Observations Less than the Analytical Limit of Detection: A New Approach

Abstract

Solutions are given for plume rise assuming a power-law wind speed profile in a stably stratified layer for point and finite sources with initial vertical momentum and buoyancy. For a constant wind speed, these solutions simplify to the conventional plume rise equations in a stable atmosphere. In a shear layer, the point of maximum rise occurs further downwind and is slightly lower compared with the plume rise with a constant wind speed equal to the wind speed at the top of the stack. If the predictions with shear are compared with predictions for an equivalent average wind speed over the depth of the plume, the plume rise with shear is higher than plume rise with an equivalent average wind speed.     

Validation of a Lagrangian model plume rise scheme using the Kincaid data set

Correct prediction of the initial rise of a plume due to momentum and buoyancy effects is an important factor in dispersion modelling. A new plume rise scheme, based upon conservation equations of mass, momentum and heat, for the Lagrangian model, NAME, is described. The conservation equations are consistent with the well-known analytical plume rise formulae for both momentum- and buoyancy-dominated plumes. The performance of the new scheme is assessed against data from the Kincaid field experiment. Results show that the new scheme adds value to the model and significantly outperforms the previous plume rise scheme. Using data from assessments of atmospheric dispersion models using the Kincaid data set, it is shown that NAME is comparable to other models over short ranges.     

A Correlation of Field Observations of Plume Rise

Data from 137 sets of plume observations, comprising nearly 1 500 data points, are correlated with two simple formulae. These formulae, one for the buoyancy-dominated rise region and the other for the stratification-dominated levelled-off region of a plume, represent an approximate form of the entrainment theory of Hoult, et al. (1968)¹ for the case of uniform atmospheric stratification and zero wind shear. The observations, which are those of the Tennessee Valley Authority and of Bringfelt (1968),⁶ were made of plumes whose source strengths ranged from 0.4 to 111 Mw and which were emitted from stacks of heights between 21 and 183 m. The two formulae are found to correlate the data equally well over all values of the stack exit and meteorological parameters, provided only that the bulk mean velocity of the stack gases exceeds the mean wind speed by at least 20%. The ratio of observed to calculated plume rise is found to be distributed log normally about the mean value.

The median rise at large distances downstream was found to differ insignificantly from that given by the effective stack height formula recommended recently¹¹ for large buoyant plumes. Based upon the correlation, two formulae are recommended for computing median plume rise at all distances downstream of the stack. The formulae include an estimate of the expected uncertainty in the predicted rise.     

Modelling plume rise and dispersion from pool fires

This paper describes an investigation into the behaviour of smoke plumes from pool fires, and the subsequent generation of empirical models to predict plume rise and dispersion from such a combustion source. Synchronous video records of plumes were taken from a series of small-scale (0.06–0.25m²) outdoor methanol/toluene pool fire experiments, and used to produce sets of images from which plume dimensions could be derived. Three models were used as a basis for the multiple regression analysis of the data set, in order to produce new equations for improved prediction. Actual plume observations from a large (20.7 m×14.2 m) aviation fuel pool fire were also used to test the predictions. The two theoretically based models were found to give a better representation of plume rise and dispersion than the empirical model based on measurements of small-scale fires. It is concluded that theoretical models tested on small-scale fires (heat output ≈70 kW) can be used to predict plume behaviour from much larger combustion sources (heat output ≈70 MW) under near neutral atmospheric conditions.     

Water flume study of the enhancement of buoyant rise in pairs of merging plumes

When multiple stacks are grouped or ganged together at a site, the effluent plumes are often observed to merge downwind, forming a single buoyant plume whose rate of rise is enhanced relative to the rise of the plumes individually. The magnitude of this rise enhancement depends on many factors, and the few available models for rise enhancement do not always agree with one another. In the present study the rise behaviour of pairs of merging, buoyant plumes was studied by physical modelling in a water flume at 1:500 scale. The experiments were conducted at several stack separation distances and various exit velocity ratios for stack pairs aligned with, or perpendicular to, the ambient flow. Limited experiments were also done with the stacks aligned at other angles to the flow. The stack releases were made buoyant by heating the source water, and the resulting plumes were measured with an array of sensitive temperature probes. From these measurements it was possible to determine the plume structure and rise rates. For small stack separations when the stacks are aligned with the ambient flow, the experimental results show that the enhanced rise is close to, and sometimes above, the maximum theoretical rise enhancement factor of 2^1/3. For the perpendicular orientation there is little or no rise enhancement. The rise enhancement for other stack orientations is somewhere between these two extremes. A plausible physical explanation for the observed behaviour is given, based on initial momentum shielding and line vortex dynamics in the merging plumes.     

