I n d . Eng. Chem. Res. 1990,29, 2093-2100
Superscripts and S u b s c r i p t s d = dissolution order g = crystal growth order 0 = zero time sat = saturation Registry No. 4-CBA, 619-66-9; T P A , 100-21-0; acetic acid, 64-19-7.
Literature Cited Bemis, A. G.; Dindorf, J. A.; Horward, B.; Samans, C. Phtalic Acids and Other Benzene Polycarboxylic Acids. Kirk-Othmer Encyclopedia of Chemical Technology, -. 3rd ed.; Wiley: New York, i g s o ; v ~ i . i i , p 732. Brown. P. M. Crvstal Aeine of Tereohthalic Acid. Ph.D. Dissertation; Po1ytech;lic Unyveisity, Ne; York, 1989. Brown, P. M.; Myerson, A. S. Crystal Aging of Terephthalic Acid. AIChE J . 1989, 35 (lo), 1749. Fujita, Y.; Takeda, A.; Tanaka, T. Behavior of 4-Formyl Benzoic Acid in Terephthalic Acid Synthesis. Gen. Chem. SOC.Diu. Pet. Chem. Present. 1968, 13 (4), 85-87. Gaines, S.; Myerson, A. S. Removal of Impurities Through Crystal Aging. AIChE Symp. Ser. 1982, 78, (No. 215), 42.
2093
Gaines, S.; Myerson, A. S. The Agglomeration and Aging of Terephthalic Acid Particles. Part. Sci. Technol. 1983, 2 , 409. Garside, J. L.; Giblaro, G.; Tauare, N. S. Evaluation of Crystal Growth Kinetics from a Desupersaturation Curve Using Initial Derivatives. Chem. Eng. Sci. 1982, 37, 1625. Hendricks, C. F.; Van Beek, H. C. A,; Heertjes, P. M. The Kinetics of the Autooxidation of Aldehydes in the Presence of Cobalt (11) and Cobalt (111) Acetate in Acetic Acid Solutions. Ind. Eng. Chem. Prod. Res. Deu. 1978, 17 (3), 260-265. Marquering, M. W. Crystal Aging of Terephthalic Acid in 90% Acetic Acid Solution. M.S. Thesis, Polytechnic University, New York, 1989. Myerson, A. S.; Saska, M. Formation of Solvent Inclusions in Terephthalic Acid Crystals. AIChE J . 1984, 30, 865. Robinson, P. A. Partition Coefficients of Terephthalic Acid. Ph.D. Dissertation, University of Strathclyde, Glasgow, Scotland, U.K., 1981. Saska, M.; Myerson, A. S. Polymorphism and Aging in Terephthalic Acid. Cryst. Res. Technol. 1985, 20, 201. Saska, M.; Myerson, A. S.Crystal Aging and Crystal Habit of Terephthalic Acid. AIChE J . 1987, 33, 848.
Received for review January 18, 1990 Accepted June 5, 1990
Facilitated Transport of COSthrough an Immobilized Liquid Membrane of Aqueous Diethanolamine Asim K. Guha, Sudipto Majumdar, and Kamalesh K. Sirkar* Department of Chemistry and Chemical Engineering, Center for Membranes and Separation Technologies, Stevens Institute of Technology, Castle Point, Hoboken, New Jersey 07030
Permeabilities and separation factors for the CO2-N2 system have been experimentally determined for facilitated transport and separation through an immobilized liquid membrane ( E M ) of an aqeuous solution of diethanolamine over a wide range of COz partial pressures. Facilitated COz transport in such a system has been modeled, and the set of coupled diffusion-reaction equations has been numerically solved. Experimentally obtained COZ-N2 separation factors at 230-516 cmHg total pressures compare very well with model predictions over the whole range of COz partial pressures. The effects of membrane thickness and downstream COz partial pressure have been numerically studied. Improved knowledge and estimates of various physicochemical parameters will substantially improve the model capability for predicting species permeability.
