370 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 41, NO. 3, JUNE 1992

Determination of Water Vapor by Microwave Spectroscopy with Application to Quality

Control of Natural Gas Achilles N. Leontakianakos, Member, IEEE

Abstract-The design and construction of a microwave spec- trometer is given. The aim of this instrument is to detect water vapor at low levels. Sinusoidal Stark field modulation is used in order to amplitude modulate the absorption of microwave energy by the water molecule, thus enhancing the sensitivity of the instrument. A semiconfocal Fabry-Perot resonator is used to hold the sample under test. The fourth harmonic of the Stark modulation frequency was used to show the quantitative pres- ence of water in the sample gas. Both atmospheric air and liquified natural gas (LNG) were used as carrier gases. The peak-to-peak intensity of the fourth harmonic was used to cal- ibrate the instrument against different amounts of water pres- ent in atmospheric air. The observed limit of this prototype is around 300 ppm water. No attempt was made to lower the de- tection limit at this point since the aim of this project was to examine the feasibility of using the fourth harmonic to deter- mine water content reliably.

I. INTRODUCTION LAR gases, i.e., gases that exhibit a molecular elec-

diation of particular wavelengths in the millimeter and centimeter ranges. The radiation sources employed in the microwave spectrum provide energy in a frequency band so narrow in comparison with most spectral lines that it can be considered a monochromatic source. This source is tunable and can be swept over a spectral line to be mea- sured or can be tuned over wide regions in search of un- known spectral lines. The resolution, easily obtainable [ 11 with these tuned electronic oscillators, is thousands of times greater than that of infrared spectrometers using prisms or gratings. Nearly all microwave spectra are mea- sured by absorption of energy by the gas molecules.

The substance to be studied is placed in an absorption cell through which radiation from the source is passed. These cells can be lengths of ordinary rectangular or cir- cular section waveguide or microwave resonant cavities. They can be enclosed resonators such as cylindrical, or cube-shaped structures, or they can be open resonators such as Fabry-Perot cells. A detector of the radiation re- cords the dip in transmitted power as the source oscillator

p4 tncal dipole, selectively absorb electromagnetic ra-

Manuscript received March 5, 1991; revised November 20, 1991. The author is with the Department of Electrical and Electronic Engi-

neering, Institute of Technology Brunei, BSB 1929, Brunei Darussalam, Southeast Asia.

IEEE Log Number 9107622.

is tuned across the absorption line of the substance. Since the invention of the maser in 1955, observation of certain microwave lines through stimulated emission has been possible, [2] and [3].

A sensitive spectrometer has been designed and devel- oped incorporating an open semiconfocal Fabry-Perot resonator as the absorption cell where the gas under ex- amination is held at low pressure. The polar gas to be detected is water vapor as it is found in the atmosphere mixed with atmospheric air or as it is found underground mixed with hydrocarbons in subterranean natural gas de- posits. In this research work both cases are focused on, and results have been generated.

The moisture content of atmospheric air is of interest to many disciplines such as meteorology, geology, avia- tion, remote sensing of the earth, etc. Similarly, the oil industry has the need to know the remnant water vapor content of natural gas when it has been dried and is sold to the customer. Also, the water content of gas has to be monitored during processing in order to ensure protection of pipelines when liquefied natural gas is pumped. Mea- surements of gas density and relative density are com- monly required, but they may not be acceptable [4] for the fiscally important measurement of the calorific value of the gas. If free water is present and the gas contains sufficient carbon dioxide and hydrogen sulphide, there can be significant corrosion in the pipes that are transporting the gas. The work presented here describes a new way ,to monitor water in hydrocarbon gases by microwave rota- tional spectroscopy.

The absorption of microwave energy due to water va- por in the short microwave region is attributed to two causes (a) a single line at frequency 22.235 GHz, and (b) the combined residual effect of all other water lines. There is a sharp peak in the absorption due to (a) at 1.34 cm amounting to about 0.2 dB Km-l * g-' of H 2 0 m-3 or 0.2 dB * 1000 * m-4 g-' [5], and the absorption caused by (b) is usually omitteu since the error involved is in- consequent, of the order of less than 1 % according to the estimates of Dennison [6] on the intensities of water lines.

