Module : 5 Gas separation

Transcription

1 Nove Searation rocesses Modue : 5 Gas searation Dr. Sirsendu De roessor, Deartent o Ceica Engineering Indian Institute o Tecnoog, Karagur e-ai: sde@ce.iitkg.ernet.in Kewords: Searation rocesses, ebranes, eectric ied assisted searation, iquid ebrane, coud oint etraction, eectrooretic searation, suercritica uid etraction Joint Initiative o IITs and IISc - Funded b MHRD age 1 o 16

2 Nove Searation rocesses Gas Searation In case o gas searation b ebranes, ig ressure eed gas is suied to one side o te ebrane and ereate coes out nora to te ebrane to te ow ressure side. Due o ig diusivit in gases, concentration gradient in te gas ase nora to te ebrane surace is sa. So, gas i resistance is negected coared to ebrane resistance. Tis eans concentration in gas ase in a direction nora to ebrane is unior weter gas strea ows arae to te surace or not. Tere are various tes o gas searation rocesses deending uon te ow caracterizations. Since te ereate coes nora to te ow direction o te eed, tis is known as sie cross ow (Fig. 5.1a). I tere is coete iing o te eed and ereate b an eterna agent (stirrer or ier), ten te coniguration is coete iing (Fig. 5.1b). I eed and ereate are in te sae direction, ten te ow is cocurrent ow (Fig. 5.1c). I te are in oosite direction, ten it is counter current ow (Fig. 5.1d). Joint Initiative o IITs and IISc - Funded b MHRD age 2 o 16

3 Nove Searation rocesses ereate Feed Fig. 5.1a: Cross Fow Reject ereat Feed Reject Fig. 5.1b: Coete Miing ereate Feed Fig. 5.1c:Co-current Reject ereate F Feed FR Reject Fig. 5.1d: Counter current Joint Initiative o IITs and IISc - Funded b MHRD age 3 o 16

4 Nove Searation rocesses In te oowing section, te working rincies and cacuations invoved in coete iing ode are considered. Tis case is ike a continuous stirred tank reactor (CSTR). Te assutions invoved are: (i) Isotera condition. (ii) Negigibe ressure dro in eed and ereate side. (iii) ereabiit o eac coonent is constant. q θq Low ressure, Feed q, Hig ressure side, q (1-θ)q Fig. 5.2: Sceatic o a coete iing coniguration wit te rocess conditions 3 In te above igure, q is tota eed ow rate (in /s) ; q 3 is outet reject ow ( /s ) ; 3 q is outet ereate ow ( /s) ; θ is raction o eed ereate q. q Overa ateria baance ieds te oowing reation. q q + q (5.1) Rate o diusion/ ereation o secies (in a binar iture o and B) is given as, q q t ( ) (5.2) Joint Initiative o IITs and IISc - Funded b MHRD age 4 o 16

5 Nove Searation rocesses were, is ereabiit o in ebrane 3 c. c 2 ; q is te ow rate o in s. c. chg ereate; is te ebrane area; t is te ebrane tickness; is eed side tota ressure (c.hg); is oe raction o in reject; is oe raction o in eed; is oe raction o in ereate; is artia ressure o in reject gas ase. Rate o ereation o secies B is given as, q ( 1 ) qb B t ( 1 ) ( 1 ) (5.3) Were, B is ereabiit o B. Dividing Eq.(5.2) b (5.3), te oowing eression is obtained. α 1 ( 1 ) ( 1 ) (5.4) Were, α B Overa coonent baance or : n overa baance o coonent resuts into te oowing equation. q q + q (5.5) Rearrangeent o above equation resuts, q q q + q (5.6) q q Deining, θ; and 1 θ, te above equation is written as, q q Joint Initiative o IITs and IISc - Funded b MHRD age 5 o 16

