Application of mathematical empirical models to dynamic removal of lead on natural zeolite clinoptilolite in a fixed bed column

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1 Indian Jurnal f Chemial Tehnlgy Vl.18, Marh 2011, pp Appliatin f mathematial empirial mdels t dynami remval f lead n natural zelite linptillite in a fixed bed lumn Marina Trg*, Nediljka Vukjević Medvidvić & Jelena Perić Faulty f Chemistry and Tehnlgy, University f Split, Teslina 10/V, Split, Cratia Reeived 25 May 2010; aepted 19 January 2011 This study examined the appliability f the mathematial empirial mdels by Bhart-Adams, Wlbrska, Thmas and Yn-Nelsn n lead remval frm aueus slutins n a fixed bed f natural zelite. Appliability f these mdels has been evaluated by fitting the experimental breakthrugh urves with the urves btained frm the applied mdel. Experimental results have shwn that the values f remval apaities alulated frm mdel are lse t the value f the experimentally btained apaity at the exhaustin pint. The Thmas and Yn-Nelsn mdels have shwn exellent fit fr all examined range f the breakthrugh urves; therefre these mdels have been used fr simulatin f breakthrugh urves fr different bed depths and flw rates. The results shw that the suessful preditin is ahieved when the empty bed ntat time (EBCT) was in the experimentally nfirmable range. Amng all examined mdels, the Thmas mdel was fund t be the mst suitable ne fr simulatin f the breakthrugh urve f lead uptake n fixed bed f natural zelite in a wide range f EBCT values. Keywrds: Zelite linptillite, Bhart-Adams mdel, Wlbrska mdel, Thmas mdel, Yn-Nelsn mdel The intensive develpment f industry is ampanied by a derease f envirnmental uality. Althugh this develpment invlves implementatin f envirnmentally aepted presses, enrmus uantities f industrial wastewaters are disharged int natural reipients. Industrial wastewaters are mstly laded with heavy metals that are nt bidegradable and tend t aumulate in auati rganisms. In rder t derease the ntent f heavy metals in the envirnment, it is neessary t treat wastewaters befre their disharge. The mst mmnly used treatments are xidatin/redutin and neutralizatin fllwed by hemial preipitatin. These treatments d nt usually ensure remval up t allwed nentratins. Fr mplete remval, the suitable presses are thse f tertiary treatment, suh as adsrptin, in exhange, membrane tehniues. The use f natural zelites as adsrbents and in exhangers bemes an imprtant alternative methd fr remval f heavy metals frm wastewaters. Elgial appliatin f natural zelites has been inreasing in the last tw deades, due t their easy explitatin, and lw sts f their pratial appliatin. Their well-knwn hemial and thermal stability in the envirnment extends the sientifi researh t pratial appliatins 1,2. *Crrespnding authr ( mtrg@ktf-split.hr) Zelites are hydrated alumsiliate mineral with a age-like struture that frmed pen hannels f 8-10 member rings. Due t ismrphi substitutin f silin with aluminium in, the negative strutural harge is urred, and is balaned by presene f sdium, alium, ptassium and magnesium ins in these hannels. Zelites are haraterized by an utstanding apability f exhange f these alkaline and earth-alkaline atins frm their struture by heavy metal atins frm aueus slutin 3-6. Uptake f heavy metal ins frm aueus slutins n natural zelite is a mplex press, whih inludes in exhange and adsrptin n the inner and uter partile surfae. It is enabled by the prus zelite struture, mineralgial hetergeneity, brken bnds and varius surfae imperfetins n the zelite partile 7. Clumn perfrmane prvides multiple repetitins f servie and regeneratin yles, whih makes it pssible t reuse the same zelite sample many times, and treatment f a large vlume f wastewater. During the regeneratin yle, a signifiantly smaller vlume f the nentrated metal ins slutin is eluted mpared t the servie yle. The regeneratin effluent ntains a high metal ins nentratin suitable fr hemial preipitatin 8,9. Many researhers are trying t desribe the experimental breakthrugh urves using mathematial mdel. Mst f develped mdels reuire a

