MODEL GAUSS UNTUK DISPERSI

PENCEMAR UDARA

Kuliah Pencemaran Udara

ADVANTAGES OF EMPLOYING ATMOSPHERIC

DISPERSION

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.

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

The method is commonly used, cheap and easily applicable.

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.

DISADVANTAGES OF EMPLOYING ATMOSPHERIC

DISPERSION

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

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

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

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

SISTEM KOORDINAT DISTRIBUSI GAUSS ARAH

HORIZONTAL DAN VERTIKAL

PLUME RISE

Several plume rise equations are available.

Briggs used the following equations to calculate

the plume rise:

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

Δh = plume rise, m

The Davidson-Bryant equation is

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

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:

MODELING Untuk memprediksi pencemaran udara Model Gauss distribusi konsentrasi Rumus menghitung C gas atau aerosol (<20 u) pada

permukaan tanah arah downwind (x):

Di mana: C = konsentrasi polutan, g/m3 m = laju emisi polutan, g/s = kecepatan angin rata-rata, m/s z = standar deviasi konsentrasi flume arah

horizontal y = standar deviasi konsentrasi flume arah vertikal H = tinggi efektif cerobonhg, m X = jarak downwind sepanjang centerline flume dari

titik sumber, m Y = jarak crosswind dari centerline flume, m

The assumptions made in the development of the above equation are:

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;

uniform emission rate of pollutants, m;

total reflection of the plume at ground z = 0 conditions; and

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

If the concentration is to be calculated along

the centerline of the plume (y = 0), further

simplification gives

The plume rise model examines a range of

stability classes and wind speeds to identify the

"worst case" meteorological conditions

Table. Stability Categories

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.

TABLE. PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD FY

TABLE 3.3 PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD FZ

Figure Dispersion coefficients, y direction

Figure. Dispersion Coefficient, z direction

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

TECHNICAL DATA AND COMPUTATION RESULTS FOR EFFECTIVE

STACK HEIGHT AND ATMOSPHERIC STABILITY

Parameter Case 1 Case 2 Case 3 Case 4

site conditionemission velocity rate m/s 17.51 38.23 19.90 36.76

inside diameter stack m 6.50 6.40 6.50 6.40

wind speed m/s 31.10;10; 3

31.10;10; 3

31.10;10; 3

31.10;10; 3

atmospheric pressure mbar 1013.00 1013.00 1013.00 1013.00

stack gas temperature K 377.83 798.83 432.83 776.53

air temperature K 298.13 298.13 298.13 298.13

stack height m 45.00 45.00 45.00 45.00

plume riseΔh pada u = 31.2 m/s m 6.50 28.22 9.21 26.67

Δh pada u = 10 m/s m 18.07 43.20 21.08 41.43

Δh pada u = 3 m/s m 60.24 144.00 70.27 138.12

efective stack height m 45 + Δh 45 + Δh 45 + Δh 45 + Δh

atmosphericstability neutral type D or B D or B D or B D or B

EMISSION LOAD FROM DATA ANALYSIS RESULT FOR

DISPERSION GAUSSIAN MODEL INPUT

Parameter Unit Case 1 Case 2 Case 3 Case 4

SO2 in exhaust g/s 0 0 241.87 241.47

Carbonmonoxide (CO) g/s 58.07 122.91 65.99 118.19

Nitrogen Dioxide(NOx) g/s 71.42 151.18 395.93 709.15

case1

Plant Operating in combined cycle fullload (Fuel Gass)

case2

Plant Operating in simple cycle GT fullload (Fuel Gass)

case3

Plant Operating in combined cycle fullload (Fuel Oil)

case4

Plant Operating in simple cycle GT fullload (Fuel Oil)

TABLE. QUALITY OF GROUND QUALITY FROM GAS EMISSION

Parameter unitCase

1Case

2Case

3Case

4Standard

Total Particle mg/m3 - - - - 150

Dioxide (SO2) mg/m3 0 0 366.54 204.30 750

Nitrogen Oxide(NOx)

mg/m3 123 123 600 600 850

Carbon Monoxide(CO)

mg/m3 100 100 100 100 -

x (km)

