Hybrid liquid membrane (HLM) system in separation technologies

journalof MEMBRANE SCIENCE

ELSEVIER

Journal of Membrane Science 111 (1996) 259-272

Hybrid liquid membrane (HLM) system in separation technologies V.S. Kislik *, A.M. Eyal Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Received 23 January 1995; accepted 25 September 1995

Abstract A novel liquid membrane system, denoted hybrid liquid membrane (HLM), was developed for the separation of solutes (metal ions, acids, etc.). It utilizes a solution of an extracting reagent (carrier solution), flowing between membranes. The membranes, which separate the carrier solution from feed and receiving (strip) solutions, enable the transport of solutes, but block the transfer of the carrier to the feed or to the strip. Blocking the carrier is achieved through membranes hydrophilic/hydrophobic or ion exchange properties, or through their retention abilities, due to pore size. The HLM-facilitated transport mechanisms have been schematically described and theoretical models have been developed to predict the rate of transport in the different separation processes. The model was tested on titanium(IV) transport from hydrochloric acid solutions. Titanium was removed by countertransport from low acidic (pH = 0.65) solutions or by co-transport from high acidic (7 mol/kg HC1) solutions, using DEHPA in benzene as a liquid carrier (membrane) solution. The efficiency of titanium transfer was studied as a function of feed, carrier and strip flow rate. Mass transfer parameters obtained were compared with model calculated data. Module optimization characteristics are discussed.

Keywords: Liquid membrane; Model equations; Titanium(IV) transport; DEHPA carrier

1. I n t r o d u c t i o n The concept of HLM transport is quite simple: a solution of an extracting reagent (carrier phase, E), flows between two membranes, which separate the carrier phase from the feed (F) and receiving (R) phases (see Figs. 1 and 2). A specific solute or solutes are extracted from feed phase, as a result of the thermodynamic conditions at the F / E interface, and are simultaneously stripped by the receiving phase due to the different thermodynamic conditions

*Corresponding author,

at the E / R interface. Similar systems have been described by other research groups such as Sirkar [1-4], Boyadzhiev [5-9], Teramoto [10-14], Kedem [15,16], Eyal [17,18] and Schlosser [19,20]. There are two general approaches to modeling liquid membrane transport mechanisms: the differential and the integral approach. According to the differential approach [6,21] all phenomena taking place in the feed or in the strip phase, such as diffusion, chemical reactions, etc., are totally ignored. The measured transfer fluxes are dependent on phenomena occurring in the bulk or at the surface of the membrane only. The integral approach [ 1 -

0376-7388/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 7 6 - 7 3 8 8 ( 9 5 ) 0 0 2 5 8 - 8

260

c o

nc c

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996) 259-272 FIE E~ c,m,,=~ =~. ~ , =E ~ .~_ c,~=,~, F ~ rane R "~"~t~_~.~_.~t. " I L " I ~ ",' s ' ~ "h.' t., ~ s ~ , ~ - - l- - J I- " I - - I ~ i II ~ ~ ' ~ ' ~- - 'I -- I' I I II 'it,~iF. t ~=~'x~~l I i

at i o

~ trot,

I

Dl,t . . . .

n

Fig. 1. Schematic concentration profile of each Ti(IV) chemical species, transported through the HLM system with hydrophobic membranes. Layers controlling the permeation rate are: hfe, feedside aqueous boundary layer; hmf, feed-side microporous membrane, immobilizedby membrane solution; her, feed-sideboundary layer of the membrane solution; her, strip-side boundary layer of the membrane solution; hmr, strip-side microporous membrane, immobilized by membrane solution; hre, strip-side aqueous boundary layer.

However, we think that (a) the assumption of the steady state mass transfer through the bulk membrane phase is oversimplified and (b) the assumption of equality of solute distribution coefficients of e xtraction m O Sandsystems. t back s eextraction, p a r isa incorrect t i o for n To develop our three-phase, HLM system model, we used the transport model simplification analysis, developed by Hu et ai. [22] for the two-phase system. Titanium, as an example for the HLM transport model verification, was chosen because of the extensive experimental data available on liquid-liquid extraction and membrane separation. [23-26]. The following model, however, is universal for any s o lute which has to be transported. T h e model is far from being exact, but it is relatively simple and useful.

2. M a s s t r a n s f e r m e c h a n i s m s

14,19,20] considers the three liquid phase system to be a closed ~ multiphase system and, therefore, takes into consideration the processes and changes in all three liquids. Most models are very sophisticated because they assume many possible types of control, nonlinear equilibria, phase interactions, etc. and need numerical methods of verification. Some are oversimplified and do not describe real transport processes. We use the approach of many researchers, formulated in Ref. [1]: 1" The °verall mass transfer rate can be c°ntr°lled by any of the diffusion resistances in the three liquid phases. 2. The aqueous and organic film resistances may be combined with membrane pore diffusion resistance in one-dimensional series of diffusion resis-

and kinetics

2.1. Transport model In general, the mass transfer rate (or flux) of any solute passing through the barrier (membrane) is a function of distance and time: J = f(x,t). At first, let us consider the flux as a function of distance.

ComJxtrtment

~

c "° ,

~.

F/E

Comptrmmat

~ r

t i

E/R

C.c~paranm~t

,,~E ~ R '~ I,__~ s~.,~ L h,,_[ ~_[.. h,,. Its~,g ~ i - ~ . . . . lE

~

I t"Jf,~l['~]' ]

I

,.

I

~o

I

I

',"1

t

~ ii__l_

lMl, i

i

i

I____.~ i "A closed system is one with boundaries across it, through which no matter may pass, either in or out, but one in which other changes may occur, including expansion, contraction, internal diffusion, chemical reaction, heating and cooling. An open system is one which undergo all the changes allowed for a closed system and in addition it can lose and gain matter across its boundaries" [27].

