Derivation of exemption formulas for air quality regulatory applications

The regulatory agencies and the industries have the responsibility for assessing the environmental impact from the release of air pollutants, and for protecting environment and public health. The simple exemption formula is often used as a criterion for the purpose of screening air pollutants. That is, the exemption formula is used for air quality review and to determine whether a facility applying for and described in a new, modified, or revised air quality plan is exempted from further air quality review. The Bureau of Ocean Energy Management’s (BOEM) air quality regulations are used to regulate air emissions and air pollutants released from the oil and gas facilities in the Gulf of Mexico. If a facility is not exempt after completing the air quality review, a refined air quality modeling will be required to regulate the air pollutants. However, at present, the scientific basis for BOEM’s exemption formula is not available to the author. Therefore, the purpose of this paper is to provide the theoretical framework and justification for the use of BOEM’s exemption formula. In this paper, several exemption formulas have been derived from the Gaussian and non-Gaussian dispersion models; the Gaussian dispersion model is a special case of non-Gaussian dispersion model. The dispersion parameters obtained from the tracer experiments in the Gulf of Mexico are used in the dispersion models. In this paper, the dispersion parameters used in the dispersion models are also derived from the Monin-Obukhov similarity theory. In particular, it has been shown that the total amount of emissions from the facility for each air pollutant calculated using BOEM’s exemption formula is conservative.

Implications:?The operation of offshore oil and gas facilities under BOEM’s jurisdiction is required to comply with the BOEM’s regulations. BOEM’s air quality regulations are used to regulate air emissions and air pollutants released from the oil and gas facilities in the Gulf of Mexico. The exemption formulas have been used by BOEM and other regulatory agencies as a screening tool to regulate air emissions emitted from the oil and gas and other industries. Because of the BOEM’s regulatory responsibility, it is important to establish the scientific basis and provide the justification for the exemption formulas. The methodology developed here could also be adopted and used by other regulatory agencies.     

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105–8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean dispersion are shown to produce results several orders of magnitude more efficiently with a loss of accuracy small compared to the absolute accuracy of advanced dispersion models near sources. The method can be readily incorporated into existing dispersion models, and may allow for additional computation time to be expended on modelling dispersion processes more accurately in future, rather than on accounting for source geometry.     

Inverse modeling to estimate LNAPL plume release timing

Methodologies are presented for dating releases of light nonaqueous phase liquids (LNAPLs) using an inverse modeling approach with simple analytical models. Models for LNAPL plume migration are presented to predict LNAPL plume velocity in the unsaturated and saturated zones as a function of basic soil and fluid properties. A relative mobility factor is introduced for LNAPL movement at the water table that depends primarily on the van Genuchten n parameter (related to the breadth of the soil pore size distribution) and the magnitude of water table fluctuations. Estimated LNAPL plume velocities compare reasonably with more rigorous numerical models, which may be used in cases where data availability warrant the greater effort entailed.Two methods of estimating release timing and its uncertainty are investigated. A direct estimation method is described that determines travel time for a single observed travel distance based on estimated soil and fluid properties. Release date uncertainty may be determined using the first order (FO) or Monte Carlo (MC) methods. The second method for estimating release date involves nonlinear parameter estimation utilizing distance vs. time measurements and other data.A case study is presented for a field site where independent estimates of release timing were obtained from a numerical modeling analysis. Release timing estimates based on direct inversion of the analytical timing model agree well with the numerical analysis. Results for a second field site indicate that release date confidence limits estimated by the FO method, assuming log-normally distributed travel times, are close to values determined by the MC method, which makes no assumption regarding the form of the travel time probability distribution.Results for a hypothetical problem indicate that LNAPL velocity and travel time may be accurately estimated if sufficient data on travel distance vs. time are available. Incorporating prior information on relevant soil and fluid properties into the objective function reduces the uncertainty in release date if prior estimates are accurate. However, biased prior estimates may lead to over- or underestimation of release date uncertainty. Simultaneous estimation of soil and fluid properties and release date is possible if prior information is available to condition the parameter estimates.     

Evaluation of the effect of meteorological data resolution on Lagrangian particle dispersion simulations using the ETEX experiment

This paper presents results from a series of numerical experiments designed to evaluate operational long-range dispersion model simulations, and to investigate the effect of different temporal and spatial resolution of meteorological data from numerical weather prediction models on these simulations. Results of Lagrangian particle dispersion simulations of the first tracer release of the European Tracer Experiment (ETEX) are presented and compared with measured tracer concentrations. The use of analyzed data of higher resolution from the European Center for Medium-Range Weather Forecasts (ECMWF) model produced significantly better agreement between the concentrations predicted with the dispersion model and the ETEX measurements than the use of lower resolution Navy Operational Global Atmospheric Prediction System (NOGAPS) forecast data. Numerical experiments were performed in which the ECMWF model data with lower vertical resolution (4 instead of 7 levels below 500 mb), lower temporal resolution (12 h instead of 6 h intervals), and lower horizontal resolution (2.5° instead of 0.5°) were used. Degrading the horizontal or temporal resolution of the ECMWF data resulted in decreased accuracy of the dispersion simulations. These results indicate that flow features resolved by the numerical weather prediction model data at approximately 45 km horizontal grid spacing and 6 h time intervals, but not resolved at 225 km spacing and 12 h intervals, made an important contribution to the long-range dispersion.     

