Quantitative Remote Sensing of Sulfur Dioxide Emissions from Industrial Plants Using Passive Fourier Transform Infrared (FTIR) Spectroscopy

Abstract

The remote monitoring and quantification of industrial gas emissions, such as sulfur dioxide (SO₂), are critical for environmental protection. This research demonstrates an integrated methodology for estimating SO₂ emission rates (kg/s) from an industrial chimney using passive Fourier transform infrared (FTIR) spectroscopy combined with atmospheric dispersion modeling. Infrared spectra were acquired at a stand-off distance of 570 m within the 7–14 $\mathsf{\mu }$m spectral range at a resolution of 4 cm⁻¹. Path-integrated SO₂ concentrations were determined through cross-sectional scanning of the gas plume. To translate these optical measurements into an emission rate, the atmospheric dispersion of the plume was modeled using the Pasquill–Briggs approach, incorporating source parameters and meteorological data. Over two experimental series, the calculated average SO₂ emission rates were 15 kg/s and 22 kg/s. While passive FTIR spectroscopy has long been applied to remote gas detection, this work demonstrates a consolidated framework for retrieving industrial emission rates from stand-off, line-integrated measurements under real industrial conditions. The proposed approach fills a niche between local in-stack measurements and large-scale remote sensing systems, which contributes to the development of flexible ways to monitor industrial emissions.

1. Introduction

The development of industrial sectors such as energy, metallurgy, chemicals, textiles, and pharmaceuticals is accompanied by an increase in emissions of harmful substances into the atmosphere [1,2,3]. These pollutants not only degrade the quality of life but also pose a serious threat to health [4,5,6].

The detection and identification of gas pollutants play an important role in environmental monitoring. It allows for tracking their sources, assessing the degree of danger, and developing effective control methods [7,8,9].

The control of sulfur dioxide (SO₂) emissions remains an urgent scientific and practical task due to the continuing high global emissions (about 75 million tons/year) [10], primarily from coal-fired power and metallurgical production, especially in the rapidly developing regions of Asia. Despite the success in reducing SO₂ emissions in developed countries, regional pollution levels remain critically high [10]. Modern epidemiological studies reveal new health risks, including long-term neurological and cardiovascular effects, even at concentrations below previously established standards [6,11]. Sulfur aerosols affect not only human and animal health but also the state of ecosystems as a whole [12]. Thus, modern control systems for SO₂ should be actively developed and implemented as a key tool for preserving the environment, minimizing environmental damage, and protecting public health in the face of increasing anthropogenic pressure.

SO₂ was selected as a representative pollutant due to its strong infrared absorption features and industrial relevance. During the combustion (melting) of copper–nickel sulfide ores, gases are released, and products associated with the oxidation of sulfides and the reduction of oxides are formed [13,14,15]. In addition to the release of water vapor and solid particles, the main gas is sulfur dioxide, which, when combined with atmospheric water, can lead to the formation of sulfuric acid and acid rain. These factors emphasize the importance of continuous monitoring of sulfur dioxide emissions.

Chimney gas emission rate measurements are typically carried out using local sensors integrated into an automatic emission control system (AECS) or a continuous emission monitoring system (CEMS) (e.g., Ref. [16]). However, this approach requires equipping every applicable chimney with sensors. Local sensors are susceptible to rapid contamination and can only measure emissions at a specific point, which leads to methodological error. Another approach is to use predictive emission monitoring system (PEMS) technologies, which are based on mathematical modeling (e.g., Ref. [17]). However, PEMS model outputs must be validated. The sample measurement methods proposed in this paper may be suitable for such verification tasks.

Currently, infrared (IR) Fourier spectroscopy [18,19], electrochemical sensing [20], differential absorption lidars [21,22,23,24,25], differential optical absorption spectroscopy [26,27,28], and non-dispersive IR spectroscopy [29,30] are widely used. For decades, various research groups have employed remote measurement techniques to analyze industrial gases such as SO₂, NO₂, etc. Xiong [31] used a UV camera with built-in NO₂ and aerosol corrections for monitoring SO₂ emissions. The authors calculated the column density (CD) with NO₂ correction, which correlates with SO₂ concentration. Lin et al. [32] applied active open-path Fourier transform infrared (OP-FTIR) spectroscopy with retroreflectors to measure concentrations (ppm) of ethylene, propylene, toluene, and other compounds at a lubricant manufacturing plant. Similarly, Polak et al. [33], Chaffin [34], and Mutua et al. [35] have used passive FTIR spectroscopy to obtain SO₂ infrared spectra and calculate path-integrated concentrations (ppm·m).

