Scholz 2013

Modeling Gas Permeation by Linking Nonideal EffectsMarco Scholz,* Thomas Harlacher, Thomas Melin, and Matthias Wessling

Chemical Process Engineering, RWTH Aachen University, Turmstrasse 46, 52064 Aachen, Germany

ABSTRACT: Conventional models for simulating gas-separation processes often neglect nonideal effects such as concentrationpolarization, the Joule-Thomson Effect, pressure losses, and real gas behavior. This study presents a comprehensive model whichaccounts for such nonideal effects and can be applied in commercial process simulations. A model of a hollow-fiber gaspermeation module was programmed in Aspen Custom Modeler. In general, pure gas measurements at a single feed pressurewere sufficient to predict the mixed gas behavior of the module. The influence of nonideal effects on the module efficiency wasinvestigated in two case studies addressing the separation of CO2/propane and CO2/methane gas mixtures. For the first case, thecurves of CO2 concentration versus module length were congruent for both ideal and realistic scenarios. The divergence of thecurves in the second case was attributed to the influence of cummulating nonideal effects. The simulations are in agreement withthe new data obtained for these gas mixtures measured at a commercial polyimide membrane module. The model predicts theexperimental gas permeation data, in particular, when nonideal effects are pronounced. Ultimately, this model can easily be usedin process simulation and enables optimization of large-scale gas separation systems.

INTRODUCTIONModels for process simulation are important for analyzing howsmall changes in gas processing efficiency translate to significantimprovements in cost-effectiveness. Exactly predicting theoperation of gas permeation modules requires the simulationof nonideal module behavior.Within the past decade, many studies have modeled gas

permeation processes. For example, Ohlrogge compiled andcompared various gas permeation modules.1 Most of thesecited models focus individually on particular nonideal effectssuch as concentration polarization, the Joule-Thomson Effect,real gas behavior, and pressure losses.The phenomenon of concentration polarization has been

extensively investigated by Mourgues and Sanchez.2 They notethat concentration polarization becomes significant when thegas permeation membrane has selectivities of 100 andpermeances of higher than 1000 GPU for the faster permeatingcomponent. Their model, however neglects real gas behaviorand assumes isothermal conditions. This model also cannot beused in flowsheeting software such as Aspen Plus to performmore complex process simulation.A few studies reported about Joule-Thomson cooling in gas

permeation.3 Rautenbach and Dahm4 investigated temperaturein gas permeation modules for separating CO2 and CH4. Cokeret al.5 programmed a model to analyze the Joule-Thomsoneffect also for CO2/CH4 separation but it cannot be applied inprocess simulators. Pressure losses on the shell side of the gaspermeation module are also not considered.Pressure losses along the flow channels of feed and permeate

are either modeled using the HagenPoiseuille type of differentialequation69 or using experimental data10 or are neglected.11 Whenpressure losses are taken into account, the pressure on the shellside of hollow fiber gas permeation modules is often assumed tobe constant.7

Often conventional gas permeation models assume ideal gasbehavior12,13 for each gas component to be separated. A fewstudies analyze the influence of real gas behavior on module

performance.1416 However, the latter focus on modelingenvelope type gas permeation modules.As shown above, conventional gas permeation models are either

unsuitable for process simulation or often do not account fornonideal effects as a whole. Thus, this current study presents a newmodel which addresses these problems: it can be used in processsimulation and it considers all of the aforementioned nonidealeffects together. The applied equations for a hollow-fibergas permeation module have been programmed using AspenCustom Modeler (ACM). Up to now only a temperaturedependent permeance was implemented. The pressure andcomposition dependence of permeance can easily be included byproviding a polynominal interpolation of mixed gas data.Using this comprehensive model, we quantify in two studies

how the accumulation of nonideal effects influence thesimulation results for the module performance. The simulationresults are verified by mixed gas membrane separation data andby literature data published by Pan.17

METHODSMathematical Description of Fundamental Equa-

tions. The Presented Model. The model of a hollow-fibermembrane module was programmed in Aspen CustomModeler (version 2006.5) which is part of the Aspen Techsimulation engine. Designed to simulate steady-state, thismodel can simulate multicomponent mixtures and can beextended to a dynamic simulation model. The modelparameters include geometric as well as material propertiessummarized in Table 1. Module properties such as the pure gaspermeances, the activation energy for the temperature dependent

Special Issue: Baker Festschrift

Received: November 21, 2011Revised: March 22, 2012Accepted: March 22, 2012

Article

pubs.acs.org/IECR

XXXX American Chemical Society A dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXX

permeance, and the heat transfer coefficient have to beobtained from experimental analysis.

