Enhancing optical quantification of combustion products using thermochemical manifold reduction
Introduction
The climate is at a tipping point, primarily due to combustion-related emissions. Oil and gas flares alone were responsible for emitting 300 Mt of CO2 globally in 2019, representing 0.9% of all CO2 emission [1], [2], [3], [4]. This figure assumes that natural gas is entirely converted to CO2; incomplete destruction of hydrocarbons can significantly increase the environmental impact of flares [5], [6], [7], [8], [9], [10], [11], since methane, the main component of natural gas, has a global warming potential of 36 times the emission of CO2, by mass [12]. Measurement techniques are urgently needed to quantify these and other emission sources, in order to fully understand the impact on climate trajectory, and establish policy and regulation to mitigate these impacts.
Emissions from large-scale combustion devices, such as oil and gas flares and gas turbines, are often quantified through probes, e.g., traversing a “rake” of thermocouples and extractive sampling ports through the flow field. This procedure suffers from a number of well-known drawbacks, chief among them the inherent locality and limited temporal resolution of the measurements. Species concentration, composition, and temperature may vary in space and time, particularly for turbulent flows, so key flow features are inevitably missed. In the case of flaring in a cross-wind, for example, the airflow across the cylindrical flare stack can cause an aerodynamic fuel stripping mechanism that produces transient and localized “pockets” of unburned fuel in the flare wake [7]. This phenomenon is difficult to capture using physical probes, leading to a severe over-prediction of flare combustion efficiency.
Optical diagnostics are useful in this context since large flow field areas may be imaged near-instantaneously, and, in some cases, gas concentrations and temperatures may be reconstructed tomographically from a large number of line-of-sight measurements [13]. Imaging-based approaches may also be used to obtain standoff or fence-line measurements, which are particularly useful in scenarios where the flow-field is difficult or impossible to access. However, in addition to spatial and temporal resolution, some degree of spectral resolution is needed to resolve concentrations of multiple species simultaneously. Particularly in the case of emission-based spectroscopy, for a mixture containing n radiatively-participating species, at least n+1 images must be obtained at independent wavelengths or over distinct spectral bands to estimate species concentrations and temperature, assuming that the measurement probe volume is well-mixed. Due to the inherent ill-posedness of the problem, and in scenarios involving heterogeneous species concentrations and temperatures, it may be necessary to have even more spectral resolution in order to obtain robust estimates of the quantities-of-interest.
In this regard, hyperspectral imaging using imaging Fourier transform spectrometers (IFTSs) is particularly appealing. IFTSs use interferometry to generate a data cube of images, each at a distinct wavelength. Each pixel in an image corresponds to a high-resolution spectrum, from which the species column densities and temperature may be inferred simultaneously by regressing a model spectrum derived from the radiative transfer equation to the measurements [14], [15], [16]. On the other hand, a major drawback of the IFTS is its poor temporal resolution compared to other types of sensors. Spectra are generated from a sequence of typically thousands of broadband images recorded as a mirror traverses across the interferometer. Higher spectral resolutions require more images, which increases the acquisition time; typical acquisition times may be on the order of 30 s in order to achieve a spectral resolution of 0.25 cm−1. This long acquisition time is not an issue for stationary targets, but, in the case of turbulent flow fields, changes in the gas state can generate artifacts in the recovered spectra [17]. For this reason, it is desirable to use the lowest resolution necessary to infer the temperature and volume fraction of each species. However, lowering the spectral resolution may increase the ill-posedness of the problem.
We propose to ameliorate this ill-posedness by introducing additional prior information via a thermochemical manifold reduction (TCMR) model. When quantifying emissions from industrial combustion applications, including flares, the focus is on the flow field downstream of the reaction zone. At this location, the gas can be envisioned as a mixture of three states: combustion products, unburned fuel, and air. Moreover, there is an implied relationship between these three states and the local temperature based on the stoichiometry and enthalpy of combustion. In the case of CH4 combustion, the number of inferred parameters may, in principle, be reduced from four (CH4, CO2, H2O, and temperature) to two: the amount of unburned fuel and the combustion products. The balance of the mixture must constitute air, and the corresponding mixture temperature may be estimated from the combustion reaction rate (amount of CO2 and H2O) and the specific heat of the mixture. This procedure is implemented on synthetic IFTS measurements on a flare in a cross-wind, with the objective of inferring the combustion efficiency. Incorporating the TCMR model into the inference process improved the CO2 column number density estimates for all spectral resolutions in relation to the standard approach. However, the TCMR does not significantly improve estimates for the unburned fuel state. Although this paper demonstrates this technique using hyperspectral measurements on flares, it can be applied to several combustion applications where it is desired to have non-intrusive methods to infer the composition and temperature quantitatively.
Section snippets
Measurement model
Inferring the species column density and temperature within each pixel of an IFTS camera amounts to solving an inverse problem in which the spectra generated from a measurement model is regressed until it matches the measured spectra. We begin by deriving the measurement model that connects the gas state to the measured spectrum for each pixel. Next, we discuss the inversion procedure used to find the species column densities. Finally, the TCMR is described for the simple case of CH4 combustion.
Synthetic data
The feasibility of the TCMR approach is assessed by considering a synthetic experiment of inferring the combustion efficiency of an upstream oil and gas flare using an IFTS. This scenario is shown in Fig. 2. Flare combustion efficiency is defined as the ratio of mass flow rates of carbon affixed to CO2 in the combustion products to that of carbon affixed to fuel (here taken to be methane) entering the flare stack. Since the mass flow rate of fuel is often unknown, e.g. in fence-line
Results and discussion
The synthetic data of 24 pixels, shown in Fig. 2, were sampled and contaminated with 10% white noise for a set of 128 measurements each, or 3072 samples in total, for each spectral resolution. The CO2, CH4, and H2O column densities are estimated for each sample in terms of their respective maximum values (x1,max, x2,max) using three different procedures and five spectral resolutions. First, the peak volume fraction of each species and peak temperature are inferred simultaneously, assuming that
Conclusions
Hyperspectral infrared imaging is a potent tool for characterizing the temperature and composition of combustion products, although this often involves solving a mathematically ill-posed problem. This study presents a novel approach to mitigate this ill-posedness by incorporating additional information via a thermochemical reduction mechanism, thereby reducing the number of inferred parameters and the statistical degrees-of-freedom in the inversion problem. The model is tested using a simulated
CRediT authorship contribution statement
R.B. Miguel: Conceptualization, Methodology, Investigation, Software, Writing – original draft. J. Emmert: Conceptualization, Methodology, Software. K.J. Daun: Conceptualization, Methodology, Writing – review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was sponsored by NSERC's FlareNet (NETGP 479641 – 15). The first author would like to acknowledge CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for the scholarship (Programa de Doutorado Pleno no Exterior/88881.128298/2016-01). The second author was suppprted by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project Nos. 215035359—TRR 129.
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