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Applied Thermal Engineering 70 (2014) 1253e1261

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Flue gas cleaning by high energy electron beam e Modeling andsensitivity analysis

Valentina Gogulancea*, Vasile LavricChemical and Biochemical Engineering Department, University POLITEHNICA of Bucharest, RO-011061, Polizu 1-7, Bucharest, Romania

h i g h l i g h t s

� A mathematical model for the electron beam flue gas treatment was developed.� The main chemical processes in both gas and liquid phases are accounted for.� The droplet generation and adsorption of gas components are taken in consideration.� The model is in good agreement with the experimental data in bibliographical sources.� The sensitivity of the process was tested using a fractional factorial white experiment.

a r t i c l e i n f o

Article history:Received 4 January 2014Accepted 14 May 2014Available online 22 May 2014

Keywords:Electron beamFlue gas treatmentSensitivity analysisHigh energyDroplet generationSO2 and NOx abatement

* Corresponding author. Tel.: þ40 724065881.E-mail address: v.gogulancea@gmail.com (V. Gogu

http://dx.doi.org/10.1016/j.applthermaleng.2014.05.041359-4311/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

The removal of sulfur and nitrogen oxides from flue gases using high energy electron beams is based onthe generation of excited molecules when the flue gas is bombarded by accelerated electrons. The excitedmolecules undergo ionization, dissociation and electron attachment to yield reactive species (ions,metastables, free radicals and electrons) which interact with the flue gas components. A complexmathematical model was built-up, which includes the main chemical processes in both gas and liquidphases together with the droplets generation and thermodynamic equilibrium between the two phases.The simulation results are in good agreement with the experimental data gathered from literature.Modeling the formation of liquid droplets and the adjacent physico-chemical phenomena provide abetter understanding of the process and a more accurate interpretation of the experimental results. Themodel enables the investigation of the treatment efficiency's sensitivity upon the main operating pa-rameters. A fractional three level factorial white experiment was designed using as parameters theirradiation dose, the water vapor content and the nitrogen oxide initial concentration of the flue gases.The removal yield of SO2 is rather insensitive to the said parameters, while, on the contrary, the removalyield of NO is very sensitive.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Growing population and the rise of industrial activities havetaken their toll on the quality of the environment. The pollutantsemitted from industrial facilities, power stations, residential heat-ing systems and engine vehicles have adverse effects on humanhealth, cause stratospheric ozone depletion, which in turn leads toclimate change, and contaminate soil and water, leading to acidi-fication and eutrophication [12].

Conventional methods for the removal of sulfur and nitrogenoxides such as flue gas desulfurization and selective catalytic

lancea).

6

reduction [14] have long proved their high removal efficiencies[29]. However, this achievement is accompanied by large energyconsumption and space requirements resulting in soaring invest-ment and operating costs [28].

Thus, new methods have been devised for the abatement ofsulfur and nitrogen oxides from flue gases. The electron beam fluegas treatment (EBFGT) is a relatively new procedure, developed inthe late 1970s by the Ebara Corporation, inwhich the pollutants aresubjected to ionizing radiation leading to the formation of a high-quality fertilizer mixture [8]. While achieving high removal effi-ciencies for both sulfur and nitrogen oxides, the process can beextended to the treatment of other gaseous pollutants and liquideffluents [16,21].

Compared with more traditional methods, EBFGT has theadvantage of scalability and simplicity in addition to being an easily

Fig. 1. Mechanism of NO removal during EBFGT treatment.

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e12611254

controllable process [5]. The technology has gradually achievedsome level of market penetration, at first with the construction of aseries of pilot plant installations in Japan, USA, Germany andPoland, among others, and, more recently, with the development oftwo industrial facilities in Poland and China [7].

However, the technology suffers, just like the conventionaltreatment methods, from large energy requirements [2] and fromreliability issues associated with the continuous operation of highenergy electron accelerators [20]. Consequently, numerous in-vestigations have been made into the possibility of reducing theenergy consumption for the process: employing hybrid irradiationmethods such as combined microwave and electron beam treat-ment [18], turning to alternative non thermal plasma generationmethods [10], fitting the plasma reactor with a catalytic layer [15],using a variety of additives such as ammonia, hydrogen peroxide[1], natural gas and hydrated lime [25]. The potential use of me-dium energy accelerators has also been investigated [5], with theprovision that a dispersed liquid phase should be introduced in thereactor before the beginning of the irradiation treatment.

