Modifid Shrinking or Modl for Rmoval of Hydrogn Sulfid with T Dsulfurizr Enguo Wang Dpartmnt of physis Lingnan normal univrsity Zhanjiang, hina -mail: 945948@qq.om Hanxian Guo Institut of oal hmial nginring Taiyuan univrsity of thnology Taiyuan, hina -mail: ghx55@6.om Abstrat Th ration btwn H S and ZnO fin partils (T dsulfurizr was studid. Th xprimnt rsults show that at th tmpratur blow 57K, th ration has stoppd bfor th omplt onvrsion of ZnO partil is obtaind. In ordr to xplain th phnomnon, th modifid shrinking or modl is put forward on th basis of th hang of th porosity of solid produt layr during th ration in th prsnt work. Th modifid shrinking or modl was applid to dsrib th xprimnt rsults of th H S rmoval ration with ZnO fin partil. Th rsults alulatd by th modl quation ar in good agrmnt with th xprimntal data, and th modl paramtrs suh as k s, D and alfaat various tmpraturs wr also obtaind. Th high diffusion ativation nrgy and th maximum onvrsion of solid ratant in th H S rmoval ration is also xplaind aording to th modifid shrinking or modl. Kywords-porosity; gas solid rations; hydrogn sulfid; zin oxid; modifid shrinking or modl INTRODUTION Nonatalyti, gas-solid rations ar of onsidrabl industrial importan and ar radily found in hmial and mtallurgial industris, and a larg numbr of xampls of this systm hav bn disussd [-5]. Svral modls hav bn applid to dsrib th kinti bhavior of ths rations. Among ths modls, grain modl [,4] or th shrinking or modl [] is oftn applid in modling th xprimntal rsults of gas-solid nonatalyti ration taking pla in th porous pllt and in th nonporous partil, rsptivly. Zin oxid dsulfurizr is usually usd for th fin lan-up of natural gas, hmial synthsis gas and ful gas, so th studis on its dsulfurization kintis hav bn rportd. For xampl, Harrison[4] studid H S rmoval with zin oxid dsulfurizr and invstigatd mthodially th orrsponding marokintis only at 57-7K. Guo [5] studid th kintis of th ration btwn H S and zin oxid (T5 dsulfurizr in th tmpratur rang of 47-67K, and obsrvd that th maximum onvrsion of zin oxid ratd with hydrogn sulfid (signd as x max was lss than %, and th maximum onvrsion inrasd with th ration tmpratur at th ration tmpraturs blow 57K. A similar phnomnon also appard in othr ration systm. Howvr, th phnomna ould not b xplaind using th abov-mntiond modls satisfatorily. So it is ssntial to advan a nw modl, whih will b alld as th modifid shrinking or modl. THE MATHEMATIAL MODELS For gas-solid ration in dns solid ratant partil, A(g + B(s (g + dd(s. ( Th shrinking or modl onsidrd that solid ratant is dns or has vry small porosity, but solid produt layr is porous. Th porosity of solid produt layr dos not hang during ration. This hypothsis is also mad in th modifid shrinking or modl. Howvr, th hypothsis that th porosity of solid produt layr will hang during th ration will b adoptd in th modifid shrinking or modl. For th sak of simplifiation, on of th simplst assumptions, that partil siz rmains unhangd during th ration whil it is not qual to initial siz of solid ratant partil, is assumd. Although this modl dos not prisly rprsnt th whol mhanism of gas-solid ration, it is th first to tak into aount th variation of th porosity of solid produt layr during th ration in th shrinking or modl. Th following hypothss ar also mad in th modifid shrinking or modl. Th ration will our at th intrfa btwn th porous solid produt layr and th unratd solid. Gas molul diffuss from th solid partil surfa to ration intrfa. Isothrmal ondition prvails. For th sak of onvnin, following assumptions will also b adoptd. Th rsistan of gas film mass transfr from gas bulk to th solid partil surfa an b ignord. Sphrial solid partils ar only onsidrd. Undr th ration ondition, th ration is first ordr with rspt to gasous ratant A, and th fft of rvrsibility on th ration an b ngltd. For ration ( taking pla in a sphrial nonporous partil, th fundamntal quations rlating th matrial balan for gasous omponnt A an b xprssd as follows.
