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2662 In d . En g. Ch em. Res. 1993,32, 2662-2670Simulation of a Urea Synthesis Reactor. 1. ThermodynamicFramework

Miguel A. Isla and Horacio A. Irazoqui'Im ti tu to de Desarrollo Tecnol6gico para la Industria Qufmica (Comej o Nacional de ZnvestigacionesCientificas y Thcnicas-Universidad Na cional del Lito ral ), Gfiemes 3450, 000 Santa Fe, ArgentinaCarlos M. GenoudF&brica de Fertilizantes P ETROS UR, Pasa Petroqulmica Argentina S.A ., Ruta 9,K m 79.4, 2804 Campa na, Argentina

A therm ody nam ic m odel for t h e system NH3-CO2-HzO-urea is developed as a supporting programof a urea synthesis reactor simulation module. Th e model covers a wide range of composition an dtemperature and can be used to predict th e behavior of th e sys tem at and removed from ureasynthesis conditions. Calculated equilibrium phase compositions and vapo r pressures a t differenttemperatures are in very good agreement with published experimental data. When used asthermodynamic suppo r t of the reactor s imulat ion module, the proposed thermodynamic modelyields good agreem ent with production-scale plant da ta. Calculated partial molal enthalpies for allcomponents in the gas and l iquid phases lead t o a satisfactory prediction of local equilibriumtemperatures. Th e solution algorithm for th e nonlinear system of phase and chemical equilibriumequations is s imple and robust. A multiple-step parame ter e stimation strategy is adop ted to regresspublished experimental data.Introduction

Urea (NH2CONHz) is produced commercially by re-action of amm onia (3 and carbon dioxide (C od ,underconditions dependingon each particular plan t technology.In m ost operating processes the synthesisreaction is carriedout in th e liquid phase, at pressures from 13 to 25 MP aand a t temperature s between 170 and 200 "C. A completesurvey of operating process technologies has been pub-lished by Chao (1967). S ubseq uently, different processhave been described by Uchino (1986) an d Stam icarbonStaff (1986).The synthesis proceeds via formation of ammoniumcarbam ate as intermediate, which then d ehyd rates to giveurea. A t pressures above ita dissociation pressure theformation of ammonium c arbam ate is fast and complete.The carbamate d ehydration reaction is slower and doesnot proceed to completion. The equilibrium conversionusually reaches values greater tha n 80% on a C02 basis(Lemkowitz et al., 1972).To overcome the limitation imposed by chemicalequilibrium on the one-pass conversion to urea, severalurea technologies include total or partial recycle ofunreacted ammonium carbamate.Unreacted C02 and NH3 present in the reactor ou tletstream a re recovered in a sequ ence of medium - and low-pressure carbamate decomposers and gas separators. Afraction of th e tota l C02 fed to the process is used in thesega s separators as a stripping a gent to aid the NH3 and C02separation from the produ ct stream. Before it is recycledto th e synthesis reactor, the stream of recovered gases iscondensed and recompressed.The rest of the fresh C02, together w ith liquid NH3 andthe recycle stream, is fed to th e tub ular synthesis reactor.A t the reactor inlet, global NHdC02 (L) nd H20IC02

* Author to whom correspondence should be addressed.0888-5885 93/2632-2662$04.00fO

Table I. Typical Reaction Feed and Outlet Streams in aTotal Recycle Urea ProcessNHa C02 carbamate outletstream feed feed recycle stream

massf low(kg/h) 16770 8310 21800 46880composition ( w t %)NHs 100 0 40.83 36.74c02 0 100 36.19 11.24H2O 0 0 21.81 19.68urea 0 0 1.17 32.34temp ("(2) 96.0 89.4 106.9 192.9

