Propane Mixtures by

In the bulk, catalyzed polymerization of propene in an industrial-scale recycle reactor, propane is an important contaminant, and for this reason it i...
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Ind. Eng. Chem. Res. 2007, 46, 1259-1269

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Modeling of the Separation of Propene/Propane Mixtures by Permeation through Membranes in a Polymerization System Marcelo T. Castoldi, Jose´ C. Pinto, and Prı´amo A. Melo* Programa de Engenharia Quı´mica, COPPE, UniVersidade Federal do Rio de Janeiro, Centro de Tecnologia, Ilha do Funda˜ o, Bloco G, Sala 115, CP 68502, CEP 21941-972, Rio de Janeiro, RJ, Brazil

In the bulk, catalyzed polymerization of propene in an industrial-scale recycle reactor, propane is an important contaminant, and for this reason it is necessary to remove it from the reaction medium in order to maintain high process productivities. In a typical industrial operation, unreacted propene/propane mixtures are purged from the recycle stream and vented to a flare, causing a significant negative impact on the process economics. Despite the potential economic advantages that membrane-based propene recovery may represent industrially, a comprehensive analysis based on a detailed mathematical model of the system is not available yet. The main purpose of this study is presenting a mathematical model to simulate the separation of propene/propane mixtures in a polymerization system using membrane modules. The model developed takes into account two extreme levels of macromixing that may be observed in the permeation module (namely, perfect mixing and plug flow), the diffusion of the gaseous mixture through the polymeric membrane, and the effect of operational variables such as temperature, pressure, flow rates, composition, and membrane area on the separation performance. It is shown that polyimide-based membranes, such as 6FDA-TMPPD (2,2-bis(3,4-decarboxyphenyl)hexafluoropropane dianhydride and 2,3,5,6-tetramethyl-1,4-phenylenediamine), may be used in permeation modules to deliver up to 5% gains in the effective propene concentration at the reactor feed, therefore increasing significantly the reactor productivity. An economic analysis shows that an economic gain of up to U.S.$1.5 million per year per polymerization plant may be attained. 1. Introduction Polypropene is a major plastic commodity with wide commercial application and of great economic importance. It is usually produced through the polymerization of propene using Ziegler-Natta catalysts. A number of important continuous polymerization processes may be found for the industrial production of polypropene: (i) the suspension process in a series of tank reactors, where the reaction occurs in liquid diluent medium, with propene being fed to the system in the gas phase;1 (ii) the bulk process in a tank reactor, where liquefied propene polymerization (also known as liquid pool polymerization, LIPP, process) is carried out, leading to a high yield and compact process;1 (iii) the bulk process in a tubular loop reactor, designed to overcome the heat transfer and mixing problems usually found in tank reactors.2 In a LIPP process, monomer, catalysts, and auxiliary reactants (such as hydrogen, used to control the polymer average molecular weight) are continuously fed into a high-pressure tank reactor, as depicted in Figure 1. Under typical operation conditions, the feed stream main contaminant is propane. The polymerization reactor effluent is, therefore, basically composed of unreacted propene, propane, hydrogen, and polypropene (catalyst inventories are typically merged to that of the polymer produced). The polymer is separated from the other components through a sudden pressure drop in a flash chamber. A lowpressure mixture of propene and propane is then recycled, and prior to reentering the reactor, it is compressed to liquid phase. The effective feeding of the reactor consists thus of a combination of fresh and recycled propene. Although the amount of propane in the fresh reactor feed stream is very small (around 0.3 wt %), its circulating amount * To whom correspondence should be addressed. Fax: +55 21 25628300. E-mail: [email protected].

Figure 1. Typical LIPP process for propene polymerization.

may increase significantly, reducing the propene concentration and the reactor productivity. The increase of the propane amount is usually prevented by purging a fraction of the recycled gaseous mixture (see Figure 1). Typically, propane concentration is maintained between 5% and 30% (weight percent) in the polymerization reactor.3 This concentration is defined based exclusively on economics reasoning, since propane is completely inert and does not participate in any polymerization stage. As the purge operation is not selective and the purged stream contains about 80% (weight percent) propene, a great amount of propene is lost for each volume of purged propane. Although the volume of purged gas is just a small portion of the new feeding, the propene lost in this way achieves amounts that may exceed 5000 tons per polymerization plant per year, representing

10.1021/ie060333q CCC: $37.00 © 2007 American Chemical Society Published on Web 01/17/2007

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Table 1. Permeability and Ideal Selectivity of Propene and Propane for a Number of Polymeric Membranes (T ) 298 K, P ) 10 atm) permeability (barrera) membrane

propene

propane

ideal selectivity

reference

PPO EC CA PEO 6FDA-44′DPE 6FDA-BAAF 6FDA-FDA 6FDA-DABA 6FDA-33′DMDB

9 52 15.2 45 0.0823 0.726 0.853 0.0475 0.263 0.15 0.115 0.188 0.0821 9.29 13.8

2.1 16 5.8 16.7 0.0020 0.0367 0.0343 0.0004 0.0067 0.0114 0.0025 0.0121 0.0040 0.5994 1.0222

4.25 3.25 2.60 2.7 41.6 19.8 24.9 124 39.4 13.2 45.1 15.5 20.7 15.5 13.5

Sridhar and Khan9 Sridhar and Khan9 Sridhar and Khan9 Lin and Freeman13 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10 Burns and Koros12 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10 Shimazu et al.10

6FDA-DSH 6FDA-BAPF 6FDA-44BAPS 6FDA-TrMPD 6FDA-TMPPD

a Barrer ) 1010 cm3 (STP) cm/(cm2 s cmHg). b PPO, poly(phenylene oxide); EC, ethylcellulose; CA, cellulose acetate; 6FDA, 2,2-bis(3,4decarboxyphenyl)hexafluoropropane dianhydride; 44′DPE, 4,4′-diaminodiphenyl ether; BAAF, 2-bis(4-aminophenyl)hexafluoropropane; FDA, 9,9′-bis(4aminophenyl)fluorene; DABA, 4,4′-diaminobenzanilide; 33′DMDB, 3,3′-dimethyl-4,4-diaminobiphenyl; DSH, 3,3′-dimethoxy-4,4′-diaminobiphenyl; BAPF, 2,2′-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane; 44BAPS, bis[4-(4-aminophenoxy)phenyl] sulfone; TrMPD, 2,4,6-trimethyl-1,3-phenylenediamine; TMPPD, 2,3,5,6-tetramethyl-1,4-phenylenediamine.

