Methane Gas Visualization Using Infrared Imaging System and

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Ind. Eng. Chem. Res. 2010, 49, 3926–3935

Methane Gas Visualization Using Infrared Imaging System and Evaluation of Temperature Dependence of Methane Gas Emissivity Anisa Safitri and M. Sam Mannan* Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas 77483-3122

Infrared (IR) camera has been used widely in the industry to visualize gases that cannot be seen by the naked eye or a visual camera. The use of an infrared camera for gas imaging offers several advantages such as faster locating of gas leaks and easier understanding on how the gas travels and disperses. In addition, several types of infrared cameras have the capability to measure the temperature of target objects especially solid body objects. However, this facility has not been applied for measurement of gas temperature due to complex analysis on the physics of infrared imaging and some uncertainties related to the radiation heat transfer processes during temperature measurement that have not been well understood. The objective of this research is to make use of the infrared or thermal imaging system to provide a concise temperature distribution of a methane gas plume presented in the infrared image. However, the current technology in infrared imaging cannot provide the true temperature of a gas plume because the emissivity value is always assumed as unity, and the actual emissivity value of the gas is not integrated in the camera’s algorithm. The visualization of dispersed liquefied natural gas (LNG) vapor from LNG spills on the ground using a midwave thermal camera is presented in this work. Two types of infrared cameras were used: Amber Radiance 1 and GasFindIR, also known in industry as hydrocarbon camera. The infrared images or thermograms show that several factors affecting the temperature measurement are weather conditions, wind rose, atmospheric attenuation due to the presence of other radiation absorbing gases along the optic path, and gas emissivity. Gas emissivity is the main uncertainty in gas temperature measurement using thermal cameras. This research proposed a method to correct the gas temperature measured by a thermal camera by applying the emissivity factor calculated from a theoretical analysis on methane gas emissivity using the band absorption method. The study demonstrates that methane gas emissivity is a strong function of gas temperature; however, the effect of optical depth is insignificant. Because in this work, the infrared camera is used to visualize the LNG vapor, temperature dependence of methane emissivity at temperatures 110-300 K is evaluated and presented in this paper. Introduction Infrared cameras have been used in industry for more than 30 years, and innovations to improve its capability have been vastly developed. The application of infrared camera varies from electrical power plants, petrochemical plants, refineries, building diagnostics, automation, marine surveying, medication, home inspection, and more others mainly in finding thermal anomalies. In the industrial plant, an infrared camera is used as a nondestructive testing tool in order to detect equipment faults and improve the safety and reliability of the system and equipment while minimizing the environmental impact and cost of operation. Recently, the use of infrared imaging technology has been expanding in the petrochemical industry as a method to detect some volatile organic compounds such as methane, benzene, and propane.1 Infrared cameras have more advantages for leak or spill detection rather than a total vapor analyizer (TVA) or “gas sniffer” because they provide area measurement rather than point by point measurement and give a real-time image of the gas plume. Infrared cameras give the option for optical imaging inspection of organic volatile compounds that cannot be reached by an organic vapor analyzer or total vapor analyzers. They are able to detect the motion of the plume and give a good contrast between the absorbing and the background gas which are the key elements for detection. Infrared imaging cameras allow one to spot several volatile compound gas leaks quickly * To whom correspondence should be addressed. E-mail: [email protected].

due to their ability to scan large areas and deliver real-time thermal images of gas leaks. The latest infrared camera for VOC detection is also designed for use in harsh industrial environments, operates in a wide temperature range of 5-122 °F (-15 to 50 °C) and can withstand water, dust, and vibrations. It also has been tested to detect several volatile compounds such as benzene, butane, ethane, ethyl benzene, ethylene, heptane, hexane, isoprene, methane, methanol, octane, pentane, 1-pentane, propane, propylene, toluene, and xylene.2 The IR imaging method allows the visualization of methane gas radiation into the atmosphere in real time, and therefore, it is suitable for rapid and accurate detection and localization of natural gas dispersion. Detection using an infrared camera is considered safer than the procedure involving a man-carried sniffing detector because the device can be placed from 5 to 20 feet away compared to the sniffer.3 Early use of infrared imaging for methane gas leak detection was conducted by Gross et al by utilizing a high-resolution IR imaging camera (∆T ) 10 mK) with a PtSi Schottky barrier focal plane array, cooled to 77 K, 256 × 256 pixels for the detection of methane radiation which had the spectral range between 3 and 5 µm.4 The infrared imaging used to measure the cloud emitted from the buried natural gas pipeline consisted of four optical components: an IR imaging camera, a narrow band filter centered at micrometers, a halogen lamp, and a diffuse IR reflector. The objective of the laboratory testing of the gas imaging done by Gross et al. was to determine the sensitivity of the infrared camera for detection of methane leak from a pipeline with an open end buried in soil and loose gravel