Performance Evaluation of Integral and Analytical Plume Rise Algorithms

The purpose of this study was to evaluate the performance of current regulatory algorithms for predicting plume rise for refinerytype sources (short stacks and a wide range of source conditions) and the performance of new or alternate algorithms which may provide better estimates. To meet the objectives, five plume rise algorithms were statistically evaluated against ten field and laboratory plume rise data bases. Two forms of the Briggs plume rise equations were tested because they are almost exclusively used in current EPA regulatory models. Two modified Briggs equations were tested to assess how simple modifications can Improve the accuracy of the estimates. The fifth algorithm was a numerical solution to the basic equations for conservation of mass, momentum, and energy often referred to as an Integral plume rise algorithm. This algorithm was selected because It handles the wide range of source and atmospheric boundary-layer conditions that affect trajectories of plumes from refinery stacks.

Ten independent plume rise data bases were assembled that covered a wide range of source and meteorological conditions. From the data bases, a total of 107 different data sets were obtained and each data set included plume rise observations versus downwind distance for one source and meteorological condition. Each model was run for each data set and the root-mean-square and mean error between model and observation was computed for use in statistically evaluating model performance.

The statistical evaluation of the algorithms showed that the rms error (considering all data bases) for the Integral plume rise algorithm was approximately 30 percent less than the errors for all other algorithms tested. This difference was significant at the 95 percent confidence level. The results suggest that improved plume rise estimates in regulatory models applied to refineries and other appropriate sources could be achieved to reduce costs and improve ambient air quality estimates through the use of an integral plume rise algorithm.     

A Theory of Plume Rise Compared with Field Observations

A theory for the rise of a plume in a horizontal wind is proposed in which it is assumed that, for some distance downwind of a high stack, the effects of atmospheric turbulence may be ignored in comparison with the effects of turbulence generated by the plume. The theory, an extension of the local similarity ideas used by Morton, Taylor, and Turner,¹ has two empirical parameters which measure the rate that surrounding fluid is entrained into the plume. Laboratory measurements of buoyant plume motion in laminar unstratified cross flow are used to estimate the empirical parameters. Using this determination of the parameters in the theory, the trajectories of atmospheric plumes may be predicted. To make such a prediction, the observed wind velocity and temperature as functions of altitude, and flow conditions at the stack orifice, are used in numerically integrating the equations. The resulting trajectories are compared with photographs, made by Leavitt, et al.,² of TVA, of plumes from 500 to 600 ft high stacks. Within 10 stack heights downwind of the stack, the root mean square discrepancy between the observed height of the trajectory above ground level and the theoretical value is 14%, which is about the uncertainty in the observed height. The maximum plume rise within the field of observation is within 15% of that predicted by the present theory.     

Stable plume rise in a shear layer

Solutions are given for plume rise assuming a power-law wind speed profile in a stably stratified layer for point and finite sources with initial vertical momentum and buoyancy. For a constant wind speed, these solutions simplify to the conventional plume rise equations in a stable atmosphere. In a shear layer, the point of maximum rise occurs further downwind and is slightly lower compared with the plume rise with a constant wind speed equal to the wind speed at the top of the stack. If the predictions with shear are compared with predictions for an equivalent average wind speed over the depth of the plume, the plume rise with shear is higher than plume rise with an equivalent average wind speed.     

