On the SO 2 Problem in Thermal Power Plants. 2.Two-steps chemical absorption modeling

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Godwin Hutchinson
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1 Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : Oct 5 On the SO Problem n Thermal Power Plant Two-tep chemcal aborpton modelng hr Boyadjev, P Popova-Krumova, M Dochnova, B Boyadjev Inttute of hemcal Engneerng, Bulgaran Academy of Scence, Acad St Angelov tr, Bl 3, 3 Sofa, Bulgara E-mal: chrboyadjev@gmalcom Abtract: The modelng of the ga aborpton n a new column apparatu for wate gae purfcaton from SО, ung twophae aborbent (ao 3 / H O upenon) preented The proce realzed n a three-zone column In the upper zone a phycal aborpton n ga-lqud drop ytem realzed and the bg convectve tranfer n the ga phae lead to a decreae of the ma tranfer retance n th phae In the mddle zone a chemcal aborpton n lqud-ga bubble ytem take place and the bg convectve tranfer n the lqud phae lead to a decreae of the ma tranfer retance n th phae The large volume of the lqud n the mddle zone caue an ncreae of the chemcal reacton tme and a a reult a further decreae of the ma tranfer retance n the lqud phae realzed The thrd zone the column tank, where the chemcal reacton take place only Keyword: aborpton, ga purfcaton, two-phae aborbent method, three-zone column, convecton-dffuon model, average concentraton model Introducton In the frt part of the paper [] wa hown, that n the cae of wate gae purfcaton from SО, ung two-phae aborbent (ao 3 /H O upenon) from ome compane (Babcock & Wlcox Power eneraton roup, Inc, Altom Power Italy, Idreco-Ingma-onortum) n the thermal power plant, the nterphae ma tranfer proce n the ga-lqud drop ytem practcally phycal aborpton a a reult of the low concentraton of the dolved SО and ao 3 n the water In thee condton the ma tranfer retance n the ga and lqud phae are R 44 and R 56, repectvely, e aborpton ntenfcaton mut be realzed by convectve ma tranfer n the ga phae (n ga-lqud drop ytem) and n the lqud phae (lqud-ga bubble ytem) Th theoretcal reult poble to be realzed n a three-zone column In the upper zone a phycal aborpton n ga-lqud drop ytem realzed and the bg convectve tranfer n the ga phae lead to a decreae of the ma tranfer retance n th phae In the mddle zone a chemcal aborpton n lqud-ga bubble ytem take place and the bg convectve tranfer n the lqud phae lead to a decreae of the ma tranfer retance n th phae The large volume of the lqud n the mddle zone caue an ncreae of the chemcal reacton tme and a a reult a further decreae of the ma tranfer retance n the lqud phae realzed The thrd zone the column tank, where the chemcal reacton take place only Th dea realzed [] n an aborpton column (Fg) wth two aborpton zone The apparatu compre a cylndrcal aborpton column, ftted at t lower end wth an nlet for ubmon of wate gae Above the bottom of the aborpton column placed n a horzontal ga dtrbuton plate 3 (bell plate or any other devce provdng the cleanng bubblng ga through the aborbent n the mddle part of the column) o that between t and the bottom of aborpton column haped entrance area of the nput ga On the dtrbuton plate 3 are ntalled vertcal dtrbuton ppe 4 at the mddle of the column, the number of whch depend on the ga delvery Each of the ga dtrbuton ppe 4 covered wth concentrc bubblng cap 5, whch le on plate 3 and ha lot 6 at the bottom Between the dtrbuton ppe 4 and the bubblng cap 5 are formed paage 7, whch are open to the ppe 4 The volume between the ppe 4 flled wth aborbent upenon The upper part of the aborpton column equpped wth prnkler ytem 9, whch located above the drop eparator and outlet, provded for the purfed ga Ext 8 (of bubblng area) are aocated wth tank through ppe 3 The level of the aborbent n the bubblng zone controlled by the turn-cock The tank provded wth the turn-cock 9 Sytem prnkler 9 are connected by crculaton ppe 5 and 6 and crculaton pump 8 wth the tank Fg A tangental nlet of the ga phae [3] lead to a gnfcant decreae of the velocty radal non-unformty below the ga dtrbuton plate 3 Th effect ncreae after ga dtrbuton n the ppe 4 and a a reult the ma tranfer rate n the ga phae ncreae [4-8] IJER@5 Page 557

