Propane Separation Using SiCHA - Industrial

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Propylene/Propane Separation Using SiCHA Mona Khalighi, Y. F. Chen, S. Farooq,* I. A. Karimi, and J. W. Jiang Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576 ABSTRACT: Separation of propylene/propane mixture with new 8-ring zeolite, pure silica chabazite (SiCHA), has been studied in this work. Since the diffusion of propane molecules in SiCHA is extremely slow, thus equilibrium information for propane has been indirectly estimated using available uptake data at 80 °C and 600 Torr. Moreover, molecular simulation has been used to obtain equilibrium information of propylene and propane and verify our estimation. The ideal kinetic selectivity of propylene/ propane mixture is ∼28 at 80 °C, which increases with decreasing temperature. A four-step, kinetically controlled pressure swing adsorption process has been suggested for this separation and studied in detail using a nonisothermal micropore diffusion model, developed and verified in an earlier study. In this model, Langmuir isotherm represents adsorption equilibrium and micropore diffusivity depends on adsorbate concentration in the micropores, according to chemical potential gradient as the driving force for diffusion.

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INTRODUCTION The separation of olefin/paraffin mixtures is a crucial operation in the petrochemical industry. The separation of propylene/ propane is probably the most common and important example.1 The industry uses two main feed mixtures for this separation. The first is the byproduct from the steam cracking of liquid feedstocks such as naphtha, and the second is the offgases from the fluid catalytic cracking (FCC) units in refineries.2 The former has 50%−60% propylene, while the latter has 80%−87% propylene. Cryogenic distillation is the current method for separating propylene/propane mixtures to get 99 mol % propylene.3 It is a difficult separation requiring high reflux ratios, much energy, and tall columns, because of the small difference in the volatilities of propylene and propane.4 Therefore, economical alternatives for the separation of propylene/propane mixtures are highly desirable. Furthermore, most applications require both propylene and propane in high purities. For instance, 99% pure propylene is the raw material for polypropylene, which is a polymer with extensive applications. Similarly, 90% pure propane is used for various purposes such as fuel for engines, oxy-gas torches, barbecues, etc.5 A pressure swing adsorption (PSA) process can be an attractive alternative for propylene/propane separation, because of its expected low energy demand.6 An adsorption-based separation is usually based on three possible mechanisms:6,7 equilibrium separation, kinetic separation, and steric separation. An adsorbent’s physicochemical structure and the adsorption characteristics of gaseous components on that adsorbent determine the separation mechanism. Equilibrium separation results from the difference in the adsorption strengths of component gases on a solid adsorbent. Kinetic separation relies on the difference in the adsorption rates of the component gases. Lastly, steric separation depends on the molecular sieving properties of crystalline microstructures of the adsorbent. Selecting the right adsorbent is the first and most critical step in developing an adsorption-based separation process. Two metrics have been proposed in the literature to guide this selection: equilibrium and kinetic selectivity.8 The former is © 2013 American Chemical Society

defined as the ratio of Henry’s constants for a Langmuirian system. It is suitable for equilibrium-based separations. In contrast, kinetic selectivity is more appropriate for kinetic separations. In the Henry’s law limit, where the adsorption and diffusion are uncoupled, kinetic selectivity is obtained by multiplying the equilibrium selectivity by the square root of the limiting diffusivity ratio. The ratios of Henry’s constants and those of diffusion coefficients for propylene and propane in several adsorbents3,4,9−11 studied in the literature are compiled in Table 1. It is evident from the table that pure silica chabazite Table 1. Summary of Henry’s Constant and Diffusivity Coefficient for Propylene/Propane in Available Adsorbents at 80° C adsorbent

Kpropylene/ Kpropane

Dpropylene/ Dpropane

kinetic selectivitya

4A zeolite 13X zeolite 5A zeolite AgNO3/SiO2 AlPO4 Ag+ exchanged resin SiCHA

12.43 29.1 9.32 11.3 12 562.8 0.38

321 0.6 0.71 1.8 3 0.3 5023

223 b b b b b 28

a

Kinetic selectivity = (Kpropylene/Kpropane)(Dpropylene/Dpropane)1/2. bDiffusion ratio is not high enough to exploit kinetic selectivity.

(SiCHA), which is a new eight-ring silica zeolite, shows high kinetic selectivity between propylene and propane.12,13 However, this adsorbent has received limited attention. Kinetic separation using this new adsorbent could be an attractive option for separating propylene/propane. SiCHA in particular exhibits the highest diffusivity ratio (∼104) for propylene over propane among the known adsorbents. SiCHA is a synthetic, pure silica zeolite having the chabazite (CHA) structure. Its Received: Revised: Accepted: Published: 3877

October 3, 2012 January 24, 2013 January 25, 2013 February 26, 2013 dx.doi.org/10.1021/ie3026955 | Ind. Eng. Chem. Res. 2013, 52, 3877−3892

