[2013 ahmad lau shariff] temperature pressure dependence membrane permeance process economics hollow...

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Temperature and pressure dependence of membrane permeance and itseffect on process economics of hollow ber gas separation systemFaizan Ahmad, K.K. Lau n , A.M. Shariff, Yin Fong YeongChemical Engineering Department, Universiti Teknologi PETRONAS, Bandar Sri Iskandar, Perak 31750, Malaysia

a r t i c l e i n f o

Article hi story:Received 20 September 2012

Received in revised form9 November 2012Accepted 25 November 2012Available online 7 December 2012

Keywords:Gas separationProcess simulationHollow ber membrane Joule thomson effectMembrane permeance

a b s t r a c t

Conventional hollow ber models in process simulators usually assume constant membrane permeancei.e., independent of pressure and temperature. In this work, hollow ber membrane model has beenproposed to cater the effects of temperature and pressure on membrane permeance. The proposed model isincorporated with Aspen HYSYS as a user dened unit operation in order to study the performance of gasseparation system. The simulated model is validated by experimental and published data. The temperaturedrop due to Joule Thomson effect and its contribution to the change in membrane permeance has also beeninvestigated. Similarly, the effect of pressure on membrane permeance has been studied. The inuence of these effects on the separation performance and process economics has been investigated for theseparation of CO 2 from natural gas. The proposed hollow ber membrane model has potential to beapplied for design, optimization and scale up of wide range of gas separation systems.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Membrane based gas separation is an important unit operation

in many industrial separations such as pharmaceutical, biotech-nology, petrochemical and gas processing [1,2]. Hollow bermembrane module is attracting wide range of applications dueto its convincing capabilities, e.g., high efciency/volume, lowerenergy requirement, chemical-free operation, etc [3] .

The modeling of hollow ber membrane separation has beenstudied by number of investigators since the development of rstmathematical model for membrane gas separation by Weller andSteiner [4] . Thorman et al. [5] incorporated the effect of pressuredrop in a study on the binary mixtures separations employingsilicone rubber capillaries. A model for practical representation of gas separation using high ux, asymmetric hollow ber mem-brane has been presented by Pan [6] .

A new approach has been presented and analyzed by Thundyil

and Koros [7] in order to solve the mass transfer problem posedby the permeation process in hollow ber membrane separator.Rautenbach et al. [8] studied a variation in ber properties thataffects the performance of defect free hollow ber membranemodules for air separation. Similarly, Lemanski and Lipscomb [9]presented a theoretical and experimental study of the effects of variable ber properties on countercurrent hollow ber gasseparation module performance.

Zhao et al. [10] developed a mathematical model to describe ahollow ber membrane separator for binary gases includingwater vapors under low feed gas pressure and vacuum. Moreover,

Jin et al. [11] studied the modeling and control of CO 2 separationprocess with hollow ber membrane modules.

Recently, Katoh et al. [3] proposed a new simulation model thatdeals with the dynamic simulation of hollow ber membraneseparation. The relaxation method is applied to solve the governingordinary differential equations for transport across the membrane,mass balance and pressure distributions in a hollow-ber mem-brane module. Khalilpour et al. [12] analyzed hollow ber separa-tion and proposed a general nite difference method coupled withGaussSeidel algorithm for the solution of the non-linear membranedifferential algebraic equations.

Model-based process design is a quantitative approach thatincludes developing or obtaining a detailed mathematical model forthe process and identifying the most important design variables

which affect the process [13] . Different commercial process simula-tors are available to evaluate the operating conditions and optimizethe design congurations [14] . Aspen HYSYS is one of the commonlyused process modelling and simulation software. It provides acomponent based framework that can easily be customized, updatedand maintained to meet changing user requirements [15] . A built inmodel for membrane separation system is not available in thestandard version of Aspen HYSYS but it can be implemented alongwith its solution procedure by using Visual Basic (VB) or C subroutine.

Many studies have been done to propose a exible mathematicalmodel in process simulator within the last decade. Rautenbach et al.[16] developed a simple cross ow membrane model in AspenPlus

Contents lists available at SciVerse ScienceDirect

journal homepage: ww w.elsevier.com/locate/memsci

Journal of Membrane Science

0376-7388/$- see front matter & 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.memsci.2012.11.070

n Corresponding author. Tel.: 605 3687589; fax: 605 3656176.E-mail addresses: [email protected] (F. Ahmad) ,

[email protected] (K.K. Lau) .

Journal of Membrane Science 430 (2013) 4455
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without consideration of pressure drop. Tessendorf et al. [17]implemented a membrane model for gas separations based onequation oriental approach in external process simulator OPTISM.Davis [18] also implemented a hollow bre membrane model inAspen HYSYS with the assumption of negligible pressure dropwithout external custom programming. Chowdhury et al. [14]presented a numerical solution approach to implement an existingmodel by Pan [6] in AspenPlus for co-current and counter current

membrane congurations. In addition, Hussain et al. [19] imple-mented a one-dimensional isothermal model in Aspen HYSYS forthe feasibility study of CO 2 capture ue gas by a facilitated transportmembrane. Peters at al. [20] performed simulation analysis withAspen HYSYS for amine absorption and membrane separation.Recently, we proposed a new method to implement a simple crossow model in Aspen HYSYS for CO 2 capture from natural gas [21] .

Based on the published literature [14 ,16 19 ,21 ], it can beconcluded that there is limited membrane model available forhollow ber membrane module in commercial simulator. All of the above proposed models do not deal with non ideal effectssuch as pressure and temperature dependence of membranepermeance.

An expansion of the residue gas at higher pressure in amembrane module to lower pressure gas in the permeate streamcan result in a change of temperature. The common example of this phenomenon is Joule Thomson (JT) cooling of the gas passingthrough adiabatic expansion valve [22] . Membrane permeance isdependent on temperature and pressure. Thus, pressure dropacross the membrane and temperature drop due to JT effect causechange in membrane permeance.

