Study on Heat and Mass Transfer During Urea Prilling Process

Transcription

1 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 Study on Het nd Mss Tnsfe Duing Ue Pilling Pocess Ali Mehez, Ahmed Hmz H. Ali, W. K. Zh, S. Ookw, nd M. Suzuki Abstct Ue ills e oduced in the illing towes whee solidifiction-cooling ocess tkes lce. The mbient i is used s the cooling i stem fo this ocess. In hot dys, the temetue of the oduct t the bottom of the towe e hot tht cnnot be cked diectly. In ddition, in hot/ humid dys, the ills fom lms nd ckes with ech othe nd on the scubbe. A mthemticl model bsed on the hydodynmics, het, nd mss tnsfe between the ue nd the cooling i is develoed. A numeicl technique with n exlicit scheme is used to solve the model. The model esults descibe the vition of the temetue nd moistue long the dius of the ticle. Hence, the model esults intoduce n inteettion of the oblem of cking nd lms fomtion es becuse of the incomlete solidifiction of the ills t the bottom of the towe. In ddition, the esults edict the qulity of the oduct unde diffeent oeting conditions of the mbient cooling i. Index Tems Numeicl simultion, ue solidifiction, Het nd mss tnsfe, mthemticl modeling. I. INTRODUCTION Ue is mketed s solution o in the solid fom. Ue in solid fom is oduced in the finl ocess stge by eithe gnultion o illing. Tnsfomtion of ue fom melt to solid ills tkes lce in the ue illing towe. In the illing ocess, ue melt is umed to the to of 50 to 60 mete (bove gound) cylindicl concete towe whee it is fed to the illing device tht clled otting bucket. The otting bucket is sieve-like cylindicl o conicl dum tht ottes bout its xis. Liquid jets emege fom the vious holes on the cuved sufce of the dum, nd bek u due to centifugl nd cilly instbility. The liquid ue dolets fomed fll downwd the illing towe. A countecuent cooling i stem entes fom intke oenings locted ound the cicumfeence of the towe t height oximtely 7 metes fom the gound level of the towe. Het nd mss tnsfe between the downwd ue Mnuscit eceived August 5, 01; evised Setembe 5, 01. The fist utho is suoted by scholshi fom the Mission Detment, Ministy of Highe Eduction of the Govenment of Egyt which is gtefully cknowledged. Ali Mehez, Ahmed Hmz H.Ali e with Enegy Resouces nd Envionmentl Engineeing Detment, Egyt- Jn Univesity of Science nd Technology E-JUST, New Bog Elb, Alexndi, Egyt (emil: li.mehez@ejust.edu.eg, hmed.hmz@ejust.edu.eg). W. K. Zh is with Physics nd Engineeing Mthemtics Detment, Fculty of Engineeing, Tnt Univesity, Tnt, Egyt (emil: wzh@f-eng.tnt.edu.eg). S. Ookw, nd M. Suzuki e with Detment of Chemicl Engineeing, Gdute School of Science nd Engineeing, Tokyo Institute of Technology, Tokyo, Jn (emil: sokw@chemeng.titech.c.j, mski@chemeng.titech.c.j). dolets nd the uwd cooling i stem long the height of the towe occus, nd thus solidifiction-cooling ocess tkes lce. The oduct, ue ills, goes fom the towe bse to conveyo belt whee it hs collected nd cked. The i stem exhust fom the towe though the exhusted stkes locted t the to of the towe whee it seds in the suounding envionment. As mbient i is used in the ocess of cooling nd solidifiction of the ills inside the towe, thus both the dy bulb temetue nd humidity of the mbient i highly ffect the qulity of the finl oduct. In this study, cse study of illing ocess in Abu Qi Fetilizes Co, Alexndi, Egyt is consideed. Bsed on the eoted infomtion fom the comny tht is in some dys in summe session, the ills e hot to the limit tht cnnot be cked diectly. The dely in the cking ocess leds to decese in the yely comny oduction. In ddition, in humid/ hot dys, the lm of ills foms t the bottom