10.1021/ie901340g  2010 American Chemical Society Published on Web 03/25/2010

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

in a depth of approximately 15 cm at a flow rate of 0.1 L/min. In the experiment, the effect of the wind force and moisture level of the soil was not considered. The result of this experiment showed that the leak rate down to 0.1 L/min was still detected by the IR imaging camera. The methane cloud is visible as dark areas in the image, the concentrations detected are 0.56% in the region above the leak and 0.03% in the tail of the cloud.4 The sensitivity of the IR imaging was estimated from the relative contrast of the absorbing gas and the background gas. Temperature difference as low as 10 mK can be resolved on a temperature background of 300 K. Infrared imaging was also utilized by Leak et al.5 to visualize liquefied natural gas (LNG) vapor dispersion. The infrared camera used was the HAWK camera system built by Leak Surveys Inc. It consisted of a modified Indigo Merlin MID camera with a spectra range of 1-5.4 µm. The detector was made of 30 × 30 µm indium antimonide (InSd) with 320 × 256 pixel array. The cooler system used was a Stirling cooler which provided the system with a NEDT (noise equivalent delta temperature) of no more than 18 mK; hence, the sensitivity was relatively high. The camera consisted of an optical module for image information, detection module for conversion of the optical image into an electrical signal, and an electric module for conditioning and data processing. The role of the optical module was to concentrate the radiation energy from the target object to form an image in the focal plane. It contained lenses and mirrors made of materials which have high refractive index, i.e., germanium, silicon, and zinc sulfide.5 This research focuses on the utilization of an infrared imaging system to visualize the LNG vapor cloud from an LNG spill on the ground. The aim is to study the behavior of the gas plume demonstrated from the thermograms, and study factors affecting the temperature measurement using an infrared imaging camera. The final objective of this research is to classify the main uncertainties in temperature measurement using an infrared camera and provide an approach to reduce the uncertainties so that the actual distribution of the gas temperature can be specified. Current technology in infrared imaging cannot provide the true temperature of the gas plume because the emissivity value is always assumed as unity, and the actual emissivity value of the gas is not integrated in the camera’s algorithm. Therefore, this research gives a theoretical approach on estimating the methane gas emissivity at different temperature. The practical application of this work is that by knowing the emissivity of methane gas at different temperatures, the actual temperature profile from the thermogram can be predicted. The dispersion model can be used to calculate concentration profile of a gas plume as long as the weather conditions are known. Having the temperature profile of the gas plume and the concentration profile attained from the dispersion model, the correlation between temperature and concentration of the methane gas plume can be further developed. Eventually, the infrared camera is not only used to locate gas releases in natural gas industry but also can be applied to measure the temperature of the gas and from the temperature-concentration correlation so that the flammability distance or range of the methane gas plume can be identified. Methodology Two types of infrared cameras were used for the visualization of the LNG vapor cloud: Amber Radiance 1 thermal camera and FLIR System Gas FindIR. Both infrared cameras worked in the midwave infrared range. The Amber Radiance 1 thermal

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camera was able to provide a temperature profile of the scenes taken during the experiments. The operating temperature of this camera was between 23 and 149 °F with thermal sensitivity 0.08 °F at 73.4 °F. The FLIR System Gas FindIR was a dual camera detector system: one detected targets in very narrow infrared wavelength and one detector acted as a reference. For this reason, this infrared camera could detect most of hydrocarbons within the narrow wavelength. Infrared camera measured the radiation that appeared to emanate from an object. The system calibration converted the output voltage to temperature. The calibration provided a twodimensional representation of the surface temperature. An object emitted energy from its internal molecular vibration. The emitted energy from an object depends on the surface temperature and surface characteristics. The camera detected the amount of flux impinging upon a detector. By knowing the detector’s spectral responsivity, the electrical signal could be determined and amplified to create a visible image.6 The temperature of an object depends on its physical properties such as heat capacity and specific heat in which the quantity varies with the material phase.2,6 Heat measurement using a thermal imaging system was conducted either qualitatively or quantitatively. Qualitative measurements compared the thermal condition of identical or similar objects under the same or similar operating conditions and observed the anomaly identified by the variation of intensity without assigning temperature. This technique was simple, and adjustment to the thermal imaging to compensate for atmospheric conditions or surface emissivity was not required. Quantitative measurements provided the temperature of the object. The condition of the object was determined by its temperature, the increase or decrease of the temperature is compared to the background condition that has been predetermined.7 The FLIR System Gas FindIR provided the qualitative heat measurement of the object while Amber Radiance 1 presented the quantitative measurement. The infrared ability to measure temperature is based on the Stefan-Boltzmann law which describes the total maximum radiation that can be released from a surface. In a thermal imaging system, it is assumed that the target and its background are ideal blackbodies. However, real materials are not ideal blackbodies; their surface quality is described by their emissivities.7 The Stefan-Boltzmann law described the total rate of emission per unit surface area from agitated atoms that release their energy through radiation given as follows:2,6 M ) σT4

(1)

where T is the absolute temperature [K], and σ is the Stefan-Boltzmann constant ) 5.6 × 10-8 [m-2 K-4]. The detector response is given by output voltage as follows:2,6 Vdetector ) kRDM

(2)

