Gas flaring is an important source of atmospheric soot–black carbon, especially in sensitive Arctic regions. However, emissions have traditionally been challenging to measure and remain poorly characterized, confounding international reporting requirements and adding uncertainty to climate models. The sky-LOSA optical measurement technique has emerged as a powerful means to quantify flare black carbon emissions in the field, but broader adoption has been hampered by the complexity of its deployment, where decisions during setup in the field can have profound, non-linear impacts on achievable measurement uncertainties. To address this challenge, this paper presents a prescriptive measurement protocol and associated open-source software tool that simplify acquisition of sky-LOSA data in the field. Leveraging a comprehensive Monte Carlo-based general uncertainty analysis (GUA) to predict measurement uncertainties over the entire breadth of possible measurement conditions, general heuristics are identified to guide a sky-LOSA user toward optimal data collection. These are further extended in the open-source software utility, SetupSkyLOSA, which interprets the GUA results to provide detailed guidance for any specific combination of location, date–time, and flare, plume, and ambient conditions. Finally, a case study of a sky-LOSA measurement at an oil and gas facility in Mexico is used to demonstrate the utility of the software tool, where potentially small regions of optimal instrument setup are easily and quickly identified. It is hoped that this work will help increase the accessibility of the sky-LOSA technique and ultimately the availability of field measurement data for flare black carbon emissions.
Gas flaring is a routine practice in the oil and gas industry in which
producers and refiners burn excess or unwanted gases in open-atmosphere
flames, typically from vertical pipe stacks. Flaring is generally preferable
to the venting of gases to the atmosphere because it reduces carbon dioxide
(CO
With the addition of BC to the Gothenburg protocol in 2012 (United Nations Economic Commission for Europe (UNECE), 2012), 34 countries are now legally bound to report, where data are available, BC emissions under UNECE's Convention on Long-Range Transboundary Air Pollution, including the European Union, Russia, the United States of America, and Canada. To attribute – and, hence, report and regulate – soot–BC emissions from various sources, emission factors that relate soot–BC emissions to a measure of industrial activity are required. Unfortunately, for gas flaring, commonly employed soot emission factors are crude single-valued parameters that link emitted soot mass to volume or mass of gas flared regardless of flare design, gas composition, or operating conditions. This contrasts with numerous studies that have observed a significant influence of flare gas composition and flame aerodynamics on soot emissions (Becker and Liang, 1982; Conrad and Johnson, 2017; McEwen and Johnson, 2012) and even soot properties (Conrad and Johnson, 2019; Trivanovic et al., 2020). Further soot yield data are needed, particularly for real-world flares under field conditions, to develop and validate accurate flare soot–BC emission factor models.
At present, there are only two published methods for the quantitative
measurement of soot–BC emissions from individual in-field flares. One
technique employs aircraft-based sampling of a flare plume (Gvakharia
et al., 2017; Weyant et al., 2016), where measurements of soot, methane, and
CO
The key component of a sky-LOSA measurement is the quantification of plume soot loading using image data, via analysis and modelling of radiative transfer through the atmospheric flare plume at the measurement wavelength. For each acquired image, soot mass column density is resolved pixel by pixel over a control surface within the image plane and combined with simultaneously measured velocity (obtained via image correlation velocimetry) to permit mass emission rate calculation. Uncertainties in sky-LOSA-calculated emission rate are computed under a Monte Carlo (MC) framework and are dominated by uncertainties that affect computation of soot mass column density. While these uncertainties are influenced by numerous parameters considered within the MC analysis, they are also sensitive to the positioning and pointing of the sky-LOSA camera relative to the horizon and sun. Consequently, a sky-LOSA user must position the camera according to several constraints, which may be heuristic but can also vary with uncontrollable measurement parameters. To make the measurement technique accessible to end-users, enabling an increase in flare soot emissions data, a standardized data acquisition protocol for sky-LOSA is required.
