Paraffin Separations and Olefin Purification

Horvath-Kawazoe (H-K) model (using the Cheng-Yang version for spherical pores and correction for .... based simply on a known pore size distribution (...
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Ind. Eng. Chem. Res. 1999, 38, 3614-3621

New Sorbents for Olefin/Paraffin Separations and Olefin Purification for C4 Hydrocarbons Joel Padin and Ralph T. Yang* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136

Curtis L. Munson Separations Technology, Chevron Research and Technology Company, Richmond, California 94802-0627

New adsorbents for olefin/paraffin separations are synthesized by incipient wetness impregnation and ion exchange of Ag+ cations on high-surface-area substrates. The separation/purification is achieved by selective adsorption of olefins and/or dienes by π-complexation. It was shown that the monolayer AgNO3/SiO2 sorbent has a selective adsorption ratio of 8.33 for butene/butane at 70 °C and 1 atm. The isotherm linearity for olefin is ideally suited for cyclic adsorption-desorption processes. Moreover, the performance of the π-complexation sorbent (AgY zeolite) for the purification of butene by removal of trace amounts of butadiene was found to be superior to that of sorbents based on physical adsorption (5A zeolite and NaY). It was also shown that the Horvath-Kawazoe (H-K) model (using the Cheng-Yang version for spherical pores and correction for isotherm nonlinearity) is capable of predicting the adsorption behavior of the C4 hydrocarbons on 5A zeolite. Because the H-K model only involves dispersion forces, it underpredicts for gas-solid systems in which other forces also exist such as electrostatic and π-complexation. C4H6/C4H8 on 5A zeolite is one of these systems. Introduction Olefin/paraffin separations represent a class of most important and also most costly separations in the chemical industry. Cryogenic distillation has been used for over 60 years for these separations.1 They remain the most energy-intensive distillations because of the close relative volatilites.2 The most important olefin/ paraffin separations are for the binary mixtures of ethane-ethylene and propane-propylene. A number of alternatives have been investigated.3 The most promising one appears to be separation via π-complexation. Separation via π-complexation is a subgroup of chemical complexation where the mixture is contacted with a second phase containing a complexing agent.4 The advantage of chemical complexation is that the bonds are stronger than those formed by van der Waals forces alone. Therefore, it is possible to achieve high selectivity and high capacity for the component to be bound. At the same time, the bonds are still weak enough to be broken by using simple engineering operations such as raising the temperature or decreasing the pressure. This picture has been illustrated by the bond energy-bond type diagram of G. E. Keller.4 π-Complexation pertains to the main-group (or dblock) transition metals, i.e., from Sc to Cu, Y to Ag, and La to Au on the periodic table.5 These metals or their ions can form a σ-bond to carbon and, in addition, the unique characteristics of the d orbitals in these metals or ions can form bonds with unsaturated hydrocarbons (olefins) by backdonation. This type of bonding is broadly referred to as π-complexation. π-Complexation has been previously considered for olefin/paraffin separation and purification by employing liquid solu* Corresponding author. Telephone: (734) 936-0771. Fax: (734) 763-0459. E-mail: [email protected].

