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Hazardous gas treatment using atmospheric pressure microwave discharges This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2005 Plasma Phys. Control. Fusion 47 B589 (http://iopscience.iop.org/0741-3335/47/12B/S43) Download details: IP Address: 153.19.47.244 The article was downloaded on 30/09/2009 at 07:54 Please note that terms and conditions apply. The Table of Contents and more related content is available HOME | SEARCH | PACS & MSC | JOURNALS | ABOUT | CONTACT US
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Hazardous gas treatment using atmospheric pressure microwave discharges

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2005 Plasma Phys. Control. Fusion 47 B589

(http://iopscience.iop.org/0741-3335/47/12B/S43)

Download details:

IP Address: 153.19.47.244

The article was downloaded on 30/09/2009 at 07:54

Please note that terms and conditions apply.

The Table of Contents and more related content is available

HOME | SEARCH | PACS & MSC | JOURNALS | ABOUT | CONTACT US

INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION

Plasma Phys. Control. Fusion 47 (2005) B589–B602 doi:10.1088/0741-3335/47/12B/S43

Hazardous gas treatment using atmospheric pressuremicrowave discharges

Jerzy Mizeraczyk, Mariusz Jasinski and Zenon Zakrzewski

Centre for Plasma and Laser Engineering, Institute of Fluid Flow Machinery, Polish Academy ofSciences, Fiszera 14, 80-231 Gdansk, Poland

E-mail: [email protected]

Received 1 July 2005Published 9 November 2005Online at stacks.iop.org/PPCF/47/B589

AbstractAtmospheric pressure microwave discharge methods and devices used forproducing non-thermal plasmas for control of gaseous pollutants are describedin this paper. The main part of the paper is concerned with microwavetorch discharges (MTDs). Results of laboratory experiments on plasmaabatement of several volatile organic compounds (VOCs) in their mixtures witheither synthetic air or nitrogen in low (∼100 W) and moderate (200–400 W)microwave torch plasmas at atmospheric pressure are presented. Three typesof MTD generators, i.e. low-power coaxial-line-based MTDs, moderate-powerwaveguide-based coaxial-line MTDs and moderate-power waveguide-basedMTDs were used. The gas flow rate and microwave (2.45 GHz) powerdelivered to the discharge were in the range of 1–3 litre min−1 and 100–400 W,respectively. The concentrations of the processed gaseous pollutants werefrom several to several tens of per cent. The results showed that the MTDplasmas fully decomposed the VOCs at a relatively low energy cost. Theenergy efficiency of decomposition of several gaseous pollutants reached1000 g (kW-h)−1. This suggests that MTD plasmas can be useful tools fordecomposition of highly concentrated VOCs.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Emission of SO2, NOx (NO + NO2), CO, COx , volatile organic compounds (VOCs) and othergaseous pollutants into the atmosphere affects our environment greatly. These emissions causeacid rains, depletion of the ozone layer, the greenhouse effect, etc. Human beings, animalsand plants suffer due to the direct and indirect influence of the gaseous pollutants.

Therefore, efficient methods for the control and reduction of gaseous pollutant emissionare strongly required. Nowadays conventional methods, e.g. adsorption, absorption and

0741-3335/05/SB0589+14$30.00 © 2005 IOP Publishing Ltd Printed in the UK B589

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catalytic combustion, do not seem to be sufficiently efficient [1, 2]. Recently the potentialof atmospheric pressure thermal [1–7] (e.g. dc torches from plasmatrons, RF torches) and non-thermal [2, 8–15] (e.g. electron beam, dc and pulsed corona discharges, corona dischargesin packed-bed reactors, dielectric barrier discharges, surface discharges, microwave torchdischarges (MTDs)) plasma methods for reduction of gaseous pollutants, have been tested.The majority of the non-thermal plasma methods have been tested for elimination of gaseouspollutants (SOx , NOx , VOCs) in relatively low concentrations (up to 1000 ppm (0.1%)) in aworking gas. The MTD method has been used for elimination of gaseous pollutants (mainlyVOCs) of relatively high concentrations (up to tens of per cent)).

An MTD at atmospheric pressure can be classified as a non-thermal plasma at elevated gastemperatures (up to 4000 K). This temperature is too low to result in a local thermal equilibrium(LTE) of the plasma but can be helpful in the decomposition of stable VOC molecules.