2 124 INDIAN J. CHEM. TECHNOL., MARCH 2011 preliminary determinatin f the istherm and mass-transfer parameters, whih reuires additinal experimentatin and a nn linear urve-fitting. The mathematial mplexity and/r the need t knw many parameters frm different experiments make these mdels rather innvenient fr pratial use. Mrever, the analytial slutins f differential euatin-based mdels fr the prpsed rate mehanism are nt available Fr that reasn, varius mathematial empirial mdels have been develped t predit the dynami behaviur f the lumn This study has applied empirial mdels by Bhart-Adams, Wlbrska, Thmas and Yn-Nelsn fr desribing f lead remval frm aueus slutins n a fixed bed f natural zelite. Theretial Bakgrund Bhart-Adams mdel Bhart and Adams prpsed an euatin fr design f the arbn adsrptin lumn. The mdel assumes that the adsrptin rate is prprtinal t bth the residual apaity f the ativated arbn and the nentratin f the srbing speies, mainly determined by surfae adsrptin n the adsrbent surfae sites, and is used fr desriptin f the initial part f the breakthrugh urve 2,13-17 : ln( -1) = ln (e k H ν -1) - k t...(1) where is initial slute nentratin (mml/l), is effluent slute nentratin (mml/l), k is rate nstant (L/mml h), is remval apaity (mml/l), H is bed depth (m), v is linear flw velity (m/h) and t is servie time (h). Beause the expnential term is usually muh k H ν larger than unity ( e >> 1) and with the assumptin that the nentratin range is nsidered t be lw, e.g., effluent nentratin < 0.15, the Bhart Adams euatin (1) an be written as: ln( ) = k H t k...(2) v Value f remval apaity in mml/g is alulated as fllws 17 : BVS = =...(3) m ρ Where is remval apaity (mml/g), BV S is fixed bed vlume(l), m is mass f the bed (g) and ρ is apparent density f the srbent in the fixed bed (g/l). Frm E. (2), the values desribing the harateristi peratinal parameters f the lumn (k AB, and ) an be determined frm the plt f ln / versus t at a given bed depth, initial nentratin and flw rate thrugh the lumn. Wlbrska mdel The next simplified adsrptin mdel was derived by Wlbrska. The mdel is based n the general euatin f mass transfer fr the diffusin mehanism fr lw nentratin range f breakthrugh urves. The mass transfer in the fixed bed adsrptin is desribed by the fllwing euatins 15-18,20-23 : t b b + v + = D H t ax 2 b 2 H...(4) where b is slute nentratin in the bulk slutin (mml/l) and D ax is axial diffusin effiient (m 2 /h). The external diffusin harater f the press with a nstant kineti effiient makes it pssible t derive the fllwing frm f the kineti euatin: = -v m =β a ( b - i )...(5) t H where i is slute nentratin at the slid/liuid interfae (mml/l), v m is migratin rate f the slute thrugh the fixed bed (m/h) and β a is kineti effiient f the external mass transfer (h -1 ). Fr the slutin f the differential euatin (5) the fllwing is assumed: i << b, v m << v, axial diffusin is negligible D ax 0 as t 0, b =, and E. (5) bemes: ln βa βa H = t...(6) ν Frm the linear dependene ln / versus t, mdel parameters β a and an be determined. The linear dependene f the Bhart Adams euatin is the same and rrespnds t the same mehanism as the Wlbrska euatin; therefre the same plts are used in alulatin f parameters fr bth mdels.