Distance H Fig. 2. Schematic concentration profile of each Ti(IV) chemical species, transported through the HLM with hydrophilic or ion-exchange membranes. Layers controlling the permeation rate are the same as those in Fig. 1 except for: hmf, feed-side microporous membrane is immobilized by feed aqueous solution; hm~, strip-side microporous membrane is immobilized by strip aqueous solution.

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996) 259-272

Three liquids, having bulk metal concentration [M] F, [M] E and [M]R, constant volumes VF, VE and VR, respectively, are separated by two membranes with the same working area S. Stirring of bulk liquids is effective in such a way that the aqueous (hee'hre) and the °rganic (hef' her) b°undary layers become sufficiently thin and constant. Concentration profiles in the HLM system with hydrophobic membranes are demonstrated in Fig. 1, while those containing hydrophilic or ion exchange membranes are demonstrated in Fig. 2. Using the concept of the one-dimensional series of diffusion resistances, and regarding the principle of resistance additivity [1-14,19-22], the overall mass transfer coefficients (or permeability coefficients [29,30]) K F on the feed side and K R on the strip side are related to the film mass transfer coefficients:

interface. Efficiency of the separation hinges directly on the distribution of solute in the steady-state layers. Using Giddings' analysis [34] of such a system we obtain: [( ~) ( J0)] h In C / Co - ~ = U-(4) D According to [2-20,28-30,32] the mass transfer coefficient of every layer, k i, is Di k~ = ~

kfekmfkefE F kfekef + kfekmf + kmfkefE F

krekrarker KR= kmrkerE R "t-kmrkre "k kreker

( (1)

(2)

For hydrophilic or ion exchange membranes kfekmfkefEF K F = kfekmf+kfekefEF+kmfkefEF

KR=

krekmrker kmrkerE R -I- krekerE R -b kmrkre

(1') (2')

Individual film mass-transfer coefficients may be determined by the following considerations. According tO postulates of non-equilibrium thermodynamics [31], the general equation that relates the flux, J, of the solute to its concentration, C, and its derivative, is [32]: dC J = UC - D - -

(5)

where D i is the free diffusion coefficient of the solute in the layer and h i is the thickness of the layer [28]. Replacing Eq. (4) with Eq. (5) we obtain

For hydrophobic membranes K F=

(3)

dx where U is the flow rate and D is the sum [33] of all "effective" diffusion coefficients, Referring to the equation of continuity, as x approaches zero, the steady-state zones or layers are formed next to the phase's interface (but not for the bulk phases, where x >> 0). Separation then occurs by differential displacement permeation through the

261

ki=U

[( In

Jss~ [ Ci-----~-)//~Ci_ I

Jss)]}-' U

(6)

where C i is the concentration of the solute in the bulk solution at time of sampling ti; C~_ 1 is the concentration of the solute in the same solution at time of previous sampling t/_ ~. According to Sirkar [28] assumption, diffusion mass transfer rate through a membrane having a solvent-filled pore (hydrophobic), or an aqueoussolution-filled pore (hydrophilic or ion-exchange) may be expressed through the diffusion coefficients of the solute in the respective interface layers: For hydrophobic membranes Def em kmf - -

hmf~.m

Der em kmr - hmrrm

(7)

(8)

For hydrophilic or ion exchange membranes Df~ 15m kmf - - (7') hmf "am DreEm kmr (8') hmrrm were cm is the membrane porosity and rm is the membrane tortuosity.

V.S. Kislik,A.M.Eyal/ Journalof MembraneScience1ll (1996)259-272

262

These expressions are valid when the following assumptions are held: there is unhindered diffusion of the solute (solute dimensions× 102 < pore dimensions); the membrane is symmetric and completely wetted by the designated phase; no two-dimensional effects occur. Applicability of these expressions for charged membranes is doubtful because of hindered diffusion of solute in their pores, but it may be evaluated experimentally. One more serious simplification: we extend the influence of the flow velocities inside the membrane pores. Another way of evaluating mass transfer coefficients through the membranes may be proposed, providing the membranes possess the same properties (diffusion resistance, porosity, tortuosity, etc.), They may, however, be of different thicknesses. It is clear from Eq. (4) that diffusion coefficients (exactly U / D , where U is known) of the solute through the feed-side and strip-side membranes may be evaluated as a slope of the plots:

-In

=f(h~)

(9)

we can derive the transport rate and distribution relation equations for metal permeating species: i a[ixA1

VFI~)=

\

--SKF([M]FVF--[M]EVE)

(11)

V [ O[M]E ] E/ dt } = SKF([M]FVF-- [M]EVE)

- SKR([~I]EV E -- [M]RVR)

(12)

From the overall material balance of the system: Q0 VF VE __ [M]R = V--R" Rv--[M]F-- "R~--7-'[M]E

(13)

where [M]°, [~]o and [M]° are initial concentrations of a metal specie in the feed, membrane and strip phases, respectively; Q0 is the overall initial quantity of the solute in the HLM system. The system described by Eqs. (l 1)-(13) results in an analytical solution under the assumption that the mass transfer coefficients are constant 2 (at flow or stirring rates constant). The following are a complete set of model equations: [M]F = -~ "b Cley't--k C2 ey2t

(14)

F

In

R=/(hmr)

(10)

We can, now, experimentally determine individual mass transfer coefficients of the solute (for example, titanium compound) in every layer and membrane. Thus, overall mass transfer coefficients of the feed ( K c F ) and strip ( K c R ) sides of the HLM system may be calculated according Eqs. (1), (2) or (1'), (2'). After analyzing the concentration profiles in the system as a function of distance, we can consider them as a function of time. Introducing the assumptions as linear concentration gradients, concentration of the metal permeating species are lower then that of the carrier in the membrane phase, and instantaneous interfacial chemical reactions and local reaction equilibria at the interfaces [220,28-32]

;+c'e'''('+ kFSy' / ( kFS ~E

+ C 2 ey2t 1 +

Q0 VF VE [M]R = - - -- [M]F -- [ M ] E - VR ~R VR 2S( K F + K R ) a = /3 = 3S2KFKR S2 3' = KFKR77-,Q ° VF _ Q0 -- 0 3' [ M]°VF + [M]EVE + [M]0RVR fl 3VF 3VF

(15)

(16) (17) (18) (19)

(20)

2 In the real continuous HLM system mass transfer coefficients

K~ and K R may be close to constant at the stabilized conditions of the process (acidity or pH, temperature, flow rates etc.).