A few studies examined temperature change due to JouleThomson (JT) effect in membrane based gas separation. Rautenbachand Dahm [23] investigated temperature change in gas permeationmodules for separating CO 2 and CH 4 . Cornelisson [24] also con-tributed to study the heat effect on gas permeation. Coker et al. [22]proposed a model for the JouleThomson effect in CO 2 /CH4 separa-tion but it has not been applied in process simulators. Scholoz et al.[25] linked non ideal effects including JT effect in the gas permeationmodeling but has not presented the effect of variable permeance(due to change in temperature and pressure) on performance andeconomics of gas separation system.

In this paper, an experimentally validated hollow ber mem-brane model considering temperature and pressure dependence of membrane permeance would be implemented in Aspen HYSYS asuser dened unit operation using nite element method in VisualBasic (VB) sub routine. The paper demonstrates the case study of CO2 removal from natural gas by hollow ber membrane. Thecomparison of ideal model with constant permeance and non idealmodel with variable permeance (due to temperature and pressureeffects) would be made to evaluate the inuence of this non idealeffect on the separation efciency and process economics (gasprocessing cost) of membrane separation system.

2. Mathematical method

2.1. Mathematical model

The radial cross ow model (shell side feed) for hollow bermembrane module is schematically represented in Fig. 1. Thebundle of bers is sealed at one end using epoxy The other end of ber bundle is kept open to allow the ow of gases. The berbundle is housed in the middle of shell. Feed gas is introduced inthe system from the shell side that ows radially inward perpen-dicular to the bers toward the centre. The permeate into the

bers ows axially along to the permeate collector. As a result,

ow rates and compositions vary axially as well as radiallymaking it two dimensional model [7] .

The separation efciency of two components ( i, j) is a mea-sured by the ratio of their permability known as selectivity. It isgiven by

a ij P iP j

1

For a binary gas mixture, the local permeation rate at any pointin the stage over a differential membrane area, dAm is as follows

ydV P 1

d ph x pl y dAm 2

1 y dV P 2d ph 1 x pl 1 y dAm 3

Dividing Eq. (2) by Eq. (3) , we get

y1 y

a x pl= ph y1 x pl= ph 1 y 4

where P 1 and P 2 are the permeabilities of pure gas components(CO2 and CH 4 in this work), x and y are the feed and permeatecomposition at any point along the membrane, d is the membranethickness and a is the membrane selectivity [26] .

One of the approach used to solve this two dimensional modelis succession of states or nite element method. The mainadvantage of nite element method over solution of differentialequations is that it is easy to incorporate non ideal effects in theformer method such as permeate pressure drop in the ber andtube sheet, Joule Thomson (JT) effect, pressure and temperaturedependence of membrane permeability etc. The method dividesthe membrane area into a number of elements having constantdriving force and specied inlet conditions, computing the masstransfer and this obtaining the outlet conditions [7] .

Hollow ber membrane module is mainly characterized by[7,27 ,28 ]

(a) Dimensions of bers bundle (such as ber length, L and radiusof ber bundle, R)

(b) Inner and outer diameter of the bers, d i and do(c) Measure of packing density and porosity: The packing density

of hollow ber membrane module is dened as the

Tube sheet

PermeateEnd

Feed End

r

Ii=1

i=N

j=1 j=M

z

II

III

IV

I

II

III

IV

Retentate End

Sealed endsheet

Epoxy Tube Sheet (closed end)

Shell sideTube side (Fiber Bundle)

Epoxy Tube Sheet (Open end)

Permeate

Feed

Retentate

Fig. 1. Schematic diagram of Hollow ber membrane separation (shell-side feed).(a): Types of element in the tube side (ber bundle) of the module [7] .

F. Ahmad et al. / Journal of Membrane Science 430 (2013) 4455 45
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fraction of the cross section area of all bers over the crosssection area of the module.

n f A f Am

n f dodm

5

where n f is the number of bers, A f is the cross section area of bers and Am is the cross section area of module. Furthermore;number of bers/cross sectional area of ber ( N f ), porosity of ber

bundle ( e) and membrane area/bundle volume ( A/V ) are con-nected as follows.

N f 1p =4 do

2 6

AV 4 1 e do 7

The model will consider the specic bundle area, and divide itup into a predetermined number of elements (index i in theradial direction and index j in the axial direction). The niteelement is assumed to exist at radius r from the centre of thebundle having radius of Dr and length of D z. The membraneseparation area of each nite element is determined by it volume

( 2p r Dr D z ) and specic area of membrane bundle (membranebundle area/unit volume of membrane bundle) as follows.

A 2p Dr D z 1 =do 8

In the case of radial cross ow, there are four types of elementsdepending upon their radial and axial location in the tube side(ber bundle) of the module as shown in Fig. 1a The computationproceeds from the Type 1 to Type 3 elements till the end of bundle and then starts again from Type 2 elements through thesuccession of Type 4 elements [7] .

For a binary system, the permeate composition, y1 (fasterpermeating component) in the rst and second types (Type1 and Type 2) of nite elements is given in terms of mole fractionof the shell side, x1 (faster permeating component) as follows.

y1 a 1b x1 1 b a 1b x1 1 b 2

4ab x1 a 10:5

2 a 1

9

where a is the selectivity of membrane and b is the pressure ratioof higher pressure side to lower pressure side. The ow rate intothe nite element of the permeate side is given by

DQ P 1 =d ph x1 i 1 , 1 pl y1 i,1 P 2 =d ph: x2 i 1 ,1 pl y2 i,1 : A 10 where x2 1 x1 and y2 1 y1 (Binary component gas mixture)

Similarly, the shell side ow rate, Q s ( i, 1) and permeate sideow rates, Q T (i, 1) contacting the next element are given by

Qs i,1 Qs i 1 , 1 DQ 11

Q T i,1 DQ 12

The shell side composition x1 (i, 1) of respective element isgiven by

x1 i,1 Qs i 1 , 1 x1 i 1 , 1 Q T i,1 y1 i, 1 =Qs i,1 13

For elements in contact with feed (Type 1), the sufxes ( i 1, 1)are replaced with feed conditions such as Q f and x f . These elementswill not have any preceding elements in the radial direction [7].

