api 931 chapter 6 dispersion of gases

MANUAL ON DISPOSAL OF REFINERY WASTES

VOLUME ON ATMOSPHERIC EMISSIONS

CHAPTER 6-DISPERSION OF GASES

AMERICAN PETROLEUM INSTITUTE Division of Refining 1801 K Street, N.W.

Washington, D.C. 20006

Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for the manufacture, sale, or use in connection with any method, apparatus, or product covered by letters patent, nor as insuring anyone against liability for infringement of letters patent.

API publications may be used by anyone desiring to do so, and every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them. However, the Institute makes no representation, warranty, or guarantee in connection with API publications and hereby expressly disclaims any liability or responsibility for loss or damage resulting from their use; for any violation of any federal, state, or municipal regulation with which an API publica-tion may conflict; or for the infringement of any patent resulting from the use of an API publication.

Copyright 1974 American Petroleum Institute

I

FOREWORD

This chapter describes environmental conditions at the probable site of refinery construction and the effects of these conditions on plume rise, atmospheric dis-persions, and ground level concentrations. Meteorological aspects are discussed at some length. Ground level concentrations of pollutants should be determined from the most accurate existing predictive techniques prior to actual construction. This will ensure that specific requirements are not exceeded.

In evaluating plume rise and atmospheric dispersion, an eclectic approach is used. The result is one formula for the determination of plume rise and one set of formulas for the determination of ground level concentrations. For refineries located where abnormal conditions are not encountered, these equations represent a suitable tool for the design engineer to use in estimating ground level concentra-tions and thereby determining the required stack heights. (High-velocity vents are not covered by these equations.)

The predictive techniques presented herein are applicable to estimating atmos-pheric dispersion at a single source of emission over uncomplicated terrain, when mean wind speed and direction can be determined. The equations enable determina-tion of ground level concentrations for an elevated source and for a ground level source. Predictive techniques for estimating atmospheric dispersions of emissions from multiple sources are also included. Dispersion coefficients are most applicable to ground level releases, but they have been applied to stack releases as well. Within the layer in which diffusion occurs, it is assumed that stability characteristics remain constant.

When designing a refinery facility, neither this approach nor any textbook approach is sufficient in cases of unusual atmospheric conditions or irregular topography. Handling these conditions requires a high degree of expertise and may involve the use of other predictive aids, such as wind tunnels .

iii

CONTENTS


6. J Typical Regulatory Requirements .... 6.2 Environmental Conditions at Construction Site ................. .

6.2.1 Temperature ..... 6.2.2 Wind Motion and Turbulence .. 6.2.3 Lapse Rate....... . .................... . 6.2.4 Stable and Unstable Air ..... 6.2.5 Inversions ... 6.2.6 Influence of Local Terrain ..

6.3 Behavior of Plumes .. 6.3.1 Plume Types and Characteristics ... 6.3.2 Influence of Wind Fluctuation .... 6.3.3 Plume Dilution and Diffusion .. 6.3.4 Effects of Obstructions, Eddies, and Downwash ... . 6.3.5 Plume Rise and Plume Rise Formulas ................... . 6.3.6 Limitations and Reliability of Predictive Techniques .............. . 6.3.7 Behavior of Flare Plumes .. . ............ .

6.4 Atmospheric Dispersion Theories 6.4.1 Background ... 6.4.2 Basic Formulas .................................. . 6.4.3 Parameters and Dispersion Coefficients ..... 6.4.4 Influence of Atmospheric Conditions ... 6.4.5 Dispersion of Aerosols and Particulate Matter ... 6.4.6 Multiple Sources.......... ...... ...... ........ . 6.4.7 Wind Tunnel and Other Studies ...... .... . 6.4.8 Limitations and Reliability of Predictive Techniques ...

6.5 Cooling Tower Plume Rise.. . .............. . 6.5.1 Background... ............ . .. 6.5.2 Analysis of Plume Rise and Plume Behavior ... 6.5.3 Plume Condensation and Precipitation. 6.5.4 Minimizing Visible Plumes... ......... .

6.6 Sample Calculations .... 6.6. J Refinery Boiler Stack ... 6.6.2 Process Heaters and Stacks .... 6.6.3 Catalytic Cracking Units ... 6.6.4 Flares...... .... . 6.6.5 Storage Tanks .... . 6.6.6 Product Loading .. . 6.6.7 Roof Vents ....

REFERENCES ... APPENDIX-ABBREVIA nONS AND SYMBOLS ..

v

PAGE 6-1 6-1 6-1 6-2 6-3 6-3 6-4 6-4 6-5 6-5 6-6 6-6 6-7 6-7 6-8 6-9 6-11 6-11 6-11 6-13 6-13 6-14 6-16 6-16 6-17 6-\8 6-18 6-18 6-20 6-21 6-24 6-24 6-24 6-27 6-28 6-29 6-30 6-33 6-33 6-35

',1ANUAL ON DISPOSAL OF REFINERY WASTES VOLUME ON ATMOSPHERIC EMISSIONS


Typical Regulatory Requirements

1': i,'c!cr~d Air Quality Standards, or the current _,::1"011[\, are outlined in the Federal Register. I * ',,' .1."C standards appear in tabular form in the Air .\ " r \ ('irS of May 3,1971, and are reproduced in

i ,doic 6-1 also gives the levels at which the .. ""'1,111 contaminants affect human health and

" Department of Health, Education and ,,",,: . :,' '.1' ",ued a series of six publications on the ."If',,[ " \ i r l)uality Criteria, t The subject of each

".~, "';:"1 I', olle of the six common contaminants:

. !!\ ilks. :1 ,']l)Jl0xide.

"!;lil'al Oxidants,

i ',(IS on pages 6-33 and 6-34, r I, 'Tl1 :)'Jperintendent of Documents. U.S. Govern~

: ';lIi,':, Washington, D,C, 20402.

These publications define the contaminants and describe their properties and their effects on human health and welfare, animals, and vegetation. The human health category includes toxicology data and effects on the respiratory and nervous systems. Standard test methods are also included.

6.2 Environmental Conditions at Construction Site

The three most important factors of weather in all parts of the world are temperature, wind, and precipita-tion. For our purpose, however, the primary concerns are temperature and wind.

6.2.1 TEMPERATURE

Temperature can vary widely because it is influenced by geographical location and seasonal change. The lowest and highest recorded readings in the United States are - 66 F and + 134 F at Yellowstone Park and

I able 6-1 ~Federal Air Quality Standards and levels at Which Effects Show in Humans

fIn);.:uIJIt:\ . Annu~l~ ~~llJl1t:tric mean, [J.g per ell m 'h., ... Ilr Cl)nc, :1.g per ell mt

. s.uur (h,des: Annu.d ,lfIth aver. f.Lg per ell m 'h, ~-~-hr (llne, ag per ell mil \f,l, ;-hr cune. tJ.g per ell m!1 C.l.t~n \1t1no\l-l .' \ . ut::.

,:,,u ~':lr ('{me, mg per ell ml! J\ I'il[ ":unc, mg per ell mil

"x"'h,hcmical Oxidants' 0:- '. t'nr l11ax. :1.g rer ell mi i

If ..!r".Jrthln~' "..1.\ -'hr ('!.)nc 6-9 am,

. ..:. per cu m ", -,

'''cn (hides: ,d .trith aver, iJ.g per eu m

'" 1\ ~l\'l'r, 'J..g per ell m Fnkral criteria.

hv June I, 1975. ~ l'lllit un enforcement.

Ili,-, .lnd crops. 1 " h

6-2 DRW MANUAL-ATMOSPHERIC EMISSIONS

Death Valley, respectively. Temperature may also vary considerably on a diurnal basis.

The most fundamental temperature variation is caused by the annual change in the angle of incidence of sun rays (i.e., the slow decrease in air temperature when moving from the equator to a latitude of 90 degrees at the poles). One other fundamental variation, apart from the seasonal variation, is caused by the presence of large land masses or large oceans. Thus the greatest seasonal and diurnal temperature variations occur near the largest land masses, which absorb heat rapidly in the summer and radiate (lose) heat rapidly in the winter. This is especially true for most interior sections of the United States and Canada.

The horizontal distribution of air temperature for large or small areas is shown by isotherms (lines drawn on maps to connect points of equal temperature). On a world map, the isotherms show an irregular distribu-tion, which varies greatly from summer to winter and from one continent to another.

General weather data for the United States and Canada (including temperature and temperature ranges, precipitation, and wind velocities) are given in API Bulletin 2513. 2 More complete climatological data for a greater variety of locations are furnished by the U. S. Environmental Data Service, Environmental Science Services Administration (Commerce Depart-ment). Data available include standard 30-year averages of temperature, precipitation, and wind velocity. Wind rose data are also available.

6.2.1.1 Seasonal Variations

At any location, seasonal temperature variations are caused primarily by the angle of incidence of sun rays to the earth. In the summer, sun rays are more nearly perpendicular than in the winter. As the rays become more perpendicular, the hours of daylight and the total radiant energy received (insolation) increase.

Seasonal temperature variations range from a low at the equator, where the monthly average temperature variation may not exceed 5 F for the entire year, to a high in northerly latitudes, where average monthly temperature variations may exceed 100 F.

6.2.1.2 Diurnal Variations

Daily temperature variations are caused by radiant energy received from the sun during the day and dis-sipated by the earth surface at night. These variations are usually greater in summer than in winter and are naturally at a minimum when the sky is covered.

On land, the highest atmospheric temperatures are usually experienced between I :00 I'm and 4:00 pm;

the lowest temperatures occur around sunrise. Diurnal variations are most pronounced in desert areas and least pronounced in moist, wooded areas. Thus daily temperature variations for wooded areas may not exceed 10 F, while those for desert areas may be as much as 120 F.

6.2.2 WIND MOTION AND TURBULENCE

Wind may be defined as the movement of air in a more or less horizontal direction. Turbulence is irregular air motion caused by eddies superimposed upon a general flow. Air currents, as contrasted with wind, denote vertically moving air columns.

