Research Article Kinetic Modeling of a Heterogeneous

Research ArticleKinetic Modeling of a Heterogeneous Fenton OxidativeTreatment of Petroleum Refining Wastewater

Diyarsquouddeen Basheer Hasan12 Abdul Aziz Abdul Raman1

and Wan Mohd Ashri Wan Daud1

1 Department of Chemical Engineering Faculty of Engineering University of Malaya 50603 Kuala Lumpur Malaysia2 National Research Institute for Chemical Technology PMB 1052 Zaria Nigeria

Correspondence should be addressed to Abdul Aziz Abdul Raman azizramanumedumy

Received 28 August 2013 Accepted 1 December 2013 Published 29 January 2014

Academic Editors H Kazemian and I Ortiz

Copyright copy 2014 Diyarsquouddeen Basheer Hasan et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The mineralisation kinetics of petroleum refinery effluent (PRE) by Fenton oxidation were evaluated Within the ambit of theexperimental data generated first-order kinetic model (FKM) generalised lumped kinetic model (GLKM) and generalized kineticmodel (GKM) were tested The obtained apparent kinetic rate constants for the initial oxidation step (1198961015840

2) their final oxidation

step (11989610158401) and the direct conversion to endproducts step (1198961015840

3) were 1012 378 and 024minminus1 for GKM 098 098 and nil minminus1

for GLKM and nil nil and gt0005minminus1 for FKM The findings showed that GKM is superior in estimating the mineralizationkinetics

1 Introduction

Petroleum Refinery Effluent (PRE) is refractory wastewatercomposing of complex aromatics organic and inorganicconstituents [1] Pollutants from refineries have been iden-tified as highly toxic and comparatively more refractory tonatural degradation compared to other industrial streams[2 3] There are literature reports on the treatment of thiscategory of wastewater by the traditional processes namelycoagulation flocculation membrane adsorption and others[4ndash6] However the biological process is the most widelyused on industrial scale [1] Generally these processes are notideal as they only succeed in contaminants transfer from onephase to another or partially degrade PRE [2 7] Among theproblems of these conventional methods are high treatmentand disposal cost of the produced sludge and high electricalconsumption due to use of UV lamps and pumps [4 8]

A treatment method proven to be effective in treat-ment of varied refractory-containing organic wastewaters isAdvanced Oxidation Processes (AOPs) [2 3 9] Basicallythe efficiency of the oxidative processes is driven by highlyreactive free hydroxyl radicals ( ∙OH) which are generated in

situ [10 11] In this regard Fenton and Fenton-like oxidationwhich fall under the category of AOPs have been wellproven to effectively mineralize and degrade a variety ofrefractory organics in water [10 12ndash14] Fenton oxidativeprocesses merit among others as they do not produce anytoxic substances in water environment [12] In additionthe process is commonly used due to the simplicity of theequipment safe operation minimal sludge generation highorganic destruction efficiency and readily available reagents[3 15ndash17] ∙OH is generated by decomposition of hydrogenperoxide with a transition metal catalyst in Fenton oxidativeprocesses [18] Fenton reactions are complex but it can berepresented with a cyclic loop starting with oxidation offerrous iron(II) to ferric iron(III) and closing with reductionof iron(III) to iron(II) by the same hydrogen peroxide [19]

Generally iron ions at acidic conditions are mostlyemployed In the case of utilizing Fe2+ as the catalyst sourcethe process is referred to as classical Fenton oxidation Onthe other hand when other transition metals are used theoxidation becomes Fenton-like Notable transition metalsused are Fe2+ Cu2+ Mn2+ and Ag+ However classicalFenton oxidation is widely adopted as Fe2+ shows superior

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 252491 8 pageshttpdxdoiorg1011552014252491

2 The Scientific World Journal

catalytic activity in comparison to the other transition metals[20] However a form of heterogeneous Fenton-like systemthat uses zerovalent nanoparticles iron (nZVI) catalysts(Fe0) has been found to be efficient in the remediation ofpolluted wastewater This is mainly due to their large specificsurface area high surface reactivity and ability to penetrateinto zones that are inaccessible to microsize solid catalystsThis may account for the observed improved mineralisationefficiency and biodegradability of Fe0 over Fe2+ reported byKhan and co-workers [21]

Despite numerous literature related to Fenton oxidationof recalcitrant waste streams data is scarce on its applicationto PRE treatment Specifically the literature reports arelimited to those completed by Coelho et al [22] and recentlyby our group [23] However the process kinetics were notaddressed in both works This is understandable consideringthat regardless of abundant research on Fenton reaction thereaction mechanism and kinetics of Fenton reaction haveseldom been investigated in detail [24] The study of processkinetics is very significant and a key component in the designof industrial units [13] Therefore a study of PRE Fentonoxidation kinetics would provide a guide on application ofFenton oxidation Based on the literature review there is anoverall lack of information on kinetics of PRE mineralisationby Fenton oxidation or other advanced oxidation processesThus establishing a kinetic model is very important

The specific objective of this study is to investigate theFenton oxidative mineralisation kinetics of PRE in the con-text of providing insight into the reaction process and exper-imentally establishing themost suitablemodel that representsthe treatment process nZVI heterogeneous catalyst (Fe0) wasemployed at the optimised parameters for the mineralisationof the PRE [23] Kinetic studies were conducted on the basisof the mineralisation pathway suggested in the literature

2 The Fenton Equations

There are different postulations to the number of groupsforming themain Fenton oxidation [25]Howevermost stud-ies have reported that the generally accepted Fenton oxidativereactions involve few main reactions which are divided intotwo groups First the reaction of inorganic species such asFe0 Fe2+ Fe3+ H

2O2 ∙OH and HO∙

2(reaction (1)) [11]

Fe0 +H2O2+ 2H+ 997888rarr Fe2+ + 2H

2O

Fe2+ +H2O2997888rarr Fe3+ +OHminus + ∙OH

Fe3+ +H2O2997888rarr Fe2+ +HO∙

2+H+

Fe3+ +HO∙2997888rarr Fe2+ +O

2+H+

(1)

