Dilution of Waste Stack Gases in the Atmosphere’ PHIL E. CHURCH University of Washington, Seattle, Wash.
Q
Experimental field work on dilution of stack gases at the Hanford Works site was conducted by forcing a continuous stream of oil-fog up a stack, 16 inches in diameter and 200 feet high, and measuring, photoelectrically, the comparative concentration (stack concentration considered as 1) of the oil-fog and mixed air at known distances from the stack under known conditions of vertical temperature gradients and wind speed. Under thermally unstable conditions with low wind speed, stack gases will intersect the ground close to the stack and may be diluted
with as little as 300 volumes of air. With higher wind speed, the stack distance becomes greater and the dilution much greater. With neutral stability (mechanically mixed) stack gases will intersect the surface some 8 to 10 stack heights downwind. This condition occurs when the wind is in excess of 20 miles per hour. When the air is stable stack gases remain embedded in a thin horizontal layer which widens, thickens, and dilutes slowly downwind. Mixing with as little as 400 volumes of air in more than 0.5 mile has been measured.
E ’
t o 1 volume ih 3000 volumes of air were used each time the instrument WBS calibrated. The instrument would measure concentrations as low as 1/50,000 of t h a t in the stack. The same type of instrument was used t o determine the dilution when the plume did not come to the ground, except that t h e suction necessary t o draw the diluted sample into the instrument was produced by a n aspirator device which operated when there was wind. The instrument and wires t o t h e indicating meter o n the ground were supported b y a small barrage balloon. The smoke generator produced a dense white cloud of very stable, condensed oil particles about 0.6 micron in diameter. The terminal velocity of the falling droplets was about 0.2 inch per hour. After passing through the blowers and 10 feet of the stack, the temperature of the oil-fog was about 133” F. No observations were made of its temperature at the top of the stack, but it was assumed there would be only a minor temperature difference between the atmosphere and the oil-fog; essentially the oil-fog was considered as “cold” smoke with a negligible lift owing t o its temperature. T h e volume of air forced u p the stack was 5500 cubic feet per minute and the oil consumption, t o produce the oil-fog, was held at about 65 gallons per hour. The concentration of oil-fog in the stack was considered as unity. All dilutions hereafter mentioned are expressed as the number of volumes of air with which a unit volume of oil-fog had been mixed. Thus, B dilution figure of 500 indicates a concentration of oil-fog of 1/500 that in the stack.
in the history of the Manhattan District Project, it was necessary to obtain all possible information on waste gas problems t h a t might arise at the Hanford Works. It was decided to study this problem in the field because of the scanty literature at t h a t time (1, 8, 11, 12) dealing with the amount of dilution t h a t waste gases from industrial stacks undergo. Since World War I1 many papers on the general problem of dispersion of atmospheric pollution have appeared (9-6,7,9,10,13-16). The primary assumption underlying the present investigation was that the general characteristics of mixing and the amount of dilution of waste stack gases when discharged into the atmosphere were dependent upon meteorologigal conditions. T o obtain data on these properties, equipment for simulating a stack and its output was assembled at the location of one of the operating units.
a
The stack was erected on smooth flat terrain covered with grass and sagebrush; only one building, about 40 feet high, was within a 2000-foot radius. The equipment consisted of a W i n c h stack, 200 feet high, through which, b y means of blowers, the whole discharge of a n Army M-1 “smoke” (oil-fog) generator was ejected into the air. The stack was provided with 1.25-inch jet pipes at each 50-foot interval (up t o 150 feet) through which was ejected enough oil-fog t o act as tracers for air flow a t the various altitudes. At each 50-foot level up t o 200 feet a shielded thermocouple was suspended and connected to a precision potentiometer in the nearby office building. Recording anemometers were placed a t 16 and 60 feet, and a recording anemometer and a wind vane at 200 feet. This instrumental arrangement provided d a t a on the lapse rate, t h e wind speed, the change of speed with height and the wind direction at the top of the stack. T o determine the amount of dilution, use was made of a photoelectric instrument, so designed t h a t a chance in the clarity of the air drawn between a light of fixed intensity and the photoelectric cell changed the current output of the cell. This photoelectric vapor densitometer was extremely sensitive, rapid in action, and rugged. It was mounted in a truck capable of going over almost any type of terrain. T h e air with the diluted oil-fog was drawn continuously through t h e instrument by suction from the windshield wiper. Each day, or more often, the “densitomet& was calibrated by drawing from the stack a known volume of oil-fog, mixing it with a known volume of air, and then forcing this mixture through the instrument. Several different concentrations of mixture from 1 volume of oil-fog in 500 volumes of air 1 Presented before the Division of Industrial and Engineering Chemistry, Symposium on Atmospheric Contamination and Purification, a t the SOCIETY,San Francisco, Calif. 115th Meeting of the AMERICAN CHEMICAL Other papers of this symposium were printed in the November issue of I N D U S T R I A L A N D ENCINEERINQ CHEMISTRY.