CO (μg/Nm3)

SO2 (μg/Nm3)

NOx (μg/Nm3)

x (km)

CO (μg/Nm3)

SO2 (μg/Nm3)

NOx (μg/Nm3)

0.1 2.83408E-12 0 3.48592E-12 4.1 21.76794836 0 26.77457648

0.3 22.83344175 0 28.08513335 4.5 18.18240924 0 22.36436337

1.7 109.8876133 0 135.1617643 7.3 7.083617335 0 8.712849322

1.9 90.94381769 0 111.8608958 7.7 6.381790196 0 7.849601942

2 83.14942757 0 102.2737959 7.9 6.069548616 0 7.465544797

2.1 76.26668649 0 93.80802438 8.1 5.779793059 0 7.109145463

2.5 55.57921767 0 68.36243773 8.5 5.25954176 0 6.469236365

2.7 48.18692878 0 59.2699224 8.7 5.025518561 0 6.18138783

2.9 42.1513305 0 51.84613651 8.9 4.806866589 0 5.912445904

3.1 37.16669264 0 45.71503195 9.1 4.602266873 0 5.660788254

3.3 33.00669802 0 40.59823857 9.3 4.410538912 0 5.424962862

3.7 26.52255457 0 32.62274212 9.7 4.061568557 0 4.995729325

3.9 23.9703639 0 29.4835476 9.9 3.902515498 0 4.800094062

4.1 21.76794836 0 26.77457648 10.1 3.752689288 0 4.615807824

Dispersion model CO and NOx on centerline, u = 3 m/s

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00-1.00

0.00

1.00

0.00

90.00

180.00

270.00

365.00

400.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00-1.00

0.00

1.00

0.00

35.00

75.00

115.00

150.00

200.00

LINE SOURCE APPLICATION

A six-story hospital building is located 300 m east and downwind from an expressway. The expressway runs north-south and the wind is from the west at 4 m/s. It is 5:30 in the afternoon on an overcast day. The measured traffic flow is 8000 vehicles per hour during this rush hour and the average vehicle, traveling at an average speed of 40mph, is expected to emit 0.02 g/s of total hydrocarbons. Concentrations at the hospital are required as part of a risk assessment study. How much lower, in percent, will the hydrocarbon concentration be on top of the building (where the elderly patients are housed) as compared with the concentration estimated at ground level? Assume a standard floor to be 3.5 m in height

q = source strength per unit distance, g/(s •

m)

HQ = effective stack or discharge height, m

u =wind speed, m/s

oz = vertical dispersion coefficients, m

Pada Ground Level

Pada Gedung Lantai 6

LINE SOURCE APPLICATION

Concentrations from infinite line sources, when the wind is not perpendicular to the line, can also be approximated.

If the angle between the wind direction and the line source is Φ.

This equation should not be used when Φ is less than 45°.

A power plant burns 12 tons of 2.5% sulfur content coal per hour. The effective stack height is 120 m and the wind speed is 2m/s. At one hour before sunrise, the sky is clear. A dispersion study requires information on the approximate distance of the maximum concentration under these conditions. {Hint: Calculate concentrations for downward distances of 0.1, 1.0, 5, 10, 20, 25, 30, 50 and 70 km.)

Model Line Source, 2 way

Kelompok I : 2 way sejajar, angin tegak lurus

Kelompok II: 2 way tdk sejajar, angin tegak lurus

salah satu jalan

Kelompok III : sama dengan kelompok I, angin tidak

tegak lurus jalan

Kelompok IV : sama dengan kelompok II, angin

tidak tegak lurus jalan

Inputan (variabel) : data angin, data lalu

lintas(kepadatan kendaraan dan beban emisi),

stabilitas atmosfer

Hasil (output) :

Konsentrasi polutan di ambien tiap titik yang

dihitung

Grafik dispersi polutan mulai dari sumber