Another method to reduce the energy consumption and theoperating costs is the investigation of more appropriate reactorconfigurations [23], either experimentally or through the use ofmathematical modeling [8]. The first mathematical models devel-oped started from the simplest reaction systems, formed only of N2,O2 and NO, considering as little as 29 chemical reactions [22] andhave been gradually improved to include over 850 chemical re-actions in the gas phase [26]. However, the size of the kinetic sys-tem greatly impacts the computational capacity so, more recentmodeling studies have only taken into consideration a fraction ofthese chemical reactions [6,11] or have resorted to empirical orsemi-empirical approaches [9]. Despite early interest in modelingthe liquid phase phenomena taking place during irradiation [19],the low liquid to gas ratio experimentally observed [32] has leadresearchers to neglect the formation and behavior of this liquidphase in their modeling efforts. However, experimental evidenceshows that the introduction of fine water droplets, even in smallamounts, in the irradiation chamber can lead to serious energysavings and lowers the operating costs [5].

The aim of the current paper is to advocate a complex mathe-matical model, considering 90 gas phase and 32 liquid phasechemical reactions that can accurately describe the behavior of thesulfur and nitrogen oxides subjected to electron beam irradiation.The model is, then, used to investigate the treatment efficiency'ssensitivity upon the main operating parameters.

2. Theoretical aspects

The treatment of flue gases with electron beams is based on thegeneration of high energy electrons that ionize the components ofthe gas carrying the pollutants and give rise to a series of reactivespecies: ions, radicals, metastables, etc. These in turn react with themain components of the flue gas (N2, O2, CO2, H2O) and promotethe transformation of sulfur and nitrogen oxides into their corre-sponding acids. Ammonia is added to the gas stream with the aimof neutralizing the acids to ammonia sulfate and nitrate e whichare collected in an electrostatic precipitator [6,7].

The mathematical model proposed in this work follows themain physico-chemical phenomena occurring in both gas andliquid phases during the irradiation treatment. The inclusion of theliquid phase phenomena together with the thermodynamic equi-librium between the liquid and the gas phases represents anoriginal approach in modeling the electron beam treatment, onethat proves relevant in the light of more recent energy-reducingdevelopments, i.e. introducing fine water droplets in the irradia-tion chamber [5].

Despite being slighted in the mathematical modeling of theelectron beam treatment of exhausts for the last decade, themodeling of liquid phase phenomena proved to be relevant in theeconomy of the process [5]. Our paper proposes new approaches tothe liquid phase modeling as well as a more extended kinetics: 19chemical species and 32 chemical reactions, listed in theSupplementary material.

2.1. Generation of reactive species

Radiation energy is absorbed by the gas components whichundergo ionization, excitation, dissociation and charge transferreactions. These processes are referred to as primary radiolysisphenomena and have a time scale in the range of 10�14e10�7 s. As ithas proven quite difficult to accurately determine the rates of thesereactions, the notion of electrochemical yield (G e value) has beenintroduced to account for the number of molecules or ions pro-duced or destroyed per 100 eV of absorbed ionizing energy. Theinteractions between fast electrons and the gas components aredescribed by Eqs. (1)e(4) [27], which are the most cited inliterature.

4:14N2/0:885N2Dþ 0:295N2Pþ 1:87N4Pþ 2:27Nþ2

þ 0:69Nþ þ 2:96e�(1)

5:3O2/2:98O� þ 2:25O1Dþ 2:07Oþ

2 þ 1:23Oþ þ 3:3e� (2)

6:7H2O/0:51H2 þ 4:25OH� þ 4:15Hþ 0:46O3P

þ 1:99H2Oþ þ 1:99e�

(3)

7:54CO2/4:72COþ 5:16O� þ 2:24COþ

2 þ 0:51COþ

þ 0:07Oþ þ 2:82e�(4)

2.2. Chemical reactions in gas phase

The species produced by the abovementioned primary radiol-ysis phenomena react further with each other giving rise to acomplicated reaction system. During these secondary radiolysisphenomena, the reactants undergo ioneion recombination, radi-caleneutral and radicaleradical reactions as well as molecular re-actions. The most complex models consulted accounted for theoccurrence of over 850 chemical reactions in the gas phaseinvolving more than 100 neutral and charged species [27].