The irregular heating of the earth produces irregular heating of the air at the surface, which, in turn, causes irregularity in pressure. Although these pressure varia-tions are relatively small, they cause wind. The velocity of the resultant wind is directly proportional to this pressure differential.

Although pressure gradient is the predominant factor, there are other factors that influence the magnitude and direction of air movements in both a horizontal and vertical direction. Vertical air movements, or air cur-rents, are discussed in Paragraphs 6.2.3 and 6.2.4.

In any locality and for any particular season the frequency and intensity with which the wind blows from any given direction are fairly constant. These data are available as wind roses (wind charts) and will show, for example, that the wind will blow from the Southwest for 45 percent of the time at an average velocity of 15 miles per hour. The other 55 percent of the time wind direction is distributed among the other 15 points of the compass and includes a period of calm.

For control of air pollution, the following information is valuable:

I. The constancy or persistency of the wind from a given direction over a period of time.

2. The variation of the horizontal wind speed and direction with height. (Where the ground is reasonably level, the effects of ground friction on wind will nor-mally cancel out at a height of 1,500 to 2,000 feet. Figure 6-1 3 shows the effect of ground friction.)

Although horizontal changes are normally less significant in areas a way from urban centers, this may not be true in cases of irregular ground terrain or unusual thermal effects. Since air is a fluid, its move-ment in a horizontal direction is usually characterized by laminar or streamline flow, unless disruptive influences are present. Disruptive influences tending to cause turbulence include:

DISPERSION OF GASES 6-3

GRADIENT

'liND SPEED (m/sec.) ,'!(\I1:11 drag reduces the wind speed close to

'" "-,\ ! 11,lt ((lund at the gradient level. The profile III I'> -..table is usually steeper than that found

-, - U"ln~e of Wind Speed Profile with Stability.

,C[,. lIillCh can be caused by natural :"":trilles (hills or irregular ground

"rlilicial barriers (buildings and in-

"I'([,;)n. which occurs when the land ""leT I pr colder) than the air itself and

m .. "", "r Ir,'nts. which are usually indicative of chane", I'rontal disturbances may be strong .JnJ ,Ire qU11e common in some areas, relatively

.. (llhn,

tUrtluklll ;Ilr motion influences effective stack Jill' [lossibility of turbulence should

C1:Je\.lt.!crl"d : 11 [ill..' "tack design.

1 :~"" . ,:,' cdll he dclined as the vertical temperature V ... "'~: ':: ck" tl) the vertical temperature distribu-':O.t:r'l'.

::"""piJere, The temperature of the atmos-I',tlls, or "Ia pses," with increasing

'" :",' ,,( the increasing distance from the "'rface of the earth, The normal or

: Ie' is 3,5 F per 1,000 feet (6.5 C per ,:11 that is not in vertical motion. This

:','rCltllre gradient shows considerable varia-

tion from one locality to another and periodically shows considerable variation within the same locality.

From the point of view of meteorology and of dis-persion of gases, further classifications of the lapse rate are required. These classifications refer to air that is in vertical motion:

1. Dry adiabatic (constant heat content) lapse rate refers to a change in air temperature due to a change in pressure of the air in vertical motion. Rising air expands due to decreasing pressure causing the temperature to faiL Falling air compresses causing the temperature to rise. This rate of temperature increase or decrease is constant for air that is dry (not saturated) and has a value of 5.5 F per 1,000 feet (10 C per kilometer). 2. Moist or wet adiabatic lapse rate refers only to rising air saturated with moisture at that temperature. This rate is 3.2 F per 1,000 feet (5.8 C per kilometer).

Descending air always warms at the dry adiabatic rate. The occurrence of saturation in the atmosphere modifies the adiabatic relationship between temperature and pressure by the value of the latent heat of evapora-tion (or condensation), which explains the lower adiabatic lapse rate for moist air.

Typical examples of lapse rates for air that is not in vertical motion are given by Donn. 4 These examples also indicate the effects of inversion (increase in air temperature with increasing altitude). An understand-ing of lapse rate is important because the relationship between the existing lapse rate and the adiabatic lapse rate determines whether the atmosphere is stable or unstable. It should be noted that the existing lapse rate for air not in vertical motion can and does vary widely, while the values for dry and moist adiabatic lapse rates (as in vertical motion) are always constant.

6.2.4 STABLE AND UNSTABLE AIR

The atmosphere is either stable or unstable depending upon its ability either to resist or to augment vertical motion, Atmospheric stability or instability is directly related to temperature gradients or lapse rates. If the existing lapse rate is less than the adiabatic lapse rate, the air is stable, if it is greater, the air is unstable. There are various degrees of conditional stability and neutral ,t', bility in which the existing lapse rate is greater than the moist adiabatic lapse rate, but less than the dry adiabatic lapse rate. Also, if a rising parcel of unstable air enters a new stratum where the existing lapse rate is lower than the adiabatic rate, the previously unstable air will become stabilized at that height.

In a mass of stable air there is little or no vertical activity to sweep it aloft. Smoke, dust, minute water

DRW MANUAL-ATMOSPHERIC EMISSIONS

droplets, and other airborne prod ucts collect in the lower atmosphere to limit visibility. The presence of fog, smog, mist, or haze is indicative of stable air. Under such conditions, smoke from industrial stacks, after losing its initial heat and velocity, will trail off in a horizontal plane. Automobile exhaust and other fumes will lie close to the surface.

In unstable air the vertical lifting sweeps aloft smoke, dust, and other haze-producing products. Good visibility is an indication of instability.

For the purpose of further estimating atmospheric dispersion, atmospheric turbulence is categorized into the following six types which are coded to correspond to Table 6-2:

I. Extremely unstable (A). 2. Moderately unstable (B). 3. Slightly unstable (C). 4. Neutral conditions (D). 5. Slightly stable (E). 6. Moderately stable (F). Table 6-2 details the relationship of atmospheric turbulence to weather conditions.

Table 6-2-Relation of Turbulence Types to Weather Conditions

Daytime Insolation Nighttime Conditions ~-----.-~-.~-------... ,----~------...

Surface Thin Over-Wind cast or < 3/8 Speed Strong Moderate Slight > 4/8 Cloudiness'

(m/sec) Cloudi-ness *

2 A A-B B 2 A-B B C E F 4 B B-C C D E

5-6 C CoD D D D 6 C D D D D

"'The degree of cloudiness is that fraction of the sky above the local apparent horizon that is covered by clouds. The neutral class (D) should be assumed for heavy overcast conditions, day Of night.

6.2.5 INVERSIONS

Temperature inversions occur when the temperature of the air increases with altitude. A common cause of inversion is rapid cooling of the ground at night by radiation. The surface air is then cooled by convection so that the air temperature some distance from the ground is higher than the air temperature at or near ground surface. Inversion can also be caused by air masses, or fronts, and occasionally by turbulence. In Los Angeles it is caused by cool marine air forcing its way under warmer continental air. Both masses of air are then trapped by the adjacent coastal mountains.

When an inversion occurs, the existing lapse rate is negative, and therefore always less than the adiabatic

lapse rate. This results in extreme air stability. Under these conditions plumes generally tend to disperse downward, thus decreasing effective stack height. Since most elevated inversions are higher than 500 feet, this would apply to most stacks. If a stack is designed for a location with a condition favorable to inverSIOn, two design possibilities should be considered:

I. Design the stack with sufficient height so that the stack exit will be above most inversion layers.

2. Design the stack exit gas velocity and exit gas temperature so that the plume will rise above inversion, or will at least provide good penetration.

Frequently the inversion layer is sufficiently high so that neither of these alternatives is possible.

With most stacks a critical wind velocity causes maximum ground level concentrations of pollutants at moderate wind speeds. Under these conditions, in-creasing the physical stack height further elevates the plume, thus reducing ground level concentrations. Increasing stack gas velocity or temperature has no significant effect on these ground level concentrations.

6.2.6 INFLUENCE OF LOCAL TERRAIN

Local terrain can have a pronounced influence on weather and weather characteristics such as air stability. A wind proceeding over a level area changes direction on reaching hills, high structures, or mountains so that the obstruction can usually be cleared. Air that is forced to rise to pass over such obstructions mayor may not become unstable depending upon the speed of ascent, humidity conditions, and contrast between the cooling rate of the rising air and the lapse rate of the surrounding air. In the Los Angeles area the incoming cool marine air does not have sufficient momentum to clear the mountains, resulting in inversion and very stable air.

As discussed previously, the type of terrain-rocky, sandy, or wooded-influences the magnitude of daily temperature variations. The smaller the daily tempera-ture variation, the greater the tendency toward stable air.

Areas of strong topographic relief also experience air currents (breezes). These breezes are usually upward during the day when the valley floor is relatively warm, and downward at night when the obstruction cools faster than the sheltered valley below.

The major effect of local terrain on weather is the extent to which it introduces instability into air move-ments or promotes turbulence and eddy currents. These in turn directly affect gas dispersion.


TYP

6-.6 DRW MANUAL-ATMOSPHERIC EMISSIONS

Analyses of these plume types indicate that in-stability is usually less desirable than stability or near-neutral stability. This is true because air turbulence may cause plume concentrations to appear on the ground in relatively close proximity to the stack. Fumigation involving a high inversion is probably the least desirable condition because vertical upward dispersion is inhibited and light to heavy ground concentrations may appear over large areas.

Complete analyses cannot be based on atmospheric conditions alone but must include an evaluation of the effluent gas and other parameters such as wind speed and wind shear and the effect of any obstructions.

6.3.2 INflUENCE OF WIND FLUCTUATION

The previo'i~ discussion of plume characteristics is presented in terms of atmospheric condition (stability or instability). Although this property is probably the most important overall indicator of plume character-istics (particularly for conditions such as fanning or fumigation), wind movement and any associated turbulence constitute other important variables. Wind shear, a measure of change in horizontal wind speed and direction with height, must also be considered. Wind and associated characteristics affect plume dilution, plume diffusion, and plume rise, although these terms are to some extent interrelated.

