Oxidative degradation of textile waste water Modeling reactor performance

OXIDATIVE DEGRADATION OF TEXTILE WASTE WATER.MODELING REACTOR PERFORMANCEE.BALANOSKY 1,F.HERRERA 1,A.LOPEZ 2and J.KIWI 1*1Swiss Federal Institute of Technology,1015,Lausanne,Switzerland and 2IRSA,Water Research Institute,Department of Water Chemistry and Technology,Experimental Laboratory,20123Bari,Italy(First received 1July 1998;accepted in revised form 1March 1999)Abstract ÐThis study reports on the Fenton and photo-assisted Fenton treatment of textile waste waters from nano®ltration of biologically treated secondary textile industry e uents produced in a large scale plant in Northern of Italy.The in¯uence of the hydrodynamic and chemical parameters a ecting the degradation of the non-biodegradable residues of textile waters being continuously replaced near the light source were studied in a ¯ow reactor.Cu 2++Fe 2+/3+-ions mediated oxidation processes under light analogous to the Haber±Weiss cycle were found to be suitable to degrade the recalcitrant part of the textile waters after the initial biological treatment.The optical absorption of the iron-chromophore and the spectral emission of the light source used but not the intensity of the applied light were the most important factors determining the kinetics and e ciency of the applied treatment.A single polynomial exponential expression was constructed for the treatment of the experimental data to make the most economical use of the oxidant,electrical energy and processing time.This approach allowed the prediction of the lowest ®nal TOC values when optimizing the main variables a ecting the degradation via phenomenological modeling.Insight is given into the way of handling simultaneously the optimization of ®ve chemical and physical variables intervening in the degradation process by way of a program on a desk computer.As a result the data from the degradation runs were used to evaluate the coe cients of the polynomial exponential expression rendering 2D-contour surface plots.A correlation factor >95%was found between the experimental and the values predicted by the mathematical expression following an exponential decay law.#1999Elsevier Science Ltd.All rights reservedKey words Ðwaste water from membrane concentrates,¯ow reactors,multivariable modeling,exponen-tial function,Fenton,photo-assisted Fenton reactionsINTRODUCTIONIncreasing water consumption for industrial and domestic use is leading to potential water shortages within much of Southern Europe.European indus-try is also facing increasing costs for the water it rge volumes of water are commonly used in textile and this type of industry,which is wide-spread throughout Europe,is a good candidate for the development of improved methods for water recycling.Waste waters from the textile waters con-tain many types of pollutants such as dyes,deter-gents,insecticides,fungicides,grease and oils,sul®de compounds,solvents,heavy metals and inor-ganic salts and ®bers.The recalcitrance and biotoxi-city of many of these pollutants means that biological treatment cannot remove all of them.There is a need at present of treatments to recycle these e uents since the remaining membrane con-centrates still contain recalcitrant organic pollu-tants.To comply with the European water use directives (European Economic Community EEC,1982)these concentrates cannot be recycled back to the aerobic biological stage or discharged into receiving water bodies without additional chemical degradation treatments such as ozonization (Rozzi et al .,1997;Lopez et al .,1998)or by using Advanced Oxidation Technologies (AOTs).The lat-ter option is dealt in the present study in a photo-reactor aiming at an adequate degradation e ciency in a cost e ective operation.Reactors for pollution abatement,prevention or elimination via Fenton reactions have been recently reported (Bandara et al .,1997;Balanosky and Kiwi,1998).Application of photochemical reactions have attracted considerable attention during the last decade in the environmental domain (Halmann,1996).Photocatalytic