = is the gravitational settling velocity (m/s),

Ur = is the approach wind speed at 10m (m/s),

" = is the proportionality constant in the relationship between flux from the pit and the product  of Ur and the concentration in the pit (Thompson, 1994).

The gravitational settling velocity, vg, is computed as described in Section 1.3.2 for each particle size category. Thompson (1994) used laboratory measurements of pollutant residence times in a variety of pit shapes typical of actual mines and determined that a single value of " = 0.029 worked well for all pits studied.

The adjusted emission rate (Qi) for each particle size category is then computed as:

Formula

Where Q is the total emission rate (for all particles) within the pit, Ni is the original mass fraction for the given size category, and g is the escape fraction calculated from Equation (1-68). The adjusted total emission rate (for all particles escaping the pit), Qa, is the sum of the Qi for all particle categories calculated from Equation 1-69. The mass fractions (of particles escaping the pit), Nai, for each category is:

Formula

Because of particle settling within the pit, the distribution of mass escaping the pit is different than that emitted within the pit. The adjusted total particulate emission rate, Qa, and the adjusted mass fractions, Nai, reflect this change, and it is these adjusted values that are used for modeling the open pit emissions.

The following describes the specification of the location, dimensions and adjusted emissions for the effective area source used for modeling open pit emissions. Consider an arbitrary rectangular-shaped pit with an arbitrary wind direction as shown in Figure 1-10. The steps that the model uses for determining the effective area source are as follows:

1. Determine the upwind sides of the pit based on the wind direction.

2. Compute the along wind length of the pit (R) based on the wind direction and the pit geometry . R varies between the lengths of the two sides of the rectangular pit as follows:

Formula

where L is the long axis and W is the short axis of the pit, and 2 is the wind direction relative to the long axis (L) of the pit (therefore 2 varies between 0E and 90E). Note that with this formulation and a square pit, the value of R will remain constant with wind direction at R = L = W. The along wind dimension, R, is the scaling factor used to normalize the depth of the pit.

3. The user specifies the average height of emissions from the floor of the pit (H) and the pit volume (V). The effective pit depth (de) and the relative pit depth (Dr) are then calculated as follows:

Formula

4. Based on observations and measurements in a wind tunnel study (Perry, et al., 1994), it is clear that the emissions within the pit are not uniformly released from the pit opening. Rather, the emissions show a tendency to be emitted primarily from an upwind sub-area of the pit opening. Therefore an effective area source (with Ae being the fractional size relative to the entire pit opening) is used to simulate the pit emissions. Ae represents a single area source whose dimensions and location depend on the effective depth of the pit and the wind direction. Based on wind tunnel results, if Dr$0.2, then the effective area is about 8% of the total opening of the mine (i.e. Ae=0.08). If Dr<0.2, then the fractional area increases as follows:

Formula

When Dr = 0, which means that the height of emissions above the floor equals the effective depth of the pit, the effective area is equal to the total area of the mine opening (i.e. Ae=1.0).

Having determined the effective area from which the model will simulate the pit emissions, the specific dimensions of this effective rectangular area are calculated as a function of 2 such that (see Figure 1-10):

Formula

and

Formula

Note that in equations 1-75 and 1-76, W is defined as the short dimension of the pit and L is the long dimension; AW is the dimension of the effective area aligned with the short side of the pit and AL is the dimension of the effective area aligned with the long side of the pit (see Figure 1-10). The dimensions AW and AL are used by the model to define the shape of the effective area for input to the area source algorithm described in Section 1.2.3.

The emission rate, Qe, for the effective area is such that:

Formula

where Qa is the emission rate per unit area (from the pit after adjustment for escape fraction) if the emissions were uniformly released from the actual pit opening (with an area of L@W). That is, if the effective area is one-third of the total area, then the emission rate (per unit area) used for the effective area is three times that from the full area.

Because of the high level of turbulence in the mine, the pollutant is initially mixed prior to exiting the pit. Therefore some initial vertical dispersion is included to represent this in the effective area source. Using the effective pit depth, de, as the representative dimension over which the pollutant is vertically mixed in the pit, the initial vertical dispersion value, Fzo, is equal to de/4.3. Note that 4.3@Fzo represents about 90% of a Gaussian plume (in the vertical), so that the mixing in the pit is assumed to approximately equal the mixing in a plume.

Therefore, for the effective area source representing the pit emissions, the initial dispersion is included with ambient dispersion as:

Formula

For receptors close to the pit, the initial dispersion value can be particularly important.

Once the model has determined the characteristics of the effective area used to model pit emissions for a particular hour, the area source algorithm described in Section 1.2.3 is used to calculate the concentration or depsosition flux values at the receptors being modeled.