In this paper we deal with atmospheric pressure MTD plasmas. Their potential use inelimination of VOCs has been widely tested.

We present results of a study of the decomposition of several VOCs: aliphatichydrocarbon (H-C)—methane, CH4; aromatic H-C—toluene, C6H5CH3; halogenated aliphaticH-Cs—carbon tetrachloride, CCl4 and chloroform, CHCl3; and aromatic chlorofluorocarbons,CCl3F (CFC-11) and CCl2F2 (CFC-12), hydrochlorofluorocarbon, CHClF2 (HCFC-22),hydrofluorocarbon, C2H2F4 (HFC-134a), and fluorocarbon, C2F6 (CFC-116), in their mixtureswith synthetic air or nitrogen. The concentrations of the processed VOCs in the MTD wererelatively high, i.e. up to a few tens of per cent.

2. Atmospheric pressure microwave discharges for hazardous gas treatment

Microwave plasmas operating at atmospheric pressure can be induced by three types ofmicrowave field applicator: (a) microwave resonant cavities [16–20], (b) microwave surfatronswith surface-wave-sustained discharges [15, 21–24] and (c) MTDs. Generally, the atmosphericpressure microwave plasmas induced using microwave resonant cavities and surfatrons aresustained within a dielectric (e.g. fused silica) tube inserted into an microwave field applicator.This can cause some problems when large power densities are deposited into the plasma,resulting in deterioration of the tube due to plasma–tube interactions. A solution to theseproblems is a microwave plasma that can be induced in ‘open’ air at the tip of an MTDapplicator. Due to the absence of an enveloping tube, no limitation to the power density isimposed by the induced plasma.

2.1. MTDs

The history of MTDs is already five decades old. MTD applicators first appeared as structuresbased on microwave coaxial line components (e.g. [25–35]). In these so-called coaxial-line-based MTDs the microwave plasma is induced in the form of a plasma ‘flame’ at the openend of a rigid coaxial line, at the tip of its inner conductor. The power-handling capability ofcoaxial-line-based MTDs is generally limited to less than 1 kW due to the low thermal strengthof the coaxial line components.

In parallel with coaxial-line-based MTD applicators, the so-called waveguide-basedcoaxial-line MTD applicators have been developed (e.g. [35–40]). In these applicators alsothe microwave plasma is induced in the form of a plasma flame at the tip of a field-shapingstructure that is similar to that of coaxial-line based MTDs. However, the microwave poweris fed into this structure from a waveguide, usually a rectangular one, at 2.45 GHz. To ensureefficient power transfer to the induced plasma, the remaining part of the waveguide-based MTD

Hazardous gas treatment B591

Figure 1. Schematic diagram of a typical MTD set-up.

consists of coaxial and rectangular waveguide elements serving as a wavemode converter fromthe TE10 mode in the rectangular waveguide to the TEM mode in the coaxial section terminatedby the field-shaping structure and as an impedance transformer. Recently, the developmentof waveguide-based MTDs has gathered momentum owing to essential improvements in theirtheory and practice developed by the Moisan’s group (the so-called torche a injection axiale(TIA) [41]).

The next modification of the waveguide-based coaxial-line MTD is the so-called TIAGOsystem, developed by the Moisan’s group [15]. In this paper we call the TIAGO system awaveguide-based MTD. In a waveguide-based MTD, the microwave power is delivered to thefield-shaping structure in the form of a conductor with a conical nozzle through a waveguide.

Since both MTDs, the coaxial-line-based one and the waveguide-based one, are flowinggas systems, they are particularly suitable for processing the various gases or materialscarried by the gases in them. The operating gas in MTDs can be delivered to their plasmaregions by radial or axial injection. In the case of radial injection, mainly for coaxial-lineMTDs, the operating gas flows in the annular channel between the inner and outer conductorsof the coaxial-shaped section and enters the plasma region radially, through a ring-shapedorifice surrounding the tip of the torch. In the case of axial injection, the operating gas flowsinside the conductor of the field-shaping structure and enters the plasma region axially, throughthe nozzle at the conductor tip.