Industrial & Engineering Chemistry Research

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crystal shape is a pseudocube 2−10 μm in size.12 Diaz-Cabanas et al.14 were the first to make synthetic CHA in pure silica form. However, Olson et al.12 and Hiden et al.13 were the first to measure the adsorption of ethane, ethylene, propane, and propylene on SiCHA. While a highly selective adsorbent is a key first step for an economic adsorption-based separation, a well-designed process, such as pressure swing adsorption (PSA), vacuum swing adsorption (VSA), or temperature swing adsorption (TSA), is equally important. The PSA process studies on propylene/ propane separation published in the literature so far are summarized in Table 2. Sikavitsas et al.11 investigated the feasibility of a PSA process using magnetically stabilized fluidized beds (MSFBs). They used Ag+-exchanged resin as a sorbent, which selectively forms Π-complexation bonds with olefins. A four-step PSA cycle including pressurization with feed, high-pressure adsorption, cocurrent high-pressure purge with high-purity product and countercurrent blowdown was proposed. Their simulations suggested that the separation in MSFBs, compared to the conventional packed beds, was enhanced due to faster transport resulting from high flow rates and smaller particle sizes, while retarded due to higher axial dispersion coefficients and larger bed voids. Their propylene recovery was only 17% with 99% purity from a 42/58 propylene/propane feed. They showed that MSFBs in PSA processes could significantly improve the performance, compared to the traditional PSA cycles based on packed beds. Rege et al.4 proposed a four-step PSA process using a monolayer of AgNO3 dispersed on silica gel substrate. This sorbent, monolayer AgNO3/SiO2, exhibited superior selective adsorption of propane through Π-complexation. They assumed equal time duration for all steps in their proposed four-step PSA process. While they obtained 99.1% propylene from an equimolar feed of propylene/propane, propylene recovery was 43.5%. In this study, they compared their result with kinetic separation using 4A zeolite. They found that equilibrium separation of propylene/propane on AgNO3 dispersed on SiO2 substrate was superior to kinetic separation on zeolite 4A. However, the recovery of their system was low. Among the commercial adsorbents, zeolite 4A exhibits the highest kinetic selectivity. Silva et al.15 studied separation of propylene/propane on zeolite 13X and zeolite 4A. While the former showed higher loading capacity and lower mass-transfer resistance, the latter’s kinetic selectivity for propylene was at least 1 order of magnitude higher. From their study, macropore and micropore diffusion seemed to dominate mass transfer in zeolite 13X and zeolite 4A, respectively. Later, Da Silva and Rodrigues16 proposed a five-step PSA process using zeolite 4A and a five-step VSA process using Zeolite 13X. Both processes produced 97%−98% pure propylene, but only at a recovery of 17%−26%. Padin et al.10 studied four-step PSA process using ALPO4-14, which has unique pore structure and separates propylene from propane sterically. They obtained 99% pure propylene from a 50/50 feed with a recovery of 52%. They also compared the separation results of ALPO4-14 with AgNO3/ SiO2 and 4A zeolite adsorbents. Purity and recovery of propylene were, respectively, 99.05% and 43.58% for AgNO3/ SiO2 and 99.97% and 23.59% for 4A zeolite. Therefore, ALPO414 showed higher recovery for 99% pure propylene, compared to 4A zeolite and AgNO3/SiO2. Grande et al.2 studied a fivestep PSA process using zeolite 4A extrudates. They used two mixtures with different propylene/propane ratios (54/46 and

85/15) diluted with 50% nitrogen. They assumed a bi-LDF approximation for mass transfer and included heat balance equations in their simulation. The 85/15 feed at 408 K gave the best performance with a simulated propylene purity of 99.43% and a recovery of 84.3%. Recently, Grande et al.17 proposed a new dual-unit VPSA technology for producing 99%-pure polymer-grade propylene (PGP) with high recovery. They proposed two VPSA units in series, using zeolite 4A with varying crystal sizes. They designed the upstream three-column VPSA unit to produce PGP, while the downstream two-column unit to produce pure propane. Propylene from the downstream unit was recycled to the upstream unit to enhance recovery. The proposed two-stage VPSA process produced 99% PGP with 95.9% recovery of propylene. The power consumption of their two-stage VPSA process was at least 20% higher than what would be required in the traditional cryogenic distillation. The above discussion suggests that most adsorption-based separation studies used almost-equimolar mixtures of propylene/propane. Only two considered an 85/15 mixture. Moreover, all the studies focused solely on obtaining 99 mol % propylene, with little regard for propane purity. Furthermore, no study has evaluated the new eight-ring zeolite, SiCHA, for this separation. Since 90% purity is also required for propane, there is a need to develop an adsorption process that separates a propylene/propane mixture into two high-purity products. This work represents the first effort at assessing a kinetically controlled PSA process for this separation using SiCHA. It is also the first work that focuses on two high-purity products, 99 mol % propylene and 90 mol % propane, as desired in practice. A four-step cycle is proposed and evaluated for the two industrially relevant feed concentrations mentioned earlier.

