ADSORPTION EQUILIBRIUM OF LIGHT HYDROCARBON MIXTURES BY MONTE CARLO SIMULATION

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1 Brazlan Journal of Chemcal Engneerng ISSN Prnted n Brazl Vol. 24, No. 04, pp October - December, 2007 ADSORPTION EQUILIBRIUM OF LIGHT HYDROCARBON MIXTURES BY MONTE CARLO SIMULATION V. F. Cabral, M. Caster and F. W. Tavares * Escola de Químca, Unversdade Federal do Ro de Janero, Phone: +(55) (21) , Fax: +(55) (21) , Cx P 68542, CEP , Ro de Janero - RJ, Brazl. E-mal: tavares@eq.ufrj.br. (Receved: May 30, 2005 ; Accepted: February 20, 2007) Abstract - The procedure presented by Cabral et al. (2003) was used to predct the adsorpton of multcomponent mxtures of methane, ethane, propane, and n-butane adsorbed on Slcalte S-115 at 300 K. The methodology employed uses the algorthm of molecular smulaton for the grand canoncal ensemble as an equaton of state for the adsorbed phase. The adsorbent surface s modeled as a two-dmensonal lattce n whch sold heterogenety s represented by of two knds of stes wth dfferent adsorpton energes. In all cases presented, the smulatons descrbed well the adsorpton characterstcs of the systems. Keywords: Adsorpton; Multcomponent mxtures; Monte Carlo smulaton. INTRODUCTION In the past few years, separaton and purfcaton processes based on adsorpton have become, n some cases, economcally feasble alternatves to unt operatons tradtonally used n the chemcal ndustry. For ths reason, the development of new methodologes capable of predctng ths phenomenon n the case of multcomponent mxtures s mportant for the desgn of new processes and for the optmzaton of exstng ones. Several methodologes have been developed to correlate adsorpton data on pure components and to predct gas mxture adsorpton. These nclude the Langmur model (Langmur, 1918), the statstcal approach (Hll, 1960), the potental model (Grant and Manes, 1966), the vacancy soluton model (Suwanayuen and Danner, 1980a, 1980b), the deal adsorbed soluton theory (Myers and Prausntz, 1965), the heterogeneous deal adsorbed soluton theory (Valenzuela et al., 1988), and twodmensonal equatons of state (Hoory and Prausntz, 1967). In recent years, molecular smulaton has become more attractve for studyng adsorpton phenomena, manly because of the ncrease n computatonal power and the development of new smulaton technques that allow yhe study of complex systems, whch would have been unfeasble n the past. A hstorcal revew of applcatons of computer smulaton to adsorpton phenomena, especally for two-dmensonal systems, has been publshed elsewhere (Steele, 2002). An advantage of molecular smulaton s that mcroscopc nformaton on the sold structure can be drectly used to develop sutable sold models for each type of real system. Examples of the use of the Monte Carlo technque n adsorpton calculatons are the work of Vlugt et al. (1999) and of Macedona and Magnn (1999). A common feature of these publcatons s that they use detaled force felds for the sold and for the flud. Even though very nterestng results have been obtaned from these smulatons, ther large computatonal effort stll lmts ther applcaton n equpment and process desgn. *To whom correspondence should be addressed