Introduction Acid gas treatment for removal of COz and H2S is of major industrial importance. The increased demand for acid gas treating and the increase in the cost of purification by conventional processes suggest a need for energy-efficient and selective gas treating technology (Astarita et al., 1983). Membrane gas separation can become a viable alternative because of its inherent simplicity, ease of control, compact modular nature, and great potential for lower cost and energy efficiency. These attractive features have stimulated significant research in the field of gas separation using polymeric as well as liquid membranes. Further, using the principle of facilitated transport, it is possible to devise highly permselective membranes (Ward, 1972). Facilitated transport of gases is important from physiological as well as engineering considerations. A number of review articles has been published on this subject in recent years (Schultz et al., 1974; Smith et al., 1977; Kimura et al., 1979; Way et al., 1982; Meldon et al., 1982; Matson et al., 1983; Sengupta and Sirkar, 1986; Noble et al., 1988). Quite a few studies have examined C02 transport through an immobilized liquid membrane (ILM) im-
* To whom all correspondence should b e addressed. 0888-5885/90/2629-2093$02.50/0
pregnated with carbonate and bicarbonate solutions (Enns, 1967; Ward and Robb, 1967; Otto and Quinn, 1971; Suchdeo and Schultz, 1974; Donaldson and Quinn, 1975; Kimura and Walmet, 1980; Jung and Ihm, 1984; Bhave and Sirkar, 1986). Apart from the carbonate/bicarbonate carrier, another group of chemicals that can facilitate COz transport is comprised of amines. In particular, aqueous solutions of diethanolamine (DEA) have long been used for COz absorption in a variety of industrial gas-cleaning processes (Astarita et al., 1983). The high COz capacity is generally attributed to the formation of carbamate (Danckwerts, 1979):
C 0 2 + R2NH
& R,NCOO- + H+ k-Am
R2NH + H++ R,NH,+ with the overall reaction being COS+ 2RzNH R,NCOO-
+ R2NHz+
(1) (2)
(3)
Here DEA is represented as RzNH. Reaction 1 is the rate-limiting step for this overall reaction. Thus, at the high-pressure side of the liquid membrane, absorption is enhanced by the forward reaction and the carrier is consumed. Similarly, at the low-pressure side, the carrier is 0 1990 American Chemical Society
2094 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
compared to reaction 1 (Danckwerts and Sharma, 19661, it is assumed to be a t equilibrium. Thus, reaction 1 controls the transport (Donaldson and Nguyen, 1980),and the rate of reaction can be written as (Blanc and Demarais, 1984) kAm
rcoz = kAm[RzNH][COz] - -[R,NCOO-][H+] (4) KAm where the brackets designate the molar concentration and
--__Figure 1. Schematic diagram of facilitated transport of COSthrough an ILM containing aqueous solution of DEA.
released because of the reversible nature of the reaction and diffuses back to the high-pressure side. The flux of reacting species is enhanced compared to that of the nonreacting species because of the combined transport of free COz and the solute-carrier complex as illustrated in Figure 1. The steady-state COz transport through such a system depends on the total carrier concentration, physically dissolved gas concentrations a t the upstream and downstream sides, liquid membrane thickness, the relative magnitudes of diffusion coefficients of solute and solute-carrier complex, and, significantly, the magnitude of reaction rate constants and the degree of reversibility of reaction. The order of reaction with respect to DEA is a matter of continuing debate (Blauhoff et al., 1983; Barth et al., 1984; Savage and Kim, 1985). Donaldson and Nguyen (1980) measured the kinetics of COPreactions with aqueous amine solutions using the 14C02facilitated membrane transport technique and provided evidence that reaction 1 is the rate-controlling step a t low DEA concentration. LeBlanc et al. (1980) and Way et al. (1987) demonstrated COz facilitation in an ion-exchange membrane soaked with ethylenediamine solution; here reaction of the unprotonated amine group with COz to form carbamate, similar to reaction 1,controls the rate and the bound amine carrier acts as a counterion in the ion-exchange membrane. The objective of this work is to develop a quantitative treatment of C02facilitation by an amine-containingliquid membrane. A complete set of equations relating simultaneous diffusion and reaction were proposed and solved numerically to estimate the facilitated flux of COz. The permeabilities of COz and N2 and the separation factors between COz and Nz through an ILM containing 20 w t 7" DEA solution have been measured over a wide range of COz partial pressures. The experimental data were compared with the predicted values obtained from the proposed facilitated transport model. Since the use of such amines in a hollow fiber contained liquid membrane (HFCLM) permeator (Majumdar et ai., 1988) has resulted in a highly efficient COz purification (Guha et al., 1989), our long-term objective is to incorporate such a permeation model into the permeator-governing equations for predicting the separation performance of a HFCLM permeator. Theory The modeling of gas separation through a facilitated transport liquid membrane requires a detailed analysis of diffusional transport coupled with chemical reaction through such a membrane. Consider the case of C 0 2 transport through aqueous DEA solution acting as a liquid membrane with an effective membrane thickness of d as shown in Figure 1. Since reaction 2 is considerably faster