Material Balance. The ACM model is based on ordinarymaterial balances for each gas component. Both countercurrentflow as well as cocurrent flow conditions can be modeled withthe presented model. Since countercurrent flow is oftenadvantegous over cocurrent flow,18 this whole study dealswith countercurrent operation (Figure 1). The differential molebalances for the retentate and the permeate are

+ =nx

n Wdd

0R(1)

+ =nx

n Wdd

0P(2)

where nR and nP refer to the molar flow rate on the retentateside and the molar flow rate on the permeate side, respectively.The flux of through the membrane is designated by n. InFigure 2W delineates the width of the module that is quantifiedas

= W dnof (3)Where the term nof and d designate the number of hollowfibers and the outer fiber diameter, respectively. The materialtransfer through the membrane n is modeled by applying thesolution diffusion model and by assuming (i) pressure-independed permeances, (ii) no coupling of the permeatingspecies, and (iii) equal chemical potentials between gas andmembrane phase.Accordingly, the flux of component j is

= n Q x p y p( )j j j jF P (4)The empirical determined permeance Qj and the partialpressure difference specify the mass transfer of the component

j through the membrane. Here, xj and yj delineate the molefraction of the gas components on the retentate side and on thepermeate side, respectively, whereby pF is the feed pressure andpP is the pressure of the permeate side.

Energy Balance. As thermodynamic effects may accompanygas permeation processes,19 it is essential to include the energybalance describing the temperature along the membranemodule. The countercurrent energy balance for the retentateside and for the permeate side are

Here, HR and HP delineate the enthalpy of the gas on theretentate side and the enthalpy of the gas on the permeate side,respectively. The temperatures on the feed side and on thepermeate side are TR and TP, respectively. The molar enthalpyof the flow permeating through the membrane is hmem.Both eq 5 and eq 6 are based on three different phenomena:

the change in enthalpy along the hollow fiber, the heat transferthrough the membrane due to temperature difference on bothsides of the membrane, and the enthalpy transferred bypermeation.The transferred heat depends on the heat transfer coefficient

k of the membrane material (mainly the porous support layer)which has to be determined experimentally or is available inliterature. As Figure 3 illustrates, the temperature and pressureto determine the molar enthalpy of the permeating stream areassumed to be equal to the temperature and pressure on thefeed side.5

Mathematical Description of Nonideal Effects. Byoperating gas permeation membrane modules, various nonidealeffects may be observed. In this current study, the followingnonideal effects are considered: (1) real gas behavior, inparticular, upon applying pressures greater than 10 bar;1 (2)pressure losses on the bore side and shell side of the module;20

(3) the Joule-Thomson effect if significant amounts of CO2permeate through the membrane;5 (4) concentration polar-ization in case of high permeable membranes.Depending on the separation process, these effects have to

be taken into account to accurately describe the moduleperformance. The real gas behavior depends on the gas

Table 1. Model Parameters for the Simulation of a HollowFiber Membrane Module

model parameters

outer fiber diameterporous support thicknessfiber lengthfiber packing densityheat transfer coefficientnumber of fiberspermeance of each componentactivation energy of each component

Figure 2. Material balance for the retentate side and the permeate sideof the gas permeation module.

Figure 1. The membrane module is divided into 100 elements. Themass and energy balances are calculated for each element.

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXB

components involved and reduces the driving force by decreasingthe partial pressure of that component. Generally, the real gasbehavior adversely affects separation performance, because thedriving force of permeation is reduced for the various gascomponents. Hence, larger membrane areas are required forseparation. Pressure losses on both sides of the membrane alsoreduce the driving force of permeation. Moreover, significanttemperature changes of the gas are caused by the Joule-Thomsoneffect. By reducing the gas temperature, the membrane selectivityincreases, whereas the permeances decreases. Concentrationpolarization negatively influences the separation performanceand may limit module performance.

Real Gas Behavior. Real gas behavior is incorporated in themodel by calculating the fugacity coefficients. Accordingly, themass transfer is assigned as

= n Q x p y p( )j j j j j j,R F ,P P (7)Where j,R and j,P delineates the fugacity coefficient of eachgas component on the retentate side and on the permeate side,respectively.Real gas behavior considers interactions of the gas molecules.

It can be determined by calculating the fugacity coefficientswhich are determined by an ACM procedure. With the use ofthe procedures in ACM an equation of state or an activitymodel must be specified. For permanent gases the SoaveRedlichKwong equation of state is applied.1 Figure 4 shows

the fugacity coefficients of methane, CO2, and propane. It canbe seen that CO2 and propane distinctly exhibit real gas

behavior whereas methane shows ideal gas behavior. At higherpressures the fugacity coefficients decrease strongly.

Pressure Losses. Pressure losses on both sides of themembrane can significantly reduce the driving force. The pressurelosses are calculated by assuming laminar flow in the bore of the fiberand on the shell side of the module.20,21 The pressure losses arecalculated by

= p

x dv

d

d 2b

id

2(8)

= p

x dv

d

d 2s

hyd

2

(9)

The terms pb and ps represent the pressure of the bore side andthe shell side, respectively. The terms did and dhyd delineate theinner fiber diameter and the hydraulic diameter of the shellside, respectively. The gas velocity is designated by v, and refers to the gas density.By assuming laminar flow on both sides of the membrane,

the friction factor can be calculated by

=Re64

(10)

Where Re is the Reynolds number. Here eq 10 is valid forReynolds numbers lower than 2300. Typical gas velocitiesrange from 0.01 to 0.38 m/s on the permeate side and 1.51.7 m/s on the retentate side. Thus, since the Reynolds numberis 220, the assumption of laminar flow is valid.

