MODELING AND SIMULATION OF AMMONIA SYNTHESIS REACTOR

Peet trool lleeuum & Cool ll IISSN 17-707 Avlle onlne t www.vuru.sk/c Petroleum & Col 48 (), 15-, 006 MODELING AND SIMULATION OF AMMONIA SYNTHESIS REACTOR Al Dsht, Kyvn Khorsnd 1, Mehd Ahmd Mrvst, Mdjd Kkvnd Reserch Insttute of Petroleum Industry (RIPI), Pzhouheshgh Blvd., Khrd, Qom Rod, Tehrn, Irn. 1 corresondng uthor, khorsndk@r.r Receved My 1, 006; cceted June 4, 006 Astrct In ths er n ndustrl mmon synthess rector hs een modeled. The rector under study s of horzontl tye. Ths rector whch s under the lcense of Kellogg Comny s equed wth three xl flow ctlyst eds nd n nternl het exchnger n ccomny wth coolng flow. The cheved modelng s one dmensonl nd non-homogenous. Consderng the sever effect of nternl het exchnger on rector oerton, t hs een smulted y clculton of flm het trnsfer coeffcents n ts tue nd shell nd then, tkng nto ccount the shell therml resstnce nd foulng coeffcent, otnng the overll het trnsfer coeffcent. So n the develoed softwre, the het trnsfer coeffcent s frst clculted usng the condtons of the nut flow to the exchnger nd then the nut flows to the frst nd second eds re clculted. The dfferentl equtons hve een solved usng Rung Kutt 4 method nd the results hve een comred wth the vlle ndustrl dt. Fnlly the clty of the develoed softwre for ndustrl lcton hs een nvestgted y chngng the rector oerton condtons nd studyng ther effects on rector outut. Key words: mmon, rector, modelng, smulton 1. Introducton Ammon Synthess s very mortnt rocess n chemcl comlexes. Ammon s the ntl chemcl mterl for vrety of ndustres. It s used n roducton of chemcl fertlzers, exlosve mterls, olymers, cds nd even coolers. Smulton cn ly n mortnt role to gve n nsght of the ndustrl unts nd hence smulton of Ammon unt s very mortnt to hel us nvestgte the dfferent oerton modes of ths unt nd otmze tht. Ammon synthess loo s the most mortnt rt of ths unt whch etter understndng of ts ottleneck cn led us to mke the oerton yeld hgher thn efore.. Ammon Synthess Loo In mmon roducton unt, the synthess loo s locted fter the syngs roducton nd urfcton unts. Ammon synthess rocess tkes lce n hgh ressure nd hence hgh ower mult cycle comressors re used to suly the requred ressure. The Kellogg synthess rector ncororted n ths loo s of horzontl tye wth three eds. To control the temerture etween frst nd second eds, n nternl het exchnger hs een used n whch the nut feed to the frst ed nd the outut gs from the sme ed hve therml exchnge. In ddton to the mentoned het exchnger, the quench gs flow s lso used for control of temerture. The nut feed to the rector, s frst dvded nto two rts, efore entrnce. One rt s consdered s feed nd the other rt s quench gs. The feed, fter enterng the rector, sses through the emty sces of the eds s well s the rector wlls nd gets slghtly heted. When rechng to the end of the rector, t sses through the shell of the nternl het exchnger nd ts temerture reches 400 ºC. Tues of the het exchnger contn the outut gs from the frst ed. Quench gs s used to control the nlet temerture of the frst ed. The requred temerture for nlet of the frst ed s 71 ºC. Outut gs,