Second the reaction of reactive species in the first groupwith the organic species (comprising of the contaminants andbyproducts) (reaction (2))

RH + ∙OH 997888rarr R∙ +H2O

R∙ + Fe3+ 997888rarr R∙ + Fe2+

R∙ + Fe2+ 997888rarr R∙ + Fe2+

R∙ +H2O2997888rarr ROH + ∙OH

R∙ +O2997888rarr ROO∙

(2)

Other reactions such as side and scavenging reactionsare depicted in reaction (3) [10 26 27] These reactions areknown to always coexist along with the main reactions [12]However they are assumed to have negligible influence on thereaction system in stoichiometrically conducted experiments[23]

H2O2+∙OH 997888rarr H

2O +HO∙

2

HO∙2+∙OH 997888rarr H

2O +O

2

∙OH+ ∙OH 997888rarr H2O2

Fe2+ + ∙OH 997888rarr Fe3+ +OHminus

(3)

Fenton reactions have been extensively discussed in theliterature [25] and the basic assumption of the modelsgenerated from these reactions can be summarised as

(i) solution in the batch reactor is completely mixed(ii) temperature is constant(iii) value of pH decreases slightly during the process

However as the variationmainly affects the Fe speciesand Fe2+ is the dominant form of Fe(II) species at pH26ndash30 these ranges are not affected by the pHchangeand thus these effects are neglected

(iv) fluctuation in concentrations of H2O2can be safely

assumed to be constant This is against the backdropthat ∙OH is a highly reactive free radical with anextremely short lifetime of nanoseconds When thecatalyst concentration within the system exceeds theoxidant there is scavenging reaction from H

2O2and

H2OThe hydroxyl radical which is very active is the

main radical and it attacks all organic substances inthe wastewater The other radicals (H

2O2 HO∙2 and

O∙2) are unable to degrade the contaminant

3 Experimental Section

31 Materials Chemicals used were of analytical gradesand used without further purification They were hydrogenperoxide (H

2O2 30 wt) sulfuric acid (H

2SO497) sodium

hydroxide (NaOH 50ww) and sodium borohydride(NaBH

4) fromMerck chemical company and ferrous sulfate

(FeSO4sdot7H2O) was used from Fisher Scientific Sdn Bhd

Malaysia FeSO4sdot7H2O and NaBH were used for the nZVI

preparation and the Fe0 obtainedwas consumed immediatelyNaBH

4was used to synthesise the catalyst at room tempera-

ture (23∘C) under Ar protection according to the proceduresdescribed by Cheng et al [28] and Xu andWang [29] Brieflythe protocol involved adding 100mL of aqueous solutionof NaBH

4(20mM) to 100mL of FeSO

4sdot7H2O (4mM)

The Scientific World Journal 3

The addition was done dropwise with constant violent stir-ring in a three-necked flask A stirring time of 90minutes wasallowed Then the nZVI deposited was washed thrice withdeionised water and vacuum dried

32 Fenton Experiment Themineralisation and degradationwere conducted at temperature of 20∘C and atmosphericpressure in a 5 L batch reactor The wastewaterrsquos initial pHwas adjusted to 3 using NaOH (2M) or H

2SO4(2M) A fixed

concentration of Fe2+ (Fenton oxidation) or Fe3+ (Fenton-likeoxidation) was transferred to the reactor containing 4 L of thePRE To initiate the reaction H

2O2was introduced under

constant stirring at 200 rpm (to homogenise the mixture)Then 125mL of the sample was periodically withdrawn atpredetermined time interval to follow the extent of minerali-sation and degradationwith timeThereafter the reactionwasterminated by spiking the sample with NaOH (2M) whichadjusted the pH to 85 plusmn 02 This consequently resulted inprecipitating iron as Fe(OH)

3which would then be filtered

using a 045 120583mfilter and subsequently analysed for the CODand TOCThe batch reactions were duplicated and the resultsobtained suggested reproducibility within an error range of3

33 Analytical Methods The chemical oxygen demand(COD) and the total organic carbon (TOC) were determinedin the liquid phase of the sampled aliquots by the closedreflux method and oxidative combustion respectively Forthe COD Hach method number 8000 was adopted wheresamples were added to Hach vials containing potassiumdichromate solution in an acid medium and digested ina HACH DR200 reactor for 120min This action reducesthe dichromate ions to chromic ions and subsequently theCOD is read from absorbance measurements in a HACHDR890 colorimeter The interferences of H

2O2with COD

measurements were eliminated by destroying residual H2O2

in the treated solution through catalase addition after the pHadjustment

TOC was measured using a Shimadzu TOC-V CSHanalyzer with an infrared detector Biochemical oxygendemand (BOD) was measured after 5 days of incubation ofa microorganism culture according to standard methods

4 Results and Discussion

41 Mineralization Profile The extent of mineralisation(TOC reduction) is considered themost suitable tomodel thekinetic reaction in a myriad wastewater TOC indicates theextent of conversion of carbon and heteroatoms componentsin organic compounds to inorganic species The procedure ismuch more accurate than COD as it measures the amountof the carbon converted directly In addition TOC measure-ment is not affected by (i) oxidation state of the organicmatter (ii) organically bound elements (nitrogen hydrogenand inorganics) and (iii) presence of organics difficult tobe oxidized completely [30] On the other hand oxygendemands determined by COD tests do not adequately reflectthe actual oxygen requirements for oxidation in wastewater

with myriad contaminants due to (i) the assumption that allthe organic materials can be oxidized by a strong oxidiz-ing agent under acidic conditions by COD proceduremdashtheassertion is not always valid as COD tests have limitation ofincomplete oxidation of some aromatic compounds and (ii)contribution to higher COD values due to easily oxidisablecompounds [31] Typically PRE contains reduced substancessuch as ferrous iron sulphides and sulphites which areknown to be easily oxidised

