CO2 facilitated transport through functionalized cation-exchange membranes

51

Journal of Membrane Scrence, 82 (1993) 51-63 Elsevier Science Publishers B V , Amsterdam

CO, facilitated transport through functionalized cationexchange membranes D. Langevin”**, M. Pinoche”, E. S6lBgny”, M. MBtayer” and R. Rouxb “URACNRS 500, Unwersttt? de Rouen, Facultk des Scrences, BP 118, 76134 Mont-Sauzt-Agnan

(France)

bFaculte’ des Sciences, Uncversrtk de Yaounde, Yaounde (Cameroun) (Received December 17,1992, accepted February 17,1992 )

Abstract The facilitated transport of CO, through a cation-exchange membrane has been studied. The cmer, monoprotonated ethylenedmmme, 1s introduced m the membrane by soaking aclchc samples in more or less concentrated neutral ethylenediamme solutions The permeability of the membrane IS determined as a function of the CO2 mole fraction m the uphill binary (COJN,) gas mixture The expenmental results have been interpreted using a transport model based on the Nernst-Planck equation The use of a highly swollen membrane enhances the lomc moblhties and leads to high selectivity and permeability Key words

cation-exchange

membranes, facdltated transport, CO, transport, tamer

Introduction The majority of the known gas sweetening processes use chemical reactions or physical absorption of CO, and H,S in towers containing liquid absorbents. For example, in the petroleum and natural gas industries commonly a low-pressure amine-based processing involves primary and secondary amines (monoand diethanolamine) for CO2 removal. Membrane separations should have an inherent advantage over the conventional separation methods because of their low capital costs and high energy efficiency, the condition is to devise highly permeable and selective membranes. The first work on facilitated transport was reported by Scholander [ 11. Since then, numerous examples of facilitated transport of VTowhom correspondence should be addressed

0376-7388/93/$06

gaseous permeates have been studied [ 2,3] ; all systems, mainly using liquid membranes, show both high selectivity and permeability. A few studies were performed on ion-exchange membranes with reactive counter-ions playing the role of mobile carriers. This latter process constitutes a new way of constructing active membranes with enhanced stability. Leblanc et al. [4] studied the transport of COP through anion- and cation-exchange membranes. The highest CO, permeabilities were obtained m a strong acid cation-exchange membrane using the mono protonated ethylenediamine (EDAH+) carrier. The membrane (110 pm thick) was composed of sulfonated polystyrene grafted onto a poly (tetrafluoroethylene) framework, having a low gel water content of 11% and a high ion-exchange capacity of 5 meq/g. The ionic carrier was introduced in the membrane by soaking it in a concen-

00 0 1993 Elsevler Science Publishers B V All nghts reserved

D Langevzn et al / J Membrane Scr 82 (1993) 51-63

52

trated EDA solution neutralized with HCl. More recently, Way et al. [5] studied facilitated transport of COz through a pertluorosulfonic acid cation-exchange membrane using the same carrier (monopositive cation of EDA). The membrane ( 200 pm thick), of low capacity (0.91 meq/g) and with a rather low water content (11 to 15% in the salt form), was converted to the reactive EDA form by immersion in an EDAH+/Clsolution. The author proposed a reaction equilibrium model usually applied to facilitated transport processes through liquid membranes. In the present paper, a highly swollen membrane, with a water content of 47%, was used in order to enhance the mobility of the species involved in the transport. Unlike the two examples mentioned above, the monopositive EDAH+ ions were introduced in the membrane by soaking H+-form samples in more or less diluted solutions of neutral EDA; the protonation of the amine in the ion-exchange material led to various concentrations of EDAH+ carrier at equilibrium. The permeability of the different samples was determined as a function of CO2 mole fraction in a binary mixture gas stream. In order to predict and interpret the observed experimental results, a model based on the Nemst-Planck equation and specific for ion-exchange membranes has been derived. This model, already applied to the facilitated transport of weak acids and bases in solutionmembrane-solution systems [ 6,7] was transposed and adapted here to gas-membrane-gas systems. Protonation of EDA. Fixing the carrier into the membrane Neutralization of ethylenediamine (EDA) in aqueous solutions gives the mono- and di-protonated species EDAH+ and EDAH:+ as follows:

NH, (CH,),NH, EDA

+H+o

NH2 (CHdzNH3+

(R.1)

EDAH+

and NH2 (gy;igNH,+

+H+o

NH,+ (z’=L& NH,+

(R.2)