We started to model the gas phase processes considering thestoichiometry proposed by Ref. [31]. Afterward, we improved ourmodel using the stoichiometry presented in Ref. [27] andcompleted with that of [22]. This way, we assembled a modelconsisting of 370 chemical reactions and 70 chemical species.

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e1261 1255

Due to the size and stiffness of the ordinary differentialequations system describing the gaseliquid processes and thecomplexity of the gaseliquid equilibrium calculations, theresulting model required a large computational time (days, upto one week), with the benefit of its high accuracy. In order toreduce the computational time still keeping a good accuracy,we performed a critical kinetic analysis of the gas-phasesystem.

This way, we excluded the chemical reactions with low reactionrates or the species with very small number concentrations. In theprocess, we gradually tested the results of the trimmed system,comparing its performance against some published experimental

Fig. 2. The solving algorithm fo

results; we ended up with the present model that takes into ac-count only 90 gas phase reactions and 40 species (see theSupplementary material) that is able to satisfactorily predict theaforementioned experimental results, while being computationallyaffordable (tens of minutes).

Sulfur dioxide is removed in the gas phase through two mainmechanisms: radio-chemical and thermal pathways. In the radio-chemical reaction series (Eqs. (5)e(12)), SO2 is oxidized by thehydroxyl and peroxyl radicals to yield the HS�O3 radical. The radicalis stabilized by reaction with molecular oxygen and forms sulfurtrioxide and sulfuric acid, the latter further reacting with the addedammonia [13,31].

r liquid phase phenomena.

Table 1Experimental conditions detailed in Ref. [9].

Experimental conditions

Experiment# Temperature (�C) Humidity (%) Dose (kGy) Residence time (s) [NO]initial (ppm) [SO2]initial (ppm) NH3 ratio

1 58.6 12.0 10.0 14.43 127 383 0.922 59.2 10.7 10.0 14.36 171 364 0.893 60.4 8.6 10.2 4.11 161 673 0.894 54.9 8.2 10.0 13.4 129 359 0.885 60.3 7.7 10.1 4.05 196 467 0.886 59.8 7.8 2.8 4.22 182 510 0.877 59.1 9.0 8.0 4.03 146 462 0.938 59.3 8.0 10.4 4.13 158 624 0.919 59.0 12.4 11.4 13.78 181 358 0.910 60.6 10.7 12.1 14.36 168 377 0.87

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e12611256

SO2 þ OH� þ N2/HS

�O3 þ N2 (5)

HS�O3 þ OH

�/H2SO4 (6)

HS�O3 þ OH

�/SO3 þH2O (7)

HS�O3 þ O2/SO3 þ HO

�

2 (8)

HS�O3 þ HO

�

2/SO3 þH2SO5 (9)

SO3 þH2O/H2SO4 (10)

HS�O3 þ O2/HOSO2O2 (11)

H2SO4 þ NH3/ðNH4Þ2SO4 (12)

The thermo-chemical pathway is described by the set of Eqs.(13)e(17): the reaction mechanism was initially proposed by Ref.[13] and refined by Ref. [4]. In the absence of irradiation, thethermo-chemical pathway is solely responsible for the removal ofsulfur dioxide, which can be as high as 40% [3].

SO2 þNH3/NH3SO2 (13)

0 1 2 3 4 5 6 7 8 9 10 1140

50

60

70

80

90

NOremovalefficiency(%)

Experiment #

ExperimentalModel

Fig. 3. Experimental vs model removal efficiencies for NO.

NH3SO2 þ NH3/ðNH3Þ2SO2 (14)

ðNH3Þ2SO2 þ 0:5O2/NH4SO3NH2 (15)

ðNH3Þ2SO2 þ H2O/ðNH4Þ2SO3 (16)

ðNH3Þ2SO2 þ H2O/ðNH4Þ2SO4 (17)

The removal of nitrogen oxides has a slightly more complexmechanism, as the pollutants simultaneously undergo oxidationreactions e the favored removal mechanism, which ultimatelyleads to the formation of nitric acid e and reducing reactions,promoted by the presence of atomic nitrogen and amidogen radi-cals [22]. The schematics of the removal process are presented inFig. 1.

