IC 9478 

INFORMATION CIRCULAR/2005

 Significant Dust Dispersion Models

 for Mining Operations

 Department of Health and Human Services

 Centers for Disease Control and Prevention

 National Institute for Occupational Safety and Health 
Information Circular 9478 

Significant Dust Dispersion Models for Mining Operations 

By W. R. Reed, Ph.D., P.E. 

DEPARTMENT OF HEALTH AND HUMAN SERVICES
 Centers for Disease Control and Prevention
 

National Institute for Occupational Safety and Health
 

Pittsburgh Research Laboratory
 

Pittsburgh, PA
 

September 2005 
ORDERING INFORMATION 

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DHHS (NIOSH) Publication No. 2005–138 
CONTENTS
 

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Page 

1 
 

Introduction ................................................................................... 2 
 

Health effects of dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 
 

Regulations pertaining to dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
 

Health and safety regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
 

Environmental regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
 

Dust propagation models and mathematical algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
 

Box model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
 

Gaussian model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
 

Eulerian model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 
 

Lagrangian model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 
 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 
 

Underground mine models ........................................................................ 6 
 

Modeling with basic mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 
 

Hwang et al. study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 
 

Courtney, Kost, and Colinet study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 
 

Courtney, Cheng, and Divers study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 
 

Bhaskar and Ramani study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 
 

Xu and Bhaskar study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 
 

Chiang and Peng study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 
 

Modeling with computational fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 
 

Wala et al. studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 
 

Brunner et al. study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 
 

Heerden and Sullivan study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 
 

Srinivasa et al. study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 
 

Surface mine models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 
 

Mine-specific numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 
 

Cole and Fabrick study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 
 

TRC environmental study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 
 

Modeling of blasting phase studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 
 

Pereira et al. study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 
 

ISC3 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 
 

ISC3 modeling technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 
 

EPA study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 
 

Cole and Zapert study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 
 

Reed et al. studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 
 

Additional models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 
 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 
 

Appendix A.—Supporting equations used with the ISC3 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 
 

ILLUSTRATIONS 

1. Emissions from haul road as handled by the ISC3 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
 

2. Representation of actual emissions from a moving haul truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
 

TABLES 

1. Summary of dust dispersion models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 
 
UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT
 

ft feet 

ft2 square feet 

ft/min feet per minute 

g/sec grams per second 

hr hours 

km kilometers 

m meters 

m/sec meters per second 

m/sec2 meters per second squared 

m2

/sec square meters per second 

m3

/sec cubic meters per second 

mg milligrams 

mg/ft3 milligrams per cubic feet 

mg/ft2

-min milligrams per square foot per minute 

mg/ft3

-min milligrams per cubic feet per minute 

mg/L milligrams per liter 

mg/m3 milligrams per cubic meter 

mph miles per hour 

sec seconds 

μm micrometers 

μg/m3 micrograms per cubic meter 
SIGNIFICANT DUST DISPERSION MODELS FOR MINING OPERATIONS
 

By W. R. Reed, Ph.D., P.E.1 

1

Mining engineer, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA. 

ABSTRACT 

Dust dispersion modeling is a subject that has had a large amount of research activity. Much of the research 

has focused on large-scale global or regional dispersion models. Other models have been created for industryspecific purposes. Furthermore, some of the past research has focused on dust dispersion modeling in the 

mining industry. This report presents the various dust dispersion models that have been developed specifically 

for the mining industry. The report first gives a brief background of the regulatory environment that helped 

to promote development of such models. It then presents an overview of the mathematical concepts used in 

this dispersion modeling. Finally, each of the various models developed for the mining industry are described, 

along with their associated mathematical algorithms and any field validation conducted on the different models. 
2 

INTRODUCTION
 

Historically and into the present day, mining operations have 

generated substantial quantities of airborne respirable dust, 

which has led to the development of lung disease in mine 

workers. Respirable dust consists of the particle size fraction of 

4.0 μm or less [Lippman 1995]. Coal worker's pneumoconiosis 

(CWP) and silicosis are lung diseases that have adversely 

impacted the health of thousands of mine workers. Depending 

on the severity of the lung disease, symptoms range from 

reduced breathing capacity to death. During 1990–1999, more 

than 15,000 deaths resulted from CWP and more than 2,400 

deaths resulted from silicosis in the mining industry [NIOSH 

2002]. 

The primary means of controlling dust generation is through 

the application of ventilating air and water sprays. Ventilating 

air dilutes generated dust and moves dust away from mine 

workers. Water is applied during the cutting, transport, and 

crushing of the mined material in an effort to suppress dust 

liberated by these processes. Although significant advances in 

dust control technology have been realized, improved mining 

practices and equipment have meanwhile led to record production levels. Higher production levels have in turn resulted in the 

generation of additional dust. Ongoing research is searching for 

new and improved controls that can be used to reduce respirable 

dust exposures of mine workers. One tool that can be used to 

investigate dust generation and dispersion is computer 

modeling. 

Modeling or simulation is a process whereby a system is 

created to simulate a real-life situation. Computer modeling is 

generally the most inexpensive and versatile method for analyzing a real-life situation and has become prevalent for solving 

problems related to physical processes, especially in research 

and development [Carroll 1987]. These simulations generally 

involve modeling a physical process and analyzing it through 

the use of a personal computer. This analysis involves trial-anderror methods applied to the model and tested with the actual 

physical process to perfect the model. Once this process is completed, the computer model can be used to identify problematic 

areas, and efforts can focus on finding solutions to address these 

particular concerns. Computer modeling of dust dispersion from 

mine sources can allow for the identification of potential hazard 

areas surrounding the source from a health and safety 

standpoint. It can also allow for the evaluation of dust control 

techniques to determine modifications necessary to improve dust 

control. 

Many computer models have been created for predicting 

pollutant dispersion. However, the number of computer models 

for predicting dust dispersion at mining operations is small in 

comparison. Many of the mine-specific dust dispersion models 

are relatively unknown and therefore unused in the mining 

industry. 

This report presents the significant dust dispersion models 

that are pertinent to the mining industry in an effort to highlight 

past and current dust modeling exercises. This review of minespecific dust dispersion models also demonstrates how these 

modeling activities have sequentially improved upon existing 

models. The models are separated on the basis of their capability for use in either underground mining or surface mining. 

The models described can be particularly useful in the research 

of dust dispersion in the mining industry. 

HEALTH EFFECTS OF DUST
 

If silica is a component of respirable dust, then the effects of 

exposure pose a very serious health concern. Crystalline silica 

in respirable dust causes more than 250 U.S. workers to die each 

year of silicosis [U.S. Department of Labor 1996]. There are 

three levels of silicosis: chronic silicosis, which generally 

occurs after 10 years of exposure; accelerated silicosis, which 

generally occurs within 5 to 10 years of exposure; and acute 

silicosis, which can occur within a few weeks to 5 years of high 

exposure to silica [U.S. Department of Labor 1996]. Silicosis 

has no cure and is generally fatal. Miners are susceptible to 

silicosis both when working underground and when working on 

the surface. 

CWP, or black lung, is a chronic disease occurring in miners 

that typically develops over a long period of respirable dust 

exposure (%20 years) and is generally fatal [NIOSH 1995]. 

Black lung, which occurs mainly in miners who work underground, is caused when respirable coal dust is a major component in the air that is breathed. Other employees who work 

coal stockpiles are also susceptible to black lung. 

In addition to the hazards of respirable dust to humans, many 

epidemiologic studies show that particulate matter less than 

10 μm in diameter (PM10) also causes harm to humans. It has 

been shown that a 50-μg/m3 increase in the 24-hr average PM10 

concentration was statistically significant in increasing mortality 

rates by 2.5%–8.5% [EPA 1996]. In relation to hospitalization 

due to chronic obstructive pulmonary disease, PM10 caused a 

statistically significant increase by 6%–25% with an increase of 

the 24-hr average PM concentration by 50 μg/m3

10 [EPA 1996]. 

Other studies have shown that children are affected by shortterm PM10 exposure and that increased chronic cough, chest 

illness, and bronchitis were associated with a 50-μg/m3

 increase 

in the 24-hr average PM10 concentrations [EPA 1996]. Longterm effects from PM10 would depend on the amount of exposure to PM10 over the life of a person. 

There are other adverse impacts from PM10 exposure in 

addition to the health effects. It is known that even small particles in the air hinder visibility, for the small particles scatter 

and absorb light as it travels to the observer from a source. This 

action results in extraneous light from sources other than the 

observed object being detected by the observer, thus impairing 

visibility [EPA 1996]. Climate change may also occur from 

PM10 exposure because the small particles in the atmosphere 
3 

absorb and reflect the radiation from the sun, affecting the cloud 

physics in the atmosphere [EPA 1996]. PM10 may also have an 

effect on materials such as paint, wood, metals, etc. The effects 

depend on the amount of PM10 in the atmosphere, the deposition 

of the PM10 on the material, and the elemental composition of 

the PM10 [EPA 1996]. 

REGULATIONS PERTAINING TO DUST 

There are two legislative acts that regulate the air quality 

from mining operations: the Federal Coal Mine Health and 

Safety Act of 1969, which was amended by the Federal Mine 

Safety and Health Act of 1977, and the Clean Air Act of 1970, 

which was amended in 1977 and 1990. The Federal Coal Mine 

Health and Safety Act of 1969 established the amount of dust 

allowable in air for health and safety purposes. The Clean Air 

Amendment of 1990 regulates air emissions from facilities from 

an environmental perspective. 

HEALTH AND SAFETY REGULATIONS 

The Federal Coal Mine Health and Safety Act of 1969 

established a limit of 2.0 mg/m3

 for respirable dust for underground and surface coal mining operations [NIOSH 1995]. If 

more than 5% quartz or silica is found in the respirable dust, 

then the limit is determined by using the following formula 

(30 CFR2

2

Code of Federal Regulations. See CFR in references. 

71.101): 

10 Φ =

% quartz 

(1)

where M ' respirable dust limit (mg/m3

) 

% quartz ' percent quartz or silica found in dust as

 a fraction 

The American Conference of Governmental Industrial Hygienists also recommends this limit for respirable dust. For metal/ 

nonmetal mining, a respirable dust standard is not enforced 

unless the level of quartz exceeds 1%. In these cases, 

a respirable dust standard is calculated by using the following 

formula: 

Φ = 10	 

% quartz + 2 (2)

The 2.0 mg/m3

 limit was based on studies conducted on 

miners in the United Kingdom. This limit was intended to prevent the formation of CWP over the working life of a miner. 

However, additional studies have found that the risk of CWP 

based on these regulations is higher than originally estimated, 

and the National Institute for Occupational Safety and Health 

has recommended lowering the limit from 2.0 mg/m3

 to 

1.0 mg/m3

 [NIOSH 1995]. 

ENVIRONMENTAL REGULATIONS 

The Clean Air Amendment of 1990 regulates emissions from 

any facility into the air and addresses toxic substances. It also 

creates the national ambient air quality standards (NAAQS) for 

the criteria pollutants: carbon monoxide (CO), oxides of nitrogen (NOx), sulfur oxides (SOx), volatile organic compounds 

(VOC), lead (Pb), and PM10 [Schnelle and Dey 2000]. NAAQS 

have been in effect for PM10 since before 1987 [Watson et al. 

1997]. As dictated by the standards, facilities are not allowed 

to emit levels of PM10 pollutants at a rate that causes the 

following standards to be exceeded [Watson et al. 1997]: 

•	 Twenty-four hour average PM10 not to exceed 150 μg/m3

 for 

a 3-year average of annual 99th percentiles at any monitoring 

site in a monitoring area. 

•	 Three-year average PM10 not to exceed 50 μg/m3

 for three 

annual average concentrations at any monitoring site in a 

monitoring area. 

The NAAQS regulations for PM10 are the maximum emission 

levels allowable in ambient air; however, states have the right 

to create stricter regulations. For example, in California the 

24-hr average for PM10 is 50 μg/m3

 and its annual average is 

30 μg/m3

 [California Air Resources Board 2003]. 

The NAAQS are also used to determine if an area can be 

classified as a nonattainment area. In determining nonattainment areas, each state is required to have in place an air 

monitoring network for different regions [Watson et al. 1997]. 