Al Dsht et l./petroleum & Col 48() 15- (006) 16 fter wrmng u, s then entered to frst ctlytc ed. Fgure 1 dects the schemtc dgrm of Kellogg horzontl rector. Fg.1 Ammon Synthess Rector - Kellogg method [1] When the gs sses the frst ed nd the recton s tken lce, ts temerture ncreses nd reches 496 ºC. It then enters the tues of the het exchnger to cool down. Gs s then entered from to of the second ed. Temerture rses gn s the recton tkes lce n the second ed. No secfc oerton s crred out etween eds two nd three. In fct these two eds ct s sngle ed whose length s twce the length of ech ed. The ctlyst of ths rector s mgnetc ferro oxde.. Mthemtcl Model By modelng of the synthess rector, temerture, concentrtons nd ressure rofles re otned. Of course testng of the model sed on the ove rmeters s cheved t the end of ech ed s ndustrl dt re not usully vlle long the length of the ed. The followng ssumtons hve een mde for ths modelng: 1. One-dmensonl Crtesn coordnte hs een consdered long wth the ulk flow.. Penetrton of mss nd het s gnored, s the flud velocty s very hgh n ndustrl scle.. Densty s constnt 4. Concentrton nd temerture on ctlyst surfce nd ulk of gs re equl. 5. The effects of enetrton resstnce n ctlyst, temerture grdent nd ctlyst nsde concentrton hve een ncororted n the equtons y coeffcent. Mterl lnce (Molr) [,] Consderng n element wth heght of Δ x nd cross secton re equl to tht of the ed we ll hve: uca x uca x + Δ x Accumulton = Consumton Producton + Outut Inut There shll e no ccumulton s the system hs een consdered to e n stedy stte. ( r ) 0 uca uca 1 x + AΔx η = x+ Δx NH Dvdng oth sdes of the equton y AΔx nd Δx 0, we ll hve:

Al Dsht et l./petroleum & Col 48() 15- (006) 17 ( r ) 0 dc u + NH η = d x Ths equton cn e re-wrtten s elow sed on the Ntrogen Converson Percentge shown y Z: dz dx ηrnh = FN A n whch the term F N A s the ntl molr flow of N. Recton Rte [,4,5,6,7,8] To clculte the rte of recton, modfed Temkn equton offered y Dyson & Smon n 1968 hs een used [4] α 1 α H NH R = NH k K N 4 NH H n whch α : Constnt whch tkes vlue from 0.5 to 0.75 n lterture [8]. k : Rte constnt for reverse recton n: N + H NH K : equlrum constnt : Actvty Actvton cn e wrtten n terms of ctvton coeffcent s elow: f = 5 f 0 f : Reference fugcty. If the reference fugcty s consdered to e 1 tm, then: f = = f = y φ P 6 1 In ths equton φ s the fugcty coeffcent nd P s the totl ressure. Below equtons re the exermentl ones for fugcty coeffcent of hydrogen, ntrogen nd mmon [4]. H 0.15 0.5 ( ) ( ) ( ).840T + 0.541 0.16T 15.98 0.011901T 5.941 = ex e P e P + 00[ e ] e P 00 φ 7 φ N = 0.94177 + 0.0858 6 6 0.7077 T + 0.477507 P φ = 0.148996 + 0.0858 T 0.448767 NH 0.114945 5 T + 0.76116 T + 0.95896 6 P P P 8 9

Al Dsht et l./petroleum & Col 48() 15- (006) 18 In ove equtons T s n terms of Kelvn nd P n terms of tmoshere. The equton of reverse mmon synthess recton hs een consdered n se of Arrhenus formt. E k = k ex RT k : Arrhenus coeffcent equl to 8.849 E : Actvton energy, whch vres wth temerture. Its men vlue s R : Gs constnt 14 kcl 40765 kmol In 190, Gllese nd Bette hve develoed the followng equton to clculte the equlrum constnt [9]. 5 7 log K =.6911 logt 505195 T + 1.84886 T 001.6 11 + +.689 T η Effect Fctor [,4,] To nvestgte the effects of temerture nd densty of the ctlyst nteror nd the dfference etween these rmeters wth those of the ctlyst surfce, n effect fctor clled η hs een defned. The generl form of the equton defnng ths effect fctor hs een gven elow []. η + T + + + + + 1 = 1 Z T 4Z 5T 6Z The ove equton s n terms of T nd converson ercentge. The coeffcents of ths equton for three dfferent ressures hve een dected n tle [4]. Pressure (r) 150 5 00 Tle. Coeffcents of the correcton fctor olynoml n terms of ressure 1 4 5 6-17.59096-8.1554-4.675759 0.07697849 0.0774149 0.05487 6.900548 6.19011 4.6875-1.0879e-4-5.54571e-5 -.4608e-5-6.4469-0.8696-11.801 4.97648e-8.7914e-8 1.540881e-8 8.97 7.88.46 Energy lnce Energy lnce s nvestgted on the sme element on whch mss lnce hs een consdered. Accumulton = Consumed Energy Produced Energy + Outut Energy Inut Energy In stedy stte, the ccumulton s zero. { ρuc T ρuc T } + AΔx( ΔH ) R 0 A 1 x Dvdng the ove equton y x+ Δx r NH η AΔ x nd = Δx 0, we ll hve: dt ρuc + ( ΔH r ) RNH η = 0 14 dx Het Cctnce The followng equton s used to determne the Het cctnce:

Al Dsht et l./petroleum & Col 48() 15- (006) 19 C ( = T + c T d ) kj = 4.184 T kmol + 15 Tle 4. Coeffcents of C olynoml for some comonent. Comonent H N CH4 Argon 6.95 6.90 4.75 4.9675-0.04567-0.075 1. ---- 5 c 0.0956 0.19 0.0 ---- 5 d -0.079-0.6861 -.6 ---- In 1967, Shh hs develoed n equton for determnton of mmon het ccty whch hs een used n our modelng [11,1]. 5 6.5846 0.6151 T + 0.66 T 9 1.5981 T + 96.1678 0.067571P + kj C PNH = 4.184 kmol. k 4 ( ) ( ) 0.5 + 1.6847 P T + 4 7 1.89 1.0095 P T 16 Recton Het Elnshe hs develoed relton n 1981 for clculton of recton het whch hs een used n our modelng [1]. 6 846.609 459.74 0.5456 + + P 5.4685T kj ΔH r = 4.184 T T 6 kmol 0.55 T + 69197 T 9157.09 17 Pressure Dro [14,15,16] To clculte the ressure dro nsde eds, Ergun equton hs een led. Ths relton for onedmensonl flow s s elow [15,16]. ( 1 ε ) z 150 μu 1 ε ρu Δ P = μ u = 1.75 18 ε d ε d As most of the ndustrl dt long the eds re not vlle, the model s tested sed on the ove vlues t the end of ech ed. Alyng mss, energy nd momentum lnce on n element, derves the mthemtcl model. Consderng ll the onts nd dscussons rsed n the revous sectons, the elow set of three dfferentl equtons re derved. dz ηrnh = dx FN A dt ρuc + ( ΔH r ) rnh η = 0 dx z dp 150( 1 ε ) μu = μ u = 1.75 dx ε d 1 ε ρu ε d 19

Al Dsht et l./petroleum & Col 48() 15- (006) 0 The 4 th order Runge Kutt roch s used to solve the ove set of equtons. As ths set of equtons s stff, ressure dro equton s frst tken out of the set nd the new set wth two equtons s solved usng Runge Kutt numercl method. At ech stge of the numercl soluton, ressure dro s clculted y mens of the temerture nd concentrton derved from tht stge nd n ths cse the three rmeters.e. temerture, ressure nd converson rte re determned. 4. Modelng Results Results tken from smulton re comred wth ndustrl dt. Inut condtons re s elow [17] : Rector nut temerture: 66 C Rector nut ressure: 16.5 r Desred temerture for nut gs flow to the frst ed: 71 C Inut flow rte to rector: 18600 kg hr Inut comoston: y 0, N = 0.6680 y 0, H = 06567006 y 0, NH = 0.0690 y 0, CH = 0.059714 4 y 0,Ar = 0.00874 The ove hs een clculted fter mxng wth quench flow nd the totl flow of the rector s kg derved s 000. hr Fg. Chnges of N converson rte long the eds Fg llustrtes the chnges of N converson rte long the three eds. It s oserved tht chnges long the frst ed re more sever thn those of the second nd thrd ones ecuse of the lower recton roduct ( N ) content n feed of ths ed. The deflecton n the curve etween frst nd second ed s ecuse of chnge n the recton seed, whch s n turn resulted from gs coolng. As no secfc oerton s crred out etween second nd thrd eds, the curve remns unform long them.

Al Dsht et l./petroleum & Col 48() 15- (006) 1 Fg. Molr frcton of the comonents long the eds Molr frcton of the comonents long the ed cn e deducted from the converson rte nd ntl mole frcton vlues. Fg dects the molr frcton of the three mn comonents of the recton. Fg 4. Pressure Chnges long the eds Fg 4 llustrtes ressure rofle long the eds. In rctce, ressure dro s more thn tht shown y modelng s n the relted smulton the ctlyst rtcles re ssumed to e shercl. Ferrte ctlyst doesn t hve regulr she whch ncreses the ressure dro. The deflecton n the curve etween frst nd second ed s resulted from the nternl het exchnger ressure dro.