2.3. Droplet formation

To model the gaseliquid thermodynamic equilibrium and theliquid radio-chemical reactions system, we started from the refer-ence works of [17,24,30]. The mathematical relationships devel-oped in these works for the sulfuric acid nucleation and gaseliquidabsorption, were tested and integrated in our mathematical model.The use of the parameterizations proposed in the referenced paperis novel; the method of [13] was computationally exhausting.

0 1 2 3 4 5 6 7 8 9 10 1170

80

90

100

SO2removalefficiency(%)

Experiment #

ExperimentalModel

Fig. 4. Experimental vs model removal efficiencies for SO2.

Table 2Model and experimental, as detailed in Ref. [9], results comparison.

Experiment# NO removal efficiency (%) Relative deviation (%) SO2 removal efficiency (%) Relative deviation (%)

Experimental Model Experimental Model

1 77.9 81.4 �4.5 93.2 96.1 �3.12 72.5 67.8 6.5 99.2 96.5 2.73 82.1 84.7 �3.2 81 83.4 �3.04 81 77.2 4.7 98.6 94.6 4.15 74 65.6 11.4 74.1 75.5 �1.96 47.3 43 9.1 89 80.8 9.27 63.7 70.3 �10.4 77.9 75.8 2.78 75.1 86.7 �15.4 84.6 82.3 2.79 74.6 70.2 5.9 97.4 95.23 2.210 76.7 74.6 2.7 99.3 95.1 4.2

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e1261 1257

The H2SO4 molecules produced in gas phase rapidly gain watervapor and nucleate to form small H2SO4/H2O droplets, condense onexisting particles or on the walls of the reactor and coagulate toform larger clusters [17].

In the present mathematical model, the assumption was thatthe condensation and coagulation processes havemuch lower ratesthan both the nucleation and the chemical processes, and thus, theyhave been neglected.

For the description of the nucleation phenomena and thecomposition of critical clusters, an empirical model was employed,valid between 300 and 400 K, with sulfuric acid concentrationsranging between 104 and 1016 molecules/cm3 and the relative hu-midity larger than 35%. The empirical Eq. (18) was used to computethe rate for nucleation, according to Ref. [24]

log Jnucl ¼ 7� 64:24� 4:7$RHþ ð6:13þ 1:95$RHÞlog½H2SO4�G(18)

where Jnucl is the nucleation rate for sulfuric acid, RH represents therelative humidity and [H2SO4]G is the sulfuric acid concentration ingas phase.

The composition of the clusters was determined using the set ofparameterized equations presented in Ref. [30].

2.4. Liquid phase phenomena

The formation of a liquid phase leads to the absorption of severalcomponents from the flue gas into the liquid, mainly SO2, HNO2,HNO3, NH3, O2, (NH4)2SO4, NH4NO3, (NH4)2SO3 and NH4NO2.Considering the relatively small concentration of these species,Henry's Law e Eq. (19) e was applied for the modeling of thegaseliquid phase equilibrium

ci ¼ pi$KH (19)

where ci ethe concentration of species i in liquid (mol/L); pi e thepartial pressure of component i in gas phase (atm); and KH e

Henry's constant for species i (mol/L atm).

Table 3Fractional simulation design.

Simulation 1 2 3 4

Case (þ,þ,þ) (þ,þ,�) (þ,�,þ) (þDose, kGy 12.2 12.2 12.2 12Humidity, % 10.3 10.3 6.8 6.NO, ppm 193 129 193 12SO2 efficiency, % 84.2 83.6 84 83NO efficiency, % 87 98.7 85.3 97

These species undergo dissociation phenomena Eqs. (20)e(27),modeled through the mass and charge balances for the corre-sponding molecular and ionic species.

H2SO4 þ H2O/HSO4� þ H3O

þ (20)

HSO4� þ H2O/SO4

2� þ H3Oþ (21)

SO2$H2O/HSO3� þ Hþ (22)

HSO3� þ H2O/SO3

2� þ H3Oþ (23)

HNO3 þ H2O/NO3� þH3O

þ (24)

HNO2 þ H2O/NO2� þH3O

þ (25)

NH3$H2O/NH4þ þ OH� (26)

H2Oþ H2O/OH� þ H3Oþ (27)

The accelerated electrons also interact with the liquid dropletsleading to a series of chemical reactions promoting the trans-formation of S(IV) to S(VI) compounds, encompassing the thirdmechanism for the removal of sulfur dioxide.