263

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996)259-272

a

/a

2

Yl = - ~ + V - 4 - - / 3

(21)

At the membrane solution-strip solution interface, for feed at low acidity (pH region) [TiE 4 • 2H2()] E -t- 2H~

Y2

2

-/3

(22)

- , [TiO]~ + + 4ttLE + H2OR

(27)

at high acidity --0VE C, =

WiC4 ~ [TiO]~ + + 4HL E + 2C1R

Y2 - Y~ (23) Yl [M] ° - ~

These reactions are characterized by equilibrium constants:

- SKF [ M ] E ~ F - [M]°

C2 = -

= [TiL4" 2H20]E[ H a]F

[H]F / 4

[~T]4[Ti " 2H20]F = E F ~ ]

KF/E

Y2 - Yl

(28)

(24) This is a set of model equations to design an HLM system for the transport of solutes. 2.2. Extraction equilibria

(29) or = [TiL4"2HC'] ( HE4IF l KtF/E ' [~--~]4 ~-EF' E[Ti" 2HC1]F

[H]F )4

(29') The transport of titanium(IV) species through HLM can be formally described as a simultaneous combination of diffusion, extraction and stripping operations occurring under non-equilibrium conditions. These systems are very complicated to analyze and therefore, some assumptions are needed for simplification. Extraction kinetics and stripping processes are much faster for most metal ions than their diffusion, and many researchers have adopted "the local extraction equilibrium" of feed-extractant and extractant-strip phases at the membrane interfaces. So, we have to analyze the chemistry of the HLM system at equilibrium conditions (thermodynamics). The chemical reactions responsible for the transport can be schematized [24,25]: at the feed solution-membrane (carrier) solution interface, for feed at low acidity (pH region)

[~--~]4

[TIE4.2HaO]E[H]2 ]

[H]2ER

(25)

[TiO]R[HT]4[CI]2 K'E/R' = [TIE4" 2HCI][H20]

-

[H--L]4[C1]2 ER

(30')

where E F and E R are the distribution coefficients of titanium ions between membrane and aqueous feed, and strip phases, respectively, and the concentration of [H20] is neglected. (EF)/ -~

~

[H] 4 ) I [H]2

(31)

or p r = K ' = KF/EKE/R

at high (> 7 mol/kg) acidity

(30)

or

K=KF/EKE/R

[Ti" 2H20]4F÷ + 4H'LE [TiL 4 • 2H20] E + 4H~

KE/R

[TiO]R[~--~]~[H20]

F

4 2) H]F[C1]R

(31')

[Ti" 2HCI] 4+ + 4HL E [TiE 4 ' 2HEllE + 4H~

(26)

K (or K') is denoted as a Driving force coefficient of the HLM system.

264

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996)259-272

Consider EF

K = KcK d where K c = E-'-Rand K d

buffered acidities, etc.). K c is an "uphill pumping" border of the HLM system.

[H]4

[H]~

(32) 3. Experimental

or

K'cK'o where K'c

K'

=

EF = - - and K~ = [H]~* [ C 1 ] ~ ER

(32') K¢ is denoted as an internal [38] (carrier) driving force coefficient, derived from the extraction distribution ratio between liquid membrane phase and feed, and receiving phases. K d (or K~) is denoted as an external driving force coefficient of the HLM system, These initial parameters are easily accessible experimentally by equilibrium extraction experiments [24]. For example, extraction of titanium(IV) from 0.1 mol/kg Ti(IV) hydrochloric acid solutions at 0.45 mol/kg (pH = 0.65), 2 mol/kg and at 7 mol/kg HC1 by 1 mol/kg DEHPA in benzene, at aq. ph./org, ph. = 5/1, have shown the initial distribution coefficients (for details, see Ref. [24]): EFI = 20 -- 25 the aqueous phase at pH = 0.65, 200 - 220 for the aqueous phase at 7.0 mol/kg HCl. E R = 1 . 5 - 2.0 EF2 =

for the aqueous phase at 2.0 mol/kg HCI. The initial distribution ratios K~ = EF/E R (internal or liquid membrane driving force coefficients) are

According to Eq. (6), individual mass transfer coefficients of titanium(IV) species in the feed, carrier, and strip interracial layers were determined experimentally. Then we explored how well the model we have developed can predict the separation behavior of the HLM system. 3.1. Materials and procedure

Di-(2-ethylhexyl) phosphate (C 16H3504P), technical grade (> 95%) was a product of Sigma, denoted-DEHPA; benzene, analytical grade, was used as diluent. The acids, bases and other chemicals used were of analytical grade. Titanium(IV) containing aqueous solutions were prepared from titanium(IV) tetrachloride, purified, a product of Fisher Scientific Company (UN-1839). Solutions with HCI concentrations of up to 2 m o l / K g were used immediately after preparation to avoid hydrolysis of Ti(IV). Titanium standard solutions were prepared from fixanals (Riedel-de-Haen) and from titanium (99.95%) granules (Aldrich). The module with circulating feed, receiver and carrier solutions at different flow rates is demonstrated in Fig. 3. The feed and receiver compartments were 10 cm 3, (H = 1 cm) and the carrier ~