i
It was assumed t h a t the oil-fog would follow directly, without appreciable lag, any and all air movements in the area occupied by the oil-fog, t h a t the presence of the oil-fog would not materially affect the air movement in any direction, and finally, t h a t the dilution of the oil-fog would represent within reasonable limits of accuracy the dilution of gaseous or minute solid particles emitted from a stack under similar meteorological conditions.
TYPES OF SMOKE PLUMES The visual plume of oil-fog has shown three clearly defined types of plumes (6),each depending on certain meteorological conditions. These three types have been named “looping,” “coning,” and “fanning”; they occur when the lapse rate is unstable, approximately neutral (with wind), and stable, respectively. Unstable Condition. When the atmosphere has a lapse rate greater than the dry adiabat, t h e plume will alternately ascend and descend or descend and ascend after leaving the stack. When it comes t o the ground, the plume will remain in contact with the ground for a short distance only as i t travels with the wind; it
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Vol. 41, No. 12
may then ascend and side to the other of later repeat this same the above-mentioned up and down motion again some distance downwind. Portions than mith negative of the plume roughly assume vertical columns downwind. The wind speed is the air flow is coma p p r o x i m a t e 1y the p i i s e d of e d d i e s same at 16, 60, and whose motions are in 200 feet, but is not in excess of 20 miles per DRY ADIABATIC RA hour when this condition occurs. T h e ground) have a slower the horizontal higher velocity than wind speed, the more WIND SPEED M P H the Ioucr poitions. n e a r 1y vertical the This evidence points Figure 1. Isolines of Least Dilution Expected at Ground from Stability columns. OS. Wind Speed t o frictionally d e There is no doubt veloped, mechanical Stack height 200 feet that the vertical cureddies whose strucrents which produce t u r e is different the ascent and descent of the plume are of thermal origin. This from those thermally produced and maintained. type of plume occurs with great regularity when the soil surface is Stable Conditions. When the lapse rate is less than the dry warmer than the air. The plume demonstrated that the descendadiabat, the plume remains in a horizontal plane gradually widcning currents were of greater time duration than the ascending ing downwind; it always stays in a thin layer vprtically. This currents, because downwind the profile of the trail showed the type of flow develops when the dcgrce of stability is about +10 X rising columns to be of smaller dimensions than the descending 10-6 per foot or more-i.e., the lapse rate is isothermal or is in an columns in the spaces between them, especially during mid-day inversion condition. Under stable conditions, the trail Kill when soil was much warmer than the air. The height to which remain in the layer in which it leveled off horizontally, and it will mixing by alternate columns may occur is definitely restricted flow a long distance over level ground. The >beet increases in to t h a t layer in which the lapse rate is superadiabatic or has vertical thickness downwind a t so slow a rate that rarely does negative stability. The degree of stability is expressed as any of the plume reach the ground (over level country) within 5 t o E = l / O X dO/dz where 0 is the potential temperature. 10 miles, Numerous observations on the rate of descent of the plume The lateral spread downwind seems intimately related t o the were made. These gave an average rate of slightly more than 4 rate of change of wind direction with height within the cloud feet per second in the summer, though the rate varied from 0 to layer; when stable conditions were present, the vertical cross more than 7 feet per second. I n winter the average was fracsection of a plume was such t h a t the left-hand edge, facing downtionally less than 3 feet per second, from the few observations obwind, was ragged, torn, and diffuse, and a t a slightIy lower altitained. Assuming a downward velocity of 4 feet pcr second, segtude than the right-hand edge, which was sharp, clearly dements of the plume would first contact the ground about 80 feet fined, and a little higher. Where smoke is ejected into a stable from the stack with a horizontal wind velocity of 7 mile per hour, layer with no shear, both edges are similar. 400 feet from the stack with a 5-mile-por-hour wind, 800 feet Change from Stable to Unstable Conditions. Some time after away with a 10-mile-per-hour wind, and 1200 feet distant with a sunrise a superadiabatic rate develops in the lowest layer and 15-mile-per-hour n ind. The above distances are computed for progressively builds upward. The time of dag when the change smoke which levels off 225 feet above the ground. from stable to unstable conditions occurs has been observed daily When the lapse rate is unstable, the plume not only loops in the for nearly 5 years. I n the period from April to mid-September, manner described above, but also swings through a wide horithe time required after sunrise for an unstable condition to dezontal angle. The higher the wind speed, the narrower the angle velop to an altitude of 200 feet is from l to 1.5 hours for a clear or through which smoke will swing. partly cloudy sky, from 1.5 to 2 hours with low broken clouds or a The above evidence indicates t h a t the unstable layer is comhigh thin overcast, and from 2 to 3 hours with a low overcast or posed of eddies thermally developed and maintained, which have other conditions obscuring the sun. In winter the corresponding components of motion in all planes. time intervals are from 1 to 2 hours longer. Neutral Stability (Dry Adiabatic Lapse Rate). Neutral stabilChange from Unstable to Stable Conditions. Positive