of the towe tht lso is not desied fo the oduct qulity. Though the oen litetue, thee e few studies discussed the modeling of the illing ocess beginning fom the wok of Bkhtin [1]. The mthemticl descition of the model eesents the Cuchy oblem fo system of fist-ode diffeentil equtions esulting descibing the dynmics nd the intenl enegy of the ticles. Bkhtin concluded tht the otimum height of the towe is tht t which the dolets becomes comletely solidified. Yun et l [] used simle shinking unsolidified coe model fo the towe-illing to intoduce new design fo the illing towe. The model ws bsed on lumed method whee the whole ticle temetue is ssumed constnt. Almdi et l [] intoduced moe enhnced model. In this study, the illing ocess ws simulted by simultneous solution of the continuity, hydodynmics, mss nd enegy tnsfe equtions. Hshemi nd Noui [4] detemined the citicl vlue of the ticle size below which no ticle cn fll down the illing towe, nd consequently cied ove to the to with the i stem nd dischged to the tmoshee. The im of this study is to build mthemticl model fo illing ocess t Abu Qi Fetilizes Co, with oductivity of 500,000 tons/ ye, locted in Alexndi, Egyt with schemtic digm shown in Fig. 1. A numeicl technique is used to solve the mthemticl model in ode to clculte the following metes within the illing towe: Velocity comonents of ticles with diffeent sizes t diffeent otting seeds of the otting dum. Temetue nd moistue content long the ticle dius. Vition of ticle vege temetue nd moistue content t diffeent oeting conditions long the DOI: /IJCEA.01.V.16 47

2 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 height of the towe. Fig. 1. A schemtic digm fo the ue illing towe II. MATHEMATICAL MODEL OF UREA PROCESS A. Model Assumtions In the deivtion of the model, the following ssumtions e consideed: 1) The dolet/ ticle e sheicl (fom exeimentl mesuements s shown in Fig. fo shot of the ticle sufce unde the electonic scnning micoscoe JSM-500 LV). ) Stedy stte fo the ue melt fed to the oty dum. ) The essue do long the towe is neglected (bout 0.01 P); theefoe, constnt essue conditions cn be lied. 4) Evotion of ue in the whole ocess, s well s the convesion of ue to mmoni nd cbon dioxide (ound 0.4% s eoted fom the comny) is neglected. 5) Rdition het tnsfe between ue ills nd the illing towe wlls is neglected (estimted bout 0.6%). 6) An dibtic ocess is consideed due to the mteil (concete low theml conductivity = W/m. K) nd lge thickness of the towe wll (0.5 m) 7) The volumetic tio of dolets/ ticles in the illing towe is nomlly vey smll (ound 0.1% only) so tht the effects of dolets/ ticles on ech othe in both het tnsfe nd movement e neglected. 8) Avege vlue of the i velocity in the xil diection is consideed (0.6 m/s mesued by the comny). B. Hydodynmics The illing towe hs cylindicl she. Thus, the illing ocess hydodynmics model is deived in the cylindicl coodintes (, θ,z ) with the unit vectos ( e,eθ,k ) in the diections of, θ nd z, esectively. The dtum of this coodinte system is tken t the i intke oenings level of the towe. Whees, fo the ticle het nd diffusion equtions, sheicl coodintes (, θ, ϕ ) e used. Thee foces ffect on the ticle duing its fll though the towe. These foces e; the weight foce F W tht cts downwd, buoyncy foce F B, nd dg foce F D both of them cts uwd s illustted in Fig.. The eqution of motion of the ticle in the medium (cooling i) is given s follows d v m = F B + F D F, W (1) dt 4 FW = m gk = ρ ( π R )gk, () 4 F B = ρ V P gk = ρ ( π R )gk, () 1 1 F D = C D A vel v C D( ρ 0 = ρ π R )vel v 0, (4) whee v is the ticle velocity, vel is the velocity of the ticle eltive to