Vdetector ) kRDσT4

(3)

where k is a constant that depends upon the specific design and RD is the detector responsivity. The algorithm of the camera’s detector for temperature measurement always assumes that the emissivity of the object is equal to unity. However, gases are considered as gray body, and the emissivity of gases are less than unity. Therefore, the appearance temperature shown in the thermogram is not the real temperature of the gas because the correct value emissivity is not used. In this research, the correct value of the emissivity

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is theoretically developed using band absorption model to obtain the correct temperature measurement using infrared imaging system. Emissivity is important physical property in heat transfer particularly when thermal radiation is significant. In the application of infrared imaging system, the value of gas emissivity is important in determining the actual amount of radiation that is emitted from the object to the camera detector. Emissivity is defined as the ratio of the actual energy emitted from a surface to the energy emitted by a blackbody at the same temperature. The total emissivity of a gas can be estimated if experimental data of monochromatic emissivity is available.7 The monochromatic emissivity is defined as Eλ Ebλ

ελi )

(4)

where Eλ is the actual monochromatic emissive power (energy per unit area at a particular wavelength) for an object surface and Ebλ is the emissive power of blackbody at that temperature given by Planck’s equation.7 Planck’s radiation law describes the energy Ebλ emitted per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + ∆λ at a temperature T. The Planck function is given as the following equation: 1 8πhc 5 exp(hc/kT λ) - 1 λ g

E(T) )

(5)

where h is Planck’s constant ) 6.6260693 × 10-34 J s, c is the speed of light ) 2.99792458 × 108 m s-1, and k is the Boltzmann constant ) 1.380 × 6504 × 10-23 J K-1. The total energy emitted per unit area is given as8

∫

∞

E)

0

ελ(Tg, X, λ)Ebλ(Tg, λ) dλ

(6)

and eventually total emissivity may be calculated from its definition as follows:

∫

∞

εT )

E ) Eb

0


∫

∞

0

and Penner,11 for hydrogen chloride by Penner and Gray,12 and for carbon dioxide by Malkmus.13 Using the total energy method, gas emissivity is calculated from the total energy radiated from a gas and the absorptivity is determined from the attenuation of blackbody radiation from the intervening gas. Hottel14 developed this method to estimate the total emissivity and absorptivity of water vapor within a nonradiating gas. In this method, the radiating gas is assumed to have a hemispherical volume at a uniform temperature and the correlation of the gas emissivity with the temperature, partial pressure, total pressure of the entire gas, and the radius of the hemisphere is determined.10 A similar method was also applied by Smith, Shen, and Friedman for a water vapor and carbon dioxide system.15 The absorption band model, also known as the band energy method, was developed by Goody in which the energy spectrum is separated into individual bands where the gas is active.16 The band energy method takes into account the effect of temperature within the active spectra of the gas. It generates the band emissivity and absorptivity in each individual band, and their sums will result in total emissivity and absorptivity of the gas. This method has been applied in the past for carbon dioxide and water vapor by Howard, Burch, and Williams,17,18 for methane at high temperature by Brosmer and Tien,19 and for carbon dioxide by Pierluissi and Maragoudakis.20 The total gas emissivity for a hemispherical volume as a function of temperature and optical depth is given in eq 7. In its spectral line, methane has nonzero spectral emissivity only within several narrow regions, and the blackbody radiation does not vary significantly in each region; thus, the average blackbody radiant energy evaluated in the center of the narrow band can be used for the entire bandwidth.8 In the band absorption method, the total emissivity is obtained by summing the band emissivity from all the bands which give signification contribution to radiation emitted by the surface, εT(Tg, X) )

∞

0

σTg4

(8)

The band emissivity can be described as a function of the average blackbody radiance and the absorption band and the temperature of the gas of interest.8

)


λi(Tg, X)

i

Ebλ(Tg, λ) dλ

∫

∑ε

ελ(Tg, X) )

(7)

There are three general approaches developed in the past to determine the emissivity and absorptivity of gas namely theoretical calculation, the total energy method, and the absorption band model.8 In theoretical calculation, gas emissivity is determined from the gas molecular transition energy. The molecular transition can be in the form of changes in electronic, vibrational, or rotational energy. A radiating gas emits energy over a range of defined frequencies, and each individual transition contributes within this range. The total radiation is the sum of the radiation intensities corresponding to these individual transitions. Theoretical calculations require the knowledge of quantum statistics, frequencies corresponding to individual transitions, the spectral line as a function of temperature, and pressure and the intensities of radiation related to the transition probabilities.9 The theoretical calculations of gas emissivities have been done in the past for carbon monoxide by Penner, Ostander, and Tsien,10 for nitric oxide by Benitez

j λ(Tg, λ¯ i)Ai(Tg, X) E σTg4

(9)

where Ai is the band absorption of the ith band. Mathematical expression of band absorption, Ai, was developed by Elsasser by assuming that spectral lines have equal intensity, line centers are equally spaced, spectral half-width is constant for all lines, and the line shape may be described by collision-broadening contour. The application of Elsasser model requires the knowledge of the effective bandwidth and its dependency of the bandwidth with the temperature.8,21 Methane has active infrared absorption regions in three wavelengths i.e. 2.37, 3.31, and 7.65 µm. The 2.37 µm band is considered as the weak or nonoverlapping band whereas the 3.31 and 7.65 µm are considered the strong or overlapping band. Penner developed a modification of the Elsasser method to calculate the effective bandwidth which was applied to the 3.31 and 7.65 µm bands of methane.8 The effective bandwidth is defined as the frequency interval in which the spectral lines have the intensity at least 0.1% of the strongest line in the corresponding branch of the vibrational-rotational band.8 The