effective losses on the order of millions of dollars per year in each plant.3 To recover part of the propene lost in the purging process, the installation of a membrane separation system for the purge stream has been suggested so that a richer propene permeate stream would be recycled to the reactor.3 As a result, an increase of the effective propene concentration in the feed stream would be obtained, improving the rate of reaction and allowing for simultaneous increase of the conversion and reactor productivity. Despite the potential economic advantages that membranebased propene recovery may represent industrially, a detailed mathematical modeling of this system is not available. The main purpose of this study is to present a mathematical model to simulate the separation of propene/propane mixtures in a polymerization system using membrane modules. The model developed takes into account two extreme levels of macromixing that may be observed in the permeation module (namely, perfect mixing and piston flow), the diffusion of the gaseous mixture through the polymeric membrane, and the effect of operational variables such as temperature, pressure, flow rates, composition, and membrane area on the separation performance. This article has been organized as follows. In section 2, a literature review of the separation of propene/propane mixtures using polymeric membranes is presented. Also, a review regarding the mathematical modeling of membrane processes focusing on the separation of propene/propane mixtures is presented. In section 3, a mathematical model is developed to describe the membrane module dynamic and steady-state behavior. This model includes the diffusion of the gaseous mixture through the polymeric membrane. The numerical details for solving the model are also presented. In section 4, the separation process is evaluated considering different operational variables and also different polymeric membranes. In section 5, the main conclusions of this study are presented. It is shown that polyimide-based membranes, such as 6FDATMPPD (2,2-bis(3,4-decarboxyphenyl)hexafluoropropane dianhydride and 2,3,5,6-tetramethyl-1,4-phenylenediamine), may be used in permeation modules in order to deliver up to 5% gains in the effective propene concentration at the reactor feed, therefore significantly increasing the reactor productivity. An economic analysis shows that an economic gain of up to U.S.$1.5 million per year per polymerization plant may be attained. Macromixing analysis of the gaseous mixture within

the module shows that, in general, plug flow behavior leads to more efficient permeation, thus resulting in smaller membrane modules. 2. Literature Overview 2.1. Membranes for the Separation of Propene/Propane Mixtures. As olefins and paraffins present similarities as far as their physical properties are concerned, separation of these hydrocarbons is a major difficulty. For instance, the boiling temperatures of propene and propane at atmospheric pressure are, respectively, -48 and -42 °C. This is the main reason the separation of propene/propane mixtures is usually carried out by cryogenic distillation. However, this separation method is highly energy demanding; very low temperatures and high pressures are needed to accomplish a reasonable separation, which results in high operational costs.4-6 Because the boiling points of propene and propane are so close, large distillation columns, containing up to 180 plates, are needed, and high reflux rates are demanded.7 Therefore, there exists great interest in the development of more economical propene/propane separation processes.8 Membrane technology can be an attractive alternative to minimize the operational costs of the separation process.6 Only recently has the separation of mixtures containing olefins and paraffins using polymeric membranes gained importance, and the available information reported on this subject is steadily increasing. Most of the studies, however, deal with the determination of diffusivity and solubility data of the gases in various polymer matrixes,4-7,9-11 with the exception of the work of the work of Burns and Koros,12 where upper bounds for selectivity/ permeability are calculated from a mathematical model and compared to the available literature data. The ideal membrane for separating propene and propane mixtures should have good permeability and high selectivity to propene. In the open literature, a number of studies may be found where polymeric membranes are tested for the separation of propene/propane mixtures. As presented in Table 1, literature data regarding the permeation of propene or propane through membranes are rarely presented for temperatures other than 298 K. However, it is expected that membrane permeability should be enhanced and selectivity should diminish as the temperature is increased.

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Data presented in Table 1 may be divided into three main groups. The first group contains poly(phenylene oxide) (PPO) as well as ethylcellulose (EC), cellulose acetate (CA), and poly(ethylene oxide) (PEO) based membranes. This group corresponds to membranes that possess high permeabilities to both propene and propane, but are more selective to propene. Ideal selectivities, obtained from permeation data of pure components, are too low to encourage their usage in large-scale applications. Group two consists of membranes presenting excellent ideal selectivities to propene at the cost of very low permeabilities, and include all 2,2-bis(3,4-decarboxyphenyl)hexafluoropropane dianhydride (6FDA) membranes with the exception of those based on phenylenediamine (TMPPD and TrMPD). The third group is composed of 6FDA-TMPPD and 6FDA-TrMPD based membranes that seem to present the best compromise between a reasonable permeability and good selectivity to propene. Another important class of membranes for the separation of propene/propane mixtures is the so-called facilitated transport membranes. The main difference of this kind of membrane is the presence of a carrier, usually a metal, that can be anchored to the polymer matrix. The carrier is added to the polymer matrix in order to facilitate the transport of propene molecules across the membrane. The most common carriers used in facilitated membranes for propene/propane separations are transition metal ions. These species react reversibly with the propene through a π-complexation mechanism, in which the olefin π-orbital interacts with the s- and d-orbitals of the metal ion. Silver in oxidation state I is the most used metal ion in membranes to carry out propene/propane separations, as it forms less stable olefin complexes in comparison to the other transition metals ions.14 Although facilitated transport membranes present better permeability and selectivity compared with some other nonfacilitated membranes, they are not considered in this work because a number of operation problems associated with carrier deactivation and loss of stability of the membrane structure are still under consideration in the open literature. 2.2. Modeling of the Separation through Membranes. The use of mathematical models for analysis, optimization, and control of processes and operations in the chemical industry has been shown to be very important.15-18 Recently, mathematical modeling tools have been applied to the design of membrane processes.19-21 The mathematical modeling of permeation modules is an important step toward the understanding of the gas separation through polymeric membranes, especially in the case of process scale-up. With the aid of a proper membrane process simulator, it is possible to understand the effect of the several operational variables such as temperature, pressure, flow rates, composition, and membrane area on the separation performance.22 The first analytical study about binary separations of gaseous mixtures (e.g., air/oxygen and helium/natural gas) through nonporous membranes was presented by Weller and Steiner.23 The mathematical model developed considered both perfect mixing and plug flow behavior of the gases on both sides of the membrane. Fick’s law was used to describe molecular diffusion of various gaseous mixtures through ethylcellulose and polystyrene membranes. As the model did not consider the effects of the module geometry, it was not possible to evaluate effects of the flow (cocurrent, countercurrent, or cross flow) in the separation module. However, the model could be used to predict the minimum possible separation and the requested