Further, the equilibrium constant of reaction 2 can be written as
A t steady state, local COP balance leads to DlAm d2[C021/dz2 = rC02
(6)
Neglecting the [H+] contribution, the electroneutrality condition a t any point can be written as [RZNCOO-] = [RZNHz+] Now for the free amine
DR,NHdZ[R2NH]/dz2= 2Fco2
(7) (8)
Assuming equal diffusivity of all species other than C 0 2 leads to [RZNH] + [RZNCOO-] + [R,NHZ+] = CT (9) where CT is the initial amine concentration. From eqs 7 and 9, one can get (10) [RJ'JHz+] = (CT - [RzNH])/2 Combining eqs 4,4a, 5, and 10 and expressing the reaction rate in terms of dissolved carbon dioxide and free amine, we get
Equation 6 can now be expressed as
Similarly, for the free amine, d2[R2NH] = 2rCo2= DR~NH dz2
Equations 12 and 13 are to be solved along with the following boundary conditions atz=O [CO,] = HIAmPu d[R,NH]/dz = 0 atz=d d[R,NH]/dz = O [COZ] = H I A m P d where HIAmis Henry's law constant for C 0 2 in aqueous DEA solution; P,, and P d are the upstream and downstream partial pressures of C02 across the liquid membrane. Equations 12 and 13 as well as the boundary conditions are nondimensionalized to
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 The total flux of COP may also be obtained from G O 2 = NCOz
+ N&NCOOd[CO2l
-Dco2 where C1 = [ C O ~ I / ( H , A ~ P J C2 = [R,NHI/C,
[ = z/d
(16) q1 = kAmCTd2/D1Am q2
(17)
= kAmCTd2/ (4KAmKPDlAmHlAmpu) =
q3
(74
kAmHlAmPud2/
DR2NH
= IzAmd2/(ZKAmKPDR2NH)
-&-
--
- DR2NCOO-
d [R2NCOO-] dz
However, from eqs 7 and 10, d[R,NCOO-] = _ -1 d[R,NH] dz 2 dz In the context of the standard assumption of equal diffusivity of all species other than C02, we get
(18) (19) (20)
At steady state, integrating across the film thickness gives
Equations 14 and 15 are to be solved along with the following boundary conditions [=O C1 = 1 dC2/d[ = 0 (21a)
-
f=1*
C2
= Pd/Pu
dC,/d[ = 0 (21b)
No exact closed form of the analytical solution to this nonlinear boundary value problem is available. Both semianalytical and numerical approaches have been used to solve such a system of equations (Jain and Schultz, 1982). The semianalytical methods include matched asymptotic expansions (Goddard et al., 1970; Kruezer and Hoofd, 1970; Smith et al., 1973),regular perturbation method (Suchdeo and Schultz, 1974), and other limiting conditions imposed on the differential equations (Friedlander and Keller, 1965; Otto and Quinn, 1971; Donaldson and Quinn, 1975; Smith and Quinn, 1979; Hoofd and Kruezer, 1981). The numerical methods involve the quasilinearization technique (Kutchai et al., 1970; Suchdeo and Schultz, 1974), a finite difference technique with nonuniform mesh size (Nedelman and Rubinow, 1981), and a technique based on the Galerkin method (Ward, 1970). More recently Jain and Schultz (1982) solved a similar problem numerically by a technique based on orthogonal collocation on finite elements introduced by Carey and Finlayson (1975). However, the solution procedure is quite complex. A simpler numerical solution procedure was adopted here. Complete numerical solution of the facilitated transport equations involved the following steps. A t first, the two second-order differential equations were converted into four first-order ordinary differential equations. Then, the system of equations was solved by using the IMSL routine BVPFD. The subroutine BVPFD is based on the PASVAS program (Pereyra, 1978), a variable-order, variable-stepsize finite difference method. However, to use the routine successfully, one had to supply initial estimates for each of the dependent variables at the selected grid points along the domain of the independent variable. In this particular case, the initial guess was generated by assuming that all the reactions were at equilibrium. Once the initial guesses were generated for a l l the variables, the problem WBS solved by using the BVPFD routine. From the numerical solution, the total flux of C02 through the liquid membrane is obtained as
Ln
total flux = No, = -Dco2 d2:[1
=
where Dq0, = DIAm. Rewriting it leads to
(22f) Defining a facilitating factor FAm as (Schultz et al., 1974) N02/NCOz
=
FAm
(23)
we get FAm
1 DR2NHCT(C2(1)- c2(0)1 =DIAmHIAm(Pu
Further, a permeability
QIAm
- Pd)
(24)
of C 0 2 defined by
leads to QlAm = DIAmHIAm(l FA^) (25) By using the known solution for C1 and C2, the facilitation factor F A m corresponding to the partial pressures of C02 (Puand p d ) can be calculated from eq 24, and the effective permeability can be calculated from eq 25.
