The Computer Simulation and Estimation of Membrane Mass Transfer Coefficients of Hollow Fiber Membrane G-L Contactors for SO 2

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1 Koean Chem. Eng. Res., Vol. 45, No. 1, Febuay, 007, pp SO o l q - h o{ m s n }o k Ç içm *Ç mk ne v k 1 * l v l o e o q 71- (006 11o 15p, 007 1o 4p }ˆ) The Compute Simulation and Estimation of Membane Mass Tansfe Coefficients of Hollow Fibe Membane G-L Contactos fo SO Removal Yong Kuk Kim, Hee Ouel Song, Hyung Keun Lee* and In-Won Kim Depatment of Chemical Engineeing, Konkuk Univesity, 1 Hwayang-dong, Gwangjin-gu, Seoul , Koea *Koea Institute of Enegy Reseach, 71- Jang-dong, Yuseong-gu, Daejeon , Koea (Received 15 Novembe 006; accepted 4 Januay 007) k l e l SO o t -k n p. l l -k p t l p SO l p, p o n p pn l m. SO p l m p t p ~ o, p v p l SO p p v p kk k. ~p o l t p SO p e p p v m. t l np q p p e m. h Abstact Hollow fibe membane G-L contactos ae widely used to emove SO emitted fom industial facilities. In this wok, the mathematical modeling and compute simulation fo hollow membane G-L contactos is caied out to analyze SO absoption behavio in hollow fibe membanes. The model is solved with the finite element method using a commecial softwae. Investigated is the dependency of SO emoval efficiency and mass tansfe chaacteistics on gas velocities, membane mass tansfe coefficients and physical popeties of contactos. The membane mass tansfe coefficients ae estimated by fitting the expeimental data with the simulated SO emoval efficiencies. In addition, a design methodology of membane contactos is suggested. Key wods: SO Removal, Membane Contactos, Hollow-fibe Membane, Membane Mass Tansfe Coefficient 1. op e to l ool o l p p l tl, l vop o l SO p t v l, k eˆ p mm v tl tp v l. p mmp o mm ~p p tn l m, l v p p l m. sp ~ p ~p p p p ~ k l eˆp f v v eˆ, -k p p p p p pl. p To whom coespondence should be addessed. inwon@konkuk.ac.k p n q l ˆ(packed towe), ˆ(spay towe), d (ventui scubbe), ˆ(bubble column) p p, v v p n l m. sp q p -k p p lp q n p p p, k~p (flooding), n lv(weeping), (loading)m p p pl k~ ~p o l p t p p v p [1]. p p q p ep t p q (micopoous hydophobic polymeic membane)p pn p, k d ~ m n q p pop e q k d l e p t (hollow fibe membane contacto) e 81

2 8 n Ë lëp Ë po p p [1-]. p t m p p n ~ p p qp v p. 1) o p p v. ~m k~p p p s l (flooding), (loading) v. ) qp v. 3) -kp p k p. 4) (module) d, d p(scale)p l(up), n(down)p np [3]. 5) ~ p k~p o l lp p l p p. p q~ p v p v m p p mm(fouling), l p p k m e p [3-4]. p p q t p pp v eˆ o l p lv p. p p qp v t n l SO l SO pp ~p o, t p, p m p ~p v l [1, 4-5]. l l l v l ol SO p q t p t l p SO l l p, p o n p pn l l e m p f p v, SO l m p t p ~p o, p v p l SO p v p kk k. ~p o l t p SO p e p v m. t l np q p p e m.. m n y -1. q o{ i m -h m s n t l p ~(SO )m k~( n ) p v p t, v q p nk ƒ v(solution diffusion mechanism)l p p lv. l l } p n nl Fig. 1 p p k~l p v k p p ~ }ov (non-wetted model), p p p l yl ~ yl k~ l p. ~ tpp p k yl p ~, k yl mp pp [1-]. Fig. 1l p P g, P M P i,, l p kp ˆ, C i, C g p ˆ. K L p k ( ) yp v ˆ, ~m k ~ pl p ~ k~ yp, v ~ pl p p pp n pl p(instantaneous eaction)p nl p k l p K L o45 o1 007 k Fig. 1. Non-wetted mode of hydophobic. p p e p [1, 5]. K G yp v ˆ, p K G ~l p ~(k d, v ) pp q (molecula diffusion)p p. p p v ˆ p. p p p s p, e (poosity), p (thickness), p (totuosity)m l p (diffusivity in membane) l p. t p nl t p (tube)p kp v pp, p p v pp e (1) p p p. D M ε = τ M R 1 ln( R R 1 ) e (1)l D M p p, ε, δ p, τ M p ˆ. R 1p p kyp, R y vp p [6]. -. s o Fig. t p l t p p ˆ p. R 1p t p v p R p t p n v p. p o l m p t kp t p n o p o (cell). l ˆ p o p o p p v ppp op l p v p. p p t t pp p p, p p v l p o p p v p tp p. SO m v p ~ t p n (shell side) tp, k p t p (lumen side) tp. t (1)