This air monitoring network measures the air for a particular 

pollutant. If the NAAQS cannot be met for one or more pollutants, then the region is designated as "nonattainment" for that 

pollutant. Nonattainment areas can have stricter standards applied for that region, and permittees may have to institute better 

pollution control technology at their facilities in order to obtain 

approvals for air quality permits [Virginia Department of 

Environmental Quality 1996]. Overall, the NAAQS regulations 

for PM10 are much stricter than the 2.0 mg/m3

 respirable dust 

limit imposed by the Mine Safety and Health Administration 

(MSHA) regulations. However, the NAAQS regulations pertain 

to ambient air, which is defined as air that is accessible to the 

general public. Therefore, the NAAQS would not apply within 

the boundaries of areas that are enclosed by a fence. 

Modeling is generally required for two reasons: 

(1) During new construction or any significant modifications/ 

expansions of an existing facility that results in an emissions 
4 

increase above the state or federal limits. This threshold 

amount can vary from state to state. For example, in 

Virginia, if a facility emits more than 250 tons of PM10 per 

year, then modeling of the emissions from the facility is 

required in order to obtain a permit [Virginia Department of 

Environmental Quality 1996]. Georgia requires that any 

facility that emits more than 100 tons of a pollutant per year 

become a Title V facility, which may require emissions 

modeling of the facility [Georgia Department of Natural 

Resources 1994]. Title V of the Clean Air Act pertains to 

regulations regarding emissions of pollutants from a facility. 

All operations, including mining and quarrying, that have the 

potential to emit greater than 250 tons per year of a regulated 

pollutant are required to obtain a Title V operating permit. 

Additionally, for 28 specific industrial categories, the 

threshold is only 100 tons per year. The individual states 

may have more stringent regulations and can require all 

facilities to be subjected to the 100-ton-per-year threshold 

and may require modeling of emissions [Heinerikson 2004]. 

(2) An ambient air monitor records a violation of an NAAQS. 

The state or other regulatory authority may conduct modeling 

to determine the cause of the violation and use the model to 

develop a control strategy to prevent future occurrences of 

NAAQS violations. Therefore, modeling may be an 

important part of obtaining an air quality permit, depending 

on the amount of PM10 emitted by the facility. 

DUST PROPAGATION MODELS AND MATHEMATICAL ALGORITHMS
 

The results from modeling the emissions of a facility are used 

to ensure that the regional air quality does not exceed the NAAQS 

or deteriorate the air quality further [Schnelle and Dey 2000]. If 

the modeling results show the facility will not cause the regional 

air quality to exceed the NAAQS or deteriorate the air quality, 

then the air quality permit will be granted. Otherwise, the air 

quality permit application will be denied. Therefore, it is important that the modeling method accurately estimate both the amount 

of pollutant a facility will emit and the pollutant's dispersion. The 

use of a modeling method that overestimates the ambient 

concentrations resulting from emissions sources at the facility may 

result in denial of an air quality-related permit, just as an 

underestimation may result in an inappropriate permit issuance. 

Modeling of pollutant dispersion is completed using 

mathematical algorithms. There are several basic mathematical 

algorithms in use: the box model, Gaussian model, Eulerian 

model, and Lagrangian model [Collett and Oduyemi 1997]. 

BOX MODEL ALGORITHM 

The box model is the simplest of the modeling algorithms. 

It assumes the airshed is in the shape of a box. The air inside 

the box is assumed to have a homogeneous concentration. The 

box model is represented using the following equation: 

dCV = QA + uC WH − uCWH in dt 

(3)

where Q ' pollutant emission rate per unit area 

C ' homogeneous species concentration within the

 airshed 

V ' volume described by box 

Cin ' species concentration entering the airshed 

A ' horizontal area of the box (L×W) 

L ' length of the box 

W ' width of the box 

u '	 wind speed normal to the box 

H '	 mixing height 

Although useful, this model has limitations. It assumes the 

pollutant is homogeneous across the airshed, and it is used to 

estimate average pollutant concentrations over a very large area. 

This mathematical model is very limited in its ability to predict 

dispersion of the pollutant over an airshed because of its inability to use spatial information [Collett and Oduyemi 1997]. 

GAUSSIAN MODEL ALGORITHM 

The Gaussian models are the most common mathematical 

models used for air dispersion. They are based upon the assumption that the pollutant will disperse according to the normal 

statistical distribution. The Gaussian equation generally used 

for point-source emissions is given as follows: 

Q

χ = 2π σσ usyz 

⎡ ⎧ ⎛ y ⎞

2 ⎫⎤ ⎡ ⎧ ⎛ ⎞ 2 ⎫⎤ ⎢ ⎪ ⎪ ⎪ H ⎪

exp ⎨−0 5. ⎜ ⎟ ⎬

⎥ ⎢ exp ⎨− 0 5. ⎜ ⎟ ⎬⎥ ⎢ ⎜σ ⎟ ⎥ ⎢ σ ⎥ ⎪ ⎝ y ⎠ ⎪ ⎪ ⎝ z ⎠ ⎪ ⎢⎣ ⎩ ⎭⎥⎦ ⎣ ⎩ ⎭⎦

(4)

where	 P ' hourly concentration at downwind distance x 

Q ' pollutant emission rate 

us ' mean wind speed at release height 

Fy, Fz ' standard deviation of lateral and vertical 

concentration distribution 

y ' crosswind distance from source to receptor 

H ' stack height or emission source height 

The terms Fy and Fz are the standard deviations of the horizontal 

and vertical Gaussian distributions that are used to represent the 

plume of the pollutant. These coefficients are based upon the 

atmospheric stability coefficients created by Pasquil and 

Gifford, and they generally become larger as the distance 

downwind from the source becomes greater. Larger standard 
5 

deviations mean that the Gaussian curve or plume has a low 

peak and a wide spread; smaller standard deviations mean that 

the Gaussian curve or plume has a high peak and a narrow 

spread [Oduyemi 1994]. 

When using this equation for calculation of pollutant 

dispersion, there are some assumptions that must be made in 

order for the equation to be valid: (1) the emissions must be 

constant and uniform, (2) the wind direction and speed are 

constant, (3) downwind diffusion is negligible compared to 

vertical and crosswind diffusion, (4) the terrain is relatively flat, 

i.e., no crosswind barriers, (5) there is no deposition or absorption of the pollutant, (6) the vertical and crosswind diffusion 

of the pollutant follow a Gaussian distribution, (7) the shape of 

the plume can be represented by an expanding cone, and (8) the 

use of the horizontal and vertical standard deviations, Fy and Fz, 

requires the turbulence of the plume to be homogeneous 

throughout the entire plume [Beychok 1994]. 

The accuracy of this model to predict pollutant concentrations has been documented to be within 20% for ground level 

emissions at distances less than 1 km. For elevated emissions, 

the accuracy is within 40%. At distances greater than 1 km, the 

equation is estimated to be accurate within a factor of 2. The 

Gaussian model also has the limitation that it cannot be used for 

subhourly prediction of concentrations [Collett and Oduyemi 

1997]. 

EULERIAN MODEL ALGORITHM 

Eulerian models solve a conservation of mass equation for a 

given pollutant. The equation generally follows the form 

[Collett and Oduyemi 1997]: 

∂ ci 2 = −U ⋅ ⋅ ∇ c i − ∇ c U D c i ′ ′ + ∇ i i + S

∂t 

(5)

where U ' U6 % UN

U ' windfield vector U(x,y,z) 

U6 ' average wind field vector 

UN ' fluctuating wind field vector 

c ' +c, % cN

c ' pollutant concentration 

+c, ' average pollutant concentration; + , denotes 

average 

cN ' fluctuating pollutant concentration 

D ' molecular diffusivity 

Si ' source term 

The wind field vector U, which is normally used, is considered 

turbulent and results in U6 and UN, which are the components of 

the turbulent wind field vector being used in Equation 5. The 

turbulent wind field vector also affects the pollutant concentration c in a similar manner with the terms +c, and cN. The term 

representing molecular diffusivity is neglected as the magnitude 

of this term is significantly small. When the rate of diffusion is 

assumed to be constant, the turbulent diffusion term L"+ci

NUN, is 

modeled as +ci

NUN, ' &KL+ci,, where K is an eddy diffusivity 

tensor. This tensor is simplified so that diffusivity transport is 

along the turbulent eddy vector, making the eddy diffusivity 

tensor diagonal and the cross vector diffusivities negligible, i.e., 

 

⎡K 0 0 ⎤ xx 

K = ⎢ 0 K 0 ⎥

, where Kxx ' ' KH, with KH being ⎢ yy ⎥ Kyy 

⎢ 0 0 K ⎥ ⎣ zz ⎦

horizontal diffusivity [Collett and Oduyemi 1997]. 

Equation 5 can be difficult to solve because the advection term 

&U6 "L+ci, is hyperbolic, the turbulent diffusion term is parabolic, 

and the source term is generally defined by a set of differential 

equations. This type of equation can be computationally expensive to solve and requires some form of optimization in order to 

reduce the solution time required. Solutions have been achieved 

by reducing the problem to one and two dimensions rather than 

using three dimensions [Collett and Oduyemi 1997]. 

LAGRANGIAN MODEL ALGORITHM 

Lagrangian models predict pollutant dispersion based on a 

shifting reference grid. This shifting reference grid is generally 

based on the prevailing wind direction, or vector, or the general 

direction of the dust plume movement. The Lagrangian model 

has the following form: 

t 

crt ( ) ∫ ∫ , = p r t r ( , ′ ′ , t ) S ( ) r ′ ′ , t dr ′ dt ′

− ∞

(6)

where +c(r,t), ' average pollutant concentration at

 location r at time t 

S(rN,tN) ' source emission term 

p(r,t*rN,tN) ' the probability function that an air

 parcel is moving from location rN at

 time tN (source) to location r at time t 

The probability function must be derived as a function of the 

prevailing meteorology, which is appropriate for sources consisting of gases. If the source of emissions consists of particles, 

then more information must be incorporated into the function, 

such as the particle size distribution and the particle density 

[Collett and Oduyemi 1997]. 
6 

This mathematical model has limitations when its results 

are compared with actual measurements. This is due to the 

dynamic nature of the model. Measurements are generally 

made at stationary points, while the model predicts pollutant 

concentration based upon a moving reference grid. This 

makes it difficult to validate the model during initial use. To 

compensate for this problem, the Lagrangian models are 

typically modified by adding an Eulerian reference grid. This 

allows for better comparison to actual measurements because 

it incorporates a static reference grid into the model [Collett 

and Oduyemi 1997]. 

SUMMARY 

These four mathematical models are the basic approaches 

used for air dispersion modeling. There are many variations 

based upon these equations. Some variations add statistical 

functions to represent the randomness of wind direction, wind 

speed, and turbulence; others include the introduction of sitespecific source terms. Because of the increased computational 

power available via personal computers, the models have 

become more complex and varied. This has resulted in the 

creation of a vast number of computer models for air dispersion. 

UNDERGROUND MINE MODELS
 

Air dispersion modeling has not bypassed the mining 

industry. A number of mine-specific models have been 

created. Most of the models that have been validated with 

testing at mine sites are those developed for underground 

mines. The focus of many of the underground mining studies 

validating the models was on respirable dust. However, these 

models also have the positive feature of having the ability to 

predict dust dispersion of all dust particle size fractions. 