{ ( ) } { ( ) }

8

Table 1. Infrared Bands of Methane band region

vibrational state

wavenumber, ω (cm-1)

2.37µ

V2 + V3 V3 + V 4 V1 + V 4 V2 + 2V4 V3 fundamental V 2 + V4 2V4 V4 fundamental

4546 4313.2 4216.3 4123 3019.3 2823 2600 1306.6

3.31µ 7.65µ

integrated band intensity, R (cm-2 atm-1)

10.235KTg B0hc

h 8π2Ic

σTg

∆ωi(Tg)erf Cio

( )

150

(10)

(11)

where J′ is any quantum number and B is the rotational constant given as B)

4

Ai ) Dio

For the harmonic-oscillator rigid-rotator model, the selection rule for the radiation transition which is governed by ∆J ) (1 can be applied.22 From Planck’s relation, the spectral line location can be derived as u ) 2BJ'

j ω(Tgω E ¯ i)

Tg ξi √X Tgo

(15)

(16)

and that for the weak or nonoverlapping band is given as:

intensity of lines of the vibrational-rotational band at constant temperature is characterized by the rotational quantum number, J: Jmax )

Ai ) ∆ωi(Tg)erf Cio

εi(Tg, X) )

1.26 3.7 4.4 0.16 300

Tg √X Tgo

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ξi

(12)

In the selection rule, any molecules advancing from level V to V′ can go either to the next higher rotational level for ∆J ) +1 or lower rotational level ∆J ) -1 with the same probability. Molecular vibrations can generate an oscillating electric dipole moment that is sufficient for both rotational and vibrational transitions which occur simultaneously. However, since the vibrational transition energy is much larger than the rotational transition energy, the spectrum of the combined transition results in an array of rotational lines that group around the vibrational wavenumber. The group with lower energy level (∆J ) -1) corresponding with the lower wavenumber portion of the band is called the P-branch and the group with the higher energy level (∆J ) +1) is called the R-branch. The branch that occurs in the vibrational energy itself where ∆J ) 0 is called the Q-branch.22 The Q-branch does not have any effect on the effective bandwidth. Several simultaneous transitions for CH4 molecules are given in Table 1. From Table 1 above, it can be indicated that for the 3.31 µ region, the R-branch of the V3 determines the upper limit and the P-branch of V2 + V4 sets the lower limit. For the 7.65 µ region, the R-branch of the V4 determines the upper limit and the P-branch of V4 sets the lower limit. Since the 2.37 µ region has low intensity, the temperature does not have a significant effect on the effective bandwidth. The effective bandwidth for both the 3.31 and 7.65 µ band regions are given as the following equations:7,10 ∆ω3.31µ ) ωV3(R)(Jmax) - ωV2+V4(P)(Jmax)

(13)

∆ω7.65µ ) ωV4(R)(Jmax) - ωV4(P)(Jmax)

(14)

The expression of the band absorption and band emissivity for the strong or overlapping band of methane is given as

εi(Tg, X) )

Tg Tgo

j ω(Tgω E ¯ i) σTg

4

ξi+ζi

√X

( )

(17)

Dio

Tg Tgo

ξi+ζi

√X

(18)

The methodology developed in this research is to be applied in LNG and the natural gas industry. LNG is stored and transported at very low temperature (-162 °C or 111 K) whereas the natural gas distribution is usually performed at ambient temperature. The major composition of natural gas is methane gas, and therefore for the application of infrared imaging for natural gas plume visualization, the emissivity of methane at temperatures between 110 K and ambient is important. This paper presents the emissivity of methane gas at temperatures of LNG vapor (110-300 K). The data of methane effective bandwidth from the experiments of Lee and Happel7 are used, and using the curve fitting method, the data are extrapolated to lower temperature. Band absorption data of methane at 7.72 cm atm at high temperature (295-1138 K) are utilized to determine the constants in eqs 12-15. Using the band absorption data, the band emissivities and total emissivity can then be predicted. Result and Discussion Texas A&M University conducted a medium-scale test of an LNG spill on concrete in November 2007 and March 2008. During both experiments, two types of infrared cameras were usedsAmber Radiance 1 thermal camera and FLIR System Gas FindIRsto visualize the LNG vapor dispersion in the atmosphere. Both infrared cameras work in the midwave infrared range. Thermograms of Dispersed LNG Vapor. In the LNG test conducted in November 2007, the average ambient temperature during the LNG spill was 12.4 °C. The Amber Radiance 1 thermal camera depicted that the highest temperature of the scene was 13.6 °C and the lowest temperature was 10.2 °C. LNG vaporizes at temperatures of 110 K, and therefore, the LNG vapor cloud will have temperatures in the range of 110 K to ambient temperature. The temperature shown from the thermal camera had a significant discrepancy with the actual LNG temperature. The temperature values shown in the thermal camera did not present the actual temperature of the gas because the camera detector assumed that the emissivity of gas was equal to unity during measurement. In addition, many other factors are the temperature measurement of the plume, including water content of the atmosphere, atmospheric attenuation, as well as reflection from other surrounding objects that are discussed in this paper. The thermogram of LNG vapor dispersion during the LNG test performed in November 2007 is shown in Figure 1. During the November 2007 test, the lowest wind speed was measured at 2.2 m/s in the south east direction and the highest was measured at 6.3 m/s in the south direction. The average humidity measured during LNG vapor dispersion was 33.4%. The figure