The theoretical value for the absorption coefficient for pure water vapor is 9.6 x lop6 cm-' [5], which is close to the observed value of 8 4 x lop6 cm-' [7]. In a more recent publication [8], the absorption coefficient is

0018-9456/92$03.00 0 1992 IEEE

LEONTAKIANAKOS: MICROWAVE SPECTROSCOPY AND QUALITY CONTROL 371

TABLE I COMPARISON OF WATER DETECTION METHODS

Principle Relative Type of of Humidity Approximate Advantages and

Hygrometer Operation Range (%) Accuracy Disadvantages ~~~

Ab03

Resistance

Piezoelectric

Dew and Frost Point

Gravimetric

Psychrometly

Coulometric

Infrared

Microwave Rotational Spectroscopy

Measure impedance of A1,0, film

Measure resistance of thin film of substance

Frequency of crystal coated.

Measure Temperature at which dew or frost is formed.

by dessicant.

water due to evapor in gas

Measure current from electrolysing water vapor.

Measure infrared Attenuation

Weigh vapor absorbed

Measure Temp. of

Measure Microwave selective attenuation

D.P. (-90, 60°C)

D.P.

D.P.

D.P.

(-90, 60°C)

(-80, 25°C)

(-80, 100'C)

D.P.

1, 100RH% ( -32 , 32°C)

(-70, 20°C) D.P.

D.P. ( -78 , 20°C)

D.P. (-45,20°C)

At present, (-50, 20"C),

( - 8 - , 20°C) in future expected

D.P.

1°C (D.P.)

5 % RH

3% RH

0.1 "C (DP)

0.1 % (vpm)

0.1 % (RH)

2 % (vpm)

2 %

100 ppm or below easily achieved

Regular Calibration, many different variants not of equal reliability. Hysteresis.

Regular Calibration. Hysteresis.

Very sensitive takes 5 h to settle.

Absolute measurement, systematic errors can exist.

Absolute Laboratory technique.

For measuring atmospheric Humidity.

Technique for lower moisture levels.

Not as selective as Microwave. Needs several It/min flow through cell, expensive.

Requires vacuum and high electric field. On line instrument, competitively priced

given to be equal to 7.21 x cm-'. The line width of the 22.235 GHz water absorption line is given by Townes and Schawlow [9] to be 14 MHz TOW' . The 22.235-GHz line is the only line that has a resonance at wavelengths longer than 1 cm. The present application of microwave rotational spectroscopy is compared to exist- ing water detection methods in Table I.

11. THEORY

The theory developed is taken from sources such as [9]- [l 11. The detailed analysis of the theory can be found in [I21 and [13]. Here, a brief outline of the theory is given for continuity. The strength, y, of one of the absorption lines of an asymmetric rotor such as the water molecule is given by:

8?r2Nf( pij I2v2 AV m-'

= 3KcT[(v - vJ2 + Av2]

where

y

N

f

attenuation per unit length of a wave propagat- ing in a gas

the number density of molecules in the absorp- tion cell

the fraction of those molecules in the lower of the two states i a n d j involved in the transi- tion

1 pi j l 2 the square of the dipole moment matrix element for the transition summed over the three per- pendicular directions in space

the frequency at which y is defined the resonant frequency or to a good approxi-

mation the center frequency of the absorption line

the half-width of the line at one-half the maxi- mum value of y

U

v,

AV

K the Boltzmann's constant T the absolute temperature c the speed of light.

If a Stark electric field is impressed on the gas its ab- sorption frequency is modulated, and this leads to the generation of harmonics of the Stark modulation [ 113. The water molecule exhibits a second-order Stark effect [9]. This means that the resonant absorption frequency of the water molecule, in this case 22.235 GHz, shifts by an amount proportional to the square of the applied electric field. The absorption of the gas is amplitude modulated at frequencies of even harmonics of the frequency of the Stark field according to Hershberger [ 113. He has shown that there is a microwave frequency very near the gas ab- sorption line for which the second harmonic of the Stark field modulation is zero, and the fourth harmonic is max- imum. The fourth Fourier component has been calculated [l 11, and its theoretical shape is shown plotted against frequency in Fig. 1. The second harmonic has been used

312 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 41, NO, 3, JUNE 1992

t

22.235 GHz Fig. 1 . The shapes of the theoretical and experimental fourth harmonic

traces.

to lock a solid state oscillator to the frequency of the gas

A Fabry-Perot resonant cavity is used to hold the gas under observation. The system is shown in Fig. 2. The impedance of the cavity can be represented by a tuned circuit G, L, and C as shown in Fig. 3. It can be shown [9] that the fractional change in voltage amplitude, AV, of the reflected wave V from the cavity at resonance with the absorbing gas in the cavity is given by:

~ 4 1 .

