Methane Gas Visualization Using Infrared Imaging System and Evaluation ofTemperature 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&MUniVersity, College Station, Texas 77483-3122

Infrared (IR) camera has been used widely in the industry to visualize gases that cannot be seen by the nakedeye or a visual camera. The use of an infrared camera for gas imaging offers several advantages such asfaster locating of gas leaks and easier understanding on how the gas travels and disperses. In addition, severaltypes of infrared cameras have the capability to measure the temperature of target objects especially solidbody objects. However, this facility has not been applied for measurement of gas temperature due to complexanalysis on the physics of infrared imaging and some uncertainties related to the radiation heat transfer processesduring temperature measurement that have not been well understood. The objective of this research is tomake use of the infrared or thermal imaging system to provide a concise temperature distribution of a methanegas plume presented in the infrared image. However, the current technology in infrared imaging cannot providethe true temperature of a gas plume because the emissivity value is always assumed as unity, and the actualemissivity value of the gas is not integrated in the camera’s algorithm. The visualization of dispersed liquefiednatural gas (LNG) vapor from LNG spills on the ground using a midwave thermal camera is presented in thiswork. Two types of infrared cameras were used: Amber Radiance 1 and GasFindIR, also known in industryas hydrocarbon camera. The infrared images or thermograms show that several factors affecting the temperaturemeasurement are weather conditions, wind rose, atmospheric attenuation due to the presence of other radiationabsorbing gases along the optic path, and gas emissivity. Gas emissivity is the main uncertainty in gastemperature measurement using thermal cameras. This research proposed a method to correct the gastemperature measured by a thermal camera by applying the emissivity factor calculated from a theoreticalanalysis on methane gas emissivity using the band absorption method. The study demonstrates that methanegas 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 ofmethane emissivity at temperatures 110-300 K is evaluated and presented in this paper.

Introduction

Infrared cameras have been used in industry for more than30 years, and innovations to improve its capability have beenvastly developed. The application of infrared camera varies fromelectrical power plants, petrochemical plants, refineries, buildingdiagnostics, automation, marine surveying, medication, homeinspection, and more others mainly in finding thermal anomalies.In the industrial plant, an infrared camera is used as anondestructive testing tool in order to detect equipment faultsand improve the safety and reliability of the system andequipment while minimizing the environmental impact and costof operation. Recently, the use of infrared imaging technologyhas been expanding in the petrochemical industry as a methodto detect some volatile organic compounds such as methane,benzene, and propane.1

Infrared cameras have more advantages for leak or spilldetection rather than a total vapor analyizer (TVA) or “gassniffer” because they provide area measurement rather than pointby point measurement and give a real-time image of the gasplume. Infrared cameras give the option for optical imaginginspection of organic volatile compounds that cannot be reachedby an organic vapor analyzer or total vapor analyzers. Theyare able to detect the motion of the plume and give a goodcontrast between the absorbing and the background gas whichare the key elements for detection. Infrared imaging camerasallow one to spot several volatile compound gas leaks quickly

due to their ability to scan large areas and deliver real-timethermal images of gas leaks. The latest infrared camera for VOCdetection is also designed for use in harsh industrial environ-ments, operates in a wide temperature range of 5-122 °F (-15to 50 °C) and can withstand water, dust, and vibrations. It alsohas been tested to detect several volatile compounds such asbenzene, butane, ethane, ethyl benzene, ethylene, heptane,hexane, isoprene, methane, methanol, octane, pentane, 1-pen-tane, propane, propylene, toluene, and xylene.2

The IR imaging method allows the visualization of methanegas radiation into the atmosphere in real time, and therefore, itis suitable for rapid and accurate detection and localization ofnatural gas dispersion. Detection using an infrared camera isconsidered safer than the procedure involving a man-carriedsniffing detector because the device can be placed from 5 to 20feet away compared to the sniffer.3

Early use of infrared imaging for methane gas leak detectionwas conducted by Gross et al by utilizing a high-resolution IRimaging camera (∆T ) 10 mK) with a PtSi Schottky barrierfocal plane array, cooled to 77 K, 256 × 256 pixels for thedetection of methane radiation which had the spectral rangebetween 3 and 5 µm.4 The infrared imaging used to measurethe cloud emitted from the buried natural gas pipeline consistedof four optical components: an IR imaging camera, a narrowband filter centered at micrometers, a halogen lamp, and adiffuse IR reflector. The objective of the laboratory testing ofthe gas imaging done by Gross et al. was to determine thesensitivity of the infrared camera for detection of methane leakfrom a pipeline with an open end buried in soil and loose gravel

* To whom correspondence should be addressed. E-mail:mannan@tamu.edu.

