Predicting the Concentration of Effluent Material within a Plume Emitted from a Tall Chimney BYD. J. MOORE Central Electricity Research Laboratories Leatherhead Surrey Received 23rd November 1972 The rates of formation of aerosols and the visual appearance of chimney plumes (including the effects of condensation of water vapour) both depend upon the dilution of the effluent gases. This dilution differs from that predicted by conventional dispersion formulae in that these latter refer to time mean concentrations whereas what is required is the dilution at any given instant in time as the plume travels downwind. The instantaneous dilution near the source depends on the turbulence induced by the plume’s movement through the atmosphere rather than the dispersive properties of the surrounding atmos- phere at the plume level.A theoreticallempirical model which has been developed to predict the trajectory of hot chimney plumes also predicts this instantaneous dilution. Dilutions calculated by this method in different conditions of wind speed and atmospheric stability for various plant emission characteristics are tabulated and compared with values obtained from field measurements. 1. INTRODUCTION If one is concerned with the concentration of material at ground level resulting from the emission from a source which is some distance away the normal practice is to sample the material over a period of time. It is then possible with the aid of various hypotheses about the nature of the dispersion of the material and possibly the rise of the plume material above the discharge point due to its buoyancy and initial vertical momentum to come to a reasonably satisfactory understanding in physical terms of the observed concentration.There are however certain aspects of plume behaviour including the rise of the plume the visibility of the plume and rates of chemical reactions within the plume which depend not on the time-averaged concentrations but on the concentration within the plume at various distances downwind at an instant in time. The time- averaged plume dimensions are the result of the meanderings of the instantaneous plume due to the large scale turbulence in the atmosphere and may bear little relation to the instantaneous dimensions. Furthermore the dilution of any large emission of material certainly within the first few hundred metres of its leaving the source is almost entirely due to its motion relative to the atmosphere and the intense mixing produced by this relative motion.Thus any information which is based on observa- tion of the dispersion of small releases of material over extended periods of time such as the Porton work reported by Sutton is irrelevant to the problems enumerated above. In the various attempts to explain the observed trajectories of buoyant plumes over the first kilometre or so of their path observations of the instantaneous dimen- sions have been made either from photographs or from lidar 3s traverses of the plume. These have in general shown that the plume diameter in so far as it can be determined from the irregular shape of the plume elements is on a given occasion 222 D.J. MOORE 223 proportional to the height of rise above the source. For a plume with substantial heat emission (i.e. several MW or more) this relation appears to hold for hundreds of metres and perhaps even to over 1 km on some occasions.2 This sort of behaviour is consistent with the assumption that the rate of entrain- ment of ambient air into the plume elements is equal to the product of the surface area of plume element exposed to the ambient air times the velocity of the plume relative to the ambient air. That is in general to the vertical velocity of the element. The constant of proportionality implicit in the above relationship is in fact a constant for a given plume element only; its value changes from element to element in a way which is not fully understood but appears to be determined by such factors as the angle of attack of the wind at the stack top the ratio of the wind speed to the effiux velocity and the initial buoyancy and its relation to wind forces on the emerging plume.Despite the complexity of the problem a number of investigators have developed models which give a very fair representation of the plume trajectories over distances out to 1 km or more. The principal differences between the models concern the idealised geometrical forms assumed for the plume elements e.g. bent-over chains of spherical puffs 