flue gas dispersion model study

Flue Gas Dispersion Model Study

CHAPTER III

3.1. ADVANTAGES AND DISADVANTAGES OF EMPLOYING

ATMOSPHERIC DISPERSION

The advantages of employing atmospheric dispersion as an

ultimate disposal method of waste gases are listed below:

1. Dispersion of the waste gases leads to the dilution of the pollutants in the atmosphere. Self-purification mechanisms of atmospheric air also assists the process.

2. Tall stacks emit gas into the upper layer of the atmosphere and lower the ground concentration of the pollutants.

3. The method is commonly used, cheap and easily applicable.4. By selecting the proper location of stacks through the use of

different models for dispersion, it is possible to significantly reduce the concentration of waste gases in the atmosphere.The disadvantages of employing atmospheric dispersion as an

ultimate disposal method of waste gases are:

1. Any particulate matter contained in the dispersed gases have a tendency to settle down to the ground level.

2. The location of the industrial source may prohibit dispersion as an option.

3. Plume rise can significantly vary with ambient temperature, stability conditions, molecular weight, and exit velocity of the stack gases.

4. The models of atmospheric dispersion are rarely accurate. They should only be used for estimation and comparative analysis.

3.2. PLUME RISE

Several plume rise equations are available. Briggs used the

following equations to calculate the plume rise:

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Where Δh = plume rise, m

F = buoyancy flux, m4/s3 = 3.7 x 10-5QH

u = wind speed, m/s

x* = downward distance, m

Xf = distance of transition from first stage of rise to the second

stage of rise, m

QH = heat emission rate, kcal/s

If the term QH is not available, the term F may be estimated by

F = (g/π)q(Ts - T)/Ts

where g = gravity term 9.8 m/s2

q= stack gas volumetric flowrate, m3/s (actual conditions)

Ts,T = stack gas and ambient air temperature, K, respectively

Many more plume rise equations may be found in the literature.

The Environmental Protection Agency (EPA) is mandated to use Brigg's

equations to calculate plume rise. In past years, industry has often

chosen to use the Holland or Davidson-Bryant equation. The Holland

equation is

where d= inside stack diameter, m

vs = stack exit velocity, m/s

u = wind speed, m/s

P = atmospheric pressure, mbar

Ts,T = stack gas and ambient temperature, respectively, K

ΔT=Ts - T

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Δh = plume rise, m

The Davidson-Bryant equation is

reader should also note that the "plume rise" may be negative in

some instances due to surrounding structures, topography, etc.

3.3. POWER PLANT EMISSION and PLUME RISE MODEL OF

DISPERSION

3.3.1. The Short-Term Dispersion Model Equations

The Short Term model provides options to model emissions from

a wide range of sources that might be present at a typical industrial

source complex. The basis of the model is the straight-line,steady-state

Gaussian plume equation, which is used with some modifications to

model simple point source emissions from stacks, emissions from

stacks that experience the effects of aerodynamic downwash.

The point source algorithms are described in bellow. The Short

Term model accepts hourly meteorological data records to define the

conditions for plume rise, transport, diffusion, and deposition. The

model estimates the concentration or deposition value for each source

and receptor combination for each hour of input meteorology, and

calculates user-selected short-term averages.

3.3.2. Point Source Emissions

The Short Term model uses a steady-state Gaussian plume

equation to model emissions from point sources, such as stacks. This

section describes the Gaussian point source model, including the basic

Gaussian equation, the plume rise formulas, and the formulas used for

determining dispersion parameters.

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3.3.3. The Gaussian Equation

The short term model for stacks uses the steady-state Gaussian

plume equation for a continuous elevated source. For each source and

each hour, the origin of the source's coordinate system is placed at the

ground surface at the base of the stack. The x axis is positive in the

downwind direction, the y axis is crosswind (normal) to the x axis and

the z axis extends vertically. The fixed receptor locations are converted

to each source's coordinate system for each hourly concentration

calculation.

The hourly concentrations calculated for each source at each

receptor are summed to obtain the total concentration produced at

each receptor by the combined source emissions. For a steady-state

Gaussian plume, the hourly concentration at downwind distance x

(meters) and crosswind distance y (meters) is given by:

where:

Q = pollutant emission rate (mass per unit time)

K = a scaling coefficient to convert calculated concentrations to

desired units (default value of 1 x 106 for Q in g/s and

concentration in μg/m3)

V = vertical term (See Section 1.1.6)

D = decay term (See Section 1.1.7)

σy , σz = standard deviation of lateral and vertical concentration

distribution (m) (See Section 1.1.5)

us = mean wind speed (m/s) at release height (See Section 1.1.3)

Equation above includes a Vertical Term (V), a Decay Term (D),

and dispersion parameters (σy and σz) as discussed below. It should

be noted that the Vertical Term includes the effects of source

elevation, receptor elevation, plume rise, limited mixing in the vertical,

and the gravitational settling and dry deposition of particulates (with

diameters greater than about 0.1 microns).