For mineralization conditions the ratio between hydro-gen peroxide and organic matter is very significant as theextent of oxidation depends on this parameter while theoxidation rate is determined by the initial iron concentration[27] The ratio yielding the lowest concentration of oxidantwas chosen in this study to allow for consumption of thereagent and to negate the need for quenching the reagentas much concentration of H

2O2might adversely affect a

subsequent biological process Thus the reagent is graduallyreduced after a batch of chemical dosing along with reactiontime andmost of the reagents would be consumed eventually[12] In addition the most effective dosing approachmdashsingledosing was adopted in the study Excessive oxidant was usedin this method andmuch of it was left available to be attackedby hydroxyl radicals [12]

As PRE is known to contain varied benzoic groupsthe appreciable mineralization observed with nZVI can beattributed to effective mineralization of nitrobenzene (NB)group of which oxidation generates a significant amount of13-dinitrobenzene (13-DNB) [32]

This byproduct of NB nitration with nitro radicals( ∙NO

2) increases the biodegradability of wastewater This

enhanced treatment is ascribed to two electron-deficientndashNO2groups and subsequent mineralization of the generated

refractory intermediates of NB hydroxylation [32]

42 Mineralisation Kinetics

421 First-Order Kinetic Model (FKM) The simplest modelFKM (5) was examined All the contaminants in PRE areassumed to be mineralized in only one step where the OHaddition results in the final products (CO

2+H2O)

PRE1198961015840

3

997888rarr CO2+H2O (4)

where 11989610158403is the apparent kinetic constant

minus119903TOCPRE= minus119889119862TOCPRE

119889119905= 1198961015840

1119862TOCPRE (5)

Based on the plot of minusln (TOCTOC119900) against time (Fig-

ure 1(a)) the apparent first-order kinetic rate constant (11989610158401)

and the corresponding correlation coefficients (1198772) of 09645between the experimental and predicted data (Table 1) it isobserved that the model could well be used to predict themineralization processThus the general assumption that themodel will not fit ab initio due to the limitation imposed bythe composition of the wastewater appears irrelevant in ourcase (for reasons discussed in Section 422)


0 50 100 150

00

02

04

06

08

Time (min)

minus02

minusln

(TO

CTO

C o)

(a)

00 02 04 06 08

00

02

04

06

08

minus02

FOKM experimental minusln (TOCTOCo)

FOKM

pre

dict

edminus

ln(T

OC

TOC o

)

(b)

Figure 1 Plots for FKM (a) kinetic and (b) predicted versus experimental

Although the 1198772 and the good agreement between thepredicted versus experimental plot (Figure 1(b)) suggestexplaining the process by the FKM the limitation imposedcalls for further exploring other robust models in addressingkinetic mineralisation of such a complex system with a vastdiversity of possible reaction pathways [13] Furthermoreas the mineralisation of PRE is attained in multiple stagesinvolving an initial oxidation step leading to transitional con-version of the contaminants to intermediates and followedby subsequent mineralization of the intermediates to theproducts [9] a simple one-step model may not be sufficientThere is need to explore other models

422 Generalized Lumped Kinetic Model (GLKM) Alumpedkinetic model that allows insight into the contribution ofPRErarr intermediates step which FKM does not account foris the simple Generalized Lumped Kinetic Model (GLKM)The simplicity of the model relates to its assumption ofnegligible influence of PRE to CO

2+H2O step To appreciate

the need for investigating the intermediates contribution webriefly looked at this step It involves addition of the produced∙OH to the aromatic heterocyclic rings and unsaturatedbonds of alkenes or alkynes [18] thereby enhancing thedegradability of aliphatic compounds However byproductsare generated along time through partial mineralisation ofthe other aromatic substances (Figure 1)These intermediatesare the results of collapse of aromatic ring during hydrox-ylation (mineralisation) which yields low molecular-weightcarboxylic acids [9 11 33]

All of the intermediates that could possibly be producedare lumped into INT the parent organic substances as PREwhile the final mineralization products are CO

2+ H2O

[9 13] The generalized degradation schemes and kineticrate constant are shown in Figure 2 with 1198961015840

1 11989610158402 and 1198961015840

3

as the apparent first-order kinetic rate constants for theinitial oxidation step the final oxidation step and the directconversion to endproducts step respectively

Table 1 FKM GLKM and GLKM kinetic rate constants and statis-tical data

Parameter Kinetic modelsFKM GLKM GLKM

Kinetic rate constants1198961015840

1(minminus1) na 09836 1012481198961015840

2(minminus1) na 09791 024441198961015840

3(minminus1) 00045 ng 37852

Statistical indicators1198772 09650 09650 097361198772

adj 09621 09621 09660SSE 00257 00257 00104RMSE 00463 00463 00323

na not applicable ng negligible

Equations (6) and (7) describe the degradation of PREand intermediates respectively


119889119905= (1198961015840

1+ 1198961015840

3) 119862TOCPRE

(6)

minus119903TOCINT= minus119889119862TOCINT

119889119905= 1198961015840

1119862TOCINT

minus 1198961015840

1119862TOCPRE (7)

As the mineralization occurs through the transitionalconversion to intermediates followed by subsequent min-eralization of the intermediates to the products 1198961015840

3is then

supposedly to be much smaller than 11989610158401or 11989610158402and thus

neglected [9 34] Hence by rearranging (6) and (7) theGLKM becomes

TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158403+ 11989610158402

119890minus1198961015840

2119905minus1198961015840

2

11989610158401+ 11989610158403+ 11989610158402

119890minus(1198961015840

2+1198961015840

2)119905 (8)

The logarithmic form of (9) becomes the following

ln TOCTOC119900

= ln1198961015840

1

11989610158402

minus ln (11989610158401+ 1198961015840

2) 119905 (9)


CO2 + H2O

INT

k998400

1 k998400

2

k998400

3

PRE

Figure 2 Schematic representation of PREmineralization interme-diates and final product

From the plot ln TOCTOC119900versus time (Figure 1)

the reaction rate constants 11989610158401and 1198961015840

2 were found to be

9836 times 10minus2minminus1 and 9791 times 10minus2minminus1 respectively

The computed rate constant values were marginally differentsuggesting that the PRErarr intermediates reaction proceededat the same rate as the intermediatesrarr CO