MODELING WITH BASIC MATHEMATICAL
 

EQUATIONS
 

Hwang et al. Study
 

Hwang et al. [1974] discussed several models for 

predicting dust dispersion in an underground entry by a 

turbulent gas stream, in other words, "the prediction of dust 

dispersion after an explosion." The basic diffusion equation 

was defined as: 

2 2 2 ∂c ∂c ⎛ ∂ c ∂ c ∂ c ⎞

+ U = k ⎜ + + ⎟ ⎜ 2 2 2 ⎟ ∂t ∂ z ⎝ ∂ x ∂ y ∂ z ⎠

(7)

where c ' dust concentration (mg/L) 

U ' convection velocity (units unknown) 

k ' diffusion coefficient (units unknown) 

x,y,z ' directions of coordinate grid (units

 unknown) 

t ' time (units unknown) 

This equation can be described as using an Eulerian 

approach, as it addresses the conservation of mass and 

assumes a stationary reference grid. From Equation 7, this 

report derived mathematical interpretations of the modeling 

process for four different types of sources: point source, line 

source, moving line source, and flat plane. These resulting 

derivations are Gaussian in nature, suggesting that the 

authors shift from an Eulerian to a Gaussian approach. The 

resulting modeling equations for each type of source are 

rather lengthy and thus not fully explained here. For 

example, the equation for an instantaneous point source in 

the plane z ' z1 at the point (x1, y1) emitted at time t ' t1 is 

given below (Equation 8): 

(8) 

−{(z z − 1 )−U t( −t1 )}

4k t( −t Qe 1 ) ⎧⎪ − km π (t−t1 ) ∞ π ⎫ 22 

m xπ m x ⎪ a c = 2 ⎨ + ∑ e 2 

⋅ cos cos 

1 12 ⎬ ⋅

2ab{πk t( − t1 )}

1

⎪⎩ m=1 a a ⎭

⎪

− kn π (t−t ) ⎧ ∞ 1 π ⎫ ⎪ 2 2

2 n yπ n y1 ⎪ ⎨1 2 + ∑ e b ⋅ cos cos ⎬ n=1 a a ⎪ ⎩

⎪ ⎭
7 

where c ' dust concentration (mg/L) 

U ' convection velocity (units unknown) 

k ' diffusion coefficient (units unknown) 

x,y,z ' directions of coordinate grid (units

 unknown) 

t ' time (units unknown) 

a ' entry opening height (units unknown) 

b ' entry opening width (units unknown) 

n ' distance in a direction normal to the 

boundary or walls of the opening 

 (assumed to be for the y direction) 

(units unknown) 

m ' undefined, but assumed to be similar to 

 n except for the x direction (units

 unknown) 

Q ' point-source emission strength (units

 unknown) 

Variables n and m are not very well defined, as the explanations for these variables were insufficient to fully describe what was meant by these variables. Results of calculations of these equations were completed, but no comparisons of calculated results to actual results were given as it 

was stated that there were no measured observations available 

[Hwang et al. 1974]. 

Courtney, Kost, and Colinet Study 

Courtney, Kost, and Colinet completed a study in 1982 that 

defined dust deposition in underground coal mine airways 

[Courtney et al. 1982]. The main emphasis of this study was 

to determine an optimum schedule for rock dusting entries in 

an underground coal mine by using an airborne particle 

deposition model. Testing was completed at eight locations in 

five U.S. underground coal mines. The deposition model in 

this study was based on a model created by Dawes and Slack 

in 1954. Their model was based on the deposition of coal dust 

in a small laboratory wind tunnel. The resulting model, which 

has a Gaussian character, is defined as: 

∂m ⎛ − Kx ⎞ = Kc = Kc0 exp ⎜ ⎟ ∂t ⎝ vH ⎠

(9) 

∂m 

where ' dust deposition rate (units unknown) ∂t 

x ' distance of deposit from the dust source 

(units unknown) 

c0, c ' airborne dust concentration of particles of

 diameter D at the dust source and at x,

 respectively (units unknown) 

v ' air velocity (units unknown) 

H ' height of airway (units unknown) 

K ' rate constant, taken as Stoke's sedimentation velocity 

 K ' kD2 (10) 

where 

D ' particle diameter (units unknown) 

k ' Stoke's sedimentation constant (units

 unknown) 

k = (ρ σ− ) g

18η

(11) 

where 

D ' particle density (units unknown) 

g ' acceleration of gravity (units unknown) 

F ' density of air (units unknown) 

0 ' viscosity of air (units unknown) 

This model was found to have satisfactory results for particles 

with diameters less than 40 μm, and the exponential decay with 

distance agreed with the experimental results [Courtney et al. 

1982]. The study by Courtney, Kost, and Colinet also stated that 

Bradshaw and Godbert completed a study of the deposition rate 

of dust in the return airway of underground coal mines. The 

results of this study showed an exponential decay rate, but the 

first 23 m from the source were found to have two to four times 

more dust deposition than was calculated [Courtney et al. 1982]. 

In studies of dust deposition in underground coal mines, Ontin 

found that the deposition rate also decayed exponentially and 

that 50% of the airborne dust settled within 1.8 m of the source 

[Courtney et al. 1982]. Experimental testing demonstrated that 

Equation 9 may underpredict the deposition rate of dust at 

distances close to sources. Through testing, Courtney, Kost, and 

Colinet found that the deposition rate in pounds per square foot 

per hour was independent of the airborne particle size, but 

increased with increasing total airborne dust concentration. 

Their recommended deposition model, which is also Gaussian 

based, was as follows: 

∂m ⎡⎛ KV ⎞ ⎤ 1 = ⎢⎜ ⎟ c0 ⎥ exp {− } ∂t ⎝ S ⎠ ⎣ ⎦

(12)

Ax

∂m where ' dust deposition rate (units unknown) ∂t 

K1 ' a proportionality constant, found to be 15.6

 in this study (units unknown) 

A ' K1/v 

x ' distance along the airway (units unknown) 

c0 ' initial dust concentration (units unknown) 

v ' air velocity (units unknown) 

V/S ' volume/surface area of the airway (units

 unknown) 

This equation was stated to be correct if the airflow is 

turbulent in the airway and not laminar and if the rate of 
8 

deposition is exponential with distance [Courtney et al. 1982]. 

The study found that this model could be used for determining 

an optimum rock dusting schedule for an underground coal 

mine, but that further testing should be completed at many 

other mine sites because of the variability from one mine 

location to another [Courtney et al. 1982]. 

Courtney, Cheng, and Divers Study 

Courtney, Cheng, and Divers proposed another deposition 

model for underground coal mines in a later study [Courtney 

et al. 1986]. The study stated that the "rate of decrease of the 

airborne concentration must be equal to the deposition of the 

airborne particles onto the surfaces of the airway" [Courtney 

et al. 1986]. The model was developed using an Eulerian approach, since this statement is analogous to the conservation 

of mass and the model uses a stationary reference grid in 

underground entries. The model is represented by the 

following equation: 

∂c ∂m − vA = L

∂ x ∂t

(13)

where v ' air velocity (ft/min) 

A ' cross-sectional area of airway (ft2

) 

c ' local dust concentration (mg/ft3

) 

x ' distance along airway (ft) 

∂m ' rate of dust deposition per unit area along ∂t airway(mg/ft2

-min) 

L ' deposition surface across airway (ft) 

L ' perimeter if dust deposits on roof, walls,

 and floor 

L ' width of airway if dust deposits only on

 floor 

If the rate of dust deposition was dependent upon local dust 

concentration as stated in the study by Courtney, Kost, and 

Colinet, then Equation 13 could be represented as: 

∂c − Av = Lkc

∂ x

(14)

where the terms are the same as given in Equation 13 

 k ' dust deposition rate constant (ft/min) 

c ⎧⎛ − L⎞ ⎫ = exp ⎨⎜ ⎟ kx⎬

c ⎝ AV ⎠ 0 ⎩ ⎭

(15)

where c0 ' dust concentration at the source (mg/ft3

) 

c ' dust concentration at a distance x from

 the source (mg/ft3

) 

Equation 14 continues to use the Eulerian approach, but 

Equation 15 introduces a Gaussian component to the model. 

Experiments to test the deposition of dust with varying air 

velocities and relative humidities were conducted at an 

underground limestone mine. It was thought that deposition 

might depend on Stokes' sedimentation velocity. However, it 

was found that the deposition was dependent upon air velocity 

and that large and small particles deposited at similar rates 

along the first 300 ft away from the source in the airway. The 

larger particles had fully deposited by 500 ft away from the 

source. The rough surface of the walls of the limestone mine 

were thought to affect the deposition of smaller particles by 

trapping the larger particles. The dependence of particle 

deposition on air velocity in the airway implied a change in the 

airborne particle size distribution, which remained to be 

explained [Courtney et al. 1986]. 

The results of the study demonstrated that the median 

particle sizes were higher at the floor of the airway (6.5 μm) 

than at the roof of the airway (4.7 μm) at 100 ft away from the 

source. At distances of 500–700 ft away from the source, the 

median diameters were closer together (4.5–4.9 μm). Respirable 

dust deposition rate was shown to decrease as a function of 

distance from the source. At low air velocities, the deposition 

rates were linear. At higher air velocities, the deposition rates 

decreased as the distance from the source became greater. 

Relative humidity was found to have a negligible effect on the 

dust deposition rate [Courtney et al. 1986]. 

Ratios of deposition rates of dust onto the floor, walls, and 

roof of the airways were also presented. These deposition 

rates were dependent upon particle size, and the floor 

deposition rate was greater than the roof and wall deposition 

rate. The ratios were established by studies done by Pereles 

and Owen [Courtney et al. 1986]. 

Bhaskar and Ramani Study 

Bhaskar and Ramani [1989] described a modeling method 

for the deposition of respirable dust in an underground coal 

mine. Their report is related to Bhaskar's Ph.D. dissertation 

entitled "Spatial and Temporal Behavior of Dust in Mines: 

Theoretical and Experimental Studies," completed at The 

Pennsylvania State University in 1987 [Bhaskar 1987]. Using 

the Eulerian method, the mathematical model presented was 

defined as: 

2 ∂c ⎛ ∂ c ⎞ ∂c = Ex ⎜

⎜ ⎟⎟ −U + sources − sinks 

∂t ⎝ ∂ x

2 ⎠ ∂ x

(16)

where c ' concentration of airborne dust (units unknown) 

t ' time (units unknown) 

Ex ' dispersion coefficient (units unknown) 

x ' distance from source (units unknown) 

U ' velocity of airflow (units unknown) 
9 

The "source" term represents dust generated by cutting 

mechanisms in the underground mine; the "sink" term refers to 

the deposition of the dust on the floor, walls, and roof of the 

airway [Bhaskar and Ramani 1989]. This mathematical model 

is applied to all the particle size intervals that are represented 

in a dust cloud generated from a mining operation. 

Results of comparing the model to experiments conducted 

in an underground airway showed that the model predicted 

deposition of the dust in airways satisfactorily. The model 

tended to predict better at lower airway air velocities than 

higher velocities. Also, total dust size was better predicted 

than respirable dust size [Bhaskar 1987]. 

Detailed explanations for the processes used in creating 

this model are given by Ramani and Bhaskar [1988]. The 

processes considered are particle deposition, deposition by 

convective diffusion, deposition due to gravity, coagulation, 

collision mechanisms, and reentrainment [Ramani and Bhaskar 

1988]. Particle deposition is related to mass transfer of a 

particle to the immediate adjacent surface; this represents 

deposition onto the roof and walls of the airway and is 

represented by Brownian diffusion, eddy diffusion, or 

sedimentation. Deposition by convective diffusion refers to 

deposition caused by eddies in turbulent flow and represents 

deposition onto the walls. Deposition due to gravity uses the 

particle's gravitational velocity to determine the deposition of 

the particle onto the floor of the airway. Coagulation and collision mechanisms are related and are based upon the interaction of the particles with one another. These two processes 

are important in determining the airborne particle size 

distribution and therefore important in determining the amount 

of dust deposited onto the airway surfaces. They take into 

account forces such as electrostatic charge, Van der Waals 

forces, and the nature of the colliding particle's surfaces. 

Reentrainment evaluates the amount of dust that is generated 

from dust that has already been deposited. Dust may be 

reentrained due to the shear forces from the velocity of air in 

the airway exceeding the cohesive force of the particle on the 

surface. This process is dependent upon the air velocity in the 

airway [Ramani and Bhaskar 1988]. 

Xu and Bhaskar Study 

Xu and Bhaskar [1995] built on the work of Ramani and 

Bhaskar and conducted additional studies to further characterize particle deposition in underground coal mine entries. 

Better understanding of this process would allow for the 

formation of improved modeling techniques in the future. 

These studies determined the deposition velocities for coal 

dust in an underground mine airway. Deposition velocity 

consists of two components in turbulent flow: deposition 

velocity due to gravity and deposition velocity due to diffusion 

or turbulent deposition. Turbulent deposition occurs from the 

breakaway of eddies from the main airflow through the airway. 

Particles are transported to the wall by these eddies and have 

sufficient momentum to penetrate the stagnant air along the 

wall and remain at this location. Turbulent deposition, which 

is stated to be dominant for fine particles, was shown to be 

independent of particle size and airflow, but dependent upon 

particle density as air velocity increased. In contrast, the particle properties and air velocities influence gravitational deposition velocities more than they affect turbulent deposition 

velocities [Xu and Bhaskar 1995]. 

