Equilibrium sorption of crude oil by expanded perlite using ......A. Alihosseini et al. 592 Moreover, expanded perlite is commonly used in the processing of vegetable fat, juice, beer

A. Alihosseini et al.

ABSTRACT : During the past decades, a significant increase occurred in accidental oil spill in the aquatic environments.In this regard, oil spill in Marine freshwater is still considered as a major environmental hazard. In this research, theexperimental data on the sorption capacity of expanded perlite to crude oil were correlated with the equilibriumisotherm of Langmuir, Freudlich, Tempkin and the three parameter Redlich-Peterson isotherms. The results obtainedfrom each specified isotherms were compared and accuracy of the models were favorably discussed. Accuracy of eachmodel using the error function were evaluated. Moreover, the effect of type of objective function on the final resultswas investigated. To bring up the idea; the sum of square of the average squares of the errors, the sum of the squares ofthe errors, the hybrid fractional error function, Marquardt’s percent standard deviation and Chi-Square objectivefunction were used and the accuracy was obtained using each objective function. The results showed that the Redlich-Peterson model can better represent the equilibrium isotherm data for the crude oil to be up taken on the expandedperlite.

Keywords: Adsorption isotherms; Crude oil; Expanded perlite; Sorption capacity

Equilibrium sorption of crude oil by expanded perlite using different adsorption isotherms at 298.15 k

1*A. Alihosseini; 2V. Taghikhani; 2A. A. Safekordi; 2D. Bastani

1Department of Chemistry, Islamic Azad University, Ilam Branch, Ilam, Iran

2Department of Chemical and petroleum Engineering, Sharif University of Technology, Tehran, Iran

Int. J. Environ. Sci. Tech., 7 (3), 591-598, Summer 2010ISSN: 1735-1472© IRSEN, CEERS, IAU

Received 24 October 2009; revised 5 January 2010; accepted 28 April 2010; available online 1 June 2010

*Corresponding Author Email: [email protected] Tel./Fax: +9821 6686 1155

INTRODUCTIONSorption techniques widely assists in high-quality

treated effluents. For this reason, sorption process hasbeen investigated as a method of removing crude oilfrom seawater (Riazi and Al-Enezi, 1999; Yuh et al.,2005; Abdel-Ghani et al., 2009). Exfoliated graphite(Kawahara et al., 2002) and activated carbon (Yoko etal., 2002; Chen et al., 2010) are high effective for theremoval of spill oil from seawater (Ingaki et al., 2001).However, the use of exfoliated graphite and activatedcarbon may not be suitable in developing countriesbecause of its high cost. Thus, it is more suitable touse adsorbents such as clay minerals, peat and woodpowder (McKay and Ho, 1998; Ghalambor, 1999;Mahvi, 2008).

Among them, clay minerals (Adams et al., 2008) suchas perlite has received great deal of attention. Perlitehas a low density, high surface area and a low thermalconductivity. Also, since most perlite samples havehigh silica content (usually greater than 70 %), theyare high privileged with adsorptive characteristics(Dogan et al., 2000). The adsorptive character of perlite

is due to the silanol groups formed by silicon atoms onthe surface of perlite (Acemioglu, 2005). The types ofsilanol groups are shown as follows:

Moreover, below the hydrous oxide surface groupsin alumina are shown:

The silicone atoms at the surface tend to maintaintheir tetrahedral coordination with oxygen. Theycomplete their coordination at room temperature byattachment to monovalent hydroxyl groups, formingsilanol groups. The surface of perlite becomes morenegatively or positively charged according to the pH ofthe medium. This situation affects sorption capacity. Also, expanded perlite is an inert chemical which couldbe used as excellent filter aid and as filler in variousprocesses and materials (Polatli et al. , 2001).

Si OH

OH

HO Si

OH

OHHO

Si

OH

OHOH

OHAl −≡ Or = AlOH

OH

(1)

A. Alihosseini et al.

592

Moreover, expanded perlite is commonly used in theprocessing of vegetable fat, juice, beer in food industry.It is also used in cleaning of dams and ponds in aquaticenvironment, in obtaining of a clear liquid as a filterproduct, growing of seed and regularizing of the soil inagriculture and in so many other industrial applications.Adsorption has been an effective separation processfor a wide variety of applications (Sylwia, et al., 2003;Nameni et al., 2008). The most widely used adsorbentfor industrial applications is exfoliated graphite andactivated carbon (Malik, 2004; Gueu et al., 2007;Hussein et al., 2008). The analysis of the isotherm datais important to develop an analytic equation whichaccurately represents the results and could be usedfor design purposes (Louis et al., 1998; Pandey et al.,2010). The most well-known isotherms applied in solid-liquid systems are the theoretical equilibrium isotherms,including Freundlich (Freundlich, 1906; Wu et al., 2001)as the earliest known relationship; Langmuir (Langmuir,1918) the best known and most often used isotherm forsorption of solute from a liquid solution and Redlich-peterson (Redlich and Peterson, 1959) containing threeparameters isotherms. In addition, the latter is anequation comprised of Freundlich and Langmuirisotherms and Tempkin (Tempkin and Pyzhev, 1940)isotherm which represents data equilibrium ofadsorption.