For Type 3 and Type 4 elements, shell and tube ow rates andcompositions are known and mass transport is measured bysolving the following equations

DQ P 1 =d ph x1 i 1 , j pl y1 i, j P 2 =d ph: x2 i 1 , j pl y2 i, j : A14

DQ 1 P 1 =d ph x1 i 1 , j pl y1 i, j : A 15 Qs i, j Qs i 1 , j DQ 16

Q T i, j Q T i 1 , j DQ 17

x1 i, j Qs i 1 , j x1 i 1 , j DQ 1

Qs i, j 18

y1 i, j Q T i 1 , j y1 i 1 , j DQ 1

Q T i, j 19

For elements in contact with feed (Type 3), the sufxes ( i 1, 1)are replaced with feed conditions such as Q f and x f . Solving theabove set of equations, mass transport across the membrane for theeach element can be computed. Using same approach for all theelements, computation proceeds from the epoxy sealed end of thehollow ber tubes to the tube-sheet end of these bers [7].

In addition, viscosity of gas mixture is calculated by Wilkesmethod while viscosity of pure components and their tempera-ture dependence are determined using Lucas method [29] . Theassumptions that follow the suggested model making it applic-able only for ideal conditions are:

1. It holds only for the binary gas mixture. Even though it is anideal assumption, yet it is a rst step to understand realisticmodeling and simulation of many important separations[6 ,7,10 ,11 ,19 ,21 ,30 ,31 ] such as CO 2 -methane separation inthe current work.

2. The shell side pressure variations are negligible (due toconstant bulk ow in an axial direction) while the permeateside pressure drop is determined by HagenPoiseuille[6 ,7,10 ,17 ,19 ,21 ].

3. The system operates at isothermal conditions [6,7,10 ,14 ,17 ,19 ,21 ,31 ]

4. Membrane permeability is assumed to be independent of thetemperature and pressure [3 ,6,7,10 ,11 ,14 ,19 ,21 ,30 ]

2.2. Temperature and pressure dependence of membrane permeance

One of the limitations in the proposed mathematical model isthe assumption (discussed in previous Section 2.1 ) that systemoperates at isothermal conditions. Experiments [32] clearly indi-cate that, in a number of separations problems, deviations fromisothermal conditions occur which cannot be neglected. The mainreason for temperature change is Joule Thomson effect whichoccurs when non-ideal gases are expanded [23] .

In the separation of CO 2 from natural gas, the permeatetemperature decreases as a direct consequence of the JouleThomson effect. The observed temperature decrease on the highpressure side is an indirect consequence of the JT effect since heatis transported across the membrane along with enthalpy due tothe permeation of mass through the membrane. Both lead to adecrease of the membrane temperature along the module [23] .Thus the module temperature may change and affect its separa-tion performance in case of non-ideal mixtures. This is especiallytrue for cases involving high membrane permeance values such asCO2 /CH4 separation [27] .

The JT coefcient m JT must be calculated in order to studythe JT expansion effect on the gas passing through the membrane.The calculation procedure is elaborated by Maric [33 ,34 ]. Thegeneral equations are provided as follows

m JT R g T 2

r C m , p

j Z j

T p20

F. Ahmad et al. / Journal of Membrane Science 430 (2013) 445546


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C m , p C p

M

C PI R g T T 00 20

M

21

where R g is univeral gas constant, C m , p is molar heat capacity, C PI isthe ideal heat molar capacity, M is molar mass, 0 and 00 are therst and second derivatives of the gas fugacity coefcient. Therst derivative of the compression factor with respect to tem-perature is

Z RTZ 2 P58n 13 C

n 0n Dnn pZ TZ 00 Z 1 R TZ 2 pT Z 1 22 where

Dnn bn c n kn r r kn r r bn ec nr r kn 23

Z 1 Br m r r X18

n 13C nn X

58

n 13C nn bn c nkn r r kn r r bn e c nr r kn 24

Z 0 B K 3 X18

n 13C nn 25

Z 00 B0 K 3

X18

n 13C n 0n 26

Z 1 Z 0 X58

n 13C nn K

3 b2n c n kn 2bn kn c n kn r r kn r r kn r r bn1 e c n r knr

27

where, r m is gas mixture molar density, r r is reduced density, B issecond virial coefcient, kn and bn are equation of state para-meters and C n

n is temperature composition dependent coef-cient. Therefore, the nal analytical equation for JouleThomsoncoefcient is given by

m JT RT 2

r M

CPI RT T 00 2 0 RTZ

2

P58n 13 C

n

n Dn

n r Z TZ00 Z 1 RTZ 2 r TZ 1 28

The temperature drop due to JT effect can thus be calculated asfollows

DT T h T l m JT ph pl 29 Membrane permeance is dependent on temperature and

pressure described by Arrhenius and partial immobilizationmodels [35 ,36 ]. Paul and Koros [37] presented the rst partial-immobilization model based on the concentration gradient. Themodications to the Ficks law for diffusion were done byintroducing a new diffusion coefcient DH for the mobility of the Langmuir mode species. A simplied permeance expression isderived as [38 ,39 ]

P K DDD1 FK =1 bp 30 where F DD/DH and K C H b/K d . DD the Henrys diffusion coef-cient and DH is the Langmuir diffusion coefcient. The parameterb is explained conceptually as the afnity of the gas molecules toget absorbed in the holes, C H is the total concentration of theseholes in that polymer, and K D is the Henrys law dissolutionconstant.

Generally, the gas transport process through polymer mem-branes can be considered as an activated process which indicatesthat we can represent the temperature dependence of perme-ability by an Arrhenius-type equation [35 , 39]

P P oexp E p

R g T 31

where P o is the pre-exponential factor independent of tempera-ture and E p is the activation energy for permeation.

Safari et al. [39] examined different forms of equations basedon partial immobilization and Arrhenius models and presentedthe following form that includes pressure and temperature effectsimultaneously.

P aexp bR g T

cexp d=R g T 1 e=T

p 32

where a, b, c , d and e are model constants, R g is universal gasconstant, p is pressure and T is temperature at which permeancehas to be calculated. The above equation shows good agreementboth with theory and experimental data [39] .