oxidative degradation pro-cesses (Walling,1975)based on the generation of the ÁOH radical from H 2O 2in the presence of Fe-ions have been shown to be enhanced by light (Ruppert et al .,1993).The application of the light enhanced Fenton reaction to the e uents of theWat.Res.Vol.34,No.2,pp.582±596,2000#1999Elsevier Science Ltd.All rights reservedPrinted in Great Britain0043-1354/99/$-see front matter582/locate/watresPII:S0043-1354(99)00150-5*Author to whom all correspondence should be addressed.Fax:+41216934111.textile industry(Nadtochenko and Kiwi,1997) explored in this work has been applied in the last few years to organic degradation like carboxylic acids(Halmann,1996),nitrophenols(Kiwi et al., 1994),pesticides like2,4-D(Sun and Pignatello, 1993)and quinolines(Nedoloujko and Kiwi,1997). This study aims at the construction of a single polynomial exponential expression for the values of TOC that can integrate the numerical values found during the degradation(Khuri and Cornell,1987) by way of two dimensional contour plots.The orig-inality of this new approach is that it avoids the use of powerful computers when handling systems com-prising more than2and up to8variables as carried out in our laboratory.Our approach required only a desk computer and a commercially available pro-gram to process the experimental data(Balanosky and Kiwi,1998).MATERIALS AND METHODSMaterialsThe textile waste waters after membrane concentration in the Northern Italian plants showed COD of 6002(30mg O2/l)equivalent in most cases to a TOC of 150mg C/l.The pH was H7.5.About50%of the material in the concentrate had a molecular weight(MW) >300,000(range of200,000±500,000).Less than30%had a MW between3000±10,000.The Fenton reagent used Mohr's salt as an iron II source(ammonium ferrous sulfate hexahydrate,FeH8 N2O8S2Á6H2O)and H2O2(30%w/w)Fluka p.a.as received.The Fe3+-ions and Cu2+-ions(CuSO4Á5H2O) were added at the beginning of each run.The consump-tion of H2O2during the reaction was followed by the Merckoquant1test(Cat Merck No.1.10011.01)for per-oxides which detected peroxides between0.4and25mg/l. This is a colorimetric test for organic or inorganic com-pounds which contain a peroxide or hydroperoxide group. Peroxidase(POD)transfers oxygen from the peroxide to an organic redox indicator,which is then converted to a blue colored oxidation product.The strips impregnated with these dye develop the blue color in15s after1s con-tact with the peroxide in solution.The textile waste waters with pH around7were acidi®ed with H2SO40.1to1M for the Fenton treatment.ReactorA Philips36W(1.20m long and26mm in diameter, TLD36W/08)black actinic light source was employed in such a way that its center passed through the focal axis of the reactor.Most of the degradation runs employedthis Fig.1.Schematic of the reactor used during the degradation of the membrane concentrates.Photo-oxidation of textile waters583light source.The lamp radiation was centered at l =366nm with a l -distribution between 330and 390nm.A 140W Philips lamp with the same l -distribution but 140W power (140W/05)was used to compare the e ect of the variation of light intensity on the degradation rate.A third light source distribution (TL 140W/03,Philips)centered at l =420nm (390<l <505nm)was also used to test the e ect of l on the light source during the degra-dation process.Figure 1shows the schematic of the photo-reactor used.In batch mode operation the waste waters with the added iron is mixed with H 2O 2pumped by a peri-staltic pump from the H 2O 2reservoir.The solution is re-cycled through the reactor by a second peristaltic pump located at the right of the sampling port.During ¯ow mode reactor operation the 20liter solution used is fed from the feeding tank shown in the lefthand side of Fig.1and cycled only once through the reactor.Batch recycling of the waste waters did not involve pumps B and D in Fig.1and the samples for analyses were taken from the mixing ¯ask as shown in this ®gure.During the ¯ow-recy-cling experiments all the pumps [Fig.1(A)±(D)]were used and the