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Figure 1. Infrared images of LNG spill on water during November 2007 test at Brayton Fire School.

Figure 2. Infrared images of LNG spill on water during the March 2008 test at Brayton Fire School.

shows that due to the effect of the weather condition and change in wind direction the LNG plume shape is changing over time. Another LNG test was conducted in March 2008 when the ambient temperature was measured at 15.7 °C during the LNG vapor dispersion experiment. The infrared images of LNG vapor dispersion during the March 2008 test are shown in Figure 2. The Amber Radiance 1 thermal camera showed that the highest temperature of the scene was 16.9 °C and the lowest temperature was 13.7 °C. During the March 2008 test, the lowest wind speed was 0.9 m/s and the highest was 2.7 m/s in the east direction. The average humidity measured during LNG vapor dispersion was 38.2%. In the thermograms, temperature was presented as the gray shade in the image. Depending on the polarity of the camera, a lighter shade can represent higher or lower temperature. In the thermograms shown in Figures 1 and 2, lighter shades depicted higher temperature and therefore darker shades represented lower temperature. The shade or color gradation is determined from the radiation intensity that is absorbed and emitted by the target. From the thermograms shown above, it is clear that background or ambient conditions determine the infrared image

quality. The ambient conditions affect the color contrast and sharpness of the image. The higher ambient temperature showed better contrast between the methane gas plume and the background. The wind effect which determined the turbulence of the gas plume can also be seen from the figures. The wind velocity during the experiments is higher in the November 2007 test compared to that of the March 2008 test. It can be observed that the gas dispersion is steadier for a lower wind velocity. The radiation emitted from and to an object fluctuates due to the presence of atmospheric transmittance. The atmosphere is composed of numerous gases and aerosols which absorb and scatter radiation as they travel from the target to the thermal imaging system. This reduction in radiation is called the atmospheric transmittance. The radiation accumulated along the line of sight due to the scattering of ambient light into the lineof-sight causes the reduction of the target contrast.6,23 The radiation that reaches the imaging system is the sum of attenuated target radiation and the path radiance. The magnitude of the transmittance and path radiance depends upon the atmospheric constituents, path length, and spectral response of the thermal imaging system. However, the atmosphere was constantly changing over time, and therefore, it is impossible


to assign a single number to the transmittance or path radiance. Infrared path radiance occurred primarily due to atmospheric self-emmitance. It was independent of the target temperature and was seen even if the target is not present. Path radiance complicates target temperature measurements but its effect only becomes a problem over very long path lengths when the transmittance is low.6,23 In addition to the atmospheric transmittance, the atmospheric content also affected the radiation absorbed and emitted by the target object. Water vapor or absolute humidity was a major absorber in the infrared region. However, transmittance was not linearly related to absolute humidity. As the water vapor increased (the absolute humidity increases), the transmittance decreased. Aerosols changed the amount of radiation primarily by scattering the radiation out of the line of sight. As the particle size grew, the scattering coefficient increased at all wavelengths and the transmittance decreased.6,23 The water vapor in the atmosphere absorbed and scattered the radiation which results in reduction of the target signature. The higher the water vapor content, the greater the effect of reduction of the target signature. Aside from that, H2O also radiated energy at ambient temperature that accumulated along the line from the target gas to the camera detector which results in the reduction of target contrast. However, the effect of water vapor in reducing the radiation energy had not been quantitatively examined in this work, and further research can be performed toward analyzing the water vapor or absolute humidity on LNG vapor dispersion. Other than water vapor and atmospheric content, some reflectances from the surrounding objects also attenuated the radiation traveling from the target to the camera; for example, the reflectance from metal structure or water tanks in the vicinity of experiment location. Yet, in this work, the effect of the reflectance from surrounding objects was considered insignificant. Emissivity Profile of Methane Gas at Different Temperatures. The most important factor in the temperature measurement using an infrared imaging system is to understand the emissivity of the gas. Because the thermal camera always assumes the emissivity of the object is equal to unity, the apparent temperature depicted in the thermogram did not reflect the true temperature of the gas. If the emissivity of the gas is not known, the temperature measured using thermal imaging system does not have any significance, and thus, the values will be meaningless. This work provides the determination of methane gas emissivity at low temperature using band absorption model. Most objects do not emit all the radiation; they only emit a fraction of it. The ratio of the actual radiation from an object compared to that of an ideal blackbody is known as emissivity. The emissivity varies with wavelength, the object’s shape, temperature, surface quality, and viewing angle.7 The thermal imaging system measures the object’s temperature by assuming that the emissivity is equal to unity. When emissivity is not known, it is misleading to assume the apparent temperature as the true temperature of the object. The discrepancy between the apparent and true temperatures becomes larger for lower emissivity. Therefore, the emissivity is the main uncertainty in temperature measurement using an imaging system. This research aims to estimate the emissivity of methane at low temperature between 110-300 K. There has been no study in the past to evaluate the methane emissivity within this temperature range; however, a correlation had been developed by Elsasser and some experiments had been done to measure the band absorption for methane at medium-high temperature (295-1138 K) by Lee and Happel.8 Using this information,