Chiang and Peng Study 

Chiang and Peng [1990] worked on the development of dust 

distribution models for underground coal longwall faces. Their 

approach used a statistical technique, which includes a Gaussian 

component, to predict dust concentrations at different locations 

along a longwall face. Their resulting report [Chiang and Peng 

1990] describes the forces that have an impact on a dust particle 

and is the first mining research report to include deposition 

velocities in stationary air. The research also included suspended time and traveling distances of these same particle sizes 

when air velocity is 2.5 m/sec in an entry having a height of 2 m. 

Chiang and Peng's report describes field studies conducted 

at several underground coal longwall mines to determine 

airflow patterns both in the plan and cross-section views along 

the longwall face. As within pipeflow, the maximum airflow 

velocity is generally located in the center of the longwall 

crosscut, but can be shifted to one side or the other depending 

on the location of other equipment (shearer, supports, and 

conveyor) in the crosscut [Chiang and Peng 1990]. 

A model of the airflow distribution was created, resulting 

in the following polynomial equation [Chiang and Peng 1990]: 

f x(Y,Z) ' A % BY % CZ % DY2 % EZ2 % FYZ (17) 

where Y ' horizontal axis along the floor originating at the

 face and directed toward the gob (m) 

Z ' vertical axis along the coal face and directed

 toward the roof (m) 

A, B, C, D, E, and F are coefficients that represent 

proportionality constants that were derived from regression 

analysis of measured velocity readings from different locations 

in and along the longwall crosscut. 

The airflow model led to the development of the longwall 

dust dispersion model. This dispersion model uses the following equation to calculate the time-weighted-average dust 

concentration in the entryway [Chiang and Peng 1990]: 

20

N x ( ) = N D x dt ( , ) ∫0 (18)

where 

⎡ − MD x 2 ⎛ D ⎛ D ⎞ ⎤ 1− e ⎛ N ( )⎞ N ( )⎞ 01 02 ⎢ ⎜⎜ ⎟ + ⎜ ⎟⎟ ⎥ ⎜ ⎟ 1 ⎢ MD2 ⎝⎝ V ⎠ ⎝ V ⎠⎠ ⎥ ( , ) = ⎢ 1 2 NDx ⎥ Tc ⎢ ⎛ 1 1 ⎞ ⎥ ND − ) ⎜ + c d ( )( Lx + ⎟ + N DT c ( ) ⎢ ⎥ ⎝V V ⎠ ⎣ 1 2 ⎦

(19)
10 

where N6 ' time-weighted-average concentration at

 location x (mg/m3

) 

Tc ' mean time of a complete mining cycle

 (sec) 

D ' particle size (μm) 

L ' length that shearer must travel to

 complete one cut (m) 

V1, V2 ' velocity of the shear: V1 ' head to tailtail entry; V2 ' tail to headgate entry

 (m/sec) 

Td ' mean idle time for a complete mining

 cycle (sec) 

N01(D) ' size composition function of the source

 at the cross-section right behind the

 shearer on the return side for the

 head-to-tailgate entry trip (μm) 

N02(D) ' size composition function of the source

 at the cross-section right behind the

 shearer on the return side for the tail-to­

 headgate entry trip (μm) 

Nc(D) ' size composition function of the source

 at the cross-section on the intake side 

 of the shearer (assumed to be constant)

 (μm) 

Apgm M = V ua

(20) 

where p ' specific weight of dust 

particles (mg) 

g ' acceleration of gravity (m/sec2

) 

A ' ratio of entry perimeter to effective ventilation

 air (units unknown)
 

Va ' mean air velocity (m/sec)
 

u ' air viscosity (units unknown)
 

m ' unknown (units unknown)
 

In order to use these equations to calculate the timeweighted-average dust concentration at a location, four 

assumptions were made [Chiang and Peng 1990]: 

1. The dust generation sources in the longwall are 

considered to be generating dust at a constant rate. 

2. The shearer cuts coal in the head-to-tailgate direction 

and cleans the bottom from the tail-to-headgate direction. The 

supports are always advanced during the clean trip, and the 

distance from the shearer and the advancing support is 

constant throughout the trip. 

3. The dust concentration is higher on the return side than 

the intake side. 

4. The velocity of the shearer is constant in either 

direction. 

It should also be noted that the integration limits of 0 to 20 in 

Equation 18 represent the particle size classes from 0 to 

20 μm. This model was tested with data from the field studies 

that were completed to create the airflow distribution model 

and agreed well with the field study results [Chiang and Peng 

1990]. It was found that air velocity is very important in dust 

particle distribution. Increasing the entry airflow and the dust 

generation from the source by corresponding magnitudes also 

increased the dust concentrations in the entryway. However, 

increasing the dust generation from the source by an amount 

that is half the magnitude of the entry airflow increase lowered 

the dust concentrations in the entryway [Chiang and Peng 

1990]. This showed that eliminating the dust generation was 

very important in reducing the dust concentrations in the 

entryways. Changes in the specific weights of coal were also 

reviewed with this model, and it was found that no significant 

changes in dust concentrations occurred [Chiang and Peng 

1990]. 

MODELING WITH COMPUTATIONAL FLUID
 

DYNAMICS
 

Wala et al. Studies
 

Wala et al. [1997, 2001] describe using computational 

fluid dynamics (CFD) to characterize airflow in mine entries. 

CFD is a numerical analysis method used to solve fluid flow 

problems with a computer. This method generally follows an 

Eulerian approach, which is applied to the airflow modeling 

[Anderson 1995]. However, it can also incorporate the 

Lagrangian algorithm. The Lagrangian method is applied to 

the particles that are subjected to forces of gravity and airflow. 

The forces (gravity and airflow) are based on an Eulerian 

reference frame, whereas the Lagrangian algorithm is used to 

characterize the advection and diffusion processes that occur 

among the individual particles and influence each particle's 

trajectory [Collett and Oduyemi 1997]. 

The basis of CFD is the fluid flow motion equations for a 

Newtonian fluid, shown in tensor form: 

∂ ρ ∂ ρ( ui ) + = 0

∂t ∂ xi

(21)

⎡ ⎛ ∂u ⎞ ⎤

∂ λ k ⎢ ⎜ ⎟ ⎥ ⎢ ∂ p ⎝ ∂ xk ⎠ ⎥ − + +

∂u j ∂u j ⎢

⎢ ∂ x j ∂ x j ⎥

⎥

ρ + ρu = ⎢ ⎥ ∂t k ∂ xk ⎛ ⎡ ∂u ∂u j ⎤ ⎞ ⎢ ⎜ i ⎟ ⎥ ∂ μ ⎢ + ⎥ ⎢ ⎜ ⎟ ∂ x ∂ x ⎥ ⎝ ⎣⎢ j i ⎦⎥ ⎠ ⎢ + ρ f ⎥ ⎢ ∂ x ⎥ ⎣ i ⎦

(22)
⎡ ⎛ ⎤ ∂ T ⎞ ⎢ ∂ ⎜

⎜ k ⎟

⎟ ⎥ ⎢ ∂uk ⎝ ∂ x j ⎠ ⎥

∂e ∂e ⎢ − p + + ⎥

ρ + ρu = ⎢ ∂ x ∂ x k j ⎥ ∂t ∂ xk ⎢ 2 ⎥ ⎢ ⎛ ∂uk ⎞ ⎛ ∂ui ∂u j ⎞ ∂u j ⎥ λ ⎜ ⎟ + μ ⎜

⎜ + ⎟ ⎢ ⎟ ⎝ ∂ xk ⎠ ⎝ ∂ x j ∂ xi ⎠ ∂ xi ⎥ ⎣ ⎦

(23)

where D ' fluid density (units unknown) 

t ' time (units unknown) 

xi ' ith orthogonal axis of the coordinate space

 (units unknown) 

ui ' velocity components in the xi direction (units

 unknown) 

p ' pressure parameter (units unknown) 

μ ' dynamic viscosity coefficient (units unknown) 

8 ' second viscosity coefficient (units unknown) 

fj ' component of body force in the xj direction

 (units unknown) 

e ' internal energy of the fluid (units unknown) 

k ' thermal conductivity of the fluid (units

 unknown) 

T ' temperature (units unknown) 

The computerized process of CFD replaces the partial 

derivatives shown in Equations 21–23 with simpler discretized 

algebraic equations that are used to solve fluid flow values at 

discrete points in the system [Wala et al. 1997]. 

Several CFD simulations were conducted based on actual 

underground openings of a continuous mining operation. The 

computer program used by Wala et al. to execute the CFD for 

the airflow studies was CFD2000 version 2.2c. These studies 

produced airflow patterns that show the individual velocity 

vectors of airflow in underground mine openings and ventilation shafts. These patterns were experimentally validated 

using pressure and velocity measurements [Wala et al. 1997] 

and a new measurement method called particle image 

velocimetry (PIV) [Wala et al. 2001]. PIV uses a digital 

camera and a light source (usually a laser) to capture images 

of moving particles released into the airflow at specified 

intervals. At least two images are required to calculate the 

individual discrete flow vectors of the total airflow. This 

measurement method is described by Wala et al. [2001] and 

Turner et al. [2002]. PIV has been evaluated with CFD, but it 

has not yet been evaluated with experimental pressure and 

velocity measurements in mine openings [Turner et al. 2002]. 

Wala et al. only indicate the use of CFD at mine sites for 

airflow evaluation. However, they mention that CFD could be 

used for gas (i.e., methane) and dust dispersion, and they list 

several references pertaining to studies completed at mine sites 

that evaluated CFD for this possibility [Wala et al. 1997]. 

Additional studies have been done by Bennett et al. [2003a,b], 

which show that CFD has the ability to predict air contaminant 

concentrations in indoor occupational environments. Although 

not directly related to mining operations, these studies confirm 

that CFD can be used for gas and dust dispersion in 

underground mine openings. 

11 

Brunner et al. Study 

Brunner et al. [1995] completed a computer simulation to 

evaluate the use of CFD to calculate the airflow velocity 

required to prevent the backlayering of smoke from a mine fire 

against the ventilation flow [Brunner et al. 1995]. The computer simulation was completed on a vehicle mine fire wherein 

the vehicle was 2.4 m wide by 2.7 m high. The mine opening 

was 4.0 m wide by 4.5 m high by 200 m long. Three ventilation airflow velocity scenarios were executed: 0.5 m/sec, 

0.75 m/sec, and 1.0 m/sec. Backlayering was predominant to 

100 m against the ventilation airflow at an airflow velocity of 

0.5 m/sec. At 0.75 m/sec airflow velocity, the backlayering 

was further diminished, and at 1.0 m/sec airflow velocity the 

backlayering was entirely eliminated [Brunner et al. 1995]. 

These results were not validated with field studies. 

Heerden and Sullivan Study 

Heerden and Sullivan [1993] used CFD to evaluate dust 

suppression of continuous miners. This study was a computer 

simulation that calculated the airflow patterns in an underground entry containing a continuous miner. Individual 

airflow velocity vectors were plotted of the total airflow 

throughout the entry. Dust dispersion was determined qualitatively by assuming the dust particles would follow the individual airflow velocity vector, i.e., only trends in dust dispersion could be considered [Heerden and Sullivan 1993]. 

This simulation was used for different machine operational 

parameters and also for determining the effect of the rotating 

head of the miner on dust dispersion. The individual airflow 

vector results were stated to have been verified experimentally, 

although details of the comparison were not given. Applications for methane concentration dispersion were also 

discussed [Heerden and Sullivan 1993]. 

Srinivasa et al. Study 

Srinivasa et al. [1993] also completed a computer simulation for modeling airflow velocities and dust dispersion in an 

underground opening. This simulation was conducted on a 

longwall face and included the effects of the shearer and 

supports on the airflow. Dust particles were assumed to be 

inertialess and had no effect on the airflow patterns. 

Individual airflow velocity vector patterns were calculated 

using FIDAP, a CFD program created by Fluid Dynamics 

International (now available from Fluent, Inc.). The airflow 

patterns were calculated first, then the dust concentrations 

were calculated separately using the following equations. 