r r A k r D s A, R>r>r. ( In Eq.(8, is porosity, and an b rprsntd as follows. Th bounding onditions ar A= A at r=r and A= A at r=r. Initial ondition is r =r at t=. In Eq.(, r, R ar th siz of th moving ration intrfa and on of th solid partil surfa, rsptivly, and r is th initial siz of solid partil. A, A and A ar th onntration of gasous omponnt A in th bulk phas, on in th porous produt layr, and on on th surfa of th unratd or, rsptivly. k s, D ar ration rat onstant and fftiv diffusivity, rsptivly. Intgrating Eq.(, w hav A A ksr. ( D r R Matrial balan for solid omponnt B an b writtn as follows. At ration surfa dr k ( s A. (4 Its initial ondition is th sam as on of Eq.(. Rplaing Eq.(4 with Eq.( obtains dr k s A = ρ k sr. ( D r R Solid ratant onvrsion x is dfind as follows. / (5 x r r. (6 ombining Eqns.(5 and (6 givs ks r A k r ( x s ( x / D (( x. r R Aording to litratur[4], th fftiv diffusivity of th gasous ratant A in solid produt layr an b writtn as (7 D D (8 x. (9 x /( Z In Eq.(9, Z is th volum of solid produt pr volum solid ratant. is th ratio of th inras amount of partil volum during th ration to its thortial inras amount, and is dfind as follows. R / r. ( Z Whn Z<, porous solid produt forms and, so th modifid shrinking or modl an b rdud to th shrinking or modl. Rplaing Eq.(7 with Eqns.(8-( yilds ( x x /( Z 6 ( x ( (( x x * [ ( Z ] ( ksa In Eq.(, t* = t, dimnsionlss ration tim, r ksr and, Thil modul numbr. Its initial 6D ondition is x= at t*=. It an b found from Eq.( that for th ration with Z> and <, th ration rat was narly zro whn x approahs whih implis that it is possibl for th solid ratant to b onsumd inompltly aftr th ration, and th maximum onvrsion of solid ratant is qual to whnand Whn, thr ar no analyti solutions for Eq.(, so numrial solution should b adoptd. In solving this quation, Rung-Kutta mthod is applid,so that th ration bhavior an b analyzd. KINEITI MODELING OF H S REMOVAL WITH ZnO T typ ZnO dsulfurizr with =4.598* - mol/m, r =.6* -6 m was prourd from Nanjing hmial Enginring ompany. Th physial proprtis of th sampl and th xprimntal pross hav bn dsribd lswhr[5]. Th xprimnts wr arrid out using a thrmogravimtri analysis apparatus with flow rat of 7 ml/min whr th rsistan of gas film mass transfr ould b ignord. Th tmpratur was varid from approximatly 47K to 6K with th H S onntration of.55 mol% in th mixtur gass of N, H S and H. Th thrmogravimtr
produd a ontinuous rord of th wight of th solid during th ration. Th hang in th wight was onvrtd dirtly to ZnO onvrsion, and th onvrsion tim data wr obtaind. Figur givs th xprimntal onvrsiontim data obtaind using thrmogravimtr at various ration tmpraturs. It an b sn from ths data in Figur that th inras in ration tmpratur lads to an inras in ration rat. It should b pointd out that th H S onntration ould also afft th onvrsion tim data for th H S rmoval ration. Th ration is first ordr with rspt to th onntration of H S, whih has bn vrifid [5]. For th H S rmoval ration with ZnO, Z is qual to th ratio of th molar volum of dns ZnS partil to on of dns ZnO partil, and is assumd to b.6. On putting th valus of A, r and Z in Eq.(, w obtain 4 * 4.58* k S.6* D 6 ( x ks x /.6 ( x ( (( x (.6 x ( Figur shows th ZnO onvrsions alulatd using th modifid shrinking or modl as funtion of th ration tim by th itration mthod. Th optimisd k s, D andin Eq. ( an b obtaind by making th omparison btwn th xprimntal data and th on alulatd by th modl so as to mak th orrlation offiint maximum. TABLE I. DETERMINATION OF THE MODEL PARAMETERS Tmp 6 k s D R a K mol/m min mol/m min 47.48.974.49.997 5.6.84.9.994 5.8.6.5.99 57.99.494 5.4.996 59. 4.485 7.59.9964 68.5 4.668.664.996 6. 5.8 6.84.9957 a. R is orrlation offiint. onvrsion, x onvrsion, x.8.6.4. 4 5 6 Tim, t (min FIGURE. Plot of th onvrsion of ZnO vrsus tim at ration tmpraturs of 6K, 68 K, 59K, 57K, 5K,.8.6.4. 5K, * 47K. 4 6 Tim, t (min FIGURE. omparison of th prditd valu of th ZnO onvrsion vrsus tim and th xprimntal data It an b sn from Figur that th data alulatd using th modifid shrinking or modl is in good agrmnt with th xprimntal ons obtaind. So this modl maks it possibl to prdit ZnO onvrsion as funtion of th ration tim. Th ativation nrgy for th hmial ration and th fftiv diffusion offiint of th gasous ratant an b stimatd by an Arrhnius plot, as shown in Figur. It an b sn that thr is a good linar rlationship btwn ln(k s as wll as ln(d and th riproal of ration tmpratur. So Arrhnius rlations for th rat onstant and th fftiv diffusion offiint ar givn by th following quations. k s =.55* -4 xp(-89/8.4t ( D =.57* -6 xp(-59758/8.4t (4