(W) ole ratios are kep t close to 4.0 and 0.7, respectively.Typical inlet and outlet streams conditions are describedin Table I.Over the past 50 years a sustained effort has been p uton the chemical and thermodynamic modeling of thesystem NH3-COz-HzO at a nd far from urea formationconditions. In the pioneering work of Fdja cq ue s (1948)a single reversible reaction for urea forma tion2NH3(1)+ COz(l)e HzCONH2(1)+ H20(1) (1)

was proposed. This oversimplified model overlooks theimportan t fact that, a t least, two independent reactionscontribute significantly to the equilibrium composition:the carbamate formation reaction and the carbamatedehydration reaction.In later work (Kawasumi, l952,1953a,b, 1954; Mavrovic,1971) the reaction schem e2NH3(l)+ C02(1)- H20CONH,(1) (2 )

NH20CONH,(1) NH2CONH2(1)+ H20(1) (3)was proposed. This more realistic starting point leavesthe way open for a more detailed treatment of chemical

0 1993 American Chemical Society

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Ind. E ng. Chem. Res., Vol. 32 , No. 11,1993 2663CO,(g) - OZ(1) (4)quilibrium. Th is possibility was lost because the ther-modynamic model of chemical equilibrium bu ilt on thisreaction scheme considered each mole of ammoniumcarbam ate presen t a t equilibrium as if it effectively were1 mol of free COz plus 2 mol of free "3 With thissimplifying assumption, e quilibrium composition can bedeterm ined with a single extent of reaction. However,th e model is insufficient to describe simultaneous chemicalan d phase equilibrium a t synthesis conditions, or chemicalequilibrium in the liquid phase far from urea synthesisconditions.Lemkowitz et al. (1973) considered eqs 2 and 3 asindependent reactions, each one with its own extent ofreaction. They solved chemical an d gas-liquid equilibriausing experimental values of the reaction equilibriumconstants. Henry's c onstants of NH3 and COZ weremeasured considering the reaction mixture a s a solvent.Bubble points of liquid reaction mixtures an d dew pointsof gas mixtures were predicted with the assumption ofideal behavior of gas an d liquid phases.Considering the severe conditions a t which the synthesisreaction is conducted and that the liquid phase is anelectrolytic solution, it can be concluded that this sim-plifying assumption limits th e validity of th e model whenthe system is removed from th e conditions a t which the

empirical constants were determined.There are abu ndant experimental data reported on thechemical equilibrium of th e synthesis reaction in th e liquidphase (Kawa sumi, l952,1953a,b, 1954; Kotu la, 1981; Inoueet al., 1972a,b). Th e conversion of COZ o urea has beenmeasured for different initial values of t he N H3/COz an dH20/C02 mole ratios and for different temperatures inthe range of interest for urea synthesis. On the basis ofthe reported data, Gorlovskii and Kucheryavyi (1980)developed a useful correlation to predict t he eq uilibriumconversion within a wide range of initial conditions.Th e thermodynam ic models for the system NH3-COz-HzO -urea reviewed so far in th is section deal with chemicaland phase equilibria.Th e rigorous simulation of critical equipm ent in ureasynthesis processes also requires th e accurate calculationof local temperatures. Therefore, the supporting ther-mody namic model for th e NH3-COz-HzO-urea mixtu remust be able to estimate partial molal enthalpies for allcomponents in the gas and liquid phases.In th e particular case of modeling and simu lation of th esynthesis reactor, local reaction rates m ust be predicted.This puts on th e supporting thermodynamic model theburde n of predicting the local composition an d temper-ature a t any point in the reaction volume (Kummel et al.,1981; Kucheryavyi a nd Gorbushenkov, 1970).This paper is intended to develop a thermodynamicmodel capable of suppo rting a rigorous reactor simulation

program (Irazoqui et al., 1993). The model parameterswill be estimate d by regression of published o peratin g dat afrom pilot-scale plants a nd from laboratory d ata found inthe literature.React ion Scheme

Th e behavior of th e system NH3-COz-HzO has beenextensively studied under conditions removed from thosea t which urea is formed (Edwards et al., 1978;Pawlikowskyet al., 1982; Kawazuishi and Prausn itz, 1987; Gop pert a ndMau rer, 1988). T he chemical model on which this bodyof work is based does not include urea either as a reactantor as a product.