2 598 V. F. Cabral, M. Caster and F. W. Tavares For engneerng problems, the use of less detaled models, whch stll address the major aspects of adsorpton phenomena, represents a feasble compromse. Several papers have followed ths approach. In these publcatons, the authors supposed that the adsorbent surface s represented by a twodmensonal square lattce of M actve stes. Ramrez-Pastor et al. (1995) studed the adsorpton of dmers on heterogeneous surfaces, usng expermental adsorpton sotherms for O 2 and N 2 adsorbed on zeoltes 5A and 10X to test the relablty of ther smulaton model. The parameters of the smulaton model were adjusted to ft the expermental data. Ramrez-Pastor et al. (2000) used Monte Carlo smulatons to study the adsorpton of nonnteractng homonuclear lnear k-mers on heterogeneous surfaces. The authors modeled the heterogeneous surface wth two knds of stes. These stes formed square patches dstrbuted at random or n a chessboardlke-ordered doman on a twodmensonal square lattce. Bulnes et al. (2001) studed the adsorpton of bnary mxtures on heterogeneous solds usng Monte Carlo smulatons n the framework of the lattce gas model. Cabral et al. (2003) proposed a new methodology for correlatng the adsorpton of pure components and for predctng the adsorpton of bnary and ternary mxtures on homogeneous and heterogeneous solds. The methodology proposed by the authors uses the algorthm of molecular smulaton n the grand canoncal ensemble as an equaton of state for the adsorbed phase. In ths technque, the chemcal potental ( ), the total number of adsorpton stes (M), and the temperature (T) are specfed. In all cases presented, the smulatons descrbed the adsorpton characterstcs of systems. The results obtaned for the adsorpton of the bnary mxtures of propane-co 2 and propane-h 2 S, whch are strongly nondeal, were qute satsfactory, showng the potental of ths technque for the descrpton of real systems. In ths paper, the methodology proposed by Cabral et al. (2003) representng the adsorbent surface as a two-dmensonal square lattce, s used. The parameters of the smulaton model are ftted usng expermental data for the adsorpton of pure components and a fttng procedure analogous to that performed n the case of a usual equaton of state for determnaton of the PVT propertes of a flud. The model s then used for predctng the adsorpton of bnary, ternary, and quaternary mxtures of methane, ethane, propane, and n-butane on Slcalte S-115 (Abdul-Rehman et al., 1990). The outlne of the paper s as follows: n the next secton, the Monte Carlo technque s presented brefly. In the thrd secton, we present the smulaton model used n ths work. Next, we present the strategy used for parameter fttng. We then present our predctons for adsorbed bnary, ternary, and quaternary mxtures. Fnally, n the last secton, we present our conclusons. MONTE CARLO SIMULATION The methodology used n ths work employs the Monte Carlo method for a grand canoncal ensemble (T, M, 1, 2,, nc specfed). Accordng to the Metropols algorthm (Allen and Tldesley, 1987), ths technque conssts of three basc movements: dsplacement, nserton, and removal of an adsorbed molecule. The transton probablty from a confguratonal state o to a new state n s expressed by n P on mn1, (1) o n where s the rato between the probablty o denstes of the confguratonal states o and n. The movement s accepted when the probablty Po n s hgher than a number randomly generated between 0 and 1. In ths work, the random numbers are generated usng the routne ran2 from Press et al. (1992). More detals about each movement can be found n Cabral et al. (2003). SIMULATION MODEL The chanlke molecule used n ths work s modeled as m nteracton centers at a fxed separaton, whch s equal to the horzontal and vertcal dstances between neghbor stes on the lattce. In the adsorpton process, we assume that each molecular segment occupes a sngle adsorpton ste. Each molecular segment nteracts wth at most four neghborng stes,.e., the number of neghborng stes of each ste on the lattce s four. Ths parameter s named coordnaton number (Z). Fgure 1 shows a chanlke molecule composed of four segments n three possble confguratons. The sold lattce s modeled as a square matrx wth the dmensons 100 x 100 (M = 10000), n Brazlan Journal of Chemcal Engneerng

3 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 599 whch the sold heterogenety s represented by two knds of stes, characterzed by the energes a and b. The stes that have a stronger bond (hgher energy: ) to the adsorbate are called actve stes a and the fracton of actve stes s a. For each fracton of actve stes, several topologes can be generated, each of them characterzed by a random dstrbuton of square grans wth a specfc number of stes. To vsualze ths statement, Fgure 2 shows a sold square lattce (M = 1600) wth a fracton of 30% of ts actve stes and clusters (grans) of stes havng dmenson Dg 4. In order to mnmze the effect of the sold sze, perodc boundary condtons are consdered, both for dstrbutng the grans of actve stes on the sold and for movng molecules on the lattce. The square lattce s replcated throughout space to mmc an nfnte sold. In the course of a smulaton, f a molecule moves n the central lattce, ts perodc mage n each of the neghborng lattces moves n the same way. Thus, f a segment leaves the central lattce from one face, one of ts mages wll enter the central lattce through the opposte face. More detals of the perodc boundary condtons can be found elsewhere (Allen and Tldesley, 1987). Fgure 1: Chanlke molecule model. Fgure 2: Illustratve dagram of the 40x40 square lattce wth 30% of actve stes, randomly dstrbuted n grans wth the dmenson Dg=4. Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

