Effect of a Vector Wall on the Thermal Field in a SRU Thermal Reactor

Transcription

1 Effec of a Vecor Wall on he Thermal Feld n a SRU Thermal Reacor Chun-Lang Yeh and Tzu-Ch Chen Absrac The effecs of a vecor wall on he hermal feld n a SRU hermal reacor are nvesgaed numercally. The FLUENT commercal code s employed o smulae he reacng and flud flow n a SRU hermal reacor. Praccal operang condons from a perochemcal corporaon n Tawan are used as he nle boundary condons. I s found ha he specfc arrangemen of a spral-ype vecor wall holes resuls n a spral moon behnd he vecor wall and hereby ncreases he resdence me. In mos cases, he average emperaure n zone s ncreased due o beer mxng. The emperaure dfference across a vecor wall becomes smaller due o beer mxng. Among he locaons of vecor walls nvesgaed, zone emperaure s he hghes when he vecor wall s locaed a 4m away from he zone corner and s he lowes when he vecor wall s locaed a 6m away from he zone corner. The 36-hole spral-ype vecor wall produces he sronges spral moon, he hghes average emperaures n he hermal reacors and he maxmum sulfur concenraons a he ex. Index Terms SRU hermal reacor, choe rng, vecor wall, hermal feld. I. INTRODUCTION The mos frequenly used desulfurzaon process s he Claus process whch convers he hydrogen sulfde n naural gas or crude ol no sulfur elemens and hereby reduces he formaon of oxysulfde. Sulfur recovery un (SRU) hermal reacor s he mos mporan equpmen n sulfur plan. I can conver he ammona, hydrogen sulfde and hydrocarbons n he reacans no sulfur. Mos of he sulfur elemens are recovered from he SRU hermal reacor. The frs on of SRU based on Claus process s composed of a burner, a hermal reacor and a wase hea exchanger. Confguraon and dmensons of he frs on of SRU for a ypcal peroleum refnery are shown n Fg.. The nner surface of a SRU hermal reacor s faclaed by refracory o proec s wall. The neror of he SRU hermal reacor s dvded no wo zones by a choe rng o ncrease resdence me and enhance chemcal reacon. An abrup emperaure rse or excessvely hgh emperaure may lead o deeroraon of he refracory. Therefore, he operang emperaure range suggesed by vendor for he operaon of a SRU hermal reacor should be srcly followed. Because he operang emperaure of he SRU hermal reacor s very hgh and he hydrogen sulfde n he reacans s a hghly acd gas, he refracory and hea exchangng ubes may be deeroraed. Manuscrp receved Ocober 0, 07; revsed January 8, 08. Ths wor was suppored n par by he Mnsry of Scence and Technology, Tawan ROC, under conrac MOST 05--E The auhors are wh he Naonal Formosa Unversy, Huwe, Yunln, Tawan (e-mal: clyeh@nfu.edu.w; asf55030@gmal.com). Exsen researches of he SRU hermal reacors are concenraed on he dscussons of praccal operaon problems and are revewed n he auhor s prevous sudes []-[3]. Facors nfluencng he operaon of a SRU hermal reacor nclude () he operang condons, () geomery of he reacor, (3) he use of a choe rng and (4) he use of a vecor wall. In he auhor s prevous sudes, he nfluence of operang condons, ncludng mass fracons [], nle ar quanes and he nle oxygen mole fracons [] were suded. In addon, he nfluence of sreamlned geomeres of a SRU hermal reacor was nvesgaed and he effecs of a choe rng and a vecor wall were analyzed and compared [3]. However, n he analyss of a vecor wall n he auhor s prevous sudes [3], only a praccal vecor wall s analyzed. To undersand he effec of a vecor wall n more deal, a paramerc sudy of he vecor wall s performed n hs paper. The effec