the i nd v 0 is the unit vecto of the eltive velocity. The dg coefficient CD is detemined by the fomul of [4] fo the nge of the ticle Reynolds numbe Re between < Re < =, 0 (5) Re C D. 5 ρ v z D whee Re =. μ The vege i velocity is v z in z-diection nd the ticle dimete is D. The ojection of the vecto eqution in the diection (, θ,z ) esulted in thee diffeentil equtions tht solved using 4th ode Runge-Kutt method using oite initil condition fo the ticle velocity. Fig. - Fig. -b Fig.. SEM imges fo the ue ticles illusttes ticle sheicity () nd intenl section (b) C. Enegy Blnce Fig.. Foces ffect on the ticle duing its fll Het tnsfe between the ticles nd the cooling i tkes lce long the height of the towe. Thee zones of stte hve been ssumed fo ech ticle s it flls fom the to to the bottom of the illing towe. In the fist zone, the liquid dolet loses its sensible het to the cooling i until it eches the cystlliztion temetue. In the second zone, solid lye δ ( z ) begins to e on the sufce of the dolet, nd hence two hses exist in ech dolet liquid nd solid. Het fom the coe of the ticle tnsfes to the mbient i by conduction though the liquid nd solid hses of the ills. In this stge, the solid lye moves towd the cente decesing the liquid hse until the dolet becomes comletely solid. In the lst zone, the solid ticle loses 48

3 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 sensible het nd futhe cooling tkes lce until the ticle exits fom the bottom of the towe t cetin temetue. The thee zones e shown in Fig. 4. Ue ticle size distibution (sieve nlysis) ws detemined by exeimentl mesuements using nlyticl sieve shke fo smle of 700 g tken fom the bottom of the illing towe. The Gussin distibution of the smle esults in n vege ticle dimete of 1.6 mm. K l = δ ( z ) + K s = δ ( z ) = ρlv z dδ dz (11) The i temetue vition long the towe is obtined fom the following eqution, Fig. 5. Fig. 4. Thee zones of the illing towe ρ v z C d T dz 6ε = hv T d ( ( ) ( z) ) l,s R T (1) Fo sheicl ticle, the temetue vition only in the dil diection nd unifom initil temetue t the to of the towe T init is consideed. The govening eqution fo the het tnsfe in liquid nd solid hses duing the thee zones, ssuming constnt density ρ, secific het C, nd theml conductivity K fo the solid nd liquid hses of the ue, is given s follows T T l l Cv z = K + 0 < Fo < R, zto < z < zinit, And 0 < < δ( z ), zinit < z < z finl, Fo δ ( z ) < < R, zinit < z < z finl, And 0 < R, z < z z. < finl < bottom (6) s T s K s Cvz = K ρ + (7) The govening equtions e subjected to the symmety condition t the coe of the ticle nd convection boundy condition t the oute sufce of the ticle. whee the het tnsfe coefficient is obtined fom the Rnz-Mshll s eqution [] s follows Consideing d is the vege dimete of the ticles, nd ε is the fction of the towe volume occuied by the ue ills. D. Mss Blnce The moistue is extcted fom the ills duing thei fll downwd the illing towe by the humid cooling i. The tnsient vition of the moistue in the dil diection of the ills is given by with unifom initil moistue content of the ticle M init, symmety boundy condition t the ticle coe nd convection mss tnsfe t the oute sufce v z M M = D + M D = h = M R = R D M W ( z) (1) mss (14) The mss tnsfe coefficient h mss is detemined lso fom the eqution of Rnz-Mshll given s follows [5] 1/ 1/ Sh = Re Sc (15) Fo 0 < Re < 00, 0 Sc 50, l, s K = hv ( T l,s ( R ) T ( z) ) = R Fo 0 < Re < 00, < P < 80, (8) / 1 1/ Nu = Re P (9) whee Nu nd P e the dimensionless Nusselt nd Pntdl numbes, esectively. In the second zone, solidifiction ocess tkes lce. This is the well-known two-hse Stefn Poblem with the conditions t the intefce δ ( z ). T l ( δ ( z ),z ) = T s( δ( z ),z ) = T m (10) ρ v Fig. 5. Slb of the towe with height dz z dw dz = h mss 6ε d ( M ( ) W ( z) ) R (16) whee Sh nd Sc e the dimensionless Shewood nd W z is the bsolute Schmidt numbes, esectively, nd ( ) 49