Al Dsht et l./petroleum & Col 48() 15- (006) Fg 5. Temerture Chnges long the eds Fg 5 llustrtes the temerture chnges long the eds. In frst ed, s the mmon concentrton s low, the recton rte s very hgh nd the temerture ncreses long the ed whle rochng equlrum t ts end (the sloe of the curve s reduced long the ed). After frst ed, gs s cooled down n nternl het exchnger cusng tht to get fr from equlrum. As t s oserved n the fgure, the gs roches equlrum t the end of thrd ed nd the temerture chnge s low. As revously mentoned, one of the cltes of the develoed softwre s nvestgton of chnges n the unt oututs. Anlyss of these results, cn led us to fnd ottlenecks nd hgh roducton wys, etc. Fg. 6 nd 7 llustrte some of the results. Fg 6. Effect of chnges n flow rte on dfferent rmeters

Al Dsht et l./petroleum & Col 48() 15- (006) 5. References Fg 7. Effect of chnges n nut NH concentrton on dfferent rmeters [1] R.W. Mssen, C.A. Mms, B.A. Svlle, Introducton to Chemcl Recton Engneerng & Knetcs, Wley, 1999. [ J. Morud, The dynmcs of Chemcl Rectors Wht Het Integrton, Ph.D thess, 1995. [] S. S. Elnshe, M. E. Ashr And A. S. Al. Ud, Smulton nd Otmzton of n Industrl Ammon Rector, Ind. Eng, chem.. Res, Vol. 7,. 015, 1988. [4] D.C. Dyson nd J.M. Scon. A Knetc Exresson Wth Dffuson Correcton for Ammon Synthess on Industrl Ctlyst, Ind. Eng. Chem. Fundmentl, Vol. 7, No. 4,. 605, 1986. [5] P.P. Sngh nd N. Srf Smulton of Ammon Synthess Rector, Ind. Eng. Chem. Process Des. Dev, Vol. 18, No.,. 04, 1979. [6] P. Stoltze nd J. K. Norshov, An Inter erdton of the Hgh-ressure Knetcs of Ammon Synthess Bsed on Mcroscoc Model J. Ctl, Vol. 1,. 1, 1988. [7] L. D. Gnes, Otml Temertures for Ammon Synthess Converters, Ind. Eng. Chem, rocess Des. Dev, Vol. 16, No.,. 81, 1977. [8] A. Nelsen, An nvestgton on Promoted Iron Ctlysts for the Synthess of Ammon, rd Ed, Jul. Gjellerus, Coenhgen, 1968 [9] L. J. Gllese, J. A. Bette, Phys. Rev., Vol. 6,. 74, 190 [] L. D. Gnes, Ammon Synthess Loo Vrles Investgted By Stedy-Stte Smulton, Chem. Engng Sc, Vol. 4,. 7, 1970. [11] B. Elverse, S. Hwkns, W. Russey, G. Schulz, Ullmn's Encycloed of Industrl Chemstry, 5 th Ed, Vol. A, 199. [1] M. J. Shh, Control Smulton n Ammon Producton, Ind. Eng. Chem., Vol 59, No 1, 7, 1967. [1] A.T. Mhfouz, S.S. Elshshn, nd S.S.E.H. Elnshe, Stedy-Stte Modellng And Smulton of n Industrl Ammon Synthess Rector I. Rector Modelng, Modelng Smulton & control, B, ASME ress, Vol., No.,. 1, 1987. [14] S.S.E. H. Elnshe nd S.S. Elshshn, Modelng, Smulton, nd Otmzton of Industrl Fxed Bed Ctlytc Rectors, G&B Scence, 199. [15] S. Ergun, Flud Flow Through Pcked Columns, Chem. Engng. Prog., Vol 48, No,. 89, 195. [16] F. Zrd, D.Bonvn, Modellng, Smulton nd *Vldton for n Axl- Rdl Ammon Synthess, Chem. Engng Sc., Vol. 47, No. 9-11,. 5, 199. [17] Feslty Study on Technology Trnsfer nd Loclzton of Ammon Synthess Process n Irn, Project reort, Reserch Insttute of Petroleum Industres, 001.