Even though the ratio of liquid to gas in the irradiation chamberis relatively low (~10�6), the liquid processes show a significantimpact on the overall removal efficiency for sulfur dioxide andprovide a better understanding of the process.

Unlike the approach of [19], who also considered bothgaseliquid phenomena, but assumed that the liquid phase is insteady state, in our model both phases are in a dynamic regime.This assumption leads to a system of ordinary differential equationsfor the liquid phase mass balance too, as opposed to a system ofalgebraic equations [19].

5 6 7 8

,�,�) (�,þ,þ) (�,þ,�) (�,�,þ) (�,�,�).2 8.2 8.2 8.2 8.28 10.3 10.3 6.8 6.89 193 129 193 129.7 83.1 82.3 83.8 83.2.9 65 85.1 63.3 83

Table 4Fractional simulation results.

Simulationnumber

qDose(%)

qHumidity

(%)qNO initial

concentration

(%)

Sensitivity

NO removalrelative yield (%)

SO2 removalyield relative (%)

1 19.6 19.8 19.9 2.7 1.02 �19.9 16.5 0.23 �19.8 19.9 0.7 0.74 �19.9 15.6 0.45 �19.6 19.8 19.9 �23.3 �0.46 �19.9 0.5 �1.37 �19.8 19.9 �25.3 0.58 �19.9 �2.0 �0.2

Fig. 6. NO removal efficiency function of humidity and initial NO concentration atdifferent irradiation dose.

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e12611258

3. Solving algorithm

The majority of the mathematical models to date has either anempirical approach or only takes into consideration the gas phasechemistry of the process. The mathematical model developed inthis work was solved using Matlab™ (MathWorks®, Natik, MA)programming environment and was structured to describe in detailthe main phenomena involved in the treatment of flue gases withhigh energy electron beams.

3.1. Gas & liquid phase transformations

The mass balance for each of the components (free radicals,ionic species and molecular compounds in both gas and liquidphases) was written using Eq. (28), according to [31],

dcidt

¼ Gi$D*$Xi þ rate of formation� rate of decomposition

(28)

where ci represents the concentration of the reactive species i; D* isthe irradiation rate; Xi denotes the molar fraction of the species iand Gi is the corresponding radio-chemical yield. The first termaccounts for the generation of reactive species via irradiation whilethe rates of formation and disappearance are associated to thechemical reactions involved in the treatment process.

Fig. 5. SO2 removal efficiency function of humidity and initial NO concentration atdifferent irradiation dose.

The mass balance equations for both liquid and gas were solvedtogether using an in-housewritten routine specifically designed forsystems of stiff ordinary differential equations.

3.2. Condensation process

After each integration step, the integrator halts and the numberand composition of sulfuric acidewater clusters freshly generatedis computed using the parameterizations presented in the previouschapter. Subsequently, the concentrations of sulfuric acid andwaterin the gas phase are adjusted to account for the nucleation phe-nomenon and the liquid to gas volume fraction of is recalculated, aspresented in Fig. 2.

Fig. 7. NO removal efficiency function of dose and initial NO concentration at differenthumidity content.

Fig. 8. SO2 removal efficiency function of dose and initial NO concentration at differenthumidity content.

Fig. 10. NO removal efficiency function of dose and humidity at different initial NOconcentration.

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e1261 1259

3.3. Absorption phenomena

Following the nucleation calculation, the solving strategy goeson to determine the rate at which the gas phase components areabsorbed in the liquid. To compute the number of moleculesabsorbed in the liquid at the current integration time t, the Henry'slaw (Eq. (19)) is the starting point. The molar concentration getssubstituted with the number concentration for the species n, (Eq.(29)), and the value of Henry's constant is adjusted by dividing it toAvogadro's number in an effort to reduce the computational time(Fig. 2).