2 Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : Oct 5 The prnkler ytem 9 lead to the decreae of the velocty radal non-unformty n the lqud phae and a a reult the ma tranfer rate n the lqud phae ncreae too Phycal aborpton modelng n the upper zone et conder the aborpton column of Fg wth a dameter D [m], where l [m] the heght of the upper zone between bubblng cap 5 and prnkler ytem 9 (ga-lqud drop ytem zone) and l [m] the heght of the mddle (lqud-ga bubble ytem) zone between dtrbuton plate 3 and the lqud urface (practcally the bubblng cap 5 heght) The dameter of the ga dtrbuton ppe 4 D [m], the bubblng cap 5 dameter D [m] and n t number The ga and lqud flow rate n the column are Q and Q [m 3 ], the nlet velocte n the ga and lqud phae are u and are hold-up coeffcent, repectvely: u [m ] and, Q Q πd u u F F F 4 Q Q Q Q Q Q,,,, The aborber workng volume W [m 3 ] n the mddle zone : () πd W F nf l, F () 4 et conder the phycal aborpton n ga-lqud drop ytem [] n the upper zone of the column (Fg ), where the radal non-unformte of the velocte dtrbuton n the ga and lqud phae abent, practcally Th a reult [3] of the tangental nlet of the ga phae n the column, the ga dtrbuton ppe 4 n the mddle column zone and the prnkler ytem 9 n the upper column zone In thee condton the radal non-unformte of the concentraton dtrbuton n the ga and lqud phae abent too and poble to be ued average concentraton value over the cro-ectonal area of the column In the upper zone a convecton-dffuon model [, 4, 5] poble to be ued for a counter-current aborpton proce n z, r, z, r, two cylndrcal coordnate ytem - z z l where c c z and c c z, are the axal dtrbuton of the average SО concentraton n the ga and lqud phae: d c d c u D k c c dz dz dc z, c c, ; dz z d c d c z u D k c c dz dz dc, c,, dz z ; ; (3) equal to the outlet SО concentraton n the ga phae from the c l ), the Henry number mddle zone ( hemcal aborpton modelng n the mddle zone The ga bubblng n the aborbent volume W n the mddle zone create an deal mxng regme and a a reult the concentraton [kg-molm 3 ] of SО ( c ) and ao 3 ( c 3 ) n the lqud phae are contant, where c 3 practcally the maxmal (equlbrum) olublty of ao 3 n water The ma flow rate [kg-mol ] of SО at the nlet and outlet of the column are Qc and Q c l, where c and c l are the SО concentraton (kg-molm -3 ) n the nput and output ga flow The dfference between them the SО aborpton rate V [kg-mol ] n the column: V Q c c l (4) The chemcal reacton rate V [kg-molm 3 ] between SО and ao 3 n the mddle zone poble to be preented a: V k c c, 3 where k the chemcal reacton rate contant (5) The concentraton of SО ( c ) n the lqud phae n the mddle zone a contant f the SО aborpton rate V n the column equal to the amount of SО (V W), react chemcally wth ao 3 n the mddle zone, e The axal dtrbuton c 3 Q c c l (6) c z of the average SО concentraton n the ga phae n the mddle zone poble to be obtaned a a oluton of the problem: d c d c u D k c c ; dz dz dc z, c c, ; dz z where k ( - ) the nterphae ma tranfer coeffcent n the lqud-ga bubble zone The mathematcal model of the SО aborpton, ung two-phae aborbent (ao 3 /H O upenon), n the column on the c c l The Fg the et of equaton (3), (6), (7), where quanttatve decrpton of the proce need the model' generalzed (dmenonle) varable 3 eneralzed (dmenonle) varable model The maxmal value of the varable wll be ued a cale n the generalzed varable: (7) where c the nlet concentraton of SО n the ga phae, IJER@5 Page 558

3 Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : Oct 5 z z z c Z, Z, Z,, l l l c c c c c,,, c c c c If put (8) n equaton (3), (6), (7), the model of SО aborpton n a three-zone column ha the form: d K Pe ; Z,, Z Z d K Pe ;,, Z d Pe K ; Z,, Z 3 (8) (9) () () Q () In (9)-() are ued the next dmenonle parameter: 4 Indutral condton ul u l u l Pe, Pe, Pe, D D D kl kl k l K, K, K u u u (3) et conder (Fg) an ndutral aborpton column wth a dameter D = 8 [m], where l = 69 [m] the heght of the upper zone between bubblng cap 5 and prnkler ytem 9 (ga-lqud drop ytem zone) and l = m the heght of the mddle (lqud-ga bubble ytem) zone between dtrbuton plate 3 and the lqud urface (practcally the bubblng cap 5 heght) The aborpton proce characterzed by the average ga velocty u 44 [m ], average lqud drop velocty u 375 [m ] (durng the extence of the drop 8 []), 4 nlet SO concentraton n the ga phae c [kg-molm -3 ], nlet SO concentraton n the lqud phae c [kg-molm -3 ], lqud [m 3 ] / ga [m 3 ] rato ( 98, ), Henry number 55, dffuvty of SО 5 n the ga (ar) D 3 [m ] and lqud (water) D 67 wll be 94% 9 [m - ] phae The dered aborpton degree From preented ndutral condton and (3) follow: Pe 77, Pe 55, 6 K u Pe 4, 75 6 K u and the model (9)-() ha a convectve form: K ; Z, (4) (5) 379 K ; Z, (6) K ; Z, (7) 3 4 Algorthm for model equaton oluton 4 Upper zone model Q (8) The oluton of the model equaton of the upper zone ue the next teratve Algorthm I: Soluton of the problem Preentaton of 3 Soluton of the problem K ; Z, (9) a a polynomal a a Z a Z K a a Z a Z 34, () Z,,,,, where,, the teraton number 4Preentaton of,, 5 Soluton of the problem a a polynomal b b Z b Z, K b b Z b Z, Z, 6Preentaton of,, The STOP crtera : a a polynomal 4 a a Z a Z (), () IJER@5 Page 559