tions containing silver (Ag+) or cuprous (Cu+) ions.1,3,6-8 While gas-solid operations can be simpler as well as more efficient, particularly by pressure-swing adsorption (PSA), the list of attempts for developing solid π-complexation sorbents is a brief one. CuCl has been considered in the powder form for olefin/paraffin separations.9-11 However, CuCl in the solid particulate form does not have a high surface area and, therefore, has a low olefin adsorption capacity. Ag+ cations dispersed on solid have also been considered. Hirai and co-workers have published a series of papers and obtained patents on Ag+ resins.12,13 They recognized that polymeric resins do not adsorb large amounts of low paraffins such as C2H6 and C3H8. Unfortunately, they used a number of anion (not cation) exchange resins. The resins were used only as supports for Ag+ salts (halides were used) but not to effectively disperse the silver cations. The only commercialized solid sorbent for π-complexation is CuCl/γ-Al2O3 (or other Cu+ salts) for CO removal and separations involving CO.14 It should also be noted that the commercially available sorbents do not have significant selectivities for olefins over their corresponding paraffins. Also, the use of these commercial sorbents might require additional operations.14-17 Yang and Kikkinides18 had success in preparing Ag+exchanged cation-exchange resin and also monolayer CuCl/γ-alumina for olefin/paraffin separations. Ionexchanged Y-type zeolites containing Ag+ and Cu+ were also tried, but their selectivities were hindered because the paraffins were also strongly adsorbed by the bare zeolite surface. Unlike the zeolite surface, the CuCl surface adsorbs few low molecular weight paraffins. Therefore, it would be a great advantage to be able to spread a near monolayer of CuCl on a zeolite to create an effective sorbent. Previous work by Xie and Tang19 demonstrated that it is possible to spread a near monolayer of CuCl on several types of zeolites. However,

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it was not determined in this work whether spreading of CuCl caused a partial or total blockage of the zeolite pores, which would lead to a reduction in rates of adsorption or in total adsorption capacity. Another type of possible candidates for substrate for π-complexation sorbents are pillared interlayer clays (PILC). PILCs are a new class of aluminosilicate material which have attracted increasing interest for both adsorption and catalysis because of their unique structural and chemical properties.20,21 In previous work by Cheng and Yang,20 olefin-specific sorbents were synthesized using the thermal monolayer dispersion technique. However, the capacities obtained from these sorbents did not make them suitable candidates for commercial use. More recently, a number of π-complexation adsorbents have been developed for olefin/paraffin separations. These include Ag+-exchanged resins22 and AgNO3/ SiO2.23 These π-complexation sorbents provided excellent olefin capacities and selectivities. They have been shown to be superior to sorbents that separate olefins from paraffins based on kinetic separation such as 4A zeolite.23 Several opportunities exist for the application of π-complexation-capable sorbents in the fractionation of C4 streams. The C4 streams obtained from various hydrocarbon cracking operations contain many important chemicals. The absolute amounts and compositions of the C4 fraction obtained from cracking are substantially affected by the type of cracking, severity of cracking conditions, and feedstock.24 The C4 fraction cannot be separated into its components economically by simple distillation because of the close proximity of their boiling points. Several separations methods have been developed for this application ranging from the selective reaction of isobutene to extractive distillation of 1,3-butadiene. The remaining C4 stream consists primarily of n-butenes and butanes. This stream can be further separated by selective adsorption of the n-butenes on π-complexation-capable sorbents. Another area where π-complexation sorbents can make an impact is in the purification of normal R-olefins (NAO). NAOs are chemical intermediates used to make a variety of products. The largest uses for NAOs are in the production of alcohols (via oxo chemistry), as comonomers for polyethylene production, and in the synthesis of poly(R-olefins), which are used in synthetic lubricants. Also, oligomerization of n-butenes to more valuable octenes is an effective way of upgrading their value.25 A variety of catalysts have been developed for this reaction. The most common metal-based catalyst used in this application involves nickel. However, one common concern in all of the above applications is the need for ultrapure olefins with very low levels of 1,3butadiene (C3H6). It has been shown by Podrebarac and co-workers26 that the nickel-based catalyst used in the oligomerization of n-butenes can be severely deactivated in the presence of small traces of C4H6 in the feed. The last part of this paper will address the feasibility of using the Horvath-Kawazoe (H-K) equation to predict isotherm behavior. A theoretical formulation was developed by Horvath and Kawazoe27 for calculating the micropore size distribution of a carbon molecular sieve from nitrogen isotherms at 77 K. It has since been applied to determine the micropore size distribution of a variety of other systems such as zeolites.28-30 The appeal of the H-K model is not only its simplicity but its ability to capture the essential features of progressive