Joule-Thomson Effect. The permeation of a gas through amembrane can be compared to an isenthalpic decompressionwhich is accompanied by a change in temperature from the feedto the permeate side and is characterized by

=h x T p h y T p( , , ) ( , , )R R R F P P P P (11)Here hR and hP delineate the molar enthalpy on the retentateside and on the permeate side, respectively. Table 2 depicts the

Joule-Thomson coefficients for various gases. In particular,since CO2 has a high Joule-Thomson coefficient, applicationsinvolving CO2 at high feed pressures are prone to largetemperature changes in the module.The permeance and the selectivity of the membrane material

are dependent on temperature19 and the Joule-Thomson effectmay change the temperature in the gas permeation module.Permeance as a function of temperature is described by usingthe following Arrhenius type equation.21,23,24

=

Q T Q

ET T

( ) exp1 1

j j009 (12)

Figure 3. Illustration of the Joule-Thomson Effect by gas permeationthrough a membrane.

Figure 4. The fugacity coefficients of methane, CO2, and propane as afunction of temperature at a pressure of 10 and 50 bar.

Table 2. Joule-Thomson Coefficients at 30 C and 10 bar22

constituent J-T coefficient [K/(bar)]

H2 0.03N2 0.20O2 0.26CH4 0.42CO2 1.05C3H6 1.95C3H8 2.03


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXC

Where E is the activation energy and 9 is the molar gasconstant. The reference permeance Qj0 is determined at thereference temperature T0. With regard to glassy polymermembranes, it is a well-known fact that higher temperatureslead to reduced selectivities and increased permeabilities.Reduced temperatures may also cause condensation of

condensable gas components. Condensation have to be avoidedsince acidic gases might dissolve in the condensate and couldattack the membrane material. Furthermore, a liquid film ordroplets on the membrane surface would induce an additionalmass transfer resistance, thereby reducing the flux through themembrane.A physical property database in ACM can be used to monitor

phase changes in the membrane module. The dew pointtemperatures as well as the gas temperatures are determinedthis way.

Concentration Polarization. Concentration polarizationmay significantly reduce module performance by increasingthe flow through the membrane of the retained componentsand decreasing the respective flow of the preferentiallypermeating components. Figure 5 illustrates that concentration

polarization occurs in the boundary layers as well as in theporous support. Figure 5 also shows the variables presented inthe following equations. Concerning asymmetric membranes, itis assumed that the active membrane layer is located at theouter circumference of a hollow fiber. In addition it is assumedthat the feed enters the bore of the fiber. The bore side feedconfiguration is used to avoid maldistribution of the feed gas.Using outside-in operation, the gas flowing around the fiberswould suffer from preferential flow through less dense fiberpackings. Inside-out operation is preferred when the retentate isthe product gas and when high product purities are required. Inlow pressure applications (15 bar) the gas is fedon the shell side of the gas permation module due to themechanical stability of the hollow fibers.The governing equations to determine the concentrations at

the membrane surface are based on differential mass balances inthe boundary layers and in the porous support. These balancesare presented by Melin and Rautenbach.21 Within the boundarylayers, the diffusion coefficient and the boundary layer thicknesscan be replaced by the mass transfer coefficient k which isspecified by Sherwood correlations.21 The bulk concentration

xj,B and the concentration at the surface of the porous supportxj,P are linked by the following equation:

*

*=

x x

x xn

c kexp

j j

j j j

,B

,P tot (13)

where xj* and ctot delineate the local mole fraction of each gascomponent in the membrane and the total concentration of gasmolecules in the gas phase, respectively. The local mole fractionof a gas component in the membrane is determined by the ratioof the flux of the respective component through the membraneand the total flux of all gas components through the membrane.

* =

=x

n

nj

jj n

j1 (14)

The mass transfer coefficient kj on the feed side is calculated bythe following Sherwood correlation:

= Sh Re Sc

dL

1.62feed feed feed1/3

(15)

The terms Refeed and Scfeed designate the Reynolds numberand the Schmidt number on the retentate side of the gaspermeation module. Here, d and L refer to the inner fiberdiameter and the length of the fiber, respectively.The permeating molecules passing through the feed side

boundary layer subsequently enter the pores of the poroussupport layer. Concentration polarization exists in the poroussupport, and the concentration profile of the various gascomponents within the porous support is determined by adifferential mass balance. Since the thickness of the poroussupport is known, there is no need to use a Sherwoodcorrelation for determining this. Equation 16 shows theconcentration on the membrane surface xj,M to be dependenton the concentration at the interface of the porous support xj,P

*

*=

x x

x xn M

Dexp

j j

j j j

,P

,M M (16)

where M is the molar weight, M is the support thickness, andthe terms and Dj delineate the porosity of the porous supportand the diffusion coefficient of component j, respectively. Thediffusion coefficients are available in the Aspen Propertiesdatabase. The diffusion coefficients are determined by theDawsonKhouryKobayashi model for pressures higher than1 atm. For pressures lower than 1 atm the ChapmanEnskogWilkeLee model is applied. Detailed information on thecorrelations to determine the diffusion coefficients can befound in the Aspen Properties help27 which uses the datapublished by Bird et al.28

Analogous to the calculation of the concentration polarization atthe feed side, the mass transfer through the membrane determinesthe concentration profile on the permeate side:

*

*=

y x

y xn

c kexp

j j

j j j

,M

,B tot (17)

Here, the terms yj,M and yj,B designate the permeate concentrationat the membrane surface and the bulk concentration on the

Figure 5. Concentration polarization considering bore side feed andthe active membrane layer on the outer fiber diameter.