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The coordinate system used in making atmospheric dispersion

estimates of gaseous pollutants, as suggested by Pasquill and modified

by Gifford, is described below. The origin is at ground level or beneath

the point of emission, with the x axis extending horizontally in the

direction of the mean wind. The y axis is in the horizontal plane

perpendicular to the x axis, and the z axis extends vertically. The

plume travels along or parallel to the x axis (in the mean wind

direction). The concentration, C, of gas or aerosol at (x,y, z) from a

continuous source with an effective height, He, is given by:

where He = effective height of emission (sum of the

physical stack height, Hs and the plume rise, Δh), m

u = mean wind speed affecting the plume, m/s

m = emission rate of pollutants, g/s

σy , σz = dispersion coefficients or stability parameters, m

C = concentration of gas, g/m3

x,y,z = coordinates, m

The assumptions made in the development of the above equation

are:

(1)the plume spread has a Gaussian (normal) distribution in both the horizontal and vertical planes, with standard deviations of plume concentration distribution in the horizontal and vertical directions of av, and oz, respectively;

(2)uniform emission rate of pollutants, m; (3)total reflection of the plume at ground z = 0 conditions;

and (4)the plume moves downstream (horizontally in the x

direction) with mean wind spead, u. Although any consistent set of units may be used, the cgs system is preferred.

For concentrations calculated at ground level (z = 0), the

equation simplifies to

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If the concentration is to be calculated along the centerline of the

plume (y = 0), further simplification gives

In the case of a ground-level source with no effective plume rise

(He = 0), the equation reduces to

It is important to note that the two dispersion coefficients are the

product of a long history of field experiments, empirical judgments, and

extrapolations of the data from those experiments. There are few

knowledgeable practitioners in the dispersion modeling field who would

dispute that the coefficients could easily have an inherent uncertainty

of ±25%.

3.3.4. Case of Meteorogical Conditions

The plume rise model examines a range of stability classes and

wind speeds to identify the "worst case" meteorological conditions, i.e.,

the combination of wind speed and stability that results in the

maximum ground level concentrations. The wind speed and stability

class combinations used are given as bellow. The six applicable

stability categories for these coefficients are shown in the following

table:

Table 3.1 Stability Categories

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Note that A, B, C refer to daytime with unstable conditions; D

refers to overcast or neutral conditions at night or during the day; E

and F refer to night time stable conditions and are based on the

amount of cloud cover. "Strong" incoming solar radiation corresponds

to a solar altitude greater than 60 o with clear skies (e.g., sunny

midday in midsummer); “slight” insolation (rate of radiation from the

sun received per unit of Earth’s surface) corresponds to a solar altitude

from 15 o to 35 o with clear skies (e.g., sunny midday in midwinter).

Equations that approximately fit the Pasquill-Gifford curves

(Turner, 1970) are used to calculate Fy and Fz (in meters) for the rural

mode. The equations used to calculate Fy are of the form:

where:

In Equations the downwind distance x is in kilometers, and the

coefficients c and d are listed in Table. The equation used to calculate

Fz is of the form:

where the downwind distance x is in kilometers and Fz is in

meters. The coefficients c,d, a and b are given in Table 3-2 and Table

3-3.

Table 3.2 Parameters Used To Calculate Pasquill-Gifford Fy

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Table 3.3 Parameters Used To Calculate Pasquill-Gifford Fz

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* If the calculated value of Fz exceed 5000 m, Fz is set to 5000 m.

** Fz is equal to 5000 m.

For the A-B, B-C, and C-D stability categories, one should use the

average of the A and B values, B and C values, and C and D values,

respectively. Figure 1 and 2 provide the variation of σy and σz with

stability categories and distances.

Figure 3.1 Dispersion coefficients, y direction.

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Figure 3.2 Dispersion Coefficient, z direction

Throughout the model, with the exception of the Schulman-Scire

downwash algorithm, the dispersion parameters, σy and σz, are

adjusted to account for the effects of buoyancy induced dispersion as

follows:

where Δh is the distance-dependent plume rise. (Note that for

inversion break-up and shoreline fumigation, distances are always

beyond the distance to final rise, and therefore Δh = final plume rise).