For the stoichiometric dissociation con(Kf = &ants of EDAH+ and EDAH;+ and K~=CEDAH+CH+/ 61DAcH + I CEDAH+ cEDAq+ ) Jensen and Christensen [8] have found 6.78~10~” and 6.3~10-~ mol-1-l respectively at 18 ’ C. The real dissociation constants in solution can be written as: KI

=%DA~H+/%DAH+ EU~A~H+/UZEDAH+

K,K,

=aEDA(aH+

-Kf

(1)

-KfKb

(2)

)2/%DAHj+

"UEDA(?TZH+)'/~~ZED,+~+

where a is the molal activity and m is the modal concentration assuming a, N m, N c,. When a sulfonic acid membrane is immersed in an EDA solution, the neutral EDA absorbed by the membrane reacts with the acidic groups, forming EDAH+ and EDAH;+ counter-ions following (R.l) and (R.2). The resulting equilibrium is summarized in Table 1 which describes the general case of a gas/solution/ionexchange membrane equilibrium. In the present system, EDA is the neutral species S, OH(resulting from hydrolysis of EDA) is the coion Y and H+, EDAH+ and EDAH;+ are the counter-ions i and]. Apparent constants in the ion-exchange material can be expressed by [ 91:

K: =aEDAm*H+/m&AH+=K~Ic&AH+

(3)

53

D Langeurn et al /J Membrane SC&82 (1993) 51-63 TABLE 1 Gas/solutlon/lon-exchange membrane eqmhbnum Species 1

Gas Neutral S

Remark

Phases Solution

Membrane apa:

P.

p partlalpressure

m.=a. ma=o.p6

rn: =A,m,

a molal actlvlty* m molal concentration r molal solublhty coeficlent 1 molal dlstnbutlon coefficient

Co-Ions Y

ml

my

rn;rQ

Donnan exclusion

Counterions

ml

m,

m:

m: fixed charge molahty

Xz,m,=my

It,m: =m:

z lonlc charge

(mY

K; molal selectivity coeffkent m the exchange r/l [lo]

891

_-;i’ (M”

(rn:)‘

’ (rn,)=’

*In thurtable molal scale has been chosen to descnbe equdlbnum because It mvolves the same reference (quantity of water) m solution and m the membrane [ 7,101 Nevertheless it 1s easy to relate molahty and molanty using conversion factors c,=pm, in solution c: =p*m: m the membrane 80 that c:=uP+/Ph, where, for dduted solutions, p IS the density of the solvent (c, 2: m, m water), p* IS a swelling parameter (g of water per cm* of swollen membrane), andp*/p IS approxunately the fractional pore volume of the membrane

1

where stars refer to the membrane and ‘cf are the molal ion-exchange selectivity coefficients. From eqns. (l)-(4) we obtain the equilibrium distribution of the species. Figure 1 represents the fraction (N 1’= z, m:/m: ) of ionic sites of a cation-exchange membrane occupied by the counter-ions EDAH+ and EDAH;+, computed as a function of the logarithm of the overall EDA concentration c, in the equilibrium solution. The selectivity constants KJwere assumed equal to unity so that K: N Kf and

Kg-K$. This diagram shows how the (EDA solution)-(acid form membrane) equilibrium can

6

se4

.2

0 4

3

2

1

-log

C+

O

Fig 1 [EDA solution] - [cation-exchange membrane] equllbnum Fraction N: of lonlc sites occupied by counterions EDAH+ and EDA@+ as a function of the decimal loganthm of the overall EDA concentration ct m the equlhbnum solution Computed from eqns ( 1)- (4) assuming K{= 1 Membrane mltmlly m the H+ form

D Langewn et al /J Membrane SCL82 (1993) 51-63

54

be used to convert a sulfonic acid membrane to the mixed EDAH+-EDAH;+ form, controlling efficiently the distribution of the counter-ions with a view to a facilitated transport application.