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ADSORPTION PARAMETERS FOR SiCHA The lack of adequate experimental studies on the adsorption of propylene and propane in SiCHA poses a major challenge in developing and simulating a SiCHA-based PSA process. To date, the lone experimental study on SiCHA is the one by Olson et al.12 It employed a thermogravimetric method to measure the dynamic uptakes of propylene and propane at 600 Torr. It reported uptake data at 30 and 80 °C for propylene, and only at 80 °C for propane, because of the extremely slow diffusion of the latter. For the same reason, the study could not measure the equilibrium loading for propane. However, it reported equilibrium data for propylene at 30, 45, 60, 80, and 100 °C. Using their lone uptake data for propane at 80 °C, Olson et al.12 estimated its diffusivity in SiCHA, but mentioned nothing about the saturation or equilibrium loading they may have used for that estimation. In their study, the uptake data was indirectly analyzed to shed some light on the equilibrium isotherm of propane on SiCHA. In addition, the equilibrium and uptake data for propylene and the uptake data for propane reported by Olson et al.12 have been reanalyzed. Our results are somewhat different, which are discussed next. Equilibrium Parameters. For propylene, Olson et al.12 reported isotherm data at 30, 45, 60, 80, and 100 °C, and fitted a separate Langmuir isotherm, given by eq 1 for each temperature: qe qs 3878

=

bp 1 + bp

(1)

dx.doi.org/10.1021/ie3026955 | Ind. Eng. Chem. Res. 2013, 52, 3877−3892

3879

pressurization with feed, high-pressure adsorption, cocurrent depressurization to an intermediate pressure, cocurrent purge with propylene product, and countercurrent blowdown

pressurization with feed, high-pressure adsorption with feed and purge product, high-pressure cocurrent purge with part of the C3H6-rich product obtained in blowdown step, countercurrent blowdown to a low pressure

five-step36

four-step6

five-step2

five-step37

pressurization, adsorption, rinse, cocurrent depressurization to intermediate pressure and counter-current blowdown

pressurization, adsorption, rinse, cocurrent depressurization to intermediate pressure (for five-step) and counter-current blowdown

pressurization with feed, high-pressure adsorption, cocurrent depressurization to an intermediate pressure, cocurrent purge with propylene product, and countercurrent blowdown

five-step16

four-step

50% propylene, 50% propane PH = 1 atm, PL = 0.1 atm, T = 393 K

pressurization with feed, high-pressure adsorption with feed gas, high-pressure cocurrent purge with part of the compressed C3H6-rich product, countercurrent blowdown

fourstep10

PH = 2.46 atm, PL = 0.098 atm, PM = 0.49 atm (for five-step), T = 408 K 54:46 propylene/ propane diluted in N2; PH = 4.98 atm, PL = 0.098 atm, PM = 0.49 atm (for 5-step), T = 433 K 85:15 propylene/propane diluted in N2

50% propylene, 50% propane PH = 2.46 atm, PL = 0.098 atm, PM = 0.49 atm (for five-step), T = 343 K

(85% propylene and 15% propane), (50% propylene and 50% propane) PH = 7 atm, PL = 0.2 atm, T = 393 K

25% propylene, 25% propane, 50% nitrogen PH = 5 atm, PM = 0.5 atm, PL = 0.1 atm, T = 423 K

25% propylene, 25% propane, 50% nitrogen PH = 5 atm, PM = 0.5 atm, PL = 0.1 atm, T = 423 K


pressurization with feed, high-pressure adsorption, high-pressure purge with high-purity olefin, countercurrent blowdown

four-step4


feed composition and operating conditions

pressurization with feed, high-pressure adsorption, high-pressure purge with high-purity olefin, countercurrent blowdown

steps

fourstep11

PSA cycle

Table 2. Summary of PSA Processes for the Separation of Propane/Propylene Mixtures

4A zeolite

purity = 99.43%, recovery = 84.3%

purity = 91%, recovery = 97% purity = 99%, recovery = 63%

Ag/SBA-15

AlPO4-14

AgNO3/SiO2

AlPO4-14

purity = 99.24%, recovery = 75% purity = 99.18%, recovery = 72% purity = 98.52%, recovery = 71% purity = 98.65%, recovery = 64%

purity = 98%, recovery = 19%

purity = 97%, recovery = 26%

purity = 99.38%, recovery = 52%

AgNO3/SiO2

13X zeolite

4A zeolite

AlPO4-14


purity >99%, recovery = 17%

Ag+ exchanged Amberlyst 15 Resin AgNO3/SiO2

performance for propylene

adsorbent

Industrial & Engineering Chemistry Research Article



⎛ ΔH ⎞ ⎟ b = b0 exp⎜ − ⎝ RT ⎠

(2)

4A zeolite

where b is the Langmuir constant, qe the equilibrium loading at partial pressure p, and qs the saturation loading. Using eq 1, they reported five separate values for qs and b. However, for the Langmuir isotherm to be thermodynamically consistent, qs must be independent of temperature. Hence, the propylene equilibrium data for different temperature were simultaneously regressed with eqs 1 and 2 to obtain temperature-independent qs, b0, and ΔH. This procedure gave us qs = 125.2 mg/g, ΔH = −33.08 kJ/mol, and b0 = 4.55 × 10−8/torr for propylene. The mean square error (MSE) corresponding to these equilibrium parameters were 5.07. The experimental data and corresponding Langmuir model fit are shown in Figure 1. With this, we have the required equilibrium isotherm parameters for propylene.