Particle motion was calculated as follows: 

P i F P P F P F ρ = F u − u + ρ − ρ g + ρ − ρ f

∂

∂

u

t

P 

Di ( i ) ( ) i ( ) i (24)
12 

where subscripts/superscripts F and P refer to fluid phase and

 particle phase, respectively 

D ' density (units unknown) 

t ' time (units unknown) 

ui ' velocity in the i direction (units unknown) 

fi ' body force vector (units unknown) 

gi ' gravitational force vector (units unknown) 

μF 

F D = 18 2 CD DP 

(25)

μ ' dynamic viscosity (units unknown) 

CD ' drag coefficient (units unknown) 

D ' particle diameter (units unknown) 

The trajectory equation was given as: 

∂ xi P = ui ∂t 

(26)

The advection-diffusion equation for the dispersed particles or 

pollutants was given as [Srinivasa et al. 1993]: 

⎡∂c ⎤ ⎢ i j ⎥ = ( j) j ρ + uc ραc + Q ∂t ⎣ ⎦

(27)

where D ' density (assumed to be particle density) (units

 unknown) 

t ' time (units unknown) 

cj ' concentration of jth pollutant (units unknown) 

" ' mass diffusivity (units unknown) 

Q ' a source term (units unknown) 

Simulations were conducted on a longwall face, and the 

outcomes were compared with experimental results. The 

airflow velocities and the dust concentrations compared well 

across the cross-section of the entry perpendicular to the 

longwall face [Srinivasa et al. 1993]. Several simulations were 

conducted to test the effectiveness of an air curtain, semi-seethrough curtains, and air-powered scrubbers in the walkway. 

The simulation conducted on the air curtain demonstrated 

only a 15%–20% reduction of dust concentrations from the 

high concentration area to the walkway of the longwall section 

only if an air curtain quantity >0.05 m3

/sec was maintained. 

It was stated that an airflow quantity >0.05 m3

/sec for an air 

curtain is not practical [Srinivasa et al. 1993]. The air curtain 

simulation results were stated to correspond with the results of 

a study conducted by Hewitt in 1990 [Srinivasa et al. 1993; 

Hewitt 1990]. 

The simulation of the semi-see-through curtain maintained 

along the spill plate of the armored face conveyor 

demonstrated a 25%–30% reduction in dust concentrations 

from the face to the walkway. It was not stated if these results 

were verified experimentally [Srinivasa et al. 1993]. 

The simulation of the air-powered scrubber established that 

there was a 40%–50% protection efficiency associated with 

the scrubber at a distance of 2.1 m downstream [Srinivasa 

et al. 1993]. The simulation agreed to within 10% of the 

experimental results [Srinivasa et al. 1993]. No details of the 

experimental procedure were given. 

As a result of this study, Srinivasa et al. concluded that 

CFD as a tool for predicting dust dispersion can be used to 

modify and improve dust control techniques. 

SURFACE MINE MODELS
 

The dust dispersion models used in surface mining have 

generally been adapted from existing industrial air pollution 

models. The surface models do not focus on a particular size 

fraction and are applicable to all particle sizes. All of these 

models, described below, are based on mathematical algorithms described earlier. 

MINE-SPECIFIC NUMERICAL MODELS 

Cole and Fabrick Study 

A number of models have been created for surface mining 

operations. Cole and Fabrick [1984] discuss pit retention of dust 

from surface mining operations. In their report, they mention a 

study completed by Shearer stating that approximately one-third 

of the emissions from mining activities escape the open pit. This 

is a very simplistic model that is representative of the box model 

algorithm. Further discussions are provided for a Gaussian 

plume model described by Winges. This model calculates the 

mass fraction of dust that escapes an open pit using the 

following mathematical model [Cole and Fabrick 1984]: 

1

ε =

+

⎛

⎝ 1 ⎜

V 

K 

d 

z 

⎞

⎠

⎟ H 

(28) 

where g ' mass fraction of dust that escapes an open pit 

Vd ' particle deposition velocity (m/sec) 

K ' 2

z vertical diffusivity (m /sec) 

H ' pit depth (m) 

Fabrick also created an open-pit retention model based upon 

wind velocity at the top of the pit. This model, based on a 

Gaussian algorithm, is given as [Cole and Fabrick 1984]: 
⎡C ⎛ 1 w⎞⎤

ε = −Vd ⎢ ⎜ + ⎟⎥ 1 ln 

u ⎝ 2 4 ⎠ ⎣ ⎦

13 

(29)

where , ' mass fraction of dust that escapes an open pit 

Vd ' particle deposition velocity (m/sec) 

u ' wind velocity at the top of the pit (m/sec) 

C ' empirical dimensionless constant equal to 7 

w ' pit width (m) 

The deposition velocity in both models was based on a 

gravitational settling velocity determined by Stoke's law. 

A comparison was completed using both models, and the 

results agreed well with each other and with the study by 

Shearer stating that one-third of the emissions from mining 

activities escape the open pit. 

TRC Environmental Study 

Several open-pit dust models are discussed in a study done 

for EPA by TRC Environmental Consultants [1995]. These 

include the models previously discussed by Cole and Fabrick. 

Another model, created by Herwehe in 1984, is a computer 

simulation using finite-element analysis. It takes into account 

many factors such as wind conditions, surface roughness, 

complex terrain, atmospheric stability, pollutant sources, 

particulate terminal settling and deposition velocities, and 

surface particulate accumulation [TRC Environmental 

Consultants 1995]. However, it was stated that this model 

may not give good results for open pits with pit angles greater 

than 35° from the horizontal or in stable atmospheres. This 

model also has not been tested with field results [TRC 

Environmental Consultants 1995]. Another model, the FEM 

(three-dimensional Galerkin finite-element model), which was 

not created specifically for the mining industry, was mentioned 

as one that could be modified for use in predicting dispersion 

of dust from open pits. Its drawback was that it required a 

very large computer to run the model. This model has also not 

been tested with field data. Both the Herwehe and FEM 

models use the concept of CFD in that they solve the NavierStokes equations for fluid motion to obtain particle dispersion 

results. 

Modeling of Blasting Phase Studies 

Modeling of dust dispersion for specific mining operations 

has been completed for the blasting phase through two studies. 

At the Kalgoorlie Consolidated Gold Mines Pty. Ltd., 

a computer program was created to determine dust dispersion 

from blasting operations. This program uses meteorology, 

bench height, blast design information, and rock density to 

predict the behavior of dust from blasting. It accounts for 

absorption of the dust on the pitwalls and for reflection of the 

dust off the pitwalls. The dust concentrations are calculated 

using settling velocities for different particle sizes and 

densities. The program is designed to determine if blasting 

will have an impact on a nearby town [Wei et al. 1999]. 

Another model for predicting dust dispersion from blasting 

operations has been created by Kumar and Bhandari [2002]. 

This model uses a gradient transport theory or an Eulerian 

approach, considering atmospheric stability and wind velocity 

and direction for computing dust concentrations at different 

distances from the blast [Kumar and Bhandari 2002]. Two 

integral equations are presented representing the dust dispersion model for the blast. However, none of the equation 

terms were defined in the study. No mention of any field 

validation of these models was given by Wei et al. or by 

Kumar and Bhandari. 

Pereira et al. Study 

Pereira et al. [1997] used a Gaussian dispersion equation 

to predict dust concentrations from the stockpiles of an 

operating surface mine in Portugal. The following equation is 

presented: 

⎡ 2 ⎤ ⎡ 2 ⎤ Q 1 ⎛ ⎞ ⎛ ⎞ ⎢ yr ⎥ 1 e − r c = exp − ⎜

⎜ ⎟⎟ exp ⎢− ⎜ ⎟ ⎥

2πσ σ u ⎢ 2 σ ⎥ ⎢ 2 ⎝ σ ⎠ ⎥ yz ⎝ y ⎠ z ⎣ ⎦ ⎣ ⎦

h z (30)

where 

c ' pollutant concentration at location receptor 

 ' (xr, yr, zr) due to the emissions at source 

 ' (0, 0, he) (units unknown) 

Q ' emissions rate (units unknown) 

Fy, Fz ' horizontal and vertical standard deviations

 or dispersion coefficients, respectively 

(units unknown) 

6u ' average horizontal wind speed (units

 unknown) 

he ' effective emissions height (units unknown) 

This equation was used to create risk maps of air quality for 

locations surrounding the mine site. No experimental validation was performed to determine the accuracy of these maps to 

actual conditions [Pereira et al. 1997]. 

ISC3 MODEL 

Dust dispersion modeling for surface mining operations, as 

required for air quality protection, is generally completed 

using an established model—the Industrial Source Complex 

model (ISC3) created by EPA. No other dust dispersion model 

has impacted the surface mining industry as much as the ISC3 

model. This model was created by EPA to predict pollutant 

dispersion from industrial facilities and is available as a 

computer program from the EPA website [EPA 2005]. The 

pollutants for which it is designed include CO, NOx, SOx, 

VOC, Pb, and PM10. 

This model also includes a subroutine for modeling flat/ 

complex terrain and has the ability to model dispersion from 
14 

four types of emissions sources: point, which are typically 

stacks; volume, which are typically buildings; area, which are 

typically haul roads or storage piles; and open pit. In addition, 

the ISC3 model can calculate the deposition rates of PM10 by 

using the deposition routine included in the model. 

Modeling of dust dispersion at surface mining operations 

generally focuses on PM10. The ISC3 model is particularly 

important to mining operations because state environmental 

permitting agencies often require its use for modeling dust 

dispersion from mining operations. The reason is that the 

ISC3 model is listed in 40 CFR 51, appendix W, as a 

"preferred air quality model." This designation means that this 

model can be used without a formal demonstration of 

applicability (40 CFR 51, appendix A of appendix W). 

An alternative model could possibly be used, but an extensive 

amount of justification would be required if an agency would 

even consider it for use. Therefore, a special review of the 

ISC3 model is presented here. 

ISC3 Modeling Technique 

The ISC3 model is based on the Gaussian equation for 

point-source emissions, which is given as the following for the 

ISC3 model [EPA 1995c]: 

2 

QKVD ⎡ ⎛ y ⎞ ⎤

χ = exp ⎢− 0 5. ⎜ ⎟ ⎥ ⎜ ⎟ 2π σσ u ⎢ σ ⎥ s y z ⎝ y ⎠ ⎣ ⎦

(31)

where Q ' pollutant emission rate (g/sec) 

K ' scaling coefficient to convert calculated

 concentrations to desired units (default

 value of 1×106

) 

V ' vertical term (dimensionless) 

D ' decay term (dimensionless) 

us ' mean wind speed at release height (m/sec) 

Fy, Fz ' standard deviation of lateral and vertical

 concentration distribution (m) 

P ' hourly concentration at downwind distance 

 x (μg/m3

) 

y ' crosswind distance from source to 

 receptor (m) 

A series of supporting equations must be used with this 

equation. These equations are listed in appendix A of this 

report. 

In order to describe how the ISC3 model works, a brief 

description of the modeling methodology is presented here. The 

ISC3 model calculates the PM10 concentrations for receptor locations, which are based on a Cartesian coordinate system where 

each source and receptor has an X and a Y coordinate. These 

coordinates are input into the downwind and crosswind distance 

equations shown in Equations A–2 and A–3, respectively (see 

appendix A). These equations calculate the downwind distance 

x and crosswind distance y, which are input into Equation 31. 

Hourly meteorological data can be obtained from the EPA 

website [EPA 2005]. The data are acquired from 

meteorological monitoring stations operated by the National 

Weather Service or other individual facilities. The data are 

processed through another program called RAMMET, which 

is distributed by EPA along with the ISC3 model. This 

program uses the meteorological data to calculate the mixing 

height zi

. The mixing height is used in Equations A–9 or 

A–10. The program then organizes the data into a format 

readable by the ISC3 program. The data are then read into the 

ISC3 model for use in Equation 31. 

Once all the data are entered, Equation 31 calculates the 

PM10 concentration P at the coordinates of the receptor. 

Generally, there is more than one receptor, and they are 

aligned in a grid format. PM10 concentrations P are calculated 

for each receptor point in the grid, with the emission source 

being stationary. These calculations are completed for each 

hour of available meteorological data. The modeled 

concentrations can be presented as hourly concentration values 

or as longer-term average concentrations, such as 24-hr 

averages or annual averages for a given receptor. The 

resulting grid of PM10 concentrations allows for the creation of 

contour maps of the dispersion modeling results, where the 

contours represent the concentrations of PM10. The user's 

guide by EPA [1995b,c] explains in greater detail how to 

operate the program. 