pore filling. The H-K model provides a one-to-one function between the pore size and the relative pressure at which the pore is filled. The original model was derived for slit-shaped pores, and it has since been improved to account for different adsorbent geometries, such as cylindrical31 and spherical pores,32,33 by considering the curvature effects of the pore walls. Also, improvements in the H-K model have been made to account for nonlinear behavior in the adsorption isotherm.33 Also, the work of Cheng and Yang34 demonstrated that the H-K model is capable of predicting isotherms of the adsorbate at other temperatures and also of predicting isotherms for other adsorbates at the same temperature. In this work, we have studied the feasibility of using the π-complexation-capable sorbents developed for the separation of butenes from butanes. Also, we have developed new sorbents capable of purifying an olefin stream by removing trace amounts of 1,3-butadiene. Furthermore, we continue to explore the possibility of applying the improved H-K model to predict isotherms based simply on a known pore size distribution (PSD) and physical properties of the adsorbent and adsorbate. Experimental Section New adsorbents for olefin/paraffin separations are synthesized by effective dispersion of Ag+ cations on high-surface-area substrates. AgNO3 (Strem Chemicals) is dispersed on a SiO2 (Strem Chemicals) surface using the standard incipient wetness technique. This technique yields the best sorbents that showed the highest selectivities, olefin capacities, and reversibilities, and fastest rates.35 Our previous studies have demonstrated the ability of these materials to separate ethaneethylene and propane-propylene mixtures effectively and competitively.23 Also, they have been shown to be superior to kinetic separations-based sorbents for the above applications. The incipient wetness impregnation technique involves preparing a solution of the salt to be dispersed at a concentration that is determined by the desired loading of the salt. The solution is then mixed with the substrate, where it is imbibed by the substrate because of incipient wetness. After the substrate has imbibed the solution containing the salt into its pore structure, the sample is heated to remove the solvent. Care needs to be taken when selecting solvents for use in this technique. First, the salt needs to be soluble in the solvent to a sufficient extent to allow enough salt to be dissolved in the volume of solution that is equal to the pore volume of the substrate. Second, the solvent selected needs to be able to wet the surface of the substrate. AgNO3/SiO2 at a weight ratio of 1.08 was the sorbent utilized in this work. The optimum loading of AgNO3 was determined by varying the salt content of each sample and measuring its olefin adsorption and olefin/paraffin selectivity. Results are only shown for the optimum loading of 1.08. Because AgNO3 is highly soluble in water, it was chosen as the solvent. Also, because SiO2 has a high affinity for water, this also ensures proper wetting of the substrate and therefore proper dispersion of the salt. A 1.2 M solution of AgNO3 was prepared. A volume of the solution equal to the total pore volume of the SiO2 sample was brought in contact with the substrate, so that a AgNO3/SiO2 ratio equal or close to 1.08 was achieved. The sample was then heated for 4 h at 105 °C in air to remove the water. The ratio

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of the resulting sample was calculated at 1.08, and the sample was used without further treatment. The BET surface area of this sorbent was measured by nitrogen adsorption at 77 K at 138 m2/g. The decrease in surface area in the sorbent when compared with the substrate is due to blockage of some pores by the AgNO3 salt. As mentioned in the previous section, one area of interest is the purification of an olefin stream, specifically, removal of trace amounts of C4H6 from a saturated 1-butene (C4H8) stream. For this application, the bond between the adsorbate and the adsorbent must be very strong in order to adsorb significant amounts of C4H6 at low partial pressures. Zeolites were selected as the substrates because of their high Henry’s law region adsorption for hydrocarbons. Specifically, zeolite types A and Y were selected. The dispersion of Ag+ cations was accomplished using ion exchange. The chemistry of ion exchange in zeolites is well documented.36 All exchanges were performed similarly. They involved vacuum filtering and washing of the zeolite with deionized water. Compared to the original cation-exchange capacity (CEC), each solution contained 10-fold cation equivalents. This procedure ensured 100% exchange. For A (Linde) and Y (supplied through Strem Chemicals) zeolites, the starting forms contained Na+ cations. The zeolites used were in powder form (binderless). Prior to use, the zeolite samples were degassed in vacuo at 350 °C for several hours. The silica gel based samples were degassed in situ by heating to 150 °C in helium. Isotherms and uptake rates were measured utilizing both a Micromeritics ASAP 2010 and a Shimadzu TGA50 microbalance and following the procedures described in Ackley and Yang.37 Surface area measurements were made using the Micromeritics ASAP 2010 and were performed using nitrogen adsorption at 77 K. The hydrocarbons used as the adsorbates were 1,3-butadiene (CP grade, Matheson, minimum purity 99.0%), and 1-butene (CP grade, Matheson, minimum purity 99.5%), n-butane (CP grade, Matheson, minimum purity 99.0%), and helium (prepurified grade, Metro Welding, 99.995%) was used as the carrier gas and as the regeneration gas. The gases were used without further purification. Results and Discussion Equilibrium Isotherm Model. Because the adsorption of paraffin molecules involves physical adsorption only, it can be modeled well by the Langmuir isotherm with two parameters shown in eq 1. However, the