The objective of this work is to complete a general uncertainty analysis (GUA) for the sky-LOSA measurement technique that provides uncertainty-based guidance to an end-user regarding the setup of equipment and acquisition of sky-LOSA data through an accompanying open-source software tool. A summary of sky-LOSA theory, referring to derivations in previous works, is first provided in Sect. 2 of this paper. The GUA methodology is summarized in Sect. 3, including special provisions necessary to reduce the computational burden of the MC-based approach (Sect. 3.1 and Appendix A). Representative results from the MC GUA are shown in Sect. 4.1, and general heuristics for the acquisition of sky-LOSA data, including new observations based on MC GUA results, are summarized in Sect. 4.1.1 and 4.1.2. To provide case-by-case guidance, a new open-source software tool to calculate sky-LOSA measurement uncertainty is introduced in Sect. 4.2. Finally, in Sect. 4.3, the software tool is used in a case study that analyzes optimal camera positioning for flare measurements at a gas refining and transport facility in Campeche, Mexico. This work enables a consistent approach for the selection of sky-LOSA camera positioning and pointing to minimize measurement uncertainties, ultimately contributing to the standardization of the sky-LOSA measurement technique.
The generalized sky-LOSA theory was summarized in full by Johnson et al. (2013) and has been the
subject of a variety of validation efforts
(Conrad et al., 2020a, b; Johnson et al., 2010). Development of the theory begins with Fig. 1, which shows an example sky-LOSA image for
computation of time-resolved soot emission rate from a soot-laden flare
plume in the Montney formation of Alberta, Canada. A highly linear,
grayscale, scientific-CMOS camera (e.g., pco edge 5.5) is used to obtain
upwards of 10 min of high-speed image data of the flare and turbulent,
soot-laden, atmospheric plume. Pseudo 16-bit images are acquired at
frame rates of 25–50 Hz with a narrow mid-visible bandpass filter
(
Sample sky-LOSA image of the flare and atmospheric plume, which is
under slight crosswind in this example. A control surface (
Overlaid in Fig. 1 is an example control
surface (
Figure 2 shows an example
positioning and pointing of the sky-LOSA camera and an optical axis (LOS) within
the surrounding sky dome. For a given LOS, a Cartesian coordinate system is
defined where the positive
Schematic of a sky-LOSA measurement under the hemispherical sky
dome showing the camera's optical axis relative to the horizon
(
Using the mean value theorem, a path-averaged source radiant intensity
(
According to Eq. (8), sky-LOSA computation of
soot mass column density is a function of the position of the camera and
sun, field-observed plume transmittance, skylight intensity distribution and
solar irradiance (through
For end-users of sky-LOSA, the sensitivity of measurement uncertainty to
camera pointing necessitates a standardized (and ideally simple) data
acquisition protocol to optimize camera position and pointing under general
conditions. This would allow a priori setup decisions to minimize or
constrain uncertainties within reasonable limits. An acquisition protocol
must therefore be constructed using quantitative knowledge of measurement
uncertainty in sky-LOSA-computed soot mass column density. Restated in the
context of the above theory, the objective of this work is to quantify via a
comprehensive general uncertainty analysis the uncertainty in
sky-LOSA computation of soot mass column density (
The goal of the present general uncertainty analysis (GUA) is to guide a sky-LOSA user in choosing a sky-LOSA camera position and pointing to minimize measurement uncertainties. The developed software tool can also be used to give an initial estimate of uncertainties in the measured soot emission rate ahead of a more detailed post-processing analysis. To provide generalized recommendations, the GUA quantifies measurement uncertainty in soot mass column density for a selected camera pointing and other independent variables via MC analysis over uncertain variables that include all relevant soot properties. This section describes the MC method used in the present GUA including novel updates to the MC approach that are necessary to make this present work tractable. This new methodology is a significant improvement to the sky-LOSA algorithm that enables accelerated MC computation of soot column density and, hence, emission rates from sky-LOSA image data.