SO o t -k p v 83 v g = v g R ------ 1 R ----- R ------ + ln------ R 3 R 3 ------------------------------------------------------------------ R 3 ------ 4 4 R + ------ + 4ln------ R (5) -3.

3 SO o t -k p v 83 v g = v g R R R ln R 3 R R R ln R (5) -3. o o p edš v ep s (bounday condition)p p. Fig.. Hexagonal shaped unit cell of the fibe assembly. kyp SO ~m mp pp p(instantaneous eaction)p t p kyp k d e. t n l ~p p m (fully developed) (lamina flow)p. p t p p p l p t l l. pm p t l SO ~p l v ep n, p (diffusive flow) (axial) l (convective flow)l p pp v v ep. C C v z C C = z z l l SO p ˆ. v z t l ~m k~p l ˆ [7-8]. o v z t m t n p o vp n l p. t p p o p p e (3)l p p. v l = v l R 1 o ep R 1p t p p v p p. t p n p o p n p n p k. p t t pp p p, p p v l p o p p v p tp p. v g e (4). v g 4 P R R = R + 4 ln µl ( R ) t n p pn l e (5) p [1]. () (3) (4) 1) = R 1, 0 z Ll C = 0 C ) = R, 0 z Ll = C 3) =, 0 z Ll = 0 4) z = 0, R l C = C 0 5) z = L, R l C C = 0 z ~ w s p t l SO m p p(instantaneous eaction) l p p. w s p p ~ ˆ p, w s p tkl p p p ˆ. w s p tp SO ˆ, w s p l p convective flux ˆ. -4. o ƒ o ~p t n p SO m v p ~p m t p Œ ~p v l p. t l tp SO m v p ~ t SO p Chapman-Enskog el p m [9]. t p p p p sq n, ~ q p qp p p q, p p ~p qo (mean fee path) qp ~ Knudsen l p p. Knudsen pp e(6) p p [9]. T D K = 9700 poe M A l D K Knudsen [cm /s], poe p v (cm), T m [T] M A p ~ p q [g/mol]p ˆ. Knudsen p t kp pp e (7) p ~p m Knudsen p e p p [7, 9] = D M D AB D K l l D M t k ~p [cm /s], D AB Chapman-Enskog el p p [cm /s] p D K Knudesen [cm /s] ˆ. Koean Chem. Eng. Res., Vol. 45, No. 1, Febuay, 007 (6) (7)