4 600 V. F. Cabral, M. Caster and F. W. Tavares PARAMETER FITTING The parameters of the model are the Henry constant (K b ); the amount adsorbed at nfnte pressure ( N ); the sde-nteracton energy between two adsorbed segments of a molecule at neghborng stes ( / kt ); and the parameter r a, whch s related to the surface heterogenety. The equaton for parameter r a s a b ra exp (2) kt Once the values of parameters b and r a are known, the adsorpton energy between an actve ste and a segment of molecule ( a ) s determned usng Equaton (2). In the case of homogeneous solds, b a, and therefore parameter r a s 1. In order to ft all these parameters, we use an algorthm that fnds a mnmum pont of the objectve functon of n varables (parameters). For a complete descrpton of ths algorthm, see Nelder and Mead (1965) or Gll et al. (1981). We use the nonweghted least-square functon related to devatons n the amount adsorbed as the objectve functon. Thus, n the procedure for fttng the model parameters, pressure s used as the ndependent varable. Therefore, we assume devatons only n the measurements of the amount adsorbed. More detals about the numercal aspects of ths procedure can be found n Cabral et al. (2003). In order to use the model, t s necessary to establsh a strategy to characterze the adsorbent and the adsorbates at the mcroscopc level. Next, we present the strateges used to obtan model parameters from pure component adsorpton data. Methane, Ethane, Propane, and n-butane Adsorbed on Slcalte S-115 The molecules of methane and ethane are modeled wth three segments ( m methane 3, m ethane 3 ), whereas the remanng components (propane and n- butane) are modeled wth fve segments,.e., m propane 5 and m n butane 5. These values are chosen n such a way that the amount adsorbed at nfnte pressure of each component ( N ) would become compatble wth the expermental value of ths varable, because both varables ( N and m ) must obey the followng equaton: methane methane ethane ethane N m N m propane propane bu tan e bu tan e N m N m (3) Slcalte S-115 s a sster materal to zeolte ZSM-5 (Abdul-Rehman, 1990). Ths knd of sold has two types of channels straght and zgzag channels whch are connected va ntersectons. The zgzag channels have a dameter of 5.4 Å, whle the straght channels are ellptc and wth the larger and the smaller axes beng 5.75 and 5.15 Å, respectvely. Vlugt et al. (1999) studed the adsorpton of lnear and branched alkanes on ths knd of sold through molecular smulaton usng a three-dmensonal sold and a complete force feld for the alkanes. At low pressures, the authors observed that the molecules are located at the ntersectons. Interestngly, at hgh pressures ths scenery changes and the molecules are adsorbed unformly throughout the sold. Vlugt et al. (1999) determned that the maxmum capacty of the ntersectons occurs wth the loadng of four * molecules per unt cell ( A 4 ). The sold s modeled here as a lattce wth two knds of ste. The actve stes correspond to the ntersectons that can be occuped. The fracton of actve stes ( a ) s calculated usng nformaton about the adsorpton of n-butane. Ths molecule has a maxmum capacty of nne molecules per unt cell ( max 9 ). Therefore, the fracton of actve stes s calculated usng the followng equaton: * A a 0.44 max (4) The actve stes are arbtrarly grouped n square grans wth the dmenson Dg=4. Usng propane as a reference substance, four parameters (K b, / kt, r a, and N ) are ftted. Next, three parameters (K b, / kt, and r a ) of the remanng substances are ftted. The amounts of these molecules adsorbed at nfnte pressure are calculated usng Equaton (3). In Equaton (3) t s assumed that all pure components occupy the adsorbent surface completely at nfnte pressure. In Table1 the parameters obtaned for each component are shown. Fgure 3 contans the results for the correlaton of the pure components obtaned by molecular smulaton. Brazlan Journal of Chemcal Engneerng