Experimental Section The immobilized liquid membrane technique was adopted to measure the permeabilities of N2 and C02 through an aqueous solution of DEA. The principal steps in the ILM based technique for the determination of permeability of any gas species through any aqueous solution were as follows: 1. Pure water or the aqueous solution was immobilized in the pores of a hydrophobic microporous polypropylene Celgard 2400 (25.4 pm thick with a porosity of 0.38 and average effective pore size of 0.02 pm) film by the exchange technique of Bhave and Sirkar (1986). The Celgard 2400 film was obtained from Hoechst Celanese Separations Products Divisions, Charlotte, NC. 2. The film was then put in a permeability cell, and the permeation rate of any gas species Ri through the water or aqueous solution was determined by the sweep gas technique (Bhave and Sirkar, 1986) for any given partial pressure difference across the film, Pi. The permeability of species i was calculated from the following relation: (264 Qi = [ R i t m ~ m l /[ f l i t m A m 1
2096 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 Table I. Measurement of Support Film Tortuosity Factor from Permeation Studies through Fully Exchanged ILMs Containing Water at 25 "C" pressure, cmHg L?J" io4&, cm3 106(RN2/ feed N, 231.14 282.86 360.43 438.04 515.57
sweep N, 0.14 0.17 0.23 0.27 0.33
cmdi 231.0 282.69 360.2 437.73 515.24
(STl$/s 5.081 6.137 8.085 9.558 11.544
OPure N2was used as the feed gas; (STP) cm)/(cm2s cmHg).
QN2
;\pN2)
2.20 2.17 2.24 2.18 2.24
used = 5.58
Tm
5.006 5.071 4.906 5.041 4.915 X
IO4 (cm3
The ideal separation factor at-]for two gas species is defined by ai-j = Q i / Q i (26b) The experimental setup for the measurement of gas permeability through an aqueous liquid membrane immobilized in a hydrophobic microporous film is shown in Figure 2. Feed gas (pure or a mixture) was first completely humidified and then passed over a film containing the immobilized aqueous solution in the test cell at a given pressure (usually greater than atmospheric but not necessarily). On the other side of the film, a completely humidified helium sweep gas stream was passed at essentially atmospheric pressure and a known flow rate. This flow rate and the rates of permeation of the components of the gas mixture were such that the permeated species were not present in the sweep gas at concentrations higher than, say, 2-3 mol % . This sweep gas stream was then analyzed by a Hewlett-Packard Model 5890 gas chromatograph. A Porapak N 80/100-mesh column was used for analyzing the permeated species in the sweep stream. The permeation rate was obtained easily; knowing the sweep helium flow rate and the permeated gas species content of this stream is equivalent to knowing the flow rate of that species, the latter coming about strictly due to permeation. The feed gas pressure was varied from 230 to 516 cmHg. A circular piece of fully water-exchanged Celgard 2400 with a nominal diameter of 5.1 cm was placed in the test cell. The Celgard film was supported by a thick Accurel polypropylene film (100 pm thick and 3.5 cm in diameter having an average pore size of 0.2 pm from Armak, Chicago, IL)and a porous 152.4-pm-thickfine circular stainless steel screen having the same nominal diameter as the Accurel film (Pall Trinity Micro Corporation, Cortland, NY). The membrane was sealed by a set of O-rings measuring 4.4 and 5.7 cm. Note that the pore size of Accurel is 1 order of magnitude larger than the pore size of Celgard film; thus, it offers no resistance to the transport of gas species. Accurel film was used simply as a backing to protect the Celgard film from any accidental sharp edges
ihl
BPR - BACK PRESSURE REGUMTOR CTB CONSTAU TEMPEPATURE BATH CV - CHECK V A L E FY - FEED HUMIDIFIER 'MC - FEED MIXTURE CYLINDER FTC FEED TFANSDUCER CONTROLLER GAS CHROMATOGRAPH GC W - GATE V A L E HTP HUMIDITY/TEMPERA'URE PROBE PG - PRESSURE GAUGE SGC - SWEEP GAS CYLINDER SH - SWEEP HUMIDIFIER TC TEST CELL
-
-
Figure 2. Schematic diagram of the experimental setup for gas permeability measurement through an ILM.
of the stainless steel screen employed to support the high-pressure difference across the ILM. The area available for gas permeation was 13.19 cm2. An independent measurement of the tortuosity factor of Celgard 2400 support film was first carried out at different pressures using pure N2 gas permeation through such a film having pure water in its pores. The feed gas pressure was varied from 231.14 to 515.57 cmHg. The permeation rate of N, in a helium sweep stream was measured, and the tortuosity factor of the support film was determined from eq 26a assuming the the nitrogen permeability through water was known from the literature.