of sze, arrangemen and number of holes of a vecor wall on he hermal feld n a SRU hermal reacor s nvesgaed numercally. The purpose of hs paper s o mprove he performance and safey of a SRU hermal reacor under hgh emperaure operaon. Fg.. Confguraon and dmensons of he frs on of SRU. II. NUMERICAL METHODS AND PHYSICAL MODELS In hs sudy, he FLUENT commercal code [4] s employed o smulae he reacng and flud flow n a SRU hermal reacor. The SIMPLE algorhm by Paanar [5] s used o solve he governng equaons. The dscrezaons of convecon erms and dffuson erms are carred ou by he power-law scheme and he cenral dfference scheme, respecvely. In respec of physcal models, by consderng he accuracy and sably of he models and by referrng o he evaluaon of oher researchers, he sandard -ε Model [6], P- radaon model [7] and non-premxed combuson model wh β ype probably densy funcon [8] are adoped for urbulence, radaon and combuson smulaons, respecvely. The sandard wall funcons [9] are used o resolve he flow quanes (velocy, emperaure, and urbulence quanes) a he near-wall regons. For he seady-sae hree-dmensonal flow feld wh chemcal reacon n hs sudy, he governng equaons are descrbed below, ncludng he connuy equaon, do: 0.878/mmm

2 momenum equaon, urbulence equaon (-ε Model), energy equaon, radaon equaon (P- radaon model) and combuson equaon (non-premxed combuson model wh β ype probably densy funcon). Connuy equaon: v 0 () Momenum equaon: In an neral reference frame, he momenum equaon [0] may be expressed as ( vv) p g F () where F s he possble source erm of he momenum equaon whch may nclude he body force caused by he neracon wh dspersed phases or he exra force erms caused by physcal models or numercal schemes. In Eq.(), he sress ensor may be expressed as v v vi (3) 3 where I s he un ensor, he superscrp T represens he ranspose operaor, and he hrd erm on he rgh hand sde of he equal sgn represens he volume dlaon effec. By he long-me averaged mehod, Eq.() may be convered o Reynolds-averaged Naver-Soes (RANS) equaons as follows: p u u u l uu u ' u ' (4) x x x x x 3 x l x In Eq.(4), he urbulen sresses (Reynolds sresses) may be relaed o he mean velocy graden by he Boussnesq hypohess as follows: u u u u u x x x ' ' 3 In Eq.(5), he urbulen (or eddy) vscosy may be expressed n erms of he urbulence nec energy () and urbulence dsspaon rae (ε) as: (5) C (6) As menoned above, and ε are modeled by he -ε model, as descrbed below. -ε model equaon: Turbulence nec energy () and urbulence dsspaon rae (ε) may be solved from her ranspor equaons [6] as follows: x x x x u G Gb YM S (8) u C ( G C3 Gb ) C S x x In Eqs.(7) and (8), G represens he urbulence nec energy producon and may be expressed as : G (7) S (9) where S s he modulus of mean rae-of-sran ensor defned as S S S (0) In Eq.(0), u u. S x x G b s he generaon of urbulence nec energy due o buoyancy, calculaed as T Gb g Pr x () where Pr =0.85 s he urbulen Prandl number for energy and g s he componen of gravaonal vecor n he h drecon. The coeffcen of hermal expanson, β, s defned as T () p Y M represens he conrbuon of he flucuang dlaaon n compressble urbulence o he overall dsspaon rae and can be calculaed as follows : Y M M (3) where M s he urbulen Mach number, defned as In Eq.