2+H2O reaction

This result implies that the hydroxylation of the parentorganic contaminants to intermediates cannot be negated

423 Generalized Kinetic Model (GKM) Still the GLKMimposes a limitation to the full prediction of the stagesas seen in the case of this work The contribution fromKRC in FKM is significant and thus the GKM proposed byMartins et al [13] was used to further asses the process Itallows the lumping of these chemical pollutants in additionto computing the direct mineralisation of PRE to CO

2+

H2O step This is a more holistic model as all the steps are

accounted for By rearranging (8) and (9) and taking intoaccount the direct conversion step we obtain

119862TOC119862TOC

119900

=119862TOCPRE

+ 119862TOCINT

119862TOCPRE119900+ 119862TOCINT119900

=119862TOCPRE119900

119862TOC119900

(1198961015840

1

11989610158401+ 11989610158403minus 11989610158402

119890minus1198961015840

2119905

+1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158403minus 11989610158402

119890minus(1198961015840

2+1198961015840

1)119905)

+119862TOCINT119900

119862TOC119900

119890minus1198961015840

2119905

(10)

To further simplify the model recalcitrant intermediatesconcentration at the initial step is assumed to be nil [13]Thusthe integrated and normalized form of (11) becomes

TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158402+ 11989610158403

119890minus1198961015840

2119905minus1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158402+ 11989610158403

119890minus(1198961015840

3+1198961015840

4)119905 (11)

The plot of (11) and the corresponding predicted andexperimental results are depicted in Figure 3

43 Goodness-of-Fit Statistics Four descriptive statisticalindicators were used to appraise the prediction performanceof proposed models and the produced error in account-ing for the kinetic reaction constants and assessing the fitbetween the experimental data from the models evaluated

The examined indicators were the sum of squares due toerror (SSE) 119877-square adjusted 119877-square and root meansquared error (RMSE) In the case of GKM MATLAB wasemployed (commercial version 71) due to complexity ofthe equation arising from the several constants The curvefitting toolbox was utilised and as Levenberg-Marquardt andGauss-Newton algorithms do not handle bound constraintstrust-region algorithm was implemented

Based on the results summary (Table 1) it is seen thatthere are very small deviations in descriptive performanceindices of all the models GKM only marginally variedwith FKM and GLKM and demonstrated a slightly superiorpredictive performance on the estimation of mineralizationkinetics Based on the 1198772 statistic measure it is evident thatthe fit successfully accounted for greater proportion of vari-ance as all themodels explainedasymp96 of the total variation inthe data Only 35 and 26 of the total variations were notexplained by FKMGLKM and GKM respectively Howeveras GKM contains more coefficients than the GKLM andFKM adjusted R-square statistic a generally accepted bestindicator of the fit quality in the comparison of models withthose that are nested is used Moreover as the 1198772 measuredis not an unbiased estimator of the population correlationcoefficient the effect is corrected employing the adjustedcorrelation coefficient Again similar trend was observed aswith the 1198772 with GKM being slightly better Results for SSEshow that the total deviation of the response values fromthe fit-to-the response values measured was acceptable Thelowest values of SSE (00104) for GKM against the slightlyhigher values of SSE (00257) for FKMGLKM indicated thatthe former model performed better This indicated that themodel had a smaller random error component and that the fitwould be more useful for prediction Lastly the fit standarderror and the standard error of the regression root meansquared error (RMSE) and the standard deviation of therandom component in the data were comparatively betterin the case of GKM with RMSE of 00323 compared toFKMGLKM with RMSE of 00463

In summary the results suggest that all the modelsadequately describe the kinetics However the limitationimposed on FKM and GLKM does not translate to the real-world description of the process For instance mineralizationwas very fast with respect to the other steps as the kineticrate constant (1198961015840

1) was 1012minminus1 This clearly indicates that

the initial oxidation step leading to transitional conversionof contaminants to intermediates is significantly yet notcaptured in its entirety in FKM (0minminus1) and in the caseof GLKM a mere 098minminus1 was computed (representingonly 10 of the actual value) This was expected as aromaticdegradation which is known to be very fast in contrast toaliphatic degradation [11] In the same vain rate constantof the intermediates mineralization to the final productspreceded fast too (1198961015840

2) Based on GKM the rate was asymp40

higher than that obtained in GLKM and not obtainable usingFKM Finally the direct conversion of PRE to endproductsstep (1198961015840

3) which was not possible to be captured was found

to be appreciable In contract to 45 times 10minus3minminus1 estimated


0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)

Figure 3 Plots for GKM (a) kinetic and (b) predicted versus experimental

by FKM the actual rate constant was 02444minminus1 approx-imately 98 higher than the value obtained by FKM Itis worth noting that mineralization would not have beenpossible at the rate computed from FKM especially whensteady mineralization was observed within 180 minutes ofoxidative treatment period and for fast PRE mineralization

The use of generalised models becomes necessary incertain reactions This assertion has been collaborated byseveral researchers who have elucidated that use of FKMcannot adequately describe the kinetics in systems beingcontinuously fed with H

2O2[12 35 36] for example mon-

itoring Fenton oxidation in a semicontinuous reactor wherethe overall amount ofH

2O2is distributed as a continuous feed

upon the reaction time [37]Additionally reactions not appropriately described by

FKMhave been addressed by subdividing the reaction periodinto two or three phases to fit the experimental data usingthe first-order model separately with different values ofkinetic constant (119896) [38] or use mixed first- and second-order kinetics [39] This approach may well simulate theexperimental data mathematically but not chemically [12]

This work provides useful information on complexwastewater treatment by heterogeneous nZVI Fenton systemspecifically PRE

5 Conclusions

The study presented the kineticmodeling of a nanozerovalent(nZVI) heterogeneous Fenton oxidative mineralization ofpetroleum refinery effluent (PRE) The oxidation specificvariable data was generated at constant pH of 30 and fixedratios of 2 and 20 for H