60% propylene, 40% propane PH = 1.48 atm, PM = 0.49 atm, PL = 0.148 atm, T = 423 K

Figure 1. Adsorption isotherms for propylene on SiCHA. Points represent the experimental data by Olson et al.12 and solid lines represent the Langmuir isotherm.

Unit 2: pressurization, feed, depressurization, evacuation, purge and pressure equalization

Unit 1: pressurization, feed, depressurization 1, rinse, depressurization 2, evacuation

purity = 99.31%, recovery = 90.2%

Article

In the absence of any experimental measurement of qs for propane, we argue as follows to assume that it is the same as that (qs = 125.2 mg/g) for propylene on SiCHA. SiCHA is a neutral adsorbent that interacts with propane and propylene via van der Waals forces. The slightly larger size (4.35 Å) of propane versus that of propylene (4.05 Å) allows propane to adsorb slightly more strongly than propylene7 at low to moderate pressures. The stronger adsorption of propane may also be explained from its higher critical temperature (369.9 K), compared to that of propylene (365.2 K). At high pressures and saturation loading, however, the smaller size and linear structure of propylene molecule may suggest slightly more adsorption for propylene. Given that the sizes of the molecules are very close, we believe it to be reasonable to assume that their saturation loadings are nearly equal. Therefore, we assume a value of qs = 125.2 mg/g for both propane and propylene in this study. To further justify our above argument and confirm our assumption of the qs value of propane, we employed the Monte Carlo (MC) molecular simulation described in the Appendix. We first matched our theoretical prediction of propylene isotherm at 80 °C with experimental results. Figure 2 shows that the predictions from the molecular simulation match the experimental data very well. Then, we computed the isotherm

two units and sixstep17

PSA cycle

Table 2. continued

steps

feed composition and operating conditions

adsorbent

performance for propylene


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If one assumes a concentration-independent micropore diffusivity (Dc), then eqs 4−7 have the following analytical solution:19 q 6 =1− 2 qe π

of propane using molecular simulation. Fitting Langmuir isotherms to these simulation results, we obtained qs = 127.3 mg/g for propane and 127.2 mg/g for propylene, which are identical for all practical purposes. Note that this predicted qs value matches quite well with our estimated value of qs = 125.2 mg/g for propylene from Olson’s experimental equilibrium data.12 Determination of the other Langmuir isotherm parameter for propane and reanalysis of the kinetic parameters for propylene and propane are discussed next.

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∞

n=0

⎛ −(2n + 1)2 π 2D t ⎞ 8 c ⎜ ⎟ exp (2n + 1)2 π 2 4l 2 ⎝ ⎠

n=1

(8)

Figure 3. Experimental and simulated uptake data for propylene in SiCHA at 30 °C and 600 Torr.

KINETIC PARAMETERS Olson et al.12 measured the uptake of propylene at 600 Torr and at two temperatures (30 and 80 °C). However, they reported uptake data for propane at 80 °C only. Pure gas uptakes in SiCHA were used. They used analytical solution of the diffusion model for planar geometry subjected to a constant boundary condition18 to compute the micropore diffusivity for both propane and propylene.

∑

∑

⎛ n2π 2D t ⎞ 1 c ⎜ ⎟ exp 2 n2 r ⎝ c ⎠

If one does not make that assumption, and allows diffusivity to vary with concentration as in Dc = Dc0/(1 − q/qs), then eqs 4−7 must be solved numerically. We used the method of orthogonal collocation. Thus, it is possible to use the above three approaches to model the uptake data of Olson et al.12 for propane and propylene at 600 Torr, and estimate both qe and micropore diffusivity values (Dc or Dc0). Figures 3 and 4 show the uptake of propylene at 30 and 80 °C, respectively, and the above three fitted models. The

Figure 2. Propylene and propane equilibrium isotherm in SiCHA at 80 °C obtained from Monte Carlo (MC) simulation are compared with experimental data and Langmuir model estimates, respectively. The Langmuir model parameters were obtained indirectly from the uptake data of Olson et al.12

q =1− qe

∞

(3)

However, it is not clear if they extracted both Dc and qe from eq 3, or they assumed qe and extracted Dc. For propane, they reported only Dc and not qe. SiCHA used in the study were three-dimensional (3D) crystals rather than planar sheets. Thus, eq 3 is not the most appropriate choice for describing the uptake of propylene and propane on SiCHA. A more appropriate and general approach would be to assume a spherical geometry.8 ∂q ∂q ⎞⎤ 1⎡∂⎛ = 2 ⎢ ⎜r 2Dc ⎟⎥ ∂t ∂r ⎠⎦ r ⎣ ∂r ⎝

∂q ∂r

Figure 4. Experimental and simulated uptake data for propylene in SiCHA at 80 °C and 600 Torr. (4)

spherical model with concentration-dependent micropore diffusivity represents the best fit with the least MSE at both 30 and 80 °C. At 30 °C, its MSE is 15, versus 17 for the constant micropore diffusivity spherical model (eq 8) and 19 for constant micropore diffusivity planar model (eq 3). At 80 °C, it is 2.1, versus 3.3 for eq 8 and 7.0 for eq 3. The MSE for 30 °C is higher than at 80 °C. The qe values are very similar