(4), a (= RT M (4) a ) s he speed of sound. The values of urbulence model consans C ε, C ε, C μ, σ and σ ε are as follows : C ε =.44, C ε =.9, C μ =0.09, σ =.0, σ ε =.3 The value of urbulence model consan C 3ε s calculaed from he followng equaon C 3 v anh u (5) where v s he componen of he flow velocy parallel o he gravaonal vecor and u s he componen of he flow velocy perpendcular o he gravaonal vecor. Energy equaon: The governng equaon for conservaon of energy s as follows []: (6) v E p eff T h J eff v Sh where eff s he effecve conducvy ( eff = +, s he urbulen hermal conducvy). The frs hree erms on he rgh-hand sde of Eq.(6) represen energy ransfer due o conducon, speces dffuson, and vscous dsspaon, respecvely. S h ncludes he hea of chemcal reacon, and any oher volumerc hea sources. E on he lef-hand sde of Eq.(6) s defned as follows : p E h where sensble enhalpy h s defned for deal gases as v (7) h Y h (8) where Y s he mass fracon of speces, and h s defned as 44

3 h T 98.5K C p, dt (9) P- radaon model equaon: The P- radaon model [7] s based on he expanson of he radaon nensy no an orhogonal seres of sphercal harmoncs. If only four erms n he seres are used, he followng equaon s obaned for he radaon flux q r : where q r G (0) () 3 a S C S In Eq.(), a s he absorpon coeffcen, σ s s he scaerng coeffcen, G s he ncden radaon, and C s he lnear-ansoropc phase funcon coeffcen. The ranspor equaon for ncden radaon G s: 4 G ag a T SG 4 () where σ s he Sefan-Bolzmann consan and S G s a user-defned radaon source. Combnng Equaons (0) and (), he followng equaon s obaned: q ag 4a T (3) 4 r S G The expresson for q n Eq.(3) can be drecly r subsued no he energy equaon (6) o accoun for hea sources (or sns) due o radaon. Non-premxed combuson model wh β ype probably densy funcon: The bass of he non-premxed modelng approach s ha he nsananeous hermochemcal sae of he flud s relaed o a conserved scalar quany nown as he mxure fracon, f. The mxure fracon can be wren n erms of he mass fracon as [8] Z Z, ox f (4) Z Z, If a ondary sream (anoher or oxdan, or a non-reacng sream) s ncluded, he and ondary mxure fracons are smply he elemenal mass fracons of he and ondary sreams, respecvely. The sum of all hree mxure fracons n he sysem (, ondary sream, and oxdzer) s always equal o :, ox f f (5) fox The Favre mean (densy averaged) mxure fracon equaon ( f ) s f f Sm Suser (6) where he source erm S m s due solely o he ransfer of mass no he gas phase from lqud droples or reacng parcles (e.g., coal). S user s any user-defned source erm. In addon o solvng for he Favre mean mxure fracon, FLUENT solves a conservaon equaon for he mxure fracon varance, f f f Cg f Cd f Suser (7) where f f f. The defaul values for he consans, C g, and C d are 0.85,.86, and.0, respecvely, and S user s any user-defned source erm. In respec of urbulence-chemsry neracon, he assumed-shape probably densy funcon (PDF, p(f)) approach s appled n hs sudy. The probably densy funcon descrbng he emporal flucuaons of f, p(f), n he urbulen flow can be used o compue he averaged values of varables (e.g. speces fracons, densy, and emperaure) ha depend on f. For a sngle-mxure-fracon sysem, densy-weghed mean speces mass fracons and emperaure can be compued as ) 0 p( f ) ( f df (8) whle he mean me-averaged flud densy can be compued as p( f ) df (9) 0 ( f ) On he oher hand, when a ondary sream exss, he nsananeous values depend on he nsananeous mxure fracon, f, and he ondary paral fracon, p,.e. φ =φ (f,p ), where f, p and f (ondary mxure fracon) are correlaed by f = p ( - f ) (30) Mean values of speces mass fracons and emperaure when a ondary sream exss are calculaed as 0 p ( f ) p ( p ) ( f, p ) df dp (3) 0 where p s he PDF of f and p s he PDF of p. The mean flud densy when a ondary sream exss can be compued as p ( f 0 0 ( f, p) ) p ( p ) df dp (3) In hs sudy, he β ype probably densy funcon s chosen o accoun for he urbulence-chemsry neracon. The β ype PDF shape s gven by he followng funcon of f and f : f f p f f f df (33) where f f ; f f f ; f and f are he f f f mean mxure fracon and mxure fracon varance of f, respecvely, and her values are solved from Eqs.