maximum area, for certain simulation scenarios. It was possible, thus, to determine membrane area limits and separation efficiencies. Naylor and Backer24 analyzed the case where the permeate stream is extracted transversal to the membrane and the module feed stream is assumed to have plug flow behavior. The plug flow model with Fickian diffusion was solved analytically and presented very good results for real conditions of mass transfer in asymmetrical membranes. Blaisdell and Kammermeyer25 performed permeation experiments using silicon tubes as membranes and considered the separation of helium-oxygen mixtures. Their data were successfully represented by a mathematical model that was solved numerically. The model considered both co- and countercurrent flow patterns in the permeation system. Doong et al.26 developed mathematical models for the prediction of the total molar flux and selectivity in permeation of toluene, p-xylene, and mesitylene through polyethylene plane membranes, using the concepts from the free volume theory of Cohen and Turnbull,27,28 which allowed for the prediction of diffusion coefficient values for permeation through the membrane. Their mathematical model was solved numerically. Sridhar and Khan9 simplified mathematical models presented in the literature for the co- and countercurrent flow patterns in plane membranes, obtaining a generic model for the description of the permeation of propene and propane through ethylcellulose, cellulose acetate, poly(phenylene oxide), and polysulfone membranes. In their model, Fickian diffusion was used. Numerical simulation results showed that ethylcellulose membranes have better performance among the polymeric membranes studied. Mariott et al.19 developed a generic mathematical model for a separation process using membranes considering several geometrical arrangements (i.e., plane, spiral, tubular, and hollow fiber membrane types). Their model is constituted by submodels used to describe the flow on each side of the membrane, in terms of balances of mass, moment, and energy, and characterize the membrane separation properties. A numerical solution using orthogonal collocation on finite elements was proposed. Their model presented very good agreement with experimental data from the literature. Wada29 developed a mathematical model for the separation of an ethanol-water mixture by pervaporation using MaxwellStefan’s equations to describe permeation through poly(vinyl alcohol) membranes. A orthogonal collocation was used to solve the model equations. Wada’s experimental data were successfully compared against the model predictions. Fernandes et al.30 also used Maxwell-Stefan’s approach to develop a permeation model for the phase inversion process during plane membrane preparation. A numerical solution was proposed for the model equations. In their process, solvent and additive permeation occurs from the inner side of the polymeric film to the immersion bath and vice versa. It is important to point out that the permeation phenomena occurring within the membrane are similar to those found in membrane permeation systems, allowing similar equations to be used. Iza´k et al.31 performed simulation studies comparing both Maxwell-Stefan and Fickian mathematical models for gaseous transport of binary mixtures of pentan-1-ol/toluene and hexan1-ol/toluene through dense and plane polyethylene membranes, and concluded that binary mixtures present strongly nonlinear behavior as far as solubility and diffusivity of the compounds

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w1 + w2 ) 1 m)

PV M h RT

(2) (3)

where Figure 2. Scheme of the membrane module with perfect mixing behavior.

in the membranes are concerned. Experimental data were successfully compared to the simulation results obtained numerically. Although the separation of propene/propane mixtures through membrane processes has been experimentally analyzed in previous publications, the detailed analysis of the performance of membrane separation modules in actual polymerization environments is still lacking. Also, the analysis of macromixing effects on the performance of membrane separation modules has not been fully characterized. This paper presents a model to describe the separation of propene/propane mixtures through membrane separation modules and to characterize the importance of macromixing effects on the separation performance. 3. Mathematical Modeling The mathematical modeling of the membrane modules has been divided into two parts: one related to the modeling of the macroscopic flow within the module itself, and the other related to the modeling of the molecular diffusion of propene and propane through the polymeric membrane. For the first part, two extreme levels of macromixing, i.e., perfect mixing behavior and piston or plug flow behavior, were considered. Although perfect mixing behavior has been investigated since the 1950s23 and nowadays most membrane separation modules are based on more complex flow patterns, this model has been added into this work for the sake of completeness of the macromixing module behavior analysis. From the simulation with perfect mixing conditions, it is possible to analyze more appropriately mixing deviations and their impact on process performance. In what follows, the mathematical models for each part are presented. 3.1. Perfect Mixing Behavior. Figure 2 presents the sketch of the membrane module. The membrane divides the module into two main sections: one receiving the feed flow rate, called the feed section, and the other one past the membrane, called the permeate section. The flow rate leaving the module through the feed section is called the retentate flow rate, and the flow rate leaving the module through the permeate section is simply called the permeate flow rate. Because of the polymeric membrane selectivity characteristics, the permeate flow rate is richer in propene. It is admitted that gases are completely mixed on the feed side of the membrane. The permeation takes place uniformly and isothermally in the whole extension of the membrane, as presented in Figure 2. In Figure 2, A represents the membrane area available for permeation/diffusion. The permeate fluxes per unit area of propene and propane are given by j1 and j2, respectively, and are obtained from the equations related to the permeation though the membrane, as discussed in section 3.3. A mass balance over the feed section of the module under nonsteady-state conditions leads to the following differentialalgebraic system of equations:

dw1 1 ) [(w1e - w1)qe - (1 - w1)j1A + w1j2A] dt m

(1)

w1 w2 1 + ) M h M1 M2

(4)

and M1 and M2 are molecular masses of propene and propane, respectively. Equations 1-3 constitute the basic model for the perfect mixed module. 3.2. Plug Flow Behavior. The other extreme of macromixing considered here is the plug flow module. In the plug flow module the gas flow through the feed section takes place in such a way that no mixing is expected in the flow direction, but complete mixing is expected in any other direction. This behavior implies that a concentration distribution is obtained along the flow direction. In order to cope with such a flow scheme, the flow direction in the feed section was divided into subsections, each one with a concentration of propene and propane. Due to the lateral withdrawal of both propene and propane, the flow rate along the feed section continuously decreases. Figure 3 presents the details of the piston flow module. A mass balance of component i in the feed section results in