~ 1

1

1

K'c = 1 0 0 - 1 5 0

Of course, during the transport process in the closed HLM system the distribution ratio will change in accordance with changing feed and strip phase conditions (acidities, titanium concentration, etc.). At K c ~-I(E F = E R) concentration of titanium(IV) in the carrier solution should be [Ti]RE R (the system at equilibrium). Therefore, E R may be denoted as an irreversible coefficient of the HLM for both, closed and open [27] systems (flowing feed, strip streams,

[X,k._.~

~NN,..~

~k,x._.~

Fig. 3. Schematic diagram of the HLM system: F, E and R, compartments of the feed, membrane (carrier) and receiving (strip) solutions, respectively; M, membranes; I and 2, inlet and outlet of the feed, carder and strip solutions. Gaskets, made of Vytone,

were insertedbetweencompartmentsand membranes.

V.S. Kislik, A.M. Eyal / Journal of Merabrane Science 111 (1996) 259-272

compartment was 5 cm 3 ( H = 0.5 era). A microporous hydrophobic polypropylene membrane (Celgard ® 2400; thickness 25 /xm, Celanese Co., USA) was used. The membrane working area was 10 cm 2. Circulation of the liquids (feed, carrier and strip solutions) through the module, and supply reservoirs at different flow rates, was carried out by a Masterflex tubing pump system (from Cole-Parmer Co.) with Norprene tubes. Flow rates varied from 6 to 60 cm3/min. Experiments were conducted at flow velocities, fixed in turn, in two compartments, and varied in the third compartment. For example, testing influence of the feed flow rate, experiments were conducted with various flow velocities only in the feed compartment; but constant and equal (12 cm3/min) in the carrier and receiving compartments during the experiments. Similar experiments were conducted testing the effects of varying the carrier and strip flow rates. To avoid the organic phase breaking through to

265

the feed and strip aqueous phases [1-4,10-14,21,22] a pressure differential was maintained (for details, see Ref. [26]). 0.1 m o l / k g Ti(IV) chloride solutions, at an HCI acidity of 0.45 m o l / k g (pH = 0.65) and 7 mol/kg, were prepared as a feed phase. A 2 mol/kg HCI solution was used as the strip (receiving) phase The carrier solutions used were 1 mol/kg DEHPA in benzene. Solution volumes in all experiments were the same: Vfeed= Vstr~p = 250 cm 3 and Vca~r~er = 50 cm 3. The feed, strip and carrier solutions were sampled periodically and the titanium concentration and acidity (or pH)were measured. The spectrophotometric determination techniques of titanium, DEHPA and benzene in the aqueous solutions (feed and strip) were described previously [24]. The spectrophotometer systems used were Spectronic 2000 (Bauch and Lomb) or Hitachi U2000.

Table 1 Individual and overall mass transfer coefficients obtained using only extraction-back extraction motivated transport equations. Initial titanium(IV) concentration in the feed phase 0.1 m o l / k g No. Feed phase Flow acidity velocity

(mol/kg)

Steady state [Ti] flux from feed ( J F X 10 -8) (cm3/s) ( m o l / c m 2 s)

Steady state [Ti] flux to carrier ( J E X 10 - 8 ) ( m o l / c m 2 s)

Steady state kctf, ) [Ti] flux to strip ( J R X 10 -1°) ( m o l / c m 2 s) ( c m / s )

kc(e0 = kc~er) X 10- 2

kc(re) X 10- 2

DEX 10-2

kc(m0= KcF X kc(mr,)< 10- 3 10- ~

KcR X 10_ 5

(cm/s)

(cm/s)

(cm2/

(cm/s)

(m/s)

(m/s)

11

12

s) 1 2 3 4 5 6 7 8 9 10

1

2

3

4

7.0

0.1 0.2 0.4 0.6 1.0 0.1 0.2 0.4 0.6 1.0

1.91 2.78 3.47 3.99 4.34 3.30 5.21 7.29 8.33 9.55

1.04 2.77 4.86 6.94 7.99 3.82 5.21 7.29 8.33 9.38

0.45 pH ~ 0.65

5

6

7

8

0.69 1.56 6.08 12.15 15.63 0.35 3.13 14.76 38.19 112.85

0.86 1.1 1.8 2.3 3.5 47 56 73 92 130

1.2 2.2 4.2 6.1 10 1.1 2.1 4.0 5.9 9.8

1.5 2.7 4.5 6.3 10 1.3 2.0 3.5 4.9 7.5

9

10

6.2

0.47

0.36

2.8

3.78 4.55 5.78 6.33 7.15 124 168 227 269 326

2.5 3.2 3.7 4.0 4.2 43 68 97 120 150

Notes: 1. Results, represented in columns 3 and 6, were obtained at various feed flow velocities (column 2) and fixed (U = 0.2 cm3/s) carrier and strip solutions flow velocities. Results in columns 4 and 7 were obtained at various carrier solution flow velocities and fixed (U = 0.2 c m a / s ) feed and strip solutions flow velocities. Results in columns 5 and 8 were obtained at various strip solution flow velocities and fixed (U = 0.2 c m 3 / s ) feed and carrier solutions flow velocities. 2. Coefficient D E in column 9 is defmed as an "effective" diffusion coefficient because its magnitude is far from the real diffusion coefficient of titanium complexes in liquids, which resulted from some assumptions (see text). Eq. (6) at U---, 0 becomes undefined, however, for the calculation of mass-transfer coefficients of solutes (for example, titanium species) at visible flow velocities, this parameter (coefficien0 is quite applicable.