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXD

permeate side, respectively. The mass transfer coefficient kj on thepermeate side is calculated by Sherwood correlation:

=

Sh Re Sc

d

L1.62per per per

hyd1/3

(18)

Whereby, Reper and Scper delineate the Reynolds number and theSchmidt number on the permeate side. Concerning the shell sideof the hollow fiber gas permeation module a hydraulic diameterdhyd is determined. Since the boundary layer thickness is muchsmaller than the outer fiber diameter, it is reasonable to use thebalances for flat sheet membranes.Equations [eq 13, eq 16, and eq 17] indicate that

concentration polarization depends on the flux through themembrane. The higher the flux is the more pronounced theinfluence of concentration polarization is. In the following wepresent membranes with low flux levels but high selectivity asdescribed in Visser et al.29

Additional Relevant Nonideal Effects. Multicomponentmass transport in glassy polymer membranes is often affectedby three phenomena:3032 (a) competitive sorption at low feedpressures and a resulting mutually affected transport of thegases, (b) penetrant induced plasticization at high feedpressures, and (c) frame of reference effects. These threeeffects are not considered in this study. Chern et al.33 haveevaluated the influence of feed pressure and composition-dependent permeance by applying the dual-sorption model.They compared the dual-sorption model to constantpermeance data and found a roughly 514% change in mostof the process variables. However, an appropriate mass transfermodel to include the pressure and composition dependence ofthe permeance can easily be incorporated in the presentedmodel by using a polynominal interpolation of mixed gaspermeation data.Al-Juaied and Koros32 present a model which takes the frame

of reference into account. They report that the diffusion of thegas molecules through the membrane is accompanied by aconvective flow of gas molecules which is referred to as bulkflux. The influence of the bulk flux is pronounced when thesorption of gas molecules in the polymer is significant (highpressure). As a result of the nonselective bulk flux the selectivityof the membrane is reduced at elevated pressures. Themathematical description of the frame of reference effects canaccount for the pressure dependence of the selectivity in theseparation of CO2 and CH4

32 as well as in the separation ofC3H6 and C3H8.

34 Mathematically, the bulk flux contributioncan be accommodated as well in the equation describing themembrane transport. In this current study it is of no relevancesince the membrane swelling is low.Additionally, minor components like water or higher

hydrocarbons may effect membrane properties and in particularthe permeances.35 However, the selectivity is only influencedwhen the reduction of permeance is different for the variousgases. Gales et al.36 have reported on the effect of volatileorganic compounds (VOCs) on the separation of air and VOCsusing PDMS membranes. They conclude that their simplemodel is able to predict the separation well, although themembrane material swells at elevated feed pressures andapplying increased VOC concentrations. Al-Juaied and Koros37

have reported on the impact of heavy hydrocarbons (in ppmrange) on the permeance of CO2 and CH4 in hollow fiberpolyimide membranes. They found that permeances significantly

increases when toluene is exposed to the membrane at lowtemperatures only.A fourth nonideal effect may be pressure losses at the entry

and the exit ports of the module. Such effect need to beaccounted for by measuring the friction factor belonging tospecific module geometry. They can easily be included in thepresented model by adding pressure loss correlations to theoverall module related pressure loss.Application of the Model in Process Simulation. The

Aspen Custom Modeler model can easily be integrated into theprocess simulator Aspen Plus. The parameters of the model canbe selected individually to cover the various nonideal effects.The user should carefully select an appropriate set of equationswhich characterizes the separation task to be investigated.Membrane Module. he permeances applied in this simula-

tion study were obtained from pure gas measurements. Todetermine the pure gas permeances, the gas permeation modulewas operated in dead end mode by closing the retentate valve.Both, the pressure on the feed side and the pressure on thepermeate side as well as the permeate flow rate were measured.Hence, the permeance is the ratio of the flow rate and the productof transmembrane pressure difference and membrane area.Furthermore, experimental mixed gas data was obtained with

an industrial hollow fiber polyimide gas permeation module(UBE Industries, Ltd.). Used here was a gas permeation testfacility allowing the simulatenous mixing and analysis of sevendifferent gases. The gas permeation module was placed in aheating cabinet to control the feed temperature and moduletemperature. Subsequently, the simulation data which uses puregas permeances was compared to the data of the mixed gasexperiments. Various feed flow rates were specified, and theflow rates as well as the mole fractions were measured. Adetailed description of the gas permeation test facility as well asinformation on the measurement procedure will be publishedelsewhere for the separation of carbon monoxide and argon.Table 3 summarizes the module properties. The fiber

diameters were measured microscopically and the number of

fibers were counted. The module diameter and the fiber lengthcould be measured.

RESULTS AND DISCUSSIONModel Validation. For the system CO2/propane we would

like to evaluate how the model data and experimental dataagree. CO2 permeates selectively over the membrane enrichingin the permeate. Table 4 shows the parameters applied in thismodel validation.