(6) and (7). III. RESULTS AND DISCUSSION Fg. shows he numercal model of he SRU hermal reacor. In Fg., he hea exchanger on consss of 9 coolng ubes of dameer 0.5m, llusraed schemacally n Fg. 3. The hea absorpon rae of each hea exchangng ube s 40,000 W/m and he oher walls are adabac. No slp condon s appled on all sold walls. The ex of he hea 45

4 exchanger on s conneced o he subsequen equpmen a 300K and am by a ppe of.37m n dameer and.5m n lengh. (b) usng a 36-hole vecor wall 6m away from he zone corner Fg.. Numercal model of he SRU hermal reacor. (c) enlarged vew and arrangemen of a 6-hole vecor wall Fg. 3. Illusraon of he arrangemen of hea exchangng ubes. In hs sudy, wo cases of oxygen supples are nvesgaed: he normal oxygen supply and he rch oxygen supply. The rch oxygen supply s desgned o ncrease he sulfur recovery. Boundary condons (ncludng he speces composons, emperaure, pressure and velocy) a he acd gas nle holes of zone and zone as well as a he ar nle hole are lsed n Table I. (d) enlarged vew and arrangemen of a 36-hole vecor wall (spral-ype) TABLE I: BOUNDARY CONDITIONS AT ACID GAS AND AIR INLET HOLES Oxygen-normal supply Oxygen-rch supply_ Locaon Acd gas Acd gas Ar nle Acd gas Acd gas Ar nle (zone ) (zone ) (zone ) (zone ) Speces mole fracon (%) O N H O CO H S CH C H NH P (N/m ) V (m/) (radal) (Radal) 34.(Tangenal) 9.8(Tangenal) Turbulence nec energy s 0% of he nle mean flow nec energy and urbulence dsspaon rae s compued from Eq.(). 3/ 4 C 3/ (34) l where l=0.07l and L s he hydraulc dameer. Fg. 4 shows he numercal models of SRU hermal reacor wh a choe rng or a vecor wall. (a) usng a choe rng 6m away from he zone corner (e) a 36-hole vecor wall (nclned-opposng ype) (f) hole confguraon and dmenson of a vecor wall Fg. 4. Numercal models of SRU hermal reacors. Fg. 5 shows he comparson of cross-onal average emperaure for SRU hermal reacors wh a choe rng or a spral-ype vecor wall a x=4m, 6m and 8m, respecvely. I s observed ha zone s a hgher emperaure regon whle zone s a lower emperaure regon. Ths s because he operang condons shown n Table I s a rch (or ar lean) condon. The supply o zone s larger han o zone. The average emperaure for he oxygen-rch supply s hgher han ha of oxygen-normal supply because of he more complee combuson. Temperaure decreases abruply across he choe rng or vecor walls because of converson of hermal energy no nec energy due o flow acceleraon. The specfc arrangemen of a spral-ype vecor wall holes resuls n a spral moon behnd he vecor wall and hereby ncreases he resdence me. The average emperaure n zone s ncreased due o beer mxng. 46