It is important to characterize the emissions source 

correctly before conducting the dispersion modeling 

calculations. It must be determined if the source is a point, 

volume, area, or open-pit source, because mischaracterization 

of a source can impact modeled concentrations by an order of 

magnitude. In addition, the correct dimensions of the source 

must be input, as incorrect dimensions can cause large 

variances in modeled concentrations. The mischaracterization 

of the emissions source is a common cause of inaccuracy that 

can be eliminated if the source is characterized correctly. To 

eliminate this as a cause of inaccuracy, the National Stone, 

Sand, and Gravel Association (NSSGA) has begun work on a 

guidance document on characterizing sources [Heinerikson 

2004]. 

EPA Study 

There have been very few studies completed to determine 

the ability of the ISC3 model to accurately predict PM10 dispersion from surface mining operations. EPA completed a 

large-scale study at a surface coal mine in Wyoming in 

1994–1995. This study, done in three phases [EPA 1994a,b; 

1995a], reviewed the entire mining operation for dust 

dispersion. The emissions factors from the EPA's AP–42 were 

used to determine the amount of emissions from the operation. 

These emissions were then input into the ISC3 model to complete dispersion modeling. Field testing to validate the ISC3 

model was completed by placing six PM10 sampling stations 

throughout the surface mining operation. The sampling 
15 

equipment used at each station was the Wedding PM10 

Reference Sampler. The six stations were used in addition to 

three existing PM10 sampling stations located at the mine site 

to fulfill air quality permitting requirements [EPA 1994a]. The 

sampling stations were placed on both the upwind and 

downwind side of major excavating operations. Weather data 

were recorded throughout the duration of the test, and time 

studies of equipment operation were completed. The testing 

occurred over a period of 2 months, with air sampling 

occurring every other day [EPA 1994a]. The modeling results 

of the operations were compared to the actual measurements 

from the sampling network. 

The EPA study documents that there is a significant 

overprediction of PM10 emissions from the surface coal mining 

operation by the ISC3 model [EPA 1995a]. This report has a 

statistical protocol that defines significant overprediction as an 

overprediction of more than a factor of 2 at a single site where 

modeled versus measured results are compared [EPA 1994b]. 

No attempt to determine the source of the overprediction of 

PM10 was made in this study. Consequently, it is not known 

whether the overprediction was caused by the emission 

estimation methods (AP–42) or by the dispersion model. 

Cole and Zapert Study 

Cole and Zapert [1995] completed a study, submitted to 

the NSSGA, to test the ISC3 model at three Georgia stone 

quarries. It was stated that the ISC3 model had a history of 

overpredicting particulate concentrations based on data 

obtained by the U.S. Department of Energy's Hanford, WA, 

site [Cole and Zapert 1995]. This study calculated emission 

rates for operations, modeled the dispersion of the emitted 

particulates, and compared modeled versus measured 

particulate concentrations for each of the three stone quarries. 

The model testing methodology was similar to that used in the 

EPA study [EPA 1994a,b; 1995a]. The number and type of 

PM10 sampling stations are unknown. However, it can be 

determined that there were at least two sampling stations at 

each site because there was a primary downwind site and a site 

located upwind of the prevailing winds to allow for subtraction 

of ambient PM10 concentrations. Once the comparison of 

modeled versus measured results was completed, it was 

determined that the model overpredicted the actual PM10 

concentrations in a range of a factor of less than 1 (87% 

overprediction) to a factor of 5 [Cole and Zapert 1995]. 

The Cole and Zapert study concluded that there could be two 

reasons for the overprediction. One was that the ISC3 model 

failed at that time to account for any deposition of the particulates. The other reason was that the emissions factor for unpaved 

roads overpredicts the amount of emissions from haul trucks. 

The emissions factor was cited as the primary possible cause of 

overprediction because during the study it was noted that the 

hauling operations contributed 79%–96% of the PM10 emissions 

from the entire quarrying operation [Cole and Zapert 1995]. 

EPA has been modifying a deposition routine for the ISC3 

model, but no literature has been found where testing has been 

completed using the deposition routine in the ISC3 model. 

Cole and Zapert used an initial deposition routine created by 

EPA and found that it reduced the modeled results by 5%. 

However, even with this reduction in modeled PM10 

concentrations, there is still a significant overprediction. This 

has led the NSSGA to embark on a series of studies published 

during 1991–2001 that attempt to better quantify the PM10 

emissions from haul trucks [Richards and Brozell 2001]. 

Reed et al. Studies 

Reed et al. [2001] completed a study on the ISC3 model 

using a theoretical rock quarry. The study also concluded that 

hauling operations contributed the majority of PM10 

concentrations and that the haul truck emissions factors may 

be part of the cause of the overprediction of PM10 

concentrations by the ISC3 model. However, further analysis 

of the data provided by the Cole and Zapert study presented 

another hypothesis explaining the cause of the ISC3's 

overprediction. This hypothesis stated that since the majority 

of the sources producing PM10 at surface mining operations are 

moving or mobile sources, the ISC3 model cannot accurately 

predict dust concentrations from mining operations because it 

is a model designed for predicting dust dispersion from 

stationary sources. This led to further investigations on dust 

dispersion modeling at surface mining operations, focusing on 

modeling the dispersion of dust generated from haul trucks. 

Reed [2003] described a model called the Dynamic 

Component Program that can be used for predicting dust 

dispersion from haul trucks. The model is a modification of 

the ISC3 model created in Microsoft's Visual Basic and 

validated through testing at two surface mining operations. 

The model is based on a Gaussian equation similar to that used 

by the ISC3 model [Reed et al. 2002]: 

2 ⎡ ⎤

χ = QKexp ⎢− 05. 

⎛

⎜ y ⎞⎟

⎟ ⎥ ⎜ 2π w σ σ ⎢ σ ⎥ syz ⎝ y ⎠ ⎣ ⎦

(32)

where Q ' pollutant emission rate (g/sec) 

K ' scaling coefficient to convert calculated

 concentrations to desired units (default

 value of 1×106

) 

ws ' mean wind speed at release height (m/sec) 

Fy, Fz ' standard deviation of lateral and vertical

 concentration distribution (m) 

P ' hourly concentration at downwind 

distance x (μg/m3

) 

y ' crosswind distance from source to 

 receptor (m) 
16 

Equation 32 is similar to Equation 31 used in the ISC3 model 

except that Equation 32 eliminates the use of the vertical and 

the decay terms. The major difference between the Dynamic 

Component Program and the ISC3 model is the methodology 

of applying the source emissions when predicting dust dispersion from that source. 

The overprediction of dust dispersion by the ISC3 model 

occurs because the model applies the total emissions of the 

mobile sources to a specific area source. This application creates a constant uniform distribution of emissions over this 

specified area, as shown in Figure 1.

Figure 1.—Emissions from haul road as handled by the 

ISC3 model. 

 In actual field 

conditions, however, the emissions from traffic or a mobile 

source are not uniform [Micallef and Colls 1999]. Figure 2 

shows how the emissions from a moving haul truck actually 

occur. 

Figure 2.—Representation of actual emissions from a 

moving haul truck. A, arrows represent emissions at 

time tn; B, arrows represent emissions at time tn%1. 

They act more like a moving point source rather than 

the continuous uniform emission distribution that the ISC3 

model uses. A moving point source is more representative 

because the emissions occur abruptly as the emissions source 

approaches a point, then the emissions slowly dissipate as the 

sourcemoves away from the point [Reed et al. 2002]. At a 

mining facility, this moving point source will move along a 

predictable path from the pit to the processing operations. The 

Dynamic Component Program uses the moving point-source 

methodology for predicting dust dispersion of haul trucks. 

This methodology should improve the ability to predict dust 

dispersion from haul trucks at surface mine sites. 

Field studies at two surface mine locations—one stone 

quarry and one coal mine—were conducted to validate the 

results of the Dynamic Component Program with actual measurements. The results of the field studies showed that the Dynamic Component Program was an 85% improvement over the 

ISC3 model in predicting dust dispersion from haul trucks 

[Reed 2003]. However, the Dynamic Component Program is 

still in its infancy and can currently only predict dust dispersion of haul trucks traveling in a straight line. More work 

is required to perform modeling on haul trucks traveling haul 

roads that contain curves and to continue validating the model 

to ensure its accuracy. 

ADDITIONAL MODELS
 

Two other dispersion models, although not developed 

specifically for the mining industry, have been used to model 

pollutant dispersion at surface mines: CALPUFF and 

AERMOD. These models are also available from the EPA 

website [EPA 2005]. 

CALPUFF is also an EPA-preferred air quality model. It 

is a Lagrangian model that uses continuous puffs to simulate 

emissions from sources [EPA 1998b]. It has applicability for 

many different pollutants, including PM10. The ability of the 

CALPUFF model to simulate the effects of temporally and 

spatially varying meteorological conditions that occur more 

often over long pollutant transport distances makes it suitable 

for the prediction of long- range pollutant dispersion (>50 km). 

Conversely, the ISC3 model is appropriate for short-range 

pollutant dispersion because it requires constant steady-state 

meteorological conditions (<50 km) (40 CFR 51, appendix A 

of appendix W) [EPA 1998a]. The sources of data input into 

the CALPUFF model are similar to those of the ISC3 model, 

and the calculated results are concentrations that are output in 

a format similar to the ISC3 model (40 CFR 51, appendix A of 

appendix W). Studies have been conducted to verify the 

CALPUFF model results, but none have been conducted at 

mine sites. However, it has been determined that CALPUFF 

can produce results similar to the ISC3 model. Generally, 
17 

CALPUFF produces higher dispersion concentrations than 

those simulated by the ISC3 model for tall sources at close 

proximity to the source. However, at distances farther away 

from the source, the trend reverses, with the ISC3 model 

yielding higher dispersion concentrations than those simulated 

by CALPUFF [EPA 1998b]. 

AERMOD is the proposed replacement model for the ISC3 

model. AERMOD's inputs and outputs are similar, and it has 

been improved significantly over the ISC3 model. Evaluations 

were conducted comparing AERMOD with the ISC3 model. 

These evaluations showed that, overall, AERMOD predicted 

pollutant concentrations that were closer to the actual 

measured concentrations than the ISC3 model. The two 

models produce relatively similar results for flat terrain. 

However, the largest amount of improvement was shown when 

comparing the two models in complex terrain. For the analysis 

conducted, AERMOD's short-term results varied from 0.67 to 

1.12 times the observed results, whereas the ISC3 model's 

short-term results varied by 0.67 to 8.5 times the observed 

results [EPA 2003a]. Although AERMOD is a significant 

improvement over the ISC3 model, it is still in the beta-testing 

stage and has not yet been listed as a "preferred air quality 

model" in 40 CFR 51, appendix A of appendix W [EPA 

2003b]. However, it is being distributed as AERMOD beta 

test version 02222. 

SUMMARY
 

A number of studies have been discussed in this report on 

mathematical modeling techniques, dust propagation models 

for underground mining, and dust propagation models for 

surface mining. Table 1 summarizes the dust dispersion 

models discussed in this report. 

Table 1.—Summary of dust dispersion models 

Model Algorithm type Tested at 

mine site? 

EPAapproved? 

Underground:

 Hwang, Singer, and Hartz ................... Eulerian/Gaussian No No

 Dawes and Slack .......................... Gaussian Yes No

 Courtney, Kost, and Colinet .................. Gaussian Yes No

 Courtney, Cheng, and Divers ................ 

 Courtney, Cheng, and Divers modified ......... 

Eulerian 

Eulerian/Gaussian 

Yes 

Yes 

No

No

 Bhaskar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eulerian Yes No

 Chiang and Peng .......................... Gaussian Yes No

 Wala computational fluid dynamics (CFD) ...... 

 Srinivasa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Eulerian 

Eulerian 

Yes 

Yes 

No

No 

Surface:

 Shearer ................................. Box Yes No

 Winges ................................. 

 Fabrick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Gaussian 

Gaussian 

No 

No 

No

No

 Herwehe finite-element ..................... Eulerian No No

 3-D Galerkin finite-element model (FEM) ....... Eulerian No No

 Kalgoorlie Consolidated Mines model .......... 

Kumar and Bhandari ....................... 

Unknown 

Eulerian 

Unknown 

No 

No

No

 Pereira, Soares, and Branquinho ............. 

ISC3 model .............................. 

Gaussian 

Gaussian 

No 

Yes 

No

Yes

 Dynamic Component Program [Reed 2003] ..... 

 CALPUFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Gaussian 

Lagrangian 

Yes 

Tested, but not 

No

Yes

at mine site 

 AERMOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaussian Tested, but not Pending 

at mine site 

 A review of the dust dispersion models for surface mining shows that 12 different models 

have been created. Of these, only three have been tested at actual mining operations. The tested models are the Shearer 

model, which states that one-third of the mining emissions 

escape the open pit; the ISC3 model; and the Dynamic 

Component Program. The ISC3 model is the only model 

accepted by EPA for conducting dispersion modeling on 

surface mining facilities and has a documented history of use 

in the mining industry. 

In contrast to the surface mining models, eight out of the 

nine models developed for underground mining operations have 

been field tested. It is notable that these models have been 

developed for underground coal operations except CFD, which 

has been adapted for underground mining use. It should also be 

noted that, unlike surface mining, there is no single accepted 

model for predicting dust dispersion in underground mining. 
18 

The research completed for both the surface and 

underground models is important to the development of dust 

dispersion models. The evaluations conducted on underground mining models can be particularly important as they 

are a good basis for characterizing the prediction of dust 

concentrations and the deposition of dust. Underground mine 

openings are a more constant environment in that the airflow 

velocities and directions are less variable than on the surface. 

This "stable" (i.e., less varying) environment 

facilitates the characterization of the dust dispersion properties, whereas the evaluations conducted on surface mine 

operations can be more difficult to interpret due to the more 

variable environment. In either case, this important 

information can be applied to the future development of both 

underground and surface mining models. It is undoubtedly 

certain that future work will continue, as there is an everpresent need to improve upon the dust dispersion modeling of 

mining facilities. 

REFERENCES
 

Anderson JD Jr. [1995]. Computational fluid dynamics: the basics with 

applications. New York: McGraw-Hill. 

Bennett JS, Crouch KG, Shulman SA [2003a]. Control of wake-induced 

exposure using an interrupted oscillating jet. Am Ind Hyg Assoc J 64(1): 

24–29. 

Bennett JS, Feigley CE, Khan J, Hosni MH [2003b]. Comparison of 

emission models with computational fluid dynamic simulation and a proposed 

improved model. Am Ind Hyg Assoc J 64(6):739–754. 

Beychok MR [1994]. Fundamentals of stack gas dispersion. 3rd ed. 

Milton R. Beychok: Newport Beach, CA. 

Bhaskar R [1987]. Spatial and temporal behavior of dust in mines: 

theoretical and experimental studies [Dissertation]. University Park, PA: The 

Pennsylvania State University, Department of Mineral Engineering. 

Bhaskar R, Ramani RV [1989]. Dust flows in mine airways: 

a comparison of experimental results and mathematical predictions. In: 

Frantz RL, Ramani RV, eds. Publications produced in the Generic Mineral 

Technology Center for Respirable Dust in the year 1988. Washington, DC: 

U.S. Department of the Interior, Bureau of Mines, Office of Mineral Institutes, 

pp. 31–39. 

Brunner DJ, Miclea PC, McKinney D, Mathur S [1995]. Examples of the 

application of computational fluid dynamics simulation to mine and tunnel 

ventilation. In: Proceedings of the Seventh U.S. Mine Ventilation Symposium 

(Lexington, KY, June 5–7, 1995). Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 479–484. 

California Air Resources Board [2003]. Ambient air quality standards for 

particulate matter. [http://www.arb.ca.gov/research/aaqs/pm/pm.htm]. Date 

accessed: May 2005. 

Carroll JM [1987]. Simulation using personal computers. Englewood 

Cliffs, NJ: Prentice-Hall, Inc. 

CFR. Code of Federal regulations. Washington, DC: U.S. Government 

Printing Office, Office of the Federal Register. 

Chiang HS, Peng SS [1990]. Development of dust distribution models 

for working faces. Vol. 1. Distribution model of airborne dust in longwall 

faces. Morgantown, WV: West Virginia University, Department of Mining 

Engineering. U.S. Bureau of Mines (USBM) grant No. G1135142, USBM 

open file report (OFR) 20–94. 

Cole CF, Fabrick AJ [1984]. Surface mine pit retention. J Air Pollut 

Control Assoc 34(6):674–675. 

Cole CF, Zapert JG [1995]. Air quality dispersion model validation at 

three stone quarries. Englewood, CO: TRC Environmental Corp. TRC 

project No. 14884 for the National Stone Association, Washington DC. 

Collett RS, Oduyemi K [1997]. Air quality modelling: a technical review 

of mathematical approaches. Meteorol Applic 4(3):235–246. 

Courtney WG, Cheng L, Divers EF [1986]. Deposition of respirable coal 

dust in an airway. Pittsburgh, PA: U.S. Department of the Interior, Bureau of 

Mines, RI 9041. NTIS No. PB 87–139424. 

Courtney WG, Kost J, Colinet JF [1982]. Dust deposition in coal mine 

airways. Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines, 

Technical Progress Report (TPR) 116. NTIS No. PB 82–194853. 

EPA [1994a]. Modeling fugitive dust impacts from surface coal mining 

operations: phase I. Research Triangle Park, NC: U.S. Environmental 

Protection Agency, Office of Air Quality Planning and Standards, Technical 

Support Division, EPA publication No. EPA–454/R–94–024. 

EPA [1994b]. Modeling fugitive dust impacts from surface coal mining 

operations: phase II – model evaluation protocol. Research Triangle Park, 

NC: U.S. Environmental Protection Agency, Office of Air Quality Planning 

and Standards, Technical Support Division, EPA publication No. EPA–454/ 

R–94–025. 

EPA [1995a]. Modeling fugitive dust impacts from surface coal mining 

operations: phase III – evaluating model performance. Research Triangle 

Park, NC: U.S. Environmental Protection Agency, Office of Air Quality 

Planning and Standards, Emissions, Monitoring, and Analysis Division, EPA 

publication No. EPA–454/R–96–002. 

EPA [1995b]. User's guide for the industrial source complex (ISC3) 

dispersion models. Vol. I. User instructions. Research Triangle Park, NC: 

U.S. Environmental Protection Agency, Office of Air Quality Planning and 

Standards, Emissions, Monitoring, and Analysis Division, EPA publication 

No. EPA–454/B–95–003a. 

EPA [1995c]. User's guide for the industrial source complex (ISC3) 

dispersion models. Vol. II. Description of model algorithms. Research 

Triangle Park, NC: U.S. Environmental Protection Agency, Office of Air 

Quality Planning and Standards, Emissions, Monitoring, and Analysis 

Division, EPA publication No. EPA–454/B–95–003b. 

EPA [1996]. Executive summary. In: Air quality criteria for particulate 

matter. Vol. I. Research Triangle Park, NC: U.S. Environmental Protection 

Agency, National Center for Environmental Assessment, EPA publication 

No. EPA/600/P–95/001aF, pp. 1–1 to 1–21. 

EPA [1998a]. A comparison of CALPUFF modeling results to two tracer 

field experiments. Research Triangle Park, NC: U.S. Environmental 

Protection Agency, Office of Air Quality Planning and Standards, Emissions, 

Monitoring, and Analysis Division, EPA publication No. EPA–454/ 

R–98–009. 

EPA [1998b]. A comparison of CALPUFF with ISC3. Research 

Triangle Park, NC: U.S. Environmental Protection Agency, Office of Air 

Quality Planning and Standards, EPA publication No. EPA–454/R–98–020. 

EPA [2003a]. AERMOD: Latest features and evaluation results. 

Research Triangle Park, NC: U.S. Environmental Protection Agency, Office 

of Air Quality Planning and Standards, Emissions, Monitoring, and Analysis 

Division, EPA publication No. EPA–454/R–03–003. 

EPA [2003b]. Comparison of regulatory design concentrations: 

AERMOD vs ISCST3, CTDMPLUS, ISC-PRIME. Research Triangle Park, 

NC: U.S. Environmental Protection Agency, Office of Air Quality Planning 

and Standards, Emissions, Monitoring, and Analysis Division, EPA 

publication No. EPA–454/R–03–002. 

EPA [2005]. Technology transfer network support center for regulatory 

air models. [http://www.epa.gov/scram001/tt22.htm]. Date accessed: May 

2005. 

Georgia Department of Natural Resources [1994]. Procedure to calculate 

a facility's "potential to emit" and to determine its classification. Atlanta, GA: 

Georgia Department of Natural Resources, Environmental Protection 

Division, Air Protection Branch, October 16. 

Heerden J, Sullivan P [1993]. The application of CFD for evaluation of 

dust suppression and auxiliary ventilating systems used with continuous 

miners. In: Proceedings of the Sixth U.S. Mine Ventilation Symposium (Salt 

Lake City, UT, June 21–23, 1993). Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 293–297. 
19 

Heinerikson A [2004]. Memorandum of June 3, 2004, from Arron 

Heinerikson, Trinity Consultants, Olathe, KS, to W. R. Reed, NIOSH 

Pittsburgh Research Laboratory, Pittsburgh, PA. 

Hewitt A [1990]. Respirable dust sampling, research, and control in 

underground coal mines. In: Proceedings of Minesafe International Conference. Perth, Australia: Chamber of Mines and Energy of Western 

Australia. 

Hwang CC, Singer JM, Hartz TN [1974]. Dispersion of dust in a channel 

by a turbulent gas stream. Pittsburgh, PA: U.S. Department of the Interior, 

Bureau of Mines, RI 7854. NTIS No. PB 233 492. 

Kumar P, Bhandari S [2002]. Modeling of near source dust dispersal 

after surface mine blast in weak wind over undulated terrain in tropical 

conditions. In: Bandopadhyay S, ed. Application of Computers and Operations Research in the Mineral Industry: Proceedings of the 30th International 

Symposium. Littleton, CO: Society for Mining, Metallurgy, and Exploration, 

Inc., pp. 677–685. 

Lippmann M [1995]. Size-selective health hazard sampling. In: 

Cohen BS, Hering SV, eds. Air sampling instruments for evaluation of 

atmospheric contaminants. 8th ed. Cincinnati, OH: American Conference of 

Governmental Industrial Hygienists, pp. 81–119. 

Micallef A, Colls JJ [1999]. Measuring and modelling the airborne 

particulate matter mass concentration field in the street environment: model 

overview and evaluation. Sci Total Environ 235(1–3):199–210. 

NIOSH [1995]. NIOSH criteria for a recommended standard: Occupational exposure to respirable coal mine dust. Cincinnati, OH: U.S. Department 

of Health and Human Services, Public Health Service, Centers for Disease 

Control and Prevention, National Institute for Occupational Safety and Health, 

DHHS (NIOSH) Publication No. 95–106. 

NIOSH [2002]. NIOSH hazard review: Health effects of occupational 

exposure to respirable crystalline silica. Cincinnati, OH: U.S. Department of 

Health and Human Services, Public Health Service, Centers for Disease 

Control and Prevention, National Institute for Occupational Safety and Health, 

DHHS (NIOSH) Publication No. 2002–129. 

Oduyemi K [1994]. Modelling dispersion of pollutants with a simple 

software: it is a practical approach. In: Zanetti P, ed. Computer techniques 

in environmental studies V. Vol. 1. Pollution modeling. Southampton, U.K.: 

Wessex Institute of Technology Press, pp. 25–32. 

Pereira MJ, Soares A, Branquinho C [1997]. Stochastic simulation of 

fugitive dust emissions. In: Baafi EY, Schofield NA, eds. Wollongong '96, 

Fifth International Geostatistics Congress. Vol. 2. Dordrecht, Netherlands: 

Kluwer Academic Publishers, pp. 1055–1065. 

Ramani RV, Bhaskar R [1988]. Dust transport in mine airways. In: 

Frantz RL, Ramani RV, eds. Publications produced in the generic mineral 

technology center for respirable dust in the year 1984. Washington, DC: U.S. 

Department of the Interior, Bureau of Mines, Office of Mineral Institutes, 

pp. 25–31. 

Reed WR [2003]. An improved model for prediction of PM10 from 

surface mining operations [Dissertation]. Blacksburg, VA: Virginia 

Polytechnic Institute and State University, Department of Mining and 

Minerals Engineering. 

Reed WR, Westman EC, Haycocks C [2001]. An improved model for 

estimating particulate emissions from surface mining operations in the eastern 

United States. In: Securing the Future – Proceedings of the International 

Conference on Mining and the Environment (Skellefteå, Sweden, June 

25–July 1, 2001). Stockholm, Sweden: Swedish Mining Association, 

pp. 693–702. 