PI. CO,-Hz0

system

According to Henry’s law the equilibrium CO, concentration in water is proportional to its partial pressure pcoz in the gas phase:

Reactions and transport mechanism EDA-CO,

7.94x1O-1’ and 4.78~10~~ mol-1-l at 18°C

system

Aqueous solutions of amines are widely used in the chemical industry for the removal of carbon dioxide from gas mixtures. Monoamines are known to form with CO2 amine salts of carbamic acids [ 111. Several authors have studied the ethylenediamine-CO2 chemistry in aqueous solution. Hiklta et al. [ 121 showed that the principal reaction, the formation of the carbamic acid zwitterion (EDACO, ) following: CO, +NH, (CH&NH+

cc02

=

SC02

(6)

PC02

where sco2 is a molar solubility coefficient which is 3.92x 10T2 mol-l-l-atm-l at 18°C 1131. CO, reacts slowly with water to form hydrogencarbonate and a hydrogen ion following [ll]: C02+HzOoHC03

+H+

(B-6)

with a first order rate constant given as a function of temperature by:

EDA

NH,+ (CH,),NHCOOEDACO2

(B.3)

log K6 = 329.850 - 110.541 log T- 17265.4 T (7)

is a fast second order reaction; its rate constant k3 is given as a function of the temperature by the empirical law:

The reaction:

log kS = 13.49 - 2799/T

is instantaneous. The corresponding first and second stoichiometric ionization constants defined by Ke =CH+ cHC0,-/cC02 and K;Z= cH+&,+CO,can be calculated from:

(5)

In aqueous solution, EDACO, dissociates: NH,+ (CH,),NHCOO-o EDACO2

H+ +NH, (CH,),NHCOOCARB

(R.4)

+H+

(B.7)

-log KJ = +3404.7/T-14.843+0.03279

T (8)

By hydrolysis the monocarbamate (CABB ) can liberate hydrogencarbonate and EDA:

and -log K;S = +2902.4/T-6.498+0.0238

NH,(CH,),NHCOO-+H,Oo NHz(CH2)2NHz +HCO,

HCO, oCO;-

(B.5)

The reported values of the stoichiometric equilibrium constants Kl= CCARJ$H+/CEDAC~ and are respectively Kd = CEDACHCO,- /CCARB

T

(9)

In basic solutions, CO2 reacts simultaneously with hydroxyl ions: CO, +OH-oHC0,

(B.8)

This reaction is second-order in the forward di-

Membrane SC&82 (1993) 51-63

D Langemn et al /J

55

Referring to reaction (R.3) and other CO,amine reactions, reaction (R.9) can reasonably be assumed to be fast. Its stoichiometric equilibrium constant in solution is obtained by combmation of the constants Kf , KJ, Ka, Kb and KQ :

rection, the rate constant k8 is given by the expression: log k8 = 13.635 - 2895/T

(10)

Transport mechun8sm In a sulfonic membrane converted to the mixed EDAH+-EDAH;+ form, the unprotonated amine group of EDAH+ behaves like a primary or secondary mono-amine. The most obvious reaction of CO, is therefore (in agreement with Leblanc et al. [4] and Danckwerts et al [ll] ) the formation of carbamic acid zwitterion (EDACO,) in the liquid phase of the swollen membrane following: CO, +2NH2 (CH,),NH,+ EDAH+

NH,+ (CH,),NH,+ EDAH;+

o

Kg

=CEDAH$+

CEDACO~/CCO~

=KfK$/(KdKdK;)

)”

(11)

From the numerical values of the constants, Kg is equal to 1.13~10~ I-mol-’ at 18°C. Considering the reaction of COZ in an EDA solution partially neutralized with HCl, a situation that may be extended to the swelling liquid in the sulfonic membrane, computation of the equilibrium distribution of the different species [ 141 shows that EDAH+, EDAH;+ and EDACOz are highly preponderant in the systern for CO, pressures up to 1 atm.

(R.9)

+NH,+ (CH2)2NHCOOEDACOz

co2

high

(CEDAH+

(32

cation-exchange Membrane

pressure side

CO2

+

EDAH

zEDAH+ ++

pressure side

W

+ EDACO2

!

[CO21 -

low

I

[EDAH:+]

-

-

kEDAH+l

[EDACO21

-

[CO21 __j

+

[CO21 I

EDAH;+ 63

CO2

+

2EDAH+

Fig 2 Schematic dmgram of the CO, faclhtated transport mechanism through a cation exchange membrane inserted between two CO,-N2 gas mixtures