Development and Evaluation of the PRIME Plume Rise and Building Downwash Model

ABSTRACT

A new Gaussian dispersion model, the Plume Rise Model Enhancements (PRIME), has been developed for plume rise and building downwash. PRIME considers the position of the stack relative to the building, streamline deflection near the building, and vertical wind speed shear and velocity deficit effects on plume rise. Within the wake created by a sharp-edged, rectangular building, PRIME explicitly calculates fields of turbulence intensity, wind speed, and streamline slope, which gradually decay to ambient values downwind of the building. The plume trajectory within these modified fields is estimated using a numerical plume rise model. A probability density function and an eddy diffusivity scheme are used for dispersion in the wake. A cavity module calculates the fraction of plume mass captured by and recirculated within the near wake. The captured plume is re-emitted to the far wake as a volume source and added to the uncaptured primary plume contribution to obtain the far wake concentrations.

The modeling procedures currently recommended by the U.S. Environmental Protection Agency (EPA), using SCREEN and the Industrial Source Complex model (ISC), do not include these features. PRIME also avoids the discontinuities resulting from the different downwash modules within the current models and the reported overpredictions during light-wind speed, stable conditions. PRIME is intended for use in regulatory models. It was evaluated using data from a power plant measurement program, a tracer field study for a combustion turbine, and several wind-tunnel studies. PRIME performed as well as or better than ISC/SCREEN for nearly all of the comparisons.     

Opacity of monodisperse sulfuric acid aerosols

The plume opacity and droplet diameters of a monodisperse sulfuric acid aerosol were calculated as a function of the initial H₂SO₄ concentration, initial H₂O concentration and final gas temperature after cooling from an original stack gas temperature of 300°C. Calculation assumptions include heterogeneous heteromolecular condensation of H₂SO₄ and H₂O onto monodisperse nuclei of 0.05 μm dia., three aerosol particle nuclei concentrations of 10⁶, 10⁷ and 10⁸ cm⁻³ (at 300°C and 760 mm Hg); and a stack or plume diameter of 6 m. The calculated results show that for the conditions considered and with the stack temperatures in excess of 125°C, initial H₂SO₄ stack gas concentrations of 10ppm or less will result in calculated opacities of less than 20 % for a plume diameter of 6 m. The results show that the calculated opacity is significantly affected by the initial H₂SO₄ and initial H₂O concentrations and the final gas temperature. The increases in the calculated opacities upon cooling of the stack gases are similar in general to the increases in the measured opacities between instack and outstack reported by Nader and Conner (1978) for an oil-fired boiler.     

A modeling study of SOx-NOx-Hydrocarbon plumes and their transport to the background troposphere

A model which emulates the behavior of urban-industrial plumes has been developed and used to analyze the chemical reaction processes occurring as a polluted air mass is transported from an urban area. A 73-step reaction mechanism describing hydrocarbon/NO_xSO_x chemistry was used, with photolytic rate constants depending on the latitude, time of day and time of year. The model includes the physical processes of plume dilution, entrainment and dry deposition, and is simulated under a diurnally varying mixing layer or neutral atmospheric stability conditions.Simulation results are compared with reported field measurements for plumes from St. Louis, Milwaukee, and a power plant plume entrained in the Milwaukee urban plume. The agreement with field concentrations and SO₂ transformation rate data is good, the latter ranging from 1 to 12 % h⁻¹. The study was extended to hypothetical plumes for parametric analysis. In every case considered, the classic O₃ peak occurred at about 3:30 p.m., essentially independent of initial concentrations and plume departure time. The analysis also indicated that substantial SO₂ oxidation via homogeneous gas phase chemistry can occur at night-time, the prerequisite being a high HG/NO_x ratio.     

Improving Plume Rise Prediction Accuracy for Stable Atmospheres with Complex Vertical Structure

Accurately predicting the rise of a buoyant exhaust plume is difficult when there are large vertical variations in atmospheric stability or wind velocity. Such conditions are particularly common near shoreline power plants. Simple plume rise formulas, which employ only a mean temperature gradient and a mean wind speed, cannot be expected to adequately treat an atmosphere whose lapse rate and wind velocity vary markedly with height. This paper tests the accuracy of a plume rise model which is capable of treating complex atmospheric structure because it integrates along the plume trajectory. The model consists of a set of ordinary differential equations, derived from the fluid equations of motion, with an entralnment parameterization to specify the mixing of ambient air into the plume. Comparing model predictions of final plume rise to field observations yields a root mean square difference of 24 m, which is 9 % of the average plume rise of 267 m. These predictions are more accurate than predictions given by three simpler models which utilize variants of a standard plume rise formula, the most accurate of the simpler models having a 12% error.     