Ind. Eng. Chem. Res. 2010, 49, 3926–39353926

10.1021/ie901340g 2010 American Chemical SocietyPublished on Web 03/25/2010

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 moisturelevel of the soil was not considered. The result of this experimentshowed that the leak rate down to 0.1 L/min was still detectedby the IR imaging camera. The methane cloud is visible as darkareas in the image, the concentrations detected are 0.56% inthe region above the leak and 0.03% in the tail of the cloud.4

The sensitivity of the IR imaging was estimated from the relativecontrast of the absorbing gas and the background gas. Tem-perature difference as low as 10 mK can be resolved on atemperature background of 300 K.

Infrared imaging was also utilized by Leak et al.5 to visualizeliquefied natural gas (LNG) vapor dispersion. The infraredcamera used was the HAWK camera system built by LeakSurveys Inc. It consisted of a modified Indigo Merlin MIDcamera with a spectra range of 1-5.4 µm. The detector wasmade of 30 × 30 µm indium antimonide (InSd) with 320 ×256 pixel array. The cooler system used was a Stirling coolerwhich provided the system with a NEDT (noise equivalent deltatemperature) of no more than 18 mK; hence, the sensitivity wasrelatively high. The camera consisted of an optical module forimage information, detection module for conversion of theoptical image into an electrical signal, and an electric modulefor conditioning and data processing. The role of the opticalmodule was to concentrate the radiation energy from the targetobject to form an image in the focal plane. It contained lensesand 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 imagingsystem to visualize the LNG vapor cloud from an LNG spillon the ground. The aim is to study the behavior of the gas plumedemonstrated from the thermograms, and study factors affectingthe temperature measurement using an infrared imaging camera.The final objective of this research is to classify the mainuncertainties in temperature measurement using an infraredcamera and provide an approach to reduce the uncertainties sothat the actual distribution of the gas temperature can bespecified.

Current technology in infrared imaging cannot provide thetrue temperature of the gas plume because the emissivity valueis always assumed as unity, and the actual emissivity value ofthe gas is not integrated in the camera’s algorithm. Therefore,this research gives a theoretical approach on estimating themethane gas emissivity at different temperature.

The practical application of this work is that by knowing theemissivity of methane gas at different temperatures, the actualtemperature profile from the thermogram can be predicted. Thedispersion model can be used to calculate concentration profileof a gas plume as long as the weather conditions are known.Having the temperature profile of the gas plume and theconcentration profile attained from the dispersion model, thecorrelation between temperature and concentration of the meth-ane gas plume can be further developed. Eventually, the infraredcamera is not only used to locate gas releases in natural gasindustry but also can be applied to measure the temperature ofthe gas and from the temperature-concentration correlation sothat the flammability distance or range of the methane gas plumecan be identified.

Methodology

Two types of infrared cameras were used for the visualizationof the LNG vapor cloud: Amber Radiance 1 thermal cameraand FLIR System Gas FindIR. Both infrared cameras workedin the midwave infrared range. The Amber Radiance 1 thermal

camera was able to provide a temperature profile of the scenestaken during the experiments. The operating temperature of thiscamera was between 23 and 149 °F with thermal sensitivity0.08 °F at 73.4 °F. The FLIR System Gas FindIR was a dualcamera detector system: one detected targets in very narrowinfrared wavelength and one detector acted as a reference. Forthis reason, this infrared camera could detect most of hydro-carbons within the narrow wavelength.

Infrared camera measured the radiation that appeared toemanate from an object. The system calibration converted theoutput voltage to temperature. The calibration provided a two-dimensional representation of the surface temperature. An objectemitted energy from its internal molecular vibration. The emittedenergy from an object depends on the surface temperature andsurface characteristics. The camera detected the amount of fluximpinging upon a detector. By knowing the detector’s spectralresponsivity, the electrical signal could be determined andamplified to create a visible image.6 The temperature of an objectdepends on its physical properties such as heat capacity andspecific heat in which the quantity varies with the materialphase.2,6

Heat measurement using a thermal imaging system wasconducted either qualitatively or quantitatively. Qualitativemeasurements compared the thermal condition of identical orsimilar objects under the same or similar operating conditionsand observed the anomaly identified by the variation of intensitywithout assigning temperature. This technique was simple, andadjustment to the thermal imaging to compensate for atmo-spheric conditions or surface emissivity was not required.Quantitative measurements provided the temperature of theobject. The condition of the object was determined by itstemperature, the increase or decrease of the temperature iscompared to the background condition that has been predeter-mined.7 The FLIR System Gas FindIR provided the qualitativeheat measurement of the object while Amber Radiance 1presented the quantitative measurement.