8p and the expression for the relative velocity which some- times includes additions to the vertical velocity with various weighting factors.'O* '' The other source of difference is the assumptions made about the way in which the atmospheric turbulence eventually assumes the major role in the dispersion when the plume elements have become so diffuse that their physical properties (i.e.turbulence and density) are no longer distinguishable from those of the surrounding air. A comprehensive test of a trajectory equation based on the recombining plume model has been shown to give mean errors of around 10-15 % in determining plume heights over a wide range of meterological conditions distances downwind and plant capacities. In this short paper it is not intended to explore in any depth the difference between the various plume models.They are sufficiently similar for the differences between them to be relatively small compared with the differences between concentrations calculated from their basic assumptions and concentrations calculated for an inert plume model. Here we shall show where the use of such a model which assumes that the plume behaves as though it were no different from the surrounding atmosphere as far as dispersive properties are concerned will lead to serious over estimates of " in-plume " concentrations. 2. THE INERT PLUME We consider the dimensions at any instant in its time of travel of an element of the plume which contains material which has been emitted into the atmosphere without in any way changing its dispersive properties. For an emission of any size this is clearly impossible and furthermore if we consider a true point source with a finite emission the concentration at the source is infinite.In practice stack emissions are usuaIly diluted with air or at least nitrogen so that the material is apparently emanating from a point source some distance upstream of the actual source. The familiar gaussian distribution of material is in fact due mainly to the meander- ings of the plume axis over the period during which the effluent is being sampled. Most truly instantaneous traverses of the plume e.g. by laser rangefinder indicate a "top-hat " distribution of material but then the traversed plumes have not been inert. Some attempts to calculate instantaneous dimensions from smoke puff photographs (e.g.by Gifford 12) have made assumptions about the distribution of material in the plume. EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES If we consider that the instantaneous plume has a " top hat " distribution of material that the axis of the time-average plumes remains within the instantaneous plume for most of a given sampling period but points removed vertically or in the cross wind direction are out of the plume for an increasing proportion of the period as one moves away from the axis then one could represent the instantaneous concen- tration by the axial concentration of the meandering time-average plume. This would give an underestimate of the instantaneous plume concentration because the time-average axis would occasionally be out of the plume.However for purposes of comparison with the self-diluting plume models it will be assumed that the axial concentration in the time-average plume for sampling times of several minutes is a reasonable estimate of the average concentration within the plume elements. Such concentrations as functions of distance from the source or time of travel through the atmosphere may be readily estimated from the data presented e.g. by Pasquill l3 and reproduced in convenient graphical form as in " Meterology and Atomic Energy ". Following Pasquill we write an expression for this axial concentration C1 = Q(xf' q)/(27cxp+qU0,aYl) where C1 is the axial concentration (units m-3) at distance x/m downwind. Q is the rate of emission of the material considered (units r1).x1 is the distance down- wind at which the vertical and cross wind concentration distributions have standard deviations crzl and crY1 respectively (m).0 is the mean wind speed (m s-I). p and q are numerical constants whose values lie between 0.5 and 1.0. If we wish to sub-stitute time of travel t in place of distance x then we replace x by Ot in eqn (2.1). Eqn (2.1) may be written in the form where B = 2nazl~,,,/(x~f4) and may be regarded as a constant on any given occasion but whose value will vary with meterological conditions. Qh = the rate of heat emission in MW. Expressing the concentration in the form given by eqn (2.2) is convenient for comparison with the concentrations deduced for buoyant plumes which follow in section 3 below. 