For a given (modelled) skylight intensity distribution, measured or modelled
solar irradiance, camera pointing, and set of soot properties, the
1SA-estimated inscattering correction (
One such means is through a Fourier–Legendre expansion of the SPF. For an
arbitrary set of randomized soot properties
Introduction of the Fourier–Legendre-expanded SPF into the sky and sun
components of the inscattering correction (
While the incident intensity-normalized solar horizontal irradiance
(
The standard CIE sky models have found good utility in a variety of fields,
from urban planning (e.g., Acosta et al., 2014) to
building design (e.g., Wong, 2017); however, the models
naturally suffer from directionally dependent error in skylight intensity.
This is particularly true for overcast and partly cloudy skies since the
models, which are smooth functions, do not capture steep gradients in
skylight intensity due to cloud structures. Thus, there is some additional
uncertainty in sky-LOSA-computed soot mass column density through use of a
single CIE sky model in the MC method. To permit capture of CIE sky model
error in the GUA, like skies were sorted into sky “categories” that have
similar properties but differing model coefficients and, hence, directional
variability. The derived sky categories (
Sky categories derived to propagate error in the CIE sky models through the sky-LOSA algorithm computing soot mass column density.
Sky category A corresponds to overcast and partly cloudy conditions with an
obscured sun. Typical turbidity factors of the component skies (
Table 2 summarizes the independent, pre-computed,
and random variables required to compute soot mass column density under the
GUA MC framework. There are five independent variables that define the
pointing of the camera relative to the sun (
Summary of independent, random, and pre-computed variables in the GUA.
To enable an objective comparison of sky-LOSA uncertainty as a function of
the independent variables, a parameter describing the
Figure 3 shows relative uncertainty results at
different camera pointings for an example sky-LOSA measurement
scenario of a flare with 90 % observed plume transmittance. The selected
solar zenith angle (
Example MC results at solar noon on the summer solstice in Fort
St. John, British Columbia – solar zenith (
There are two observable trends in the data of Fig. 3 that persist through all measurement conditions.
Firstly, the relative uncertainty is a strong function of the solar
scattering angle,
The mechanism for the decrease in relative uncertainty with increasing
Central tendency (median; left logarithmic axis) and relative
uncertainty (CV
The second trend in Fig. 3 that is generally seen
across all measurement conditions is the sensitivity of relative uncertainty
to the camera inclination angle (
Percentage relative uncertainty in soot mass column density for a
relative solar azimuth (
Figure 5 also shows that the CV
Upon arrival at a measurement facility, the sky-LOSA user's first task is to
determine the position of the sky-LOSA camera for data acquisition. This
important decision can be made by considering viable camera pointings from
GUA MC data through constraints on
Summary of constraints regarding camera pointing relative to the
horizon and sun as a function of plume transmittance (
One additional consideration in the pointing of the sky-LOSA camera is the direction of plume propagation. Under quiescent conditions, buoyancy-driven flare plumes will propagate vertically away from the flare stack; however, under sufficiently strong crosswinds, the flame and plume can bend over and propagate horizontally, parallel to the wind direction. In this latter case, if the plume propagates towards or away from the sky-LOSA camera, turbulent plume structures of differing vorticity become overlapped from the camera's perspective. Therefore, it is best to position the sky-LOSA camera such that it points orthogonally to the wind direction, which minimizes out-of-image plane motion of the plume and yields the best data for velocimetry calculations. This should be viewed as a weak constraint on sky-LOSA data acquisition however, since the effect of uncertainty in estimated velocity on mass emission rate is generally negligible compared to that of column density uncertainty.