The infrared ability to measure temperature is based on theStefan-Boltzmann law which describes the total maximumradiation that can be released from a surface. In a thermalimaging system, it is assumed that the target and its backgroundare ideal blackbodies. However, real materials are not idealblackbodies; their surface quality is described by their emis-sivities.7 The Stefan-Boltzmann law described the total rateof emission per unit surface area from agitated atoms that releasetheir energy through radiation given as follows:2,6

where T is the absolute temperature [K], and σ is theStefan-Boltzmann constant ) 5.6 × 10-8 [m-2 K-4].

The detector response is given by output voltage as follows:2,6

where k is a constant that depends upon the specific design andRD is the detector responsivity.

The algorithm of the camera’s detector for temperaturemeasurement always assumes that the emissivity of the objectis equal to unity. However, gases are considered as gray body,and the emissivity of gases are less than unity. Therefore, theappearance temperature shown in the thermogram is not thereal temperature of the gas because the correct value emissivityis not used. In this research, the correct value of the emissivity

M ) σT4 (1)

Vdetector ) kRDM (2)

Vdetector ) kRDσT4 (3)

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 3927

is theoretically developed using band absorption model to obtainthe correct temperature measurement using infrared imagingsystem.

Emissivity is important physical property in heat transferparticularly when thermal radiation is significant. In the ap-plication of infrared imaging system, the value of gas emissivityis important in determining the actual amount of radiation thatis emitted from the object to the camera detector. Emissivity isdefined as the ratio of the actual energy emitted from a surfaceto the energy emitted by a blackbody at the same temperature.The total emissivity of a gas can be estimated if experimentaldata of monochromatic emissivity is available.7 The monochro-matic emissivity is defined as

where Eλ is the actual monochromatic emissive power (energyper unit area at a particular wavelength) for an object surfaceand Ebλ is the emissive power of blackbody at that temperaturegiven by Planck’s equation.7

Planck’s radiation law describes the energy Ebλ emitted perunit volume by a cavity of a blackbody in the wavelengthinterval λ to λ + ∆λ at a temperature T. The Planck function isgiven as the following equation:

where h is Planck’s constant ) 6.6260693 × 10-34 J s, c is thespeed of light ) 2.99792458 × 108 m s-1, and k is theBoltzmann constant ) 1.380 × 6504 × 10-23 J K-1.

The total energy emitted per unit area is given as8

and eventually total emissivity may be calculated from itsdefinition as follows:

There are three general approaches developed in the past todetermine the emissivity and absorptivity of gas namelytheoretical calculation, the total energy method, and the absorp-tion band model.8 In theoretical calculation, gas emissivity isdetermined from the gas molecular transition energy. Themolecular transition can be in the form of changes in electronic,vibrational, or rotational energy. A radiating gas emits energyover a range of defined frequencies, and each individualtransition contributes within this range. The total radiation isthe sum of the radiation intensities corresponding to theseindividual transitions. Theoretical calculations require theknowledge of quantum statistics, frequencies corresponding toindividual transitions, the spectral line as a function of temper-ature, and pressure and the intensities of radiation related tothe transition probabilities.9 The theoretical calculations of gasemissivities have been done in the past for carbon monoxideby Penner, Ostander, and Tsien,10 for nitric oxide by Benitez

and Penner,11 for hydrogen chloride by Penner and Gray,12 andfor carbon dioxide by Malkmus.13

Using the total energy method, gas emissivity is calculatedfrom the total energy radiated from a gas and the absorptivityis determined from the attenuation of blackbody radiation fromthe intervening gas. Hottel14 developed this method to estimatethe total emissivity and absorptivity of water vapor within anonradiating gas. In this method, the radiating gas is assumedto have a hemispherical volume at a uniform temperature andthe correlation of the gas emissivity with the temperature, partialpressure, total pressure of the entire gas, and the radius of thehemisphere is determined.10 A similar method was also appliedby Smith, Shen, and Friedman for a water vapor and carbondioxide system.15

The absorption band model, also known as the band energymethod, was developed by Goody in which the energy spectrumis separated into individual bands where the gas is active.16 Theband energy method takes into account the effect of temperaturewithin the active spectra of the gas. It generates the bandemissivity and absorptivity in each individual band, and theirsums will result in total emissivity and absorptivity of the gas.This method has been applied in the past for carbon dioxideand water vapor by Howard, Burch, and Williams,17,18 formethane at high temperature by Brosmer and Tien,19 and forcarbon dioxide by Pierluissi and Maragoudakis.20