q)

qmpbbP 1 + bpP

(1)

adsorption of olefin molecules on AgNO3/SiO2 includes both physical adsorption and chemisorption (via π-complexation). Therefore, a different model is required to account for chemisorption. The isotherm model developed by Yang and Kikkinides18 to account for both interactions is shown in eq 2. The first term accounts

q)

qmc 1 + bcPes qmpbbP + ln 1 + bpP 2s 1 + b Pe-s

(2)

c

for physical adsorption, while the second term represents contributions by chemisorption. The second term also takes into account the energetic heterogeneity of

Figure 1. Equilibrium isotherms of C4H6, C4H8, and C4H10 at 70 °C on SiO2 at 70 °C. Lines are fittings with eqs 1 and 2. Table 1. Fitting Parameters for Isotherms of C4H6, C4H8, and C4H10 at 70 °C on SiO2 and AgNO3/SiO2

C4H6 SiO2 AgNO3/SiO2 C4H8 SiO2 AgNO3/SiO2 C4H10 SiO2 AgNO3/SiO2

qmp (mmol/g)

qbp (mmol/g)

qmc (mmol/g)

bc (atm-1)

s

1.55 1.12

12.5 0.47

4.44

0.0021

12.4

1.53 1.53

4.86 0.34

4.2

0.0067

9.4

1.89 0.235

1.31 2.09

the surface ion sites available for complexation. While eq 2 contains five parameters, only two of them are true fitting parameters.18 The other three parameters have certain constraints imposed on them in order for them to have physical meaning. Empirical values for s are available from the literature.38,39 For each adsorbent, the corresponding paraffin data were used first to obtain the two parameters in the Langmuir isotherm. Therefore, eq 2 was used to fit the olefin adsorption data with imposed values or constraints on qmp, bp, and s, leaving only qmc and bc as true fitting parameters. The adsorption branches of the isotherms were used to fit the models. Bulk Separation of Olefin/Paraffin C4’s. As mentioned in the previous section, the olefin/paraffin separation of C4’s by distillation is very difficult because of the similarity of the boiling points. The strategy for developing a sorbent capable of separating olefin from paraffins is to disperse Ag+ cations over a high-surfacearea substrate. The Ag+ cations are capable of selectively adsorbing olefins by π-complexation. The sorbent discussed in this section is AgNO3 dispersed over SiO2 at a loading of 1.08 g of salt/g of substrate. To establish a baseline for comparison, equilibrium adsorption data for 1,3-butadiene (C4H6), 1-butene (C4H8), and n-butane (C4H10) on SiO2 at 70 °C were measured and shown in Figure 1. The equilibrium data for C4H6, C4H8, and C4H10 were fitted to eq 1. Fitting parameters for these isotherms are shown in Table 1. Equilibrium capacities at 70 °C and 1 atm were measured at 1.48, 1.30, and 1.03 mmol/g, respectively. As expected, the SiO2 surface provides no significant selectivity among the hydrocarbons. The pore volume and surface area of the SiO2 utilized were measured by the BET method as 0.46 cm3/g and 670 m2/g, respectively.