3. Experimental

The main parts of the experimental set-ups used in this investigation were a microwavegenerator (magnetron), a MTD generator, a microwave supplying and measuring systemand a gas supplying system (figure 1). The microwave power (2.45 GHz) was supplied tothe MTD from a magnetron. Depending on the required microwave power, the microwavepower was supplied to the MTD generator by the coaxial cable or the rectangular waveguide.Three types of microwave plasma generator were tested: the low-power coaxial-line-basedMTD generator (figure 2), the moderate-power waveguide-based coaxial-line MTD generator(figure 3) and the moderate-power waveguide-based MTD generator (figure 4). The MTDgenerators ensure optimal transfer of microwave power to the discharge plasma and ensure

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Figure 2. Schematic of the low-power coaxial-line-based MTD generator and plasma reactor usedfor processing gas mixtures.

Figure 3. Schematic of the moderate-power waveguide-based coaxial-line MTD generator andplasma reactor used for processing gas mixtures.

the mode conversion (e.g. conversion of the mode in the waveguide to the mode in coaxialstructure). In all microwave plasma torches, the operating gas flowed through the inner ductof the coaxial line section of the torch system and exited through an outlet (a kind of nozzle)ending it. The gas flow rate was automatically controlled by a mass flow controller (HastingsInstruments). In the torch, the plasma was sustained at the tip terminating the inner conductorof a coaxial line duct. The inner conductor protruded slightly beyond the end of the outerconductor. The plasma was generated in the form of a ‘plasma flame’ above a nozzle withina quartz reactor. The composition of the gas mixtures before and after plasma processing wasdetermined using a FTIR spectrophotometer operating in the range 4000–1000 cm−1.

3.1. Low-power coaxial-line-based MTD

The experimental set-up with the coaxial-line-based MTD generator is shown in figure 2.Microwave power (2.45 GHz) of about 70–100 W was supplied to the torch system througha standard 50 � coaxial cable with the use of a coupler (microwave antenna). There was

Hazardous gas treatment B593

(a)

(b)

Figure 4. Schematic of the moderate-power waveguide-based MTD generator and plasma reactorused for processing gas mixtures (a) and the nozzle region (b).

a mica foil between the coupler and the inner coaxial conductor. The mica foil improvedthe microwave coupling by increasing the capacitance between the coupler and inner coaxialconductor. The impedance-matching function was performed by using one intrinsic tuningelement in the form of a movable plunger located between the inner and outer conductors. Thecoaxial-line movable plunger allowed the reflected power to be minimized.

3.2. Moderate-power waveguide-based coaxial-line MTD

The experimental set-up with the waveguide-based coaxial-line MTD generator is shownin figure 3. The idea of such a generator, designated TIA, was described in [41]. In thiscase the microwave power (2.45 GHz), about a few hundred watts, was supplied to themicrowave plasma torch from a magnetron via a standard WR-430 rectangular waveguide.

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Figure 5. Illustration of the double-nozzle moderate-power waveguide-based MTD generator.

The mode conversion and impedance-matching functions were performed using a impedancematching system consisting of a conventional waveguide-to-coaxial line transition consistingof two intrinsic tuning elements in the form of movable plungers. Both the two movableplungers allowed the reflected power to be minimized.

3.3. Moderate-power waveguide-based MTD

The experimental set-up with the waveguide-based MTD generator is shown in figure 4.The idea of such a generator, termed TIAGO, was recently proposed by Moisan et al [15].Microwave (2.45 GHz) power of about a few hundred watts was supplied from a magnetronvia a standard WR-430 rectangular waveguide to the field-shaping structure in the form ofa conductor with a conical nozzle (figure 4(b)). The impedance-matching function wasperformed using one intrinsic tuning element in the form of a movable plunger placed inthe waveguide. The movable plunger allowed the reflected power to be minimized. Themain advantages of the waveguide-based MTD generator are its compactness, simplicityand smooth impedance matching (low sensitivity to changes in the operating conditions).Furthermore, it is possible to arrange single-nozzle waveguide-based MTD generators in arraysto form a compact multi-discharge system, suitable for high gas throughput. Figure 5 showsdouble-nozzle waveguide-based MTD generators with the nozzles located along or across thewaveguide. Figure 6 shows a multi-nozzle waveguide-based MTD generator in which thenozzles are located both along and across the waveguide.

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Figure 6. Schematic of the multi-nozzle moderate-power waveguide-based MTD generator.