=0 (0, t )

(5)

q|(rc , t ) = qe

(6)

q|(r ,0) = 0

(7) 3881



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(∼119 mg/g at 30 °C and ∼89 mg/g at 80 °C) from all three models, as listed in Table 3. Interestingly, in addition to the

obtained qe = 108.7 mg/g at 80 °C and 600 Torr. Using this equilibrium concentration value with qs = 125.2 mg/g previously estimated, we calculated b = 0.011/torr for the Langmuir isotherm. Thus, the dimensionless Henry’s constants for propylene and propane at 80 °C were 379.7 and 999.3, respectively. The higher value of propane, compared to propylene, is consistent with what has been observed with ethane and ethylene, and is due to the higher van der Waals interactions of paraffins versus olefins with SiCHA.12 The equilibrium data for propylene in SiCHA at 80 °C calculated using these Langmuir isotherm parameters are compared with the predictions from MC simulation in Figure 2. The last important parameter for adsorption is the isosteric heat of adsorption for propane, which is normally computed from the variation of b = b0 exp(−ΔH/RT) with temperature. Olson et al.12 reported a ΔH value of −33.5 kJ/mol for propylene, but none for propane. Therefore, we again employed MC simulations (detailed in the Appendix). From these simulations, we obtained ΔH = −29.16 kJ/mol for propylene and ΔH = −30.94 kJ/mol for propane. The higher value for propane is again consistent with that observed with ethane versus ethylene, and, as already explained in relation to the Henry’s constant values, is due to the higher van der Waals interactions of paraffins versus olefins with SiCHA.12 Instead of using these values as is, we chose ΔH = −33.08 kJ/mol for propylene obtained in our reanalysis discussed earlier and used the ratio of ΔH values obtained from MC simulations as the scaling factor to compute ΔH = −33.8 × [(−30.94)/(−29.16)] = −35.5 kJ/mol for propane. Table 4 summarizes the kinetic and equilibrium parameters for propylene and propane.

Table 3. Equilibrium and Diffusivity Information Obtained from the Uptake of Propylene and Propane in SiCHA at 600 Torr model

qe (mg/g)

Propylene @ 30 °C 119.13 119.75 118.66 120.00 Propylene @ 80 °C analytical (spherical) 88.61 numerical (spherical) 89.16 analytical (planar) 88.07 analytical (planar, Olson) 90.00 Propane @ 80 °C analytical (spherical) 116.45 numerical (spherical) 108.77 analytical (planar) 90.55 analytical (planar, Olson) 90.00

analytical (spherical) numerical (spherical) analytical (planar) analytical (planar, Olson)

a

D/r2 (1/s)

MSEa

2.95 6.71 1.03 4.70

× × × ×

10−05 10−05 10−04 10−04

17 15 19 26

8.10 1.73 2.52 1.50

× × × ×

10−05 10−04 10−04 10−03

3.34 2.19 7.08 42.3

6.07 3.45 2.13 7.60

× × × ×

10−08 10−08 10−07 10−07

0.211 0.203 0.132 0.588

MSE = mean square error.

differences in the values from the three models, some discrepancy also exists between the values reported by Olson et al.12 and those computed by us from eq 3. Figure 5 shows the uptake of propane at 80 °C and our predictions from the three models. The MSEs for all three

Table 4. Kinetic and Equilibrium Parameters for Propylene and Propane at 80 °C kinetic/equilibrium data 2

D/r (1/s) b (1/torr) isosteric heat (kJ/mol) qs (mg/g) Henry’s constant

propylene 1.73 × 10 0.004 −33.08 125.2 379.7

−4

propane 3.45 × 10−8 0.011 −35.5 125.2 999.3

The above discussion achieves our complete characterization of both equilibrium and kinetic properties of propane and propylene, which is needed for PSA simulations, and allows us to compute adsorption selectivities as follows. Kinetic and Equilibrium Selectivity. Majumdar et al.20 showed that, for a kinetically controlled adsorption process, the effective kinetic selectivity given by eq 9 is time-dependent, and gives a more-realistic representation of an adsorbent’s separation potential, compared to ideal selectivity. The effective kinetic selectivity can be simplified to the ideal kinetic selectivity (eq 10) under three simplifying assumptions of (i) short contact time, (ii) uncoupled diffusion and constant diffusivity, and (iii) linear or Langmuir isotherm. In contrast to the effective selectivity, this ideal kinetic selectivity considers the loading in the micropores only and not the nonselective storage capacity of macropores.