Following selection of a permissible sky-LOSA camera position, the imaging
optics must be chosen. Prime (fixed focal length) lenses are employed in the
sky-LOSA technique to avoid ambiguity in optical magnification and, hence,
spatial scaling of the image. The most appropriate prime lens for the
studied flare is one that maintains the entirety of the flare flame well
within the image during the data acquisition period. This helps to ensure
that a control surface within the image plane that transects the plume and
encloses the flame can be derived, as shown in Fig. 1. For a flame that is relatively unsteady – i.e.,
moving with the wind – it is suggested to keep the flare flame
approximately one-quarter of the smallest image dimension. By contrast, if
the flame is steady, a flame length of approximately one-third of the
smallest image dimension should be targeted. For the sky-LOSA camera used by
the authors (minimum sensor dimension of
With an appropriate lens selected, the user must then choose imaging
parameters that influence the exposure and focus of the image. The objective
is to obtain an image that maximizes the digital signal while minimizing
exposure time and ensuring the flame is in focus. In the authors'
experience, this can be obtained with a lens aperture close to full-open
(typically
While the camera pointing heuristics presented in
Table 3 can be used to ensure that
Figure 6 shows a flow chart describing the
SetupSkyLOSA software's main procedure. For a user-inputted location and time, the
software first determines the current position of the sun using an
integrated solar position calculator – a MATLAB implementation of the
National Renewable Energy Laboratory's (NREL's) Solar Position Algorithm
(SPA) (Reda and Andreas, 2008). The SPA returns the solar
zenith (
Flow chart of the main procedure of the SetupSkyLOSA software tool. The user
provides the location, Gregorian date, time zone, and local time, which are
used to compute the corresponding solar position using the Solar Position
Algorithm of the National Renewable Energy Laboratory
(NREL; Reda and Andreas, 2008). Then, with data on
ambient conditions and observed plume transmittance, the software tool plots
the desired statistic of soot mass column density over the
At this point, the software has computed
SetupSkyLOSA also includes several added utilities to support optimal positioning and
pointing of the sky-LOSA camera. Firstly, using the same pinhole camera
model that enables spatial scaling of the image, the software tool can
optionally overlay the approximate extent of the image sensor in the
The utility of the novel software tool, SetupSkyLOSA, is shown in this section via a
case study of a sky-LOSA measurement at a real oil and gas facility. The
Atasta Gas Processing and Transport Centre (Centro de Proceso y Transporte
de Gas Atasta) is a midstream oil and gas facility near Atasta, in the
Mexican state of Campeche. The facility is under the jurisdiction of
Petróleos Mexicanos and receives sour gas and condensates from the
Cantarell offshore oil field for processing and transport to the national
market. As shown in Fig. 7a, the Atasta facility is
located 35 km west of Ciudad (Cd) del Carmen and approximately 5 km south of
the shore of the Bay of Campeche. The facility occupies approximately
1 km
For this case study, a sky-LOSA measurement of soot emissions from the
central flare stack at the Atasta station was considered as indicated in
Fig. 7b, the base of which is located at
18 The sky-LOSA measurements occur on 13 May 2021, which is the date of that
year that the sun most closely reaches the solar zenith ( Predicted sky conditions are uncertain and may change between overcast and
fully clear conditions throughout the day. Wind speed is predicted to be low and the flare is strongly buoyant. The flare stack is 30 m in height, and the horizontal stand-off distance of
the sky-LOSA camera is limited to 250 m or less due to available optics. The flare is lightly sooting, with an observed transmittance of
approximately 90 % (
Assumption 2 implies that sky-LOSA data acquisition may occur under
skies represented by any of sky categories A–D. Furthermore, assumption
3 suggests that the soot-laden flare plume propagates vertically from
the flare stack, and, therefore, the constraint on camera position with
respect to wind direction is unimportant. The sky-LOSA user wishes to obtain
sky-LOSA data with minimal measurement uncertainty, while also avoiding
re-location of the sky-LOSA camera throughout the day, if possible.