Figure 7. Image of the atmospheric-pressure nitrogen MTD flame, recorded using a videocamera. Microwave power, 200 W; nitrogen flow rate, 1 litre min−1 The length of the flame core isabout 3 cm.

Nowadays, the maximum power of magnetron heads may be a few kilowatts or more, andso it is possible to use a high-power-waveguide-based MTD which can work at a microwavepower of several kilowatts with a relatively high gas flow rate (100–200 litre min−1).

4. MTD parameters

The MTD flame resembles a candle flame with two distinct zones: an inner core and anouter ‘envelope’ (figure 7). Some parameters of the MTD plasma were described in [42–46]for both zones. According to the authors with a microwave power of several hundredwatts delivered to the MTD, the nitrogen temperature, electron temperature and electrondensity in the flame core are about 1500 K, 20 000 K and 1021 m−3, respectively. In theflame envelope, just above the flame core, the nitrogen temperature is higher (4000 K),while the electron temperature (17 000 K) and density (1020 m−3) are lower than those in

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(a) (b)

Figure 8. Electron density, ne in argon MTD flame (0.5 mm above the nozzle) as a function ofmicrowave power (a) and as a function of distance above the nozzle (b).

(a) (b)

Figure 9. Images of MTD flame (waveguide-based MTD generator). Flow structures in (a) argonand (b) nitrogen. Gas flow rate, 1 litre min−1; microwave power, 200 W.

the core. Jasinski et al [43] measured the nitrogen temperature in the flame envelope, justabove the flame core, at 3700 ± 500 K, regardless of the microwave power (100–400 W) andnitrogen flow rate (1–3 litre min−1). This is due to the almost linear increase in the MTDflame volume with increasing microwave power, which causes the microwave power deliveredto a unit volume of the flame to remain constant, resulting in a constant gas temperature.In contrast to the gas temperature, the electron density increases with increasing microwavepower (figure 8(a)). As shown in figure 8(b), the electron density decreases with increasingdistance above the nozzle (distance AN). The beginning of the linear part is about 5 mm AN.We can suppose that it is the beginning of the plasma sustained by the surface wave.

The few MTD plasma parameters cited above suggest that the nitrogen MTD plasma is notin thermodynamic equilibrium (the neutral gas and, likely, ion temperatures are much lowerthan that of the electrons).

In general, the plasma flame consists of a hot ‘candle-like’ flame and an operating gasflow from the microwave torch nozzle (figure 9). When the operating gas was nitrogen, the

Hazardous gas treatment B597

candle-like flame was not located coaxially around the nozzle (figure 9(a)). The nitrogen flowis mostly a laminar jet which becomes turbulent with increasing flow velocity and decreasingmicrowave power.

The argon plasma flame structure is different. The candle-like flame is located almostcoaxially around the nozzle (figure 9(b)). In contrast to the nitrogen plasma flame, the operatinggas exiting the nozzle flows through the candle-like flame. The argon flow has the typicalstructure of a turbulent jet which is not changed by microwave power and gas flow rate.

Thus, the interaction between the candle-like flame and the operating gas flow depends onthe kind and velocity of the operating gas and microwave power. In particular, this interactionis pronounced for nitrogen.

Our investigation showed that the structure of the MTD flame depends on the kind ofoperating gas, its velocity and the microwave power delivered to the plasma. The position ofthe operating gas jet in relation to the position of the microwave flame is important for thechemical kinetics of the processed gases in the flame and its optimization.

5. Hazardous gas treatment using MTDs—results

In our investigations the decomposition of VOCs—methane (CH4), carbon tetrachloride(CCl4), chloroform (CHCl3), toluene (C6H5CH3), chlorofluorocarbons (CCl3F (CFC-11) andCCl2F2 (CFC-12)), a hydrochlorofluorocarbon (CHClF2 (HCFC-22)), a hydrofluorocarbon(C2H2F4 (HFC-134a)) and a fluorocarbon (C2F6 (CFC-116))—in their mixtures with syntheticair or nitrogen and of nitrogen oxides (NOx) in their mixtures with N2 or Ar in a microwavetorch plasma at atmospheric pressure was tested.