Table 3. Membrane Module Properties

model parameters unit value

outer fiber diameter m 415porous support thickness m 74fiber length m 0.2module diameter m 0.038number of fibers 3380

Table 4. Parameters Applied for Model Validation

variable value unit

feed pressure 3 barfeed temperature 50 Cfeed mole fraction propane 0.5


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXE

Figure 6 shows that the experimental results for the retentateflow rate vs feed flow agree well with the simulation curve for

the system CO2/propane. For the permeate, however, theexperimental data are different from the simulated ones. Thismaybe within the accuracy of measurement. Since flow rate ofthe permeate is low, the experimental data for permeate flowmay be inaccurate. A second reason may well be a strongpressure- and concentration-dependence of the permeance dueto the glassy nature of the polymer which is addressed in theparagraph on additional nonideal effects.Figure 7 depicts the propane mole fraction in the retentate

and the CO2 mole fraction in the permeate for both simulation

as well as experimental data. It can be seen that in both casesthe simulations agree very well with the empirical data.To demonstrate the applicability of the model for

applications in which high pressures (>35 bar) as well asmultiple components are to be separated, the model wascompared to experimental data published by Pan.17 Figure 8

shows the permeate mole fraction of CO2, CH4, C2H6, andC8H8 as a function of stage cut. Regarding the model data aswell as the experimental data, the model predicts theexperimental data well.Case Studies to Evaluate Model Performance. To

investigate the effect of nonideal module operation, two casestudies were performed analyzing the separation of propaneand CO2 and the separation of methane and CO2. Both studiescompare ideal and real module conditions. In the latter case, allaforementioned nonideal effects were taken into account. Toanalyze the influence of the nonideal effects individually, theideal module operation was simulated respectively with eachsingle nonideal effect. Both systems, the separation of propaneand CO2 as well as the separation of methane and CO2, areselected such that Joule-Thomson cooling and real gas behaviorare pronounced.

Case Study on the Separation of Propane and CO2. Table 5summarizes the parameters applied in the simulation of the

separation of CO2 and propane, which were obtained from puregas measurements. The heat transfer coefficient and the ratiosof the activation energy and the universal gas constant E/9were estimated based on data provided by Melin andRautenbach.21 Moreover, Table 3 shows the module propertiesfor the polyimide gas permeation module.

Figure 6. Separation of CO2/propane. The retentate and permeateflow are presented as a function of the feed flow rate. The curvespresent the simulation results. The symbols represent the empiricaldata points. The temperature is 50 C, the feed side pressure is 3 bar,the permeate side pressure is 1 bar, the CO2 permeance is 203 GPUand the C3H8 permeance is 0.23, respectively.

Figure 7. Separation of CO2/propane. The retentate mole fraction ofpropane and permeate CO2 mole fractions are shown as a function offeed flow. The curves illustrate the simulation results and the symbolsrepresent the empirical data points. The temperature is 50 C, the feedside pressure is 3 bar, the permeate side pressure is 1 bar, the CO2permeance is 203 GPU, and the C3H8 permeance is 0.23, respectively.

Figure 8. Comparing the model to experimental data reported byPan.17 The lines represent the simulation results obtain by thepresented model. The dots indicate the experimental data by Pan.Feed temperature is 10 C, the feed pressure is 35.28 bar, thepermeate pressure is 0.928 bar, and the feed composition is 0.485CO2, 0.279 CH4, 0.1626 C2H6, and 0.0734 C3H8, respectively.Permeances (GPU): 40.05 CO2, 1.11 CH4, 0.31 C2H6, and 0.06 C2H8.

Table 5. Parameters Applied for Simulation in theSeparation of CO2 and Propane Using a Polyimide HollowFiber Membrane Module

variable value unit

feed pressure 10 barfeed temperature 40 Cheat transfer coefficient 4 (W/(m2 K))feed mole fraction propane 0.5Permeance CO2 203 GPUPermeance C3H8 0.23 GPU

ECO29

1000 K

EC H3 89 2000 K


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXF

Figure 9 shows the retentate CO2 mole fraction for idealmodule operation and for the real module operation where the

considered nonideal effects are accumulated. The latter case isreferred to as accumulated effects. Since the difference betweenthe individual nonideal effects and ideal module operation isnot pronounced, all the effects (i.e., concentration polarization,the Joule-Thomson Effect, pressure losses and real gasbehavior) are considered as a whole. Here, the curves depictingthe Joule-Thomson effect and real gas behavior are congruentwith the curve showing the accumulated effects. Analogously,the curves for concentration polarization and pressure lossesare congruent with the curve for ideal operation.Figure 10 presents the permeate CO2 mole fraction for ideal

module operation and the accumulated effects module

operation. Compared to Figure 9 the difference between bothoperation conditions is more pronounced. However, the CO2mole fraction at the permeate outlet is almost equal for bothideal module operation and the accumulated effects moduleoperation. Thus, here the difference between both operationconditions is insignificant. Consequently, in this case the simplemodel assuming ideal gas behavior and neglecting nonidealeffects may be applied in process simulation. However, anappropriate mass transfer equation is required in order to

describe the influence of feed pressure, feed temperature, andgas composition on the permeance.Figure 11 shows the temperature distribution as well as the

dew point temperature for the retentate side of the hollow fiber

gas permeation module. Since the dew point temperature onthe permeate side is less than 87 C and condensation of therespective gases is not expected, the dew point temperature curvesare not shown in Figure 11. Propane and CO2 have a distinct JouleThomson coefficient; hence, the feed gas cools down along thelength of the module. However, the gas temperatures are notlower than the dew point and condensation does not occur, evenat feed pressures as high as 14 bar.