The total gas emissivity for a hemispherical volume as afunction of temperature and optical depth is given in eq 7. Inits spectral line, methane has nonzero spectral emissivity onlywithin several narrow regions, and the blackbody radiation doesnot vary significantly in each region; thus, the average blackbodyradiant energy evaluated in the center of the narrow band canbe used for the entire bandwidth.8

In the band absorption method, the total emissivity is obtainedby summing the band emissivity from all the bands which givesignification contribution to radiation emitted by the surface,

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

where Ai is the band absorption of the ith band.Mathematical expression of band absorption, Ai, was devel-

oped by Elsasser by assuming that spectral lines have equalintensity, line centers are equally spaced, spectral half-width isconstant for all lines, and the line shape may be described bycollision-broadening contour. The application of Elsasser modelrequires the knowledge of the effective bandwidth and itsdependency of the bandwidth with the temperature.8,21

Methane has active infrared absorption regions in threewavelengths i.e. 2.37, 3.31, and 7.65 µm. The 2.37 µm band isconsidered as the weak or nonoverlapping band whereas the3.31 and 7.65 µm are considered the strong or overlapping band.Penner developed a modification of the Elsasser method tocalculate the effective bandwidth which was applied to the 3.31and 7.65 µm bands of methane.8 The effective bandwidth isdefined as the frequency interval in which the spectral lines havethe intensity at least 0.1% of the strongest line in the corre-sponding branch of the vibrational-rotational band.8 The

ελi )Eλ

Ebλ(4)

E(T) ) 8πhc

λ5

1exp(hc/kTgλ) - 1

(5)

E ) ∫0

∞ελ(Tg, X, λ)Ebλ(Tg, λ) dλ (6)

εT ) EEb

)∫0

∞ελ(Tg, X, λ)Ebλ(Tg, λ) dλ

∫0

∞Ebλ(Tg, λ) dλ

)

∫0

∞ελ(Tg, X, λ)Ebλ(Tg, λ) dλ

σTg4

(7)

εT(Tg, X) ) ∑i

ελi(Tg, X) (8)

ελ(Tg, X) )Ejλ(Tg, λ̄i)Ai(Tg, X)

σTg4

(9)

3928 Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

intensity of lines of the vibrational-rotational band at constanttemperature is characterized by the rotational quantum number,J:

For the harmonic-oscillator rigid-rotator model, the selectionrule for the radiation transition which is governed by ∆J ) (1can be applied.22 From Planck’s relation, the spectral linelocation can be derived as

where J′ is any quantum number and B is the rotational constantgiven as

In the selection rule, any molecules advancing from level Vto 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 dipolemoment that is sufficient for both rotational and vibrationaltransitions which occur simultaneously. However, since thevibrational transition energy is much larger than the rotationaltransition energy, the spectrum of the combined transition resultsin an array of rotational lines that group around the vibrationalwavenumber. The group with lower energy level (∆J ) -1)corresponding with the lower wavenumber portion of the bandis called the P-branch and the group with the higher energylevel (∆J ) +1) is called the R-branch. The branch that occursin the vibrational energy itself where ∆J ) 0 is called theQ-branch.22 The Q-branch does not have any effect on theeffective 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 andthe P-branch of V2 + V4 sets the lower limit. For the 7.65 µregion, the R-branch of the V4 determines the upper limit andthe P-branch of V4 sets the lower limit. Since the 2.37 µ regionhas low intensity, the temperature does not have a significanteffect on the effective bandwidth. The effective bandwidth forboth the 3.31 and 7.65 µ band regions are given as the followingequations:7,10

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

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

The methodology developed in this research is to be appliedin LNG and the natural gas industry. LNG is stored andtransported at very low temperature (-162 °C or 111 K) whereasthe natural gas distribution is usually performed at ambienttemperature. The major composition of natural gas is methanegas, and therefore for the application of infrared imaging fornatural gas plume visualization, the emissivity of methane attemperatures between 110 K and ambient is important. Thispaper presents the emissivity of methane gas at temperaturesof LNG vapor (110-300 K). The data of methane effectivebandwidth from the experiments of Lee and Happel7 are used,and using the curve fitting method, the data are extrapolated tolower temperature. Band absorption data of methane at 7.72cm atm at high temperature (295-1138 K) are utilized todetermine the constants in eqs 12-15. Using the band absorptiondata, the band emissivities and total emissivity can then bepredicted.

Result and Discussion

Texas A&M University conducted a medium-scale test ofan LNG spill on concrete in November 2007 and March 2008.During both experiments, two types of infrared cameras wereusedsAmber Radiance 1 thermal camera and FLIR System GasFindIRsto visualize the LNG vapor dispersion in the atmo-sphere. Both infrared cameras work in the midwave infraredrange.