samples for analyses were taken from the outlet as marked in this ®gure.The H 2O 2was added by means of a peristaltic pump into the mixing ¯ask as before during batch mode operation.Analyses in solutionTotal organic carbon (TOC)was monitored with a Shimadzu 500provided with an automatic auto sampler.The data processing of the TOC analyzer rejects automati-cally values with deviations >3%during the determi-nation of the TOC value which is found from at least three experimental determinations.Spectrophotometric measurements were carried out with a Hewlett±Packard 386/20N diode array.The technique to determine the Mw involved correlation measurements by low angle scattering on a Chromatix KMX-6instrument equipped with a 64channel correlator.The error in the experimental determi-nation by the latter technique was H 10±15%.RESULTS AND DISCUSSIONReactor dark and photo-assisted Fenton pretreat-ment.Batch-recycle reactor (1.4liter)mode oper-ationThe Fenton reagent a mixture of H 2O 2and Fe-ions (Walling,1975)is a powerful oxidant of or-ganic compounds,the ÁOH radical being the pri-mary reactive species insolutionFig.2.(a)Reduction in the TOC values with time of the waste waters of membrane concentrates in the dark and under actinic light (36W)at pH 2.8.Batch mode recirculation of 270ml/min was used along the addition of H 2O 2at the speci®ed feeding rates for solutions containing Fe 3+(74mg/l).Experiments in the dark are denoted by solid points and experiments under light are denoted by open points in all ®gures.For the variation of other experimental parameters see the captions in the ®gure.(b)Reduction in the absorbance of the waste waters at l =400nm (d =1cm).Other experimental conditions as in (a).The inset shows:trace 1,the absorbance of the membrane concentrates used (d =0.1cm),trace 2,the absorbance of the Fe 3+(aq)band and in trace 3,the superimposed spectral emission of the actinic source (36W)in arbitrary units.(c)Reduction of TOC of the waste waters with time as a function of the variation of the recirculation rate used during reactor batch-mode recycling operation.Other exper-imental conditions as in (b).E.Balanosky et al.584Fe 2 H 2O 24Fe 3 OH À OH1Light irradiation accelerates the Fenton reaction (Fe 2+/H 2O 2)and the photolysis of Fe 3+complexes yielding oxidative radicals and regenerating Fe 3+through the photolysis of the Fe 3+-organics com-plexes or its intermediates in solution specially or-ganic acids (Zepp et al .,1992;Kiwi et al .,1994)Fe 3 H 2O 24Fe 2 HO 2 H2Figure 2(a)presents the amount of TOC decrease of the waste waters due to H 2O 2or Fenton reagentin solution as a function of time up to 2h.The results show than in the dark (solid points,trace 1)adding H 2O 2no degradation was observed.Adding only H 2O 2a minor degradation was attained under light irradiation as seen by the open points in traces 2±4.When Fe 3+-ion was added (74mg/l or 1.32Â10À3M)in the presence of H 2O 2a 25%degradation of the initial TOC was observed within 2h as shown in Fig.2(trace 5).The dark mineral-ization in trace 5is seen to reach a plateau.This means that intermediates precluding furtherdegra-Fig.2(continued )Photo-oxidation of textile waters 585dation are produced in solution during dark degra-dation of these textile waters.The e ect of a signi®cant increase in the Fe-ion concentration in solution was tested next.The increase of ®ve and ten times of the amount of iron is shown in the lower part in traces 8and 9.An accelerated TOC decrease takes place.The degra-dation in the latter two traces is comparable to the degradation observed during light processes at an iron level 5to 10times lower.The light enhance-ment has been ascribed to photolysis of Fe-com-plexes which are light sensitive involving the photoreduction of Fe 3+to Fe 2+-ions with ad-ditional generation of ÁOH radicals (Ruppert et al .,1993).Under light,lower Fe-sludge will be formed after treatment with bene®cial e ects during the dis-posal and redissolution of the iron in solution.A one pass for the 1.4liter waste water used in the reactor in