5 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 601 Table 1: Parameters for methane, ethane, propane, and n-butane adsorbed on Slcalte S-115 at a temperature of 300K. Parameters Substances K b (kpa -1 ) r a / kt N (mol/kg) Methane Ethane Propane n-butane (c) (d) Fgure 3: Adsorpton sotherms for methane, ethane, propane (c), and n-butane (d) on Slcalte S-115 at 300 K. Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

6 602 V. F. Cabral, M. Caster and F. W. Tavares PREDICTIONS FOR MIXTURES Results of the predcted behavor of adsorbed bnary mxtures are presented n two dagrams. In the frst the mole fracton of component 1 n the gas phase, Y(1), s shown as a functon of the mole fracton of component 1 n the adsorbed phase, X(1), and n the second dagram presents the adsorbed amount versus the mole fracton of component 1 n the adsorbed phase, X(1) s shown. For each smulated pont, Monte Carlo steps are performed to allow the system to reach equlbrum. The average propertes of the system are computed after the performance of 10 5 Monte Carlo steps. Ths procedure s repeated ten tmes, for dfferent randomly generated solds wth the same fracton of actve stes and the same gran dmenson. The overall average and the standard devaton of the propertes at each pont are then calculated wth 100 averaged values. Each Monte Carlo step s composed of one attempt to move, nsert, and remove dfferent molecules n the system. The proposed smulaton model needs combnng and mxng rules, n the same way that an equaton of state appled to determne the PVT propertes of a gas mxture does. The followng mxng rule s used to determne the amount of mxture adsorbed at nfnte pressure ( N ): 1 N mx nc 1 x N mx (5) where x s the mole fracton of component n the adsorbed phase. The followng combnng rule, suggested by Romanelo (1991), s used to calculate the cross-contact energy ( / kt ): k kt m km kt 1 2 Bnary Mxtures m kk k k m (6) Abdul-Rehman et al. (1990) studed the bnary mxtures of methane(1)-ethane(2), methane(1)- propane(2), methane(1)-n-butane(2), and ethane(1)- propane(2) adsorbed on Slcalte S-115 at 345 and 655 kpa and a temperature of 300 K. All mxtures have nearly deal behavor. Methane(1)-Ethane(2) at 345 and 655 kpa The expermental data for the methane(1)- ethane(2) mxture are avalable at pressures of 345 (Fgure 4) and 655 kpa (Fgure 5). In these fgures, we present comparsons of the predctve calculatons from molecular smulaton wth expermental data. In both cases, the smulatons produced smlar predctons of mole fracton adsorbed. An unexpected behavor related to the amount adsorbed s observed n ths system. We expected that by ncreasng the pressure, the amount adsorbed would ncreases; however, ths behavor s not observed expermentally (see Fgures 4 and 5). In general, the smulatons predct well the behavor of the mxture. The largest devatons are found at 655 kpa. Fgure 4: Phase-equlbrum dagram and total amount adsorbed for methane(1)-ethane(2) on Slcalte S-115 at 345 kpa and 300 K. Straght dotted lne s for X(1)=Y(1). Brazlan Journal of Chemcal Engneerng