In Eq. (29), VL represents the volume of the liquid phase (cm3)and Nt

nL is the number of molecules present in the liquid after thecurrent integration step. This number can be expressed as the sum

Fig. 9. SO2 removal efficiency function of dose and humidity at different initial NOconcentration.

between the already existing number of molecules absorbed in theliquid phase ðNt�1

nL Þ and the freshly absorbed molecules ðDLnÞ;

computed according to Eq. (30) (Fig. 2).Thus the concentration of the species in the liquid phase should

be computed using Eq. (31). For the right part of Henry's law, thepartial pressure of the gas molecules can be expressed using Eq.(32), where Nt

nG is the number of molecules of species n in the gasphase at time t, Kgas stands for the total number of molecules in thegas phase and psystem is pressure of the system, set at 1 atm.

Going back to Henry's law, substituting and rearranging, thenumber of molecules freshly absorbed in the liquid is computedusing Eq. (33) (Fig. 2).

3.4. Dissociation phenomena

With the number concentrations of the main componentsdetermined from the previous step, a mass and charge balance iswritten in the form of a system of 15 non-linear equations, solvedusing Matlab's built e in routine fsolve. The concentrations of thespecies are adjusted one final time both in gas and liquid and thestiff differential equation solver passes to the next integration step(Fig. 2).

4. Results and discussion

The simulations of the proposed mathematical model werecompared against the experiments detailed in Ref. [9], who per-formed a series of pilot scale tests in order to develop an empiricalmodel for the EBFGT. The selected experimental conditions arepresented in Table 1, keeping in mind that the experiments wereperformed using double stage irradiation e thus doubling the re-action time.

The model shows a good prediction capability, see Figs. 3 and 4,with a mean error of 8.3% in the case of NO and 4.1% for SO2. Thecomparison between the model predictions and the experimentalresults obtained by Ref. [9] shows that the mathematical model isable to predict in a consistent and accurate manner the behavior ofsulfur and nitrogen oxides when subjected to electron beam irra-diation (Table 2).

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e12611260

Bothmodeling and experimental results show that in the case ofnitrogen oxide a steep decrease in irradiation dose is mirrored by asimilar drop in the removal efficiency (especially in the case ofsimulation 6). Moreover, the increase of the irradiation dose abovethe level of 10.2 kGy has only a marginal effect on the removalefficiency for both pollutants, as seen for the tenth experiment. Theinitial concentration of nitrogen oxide and the humidity percentshow marked effects on the overall efficiency of the process; themodel being in good agreement with the experimental findings edisplaying improved removal at higher humidity values (experi-ment 1 vs experiment 4) and lower performances for high NOconcentrations.

The best agreement between the simulation results and theexperimental data are registered for the third simulation, showing83.4% removal efficiency for sulfur dioxide, against 81% reported forthe experiment, and 84.7% for nitrogen oxide, against 82.1% ob-tained in the experiment; the results obtained using the empiricalmodel proposed in the original work were 81.1% and 76.5%respectively.

The nitrogen oxide and sulfur dioxide are removed with com-parable efficiencies from the flue gas, mainly due to the high irra-diation rate and suitable water vapor content of the gases. Therelatively small removal efficiency for SO2 (efficiencies as high as95% have been reportedly obtained in industrial installations) isexplained by the reduced residence time in the irradiation cham-ber, which diminishes the contribution of the thermo-chemicalreaction pathway.

4.1. Sensitivity analysis

In order to thoroughly investigate the sensitivity of the mathe-matical model, a fractional factorial white experiment was pro-posed, using the experimental conditions for which our model bestmatched the experimental data (see Table 2, experiment 3). Theselected parameters are the absorbed dose, the humidity and theinitial NO concentration and their combination for the additionalsimulations are presented in Table 3. Due to the lack of reliabletemperature e absorbed dose dependencies in the open literature,the temperature was disregarded as parameter in the whiteexperiment we envisaged to study the sensitivity of our model tothe main operating parameters.

The sensitivity analysis results are presented in Table 4 in termsof relative deviations q, which are computed using the relation(34):

q ¼ pm � pref

pref(34)

where pm represents the modified value of the parameters oryields, while pref stands for the reference values.