Case Study on the Separation of Methane and CO2. Theseparation of CO2 and CH4 was investigated by analyzingwhether nonideal effects influence the mole fraction of CO2 onthe retentate and the permeate side. Table 6 summarizes the

simulation parameters. The heat transfer coefficient and theratios of the activation energy and the universal gas constantE/9 were assumed based on published experimental data.21Table 3 presents the properties of a polyimide gas permeationmodule applied in the simulation.Figure 12 presents the CO2 mole fraction on the retentate

side of the gas permeation module as a function of modulelength. Here, the nonideal effects are more marked, whereasthe effect of pressure loss and concentration polarization are

Figure 9. Separation of CO2/propane: ideal and real mole fraction ofCO2 on the retentate side of the gas permeation module as a functionof module length.

Figure 10. Separation of CO2/propane: ideal and real mole fraction ofCO2 on the permeate side of the gas permeation module as a functionof module length.

Figure 11. Separation of CO2/propane: gas temperature for theretentate and the permeate side as well as the dew point temperatureon the retentate side at a feed pressure of 14 bar and a feed pressure of10 bar as a function of module length.

Table 6. Parameters Applied for Simulating the Separationof CO2 and CH4 Using a Polyimide Hollow Fiber MembraneModule

variable value unit

feed pressure 10 barfeed temperature 40 Cheat transfer coefficient 4 (W/(m2 K))feed mole fraction methane 0.5permeance CO2 203 GPUpermeance CH4 10 GPU

ECO29 1000 K

ECH49 2000 K


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXG

negligible as the respective curves are congruent with the curvefor ideal operation. It can be seen that the real gas behavior hasthe strongest impact on the separation performance. The JouleThomson cooling also has an impact on the CO2 mole fractionbut it is less pronounced.Figure 13 illustrates the CO2 mole fraction on the permeate

side of the gas permeation module as a function of module

length. The impact of concentration polarization and pressurelosses can be neglected here. Compared to Figure 12 thedifference between ideal module operation and the accumu-lated effects module operation is more pronounced. The mostimportant contribution to nonideal module operation is observedfor the Joule-Thomson effect and for the real gas behavior. Asthe various nonideal effects are interdependent, the curves for theindividual effects cannot be summed up to obtain the curve inwhich all the aforementioned effects are taken into account(accumulated effects case). Hence, the superposition principlecannot be applied.Pressure-Dependent Permeance. In general the feed

pressure and in particular the partial pressure of CO2 influencesthe permeation of the gas molecules through the membranematerial38 and hence a pressure-dependent permeance is

analyzed separately in this paragraph. Here, the separation ofCO2 and C3H8 is considered. Figure 14 depicts the permeance

of CO2 and C3H8 as a function of feed pressure. The characteri-stics of the permeance are based on theoretical consideration.At low pressure competitive sorption will reduce permeance,whereas at high pressures plasticization becomes significantresulting in an increased permeance. It is assumed that due tocompetitive sorption the permeance reduces by 20% at apressure of 12 bar compared to the permeances at a pressureof 1 bar. Furthermore, it is assumend, that the permeancesincrease by 20% at a feed pressure of 30 bar. Hence, thepermeance can be described by a second order polynomial.38 Inaddition, the selectivity is assumed to be constant. However,this assumption is rather unrealistic.38 It is essential to includean adequate description of the pressure-dependent permeationequation in order to account for the pressure and thetemperature influence as well as the impact of the permeatingcomponents.To compare the different feed pressure levels the pressure

ratio across the membrane is kept constant at 10. Two differentcases were considered in which one assumes constantpermeances and one calculates the module performance witha pressure-dependent permeance.Figure 15 shows the CO2 mole fraction in the retentate as

a function of module length for feed pressures of 10, 30, and50 bar. At low feed pressure the difference between constantand pressure-dependent simulations is less pronounced. Atpressures of more the 30 bar the differences between the case inwhich constant permeances are assumed and the pressure-dependent case becomes significant.In Figure 16 the CO2 mole fraction in the permeate is

illustrated as a function of module length for feed pressures of10, 30, and 50 bar. For pressures of more than 30 bar thedifference between both cases is pronounced.According to the simulation results an appropriate description

of the mass transfer through the membrane is essential. Thisrequires a detailed experimental investigation to determine themixed gas permeances at elevated pressures. However, complexmass transfer equations can easily be incorporated in the existingmodel.Compared to the aforementioned nonideal effects (Joule-

Thomson Effect, concentration polarization, pressure losses,real gas behavior) the temperature- and pressure-dependence ofthe permeance may even have a more pronounced effect on

Figure 12. Mole fraction of CO2 on the retentate side as a function ofmodule length. The distribution of CO2 is presented for the variousnonideal effects as well as for the ideal module operation and theaccumulated effects module operation, separating CO2 and CH4.