3 TRGO et al.: MATHEMATICAL EMPIRICAL MODELS TO DYNAMIC REMOVAL OF LEAD 125 Thmas mdel The Thmas mdel is ne f the mst general and widely used. The mdel is appliable in system with a nstant flw rate and n axial dispersin, and its behaviur mathes the Langmuir istherm and the send-rder reversible reatin kinetis. The mdel has the fllwing frm 13,24-26 : 1 = k Th 1 + exp ( m 0 V (7) where k Th is rate nstant (L/mml h), is flw rate (L/h), m is mass f the bed (g) and V is effluent vlume (L). The linearizatin f E. (7) yields: kth m kth ln( -1) = - V... (8) Frm the linear dependene f ln[( /)-1] versus V, the remval apaity and rate nstant k Th an be determined. Yn-Nelsn mdel Yn and Nelsn have develped a relatively simple mdel fr a single mpnent system. If A is a fratin f the slute being adsrbed in bed, and P is the fratin f the slute that remains in the effluent, the rate f adsrptin an be expressed as 11,15-16,19, 27 : da = k dt YN ( t τ ) where k YN is rate nstant (h -1 ). (9) With the substitutin P = 1- A, and if A = 0.5 at time τ, the integratin f E. (9) yields: n ( ) = k ( t τ ) (10) 1 YN where τ is time when / 0.5, h. Frm the linear dependene f ln[/( -)] versus time t, the mdel parameters k YN and τ an be determined fr a given bed depth, flw rate and initial nentratin. Euatin (10) an be written as: 1 t = τ + ln ( )... (11) k - YN If the 50 % f breakthrugh is mpleted at t = τ, the bed will be exhausted at t = 2τ. Fr a symmetrial breakthrugh urve the uantity f slute adsrbed at time τ euals half f the remval apaity, and it is alulated relative t the initial nentratin and flw rate: τ =... (12) m Table 1 shws the euatins f used mathematial empirial mdels. Experimental Sample preparatin The natural zelite sample ntaining 80% f linptillite riginates frm the Vranjska Banja (Serbia) depsit. The sample was rushed and sieved t the tw partile size fratins f mm and Mdel Bhart- Adams Wlbrska Thmas Yn- Nelsn Table 1 Mathematial relatins, rrespnding parameters and breakthrugh urves euatins f used mdels Mathematial euatin ln( ) = k ln ln( ln( = β a -1) = ) - k = k Th t k βa H t - v YN m k Th - V H v Linear dependenes ln(/ ) vs. t Mdel parameters Breakthrugh urve k,, = exp[ (k t) (k H/ v) ] βa t βa H = exp ln(/ ) vs. t β a, ( ) ( ) v 1 = ln[( /)-1] vs. V k Th, k Th 1+ exp ( m - V) (t -τ) ln[/( -)] vs. t k YN, τ, exp = 1+ exp [ kth (t τ) ] [ kth (t τ) ]

4 126 INDIAN J. CHEM. TECHNOL., MARCH mm and rinsed in dubly distilled water in rder t remve impurities. After drying at 60 C, the samples were stred in the exsiatr. The results f XRD and hemial analysis f natural zelite are reprted elsewhere 8. Clumn study The experiments were perfrmed using tw glass lumns with the inner diameter f 12 mm and a height f 500 mm filled with zelite samples up t 115 mm, rrespnding t the bed vlume f 13 m 3. The examinatin f Pb 2+ remval n the zelite was arried ut with slutins f different initial nentratins ( = mml Pb/L) prepared by disslving f Pb(NO 3 ) 2 in dubly distilled water withut setting the initial ph value. Lead nentratins were determined mplexmetrially in the aid medium, using a highly seletive indiatr methylthymlblue 28. Servie yles were perfrmed by passing the lead slutin thrugh the fixed zelite bed using dwn flw mde. The flw rates f lead slutin were kept in range f 1-3. The flw nstany was maintained using a vauum pump. At seleted time intervals the lead nentratin in effluent was determined. The press was stpped when the Pb nentratin in the effluent beame eual t the initial nentratin in the influent. After eah servie yle, the regeneratin was perfrmed with the NaNO 3 slutin. The experimental results with breakthrugh and regeneratin urves are presented earlier 8. In this wrk, the experimentally btained breakthrugh urves have been tested by Bhart-Adams, Wlbrska, Thmas and Yn-Nelsn mdels. In rder t examine the reliability f the tested mathematial mdels, anther fur servie and regeneratin yles have been perfrmed using the same experimental predure with zelite partile size f mm n zelite bed depths f 80 mm and 40 mm (whih rrespnding t the bed vlume f 9.04 and 4.52 m 3, respetively) with the initial Cyle N. (Pb) mml/l nentratin f mml Pb/L and the flw rates f 1-3. Experimental nditins during servie and regeneratin yles are given in Table 2. Results and Disussin Appliatin f lumn methd in pratie reuires simulatin f the breakthrugh urves fr different experimental nditins. This predure was dne in this study thrugh the fllwing steps: (i) determinatin f experimental breakthrugh urves fr bed depth f 115 mm and different experimental nditins 8, (ii) testing f experimental breakthrugh urves by mathematial empirial mdels and alulatin f mdel parameters, (iii) evaluatin f mdels and verifiatin f alulated mdel parameters, (iv) simulatin f breakthrugh urves fr bed depths f 80 mm and 40 mm (v) experimental perfrmane f the breakthrugh urves at the bed depth f 80 mm and 40 mm and (vi) mparisn f simulated and experimental breakthrugh urves. Testing f breakthrugh urves by mathematial empirial mdels The empirial mdels by Bhart-Adams, Wlbrska, Thmas and Yn-Nelsn have been used fr a mathematial desriptin f the previusly published experimental results fr eight servie yles 8. These servie yles were perfrmed fr the zelite bed depth f 115 mm, initial nentratin f mml Pb/L, flw rates f lead slutin f 1-3, and fr zelite partiles size f mm and mm. Calulatins were arried ut by linear regressin analysis. The regressin effiient R 2 was alulated as indiatr f fitting f experimental pints with mathematial euatins f mdels given in Table 1. Slpe and interept were used fr alulatin f mdel parameters, and they are shwn in Tables 3-5. Evaluatin f applied mdels The euatins f mdels shwn in Table 1 inlude the remval apaity, whih is alulated frm Table 2 Experimental nditins fr servie yles and regeneratin yles γ (Pb) mg/l Servie yle BV/h γ (NaNO 3 ) g/l Regeneratin yle Bed depth 80 mm 9 th Bed depth 40 mm 10 th th th