The current study used Eqs. (20)(29) to calcualte the tem-perature drop due to JT effect and Eq. (32) to calculate theinlfuence of temperature and pressure on membrane permeance.These equations are then included with ideal hollow bermembrane model, explained in the previous section.

2.3. Process simulation and economics

The membrane units are most likely to be part of a complexprocess ow sheet along with other unit operations. Thus, it isadvantageous to introduce the membrane unit into commercialprocess simulator which will then provide a tool to simulate,design and optimize the overall process rather than an isolatedmembrane module.

In this work, hollow ber membrane model ( Fig. 1) has beeninterfaced with Process simulation programme, ASPEN HYSYS inorder to calculate permeate and retentate of the system withany number of modules, allowing complex process simulations.The programme has the possibility to use ASPEN HYSYS capabil-ities to calculate mass and energy balances and combine in theprocess model.

The equation of state was solved to calculate Joule Thompsoncoefcient at certain temperature using Visual Basic coding as apart of complete hollow ber membrane model. The model isthen interfaced as a user dened unit operation (extension) inAspen HYSYS employing Visual basic subroutine in order tocalculate permeate and product compositions, ow rates andmembrane area required for the separation. These parameters,along with methane losses, stage cut and compressor power,dene the gas processing cost (GPC) for the membrane system. Inorder to get the optimal design, it must be minimized keepingoperating conditions under consideration.

Usually, upgraded natural gas is sold on the basis of productvolume rather than of feed volume [40] . Therefore, processingcost per MSCF of product is used in the present study. It shouldalso be noted that retentate containing high methane is consid-ered as product in the current study.

The procedure to calculate the gas processing cost (GPC) isgiven in Table 1 . It includes the capital related cost (CRC), thevariable operating and maintenance cost (VOM) and the cost of CH4 lost in the permeate stream (CH 4LS) [19 ,40 ]. The cost of cooling system is included in the compressor cost (CC) as it usuallycomes along with compressors. A payout time is considered to be5 years in order to calculate the capital cost whereas projectcontingency, that covers the unpredictable elements of the project,is assumed to be 20% of the base plant cost [40] . Gas processingcost (GPC) must be minimum subject to operating conditions,material and energy balances, and individual permeator mathe-matical model [31] .

One of the approaches to design of a membrane separationprocess is to select a small number of design congurations and

optimize the operating conditions of each conguration. The nal

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optimum design is chosen to be the system with most favourableeconomics [31 ,41 43 ]. In the previous paper [21] , we have shownthat double stage with permeate recycle system (shown in Fig. 2)gives the optimum design conguration due to minimum processgas cost involved with it. In this work, non ideal effects have beenintroduced in the model and the optimum design conguration isexplored further to see the inuence of non ideal effects on theperformance and economics of the separation system.

2.4. Simulation conditions

Feed conditions for natural gas treatment plant depend mainly onthe source; therefore composition, ow rates, pressures and tem-perature of crude natural gas typical for medium sized natural gastreatment plant for removing CO 2 gas are selected. As a result, thefeed ow rate of feed gas is maintained at 50000 SCFH (1.3 MMSCF).Feed temperature is 323 K. On the other hand, feed pressure andpermeate pressures are maintained at 59.6 bar and 1.8 bar,

respectively, unless specied otherwise [7,22]. The permeance valuesused for the simulation (22 GPU for CO 2 and 0.7 for CH 4 at 50 1 C)correspond to membrane material of polyimide for the effectiveseparation layer thickness of 0.1 mm [22,44].

Modules parameters are typical for hollow ber membraneseparations used for natural gas treatment applications. Unlessspecied otherwise, the simulations are run at the ber bundleradius of 10 cm. Similarly, hollow ber module is composed of

bers having outer diameter of 0.040 cm and packing density of 50%. Lower packing density may cause ow channelling outsidethe hollow bers. In contrast, higher packing density may lead toa reduction of the ow space for shell-side feeding, which maycause higher pressure drop [27] .

Natural gas contains different amounts of CO 2 ranging fromsweet (CO 2 -free) gas in Siberia to very high CO 2 content of 90% inthe Platong and Erawa elds in Thailand [45] . The natural gas eldin the Greater Sarawak Basin (Indonesia), with estimated 46trillion cubic feet recoverable reserves, remains undevelopeddue to high CO 2 contents of 71% [45 ,46 ]. In Malaysia, 13 trillioncubic feet natural gas reserves are undeveloped due to high CO 2content that varies from 28% to 87% [46 ,47 ]. Therefore, threecases have been investigated including lower concentration feed(10% CO

2), medium concentration feed (40%) and higher CO

2concentration feed (70% CO 2 ).

3. Experimental method

Mathematical models have to be supported by experimentaldata. Thus, the proposed model is veried by experimentalmethod through comparison of the simulated and experimentsresults. The experimental set up mainly consists of hollow bermembrane module and the gas separation testing unit in whichthe module is installed to facilitate the separation mechanism.

3.1. Hollow ber membrane module

Hollow ber modules may have different congurations tomeet the needs of different applications. The current work usedcross ow (shell-side feeding) hollow ber module as shown inFig. 1. In this conguration, two tube sheets hold the ber ends inplace and separate the retentate from the permeate ow. One is aplug-sealed tube sheet in which the openings of ber ends areblocked by the epoxy resin; the other is an open-end tube sheet inwhich the bores of hollow bers are exposed [27] .

The hollow bers used for the experimental work are com-mercial (Alpha Membrane Hi-Tech Pte. Ltd, Singapore). Thematerial of membrane used is polyimide having the permeanceof 22 GPU for CO 2 and 0.7 GPU for CH 4 at 50

1 C. The bers haveouter diameter of 400 mm and inner diameter of 180 mm. The

Fig. 2. Process ow diagram (PFD) of double stage system with permeate recycle in Aspen HYSYS.

Table 1Economics parameters for gas processing cost [19] .