6.3.3 PLUME DILUTION AND DIFFUSION

Bosanquet 5 states that plume dilution caused by wind is an important factor in overall dilution and varies directly as a function of the wind velocity. The wind speed serves to alternate the concentration of particles as they are released from the stack. If other parameters remain constant and the wind s peed doubles, the number of particles in a given downward direction is halved.

In addition to dilution, wind turbulence and its effect on diffusion must also be considered. The eddy diffusion coefficient is proportional to the product of wind velocity and a function of the existing turbulence. A plume increases in diameter as a result of turbulence acting on its outer circumference. As the eddies result-ing in turbulent motion increase in size, a point is reached where they affect the entire plume, causing irregular motion downwind while having little effect on plume diameter. In normally turbulent air where various sizes of eddies coexist, a combined effect is experienced. These three conditions are illustrated in Figures 6-3, 6-4, and 6-5. I

NOTE: A plume in a hypothetical field of small turbulent motions will move in a relatively straight line, with a gradual increase in its cross section.

Figure 6-3-Plume Dispersing in a Field of Small Eddies.

NOTE: If the eddies are all very large compared to the plume dimensions, the plume will grow very little in size, but it will meander wildly.

Figure 6-4-Plume Dispersing in a Field of Large Eddies.

NOTE: The typical daytime atmosphere has eddies of an infinite variety of sizes, and a dispersing plume both grows and meandero;; as it moves downwind.

Figure 6-5-Plume Dispersing in a Field of Varied Eddies.

Various mathematical equations for diffusivity have been proposed notably by Bosanquet. However, these are usually of little practical value because the degree and type of turbulence and the various parameters involved do not permit accurate evaluation. Smith notes that "a statistical evaluation of the problem is often satisfactory if care is taken in choosing the parameters." 3 Even this representation applies only for relatively short distances downwind.


OF OBSTRUCTIONS, EDDIES, AND

',[ruction can play an important role in deter- ::c !,lllme rise and dispersion because it can disturb

,d the air flow. This disturbance or deflection , ,.1' :'!ll me dilution and diffusion.

" ,iiscussion, obstructions include not only tall ,.II! r,', and natural irregularities in the earth surface,

','''graphical features such as valleys and shore-"HI-water effect). Natural irregularities include HI depressions and unusual ground roughness. ,,::,wres located in large urban areas not only

.I",'C Il)pographic effects, but can produce thermal " \'.cli. Generally, the effects of obstructions are

" "I ilat is, they tend to result in down wash and ,:


(but not exceeding ten stack heights). This can be expressed as:

Where:

t..H = (l.6F)li(x)% I'-

(3)

F = value proportional to the rate of buoyancy (heat) emission.

x = horizontal distance downwind of the stack. I'- = wind velocity.

A regression formula 4 was developed to which the other formulas were compared. This regression formula is generally applicable to the total data available, most of which involved wind speeds in the range of 9 to 22.5 mph (4 to 10 m/sec). This formula is not generally applicable to wind velocities outside this range nor to a wide variety of stacks where local conditions have a pronounced or predominate effect.

Anderson, et al., conclude that "no rational choice can be made between various proposed empirical plume rise formulas" 10 for the determination of effec-tive stack height. It is the consensus that this observa-tion is valid for all formulas, empirical and dimensional, that have been published to date.

Nevertheless, the quest for accurate formulas con-tinues apace so that the engineer can design in com-pliance with applicable specifications. The most precise dimensional analysis is that presented by the U. S. Atomic Energy Commission II (these formulas have been reproduced by Anderson, Hippler. and Robin-son 10 in their work for API). These formulas treat momentum-dominated plumes and buoyancy-domi-nated plumes separately. In each category. for both calm days and windy days, the values of parameters are given for stable conditions and unstable conditions. Most of the constants contained in the formulas have not been determined. These determinations must be made experimentally on the basis of actual observation of plume rise.

The formula by Holland 12 involves a less rigorous approach thaI' most formulas for an ctl"ective stack height determination. Several authorities 10.13, recom-mend this formula on the basis of reasonable accuracy under various conditions. This formula is for neutral or slightly unstable conditions:

wd [ (T.' -- T") I] I1H = iJ: 1.5 + 2.68 (I0-'p) i,- I ( 4) Where:

,\' d I'-

stack exit velocity. in meters per second. stack diameter. in meters. wind velocity at stack height. in meters per

second. atmospheric pressure. in millibars. atmospheric temperature. in degrees Kelvin. stack temperature. in degree, Keh in.

This formula is on the conservative side, thus pre-senting a slight safety factor. It should be reasonably accurate for unstable conditions by using a factor of 1.1 or 1.2 and for stable conditions by using a factor of 0.8 or 0.9. These factors are recommended by Holland. 12 Conditions of extreme stability (inversion) or extreme instability (turbulence) present the usual problems.

The critical wind speed for any given atmospheric stability condition is that speed which causes a maxi-mum ground level concentration of the pollutant. Equation (4) and formulas of other authorities indicate that the plume rise (t..H) is an inverse function of wind speed, conversely, the greater the wind speed, the greater the effect of dilution. These two forces are counter-acting. There is a point of equilibrium between these two counteractive effects where the maximum ground level concentration occurs. This intermediate wind speed-the critical wind speed-varies with conditions of atmospheric stability. This wind should be used for design purposes. A method for determining critical wind speed is indicated in Paragraph 6.6.2.

6.3.6 LIMITATIONS AND RELIABILITY OF PREDICTIVE TECHNIQUES

All authorities generally agree that none of the plume rise formulas presented in the literature are uniformly applicable. As will be shown, the degree of applica-bility is related to the parameters in the equation, but accuracy is largely determined by local meteorological conditions, which are not adequately expressed in the available formulas. In the following table,lo a com-parison is made between observed and theoretical plume rise.

Formula

Bosanquet, et al. Sutton Priestley Meade

Range of Ratios of Calculated to Observed Rise

0.44 to 1.13 1.21 to 1.85 0.60 to 1.32 0.77 to 1.21

NOTE: Buoyant source, windy day.

Variations of 50 percent between calculated and observed values of :lH can occur, especially for adverse meteorological conditions (e.g., a strong inversion). This does not necessarily signify that the parameters in the equations are in error, although constants and exponential values do vary. It can indicate inadequate or inaccurate measurement of the parameters or that the measurements changed with distance downwind. Ideally, dimensionalized or empirical formulas with

1 I


,'onstants should be developed for the area ," consideration.

". 'clop equations with suitable constants, con-,I [h~ accuracy of the plume rise equations with

::,'" to wind velocity in neutral or near-neutral 1"115 of >lability. Generally, the equations are ,,'lW[[C in low to moderate wind velocities-that ,:',1 lllPh (2.3 to 9.1 m/sec). The accuracy tends

c I ':11 'e somewhat for lower or higher wind veloci-!" is not generally important because t1H is a

"I" Ilii'h figure for low wind velocities, thus '" II" '! !!round concentrations. At high wind

:', dilution effects preclude high concentrations, 1 "line of the plume is occasionally swept to

,l:lnd. III,' rl'asoning with reference to wind velocities IIp[llleS to unstable air except that the factor

I ".,jiIV usually produces an increase in average '. !'!'I~ilt. This is reflected in equation (4) by use of

:111' ;'1 1,1 or 1.2 applied to t1H. Unfortunately, ., ,':I;,rl\, with strong instability, the higher stack

'I ""'1' 'lot overcome the effect of looping, which "'[lei uce undesirable ground concentrations at I',ilort distances downwind from the stack.

It a I reg uent occurrence. ,',:[I"t deviation from these equations is

", '1',','0 wilen there is an inversion above the stack , :.ilion) where the most precise results should

""hlC, 1'


1.0

0.9

0.8

./ .-- ~.6.LX

/ ~ b,L 5~;; (i-t) b,X -b,J.,

X --l


..... __ .. " ~ .. r'f~ctive Stack Height, H.

','111. t he method may ,I ,,'\ ,'1 concentrations ,,""tltute a problem). "!llur dioxide or other

',"'''Ied ,n the following _-, .. ",,;' ,'! ,II'"~ by using effective

,1'1.111 "n ( I ).

.- UI\Dl!r510n 1 neories

,;; c 1',lS,il fuel contains .. "mitted into the

, "II' concern with these ,II, " primarily at what " lliey come in contact

"111 ,hurt-term and long-, 1 i'IC\ iously, these con-

,,'ceI certain prescribed

,I ',lirly predictable tra-,'"" hoth downwind and

",'IIIi\. however, it is sub-'1l1l1 forces resulting in " 'ill'cading of contam-

""lined somcwhat impre-'c' \ lliues of a frequency

"lilt concentration) from the ',' "liues. Dispersion is

",Ill, Whcn diffusion occurs, ,I Ill\)\'C from a region of "I' lower concentration. III"table atmospheric con-

k IIlCtlC energy and thermal i,,~ pluille-all of which con-

tribute to the vertical component of rise. Turbulence is defined as "the random character of the velocity of a fluid-in contrast to the constancy of such a velocity in steady streamlined flow." 16 Wind turbulence is always present with eddies varying from small to large scale. The strength and time intervals of these eddies range from large in highly unstable regions to small in highly stable meteorological regions. It is apparent that no mathematical derivation (formula or set of formulas) yields an absolutely accurate value for ground level concentrations. Also the dispersion parameters that are available in the literature are average values for a definite period of time. These parameters can become less accurate if modified to another time base .

Even if all parameters could be accurately deter-mined, a physical impossibility, the relationship of these parameters to time and distance is variable rather than fixed. The predictive calculations of the ground concentrations (on which design is based) must not represent either overestimations, which result in unnecessarily expensive design, or underestimations, which may result in ground concentrations above the accepted standards.