Given the known GPS coordinates of the flare stack, measurement date, and approximate plume transmittance, SetupSkyLOSA can be used to constrain sky-LOSA
camera pointing for any sky condition and time of the day based on the
CV
Using the uncertainty data in Fig. 8a–d, the positioner
utility of SetupSkyLOSA can be employed to highlight where the sky-LOSA camera may be
positioned relative to the flare stack. This was performed for each of the
sky categories using the uncertainty threshold of 16.5 %. Permissible
camera positions were output in .kml format by the positioner utility and
are overlaid on a map of the Atasta facility in Fig. 8e and are quite different for each of the sky
categories. Permissible camera positions for sky category B exist beyond a
small region near the stack tip, while those for sky category A are within
an annular region surrounding the flare stack – since the lower limit on
the camera inclination angle in Fig. 8a imposes a
maximum permissible stand-off distance. Sky category D contains two
permissible regions – one to the south and one to the north of the flare
stack – while the most-constrained sky category C has one relatively small
region to the north of the flare stack. Recalling assumption 2 that
predicted sky conditions were uncertain, the sky-LOSA user should ideally
position the camera at the intersection of the sky-category-dependent
permissible regions. This small area is outlined in black in the figure,
This case study shows the remarkable utility of the SetupSkyLOSA software tool. The tool quickly provides resolved measurement uncertainty data from the GUA that would otherwise require millions of MC analyses to compute. These uncertainty data enable optimal sky-LOSA camera positioning and pointing and also represent a first-order estimate of soot emission rate uncertainties that are computed in post-processing. Together with the additional utilities and general camera heuristics, this software tool permits a sky-LOSA user to obtain optimal sky-LOSA data that minimize measurement uncertainties under generalized conditions.
A comprehensive Monte Carlo-based general uncertainty analysis (GUA) has been used to develop heuristics constraining the pointing and positioning of sky-LOSA equipment for measurement of soot–black carbon emissions from gas flares. The GUA identifies generalized constraints based on predicted measurement uncertainties in soot mass column density, computed using sky-LOSA. The results show that equipment setup constraints can be classified based on the conditions of the sky, relative positioning of the sun, and inclination angle of the camera. With additional heuristics on camera optics and imaging parameters, the presented results provide generalized guidance to greatly simplify acquisition of optimal sky-LOSA data in the context of complex, non-linear measurement uncertainties. These are further extended in the open-source software utility, SetupSkyLOSA, which interprets the GUA results to provide detailed guidance for any specific combination of location, date–time, and flare, plume, and ambient conditions. Furthermore, software-displayed soot mass column density statistics provide the user with a first-order estimate of measurement uncertainty in soot–black carbon emission rate that otherwise is only computable during post-processing. The case study using SetupSkyLOSA to identify optimal equipment setup at a real oil and gas facility in Mexico demonstrates the utility of this new software tool, which as an open-source application can hopefully facilitate broader use of the sky-LOSA technique and ultimately help increase the knowledge base of soot–black carbon emissions from gas flares.
For the prior probability distributions of soot properties derived by
Johnson et al. (2013), the total order of
soot coefficients required to represent the soot SPF according to the
procedure of Schuster (2004) was typically
As noted in Sect. 2, ground-level solar normal
irradiance –
The ratio of solar normal to diffuse horizontal irradiance is complex to
quantify in a general sense as it is a function of atmospheric composition.
However, for the purposes of the present GUA it is modelled as follows:
To model some amount of unknown uncertainty due to the use of “typical”
metrics listed in the literature, an additional randomized variable (
The developed software tool and associated data are available online as
open-source and build distributions (
Both authors conceptualized the research and developed the methodology. MRJ was responsible for funding acquisition, project administration, provision of resources, and supervision. BMC curated the data, performed the formal analysis and investigation, developed the software, and produced the original manuscript including visualizations. Both authors reviewed and edited the manuscript throughout the publication process.
The authors declare that they have no conflict of interest.
We are grateful for the support of Michael Layer (project manager, Natural Resources Canada) for championing this and related projects and to Brian Crosland (Natural Resources Canada) for lending computational resources.
This research has been supported by Natural Resources Canada (grant no. CH-GHG IETS-19-103) and the Natural Sciences and Engineering Research Council of Canada (NSERC, grant nos. 479641, 06632, 522658).
This paper was edited by Oleg Dubovik and reviewed by three anonymous referees.