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Table 2. Effective Band Widths of Methane Gas at 3.31 and 7.65 µ8 3.31 µ band

7.65 µ band

T (K) Jmax ωV3(R) ωV2+V4(P) ∆ω (cm-1) ωV4(R) ωV4(P) ∆ω (cm-1) 295 373 473 573 673 773 873 973 1073 1173 1273 1473 1673 1873 2073 2273

20 23 25 28 30 32 34 36 38 40 42 45 48 50 53 56

3207 3231 3246 3268 3282 3296 3309 3322 3335 3347 3357 3377 3393 3404 3419 3433

2706 2688 2676 2658 2646 2634 2622 2610 2598 2585 2573 2555 2536 2524 2505 2486

501 543 570 610 636 662 687 712 737 762 784 822 857 880 914 947

1396 1404 1408 1413 1413 1419 1422 1422 1422 1422 1422 1422 1422 1422 1422 1422

1190 1172 1160 1142 1130 1118 1106 1094 1081 1069 1057 1038 1020 1007 988 970

206 232 248 271 283 301 316 328 341 353 365 384 402 415 434 452

methane gas emissivity is estimated by fitting the data from Lee and Happel into the Elsasser correlation to obtain the constants in eqs 12-15 above. With the known constants, the data is then extrapolated to calculate the band emissivities and total emissivity of methane at low temperature. The effective bandwidth for methane gas in the 3.31 and 7.65 µ band data from Lee and Happel is shown in Table 2. The absorption band of methane at gas 2.37 µ does not depend on the effective bandwidth thus the band absorption only depends on the gas temperature and the optic length. By plotting the effective bandwidth data for methane given in Table 2, the relationship of effective bandwidth to temperature for the 3.31 and 7.65 µ bands can be obtained and used to calculate the effective bandwidth at lower temperature. The plot of the effective bandwidth as function of temperature is given in Figure 3. The relationship between temperature and effective bandwidth for methane at 3.31 µ is

( )

∆ω3.31µ Tg ) (∆ω3.31µ)0 Tgo

0.311

(19)

And the relationship for methane at 7.65 µ is given as follows:

( )

∆ω7.65µ Tg ) (∆ω7.65µ)0 Tgo

0.377

(20)

The data of methane absorption at three different wavelengths (2.37, 3.31, and 7.65 µ) as a function of temperature obtained by Lee and Happel in 1964 is presented in Table 3. The absorption band for methane gas at the 2.37 µ wavelength is plotted against temperature to find the constants Dio and (ξi + ζi) in eq 14 as given in Figure 4. The relationship between the temperature and absorption band for methane at 2.37 µ is

( )

A2.37µ Tg ) (A2.37µ)0 Tgo

0.534

(21)

The value of the constant (ξi + ζi) obtained from the plot is -0.534, and by taking Tgo ) 295 K, the constant Dio is equal to 38.2 with standard deviation equal to 3.7. Thus for the 2.37 µ band, eq 14 can be rewritten as follows: Ai,2.37µ ) 38.2

( ) Tg 295

-0.534

√X

(22)

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Figure 3. Effective bandwidth of methane at different temperatures for the (a) 3.31 and (b) 7.65 µ bands.

Table 3. Band Absorption of Methane at 7.72 cm atm Optical Depth at Different Temperatures8 T (K)

A2.37µ (cm-1)

A3.31µ (cm-1)

295 375 378 471 473 569 668 674 768 873 873 974 1008 1079 1084 1118 1138

106.3 102.3

193.2 189.5 187.9 181.3 184.1 192.3 214 221 234.2 238.7 242.3 265

85.7 88.2 71.8 60.7 53 66.6 58.7 56.8 63.2 51.6 61.9

A7.65µ (cm-1) 124 126 131.8 129.9 139.5 146 149.9 152.3 152.9 151.7

{ ( )