266

V.S. Kislik, A.M. Eyal /Journal of Membrane Science 111 (1996) 259-272

Titanium fluxes from the feed through the carrier to the strip solutions were calculated using relations, described elsewhere [26]. Individual mass transfer coefficients at one-dimensionally facilitated titanium transport were determined:

species in the feed carrier and strip solutions and were evaluated by extrapolating the plots of t~ = f ( U ) to U ~ 0.

4. Results and discussion

kc(fe)i=UFj(-ln[([Ti]F-JSsl '

Thec°rrelati°nfact°rbetween[Ti]iandJss/Uiin

UFj ]

-Jss I U ]F,], J/

(

/ [Ti]F(i- I) -J] ( for feed layer)

(33)

1

-~kc(eo,(or kc,er),) = UEj +In / ([Ti]E(,_,

k¢,fe)' = UF~{-- ln([TllF, . )/([TqF,_,,)} . -1

[ T i ] e,-

kc(fe), =

)])

(33')

7 kcCef)~(Orkccer)') = UEj{+_In([Ti]E,)/([Ti]E,,_,,)] } -I

(34')

URj{ln([Ti]R,)/([Ti]Rv_ 1~)} -I

(35')

(34)

where "plus" (positive) is at increasing concentrations vs. time and "minus" (negative) is at decreasing ones

kc~r~)' { [( ass] = U% In [Ti]R,URj ] -1 / [Ti]R,_,

I" t rtTijF,~_~,I/~,tTijF, 1 atr 1 ~ H-' 1 UFAIn,

1

UE,JSs

(for carrier layers)

(

Eqs. (33)-(35) has been checked in the range U = 0.1-1.0 cm3/s. Results showed that [Ti] > Jss/U: in the feed solutions, more than 4 orders; in the carrier solutions, about 3 orders; in the strip solutions, more than 1.5 orders. It means that the JsJU ratio may be excluded from Eqs. (33)-(35). We, therefore, obtain:

Jss )]} U%

(for stfip layer) (35) where UvJ, U E) , U RJ are j-flow velocities, JF ~, JEss,JR,are fluxes at steady state, [Ti]F,, [Ti]E,, [TieR are concentrations of titanium(IV) species, sampled at time i, in the feed, carrier and strip solutions, respectively. Mass transfer coefficients of titanium species through the membrane were calculated, using Eqs. (7) and (8). D E represents the "effective" diffusion coefficients (see note 2 of Table 1) of the titanium

kc(re)i ~-

These equations are the same 3 as those used by other researchers [1-20]. Individual mass transfer coefficients, represented in Table 1, were calculated using Eqs. (33')-(35'). Concentration profiles of titanium(IV) species in the feed, carrier, and strip solutions were calculated using model equations. Comparison of the experimental and the simulated data shows that: -Diffusion of titanium(IV) species through the feed aqueous boundary layer does not control the transport rate. Thus, variations of the feed flow-rate have little effect on the titanium transport performance. -The magnitudes of individual titanium masstransfer coefficients are similar at carrier or strip

3 Referenced authors obtained Eqs. (3Y)-(35') by considering

the basic Stokes-Einsteinequation [28,35-37]. We obtainedthem as a particular case from Eq. (6), based on the kinetics of

irreversibleprocesses(non-equilibrium thermodynamics).

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996)259-272

flow rates variations. Resistance to diffusion in the carrier solution layers and membrane pores, is not a rate controlling step, since the overall mass-transfer coefficients on the strip side of the HLM are two orders less than that on the feed side. Thus, rate-controlling steps could act as resistance of the strip solution layer, or the interfacial back-extraction reaction rate. -Dependence of titanium transport rate to the strip on strip-flow rate is much stronger at low acidity feed than at high acidity feed. Thus, we can conclude that the interfacial back-extraction reaction rate is a rate-controlling step of titanium transport in the HLM system, - A t high acidity feed solutions, discrepancies between experimentally obtained and theoretically calculated data for titanium concentration in the strip phase, are 15-30 times or 15-230 times at feed flow or strip flow rate variations, respectively, - A t low acidity feed solutions the discrepancies are about 4.5 times at feed flow rate variations (independent of it), or 1-112 times at strip flow rate variations, These differences between the experimental and the simulated data have the following explanation, According to the model, mass transfer of titanium from the feed through the carrier to the strip solu-

267

tions is dependent on the resistances: boundary layer resistances on the feed and strip sides, resistances of the free carrier and titanium-carrier complex through the carrier solution boundary layers, including those in the pores of the membrane, and resistances due to interfacial reactions at the feed-and strip-side interfaces. In the model equations we took into consideration only mass transfer relations, motivated by internal driving force (forward extraction-back extraction distribution ratio, Kc). Mass transfer relations, motivated by external driving force (proton concentration gradients at low acidity feed solutions, and proton and Cl-anion concentration gradients at high acidity feed solutions) between feed and strip phases, indicated by K d coefficient, were not considered. Thus, resistances to the titanium transport, due to diffusion kinetics through the feed and strip boundary layers of protons or protons and Cl-anions, generated at the feed-membrane and strip-membrane interfaces [see Eqs. (25)-(28)], resistance to free carrier molecules diffusion through the boundary layers of the carrier solution and through the membrane pores opposite to titanium direction, were not taken into account. There are two ways to evaluate individual mass transfer coefficients of these processes: 1. by sampling and determining proton and Cl-anion concentrations in the feed and strip phases, and

Table 2 Individual and overall mass-transfer coefficients accounting for coupling effects of the titanium transport (external driving force). Combined overall mass-transfer coefficients No.