Results and Discussion The tortuosity factors of the liquid membrane support film, obtained at different feed pressures are reported in Table I. A tortuosity value of 5 was obtained for the pressure range studied. In these calculations, the permeability value of N, through water was considered to be 5.58 X lo4 (cm3(STP) cm)/(cm2s cmHg) (Bhave and Sirkar, 1986). Table I1 illustrates the permeation and separation behavior of CO2-N2 mixtures through the fully exchanged Celgard ILM containing an aqueous 20 wt % DEA solution. Two different gas mixtures containing 5% coz-95% Nz and 25% coz-75% Nz were used as the feed. The total pressure of the feed mixture was kept between 231.14 and 515.57 cmHg. The partial pressure of CO, was varied in
Table 11. Permeation and Separation Behavior of C02-N2Mixtures through Fully Exchanged Celgard ILMs Containing Aaueous 20 wt % DEA Solutionso separation i03RN cm3 1o3RCO2, cm3 total P, factor U N *C02? cmHg cm$ cmHg (ST$)/s (STP)/s ~O'QN, 1O9Qco, (QcoJ QNJ 268.63 282.9 11.65 0.1826 1.747 482.46 276.2 2.2506 0.2294 15.15 342.31 360.4 1.666 362.20 217.41 2.2546 415.97 0.2680 438.0 18.64 1.646 296.10 179.89 2.2069 489.64 0.3165 515.6 22.13 246.97 153.40 2.2384 1.610 231.1 173.26 87.92 0.1323 55.15 1.938 170.4 3.7037 79.07 212.03 0.1557 282.8 67.92 1.887 149.20 3.9436 270.23 75.61 0.1906 360.4 87.86 1.753 132.54 4.684 63.94 0.2262 438.0 112.48 4.722 328.39 1.759 107.23 55.85 515.6 4.948 386.55 0.2707 97.40 1.744 126.53 OTemperature = 25 "C;flat film area = 13.19 cm2; tortuosity values were taken from Table I; cm)/(cm2s cmHg).
QN2
and
QCO?
values were in (cm3 (STP)
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2097 Table 111. Estimated Permeability of N2through a n Aqueous Solution of 20 w t % DEA a t 25 OC" wt% 103cT, 1O'Dih: 1 0 5 ~ ~ ~ $ DEA mol/cm3 cmz/s cmz/s 104~~,b 1 0 9 20 1.9429 2.34 1.43 1.76 4.12 "Qi values are expressed in (cm3 (STP) cm)/(cmz s cmHg).
~
~
~109~~,d ~ 2.52
values are expressed in mol/(cm3 cmHg) and calculated by using eq 29.
Di values are obtained from eq 27. Di values are obtained from eq 28. Table IV. Observed and Predicted C02-N2Separation Factors i n 20 w t 70 DEA Solution at Various Partial Pressures of C02 total P,cmHg Pu, cmHg Pa,cmHg AF'CO,, cmHg FA," 10gQc02n FAmb 109QCo; 'a, aAm b alXp Fgc 282.86 360.43 438.0 515.57 231.14 282.86 360.43 438.00 515.57
12.73 16.22 19.71 23.20 57.79 70.71 90.11 109.50 128.89
1.08 1.07 1.07 1.07 2.64 2.79 2.25 2.27 2.36
11.65 15.15 18.64 22.13 55.15 67.92 87.86 107.23 126.53
4.40 3.57 3.07 2.64 0.95 0.77 0.62 0.50 0.41
835.9 708.3 630.5 562.9 302.3 274.2 250.4 232.7 218.7
6.63 5.43 4.70 4.05 1.53 1.25 1.01 0.83 0.68
721.8 608.0 538.9 477.8 239.2 212.6 189.8 172.8 159.1
331.7 281.1 250.2 223.4 119.9 108.8 99.4 92.3 86.8
286.4 241.3 213.9 189.8 94.9 84.4 75.3 68.6 63.2
'Diffusivity value calculated from eq 27. bDiffusivity value calculated from eq 28. CProcedure for calculating Appendix.