56

The liquid phase is found to be always weakly basic or weakly acid so that the rate of formation of carbonate, by (R.6) and/or (R.8), is finally negligible as suggested by Danckwerts and Sharma for the COz-amine systems [ 111. Reaction (R.9) is therefore considered as the preponderant step in the CO, facilitated transport mechanism through an EDAH+EDAH;+ sulfonic membrane. Figure 2 represents schematically this mechanism which involves (i) the formation of the zwitterion carbamic complex (EDACO,) on the high CO, pressure side of the membrane; (ii) the diffusion of the free permeate and the parallel diffusion of the complex towards the low COz pressure side, coupled to the interdiffusion of the two counter-ions EDAH+ (the carrier) and EDAHif+ ; (iii) the complex dissociation on the low pressure side. Only the gaseous COz can enter and leave the membrane and a net flux of CO, is produced following the permeate pressure gradient. Assuming fast reactions, so that the ratio of reaction time to diffusion time is low, this transport system can be described by a reaction equilibrium model. The value of the formation constant (Kg ) of the permeate-carrier complex EDACO, is particularly favourable to a facilitated transport process which needs a complex of intermediate stability [ 71.

D Langevwz et al /J

Membrane Scr 82 (1993) 51-63

number of complexed COz molecules per ionexchange site: n* = nz = q/2 corresponds to the of the carrier, N&An+ = saturation =q-2n* is the fraction of the mInAn+lmZ ionic sites balanced by EDAH+, N&-,AH~+=2 rngDAH2+ I rnz = 1 - q+ 2n* is the fraction of the ionic &es balanced by EDAH;+. The COz mola1 activity cco, is proportional to the pressure pcoz (according to Table 1, acOz= ~cozpcoz, where acoz is the molal solubility coefficient of CO2 in water). The overall molality of the carrier (EDAH+ and its derivatives) in the membrane is rn: = mgDAH++ rngDAHg+ + m&AC02 and the overall CO, (free and complexed) molality is defined by rng = m&AC02 + mEo2. The membrane molality mEOz 1s deduced from the activity by (cf. Table 1) where Acoz is a Go2 =&0zaC02 molal distribution coefficient. An apparent equilibrium constant K& can be defined in the membrane for reaction (R.9) according to eqns. (3) and (4): KG = mhCo2 &bU-I~+/

bCOz(mgDAH+

J21

(12)

This constant can be related to the stoichiometric constant Ki (cf. eqn. 11) by: (13) wrth K,=~,DAC,~EDAH~+/[~~O~(~EDAH+)I~

Modeling

Definrtuxzs The membrane carrier content is characterized by the fraction q of the ion-exchange sites initially occupied by EDAH+ counter-ions; considering reaction (R.9) only EDAH+ can react with COz, however EDAH:+ (initial fraction 1- q) participates in the equilibrium. At equilibrium n* = m&acoJm~ defines the

=

Ki (assuming m, N c, in solution). A EDACOzis the molal distribution coefficient of the neutral complex EDAC02 and JC~~~~

is the molal selectivity constant m the EDAH+EDAH;+ ion exchange.

Effect of the membrane carrw content From the definitions above K& can be rewritten as:

K&=n*(l-q+2n*)/[2aco,(q-2n*)2]

(14)

D Langevtn et al /J

Membrane Scz 82 (1993) 51-63

A=A

-3

-2

-1

AsA"

0

1

2

[Al

3

Fig 3 Eqmhbnum between COz gaseous phase and carrier contammg membrane Number n* of complexed COz molecules per ion-exchange site from eqn (14) as a function of the parameter A (see text) for different tamer contents 1 (0 25,0 5, 0 75 and 1) A 1s defined such that the l/2 saturation points of the different curves are on the same vertrcal A=0 For transport, the vertical lines A =A’ and A =A” correspond to upstream (p& ) and downstream (pEo,) CO2 actrvrtles and define upstream n*’ and downstream numbers n*” for each value of q

Figure 3 shows the number n* calculated (with the simplifying assumption: K& N KQ) for different carrier contents q as a function of the COB activity represented by the quantity A+=loga,o,+(logK;fb). The origin shift (log K;lb ) = log [ 4 K&q/ (2 - q) ] represents a conditional equilibrium constant depending on g and defined such that A = 0 at half saturation of the carrier (when n*=n,*/2=~/4) [7]. When the membrane is placed between two gas mixtures with different CO, partial pressures (p&o2 and pEo, ), assuming that the interfaces are in equilibrium with the gaseous phases (i.e. disregarding gaseous boundary &ffusion layers), a transmembrane flux of EDACO, arises from the difference between the numbers n* at the upstream (n*' ) and the downstream (n* u ) interfaces. For a given ratio P~o2lP~o29 the difference (n*’ - n*” ) and therefore the flux are highly depend on the carrier content q and on the mean pressure. This is shown in Fig. 3 where A’ and AN correspond

to

upstream

downstream phases lo&z& /&oz) = log(p~oz/p~o~ ), from the definition of A].