5 TRGO et al.: MATHEMATICAL EMPIRICAL MODELS TO DYNAMIC REMOVAL OF LEAD 127 Experimental nditins Cyle N. Table 3 Parameters f the Bhart-Adams and Wlbrska mdels fr different experimental nditins (Pb) mml/l Parameters f the mdels k L/(mml h) mml/l mml/g β a R 2 h -1 Partile size mm 2 nd rd th th th th Partile size mm 2 nd Cyle N. (Pb) mml/l Table 4 Parameters f the Thmas mdel fr different experimental nditins k Th L/(mml h) mml/g Partile size mm 2 nd rd th th th th Partile size mm 2 nd Experimental nditins Cyle N. (Pb) mml/l Table 5 Parameters f the Yn-Nelsn mdel fr different experimental nditins Parameters f the mdel k YN h -1 τ h mml/g Partile size mm 2 nd rd th th th th Partile size mm 2 nd R 2 R 2 the linear dependenes f all mdels. Table 6 mpares alulated values with the experimental breakthrugh and exhaustin apaities B and E. The alulated values f remval apaities are very lse t the experimental apaities at the exhaustin pint E, whih indiate the appliability f tested empirial mdels. The parameters f eah mdel frm Tables 3-5 have been inserted int euatins f breakthrugh urves in Table 1, and fr the hsen values f time and vlume, the values f / have been alulated fr eah kineti euatin. The alulated values f / versus t r V have been used t plt the breakthrugh urves that were then mpared with the experimental nes in Figs 1 and 2. Figure 1 shws the mparisn f experimental and alulated urves fr the Thmas mdel, while the Fig. 2 shws that mparisn fr the Bhart-Adams, Wlbrska and Yn-Nelsn mdels. Bth figures shw the bviusly very gd agreement f the Thmas and Yn-Nelsn mdels with experimental pints fr all examined ranges n the x-axis. Therefre, these mdels have been applied in simulatin f breakthrugh urves fr bed depths f 80 mm and 40 mm.