An experimental verification of a theoretical model for the dispersion of a stack plume heavier than air

Experiments were carried out in a windtunnel to test the theoretical model for the dispersion of a stack plume heavier than air developed by Ooms et al. (1974, First Int. Symp. on Loss Prevention and Safety Promotion in the Process Industries, The Hague). Particular attention was paid to the initial conditions which have to be supplied in order to make model calculations possible. A good agreement between experimental results and model predictions was found for the plume path and the density distribution along the plume axis. The velocity distribution inside the plume was less well predicted.     

A new mixed segment-puff approach for dispersion modeling

This paper presents a new mixed methodology for realistic and cost-effective simulation of shortterm air quality dispersion phenomena using the Gaussian formula. The method can be applied to shortrange, intermediate and, especially, long-range transport simulations. Pollutant dynamics are described by the temporal evolution of plume elements, treated as segments or puffs according to their size. While the segments provide a numerically fast simulation during transport conditions, the puffs allow a proper simulation of calm or low-wind situations.The methodology is incorporated into a computer package (AVACTA II, Release 3) that gives the user large flexibility in defining the computational domain, the three-dimensional meteorological and emission input, the receptor locations, and in selecting plume rise and sigma formulas. AVACTA II provides both pollutant concentration fields and dry/wet deposition patterns. The model uses linear chemistry and is applicable to any two-species reaction chain (e.g., SO₂ and SO²⁻₄) where this approximation is reasonable and an appropriate reaction rate is available.     

Plume Rise Determination-A New Technique Without Equations

Information on plume rise is important in determining the resulting concentrations of a pollutant on the ground. Practical use of plume rise values may be made in connection with stack design, the use of urban air pollution models, and in evaluating the hazards to a population complex.

This paper presents a new equationless technique for estimating plume rise as well as a comparison of seventeen commonly used plume rise formulas. Data from 10 sets of experiments, involving 615 observations and 26 different stacks, were used to study the relation between plume rise and related meteorological and stack parameters.

An independent data set was used to test the derived methods for determining plume rise. These data were obtained by Bringfelt of Sweden and contained measurements from stacks smaller than that at the Argonne National Laboratory to those approaching the TVA stacks.

A significant improvement in the prediction of plume rise from meteorological and stack parameters resulted from the use of a new technique called the Tabulation Prediction Technique. This is a method whereby an estimate of the value of a dependent variable may be obtained from information on the independent variables. Combinations of the independent variables—wind speed, heat emission rate, momentum rate, and stability—are arranged in an ordered sequence. For each combination of independent variables, the cumulative percentile frequency distribution of the dependent variable based on past measurements is given along with other statistics such as the mean, standard deviation, and interquartile range, i.e., the difference in plume rise between the 75th and 25th percentile values. Thus, one may look up the combination of independent variables just as one looks up words in a dictionary to obtain the percentile frequency distribution of the dependent variable. The mean, for each combination of independent variables may be considered as the best estimate for the given conditions.     

Monte Carlo simulation of nitrogen oxides dispersion from a vehicular exhaust plume and its sensitivity studies

The pollutant dispersion behavior from the vehicular exhaust plume has a direct impact on human health, particularly to the drivers, bicyclists, motorcyclists, pedestrians, people working nearby and vehicle passengers. A two-dimensional pollutant dispersion numerical model was developed based on the joint-scalar probability density function (PDF) approach coupled with a k–ε turbulence model to simulate the initial dispersion process of nitrogen oxides, temperature and flow velocity distributions from a vehicular exhaust plume. A Monte Carlo algorithm was used to solve the PDF transport equations in order to obtain the dispersion distribution of nitrogen oxides concentration. The model was then validated by a series of sensitivity experimental studies in order to assess the effects of vehicular exhaust tailpipe velocities, wind speeds and chemistry on the initial dispersion of NO and NO₂ mass concentrations from the vehicular exhaust plume. The results show that the mass concentrations of nitrogen oxides decrease along the centerline of the vehicular exhaust plume in the downstream distance. The dispersion process can be enhanced when the vehicular exhaust tailpipe velocity is much larger than the wind speed. The oxidation reaction of NO plays an important role when the wind speed is large and the vehicular exhaust exit velocity is small, which leads to chemical reduction of NO, and the formation and accumulation of NO₂ in the exhaust plume. It is also found that the effect of vehicular exhaust-induced turbulence in the vicinity of the exhaust tailpipe exit is more dominant than the effect of wind turbulence, while the wind turbulence gradually shows a significant role for the dispersion of nitrogen oxides along with the development of exhaust plume. The range of dispersion of nitrogen oxides in the radial direction is increased along with the development of vehicular exhaust plume.     