Reasonable accuracy can be obtained, particularly when practical limitations are applied to time involved and distance downwind. Wind tunnel models and other meteorological studies can be useful under certain conditions to augment calculated results (see Paragraph 6.4.7). This is particularly true for complex situations, such as the disturbance of plume flow resulting from structural obstructions or topographic irregularities.

6.4.2 BASIC FORMULAS

The basic formulas have been well presented by various authorities including Sutton and Bosanquet, while modifications to these formulas have been in-dicated by Pearson, Pasquill, Turner, and Gifford. In general, these formulas do not vary greatly and involve expressions of the probability curves developed by Karl Gauss. The so-called Gaussian curves were originally applied to indicate deviations from presumed known values, involving either experimental or statistical studies.

The Gaussian curve has been found applicable under most conditions for the determinations of downwind atmospheric concentrations resulting from a stack plume. The dispersion equations herein assume a Gaussian distribution in both horizontal and vertical planes-that is, the equations incorporate deviations on a probability basis, ~!I (horizontal) and ~, (vertical), and have been developed from the work of Ogura,


Frenkiel, Pasquill, and Gifford. The major differences in the various dispersion formulas involve the dispersion coefficients and the way they vary with atmospheric stability and distance downwind. The formulas herein are recommended since the standard deviations are related graphically to a more comprehensive definition of atmospheric conditions and only two dispersion parameters are involved.

The Gaussian distribution curve as applied to the distribution of atmospheric contaminants is shown in Figure 6-8, in which y (value of the relative concentra-tion) varies from to 100 percent when plotted against values of x - x/cr. The deviation values or dispersion co-efficients, cry and cr" are discussed later in this section. The value of x represents any point directly downwind of the plume flow, and x represents the distance in meters from x. Characteristics of the Gaussian dis-tribution curve are described in greater detail by Turner. IJ

The Gaussian curves retain the same general bell-shape at any distance downwind, but with increasing distances downwind the curves become flatter and wider. It should be noted that these curves refer to distribution of contaminants only, as induced by dispersion-that is, the dispersion coefficients.

The equations for determining the concentration of gas or particles are given below. The effective stack height (H) is determined by estimating plume rise and adding the physical stack height. All equations are for particles equal to or less than 20 microns in diameter.' The equations are for a single source of emission at effective stack height (H)t when there is no particle deposition or reaction at the surface. The equations are as follows:

X(x,y,z;H) = _. exp - - -Q [' (Y)'] 7:2 cru cr~ (1. 2 cr" { [ '(2-H)'] [1(-+H)'Jl exp- 2 ~-;:- + exp - 2 ~:- f (8)

'See Paragraph 6.4.5 for discussion of particles up to 44 microns and 60 microns in diameter.

tNote that when H ~ 0, as for a ground level release source, value for H is equal to the plume rise (tlH).

10 0.9 0.8

0.7 0.6

Y 0.5 OA 0.3 0.2 01 0.0

Figure 6-8-Gaussian Distribution Curve.

Where: X concentration at any particular point In

x y z Q

space, in grams. distance downwind. distance crosswind from x-axis. vertical distance above ground. uniform rate of emission, in grams per

second. cr y = standard deviation of plume diffusion in the

horizontal. cr, = standard deviation of plume diffusion in the

vertical. tL = wind velocity, in meters per second.

For concentrations calculated at ground level, equation (8) simplifies to:

X(x,y,O;H) = ~L exp [- ! (l')'J cry cr, tL 2 cry

exp [ - ~ (~),J (9) A still simpler equation can be applied to ground

level concentrations calculated along the centerline of the plume (i.e., y = 0):

X(x,O,O;H) = _(l~ exp [- ! (.l!)'] (10) cry cr, tL 2 cr,

For a ground-level source with no effective plume rise, the resulting equation is:

Q X(x,O,O;O) = r. --cr 11 cr z [J.

(II)

The accuracy of the mean value of X so determined is proportional to the accuracy of the mean value of the wind velocity (tL) and is also directly related to the pre-cision involved in choosing the diffusion coefficients. Since diffusion (or dispersion) coefficients are based on a 10-minute sampling time, shorter sampling times yield somewhat higher values for ground level con-centration, while longer sampling times result in decreased concentrations. For slightly unstable and neutral conditions, the higher values approximate I percent for 3 minutes, while longer sampling times may yield lower concentrations approximating 50 per-cent for 4 hours. These variances occur because a plume meanders and increases in diameter as it travels downwind. As a result, cry increases with sampling time.

The concentrations given previously are averages and can be exceeded under certain conditions. It can be shown that maximum concentrations occur when cr, = Hh/f. This maximum value is obtained by the equation:

( 2Q ) (cr,) Xmax = e 7r.~H2 ;.-;: (12) Where:

e = the base of the natural logarithm, 2.718.

T ,

-'


l11e value of the effective stack height varies with wind ,pecd and stability conditions. Inversion lids, especially

,ct appreciable heights (2,000 feet or over), do not ",Jrmally present a problem since their effect on plume ",persion is negligible except at appreciable distances 'rom the source. This is not true in the special case of ,,". crsion break-up fumigation.

I nversion break-up fumigation can occur on sunny "l1omings following cool nights; this produces a mild ','.crsion. The radiant heat absorbed by the earth heats

.,Ir adjacent to the ground by convection so that the "lire layer under the inversion is mixed vertically.

,oer these conditions, relatively high concentrations :"e found at ground levels for periods ranging up to 'Ile hour.

,he ground fumigation concentration at a near ':lXimum value can be approximated by:

z,(x.)"O;H) = Q exp [- ~ (_L)] (13) V2 IJ.crylh l cr"1 : Vlrere:

0'0 = the value of cry for stable conditions plus Ys the effective height of emission.

ill H + 2:J. = h + !:J.H + 2cr .

Turner's term :J II! is used in equation (13) rather Ikm cr" so that estimated calculations for XI will not be ",,,htly higher than actual concentrations. Under ""nigation conditions, additional horizontal spreading .:curs when vertical diffusion is limited by an inversion

layer. Equation (13) is applicable to conditions down-wind of the stack, but not for areas close to the stack base. Its greatest applicability is for relatively long downwind distances, perhaps greater than 5 or 6 kilometers.

Equations (I) through (13) can be programmed for the computer to provide both rapid and accurate solutions to problems. There are many advantages of this modern technology; probably the most important is savings in time particularly, when dealing with multiple sources. In turn, the time saving permits better economic evaluation of the processing options available (e.g., whether a reduction in the number of stacks is economical or enables the refiner more readily to meet air quality standards). Complicated economic studies of this type are not practical when computer programs are not available.

For relatively simple problems, Turner 13 has devel-oped a solution for exponents, in which the exponential function is reduced by table to a simple mathematical multiplier. This method is recommended when a computer program is not available or for occasional usage of the equations.

In concluding this section on equations, it should again be emphasized that for practical purposes there is little difference in the various proposed equations.

6.4.3 PARAMETERS AND DISPERSION COEFFICIENTS

The parameters in equation (13) are the determinants of the calculated concentrations at any point in space downwind of the source. The parameters are Q, H, IJ., X, y, z, and cru and cr,; all except cry and cr, have been previously defined. It is obvious that the accuracy of the calculated concentrations depends on the accuracy with which these parameters are determined. Param-eters x, y, and z can be accurately determined: Q and IJ. should present no serious problem, although H can be troublesome as previously indicated.

Probably the most difficult parameters to determine accurately, particularly if atmospheric stability con-ditions are not precisely known, are the standard deviations (dispersion coefficients) of plume concentra-tion distribution, :Jy (horizontal) and cr, (vertical). In addition to varying with atmospheric turbulence, these factors also vary with wind speed and surface topography and increase with distance from the source. The data presented later assume relatively open country and a height not exceeding several hundred meters above the ground. The values plotted are more accurate for suburban than for urban areas.

Several authors relate these deviations to only three sets of turbulent conditions (e.g., low, average, and moderate) while others, including Sutton, recognize four sets of stability conditions. The six stability or turbulence conditions proposed by Pasquill are described in Paragraph 6.2.4. This is a more sophisti-cated approach (see also Table 6-1) and is used by CONCA WE: 8 Anderson, Hippler, and Robinson; 10

~urner; 13 and many others. Obviously, the actual stability conditions may be at any value (e.g. halfway between moderately unstable and slightlY unstable).

The standard deviations, cr, and Gu, are expressed in meters as functions of the distance downwind for each of six different meteorological conditions. Graphs for these conditions are shown in Figures 6-9 and 6-10. These graphs represent diffusion caused by horizontal forces (e.g., variations in wind direction) and vertical forces (e.g., atmospheric stability and instability). The accuracy of assessment of stability conditions and the validity of the graphical representations determine the accuracy of the calculated concentrations.

6.4.4 INFLUENCE OF ATMOSPHERIC CONDITIONS

Atmospheric conditions and the methods of defining and estimating them are of paramount importance in

6-14 DRW MANUAL--ATMOSPHERIC EMISSIONS

~ f-!" z !!! (.) iL LL UJ 0 (.)

z Q In a: UJ 0.. In C ...J

~ z 0 N

~ :r b>o

104

5

2

103

5

2

102

5

2

101

A Extremely unstable B Moderately unstable C - Slightly unstable

4 X 100 L.----1----1.....L.LLI.l.li. __ -'--'-J-J..1..U-'"-_'--.J-J-W.J....L.I.J 102 2

DISTANCE FROM SOURCE. M

Figure 6-9-Loterol Diffusion, ~y, vs. Downwind Distance from Source for Posquill's Turbulence

Types.

determining actual ground level concentrations and in developing the equations used for predicting ground level concentrations. This is apparent by the terms used in the equations.