2O2 PRE andH

2O2 Fe0 respectively

The data was fitted to three different models first-orderkinetic model (FKM) generalised lumped kinetic model(GLKM) and generalized kinetic model (GKM)

Based on the results obtained and the four descriptivestatistical indicators used for appraisal of the predictionperformance of proposed models only small deviations

were observed and the data fitted satisfactorily generallyAlthough GKM demonstrated a slightly superior predictiveperformance on the estimation of mineralization kineticsin comparison to FKM and GLKM the correspondingpredictive kinetic rate values varied significantly With themost significant step being the initial oxidation step leadingto transitional conversion of contaminants to intermediatesonly 10 of the actual value was captured by GLKM andthe limitation of FKM does not allow for determining thecontribution of this stepThe second fastest stepwas the inter-mediates mineralization to the final products (1198961015840

2) Again

the rate predicted by GLKM was asymp40 lower than the valueobtained in GLKM and naturally not obtainable using FKMConsidering that GKM is able to predict simultaneously allthe steps of PRE hydroxylation it is deemed to be the mostsuitable model

This work provided useful information on complexwastewater treatment kinetics by heterogeneous nZVI Fentonsystem specifically PRE

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful to the University of Malaya HighImpact Research Grant (HIR-MOHE-D000037-16001) fromthe Ministry of Higher Education Malaysia which finan-cially supported this work

References

[1] B H Diyarsquouddeen W M A W Daud and A R Abdul AzizldquoTreatment technologies for petroleum refinery effluents areviewrdquo Process Safety and Environmental Protection vol 89 no2 pp 95ndash105 2011


[2] H Sun X Feng S Wang H M Ang and M O TadeldquoCombination of adsorption photochemical and photocatalyticdegradation of phenol solution over supported zinc oxideeffects of support and sulphate oxidantrdquo Chemical EngineeringJournal vol 170 p 270 2011

[3] M Bayat M Sohrabi and S J Royaee ldquoDegradation of phenolby heterogeneous Fenton reaction using Feclinoptiloliterdquo Jour-nal of Industrial and Engineering Chemistry vol 18 no 3 pp957ndash962 2012

[4] G Zelmanov and R Semiat ldquoPhenol oxidation kinetics inwater solution using iron(3)-oxide-based nano-catalystsrdquoWaterResearch vol 42 no 14 pp 3848ndash3856 2008

[5] L Augulyte D Kliaugaite V Racys et al ldquoMultivariate anal-ysis of a biologically activated carbon (BAC) system andits efficiency for removing PAHs and aliphatic hydrocarbonsfrom wastewater polluted with petroleum productsrdquo Journal ofHazardous Materials vol 170 no 1 pp 103ndash110 2009

[6] M H El-Naas S Al-Zuhair and M A Alhaija ldquoReductionof COD in refinery wastewater through adsorption on date-pitactivated carbonrdquo Journal of Hazardous Materials vol 173 no1ndash3 pp 750ndash757 2010

[7] E C Catalkaya and F Kargi ldquoAdvanced oxidation and min-eralization of simazine using Fentonrsquos reagentrdquo Journal ofHazardous Materials vol 168 no 2-3 pp 688ndash694 2009

[8] J Bandara C Pulgarin and P K J Peringer ldquoChemical (photo-activated) coupled biological homogeneous degradation of p-nitro-o-toluene-sulfonic acid in a flow reactorrdquo Journal ofPhotochemistry and Photobiology A vol 111 no 1ndash3 pp 253ndash263 1997

[9] B Iurascu I Siminiceanu D Vione M A Vicente and AGil ldquoPhenol degradation in water through a heterogeneousphoto-Fenton process catalyzed by Fe-treated laponiterdquo WaterResearch vol 43 no 5 pp 1313ndash1322 2009

[10] C T Benatti C R G Tavares and T A Guedes ldquoOptimizationof Fentonrsquos oxidation of chemical laboratory wastewaters usingthe response surface methodologyrdquo Journal of EnvironmentalManagement vol 80 no 1 pp 66ndash74 2006

[11] D Hermosilla M Cortijo and C P Huang ldquoThe role of ironon the degradation and mineralization of organic compoundsusing conventional Fenton andphoto-FentonprocessesrdquoChem-ical Engineering Journal vol 155 no 3 pp 637ndash646 2009

[12] H Liu X Z Li Y J Leng and C Wang ldquoKinetic modeling ofelectro-Fenton reaction in aqueous solutionrdquo Water Researchvol 41 no 5 pp 1161ndash1167 2007

[13] R C Martins R J G Lopes and R M Quinta-FerreiraldquoLumped kinetic models for single ozonation of phenoliceffluentsrdquoChemical Engineering Journal vol 165 no 2 pp 678ndash685 2010

[14] J M Abdul M Kumar S Vigneswaran and J KandasamyldquoRemoval of metsulfuron methyl by fenton reagentrdquo Journal ofIndustrial and Engineering Chemistry vol 18 no 1 pp 137ndash1442012

[15] A Lopez G Mascolo A Detomaso G Lovecchio and GVillani ldquoTemperature activated degradation (mineralization) of4-chloro-3-methyl phenol by Fentonrsquos reagentrdquo Chemospherevol 59 no 3 pp 397ndash403 2005

[16] M S Lucas and J A Peres ldquoDecolorization of the azo dyeReactive Black 5 by Fenton and photo-Fenton oxidationrdquo Dyesand Pigments vol 71 no 3 pp 236ndash244 2006

[17] M Karatas Y A Argun and M E Argun ldquoDecolorization ofantraquinonic dye Reactive Blue 114 from synthetic wastewater

by Fenton process kinetics and thermodynamicsrdquo Journal ofIndustrial and Engineering Chemistry vol 18 no 3 pp 1058ndash1062 2012

[18] E Neyens and J Baeyens ldquoA review of classic Fentonrsquos peroxida-tion as an advanced oxidation techniquerdquo Journal of HazardousMaterials vol 98 no 1ndash3 pp 33ndash50 2003