AV QXa I/ 27r

-

where Q = the quality factor of the cavity, and Q X / 2 n can be conveniently written as LeR, the effective electric path length in the cavity. Then:

(3)

where x is the fractional abundance of the gas in the cav- ity, and a is approximately equal to xy. It can also be shown [12] that:

K - - 2 - AV v 1 - cos 4wt (4)

where K = a system constant. A phase-sensitive detector locked on the frequency of

the fourth harmonic is used to extract it from the com- posite signal shown in (4) above, where the signal is pro- portional to the fractional abundance of the water vapor in the cavity.

111. SYSTEM DESCRIPTION The microwave spectrometer designed to determine the

water vapor content of atmospheric air or natural gas em- ploys a Wiltron programmable scanning source, an open semiconfocal Fabry-Perot resonator of diameter 100 mm and radius of curvature 186 mm as the cell where the sam- ple is held, and, finally, a sensitive microwave detector diode, H.P. 33330C, is used to measure the attenuation of microwave energy.

The gas is held in a sealed Teflon cup in the Fabry- Perot resonator under vacuum conditions. The Stark field is impressed on the sample by a wire grid stuck on the flat

[air cyllnd.)-(sieve H b l e n d e r H i l t w m n s I tali br tube

t t o display

Fig. 2. Complete system of the microwave water spectrometer

Stark field wire grid

Teflon /

L {T-Gt: 9

(b) Fig. 3 . Schematics of (a) physical reflection Fabry-Perot cavity and (b)

electric equivalent of the gas containing resonant cavity.

side of the cup. The microwave energy is coupled to the resonator via an iris of dimensions 5 x 1 mm through a vacuum-sealed energy transparent window. The compos- ite signal from the microwave detector diode is amplified in an 85-db wideband amplifier and then is passed through the high quality factor bandpass gyrator filter.

The microwave source is set to oscillate at the reson- ating frequency of the cavity which is the water line fre- quency. Any mismatch between the cavity and Hybrid “T” is eliminated by the three-stub tuner. When water is detected in the cavity, then the newly generated reflected waves travel back through the Hybrid “T” to the detector where they register their presence. A gas blender was used to mix two streams of gas in any ratio between 0.02 and 1.00 with a resolution of 0.02. Air from the laboratory was bled in to give a single volume reading at the current ambient humidity. Air from a compressed air bottle was dried over a molecular sieve, and the water content of the

LEONTAKIANAKOS: MICROWAVE SPECTROSCOPY AND QUALITY CONTROL

80'

30 20. 10

0

resulting air had less than 50 ppm water content, so it was considered to be effectively dry for the experiments that followed. The dry air was then mixed with the laboratory air supply to give a range of mixtures.

The wet and dry air mixture was analyzed for water content using two methods: (a) by gravimetry, where after adsorption onto phosphorous pentoxide the weight of the wet sample was compared to the weight of the dry sam- ple, and (b) by hydrometry over a wet and dry bulb hy- drometer. During the course of these experiments the hu- midity of the laboratory air was found to be between 10000 and 8000 ppm which in relative humidity terms is translated to around 50 and 55 % over the period of a few days. The blended air was introduced into the spectrom- eter at a cavity pressure of 3.5 k 0.5 f lo-* mbar, which was maintained throughout the experimentation course.

;/ ,

. - - . . . - -

Intensity of . second harmonic Bandwidth

(mV 1 (KHz)

1300

I200

I I Q O

1000

930

800

700

600

500

400 IV. RESULTS The fourth harmonic was detected, and the shape of it

is shown in Fig. 1. In order to minimize the distortion of the shape of the water line and to keep it below saturation, the microwave power was kept to around 6 dbm.

At a pressure of 5.5 X lop3 mbar the water content was kept constant at 10000 ppm, and the power of the energy coupled to the cavity was varied. The complete set of results for this experiment is shown in Fig. 4, where the intensity and bandwidth variation in conjunction with power input to the cavity are plotted along the curves ABC and DEF, respectively. Then the sample pressure was in- creased further to 3.5 X mbar. The new sets of re- sults of intensity and bandwidth are shown along the curves GHI and JKL, respectively.

It is seen that the increased pressure has increased the saturation level of the line from 2 dbm at 5.5 x mbar to almost 3 dbm at 3.5 X mbar. This observation has to be taken into consideration when minute samples of gas are examined, with the requirement of an undis- torted line shape. As seen, the width of the line for both pressure values did not change appreciably.