The results of this white experiment show that at higher levelsof irradiation, higher removal efficiencies of NOx and SO2 are ob-tained. In accordance with literature data, our model predicts thatthe sulfur dioxide is affected to a lower degree (see Fig. 5) than thenitrogen oxide. For sulfur dioxide high removal efficiencies areobtained using doses as low as 4e6 kGy; the removal efficiencyreaching a plateau for doses increased above this level. Overall, thebehavior of sulfur dioxide is only slightly affected by the changes inthe operating conditions, see Table 4: the highest sulfur dioxideremoval efficiency was registered for high humidity, irradiationdose and initial NO concentration (84.2%) while the minimumremoval efficiency was 82.3%.

In contrast, the removal efficiency for NO has a significantsensitivity to these operating parameters, as depicted in Table 4. Itsignificantly improved by the increase in the absorbed irradiation

dose, as seen in Fig. 6. For the irradiation dose of 12.2 kGy, theremoval efficiency has values above 85% in all cases while for thelower doses, efficiencies as low as 63e65% are obtained. The higherirradiation dosage promotes the formation of free radicals withgreat oxidizing capacity which in turn favor a higher NO removalefficiency.

Similarly, the increase in the humidity content of the flue gasaids the formation of hydroxyl free radicals during the primary andsecondary radiolysis phenomena, accounting for the increase in theremoval rate of nitrogen oxide, depicted in Fig. 7. In addition to this,the increase of humidity promotes the nucleation associated phe-nomena and enhances the rate of the physico-chemical processesin the liquid phase, slightly improving the sulfur dioxide removalprocess as shown in Fig. 8.

The NO initial concentration is also a significant factor affectingthe removal efficiencies of the gaseous pollutants, presented inFigs. 9 and 10. It has been proved that lower initial concentrationsof nitrogen oxide have a positive impact on the removal of nitrogenoxide: a lower initial number of NO molecules leads to a higherefficiency for the interactions between them and the oxidizingradicals responsible for their removal, resulting in a better perfor-mance for the NO abatement. However, the sulfur dioxide's removalis negatively impacted as the pollutants interact with each otherduring the irradiation treatment and the decrease in the initial NOconcentration is followed by a decrease in the rate of these mo-lecular interactions.

5. Conclusions

The results obtained from the proposed new mathematicalmodel are in good agreement with published experimental datafrom literature. The model predicts with good accuracy the per-formances obtained experimentally for a relatively large array ofoperating conditions: in the majority of cases the departure modele experiment is within the experimental error range. Moreover, themodel is more accurate in predicting the sulfur dioxide behavior, asits removal pathway, despite being more complex, involves fewerradio-chemical reactions.

In the best case scenario, the predicted nitrogen and sulfur ox-ides' removal efficiencies are very similar to those obtainedexperimentally for a residence time of 4.11 s and an irradiation doseof 10.2 kGy being closer than those predicted by the empiricalmodel in the case of nitrogen oxide. Nitrogen oxide's slightly betterremoval can be explained by the low initial concentration of thispollutant and the high irradiation rate.

The factorial white experiment has proved the capacity of thisnew mathematical model to capture the sensitivity of the process,showing that both these parameters have a marked effect on theremoval efficiency of the nitrogen oxides: even small positive var-iations in initial pollutant concentration (in the range of tens ofppm) lead to significantly poorer performance for the process, ingood agreement with the experiments.

The increase in irradiation dose and humidity content have anotable beneficial effect on the abatement of nitrogen oxide fromflue gases, the former being almost entirely removed from the gasin the most favorable scenario (high humidity and irradiation doseand low initial concentration).

However, increasing the irradiation dose has a negative effect onthe energy consumption of the process and may lead to mainte-nance problems for the accelerators in the long-run. In addition tothis, the water vapor content reduces the temperature of the fluegases and poses problems for the equipment, both factors leadingto greater operating and investment costs.

The sulfur dioxide's removal efficiency shows small improve-ments with the increase of irradiation dose and humidity content of

V. Gogulancea, V. Lavric / Applied Thermal Engineering 70 (2014) 1253e1261 1261

the flue gases. The removal of sulfur dioxide is negatively impactedby the addition of a less than stoichiometrical quantity of ammonia,the small nitrogen oxide initial concentration and the relativelyshort residence time.

The new mathematical model proposed for characterizing theabatement of sulfur and nitrogen oxides can predict in a consistentmanner the overall process efficiency of the irradiation beamtreatment for flue gases while showing appropriate sensitivityagainst the main operating parameters.

Appendix A. Supplementary material

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.applthermaleng.2014.05.046.

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