Simplified contaminant source depletion models as analogs of multiphase simulators

Four simplified dense non-aqueous phase liquid (DNAPL) source depletion models recently introduced in the literature are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. The spill and subsequent dissolution of DNAPLs was simulated in domains having different hydrologic characteristics (variance of the log conductivity field=0.2, 1 and 3) using the multiphase flow and transport simulator UTCHEM. The dissolution profiles were fitted using four analytical models: the equilibrium streamtube model (ESM), the advection dispersion model (ADM), the power law model (PLM) and the Damkohler number model (DaM). All four models, though very different in their conceptualization, include two basic parameters that describe the mean DNAPL mass and the joint variability in the velocity and DNAPL distributions. The variability parameter was observed to be strongly correlated with the variance of the log conductivity field in the ESM and ADM but weakly correlated in the PLM and DaM. The DaM also includes a third parameter that describes the effect of rate-limited dissolution, but here this parameter was held constant as the numerical simulations were found to be insensitive to local-scale mass transfer. All four models were able to emulate the characteristics of the dissolution profiles generated from the complex numerical simulator, but the one-parameter PLM fits were the poorest, especially for the low heterogeneity case.     

A robust approach for iterative contaminant source location and release history recovery

Contamination source identification is a crucial step in environmental remediation. The exact contaminant source locations and release histories are often unknown due to lack of records and therefore must be identified through inversion. Coupled source location and release history identification is a complex nonlinear optimization problem. Existing strategies for contaminant source identification have important practical limitations. In many studies, analytical solutions for point sources are used; the problem is often formulated and solved via nonlinear optimization; and model uncertainty is seldom considered. In practice, model uncertainty can be significant because of the uncertainty in model structure and parameters, and the error in numerical solutions. An inaccurate model can lead to erroneous inversion of contaminant sources. In this work, a constrained robust least squares (CRLS) estimator is combined with a branch-and-bound global optimization solver for iteratively identifying source release histories and source locations. CRLS is used for source release history recovery and the global optimization solver is used for location search. CRLS is a robust estimator that was developed to incorporate directly a modeler's prior knowledge of model uncertainty and measurement error. The robustness of CRLS is essential for systems that are ill-conditioned. Because of this decoupling, the total solution time can be reduced significantly. Our numerical experiments show that the combination of CRLS with the global optimization solver achieved better performance than the combination of a non-robust estimator, i.e., the nonnegative least squares (NNLS) method, with the same solver.     

A robust approach for iterative contaminant source location and release history recovery

Contamination source identification is a crucial step in environmental remediation. The exact contaminant source locations and release histories are often unknown due to lack of records and therefore must be identified through inversion. Coupled source location and release history identification is a complex nonlinear optimization problem. Existing strategies for contaminant source identification have important practical limitations. In many studies, analytical solutions for point sources are used; the problem is often formulated and solved via nonlinear optimization; and model uncertainty is seldom considered. In practice, model uncertainty can be significant because of the uncertainty in model structure and parameters, and the error in numerical solutions. An inaccurate model can lead to erroneous inversion of contaminant sources. In this work, a constrained robust least squares (CRLS) estimator is combined with a branch-and-bound global optimization solver for iteratively identifying source release histories and source locations. CRLS is used for source release history recovery and the global optimization solver is used for location search. CRLS is a robust estimator that was developed to incorporate directly a modeler's prior knowledge of model uncertainty and measurement error. The robustness of CRLS is essential for systems that are ill-conditioned. Because of this decoupling, the total solution time can be reduced significantly. Our numerical experiments show that the combination of CRLS with the global optimization solver achieved better performance than the combination of a non-robust estimator, i.e., the nonnegative least squares (NNLS) method, with the same solver.     