Reed WR, Westman EC, Haycocks C [2002]. The introduction of a 

dynamic component to the ISC3 model in predicting dust emissions from 

surface mining operations. In: Bandopadhyay S, ed. Application of 

Computers and Operations Research in the Mineral Industry: Proceedings of 

the 30th International Symposium. Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 659–667. 

Richards J, Brozell T [2001]. Air quality monitoring and emission factor 

development: 1991–2001. Alexandria, VA: National Stone, Sand and Gravel 

Association. 

Schnelle KB, Dey PR [2000]. Atmospheric dispersion modeling 

compliance guide. New York: McGraw-Hill. 

Srinivasa RB, Baafi EY, Aziz NI, Singh RN [1993]. Three dimensional 

numerical modelling of air velocities and dust control techniques in a longwall 

face. In: Proceedings of the Sixth U.S. Mine Ventilation Symposium (Salt 

Lake City, UT, June 21–23, 1993). Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 287–292. 

TRC Environmental Consultants, Inc. [1995]. Dispersion of airborne 

particulates in surface coal mines: data analysis. Washington, DC: U.S. 

Environmental Protection Agency, Office of Air and Radiation, Office of Air 

Quality Planning and Standards. 

Turner D, Wala AM, Jacob J [2002]. Experimental study of mine face 

ventilation system for validation of numerical models. In: De Souza E, ed. 

Proceedings of the North American/Ninth U.S. Mine Ventilation Symposium 

(Kingston, Ontario, Canada). Lisse, Netherlands: Balkema, pp. 183–189. 

U.S. Department of Labor [1996]. Preventing silicosis. Washington, DC: 

U.S. Department of Labor, October 31. 

Virginia Department of Environmental Quality [1996]. Business and 

industry guide to environmental permits in Virginia. Richmond, VA: Virginia 

Department of Environmental Quality. 

Wala AM, Stoltz JR, Jacob JD [2001]. Numerical and experimental study 

of a mine face ventilation system for CFD code validation. In: Proceedings 

of the Seventh International Mine Ventilation Congress (Krakow, Poland, 

June 17–22, 2001), pp. 411–417. 

Wala AM, Yingling JC, Zhang J, Ray R [1997]. Validation study of 

computational fluid dynamics as a tool for mine ventilation design. In: 

Ramani RV, ed. Proceedings of the Sixth International Mine Ventilation 

Congress (Pittsburgh, PA, May 17–22, 1997). Littleton, CO: Society for 

Mining, Metallurgy, and Exploration, Inc., pp. 519–525. 

Watson JG, Chow JC, DuBois D, Green M, Frank N, Pitchford M [1997]. 

Guidance for network design and optimum site exposure for PM2.5 and PM10. 

Research Triangle Park, NC: U.S. Environmental Protection Agency, Office 

of Air Quality Planning and Standards. 

Wei Y, Ayotte K, Howard R [1999]. KCGM blasting dust modelling and 

management system. In: CSIRO Exploration and Mining Research Review. 

Commonwealth Scientific and Industrial Research Organisation, Division of 

Exploration and Mining, Australia, pp. 204–205. 

Xu L, Bhaskar R [1995]. A simple model for turbulent deposition of 

mine dust. In: Proceedings of the Seventh U.S. Mine Ventilation Symposium 

(Lexington, KY, June 5–7, 1995). Littleton, CO: Society for Mining, 

Metallurgy, and Exploration, Inc., pp. 337–343. 
20 

APPENDIX A.—SUPPORTING EQUATIONS USED WITH THE ISC3 MODEL 

The following equations are all required in order to use the Gaussian equation for pollutant dispersion. 

This information is taken directly from EPA [1995c]. 

The Gaussian equation for point source emissions 

2 

QKVD ⎡ ⎛ y ⎞ ⎤

χ = exp ⎢− 0 5. ⎜ ⎟ ⎥ ⎜ ⎟ 2π σσ u ⎢ σ ⎥ syz ⎝ y ⎠ ⎣ ⎦

(A–1)

where Q ' pollutant emission rate (g/sec) 

K ' scaling coefficient to convert calculated concentrations to desired units (default

 value of 1×106) 

V ' vertical term (dimensionless) 

D ' decay term (dimensionless) 

us ' mean wind speed at release height (m/sec) 

Fy, Fz ' standard deviation of lateral and vertical concentration distribution (m) 

P ' hourly concentration at downwind distance x (μg/m3) 

y ' crosswind distance from source to receptor (m) 

Downwind and crosswind distances 

x ' &(X(R) & X(S))sin(WD) & (Y(R) & Y(S))cos(WD) (A–2) 

where x ' downwind distance (m) 

X(R) ' x coordinate of receptor (m) 

Y(R) ' y coordinate of receptor (m) 

X(S) ' x coordinate of source (m) 

Y(S) ' y coordinate of source (m) 

WD ' direction from which wind is blowing (angle measured clockwise from north)

 (degrees) 

y ' &(X(R) & X(S))cos(WD) & (Y(R) & Y(S))sin(WD) (A–3) 

where y ' crosswind distance (m) 

X(R) ' x coordinate of receptor (m) 

Y(R) ' y coordinate of receptor (m) 

X(S) ' x coordinate of source (m) 

Y(S) ' y coordinate of source (m) 

WD ' direction from which wind is blowing (angle measured clockwise from north)

 (degrees) 
21 

Wind speed profile 

⎛ hs ⎞ p	 

u = u ⎜ ⎟ s ref ⎜ ⎟ 	 ⎝ zref ⎠
 

(A–4)

where	 us ' mean wind speed at release height (m/sec) 

uref ' observed wind speed from a measured reference height (zref) (m/sec) 

hs ' stack height (m) 

p ' wind profile exponent (dimensionless) 

zref ' measured reference height for wind speed (m) 

Default values 

Stability category Rural exponent Urban exponent
 

A . . . . . . . . . . . . . . . . . 0.07 0.15 
 

B . . . . . . . . . . . . . . . . . 0.07 0.15 
 

C................. 0.10 0.20 
 

D................. 0.15 0.25 
 

E . . . . . . . . . . . . . . . . . 0.35 0.30 
 

F . . . . . . . . . . . . . . . . . 0.55 0.30 
 

Plume rise due to momentum 

⎛ v ⎞ s h = h′ + 3d	 ⎜ ⎟ e s s ⎝ u s ⎠ (A–5)

where	 he ' plume rise (m) 

hNs ' stack height (m) 

ds ' inside diameter of stack (m) 

vs ' exit velocity of stack gas (m/sec) 

us ' mean wind speed (m/sec) 

Dispersion parameters (Fy, Fx) 

Fy ' 465.11628(x)tan(TH) (A–6) 

where TH ' 0.017453293[c&d ln(x)] (A–7) 

where x ' downwind distance (km)

 c,d ' coefficients 

Coefficient default values 

Pasquill stability 

category
 c d

A . . . . . . . . . . . . . . . . . . . . . 24.167 2.5334
 

B . . . . . . . . . . . . . . . . . . . . . 18.333 1.8096
 

C..................... 12.500 1.0857
 

D..................... 8.333 0.72382
 

E . . . . . . . . . . . . . . . . . . . . . 6.250 0.054287
 

F . . . . . . . . . . . . . . . . . . . . . 4.1667 0.36191
 
22 

The Pasquill stability category refers to the stability of air layers near the ground. It is based upon wind 

speed and insolation (incoming solar radiation) [Schnelle and Dey 2000]. The following table defines the 

six categories. 

Pasquill-Gifford stability categories 

Surface wind 

(measured at 

33 ft) (mph) 

4.5 . . . . . . . . 

Daytime insolation 

Strong Moderate 

A A–B 

Slight 

B 

Nighttime cloudiness 

Thinly overcast or #3/8 cloudiness $4/8 cloudiness 

— — 

4.5–6.7 .... A–B B C E F 

6.7–11.2 . . . B B–C C D E 

11.2–13.4 . . C C–D D D D 

>13.4 . . . . . C D D D D 

A Extremely unstable. B Moderately unstable. C Slightly unstable. 

D neutral. E Slightly stable. F Moderately stable.

 NOTE.—Insolation is the rate of radiation from the sun received per unit of earth's surface. 

Strong insolation corresponds to sunny midday in summer. Slight insolation corresponds to 

similar conditions in winter. For A–B, B–C, and C–D, average values are taken. Night refers to 

1 hr before sunset to 1 hr after dawn. Regardless of wind speed, the neutral category D should 

be assumed for overcast conditions during day or night and for any sky conditions during the 

hour preceding or following night.

 Source: Schnelle and Dey [2000]. 

F z ' axb (A–8) 

where x ' downwind distance (km) 

a,b ' coefficients 

Default values 

Pasquill 

stability 

category 

A ....... 

x

(km) 

<0.10 

a

122.800 

b

0.94470 

Pasquill 

stability 

category 

E ........ 

x

(km) 

<0.10 

a

24.260 

b

0.83660 

0.10–0.15 158.080 1.05420 0.10–0.30 23.331 0.81956 

0.16–0.20 170.220 1.09320 0.31–1.00 21.628 0.75660 

0.21–0.25 179.520 1.12620 1.01–2.00 21.628 0.63077 

0.26–0.30 217.410 1.26440 2.01–4.00 22.534 0.57154 

0.31–0.40 258.890 1.40940 4.01–10.00 24.703 0.50527 

0.41–0.50 346.750 1.72830 10.01–20.00 26.970 0.46713 

0.51–3.11 453.850 2.11660 20.01–40.00 35.420 0.37615 

>3.11 — — >40.00 47.618 0.29592 

B . . . . . . . <0.20 90.673 0.93198 F ........ <0.20 15.209 0.81558 

0.21–0.40 98.483 0.98332 0.21–0.70 14.457 0.78407 

>0.40 109.300 1.09710 0.71–1.00 13.953 0.68465 

C . . . . . . . All 61.141 0.91465 1.01–2.00 13.953 0.63227 

D . . . . . . . <0.30 34.459 0.86974 2.01–3.00 14.823 0.54503 

0.31–1.00 32.093 0.81066 3.01–7.00 16.187 0.46490 

1.01–3.00 32.093 0.64403 7.01–15.00 17.836 0.41507 

3.01–10.00 33.504 0.60486 15.01–30.00 22.651 0.32681 

10.01–30.00 36.650 0.56589 30.01–60.00 27.074 0.27436 

>30.00 44.053 0.51179 >60.00 34.219 0.21716 

Source: EPA [1995c]. 
23 

Vertical term 

V 

z h z h r e 

z 

r e 

z 

= − ⎛ −

⎝

⎜ ⎞

⎠

⎟ ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

+ − ⎛ +

⎝

⎜ ⎞

⎠

⎟ ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ exp . 05 exp . 05 

2 2 

σ σ

H H H H 

z z z z 

+ − ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

+ − ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

+ − ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

+ − ⎛

⎝

⎜ ⎞

⎠

⎟

⎡

⎣

exp . exp . exp . exp . 0 5 05 05 ⎢ 0 5 1 

2 

2 

2 

3 

2 

4 

2 

σ σ σ ⎢ σ

⎤

⎦

⎥

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭ = ⎪

∞

∑i 1 

(A–9) 

where he ' hs % )h 

he ' plume height (m) 

hs ' stack height (m) 

)h ' plume rise (m) 

H1 ' & zr (2izi & he) 

H2 ' zr % (2izi & he) 

H3 ' zr i & (2iz % he) 

H4 ' zr % (2izi % he) 

zr ' receptor height above ground (m) 

zi ' mixing height (m) 

2πσ z V = zi 

(A–10)

This form (Equation A–10) is used to save on computational time without sacrificing accuracy. 

There are variations of the vertical term depending on the routine used in calculating dispersion. 

Decay term 

⎛ x ⎞ For R > 0 D = exp ⎜ − ψ ⎟ ⎝ us ⎠

(A–11) 

D'1 For R ' 0 

where R ' decay coefficient 

0 693 . ψ = T 1

2 

(A–12) 

T1/2 ' pollutant half life (sec)
 

x ' downwind distance (m)
 

us ' mean wind speed at release height (m/sec)
 

Default value of R ' 0 unless specified. 
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For information about occupational safety and health topics contact NIOSH at: 

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