Modeling Of The Reactor-Crystallizer Unit In A Phosphoric Acid Production Plant

Transcription

1 Modelg Of The Reacto-Cystallze Ut I A Phosphoc Acd Poducto Plat a Kyakos Theodosads, a Athaasos I. Papadopoulos, a,b Paos Sefels a Chemcal Pocess Egeeg Reseach Isttute, CERTH, P.O. Box 60361, Them-Thessalok, Geece b Depatmet of Mechacal Egeeg, Astotle Uvesty of Thessalok, P.O. Box 484, Thessalok, Geece Ths pape descbes a ew appoach the modelg of the dssoluto of phosphate ock ad ts subsequet coveso to phosphoc acd (H 3 PO 4 ) afte t has bee teated by sulfuc acd a cotuously sted tak. The eacto s cosdeed as a set of tecoected modula cells of ufom bulk lqud phase cocetato ad tempeatue. Wth each cell a detaled dyamc model that copoates the flm theoy to descbe the multcompoet dffuso ad eacto aoud the ock patcles s developed. The geealzed Maxwell-Stefa equatos modfed to accout fo electolyte soluto ae used fo the calculato of the fluxes fo the mola ad oc compoets though the flm. The poposed eacto epesetato ca accommodate o-ufom cocetato dstbuto wth the eacto ad futhe allow the detaled modelg of the lqud-sold tefacal pheomea. 1. Itoducto The heat of the poducto pocess the phosphoc acd dusty s the eactocystallze ut. The ma goals of the pocess ae the hgh coveso of the phosphate ock ad the hgh ecovey ate of the poduced phosphoc acd. The fome s acheved by allowg suffcet cotact tme fo the phosphate ock the eacto ad the latte by matag those eacto codtos that would allow the pope fomato of the gypsum cystals (Becke, 1989). Theefoe, motog, cotol ad optmzato of the eacto opeatg codtos s absolutely ecessay. The ecycle ate of the phosphoc acd soluto to the eactos, the cocetato of solds the feed, the sulfuc acd cocetato the eacto ad the sze of the poduced cystals at the outlet ae factos that have sgfcat effect achevg the poduct qualty specfcatos (fo the poduct acd cocetato) ad mmzg the eegy cosumpto of the pocess. Howeve, pocess desg ad optmzato of the eacto eque the developmet of accuate ad elable models that ca accuately pedct the behavo of the ut. Multple teactg physcal ad chemcal pheomea take place sde the eactocystallzato ut used phosphoc acd plats. These geeally volve dffuso of the eactats (H + ) fom the bulk of the lqud soluto to the suface of the sold patcles of the phosphate ock, eacto that leads to the dssoluto of the phosphate ock at ts suface, dffuso of the poducts (e.g., PO 4-3, Ca +2 ) fom the suface of the sold to the bulk phase of the lqud soluto ad fomato of a ew sold phase (CaSO 4 2H 2 O cystals). Due to the fact that most of the eactos each the equlbum vey fast,

2 dffuso becomes the lmtg step the dssoluto of the phosphate ock ad the ctcal stage the fomato of the gypsum cystals. Most models foud lteatue (Goa, 1977, Abu-Eshah, 2001) attempt to descbe the behavo of the eacto system based o smplfed balace equatos. The age dstbuto fuctos that ae used ae based maly o empcal coelatos that mpose lmtatos o the age of applcato fo the model. Futhemoe, lteatue models do ot cosde the effects of cocetato gadets wth the eacto, multcompoet dffuso of oc compoets ad the dyamc behavo of the ut. The peset wok focuses o the developmet of a eacto model that s cossted of a umbe of tecoected modula cells that accuately descbe the multcompoet dffuso usg the geealzed Maxwell-Stefa equatos adapted fo oc solutos ad eactve pheomea aoud the ock patcles steady state ad dyamc codtos. 2. Model Fomulato The model volves the descpto of mass tasfe pheomea ad chemcal eactos the sold-lqud teface usg the th flm model (Taylo & Ksha, 1993) wth a sgle cell. Accodg to the th flm model mass tasfe esstace s lmted a flm ego adacet to the lqud-sold teface. The basc assumptos of the model ae: () oe-dmesoal mass taspot omal to the teface, () pefectly mxed bulk lqud phase wth ufom tempeatue ad composto ad () mpemeable sold phase ad mola compoets wth a ufom phosphate composto. Fo desg puposes these assumptos ca be safely cosdeed as vald fo omal opeatg codtos. Chemcal eactos ae cosdeed to take place both the flm ad the bulk lqud phase egos. A gaphc epesetato of the flm model s show Fgue 1. Fgue 1. Schematc epesetato of the th flm model the lqud-sold teface. The mass balace fo a sgle ut/cell the bulk phase of the lqud the eacto mxtue s gve by Equato (1).