CFD model simulation of dispersion from chlorine railcar releases in industrial and urban areas

To assist in emergency response decisions and planning in case of releases of pressurized liquefied chlorine from railroad tank cars in industrial sites and cities, the FLACS Computational Fluid Dynamics (CFD) model has been used to simulate the transport and dispersion of the dense chlorine cloud. Two accident locations are studied: an actual railcar accident at an industrial site in Festus, MO, and a hypothetical railcar accident at a rail junction in the Chicago urban area. The results show that transport of a large dense gas release at ground level in an industrial site or large city could initially extend a hundred meters or more in the upwind and crosswind directions. The dense cloud may follow terrain drainage, such as river channels. Near the source, the obstacles tend to slow down the dense gas cloud and may constrain it and cause increased concentrations. Farther downwind, the obstacles may cause enhanced mixing and dilution once the cloud has grown larger. In some cases, significant amounts of cloud mass may become “trapped” in obstacle wakes for many minutes after the main cloud has passed. Although the CFD model can account for the details of the flow and dispersion much better than standard widely-used simple dense gas models, many similarities are found among the various models in their simulated variations with downwind distance of the maximum cloud centerline concentration.     

Influence of rate-limited sorption on the cleanup of layered soils by vapor extraction

The conditions under which rate-limited sorption is important for cleanup of layered soils by vapor extraction are investigated. The investigation includes two steps: (a) the cleanup time is estimated for a number of scenario cases by means of a numerical model and (b) the numerical results are approximated using analytical solutions derived for simplified models. In this way, equations are derived, which give insight into the influence of different parameters characterizing the properties of the soil, the geometry of the formation, the mass transfer mechanisms in it, and the distribution of the contaminant mass in the different phases (gas phase, water phase and solid phase). The numerical model used is based on the advection-dispersion differential equations for Darcian isothermal airflow, local equilibrium contaminant mass transfer between gas phase and soil water and first-order kinetics for mass transfer between soil water and solid phase. The numerical results are approximated combining an analytical solution to estimate cleanup time in layered formations for local equilibrium sorption, which has been presented in a previous work (J. Contam. Hydrol., 36 (1999) 105). with an analytical solution based on the well-mixed reservoir model under consideration of rate-limited sorption. The analytical approximation of the cleanup time is in reasonable agreement with the numerical results and allows its estimation with small computational effort.     

Development and evaluation of the PRIME plume rise and building downwash model

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.     

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.     

A Gaussian puff model with optimal interpolation for air pollution modelling assessment

A Gaussian plume model was modified to simulate the dispersion of non-reactive air pollutants under non-homogeneous wind conditions through a multi-puff approach. It was applied to the city of Lisbon and evaluated by comparison with measured sulphur dioxide data, showing a reasonable skill to estimate the transport and dispersion of pollutants under complex wind field and different atmospheric conditions. The modelling results were integrated with observed data, based on correlation functions determined from historical values, to obtain the improved analytical results by using optimal interpolation. A significant improvement over the predictions by the Gaussian puff model alone was achieved.     

An analytical solution for vertical transport of volatile chemicals in the vadose zone

An analytical solution is presented for one-dimensional vertical transport of volatile chemicals through the vadose zone to groundwater. The solution accounts for the important transport mechanisms of the steady advection of water and gas, diffusion and dispersion in water and gas, as well as adsorption, and first-order degradation. By assuming a linear, equilibrium partitioning between water, gas and the adsorbed chemical phases, the dependent variable in the mathematical model becomes the total resident concentration. The general solution was derived for cases having a constant initial total concentration over a discrete depth interval and a zero initial total concentration elsewhere. A zero concentration gradient is assumed at the groundwater table. Examples are given to demonstrate the application of the new solution for calculating the case of a non-uniform initial source concentration, and estimating the transport of chemicals to the groundwater and the atmosphere. The solution was also used to verify a numerical code called VLEACH. We discovered an error in VLEACH, and found that the new solution agreed very well with the numerical results by corrected VLEACH. A simplified solution to predict the migration of volatile organic chemical due to the gas density effect has shown that a high source concentration may lead to significant downward advective gas-phase transport in a soil with a high air-permeability.     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

Impact of transverse and longitudinal dispersion on first-order degradation rate constant estimation

A two-dimensional analytical model is employed for estimating the first-order degradation rate constant of hydrophobic organic compounds (HOCs) in contaminated groundwater under steady-state conditions. The model may utilize all aqueous concentration data collected downgradient of a source area, but does not require that any data be collected along the plume centerline. Using a least squares fit of the model to aqueous concentrations measured in monitoring wells, degradation rate constants were estimated at a former manufactured gas plant (FMGP) site in the Midwest U.S. The estimated degradation rate constants are 0.0014, 0.0034, 0.0031, 0.0019, and 0.0053 day(-1) for acenaphthene, naphthalene, benzene, ethylbenzene, and toluene, respectively. These estimated rate constants were as low as one-half those estimated with the one-dimensional (centerline) approach of Buscheck and Alcantar [Buscheck, T.E., Alcantar, C.M., 1995. Regression techniques and analytical solutions to demonstrate intrinsic bioremediation. In: Hinchee, R.E., Wilson, J.T., Downey, D.C. (Eds.), Intrinsic Bioremediation, Battelle Press, Columbus, OH, pp. 109-116] which does not account for transverse dispersivity. Varying the transverse and longitudinal dispersivity values over one order of magnitude for toluene data obtained from the FMGP site resulted in nearly a threefold variation in the estimated degradation rate constant-highlighting the importance of reliable estimates of the dispersion coefficients for obtaining reasonable estimates of the degradation rate constants. These results have significant implications for decision making and site management where overestimation of a degradation rate may result in remediation times and bioconversion factors that exceed expectations. For a complex source area or non-steady-state plume, a superposition of analytical models that incorporate longitudinal and transverse dispersion and time may be used at sites where the centerline method would not be applicable.     