Thermograms of Dispersed LNG Vapor. In the LNG testconducted in November 2007, the average ambient temperatureduring the LNG spill was 12.4 °C. The Amber Radiance 1thermal camera depicted that the highest temperature of thescene was 13.6 °C and the lowest temperature was 10.2 °C.LNG vaporizes at temperatures of 110 K, and therefore, theLNG vapor cloud will have temperatures in the range of 110 Kto ambient temperature. The temperature shown from thethermal camera had a significant discrepancy with the actualLNG temperature. The temperature values shown in the thermalcamera did not present the actual temperature of the gas becausethe camera detector assumed that the emissivity of gas was equalto unity during measurement. In addition, many other factorsare the temperature measurement of the plume, including watercontent of the atmosphere, atmospheric attenuation, as well asreflection from other surrounding objects that are discussed inthis paper.

The thermogram of LNG vapor dispersion during the LNGtest performed in November 2007 is shown in Figure 1. Duringthe November 2007 test, the lowest wind speed was measuredat 2.2 m/s in the south east direction and the highest wasmeasured at 6.3 m/s in the south direction. The average humiditymeasured during LNG vapor dispersion was 33.4%. The figure

Table 1. Infrared Bands of Methane8

band regionvibrational

statewavenumber,

ω (cm-1)

integrated bandintensity,

R (cm-2 atm-1)

V2 + V3 4546 1.26V3 + V4 4313.2 3.7V1 + V4 4216.3 4.4

2.37µ V2 + 2V4 4123 0.16V3 fundamental 3019.3 300V2 + V4 2823

3.31µ 2V4 26007.65µ V4 fundamental 1306.6 150

Jmax ) �10.235KTg

B0hc(10)

u ) 2BJ' (11)

B ) h

8π2Ic(12)

∆ω3.31µ ) ωV3(R)(Jmax) - ωV2+V4(P)(Jmax) (13)

∆ω7.65µ ) ωV4(R)(Jmax) - ωV4(P)(Jmax) (14)

Ai ) ∆ωi(Tg)erf{Cio( Tg

Tgo)�i

√X} (15)

εi(Tg, X) )Ejω(Tgω̄i)

σTg4

∆ωi(Tg)erf{Cio( Tg

Tgo)�i

√X} (16)

Ai ) Dio( Tg

Tgo)�i+�i

√X (17)

εi(Tg, X) )Ejω(Tgω̄i)

σTg4

Dio( Tg

Tgo)�i+�i

√X (18)

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 3929

shows that due to the effect of the weather condition and changein wind direction the LNG plume shape is changing over time.

Another LNG test was conducted in March 2008 when theambient temperature was measured at 15.7 °C during the LNGvapor dispersion experiment. The infrared images of LNG vapordispersion during the March 2008 test are shown in Figure 2.The Amber Radiance 1 thermal camera showed that the highesttemperature of the scene was 16.9 °C and the lowest temperaturewas 13.7 °C. During the March 2008 test, the lowest wind speedwas 0.9 m/s and the highest was 2.7 m/s in the east direction.The average humidity measured during LNG vapor dispersionwas 38.2%.

In the thermograms, temperature was presented as the grayshade in the image. Depending on the polarity of the camera, alighter shade can represent higher or lower temperature. In thethermograms shown in Figures 1 and 2, lighter shades depictedhigher temperature and therefore darker shades representedlower temperature. The shade or color gradation is determinedfrom the radiation intensity that is absorbed and emitted by thetarget.

From the thermograms shown above, it is clear that back-ground or ambient conditions determine the infrared image

quality. The ambient conditions affect the color contrast andsharpness of the image. The higher ambient temperature showedbetter contrast between the methane gas plume and thebackground. The wind effect which determined the turbulenceof the gas plume can also be seen from the figures. The windvelocity during the experiments is higher in the November 2007test compared to that of the March 2008 test. It can be observedthat the gas dispersion is steadier for a lower wind velocity.

The radiation emitted from and to an object fluctuates due tothe presence of atmospheric transmittance. The atmosphere iscomposed of numerous gases and aerosols which absorb andscatter radiation as they travel from the target to the thermalimaging system. This reduction in radiation is called theatmospheric transmittance. The radiation accumulated along theline of sight due to the scattering of ambient light into the line-of-sight causes the reduction of the target contrast.6,23 Theradiation that reaches the imaging system is the sum ofattenuated target radiation and the path radiance. The magnitudeof the transmittance and path radiance depends upon theatmospheric constituents, path length, and spectral response ofthe thermal imaging system. However, the atmosphere wasconstantly changing over time, and therefore, it is impossible

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.