7 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 603 Fgure 5: Phase-equlbrum dagram and total amount adsorbed for methane(1)-ethane(2) on Slcalte S-115 at 655 kpa and 300 K. Straght dotted lne s for X(1)=Y(1). Methane(1)-Propane(2) at a pressure of 345 kpa In ths mxture, propane s adsorbed preferentally on Scalte S-115. Ths behavor can be confrmed by analyzng the expermental data on pure components at the same pressure as that of the mxture. As n the case of the prevous mxture, the expermental data show an ncrease n the amount of mxture adsorbed when compared to the amount of pure components adsorbed at the same temperature. Ths behavor s not predcted by smulatons that show systematc devatons n the predcton of amount adsorbed. Indeed the smulatons are consstent wth the amount adsorbed at the lmt of the pure component. However, n general, the smulatons satsfactorly represent ths system. In Fgure 6 a comparson of the expermental data wth those obtaned by smulatons s presented. Methane(1)-n-Butane(2) at a pressure of 345 kpa In Fgure 7 results of adsorpton are presented for the methane(1)-n-butane(2) mxture. In ths system, there s a strong preference for adsorpton of n- butane n ths mxture. The smulatons predct well the behavor of ths system. However, the smulatons slghtly overpredct the adsorpton capacty of the mxture. Fgure 6: Phase-equlbrum dagram and total amount adsorbed for methane(1)-propane(2) on Slcalte S-115 at 345 kpa and 300 K. Straght dotted lne s for X(1)=Y(1). Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

8 604 V. F. Cabral, M. Caster and F. W. Tavares Fgure 7: Phase-equlbrum dagram and total amount adsorbed for methane(1)-n-butane(2) on Slcalte S-115 at 345 kpa and 300 K. Straght dotted lne s for X(1)=Y(1). Ethane(1)-Propane(2) at a Pressure of 345 kpa The results for the ethane(1)-propane(2) mxture are presented n Fgure 8. Ths mxture seems to have a maxmum on the curve of adsorbed moles. Ths behavor should ndcate a devaton from dealty by the adsorbed soluton. However, ths behavor s not confrmed by the phase dagram of ths system, whch does not show nversons n the selectvty of components. The smulatons predct well the behavor of ths system n terms of mole fracton adsorbed. In the case of the amount adsorbed, the smulatons do not predct the maxmum on the curve of adsorbed moles, but rather a contnuous ncrease n ths varable wth the ncrease n gas mole fracton of ethane Y(1). Fgure 8: Phase-equlbrum dagram and total amount adsorbed for ethane(1)-propane(2) on Slcalte S-115 at 345 kpa and 300 K. Straght dotted lne s for X(1)=Y(1). Brazlan Journal of Chemcal Engneerng

9 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 605 In Fgure 9 the average devatons of adsorbed mole fracton ( X()%) and the average relatve devatons of amount adsorbed ( N R ads % ) are presented for each bnary mxture. The defntons of these devatons are respectvely gven by: np exp cal j j (7) j1 100 X()% X() X() np j1 exp jads exp jads cal jads np R 100 N N N ads % np (8) N where np s the expermental number of ponts of each exp cal set of expermental data; X() j and X() j are respectvely the expermental adsorbed mole fractons of speces and those obtaned from smulatons; and N and N are the expermental adsorbed mole exp ads cal ads numbers and those obtaned from smulatons. The number allocated for each bnary mxture corresponds to the order n whch that mxtures appear n the text. Therefore, the numbers from 1 to 5 are related to the mxtures of methane-ethane at 345 and 655 kpa, methane-propane, methane-butane, and ethanepropane, respectvely. Fgure 9: Average devatons of adsorbed mole fracton ( X()%) and the average relatve devatons of amount adsorbed ( N R ads % ), calculated for each bnary mxture. Each number holds for a mxture,.e., 1 for methane-ethane at 345 and 2 for methane-ethane at 655 kpa, 3 for methane-propane, 4 for methane-butane, and 5 for ethane-propane. Ternary Mxtures Abdul-Rehman et al. (1990) also presented expermental data on three ternary mxtures: methane(1)-ethane(2)-propane(3), methane(1)- ethane(2)-n-butane(3), and methane(1)-propane(2)- n-butane(3). Here, we show that our procedure can descrbe well the adsorpton of these mxtures. Methane(1)-Ethane(2)-Propane(3) at 345 kpa and 300 K In Fgures 10 and 11 present the performance of smulatons n predctng the adsorpton of ths ternary mxture are presented. In Fgure 10 the adsorbed mole fracton of methane and ethane as a functon of the gas mole fracton of methane s shown, specfyng that the rato of the gas mole fractons of ethane to propane s 2.77,.e., Y(2)/Y(3) = In ths fgure, the profle for adsorbed mole fracton of ethane ntercepts the straght lne Y(2)=X(2). Thus, an ncrease n the gas mole fracton of ethane produces an nverson n adsorpton selectvty for ths system. In the stuaton where there s low concentraton of methane n the gas phase, the adsorbed mole fracton of ethane s smaller than n the gas phase. Hs behavor s nverted for a hgh concentraton of methane n the gas phase. In Fgure 11 the adsorbed mole fracton of propane and the amount adsorbed as functons of gas mole fracton of methane are presented. In general, the smulatons descrbe well the features of ths ternary mxture. For these predctons, the average devatons of adsorbed mole fracton ( X()% ) of methane, ethane, and propane are determned to be 8.3, 4.4, and 12.7% respectvely, whereas the average relatve devatons as a functon of amount adsorbed ( N R ads % ) s calculated as 9.5%. Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