Total plant investment (TPI ): TPI TFI SC

Membrane module cost (MC) $ 5/ft 3

Installed compressor cost (CC) $ 8650 *(W cp /Zcp )0.82

Fixed cost (FC) MC CCBase plant cost (BPC) 1.12 * FCProject contingency (PC) 0.20 * BPCTotal facilities investment (TFI) BPC PCStart up cost (SC) 0.10 * VOM

Annual variable operating andmaintenance Cost ( VOM):

VOM CMC LTI DL LOC MRC UC

Contract and material maintenancecost

0.05 * TFI

(CMC) 0.015 * TFILocal taxes and insurance (LTI) $ 15/hDirect Labor cost (DL) 1.15 * DL Labor overhead cost (LOC) $ 3/ft 2 of membraneMembrane replacement costs (MRC) $ 0.07/kw hUtility cost (UC)

Annual cost of CH 4 lost inpermeate (CH4 LS):

CH4 LS NGLS * NHV * NWP

Annual natural gas lost (NGLS) NGLS 365 * OSF * L f * yP (CH4 ) * x f (CH4 )

Gas processing cost (GPC) GPC (CRC CH4 LS VOM) /[365 * OSF *L f * (1SCE) * 1000

Annual capital related cost (CRC) 0.2 * TPIMembrane life ( t ) 4 yearsWellhead price of crude natural gas $ 2/MMBTUHeating value of natural gas 1066.8 MMBTU/MMSCFOn stream factor (OSF) 96%Compressor efciency ( Zcp ) 0.8



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required ber numbers and ber length are calculated based onthe diameter of hollow bers and the length of module with anassumption of 4050% packing density. Fifty bers having lengthof 28 cm have been cut for the purpose of bench-scale testing inthe current study.

Using the same procedure for bundle preparation as explained inthe published literature [27,48 ], the bers are cut to a desired lengthand visibly defective bers are removed. Finally, the remaining

bers are placed in parallel order while putting them together as aber bundle. A piece of barrier lm (Paralm M s ) has been taken,stretched and wrapped it on one end of the ber bundle. The end of the ber bundle will become denser because of the shrinkage of thelm. The wrapped side is cut with a sharp razor blade to yield asmooth end. The end has to be encircled with string in order to besure that its diameter is less than the shell diameter.

The shells made of stainless steel (SS 316) having outer diameterof 1/2 in (1.27 cm) and 1 in (2.54 cm) are used in this study. In orderto assemble the module, the shell is placed vertically on a holderwith enough space under it to accommodate the ber bundle. Withthe help of string, ber bundle is housed in the shell.

The void space between the bers and the internal wall of theshell was potted i.e., lled with epoxy glue (Loctite s E-30CL Hysol s adhesive). The purpose is to isolate the permeate streamfrom the retentate stream. Unlike the open side, the other side of bers are completely sealed by the epoxy glue to form a dead end.The glue hardens in several minutes but reaches the maximumstrength in 24 h. The openings of the bers have to be inspectedcarefully to make sure that all of them are properly embedded inglue and not closed or deformed by cutting.

3.2. Gas separation testing unit

Hollow ber membrane module is installed in the experimen-tal set up as shown in Fig. 3. The testing unit mainly consists of

gas cylinders, mass ow controllers, compressor, and infraredanalyser. Natural gas (with impurities) and pure methane can beused alternatively in the set up. In addition, nitrogen is used forpurging the separation system. In the current study, puremethane and CO 2 are used to evaluate the performance of separation system. Thermocouples and pressure gauges areinstalled before and after the permeation test cell to monitorthe temperature and pressure drop across the membrane module.

Furthermore, a back pressure regulator is xed after the mem-brane module in order to generate trans-membrane pressurerequired for the separation of gases. The whole system exceptfeed cylinders and compressor is placed in an oven to maintainthe temperature of system and isolate from external effects.Coriolis ow meters are used to measure the mass ow rates of streams. Similarly, Infrared analyzer is used to measure thecomposition of feed, permeate and retentate streams. They areconnected to data acquisition system in order to record the gasconcentrations of streams at different times.

4. Results and discussions

4.1. Model validation

To demonstrate the applicability of the model, the simulatedmodel with non ideal effects is validated with experimentsperformed in laboratory. Feed gas containing 50% CO 2 is main-tained at 10 l per minute ow rate while at temperature of 50 1 C.On the other hand, feed pressure is maintained at 10 bar. Thenumber of bers is xed to 50 and CO 2 concentration in the feedgas is varied from 10% to 70% in order to nd the temperaturedrop across the membrane measured by thermocouple installedin the equipment. The experimental results are compared withsimulated results for the simplest design conguration with no

Natural gas CH4 CO2 N2

Feed Vessel

Hollow FiberMembrane Module

Static mixer

F

Flow meter

T

Thermocouple

P

Pressure guage

F

TPBackpressure

Regulator

Pressure guage Thermocouple

F

Flow meter

Flow meter

P T

Pressure guage Thermocouple

Infrared Analyzer

Flowcontroller

Data AcquisitionSystem (Computer)

Fig. 3. Flow sheet of gas separation testing unit for experimental validation.



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recycle stream as shown in Fig. 4. It can be seen that suggestedmodel is in agreement with experimental results with maximumpercentage error less than 8%. The small difference in valuesmight be due to the experimental errors and precision limitationsof instruments (thermocouples).

The non ideal model is further compared to experimental datapublished by Pan [6] as shown in Fig. 5. The data is based on theexperiments performed on sour natural gas. Feed conditions used

are 48.5% CO 2 , 27.9% CH4 , 16.26% C2 H6 and 7.34% C 3H8 . Themembrane material is cellulose acetate with permeance values of 40.05 for CO 2 , 1.11 for CH 4 , 0.31 for C 2H6 and 0.06 for C 3 H8 [6] .Thus, it can be assumed that most of heavy hydrocarbons (such asC2 H6 and C 3H8 ) pass to the retentate/product without permeatingthough the membrane. The simulations are performed in AspenHYSYS on the basis of 48.5% CO 2 and 27.9% of CH 4 in the feed withmembrane permeance values of 40.05 and 1.11, respectivelywhile allowing other components to pass across the modulewithout permeation.

The temperature and pressure values of the gas are 10 1 C and35.28 bars, respectively, while the permeate pressure is 9.28 bar.The selectivity is assumed to be 25. The same process conditionsare maintained for the simulated model and compared with theexperimental data. Fig. 5 shows that the suggested model givesgood approximation to the experimental data with maximumpercentage error less than 3%.