Figure 5. Experimental and simulated uptake data for propane in SiCHA at 80 °C and 600 Torr.

models are in the range of 0.1−0.2, but qe values vary significantly from 90 mg/g to 116 mg/g, as presented in Table 3. This variation is due to the fact that the uptake of propane versus √t is almost linear, which implies that it may be difficult to estimate qe reliably. The simulated qe value, based on MC, is 103.4 mg/g, which is in good agreement with the value obtained from the micropore diffusion model including concentration dependence of micropore diffusivity (108.7 mg/g). The micropore diffusion model with concentration-dependent diffusivity is the most appropriate description for the uptake of propylene and propane on SiCHA. For propane, we

ηk ,effective =

3882

⎛ qp(t ) ⎞ ⎜ ⎟ ⎝ c0 ⎠ propylene ⎛ qp(t ) ⎞ ⎜ ⎟ ⎝ c0 ⎠ propane

(9)


Industrial & Engineering Chemistry Research ⎛K propylene ηk,ideal = ⎜⎜ K ⎝ propane ⎛ K propylene ⎞ ⎟⎟ ηE = ⎜⎜ ⎝ K propane ⎠

Dpropylene ⎞ ⎟ Dpropane ⎟⎠

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PVSA PROCESS MODEL

We began our study with a five-step PVSA cycle comprised of (1) pressurization with feed, (2) high-pressure adsorption with feed, (3) cocurrent rinse with the propylene product from Step 5, (4) cocurrent blowdown to intermediate pressure, and (5) countercurrent evacuation. In this cycle, propane is collected in Steps 2 through 4, and propylene in Step 5. However, our simulations revealed that propane passes through the bed virtually unadsorbed due to its low diffusivity. Thus, Steps 2 and 3 deliver most of the propane, and Step 4 gives little propane. In other words, Step 4 essentially produces propylene, and thus has the same role as Step 5. Clearly, Step 4 in this fivestep cycle seems redundant and can be eliminated. Its elimination does not compromise recoveries, because product purity specifications automatically fix product recoveries in a binary separation when there are only two useful products and no waste stream. This is evident from the following equations obtained via simple mass balance:

(10)

(11)

where η is the selectivity, qp(t) the adsorbed amount of component i at a certain time t, c0 the gas concentration in the external fluid phase, K the dimensionless Henry’s constant, and D the micropore diffusivity. Using the independent unary equilibrium and kinetic parameters estimated previously, we computed the selectivities for propylene/propane in SiCHA. Figures 6a and 6b show the

Re1 =

z 2Pu1(1 − Pu 2) − z1Pu1Pu 2 1 × (1 − Pu1)(1 − Pu 2) − Pu1Pu 2 z1

(12)

Re 2 =

z1Pu 2(1 − Pu1) − z 2Pu1Pu 2 1 × (1 − Pu1)(1 − Pu 2) − Pu1Pu 2 z2

(13)

where Rei, zi, and Pui are the recovery, feed mole fraction, and purity of component i. Moreover, the four-step cycle should also consume less energy than the five-step cycle. Thus, we eliminate step 4 and study a four-step PVSA cycle for SiCHA (Figure 7).

Figure 6. Effective kinetic selectivity of propylene over propane in (a) SiCHA at 353 K and 266 kPa and in (b) 4A at 353 K and 10 kPa. The selectivity at t = 0 is a small nonzero value.

time-dependent effective selectivities of propylene over propane in SiCHA and 4A zeolite, according to eq 9. These figures show that the selectivity passes through a maximum at a short contact time, and then it gradually reaches the equilibrium selectivity limit. The maximum effective selectivity of propylene over propane in SiCHA is 32, the equilibrium selectivity (eq 11) is around 0.4, and the ideal kinetic selectivity is 28 at 80 °C. Even though the equilibrium selectivity is lower than unity, the kinetic selectivity seems sufficient for a kinetically selective PSA process, and, in fact, can be increased significantly by lowering the temperature. As may be seen from Table 1, the alumina-rich zeolites exhibit higher equilibrium selectivity for propylene/ propane than pure SiCHA. Because of the electrostatic forces arising from the exchangeable cations, the olefins are adsorbed more strongly than the corresponding paraffins. The maximum effective selectivity of propylene over propane in 4A is 190, the equilibrium selectivity is 12.43, and the ideal kinetic selectivity is 223 at 80 °C.

Figure 7. Schematic diagram of the PSA cycle. Legend: (1) pressurization, (2) high-pressure adsorption, (3) rinse, and (4) countercurrent evacuation. 3883



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In the evacuation step, propylene product is collected in a tank and a part of this product is recycled to the rinse step as heavy reflux. Since rinse duration and amount of gas that is recycled to this step are known, we can calculate the rinse velocity using the following equation: vrinse