4 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 humidity of the i t the slb level. The vition of the bsolute humidity of the i is detemined fom the mss blnce s follows III. SOLUTION SCHEME The enthly method is oosed fo the solution of enegy evlution duing the towe. The enthly method is well-known method used fo solving the moving boundy oblems e in the hse chnge henomen [6]. In this method, n enthly function E (T ), which is the totl het content of the substnce, is used to eesent the eqution. Accodingly, Eq. 6 nd Eq. 7 cn be witten in one eqution tht will be s follows solution of the mss blnce equtions to obtin the vition of the ticle moistue content. The exlicit scheme is solved using ste size of 0.1 m (the towe height is 50 m) in z diection nd 0.05 mm in diection. The oeting conditions used in the esent esults e oduced in Tble I s eoted fom Abu Qi Fetilizes Co., while the theml nd chemicl oeties of ue e obtined fom [7] nd illustted in Tble II. E T K v z = K + (17) Fig. 6- The govening eqution is subjected to the sme boundy conditions. The solution domin (,z ) is discetized into N, M intevls in nd z diections with ste sizes d nd dz, esectively, Fig.6 TABLE I OPERATING CONDITIONS FROM THE COMPANY Vible Vlue Towe Height 57 [m] Towe Dimete 18 [m] Roty dum conic ngle [deg.] Rotting seed of the dum 55[m] Temetue of inlet ue melt 140 [ C] Moistue content of inlet ue melt 0.5 [% weight] Amount of ue melt 7487[Kmol/dy] Density of i [Kg/ m] Viscosity of the i x10-5 [P. s] Secific het of the i [KJ/ Kg. K] Totl flow te of the cooling i 50,000[Nm/h.] Pticle vege size 1.6 [mm] Vible TABLE II PROPERTIES OF UREA FROM [7] Vlue Density of ue melt 10 [Kg/ m] Melting oint of ue 1 [ C] Theml conductivity of ue.651x10-5 [KW/ m. K] Secific het of ue 1.4 [KJ/ Kg. K] Melting het of ue 4 [KJ/ Kg] Fig. 6. b Fig. 6. Discetiztion of the ticle dius () nd the solution domin (,z ) (b) Fig. 7- Fig. 7-b The fowd finite diffeence fomul is lied fo the deivtive of the enthly. Whees, the centl diffeence fomul is lied fo the fist nd second deivtives of the temetue. An exlicit scheme is obtined to get the temetue vition of the ticle long its dius t diffeent heights of the towe, consideing the singulity of the het eqution t the coe of the ticle esulting fom the symmety condition. Fo the iside in the enegy model, the fowd divided diffeence scheme is used fo the i temetue deivtive. The sme ocedue is lied fo the Fig. 7-c Fig. 7. Rdil, tngentil, nd xil velocity with diffeent ticle dimetes 50

5 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 IV. RESULTS AND DISCUSSION The thee comonents of the ticle velocity, dil, tngentil nd xil, e clculted fom the hydodynmic nlysis fo diffeent ticle sizes s shown in Fig. 7-, b, c, esectively. The esults show tht the lge the ticle dimete, the highe the oscilltion of both dil nd tngentil velocity befoe eching the zeo vlue. The cose ticles, dimete of mm o lge, hve highe xil velocity thn the fine ones. As mentioned, the melt is fed to otting conicl dum with vible dius long the height of the dum. Diffeent dolets fom diffeent sections of the dum hve distinct mlitude of oscilltion of the dil nd tngentil velocity, whees vible dum dius hs slice effect on the xil velocity s seen in Fig. 8-, b, c, esectively. A simil effect is obtined fo chnging the otting seed of the dum s illustted Fig. 9-, b, c, esectively. Incesing