6 128 INDIAN J. CHEM. TECHNOL., MARCH 2011 Simulatin f breakthrugh urves by Thmas and Yn- Nelsn mdels The simulatin the breakthrugh urves fr zelite bed depths f H = 80 and 40 mm is perfrmed using empty bed ntat time (EBCT) values and the Thmas and Yn-Nelsn mdel parameters alulated fr bed depth f 115 mm. EBCT inludes the bed depth and flw rate, and an be expressed as: 2 H H d π H EBCT = = =... (16) v /A 4 where A is rss-setinal area f the lumn (m 2 ) and d is lumn diameter (m). The values f EBCT have been alulated, and are given in Table 7. The EBCT fr the bed depth f Cyle N. Table 6 Cmparisn f experimentally btained breakthrugh B and exhaustin apaities E with alulated remval apaities Experiment B mml/g E mml/g Bhart-Adamsand Wlbrska Thmas mml/g Yn-Nelsn Partile size mm 2 nd rd th th th th Partile size mm 2 nd Fig. 1 Cmparisn f experimental (pints) and breakthrugh urves alulated by the Thmas mdel (line) fr different (a) flw rates, (b) initial lead nentratins and () zelite partile sizes Fig. 2 Cmparisn f experimental (pints) and breakthrugh urves alulated by the Bhart-Adams and Wlbrska mdels (dashed line) and Yn-Nelsn (full line) fr different (a) flw rates, (b) initial lead nentratins and () zelite partile sizes

7 TRGO et al.: MATHEMATICAL EMPIRICAL MODELS TO DYNAMIC REMOVAL OF LEAD mm is in range min, while fr bed depths f 80 mm and 40 mm is in range min. In rder t evaluate the mdel parameters fr the range f EBCT= min, the plts f Thmas and Yn-Nelsn mdel parameters (, k TH, k YN and τ, see Table 1) versus EBCT and flw rate are given n Fig. 3. Fr the values f EBCT 9.04 min and 4.52 min, the parameters f the Thmas and Yn-Nelsn mdel have been evaluated frm Figs 3a and 3. Fr the values f EBCT 2.26 min and 1.51 min, the same Table 7 Values f the EBCT fr different flw rates at examined bed depths ( (Pb)=1.026 mml/l) H=115 mm H=80 mm H=40 mm, EBCT, min parameters have been evaluated frm Figs 3b and 3d. Evaluated values are given in Table 8. The values f evaluated parameters have been inserted int the euatins f breakthrugh urves in Table 1, and fr the hsen values f time and vlume, the / was determined fr the Thmas and Yn-Nelsn mdels. The alulated values f / versus t r V have been used fr pltting f simulated breakthrugh urves fr bed depths H = 80 mm and 40 mm (Fig. 4.). Cmparisn f simulated and experimental breakthrugh urves The effiieny f simulatin was established by mparing the simulated urves with the urves prvided in new experiments at nditins given in Table 2. Their mparisn is shwn in Fig. 4, where lines indiate the simulated urves and pints the experimental results. Table 9 shws the Table 8 Parameters f the Thmas and the Yn-Nelsn mdels evaluated frm Fig. 3 Mdel Thmas Yn-Nelsn Parameter f the mdel H =80 mm =1 EBCT = 9.04 min =1 EBCT = 4.52 min =2 EBCT = 2.26 min =3 EBCT = 1.51 min k Th, L/(mml h) , mml/g k YN, h τ, h Fig. 3 Plts f mdel parameters versus EBCT and flw rate fr (a) and (b) the Thmas mdel; () and (d) the Yn-Nelsn mdel

8 130 INDIAN J. CHEM. TECHNOL., MARCH 2011 Mdel Thmas Yn-Nelsn Experiment Fig. 4 Cmparisn f simulated and experimental breakthrugh urves fr different bed depths, i.e., EBCT Table 9 Cmparisn f the values f breakthrugh t B and exhaustin times t E frm experimental and simulated urves Parameter f the mdel H =80 mm =1 EBCT = 9.04 min mparisn f breakthrugh and exhaustin times t B and t E fr experimental and simulated urves. Results in Fig. 4 and data in Table 9 shw a gd fit f bth mdels when EBCT = 9.04 and 4.52 min, while nly the Thmas mdel shws a gd fit fr EBCT = 2.26 and 1.51 min. The results nfirm that EBCT is the harateristi parameter fr preditin f the lumn press. The hange f the bed depth and flw rate, at the nstant nentratin and lumn diameter, affets the EBCT values. Therefre the gd fitting f the experimental and simulated urves is bserved when the values f EBCT are in the experimentally nfirmable range. This is imprtant fr saling up f the labratry experiment. Fr example, when the =1 EBCT = 4.52 min =2 EBCT = 2.26 min =3 EBCT = 1.51 min t B, h t E, h t B, h t E, h t B, h t E, h lumn diameter inreases linearly, the nstant EBCT value shuld be maintained with the apprpriate values f bed depth and flw rate. Cnlusins The remval f lead ins frm aueus slutins n a fixed bed f natural zelite an be desribed by empirial mdels f Bhart-Adams, Wlbrska, Thmas and Yn-Nelsn. The alulated values f remval apaities () are very lse t the experimental apaities at the exhaustin pint ( E ) whih is determined by graphial integratin f area abve breakthrugh urve up exhaustin pint 8. The Thmas and Yn-Nelsn mdels shw exellent fitting fr all examined range f breakthrugh urves at bed depth f 115 mm. Therefre, the Thmas and