Ai,3.31µ ) ∆ωi(Tg)erf 0.207

161.7 254.8 164.7

51 52.8

279.2 273.7

Equation 12 is used to fit the data for the strong or overlapping band (3.31 and 7.65 µ). For the 3.31 µ band, the plot of absorption band against the temperature demonstrates two different regions as shown in Figure 5: (1) at T < 473 K, the absorption band decreases as the temperature increases, and (2) at T g 473 K, the absorption band increases with temperature. For methane at the 3.31 µ wavelength, Figure 6a shows the plot of erf-1(Ai/∆ωi) against temperature at T < 473 K and Figure 6b is the plot for methane at T g 473 K. The constants, ξi, obtained from these plots are -0.477 for T < 473 by setting Tgo ) 295 K and, for T g 473 K, ξi ) 0.185 by setting Tgo ) 473 K. The value of constant Cio for T < 473 K is equal to 0.129 with standard deviation ) 0.001. Thus for the 3.31 µ band at T < 273, eq 12 can be rewritten as follows:

{ ( )

Ai,3.31µ ) ∆ωi(Tg)erf 0.129

-0.477

Tg Tgo

√X

}

relationship between erf-1(Ai/∆ωi) and temperature for methane gas at the 7.65 µ band. The value of the constant ξi obtained from the plot is -0.177 and by taking Tgo ) 295 K the constant Cio is equal to 0.207 with standard deviation ) 0.005. Thus for the 7.65 µ band, eq 12 can be rewritten as follows: Tg Tgo

-0.177

}

√X

(25)

Band emissivity is determined from eq 6. The band emissivity at certain temperature and optical depths is the product of absorption bandwidth with the Planck radiation function divided by the total energy emitted by a perfect blackbody at that temperature determined by the Stefan-Boltzmann law. The band emissivities of methane gas at temperature 110-350 K are given at three active wavelengths in Figure 9a-c. The total emissivity is the sum of band emissivities. The total emissivity of methane gas at temperature 110-350 K is given in Figure 9d.

Figure 4. Band absorption of methane gas as a function of temperature for methane gas at the 2.37 µ wavelength and 7.72 cm atm optical length.

(23)

The value of constant Cio for T g 473 K is equal to 0.103 with standard deviation ) 0.003. Thus for the 3.31 µ band at T g 273, eq 12 can be rewritten as follows:

{ ( )

Ai,3.31µ ) ∆ωi(Tg)erf 0.103

Tg Tgo

-0.185

√X

}

(24)

For the 7.65 µ band, the plot of absorption band against the temperature is shown in Figure 7 and Figure 8 gives the

Figure 5. Band absorption of methane gas as a function of temperature for methane gas at 3.31 µ and 7.72 cm atm.


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Figure 6. Plot of erf-1(Ai/∆ωi) for methane gas at 3.31 µ, 7.72 cm atm, and at (a) T < 473 and (b) T g 473 K.

Figure 7. Absorption band of for methane gas at 7.56 µ and 7.72 cm atm. Figure 8. Plot of erf-1(Ai/∆ωi) for methane gas at 7.65 µ.

From the figure above, it is shown that the band and total emissivity of methane gas at lower temperature is a strong function of temperature. The effect of optical depth is not highly significant to emissivity measurement for methane at lower temperature. From the calculation of total emissivity using band absorption method, it is evident that the emissivity of methane gas at low temperature (110-300 K) is much less than unity. Therefore, the temperature measurement using thermal camera assuming the emissivity equal to unity will not give a valid temperature measurement of methane gas. The emissivity value obtained in this work will be used as correcting factors in measuring the gas temperature. The temperature of the gas can be determined from the different amount of radiation emitted from the target and the background. For a target cooler than its background, the power difference is ∆M ) MB - MT

(26)

∆M ) ε(TT)σ(TB4 - TT4)

(27)

where TT and TB are the target and background temperatures, respectively. It is practical to specify it by its target-background difference (∆T) where ∆T ) TT - TB. ∆M ) ε(TT)σ[TB4 - (TB - ∆T)4]

(28)

∆M ) ε(TT)σ[4TB3∆T - 6TB2∆T2 + 4TB∆T3 - ∆T4]

(29) ∆M depends on the temperature difference and background temperature. The emissivity value ε(TT) is applied to calculate the actual radiation emitted to the target.

Conclusions The use of infrared (thermal) camera has been applied in LNG system to visualize the LNG vapor dispersion. The quality of the thermal image (thermogram) as well as the thermal reading of the gas visualization highly depends on the conditions during the experiments. Those factors include wind conditions, atmospheric transmittance, atmospheric content, absolute humidity, and emissivity of the gas. Uncertainty related to emissivity is the most significant factor in the temperature measurement of the dispersed gas and in this research the emissivity of methane gas at low temperature has been quantitatively analyzed using the band energy method. The emissivity of methane at low temperature is important to be identified since the LNG vaporizes at 110 K, and thus, the emissivity value is analyzed from this temperature. The available published data in the past provided the absorption of methane at temperatures from 295 to 1198 K; however, no data was available for temperatures lower than 295 K. Hence, the initial assumption for estimating the emissivity to lower temperature is to evaluate the trend of the available data and with the method of curve fitting and extrapolation the data is projected to lower temperature. The result shows that emissivity of methane gas significantly increases as the temperature increased for temperature range between 110 and 300 K. An infrared camera is an effective mean to visualize the LNG vapor cloud qualitatively; however, one cannot rely on direct temperature measurement given by the thermal imaging camera since a lot of parameters such as atmospheric transmission, solar radiation intensity, and air content can affect measurement as well as high uncertainty due to unknown emissivity values of