4.2. Temperature and pressure effects

Stage cut has a large impact on the gas thermodynamicsproperties and contributes to temperature drop. As an initial step,the membrane permeation properties are taken to be constant atthe values characteristic of the feed temperature (50

1

C) in order

to isolate the effect of temperature changes entirely due toexpansion-driven cooling. The feed pressure is maintained at59.6 bar while permeate pressure at 1.8 bar. Fig. 6 reports theeffect of stage cut on temperature change across the module fordifferent feed concentrations of CO 2 . It can be observed thattemperature change across the module can be as large as 40 C andis strongly dependent upon the stage cut as well as CO 2 concen-tration in the feed. At the same stage cut, gas mixtures with more

CO2 in the feed experience larger temperature decreases from thefeed to residue ends of the module. It is due to the reason thatfeed composition changes not only the amount of permeating gasacross the ber wall but also the thermodynamic properties (suchas heat capacity and PVT properties) of the gas mixtures in theresidue and permeate streams [22] .

In general, gas permeance values are taken to be independentof temperature in order to isolate the inuence of gas-phasecomposition and stage cut on expansion-driven temperaturechanges. However, signicant temperature changes across themodule are observed. Thus, simulations are performed in order tostudy the effect of stage cut and temperature drop on membranepermeance of CO 2 and CH 4 . As an example, the effect of stage cutand temperature drop on CO 2 permeance for higher concentrationfeed (70% CO

2) is shown in Fig. 7. Similarly, the effect of stage cut

and temperature drop on CH 4 permeance for higher concentrationfeed (70% CO 2 ) is shown in Fig. 8. It can be seen that permeance of both CO 2 and CH 4 decreases with the increase in stage cut. It isdue to the reason that the increase in stage cut increases thetemperature drop which results in change of CO 2 and CH 4permeance being dependent on temperature.

Feed pressure due to partial pressure of gases in the feed alsoaffects the membrane permeance. It is due to the reason that themass transport of membranes for the separation of CO 2 /CH4mixtures is determined by competitive sorption and plasticization

20

25

30

35

40

45

50

0 20 40 60 80 T e m p e r a

t u r e o

f p e r m e a

t e s

t r e a m

( C )

CO2 contents in feed (%)

Experimental

Simulated (Non ideal)model

Fig. 4. Model validation with experimental results at feed temperature 50 1 C,feed pressure 10 bar, feed ow rate 10 l/min and number of bers 50.

0.7

0.75

0.8

0.85

0.9

0.95

1

0.4 0.45 0.5 0.55 0.6 0.65

P e r m e a

t e C O 2 m o

l e f r a c

t i o n

Stage Cut

Experimental data byPan [10]

Simulation results bysuggested model

Fig. 5. Model Validation with published literature by Pan [10] .

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60

T e m p e r a

t u r e

D r o p

( C )

Stage Cut

10 % CO2

40 % CO2

70 % CO2

Fig. 6. Effect of stage cut on temperature drop (Feed temperature 323 K).

0

5

10

15

20

25

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60

P e r m e a n c e o

f C O 2 ( G P U )

T e m p e r a

t u r e

d r o p

( C )

Stage Cut

Temperature drop

Permeance of CO2

Fig. 7. Effect of stage Cut on CO 2 permeance of for 70% CO 2 feed.



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[49 ,50 ]. Fig. 9 shows the effect of pressure ratio on the CO 2 andCH4 permeance of the membrane material for the higher CO 2concentration feed. It can be seen that permeance value increaseswith the increase in pressure ratio and vice versa. Thus, pressureratio is an important factor to determine the non ideal permeanceof the separation system.

4.3. Membrane performance study

A case study of CO 2 separation from methane was performed inorder to evaluate the performance of non-ideal model (with tem-perature and pressure effects on membrane permeance) in terms of product/retentate composition, methane loss and stage cut. More-over, it is compared with ideal model having constant permeance.

Fig. 10 (a) reports the mole fraction of CO 2 on the retentate/product side of the system as a function of ber length for feedCO2 composition of 10%. It can be seen that mole fraction of CO 2decreases with the increase in ber length of module. The reasonis that the increase in ber length (or membrane separation area)improves the amount of CO 2 permeating through the membraneleading to lower retentate/product CO 2 composition. It can also beobserved that non ideal model (variable permeance) shows higherCO2 composition in the retentate/product for the same berlength in comparison with the ideal model (constant permeance).The maximum difference between ideal and non ideal models atthe same ber length is almost 18%. It is due to the fact thatmembrane permeance of CO 2 decreases as a result of pressuredrop and resultant temperature drop due to JT effect as explainedin the previous section. As a result of membrane permeancechange in non ideal model, the composition of CO 2 increases inretentate/product.

Methane (CH 4) loss can be described as the percentage of methanelost in the permeate stream to the methane present in the feed

stream. It increases with the increase in ber length due to increase of

membrane separation- area and vice versa [7]. Fig. 10(b) presents themethane loss as a function of ber length for both ideal and realscenario. Methane loss increases with the increase in ber length asexpected but it is less pronounced in non ideal case (with maximumdifference of 6%) where permeance of both CO 2 and CH 4 decreaseswith the temperature and pressure drop.

Fig. 10 (c) shows the effect of ber length on stage cut. Stagecut increases with the increase in ber length. For the same berlength, non ideal case shows lower stage cut in comparison withideal case with maximum difference of 4%. It is due to the reasonthat ow rate of permeate stream decreases due to decrease inpermeance of CO 2 and CH 4 . As a result, stage cut being ratio of permeate ow rate to feed ow rate, gets reduced for the nonideal case. The results are consistent with those obtained by Safariet al. [39] and Schloz et al. [25] .