Fig.1decreases the TOC by 3.7ppm.The solution used in batch experiments (1.4liter)was recirculated at 270ml/min and the TOC con-tent decreased from 150to 65in 120min as shown in Fig.2(a)trace 6.To recirculate 1.4liters we need 5.2min,so in 2h the 1.4liters is recirculated about 23times.A one pass of the 1.4liter solution through the reactor therefore a ords a reduction of 3.7ppm in the initial TOC.This latter estimate seems to be valid considering the initial 10min of degradation in Fig.2(a)(trace 6)since the reduction of TOC is seen to be near exponential in nature.Traces 3,4and 6in Fig.2(a)show that the TOC reduction depends on the rate of H 2O 2addition.The initial TOC was reduced by about 56%for anH 2O 2addition rate of 150m l/min/l.The H 2O 2con-centration in the reacting solution is H 1.05mM.A lower H 2O 2addition rate of (75m l/min/l)did not a ord su cient oxidant concentration in solution for the reaction to proceed favorably.Higher rates of oxidant than 150(m l/min/l)as shown in trace 4(300m l/min/l)were observed to be detrimental for an adequate degradation kinetics since after the in-itiation step the propagation step would be hin-dered by an excess H 2O 2acting as an ÁOH radical scavenger (Sychev and Isak,1995)H 2O 2 OH 4H 2O HO3Figure 2(b)shows the reduction in optical absor-bance from A =1.0to about A =0.43(l =400nm)within 2h.The decoloration of the textile waters during the treatment was a primary goal of the pre-sent study since European treatment facilities are often unable to meet e uent color standards for waste waters containing non-biodegradable dyes (EEC,1982;Swiss Drinking Standards,1983).The initial absorption is due to two main components:(a)the aromatic and aliphatic compounds in the waste water solution and (b)the absorption of the existing Fe(III)-aqua complex(es).The results pre-sented in Figs 2(a)and (b)can be understood in terms of the Fe 3+-ion being the absorbing chromo-phore in the oxidative reaction media.The inset in Fig.2(b)presents the absorbance of the waste-waters,Fe 3+-ions and in relative units the superim-posed emission of the 36W actinic source.The inset shows that the Fe 3+-ion was practicallytheFig.2(continued )E.Balanosky et al.586only absorber of the actinic light between330and 390nm.While the concentrations of the complexes of Fe3+in solution:Fe(OH)2+with e366nm=275MÀ1cmÀ1(Zepp et al.,1990)and Fe2(OH)4+2with e366nm=1000MÀ1cmÀ1(Knight and Sylva,1975)decrease after the beginning of the reaction,the optical absorption of the Fe(II)gener-ated in solution increases due to the charge transfer band associated with the Fe(H2O)2+6.The latter band does not absorb at l=366nm the maximum emission l of the actinic lamp used.Its absorption begins at l=265nm with l254nm=20MÀ1cmÀ1 (Balzani and Carassiti,1970).The inset in Fig.2(b) presents the absorbance of the waste waters,of the Fe3+-ions superimposed emission of the actinic36 W source(in relative units).H2O2presents a mean-ingful absorption only below l=300nm at the con-centrations used in Fig.2.At any given time the main absorption in solution would be due to Fe3+/ Fe2+coexisting in solution.The reduction of the TOC of a solution of textile waste water was treated in the reactor under light (36W)at pH=2.8,adding74mg Fe3+and150m l/ min/l to see the e ect of the recirculation rate on the degradation rate.Fig.2(c)shows the experimen-tal results of these runs.A higher degradation rate was observed with a faster recirculation rate in sol-ution up to a de®ned limit.Beyond recirculation rates of270ml/min or10.8Â10À3msÀ1,the TOC degradation rates increased only marginally.This is specially noteworthy when the system is operated with a recirculation rate below270ml/min or 10.8Â10À3msÀ1[see Fig.2(c)].In view of the results obtained this latter recirculation rate(resi-dence time of0.062h)was used during batch mode operation throughout this study.The Reynolds number for the reactor under con-sideration was160for a rate of10.8Â10À3msÀ1 far below the limit of turbulent¯ow(H2000).This clearly indicates that laminar¯ow is taking place