stability ity occurs only when wind velocities of 20 miles per hour or more first forms in the air layer next to the ground about the time the are attained, When this condition is present the plume assun sets. When the degree of stability reaches f10 X ~ u m e sthe shape of a narrow cone, the axis of vvhich appears, per foot in the loKest 50 feet, no more oil-fog romes to the ground. when viewed on the profile, to be inclined a t a small angle toAppreciable vertical currents are still present above 50 feet, but ward the ground downwind. This angle is so small that, coupled the amplitude of vertical movement is greatly reduced. As the with the gradual widening of the trail, the first fringes of the layer with positive stability becomes thicker and the degree of plume reach the ground about 1600 t o 2000 feet from a 200-foot this stability increases in value, the plume is confined to a thinstack. At t h a t distance from the stack the upper boundary ner and thinner layer. of the plume was still estimated to be no higher than the stack There is an intermediate stage between truly stable and un. top. stable conditions which occurs when the stability is between zero Not only does the plume widen slowly downwind, but i t also per foot and the wind is less than about 20 and +IO X swings through a much smaller angle than under unstable condimiles per hour. Under these conditions the oil-fog will rarely tions. Records shon- the arc of swing t o be in the neighborhood come to the ground; more often as the lapse rate approaches the of 30" to 40" with flow undisturbed by buildings or topographic dry rate and less often as the positive stability increases. features. The time interval for the plume to swing from one
December 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY DILUTION
During a period of nearly 6 months a total of more than 40,000 individual readings was obtained from clouds of oii-fog. These readings were procu ed over a wide range of stability, wind velocity, and wind direction. About 36,000 readings were made at the ground, most of them when looping was occurring; a small number were procured under coning conditions, and the remaining 4000 readings were obtained when fanning was in progress. Unstable Conditions. A small fraction of the field readings and supporting meteorological data was subjected t o statistical analysis. The results were not particularly outstanding. The simple correlation coefficients between the least dilution and various parameters were as follows: wind speed a t 60 feet, +0.51; distance from stack (horizontal), f0.28; stability, -0.16. These were the only coefficients of any statistical significance, but were not high enough to be usable. Hence, the data were subjected to a different type of analysis. It was necessary to know what least dilutions could be expected a t the ground from meteorological elements that could be instantaneously observed a t various levels from a fixed location, The elements most easily observed are wind speed and temperature. (The wind direction must also be known, but for other reasons.) Wind speed and vertical temperature differences a t any and every instant can be translated to the general behavior of the plume, whether or not the plume would come to the ground, the distance downwind where it would first strike the ground if it comes to the ground, and the least dilution (maximum concentration of pollutant) expected a t the ground level where the plume first comes to the ground. To put such information in usable form, the least dilutions observed from field readings were plotted on a graph in which the stability was the ordinate and wind speed the abscissa. The distribution of these least dilution values fell in such an orderly arrangement that isolines could be drawn of the least dilution values expected a t the ground. The wind speed governs the distance downwind at which the plume will first intersect the ground; the greater the instability the greater the vertical velocity of the downdrafts; the instability is only roughly related t o the wind speed during the day. Figure 1 shows isolines of least dilution at the ground. Multiplying the wind speed in feet per second by the number of seconds it will take for a descending segment of the plume t o reach the ground gives the distance from the stack where the plume will first intersect the surface. If the wind speed is greater than 20 miles per hour, the plume will reach the surface about 10 stack heights downwind. On several occasions the oil-fog plume came to the ground within 40 feet of the base of the stack. Obviously it was when there was a high degree of instability and nearly calm. Unfortunately, no densitometer readings were made on those occasions, but it can be safely said that from eye observations the oilfog appeared as dense, if not denser, than that measured numerous times within 400 feet of the stack base, and much denser than that a t greater distance from the stack. The amount of dilution is more nearly in inverse proportion to the distance of smoke travel from the top of the stack to where the smoke intersects the ground than the horizontal distance from the stack base. Little attempt has been made to compute the average dilution of the plume segments that reached the ground because normally the dilution ranges from infinity to a minimum value and back to infinity in a n irregular manner along a longitudinal section of the plume segment. Tentatively, dilutions on the surface may be set as approximately 2000 at 450 feet, 4000 at 900 feet, and more than 10,000 beyond 1700 feet. Neutral Conditions. So few field readings were obtained under coning conditions, because of the dust in the air, that no figures on dilution values can be given. Eye observations of a coning plume, however, indicate less dilution than under looping but much more than when fanning is occurring.