4 Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : Oct 5 Accordng the ndutral condton the dered aborpton degree have to be 94%, e 6 The mnmzaton of the leat quare functon F K 6 (3) permt to be obtaned the model parameter K 386 A a reult the model (5)-(8) ha the form: Z 386 ;, (4) 53 ; Z, (5) K ; Z, (6) 3 Q (7) The oluton of the model equaton (4)-(7) ue the next teratve Algorthm II, where a zero teraton tep 5: Determnaton of Z a a oluton of the problem K ; Z, ; (8) where,, the teraton number Fndng 3 Soluton of the problem (4), (5), ung the algorthm (9)- () 4 Fndng 5 alculaton of, ung (7) 6 heckng 4 Ye - contnuaton of 8 No - contnuaton of 7?, 7alculaton of layng, and contnuaton of 8 STOP 4 Numercal reult The preented Algorthm I and Algorthm II are ued for the oluton of the model equaton (4)-(7), where Kg 386, K A a reult obtaned 59 and concentraton dtrbuton, whch are preented on the Fg-4 From the model equaton oluton obtaned the ga outlet (nlet) concentraton n the mddle (upper) zone of column - 689, 44 p g Z Fg Evoluton of SО concentraton n the ga phae g K 386, K, Z Fg 3 Evoluton of SО concentraton n the lqud phae g K 386, K, Fg 4 Evoluton of nlet SO concentraton n the Z IJER@5 Page 56

5 Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : Oct 5 ga phae g K 386, K, 59 onderng the dered outlet ga concentraton n the column wa Z 6 a,, then from the oluton of the model equaton can be determne the nterphae ma tranfer coeffcent n the upper zone of the column and permt to be obtaned requred heght of the upper part of the column l 69Z 587 m, Z 85 The ncreae of the aborber workng volume W n the mddle zone () lead to the decreae of the concentraton of SО ( c ) n the lqud phae (6) and practcally = In thee condton, the heght of the upper part of the column (l ) decreae, f the nterphae ma tranfer coeffcent (K) n the mddle zone ncreae Thee reult are preented on the Fg 5 oncluon The modelng of the ga aborpton n a new column apparatu for wate gae purfcaton from SО, ung two-phae aborbent (ao 3 /H O upenon) preented An algorthm for olvng a ytem of model equaton propoedthe dtrbuton of the SО concentraton n the two zone of the column hown and the effect of the ma tranfer rate n the mddle zone of the column on the total ma tranfer rate demontrated The ncreae of the aborber workng volume W n the mddle zone of the column lead to the decreae of the nlet concentraton of SО In thee condton, the heght of the upper part of the column ( l ) decreae Increang the ntenty of the bubble zone at the bottom of the column (nterphae ma tranfer coeffcent) can reult to a gnfcant reducton of the heght n the upper part of the apparatu, and thu the entre heght of the apparatu ,5,5,5 3 K Fg 5 Heght of the upper part of the column (l ) a functon of nterphae ma tranfer coeffcent (K) n the mddle zone Reference Boyadjev, hr, Dochnova, M, Popova-Krumova, P, Boyadjev, B, On the SO problem n thermal power plant Aborpton procee modelng, n pre Boyadjev, hr, Boyadjev, B, Dochnova, M, Popova- Krumova, P, Method and apparatu for ga aborpton, Patent applcaton 68, 3 Boyadjev, hr, Boyadjev, B, Dochnova, M, Popova- Krumova, P, olumn reactor for chemcal procee, Utlty model, applcaton number 464, 3 v Boyadjev, hr, Theoretcal hemcal Engneerng Modelng and mulaton, Sprnger-Verlag, Berln Hedelberg, v Dochnova, M, Boyadjev, hr, On the column apparatue modelng, Int J Heat Ma Tranfer,, vol 55, p 675 v Boyadjev, hr, Dffuon model and cale-up, Int J Heat Ma Tranfer, 6, vol 49, p 796 v Boyadjev, hr, Modelng of column apparatue, Tranacton of Academenergo, 9, 3, p7 v Boyadjev, hr, A new approach for the column apparatue modelng n chemcal engneerng, J Appl Math:Advance and Aplcaton, 3, vol,, p 3 IJER@5 Page 56

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy: BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,