Air, N2 or Ar was used as a carrier gas to dilute and transport the gaseous pollutants tothe MTD. The composition of the gas mixtures before and after the plasma processing wasdetermined using a FTIR spectrophotometer operating in the range 4000–1000 cm−1. Forexample, figure 10 shows the FTIR spectra of a Freon mixture in N2 (2% vol.) before (a)and after (b) low-power coaxial-line-based MTD processing. In this case, the volume ratio ofCFC-12 : HCFC-22 : HFC-134a was 18 : 73 : 9. The microwave power and gas flow rate were100 W and 1 litre min−1, respectively. Due to the use of N2 as a carrier gas, the spectrumafter plasma processing is pure. There were no toxic compounds (e.g. phosgene or dioxins)produced when air was used as the carrier gas.

In these investigations the concentrations of the processed gaseous pollutants wererelatively high, i.e. around a few per cent. The use of higher microwave power (200–400 W)allowed us to increase the initial concentration of the processed gaseous pollutants toseveral tens of per cent. For example, when using the moderate-power waveguide-basedMTD generator for decomposition of a chlorofluorocarbon, CCl3F (CFC-11), the initialconcentrations of CCl3F in air or nitrogen were in the range 10–50% vol.

The performance of the moderate-power waveguide-based MTD when used for CFC-11decomposition in N2 is illustrated in table 1 and figures 11 and 12.

The efficiency of decomposition of CFC-11 in the nitrogen MTD as a function of the gasflow rate at a microwave power of 400 W is shown in figure 11. As can be seen from it, theCFC-11 decomposition efficiency is high and approaches 100% when the initial concentrationof CFC-11 is 10%, almost regardless of the gas flow rate. However, when the initial CFC-11concentration is 50%, the CFC-11 decomposition efficiency reaches 100% only if the gas flowrate is 1 litre min−1, decreasing to about 60% with increasing gas flow rate to 3 litre min−1.We observed that the MTD flame volume decreases with increasing gas flow rate. So, withincreasing gas flow rate, the resident time decreases not only due to the increasing gas velocitybut also due to the decreasing MTD flame volume. As shown in figure 11, with increasing

B598 J Mizeraczyk et al

(a)

(b)

Figure 10. FTIR spectra of Freon mixture in N2 (2% vol.) before (a) and after (b) low-powercoaxial-line-based MTD plasma processing. The volume ratio of CFC-12 : HCFC-22 : HFC-134awas 18 : 73 : 9. Microwave power, 100 W, gas flow rate, 1 litre min−1.

Table 1. Selected values of the specific energy density, decomposition efficiency, removal rate andenergy efficiency of decomposition of a chlorofluorocarbon (CCl3F (CFC-11)) in its mixture withnitrogen in a moderate-power waveguide-based MTD.

SpecificInitial Microwave Flow energy Destruction Removal Energyconcentration power rate density efficiency rate efficiency(%) (W) (litre min−1) (kW-h m−3) (%) (g h−1) (g (kW-h)−1)

50 300 1 5.0 100 170 57050 400 3 2.2 60 310 77550 200 2 1.7 60 210 1000

gas flow rate, the resident time decreases, resulting in a lower value of the decompositionefficiency.

As shown in figure 12, the efficiency of decomposition of CFC-11 in the nitrogen MTDfor different gas flow rates and initial concentrations of CFC-11 increases with increasingmicrowave power delivered to the discharge. It is almost 100% even for a relatively highinitial CFC-11 concentration of 50% if the microwave power is higher than 300 W (except inthe case when the gas flow rate was 2 litre min−1). At CFC-11 initial concentrations lower

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Figure 11. CFC-11 decomposition efficiency as a function of gas flow rate for different initialconcentrations of CFC-11 in nitrogen: (�), 10%; and (•), 50%. The moderate-power waveguide-based MTD generator was used. The microwave power delivered to the discharge was 400 W.

Figure 12. CFC-11 decomposition efficiency as a function of microwave power for different gasflow rates and initial concentrations of CFC-11 in nitrogen: 10% (- - - -) and 50% (——). Themoderate-power waveguide-based MTD generator was used.

than 10%, the use of microwave power higher than 200 W is energetically inefficient for a gasflow rate of 1 litre min−1. At higher gas flow rates, higher microwave power is needed to fullydecompose CFC-11. However, although in such a case the removal rate is always higher (dueto a higher gas flow rate), the energy efficiency of CFC-11 decomposition is not necessarilyhigher. We observed that the MTD flame volume increases with increasing microwave power,but the gas temperature remains almost constant. So, with increasing microwave power, theresident time increases, resulting in a higher value of the decomposition efficiency.