under the present operating conditions in the reac-tor of the liquid¯ow in the reactor.For the highest recirculation rate(21.6Â10À3msÀ1)in Fig.2(c), the Reynolds number increases only to320.No increase in the turbulence near the lamp is therefore possible in the latter case.These latter values corre-spond to Reynolds numbers that continue to be well into the laminar¯ow region.When the¯ow velocity in the reactor was increased,the overall mixing in the system seems to improve and the reaction rate was seen to increase.The TOC reduction as a function of pH for sol-utions containing(a)Fe3+-ions and solutions con-taining and(b)an equimolar mixture of Fe3+and Cu2+(0.066M of each cation)along H2O2was explored in separated experiments.In both cases at pH>2.8,a lower degradation rate was observed because the Fe(H2O)3+6(pK a2.79)deprotonates to Fe(H2O)5OH2+(Knight and Sylva,1975)and Fe(H2O)4OH+(Faust and Hoigne,1990)slowing down the latter process.The degradation of textile waters proceeds more favorably via protonated Fe-species in solution for Fenton-like processes.At pH I2.8,the photolysis of Fe(OH)2+generates additionalÁOH radicals in solution(Ruppert et al., 1993;Zepp et al.,1992).When Cu2+is added besides Fe2+-ions in solution(b),acceleration of the degradation was observed in comparison to sol-utions containing only Fe-ions(a). Degradation involving light and dark periods Figure3presents the results for the degradation of textile waste waters using the36W actinic light source.The results presented in Fig.3are based on a Fenton system using equimolar concentrations of Fe3+and Cu2+-ions.Di erent illumination times were tried to generate the photosensitive intermedi-ates that would continue degrading in the dark. Subsequently a dark reaction period in Fig.3shows a modest TOC decrease from63to55(mg C/l) which shows the inhibiting e ect of the intermedi-ates formed in the dark for further degradation. When light was applied for1h period after19h dark reaction,a signi®cant reduction in TOC values was observed(the right-hand side of Fig.3).The hydroxyl radical produced in equations(1)and(2) reacts with RH(the organic compounds of the tex-tile waste water)RH OH4R H2O or RHOH 4 The TOC decrease observed from the beginning of the reaction in Figs2and3suggest a degradation mechanism through iron-organic complexes(Sawyer et al.,1993)RCOOÀFe 2 4h n R CO2 Fe2 5 where the®rst term in equation(5)represent an LMCT complex due to the photolysis of the Fe(III)±polydentate species containing ligand inter-mediates leading to mineralization(Figs2and3). The inset in Fig.3presents the reduction in absorbance of the textile e uents as used in Fig.3 after3h of actinic light irradiation.The ensuing dark reaction hours is seen to further reduce the absorbance from A=0.24to A=0.11within22h. The inset in Fig.3shows an increase in trans-mission from7%(initial)to58%for textile waters after3h reaction under light.Figure3shows the oxidation and decoloration(inset)of textile waters of making possible the recycling of these e uents for further use.In¯uence of Cu(II)in the photo-oxidation process When Cu2+-ions were added to a solution con-taining Fe3+-ions a more e cient degradation rate was observed.Cu2+-ion is a more energetic oxidant than iron-ion as re¯ected by the potentials Cu2+/ Cu+(0.16V)vs Fe3+/Fe2+(0.77V).When Cu2+Photo-oxidation of textile waters587is used alone as photocalyst in the presence of H 2O 2,the degradation was observed to be kineti-cally slower and less e cient than when using only Fe 2+(Mohr's salt).The R Áradical in the right-hand side equation (4)seems to react with the Cu 2+added in solution by equation (6).The intermediate Cu +undergoes reaction with Fe 3+regenerating Fe 2+-ion (Kiwi et al.,1994).Therefore,an ad-ditional channel due to the added Cu +-ions would be available to enhance the recycling kinetics Fe 2+/Fe 3+/Fe 2+R Cu 2 4R Cu6Cu Fe 3 4Cu 2 Fe 27E ect of the wavelength of irradiation and light intensity used during the degradation process The degradation of textile waters was studied as a function of