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Figure 2. Equilibrium isotherms of C4H8 on AgNO3/SiO2 at 70 °C. Lines are fittings with eqs 1 and 2.

Figure 3. Adsorption/desorption behavior of C4H8 on AgNO3/SiO2 at 70 °C.

Equilibrium isotherms for C4H8 and C4H10 on AgNO3/ SiO2 at 70 °C are shown in Figure 2. The equilibrium data for C4H8 and C4H10 were fitted to eqs 1 and 2. Fitting parameters for these isotherms are shown in Table 1. Equilibrium capacities for C4H8 and C4H10 at 70 °C and 1 atm were measured at 1.25 and 0.15 mmol/ g, respectively. Diffusion of all C4’s on this sorbent was fast, with 100% uptake reached in less than 3 min. It appears that there was not an increase in C4H8 adsorption upon spreading of AgNO3 on the SiO2 surface. However, the true effect of spreading AgNO3 becomes apparent when one compares the amount of C4H8 adsorbed per square meter of surface area. The surface area of the AgNO3/SiO2 sorbent was measured at 138 m2/g. Therefore, the amount of C4H8 adsorbed per square meter of surface area increased from 1.94 × 10-3 in the SiO2 sample to 9.06 × 10-3 mmol/m2 in the AgNO3/SiO2 sample. This was a 4-fold increase in olefin adsorption per unit area. Simultaneously, paraffin adsorption was decreased from 1.03 to 0.15 mmol/g. Moreover, the pure component adsorption ratios for C4H8/C4H10 on SiO2 and AgNO3/SiO2 were calculated at 1.26 and 8.33, respectively. Another interesting feature of the isotherm is its steepness above the knee. This feature indicates that the sorbent possesses a good working capacity for PSA applications. The sorbent also exhibited good desorption behavior. The desorption behavior for C4H8 on AgNO3/SiO2 at 70 °C is shown in Figure 3. While the C4H8 adsorption in Figure 3 exhibits a slight hysteresis, it should not significantly affect the sorbent’s usefulness for PSA-type applications. Also,

Figure 4. Equilibrium isotherms of C4H6 and C4H10 on AgNO3/ SiO2 at 70 °C. Lines are fittings with eqs 1 and 2.

evidence of polymerization or coking was not observed at the temperatures at which the sorbents were tested. Although it seems feasible to utilize a AgNO3/SiO2 sorbent for bulk separation of C4H8 and C4H10, it is not possible to utilize this sorbent for bulk separation of C4H6 from C4H8. Equilibrium isotherms for C4H6 and C4H10 on AgNO3/SiO2 at 70 °C are shown in Figure 4. The equilibrium data for C4H6 and C4H10 were fitted to eqs 1 and 2. Fitting parameters for these isotherms are shown in Table 1. Equilibrium capacities for C4H6 and C4H8 at 70 °C and 1 atm were measured at 1.50 and 1.25 mmol/g, respectively. Adsorption of C4H6 on AgNO3/ SiO2 is only 20% greater than C4H8. This makes AgNO3/ SiO2 a poor candidate for bulk separation of C4H6 from C4H8. This behavior is expected because both adsorbates are capable of complexation with the Ag+ on the sorbent. This is due to the olefinic nature of both C4H6 and C4H8. However, on the basis of the adsorption data shown in Figure 4, one can observe that it is possible to separate C4H6 from C4H10 using a AgNO3/SiO2 sorbent. Purification of Olefin C4’s via π-Complexation. In this section, the feasibility of using π-complexationcapable sorbents to purify an olefin stream containing trace amounts of impurities is discussed. Currently, there are no commercially available sorbents capable of purifying an olefin stream. This particular application requires the removal of trace amounts of C4H6 from an unsaturated C4H8 stream. The sorbent must be capable of lowering the partial pressure of C4H6 from 0.001 to 0.0002 atm, at a total pressure corresponding to the saturated pressure of 1-butene at 120 °C. Moreover, the sorbent needs to be able to adsorb significant quantities of C4H6 at 0.001 atm. Commercially available 5A (CaA) zeolite from Linde was tested for this application. Low-pressure equilibrium isotherms for C4H6 and C4H8 on 5A zeolite at 120 °C are shown in Figure 5. From the isotherm data, it can be observed that the low-pressure adsorption behavior of this material was acceptable. At the required partial pressure of 0.001 atm, this sorbent adsorbed 0.45 mmol/g of C4H6. The working capacity of this sorbent between 0.001 and 0.0002 atm is also acceptable. It was measured at approximately 0.4 mmol/g. Diffusion of C4H6 and C4H8 on 5A zeolite at 120 °C was 100% complete in less than 2.5 min. The separation factors were calculated using eq 3,40 using pure-component