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Figures 11 and 12 show that the efficiency of decomposition of gaseous pollutants increaseswith increasing resident time. In the case of the MTD, the resident time can be changed bychanging both the gas flow rate and the microwave power delivered to the discharge.

As can be seen from table 1, the best values of the specific energy density, theremoval rate and the energy efficiency of CFC-11 decomposition were 1.7 (kW-h) (N m3)−1,310 g(CFC-11) h−1 and 1000 g(CFC-11) (kW-h)−1, respectively, depending on the gas flow rateand microwave power delivered to the discharge. The best conditions for CFC-11 destruction(highest decomposition efficiency at relatively attractive values of the removal rate and energyefficiency) occurred for CFC-11 initial concentration, gas flow rate and microwave powervalues of 50%, 1 litre min−1 and 300 W, respectively.

The energy efficiency and rate of CFC-11 removal obtained in the present experimentare superior to those with other plasma methods (e.g. corona [26], gliding [47] and arc [48]discharges or low-power MTD [49, 50]) used for this purpose.

Traces of CF4, CF3CN and SiF4 are found from the absorption peaks as by-products in theexit gas. Here we must note that oxygen compounds, such as COCl2, COF2, CF3NO, CF3NO2,NOx , CO and CO2, usually present when processing Freons in air [49,50]), were not monitoredin the after-process spectrum in the present experiment. Also, carbon (C), chlorine (Cl2) andfluorine (F2) were found in the by-products. The carbon deposit could be easily seen on thereactor walls. The chlorine and fluorine were detected by observing the changes in the colour ofa paper wetted with potassium iodide and starch solution. These gases were removed from theexit gas by passing it through a container with CaCO3 [51] (other possible filters are activatedcarbon [52, 53], zeolite filter [53] and fluidized CaO particles [54]).

As determined in this experiment, the efficiency of CFC-11 decomposition in a moderate-power MTD operating in atmospheric-pressure synthetic air was almost 100%, at an initialCFC-11 concentration, gas flow rate and microwave power of 50%, 2 litre min−1 and 400 W,respectively. This shows that the CFC-11 decomposition efficiency in the air MTD is higherthan that in the nitrogen MTD (82%) with the same operating parameters. The by-productsof CFC-11 decomposition in the air MTD were Cl2, F2, CO, CO2, COCl2, CF3CN, CF3NO,CF3NO2, CF4 and COF2. In contrast to the low-power MTD processing of Freons in air [23,24],nitrogen oxides were not produced in the present case. This might be because of the higherinitial concentration of CFC in this experiment because, as was shown in [49,50], the productionof nitrogen oxides in MTDs decreases with increasing initial concentration of Freons.

Taking into consideration the by-products, we propose the use of N2 as a carrier gasinstead of air. The results of this investigation encourage us to propose a hybrid system forFreon (CFC or HCFC) decomposition consisting of an atmospheric-pressure nitrogen MTDand a scrubber [55]. In the Freon destruction system, a pressure swing adsorbent unit (PSA)has been proposed for supplying the MTD unit with nitrogen at a reasonable cost (figure 13).

6. Conclusions

The results of this investigation show that several gaseous pollutants can be completelydecomposed in MTD plasmas.

The energy efficiency of decomposition of several gaseous pollutants (VOCs) using MTDsis better than with other plasma methods.

The decomposition of several gaseous pollutants by MTDs in air is accompanied with theproduction of harmful or toxic products (e.g. NOx , COCl2). So we propose the use of N2 as acarrier gas.

A multi-nozzle MTD system can be used to increase the rate of decomposition of storedVOCs.

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Figure 13. Schematic diagram of the atmospheric-pressure nitrogen MTD system used for VOCdestruction.

Therefore, the possible operation at a lower average power makes MTD devices morereliable and cheaper for gas treatment.

Acknowledgments

This research was supported by the Institute of Fluid Flow Machinery, Polish Academy ofSciences under the programmes IMP PAN O3Z3T2 and O3Z1T1. The authors are grateful toProfessor J S Chang for helpful discussions.

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