Figure 13. Mole fraction of CO2 on the permeate side as a function ofmodule length. The distribution of CO2 is presented for the variousnonideal effects as well as for the ideal module operation and theaccumulated effects module operation, separating CO2 and CH4.

Figure 14. Permeances of CO2 and C3H8 as a function of feedpressure. The selectivity is assumed to be constant.


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXH

module performance. Hence, the interaction between nonidealeffects related to the permeation through the membranematerial as well as nonideal effects related to module operationneed to be considered for an adequate description of moduleperformance.

CONCLUSIONSThe presented model of a hollow fiber gas permeation moduleprogrammed in Aspen Custom Modeler predicts experimentaldata under nonideal conditions.Whereas conventional gas permeation models generally focus

on individual nonideal effects, our model links as a wholeconcentration polarization, the Joule-Thomson Effect, pressurelosses, and real gas behavior.In particular, the separation of CH4 and CO2 exhibits

nonideal behavior (a) through the Joule-Thomson coolingalong the length of the module and (b) through real gasbehavior. Thus, these effects have to be taken into account for alarge-scale process design where multiple membrane stages are

integrated or different unit operations are combined in hybridprocesses. As the case studies on separating CH4/CO2 andC3H8/CO2 demonstrate, it is important that the processdesigner chooses the appropriate set of equations for nonidealeffects as well as their respective parameters that depend on theseparation task at hand.We anticipate the effect of the complex permeation

properties in glassy polymers at very low as well as at highfeed pressure to be significant. This analysis will be addressed ina separate publication.Ultimately, the presented model represents more realisticly gas

permeation behavior in large-scale hollow fiber modules andpotential for future application in gas separation, in particular, forflue gas treatment, biogas upgrading, and natural gas purification.

AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

ACKNOWLEDGMENTSThis work was supported partially by the Alexander vonHumboldt Foundation. We are grateful to Dr. TorstenBrinkmann (Helmholtz-Zentrum Geesthacht) for his helpfulinsights about modeling in Aspen Custom Modeler and toMary-Joan Blumich for editing the manuscript.

REFERENCES(1) Krause, B.; Gohl, H.; F., W.; Ohlrogge, K.; Ebert, K. Membranen;Wiley-VCH: Weinheim, Germany, 2006.(2) Mourgues, A.; Sanchez, J. Theoretical analysis of concentrationpolarization in membrane modules for gas separation with feed insidethe hollow-fibers. J. Membr. Sci. 2005, 252, 133144.(3) Gorissen, H. Temperature changes involved in membrane gasseparations. Chem. Eng. Process. 1987, 22, 6367.(4) Rautenbach, R.; Dahm, W. Gas permeationmodule design andarrangement. Chem. Eng. Process. 1987, 21, 141150.(5) Coker, D.; Allen, T.; Freeman, B.; Fleming, G. Nonisothermalmodel for gas separation hollow-fiber membranes. AIChE J. 1999, 45,14511468.(6) Tessendorf, S.; Gani, R.; Michelsen, M. Modeling, simulation andoptimization of membranebased gas separation systems. Chem. Eng.Sci. 1999, 54, 943955.(7) Kaldis, S.; Kapantaidakis, G.; Papadopoulos, T.; Sakellaropoulos,G. Simulation of binary gas separation in hollow fiber asymmetricmembranes by orthogonal collocation. J. Membr. Sci. 1998, 142, 4359.(8) Thundyil, M.; Koros, W. Mathematical modeling of gasseparation permeatorsfor radial crossflow, countercurrent, andcocurrent hollow fiber membrane modules. J. Membr. Sci. 1997, 125,275291.(9) Murad Chowdhury, M.; Feng, X.; Douglas, P.; Croiset, E. A newnumerical approach for a detailed multicomponent gas separationmembrane model and AspenPlus simulation. Chem. Eng. Technol.2005, 28,.(10) Marriott, J.; Srensen, E. A general approach to modellingmembrane modules. Chem. Eng. Sci. 2003, 58, 49754990.(11) Davis, R. Simple gas permeation and pervaporation membraneunit operation models for process simulators. Chem. Eng. Technol.2002, 25, 717722.(12) Rautenbach, R.; Knauf, R.; Struck, A.; Vier, J. Simulation anddesign of membrane plants with AspenPlus. Chem. Eng. Technol. 1996,19, 391397.

Figure 16. Mole fraction of CO2 in the permeate as a function ofmodule length. The solid lines represent the case in which constantpermeances are assumed. The dashed lines illustrate the case in whichpressure-dependent permeances are applied in the simulation. Thefeed pressure is varied between 10 and 50 bar, whereby the pressureratio across the membrane is fixed at 10.

Figure 15. Mole fraction of CO2 in the retentate as a function ofmodule length. The solid lines represent the case in which constantpermeances are assumed. The dashed lines illustrate the case in whichpressure-dependent permeances are applied in the simulation. Thefeed pressure is varied between 10 and 50 bar, whereby the pressureratio across the membrane is fixed at 10.