GM tank ⎛ R gTg ⎞ = ⎜ ⎟ trinseAε ⎝ PH ⎠

Overall mass balance for Steps 1 and 4: ±

where G is the reflux ratio, Mtank is the molar amount of product collected in the tank, trinse the rinse duration, A the column cross-sectional area, Rg the universal gas constant, ε the bed porosity, Tg the gas temperature, and PH the operating pressure of the rinse step. To simulate this process, we use the following isobaric and nonisothermal model based on intraparticle micropore diffusion with concentration-dependent diffusivity.21 Model Equations. We assume the following: (1) The ideal gas law applies. (2) The system is isobaric. (3) Axially dispersed plug flow model describes the flow pattern. (4) The adsorbent consists of uniform microporous crystals. (5) The extended Langmuir isotherm using independently estimated single component parameters describes the mixture equilibrium. (6) The macropore resistance is negligible. (7) The chemical potential gradient is the driving force for micropore diffusion. (8) Temperature gradients along the radii of the column and microparticle are negligible. (9) The gas and adsorbent particles are in thermal equilibrium everywhere in the bed. (10) Lumped coefficients account for the heat transfer between the bed and column wall and that between the column wall and external surroundings. With these assumptions, the following equations describe the four-step PSA process. The plus sign (+) holds for the cocurrent flow from z = 0 to z = L (column length) and the minus sign (−) holds for the countercurrent flow from z = L to z = 0. Gas-phase mass balance for component i (A = propylene, B = propane): ∂vci ∂c 1− − DL 2 ± + i + ∂z ∂t ε ∂z

ε ⎛⎜ ∂qpi̅ ⎞⎟ ⎜ ∂t ⎟ = 0 ⎠ ⎝

∂t

= εp

∂q ̅ ∂ci + (1 − εp)ρc ci ∂t ∂t

∂t

=

3 ∂qci Di rc ∂r

∂Cv 1−ε + ∂Z ε

∑ i

∂qpi̅ ∂t

⎛

n

∑ ⎜(−ΔHi − cpaTg)ρc i=1

(19)

⎝

∂qci̅ ⎞ 2hw (Tg − Tw ) ⎟− ∂t ⎠ εR w

(20)

where cpa, cps, and cpg are the molar specific heat capacity of the adsorbed gas (that we assume it has the same value as cpg), specific heat capacity of the adsorbent and molar specific heat capacity of the gas mixture, respectively. λ is the axial heat dispersion, calculated from the correlation by Wakao.22 The term −ΔHi represents the isosteric heat of adsorption for component i, Tw is the wall temperature, hw is the film heattransfer coefficient between the adsorption bed and the column wall, Rw is the column (inside) radius. Wall heat balance: ρw cp w

∂Tw ∂ 2T = K w 2w + αwihw (Tg − Tw ) ∂t ∂z

(15)

− αwoh0(Tw − T∞)

(21a)

α wi =

2R w e(2R w + e)

(21b)

α wo =

2(R w + e) e(2R w + e)

(21c)

(16)

where cpw and ρw are the specific heat and density of the column wall, respectively. αwi is the ratio of the internal surface area to the volume of the column wall, e is the wall thickness, αwo is the ratio of the external surface area to the volume of the column wall, h0 is the convection heat-transfer coefficient between the wall and the surroundings, Kw is the wall thermal conductivity, and T∞ is the constant ambient temperature. The pressure change with time in Step 1 is represented by23

Overall mass balance for Steps 2 and 3: ±

=0

2 cpg ∂(vP) cpg ∂P (1 − ε) λ ∂ Tg − + − 2 ε ∂z ε R g ∂z R g ∂t

=

(17)

r = rc

∂t

⎡ (1 − ε) ⎤ ∂Tg ⎢ (cpa ∑ qpi̅ + ρs cps)⎥ ⎢⎣ ε ⎥⎦ ∂t i

Mass transfer into micropores:

∂qci̅

i

∂qpi̅

Gas-phase energy balance:

Mass transfer into macropores: ∂qpi̅

∑

In the above equations, C = ∑ci is the total gas phase concentration, ci = Pyi/(RgTg) is the concentration of component i in the bulk gas phase, P is the total gas pressure, yi is the mole fraction of component i in the bulk gas phase, Tg is the gas temperature in thermal equilibrium with the adsorbed phase, Rg is the universal gas constant, v is the interstitial velocity, DL is the axial dispersion coefficient, qp̅ i is the average adsorbed concentration of component i per unit adsorbent particle volume, q̅ci is its average adsorbed concentration per unit crystal mass, qci is the local adsorbed concentration per unit crystal volume along the crystal radius, ρc is the crystal density, ε is the bed porosity, εp is the adsorbent particle porosity, and t is the adsorption time. Note that v is computed from eq 18 or 19. The boundary conditions for eqs 14, 17, and 19 vary with each step in the PSA cycle and are discussed later in this work.

(14)

∂ 2ci

∂Cv ∂C 1−ε + + ∂Z ∂t ε

=0 (18) 3884



Article

P = PH − (PH − PL) exp( −a1t )

Pressure change with time in Step 4 is represented by P = PL + (PH − PL) exp( −a 2t )

∂qi

(22) 23

∂r (23)

qi|r = R c

where PL and PH are the low and high pressures in the pressurization and evacuation steps. The constants in eqs 22 and 23, a1 and a2, are assumed to have values of 0.15 and 0.05/ s, respectively, such that the pressure changes are completed within the durations of these steps. Boundary conditions for Steps 1, 2, and 3:

qis

DA =

∂ ci ∂z 2

∂ci ∂z

= −v|z = 0 (ci|z = 0− − ci|z = 0 ) (24a)

z=0

DB =

=0 (24b)

z=L

λ ∂Tg = −Ccpgv|z = 0 (Tg|z = 0− − Tg|z = 0 ) ε ∂z

∂T −K w w ∂z

= βh0(Tw − T∞) z=L

= z=0

= z=0

∂Tg

∂z

Pu 2 =

(24e)