[AA=A’-A”

and

=

Relatum between the fluxes In transport conditions, the reaction equilibrium model interrelate the concentrations of the involved species through the equilibrium constant K& in each point of the membrane. In the steady state, assuming constant individual diffusion coefficients, relations between the fluxes of the different species are derived from the Nernst-Planck equation: J,= -o:[dc:/dx+z,c:(F/RT)d~/dx]

(15)

with i=COz, EDAC02, EDAH+ and EDAH;+ and where J is the flux density, c* the molar concentration in the membrane, x the distance measured perpendicularly to the membrane, z the electrical charge, F Faraday’s constant, R

58

D Langemn et al / J Membrane Set 82 (1993) 51-63

the gas constant, T the absolute temperature and $ the electric potential. This equation involving molar concentrations c: is easily deduced from molalities (c: =p*m:, see note of Table 1) and can be rewritten as: -z,(F/RT)d@/dx=d(ln

1 +D$o&oz 8=1/[

D*

1

EDACO&DACOz

1

4 'D~DAR+c~DAH+'D~AH~+c~DA~+

>I

c:)d.r+J~/D:c: (16)

Applying to the four species and using linear combination this equation leads to the first relation:

Concentratwz profiles The overall flux JR can be related to the overall CO, concentration cg by Fick’s first law:

JR = - D:dc:/dx

(29)

where DE is an x dependent diffusion coefficient. Equation (19) and (CA =c&. +ci!&& we: d In [( d[ln(a

-J,/D*,=dcB/dx=dc~,,/dx+dc~,,,,/~ K&)]/dx=O

(17)

) from the definition of the with CX=l/(p*Acoz constant K& . The overall flux of CO, (free and complexed), independant of X, is defined by: JR=JCO~+JEDACO~

Jcon= U-PP)JR

and therefore, applying Fick’s law to CO2 and EDAC02 diffusion:

JRDA=Jco,/DEo,+ JEDACOZ/D;DACOZ Equations (19) and (22) lead to:

(19)

and finally to the expression of the variable diffusion coefficient: DZ=Di?o$i+i~Aco~

/[(~-B)DBDAco~+BDEo~I (23)

For a known JR and for a given pcoz , n*, rn: , c: and cg are calculated from eqn. (14), /? and

J, from eqn. (19) and eqn. (23) gives Dg .To compute the concentration and flux profiles, constant increments Apcoz were related to variations AX of the distance across the membrane using eqn. (20) :

J R= -DT,dcg/dx-D;Acg/Ax with:

(22)

(18)

Considering that the electric current is nil across the membrane (JEDm + + ~JED~;+ = 0) and that the overall carrier concentration c: is independent of x (dc:/dx= 0 so that eqns. Jt= &DAH+ +&DAH~+ +JEDAco~=~), (17) and (18) yield a relation between the individual fluxes and the constant JR:

J EDACOz 'PJR J EDAH+ = -2pJl3 J EDAH;+=/%

(21)

(24)

D Langemn et al /J

59

Membrane SC&82 (1993) 51-63

For example, starting the pressure incrementation frompco, =pboz at the upstream interface (le= 0 ) , the calculation is stopped when the downstream interface is reached (x = 1) and the downstream pressure p go2 is obtained. Experimental procedure

Membrane preparation The ion-exchange membrane samples (Permion, sulfonated styrene-divinylbenzene in a fluorinated matrix) first conditioned by 3 or 4 acid-base cycles (NaOH 1 M-HCl 1 M), were converted to the H+ (or Na+ ) form by an excess of HCl (or NaCl+ NaOH) and washed in pure water. The Na+ form was used as a nonreactive membrane reference. Membranes in H+ form dipped in 0.1, 0.01 and 0.001 mol-I-’ neutral EDA solutions were converted into the mixed EDAH+/EDAHg+ form yielding fl fractions of 0.94,0.67 and 0.28 according to Fig. 1. hydrolysis (2 In order to prevent EDAH+oEDAHg+ + EDA) after treatment, the membranes (except some samples) were not washed but quickly blotted with filter paper. Swelling (0.47 g H,O/g swollen membrane), ion-exchange capacity (2.2 meq/g dry membrane) and thickness (ZzO.01 cm) were determined using classical methods [ 10,141.