1 2 3 4 5 6 7 8 9 10

Feed phase acidity (mol/kg)

Flow velocity (cma/s)

kd(fe) (m/s)

1

2

3

7.0

0.1 0.2 0.4 0.6 1.0 0.1 0.2 0.4 0.6 1.0

0.802 0.798 0.895 0.980 1.10 0.190 0.227 0.295 0.412 0.524

0.45 pH = 0.65

kd(mf+el) = kd(mr+er) (m/s) 4 -

0.60 0.63 0.69 0+76 0.83 0.465 1.12 6.25 60.0 100.0

kd(re) (m/s) 5 0.625 0.647 0.697 0.765 0.835 -0.785 2.69 4.94 6.01 16.73

KdF (m/s) 6 2.38 2.99 3.01 3.38 3.38 0.135 0.189 0.282 0.409 0.521

KdR (m/s) 7 15.2 23.1 70.3 125.0 147.6 1.14 1.09 2.76 5.46 14.33

K F X 10 -2 (m/s) 8 0.90 1.36 1.74 2.14 2.41 1.67 3.18 6.4 11.0 17.0

K R × 10-4 (m/s) 9 3.80 7.40 26.00 50.00 62.00 1.00 7.40 26.80 65.50 215.00

Notes: 1. For an explanation of the results, represented in columns 3, 4 and 5, see note 1 of Table I. 2. The meaning of the negative mass transfer coefficients in columns 4 and 5 is not a real case, but was used for feasibility of calculations [see Eqs. (33')-(35'), (36) and (37)]. We stated that the model calculated concentrations of the solute will be in the numerator and the experimentally obtained ones in the denominator (see text). Therefore, if the magnitude of experimentally obtained concentration prevails the model calculated one, the mass transfer coefficient will be "negative".

10 . 3

10-1

0.0

0

*

~

+

o

.

o

High acidity feed • KdF

~

o

.

o

'

0.4

0

+

'

0.6

o

'. 0 8

Low acidity feed • K~

'o

o

+

•

1.

o

Feed flow rate, U, cm3/sec

'

0.2

o

~

KcF

I~

I~

0.2 0.4 1 '0 016 0.8 F e e d f l o w r a t e , U, c m 3 / s e c

,

+

o

KcF

1.2

1.2

10 2

re)

.~

1 0 " 2'1]

1°"I

1oO

10 1 --~

~

~

m

4

10"3

10 . 2

10-1

100

101

102

== lO"

~

=

~,

0 ¢J

~

. ¢I ~

~

~

~J

0.0

!

•¢t 10" 5 ] ~ 0.0

lO'4.~

~ 1°"3

~

~

-~ lO3

~

, 0.4

+

o

•

, 0.6

+

o

•

, O.S

High acidity feed • KdR o

•

KcR

, 0.4

0 6

,

+

o

, 0.8

1,0

,

+

0

•

o

S t r i p flow rate, U, cm3/sec

0 2

o

•

Low acidity feed • KdR

KR

KR

110

+

o

•

S t r i p flow rate, U, cm3/sec

0 2

'.

+

o

•

KcR

o ,.

+

•

d)

+

+

o

•

+

1.2

12

Fig. 4. The effect of feed or strip flow variationson the overall mass-transfercoefficientsat co- (a and c) and counter-(b and d) transport of titanium species.

,~= 10"~

=,

O

I=

b)

+

+

+

,,~

0.0

10"2o

10 "1

10 0

101

"~1o °

u

¢~

""

o

o

t~

~

~"

~.

~:

"~

269

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996) 259-272

High acidity (7 mol/kg HCL) feed

Low acidity ( pH=0.65 ) fe,e,d

a)., b). :U F = 0.4 cm3/sec; U E = U R = 0.2 cm3/~c

10 +1

a).

10 +I"

lO+C

b).

lo+o

~'~="8"2'10"1' 10 "* . . . . . . . . . . . . .

'~ 10-1' "" " -n - = - ,~ ' - - "-n - -- "="o 10-2-

' = ) 5 " 1 0 +-4 10-10+515-10 +5 Time, sec

10-6 .0

10-6 ~ 0

: t t 5 - 1 0 .+.4 10-10+515"10+5 Time) sec

c),)d). :UF = 0.4 cra~lsec,U F = U R = 0.2 cra~/sec

i0+I .

i0+I -

c).

lO-l-O .

-

,.o ' ' ' ' ' ~ w m ~ I . ~ ' "

.~_ 10-1, ; ' ~ : - . - , ~ - o O E

_=

~_ 10-1. ~ = ~

,a,,,~-

c

.

.

.

o

.

•

--o

O

E 10-2~ ~ °I0-3" ' *-4- - 1 0/

10-2,

.., !

d).

10+0

~'q

@ 10-3' '-4. * ' * ':' 1 0

E lO-5.

~ .O.,=- o . . . - - ~ ~

~. lO-5

10-6

!

,

i 5 - 1 0 +4 10-10+515-10+5 Time, sec

0

10-6

! 0

I

I

5-10+4 1 0 - 1 0 + 5 1 5 . 1 0 + 5 Time, sec

¢),, f). :UR = 0.4 cm~/sec UF = U , ~ 0.2 cm31sec

10+1-

I0 +]

I0

)"

I0 +(

lO-1~,.~

'~ ~o-~ ,o-

-o---o

~ ~o-1 ~

-o

Feed:

o

o

~ lO-2

._o..-o-- ~

ll >-"

1o-~-Ii 1 0 - 6 Ii 0

.o

~-o

~ ,o-5 I

I

I

5"10+4 I0"I0+515"10+5 Time, see

Calculated Expcdm.

.... C_,a..rfie~. •

10_6; i

0

Calculated Experh~.

:

I

i

5 . 1 0 +4 1 0 - 1 0 + 5 1 5 - 1 0 + 5 Time, sec

Srip: ~ " - - C,,alculzte,d 0 F,.xperim.