Linear regression and least square method werefrequently used to determine the most fitted modelthroughout the years and finding the parameters ofthe models, respectively. However, transformations ofnon-linear isotherm equations to linear form implicitlyalter their error structure and may also violate the errorvariance and normality assumption of standard leastsquares. In this study, a comparison of linear regressionand five different error functions as: a) the sum ofsquare of the average squares of the errors (ERAV). b)The sum of the squares of the errors (ERRSQ). C) Thehybrid fractional error function (HYBRID). d)Marquardt’s percent standard deviation (MPSD). e)Chi-square analysis (χ2) were examined of fourisotherms (Langmuir, Freundlich, Redlich-Peterson andTempkin) and have been applied to the experiment ofcrud oil sorption on expanded perlite(Marquardt, 1963;Allen et al ., 2003)

In this work, cost-effective expanded perlite sampleswere selected as a sorbent for the investigation ofsorption isotherm of crude oil from oil and seawatermixing. Perlite is glass volcanic rock varying in color

from gray to black When it is heated to elevatedtemperatures (850-1100 oC), it expands to 35 times itsinternal volume and called as ‘expanded perlite’ (Bastaniet al., 2006).

MATERIALS AND METHODSThe successful representation of the dynamic

adsorptive separation of solute from solution onto anadsorbent depends upon a good description of theequilibrium separation between the two phases.Adsorption equilibrium is the amount of solute beingadsorbed onto the adsorbent and equal to the amountbeing desorbed. At this point, the equilibrium solutionconcentration remains constant. By plotting solidphase concentration against liquid phase concentrationgraphically, it is possible to depict the equilibriumadsorption isotherm. There are many theories relatingto adsorption equilibrium.

Langmuir isothermThe Langmuir isotherm theory assumes monolayer

coverage of adsorbate over a homogenous adsorbentsurface. Graphically, plateau characterizes the Langmuirisotherm. Therefore, at equilibrium, a saturation pointis reached where no further adsorption can occur.Sorption is assumed to take place at that site. In Eq. 2,KL and aL are the Langmuir isotherm constants while Ceis the oil weight in the liquid phase and qe is the oilweight in the solid phase at equilibrium state.

The Langmuir constant, KL and aL are evaluated ofthe linearization of Eq. 2. The linear expression takesthe following form:

Hence, by plotting Ce/qe against Ce, it is possible toobtain the value of KL from the intercept (1/KL) and thevalue of aL from the slope (aL/KL). The theoreticalmonolayer capacity is Q0 and is numerically equal to(KL/aL). The Langmuir equation is applicable tohomogeneous sorption where the sorption of eachmolecule has equal sorption activation energy. Theequation is thermodynamically consistent and followsHenry’s Law at low concentrations. Therefore, as Ce

eL

eLe Ca

CKq

+=

1(2)

L

eL

Le

e

KCa

KqC

+=1 (3)

A. Alihosseini et al.Int. J. Environ. Sci. Tech., 7 (3), 591-598, Summer 2010

593

becomes lower, aLCe is much less than unity and qe,that is, analogous to Henry’s Law.

Freundlich isothermThe Freundlich expression is an exponential

equation and therefore, assumes that as the adsorbateconcentration increases with the concentration ofadsorbate on the adsorbent surface. Theoretical, usingthis expression, an infinite amount of adsorption canoccur.