COz(l)+ 2NH3(l)- ,NCOO- + NH4+ (7)COz(l)+ NH3(l)+ HzO(l)- CO; + NH; (8)HCO; + NH3(l)- 0:- + NH,+ (9)

NH3(1)+ HzO(l)- O- + NH; (10)HzO(l)* HO - + H + (11)

This system of reactions does not account for analternative way to dissolve COZdifferent from the pro-duction of ionic species. Except for th e negligible amo untth at remains unrea cted, all of th e COz dissolved has beenused to form H e@-, c03'-, and HzNCOO- anions.This confers some lack of flexibility to t he scheme, whichfor intermediate to high concentrations leads to overes-timation of the ionic strength of the mixture.Undissociated carbamic ac id formed from dissolved COzand NH3 according to

(12)may be pres ent in th e NH3-COz-HzO mixtu re undercertain conditions (H atc h an d Pigford, 1962;Buckinghame t al., 1986).Partial dissociation of ammonium carbamate can beincluded by considering the equilibrium

(13)together with eq 7.At high ammonia and carbon dioxide concentrationsand for temperatures above 160 "C, the urea synthesisreaction

(14)must also be taken into account.Although the objective of this work is to develop athermodynamic subprogram to assist an urea synthesisreactor simu lator, all of the above chem ical reactions mustbe taken into account in order to profit from experimentalda ta taken u nder d ifferent conditions, even if they weremeasured outside the synthesis range.In this way, no a priori restrictions on the degrees offreedom of th e chemical system are imposed. Th e valuesof th e param eters ob tained by regression of th e availableexperimental da ta will show which of th e reactions in th escheme are relevant an d which are not under ureasynthesisConditions. However, chemical reactions with negligibleequilibrium reaction extents will be disregarded in thefinal version of th e phase a nd chemical equilibrium modelto avoid unnecessary time-consuming iteration loops tobe executed in each call to t he thermodynamic supp ortingprogram.

COz(l)+ NH3(l)* H,NCOOH(l)

C02(1)+ 2NH3(l)- ,NCOONH,(l)H,NCOO- + NH; - zNCONHz(l)+ HzO(l)

Activ ity Coeff ic ientsMost of the work published on the chemical andthermodynamic modeling of the system NH3-COz-HzO

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2664 Ind. E ng. Chem. Res., Vol. 32, No . 11, 1993deals with solutions from dilute to moderate concentrationsof NH3 and C02 in water. Under suc h circumstances itis natural t o choose the pu re liquid a t the systemtemperature, T,and pressure,P , as the stan dard state forwater an d th at of infinite dilution in pure w ater for CO2an d nonvolatile species.A t synthesis conditions ammonia is fed t o th e reactorin great excess over its stoichiometric ratio to CO2. Ureaand water, already present in the recycle stream, areproduced in equal molar quan tities by the urea synthesisreaction, representing together m ore tha n 50%of th e outletstream mass flow rate.In thi s situation, it is convenient to choose the pureliquid a t the system temperature, T, an d pressure, P , asthe stand ard state for ammonia, water, and urea andinfinite dilution in pure water as th e stand ard sta te forthe remaining components in the mixture.To estimate th e activity coefficients n the mixture 3-C02-Hz0, Bernardis et al. (1989) used an extendedUNIQUAC model (Sander e t al., 1986a,b). In this paper,some of the most impo rtant binary interaction para mete rsare considered as functions of the tem peratu re a nd of th eionic strength of th e mixture. It is noticeable th e strongdependence found for the binary interaction parameterson the ionic strength, which seems to be an indirect wayto compensate for the inherent limitations of th e adoptedreaction schem e to interp ret the chemical changes occur-ring in the medium far from synthesis conditions.In this paper, the chemical reaction system discussedin the previous section is adopted. Activity coefficientsare predicted by means of the UNIQUAC extendedequationIn yi(T,x)= In yy (x) + In y?(T,x ) + In yFH (T,x ) (15)where th e combinatorial, yic(X), and the residual, TiR(T,x),contributions t o ac tivity coefficients are given by

and

respectively. T he Debye-Htickel contribution for nonionicspecies (Sander e t al., 1986a), isIn y F H ( ~ , x )( 2 ~ / b ~ ) ~ , [ 1 +~ ~ / ~1 / ( 1 + b ~ / ~ )