4 84 n Ë lëp Ë po Fig. 3. Concentation contou and total flux pofiles in hollow membane shell side ( = m/s, v g =4.3m/s). 3. y COMSOL p FEMLAB[10]p t SO p ~p o, p v p l v s l k p p, p s l SO m g p p o p t l p SO (contou plot)m ~ (total flux)p Fig. 3l e m. ~p o v g =4.3m/sp p v = m/s p np t n p SO ˆ p. p ny p t p y (R )p ˆ m y p t p t vp k p v ( )p ˆ. nyp SO p o(nondimensional) ˆ. k yl tp SO ny p p l t p ~ mp pl p. ~ yp v l ~p kvp p. t p p pl ny p m y SO p p p p t p n p SO l l p t lvp lt. Fig. 4 t p l t t p pl p ~p o l ˆ p lt p. ~p o p ƒvl SO l p kyp p p lt p. 3-. s n i SO o l l v l l e p SO p e p l p v ( ) m ~ o l p m. e l n t p o45 o1 007 k Fig. 4. Outlet concentation pofile with gas velocity ( = m/s). Table 1. Specification of the hollow fibe membanes Popeties Philos Cel Module Diamete (m) Length (m) VolumesG(cm 3 ) Fibe Mateial Polypopylene Polypopylene I.D (µm) O.D (µm) Poe size (µm) Poosity ( ) - 30 Packing density Numbe of fibe Fig. 5. Expeimental (Philos08-00) & calculated esults of SO emoval efficiency.

5 SO o t -k p v 85 Fig. 6. Expeimental (cel03-00) & calculated esults of SO emoval efficiency. Fig. 7. Simulation esults of effects of Gaetz and Shewood numbe in outlet concentation. p Table 1l ˆ l [11]. Philos08-00p Philos p Philosep p 00 p t p lp p, Cel03-00p Celgad p Liqui-cel p 00 lp p. Fig. 5m Fig. 6p v p l SO pp ˆ. ~ o p v l SO pp o p v l pp qkvp k p. p l SO pp k p p. v p p v pp, ~ o p ƒvl pp p qpp l t p. p p ƒv k dp l ~ o p m p lvp k p. Fig. 5l p p pn l ƒ l lp pp e p. e (Ë)p t (Philos08-00)p e p SO pp. p m/sl e l p p pp k p. p Philos08-00p t p v p m/sl p k p. p p l p, m k nl el p pp l l p t p p p v kk l ep e p SO p ƒ l p e ˆ SO pp l p m. Fig. 6p Cel03-00l l p p e l lp SO p lp SO pp p. l p m/sp. Cel03-00p nl Philos08-00p nl p o l SO pp, e lp pp p p p p. p p qp p v nl pp ~ o l pp p. Philos08-00l ~o p 4 m/s v 0Íp pp p, Cel03-00p nl k 60Í p p pp p q m l p t p t p l o } e p, p Gzm Sh l Fig. 7p k p. Fig. 7p Gz(gaetz numbe)l p Sh(shewood numbe)l ˆ p l p Gzm Sh pp el p p. v g d Gz = L R Sh = o el v g ~p o [m/s], d t n p v [m] k dp [m /s], Lp t p p Rp t n p [m]p. p t p p } n p p pp l p p lv. 1) p v(,,, )p p v, p e p p. ) p Sh. 3) Gz-Sh pn o q pp ~ m Sh l l pl Gz p }. 4) Gz p p k p ~, t p v p p l t p p p, p t o lp p m l Fig. 7p pn l 95Íp SO o 00 p t p v t p o t p p p. p Philos08-00 p p m/s, p Sh 0.464p. SO pp 95Í p SO 0.05p, Fig. 7l p Shm l k 0.6p Gz lp p. t p 00 p n o p 16 L/minp o p 4. m/s, SO m /sp p t p p Lp 0.65 mp. v, 95Í SO p pp o t p 00 n t p p k 0.65 m lk p k p. (7) Koean Chem. Eng. Res., Vol. 45, No. 1, Febuay, 007