∂Ci ∂Ci ∂V ) -Ci - V - jiR ∂t ∂z ∂z

(5)

where Ci is the molar concentration of species i in the feed section, R is the ratio between the membrane area and the volume of the module, and V is the flow velocity, given by

V)

qT AtF

(6)

In eq 5, ji stands for the permeate flux per unit area of either propene or propane and is obtained from the equations related to the permeation though the membrane, as discussed in section 3.3. In eq 6, At is the total cross-sectional area in the feed section. The average density of the gaseous mixture in the feed section is calculated from

F)

(

)

w 1 w2 + F1 F2

-1

(7)

where w1 and w2, the mass fractions of propene and propane in the feed section, respectively, are calculated from

wi )

qi qT

(8)

The change in the flow rate through the feed section is obtained from the following equation

∂qi ) -jil ∂z

(9)

where l is the length of the module in the flow direction. Finally, the total mass flow rate, qT, is given by

qT ) q1 + q2

(10)

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Figure 3. Scheme of the plug flow module type.

Equations 5-10 constitute a set of coupled algebraic-partial differential equations. To solve this system, eq 5 was discretized using a finite difference scheme, as illustrated in Figure 3. The boundary conditions are given at the module entrance

q(z)0) ) qe ) qe0 Ci(z)0) ) Cie ) Cie0

(11)

3.3. Permeation through the Membrane. Molar fluxes j1 and j2 result from the concentration difference of both propene and propane in both sides of the membrane. It is assumed that the mass transport takes place through molecular diffusion through the polymeric matrix of the membrane. No mass transport due to any convection mechanism is expected since the separation occurs in a dense membrane. A classical approach considering that the molecular diffusion may be described by Fick’s law was adopted. This is a very reasonable assumption as the mass transport may be considered binary (for the polymer matrix is static) and due to the nonpolarity of the diffusional species. The dimensionless molar balance permeation through the membrane is given by

∂φi 1 ∂DiM ∂φi DiM ∂2φi ) 2 + 2 ∂t L ∂x ∂x L ∂x2

(12)

Kie[φie - hieφi(0,t)] ) -

DiM ∂φi| | L ∂x |x)0

(13)

Kis[hisφi(1,t) - φis] ) -

DiM ∂φi| | L ∂x |x)1

(14)

∀x

(15)

φi(x,0) ) 0,

where φi is the dimensionless concentration of the component i (propene or propane) normalized by the correspondent feed concentration at the permeation module; hie and his are the partition constants at the feed and permeate sides of the membrane, respectively; Kie and Kis are mass transfer coefficients at the feed and permeate sides of the membrane, respectively; φis is the dimensionless concentration of the component i at the permeate side; φie is the dimensionless concentration of the component i on the feed side of the membrane, obtained from the material balance for the modules. One may notice that variable diffusivities are considered in order to account for the swelling effects, commonly found for polymeric membranes. It should also be noticed that molar fluxes j1 and j2 are given by the absolute value of the righthand side of eq 13. In eqs 12-14 DiM is the mutual diffusion coefficient. There are a number of diffusion coefficient models in the open literature. Among them, the Vrentas-Duda32 model was chosen in this work because it is the most studied and accepted model to describe molecular diffusion through dense polymeric membranes.33-41 The details of the mutual diffusion coefficient

Figure 4. Propene dimensionless concentration in the membrane system (L ) 1 µm, Kie ) Kis ) 0.01, hie ) his ) 1, DiM ) 27.4 × 10-10 cm2/s).

calculation and the model numerical solution may be found in the Appendix. 4. Results and Discussion In what follows, results are initially presented for a set of simulations considering the 6FDA-TMPPD membrane system alone, i.e., simulations considering only the permeation process. It is intended to investigate membrane swelling and selectivity characteristics at different process conditions. Afterward, a thorough analysis of the performance of the membrane modules is carried out at two limiting cases of macromixing behavior, i.e., at plug flow and perfect mixing conditions, and different operation temperatures and available membrane areas. Then, a comparison among the performances of the membrane modules using different types of membranes is performed. Finally, an economic evaluation of the implementation of the membranebased separation system in an industrial polymerization process is presented. 4.1. Permeation through the Membrane. Except when explicitly stated otherwise, the simulations presented in this section consider a working temperature of 333 K and feed pressure of 10 atm, and a constant upstream (feed side) concentration of propene of 80% (weight percent). Also, the permeate side of the membrane is assumed to be under vacuum conditions. The membrane thickness used for the simulations is 5 µm, as suggested by Baker et al.3 It may be emphasized that, according to the open and patent literature, values for membranes used for the separation of propene/propane are typically in the range of 1-50 µm. Permeability and selectivity of both propene and propane in the 6FDA-TMPPD membrane system are given in Table 1. Figure 4 shows concentration profiles of both propene and propane along the membrane at the steady-state conditions. The influence of the Vrentas-Duda mutual diffusion coefficient on the concentration profiles can be seen. When the diffusion coefficient is not constant, profiles are no longer linear. The most important consequence of this situation is that, by considering a nonconstant diffusion coefficient, molar fluxes at the membrane permeate side are significantly lower than those obtained for the linear concentration profile. Therefore, taking into account the interaction of the diffusing molecules with the polymer matrix improves the proper calculation of permeate molar fluxes. In Figure 5, the influence of the temperature on membrane selectivity and area is presented. It may be observed that temperature effects are not significant at temperatures below

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Figure 5. Molar fractions in the permeate stream and membrane area as a function of operation temperature (P ) 10 atm).