The model uses either a polar or a Cartesian receptor network as

specified by the user. The model allows for the use of both types of

receptors and for multiple networks in a single run. All receptor points

are converted to cartesian (X,Y) coordinates prior to performing the

dispersion calculations.

In the Cartesian coordinate system, the X axis is positive to the

east of the user-specified origin and the Y axis is positive to the north.

For either type of receptor network, the user must define the location

of each source with respect to the origin of the grid using Cartesian

coordinates. In the polar coordinate system, assuming the

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X( R ) = rsinθ - Xo

Y( R ) = rcosθ - Yo

origin is at X = Xo, Y = Yo, the X and Y coordinates of a receptor

at the point (r, θ). The downwind distance is used in calculating the

distance-dependent plume rise and the dispersion parameters.

The wind power law is used to adjust the observed wind speed,

uref, from a reference measurement height, zref, to the stack or

release height, hs. The stack height wind speed, s, is used in the

Gaussian plume equation, and in the plume rise formulas. The power

law equation is of the form:

where p is the wind profile exponent. Values of p may be

provided by the user as a function of stability category and wind speed

class. Default values are as follows:

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

The stack height wind speed, us, is not allowed to be less than 1.0

m/s.

The mixing height used for neutral and unstable conditions

(classes A-D) is based on an estimate of the mechanically driven

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mixing height. The mechanical mixing height, zm (m), is calculated

(Randerson, 1984) as

zm = 0.3 u*/f

where: u* = friction velocity (m/s)

f = Coriolis parameter (9.374 x 10-5 s-1 at 40 (latitude)

Using a log-linear profile of the wind speed, and assuming a

surface roughness length of about 0.3m, u* is estimated from the 10-

meter wind speed, u10, as

u* = 0.1 u10

Substituting for u* in Equation 2 we have

zm = 320 u10.

The mechanical mixing height is taken to be the minimum

daytime mixing height. To be conservative for limited mixing

calculations, if the value of zm from Equation is less than the plume

height, he, then the mixing height used in calculating the concentration

is set equal to he + 1. For stable conditions, the mixing height is set

equal to 10,000m to represent unlimited mixing.

Wind speed at elevation from known wind speed and elevation

where u = wind speed at height h, (m/s)

u0 = wind speed at anemometer level h0, (m/s)

n = coefficient, approximately 1/7

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http://www.ajdesigner.com/phpdispersion/wind_speed_elevation_equation.php


3.4. STACK DESIGN RECOMMENDATIONS

As experience in designing stacks has accumulated over the

years, several guidelines have evolved.

1. Stack heights should be at least 2.5 times the height of any

surrounding buildings or obstacles so that significant turbulence

is not introduced by these factors.

2. The stack gas exit velocity should be greater than 60 ft/s so that

stack gases will escape the turbulent wake of the stack. In many

cases, it is good practice to have the gas exit velocity on the

order of 90 or 100 ft/s.

3. A stack located on a building should be set in a position that will

assure that the exhaust escapes the wakes of nearby structures.

4. Gases from the stacks with diameters less than 5 ft and heights

less than 200 ft will hit the ground part of the time, and the

ground concentration will be excessive. In this case, the plume

becomes unpredictable.

5. The maximum ground concentration of stack gases subjected to

atmospheric dispersion occurs about 5-10 effective stack heights

downwind from the point of emission.

6. When stack gases are subjected to atmospheric diffusion and

building turbulence is not a factor, ground-level concentrations

on the order of 0.001-1% of the stack concentration are possible

for a properly designed stack.

7. Ground concentrations can be reduced by the use of higher

stacks; the ground concentration varies inversely as the square

of the effective stack height.

8. Average concentrations of a contaminant downwind from a stack

are directly proportional to the discharge rate; an increase in the

discharge rate by a given factor increases ground-level

concentrations at all points by the same factor.

9. In general, increasing the dilution of stack gases by the addition

of excess air in the stack does not affect ground-level

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concentrations appreciably. Practical stack dilutions are usually

insignificant in comparison to the later atmospheric dilution by

plume diffusion. Addition of diluting will increase the effective

stack height, however, by increasing the stack exit velocity. This

effect may be important at low wind speeds. On the other hand if

the stack temperature is decreased appreciably by the dilution,

the effective stack height may be reduced.

10. Stack dilution has an appreciable effect on the

concentration in the plume close to the stack.

These 10 guidelines represent the basic design elements of a

stack "pollution control" system. An engineering approach suggests

that each element be evaluated independently and as part of the whole

control system. However, the engineering design and evaluation must

be an integrated part of the complete pollution control program.

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flue gas dispersion model study

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