the range of about 12 to 129 cmHg while that of N, was increased from about 220 to 492 cmHg. From the measured permeation rate of Nz and COz, the permeability values of N2 and CO, through 20 wt % DEA solution were calculated by using eq 26a. The tortuosity value corresponding to the total pressure was taken from Table I. Since N2 is a nonreactive species, the permeability of Nz remained almost constant for the pressure range studied. An average value of 1.75 X (cm3 (STP) cm)/(cm2s cmHg) was obtained in the present studies. However, as indicated in Table 11, the permeability of COz as well as the CO2-N2 separation factor vaired widely. The permeability of the nonreacting species like Nz can be also estimated from the product of diffusivity and solubility through the solution. Sada et al. (1978) have studied the diffusivity and solubility of gases in aqueous solutions of amines. The diffusivity values of different gas species were estimated in two ways. In the first method, the variation of the diffusivity of N 2 0 in an aqueous solution of DEA measured by Sada et al. (1978) was used. The diffusivity value was correlated with the concentration of DEA solution by the following equation:
Di,/Diw
= ( D h / D w ) ~ ,= o 1.0 - 1.1352 X 10-4CT (27)
In the second method, the diffusivity value was estimated by the Stokes-Einstein equation DiAm/Diw
=
(28)
(WAm/Ww)-'
using the viscosity values measured by Sada et al. (1978). Similarly, the solubility of N20 measured by Sada et al. (1977) was correlated by the following equation (Blanc and Demarais, 1984)
+
In (HiAm/Hiw) = 1.0406 X + 6.8433 X 104CT 1.33633 X 1O-*CTZ- 1.1549 X 10-12CT3(29) Table I11 provides the estimated diffusivity, solubility, and permeability values of N2 through an aqueous 20 w t % DEA solution. The nitrogen permeability value (1.75 X lo* (cm3(STP) cm)/(cm2s cmHg)) obtained in this set of measurements is significantly less than the estimated values. Note that the results of Sada et al. (1977,1978) were obtained in the absence of COBgas. I t is most likely that when COz is present along with N,, the N, permeability value gets reduced further due to the presence of other ions, e.g., R2NC00- and R2NHz+,in the liquid membrane formed by reaction 3, which will lower the solubility of Nz. This
276.2 217.4 179.9 153.4 87.9 79.1 75.6 63.9 55.8
FE
6.34 4.78 3.78 3.08 1.34 1.10 1.01 0.70 0.48
is shown in the
Table V. Physicochemical Parameters Used solubility H,, = 4.45 X mol/ Danckwerts and Sharma (1966) (cm3 cmHg) diffusivities D,, = 1.92 X cmz/s Danckwerts and Sharma (1966) D, NF = 3.83 X lo* cmz/s Thomas and Furzer (1962) equill2brium and rate constants K, = 2.5 X lo* Danckwerts and Sharma (1966) K P = 1.666 X 10l2 cm3/mol Danckwerts and Sharma (1966) ,k = 4.0 X lo5 (cm3/mol)/s Donaldson and Nguyen (1980)
kind of "salting out" effect has been reported earlier by Ward and Robb (1967) for COz/Oz separation and by Way et al. (1987) for COZ/CH4separation. The observed separation factors of CO, and N2 through a 20 wt 5% DEA solution at different partial pressures of CO, have been compared with the numerical simulation results based on the theoretical analysis and are presented in Table IV. The partial pressure of CO, in the downstream side was maintained at about 1 cmHg as long as the upstream partial pressure of COz was below 24 cmHg. However, when the upstream partial pressure of CO, exceeded 24 cmHg, the downstream partial pressure was maintained around 2.5 cmHg. Permeability values of COP as well as separation factors between COz and N2 sharply decreased with the increase of APco, up to a certain value since the reaction rate controlled the transport for lower APco, values. A t higher APco,, the reactive liquid membrane no longer acts as a facilitating membrane, and the premeability values and separation factors are simply governed by the reduction in solubility and diffusivity of gas species in that ionic solution. Physicochemical parameters used for the predictions are given in Table V. The physical solubility of COPwas determined from eq 29 and the diffusivity from either eq 27 or eq 28. However, common practice is to use eqs 27 and 29 only (Savage and Kim, 1985; Blanc and Demarais, 1984). Note that in the present analysis the observed separation factor data, shown in Figure 3, were predicted better by considering eqs 28 and 29. Though the present model predicted the separation factors quite well, the permeability values of CO, were always overpredicted to a great extent. This could be due to uncertainties in the estimation of other parameters, such as diffusivity of amine, rate constants, and reaction orders with respect to DEA, which have considerable effects on the prediction (Donaldson and Nguyen, 1980). The experimental diffusivity of amine (Thomas and Furzer, 1962),
2098 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
80
;C
4C
62 "
'52
83
'2:
-
*LC
- 7 cln
-22'
~
y
Figure 3. Observed and predicted separation factors of CO2-NZ through an ILM containing aqueous 20 wt 70 DEA solution.