Figure 7. Propene concentration (weight percent) in the retentate stream as a function of membrane area at P ) 10 atm and (a) T ) 323 K, (b) T ) 333 K, and (c) T ) 343 K.

Figure 6. Propene concentration (weight percent) in the permeate stream as a function of membrane area at P ) 10 atm and (a) T ) 323 K, (b) T ) 333 K, and (c) T ) 343 K.

333 K, but are important above this temperature. Selectivity to propene is highly affected as temperature increases. This is due to the fact that, as temperature increases, free volumes in the polymer matrix are enlarged. Although this expansion may enhance propene diffusion within the membrane, it may also enhance the larger propane molecules to diffuse as well. In the limiting case, permeate molar fractions would be equal to those found in the feed side of the membrane. As far as membrane area is concerned, calculations were performed in such a way that a flow rate of 100 kg/h propene is obtained in the permeate section of the membrane. As shown in Figure 5, membrane area is highly reduced as temperature

increases. This is an expected result as permeabilities are enhanced as temperature increases, at the cost of a significant decrease in selectivity, as discussed above. Also, the decrease in the membrane area is only moderately affected by temperature above 333 K. In view of the discussion presented above, the temperature 333 K seems to present the best compromise between selectivity (evaluated from the molar fractions at the permeate side) and permeability (evaluated from the membrane area calculated) to separate propene and propane in an industrial process. 4.2. The Permeation Module. The methodology used to simulate the membrane module considered here is described as follows. The feed stream is composed of a gas mixture consisting of 80% (weight percent) propene and 20% (weight percent) propane. Different feed flow rates (100, 300, 500, 700, and 1000 kg/h) may be imposed on the module in order to evaluate the effect of the average residence time on the separation efficiency. Simulations are performed at an operation feed pressure of 10 atm and temperatures 323, 333, and 343 K. The permeate side of the membrane is assumed to be under vacuum conditions. For each simulation, two levels of macromixing are considered, as described in section 3. Results are analyzed in terms of the propene molar fraction in the permeate and retentate streams and the operation stage-cut (ordinates) as a function of the membrane area needed to achieve a given

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Figure 9. Membrane area and amount of propene lost in the retentate stream as a function of feed flow rate of the module (T ) 333 K, P ) 10 atm, 100 kg/h propane removal).

Figure 10. Propene recovered in the permeate stream as a function of available membrane area (T ) 333 K, P ) 10 atm, 100 kg/h propane removal).

Figure 8. Stage-cut as a function of membrane area at P ) 10 atm and (a) T ) 323 K, (b) T ) 333 K, and (c) T ) 343 K.

separation efficiency (abscissas). Feed flow rates and temperatures are parameters in the various curves presented. Figure 6 shows steady-state propene concentrations in the permeate stream of the module as a function of the available membrane area at different temperatures and macromixing levels. It is shown that propene concentrations in the permeate stream may be significantly reduced with the increase of the membrane area. The explanation for this behavior is given as follows. For a given feed flow rate, as the available membrane area increases, the volume of the retentate side of the module also increases. This leads to an increase in the mean residence time the gas mixture spends flowing through the retentate side of the module. Because the membrane is not solely selective to propene, as the residence time in the retentate side increases, more propane permeation is observed, thus reducing the propene concentration in the permeate side of the module. The same behavior is observed when a fixed membrane area is chosen and the feed flow rate is varied. Higher feed flow rates decrease the mean residence times in the retentate side of the module, allowing for a more selective permeation through the membrane. As far as the operation temperature is concerned, it is shown that temperature has a dramatic negative effect on the separation performance. As discussed in section 4.1, as temperature increases, the polymer matrix undergoes a thermal expansion that ultimately leads to an increase of the molar flux of propane along the membrane. Therefore, higher operation temperatures

result in lower permeate propene concentrations for the same available membrane area. The last point concerns the effect of the macromixing behavior of the module and its influence upon the separation efficiency. Figure 6 shows that, regardless of the chosen membrane area, operation temperature, and feed flow rate, plug flow behavior usually leads to higher propene concentration in the permeate stream. The retentate side of the membrane module is analogous to a chemical reactor. Here, lateral withdraw (due to the presence of the membrane) assumes the role of the bulk chemical reaction. It is well-known from classical chemical reaction engineering that, for a given volume, plug flow behavior generally implies the largest attainable conversion. This explains the better separation efficiencies observed for the membrane module operating under plug flow regime. Figure 7 shows steady-state propene concentration in the retentate stream of the module as a function of the available membrane area at different temperatures and macromixing levels. It is shown that propene concentration in the permeate stream decreases with the increase of the membrane area. For a given feed flow rate and macromixing level in the module, as the available membrane area increases, the mean residence time the gas mixture spends in the retentate side increases. The increase in the mean residence time leads to an increase in the overall molar flux of propene, thus decreasing its concentration in the retentate stream. The same analysis is valid when one considers a fixed membrane area and increases the feed flow rate of the module, as presented in Figure 7. The analysis of the effects of temperature and macromixing level in the retentate side of the membrane on the concentration of propene in the retentate stream is analogous to the case of the permeate stream, presented above. Figure 8 shows steady-state module stage-cut values as a function of the available membrane area at different tempera-

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Table 2. Data for the Membranes Investigated solubility (cm3 (STP)/cm3 cmHg) polymer matrix

density

PEOa 6FDA-DABAb 6FDA-TMPPDb a

Lin and Freeman.13

(g/cm3)

1.124 1.459 1.325 b

diffusivity × 1010 (cm2/s)