di erent light sources (a)a 36W Philips actinic light source with a maximum at l =366nm,(b)a 40W Philips light source centered at l =420nm and ®nally (c)a 140W actinic light source with the same l -distribution as in (a).An increase in intensity did not favorably a ect the degradation kinetics when an actinic light source with a maximum at l =366nm was used as seen when the results of degradation runs of (c)were compared with (a).This indicates that the degra-dation kinetics does not depend on the intensity of the light used but on the amount of light absorbed by the active chromophore.A slower degradation rate was observed when using the visible lightcen-Fig.3.Decrease in the TOC with time of the waste waters under light irradiation with an actinic source of 36W for 3h,followed by a dark reaction period (19h).Subsequently,light is applied again for 2h (L).Batch mode operation of the reactor with a recirculation rate of 270ml/min and an H 2O 2addition rate of (150m l/min/l).The solution was pH 2.8and contained Fe 3+(37mg/l)+Cu 2+(42mg/l).Theinset shows the decrease of absorbance (l =400nm)within the reaction time.E.Balanosky et al.588tered at l =420nm in run (b).This is understood in terms of the lower Fe 3+-ion absorption for the spectral irradiation of this light source centered at longer l s.Flow-recycle reactor (20liter)studies of membrane concentratesThe oxidation kinetics for textile waste waters in batch reactor operation was systematically studied as a function of the amount of the H 2O 2addition,the amount of Fe 3+and Cu 2+-ions,the reactor ¯ow,the recirculation rate,the solution pH and the type and intensity of the light source.The infor-mation of the preliminary optimization in batch mode operation was used next during reactor ¯ow mode operation.A feeding tank of 20liters is used for the textile waters during the ¯ow experiments (Fig.1).Figure 4shows the results for the degra-dation of textile waters in reactor ¯ow mode oper-ation.A signi®cant reduction of the initial TOC is seen during the ®rst 3h irradiation followed by a more modest reduction in the dark.The inset in Fig.4reports the reduction of optical absorbance (A )during the run.The reduction of both TOC and A follow the same pattern as the values reported in Fig.3for reactor batch mode oper-ation.The only di erence stems from the fact that a longer residence time is needed during reactor ¯ow mode operation (120ml/min or a residence time of 0.138h)as compared to the value in batch reactor operation (270ml/min or a residence time of 0.062h).As expected longer contact times were necessary for the degradation of 20liters in a ¯ow experiment than in batch mode using only 1.4liters.Fig.4.Decrease of the TOC with time for the waste waters of a 20liter reservoir during reactor ¯ow mode operation.Other experimental conditions:actinic light (36W),pH 2.8,H 2O 2addition rate (150m l/min/l),reactor through ¯ow 120ml/min.The feeding tank of 20liters containing Fe 3+(420mg)+Cu 2+(480mg).The inset shows the reduction of the absorbance of the initial solutionwith time (d =1cm).Photo-oxidation of textile waters 589The results obtained in the¯ow mode sound encouraging since they point out the possibility of degrading larger quantities of textile waters using low energy actinic light(36W)with low consump-tion of electrical energy in a cost e ective process. Statistical modeling(phenomenological)of the degradation parameters.Exponential function Some years ago a statistically signi®cant method-ology was developed to model a process by per-forming a set of well chosen experiments(Box et al.,1978).The present study addresses the problem of constructing a mathematical model based on a single polynomial exponential expression®tting the experimental data as presented in Figs2±4.Contour plots(curves of constant response)giving the minima of the TOC achieved during photodegrada-tion(Figs2±4)are determined through equation(8) following an exponential form for the modeling of the data(Khuri and Cornell,1987).This method-ology has been applied for the main variables