6 86 n Ë lëp Ë po : adius of hollow fibe [m] R 1 R Sh T v g : inside adius of hollow fibe [m] : outside adius of hollow fibe [m] : fee suface adius of hollow fibe [m] : Shewood numbe (= R/ ) [ ] : tempeatue [K] : gas velocity [m/s] <v g > : aveage gas velocity [m/s] z : axial coodinate on the hollow fibe Fig. 8. Hollow fibe lengths of Gas velocity and Sh-numbe fo 95 SO emoval efficiency. t p 00 p SO pp 95Íp Sh(0.05, 0.1, , 1, 1.5)m o (0.55, 1.05, 1.58,.1, 3.15, 4.)l t pp ˆ Fig. 8 p ˆ p. 4. t SO p o l t n p o p tp SO l v ep n o, p v ( ) p l SO p l l m. ep SO p e l p l t l n p v m. p v pn l t p ql n t p, p, ~ o p q p p e m. pm p l l t p v, v p l, SO l q t q q p. k C : dimensionless concentation of SO [-] C 0 : dimensionless initial concentation of SO [-] d : inne hollow diamete [m] : gas diffusion coefficient [m /s] D K : Kundsen diffusion coefficient [cm /s] D M : diffusion coefficient of a gas in s membane poe [cm /s] Gz : Gaetz numbe (= v g d / L) [ ] K G : feed gas mass tansfe coefficient [m/s] K L : Liquid absobent mass tansfe coefficient [m/s] : membane mass tansfe coefficient [m/s] L : membane length [m] M : gas molecula weight [g/mol] P : pessue [atm] m m P : Pessue diffeence along hollow fibe [atm] τ M : totuosity of membane [ ] ε : poousity of membane [ ] µ : viscosity of gas [kg m/s] y 1. Kaoo, S., Gas Absoption Studies in Micopoous Hollow Fibe Membane, Stevens Institute of Technology, Ph.D. Dissetation, Stevens Institute of Technology, USA(199).. Kao, S. and Sika, K. K., Gas Absoption Studies in Micopoous Hollow Fibe Membane Modules, Ind. Eng. Chem. Res., 3(4), (1993). 3. Zhang, Q. and Cussle, E. L., Micopoous Hollow Fibes fo Gas Absoption: I. Mass Tansfe in the Liquid, J. Memb. Sci., 3(3), 31-33(1985). 4. Zhang, Q. and Cussle, E. L., Micopoous Hollow Fibes fo Gas Absoption: I. Mass Tansfe in Acoss the Membane, J. Memb. Sci., 3(3), (1985). 5. Keulen, H., Smoldes, C. A., Vesteeg, G. F. and Swaaij, W. P. M. van, Micopoous Hollow Fibes Membanes as Gas-liquid Contactos: Pat. Mass Tansfe with Chemical Reaction, J. Memb. Sci., 78(3), 17-38(1993). 6. Wang, S., Xu, S. and Qin, Y., Mass Tansfe in Membane Absoption-desoption of Ammonia fom Wate, Chinese J. Chem. Eng., 1(3), (1993). 7. Qin, Y., Joaquim M. S. Cabal and Shichang Wang, Hollowfibe gas Membane Pocess fo Removal of NH 3 fom Solution of NH 3 and CO, AIChE, 4(7), (1996). 8. Li, K., Wang, D., Koe, C. C. and Teo, W. K., Use of Asymmetic Hollow Fibe Modules fo Elimination of H S fom Gas Steams Via a Membane Absoption Method, Chem. Eng. Sci., 53(6), (1998). 9. Waen, L. M., Smith, J. C. and Pete Haiott, Unit Ope. Chem. Eng., 6 th Edition, McGaw Hill(001). 10. FEMLAB Use s Guide, COMSOLAB(004). 11. Kim, I. W., Pak, H. H., Lim, C. W., Jo, H. D., Song, H. O. and Lee, H. K., Effect of Membane Mateial and Absobent Type on SO Removal Using Micopoous Hollow-fibe Membane G-L Contactos, KIGAS, 10(), 14-1(006). o45 o1 007 k

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