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Stable Conditions. When the oil-fog remained aloft, the pattern of mixing was entirely different from that under an unstable or neutral lapse rate. Under light and moderate wind velocities and with a ground inversion, the smoke remained a t approximately the stack height, or slightly higher, and the plume took on the shape of a gradually widening ribbon that continued for great distances downwind. Dilution was much less per unit distance downwind than during looping conditions, and the dilution appeared to be unaffected by the wind speed at the stack top. However, the less the wind speed, the steeper the inversion that can occur. The critical wind velocity which would prevent an inversion from forming was from 16 to 20 miles per hour, but, with an existing inversion, a wind of 22 to 25 miles per hour was necessary to reduce the stability to +10 X l0-6per foot. Lastly, the dilution within the plume was much more uniform than when the trail is looping. When the absolute least dilution wm plotted against stability, wind speed, and distance from the stack, it was found that a t a constant distance the dilution decreased with increasing stability until a value of about +40 X lom6per foot was attained, but with a still higher degree of positive stability dilution increases (Table I).
Table I.
Effect of Stability on Dilution
(Distance from stack, 2800 feet) Stability 10-8 per foot +4 +16 Least difution 1200 800
2% -E
&E
The absolute least dilution, when plotted against distance regardless of stability, follows closely the equation below over the distance range of 3000 to 7300 feet from the stack:
Y. =
a
+ bX
where a = 400, b = 0.47, Y o = absolute least dilution, and X = stack distance (in feet) - 3000. For 159 individual clouds investigated, the average least dilution over the above distance range follows the equation:
Ye
=i
a
+ bX
where a = 2400, b = 1.0, Y,= average least dilution, and X = stack distance (in feet) - 3000. Simple correlation coefficients between least dilution and various parameters for a portion of the data are as follows: wind speed, +0.02; distance from stack (horizontal) in feet, +0.37; stack distance squared, +0.68. There appears to be no definite relation between wind speed and dilution except as the speed affects the stability. Using the average of the mean dilutions of the individual clouds, or the average of each 40 successive readings, if the cloud yielded more than that number of readings, and plotting these dilutions against horizontal stack distance only, the dilution was found to increase with distance according to:
where Y, = average dilution and X, = stack distance (in feet). The average dilution at various stack distances is given in Table I1 and is extrapolated for distances less than 3000 feet.
Table 11.
Average Dilution
Staokdietsnae feet 1000 2000 3000 4000 5000 6000 Average dilution 700 1900 3600 6400 7500 9700
7000 11,600
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The data presented here should be generally applicable to conditions similar to those prevailing when these tests were carried QUt.
Vol. 41, No. 12
(3) Davidson, W. F., Bull. Am. Meteor. Soc., 27, 547-9 (1946). (4) Dept. Scientific and Industrial Research, Tech. Paper 1, At-
mospheric Pollution Research, London, H.M. Stationery Office, 1945. ( 5 ) Dobson, G. hl. (1948).
ACKNOWLEDGMENT
This report would not have been possible without the able assistance of a number of othws, especially C. A. Gosline, Jr., E. I . du Pont de Nemours & Company; J. F. Mattingly, U. S. Weather Bureau, Evansville, Ind.; and 0. H. Newton, U. 8. Weather Bureau, Brownsville, Tex. LITERATURE CITED (1) Bosanquet, C. H., and Pearson, J. L., Trans. Faraday SOC.,32, 1249-63 (1936) ( 2 ) Brooks, F.A,, Agr. Eng., 28, 233-40 (1947). e
B.,Quart. J . R o y . Meteor.
Soc., 74, 133-43
(6) Etkes, P. W., and Brooks, C. F., Monthly Weather Rev., 46, 45960 (1918).