5 wh choe rng a x=4m wh 6-hohe vecor wall a x=4m wh 8-hohe vecor wall a x=4m wh 36-hohe vecor wall a x=4m (a) a x=4m wh choe rng a x=6m wh 6-hohe vecor wall a x=6m wh 8-hohe vecor wall a x=6m wh 36-hohe vecor wall a x=6m (b) a x=6m (b) usng a 36-hole spral-ype vecor wall a x=4m Fg. 6. Sream races for he SRU hermal reacors usng a choe rng or a spral-ype vecor wall. Fg. 7 shows he comparson of cross-onal average emperaures for SRU hermal reacors wh spral-ype vecor walls a dfferen locaons. I can be seen ha zone emperaure s he hghes when he vecor wall s locaed a x=4m and s he lowes when he vecor wall s locaed a x=6m. The locaon x=6m s more suable for proecng zone wh choe rng a x=8m wh 6-hohe vecor wall a x=8m wh 8-hohe vecor wall a x=8m wh 36-hohe vecor wall a x=8m wh 6-hohe vecor wall a x=4m wh 6-hohe vecor wall a x=6m wh 6-hohe vecor wall a x=8m (c) a x=8m Fg. 5. Comparson of cross-onal average emperaure for SRU hermal reacors wh a choe rng or a spral-ype vecor wall (oxygen-normal supply) (a) wh a 6-hole spral-ype vecor wall a dfferen locaons The spral moon caused by a vecor wall can be seen from Fg. 6 whch shows sream races for he SRU hermal reacors usng a choe rng or spral-ype vecor walls a x=4m for an oxygen-normal operaon. I s observed ha a 36-hole spral-ype vecor wall produces he sronges spral moon and herefore produces he hghes average emperaure, as can be seen from Fg. 5. I s also observed ha he average emperaure across a vecor wall becomes more unform due o beer mxng wh 36-hohe vecor wall a x=4m wh 36-hohe vecor wall a x=6m wh 36-hohe vecor wall a x=8m (b) wh a 36-hole spral-ype vecor wall a dfferen locaons Fg. 7. Comparson of cross-onal average emperaure for SRU hermal reacors (oxygen-normal supply). (a) usng a choe rng a x=4m In a praccal SRU hermal reacor, he refracory may be rupured due o hgh emperaures, for example, near he zone corner. Fg. 8 shows he emperaure profles for a SRU hermal reacor usng a choe rng or spral-ype vecor walls. The maxmum emperaure n he hermal reacor and he sulfur concenraon a he ex are also labeled n he fgures. I can be observed ha he 36-hole spral-ype vecor walls produce he hghes average emperaures n he hermal 47

6 reacors and he maxmum sulfur concenraons a he ex due o he bes mxng. he sulfur concenraon a he ex are also labeled n he fgures. Compared wh Fg. 8(d), s seen ha he 36-hole spral-ype vecor wall produces a hgher average emperaure n he hermal reacor and a larger sulfur concenraon a he ex due o beer mxng, as analyzed n Fg. 9 and Fg. 0. (a) wh a choe rng a x=4m (b) wh a 36-hole spral-ype vecor wall a x=4m 000 wh choe rng a x=6m wh nclned-opposng 36-hohe vecor wall a x=6m wh spral 36-hohe vecor wall a x=6m Fg. 9. Comparson of cross-onal average emperaures for SRU hermal reacors wh a choe rng or 36-hole vecor walls of dfferen arrangemens a x=6m (oxygen-normal supply). (c) wh a choe rng a x=6m (d) wh a 36-hole spral-ype vecor wall a x=6m (a) oxygen-normal supply (spral) (e) wh a choe rng a x=8m (f) wh a 36-hole spral-ype vecor wall a x=8m Fg. 8. Temperaure profle for a SRU hermal reacor (oxygen-normal supply). To nvesgae he effec of arrangemen of he vecor walls, Fg. 9 shows he comparson of cross-onal average emperaures for SRU hermal reacors wh a choe rng or 36-hole vecor walls of dfferen arrangemens a x=6m. I s seen ha he 36-hole vecor walls produce hgher cross-onal average emperaures han he choe rng. The spral-ype arrangemen produces a hgher cross-onal average emperaure han he nclned-opposng-ype arrangemen due o beer mxng. Ths can be observed from Fg. 0 whch shows he comparson of sream races for SRU hermal reacors wh a 36-hole spral-ype vecor wall or a 36-hole nclned-opposng-ype vecor wall a x=6m. Fg. shows he emperaure profles for a SRU hermal reacor usng a 36-hole nclned-opposng-ype vecor wall a =6m. The maxmum emperaure n he hermal reacor and (b) oxygen-normal supply (nclned-opposng) Fg. 0. Comparson of sream races for SRU hermal reacors wh a 36-hole spral-ype vecor wall or a 36-hole nclned-opposng-ype vecor wall a x=6m. Fg.. Temperaure profle for a SRU hermal reacor wh a 36-hole nclned-opposng-ype vecor wall a x=6m (oxygen-normal supply). IV. CONCLUSION In hs paper, he effecs of sze, arrangemen and number 48