3.BUOYANT PLUME For the sake of simplicity we consider a plume of material with the same density at ambient temperature and pressure as the ambient air emitted into an atmosphere in which the potential density (i.e. the density referred to a standard pressure) is not changing with height. The simpler plume models then indicate that the concentration of material within a plume element is given by where C2 is the concentration in a plume element which has risen a height z above the source. rn is a numerical constant with a value between 2 and 3 depending on the assumed nature of the plume elements (i.e. 2 if they are conical or cylindrical 3 if they are spherical or any other closed configuration). A may be a constant if the heat content of a plume element is assumed to remain invariant with distance from the source or may be a function of distance if the heat content of the element is changing with distance.Its dimensions are mz-m. It may be a function of the D. J. MOORE wind speed. The various expressions forplume rise in the above assumed meterological conditions are of the form l8 z = AIQLxs//U (3.2) if one ignores the initial momentum of the plume and assumes that the rate of entrain-ment is proportional to the vertical velocity. Here Y is a numerical constant equal to $ for the two dimensional (conical etc.) models and + for the 3-dimensional (spherical etc.,) models. s is a numerical constant with values between 3 and $-and Al is a parameter equal to (g/p,CpO)'A2where g is the acceleration of gravity (m s-~),Cpis the specific heat at constant pressure of the effluent (MJ kg-l K-l) pe is the density of the ambient air (kg m-3) 8 is the absolute temperature of the ambient air reduced to standard pressure (K) A2 is a parameter of dimensions (m ~-~)-(~'-')m(~-('+~)) which represents the effect of such factors as the initial length of plume material within a plume element and the dependence of the rate of entrainment factor on the wind speed etc.Substituting for z in eqn (3.1) from eqn (3.2)we arrive at c2= (Q/Q~)Q;-~~/(A~x~~D~ (3.3) -") where A = AAY. The buoyant plume model used above would estimate the maximum dilution due to relative motion at a given distance downwind. If the atmosphere were stably stratified (i.e.the potential density were decreasing with height) then the plume would rise less rapidly than eqn (3.2) indicates the difference becoming more marked as the distance from the source increased. For practical purposes it would be sufficient to assume that the plume followed eqn (3.2) out to some distance xT where X is proportional to the stability parameter ((g/p,D2) I (dpe/&) 1 )* and is roughly equal to 120 U m for isothermal conditions in light winds. If one is concerned with a plume of gas with a density at ambient temperature and pressure which differs appreciably from that of air then Qhin eqn (3.1) (3.2) and (3.3) may be replaced by the term (VApCJI),where is the total volume rate of emission of the effluent (m3 s-l) (i.e. of all the gases being emitted from the stack not just the material being considered) Ap is the difference in density between the ambient air and the effluent (kg m-3).4. COMPARISON OF INERT AND BUOYANT PLUME MODELS The ratio of the plume concentrations calculated from the inert and buoyant plume models mentioned above may be obtained from eqn (2.2) and (3.3) and is equal to C1/C2 = QcrA3/(Bx(~+~ -ms)Um). (4.1) If we wish to use the dilution given by the buoyant plume model out to a distance xEwhere the value of C1/C2is equal to 1 and the inert plume dilution beyond this distance then xEis given by xE = Q~mr/(P+q-ms))(A31B)(l/(P+q-ms))/V(m/(P +4-ms)). (4.2) The equivalent time of travel to xE,tE,will be tE = xE/u= Q~~r/(p+q-ms))(A3/B)(l/(p+q-ms))/~(m(l -s) +~+dl(p+q-ms).