All these results are repeated for medium CO 2 feed concentrationof 40% as shown in Fig. 11 and higher concentration of 70% as shownin Fig. 12. It can be seen that the performances at the higher feedconcentration is an amplication of the results obtained at the lowerfeed concentration. For example, the maximum difference between

ideal and non ideal cases for retentate/product CO 2 composition is

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0

5

10

15

20

25

0 10 20 30 40 50 60

P e r m e a n c e o

f C H 4 ( G P U )

P e r m e a n c e o

f C O 2 ( G P U )

Pressure Ratio

CO2

CH4

Fig. 9. Effect of pressure ratio on membrane permeance of CO 2 and CH4 for 70%CO2 feed.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 100 200 300 400

R e

t e n

t a t e C O 2

C o m p o s

i t i o n

( % )

Fiber length (cm)

Ideal model (constantpermeance)

Non-ideal model(variable permeance)

Fiber length (cm)

0 100 200 300 4000

5

10

15

20

25

M e

t h a n e

l o s s

( % )


Non-ideal model

(variable permeance)

100 200 300 40000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

S t a g e

C u

t

Fiber length (cm)


Non-ideal model

(variable permeance)

Fig. 10. Comparison of (a) retentate CO 2 composition (b) Methane loss (c) stagecut by ideal model (constant permeance) with non ideal model (temperature andpressure dependent permeance) for 10% CO 2 feed.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60

P e r m e a n c e o

f C H 4 ( G P U )

T e m e r a

t u r e

d r o p

( C )

Stage Cut

Temperature drop

Permeance of CH4

Fig. 8. Effect of stage cut on CH4 permeance of for 70% CO 2 feed.



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increased to 10% (for 40% CO 2 concentration feed) and 15% (for 70%CO2 concentration feed). More concentration of CO 2 in feed causesmore temperature drop due to JT effect that leads to decrease inmembrane permeance. As a result, retentate CO 2 composition tendsto increase while stage cut and methane loss tend to decreasefurther for non ideal model.

4.4. Process economics study

In order to evaluate the process economics of the system, feedgas composition of CO 2 is xed at 40% while methane purity at96% (4% CO2 in retentate stream) and the effect of ber length onthe compressor power requirement and gas processing cost hasbeen investigated both for the ideal and non ideal case of membrane permeance. The simulations conditions are same asmentioned in the Section 2.4 (Feed pressure 59.6 bar, permeatepressure 1.8 bar, feed temperature 323 K and feed owrate 1.3 MMSCF). The compressor efciency of 80% is used asshown in Table 1 .

The effect of membrane module characteristics on the com-pressor power requirement has been investigated for the pro-

posed design conguration (double stage with permeate recycle)

The compressor power is given by the expression [51] .

W cp hp R g T X2

n 1Q p, n ln

ph pl,n n 1:341 33

where Q p is the permeate ow rate, n is the index of membranestage, T is the temperature and R g is ideal gas constant.

Fig. 13 shows the comparison of ideal and non ideal model forcompressor power as a function of ber length. It can be seen thatcompressor power requirement increases with the increase inber length. In fact, these ber length change the membraneseparation area which causes the change of stage cut as explainedin the previous section. Keeping the feed ow rate constant, thechange in stage cut would mean the change in permeate owrate. It can be seen from Eq. (33) that compressor power dependson the permeate ow rate along with feed and permeate pres-sures. Thus, the change in permeate ow rate change results inchange of compressor power requirement accordingly. It can alsobe observed that compressor power requirement change is lesspronounced in non-ideal case for the same ber length. The

maximum difference between compressor power for ideal and

0

5

10

15

20

0 100 200 300 400

R e

t e n

t a t e C O 2

C o m p o s

i t i o n

( % )

Fiber length (cm)

Ideal model (contstantPermeance)Non ideal model (variablepermeance)

05

10

15

20

25

30

35

40

0 100 200 300 400

M e

t h a n e

l o s s

( % )

Fiber length (cm)


Non ideal model (variablepermeance)

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 100 200 300 400

S t a g e

C u

t

Fiber length (cm)

Ideal model (constantpermability



0

5

10

15

20

25

30

35

0 100 200 300 400

R e

t e n t a

t e C O 2 C o m p o s

i t i o n

( % )

Fiber length (cm)



0

10

20

30

40

50

60

M

e t h a n e

l o s s

( % )

Fiber length (cm)



0 100 200 300 400

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 100 200 300 400

S t a g e

C u

t ( % )

Fiber length (cm)




http://-/?-http://-/?-


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non ideal case at the same ber length is 6%. It is explained by thereason that compressor power mainly depends on the permeateow rate and thus stage cut. With the decrease in stage cut due todecrease of membrane permeance for gases, there will be lowrequirement of compressor power in non-ideal case wheremembrane permeance is dependent on temperature and pressure.

The effect of ber length on gas processing cost (GPC) for bothideal and non ideal cases is shown in Fig. 14. It can be noted thatlarger ber lengths yield higher GPC. It is due to the reason that GPCmainly depends on membrane module cost (MC), compressor cost(CC) and annual cost of CH 4 lost in permeate (CH 4LS) as shown inTable 1 . With the increase in membrane area (or ber length), theabove mentioned costs increase resulting in the increase of GPC.It can also be observed that non-ideal case show less GPC incomparison with ideal case (maximum difference of 8%) for thesame ber length. As stage cut and a compressor power requirementis decreasing with the decrease in membrane permeance, it leads toreduce the GPC of the membrane separation system.

In order to see the effect of higher concentration CO 2 feed onprocess economics, the above procedure is repeated for 70% CO 2in feed gas as shown in Fig. 15 (for compressor power) and Fig. 16(for gas processing cost). It can be observed that the differencebetween performance of ideal and non ideal models are morepronounced in the case of higher CO 2 composition feed. Forexample, the maximum difference between ideal and non idealcases for gas processing cost is increased from 8% (for 40% CO 2concentration feed) to 15% (for 70% CO 2 concentration feed). It isdue to the reason that higher CO 2 in feed leads to increase intemperature drop. As a result, membrane permeance reduceswhile contributing to further decrease in compressor power and

gas processing cost.