7 of holes of a vecor wall on he hermal feld n a SRU hermal reacor are nvesgaed numercally. I s found ha he specfc arrangemen of a spral-ype vecor wall holes resuls n a spral moon behnd he vecor wall and hereby ncreases he resdence me. In mos cases, he average emperaure n zone s ncreased due o beer mxng. The emperaure dfference across a vecor wall becomes smaller due o beer mxng. Among he locaons of vecor walls nvesgaed, zone emperaure s he hghes when he vecor wall s locaed a 4m away from he zone corner and s he lowes when he vecor wall s locaed a 6m away from he zone corner. The locaon 6m away from he zone corner s more suable for proecng zone. The 36-hole spral-ype vecor wall produces he sronges spral moon, he hghes average emperaures n he hermal reacors and he maxmum sulfur concenraons a he ex. The fndngs of hs paper are helpful o mprove he performance and safey of a SRU hermal reacor under hgh emperaure operaon. REFERENCES [] C. L. Yeh, The effec of mass fracon on he combuson and flud flow n a sulfur recovery un hermal reacor, Appled Scences, vol. 6, Issue, p. 33, 06. [] C. L. Yeh, The effec of nle ar quany and nle oxygen mole fracon on he combuson and flud flow n a sulfur recovery un hermal reacor, Transacons of he Canadan Socey for Mechancal Engneerng. vol. 4, no., pp , 07. [3] C. L. Yeh, Numercal analyss of he effecs of sreamlnng geomery and a vecor wall on he hermal and flud flow n a SRU hermal reacor, Transacons of he Canadan Socey for Mechancal Engneerng. vol. 40, no. 5, pp. 8-80, 06. [4] ANSYS FLUENT Theory Gude, ANSYS Inc., 009. [5] S. V. Paanar, Numercal Hea Transfer and Flud Flows, New Yor: McGraw-Hll, 980. [6] B. E. Launder and D. B. Spaldng, Lecures n Mahemacal Models of Turbulence, London England: Academc press, 97. [7] R. Segel and J. R. Howell, Thermal Radaon Hea Transfer, Washngon DC: Hemsphere publshng corporaon, 99. [8] Y. R. Svahanu and G. M. Faeh, Generalzed sae relaonshps for scalar properes n non-premxed hydrocarbon/ar flames, Combuson and Flame, vol. 8, pp. -30, 990. [9] B. E. Launder and D. B. Spaldng, The numercal compuaon of urbulen flows, Compuer Mehods n Apped Mechancs and Engneerng, vol. 3, no., pp , 974. [0] G. K. Bachelor, An Inroducon o Flud Dynamcs, Cambrdge Unversy press, Cambrdge England, 967. [] A. Bean, Convecon Hea Transfer, ond ed., Wley, New Yor, 995. C. L. Yeh s currenly a professor of he Deparmen of Aeronaucal Engneerng, Naonal Formosa Unversy, Huwe, Yunln, Tawan, ROC. He receved B.S. n 987, M.S. n 989 and Ph.D. n 993 degrees from Naonal Cheng-Kung Unversy, Tanan, Tawan, ROC. Dr. Yeh has served as an engneer n CTCI Corporaon, he larges engneerng, procuremen, and consrucon frm n Tawan, from 995 o 997, and as a consulan o Formosa Perochemcal Corporaon n Tawan, snce 007. He s also he auhor and revewer of research papers n he area of flud mechancs, hea ransfer, chemcal reacon, vbraon, and sress analyss. T. C. Chen s currenly a graduae suden of he Deparmen of Aeronaucal Engneerng, Naonal Formosa Unversy, Huwe, Yunln, Tawan, ROC. He receved he B.S. degree n 06 from Naonal Uned Unversy, Maol, Tawan, ROC. He s currenly worng under he supervson of Dr. C. L. Yeh n he area of compuaonal flud dynamcs and chemcal reacon for hs M.S. degree. 49