-
Figure 5. Effect of membrane thickness variation on separation factor of C0,-N,; upstream and downstream partial pressures were the same as those of the experimental data. 320
240
280
i
______ - SIMULATION WITH Pd = . c w
\
0 1
i---
00
0 2
-
0 6
0 4
-
08
0 C '
-A 000
a
'G
t Figure 4. Dimensionless concentration and gradient profiles of amine across the length of the membrane for two different COz partial pressure conditions.
measured in the absence of reaction, was used. The equilibrium constants KAmand Kpat 20 O C were obtained from Danckwerts and Sharma (1966), who reported that the values of the equilibrium constants are influenced substantially by the ionic strength of the solution; it is not generally possible to make accurate allowance for this. In addition, most of the previous investigators have studied only the forward reaction in the absence of significant carbamate product, which will have a noticeable effect on all these parameters (Donaldson and Nguyen, 1980). Facilitated transport of COPthrough monoethanolamine (MEA) solution has been analyzed by Smith and Quinn (1979). They used the analytical solution introduced by Donaldson and Quinn (1975) derived under the limiting condition of constant carrier concentration. Donaldson and Nguyen (1980) applied the same model to predict the reaction kinetics of C 0 2 with mono-, di-, and triethanolamine. However, this model is valid only for very low COB partial pressure and large excess of carrier concentration. Such restrictions were not imposed in the present analysis. Thus, it is necessary to demonstrate the profiles of amine and its gradient across the membrane as shown in Figure 4. These profiles were obtained from the numerical solution of our model corresponding to two extreme experimental C 0 2 partial pressure conditions. The local concentration of amine and its gradient strongly depend on the magnitude of partial pressure of COz at the two boundaries. Further, the amine concentration varies considerably along the membrane. Apart from physicochemical parameters, the film thickness is likely to have a considerable effect on the separation factor between C02 and N2. The effect of membrane thickness variation is shown in Figure 5 . The actual membrane thickness in the present ILM experiment
7
90
40
6C
-"-pco2
80 CW
-
'C0
'?^
'
I-0
c
Figure 6. Effects of downstream partial pressure and membrane thickness on the separation factor of C02-N2.
is around 125 pm ( ~ ~ t , )We . find that a membrane thickness between 101 and 127 pm provides a reasonable description of the observed behavior. However, the higher the membrane thickness, the greater is the residence time and, therefore, higher is the facilitation. Note that the highest facilitation factor can be obtained only at equilibrium, which can be achieved if the membrane thickness is sufficiently large. The reaction rate and membrane thickness are interrelated in such a way as to achieve a higher separation factor by increasing the membrane thickness results in the reduction of species flux. The effect of downstream partial pressure on CYCO~-N~ is shown in Figure 6. This suggests that at low APco, both upstream and downstream partial pressures of C 0 2 have significant effects since both absorption and desorption rates are affected by them. The permeability of C 0 2through a hybrid solvent like poly(ethy1ene glycol)/diethanolamine (PEG/DEA) was studied for the selective removal of C 0 2 from COZ-O2 mixture (Meldon et al., 1986) and from CO2-CH4 mixture (Meldon and Nair, 1986). A much higher permeability of COz was observed here through a 20 wt % aqueous DEA solution compared to the values obtained through a 2 M DEA/PEG solution (Meldon and Nair, 1986) under similar feed partial pressure of C 0 2 . This is mainly due to the much lower permeability of C02 through PEG compared to water. We can also compare the calculated Qco I d and CY,.., values for such 20 w t % DEA membrane at high APco, and low value of membrane thickness with those for commercially available polymeric membrane. Kulkarni et al. (1983) reported a specific C 0 2 permeation rate through
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2099 commercial polysulfone membrane (used in Monsanto’s cm3 Prism separator) as [QC02/d]polys~fone = 4.2 X (STP)/(cm2s cmHg); the separation factor for the C02-N2 system was around 38. For a 20 wt % DEA solution as the liquid membrane (thickness of 25 pm), the calculated specific permeation rate corresponding to high P, = 135 cmHg and Pd= 2.5 cmHg is [Qco,/d]b = 4.84 X cm3 (STP)/(cm2s cmHg), and the separation factor is around 49. The values [Qc /dIb and ai-i for much lower partial pressure can easily%e at least 3 times the values for the polymeric membranes. Thus, the specific permeation rate and separation factor through the thin DEA based liquid membrane can be very large and highly attractive.