270

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996) 259-272

free carrier concentration in the carrier solution during experiments with flow rate variations, and 2. by comparing the experimentally obtained titanium concentration profiles with model predicted ones, which were calculated using only mass transfer coefficients, K c. We used the second, simpler way. Individual external mass transfer coefficients, k d, (see Table 2), were evaluated using Eqs. (33')-(35'), where [Ti]v , [Ti]E, and [Ti]R were taken from model calculated data and [Ti]ri_,, [~Fi]Ei_, and [Ti]R,_ ~were

rate-controlling step of titanium transport is the back-extraction reaction rate at the membrane-strip interface. In the case of high acidity feed (co-transport), mass-transfer coefficient values approach a constant when the feed or strip flow rates are above 0.6 cm3/s. Below this border the dependence may be evaluated by the following equations:

experimentally obtained data under the same conditions and sampling time, t~. Overall mass transfer coefficients KdF on the feed side and KdR on the strip side were calculated by the following equations:

In the case of low acidity feed (counter-transport), the dependence is evident in all ranges of flow rates studied and may be evaluated by: K F = - 1.53e -3 + 0.174e -2U~ (42)

K~F = kd(fe) X kd(mf+ef)

KR = -- 4"59e-4 + 2"37e-2V~

(36)

kd(fe) + kd(mf+ef) and KdR = kd(re) X

kd(mr+er)

(37)

kd(re) + kd(rnr+er) The overall mass transfer coefficients of the HLM system [see Eqs. (32) and (32') were calculated by equations: K F = KcF )< KdF

(38)

and K R = KcR )< KdR

(39) Fig. 4 shows the dependence of the titanium transport internal driving force coefficients, K c, external driving force coefficients, K d, and overall mass transfer coefficients, K, on feed flow rate (Fig. 4a and Fig. 4b) or strip flow rate (Fig. 4c and Fig. 4d) variations. It is clearly seen that in most cases the resistivity to titanium transport of protons, and Cl-anions diffusion is much lower than that of titanium species themselves. Ka in the feed aqueous phase layer at low acidity is the only exception. It is evident that in both co-transport (high acidity feed) and counter-transport (low acidity feed) t h e

KF = 6"04e-3 + l'9e-2U~ K R = - 2.17e-4 + 6.9e-3uR

(40) (41)

(43)

Fig. 5 shows examples of concentration profiles of titanium species in the feed carrier and strip solutions, obtained experimentally (dotted curves) and calculated, using model equations and combined overall mass-transfer coefficients (continuous lines). There is a good correlation between experimental and simulated data. Comparing the simulated results with the experimental data, it appears that at higher flow rates, where boundary layers resistance becomes less important, membrane-strip interfacial reaction kinetics dominates as a rate controlling step for titanium transport. It should be mentioned, that in the case of titanium(IV) treatment, the HLM does not result in significant transport rate improvements, in comparison with the HFCLM (hollow-fiber contained liquid membrane) of Sirkar. Membrane fouling may be lessened. However, the HLM has some decisive advantages for many solutes (metals, carboxylic, amino acids, etc.) when diffusion of large organic complexes through the filled membrane pores and carrier solution is more limiting. Model analysis shows that the solute (titanium) concentration enrichment cannot exceed the value of [ T i ] E / E R (titanium concentration in the carrier

Fig. 5. Effect of the feed (a and b), carrier (c and d) or strip (e and f) solutions flow velocity variations on the concentration profiles of titanium(IV) transfer through the HLM. Comparison of the calculated (continuous lines) and experimentally obtained data (dotted curves).

V.S. Kislik, A.M. Eyal / Journal of Membrane Science 111 (1996) 259-272

phase/back extraction distribution coefficient), or [Ti]F E F / E R. Thus, extraction distribution parameters control the enrichment ability of the HLM. Most researchers [1-20] propose the application of processes, based on the steady state of the system, Experimental and model simulation data show much higher mass-transfer rates through the HLM, with titanium concentration in the carrier solution, reaching its maximum. At this stage, both, the internal (extraction-back extraction distribution ratio) and the external (coupling) driving forces, motivate the titanium transport in an optimal way. At a steady state transport, proposed by most researchers, titanium permeation is motivated mostly by an external driving force and the fluxes are about an order lower. A much more effective H L M module, with continuously flowing feed (open system), can be designed if the feed side membrane area S F and the feed flow rate U F enable us to obtain a fixed titanium feed outlet concentration at a contact time, close to that at the maximum on the simulated concentration profile of the carrier solution (see Fig. 5). One more advantage of the HEM system is realized from theoretical simulations. At feed side resistances not controlling the solute transport (as in the case with titanium) the fluxes of the solute to the strip are approaching these in the SLM systems, but without many drawbacks of the latter,

5. Conclusions A theoretical model has been developed for titanium(IV) transport through D E H P A in benzene, as a carrier solution, from the feed to the strip hydrochlotic acid aqueous solutions. There is good correlation between experimental and simulated data. Most parameter variables needed for the HLM module design, may be obtained by performing a number of experiments: feed, carrier, strip-flow variations and extraction distribution data. Optimal utilization of the membrane area is the main objective to be considered when designing the HLM module, At co-transport of titanium(IV) from the high acidity feed solution (7 m o l / k g HC1) to the 2 m o l / k g HCI strip solution or counter-transport from low acidity feed (pH = 0.65) to the same strip the model shows that the interfacial back-extraction reaction

271

rate controls the overall permeation. Increasing strip side membrane area and strip flow rate the total mass transfer rate may be improved considerably. The HLM module should be operated in such a way so as to achieve maximum mass transfer rate, i.e. by increasing strip side interfacial area and decreasing strip boundary layer resistance at a given total (feed and strip) membrane area. That kind of the HLM module may be based on hollow-fiber [3-6] or spiral [12-16] membrane types of modules.