(4.3) EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES Eqn (4.2) and (4.3) are valid only if A3 is not a function of distance from the source and/or wind speed. In some of the models e.g. the recombining plume model A3 is in fact assumed to be proportional to D and inversely proportional to x. In this case t = (A,lB)4Q~D-9 where A3 = A,D/x. Although expressions like (4.3) appear rather complicated their interpretation is fairly straightforward. All the models indicate that the term in the denominator of the exponents is small ie. ms is only slightly smaller than pfq (or (1+p+q) in the case of the recombining plume model). The term mr is however a fairly large fraction and the numerator of the exponent of is about 2. This means that tE varies rapidly (i.e.as the third or fourth power) of Qhand even more rapidly (i.e. as the ninth or greater power) of l/o. Hence for practical purposes there are wide ranges of low wind speeds and high heat emissions where the buoyant plume model is valid for calculating concentrations while the dispersion or inert plume model may be used in strong winds for most sources and in all but the lightest winds for very small sources. Since by the same reasoning eqn (4.1) indicates that C1/C2is a very slowly varying function of distance from the source (or time of travel) it follows that in border-line cases either model may be used over a considerable range of time or distance without serious error. The precise values of plume concentrations for given values of 0 and Qh will depend on the values chosen for A3 or A4 and B and the parameters p q rn r and s i.e.on the plume rise and dispersion models used. Table 1 shows some values of the concentrations calculated from eqn (2.2) using values of p+q and B consistent with plume dimensions at seueral kilometres from the sources and from eqn (3.3) using the plume rise equation of Briggs C2(BR) and Lucas l6 C2(LU) (see Pasquill 15) modified to take account of distance down- wind but not of stability or atmospheric turbulence.'* The plume rise model has relatively little effect on the calculated concentrations but the dilutions in light winds are very much greater than with the inert plume model when one is considering the large heat sources even though the dispersion parameters used are appropriate to unstable meteorological conditions.In very stable conditions the buoyant plume dilutions would remain effectively constant after something like 120 m or so of travel (i.e. 120 s in a 1 m s-I wind). Even so the plumes are much more diffuse than the inert plumes; consequently serious errors could be made both in estimates of plume visibility and in chemical reaction rates in plumes if the inert models were used in these sort of conditions. Taking 1 m s-I as the worst condition concentrations at 120 m downwind would be 1652 and 1181 p.p.h.m. for the C2(BR) and C,(LU) models respectively. Atmos-pheric dilution might be considered negligible in these conditions and the plumes would then drift downwind with little further dilution.Size of source would have comparatively little effect since eqn (3.3) shows C,varies as a small power of Qh but the concentration is directly proportional to the S02/MJratio. 5. COMPARISON WITH EXPERIMENTAL DATA Comprehensive data on peak concentrations of SO2 at several km from the Keystone Power Plant are available. The ratio of S02/MJ was about 0.8 times that assumed in table 1 and the plant was emitting heat at an average rate of 100 MW D. J. MOORE during the period of the measurement (1967-69).20 C2(BR) and C2(LU)would be about 0.8(+)* and 0.8($)* times the concentration at the same time of travel for the 300 MW source in table 1 i.e. 916 and 717 p.p.h.m. for 120s travel at 1 ms-'. With these emission conditions the highest concentration observed in the plume was in fact 767 p.p.h.m.at 4.8 km downwind on 30th October 1967. At 10 km the con- centration peak was 352 p.p.h.m. Winds as light as 0.6 m s-l were recorded by pilot balloon ascent on that day. Pasquill Category F would give a concentration of 1940p.p.h.m. and Category E about 850 p.p.h.m. at 4.8 km and 707 p.p.h.m. and 296 p.p.h.m. respectively at 10 km. It appears therefore either that Category F type of dispersion is never observed from an elevated plume (or observed so seldom that several years' measurements TABLE1.-CONCENTRATION (p.p.h.m.) vol/vol SO2 FROM A SOURCE EMITTING 0.008 m3 (KEDUCED TO s.T.P.) OF SO2PER MJ OF HEAT EMITTED time CdUS) Oh CABR)'' 300 MW; CZ(LU)+ 0 1 m S-* CdST) 250 3342 621 472 954 930 500 1181 246 198 244 850 750 643 143 119 119 740 lo00 418 98 83 77 320 2000 148 39 35 25 610 u= 7ms-1 timc CI C2(BR) C2(LU) 250 352 324 290 500 125 129 122 750 68 75 73 lo00 44 51 51 2000 16 20 21 Qh= low* g= Ims-1 time CdUS) c*(BR); CZ(LU)+ CdST) 250 158 200 201 31 830 500 56 79 85 8 160 750 30 46 51 3 991 lo00 20 31 36 2 577 2000 854 C2values are calculated from the buoyant plume model using the following numerical values C2(BR) corresponds to the two-dimensional bent over cone type of plume model advocated by Briggs and others C2(LU)corresponds to the Priestley l7 type model of Lucas l6 and the recombining plume model of Moore 8s C2(BR) = Q/((0.426~)~nV), where z = 3.1 Qgx%/owhich with the assumed relation between SO2 and heat emission gives C2(BR) = 146 014Qh*0-f.t-3 C2(LU) = 3 ex/(16(0.3 13~)~n~') where z = 2.4Q4d/U which gives C2(LU) = 112 635Qtu-*t-* p.p.h.m.Taking Bxt = 2n(0.O8L*(7/U)*),l9C1was equal to 556 921 Qh/(t*u2j2L*)in unstable (US) conditions with L = 160 m for the large source; and L = 80 m for the small source.19 The Pasquill Category F values of a,,and cZwere used in stable (ST) condition^.'