Rij )

Xi/Yi Xj/Yj

(3)

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Figure 5. Low-pressure equilibrium isotherms of C4H6 and C4H8 on 5A zeolite at 120 °C.

Figure 7. Low-pressure equilibrium isotherms of C4H6 and C4H8 on NaY zeolite at 120 °C.

Figure 6. Adsorption/desorption behavior of C4H6 on 5A zeolite at 120 °C.

Figure 8. Comparison between low-pressure equilibrium isotherms of C4H6 on NaY and AgY zeolite at 120 °C.

isotherms, where Xi and Yi are the equilibrium mole fractions of component i in the adsorbed and gas phases, respectively. The above equation was based on the assumption of an ideal binary mixture. The separation factor for C4H6/C4H8 on 5A zeolite was calculated using eq 3 to be approximately 5170. The sorbent also exhibited good desorption behavior. The desorption behavior for C4H6 on 5A zeolite at 120 °C is shown in Figure 6. As can be observed from Figure 5, 5A zeolite is an acceptable sorbent. However, it might be possible to improve on this sorbent by making use of π-complexation with C4H6. This can be accomplished by ionexchanging 5A zeolite with Ag+. However, because of the size of the Ag+ cation (1.27 Å), the substitution of Ca2+ with Ag+ will lead to a net decrease in the pore opening of the type A zeolite. This reduction in pore opening will have a significant decrease in the diffusivity and, therefore, the effectiveness of the sorbent. To effectively use Ag+ cations, type Y zeolite was used as the substrate because of its larger pore opening. Lowpressure equilibrium isotherms for C4H6 and C4H8 on NaY zeolite at 120 °C are shown in Figure 7. At the required partial pressure of 0.001 atm, NaY zeolite adsorbed 0.2 mmol/g of C4H6. The working capacity of this sorbent between 0.001 and 0.0002 atm was measured at approximately 0.1 mmol/g. On the basis of the above results, the NaY zeolite will not be a good candidate for this separation. However, after ion exchange with Ag+, a considerable difference in adsorption behavior is observed.

Low-pressure equilibrium isotherms for C4H6 on NaY and AgY zeolites at 120 °C are shown in Figure 8. In this figure, one can clearly observe the effect of π-complexation bonding on the adsorption behavior of C4H6. There has been a significant shift in the C4H6 adsorption isotherm to the left because of the stronger adsorption caused by π-complexation. Whereas C4H6 adsorbed only about 0.2 mmol/g on NaY at 0.001 atm, adsorption on AgY at the same partial pressure of C4H6 increased to 1.9 mmol/g. This was almost a 10-fold improvement in the amount of C4H6 adsorbed. The working capacity of the sorbent measured between 0.0002 and 0.001 atm was 1.6 mmol/g, a 350% improvement. The low-pressure equilibrium adsorption isotherms for C4H6 and C4H8 on AgY are shown in Figure 9. From this figure and eq 3, the separation factor for the separation was calculated to be approximately 11 700. As expected, the diffusion behavior for C4H6 and C4H8 on AgY was not greatly affected by Ag exchange. Complete uptake was obtained in less than 1.5 min. Therefore, it seems feasible to utilize AgY zeolite to effectively remove trace amounts of C4H6 in an unsaturated C4H8 stream. It is interesting to note that CuCl has been incorporated on high-surfacearea alumina prepared by the sol-gel route.41 However, diffusivities for C4 molecules in sol-gel-based substrates are likely to be low. Predicting Isotherms Using the Cheng-Yang Model of the H-K Equation. Using the low-pressure data obtained in the previous section for C4H6 and C4H8 on 5A zeolite, the feasibility of using H-K formulations to derive isotherms of other molecules at subcritical temperatures will be determined. The advantage of the

Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 3619 Table 2. Molecular Property Input Parameters for the H-K Model

parameter diameter d, Å polarizability, R, cm3 magnetic susceptibility χ, cm3 density N, molecules/cm2

zeolite (oxide ion)

C4H6

C4H8

C4H10

3.0443 2.5 × 10-25 44 1.94 × 10-29 43 3.75 × 1015 43

4.2 8.64 × 10-24 45 5.33 × 10-29 45 2.68 × 1014 46

4.5 7.97 × 10-24 45 6.81 × 10-29 45 2.53 × 1014 46

5.2 8.20 × 10-24 45 8.35 × 10-29 45 2.46 × 1014 46

where T1-T4, N1, and N2 are:

T1 )

T2 )

T3 )

Figure 9. Low-pressure equilibrium isotherms of C4H6 and C4H8 on AgY zeolite at 120 °C.

T4 )

1 L - d0 1L

3

1 L - d0 1+ L

2

1 L - d0 1L

9

1 L - d0 1+ L

8

(

-

1 L - d0 1+ L

3

-

1 L - d0 1L

2

-

1 L - d0 1+ L

9

-

1 L - d0 1L

8

) (

(

) (

(

) (

(

) (

N1 ) 4πL2Na

)

(5)

) ) )

(6)

N2 ) 4π(L - d0)2NA and the minimum energies are obtained from the Lennard-Jones potential as

/12 ) /22 )

Figure 10. Differential pore size distribution of 5A zeolite calculated from C4H10 adsorption at 120 °C and the H-K equation using the Cheng-Yang model for spherical pore and correction for isotherm nonlinearity.

H-K equation is that it provides a simple method for determining the pore size distribution of a material based on an adsorption isotherm. The H-K equation renders a one-to-one function between the pore size and the relative pressure at which the pore is filled. Therefore, because the H-K equation is a one-to-one function, one can predict an adsorption isotherm based on a previously obtained pore size distribution and physical parameters of the adsorbate and adsorbent. The H-K equation described below is the Cheng-Yang version by taking into account the nonlinearity in the isotherm and the spherical curvature effects of the pore wall. The details of the derivation are available elsewhere.33

( ) (

RT ln

) [ ( )( ) ( ) ( )]

RT P 1 + RT ) ln P0 θ 1-θ 6(N1/12 + N2/22)L3 (L - L0)

3

-

d0 L

6

T1 T2 + + 12 8

d0 L

12

T3 T 4 + 90 80

(4)

Aa 4d06

(7)

AA 4dA6

and the dispersion constants may be calculated according to Kirkwood-Muller formalism as

Aa )

6mc2RaRA Ra RA + χa χA

() ()

(8)

3 AA ) (mc2RAχA) 2 The differential pore size distribution of 5A zeolite calculated from a C4H10 adsorption at 120 °C and utilizing eq 4 is shown in Figure 10. In this work, physical parameters from the published literature were used and are shown in Table 2. No fitting parameters were used in this work. On the basis of crystallographic data, the cavity size of 5A zeolite was measured at about 11 Å.36 However, the peak position in the PSD shown in Figure 10 is around 9 Å. While the broad pore size distribution pattern calculated does not entirely reflect the crystalline nature of 5A zeolite, the model produced a reasonable approximation. The use of a PSD obtained from a C4H10 isotherm was deliberate. While the PSD obtained using C4H10 is not entirely accurate, its use helps to minimize any errors due to size and shape differences between the molecules.