the otting seed of the ottoy dum leds to highe oscilltion in dil nd tngentil velocities. tht in the liquid hse due to the elese of the ltent het of cystlliztion t the intefce of solid nd melts lyes within the ticles. The temetue t the oute sufce emins oximtely constnt long the height of the illing towe. This is due to the slice vition of i temetue long the height of the towe. Fig. 11 shows the vition of the ticle vege temetue with the towe height. The esults show tht the lowe the i temetue t the inlet, the lowe the vege temetue of the ticles t the bottom of the towe. Fig. 9- Fig. 8- Fig. 9-b Fig. 8-b Fig. 9-c Fig. 9. Rdil, Tngentil, nd Axil Velocity t diffeent ms of the otting dum Fig. 8-c Fig. 8. Rdil, tngentil, nd xil velocity t diffeent sections of the otting dum The temetue vition long the dius of the ticle t diffeent heights of the towe is shown in Fig. 10. The i temetue is needed t the outlet of the illing towe. The ticles exit the illing towe (t z=0 m) with coe temetue bove the melting oint of 1 C. In ddition, cooling of the ills in the solid hse tkes lce fste thn Fig. 10-T = 0 C Fig. 10-bT = 0 C 51

6 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 it cn be seen tht the lge the i humidity t the outlet, the lge the mount of moistue tht extcted fom the ills. Hence, oduct of less moistue content is obtined. Fig. 14 illusttes the vition of the moistue content long the dius of the ticle t diffeent i humidities. Fig. 10-cT = 50 C Fig. 10. Temetue vition long the dius of the ticle t diffeent i temetue Fig. 14-b. W = 0.0 (Kg wte)/(kg dy i) Fig. 11. Vition of vege ticle temetue with the towe height Fig. 14-cW = 0.0 (Kg wte)/(kg dy i) Fig. 14. Vition of moistue content long the dius of the ticle t diffeent i humidity Fig. 1. Vition of vege ticle moistue content with the towe height Fig. 1. Vition of i humidity with the towe height Fig W = (Kg wte)/(kg dy i) The chnge in vege moistue content of the ticle long the height of the towe is shown in Fig. 1 t diffeent i humidities. Fig.1 illusttes the vition of bsolute i humidities long the towe height. Fom Fig. 1 nd Fig. 1, V. CONCLUSION Ue ills e oduced in the illing towes whee solidifiction-cooling ocess tkes lce. The mbient i is used s the cooling i stem fo this ocess. In hot dys, the temetue of the oduct t the bottom of the towe e hot tht cnnot be cked diectly. In ddition, in hot/ humid dys, the ills fom lms nd ckes with ech othe nd on the scubbe. A mthemticl model bsed on the hydodynmics, het, nd mss tnsfe between the ue nd the cooling i is develoed. A numeicl technique with n exlicit scheme is used to solve the model. The study esults e s follows: The esults show tht the velocity comonent vlues of the ticles with diffeent dimetes t diffeent oeting conditions incese with incesing the otting seed of the oty dum. This leds to n enhnced enettion of the ticles though the towe nd hence oduct of bette qulity. The model esults descibe the vition of the temetue nd moistue long the dius of the ticle. Hence, the model esults intoduce n inteettion of the oblem of cking nd lms fomtion es becuse of the incomlete solidifiction of the ills t the bottom of the towe. The vition of vege ticle temetue nd moistue content is oduced long the towe height s well s fo the iside. Thus, the model edicts the qulity of the oduct unde diffeent oeting 5