The predicted ground level concentration is affected by the wind speed with which it varies inversely, by the effective stack height (H), and by the dispersion co-efficients, cry and ~,:

I. Effective stack height, H: The ground level con-centration varies inversely as an exponential function of the stack height. The parameter, H, in turn, is related to atmospheric stability and instability as discussed previously.

2. Dispersion coefficients, ~y and cr,: The ground level concentration varies inversely with the dispersion co-efficients, cry and cr,. These, in turn, are related to the six atmospheric stability conditions (Figures 6-9 and 6-10) and to the distance downwind from the source.

In view of the importance of atmospheric stability, it might be in order to review the stability factors A to F, discussed previously (see Table 6-2). Pasquill has categorized atmospheric turbulence into six types ranging from A, extremely unstable with high turbulence, to F, stable with practically no turbulence. In view of the large number of parameters in the dispersion equations and the difficulty in achieving quantitative

3xl03 r--,--rTTTnn~~-,-rTY~,-~-,-rTTrrn

f-!" z UJ

~ LL LL

2

2

~ 10 2 ~-----,~~~~----~~~~~----~ (.)

z o In a: UJ 0.. !!!

2

c 101 ...J bN 2

A - E~trernely unstable bL.,.,tC-.."c.--7C-+-- B _ Mod.rately unstable

e - Slightly unstable 0- Neutral E Slightly stable

Figure 6-10-Vertical Diffusion, cr" vs. Downwind Distance from Source for Posquill's Turbulence

Types.

accuracy, the use of six stability conditions provides adequate coverage for the existing variations in atmos-pheric stability.

All environmental sites (refineries) are subjected to at least two of these conditions (e.g., slightly unstable, C, and neutral, D) for a major period of time. At some refineries, three or four of these conditions may be frequently encountered. Atmospheric conditions at a given location and time can change by one or more classes when moving from ground level to a height of perhaps 2,000 feet. If the condition changes by only one class (e.g., slightly unstable, C, to moderately unstable, B), the predicted ground level concentration can change by a factor of 2 or more. Accordingly, it is essential to determine accurately the stability condition immediately above stack height at time of discharge.

Anderson, Hippler, and Robinson state that even though these stability classifications are almost entirely empirical, they represent the best known approach for predicting the dispersion of pollutants. 10 Practically all recent literature on this subject is in agreement.

6.4.5 DISPERSION OF AEROSOLS AND PARTICULATE MATTER

An aerosol may be defined as a suspension of fine solid or liquid particles. The Air Quality Criteria


\lanual 17 defines particle as "any dispersed matter, '0lid or liquid, in which the individual aggregates are Llrger than single small molecules (about 0.0002 micron i" diameter) but smaller than about 500 microns." I One micron, 1iJ" is one-thousandth of a millimeter.)

In this chapter, aerosols and particulates are divided 'iltO three size classifications related to diameter only:

1. Small (arbitrarily defined as particles up to I 0iJ,): hsentially no fallout is experienced, and the standard ,tmospheric dispersion estimates are entirely applicable.

.'. Medium (arbitrarily defined as particles ranging from ! IJ," to 60iJ,): Some fallout may be experienced, par-ticularly for stable atmospheric conditions and for long ,;ownwind distances.

3, Large (arbitrarily defined as particles larger than ''(J:"l: Some fallout is predicted under all conditions. ',:lrge particles do not normally occur in stack emissions :'rom refinery processes.

The rate of free fall of any particle is defined by Stokes' Law. Stokes' Law takes into consideration the I'article density for the particle size involved. This ,'tlnsideration is important but can be disregarded for ,he purposes of predicting ground level concentrations. ;tokes' Law is applicable only to spheres. Although particle emissions are of many geometric configurations, ;he particles can be considered, for simplicity, to be 'oneres of the size that have the same settling rate as the ':clual particles. Utilizing this law, the settling velocities of particles in still air at 0 C and 760 mm pressure and with a density of I g/cu em can be plotted graphically against the particle size as shown in Figure 6-11.

Figure 6-11 shows that a particle with a diameter of 10',J. has a settling velocity of only 0.3 em/sec, which is cquivalent to a wind speed of approximately 0.007 mph. For a 60:J. diameter particle, the settling velocity is approximately 10 cm/sec, which is equivalent to a wind speed of 0.2 mph.

It is apparent from these data that small particles have a minuscule fallout rate. Medium particles, particularly those smaller than 44iJ" have a low fallout ratc which can generally be disregarded. Thus Smith 3 uses a fallout factor of less that 20 percent for emissions from elevated sources in which the mass median particle diameter is less than 20iJ" even for long distances down-wind. Csanady 18 has established that deviations of less than 5 percent can be expected if particle diameters arc smaller than 601".

In summary. some fallout is experienced in the medium-sized range-small in the lower part and significant in the higher part. Generally, particles 20iJ, or smaller have negligible fallout, while particles 44iJ,

u w ~102

~' u

LJIOI ....J u I-~IOO a..

IJ.. o

10-1 >-I-U 3/0-2 w >

(!) 10-3 z ....J l-I-W (f)

10-5~~~~~WL-W~~~~~~~ 10-1 100 101 102 103 104

DIAMETER OF PARTICLE, MICRONS

Figure 6-11 -Settling Velocity of Porticle vs. Diometer of Porticle.

or larger have significant fallout. The range of 20iJ, to 44iJ, has not been carefully explored.

With regard to refineries, particles resulting from gas combustion can be assumed to be smaller than 5:J.,19 A considerable variation is noted for particles emitted from oil-fired boilers (e.g., 10 to 99.5 percent by weight of emissions is reported as smaller than 5iJ,). In this case essentially 100 percent of the particles is smaller than 44iJ,. Some oil-fired combustion processes may be less efficient than oil-fired boilers. In other refinery combustion processes (e.g., a CO boiler) the stack emissions are usually subjected to particulate removal processes, such as cyclones or precipitators, which effectively reduce both emission and particle size.

It has been shown that occasionally for medium particles (l0iJ, to 60iJ,) and usually for larger particles fallout can occur. If vector analysis is applied to those particles that may be affected, the combination of convective velocity and terminal velocity results in what has been described as a "tilted plume." If this effect does exist and assuming similar particle densities,

~16 DRW MANUAL-ATMOSPHERIC EMISSIONS

larger particles will fall out first, followed by particles of decreasing size. Medium particles, even if present as a small percentage of the total count in refinery stack emissions, can assume a major role on a weight basis, and thereby affect a "weight" calculation.

6.4.6 MULTIPLE SOURCES

Multiple sources, as defined in this context, include only sources within the refinery. For multiple sources outside the refinery, reference is made to Anderson, et al. 10 and to Turner. 13

To determine the concentration at any given location, a reasonably accurate method involves determining the individual contribution made by each of the multiple sources. For practical purposes, any source or stack 1,250 feet * or more removed at a perpendicular distance from the x-axis (direction of wind flow) can be elimi-nated from consideration since such contribution would be negligible. The x-axis can also be defined as the line joining the major source and the point of calculation.

A typical refinery area with seven stacks (location of stacks arbitrarily chosen) is shown in Figure 6-12. The three groups of stacks (S I and S2; S3, S4, and S5; and S6 and S7) are more than 1,250 feet apart. It is assumed that all stacks emit approximately equal amounts of the pollutant under consideration. For a north wind, the concentration at a location 5,000 feet due south of SI and S2 involves the contributions of SI and S2 only. Similarly for a location due south of S3, S4, and S5, only these stacks are considered, and the same reasoning applies for a location due south of S6 and S7.

"'For heavy contaminant sources emitting more than 25 tons per day, this distance should be extended possibly to 3,000 feet or more.

N

T OS3 ,..: ...

OSI OS6 0 0

'" OS4

'"

1 OS2 OS7 OS5 1- 5000 FT. -I

Figure 6-12-Typical Refinery Area.

On the other hand, to determine the concentration at a point due east or due west of any of the seven stacks, the contributions from all seven must be considered.

The contributions from each source are obtained by the atmospheric dispersion equations, as previously indicated. It is apparent that this method can involve a varying number of calculations, depending on wind direction and velocity for each of three or more con-taminants (particulates, sulfur dioxide, and nitrogen oxides). Such calculations, even if programmed on a computer, can easily be time consuming, particularly if the refinery is located in a populated area. Depending on conditions, a calculation of this type is probably reasonably accurate.

A less accurate method, more suitable for determining ground concentrations further from the refinery (at least I mile downwind), involves only one calculation for any given wind direction and velocity for each contaminant. With this method, the multiple sources are considered as one source in the atmospheric dis-persion equation. Again, only those stack sources are considered that are at a horizontal distance (upwind) of 1,250 feet or less from the x-axis. The variable Q represents the total contaminant emission for all sources involved and H, the effective stack height, is determined as a weighted average for all individual effective stack heights under consideration. The dispersion coefficients ax, ail' and a, are determined for this weighted effective stack height, the distance being the average distance of all contributing stacks. The concentration so deter-mined represents an estimate, which may be useful for predictive purposes. In the extreme case, where there are sufficient sources to consider the uniform area source, these concentrations are dependent upon cr, only, thus increasing the accuracy of the estimate.

The foregoing approximations are applicable only to stacks discharging above the layer of heavy ground-induced turbulence. Short stacks are unpredictable and increasing their number increases the magnitude of potential error.

6.4.7 WIND TUNNEL AND OTHER STUDIES

The continuing development of basic plume rise and dispersion formulas (including methods of predicting standard deviations of plume spread) provides increased accuracy of calculated data, particularly where there are no complications of terrain, however, this technique is not infallible. Wind tunnel studies are a convenient means for obtaining data on dispersion of stack

J iJ


b. c'[Jccially in those situations where theoretical , produce the least accurate results, as in dealing

:,,'ulld-induced turbulence. The techniques and .lil""' of this method are described elsewhere.1o -d l'lnnel studies can be used effectively for ~:,.'ted building structures, a mUltiplicity of stacks,

, i,>!'ographic effects, and wide ranges of stack ,;:i,\cllv-all of which can influence plume stability ,!;'rcr,ion. The relatively simple cases of single

,1I,charging at high exit velocities above the laver are more accurately assessed when using

!cd :md empirical formulas, since performance r-: I'cll:r than predicted.