Flux measurements (Ftg. 4) The membrane (4.5 cm in diameter, effective area At=6.6 cm2) was positioned on a stainless steel porous support and inserted between the two compartments of a permeation cell. The upstream compartment (I) was supplied (flow ratef’, typically 0.5 cm3-set-l) with a gaseous mixture (100,49.9,10 and 4.1% CO2 in N2, total pressure: 1 atm) containing CO, at the inlet partial pressure (p&,z)‘n; the downstream compartment (II) was supplied (flow rate f”, typically 0.042 to 0.33 cm3-set-l) with

Fig 4 Diagram of the expenmental setup for CO2 transport measurements ( 1) feed gas mixture, (2) sweepmg gas, (3) carrier gas for gas chromatography, (4) permeation cell, (5) gas chromatograph, (6) pressure regulator, (7) needle valve, (8) humidifier, (9) flow meter, (10) temperature sensor, (11) fan, (12) regulated heatmg, (13) multlway valve

pure N2. Feed and sweeping gases were humidified in order to maintain hydration of the membrane. The composition of the outlet feed gas and of the permeate was periodically analysed using a calibrated thermal conductivity gas chromatograph and the outlet partial pressure (pboz)oUtand (pijoz)out were determined. The measurements were made in a constant temperature environment (29’ C ). The experimental steady-state flux of CO2 is given by:

JR= (P;02)o”tfn/(SRT)

(25)

where (p~oP)o”t/RT has the dimension of a concentration ( mmol-cm-3) and JR is in mmolcm-2-see- ‘. The statistically estimated error on the flux is 5%. The permeability coefficient is calculated from the flux by: Pcoz=

J~~/[b-'b,)

out- (pgoJy

(26)

assuming that the porous support of the membrane has a negligible resistance to the gas diffusion and disregarding the diffusion boundary layers. Results and discussion The experimental results are shown in Fig. 5 where JR vs. (~$0,) Outis plotted. Measure-

D Langevanet al / J Membrane Scr 82 (1993) 51-63

60

JR -hoA “- (P&z)““tlI~

(pCO:)ou’

with Pcoz =p*c~~o~D& DEoz, obtained from the slope of the linear fit of the flux data, has a value of 5.6 x 10m6cm2set-‘. EDAH+ in the membrane enhances the flux which becomes non-linear. For a given carrier content, the flux increases with (J&~)““~ at low pressure, then tends to be linear and parallel to the Na+ membrane flux for the highest pressures. These results agree well with the facilitated transport concept which predicts the highest permeabilities for the lower permeate concentrations and a saturation effect of the carrier for the highest concentrations. The facilitation factor F, which is the permeability ratio PC02/PC02~Ns+~,is a decreasing function of (p~02)o”t and an increasing function of the carrier content q. Some experimental values of JR and F are presented in Table 2 together with those of Leblanc et al. [4] and Way et al. [ 51 for comparison. For comparable experimental conditions the facilitation factors are quite similar whereas the fluxes and permeabilities are markedly higher in this work. This may be attributed to the higher mobllities

100

50

0

km

(27)

Hg)

Fig 5 COx flux Ja vs. upstream CO2 partial pressure (p&J” Theoretical curves calculated from the model usmg values of Table 3 Expenmental results (A ) Na+ membrane, (m) washedmembrane, q=O 14, (0) q=O 28, (A) q=O67, (V) q=O94 ments were made with non-reactive membranes (Na+ form) and with carrier-containing membranes (EDAH+-EDAH;+ form; ~~0.28,0.67 and 0.94) ( a washed membrane with unknown ?,Iwas also used). The Na+ membrane flux is a linear function of (P~ozPut, which denotes a constant permeability coefficient Pcoz . With consideration of the permeation flux: TABLE 2 Experrmental flux and facrlitatlon factor data

?

upstream out @6oS ) (cmHg)

JR x 10’

Pco, x log

F

Remark

(mmol-cm-2-sec-1)

(mmol-cm-*-set-‘-cmHg-‘)

0 94

3 05 756

74 34

29 6 45

24 44

This work

0 14

3 05 75 6

30 15

10 4 19

10 2

Washed membrane From Leblanc et

1

1

22

49

25 4

186

749

95

14

11

0 76 76

05 28

13 7 07

26 7 14

al 141 From Way et al [51

D Langevzn et al /J Membrane So 82 (1993) 51-63

61

TABLE 3 Parameter values used m the model computation Membrane thickness” Swelhng parametef Ionic sites molahtp