10 606 V. F. Cabral, M. Caster and F. W. Tavares Fgure 10: Profle for adsorbed mole fracton of methane and ethane as functons of the gas mole fracton of methane for the methane(1)-ethane(2)-propane(3) ternary mxture on Slcalte S-115 at 345 kpa and 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lnes are for X(1)=Y(1). Fgure 11: Profle for adsorbed mole fracton of propane and the amount adsorbed as functons of the gas mole fracton of methane for the methane(1)-ethane(2)-propane(3) ternary mxture on Slcalte S-115 at 345 kpa and 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lne s for X(1)=Y(1). Methane(1)-Ethane(2)-n-Butane(3) at 345 kpa and 300 K Results of ths ternary system are presented n Fgures 12 and 13. The average devatons of the adsorbed mole fracton ( X()% ) of each component are determned to be 6.2, 6.5, and 12.7% respectvely. The average relatve devaton as a functon of amount adsorbed ( N R ads % ) s calculated as 16.7%. Fgures 12 and 13 show the adsorbed mole fracton of every component and the amount of mxture adsorbed as a functon of gas mole fracton of methane. In these dagrams, the rato of the gas mole fractons of ethane to n-butane s fxed at Y(2)/Y(3) = As n the case of the prevous ternary mxture, the adsorbed mole fracton of ethane crosses the straght lne X(2)=Y(2), showng an nverson n adsorpton selectvty. The smulaton predcts ths nverson behavor; however ths predcton has a larger devaton than the predctons for the methane(1)-ethane(2)- propane(3) mxture. The predcton of amount adsorbed agrees qualtatvely wth the expermental data on ths mxture. Brazlan Journal of Chemcal Engneerng

11 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 607 Fgure 12: Profle for adsorbed mole fracton of methane and ethane as functons of the gas mole fracton of methane for the methane(1)-ethane(2)-n-butane(3) ternary mxture on Slcalte S-115 at 345 kpa and 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lnes are for X(1)=Y(1). Fgure 13: Profle for adsorbed mole fracton of n-butane and the amount adsorbed as functons of the gas mole fracton of methane for the methane(1)-ethane(2)-n-butane(3) ternary mxture on Slcalte S-115 at 345 kpa 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lne s for X(1)=Y(1). Methane(1)-Propane(2)-n-Butane(3) at 345 kpa and 300 K The adsorbed mole fracton of each component and the amount of mxture adsorbed as a functon of gas mole fracton of methane are presented n Fgures 14 and 15. In ths case, the rato Y(2)/Y(3) s fxed at The average relatve devaton of the amount adsorbed ( N R ads % ) s calculated as 5.5%, whereas the average devatons of adsorbed mole fracton ( X()% ) of methane, propane, and n-butane are determned to be 5.7, 1.6, and 7.4%, respectvely. The expermental data show that the adsorbed mole fracton of methane s always smaller than n the gas phase. Ths behavor s also predcted by smulatons, whch agree qualtatvely wth the expermental data on ths system. In the case of propane adsorpton, the expermental data ndcate an nverson n the selectvty of ths component. In the regon wth a low concentraton of methane n Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