Demonstration of a global modeling methodology to determine the relative importance of local and long-distance sources

A global three-dimensional (3D) transport–dispersion model was used to simulate Krypton-85 (⁸⁵Kr) background concentrations at five sampling locations along the US east coast during 1982–1983. The samplers were established to monitor the ⁸⁵Kr plume downwind of the Savannah river plant (SRP), a nuclear fuel reprocessing facility. The samplers were located 300–1000 km downwind of the SRP. In the original analyses of the measurements, a constant background concentration, representing an upper-limit and different for each sampling station, was subtracted from the measurements to obtain the part of the measurement representing the SRP plume. The use of a 3D global model, which includes all major ⁸⁵Kr sources worldwide, was able to reproduce the day-to-day concentration background variations at the sampling locations with correlation coefficients of 0.36–0.46. These 3D model background predictions, without including the nearby SRP source, were then subtracted from the measured concentrations at each sampler, the result representing the portion of the measurement that can be attributed to emissions from the SRP. The revised plume estimates were a factor of 1.3–2.4 times higher than from the old method using a constant background subtraction. The greatest differences in the SRP plume estimates occurred at the most distant sampling stations.     

Water tank measurements of buoyant plume rise and structure in neutral crossflows

In this paper, an experimental study of the rise and development of a single buoyant plume and a pair of in-line buoyant plumes is presented. The investigations were carried out at small scale in a water filled towing tank using both quantitative flow visualisation and local concentration measurements. The measured plume trajectories for a single plume were compared with the Briggs plume rise equation and predictions from a numerical integral model. Plume trajectories were studied for twin in-line plumes, with particular attention to changes in the plume trajectory, especially any additional rise that resulted from the interaction between the two plumes. Concentration field distributions in cross-sections through both single and interacting twin plumes were obtained from the local concentration measurement system. These showed how the interaction affected the plume structure, notably the double vortex system that occurs in a fully developed plume.     

Concentration field and turbulent fluxes during the mixing of two buoyant plumes

In this work an experimental study of mixing of two identical plumes, carried out in a turbulent neutral boundary layer generated in a wind tunnel, is presented. Measurements have been performed with fast flame ionisation detectors (FFIDs) and a two-component Laser-Doppler Anemometer system. Results allow the study of both the average and the fluctuating concentration field, including the turbulent vertical and longitudinal mass fluxes, in single plumes and during the interaction of two identical plumes. This information gives insight into the details of the mixing phase of the two plumes. Results of trajectories and additional rise (due to plume interactions) have been compared with previous measurements carried out in laminar cross-flows, showing similar behaviour. Concentration distributions in plume cross-sections in turbulent cross-flows differ from those measured in laminar cross-flows. Average vertical and longitudinal velocity measurements into the plume core show the strength of the shielding effect of the upwind plume and some details of interaction between the counter-rotating vortex pairs (CVPs). For large values of the alignment angle φ, between the line joining the stacks and the cross-flow, an average negative vertical velocity is measured in the middle of the plume even if its centre of mass is rising. This downward velocity is induced by the slow interaction of the CVPs and generates a vertical stretching of the plume and negative rise enhancement. Vertical turbulent fluxes change sign on the plume centreline and are of opposite sign with respect to the longitudinal turbulent fluxes. Results indicate a good linearity between vertical turbulent fluxes and concentration gradients, with different proportionality for the top and bottom parts of the plume (especially in the near field) indicating that dispersion could be described by a gradient-transfer model.