2 ln(1 + b11/2)1 (18)while in th e case of ionic species is

In y F H ( ~ , x ) -Z?AP/~/(I + (19)where

~ i j exp(-aij/T); uij # aji;ai i= ajj = 0 (23)

Table 11. Extended UNIQUAC Model: Pure ComponentParameterscomponent (i) ri Ui

0.921.001.320.911.541.711.992.16

1.401.001.120.991.441.581.922.00

where mi is th e molality of th e i ionic species referred to1000 g of mixed solvent, Mi is the molecular weight ofneutral species i, ziis th e charge num ber of a ionic speciesi; b is the distance of closest approac h between ions, z isth e coordination number (usually z = lo), ri and qi arefixed UNIQUAC volume and surface pure componentparameters (see Table 11)and aij are adjustable binaryinteraction parameters. Following Sand er et al. (1986a)b = 1.5 was ch osen and the DebyeH tickel parameter Awas taken a s the one corresponding to pure water.Activity coefficientsbased on t he symm etric convention,yi(T,X), can be related to those based on th e unsymmetricconvention,In y i o ( ~ ,x ) In y ioc(x)+ In y i0 tR( ~ ,x ) In yi0J(~ ,x)

(25)by me ans of

In yioPR(T,x) In y:(T,x) - n yimVR(T)In yioPDH(T,x)In yFH(T ,x)- n yjlPDH

In yimpc= ln(ri/r l)+ (z/2)qi n[qir1/(riql)I+ li - iZl/qlIn y i m J ? ~ -qi(ln T~~- 1 + T ~ ~ )

(27)(28)

where(29)(30)

andIn yimJ 0 (31)

give th e limiting values of t he configurational, residual,and De bye Hu cke l contributions to th e activity coefficientin therationalsymmetricscale takenasx l-1 (purewater).Following th e same criterion of Sande r et al. (1986133,the Debye-Huckel parameter A was taken as the onecorresponding to pure water.Ma thematical Model

A t global equilibrium, t he following set of non linear,partial equilibrium conditions must be satisfied (subscriptassignment to system components can be found in T able11).Phase Equil ibrium. A t phase equilibrium, the fol-lowing relationship mu st be satisfied for water ( i = 1)andammonia ( i = 2)xiri(T,x) i ( T Q - 0 ) exp(uiP/RT) = PYi@i(TQ,Y),

i = 1, 2 (32)while for carbon dioxide ( i = 3) the phase equilibriumcondition is

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x3y,O(T,x)H3,1(TPv,1(T))xp(v,"(P - P, , , (T) ) /RT)=PY3@3(TQ,Y) (33)

where x and y are arrays of the mole fractions in t he liquidan d gas phase, respectively.The fugacity coefficient of component i in the gasmixture, ai(TQ,y), s estima ted using th e equation of stateproposed by Nakamura et al. (1976).In eqs 15-33, yi(T , x ) s the activ ity coefficient of speciesi measured in the rational sym metric scale, while ?i o ( T , x )is the activity coefficient in the rational unsymm etric scale.Th e temperature dependence of the pure liquid refer-ence fugacity a t zero pressure for am monia (i = 2) , fz", ismodeled asIn f z0 (T )= ( A , / T )+ A , In T + A3T + A , (34)

In the limit of X I approaching 1 (pure water), the(35)

between Henry's constant of COz ( i = 3) in water, th ehypothetical stand ard sta te fugacity, f 3 O , and the limitingform of the activity coefficient in the rationa l symmetricscale, y3-, holds for this noncondensable solute.The dependence of In f 3 O on the system temperaturecan be modeled with a n empirical expression with th e sameform as th a t cho sen for In f2O (eq 34). Besides,

with f2" in MPa and T n K.relationship

In H3,1(T)= In r3"(T) In f 3 0 ( 2 " )

(36)which, from e qs 23,29, and 30 , can be shown to be of theform

(37)n rJT) = @ i l / T ) - &'Til + ciwhere Ci is a constant that depends on component i.In H3,1(T)= ( B l / T )+ B , In T + B3T + B4 - q3731 (38)chosen to model the tem perature dependen ce of Henry'sconstan t of COZ n water, H ~ J ,s consistent with eqs 34 ,35, and 37, as required.