^ * The values of C,(BR) and C2(LU) at 120 m downwind in a 1 m s-l (i.e after 120 s travel) would be 1652 1181 532 and 503 p.p.h.m. in columns 3,4 10 and 11 respectively. These conditions would represent the minimum dilution at greater distances in the most stable conditions. EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES fail to detect it) or that the extra dispersion caused by the relative motion has the effect of making the minimum observed dilution comparable with Category E at distances of around 5-10 km downwind of large sources.Unfortunately there do not appear to be any comprehensive " in-plume '' measurements made closer to the stack but the dimensions of the plume recorded by the various techniques described in section 1 above indicate that the concentra- tions predicted in table 1 by the buoyant plume models are more likely to be correct than the much higher concentrations predicted by dispersion models. 6. CONCLUSIONS The calculations indicate that for large heat source the dilution of buoyant plumes in light winds is much more rapid than the classical formulae would indicate.The effect is most noticeable in the early stages of the plume's travel because the plume's motion relative to the surrounding air is then at its greatest and the dilution effected by this relative motion far exceeds the diluting effect of the turbulence in the surrounding air. In very stable conditions most of the dilution probably occurs within a 100 m or so of the stack because the plume rise is completed in this distance. Further dilution will proceed at a very slow rate so that for practical purposes in-plume concentrations may be considered constant for several km after this initial rapid dilution. Even so concentrations at all distances out to 10 km would be less than those indicated by a simple application of the Pasquill Category F curves.In unstable conditions the dilution produced by relative motion is also greater than that produced by atmospheric turbulence in light winds close to the stack for large heat sources but the atmospheric diluting mechanism will become important at a much earlier stage than it does in stable conditions. When it is windy both models (atmospheric dilution and buoyant plume) give roughly the same dilutions out to several km from the source. The work was carried out at the Central Electricity Research Laboratories and the paper is published by permission of the Central Electricity Generating Board. The author is grateful to Dr. K. W. James and Mr. D. H. Lucas for helpful criticism. 0.G. Sutton Atmospheric Turbulence (Methuen London 1949). Tennessee Valley Authority Report Full Scale Study of Plume Rise at Large Electric Generating Stations (T.V. A. Muscle Shoals Alabama 1968). P. M. Hamilton Phil. Trans. A 1969 265 153. P. M. Hamilton Atmospheric Environment 1967 1 370. C. H. Bosanquet J. Inst. Fuel. 1957 30 322. R. S. Scorer Int. J. Air Pollution 1959 1 198. 'G. A. Briggs Plume Rise (U.S.A.E.C. Critical Review Series 1969). D. J. Moore Int. J. Air and Water Polution 1966 10 411. D. J. Moore Atmospheric Environment 1968 2 247. lo D. P. Hoult J. A. Fay and L. J. Forney J. Air Polution Control Assoc. 1969 19 585. G. Ooms Atmospheric Environment 1972 6 899. l2 F. Gifford J. Meteorology 1957 14 410. l3 F. Pasquill Meterological Mag. 1961 90 33. l4 Meteorology and Atomic Energy ed. D. Slade (U.S.A.E.C.1968). l5 F. Pasquill Quart. J. Roy. Meteorological Soc. 1972 97 369. l6 D. H. Lucas Atmospheric Environment 1967 1,421. C. H. B. Priestly Quart. J. Roy. Meteorological SOC.,1956 82 165. D. J. Moore Atmospheric Environment 1974 8 131. l9 D. J. Moore Adv. Geophysics-Turbulent Diflusion in Atmospheric Pollution ed. F. N. Frenkiel and R. E. Munn (1974). 2o Tennessee Valley Authority Large Power Plane Effluent Study Vol. 1 1967 and 1969 Vol. 2 1968 (U.S. Dept. of Health Education and Welfare 1970).