6 Nove Searation rocesses ( 1 θ ) + θ (5.7) Te above equation is re-organized to estiate te eed oe raction or tat in te ereate. θ 1 θ or ( θ ) 1 (5.8) θ But, q θq and te ebrane area can be estiated as oows. q t ( ) θq t ( ) (5.9) For design uroses: Tere are 7 variabes, nae,,,, θα,,,. 4 o te are genera indeendent. Case 1:,, α, are given and, θ, need to be deterined. Fro Eq. (5.3),,, α (5.1) It is a quadratic equation. We can sove or. θ is cacuated ro Eq. (5.8) θ 1 θ can be cacuated ro Eq. (5.9). Joint Initiative o IITs and IISc - Funded b MHRD age 6 o 16

7 Nove Searation rocesses Case 2:, θα,, are given and,, to be cacuated Miniu concentration o Reject Strea: I a te eed is ereated, ten θ1 and eed coosition For a vaues o θ <1, > Substitute, in Eq. (5.3). Miniu rejection coonent or a given α + ( α ) ( ) ( 1 ) (5.11) So, a eed coonent cannot be stried ower tan even wit an ininite arge ebrane area or a coete ied sste. To do tis cascade a be used. Cross Fow ode or gas ereation: ereat q θq, dq Low ressure q, Feed in ig ressure ug Fow q, q dq -d d Reject, q (1-θ)q Fig. 5.3: Sceatic o a cross ow ode Joint Initiative o IITs and IISc - Funded b MHRD age 7 o 16

8 Nove Searation rocesses Longitudina veocit in ig ressure or reject strea is ig. So tat gas is in ug ow and ows arae to ebrane. Low ressure side, ereate strea is aost ued into vacuu. So, ow is essentia erendicuar to ebrane. No iing is assued. So tat coosition varies as engt. Over a dierent ebrane area d at an oint, oca ereation rates are resented beow. Coonent baance: Coonent B baance: dq [ ] d (5.12) t B ( 1 ) dq ( 1 ) ( 1 ) d t (5.13) dq tota ow rate erendicuar to d. Dividing Eq.(5.12) b (5.13), α 1 ( 1 ) ( 1 ) (5.14) ereate coosition as a unction o reject coosition at a oint aong te engt. natica soution: Te design equation is resented beow: ( 1 θ )( 1 ) R E S u T D u α + F u F ( 1 ) E u u α F (5.15) + u F D q Were, θ , i ; u Di+ D i + 2Ei+ F ; q 1 Joint Initiative o IITs and IISc - Funded b MHRD age 8 o 16

9 Nove Searation rocesses ( 1 α ) D.5 + α ; α E DF ; F.5 ( 1 α ) R ; 2D 1 S α ( D 1) ( 2D 1) + F ; α F 2 T 1 E 1 D F u vaue o u at i i. 1 Coosition o eit: t eit,, θ * θ (cut ratio) raction o eed ereated. oe raction at te eit o ereate is estiated b overa ateria baance Mebrane area required, ( 1 θ )( 1 ) i B i ( i i) tq di (5.16) i 1+ i Were, ( D F) D i 2Ei F i and t tickness o ebrane and i B ebrane ereabiit o secies B Counter-current gas Searation: q, i q, q, Fig. 5.4: Sceatic o a counter current ow ode Joint Initiative o IITs and IISc - Funded b MHRD age 9 o 16

10 Nove Searation rocesses q, i q, q, Fig. 5.5: Sceatic o baance over a sa eeent Te sceatic o te counter current ow ode is resented in Fig. 6.4 and te sa eeent is sown in Fig Overa ateria baance: Tota ateria in Tota ateria out q q + q (5.17) Overa baance: Tota in Tota out q q + q (5.18) Secies baance over a dierentia eeent, ( ) dq ( ) dq (5.19) dq, q, d (q - dq) ( - d) In te above dierentia voue, secies baance rovides, q ( q dq)( d) + dq Joint Initiative o IITs and IISc - Funded b MHRD age 1 o 16