Th e em pirical function

Chemical Equil ibrium. Th e functional formIn K&T)= (C , , / T ) + C,: In T + C3,T + C,: (39)

was adopted t o describe the tem pera ture dependence ofthe j reaction equilibrium constant.The estimation of the parameters of the phase andchemical equilibrium model was done by a nonlinearregression of experimental data using the maximumlikelihood principle (Anderson et al., 1978).To lower the number of parameters to be regressed,exploratory runs of the parameter estimation program weremade on the basis of the chemical reaction schemedescribed by eqs 7-13.Provisional but still significant estima ted values of th emodel parameters were used to assess the relative im-portance of th e chemical reactions 7-14 in th e whole rangeof experimental conditions. By solving th e phase a ndchemical equilibrium, i t was found tha t in the temperature,pressure, an d composition range of the experimental d at aonly eqs 7 , 8 , 1 2 ,and 14 have to be considered to acco untfor th e detailed equilibrium composition. Th e remainingchemical reactions showed values of their reaction e xtentstoo low to influence th e phase an d chemical equilibriumcomposition.Therefore, th e following se t of nonlinear equa tions waschosen to describe the chemical equilibrium of the "3

Ind. E ng. Chem. Res., Vol. 32, No. 11, 1993 2665COZ-HzO-urea system over th e tem per atu re, pressure,and composition range of the experimental d a h

K,(T) = K J x ) K , ,( T ,x ) ; r = 7 , 8 , 1 2 , 1 4where

an d

Th e electroneutrality condition is automa tically satisfiedwhen th e extents of reactions 7 , 8 , 1 2 , and 14 are used t ocompute the equilibrium composition of the reactionmixture.Given the temperature of the system and the initialvalues of the N Hd C0 2 and H2 0/C02 mole ratios, the setof nonlinear equations is solved by an ite ration m ethod,according to th e following procedure:(i) Initially each of th e activity coefficients is set equ alto 1.(ii) Th e value of th e exten t of the urea synthesis reaction(eq 14) is guessed.(iii) Th e system formed by eq s 32,33, and 41-46 is solvedto obtain th e extent of the reactions 7 , 8 , and 12 in termsof the current value of the extent of reaction 14 .(iv) With t he liquid composition resulting from ste p iii,activity coefficients are calculated and substi tuted in eqs32, 33, and 41-46. Steps iii and iv are repeated untilconvergence on mole fractions is obtained.(v) With t he curren t values of th e activity coefficientsan d of th e extents of th e reactions 7 , 8 , and 12 , eq s 47 and48 are solved to obtain th e extent of reaction 14. This canbe don e by solving a quadratic equation a nd disregardingthe unphysical root. Th e algorithm returns to step ii,repeating steps ii a nd iii until t he convergence criterionimposed on the extent of reaction 14 is satisfied.Bubble pressure and bubble composition can be cal-culated by me ans of eqs 32 and 33 . In t he synthesis reactorth e presence of a gas phase is undesirable. Th e calculationof the bubble pressure at every point in the reactor isnecessary only to en sure th at th e reaction mixture is alwayssubcooled at synthesis conditions.Th e proposed calculation procedure is simple and robust.I t has the additional advantage th at i t is able to cover

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2666 Ind. Eng. Chem . Res., Vol. 32, No. 11, 1993situations in which the sy nthesis reaction shows a mea-surable progress (as in th e reactor) an d also those in whichit is negligible (as in the recycle stream). In th e latter ofthe two situations, the e xte nt of reaction 14 is set equalto zero and no iterative loop between steps ii and v isneeded.En th al py Calcu latio ns. Neglecting pressure correc-tions, the partial molal enthalpy for water ( i = 1) andammonia (i = 2) in the liquid phase (P rausnitz et al., 1980)can be approximated by