In this equation, KF and bf are the Freundlichconstants. This expression is characterized by theheterogeneity factor, bf, and thus the Freundlichisotherm may be used to describe heterogeneoussystem (Moon and Lee, 1983; Al-Duri and McKay,1988). The Freundlich equation agrees well with theLangmuir equation over moderate concentration rangesbut, unlike the Langmuir expression, it does not reduceto the linear isotherm (Henry’s Law) at Low surfacecoverage. Both these theories suffer from a drawbackthat equilibrium data over a wide concentration rangecannot be fitted with a single set of constants .Todetermine the constant Kf and bf, the linear form of theequation as shown below may be used to plot ln(qe)against ln (Ce) as:

Redlich - Petertson isothermRedlich and Peterson proposed an empirical three

parameter equation which may be used to representadsorption equilibrium over a wide concentration rangeof adsorbate. The adsorbate concentration atequilibrium condition can be computed as follows:

Where, β is a constant parameter and is normallyless than unity. This equation reduces to a linearisotherm at low surface coverage, to the freundlichisotherm at high adsorbate concentration and to theLangmuir isotherm when β=1. However, the equationcannot be linearised for easy estimation of the isothermparameter KR, aR and β. The linearization of theexpression gives the following relation:

fbeF CKqe = (4)

effe LnCbLnKLnq +=

βeR

eR

CaCK

qe+

=1 (6)

βe

R

R

Re

e CKa

KqC

+=1

(7)

Plotting Ce/qe against βeC yields a straight line

with slope= R

R

Ka and intercept =

RK1 . However,,

plotting of Eq. 7 is not applicable because of threeunknown parameters contained within the equation.Therefore, a minimization procedure is adopted tomaximize the correlation coefficient between thetheoretical data for qe predicted from Eq. 7 and thecorresponding experimental data. More often, themethod used to determine isotherm parameters is thelinear regression with transformed variables. Thequality of the fit of the experimental data with theisotherm equation is assessed on the magnitude of thecorrelation coefficient for the regression. In otherwords, the isotherm giving the correlation coefficientclosest to unity provides the best fit.

Tempkin isothermTempkin and pyzhev are considered as the effect of

some indirect adsorbate/adsorbate interaction onadsorption isotherms and suggested that because ofinteraction the heat of adsorption of all the moleculesin the layer would decrease linearly with coverage. Theamount of adsorbate can be given as below:

Eq. 7 can be expressed in its linear form as:

with

The adsorption data can be analyzed according toEq. 9 and a plot of qe versus lnCe enables thedetermination of the isotherm constant, A and B. Itwould be worth noting that the constant B is related toheat of adsorption.

Error functions In the present study, five different error functionswere examined and in each case the respective errorfunction across the liquid phase concentration rangeusing the QBasic software.

eACb

RTqe ln⎟⎠⎞

⎜⎝⎛=

(5) (8)

ee CBABq lnln += (9)

bRTB =

(10)

A. Alihosseini et al.

The sum of square of the average squares of theerrors

Here, the error function minimized the fractional errordistribution across the entire concentration range

Where, qe,calc is the equilibrium capacity (mg/g)calculated from the applied model and qe, meas is theequilibrium capacity (mg/g) obtained from theexperimental data. If data from the model are similar tothe experimental data, ERAV will be a small number; ifthey are different, ERAV will be a large number (Khanset al., 1997).

The sum of the squares of the errorsThis widely used error function has one major

drawback. The function will result in the calculatedisotherm parameters providing a better fit at the higherend of the liquid phase concentration range. This isbecause the magnitude of the errors and hence thesquare of the errors will increase as concentrationincreases.

The hybrid fractional error functionThis error function was developed in order to

improve the fit of the ERRSQ method at lowconcentration values. In this method, each ERRSQ valuewas divided by the experimental solid phaseconcentration q value. In addition, a divisor wasincluded as a term for the number of degrees of freedomfor the system, the number of data points minus thenumber of parameters within the isotherm equation.

Marquardt’s percent standard deviationThis error function was similar to a geometric mean

error distribution which was modified to allow for thenumber of degrees of freedom of the system.

594

Equilibrium sorption of crude oil by expanded perlite

2/1

1

2,, )(1

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= ∑

=

p

imeasecalce qq

pERAV (11)

( ) 21 ,, ii measecalce qqERRSQ ∑ =

−=(12)

∑= ⎥

⎥⎦

⎤

⎢⎢⎣

⎡ −

−=

p

i mease

calcemease

qqq

nPHYBRYID

1 ,

2,, )(100

(13)

( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −

−= ∑

=

p

i mease

calcemease

qqq

npMPSD

1 ,

2,,1100

(14)

( )∑=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −=

p

i calce

calcemease

qqq

1 ,

2,,2χ (15)

Chi-square analysis (χ2)The advantage of using chi-square test is to compare

all isotherms on the same abscissa and ordinate. Theequivalent mathematical statement was:

If data from model were similar to the experimentaldata, χ2 would be a small number and vice versa thevalues of χ2 of each model were shown in Table 1.