Tg (K)

propene

propane

propene

propane

223 632 679

0.263 0.163 0.496

0.155 0.027 0.420

170 0.291 27.8

106 0.014 2.44

Shimazu et al.10

tures and macromixing levels. Stage-cut values are calculated from the ratio of the permeate flow rate to the module feed flow rate. For a given feed flow rate, as the available membrane area increases, the observed response is an increase in the overall molar flux through the membrane, resulting in higher values for the stage-cut. Figure 8 also shows that higher feed flow rates, i.e., lower mean residence times of the gas mixture in the retentate side of the module, imply lower permeate fluxes along the membrane, thus reducing the stage-cut value for a given membrane area. The analysis of the effects of temperature and macromixing level in the retentate side of the membrane on the module stage-cut behavior is analogous to the cases presented above. Figures 9 and 10 presents simulation results concerning the calculation of the membrane area (and the corresponding amount of propene lost in the retentate side and recovered in the permeate side) needed to carry out the removal of 100 kg/h propane for a given module feed flow rate. This fixed value for the removal flow rate of propane is explained by the fact that it represents a typical feed flow rate of propane to the LIPP polymerization reactor, as a contaminant in the propene stream, as discussed in section 1. Figure 9 shows that, regardless of the macromixing behavior in the retentate side of the module, as the module feed flow rate increases, the necessary available membrane area to accomplish a removal of 100 kg/h propane also increases, as expected. Because of the increase of the available membrane area, an increase of the total molar flux along the membrane is also observed. As the membrane is more selective to propene, it is noticed that the amount of propene lost in the retentate side systematically decreases as the available membrane area increases. Also, as plug flow behavior in the retentate side implies higher total molar flux of propane along the membrane, lower membrane areas are necessary when compared to the case of perfect mixing. In Figure 10, the ratio of the amount of propene recovered in the permeate side to that in the membrane area is plotted against the membrane area itself. As shown, recovered propene per unit area increases significantly as the available membrane area of the module increases to values up to 4000 m2. Additional increase of the available membrane area does not imply significantly higher recovered propene flow rates. This is due to the fact that the available membrane area has been increased up to a point where retentate and permeate propene concentrations are almost equal, and the mass transfer driving force along the membrane has virtually vanished. 4.3. Other Membranes. In all simulations presented above, the membrane is constituted of a 6FDA-TMPPD polymeric matrix. Other polymeric matrixes are now considered in order to evaluate the suitability and separation performance of the membrane module to carry out propene/propane separation. Simulations with low-selectivity membranes may be used to emulate an industrial scenario once, in this case, ideal selectivities may not be obtained. Simulations were accomplished considering a module feed flow rate of 100 kg/h constituted of 80% propene (weight percent) and 20% propane (weight percent), and a membrane area of 100 m2. Membranes produced

of poly(ethylene oxide) (high permeability and low selectivity to propene) and 6FDA-DABA (high selectivity with low permeability to propene) are compared against the 6FDATMPPD membrane base case. A number of model parameters are affected when one considers a different type of membrane, namely, the polymer density, the glass transition temperature (Tg), and the values of solubility and diffusivity of the permeating species through the membrane. Table 2 summarizes the relevant data for the membranes investigated. Figure 11 presents a comparison of the separation efficiency of the membrane systems investigated, evaluated in terms of the propene concentration in the permeate stream. It is verified that, regardless of the macromixing behavior within the module, propene concentrations in the permeate stream are always higher in the 6FDA-DABA membrane. The poly(ethylene oxide) membrane presents the less encouraging results as far as the separation selectivity to propene is concerned, as expected. It should be pointed out that, in general, plug flow behavior always results in higher selectivities to propene. Figure 12 presents propene concentrations in the retentate stream for the membranes analyzed. One may observe that, given a macromixing behavior within the module, PEO-based membranes present the lower propene concentrations in the retentate stream. This is due to the fact that, because of the higher permeability and lower selectivity of this membrane, a higher propene molar flux is observed, resulting in a significant decrease of its concentration in the retentate stream. On the other hand, for the case of the 6FDA-DABA based membrane, in spite of the higher selectivity to propene, its lower permeability implies lower propene molar fluxes along the membrane, thus decreasing very moderately the propene concentration in the retentate stream. 6FDA-TMPPD based membranes present an intermediate scenario. For a given polymer membrane, plug flow behavior results in lower propene concentration in the retentate. This may be explained by noticing that the average driving force for permeation is higher at plug flow conditions, which increases the molar flux of propene along the membrane; the propene concentration in the retentate stream is decreased when this situation is compared to the perfect mixing behavior. Figure 13 presents stage-cut values for the membrane systems analyzed. 6FDA-DABA based membranes present the lower stage-cut values because the permeability characteristics of these membranes are too low when compared to the other ones, according to Table 1. Also according to Table 1, poly(ethylene oxide) based membranes present very high permeabilities to both propene and propane, thus justifying the elevated values for stage-cut. 6FDA-TMPPD based membranes present an intermediate module stage-cut behavior. The better stage-cut performance of the high permeability membrane systems with plug flow behavior is explained analogously as in the previous paragraphs. 4.4 Economic Evaluation. As already discussed in the previous sections, in an industrial-scale LIPP polymerization process, a large amount of propene is lost because contaminant propane needs to be removed from the system. The acceptable

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1267

Figure 14. Proposed implementation of the membrane module in the polymerization system. Figure 11. Propene concentration (weight percent) in the permeate stream as a function of polymer membrane and level of macromixing with the module (T ) 333 K, P ) 10 atm).

Figure 12. Propene concentration (weight percent) in the retentate stream as a function of polymer membrane and level of macromixing with the module (T ) 333 K, P ) 10 atm).

Figure 13. Stage-cut as a function of module type and membrane polymer (T ) 333 K, P ) 10 atm).

propane concentration inside the reactor depends strongly upon economic process considerations. The higher the propane concentration inside the reactor, the lower the observed propene concentration, and therefore, a decrease in the reactor productivity is expected. To avoid such a situation, purge streams in the range of 500-1000 kg/h containing, typically, 80% (w/w) propene, may be applied. Figure 14 presents the proposed implementation of the membrane module system. As presented, the gas mixture recovered in the polymer separation chamber is split into two streams before entering the refrigeration and compression system. One stream is directed to a membrane module where propene will be enriched. Both streams are then refrigerated, compressed, and sent to the reactor feed.