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Figure 9. (a) Band emissivity of methane gas at the 2.37 µ band, (b) emissivity of methane gas at the 3.31 µ band, (c) emissivity of methane gas at the 7.65 µ band, and (d) total emissivity of methane gas at different temperatures and optical depths.

the methane gas. This article provides the calculation of methane gas emissivity using the band energy method which can be further applied to estimate the actual radiation emitted from the methane gas target into the camera detector as well as the actual temperature distribution of the gas plume. By combining this study with dispersion modeling, a temperature-concentration correlation can be established. This correlation is useful to understand the extent of the dispersed gas and concentration of gas as well as to calculate the emission rate of the gas. Literature Cited (1) Holst G. C. Common Sense Approach to Thermal Imaging; SPIE Optical Engineering Press, 2000. (2) Furry; Richards; Lucier; Madding Detection of Volatile Organic Compound (VOC) with a Spectrally Filtered Cooled Mid-Wave Infrared Camera. Inframation Proceedings, 2005. (3) Madding, R. New Development in Portable Infrared Camera Technology. Hydrocarbon Process. 2006, 85 (11), 83–86. (4) Gross; Hierl; Scheurpflug; Schirl. Detection of Gas Leak Along Pipelines by Spectrally Tuned Infrared Imaging. Proc. SPIE 1998, 3493, 267–271. (5) Leak; Moore; Murthi; Mannan Application of Visualization and Thermal Detection Technique for Non-Intrusive Imaging of LNG Leaks and Plumes. 8th Annual MKOPSC Symposium Proceeding, 2005.

(6) Holst G. C., Testing and EValuation of Infrared Imaging System, 2nd ed.; JCD Publishing, 1998. (7) Caniou, J. PassiVe Infrared Detection Theory and Application; Kluwer Academic Publishing: Norwell, MA, 1999. (8) Lee, R. H.; Happel, J. C. Thermal Radiation of Methane Gas. Ind. Eng. Chem. Fundaman. 1964, 3 (2), 167–176. (9) Ostrander EmissiVity Calculations for Carbon Monoxide; California Institute of Technology: Pasedena, CA, 1951. (10) Penner; Ostrander; Tsien. The Emission of Radiation from Diatomic Gases III. Numerical Emissivity Calculations for Carbon Monoxide for Low Optical Densities at 300 K and Atmospheric Pressure. J. Appl. Phys. 1952, 23 (2), 256–263. (11) Benitez, L. E.; Penner, S. S. The Emission of Radiation from Nitric Oxide: Approximate Calculations. J. Appl. Phys. 1950, 21 (9), 907–908. (12) Penner, S. S.; Gray, L. D. Approximate Infrared Emissivity Calculations for HCl at Elevated Temperature. J. Opt. Soc. Am. 1961, 51 (4), 460–462. (13) Malkmus, W. Infrared Emissivity of Carbon Dioxide (4.3-µ Band). J. Opt. Soc. Am. 1963, 53 (8), 951–960. (14) Hottel, H. C.; Sarofim, S. F. Models of Radiative Transfer in Furnaces. J. Eng. Phys. Thermophys. 1970, 19 (3), 1102–1114. (15) Smith; Shen; Friedman. Evaluation of Coefficients for the Weighted Sum for Gray Gases Model. J. Heat Transfer 1982, 104 (4), 602–608. (16) Goody, R. M. A Statistical Model for Water Vapor Absorption. Q. J. R. Meteorol. Soc. 1952, 78 (336), 165–169. (17) Howard; Burch; Williams. Infrared Transmission of Synthetic Atmosphere. II. Absorption by Carbon Dioxide. J. Opt. Soc. Am. 1956, 46 (4), 237–241.

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 (18) Howard; Burch; Williams. Infrared Transmission of Synthetic Atmosphere. III. Absorption by Water Vapor. J. Opt. Soc. Am. 1963, 6 (2), 585–589. (19) Brosmer, M. A.; Tien, C. L. Infrared Radiation Properties of Methane at Elevated Temperature. J. Quant. Spectrosc. Radiat. Transfer 1984, 33 (5), 521–532. (20) Pierluissi, J. H.; Maragoudakis, C. E. Band Model for Molecular Transmittance of Carbon Monoxide. Appl. Opt. 1986, 25 (22), 3974–3977. (21) Modest, M. F. RadiatiVe Heat Transfer, 2nd ed.; Academic Press: New York, 2003.

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(22) Liou, K. N. An Introduction to Atmospheric Radiation, 2nd ed.; Academic Press: New York, 2002. (23) Barron, B. F. Cryogenic Heat Transfer; Taylor and Francis, 1999.

ReceiVed for reView August 27, 2009 ReVised manuscript receiVed January 21, 2010 Accepted March 3, 2010 IE901340G

Methane Gas Visualization Using Infrared Imaging System and

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