3 dm dt b b t = + ( φ R + N α ) V 1,... (1), out, cell = Whee V cell deotes the volume of the cell, φ deotes the facto of the bulk lqud volume ove the total cell volume, α t deotes the tefacal aea of the lqud pe ut volume of the cell. The total eacto ate fo each compoet ad ts mola flux ae b b deoted by R, N, espectvely. The total flow ates ad mole factos the bulk phases ae defed by: = =1 t b x = 1,... t = 1,... (2) = (3) Table 1. Reacto ad eacto compoets Idex Compoets Reactos Commets 1 H + CaSO 4 2H 2 O Ca +2 + SO H 2 O 2 SO Ca +2 4 PO F - 6 H 2 O 7 Ca 3 (PO 4 ) 2 CaF 2 H + + Ca 3 (PO 4 ) 2 CaF 2 2PO Ca +2 +2F - + H + Takes place the bulk ad flm ego of the lqud Takes place at the sold teface The fomato of the salt compoud CaSO 4 2H 2 O s cosdeed as a equlbum eacto. The eacto takes place both the flm ad the bulk ego of the lqud ad the poduct dffuses to the bulk. The total compoet eacto ates ae calculated by Equatos (4) ad (5) fo the bulk ad flm ego of the lqud phase, espectvely. b R, whee b = ν R = ν, = 1,... (4) ad b ae the eacto ates of each compoet the flm ad bulk ego of the lqud, espectvely. The tems the left-had-sde of Equato (1) accout fo the compoet mola hold-up the lqud phase whch, ts tu, s elated to the avalable lqud volume by the followg equato: m = φ d Vcell (5) t Fo multcompoet mxtues the Maxwell-Stefa equatos deved fom the ketc theoy of lquds ae used to descbe the dffuso tems. I the geealsed fom, these equatos ae gve by (Taylo ad Ksha, 1993).

4 1 = 1 Γ x η x z F RT φ η = ( x N x N ) = 1 c t Ð (6) fo = 1,... 0 < η δ whee, Γ = δ + x l γ x T, P, xk, k = 1,... 1 The electolyte atue of the compoets cluded the eacto mxtue ad the fact that the speces dffused ae os s take to accout the themodyamc popetes of the model. The actvty coeffcet γ Equato (6) coespods to the actvty coeffcet of each o cotaed the eacto mxtue ad t s calculated cosdeg the solvato effect of the os. The theoy of Ptze ad Km (1974) s used to deteme the actvty coeffcets of the electolyte compouds. The tem F φ x z Equato (6) descbes the effect of the electcal foces RT η developed betwee os the dffuso though the flm ego of the soluto. φ s the electcal potetal of each oc compoet, F s the Faaday costat ad z s used to expess the oc chage. It s cosdeed that thee s o et electcal body foce actg o the mxtue as a whole ad theefoe the codto of electoeutalty holds ad s expessed by Equato (7). = 1 c = 0 (7) z Whee, c s the cocetato of each oc compoet the soluto mxtue. The mass balace the lqud flm s gve by the fomulae: N η R = 0 fo = 0 < 1,... η δ (8) The bouday codtos fo Equato (8) ae as follows: N b b = N x = x = 1,... Gf Gf η = δ η = δ (9) Gypsum cystal fomato modelg s based o the pcple that the degee of supesatuato of calcum sulphate (CaSO 4 ) dctates both the fomato of the ucle ad the gowth of the cystals. Followg Abu-Eshah et. al., 2001, the mass facto of gypsum the total amout of sluy the eacto, B, ad the degee of supesatuato, G, ca be calculated by Equatos (10)-(12).