""',c' I!,cre is no temperature gradient in most wind lile buoyant effect produced by the thermal and ,'llcri!Y of an actual stack plume cannot be

.lte,1, rhus the wind tunnel studies are limited to '" IIII,ch building configuration, stack structures,

:,,!','crarl1ical irregularities have a marked effect Accordingly, every effort should be

"' IIlC scale model to reproduce the basic struc-. ."d lorographic effects.

h:liJcr. wind tunnel studies are more effective at " Ililld ,peeds (i.e., speeds equal to or greater than ':Ic." ncr second) where thermal or convective

r.'.".:, ::, lile air streams are small compared with the :."",:Ii mass velocity effect. Structurally the wind

t",,,.: . !!\uid have a long test section with a distance upwind equal to at least ten stack

studies are applicable to existing which usually contain multiple stacks,

where additional construction is con-These studies augment the basic formulas.

Jilliculty in using theoretical and empirical equa-alone for calculating or predicting ground con-

,Ctnlralinns has been detailed in the literature.3 \I, IIlU tunnel techniques are used in determining the

c!frcl< of varying rates of wind velocity on stack velocity tII

6-18 DRW MANUAL-ATMOSPHERIC EMISSIONS ----------------~----------------

, ,

future even better accuracy can be anticipated as more accurate values are determined for dispersion co~ efficients by means of suitable field experiments.

The use of wind tunnel and other meteorological studies, especially for the purpose of augmenting pre~ dictive techniques, is also advisable and was previously discussed. Wind tunnel studies properly conducted can serve as excellent tools for new refineries or for complex, existing refineries where new construction is proposed.

In existing refineries, whether or not new construction is contemplated, there is no substitute for sampling and analysis to determine actual ground level concentrations. This serves to indicate the degree of error, if any, in previous calculations and to indicate the magnitude of any corrections that should be applied to the standard dispersion coefficients. Sampling and analysis are valid only to the extent that the refinery is the sole source. Otherwise, it is difficult to predict the refinery con~ tribution to a definite ambient air concentration. Well planned tracer studies can assist in these cases.

6.5 Cooling Tower Plume Rise

6.5.1 BACKGROUND

Petroleum industry cooling towers were originally largely spray (atmospheric) towers of the counterflow type. When induced-draft cooling towers were devel-oped, they were originally the counterflow type, but today crossflow towers are more common and are finding extensive application in petroleum refineries. Tall natural-draft towers (i.e., hyperbolic type) have not been widely used in North America, and there arc no known refinery installations.

In the operation of cooling towers, water cooling is usually accompanied by the emission of a plume and a water drift or spray. As the saturated warm air leaves the tower and mixes with cooler ambient air, there is a tendency to form a cloud (i.e., to condense the moisture content into a visible plume of minute fog droplets). The drift results from physical entrainment of liquid particles or droplets into the rising saturated air. While evaporation losses are approximately the same for different types of towers. drift losses are higher for mechanical-draft towers than for natural-draft towers due in part to the higher velocities of ascending air.

As visible plumes travel downwind they increase the humidity, and occasionally the precipitation, of the area through which they travel. Eventually, dilution and dispersion serve to evaporate the droplets and the plume disappears some distance downwind of the tower. Plume-induced fogs from cooling towers con-

stitute a visibility hazard and can represent an icing hazard during the colder periods of the year. Thus a low to moderate wind speed, an ambient air temperature of 25 F to 60 F and a relative humidity of 70 percent or above may cause fogging (and/or icing). Under certain conditions, cooling tower plumes may merge with stack plumes. This will affect downwind concen-tration of contaminants, possibly in an adverse manner.

Mathematical models and actual experience have indicated that plume rise is directly proportional to the diameter of the plume discharge.21 On this basis, a single large tower for a given capacity is more effective in reducing visible plume formation than several smaller towers, particularly if the latter are of relatively low elevation. Also, mechanical-draft cooling towers dis-charging small diameter plumes at low elevations and at relatively low velocities are more prone to fogging conditions than natural-draft towers.

Mathematical models designed to predict plume behavior and concentrations have been correlated with actual behavior and ground concentrations with reason-able agreement. The data involved were based on tall natural-draft towers and on mechanical-draft cooling towers. The predictions herein should nevertheless be applicable to refinery cooling towers because of the lower effective emission height. As for industrial stacks, suitable allowance should be made for topographic or structural irregularities.

6.5.2 ANALYSIS OF PLUME RISE AND PLUME BEHAVIOR

There is a general similarity between the conditions affecting plume rise and plume behavior for industrial stack plumes and cooling tower plumes, although some differences do exist. One important difference is that t'"Ie larger plume from a cooling tower is related to a large effective discharge diameter. A smoke plume issues from a stack with a diameter ranging from 5 to 15 feet, while a vapor plume may be many times larger. Further, a cooling tower plume contains no con-taminants except possibly hydrocarbons and will usually evaporate while traveling downwind.

Kaylor, Kangos, Petrillo, and Tsai 22 have prepared two mathematical models for predicting plume behavior based on low and high wind conditions. The low wind model involves the turbulent jet method in which plume buoyancy is a dominant factor. In the high wind model, the mathematical model is based on the work of Pasquill and Gifford and the Pasquill-Turner stability categories previously considered. In this method, plume buoyancy is considered low or negligible.

..

f


I h~," \,,0 set, of wind conditions, low and high, I!1J' he further defined as follows:

iI,'" \',Ind: \""ind velocity is relatively low, so that c:c ""leliC and thermal energy effects of plume rise r.1\I,t be con,idered,

: High \,,1 nd: Wind velocity is relatively high and "lul11e rise (j. H) is relatively minor. I

I ;:c line of demarcation between low and high wind is :1,'rl11ally a ratio of cooling tower exit velocity to wind -t'ceu velocity or a ratio of 2: I. Higher ratios are low '1I11d. lov.n ratio'> are high wind.

I I1def low wind conditions, the cooling tower plume ;i'C' oecau'>e of the kinetic energy supplied by natural 'I Induced drafts, because the plume temperature is

,!I'll\'e am bicnt. and because plume diameter is rela-IlIl'ly large. Thi, is especially true in the case of a

L,,~e plume, which has a smaller surface-to-volume r:tll,) than a small plume. In the large plume, there is "'I1,idcrably less surface mixing, and hence a greater 1"l1dency to mamtain its temperature and reach a c"ll1parallvely higher altitude.

6,5.2.1 Turbulent Jet Method for Low Wind Conditions

For the low wind condition, Kaylor, et aI., 22 utilize t he work of Fan 21 and of Abraham 24 and postulate that 1 he cooling tower plume for low or moderate wind 'clocity a"sumes thc characteristics of a round, buoyant, '1lrbulent jd.

The turbulent jet method involves the fol:owing basic as,umptions:

I. Plume-induced turbulence prevails. 2. Round. buoyant, turbulent jet theory applied. * 3. Mixing and cntrainment mechanism takes place of dispersion mechanism. 4. Gau"ian distribution for heat, moisture, density, and velocity profiles. 5. Heat. moisture, buoyancy, and momentum con-served.

The paramders shown in Figure 6-13 are obtained by numerical solution of differential equations. The plume under llIost cond itions (except certain types of inversion) appears ,ullicj~lltIy buoyant so that it will not reach the ground, except possibly in very low concentrations, and will ultimately cvaporate. It is difficult to predict the clfect of a low inversion (e.g., 500 to \,000 feet), which IHay present some problems. Fortunately, an illvcr,ioll at this height is an infrequent occurrence.

>J


of atmospheric conditions is also relevant (see Para-graphs 6.4.3 and 6.4.4).

Kaylor, et aI.,22 verified the mathematical models by observation of visible plume behavior. These com-parisons show reasonable correlation which can, on the average, be represented by: Observed plume length = 35 + (0.91) (predicted plume length).

The actual observations were taken from three sources including a mechanical draft tower with five cells and a natural draft cooling tower. This tower was a hyper-bolic type but, as previously indicated, the general conclusions should also be applicable to low or medium height towers.

In an article by Westlin, Brenchley, and Smith, 25 the PasquiIl-Gifford-Turner method, using Gaussian dis-persion coefficients, is also used in developing a plume length equation. Field test data indicate that an excellent correlation is obtained with a multiple regres-sion coefficient greater than 0.8. In this article, however, high wind condition is defined differently and is related solely to wind velocity-that is, to a wind velocity greater than 1m/sec (7.5 mph). The Kaylor article defines high wind condition in terms of a ratio. The Westlin article is based on results from a crossftow-induced cooling tower.

As previously indicated, wind tunnel studies are advisable for complicated building structures, for a multiplicity of smoke sources or plume sources, or both, and for unusual topographic effects which might disrupt the normal flow pattern. Wind tunnel studies usually disregard any buoyant effect and are more effective at higher wind speeds. Accordingly, wind tunnel models seem to be ideally suited for predicting cooling tower plume behavior in high wind conditions. Although the cost of these studies normally precludes their use, they should be considered when the possibility of hazardous fogging or icing conditions exists.

6.5.3 PLUME CONDENSATION AND PRECIPITATION

Plume condensation is the transference from invisible to visible plume and occurs when the saturated vapors are cooled below the dewpoint. It is of practical significance to deduce whether the condensate remains in the atmosphere as a vapor plume or cloud, or whether there is further condensation to form rain.

The evaporative cooling tower evaporates a small percentage of the water to be cooled, thus releasing its latent heat of vaporization and cooling the water. The rate of evaporation can be quite high, and if only a small portion of the evaporated water is condensed, it will precipitate in the form of rain. In this discussion

it is assumed that the tower is equipped with a drift eliminator, which substantially eliminates physical carry-off of entrained water.