a ecting the degradation process:H2O2concen-tration,Fe3+-ions,sample dilution,recirculationFig.5.2D-Contour plots obtained from the exponential function for the data reported in Fig.2(a)for the pair of variables:(a)Fe3+,H2O2,(b)recirculation rate,H2O2,and(c)intensity,H2O2.E.Balanosky et al.590¯ow (time of residence)and intensity (I )of the light source.Figures 2±4show experimentally that the TOC decreases for the di erent chemical parameters fol-lowing an approximate exponential decay law.An exponential form was therefore chosen to ®t the ex-perimental data.It is possible to construct from these experimental values a function Z (representing the TOC)of a pair of experimental variables (X i ,X j ),via contour plots [Fig.5(a)±(c)]representing curves of constant response Z for the values (X i ,X j )within the experimental region (Khuri and Cornell,1987).In this way it is possible to predict the optimum values of X i ,X j that yield a minimum value of Z (TOC),i.e.the optimum numerical values for the parameters leading to the best degra-dation in terms of materials,time and energy.In order to avoid having di erent units for di er-ent variables u i ,the di erent variables are trans-formed into reduced centereddimensionlessFig.5(continued )Photo-oxidation of textile waters 591variables X i (reaction variables).Calling u i 0=(u mi-n+u max )/2the value of u i at the center of the exper-imental region,i.e.the average of the maximum and minimum values of u i used during the exper-iments,we de®ne X i =(u i Àu i 0)/D u i ,where:u i 0is the value of u i at the center of the experimental region and D u i =(u i max Àu i min )/2.The treatment of the data takes the experimental data in pairs,X 1and X 2(reaction parameters).Each graph represents a set of 48pair of values for TOC as a function of the reaction parameters.Then a simple exponential expression can be constructedZ b 0exp h s b i X ib ii X 2ib ij X i X ji 8where b 0=a Z i /N ,the average of the values of TOCover N experimental points,b i =the coe cients for the main e ect of the variable X i and b i =a i Z i X i /N,b ii =the coe cients for the quadratic e ect of the variable X i and b ii =a i Z i X 2i /N,b ij =the coe -cient for the ®rst order interaction e ect of X i and X j and b ij =a i Z i X i X j /N and s =(scaling factor)isFig.5(continued )used to adjust the®tting of the curves for the initial and®nal concentrations of the reagents.The method for calculating the coe cients b i and b ij is based on the coe cient b i s represent®rst order e ect.A set number of six experimental points are taken with eight TOC values corresponding to each of the values found for X i,i.e.48values in total.In each case,the TOC values were multiplied by the values of the corresponding X i.The48products found were added up and divided by48to®nd the coe cient for b i.Coe cients noted by b ii s represent the quadratic e ect.To®nd the b ii s value,each TOC value was multiplied by the square of the cor-responding x i,the48products were added up and divided by48.To®nd the b ij coe cients represent-ing the®rst order interaction e ect between X i and X j,the TOC values found experimentally were mul-tiplied by X i and X j and the48products added up and divided by48.Contour plots were obtained using the IGOR3.0 Program in a Power Macintosh8200/120.The regions for the minima of the Z values have been located as a function of the combination of vari-ables taken in pairs[equation(8)].The variation of TOC vs(H2O2,Fe3+)is shown in Fig.5.Similar contour plots can be drawn for TOC vs(H2O2, recirculation rate)and TOC vs(H2O2,Intensity). These plots were obtained by calculating the coe -cients of the exponential function equation(8)and drawing subsequently the contour for the respective pair of variables.The central regions for thethreeFig.6.Minima regions for TOC as a function of three reaction parameters found by the overlap of the2D-contour plots in Fig.5for(a)TOC(Z function)vs(H2O2,recirculation rate,light intensity and(b) the TOC(Z function)vs(H2O2,waste waters dilution,Fe3+-concentration.。