RESULTS AND DISCUSSION Table 1 presents the values of the parametersintroduced by the Langmuir isotherm, i.e., aL and kL,associated with the correlation coefficient obtainedfrom least square fit of the model to the correspondingexperimental data. Also, it can be seen from Table 1that the type of objective function used to obtain theregressed values of the parameters was mentioned tobe error functions. As mentioned earlier, the errorfunctions can be given by Eqs. 11-15. The values ofthe parameters can be directly used to obtain theamount of adsorbat to be sorbed onto the expandedperlite studied in this work. As observed from Table1, the correlation of the Langmuir isotherm wasperformed with the sorption experimental data ofdifferent types of crude oil onto the expanded perlite. Table 2 illustrates the values of the parametersintroduced by the Freunlich isotherm, i.e., KF and bf,associated with the correlation coefficient obtainedfrom least square fit of the model to the correspondingexperimental data. Moreover, it can be seen from Table2 that the type of objective function used to obtainthe regressed values of the parameters was mentionedto be error functions.

Redlich - Petertson isothermThe Redlich-peterson isotherm plots for sorption

of crude oils on expanded perlite are presented in Fig.1. Again, examination of the plot shows that theRedlich-peterson isotherm accurately describes thesorption behaviors of crude oil on expanded perliteover the concentration ranges studied. The Redlich-peterson isotherm constants, KR, aR, β and R2 anderrors function are presented in Table 3. Since themethod used to derive the isotherm parametersmaximizes the linear coefficient of determination, it isunsurprising that in this case, the Redlich-petersonisotherm exhibit extremely high R2 values indicating,superficially at least, that it produces a considerablybetter fit compared to the preceding two-parameterisotherms. This equation reduces to a linear isotherm

A. Alihosseini et al.

Table 1: Langmuir isotherm constants aL and KL and errors function Chi-Square R2 KL aL Oil Type 9.2314*10-1 0. 9132 0.42311 6.584*10- I. O. L

1.152*10-1 0.9356 0.4756 7.248*10-2 M. As MPSD HYBRID ERRSQ ERAV Oil Type

10.36317 1.073953 0.7860075 2.3645 I O.L 11.4567 1.15243 0.82314 2.5463 M. As

Table 2. Freundlich isotherm constants Kf and bf and errors functionOil Type KF bf R2 Chi-Square I. O. L 2.531 0.23278 0.989 5.8513*10-2 M. As 2.7846 0.2506 0.988 6.54*10-2 Oil Type ERAV ERRSQ HYBRID MPSD I. O. L 0.928562 1.081*10-2 6.5227*10-3 0. 8078 M. As 0.98251 1.15*10-2 8.754*10-3 0.9423

Table 3: Redlich-Peterson isotherm constants KR, aR, β, R2 and errors function

Oil Type KR aR β R2 Chi-Square I .O.L 5.190622 1.90345 0.78 0.999 1.025*10-2 M. As. 5.092 2.0452 0.79 0.999 4.32*10-2 Oil Type ERAV ERRSQ HYBRID MPSD I .O.L 0.1927 9.445*10-3 1.132*10-3 0.7254 M. As. 0.2841 7.458*10-3 7.674*10-3 0.9843

Fig. 1: Langmuir isotherm and model data

at low surface coverage, to the Freundlich isotherm athigh adsorbate concentration and to the Langmuirisotherm when β=1.

Tempkin isothermThe Tempkin isotherm plots for sorption of crude

oils on expanded perlite are presented in Fig. 2. TheTempkin isotherm constants, A, B, R2 and errorsfunction are presented in Table 4. Fig. 2: Frundlich isotherm and model data

The different forms non- linear isothermsThe different Non-linear forms of Redlich-peterson,

Freundlich, Langmuir and Tempkin isotherm plots andthe experimental data for sorption of crude oils onexpanded perlite are presented in Figs. 3 and 4.Therefore, drawing conclusion from the Redlich-peterson isotherm was best-fitting isotherm, followedby the Freundlich model for this sorption system.