[19] A Santos P Yustos S Rodrıguez and A Romero ldquoMineraliza-tion lumping kinetic model for abatement of organic pollutantsusing Fentonrsquos reagentrdquo Catalysis Today vol 151 no 1-2 pp 89ndash93 2010

[20] X-R Xu H-B Li W-H Wang and J-D Gu ldquoDegradation ofdyes in aqueous solutions by the Fenton processrdquo Chemospherevol 57 no 7 pp 595ndash600 2004

[21] E Khan W Wirojanagud and N Sermsai ldquoEffects of irontype in Fenton reaction on mineralization and biodegradabilityenhancement of hazardous organic compoundsrdquo Journal ofHazardous Materials vol 161 no 2-3 pp 1024ndash1034 2009

[22] A Coelho A V Castro M Dezotti and G L SantrsquoAnnaJr ldquoTreatment of petroleum refinery sourwater by advancedoxidation processesrdquo Journal of Hazardous Materials vol 137no 1 pp 178ndash184 2006

[23] B H Diyarsquouddeen A R Abdul Aziz and W M A WDaud ldquoOxidative mineralisation of petroleum refinery effluentusing Fenton-like processrdquo Chemical Engineering Research andDesign vol 90 p 298 2012

[24] M-W Chang and J-M Chern ldquoDecolorization of peach redazo dye HF6 by Fenton reaction Initial rate analysisrdquo Journal ofthe Taiwan Institute of Chemical Engineers vol 41 pp 221ndash2282010

[25] Y DuM Zhou and L Lei ldquoKinetic model of 4-CP degradationby FentonO

2systemrdquo Water Research vol 41 no 5 pp 1121ndash

1133 2007[26] V Kavitha and K Palanivelu ldquoThe role of ferrous ion in Fenton

and photo-Fenton processes for the degradation of phenolrdquoChemosphere vol 55 no 9 pp 1235ndash1243 2004

[27] A Bach H Shemer and R Semiat ldquoKinetics of phenolmineralization by Fenton-like oxidationrdquoDesalination vol 264no 3 pp 188ndash192 2010

[28] R Cheng J-l Wang andW-X Zhang ldquoComparison of reduc-tive dechlorination of p-chlorophenol using Fe0 and nanosizedFe0rdquo Journal of Hazardous Materials vol 144 no 1-2 pp 334ndash339 2007

[29] L Xu and J Wang ldquoA heterogeneous Fenton-like system withnanoparticulate zero-valent iron for removal of 4-chloro-3-methyl phenolrdquo Journal of Hazardous Materials vol 186 no 1pp 256ndash264 2011

[30] S Navalon M Alvaro and H Garcia ldquoHeterogeneous Fentoncatalysts based on clays silicas and zeolitesrdquo Applied CatalysisB vol 99 no 1-2 pp 1ndash26 2010

[31] A E Papadopoulos D Fatta and M Loizidou ldquoDevelopmentand optimization of dark Fenton oxidation for the treatmentof textile wastewaters with high organic loadrdquo Journal ofHazardous Materials vol 146 no 3 pp 558ndash563 2007

[32] B-C Jiang Z-Y Lu F-Q Liu et al ldquoInhibiting 13-dinitrobenzene formation in Fenton oxidation of nitrobenzenethrough a controllable reductive pretreatment with zero-valentironrdquo Chemical Engineering Journal vol 174 pp 258ndash265 2011

[33] K Gai ldquoAnodic oxidation with platinum electrodes for degra-dation of p-xylene in aqueous solutionrdquo Journal of Electrostaticsvol 67 no 4 pp 554ndash557 2009


[34] B H Diyarsquouddeen A R Abdul Aziz WM AW Daud andMHChakrabarti ldquoPerformance evaluation of biodiesel fromuseddomestic waste oils a reviewrdquo Process Safety and EnvironmentalProtection vol 1 p 431 2012

[35] S Malato J Caceres A Aguera et al ldquoDegradation of imida-cloprid in water by photo-fenton and TiO

2photocatalysis at a

solar pilot plant a comparative studyrdquo Environmental Scienceand Technology vol 35 no 21 pp 4359ndash4366 2001

[36] B Gozmen M A Oturan N Oturan and O Erbatur ldquoIndirectelectrochemical treatment of bisphenol A in water via electro-chemically generated Fentonrsquos reagentrdquo Environmental Scienceand Technology vol 37 no 16 pp 3716ndash3723 2003

[37] J A Zazo J A Casas A F Mohedano and J J RodriguezldquoSemicontinuous Fenton oxidation of phenol in aqueous solu-tion A kinetic studyrdquoWater Research vol 43 no 16 pp 4063ndash4069 2009

[38] W Chu C Y Kwan K H Chan and S K Kam ldquoA study ofkinetic modelling and reaction pathway of 24-dichlorophenoltransformation by photo-fenton-like oxidationrdquo Journal of Haz-ardous Materials vol 121 no 1ndash3 pp 119ndash126 2005

[39] F Emami A R Tehrani-Bagha KGharanjig and FMMengerldquoKinetic study of the factors controlling Fenton-promoteddestruction of a non-biodegradable dyerdquo Desalination vol 257no 1ndash3 pp 124ndash128 2010

International Journal of

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VLSI Design



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DistributedSensor Networks



catalytic activity in comparison to the other transition metals[20] However a form of heterogeneous Fenton-like systemthat uses zerovalent nanoparticles iron (nZVI) catalysts(Fe0) has been found to be efficient in the remediation ofpolluted wastewater This is mainly due to their large specificsurface area high surface reactivity and ability to penetrateinto zones that are inaccessible to microsize solid catalystsThis may account for the observed improved mineralisationefficiency and biodegradability of Fe0 over Fe2+ reported byKhan and co-workers [21]