5. Conclusions

The temperature and pressure dependence of membrane per-meance has been investigated for the case involving CO 2 separationfrom methane. The effect of variable permeance is included in thecross ow model for hollow ber membrane separation. The modelis then included in the process simulation (Aspen HYSYS) as a userdened unit operation along with other available unit operations inorder to investigate the membrane performance and process eco-nomics. The simulated model is validated with experimental pub-lished data where the simulated data exhibit good agreement withthe experimental and published results. The temperature drop dueto Joule Thomson (JT) cooling and its effect on membranepermeance of both CO 2 and CH 4 has been studied. Similarly, theeffect of pressure ratio on membrane permeance has been reported.The inuence of variable permeance (temperature and pressuredependent) is studied by comparing separation performance (interms of retentate/product CO 2 composition, methane loss and stagecut) and process economics (gas processing cost) with the idealmodel where membrane permeance is assumed independent of temperature and pressure. It has been shown that non ideal modelshows higher CO 2 retentate composition, lower stage cut andmethane loss in comparison to ideal model for the same berlength. It leads to lower compressor power requirements and gasprocessing cost for the non ideal hollow ber membrane model. Forhighly non ideal conditions (e.g., higher CO 2 concentration feed),non ideal effects related to module operation would be moresignicant in affecting the product quality (CO 2 retentate/productcomposition), methane loss, stage cut, compressor power and gas

processing cost of hollow ber separation systems. Thus, it is crucial

0

50

100

150

200

250

300

0 100 200 300 400 500

C o m p r e s s o r p o w e r

( h p

)

Fiber length(cm)



Fig. 13. Comparison of compressor power by ideal model (constant permeance)with non ideal model (temperature and pressure dependent permeance) at feedCO2 composition 40% and methane purity 96%.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 100 200 300 400 500

G P C ( U S D / M S C F o

f p r o

d u c

t )

Fiber length (cm)



Fig. 14. Comparison of gas processing cost by ideal model (constant permeance)with non ideal model (temperature and pressure dependent permeance) at feedCO2 composition 40% and methane purity 96%.

0

50

100

150

200

250

300

350

0 100 200 300 400 500

C o

m p r e s s o r

P o w e r

( h p

)

Fiber length (cm)


Non ideal model(variable permeance)

Fig. 15. Comparison of compressor power by ideal model (constant permeance)with non ideal model (temperature and pressure dependent permeance) at feedCO2 composition 70% and methane purity 96%.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 100 200 300 400 500

G P C ( M S C F o f p r o

d u c

t )

Fiber length (cm)


Non ideal model(variable permeance)

Fig. 16. Comparison of gas processing cost by ideal model (constant permeance)with non ideal model (temperature and pressure dependent permeance) at feedCO2 composition 70% and methane purity 96%.



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to include the effect in the proposed hollow ber membrane modelas an accurate assessment of performance and economics of gasseparation system.

List of symbols

A Membrane separation area (cm 2 )

Am Cross section area of membrane module (cm2

)Af Cross section area of ber (cm 2 )BPC Base plant cost (USD)CC Installed compressor cost (USD)CH4 LS Annual cost of methane loss in permeate (USD/year)CMC Annual contract and material maintenance cost

(USD/year)CRC Annual capital related cost (USD/year)Cp Specic Heat capacity (J/g K)CPI Ideal heat molar capacity (J/g K)Cm,p Heat molar capacity (J/mol K)DL Direct labor cost (USD/year)Dd Henrys diffusion coefcient (cm 2 /s)Dh Langmuir diffusion coefcient (cm 2 /s)d

i Inner diameter of bers (cm)

d o Outer diameter of bers(cm)dm Diameter of Membrane module (cm)Ep Activation energy for permeation (kJ/mol)FC Fixed cost (USD)GPC Gas processing cost (USD/MSCFD of natural gas product) J Gas permeation ux through membrane (MMSCF/

ft2 day)i Index of gas componentLOC Annual labor overhead cost (USD/year)LTI Annual local tax and insurance cost (USD/year)L Length of bers (cm)l Membrane life (years)M Molar mass (g/mol)MC Total cost of membrane modules (USD)MMBTU 10 6 BTUMMSCFD10 6 ft 3 /dayMRC Annual membrane replacement cost (USD/year)MSCF 103 standard cubic feet (at standard temperature and

pressure)NGLS Annual loss of natural gas (MMSCF/year)NHV Heating value of natural gas (1066.8 MMBTU/MMSCF)NWP Wellhead price of crude natural gas (USD/MMBTU)Nf Number of bers/cross section area of ber (cm 2 )n f Number of bersn index of membrane stageOSF On stream factorP Project contingency (USD)Pi Permeability of component i (mol/MPa-m 2 -s)P j Permeability of component j (mol/MPa-m 2 -s)p h Pressure on the high pressure side (bar)p l Pressure on the low pressure side (bar)Q f Feed Flow rate (cm 3 (STP)/s)Q p Permeate ow rate (cm 3 (STP)/s)Q r Product/Retentate ow rate (cm3(STP)/s)R Radius of ber bundle (cm)R g Universal gas constant (m 3 Pa/kg-mol K)SC Start up cost (USD)SCF Standard cubic feet (at standard temperature and

pressure)T Temperature (K)Th Temperature of feed (high temperature) side (K)Tl Temperature of permeate (low temperature) side (K)

TFI Total facilities investment (USD)

TPI Total plant investment (USD)UC Annual utility cost (USD/year)UCP Utility cost (USD/kw h)VOM Annual variable operating and maintenance cost

(USD/year)W cp Power requirement for compressors (hp)x1 Mole fraction of carbon dioxide on shell sidex2 Mole fraction of methane on shell side

y1 Mole fraction of carbon dioxide on tube (permeate) sidey2 Mole fraction of methane on tube (permeate) sideZ Compression factor

Greek symbols

a ij Selectivity of the membraneb Pressure ratioe Porosity of the membrane (%)^ fugacity coefcient Packing density (%)DQ Molar permeation into an element (cm 3 (STP)/s)Dr Radial increments

D z Axial incrementsd Membrane thickness (cm)r m Molar density of gas mixture (mol/cm 3 )r r Reduced densityZcp Compressor efciency (%)m JT Joule Thomson coefcient (K/bar)

Acknowledgements

This work was done with the nancial and technical supportfrom CO 2 Management (MOR) research group, Universiti Tekno-logi PETRONAS.

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