In the paper by Overcamp and Hoult,26 it is shown that "the condensation of the water vapor cannot cause rain unless the plume mixes with the aerodynamic wash of the tower, bringing the droplets in contact with the ground."

Basically, rain formation occurs when minute water droplets condense. A raindrop reaches the ground before it evaporates, while a cloud particle does not. By this definition, a raindrop has a minimum size of approximately 200 microns. In the effluent vapor plume, condensation is the dominant process for water droplets in sizes up to 40 microns. It can be shown that the average length of residence in the plume is 100 seconds or less, which is insufficient time to form droplets larger than 40 microns. Thus Overcamp and Hoult conclude that the condensation process in a vapor plume is not conducive to the formation of an appreciable number of the larger raindrops. This con-cl usion was also reached by earlier authorities, Blum (1948), Bront (1952), and Chilton (1958).

The effect of wind velocity (cross-wind effect) is important in determining whether interaction occurs between the visible plume and the aerodynamic tower wake. If interaction occurs, there will be ground precipitation; if no interaction occurs, the plume will rise and ultimately disappear downwind. The critical variables to determine whether interaction occurs were found by Overcamp and Hoult to be:

1. Speed ratio, R. R = U/IL

Where:

U = plume exit velocity. IL = wind speed.

2. Froude number. (This may not be valid for Froude numbers greater than 3.0.) 3. Reynolds number. (This may also be a factor but can usually be disregarded.)

If the speed ratio, R, is below a critical value, inter-action occurs. The critical value varies as a straight-line relationship with the Froude number-that is, the critical val ue decreases as the Froude number decreases. For a given tower exit velocity, the higher the wind speed the lower the speed ratio, thus the possibility of interaction increases.

The conclusions reached include where the plume struck the ground (2 to 4 tower heights downwind) and

f

)


. ""c,w,tation, where applicable to tall natural-;\"""" iOwers. It is reasonable to assume that

.:.;.:.1::," d()\\nwind (in terms of tower height) and ,ro, li:c total precipitation would be approxi-:.c ,ame for lower height refinery cooling '.111,' estimates of the severity of precipita-

_-:r" n"'lie for a 500 megawatt plant. These are I" Iigure 6-15.

."1 n " relative humidity of 90 percent, an exit "",.llnrc elf 40 C (104 F), and an ambient tempera-

~ (. 125 F), the precipitation would be 0.1

"ne'L1sions are interesting apart from pre-",l;sibilities. A noninteracting plume will 'Ie'lind fog hazards will be minimized; an

',:1"" plume will result in lowered visibility and . "':"1I, cOllditions at or near the ground.

MINlioAlZING VISIBLE PLUMES

111" towcrs in high humidity conditions have a . ~'.:,T,(\ I,) rrod LIce fog when the effluent air is cooled

", dew point. These visible plumes normally ., .[,"bient temperatures of 25 to 60 F and at a

. ,'. ,'i' 70 percent or higher, Temperatures below , lI,ay cause icing, .,1 IlIdllOds can be used to minimize or even

.. !;Ie Ihe plume, Probably the most positive method 'C!Pcrheating the effluent air. This method is

"d laler in greater detail. Other methods include : ';\ii()\ving:

\II~I) the length of the cooling tower with the direc-(Wil ()f the prevalent winds. , Employ drift eliminators to reduce drift to a val uc "f n()5 percent or lower. (Values of drift loss with

0.15

cr: RELATIVE HUMIDITY 1: .... 90%

~ 40% u 010 ---z-0 ;:

75 F DISCHARGE AIR

1

CONVENTIONAL FILL

WATER INLEf 15 F

WATER OUTLET 80F

Figure 6-16-CounterAow Tower.

6-22

AMBIENT AIR

1 ,

(

FAN--'

DECK'"

FILL DECKS

COILS

DRAIN AND

Figure 6-17 -erossflow Tower.

6-23

6-24. DRW MANUAL-ATMOSPHERIC EMISSIONS

6.6 Sample Calculations

6.6.1 REFINERY BOILER STACK

In a refinery having a single boiler stack 75 meters high and operating under the given conditions, what is the effective height of the stack r'or stability condition C? (See Problem 1.) Also, what is the point downwind of maximum ground concentration (see Problem 2), and what is the ground level concentration at this point for three stability conditions-B, C, and D? (See Problem 3.) The contaminant is sulfur dioxide (SO,).

6.6.1.1 Assumptions

1. Fuel is fired at the rate of 120 bbl/hr (20 tons/hr). 2. Sulfur content of fuel is 1.0 percent by weight.

3. Stack exit velocity is 12 m/sec.

4. Diameter of stack is 3 meters.

5. Wind speed is 3.4 m/hr (6.0 m/sec). 6. Atmospheric pressure is 1013 millibars.

7. Stack exit temperature is 540 F (561 K). 8. Ambient temperature is 68 F (293 K).

6.6.1.2 Problem 1

Calculate effective stack height by using Holland's formula:

j.H = v/[1.5 + 2.68 (l0-3p) V" ~"Ta)dJ = ~) [1 5 + 268 (10-3)(1013) (561-=-293) 3J 6 .. 561 = 6 [1.5 + 2.68 (10-3)(1013) (~4)3 J = 6 [1.5 + 8.145 (~~D J = 6 (1.5 + 3.98) = 32.3 meters

Whence, effective stack height is:

75.0 + 32.3 = 107.3 meters

NOTE: For a clear. sunny day, at a wind speed of 6.0 mj sec, stability condition is C. For unstable conditions the value of j.H (32.3 m) should be multiplied by 1.15, whereas for stable conditions. it should be mUltiplied by 0.85.

6.6.1.3 Problem 2

Determine the point of maximum downwind con centration. The following data are taken from Figure 6-18:

I. At stability condition B, the point of maximum down-wind concentration is 0.8 km for an effective stack height of 107.3 km.

2. At stability condition C, the point of maximum downwind concentration is 1.3 km.

3. At stability condition D, the point of maximum downwind concentration is 3.4 km.

6.6.1.4 Problem 3

Calculate the ground level concentrations at these points. The value of Zmax can be determined from the equation:

Zmax = QZiJ. X 2. max [J.

Where: Q = uniform emission rate of pollutants. iJ. = wind velocity.

The value of Q is determined from the sulfur burned. Thus,

20 tons/hr X 0.01(% sulfur) = 0.2 ton/hr or 400 bbl/hr

Given the molecular weights of sulfur dioxide and sulfur, 64 and 32, respectively:

Q = ~~ X 400 bbl/hr X 454 glIb 32 360 sec/hr

= 101 g/sec of SO,

At stability condition B:

Zm" = 1.35 X 10-5 X l~1 = 2.3 X 10-4 g/m' of SO, At stability condition C:

- I 15 10-5 ' !Q I - I 9 10 4 I 3 f SO Zmax-. X X 6--' X -g/mo 2 At stability condition D:

70 10-6 X lOl = 12 10 4 / , fSO Zm,"x = . X 6' X- g. m 0 2

6.6.2 PROCESS HEATERS AND STACKS

Stack emissions from process heaters vary from those of boiler stacks, even though the same fuel is used, because of differences in operation and design. Many process heaters use natural draft, whereas most

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1 6-25


large boilers use forced draft. Also, many refinery boilers burn gas as well as fuel oil, while process heaters are more often gas-fired and generally use a higher percentage of gas. To allow for greater variation in the combustion value of gas, more air is used in process heaters; excess air may be as high as 40 percent. Finally, process heater stacks are usually lower than boiler stacks because the lower height provides a chimney effect and a slightly negative combustion box pressure.

The concentration of nitrogen oxides (NO x ) is usually higher in a process heater stack because higher tempera-tures enable the conversion of nitrogen to oxides. Com-bustion box temperatures and stack temperatures are higher in process heaters than in boilers. Heater stacks range in temperature from 700 to 1,000 F.

Sulfur dioxide and carbon dioxide concentrations are lower in process heaters primarily because of the dilution supplied by additional excess air. In the case of carbon dioxide, an additional factor is the carbon: hydrogen ratio of gas, which is lower than that of fuel oil.

Consider a process heater with a stack height of 164 feet and a stack exit diameter of 8 feet. The stack emits 150,000 cubic feet per minute of gas at 800 F and the gas analysis shows 0.25 percent NOx (as NO,)*, 2.9 percent 0" 77.5 percent N 2 ; the balance is water vapor. The average wind speed is 15 mph (6.7 m/sec). On a sunny day, the ambient temperature is 68 F. Thus the stability category is C.

Calculate the critical wind speed (problem I). For a wind speed of 15 mph, calculate the maximum ground level concentration of NO x and the point of maximum concentration (problem 2). Calculate the ground level concentration of NOx 1.25 miles downwind from the stack (problem 3).

6.6.2.1 Assumptions

I. Stack height is 164 fcet (50 meters). 2. Stack temperature is 800 F (427 C) (700 K). 3. Ambient temperature is 68 F (20 C) (293 K). 4. Molecular weight of NO, is 46 grams per gram mole and weight is 0.129 pounds per cubic foot at N.T.P.

5. Atmospheric pressure is 10 13 millibars.

*Jt is assumed that all oxides of nitrogen are included in the 0.25 percent NO" analysis. The primary components of NO" are NO and NO, and are usually updated as NO" which has a molec-ular weight of 46. To the extent that the average molecular weight of NO, differs from that of NO-, the solutions in Problems I. 2, and 3 would require modification.

Q _ (\50,000) (0.25%) (0.129Ib/cu ft) (454 g/Ib) (29~\ - 60 sec/min 700) = (375L~8~) (0419) (375) (2~.6)

60' 60

= 154 g/sec

6,6,2,2 Problem I

Holland's equation is used to determine effective stack heights, which can be calculated for various wind speeds as follows (see Table 6-3):

~H = 1'/ [1.5 + 2.68 (lO-'p) C'~, Ta) d J Where: )', = stack exit velocity 150,000 50.3 2980 ft mm

15.1 m/sec

Substituting,

~H = 15.1 ~2.44)[1.5 + 2.68G~~~)eO~~0293)2.44J 3~8 [1.5 + 2.71 (~~) 2.44J 36.~ (5.3) 195

[1. [1.