Passive FTIR spectroscopy has been employed for several decades to remotely detect and quantify atmospheric gases, including sulfur dioxide, nitrogen oxides, and volatile organic compounds. Earlier studies primarily focused on spectral identification and retrieval of path-integrated concentrations (ppm·m), as well as on algorithmic improvements for background suppression and signal inversion. However, direct estimation of emission rates from industrial point sources typically relies on in-stack measurements or PEMS, both of which have practical limitations.

Modeling the spread of pollutants in the air includes various approaches that can be categorized based on their mathematical frameworks and scales of application. Gaussian models are based on the assumption that the pollutants are normally distributed in the atmosphere, for example, AERMOD (EPA) [36], ADMS (CERC) [37], and ISC3 [38]. Lagrangian models calculate the trajectories of individual pollution particles, accounting for wind and turbulence, for example, HYSPLIT (NOAA) [39], FLEXPART [40], and CALPUFF [41]. Eulerian models consider the atmosphere by dividing it into cells, for each of which the transport equations are solved, for example, CMAQ (EPA) [42], CHIMERE (EC) [43], and WRF-Chem [44]. Empirical models describe the scattering of clouds of heavy gas released into the atmosphere near the land surface, for example, B and McQ [45,46], and VDI Guidelines [47].

Lagrangian models effectively account for changing weather conditions and complex terrain by utilizing three-dimensional meteorological fields and adaptively calculating particle trajectories. This makes them suitable for modeling accidental emissions and long-range pollution transport. However, a significant limitation of these models is their poor suitability for accounting for complex chemical reactions in the atmosphere due to the computational difficulties associated with interacting, independently moving particles. Typically, Lagrangian models implement only the simplest chemical processes, such as radioactive decay or first-order linear reactions, while photochemical cycles, secondary aerosol formation, and other complex transformations remain beyond their scope. To solve this problem, hybrid approaches that combine Lagrangian and Eulerian methods are often used, enabling the modeling of complex atmospheric processes.

In contrast, Eulerian models have several significant disadvantages. Their primary weakness is limited spatial resolution, which leads to the “smearing” of point emission sources (such as chimneys) across the cells of the computational grid. This is especially critical for local-scale tasks where precise spatial detail is important. Furthermore, these models require substantial computing resources to increase detail; for instance, halving the grid spacing leads to an eightfold increase in computational load. They are also highly sensitive to the quality of the meteorological data, as small inaccuracies in wind or temperature fields can result in significant forecast inaccuracies.

Gaussian models are widely used for calculating pollutant dispersion from industrial chimneys due to their optimal combination of accuracy, simplicity, and established validity. This study employs the Pasquill–Briggs model to simulate sulfur dioxide (SO₂) emissions from chimneys. This approach requires a minimal set of input data, making it convenient for operational emission spread calculations. Compared to more complex Eulerian or Lagrangian approaches, the Gaussian model demands an order of magnitude fewer computational resources and less time while maintaining sufficient accuracy for industrial facilities with stationary emission sources.

In the present paper, a method for calculating SO₂ emission rates (kg/s) is presented based on passive Fourier spectroscopy and path-integrated concentration data. The Pasquill–Briggs Gaussian plume dispersion model is used to relate the measured plume cross-sections to the chimney emission rate. The novelty of this work lies in the combined implementation of cross-sectional FTIR plume scanning and dispersion model inversion for reconstruction of the total emission rate from a point source without access to the chimney, rather than in the use of passive FTIR spectroscopy itself.

2. Materials and Methods

In this paper, we applied the Pasquill–Briggs model to estimate the flue gas distribution, and by solving the inverse problem, we were able to estimate the flue gas emission rate. The Pasquill–Briggs model describes the distribution of pollutants in the atmosphere as a Gaussian distribution. This approach is based on the turbulent diffusion equation with the following key assumptions [48,49]:

• Dispersion in the horizontal and vertical planes is described by a Gaussian distribution with standard deviations ${\sigma }_y$ and ${\sigma }_z$ along the y and z axes, respectively;
• The average wind speed acting on the flow remains constant throughout the layer, and the wind direction does not change;
• The gas emission rate is constant;
• The flow can be reflected from the earth’s surface.