9 TRGO et al.: MATHEMATICAL EMPIRICAL MODELS TO DYNAMIC REMOVAL OF LEAD 131 Yn-Nelsn mdel were used in simulatins f breakthrugh urves fr bed depth 80 and 40 mm. Results shw very gd agreement f simulated and experimentally perfrmed urves when the EBCT values were in the experimentally nfirmable range. The perfrmed experiments nfirmed the signifiane f the EBCT as the main parameter fr simulatin predure. Thmas mdel has been fund t be the mst suitable ne fr mathematial desriptin and mdelling f lead remval n a fixed bed f natural zelite in a wide range f EBCT values. Aknwledgement We are thankful t the Ministry f Siene, Eduatin and Sprts f the Republi f Cratia, fr finaning the prjet ( ). Referenes 1 Kurniawan T A, Chan G Y S, L W & Babel S, Si Ttal Envirn, 366 (2006) Wang S & Peng Y, Chem Eng J, 156 (2010) Stylianu M A, Hadjinstantinu M P, Inglezakis V J, Mustakas K G & Lizidu M D, J Hazard Mater, 143 (2007) Perić J, Trg M & Vukjević Medvidvić N, Water Res, 38 (2004) Ćurkvić L, Cerjan-Stefanvić Š & Filipan T, Water Res, 31 (1997) Petrus R & Warhl J K, Water Res, 39 (2005) Trg M, Perić J & Vukjević Medvidvić N, J Hazard Mater, B136 (2006) Vukjević Medvidvić N, Perić J & Trg M, Sep Purif Tehnl, 49 (2006) Inglezakis V J & Grigrpulu H P, Mirpur Mespur Mater, 61 (2003) Warhl J K & Petrus R, Mirpur Mespur Mater, 93 (2006) Lin S H & Huang C Y, J Envirn Eng, 126 (2000) Hamdaui O, J Hazard Mater, 161 (2009) Aksu Z & Gnen F, Press Bihem, 39 (2004) Aksu Z, Press Bihem, 40 (2005) Hamdaui O, J Hazard Mater, 138 (2006) Ghrai S & Plant K K, Chem Eng J, 98 (2004) Sag Y & Aktay Y, Press Bihem, 36 (2001) Tran H H & Rddik F A, Water Res, 33 (1999) Huthins R A, Chem Eng, 20 (1973) Wlbrska A & Pustelnik P, Water Res, 30 (1996) Wlbrska A, Water Res, 23 (1989) Stefanva R Y, J Envirn Si Health, A36 (2001) Shen Y S, Yung K & Wu M H, Sep Si Tehnl, 38 (2003) Hankins N P, Pliankarm S & Hilal N, Sep Si Tehnl 39 (2004) Yan G & Viraraghavan T, Biresure Tehnl, 78 (2001) Juang R S, Ka H C & Chen W, Sep Purif Tehnl, 49 (2006) Yn Y H & Nelsn J H, Am Ind Hyg Ass J, 45 (1984) Cmplexmetri Assay Methds with Triplex, 3rd ed (E. Merk, Damstadt), p.43.

The balancing of NO concentration fluctuations by adsorption/desorption. process on activated carbon

The balancing of NO concentration fluctuations by adsorption/desorption. process on activated carbon The balaning f NO nentratin flutuatins by adsrptin/desrptin press n ativated arbn I. Ptykvá, L. Obalvá*, L. Kubňvá, K. Obručka VŠB-Tehnial University f Ostrava, Centre fr Envirnmental Tehnlgy, 17. listpadu