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Figure 11. Prediction of C4H8 adsorption isotherm on 5A zeolite at 120 °C using the Cheng-Yang model of the H-K equation. Comparison of prediction vs experiment.

Figure 13. Comparison between predicted isotherms for C4H6 and C4H8 on 5A zeolite at 120 °C.

Although the H-K model in its present form cannot completely predict isothermal behavior, it can accurately predict the correct trend in adsorption. As shown in the previous section, C4H6 adsorbs at a lower partial pressure than C4H8. This behavior was captured by the H-K model and is shown in Figure 13. To account for electrostatic interactions and other interactions such as π-complexation, further work is needed to include these forces in the H-K model. Conclusions

Figure 12. Prediction of the C4H6 adsorption isotherm on 5A zeolite at 120 °C using the Cheng-Yang model of the H-K equation. Comparison of prediction vs experiment.

To test the predictive power and accuracy of the H-K equation, the PSD obtained in Figure 10 and the physical parameters for C4H8 shown in Table 2 were used in eq 4. On the basis of the above input, a predicted isotherm for C4H8 adsorption on 5A zeolite at 120 °C was obtained. The predicted and experimental isotherms are compared in Figure 11. Similarly, a predicted isotherm was obtained for C4H6 on 5A zeolite at 120 °C and is compared to the corresponding experimental data in Figure 12. From Figures 11 and 12, one can observe the predictive ability of the H-K equation. While in both cases the H-K equation underpredicted the adsorption behavior of C4H6 and C4H8, this was expected. The H-K model only considers dispersion and repulsion interactions. Electrostatic forces are not included in its calculation of the energy potential. While C4H6 and C4H8 have large electron clouds that are negatively charged, the interaction of these electron clouds with the positive cations present in the 5A zeolite surface is not accounted for. These electrostatic interactions shift the adsorption isotherm toward a smaller partial pressure value for the pore dimension. Another reason for the difference between experiment and prediction is due to the shape of the molecules. The approximation of spherical molecules is not a good one for adsorbates studied. The Lennard-Jones potential only depends on center-to-center distances to determine the interaction energy. However, the intermolecular forces of nonspherical molecules depends also on the relative orientation of the molecules.42

The performance of π-complexation-capable sorbents for the bulk separation of C4 olefins from paraffins was found to be excellent. It was shown that the AgNO3/ SiO2 sorbent developed has excellent capacities and selectivities for this application. Its working capacity makes it a good candidate for PSA applications. Also, the performance of π-complexation sorbents for the purification of an olefin stream was found to be superior to that of sorbents based on physical adsorption (5A zeolite, NaY). In this work, it was also shown that the H-K model is capable of predicting relative (or trend of) adsorption isotherms of C4H6, C4H8, and C4H10 on 5A zeolite. Further work is in progress on developing an improved energy potential model for the H-K equation that accounts for electrostatic and π-complexation type interactions. Nomenclature A ) dispersion constant b ) Langmuir constant c ) speed of light d ) diameter of the atom do ) arithmetic mean of diameters of adsorbate and adsorbent atoms L ) defined as the radius of the spherical pores mc2 ) kinetic energy of an electron N ) density per unit area NAV ) Avogadro’s number P ) pressure P0 ) saturate vapor pressure of adsorbate q ) equilibrium amount adsorbed qm ) monolayer or saturated amount adsorbed R ) gas constant s ) heterogeneity parameter T ) absolute temperature Greek Letters R ) polarizability

Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 3621 χ ) magnetic susceptibility  ) potential energy of interaction θ ) degree of void filling Subscripts 1 ) adsorbent atom 2 ) adsorbate molecule a ) adsorbent A ) adsorbate c ) chemisorption or π-complexation p ) physical adsorption

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Received for review December 14, 1998 Revised manuscript received February 18, 1999 Accepted February 20, 1999 IE980779+