Taking these assumptions into account, the spatial distribution of the SO₂ concentration $c(x,y,z)$ from a point source with a constant wind directed along the x-axis can be represented by the following formula within the framework of the Gaussian model (see Figure 1).

$$c(x,y,z)={\displaystyle \frac{q}{2\pi {\sigma }_y{\sigma }_{z}u}}\exp {\displaystyle \frac{-y^2}{2{\sigma }_y^2}}\left(\exp {\displaystyle \frac{-{(z-H)}^2}{2{\sigma }_z^2}}+\exp {\displaystyle \frac{-{(z+H)}^2}{2{\sigma }_z^2}}\right),$$

(1)

where q is the gas emission rate [kg/s]; H is the height of the flare axis above ground level [m]; $\overrightarrow{u}$ is the horizontal wind speed along the torch axis [m/s]. In the Pasquill–Briggs model, the values of the scattering functions ${\sigma }_y$ and ${\sigma }_z$ are determined by the stability class of the atmosphere at a distance of 100 m to 10 km from the source. The stability class of the atmosphere is determined by wind speed, the degree of solar radiation, and cloud cover [50].

Taking into account the rise of the plume when modeling the dispersion of pollutants is critically important for the correct assessment of the effective height of the emission H, defined as the sum of the physical height of the source h and the vertical displacement of the plume $\Delta h$. For hot emissions characterized by significant buoyancy $(T_s\gg T_a)$, the rise of the plume is mainly due to thermal convection and is described by the semi-empirical Briggs formulas [51]:

$$\Delta h=1.6{\displaystyle \frac{{\left(F_b{x}_c^2\right)}^{1/3}}{u}}\left[{\displaystyle \frac{2}{5}}+{\displaystyle \frac{16x}{25x_c}}+{\displaystyle \frac{11}{5}}{\left({\displaystyle \frac{x}{x_c}}\right)}^2\right]{\left(1+{\displaystyle \frac{4x}{5x_c}}\right)}^{-2},$$

(2)

where $F_b$ is a flux parameter [m⁴/s³]: $F_b=g{v}_s{r}^2\left({\displaystyle \frac{T_s-T_a}{T_s}}\right)$, $g=9.81$—free fall acceleration [m/s²]; $v_s=4.36$—vertical speed [m/s]; $r=4.36$—exit radius [m]; $T_s,T_a$—the exit gas and ambient temperatures [K]; $x_c=A{F}_b^{2/5}{h}^{3/5}$—the distance downwind at which environmental turbulence begins to dominate the dispersion process is known as the critical distance [m]; $A=2.16$ [s^6/5/m^6/5].

The most important step in constructing the plume distribution is to obtain the initial parameters of the model. The basic meteorological parameters (wind speed, atmospheric stability class) required for calculations are set directly from the weather forecast at the time of the measurements. The path-integrated gas concentrations in the flux are calculated according to the direction of the data recorded on the Fourier spectrometer. The emission rate q is calculated by comparing experimentally obtained path-integrated gas concentrations of pollutants $C_{int}^E(\theta ,\phi )$ in the exhaust gas plume with the simulated values $C_{int}^T(\theta ,\phi )$, where $\theta ,\phi$ is the elevation angle and azimuth relative to the observation point. The simulation of path-integrated gas concentrations was carried out as follows:

$$C_{int}^T(\theta ,\phi )={\int }_0^{\infty }{c}_{sp}(r,\theta ,\phi )dr,$$

(3)

where $c_{sp}(r,\theta ,\phi )$ is calculated using the distribution $c(x,y,z)$, by switching to a spherical coordinate system with rotation and shifting the origin to the observation point. For the described transformations, additional parameters are introduced: the azimuth on the tube ${\theta }_s$ and the distance to the tube from the observation point $r_s$. By varying the direction of wind speed and emission rate q, the minimum discrepancy between the theoretical and experimentally measured series of values is determined:

$$\parallel C_{int}^T(\theta ,\phi )-C_{int}^E(\theta ,\phi )\parallel \stackrel{\overrightarrow{u},q}{\to }min$$

(4)

The desired value of the ejection power is determined from condition (4). The experimental concentrations were determined by remote sensing using an infrared Fourier spectrometer. The process of obtaining experimental values $C_{int}^E(\theta ,\phi )$ is presented in detail in [1]. The efficiency of SO₂ detection in the infrared range of the spectrum has been shown in [1,52].