Th ativation nrgy for th hmial ration was found to b.9kj/mol, and th ativation nrgy for diffusion in th H S rmoval ration is avragd to about 59.76kJ/mol. Obviously, th diffusion ativation nrgy is Ln( 6 ks.5 y = -7.876x + 4.9 y = -.454x + 5.547.5 -.6.7.8.9 /T(K - FIGURE. Arrhnius plots of alulatd rat onstant ( and alulatd fftiv diffusion offiint ( vry high. For th phnomnon, Guo onsidrd that th diffusion inluds both H S gas diffusion through th porous produt layr and S - and O - ion diffusion in th solid partils [5]. Th ion diffusion lads to a high diffusion ativation nrgy. Howvr, aording to th modifid shrinking or modl, th rason for th high diffusion ativation nrgy is that th porosity of solid produt layr will hang during th ration, and that th snsitivity of th porosity to tmpratur is high. As shown in Tabl I, th variation of paramtr with th ration tmpratur is obsrvd. Plot of ln(vs /T is prsntd in Figur 4. urv of bst fit was obtaind for th data of paramtr with onsidration of xprimntal rror. Th paramtr has a rlationship with tmpratur as Ln( D = 6.74*xp(-65.7/T. (5 It an b found from Eq. (5 and Figur 4 that th tmpratur for = is 57K, and that paramtr inrass with th ration tmpratur. As mntiond abov, th maximum onvrsion of solid ratant during th ration is qual towhn. So whn th H S rmoval ration with ZnO fin partil is arrid out at th tmpratur blow th 57K, th ZnO partil ould b onsumd inompltly, and th maximum onvrsion of ZnO partil drass with th ration tmpratur. Only at th tmpratur highr than 57K, ould th omplt onvrsion of ZnO partil b obtaind. ln.6. -. -.6 y = -.657x +.69 -.9.6.7.8.9.. /T(K - FIGURE 4. Rlationship btwn alulatd valu and ration tmpraturs ONLUSIONS Th modifid shrinking or modl is put forward on th basis of th hang of th porosity of solid produt layr during th ration, and an b rdud to th shrinking or modl whn th siz of ratd partil is qual to th initial partil siz. Th modifid modl is applid to xplain th xprimnt rsults of th H S rmoval ration with ZnO in a thrmogravimtri analysis apparatus btwn 47K and 6K. ompard with th shrinking or modl, th rsults alulatd by th modifid shrinking or modl ar in good agrmnt with th xprimntal data, so th ration haratristis of ZnO with H S an b dsribd by that at th tmpratur blow 57K, th ration stoppd bfor th omplt onvrsion of ZnO partil was obtaind. This phnomnon an also b intrprtd by th suggstd modl. Som paramtrs suh as k s, D and was also obtaind. REFERENES [] H. Adloo, Z. Safai, M. N. Esfahany and M. R Ehsani, Dvlopmn.t of por ntwork mthod in simulation of non-atalyti gas solid rations Study of sulfur dioxid hmisorption on oppr oxid sorbnts, hm. Eng. J.,5, pp. 95. [] P. Sha'ban Nashta and B. Khoshandam, Nonatalyti gas-solid rations in pakd bd rators: a omparison btwn numrial and approximat solution thniqus, hm.eng ommun. Vol., 4, pp. -5, DOI:.8/986445..769 [] F. M.YANG F, L. WANG,S. W. YIN, and Y. H. LI, Nonatalyti gas-solid ration modl for dirtly nitridizing silion powdr undr atmosphri prssur, J Univ Si Thnol Bijing,vol.5, Jun., DOI:.74/j.issn-5x..6. [4] P. V. Ranad and D. P. Harrison, Th variabl proprty grain modl applid to th zin oxid-hydrogn sulfid ration, hm. Eng. Si.,vol.6, 98, pp. 79-89,doi:.6/9-59(8894-. [5] S.B.Zhang H.X.Guo and S.Z.Liang, Mirokinti study of HS rmoval by T5 dsulfuurizr, J. Taiyuan Univ Thnon.vol., Spt. 99, pp. -9. 4 4
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