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXI

(13) Giglia, S.; Bikson, B.; Perrin, J.; Donatelli, A. Mathematical andexperimental analysis of gas separation by hollow fiber membranes.Ind. Eng. Chem. Res. 1991, 30, 12391248.(14) Ohlrogge, K.; Wind, J.; Scholles, C.; Brinkmann, T.Membranverfahren zur Abtrennung organischer Dampfe in derchemischen und petrochemischen Industrie. Chem. Ing. Tech. 2005,77, 527537.(15) Wang, R.; Liu, S.; Lin, T.; Chung, T. Characterization of hollowfiber membranes in a permeator using binary gas mixtures. Chem. Eng.Sci. 2002, 57, 967976.(16) Alpers, A.; Keil, B.; Ludtke, O.; Ohlrogge, K. Organic vaporseparation: Process design with regards to high-flux membranes andthe dependence on real gas behavior at high pressure applications. Ind.Eng. Chem. Res. 1999, 38, 37543760.(17) Pan, C. Gas separation by high-flux, asymmetric hollow-fibermembrane. AIChE J. 1986, 32, 20202027.(18) Scholz, M.; Wessling, M.; Balster, J. In Membrane Engineering forthe Treatment of Gases: Gas-Separation Problems with Membranes;Drioli, E., Barbieri, G., Eds.; Royal Society of Chemistry: London,2010.(19) Mulder, M. Basic Principles of Membrane Technology; KluwerAcademic: Dordrecht, The Netherlands, 1996.(20) Struck, A. Untersuchung und Optimierung von Hohlfasermodulenfu r die Stickstoffanreicherung durch Gaspermeation. Ph.D. Thesis,RWTH Aachen University, Germany, 1998.(21) Melin, T.; Rautenbach, R. Membranverfahren; Springer: Berlin,2004.(22) Linstrom, P.; Mallard, W. NIST Chemistry WebBook; NationalInstitute of Standards and Technology: Gaithersburg, MD, 1997.(23) Yampolskii, Y.; Pinnau, I.; Freeman, B. Materials Science ofMembranes for Gas and Vapor Separation, (Wiley Online Library);Wiley: West Sussex, England, 2006.(24) Koros, W.; Fleming, G. Membrane-based gas separation.J. Membr. Sci. 1993, 83, 180.(25) Rautenbach, R.; Struck, A.; Roks, M. A variation in fiberproperties affects the performance of defect-free hollow fibermembrane modules for air separation. J. Membr. Sci. 1998, 150, 3141.(26) Rautenbach, R.; Struck, A.; Melin, T.; Roks, M. Impact ofoperating pressure on the permeance of hollow fiber gas separationmembranes. J. Membr. Sci. 1998, 146, 217223.(27) Inc., A. T. Physical property methods and models manual. AspenEngineering Suite; Aspen Technology: Cambridge, MA, 2002; Vol. 10.2.(28) Bird, R.; Stewart, W.; Lightfoot, E. Transport Phenomena,2nd ed.; John Wiley and Sons: New York, 2002.(29) Visser, T.; Masetto, N.; Wessling, M. Materials dependence ofmixed gas plasticization behavior in asymmetric membranes. J. Membr.Sci. 2007, 306, 1628.(30) Visser, T.; Koops, G.; Wessling, M. On the subtle balancebetween competitive sorption and plasticization effects in asymmetrichollow fiber gas separation membranes. J. Membr. Sci. 2005, 252,265277.(31) Visser, T.; Wessling, M. Auto and mutual plasticization in singleand mixed gas C3 transport through Matrimid-based hollow fibermembranes. J. Membr. Sci. 2008, 312, 8496.(32) Al-Juaied, M.; Koros, W. Frame of reference effects on theperformance of hollow fiber membranes. Ind. Eng. Chem. Res. 2005, 44,36483654.(33) Chern, R.; Koros, W.; Fedkiw, P. Simulation of a hollow-fibergas separator: The effects of process and design variables. Ind. Eng.Chem. Process Des. Dev. 1985, 24, 10151022.(34) Das, M.; Koros, W. Performance of 6FDA6FpDA polyimidefor propylene/propane separations. J. Membr. Sci. 2010, 365, 399408.(35) Pourafshari Chenar, M.; Soltanieh, M.; Matsuura, T.; Tabe-Mohammadi, A.; Khulbe, K. The effect of water vapor on theperformance of commercial polyphenylene oxide and Cardo-typepolyimide hollowfiber membranes in CO2/CH4 separation applica-tions. J. Membr. Sci. 2006, 285, 265271.

(36) Gales, L.; Mendes, A.; Costa, C. Removal of acetone, ethylacetate, and ethanol vapors from air using a hollow fiber PDMSmembrane module. J. Membr. Sci. 2002, 197, 211222.(37) Al-Juaied, M.; Koros, W. Performance of natural gas membranesin the presence of heavy hydrocarbons. J. Membr. Sci. 2006, 274, 227243.(38) Bos, A.; Punt, I.; Wessling, M.; Strathmann, H. Plasticization-resistant glassy polyimidemembranes for CO2/CO4 separations. Sep.Purif. Technol. 1998, 14, 2739.


dx.doi.org/10.1021/ie202689m | Ind. Eng. Chem. Res. XXXX, XXX, XXXXXXJ

Documents

Scholz 2013