Table 6-3-Effective Stack Heights

i' (m/sec) 1.0 2 3 5 6.7 8

10

j.H (01) 195 98 65 39 29 24 20

h + j.H (m) 245 148 115 89 79 74 70

It is apparent that the critical wind speed is approxi-mately 5 m/ sec, or 11 mph. A more precise critical wind speed can be obtained by plotting maximum concentration vs. wind speed (see also Turner B). The critical wind speed corresponds to the highest maximum concentration on the curve. (See Table 6-4.)

Table 6-4-Maximum Concentration as a Function of Wind Speed at Stability Condition C

.... H Z'tJ./Qrnax QI .... ZIlH\X (m/sec) (m) (m2) (g/m) (g/m:l)

1.0 245 2.4 X 10-" 154 3.7 X 10-' 2 148 6.4 X 10-" 77 4.9 X 10-' 3 115 1.0 X 10-" 51 5.1 X 10-' 5 89 1.8 X 10-" 31 5.6 X 10-' 6.7 79 2.3 X 10-:' 23 5.3 X 10-' 8 74 2.7 X 10-5 19 5.1 X 10-'

10 70 2.9 X 10-" 15 4.4 X 10-'

I I I j i


6.6.2.3 Problem 2

At a wind speed of 15 mph (6.7 m/sec), the maximum concentration of NOx is 5.6 X 10-4 g/ml and will be found at a downwind distance of 0.9 km (Figure 6-18).

6.6.2.4 Problem 3

To determine the NOx concentration at a distance of 2.0 kilometers (1.25 miles) downwind of the source at the centerline of the plume and at ground level, the equation is:

Z(x,O,O;H) = Q exp [- 2! (H)'J 7C'cry crz [J. IJz

154 Z(2000, 0,0 ;H) = (3.1416) (200) (lIS) (6.7)

Where: exp [ - ~ C~~),J

x = 2000 meters at stability condition C ~ II = 200 meters cr. = 115 meters

154 [I 2J z(2000, 0,0;79) = (4.84)(10=5) exp - 2 (0.69)

z = (3.2 X 10-4) (7.88 X 10-') = 2.5 X 10-4 gicu m

This is equivalent to 250 micrograms per cubic meter.

6.6.3 CATALYTIC CRACKING UNITS

In a catalytic cracking unit, the catalyst regulator is equipped with two stages of internal cyclones in the regenerator, and the catalytic off-gases are then pro-cessed in a carbon monoxide (CO) boiler. In general, for all catalytic cracking units having CO boilers, the CO content in the tail gas will be essentially zero. The CO boiler inlet gas will contain an average of 9.5 percent CO for a fluid bed and 6.0 percent CO for an hourly bed. 28

Under the following conditions, assumed for a fluid bed unit during a 50,000-barrel day, calculate the maxi-mum ground level concentration of S02 at a wind speed of 4 m/sec (8.9 mph) and determine the location. (See Problem I.) The day is bright and sunny, stability category B.

Under the same conditions, calculate the particulate concentration at ground level at distances of 0.5 mile and 2.0 miles, and displaced horizontally 0.25 mile (0.25 mile from x-axis). Calculate these concentrations for emissions if no electrostatic precipitator is present (see problem 2) and if an electrostatic precipitator is connected to the CO boiler (see problem 3).

6.6.3.1 Assumptions

I. Stack height is 200 feet (61 meters). 2. Stack temperature is 800 F (427 C) (700 K). 3. Ambient temperature is 68 F (20 C) (293 K). 4. Wind speed is 4 m/sec (8.9 mph). 5. Atmospheric pressure is 10\3 millibars (N.P). 6. Stack diameter is 12 feet (3.66 meters). 7. Gas discharge is 600,000 cubic feet per minute (actual). 8. SO, in exit gas is 1,000 parts per million (0.1 per-cent by volume). 9. S02 emitted is 0.1827 pound per cubic foot (N.T.P.) 10. Particulate emission with no precipitator is 154 grains (10 g) per SCF. II. Particulate emission with an electrostatic precipi-tator is 15.4 grains (1.0 g) per SCF.

6.6.3.2 Problem 1

Calculate maximum downwind concentration of SO, and the point of maximum downwind concentra-tion. Use Holland's formula to obtain the effective stack height.

j,H = v~d [1.5 + 2.68 (10-'p) C-'-j.,Ia) d J Where:

v., = stack exit velocity = 60,0.000 X __ L_ 113.1 60 X 3.28

= 26.9 m 'sec

Substituting,

j,H= ~6.9~3.66)[1.5 + 2.68 (1.013)C()().ffit93)3.66J = 24.6 [1.5 + 2.71(0.581) (3.66)] = 24.6 (7.26)

178.6 X 1.10 = 196 meters (at stability con-dition B)

Thus, H = H, + j,H = 61 + 196

= 257 meters (effective stack height) Determine Q, quantity of S02 emitted in g/sec.

Q = ((>OQ.000)(O20Il(0.1:~7 Ib/cuftl (4}_~lll)G~~)

600 ~~.95) (0.419 829.5 (0.419) 347 g/sec

6--28 DRW MANUAL-ATMOSPHERIC EMISSIONS

Xm.x = (QX:J (;) = 2.7 X 10-' e:7) = 2.39 X 10- 4 glcu m

Where:

~ = 2.7 X 10-'sqm Qmax The location of maximum downwind concentration of SO, at ground level, for stability condition Band an effective stack height of 257 meters, is 1.7 kilometers (Figure 6-18).

6.6.3.3 Problem 2

Determine the particulate concentrations if no pre-cipitator is present. To calculate downwind concentra-tions, the effective stack height, H, and the total quan-tity emitted, Q, must be known. H has been calculated as 257 meters.

_ (600,000 cu ft/min)(10 g/cu ft) (?93) Q - 60 sec/min 700

= 100,000 (0.419) = 41,900 glsec The eq uation to determine particulate concentration at a finite distance is:

X(x,y,O;H) = TO _Q- exp [- I (l')'J cr"O',1L 2 cry

exp [ - ~ (~YJ For stability condition B, at 0.8 km downwind, cry = 130 m and crz = 85 m. For 2 km, cry = 290 m and cr, = 235 m.

41,900 [I (400)2J x(800,400; 257) = 7: (130) (85r (4) exp - 2 130

exp [ -1 e;n'J = 0.30 exp [ - 1/2 (3.08)'J

exp [ - 1/2 (30.2)2J

= 0.30 (8 71) (l0- 3) (1.05) (10-2) 2.74 X 10-' g leu m (at 0.5 km down-wind and 0.25 km from x-axis)

41,900 [I (400)'J Z(2000,400,0 ;257) = 7: (290)(235f( 4) exp - 2 290 exp [ -1 G~~YJ

x (2000,400,0;257) = 0.049 exp [ - 1/2 (1.38)'J

6.6.3.4 Problem 3

exp [ - 1/2 (1.09)'J

= 0.049 (3.86 X 10-1) (5.52 X 10-1) 1.1 X 10-2 g/cu m (at 2.0 km

downwind and 0.25 km from x-axis)

As indicated in the preceding data, the precipitator generally reduces particulates by approximately 90 percent overall, the reduction being greater for larger size particles. The effective stack height, H, is still 257 meters and Q is only 10 percent of its former value (i.e., 4190 g/sec). Therefore,

z(800,400,0; 257) = 2.74 X 10-1 g/Cll m x(2000,400,0; 257) = 1.1 X 10-3 g Icu m

In the preceding examples, it is assumed that par-ticulates behave as gases. This is substantially true after the particulates pass through a precipitator because the remaining particles are primarily small (under lOlL); although some medium-sized particles (lOlL to 60IL) are present. If no precipitator is present, more particles are in the medium range, and possibly some in the large range (over 60IL). The large particles, and to some extent the medium particles, suffer fallout resulting in the so-called "tilted pI ume." Thus, down-wind readings without a precipitator are higher than the values shown, especially for X(800,400,0 ;257), which is now shown as 2.74 X 10- 5 g/Cll m

6.6.4 FLARES

Calculate the total effective height of a flare plume under the following conditions:

I. Stack height is 150 feet (45.7 meters). 2. Stack diameter is 2 feet (0.61 meters). 3. Wind velocity is 15 mph (22 ft/sec) (6.7 m/sec). 4. Stack exit velocity is 0.2 sonic velocity or 1000 X 0.2 = 200 ft/sec (61 m/sec). The total effective height of the plume, H, is determined by:

H = Hs + J.FL + J.H

I


! Is = stack height. '... fL vertical component of flare length (to

yield imaginary stack height). .~ f! = plume rise above imaginary stack height

using Holland's equation.

;, has been shown that j.FL can be determined with ',)Ille degree of accuracy, but j.H is an approximation .;t hcst. regardless of the formula used. There is reason ;. helieve that j.His a relatively low figure, numerically.

lis 1"' .L

J.FL

= 45.7 meters. = constant X stack diameter (API RP 52 I)

120 X 2 = 240 feet (73.2 meters).

= FL (~~l). i ,0 obtain ;::;~~, the ratio of wind velocity (IL".) to stack . il velocity ([.I.,,) must be calculated:

~'W = ~ = 0.110 [.1.0 200

,d from Figure 6-6,

'E..1y = 044 L .

.1FL = 240 (0.44) = 105.6 feet (32.3 meters) ,'" obtain .1H from the Holland equation, the

[,)llowing data were assumed for the imaginary stack height:

I. Flare diameter is 7 feet (2.13 meters). , T. (temperature of total gases) is 600 F (589 K). 3. Tn (ambient temperature is

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