Propene losses may exceed 5000 tons of propene per industrial plant per year or more than $2.5 million in propene per year.3 This is why the possibility of recovering a portion of the purged propene is so attractive. Regarding this hypothetical 5000 tons of propene purged and lost per year, a recovery of 10% of such propene would result in a savings of U.S.$500,000 per year per plant, considering that the value of polypropene is about U.S.$1.00/kg. Implementation of a membrane-based separation system to this polymerization process would certainly result in economic benefits. Consider the situation where operational conditions of the reactor are such that it is necessary to remove 100 kg/h propane from the polymerization process. Without the separation stage, the removal of that amount may imply a purge stream of 400 kg/h propene. Implementing a separation stage and purging the module retentate stream instead, the removal of 100 kg/h propane could be carried out by purging only 100 kg/h propene, assuming a concentration of 50% (weight percent) propene in the retentate stream. In this case, propene losses represent just a quarter of that observed in the case with no separation and, additionally, without any disturbance in the operation conditions of the reactor, since the amount of propane being removed is the same fed to the system in a typical industrial operation. Now consider that the feed flow rate of the industrial polymerization reactor is 20 000 kg/h fresh propene containing 99.5% (weight percent) propene. This stream contains 100 kg/h propane. Suppose a recycle stream of 50 000 kg/h with 80% (weight percent) propene. To maintain the propane concentration constant in the reactor, a purge of 500 kg/h of the recycle stream is necessary. The effective polymerization reactor feed is composed of a stream containing 85.61% (weight percent) propene. Using a membrane separation stage to treat the whole recycle stream, to remove 100 kg/h propane, a membrane area of approximately 30 000 000 m2 would be necessary, and the permeate stream would present 80.16% (weight percent) propene. The effective feeding stream is now composed of the sum of fresh feed stream and purified recycle stream, totaling a feed containing 85.69% (weight percent) propene. The purification of the whole recycle stream is not advisable, because the membrane area necessary would be enormous. However, if only 2% (1000 kg/h) of the original recycle stream of 50 000 kg/h with 80% (weight percent) propene were purified by a membrane module with an area of 3000 m2, the effective reactor feed would be a stream with a concentration of 85.69% (weight percent) propene, composed of the sum of the fresh feed stream, recycle stream (49 000 kg/h with 80% (w/w) propene), and purified recycle stream (1000 kg/h with 88.57% (weight percent) propene). Purifying just a portion of the recycle stream (and using a membrane area 10 000 times smaller) was shown to have

1268

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Table 3. Vrentas-Duda Model Parameters parameter (cm2/s)

D0 E (cal/mol) Vs (cm3/g) K1s/γs (cm3/gK) K2s - Tgs (K) Vpj (cm3/g) Tgp (K) fpg Vp(Tgp) (cm3/g) Rp (K-1) Rcp (K-1) γp χsp a

propene 27.8 -0.24 0.90 7.04 × 10-4 -5.14 -

propane 2.438 -0.24 0.90 7.04 × 10-4 -5.14 -

membrane

Flory-Huggins

reference

0.5

Shimazu et al.10 Reis43 Reis43 Reis43 Reis43 Reis43 Shimazu et al.10 Reis43 Reis43 Reis43 Reis43 Reis43 Allcock and Lampe44

-a 0.755 679 0.026 0.86 2.87 × 10-4 3.23 × 10-4 1 -

“-” means not pertinent.

practically the same effect as purifying the whole recycle stream, in terms of increase of the effective reactor feed propene concentration. Although it may be said that it is a modest increase, it is certainly high enough to increase the productivity of the process, not to mention the recovery of more than 350 kg/h propene, resulting in an savings of 3000 tons of propene per year, totaling approximately $1.5 million per year per polymerization plant. This is a quite attractive result. Supposing the installation cost of a membrane separation module about U.S.$800.00 per square meter of membrane,42 the 3000 m2 of membrane calculated in the above case would result in a total cost of $2.4 million. Therefore, the installation investment of the module would be recovered in approximately 1 1/2 years, considering only the savings in propene. 5. Conclusions A comprehensive analysis of the membrane-based separation of propene/propane mixtures has been presented. The analysis has been applied to an industrial-scale propene polymerization process. As presented, the separation using membranes may be economically valuable for the plant site, because it may allow the partial and significant recovery of propene that would be purged from the system. The membrane system may increase up to 5% the propene concentration in the reactor feed stream, therefore improving reaction rates, conversion, and, ultimately, productivity. It has been shown that the inclusion of a membrane separation stage may generate a savings of more U.S.$ 1.5 million per polymerization plant per year in propene recovered. Besides, a simplified payoff calculation has shown that the membrane system implementation investment is returned in approximately 1 1/2 years. It has been shown that there is a compromise between the membrane area and feed flow rate to be applied in the system. Average residence time analysis has shown that larger membrane areas with larger feed flow rates result in relatively poorer separation efficiencies. A recommendation is the utilization of small membrane areas and feed flow rates. Furthermore, stagecut values are significantly higher when one operates the membrane module system with lower feed flow rates, which also leads to improvement in the propene recovery. In the comparative analysis among the polymeric membranes tested to carry out the propene/propane separation, it has been shown that good selectivities usually lead to small permeate flow rates very rich in propene. Good permeabilities usually lead to large permeate flow rates with modest propene concentration. A compromise scenario is, however, possible, when one utilizes membranes with moderate permeabilities but relatively good selectivities, such as 6FDA-TMPPD based membranes.