3. Experimental Setup

Figure 2 shows a diagram of an experiment on the remote recording of infrared chimney exhaust gas spectra.

Table 1. Main characteristics of the experimental setups.

Parameter	Value
Optical scheme	Michelson interferometer
Spectral range, $\mathsf{\mu }$m	7–14
Spectral resolution, cm−1	4
Measurement frequency, Hz	1
FOV, deg	2 × 2
Detector type	MCT, cooled up to 80 K
Operating mode	Passive (without IR source)

shows the main technical characteristics of the infrared Fourier spectrometer. The Fourier spectrometer was located on an automated pan-tilt positioner controlled via the Ethernet protocol, with the ability to automatically transmit azimuth and elevation for each measurement, along with a time reference, which makes it possible to use the Pasquill–Briggs model to calculate emissions. The positioning accuracy of the automatic pan-tilt positioner is at least 1 mrad.

4. Results and Discussion

Measurements of path-integrated gas concentrations were carried out in two series. The series were held over two days, with each episode lasting 30 min. The measurement conditions, as well as the simulation parameters, are shown in

Table 2. Measurement conditions.

Parameter	Value	Series 1	Series 2
Time duration	min	30	30
Chimney height	M	250	250
Wind speed ($H_{\nu }$ = 10 m)	m/s	3–4	5–6
Atmospheric stability class	-	D	C
Distance to the chimney R	m	570	590
Azimuth to the chimney $\alpha$	deg	55	50
Chimney exit radius r	m	4.36	4.36
Ambient air temperature $T_a$	deg C	−5	−20
Discharge temperature $T_s$	deg C	55	50
Gas flow speed $v_s$	m/s	4.5	4.5
Elevation angle $\theta$	deg	25–30	25–30
Azimuth $\phi$	deg	220–280	220–280

. Figure 3 shows the side view of the plume from the spectrometer. The middle of the crosshair shows the axis of the infrared channel. The red square is shown conditionally. Figure 4 shows an analysis of thermograms of exhaust plumes with an assessment of the temperature contrast.

Figure 4a shows the thermogram of the exhaust plume obtained using the NEC 2640 (NEC Corporation, Minato, Tokyo, Japan) high-resolution thermal camera from the same position as the spectrometer. Figure 4b shows the temperature distribution along the plume from the chimney exit (L is the distance from the chimney exit, m). The thermogram shows that on the day of the measurement, the effective temperature of the underlying surface (sky) is −38.1 °C or less, which corresponds to a temperature contrast between the exhaust plume and the underlying surface of the order of 20° or more.

The measurement conditions given in Table 2 and

Table 3. Parameters of the Pasquill–Briggs model.

Parameter	Value	Series 1	Series 2
Average source emission	kg/s	15.0	22.0
Wind direction ${\alpha }_u$	deg	121	143
Buoyant flow $F_b$	m4/s3	90	112
Critical distance $x_c$	m	359	392
The plume shifting $\Delta h$	m	146.6	105.3

show the main parameters of the Pasquill–Briggs model. The results of the calculations of the point source plume propagation are shown in Figure 5, Figure 6 and Figure 7.

The graph shown (Figure 5) illustrates the vertical profile of the SO₂ distribution for various distances from the emission source, calculated using the data from the corresponding experiment No. 1. Near the source (no more than 1000 m), in the zone of active plume rise, the concentration distribution shows a symmetrical Gaussian character (Figure 6 and Figure 7) with a maximum located at an altitude determined by Formula (2).

The analysis of the concentration isolines demonstrates a characteristic expansion in the zone of maximum elevation, followed by a stabilized spread at altitudes of about 350–400 m. Data on the height of the plume rise in a specific location allow the spectrometer to be optimally positioned for the accurate targeting of the area of maximum concentration of pollutants. Knowledge of the vertical distribution of the plume ensures the correct selection of elevation and azimuth angles during scanning, which increases the reliability of measurements of path-integrated gas concentration and minimizes errors associated with the incomplete capture of the cross-section of the plume.

To choose the optimal location for the observation point, it is necessary to combine the terrain map with data on the density and direction of winds, as well as information on the distribution of pollution sources and possible obstacles. Preliminary data on wind and emission rates allow us to estimate the pollution density in advance and determine the most suitable location for an observation point.