(7) Frost, R., PFOC. R o y . Boo., A186, 20-35 (1946). (8) Hewson, E. W., IND. ENQ.CHEM., 36, 195-201 (1944) (9) Meetham, A. R., Weather, 1, 200-5 (1946). (10) Parker, A., Nature, 155, 682-5 (1945). (11) Roberts, 0. F. T., Proc. R o y . Soc., A104, 640-53 (1923). (12) Sutton, 0. G., Ibid., A135, 143-65 (1932). (13) Sutton, 0. G., Quart. J.R o y . Meteor. Soc., 73, 257-81 (19471 (14) Ibid., pp. 426-36. (15) Ibid., 74, 13-30 (1948) Rncmvm March 7 , 1949
rner
r
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wit
S JOSEPH GRUMER Cent,ral Experinrent S t a t i o n , 77.S. B u r e a u of 'Mines, P i t t s b u r g h , P a .
T h e ability to interchange gas supplies has become important in the gas industry. New gases may not be able eo maintain stable flames in consumers' appliances. Recent studies have shown the fundamental principles of flame stabilization and entrainment of air in gas burners. This information is combined into relationships predicting the performance o f all burners in a community when fuel gases are changed, without requiring that the number of burners or their individual characteristics be known. Only certain readily obtainable data on the fuel gases concerned in the intcrchange are required. The method can be put to a practical test when data on actual fuel gases in use become available.
HE gas utility industry is occasionally forced to interchange fuel gases or supplement a low supply with gas of another kind. This may lead to serious problems, inasmuch 8s new mixtures are required to burn satisfactorily on a large number and on different types of gas appliances in use within a community. It is therefore necessary to develop a method for predicting the performance of interchanged furl gases, The A4merican Gas Association and the National Bureau of Standards ha,ve attempted to develop a method from an essentially empirical approach, but to date no completely satisfactory solution has been found ( 1 , 6). The practical method dcveloped in this paper can be used when certain readily obtainable basic data on fuel gases io be interchanged become available. The metliod is based on theoretical principles making use of the concept of boundary velocity gradients that define the flame-stability reglon and the principles of air entrainment by a fuel jet. These are combined t o develop relations which predict the rhange in burner performance when fuel gases are interchanged. FLAME-STABILITY DIAGRlJIS FOR VARIOUS FUEL GASES
Flash-back and blowoff characteristics may be studied with a burner consisting of a cylindrical tube with unrestricted port into which premixed fuel gas and air are iiitroduced a t different rates of flow. A burner flame is stable between two critical flow conditions, which are determined by the slopes of the curves of critical
stream velocity a t the boundary of the stream (10, 12, 16). If the stream-velocity distribution over the entire cross section is known, the desired slopes or, as termed by Lewis and von Elbe, critical boundary velocity gradients ( g F for flash back and g B for blowoff) can be calculated from measured critical flows for flash back and blowoff. For laminar (Poiseuille) flow, the boundary velocity gradient, g, is ( 1 2 ) g = limit (--dU/d.r) = 4Y/nR3 ?-+
? '
(1)
where V is the flow in a cylindrical tube of radius R and si is the stream velocity a t distance T from the axis of the tube. For turbulent flow of Reynolds number Re (8, 1 6 ) g = limit +R
(-dU,ldr) = V2/103R4R~1'4
(2)
The advantage of this theoretical treatment of flame stability can be seen by examining Figures 1t o 4 t)aken from ( 1 2 ) * The critical flows of natural gas-air mixtures a t \+hich flash back and blovioff were observed. with various burners are presented in Figures 1 and 2. There is a, different set of curves for each burner size. However, by plotting the data against g B instead of V F , subslantially a single curve is obtained for the burners of various size except for very small tube diameters approaching quenching distances (the minimum t.ube diameter through which flame will just pass) and for very large t,ube diameters that show tilted flames (12, 15). This is shown in Figure 3. A similar unification is obtained by plotting g B instead of VB. Figure 4, in which both g p and g B are plotted, defines the flame-stability region of natural gas-air mixtures. Similar flame-stability diagrams may be obtained for all combustible constituents of commercial fuel gases, which are hydrogen, carbon monoxide, methane, ethane, ethylene, propane, propene, and but'ane. The same is true for mixtures of these constituents with one another and with noncombustibles, such as oxygen, nitrogen, and carbon dioxide. Thus it is clear that, in principle, there is no difference between supplemeiiting fuel gases and interchanging them. A desired simplification is obtained by plott,ing fuel gas percentage as the fraction of the stoichiometric. In this way the