Despite numerous literature related to Fenton oxidationof recalcitrant waste streams data is scarce on its applicationto PRE treatment Specifically the literature reports arelimited to those completed by Coelho et al [22] and recentlyby our group [23] However the process kinetics were notaddressed in both works This is understandable consideringthat regardless of abundant research on Fenton reaction thereaction mechanism and kinetics of Fenton reaction haveseldom been investigated in detail [24] The study of processkinetics is very significant and a key component in the designof industrial units [13] Therefore a study of PRE Fentonoxidation kinetics would provide a guide on application ofFenton oxidation Based on the literature review there is anoverall lack of information on kinetics of PRE mineralisationby Fenton oxidation or other advanced oxidation processesThus establishing a kinetic model is very important

The specific objective of this study is to investigate theFenton oxidative mineralisation kinetics of PRE in the con-text of providing insight into the reaction process and exper-imentally establishing themost suitablemodel that representsthe treatment process nZVI heterogeneous catalyst (Fe0) wasemployed at the optimised parameters for the mineralisationof the PRE [23] Kinetic studies were conducted on the basisof the mineralisation pathway suggested in the literature

2 The Fenton Equations

There are different postulations to the number of groupsforming themain Fenton oxidation [25]Howevermost stud-ies have reported that the generally accepted Fenton oxidativereactions involve few main reactions which are divided intotwo groups First the reaction of inorganic species such asFe0 Fe2+ Fe3+ H

2O2 ∙OH and HO∙

2(reaction (1)) [11]

Fe0 +H2O2+ 2H+ 997888rarr Fe2+ + 2H

2O

Fe2+ +H2O2997888rarr Fe3+ +OHminus + ∙OH

Fe3+ +H2O2997888rarr Fe2+ +HO∙

2+H+

Fe3+ +HO∙2997888rarr Fe2+ +O

2+H+

(1)

Second the reaction of reactive species in the first groupwith the organic species (comprising of the contaminants andbyproducts) (reaction (2))

RH + ∙OH 997888rarr R∙ +H2O

R∙ + Fe3+ 997888rarr R∙ + Fe2+

R∙ + Fe2+ 997888rarr R∙ + Fe2+

R∙ +H2O2997888rarr ROH + ∙OH

R∙ +O2997888rarr ROO∙

(2)

Other reactions such as side and scavenging reactionsare depicted in reaction (3) [10 26 27] These reactions areknown to always coexist along with the main reactions [12]However they are assumed to have negligible influence on thereaction system in stoichiometrically conducted experiments[23]

H2O2+∙OH 997888rarr H

2O +HO∙

2

HO∙2+∙OH 997888rarr H

2O +O

2

∙OH+ ∙OH 997888rarr H2O2

Fe2+ + ∙OH 997888rarr Fe3+ +OHminus

(3)

Fenton reactions have been extensively discussed in theliterature [25] and the basic assumption of the modelsgenerated from these reactions can be summarised as

(i) solution in the batch reactor is completely mixed(ii) temperature is constant(iii) value of pH decreases slightly during the process

However as the variationmainly affects the Fe speciesand Fe2+ is the dominant form of Fe(II) species at pH26ndash30 these ranges are not affected by the pHchangeand thus these effects are neglected

(iv) fluctuation in concentrations of H2O2can be safely

assumed to be constant This is against the backdropthat ∙OH is a highly reactive free radical with anextremely short lifetime of nanoseconds When thecatalyst concentration within the system exceeds theoxidant there is scavenging reaction from H

2O2and

H2OThe hydroxyl radical which is very active is the

main radical and it attacks all organic substances inthe wastewater The other radicals (H

2O2 HO∙2 and

O∙2) are unable to degrade the contaminant

3 Experimental Section

31 Materials Chemicals used were of analytical gradesand used without further purification They were hydrogenperoxide (H

2O2 30 wt) sulfuric acid (H

2SO497) sodium

hydroxide (NaOH 50ww) and sodium borohydride(NaBH

4) fromMerck chemical company and ferrous sulfate

(FeSO4sdot7H2O) was used from Fisher Scientific Sdn Bhd

Malaysia FeSO4sdot7H2O and NaBH were used for the nZVI

preparation and the Fe0 obtainedwas consumed immediatelyNaBH

4was used to synthesise the catalyst at room tempera-

ture (23∘C) under Ar protection according to the proceduresdescribed by Cheng et al [28] and Xu andWang [29] Brieflythe protocol involved adding 100mL of aqueous solutionof NaBH

4(20mM) to 100mL of FeSO

4sdot7H2O (4mM)




2SO4(2M) A fixed







2O2with COD

















2+H2O)

PRE1198961015840

3

997888rarr CO2+H2O (4)



119889119905= 1198961015840

1119862TOCPRE (5)





0 50 100 150

00

02

04

06

08

Time (min)

minus02

minusln

(TO

CTO

C o)

(a)

00 02 04 06 08

00

02

04

06

08

minus02


FOKM

pre

dict

edminus

ln(T

OC

TOC o

)

(b)







2+ H2O


1 11989610158402 and 1198961015840

3





1(minminus1) na 09836 1012481198961015840

2(minminus1) na 09791 024441198961015840

3(minminus1) 00045 ng 37852


adj 09621 09621 09660SSE 00257 00257 00104RMSE 00463 00463 00323




119889119905= (1198961015840

1+ 1198961015840

3) 119862TOCPRE

(6)


119889119905= 1198961015840

1119862TOCINT

minus 1198961015840

1119862TOCPRE (7)


3is then



TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158403+ 11989610158402

119890minus1198961015840

2119905minus1198961015840

2

11989610158401+ 11989610158403+ 11989610158402

119890minus(1198961015840

2+1198961015840

2)119905 (8)


ln TOCTOC119900

= ln1198961015840

1

11989610158402

minus ln (11989610158401+ 1198961015840

2) 119905 (9)


CO2 + H2O

INT

k998400

1 k998400

2

k998400

3

PRE




2 were found to be



2+H2O reaction



2+



119862TOC119862TOC

119900

=119862TOCPRE

+ 119862TOCINT

119862TOCPRE119900+ 119862TOCINT119900

=119862TOCPRE119900

119862TOC119900

(1198961015840

1

11989610158401+ 11989610158403minus 11989610158402

119890minus1198961015840

2119905

+1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158403minus 11989610158402