References [l] W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Van Nostrand Reinhold, New York, 1992, p. 764. [2] R. Basu and K.K. Sirkar, Citric acid extraction with microporous hollow fibers, Solv. Exit. Ion Exch., 10(1)(1992) 119. [3] R. Prasad and K.K. Sirkar, Microporous membrane solvent extraction, Sep. Sci. Technol., 22(2/3) (1987) 619. [4] R. Prasad and K.K. Sirkar, Dispersion-free solvent extraction with microporous hollow-fiber modules, AIChE J., 34(2)

(1988) 177. [5] L. Boyadzhiev and Z. Lazarova, Study on creeping film pertraction. Recovery of copper from diluted aqueous solutions, Chem. Eng. Sci., 42(5)(1987) l l31. [6] L. Boyadzhiev, Liquid pertraction or liquid membranes State of the art, Sep. Sci. Technol., 25(3) (1990) 187. [7] L. Boyadzhiev and S. Alexandrova, Dephenolation of phenol-containing waters by rotating film pertraction, Sep. Sci. Technol., 27(10) (1992) 1307. [8] L. Boyadzhiev, Recovery of valuable metals from diluted aqueous solutions by creeping film pertraction, in G.A. Devis (Ed.), Separation Processes in Hydrometallurgy, Part 3, London, 1987, p. 259. [9] z. Lazarova and L. Boyadzhiev, Kinetic aspects of copper(If) transport across liquid membrane containing LIX-860 as a carrier, J. Membrane Sci., 78 (1993) 239. [10] M. Teramoto, H. Matsuyama and T. Yonehara, Selective facilitated transport of benzene accross supported and flowing liquid membranes containing silver nitrate as a carrier, J. Membrane Sci., 50 (1990)269. [l 1] M. Teramoto, Development of a spiral-type flowing liquid membrane module with high stability and its application to the recovery of chromium and zinc; Sep. Sci. Technol., 24(12/13) (1989) 981. [12] M. Teramoto Masaaki, Development of spiral-type supported liquid membrane module for separation and concentration of metal ions, Sep. Sci. Technol., 22(11) (1987) 2175.

[13] H. MatsuyamaHideto, Separation and concentration of heavy metal ions by spiral type flowing liquid membrane module, Water Treatment, 5 (1990) 237. [14] M. Teramoto Masaaki, Selectivity in the extraction of metals by liquid membranes, Proc. ISEC-86, Vol. 1, 1987, p. 545.

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[15] O. Kedem and L. Bromberg, Ion-exchange membranes in extraction processes, J. Membrane Sci., 78 (1993) 255. [16] O. Kedem, A. Eyal, L. Bromberg and E. Bressler, Membrane extraction in the fermentation of carboxylic acids, Israeli Pat. Appl., 101905 (1992). [17] A. Baniel, A. Eyal and E. Bressler, Extraction of electrolytes from aqueous solutions, Israeli Pat. Appl., 101906 (1992). [18] A. Eyal and E. Bressler, Industrial separation of carboxylic and amino acids by liquid membranes: applicability, process considerations, and potential advantages, Biotechnol. Bioeng., 41 (1993) 287. [19] S. Schlosser and E. Kozaczky, Method for separation of solutions by pertraction, Proc. ISEC 86, Vol. III, 1986, p. 935. [20] S. Schlosser, Hollow-fiber pertractor with bulk liquid membrane, J. Membrane Sci., 78 (1993) 293. [21] M.C. Porter, Handbook of Industrial Membrane Technnology, Noyes, USA, 1990, p. 511. [22] S. Hu, Selective removal of metals from wastewater using affinity dialysis; in: Emerging Technologies in Hazardous Waste Management, Am. Chem. Soc., 1990, p. 187. [23] V. Kislik and A. Eyal, Acidity dependence of Ti(IV) extraction: a critical analysis, Solvent Extr. Ion Exch., 11(2) (1993) 259. [24] V. Kislik and A. Eyal, Extraction of titanium(IV) by mixtures of mono- and di-(2-ethylhexyl) phosphoric acid esters, Solvent Extr. Ion Exch., 11(2) (1993) 285. [25] V. Kislik and A. Eyal, Mechanisms of titanium(IV) and some other transition metals extraction by organophosphoric acids, in D.H. Logsdail and M.J. Slater (Eds.), Proc. ASEC'93, Vol. 3, Elsevier Applied Science, 1993, p. 1353.

[26] V. Kislik and A. Eyal, Hybrid liquid membrane based transport of titanium(IV), J. Membrane Sci., 111 (1996) 273. [27] J.C. Giddings, Unified Separation Science, Wiley, 1991, p. 17. [28] W.S.W. Ho and K.K. Sirkar (Eds.), Membrane Handbook, Van Nostrand Reinhold, New York, 1992, pp. 731-763. [29] P. Danesi, Separation of metal species by supported liquid membranes, Sep. Sci. Technol., 19(11/12) (1984/85) 857. [30] P. Danesi and L. Reichley-Yinger, Origin and significance of the deviations from a pseudo first order rate law in the coupled transport of metal species through supported liquid membranes, J. Membrane Sci., 29 (1986) 195. [31] J.C. Giddings, Unified Separation Science, Wiley, 1991, p. 38. [32] J.C. Giddings, Unified Separation Science, Wiley, 1991, pp. 45-48. [33] J.C. Giddings, Unified Separation Science, Wiley, 1991, pp. 94. [34] J.C. Giddings, Unified Separation Science, Wiley, 1991, pp. 112-114. [35] J.C. Giddings, Unified Separation Science, Wiley, 1991, pp. 55-71. [36] L. Bonoli and P.A. Witherspoon, Diffusion of aromatic and cycloparaffin hydrocarbons in water from 2 to 60°C, J. Phys. Chem., 72 (1968) 2532. [37] T.K. Sherwood and J.C. Wei, Ion diffusion in mass transfer between phases, AIChE J., ! (1955) 522. [38] J.C. Giddings, Unified Separation Science, John, 1991, p. 33.