Overview of Petroleum Environmental Research Forum (PERF) dense gas dispersion modeling project

This paper provides a background for and an overview of the results of a comprehensive study of transport and dispersion of dense gas plumes over rough surfaces typical of industrial sites. The Petroleum Environmental Research Forum (PERF) 93-16 project involved model development and evaluations using observations from three wind tunnels and from the Kit Fox field experiment. Detailed discussions of the results of the research are given in the other papers in this special issue. The wind tunnel experiments produced data showing that the resulting best-fit vertical entrainment formula was close to (i.e., within about 30%) the vertical entrainment formulas already in use by current models, which were derived primarily from observations over smooth surfaces. Observations from the Kit Fox field experiment demonstrated the validity of the entrainment curves derived from the wind tunnel data. The Kit Fox data were also used to evaluate algorithms for along-wind dispersion and cloud advection speeds for short-duration releases typical of an industrial site, and to evaluate the HEGADAS dense gas dispersion model.     

Determination of Setback Distances for Livestock Operations Using a New Livestock Odor Dispersion Model (LODM)

ABSTRACT

Setback distance has been used as an effective tool to avoid odor nuisance from livestock operations. Many setback distances were guidelines that were determined by empirical methods that are considered to be lack of science base. Air dispersion models have been used to determine setback distances; however, these models do not consider the short-time fluctuations of odor. A livestock odor dispersion model (LODM) was developed to consider the short-time variations of odor and predict occurrence frequency for certain levels of odor. In this study, this model was used to predict the occurrence frequency for various levels of odor in the vicinity (10 km) of a swine farm. Using selected odor criteria, setback distances between the swine farm and nearby communities were defined. Results indicate that the LODM can be used as an effective tool to determine setback distances.

IMPLICATIONS One of the more important applications of odor dispersion models is to determine setback distances for major odor sources, such as intensive livestock operations, from nearby communities. This study provided a case study in determining directional setback distances from a typical swine farm using a newly developed livestock odor dispersion model (LODM). It is also the first study in using hourly odor frequency to determine setback distances.     

Use of tritium to predict soluble pollutants transport in Ebro River waters (Spain)

The Ebro River, in Northeast Spain, discharges into the Mediterranean Sea after flowing through several large cities and agricultural, mining and industrial areas. The Ascó nuclear power plant (NPP) is located in its lower section and comprises two pressurised water reactor units, from which low-level liquid radioactive waste is released to river waters under authority control. Tritium routinely released by the NPP was used as a radiotracer to determine the longitudinal dispersion coefficient and velocity of the river waters. Several field experiments, in co-ordination with the NPP, were carried out during 1991 and 1992. During each field experiment, the flow rate was kept constant by dams located upstream from the NPP. After each tritium release, water was sampled downstream at periodic intervals over several hours and tritium was measured with a low-background liquid scintillation counter. Velocity and dispersion coefficient were determined in river waters for several river discharges using an analytical, box-type and numerical approach to solve the one-dimensional advection-diffusion equation. The set of calibrated parameters was used to predict the displacement and dispersion of soluble pollutants in river waters. Velocity was determined as a function of river discharge and river slope, and dispersion coefficient was determined as a function of distance. Finally, sensitivity of the model predictions was studied and uncertainties of the fitted parameters were estimated.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Air Pollution Directional Risk Assessment for Siting a Landfill

Abstract

Air pollution directional risk (APDR) is an essential factor to be assessed when selecting an appropriate landfill site. Because air pollutants generated from a landfill are diffused and transported by wind in different directions and speeds, areas surrounding the landfill will be subject to different associated risks, depending on their relative position from the landfill. This study assesses potential APDRs imposed from a candidate landfill site on its adjacent areas on the basis of the pollutant distribution simulated by a dispersion model, wind directions and speeds from meteorological monitoring data, and population density. A pollutant distribution map layer was created using a geographic information system and layered onto a population density map to obtain an APDR map layer. The risk map layer was then used in this study to evaluate the suitability of a candidate site for placing a landfill. The efficacy of the proposed procedure was demonstrated for a siting problem in central Taiwan, Republic of China.