I=0 01 cm p*=O 474 (g H,0)/(cm3 rn: =2 48 meq/(gH*O)

molal solubllity coef b

aEo,=39

Eqmhbrmm constant c

K%-l8K,=18~1

Intramembranar apparent diffusion coefficients Permeantd

swollen membrane)

lo-*mmol/(gH,O)/(cmHg) 13 lo3 (gH,O)/mol

Protonated carrieP

D& = 5 6 lo-’ cm2-sec-1 D&,,+ = 17 lo-’ cm’-set-1 D&,-+ = 0 8 10m6 cm2-set-’

Permeant-tamer

Go,,col = 125 low6 cm2-set-’

earner” complex’

Membrane tamer content!

q=O 14-O 28-O 67-O 94

“Expenmental, gravimetnc and ac&metic methods ( zk1% ) bFrom literature [ 131 “Adjustment form literature, see eqn ( 11) dFrom Na+ form membrane flux measurements ( k 5% ) “Eshmate from membrane conductlvlty measurements ( f 10%) applymg Nernst-Emstem

relation to the electnc mob&y

1101 ‘Ar&netic mean of Ohm+ pE&mate from [8] andeqns

and D&m+ (1) to (4)

4/

‘; VI

3

.H

J z2 5 n 0 -1 x 2 -1

//

/

/ p

/'

/'

/'

/'

/'

/'

0'

/'

/'

1

01 0

/'

05

(eta)

1

Fig. 6 CO2 flux JR vs. the membrane earner content, calculated from the model Dotted curve: EDAH+ -Na+ form membrane, contmuous curve EDAH+-EDAH:+ form membrane ( n ) Expernnental results

of the species involved in the more water-swollen membrane we used. Measurements of N, fluxes allow estimation

of selectivity for COz over N2 defined as the ratio of the permeability coefficients Pco2/PN2. PN2 was found to be constant and equal to 5.6X lo-l1 mmol-cm-2-sec-1-cmHg-’ so that the selectivity ratio reaches 524 for (J&,,)““~ N 3.05 cmHg at q N 0.94. Figure 5 also shows the curves calculated from the theory using parametric values collected from Table 3. A good fitting of all the experimental data by the model is obtained when K,‘, is adjusted to 1.8 Kg. This should indicate an influence of the polymeric environment on the EDA-CO2 equilibrium (i.e. IC;and 1, # 1 in eqn. 13). The need to adjust Kq accounts also for the uncertainty about the value of KJ (mainly due to the discrepancy between the authors about Kf and Kd [8,15,16]) and for the experimental error on JR and on the parameters of Table 3. For the washed membrane, a good agreement between calculated and experimental fluxes is found for q = 0.14 corresponding to an equilib-

D Langevtn et al /J Membrane Set 8.2(1993) 51-63

62

rium EDA solution concentration of 2.6 x 10-4 mol-1-l in Fig. 1. The influence of the membrane carrier content on the transport rate is illustrated in Fig. 6 showmg JR vs. q values calculated for a fixed upstream (p&oz)out. The dotted curve corresponds to a mixed EDAH+-Na+ membrane; in this case, described by Way et al. [5], the flux ts proportional to q because Na+ does not participate in the EDAH+-CO, equilibrium. This is different from the case of mixed EDAH+EDAH;+ membranes (this work, continuous line) where EDAH:+ constitutes a stock of carrier. This induces the non linearity of JR vs. q m agreement with the plot of the experimental data.

Conclusion

Facilitated transport of CO, through a cation-exchange membrane functionalized with a reactive counter-ion has been studied. With a thick membrane, the reaction equilibrium model describes fairly well the observed phenomena. By adjusting just one constant, I& whose experimental value is subject to uncertainties, the agreement is quantitative. With its higher water content the membrane can be assimilated to an immobilized liquid membrane with a concentrated carrier. The neutralization of acid sites by EDA ensures an easy monitoring of the carrier content. The high flux observed is attributed to the high rate of reaction and enhanced mobilities m the swelling liquid. The study of other physical constraints, such as heat effects, being able to modulate or increase the facilitated transport rates and limits remains of interest and is the subject of our present investigations.