119890minus(1198961015840

2+1198961015840

1)119905)

+119862TOCINT119900

119862TOC119900

119890minus1198961015840

2119905

(10)


TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158402+ 11989610158403

119890minus1198961015840

2119905minus1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158402+ 11989610158403

119890minus(1198961015840

3+1198961015840

4)119905 (11)













0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)










5 Conclusions


2O2 PRE andH





2) Again





Acknowledgments


References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2SO4(2M) A fixed







2O2with COD

















2+H2O)

PRE1198961015840

3

997888rarr CO2+H2O (4)



119889119905= 1198961015840

1119862TOCPRE (5)





0 50 100 150

00

02

04

06

08

Time (min)

minus02

minusln

(TO

CTO

C o)

(a)

00 02 04 06 08

00

02

04

06

08

minus02


FOKM

pre

dict

edminus

ln(T

OC

TOC o

)

(b)







2+ H2O


1 11989610158402 and 1198961015840

3





1(minminus1) na 09836 1012481198961015840

2(minminus1) na 09791 024441198961015840

3(minminus1) 00045 ng 37852


adj 09621 09621 09660SSE 00257 00257 00104RMSE 00463 00463 00323




119889119905= (1198961015840

1+ 1198961015840

3) 119862TOCPRE

(6)


119889119905= 1198961015840

1119862TOCINT

minus 1198961015840

1119862TOCPRE (7)


3is then



TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158403+ 11989610158402

119890minus1198961015840

2119905minus1198961015840

2

11989610158401+ 11989610158403+ 11989610158402

119890minus(1198961015840

2+1198961015840

2)119905 (8)


ln TOCTOC119900

= ln1198961015840

1

11989610158402

minus ln (11989610158401+ 1198961015840

2) 119905 (9)


CO2 + H2O

INT

k998400

1 k998400

2

k998400

3

PRE




2 were found to be



2+H2O reaction



2+



119862TOC119862TOC

119900

=119862TOCPRE

+ 119862TOCINT

119862TOCPRE119900+ 119862TOCINT119900

=119862TOCPRE119900

119862TOC119900

(1198961015840

1

11989610158401+ 11989610158403minus 11989610158402

119890minus1198961015840

2119905

+1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158403minus 11989610158402

119890minus(1198961015840

2+1198961015840

1)119905)

+119862TOCINT119900

119862TOC119900

119890minus1198961015840

2119905

(10)


TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158402+ 11989610158403

119890minus1198961015840

2119905minus1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158402+ 11989610158403

119890minus(1198961015840

3+1198961015840

4)119905 (11)













0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)










5 Conclusions


2O2 PRE andH





2) Again





Acknowledgments


References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 150

00

02

04

06

08

Time (min)

minus02

minusln

(TO

CTO

C o)

(a)

00 02 04 06 08

00

02

04

06

08

minus02


FOKM

pre

dict

edminus

ln(T

OC

TOC o

)

(b)







2+ H2O


1 11989610158402 and 1198961015840

3





1(minminus1) na 09836 1012481198961015840

2(minminus1) na 09791 024441198961015840

3(minminus1) 00045 ng 37852


adj 09621 09621 09660SSE 00257 00257 00104RMSE 00463 00463 00323




119889119905= (1198961015840

1+ 1198961015840

3) 119862TOCPRE

(6)


119889119905= 1198961015840

1119862TOCINT

minus 1198961015840

1119862TOCPRE (7)


3is then



TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158403+ 11989610158402

119890minus1198961015840

2119905minus1198961015840

2

11989610158401+ 11989610158403+ 11989610158402

119890minus(1198961015840

2+1198961015840

2)119905 (8)


ln TOCTOC119900

= ln1198961015840

1

11989610158402

minus ln (11989610158401+ 1198961015840

2) 119905 (9)


CO2 + H2O

INT

k998400

1 k998400

2

k998400

3

PRE




2 were found to be



2+H2O reaction



2+



119862TOC119862TOC

119900

=119862TOCPRE

+ 119862TOCINT

119862TOCPRE119900+ 119862TOCINT119900

=119862TOCPRE119900

119862TOC119900

(1198961015840

1

11989610158401+ 11989610158403minus 11989610158402

119890minus1198961015840

2119905

+1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158403minus 11989610158402

119890minus(1198961015840

2+1198961015840

1)119905)

+119862TOCINT119900

119862TOC119900

119890minus1198961015840

2119905

(10)


TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158402+ 11989610158403

119890minus1198961015840

2119905minus1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158402+ 11989610158403

119890minus(1198961015840

3+1198961015840

4)119905 (11)













0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)










5 Conclusions


2O2 PRE andH





2) Again





Acknowledgments


References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










CO2 + H2O

INT

k998400

1 k998400

2

k998400

3

PRE




2 were found to be



2+H2O reaction



2+



119862TOC119862TOC

119900

=119862TOCPRE

+ 119862TOCINT

119862TOCPRE119900+ 119862TOCINT119900

=119862TOCPRE119900

119862TOC119900

(1198961015840

1

11989610158401+ 11989610158403minus 11989610158402

119890minus1198961015840

2119905

+1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158403minus 11989610158402

119890minus(1198961015840

2+1198961015840

1)119905)

+119862TOCINT119900

119862TOC119900

119890minus1198961015840

2119905

(10)


TOCTOC119900

=1198961015840

1

11989610158401+ 11989610158402+ 11989610158403

119890minus1198961015840

2119905minus1198961015840

3minus 1198961015840

2

11989610158401+ 11989610158402+ 11989610158403

119890minus(1198961015840

3+1198961015840

4)119905 (11)













0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)










5 Conclusions


2O2 PRE andH





2) Again





Acknowledgments


References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 150 18004

06

08

1

Time (min)

TOC

TOC o

(a)

04 06 08 1002

04

06

08

10

GKM experimental

GKM

pre

dict

ed

(b)










5 Conclusions


2O2 PRE andH





2) Again





Acknowledgments


References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Kinetic Modeling of a Heterogeneous