(49)i ( ~ , x ) H ~ O ( T ) -R P ( ~n y i / d ~where

H i o ( T )=Hi*(T )- RP(d In f i o / a T ) (50)In eqs 49 and 50,Hio(T) is the molal enthalpy of th ehypothetical liquid pure com ponent a t zero pressure an da t he system temperature andH?(T) is the molal enthalpyof th e ideal gas pure component a t the same temperature.For carbon dioxide (i = 3), th e dilute solution in pureliquid water has been chosen as the reference state. Th ecorresponding expression of th e partial m olal enthalpy inthe liquid phase is

R 3 (T , x )=R3'(7') RP ( d In y30/dT) (51)where the m olal enthalpy of CO2 in its h ypothetical liquidstandard state at zero pressure and at the system tem-perature is given by

R30(T)= H3*(T) - R P ( d lnH3,1/dT) (52)where H3,1 is Henry's constant of COZ n water, given byeq 38.Th e partial m olal enthalpies of ionic and neutral reactionproducts can be calculated using th e approp riate forms ofthe van't Hoff equation relating the standard molalenthalpies of th e reaction products t o those of the rea ctantspecies.

T he dilute solution in pure liquid water has been chosenas the reference state for all reaction products. T hecorresponding expression of th e partial m olal enthalpy inthe liquid phase isR i ( ~ , x )R i 0 ( ~R P ( ~n yi0/") (53)

whereHio(T ) is the molal enthalpy of the iproduc t speciesin its hypothetical liquid stan dard s tate a t zero pressureand a t the system temperature.Anions and cations belonging to the same electrolyteare no t independent species since their concentrations haveto satisfy th e electroneutrality condition. For this reasonit is convenient to work with pa rtia l molal enthalpies ofeach dissociated elec trolyte instea d of working with ionicpartial m olal enthalpies.T he partial m olal enthalpie s of dissociated amm onium( i = 4) bicarbonate ( i = 5) and ammonium carbamate ( i= 6) are given byH4,5(T,~)H44,50(T)RPaCca In y40/aT)+an dR4,6(T,x)= R4,e0(T)R P [ ( d n y4~/a77

(d In r5"ldT)1 (54)

(a In y6OldT)I (55)respectively, where

R 4 , 5 O ( T ) = RdO(T) R,O(T) (56)an d

R 4 , 6 O ( T ) = R4"(T)+ ; T , O ( T ) (57)are th e stand ard molal enthalpies of the electrolytes.Rearranging the van't Hoff equation written for K7(2'),K dT ) , K12(T), an d K14(T), the following expressions ofthe s tanda rd molal enthalpies of th e product species areobtained:

R4,60(7') 2H20(T)+ R30(T)+ RF(d In K 7 ( T) /d T)(58)

= H , O ( T ) + H20(T)+ R30(T)R F ( d In K , (T ) / ~T ) 59)

R8"(T) H 1 O ( T ) + 2H,O(T) + R30(T)+RP ( d In K14(T)/Xl"l (61)

Finally, th e molal enthalpy of the liquid m ixture is givenby

where x j is the m ole fraction of species j in th e mixture.P a r a m e t e r E s t i m a ti o n S t r a t e g y

The model adopted to fit the chemical and phaseequilibr ium behavior of th e NHs-CO2-HzO-urea systemcontains a total of 80 adjustable parameters. Among theseare the Ai constants of eq 34, with i = 1, ..., 4; the Bicon stan ts of eq 38, with i = 1, ...,4, and the Cij constantsof eq 39, with i = 7, 8, 12, 14 and j = 1, ..., 4. Theseequations give the pure liquid reference fugacity of NH3a t zero pressure, th e Henry's constan t of COa in water,and th e chemical equilibrium constan ts of reactions 7,8 ,12, and 14, respectively, as functions of temper ature.Th e remaining 56 adjustable parameters are UNIQUACinteraction parameters aij, with i, j = 1, ...,8, which arenecessary to model the temperature dependence of theactivity coefficients of th e componen ts in the m ixture an dto calculate their molal partial excesa enthalpy.Th e UNIQUAC interaction param eter a31 also appear sin the empirical function chosen to model the emperaturedependence of Henry's constant of C02 in H2O (eq 38)through the function