Summary The proposed model for facilitated transport of C02 through an ILM containing aqueous DEA solution provides an excellent estimate of the C02-N2 separation factor observed experimentally over a wide range of APco,. High C02 permeability coefficients as well as high separation factors between C02 and N2 were obtained. Model predictions of the permeabilities of C02 and N2 are hindered by the lack of reliable values of a number of physicochemical parameters. Acknowledgment The financial support by the New York State Energy Research and Development Authority, Gas Research Institute, and the New York Gas group is gratefully acknowledged. We thank Hoechst Celanese Separations Products Division, Charlotte, NC, for supplying us with Celgard 2400 films.
Nomenclature A,: flat membrane area, cm2 C1, Cz: dimensionless concentrations, defined by eq 16 CT: initial concentration of DEA, mol/cm3 d: liquid membrane thickness, pm Dco2: diffusion coefficient of C 0 2 in aqueous DEA solution cm2/s DR2NH: diffusion coefficient of DEA, cm2/s DiA,: diffusion coefficient of gas species i in aqueous DEA solution, cm2/s Diw: diffusion coefficient of gas species i in pure water, cmz/s F A m : facilitation factor defined by eq 24 HiAm:solubility of gas species i in aqueous DEA solution, mol/ (cm3cmHg) Hiw:solubility of gas species i in pure water, mol/(cm3cmHg) kAm: forward reaction rate constant of eq 1, (cm3/mol)/s k-Am: backward reaction rate constant of eq 1, (cm3/mol)/s KAm:equilibrium constant of eq 1 Kp: equilibrium constant of eq 2, cm3/mol Nco,: flux of COz at any location of the membrane, mol/(cm2 S)
aO2: total flux of COz, mol/(cm2 s) NR2NH: flux of DEA, mol/(cm2 S) Pd,P,: downstream and upstream partial pressures of COz across the liquid membrane, respectively, cmHg APc%pressure difference of C02across the liquid membrane, cm g q l , q2, q3, q4: dimensionless parameters defined by eqs 17-20, respectively Qi:permeability of species i, (cm3(STP) cm)/(cm2s cmHg) QIAm: permeability of COPin an aqueous solution of DEA, (cm3 (STP) cm)/(cm2s cmHg) Qih: permeability of species i in an aqueous solution of DEA, (cm3 (STP) cm)/(cm2s cmHg) Ri:permeation rate of gas species i, cm3 (STP)/s t,: thickness of flat membrane, pm T absolute temperature, K
Greek Symbols ai-j: ideal separation factor between two gas species i and j, eq 26b (: dimensionless membrane thickness, defined in eq 16 ph: viscosity of an aqueous DEA solution, CP pw: viscosity of water, CP 7,: tortuosity of flat membrane
Appendix To determine the values of the facilitation factor F b obtained experimentally (denoted by FE) for each upstream and downstream C02 partial pressure, it is necessary to estimate the permeability values of C02 through amine solution under no reaction condition. The permeability of C02 under such a condition is identified as QCozhl Bical. It is assumed that the reduction in the permeaiirity of C02 through amine compared to water under no reaction conditions would be similar to that of NZ. Thus, (AI) QCOz,AmIphysid/ QCO2,water = QNz,Am/ QN2,water The experimental permeability values of N2 through amine solution (denoted by QN2,Am) reported in Table I1 can be used here. Since F can be expressed as
substituting QCOzblphpicd
from eq A1 into eq A2 leads to
A value of 37.6 can be used for aC02-N water, the separation factor of the C02-N2 system througi pure water. The permeability value of C02 through water was considered to be 210 X lo+’ (cm3 (STP) cm)/(cm2s cmHg) (Ward and Robb, 1967). aeXp in column 11of Table IV is nothing but C Y ~ ~ , -Thus, ~ , ,F ~ yz . may be calculated from eq A3. The results are shown in column 12. They agree reasonably well with F A m b in column 7 predicted from theory.
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Received for review J u n e 22, 1989 Revised manuscript received February 6 , 1990 Accepted J u n e 8, 1990