The fourth harmonic intensity was further investigated by using different Stark field values while all the other parameters were kept constant. The results of this exper- iment are shown in Fig. 5 . The data collected for different water concentrations are shown in Table I1 and plotted in Fig. 6.

The line trace (A) represents the plot of the amplitude of the fourth harmonic signal against frequency, whereas line trace (B) represents the peak-to-peak height of it. The two traces exhibit similar slopes at the lower concentra- tion region, but they deviate considerably for higher con- centrations of water.

It was then discovered that there was a leak of atmo- spheric laboratory air of 10000 ppm water content to the cavity which prohibited any intentional further effective decrease of water vapor in the camer gas. The effect of the leak was to give a baseline plateau of the order of 350 PPm.

Finally, the carrier gas was changed to consumer calor gas (LNG) of water concentration 8000 ppm, and was in-

373

I

@'mi,,,,' - -1 er 3 entering 5 , 7 the cavity (& -

Fig. 4. Fourth harmonic intensity and bandwidth variation with pressure and power, where ABC and DEF are the intensity and bandwidth variation respectively at 5.5 x mbar, and GHI and JKL are the intensity and bandwidth variation respectively at 3.5 x lo-' mbar.

Fourth harmonic magnitude (mV)

Stark field voltage (KV) - Fig. 5. Fourth harmonic magnitude variation with Stark field voltage at a

pressure of 1 x mbar and water concentration 10000 ppm.

TABLE I1 WATER CONCENTRATION RESULTS

Water Concentration Fourth Harmonic Signal Fourth Harmonic Signal in air Curve A Curve B

(mV) (mV) ~

300 500 1300 2300 3400 4500 5400 6000 7600 9400 1000

9 10 15 20 25 30 33 35 40 45 47

13 15 18 23 30 35 40 43 52 61 65

314 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 41, NO. 3, JUNE 1992

Fourth harmonic

I amplaude (InV’

Water con entmtion in air/& VOI/V~I

d

Fig. 6. Calibration curve for water in air

306nkr A - I , Fig. 7. Fourth harmonic signal due to water in Calor gas. Apparent water

concentration in the gas is about 8000 ppm.

Fig. 8. Fourth harmonic signal due to water in Calor gas.

troduced to the cavity at a pressure of 3.5 x l o - * mbar. The pressure of the cavity was set to 6 . 0 f 0.5 X mbar. The signal obtained is shown in Fig. 7, and it in- cludes the additional effects of the ambient air leak to the cavity. The water content of the atmospheric air entering the cavity was found to be in the order of 9500 ppm. The calor gas was then dried and directed into the cavity. The signal trace obtained is shown in Fig. 8 where it can be seen that the amplitude of the fourth harmonic is reduced since the dry calor gas has reduced the concentration of water in the cavity by mixing with the air from the leak. From the pressure readings a dilution factor of 5 would be expected (i.e., 6 x - 3.5 X l o p 2 mbar), but, in fact, a decrease in peak height of 3.3 was obtained (i.e., 306-91 mV). The discrepancy is likely due to inefficient gas drying, the air leak, and experimental error all con- tributing to nonlinearities.

V. CONCLUSION A microwave spectrometer has been built to detect

water vapor content of atmospheric air, and the feasibility of the method in detecting varying levels of water vapor in LNG was successfully tested. The Stark effect method

was used, and the fourth harmonic of the Stark modula- tion frequency was employed to indicate the water content of the carrier gas.

The detectability or sensitivity of the instrument at its present state was tested, and it was found to be in the order of 300 ppm. Other polar gases of similar or lower concentrations can be examined since the Fabry-Perot cavity can be tuned to resonate at the new gas frequency by adjusting the length between its two mirrors and by reprogramming the scanning microwave source to oscil- late through a new frequency range. So a wide bandwidth spectrometer can be achieved limited only by the limits of the frequency range in which the Fabry-Perot cavity is able to resonate. Such a device can be used as an exten- sive analytical tool or as a dedicated online process and quality control unit. There is a growing interest particu- larly in chemical, oil, and energy related industries, for compound specific process control monitors. Bulk effect sensors are still the standard in these industries, but se- lective detectors offer much more control for product op- timization in many processes. Very few process control sensors are compound selective, quantitative, and have real-time output capability. Microwave rotational spec- troscopy has all of these properties plus compactness, simplicity, and reliability. Although it has great potential for process control applications not much work has been done. Levels of sensitivity of the order of subparts-per- billion can be achieved [ 161.

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