5 B 0 4 = 6 G φ ψ ( u ) 2 t avg (10) ρ 2+ 2 [ Ca ][ SO4 ] 2+ 2 [ Ca ] [ SO ] G = = 1 + S * (11) C eq 4 eq C * 5 2 ( T ) C ( ) ( ) = ρ (12) * Whee C s the satuato cocetato of calcum sulphate kg/m 3 ad C PA s the mass cocetato of the phosphoc acd the mxtue. The mass desty of the total mxtue s ρ kg/m 3. The degee of supesatuato S s calculated as the dffeece betwee the actual ad the satuato cocetato of calcum sulphate. * S = C ( ) C ( ) (13) The ete eacto ut s cosdeed as a set of tecoected modula cells. The lqud phase leavg each cell ca be dstbuted to the adacet cell below ad to the ght theeby the axal ad coss flow mxg become a adustable paamete. The lqud mola flows of each compoet each cell ae calculated by the followg elatos.,, ( axal) +, ( coss) = (14) The tempeatue wth each cell s mataed ufom. Gve the exothemc atue of the eacto, sothemal codtos ae acheved by patal evapoato of the lqud soluto. The vapo effluet cotas maly hydofluode ad wate ad s calculated fom a oveall eegy balace. The popetes of the phosphate ock patcles ae assumed ufom all cells. The eacto modula epesetato s show Fgue 2. PA Fgue 2. Schematc epesetato of the oveall eacto ut model.

6 3. Soluto appoach The method of Ptze ad Km, 1974 wll be used fo the estmato of the actvty coeffcets of the electolytes patcpatg the eacto. The patal dffeetal equatos the flm (Eq. 8) ae dscetzed usg othogoal collocato o fte elemets (OCFE). Cosequetly, the eacto model s descbed by a set of dffeetal ad algebac equatos. gproms by PSE (Pocess Systems Etepse), a advaced modelg evomet, s used fo the fomulato ad soluto of the dyamc eacto model. Ketc costats, flm thckess, ad mass tasfe coeffcets ae selected as the adustable paametes to ft the dustal data avalable fo the eacto-cystallze ut. 4. Cocludg emaks Ths wok poposes a ovel appoach modelg the eacto ut a phosphoc acd poducto plat. Multcompoet dffuso of electolyte soluto cossted of sulfuc acd, phosphoc acd ad calcum sulphate, whch essetally detemes the dssoluto ate of the phosphate ock ad the optmal fomato of gypsum cystals, has bee thooughly vestgated. Mxg effects the lage dustal sted taks has bee take to cosdeato wth the patto of the eacto to a set of tecoected modula cells of ufom cocetato ad tempeatue. The model wll eable the calculato of the optmal opeatg codtos fo the maxmzato of the phosphate ock yeld, ad the maxmzato of phosphoc acd ecovey at the hghest possble poduct cocetato fo lowe eegy equemets. Ackowledgemets The facal suppot of the Euopea Commsso ude poect ECOPHOS (INCO- CT ECOPHOS) s gatefully ackowledged. 5.Refeeces Abu-Eshah, S., I., Nza, A., J., 2001 Paametc study o the poducto of phosphoc acd by the dhydate pocess Chemcal Egeeg Joual, 81, Becke P., 1989, Phosphates ad phosphoc acd: Raw mateals, techology ad ecoomcs of the wet pocess, Macel Decke c., New Yok Goa, F., Mua, G., Vola, A., 1977 Aalyss, Smulato ad Optmzato of the hemhydate pocess fo the poducto of Phosphoc Acd fom Calcaeous Phosphotes, Id. Eg. Chem. Pocess Des. Dev., 16 (3) Ptze, K. S., Km, J. J., 1974, Joual of Ameca Chemcal Socety, 98, Taylo, R., & Ksha, R., 1993, Multcompoet mass tasfe, Wley, New Yok