7 Intentionl Jounl of Chemicl Engineeing nd Alictions, Vol., No. 5, Octobe 01 conditions of the mbient cooling i. ACKNOWLEDGMENT The fist utho is suoted by scholshi fom the Mission Detment, Ministy of Highe Eduction of the Govenment of Egyt which is gtefully cknowledged. A C D D D d NOMENCLATURE Extenl e of the ticle [m] Dg coefficient Diffusion coefficient [m/s] Pticle dimete [m] Avege ticle dimete [m] C Secific het ccity of the ue [KJ/ Kg. K] C Secific het ccity of the i [KJ/ Kg. K] E e e θ F B F D FW Locl enthly of the ticle [KJ/ Kg] Unit vecto in -diection Unit vecto in -diection Buoyncy foce [N] Dg foce [N] Weight foce [N] g Acceletion of gvity [m/ s] h v Het tnsfe coefficient [KW/ m. K] h mss Mss tnsfe coefficient [m/ s] k Unit vecto in z-diection K L M Nu P R Re Theml conductivity of the ue Ltent het of cystlliztion of ue [KJ/ Kg] Locl moistue content of the ticle [% weight] Nusselt numbe Pntdl numbe Rdius of the ticle [m] Pticle Reynolds numbe Sc Schmidt numbe Sh Shewood numbe T Temetue of cooling i [ C] T l, s Temetues of liquid nd solid ue [ C] v z Avege i velocity [m/ s] v Pticle velocity [m/ s] v el Pticle velocity eltive to the i [m/ s] v 0 Unit vecto of the eltive velocity W Absolute humidity of the cooling i ε Fction of towe volume occuied by the ticles ρ Density of ue [Kg/ m] ρ Density of i [Kg/ m] μ Kinemtic viscosity of the i [P. s] δ Intefce osition [m] REFERENCES [1] L. A. Bkhtin, A. A. Vgin, L. Y. Esiovich, nd A. N. Lbutin, Het-Exchnge clcultions in illing towes, Chemicl nd Petoleum Engineeing, vol. 14, , [] W. Yun, B. Chuning, nd Z. Yuxin, An Innovted Towe-fluidized Bed Pilling Pocess, Chin. J. Chem. Eng., vol. 15, no., , 007. [] A. Almdi, A. Jhnmii, nd N. Rhmniyn, Mthemticl Modeling of Ue Pilling Pocess, Chemicl Eng. Comm, vol. 178, , 000. [4] M. Hshemi nd F. Noui, Study on ollution evention though n integted ocess-envionmentl model in ue illing towe, Envion Model Assess, no. 11,.4 50, 006. [5] N. Wko nd S. Kgue, Het nd Mss Tnsfe in Pcked Beds, Godon nd Bech, Science Publishes, Inc, 198 [6] J. Cnk, Fee nd Moving Boundy Poblems, Oxfod Univesity Pess, USA, [7] Ullmnn, Encycloedi of Industil Chemisty, Wiley-VCH, 007. Ali Mehez ws bon in Tnt, Egyt, on Jnuy He obtined B.Sc. in Mechnicl Powe Engineeing fom Tnt Univesity, Egyt, in 006. The Cumultive vege gde is Distinction with Hono's Degee Now he is MSc. Student t Detment of Enegy Resouces nd Envionmentl Engineeing Detment, Egyt-Jn Univesity of Science nd Technology E-JUST, Alexndi, Egyt. His filled of esech inteest is mthemticl modeling of the ue illing ocess, Numeicl Anlysis. Ahmed Hmz H. Ali since My 010 is Pofesso nd Chieson of the Detment of Enegy Resouces nd Envionmentl Engineeing, Egyt-Jn Univesity of Science nd Technology (E-JUST), Egyt. Fom June 009 to now, he ws Pofesso of Refigetion nd Ai-Conditioning t Fculty of Engineeing, Assiut Univesity, Egyt. Ahmed Hmz ws bon in Egyt in Decembe 16, 196. Ahmed Hmz obtined his Doctol Degee in Engineeing in field of het tnsfe fom Muon Institute of Technology, Jn in Mch1999. Ahmed Hmz mjo field of study e Design of Renewble Enegy Utiliztion systems such s Sol Enegy Cooling Systems, Noctunl Rdition Cooling Systems, Sol Powe Genetion, Theml Enegy Stoge nd Industil Sol Heting Systems, Photovoltic (PV) nd Concenttion Photovoltic (CPV) Modules Theml Regultion systems. In ddition design nd efomnce of smll-scle theml diven chilles, convection combined with dition het tnsfe t solid boundy, combined het nd mss tnsfe. He hs moe thn 5 es ublished on Int. J nd moe thn 40 oceeding es. His cuent esech of inteest is Design of theml systems. He evious esech inteest wee Theml owe lnt imct on envionment, theml nlysis of fuel cells nd Theml nlysis fo heting nd cooling of buildings Pof. Ahmed Hmz is membe of Intentionl Sol Enegy Society (ISES), The Het Tnsfe Society of Jn, Jn Society of Mechnicl Enginees (JSME) nd Egytin Engineeing Syndictes 5