3930 Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

to assign a single number to the transmittance or path radiance.Infrared path radiance occurred primarily due to atmosphericself-emmitance. It was independent of the target temperatureand was seen even if the target is not present. Path radiancecomplicates target temperature measurements but its effect onlybecomes a problem over very long path lengths when thetransmittance is low.6,23

In addition to the atmospheric transmittance, the atmosphericcontent also affected the radiation absorbed and emitted by thetarget object. Water vapor or absolute humidity was a majorabsorber in the infrared region. However, transmittance was notlinearly related to absolute humidity. As the water vaporincreased (the absolute humidity increases), the transmittancedecreased. Aerosols changed the amount of radiation primarilyby scattering the radiation out of the line of sight. As the particlesize grew, the scattering coefficient increased at all wavelengthsand the transmittance decreased.6,23 The water vapor in theatmosphere absorbed and scattered the radiation which resultsin reduction of the target signature. The higher the water vaporcontent, the greater the effect of reduction of the target signature.Aside from that, H2O also radiated energy at ambient temper-ature that accumulated along the line from the target gas to thecamera detector which results in the reduction of target contrast.However, the effect of water vapor in reducing the radiationenergy had not been quantitatively examined in this work, andfurther research can be performed toward analyzing the watervapor or absolute humidity on LNG vapor dispersion.

Other than water vapor and atmospheric content, somereflectances from the surrounding objects also attenuated theradiation traveling from the target to the camera; for example,the reflectance from metal structure or water tanks in the vicinityof experiment location. Yet, in this work, the effect of thereflectance from surrounding objects was considered insignificant.

Emissivity Profile of Methane Gas at DifferentTemperatures. The most important factor in the temperaturemeasurement using an infrared imaging system is to understandthe emissivity of the gas. Because the thermal camera alwaysassumes the emissivity of the object is equal to unity, theapparent temperature depicted in the thermogram did not reflectthe true temperature of the gas. If the emissivity of the gas isnot known, the temperature measured using thermal imagingsystem does not have any significance, and thus, the values willbe meaningless. This work provides the determination ofmethane gas emissivity at low temperature using band absorptionmodel.

Most objects do not emit all the radiation; they only emit afraction of it. The ratio of the actual radiation from an objectcompared 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 thermalimaging system measures the object’s temperature by assumingthat the emissivity is equal to unity. When emissivity is notknown, it is misleading to assume the apparent temperature asthe true temperature of the object. The discrepancy betweenthe apparent and true temperatures becomes larger for loweremissivity. Therefore, the emissivity is the main uncertainty intemperature measurement using an imaging system.

This research aims to estimate the emissivity of methane atlow temperature between 110-300 K. There has been no studyin the past to evaluate the methane emissivity within thistemperature range; however, a correlation had been developedby Elsasser and some experiments had been done to measurethe band absorption for methane at medium-high temperature(295-1138 K) by Lee and Happel.8 Using this information,

methane gas emissivity is estimated by fitting the data fromLee and Happel into the Elsasser correlation to obtain theconstants in eqs 12-15 above. With the known constants, thedata is then extrapolated to calculate the band emissivities andtotal emissivity of methane at low temperature. The effectivebandwidth for methane gas in the 3.31 and 7.65 µ band datafrom Lee and Happel is shown in Table 2. The absorption bandof methane at gas 2.37 µ does not depend on the effectivebandwidth thus the band absorption only depends on the gastemperature and the optic length.

By plotting the effective bandwidth data for methane givenin Table 2, the relationship of effective bandwidth to temperaturefor the 3.31 and 7.65 µ bands can be obtained and used tocalculate the effective bandwidth at lower temperature. The plotof the effective bandwidth as function of temperature is givenin Figure 3.

The relationship between temperature and effective bandwidthfor methane at 3.31 µ is

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

The data of methane absorption at three different wavelengths(2.37, 3.31, and 7.65 µ) as a function of temperature obtainedby Lee and Happel in 1964 is presented in Table 3.