List of symbols

A A+ a c

D

F J K K+

quantity representing the COz activity effective area of the membrane (cm2) activity molar concentration (mol-1-l or mmolcmm3) diffusion coefficient (cm2-set-l) Faraday’s constant flow rate of the solutions (cm3-set-l) flux density (mmol-cm-2-sec-‘) equilibrium constant [f( a,,m,) ] stolchlometric equilibrium constant

[f(cz)1

n P R S S

T x

Y z

kinetic rate constant thickness of the membrane (cm) molal concentration (mmol-g-l) fraction of the ionic sites occupied by an ionic specie number of complexed CO, molecules per Ion-exchange site partial pressure universal gas constant neutral species molar solubllity coefficient absolute temperature (K ) distance parameter co-ion electric charge.

Greek

F 9 tl

; P G

parameter defined by eqn. (16) parameter defined by eqn (18) electric potential fraction of the ionic sites imtially occupied by the carrier selectivity coefficient in ion-exchange molal distribution coefficient conversion factor (from molal to molar scale ) (g-cmm3) molal solubility coefficient (mmol-g-lcmHg-l)

D Langewn et al /J

Subscripts hi R S

t

63

Membrane Sea 82 (1993) 51-63

refers to a chemical species (CO,, EDAC02, EDAH+, EDAH;+, H+) refers to the overall permeant, free and bound refers to the saturation of the ionic carrier in nz refers to the overall carrier, free and bound

Superscripts.

6

7

8

9

I N ,

refers to the upstream and downstream interfaces * refers to the membrane I,11 refers to the upstream and downstream compartments in, out refers to inlet and outlet gas mixtures

10

11

12

References P F Scholander, Oxygen transport through hemoglobm solutions, Science, 131 (1960) 585 G Broun, E S&gny, C Tran Mmh and D Thomas, Facilitated transport of CO2 across a membrane bearmg carbonic anhydrase, FEBS Letters, 7 (1970) 223 J D Way, R D Noble, T M Flynn and ED Sloan, Liquid membrane transport A survey, J Membrane Scl ,12 (1982) 239 0 H Leblanc, W J Ward, S L Matson and S G Klmura, Faclhtated transport m ion-exchange membranes, J Membrane Scl ,6 (1980) 339 J D Way, R D Noble, D L Reed, J M Gmley and LA Jarr, Fac&ated transport of CO2 m ion exchange membranes, AIChE J ,33 (1987) 480

13

14

15

16

D Langevm, M M&ayer, M LabbB, B Pollet, M Hankaom, E SBl&ny and S Roudesh, Transport-reaction through ion-exchange membranes modeling of hgand transport by a complexmg counter-ion and experiments v&h amme and polyborate ions, Desahnation, 68 (1988) 131 M MBtayer, D Langevm, B El Mahl and M Pmache, FacUated extraction and faclhtated transport of non-lonlc permeants through ion-exchange membranes influence of the stab&y of the permeant/carrler complexes, J Membrane Scl ,61 (1991) 191 A Jensen and R Christensen, Studies on carbamates XI The carbamate of ethylenedlamme, Acta Chem Stand ,9 (1955) 486 M M&ayer, D Langevm, M Hankaom, B Pollet and M LabbB, Reaction m ion-exchangers Apparent stability constants of complexes and salting-m (-out) effects, Reactive Polymers, 7 (1988) 111 F Helffench, Ion Exchange, McGraw-Hdl book Company, Inc , New York, NY, 1962, Chapt 4 and 7, pp 72-84, pp 147-156 P V Danckwerts and M M Sharma, The absorption of carbon dioxide mto solutions of alkalis and ammes, The Chemical Eng J , Ott (1966) 244 H Hlklta, S Asal, H Hlshtkawa and M Honda, The kinetics of reactions of carbon dloxlde with monolsopropanolamme, dlglycolamme and ethylenedmmme by a rapid mlxmg method, The Chemical Eng J , 14 (1977) 27 S Glasstone, Textbook of Physical Chemistry, 2nd edn , D Van Nostrand Company, Inc , New York, NY, 1958, Chap 10, pp 695 M Pmoche, Transport faclhti dans les membranes 6changeuses d’lons apphcatlon 21l’extractlon du COz d’un m&nge gazeux par le transporteur ethyliinedlamme monoproton&, Thesis, Rouen, 1989 R A Robinson and R H Stokes, Electolyte Solutions, Butterworth, Ed, P&man Press, London, 2nd edn , 1959 D H Everett and B R W Pmsent, The dlssoclatlon constant of ethylene dlammomum and hexamethylene dlammonmm ions from 0” to 6O”C, Proc Roy Sot , A215 (1952) 416