11 Nove Searation rocesses ( ) dq d q (5.2) Loca u o across te ebrane is resented, dq [ ] d t (5.21) For secies B, te oowing baance equation is rovided: B ( 1 ) dq ( 1 ) ( 1 ) d t (5.22) Cobining Eqs. (5.21) and (5.22), te oowing eression is obtained. 1 B ( 1 ) ( 1 ) (5.23) Eiinate q b using equations (5.17) and (5.18), ( ) q q + q q (5.24) Te above equation can be rearranged as ( ) ( ) q q (5.25) Bu using tis equation substitute q in equation (5.21) ten we get, ( ) ( ) d q d t d d t q [ ] [ ] B derivating tis equation and b rearranging it ina we get it as, Joint Initiative o IITs and IISc - Funded b MHRD age 11 o 16

12 Nove Searation rocesses d d q d d t ( ) + ( ) ( )( ) (5.26) Fro Eq. (5.23), α r 1 1 r 1 ( ) ( ) (5.27) Were, r. Te above equation is siiied as, 2 (1 ) r( ) α (1 )( r) (5.28) D ierentiate te above equation wit resect to, d + α (1 ) d (1 ) (1 2 ) d r (1 ) + α r + α ( r ) d d β (5.29) d Te above equation is rearranged as, ( )( ) d t d q ( ) β (, )( ) (5.3) Siiar, te eression o d d can be derived. Overa Materia Baance rovides, q q + q q + θq q ( θ ) q (5.31) 1 Overa baance resuts, q q + q Joint Initiative o IITs and IISc - Funded b MHRD age 12 o 16

13 Nove Searation rocesses ( 1 θ ) (5.32) θ For a vaue o given θ, ten (i) Guess (ii) Sove or ro equation (5.32) (iii) Ceck vaue o or soving ordinar dierentia equations. (iv) Iterate. Soved robes 1) ebrane is used to searate a gaseous iture and B wose eed rate is 4 3 q 1 c ( ST) / s and eed coosition o,.5; Te desired coosition o te reject is.25. Te ebrane tickness, t 3*1-3 c; eed side ressure 8 c Hg and ereate side ressure 2 c Hg. Te ereabiities are, 3 c ( ST). c 6 1 and o above units. ssuing coete 1 2 s. c. chg B iing ode, cacuate ereate concentration,, raction ereated θ and ebrane area ( ) required? Soution: *,, α, / are given, θ, are to be deterined Fro Eq.(), Were, + ( ) 2 b b 4ac 2a * a 1 α ; b 1 1+ α + α * * Joint Initiative o IITs and IISc - Funded b MHRD age 13 o 16

14 Nove Searation rocesses * c α * 6 1 α B 6 1 * a 1 α * * ( 1 ) 1 α α b 8 8 ( 1.25) c ( ) * α 2 2 b+ b 4ac.64 2a θ 1 θ.5 θ θ θ.76 θq ( / t)( ) 6 1 ( ) c 8 2 2) It is desired to ind te ebrane area required to searate air using a ebrane 3*1-3 c tickness wit ogen ereabiit 3 c ( ST). c and α * 1 or sc.. chg ereabiit ratio o ogen to nitrogen. F eed rate, q c 3 ( ST)/ sand raction Joint Initiative o IITs and IISc - Funded b MHRD age 14 o 16

15 Nove Searation rocesses cut θ.2; 2 c Hg and 2 c Hg. ssue, coete iing ode, cacuate ereate coosition, reject coosition and ebrane area? Soution:.21 (oe raction o ogen in air) a * * * θ θ α θ α α θ b θ + θ + α θ + α α θ + α * * * * c * 1 α b+ b 4ac + 2a ( ) ( ) θ θ 1.2 θq ( / t)( ) c ( ) Joint Initiative o IITs and IISc - Funded b MHRD age 15 o 16

16 Nove Searation rocesses Reerences: 1. C. J. Geankois, Transort rocesses and Unit Oerations, rentice Ha o India, New Dei,1997. Joint Initiative o IITs and IISc - Funded b MHRD age 16 o 16