The absorption band for methane gas at the 2.37 µ wavelengthis plotted against temperature to find the constants Dio and (�i

+ �i) in eq 14 as given in Figure 4.The relationship between the temperature and absorption band

for methane at 2.37 µ is

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

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 20 3207 2706 501 1396 1190 206373 23 3231 2688 543 1404 1172 232473 25 3246 2676 570 1408 1160 248573 28 3268 2658 610 1413 1142 271673 30 3282 2646 636 1413 1130 283773 32 3296 2634 662 1419 1118 301873 34 3309 2622 687 1422 1106 316973 36 3322 2610 712 1422 1094 328

1073 38 3335 2598 737 1422 1081 3411173 40 3347 2585 762 1422 1069 3531273 42 3357 2573 784 1422 1057 3651473 45 3377 2555 822 1422 1038 3841673 48 3393 2536 857 1422 1020 4021873 50 3404 2524 880 1422 1007 4152073 53 3419 2505 914 1422 988 4342273 56 3433 2486 947 1422 970 452

∆ω3.31µ

(∆ω3.31µ)0) ( Tg

Tgo)0.311

(19)

∆ω7.65µ

(∆ω7.65µ)0) ( Tg

Tgo)0.377

(20)

A2.37µ

(A2.37µ)0) ( Tg

Tgo)0.534

(21)

Ai,2.37µ ) 38.2( Tg

295)-0.534

√X (22)

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 3931

Equation 12 is used to fit the data for the strong or overlappingband (3.31 and 7.65 µ). For the 3.31 µ band, the plot ofabsorption band against the temperature demonstrates twodifferent regions as shown in Figure 5: (1) at T < 473 K, theabsorption 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 theplot of erf-1(Ai/∆ωi) against temperature at T < 473 K and Figure6b is the plot for methane at T g 473 K. The constants, �i,obtained from these plots are -0.477 for T < 473 by settingTgo ) 295 K and, for T g 473 K, �i ) 0.185 by setting Tgo )473 K.

The value of constant Cio for T < 473 K is equal to 0.129with standard deviation ) 0.001. Thus for the 3.31 µ band at T< 273, eq 12 can be rewritten as follows:

The value of constant Cio for T g 473 K is equal to 0.103 withstandard deviation ) 0.003. Thus for the 3.31 µ band at T g273, eq 12 can be rewritten as follows:

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

relationship between erf-1(Ai/∆ωi) and temperature for methanegas at the 7.65 µ band.

The value of the constant �i obtained from the plot is -0.177and by taking Tgo ) 295 K the constant Cio is equal to 0.207with standard deviation ) 0.005. Thus for the 7.65 µ band, eq12 can be rewritten as follows:

Band emissivity is determined from eq 6. The band emissivityat certain temperature and optical depths is the product ofabsorption bandwidth with the Planck radiation function dividedby the total energy emitted by a perfect blackbody at thattemperature determined by the Stefan-Boltzmann law. Theband emissivities of methane gas at temperature 110-350 Kare given at three active wavelengths in Figure 9a-c. The totalemissivity is the sum of band emissivities. The total emissivityof methane gas at temperature 110-350 K is given in Figure9d.

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 OpticalDepth at Different Temperatures8

T (K) A2.37µ (cm-1) A3.31µ (cm-1) A7.65µ (cm-1)

295 106.3 193.2 124375 102.3 189.5 126378 187.9471 85.7 181.3 131.8473 88.2 184.1 129.9569 71.8 192.3 139.5668 60.7 214 146674 53 221 149.9768 66.6 234.2 152.3873 58.7 238.7 152.9873 56.8 242.3 151.7974 63.2 265

1008 51.6 161.71079 61.9 254.81084 164.71118 51 279.21138 52.8 273.7

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

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

Ai,3.31µ ) ∆ωi(Tg)erf{0.129( Tg

Tgo)-0.477

√X} (23)

Ai,3.31µ ) ∆ωi(Tg)erf{0.103( Tg

Tgo)-0.185

√X} (24)

Ai,3.31µ ) ∆ωi(Tg)erf{0.207( Tg

Tgo)-0.177

√X} (25)

3932 Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

From the figure above, it is shown that the band and totalemissivity of methane gas at lower temperature is a strongfunction of temperature. The effect of optical depth is not highlysignificant to emissivity measurement for methane at lowertemperature. From the calculation of total emissivity using bandabsorption method, it is evident that the emissivity of methanegas at low temperature (110-300 K) is much less than unity.Therefore, the temperature measurement using thermal cameraassuming the emissivity equal to unity will not give a validtemperature measurement of methane gas. The emissivity valueobtained in this work will be used as correcting factors inmeasuring the gas temperature. The temperature of the gas canbe determined from the different amount of radiation emittedfrom the target and the background. For a target cooler than itsbackground, the power difference is

where TT and TB are the target and background temperatures,respectively. It is practical to specify it by its target-backgrounddifference (∆T) where ∆T ) TT - TB.