'31 = exp(-a,,/T)To calculate the reactor tem pera ture profile, the tem-

perature corresponding to each local enthalpy and com-position has to be computed. Th e accuracy of th eprediction of temper atures from molal enthalpy values atgiven compositions largely depends on th e accuracy of thecoefficients listed above.Th is is why plant measurem ents of the adiab atic mixingtempe rature of the reactor feed streams have been includedas experimental points to estimate th e model parameters,in addition to liquid-vapor an d chemical equilibrium data .These additional experimental measurements are need-ed because of the proven f act th at "...correct predictionsof the vapor phase compositions and pressures by a solutionmodel do not guarantee th at t he description of the liquidphase is correct" (P elkie et al., 1992).

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Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2667system outside urea synthesis conditions begins, takingth e initial estimates of th e model parameters as he startingpoint.In all th e regressions made so far in this procedure, th eurea synthesis reaction has been excluded from thechemical model and the interaction coefficients aj,8 andasj were both tak en equal to 0. This was done because theliquid-vapor equilibrium d ata used for th e NH3-CO2-H2O system were reported a t conditions outside those ofurea synthesis.In the following step th e synthesis reaction was takeninto acco unt, as well as he interaction between urea a ndth e other components in the mixture. Th e parameterestimation process was renewed on a se t of 48 vapor-liquidand chemical equilibrium data for the NH3-C02-H20-urea system a t synthesis conditions (Inoue et al., 1972).T o keep the num ber of adjustable parameters well belowthe number of experimental points, some of the aijinteraction parameters in th e NH3-COzH2O-urea systemwere given th e same value as tha t already estimated forthe NH3-C02-H20 system on th e basis of the experimen taldat a by Goppert and Maurer (1988).A t synthesis conditions, the liquid phase at chemicalequilibrium can be though t of asa solution of amm oniumsalts in a mixed solvent formed by excess "3 H20, andurea. Among the solutes, ammonium carbam ate is thepredominant species and the amount of free C02 in theliquid phase is negligible. T he equilibrium c oncentrationsof ammonium bicarbon ate an d carbamic acid are also verysmall compared to tha t of ammonium carbamate.Under these circumstances the aij parameters in the"3-CO2-HaO-urea sys tem correspon ding to bin aryinteractions between solutes were assigned th e same valuethey had in th e NHs-COZ-H~O ystem. The same criterionwas adopted for the interactions between carbamic acidan d bicarbonate ions with each of the com ponents of th emixed solvent.Th e only ajj parameters a djusted in this final step werethose corresponding to interactions between the compo-nents of th e mixed solvent (Le., "3 H20, and urea) andto interactions between each one of them with C02 andammonium and carbamate ions.Th e list of the param eters adjusted in this final step iscompleted with the binary interaction param eters ai,s an da ~ j ,, j = 1, ...,7, and th e parameters c1,14,c2,14,c3,14,andc4,14, related to the temperature dependence of thesynthesis reaction eq uilibrium constant. Th e multi-objective function to be minimized included the errorbetween predicted an d measured vapor equilibrium pres-sure over the reaction mixture a t urea synthesis conditions,th e error between predicted an d measured conversion ofinitial C02 to urea, and t he error between predicted andmeasured adiaba tic mixing temp erature of th e reactor feedstreams.Th e proposed phase an d chemical equilibrium modelwith th e final se t of adjusted param eters loaded was ableto a ccurately reproduc e t he behavior of th e NH3-CO2-HzO-urea system within the range of temperature andcomposition defined by the synthesis reactor inlet andoutlet streams.