12 608 V. F. Cabral, M. Caster and F. W. Tavares the gas phase, the adsorbed mole fracton of propane s smaller than n the gas phase. An ncrease n the gas mole fracton of methane to values hgher than approxmately 0.60 nverts the selectvty. The smulatons predct ths phenomenon very well. For n-butane, the expermental data shows that the adsorbed mole fracton of n-butane s larger than ts gas mole fracton for every composton of methane n the gas phase (Fgure 15). The smulatons also predct ths phenomenon. Fgure 14: Profle for adsorbed mole fracton profle of methane and propane as functons of the gas mole fracton of methane for the methane(1)-propane(2)-n-butane(3) ternary mxture on Slcalte S-115 at 345 kpa and 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lnes are for X(1)=Y(1). Fgure 15: Profle for adsorbed mole fracton profle of n-butane and the amount adsorbed as functons of the gas mole fracton of methane for the methane(1)-propane(2)-n-butane(3) ternary mxture on Slcalte S-115 at 345 kpa and 300 K and at a fxed rato of Y(2)/Y(3) = Straght dotted lne s for X(1)=Y(1). Brazlan Journal of Chemcal Engneerng

13 Adsorpton Equlbrum of Lght Hydrocarbon Mxtures 609 Quaternary Mxtures Fgure 16 shows a comparson between expermental and calculated values of mole fracton of each component adsorbed on Slcalte S-115 for dfferent vapor compostons. The average devatons of adsorbed mole fracton ( X()%) of each component are determned to be 4.1 (methane), 4.9 (ethane), 1.8 (propane), and 10.5% (n-butane). For ths quaternary mxture, the average relatve devaton of amount adsorbed ( N R ads % ) s calculated as 4.5 %. In general, the smulatons are n good agreement wth the expermental data. Fgure 16: Quaternary mxture of methane(1)-ethane(2)-propane(3)-n-butane(4) adsorbed on Slcalte S-115 at 300 K; data of Abdul-Rehman et al. (1990). CONCLUSIONS In ths work, we used the methodology proposed by Cabral et al. (2003) for correlatng the adsorpton of pure components and for predctng the adsorpton of bnary, ternary, and quaternary mxtures on Slcalte S-115. Ths methodology uses the Monte Carlo algorthm for a grand canoncal ensemble as an equaton of state for the adsorbed phase. In the case of pure components, the smulatons correlated the expermental data on methane, ethane, propane, and n-butane adsorbed on Slcalte S-115 at 300 K very well. In the case of the adsorpton of multcomponent mxtures, the smulatons showed good agreement wth the expermental data. In these predctons we used sold structure nformaton on the absorbent to obtan nsghts nto the macroscopc behavor of the systems studed. In the near future, ths knd of strategy can become a common workhorse for calculatng thermodynamc propertes for engneerng applcatons, due to progress n computer scence and n hardware technology. ACKNOWLEDGMENTS The authors acknowledge the fnancal support of the Brazlan agences CNPq and FAPERJ. REFERENCES Abdul-Rehman, H. B., Hasanan, M. A., and Loughln, K. F., Molecular Smulatons of Adsorpton Isotherms for Lnear and Branched Alkanes and ther Mxtures n Slcalte, Industral & Engneerng Chemstry Research, 29, No. 7, 1525 (1990). Allen, M. P. and Tldesley, D. J., Computer Smulaton of Lquds. Oxford Unversty Press, Oxford (1987). Bulnes, F., Ramrez-Pastor, A. J., and Pereyra, V. D., Study of Adsorpton of Bnary Mxtures on Dsordered Substrates, Journal of Molecular Catalyss A: Chemcal, 167, No. 1-2, 129 (2001). Cabral, V. F., Tavares, F. W., and Caster, M., Monte Carlo Smulaton of Adsorpton usng 2-D Models of Heterogeneous Solds, AIChE Journal, 49, No. 3, 753 (2003). Brazlan Journal of Chemcal Engneerng Vol. 24, No. 04, pp , October - December, 2007

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