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

Conclusions

The use of infrared (thermal) camera has been applied in LNGsystem to visualize the LNG vapor dispersion. The quality ofthe thermal image (thermogram) as well as the thermal readingof the gas visualization highly depends on the conditions duringthe experiments. Those factors include wind conditions, atmo-spheric transmittance, atmospheric content, absolute humidity,and emissivity of the gas. Uncertainty related to emissivity isthe most significant factor in the temperature measurement ofthe dispersed gas and in this research the emissivity of methanegas at low temperature has been quantitatively analyzed usingthe band energy method. The emissivity of methane at lowtemperature is important to be identified since the LNGvaporizes at 110 K, and thus, the emissivity value is analyzedfrom this temperature. The available published data in the pastprovided the absorption of methane at temperatures from 295to 1198 K; however, no data was available for temperatureslower than 295 K. Hence, the initial assumption for estimatingthe emissivity to lower temperature is to evaluate the trend ofthe available data and with the method of curve fitting andextrapolation the data is projected to lower temperature. Theresult shows that emissivity of methane gas significantlyincreases as the temperature increased for temperature rangebetween 110 and 300 K.

An infrared camera is an effective mean to visualize the LNGvapor cloud qualitatively; however, one cannot rely on directtemperature measurement given by the thermal imaging camerasince a lot of parameters such as atmospheric transmission, solarradiation intensity, and air content can affect measurement aswell as high uncertainty due to unknown emissivity values of

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.

∆M ) MB - MT (26)

∆M ) ε(TT)σ(TB4 - TT

4) (27)

∆M ) ε(TT)σ[TB4 - (TB - ∆T)4] (28)

∆M ) ε(TT)σ[4TB3∆T - 6TB

2∆T2 + 4TB∆T3 - ∆T4]

(29)

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 3933

the methane gas. This article provides the calculation of methanegas emissivity using the band energy method which can befurther applied to estimate the actual radiation emitted from themethane gas target into the camera detector as well as the actualtemperature distribution of the gas plume. By combining thisstudy with dispersion modeling, a temperature-concentrationcorrelation can be established. This correlation is useful tounderstand the extent of the dispersed gas and concentration ofgas as well as to calculate the emission rate of the gas.

Literature Cited

(1) Holst G. C. Common Sense Approach to Thermal Imaging; SPIEOptical Engineering Press, 2000.

(2) Furry; Richards; Lucier; Madding Detection of Volatile OrganicCompound (VOC) with a Spectrally Filtered Cooled Mid-Wave InfraredCamera. Inframation Proceedings, 2005.

(3) Madding, R. New Development in Portable Infrared CameraTechnology. Hydrocarbon Process. 2006, 85 (11), 83–86.

(4) Gross; Hierl; Scheurpflug; Schirl. Detection of Gas Leak AlongPipelines by Spectrally Tuned Infrared Imaging. Proc. SPIE 1998, 3493,267–271.

(5) Leak; Moore; Murthi; Mannan Application of Visualization andThermal Detection Technique for Non-Intrusive Imaging of LNG Leaksand 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; CaliforniaInstitute of Technology: Pasedena, CA, 1951.

(10) Penner; Ostrander; Tsien. The Emission of Radiation from DiatomicGases III. Numerical Emissivity Calculations for Carbon Monoxide for LowOptical 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 NitricOxide: Approximate Calculations. J. Appl. Phys. 1950, 21 (9), 907–908.

(12) Penner, S. S.; Gray, L. D. Approximate Infrared EmissivityCalculations 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 inFurnaces. J. Eng. Phys. Thermophys. 1970, 19 (3), 1102–1114.

(15) Smith; Shen; Friedman. Evaluation of Coefficients for the WeightedSum 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 SyntheticAtmosphere. II. Absorption by Carbon Dioxide. J. Opt. Soc. Am. 1956, 46(4), 237–241.

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 7.65µ band, and (d) total emissivity of methane gas at different temperatures and optical depths.

3934 Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

(18) Howard; Burch; Williams. Infrared Transmission of SyntheticAtmosphere. III. Absorption by Water Vapor. J. Opt. Soc. Am. 1963, 6 (2),585–589.

(19) Brosmer, M. A.; Tien, C. L. Infrared Radiation Properties ofMethane at Elevated Temperature. J. Quant. Spectrosc. Radiat. Transfer1984, 33 (5), 521–532.

(20) Pierluissi, J. H.; Maragoudakis, C. E. Band Model for MolecularTransmittance of Carbon Monoxide. Appl. Opt. 1986, 25 (22), 3974–3977.

(21) Modest, M. F. RadiatiVe Heat Transfer, 2nd ed.; Academic Press:New York, 2003.

(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, 2009ReVised manuscript receiVed January 21, 2010

Accepted March 3, 2010

IE901340G

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 3935