Finally, it has been shown here that propene recovery in a polymerization plant using a simple membrane system is a quite feasible operation, even when current available technology is considered, and that installation costs can be paid off in relatively short times. Acknowledgment The authors would like to thank CNPQ-Brazil (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico) for supporting this research and providing scholarships. Appendix The mutual diffusion coefficient, calculated by the VrentasDuda model, is presented below

( ) [

DiM ) Di0 exp -

]

Ei γ(wiVi + wpjξVpj) exp φi2(1 RT VFH 2χipφi) (16)

where Di0 is a constant with the same dimension as DiM; Ei is the effective energy per mole that a molecule needs to overcome attractive forces; R is the universal gas constant; T is the temperature; γ is a superposition coefficient; wi and wpj are the mass fractions of the component i and the jump unit of the polymer, respectively; Vi and Vpj are the critical volumes; ξ is a ratio among the volumes; φi is the volumetric fraction of the component i; χip is the Flory-Huggins coefficient. VFH is the free hole volume described by

K1s VFHp(T) VFH (K + T - Tgs) + wp ) ws γ γs 2s γp VFHp(T) ) Vp(Tgp)[fpg -

∫TT

(17)

(Rp - Rcp) dT]

gp

where Vp(Tgp) is the membrane-specific volume at the glass transition temperature; Tgp is the glass transition temperature; fpg is the fraction of the free volume of the polymer at Tgp; Rp and Rcp are the thermal expansion coefficients of the polymer and the solvent-polymer mixture, respectively. Table 3 presents the Vrentas-Duda model parameters used in this work. The data of Reis43 refer to the poly(vinyl acetate)-toluene system operated at 30 °C, and are adopted here due to lack of data concerning the (6FDA-TMPPD)-propene-propane system. The data of Shimazu et al.10 refer to the (6FDATMPPD)-propene-propane system. The value for χsp was used as suggested by Allcock and Lampe.44 The mathematical model regarding the permeation of the gas mixture through the membrane, given by eqs 12-17, was

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discretized according to the method of lines in the space variable to generate a system of algebraic-differential equations in time. The space derivatives were discretized using the orthogonal collocation method.45 A numerical analysis performed at different process operation conditions showed that nine internal collocation points guarantee the convergence of the discretization method. Literature Cited (1) Mattos Neto, A. G.; Pinto, J. C. Steady-state modeling of slurry and bulk propene polymerizations. Chem. Eng. Sci. 2001, 56, 4043. (2) Zacca, J. J. Distributed parameter modelling of the polymerization of olefins in chemical reactors. Ph.D. Dissertation, University of Wisconsin, Madison, WI, 1995. (3) Baker, R. W.; Da Costa, A. R.; Daniels, R.; Pinnau, I.; He, Z. Membrane-augmented polypropylene manufacturing. U.S. Patent 6,271,319 B1, 2001. (4) Tanaka, K.; Taguchi, A.; Hao, J.; Kita, H.; Okamoto, K. Permeation and separation properties of polyimide membranes to olefins and paraffins. J. Membr. Sci. 1996, 121, 197. (5) Staudt-Bickel, C.; Koros, W. J. Olefin/paraffin gas separations with 6FDA-based polyimide membranes. J. Membr. Sci. 2000, 170, 205. (6) Chan, S. S.; Wang, R.; Chung, T.-S.; Liu, Y. C2 and C3 hydrocarbon separations in poly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluoropropane) diimide (6FDA-1,5-NDA) dense membrane. J. Membr. Sci. 2002, 210, 55. (7) Da Costa, A. R.; Daniels, R.; He, Z.; Morisato, A.; Pinnau, I. Membrane process for the recovery of propene from chemical industry waste streams. Presented at the 6th World Congress of Chemical Engineering, Melbourne, 2001. (8) Hess, S.; Scharfenberger, G.; Staudt-Bickel, C.; Lichtenthaler, R. N. Propene/propane separation with copolyimides containing benzo-15crown-5-ether to incorporate silver ions. Desalination 2002, 145, 359. (9) Sridhar, S.; Khan, A. A. Simulation studies for the separation of propene and propane by ethylcellulose membrane. J. Membr. Sci. 1999, 159, 209. (10) Shimazu, A.; Miyazaky, T.; Maeda, M.; Ikeda, K. Relationships between the chemical structures and the solubility, diffusivity, and permselectivity of propene and propane in 6FDA-based polyimides. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 2525. (11) Krol, J. J.; Boerrigter, M.; Koops, G. H. Polyimide hollow fiber gas separation membranes: preparation and the suppression of plasticization in propane/propylene environments. J. Membr. Sci. 2001, 184, 275. (12) Burns, R. L.; Koros, W. J. Defining the challenges for C3H6/C3H8 separation using polymeric membranes. J. Membr. Sci. 2003, 211, 299. (13) Lin, H.; Freeman, B. D. Gas solubility, diffusivity and permeability in poly(ethylene oxide). J. Membr. Sci. 2004, 239, 105. (14) Duarte, L. T.; Habert, A. C.; Borges, C. P. Preparation and morphological characterization of polyurethane/polyethersulfone composite membranes. Desalination 2002, 145, 53. (15) Aris, R. Ends and beginnings in the mathematical-modeling of chemical-engineering systems. Chem. Eng. Sci. 1993, 48, 2507. (16) Elnashaie, S. S. E. H.; Alhabdan, F. M.; Elshishini, S. S. The vital role of mathematical-modeling in chemical-engineering education. Math. Comput. Model. 1993, 17, 3. (17) Levenspiel, O. Modeling in chemical engineering. Chem. Eng. Sci. 2002, 57, 4691. (18) Sargent, R. Process systems engineering: A retrospective view with questions for the future. Comput. Chem. Eng. 2005, 29, 1237. (19) Marriott, J. I.; Sørensen, E.; Bogle, I. D. L. Detailed mathematical modelling of membrane modules. Comput. Chem. Eng. 2001, 25, 693. (20) Qi, R. H.; Henson, M. A. Modeling of spiral-wound permeators for multicomponent gas separations. Ind. Eng. Chem. Res. 1997, 36, 2320. (21) Qi, R. H.; Henson, M. A. Optimal design of spiral-wound membrane networks for gas separations. J. Membr. Sci. 1998, 148, 71. (22) Kovvali, A. S.; Vemury, S.; Krovvidi, K. R.; Khan, A. A. Models and analyses of membrane gas permeators. J. Membr. Sci. 1992, 73, 1.

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ReceiVed for reView March 20, 2006 ReVised manuscript receiVed December 1, 2006 Accepted December 13, 2006 IE060333Q