When calculating the emission rate of n sources (chimneys), a linear superposition of the emissions from each individual source is applied simultaneously, taking into account the position of the sources on the terrain map $c(x,y,z)={\sum }_{i=1}^{n}c(x-x_i,y-y_i,z)$.

During Series No. 1, 15 experiments were performed to register the IR spectra of SO₂ while scanning the FTIR spectrometer along the plume. During Series No. 2, 25 experiments were performed. The results of the analysis of the two series are shown in

Table 4. Results of emission rate calculation.

Parameter	Value	Series 1	Series 2
The average value	kg/s	15.0	22.0
Average square deviation	kg/s	7.4	7.3
Coefficient of variation	%	45.2	32.8

.

Accurate emission data are not available for remote measuring, as it is difficult to perform local monitoring by simultaneously measuring gas flows in all pipes entering the chimney. Another way to estimate the emission rate may be through PEMS models. However, the PEMS data are indirect and also require validation. The above errors in the emission rate are determined to be random errors, such as errors in registering IR spectra and in determining wind speed (especially the vertical component, where the error of anemometers reaches $\pm 5\%$), as well as methodological errors related to solving the multilayer problem of atmospheric optics for determining concentrations while considering atmospheric turbulence, etc.

In addition to the described emission rate assessment, the proposed methodology can be improved to create an operational alarm system. Continuous monitoring of emission levels during time windows (for example, from 1 to 30 min on average) will allow detecting cases of exceeding regulatory or enterprise-specific thresholds. Such exceedances can serve as triggers for alarm notifications, allowing us to quickly identify abnormal emission patterns, unintended emissions, or deviations from expected operating conditions. It is important to note that this alarm function can be implemented without the need for physical access to the emission source, providing a passive additional control measure in combination with existing CEMS or PEMS systems.

The proposed methodology is not designed to replace existing advanced monitoring technologies such as in-stack CEMS or satellite-based observation systems. Instead, it corresponds to situations in which direct access to emission sources is limited, independent verification of reported emissions is necessary, or the swift implementation of a contactless monitoring solution offers significant benefits. The described method should be regarded as a complementary diagnostic and verification tool rather than a standard measurement tool replacement.

However, the proposed methodology is not species-specific. The same procedure can be applied to other infrared-active gaseous pollutants such as NO₂, HCl, H₂S, CO, NH₃, and selected volatile organic compounds, provided that suitable spectral windows and absorption cross-sections are available. Furthermore, the linearity of the Gaussian plume dispersion model allows for the extension of the approach to multiple emission sources through superposition. The method is therefore best interpreted as a general framework for the remote estimation of industrial emission rates rather than as a pollutant-specific technique. Potential applications include independent verification of CEMS and PEMS data, rapid screening of emission sources, and deployment in locations where direct in-stack monitoring is impractical.

5. Conclusions

This paper presents a consolidated methodology for estimating industrial SO₂ emission rates by integrating passive FTIR path-integrated concentration measurements with Gaussian plume inversion. The approach extends established FTIR concentration retrieval techniques by coupling them with atmospheric dispersion modeling to recover chimney emission rates under real industrial conditions. The FTIR spectrometer, operating in the mid-infrared range (7–14 $\mathsf{\mu }$m) at a spectral resolution of 4 cm⁻¹ and a scanning frequency of 1 Hz, was deployed at a distance of 570 m from the emission source.

The emission rates of sulfur dioxide were calculated using the Pasquill-Briggs Gaussian plume dispersion model. Model inputs included source parameters (chimney height, nozzle diameter, and gas exit velocity) and real-time meteorological data (wind speed and atmospheric stability class). Analysis of two distinct 30 min measurement series, conducted on separate days, yielded average emission rates of 15.0 kg/s and 22.0 kg/s, with corresponding coefficients of variation of 45.2% and 32.8%. This level of uncertainty is consistent with established dispersion modeling approaches, which report inter-model discrepancies on the order of 35% for emission rate estimations [52].

The methodology is general and transferable to other gaseous pollutants and industrial configurations, subject to meteorological constraints and spectral detectability. It provides a practical complement to conventional emission monitoring systems such as CEMS and PEMS, thus filling the niche between localized in-stack measurements and large-scale remote sensing systems, contributing to more flexible and transparent industrial emission monitoring strategies.