(24f)

∂yi

Kw

∂ci ∂z

=

∂z

(29)

⎡ ∂q /∂r ⎤ DB0 ⎢(1 − θA ) + θB A ⎥ 1 − θA − θB ⎢⎣ ∂qB /∂r ⎥⎦

(30)

100 ∫

0

t Evacuation

CC3H6v|z = 0 dt

t

t

∫0 Evacuation CC3H6v|z = 0 dt + ∫0 Evacuation CC3H8v|z = 0 dt

∂z

=0 (25a,b)

z=L

=0

∂Tw ∂z

= βh0(Tw − T∞) z=L

C totalv|z = 0 dt + ∫ 0

t Rinse

t Rinse

CC3H8v|z = 0 dt ]

C totalv|z = 0 dt

for Step 1

(26a)

v|z = 0 = v0

for Step 2

(26b)

for Step 3 for Step 4

(26c) (26d)

(1 − γ )/ γ ⎧ ⎫ ⎪⎛ P ⎞ ⎪ out ⎨ − 1⎬ dt F × Pin ⎜ ⎟ ⎪⎝ P ⎠ ⎪ ⎩ in ⎭

(33)

(34)

■

Mass balance for microparticles: ∂q ⎞⎤ 1⎡∂⎛ = 2 ⎢ ⎜r 2Di ci ⎟⎥ ∂t ∂r ⎠⎥⎦ r ⎢⎣ ∂r ⎝

∫0

ti

where F1 is the amount of propylene produced in the evacuation step. As shown in Figure 7, the pressurization and adsorption steps may require compressors, if the high pressure in the PVSA process exceeds the feed stream pressure, which is 2−3 atm in practice. Since the rinse occurs at the high pressure, a compressor is required during the rinse to increase the pressure of the heavy reflux from the evacuation step. Finally, a vacuum pump is needed for the evacuation step. Thus, if the high pressure in a PVSA cycle does not exceed the feed pressure, then the work in eq 34 involves two parts: one for the rinse, and the other for the evacuation.

(25e,f)

v|z = L = 0

v|z = L = 0

CC3H8v|z = 0 dt + ∫ 0

Wtotal (kWh/tonne of propylene) Wcompressor + Wvacuum pump = 3.6 × 42 × F1

(25c,d)

z=L

Boundary conditions for velocity:

v|z = 0 = vrinse

∫0

tAdsorption

0 tAdsorption

where component 1 is propylene and component 2 is propane, η is the compression efficiency, and γ is the adiabatic compression constant. F is the total gas flow through the compressor or vacuum pump, and Pin and Pout are the inlet and outlet pressures, respectively. For recoveries, we use eqs 12 and 13. The total energy consumption for the separation is given by

(24g)

z=L

= −K w z=0

100[∫

γ W= η(1 − γ )

=0

∂Tg

z=0

∂Tw ∂z

⎡ ∂q /∂r ⎤ DA0 ⎢(1 − θB) + θA B ⎥ 1 − θA − θB ⎢⎣ ∂qA /∂r ⎥⎦

(31)

Boundary conditions for Step 4: ∂ci ∂z

(28b)

(32)

(e + R w )2 β= e(e + 2R w )

∂z

1 + ∑i bici|r = R c

(24d)

z=L

∂yi

bici|r = R c

(24c)

=0

∂z

= θi =

To compute the purity (Pu, %) and energy consumption (W, kWh/tonne propylene), we use Pu1 =

∂Tg

(28a)

We use the following to describe the concentration dependence of diffusivity in a Langmuir system with constant intrinsic mobilities:24

2

Dl

=0 r=0

NUMERICAL SIMULATION Dell Optiplex 780 with Intel Core 2 Quad CPU Q9400 @ 2.66 GHz Processor, 8 GB of RAM is used for numerical simulation. The model equations are written in dimensionless form and solved using COMSOL Multiphysics software that employs the

∂qci

(27)

Microparticle boundary conditions: 3885



Article

finite element method. Two geometries are used: one is a line of unit length, representing the axial direction of the bed, and the other is a square of unit length and width, representing the axial direction of the bed and radial direction of the particles, respectively. Using a square to represent variable profiles within the particle along the bed is helpful in that it obviates the need to simulate a full sphere at each position in the bed; hence, it simplifies the problem and reduces the level of computation required. The partial differential equations (PDEs) that belong to bulk profiles are set up in the line geometry whereas those for microparticle profiles are set up in the square geometry. Four COMSOL files, which correspond to pressurization, adsorption, rinse and evacuation steps, are solved and exported as structures to MATLAB, which executes the cycling codes and solves these structures sequentially. The initial pressurization structure carries the initial conditions of the bed under vacuum condition to start the cycling whereas the other structures take the recorded final condition from the previous step as initial conditions. The cycling loop is continuously executed until the purity difference in five cycles dwindles to

Propane Separation Using SiCHA - Industrial

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