595

Int. J. Environ. Sci. Tech., 7 (3), 591-598, Summer 2010

Ce/q

e (g

/L)

2

4

6

8

10

12

14

16

18

20

24.3

35.2 40

48.3

52.2

57.1

66.6

72.7 92 100

147

Ce (g)Iranian o il light Medium As ian Mo del data

1.51.55

1.61.65

1.71.75

1.81.85

1.91.95

22.05

2.12.15

3.19

3.56

3.69

3.88 4

4.04 4.2

4.29

4.52

4.61

4.99

LnC (e)Iranian o il light Mo del da ta Medium as ian

Ln q

(e)

A. Alihosseini et al.

4

4 .5

5

5 .5

6

6 .5

7

7 .5

8

8 .5

9

7 .3 4 6 5 8 .2 0 1 8 .4 9 5 8 8 .92 8 7 9 .10 8 3 9 .3 15 6 9 .6 6 8 9 .8 7 0 7 10 .4 14 10 .6 0 5 11.49 2

ln C e

Ira n ia n o il lig h t M o d e l da ta M e d iu m A s ia n

Fig. 3: Redlich- Peterson isotherm and model data

Fig. 4: Temkain isotherm and experimental data

C (e

) / q

(e)

0

2

4

6

8

10

12

14

16

18

2 0

0 10 20 3 0 40 50 6 0

C (e )b

Ira n ia n il ligh t M o de l da ta M e dium A s ia n

q (e

)

596

CONCLUSIONThe equilibrium adsorption of two-type crude oil

by expanded perlite has been reported. The resultsrevealed the potential of the expanded perlite issuitable to be a low-cost sorbent for clean-up crudeoil. The equilibrium results have been modeled andevaluated using four different isotherms and five

Table 4: Tempkin isotherm constants A, B, R2 and errors function

Chi-Square R2 B A Oil Type 4.2664*10-2 0.98 0.6678 12 I.O.L

4.537*10-2 0.974 0.7845 14 M .As MPSD HYBRID ERRSQ ERAV Oil Type 3.7554 1.410318 *10-1 8.3224*10-2 0.3105 I.O.L

4.658 9.724*10-2 2.5*10-2 0.98251 M.As

different error functions including a linear transformmodel. The results showed that the equilibrium datafor all the crude oil–sorbent systems are fitted tothe Redlich-Peterson and Freundlich isothermsmodel best. The linear transform model providedhighest correlation coefficient for the case of theRedlich-Peterson isotherm (R2 = 0.999). The R2 for

A. Alihosseini et al.

597

Langmuir isotherm is 0.9132 troughs 0.93561. Besides,the sum of square of the average squares of the errors(ERAV) equal 2.36451 for Langmuir isotherm. TheLangmuir isotherm theory assumes monolayercoverage of adsorbate over a homogenousadsorbent surface. Using of the error functions foroptimization showed that often the isotherms weregenerally better represented using the ERRSQ,HYBRID and Chi-Square errors function.

NomenclatureaL: Langmuir isotherm constant (dm3/mg)aR : Redlich–Peterson isotherm constant (dm3/mg) A: Tempkin isotherm constantb: Tempkin isotherm energy constant (J/mol)bF : Freundlich isotherm exponentB: Tempkin isotherm energy constant (dm3/g)C0: Initial liquid-phase concentration (mg/dm3)Ce: Equilibrium liquid-phase concentration (mg/m3)ERRSQ: The sum of the squares of errorsHYBRID: The hybrid fractional error functionKF : Freundlich isotherm constant (dm3/g)KL: Langmuir constant (dm3/g)KR: Redlich–Peterson isotherm constant (dm3/g)MPSD: Marquardt’s percent standard deviationn: Number of isotherm parametersp: Number of data pointsqe: Equilibrium solid-phase concentration (mg/g)Qo: Monolayer capacity of Langmuir equation(mg/g)qe, calc: Calculated dye equilibrium solid phaseconcentration (mg/g)qe, meas : Measured dye equilibrium solid phaseconcentration (mg/g)R: Gas constant (J mol/K)T: Temperature (K)β: Exponent in Redlich–Peterson isotherm

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Int. J. Environ. Sci. Tech., 7 (3), 591-598, Summer 2010

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Equilibrium sorption of crude oil by expanded perlite

AUTHOR (S) BIOSKETCHESAlihosseini, A., Assistant Professor, Department of Chemistry, Islamic Azad University Ilam Branch, Ilam, Iran.Email: [email protected]

Taghikhani, V., Full Professor, Department of Chemical and petroleum Engineering, Sharif University of Technology, Tehran, Iran.Email: [email protected]

Safekordi, A. A., Full Professor, Department of Chemical and petroleum Engineering, Sharif University of Technology, Tehran, Iran.Email: [email protected]

Bastani, D., Full Professor, Department of Chemical and petroleum Engineering, Sharif University of Technology, Tehran, Iran.Email: [email protected]

How to cite this article: (Harvard style)Alihosseini, A.; Taghikhani, V.; Safekordi, A. A.; Bastani, D., (2010). Equilibrium sorption of crude oil by expanded perlite usingdifferent adsorption isotherms at 298.15 k. Int. J. Environ. Sci. Tech., 7 (3), 591-598.

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