Aslightly modified version of th e param eter e stimationprogram published by Prausnitz et al. (1980), which isbaaed on the method of Anderson et al. (1978), has beenadopted in this work.Before starting th e paramete r estimation process, a setof initial parameter estimates was generated. To thispurpose it was recognized th at different subsets amongthe m odel parameters can be related to different featuresof the system behavior.In particular, th e characteristic m inimum shown by theisotherma l bub ble pre ssure of NH3-CO2 an d NH3-CO2-H2O mixtures as a function of the COdN H3 ratio at, an doutside, urea synthesis con ditions, is ascribed t o chemicalreactions (Pelkie et al., 1992; Bernardis et al., 1989;Lemkowitz e t al., 1973).The Cij parameters included in the correlation of thechemical equilibrium constants with temperature arereasonably expected to have an impo rtant impac t on theprediction of the system behavior if the C02/NH 3 ratio istaken within the range in which the pressure minimumoccurs as a consequence of th e chemical reactions in theliquid phase.Also, a t low concentrations of NH 3 and C02 in H2O theDebye-Huckel contribution t o t he activity coefficients willtend to dom inate over the configurational and residualones, thus attenuating the impact of the UNIQUACinteraction parameters aij on the phase and chemicalequilibrium description.Therefore, to obtain initial values of the parametersClj , C2j, C3j, and C4j, for j = 7, 8, and 12, the parameterestimation program was ran on a subset of experimentalpoints of low concen tration of NH3 an d COz in H20 , andwith COdNH3 ratio about the pressure minimum. Thesepoints have been chosen among th e extensive experimentaldata published by Goppe rt and Maurer (1988). In theseinitialization runs th e UNIQUA C interaction parametersaij were taken equal to 0, while th e Ai and Bi parametersof eqs 34 and 38 were obtained from published data byGillespie et al. (1987) and by Edwards et al. (19781,respectively.The low COz/NH3 branch of the isothermal bubblepressu re curve of the NH3-CO2-HzO system ca n beinterpreted assuming that its asymptotic behavior isdominated by the NHS-H~O inary interactions and bythe chem ical reactions present. On this basis, experimentalpoints in th e low COd NH 3 region were selected from th eda ta published by Goppert and Maurer (1988)to generateinitial estimates of the a12 and a21 binary interactionparameters. Th e parameter estimation program was runon this subset of experimental points, using the initialvalues of t he par am eter s Clj, Czj, C3j, an d C4j, for j = 7,8, and 12 , obtained before an d taking th e remaining aijparameters equal to 0.

Assuming that the asymptotic behavior of the "3C02-H20 system a t large C02/N H3 atios is dominatedby the C02-Hz0 binary interactions in addition to th echem ical reaction s prese nt, initia l a13 an d a31 values wereestimated. For this, the p arameter estimation programwas run on a subset of experimental points in the largeCOdNH3 region selected from the same source as theothers. T he initia l estim ates of th e a12 an d a21 binaryinteraction param eters obtain ed before were used, aswellas those of the pa rame ters Clj, Cq, C3j , and Cdj, for j7, 8, and 12 . Th e remaining aij parameters were take nequal to 0.After th e initialization procedure has been accomplished,th e pa rame ter estimation process for th e NH3-CO2-HzO

Analysis of ResultsThere is some disagreement in the equilibrium con-version of C02 to urea reported by different autho rs (Inoueet al., 1972;Kawasumi, 1952a,b, 1953,1954;Kotula, 1981).Therefore, different parameter sets can be obtaineddepending on the set of experimental dat a used. However,the equilibrium conversionvalues predicted can be checked

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2668 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993Table 111. Equilibr ium Consta nts, Ammonia Fug acity , andCarbon Dioxide H enry's C onstant Parameters

~~ ~ ~~ ~ ~parametersfunction 1 V A 1 lOAz lO3A3 A4

In fz o ( m a ) -2.5141 2.8417 -2.5759 14.64 60function 1 V B 1 lOBz WE3 B4

InHR (MPa) -2.6560 -3.5050 6.3216 18.1575parameters

Darametersfunction I V C l i 102Cz IOSCR CAiIn Kii = 7 9.9068 7.4296 -5.3985 -20.2220i = 8 8.8226 0.8404 1.8736 -21.6135i = 12 8.1358 0.0283 -0.1005 -21.5090i = 14 -1.7352 -4.7506 9.3576 5.6601

Table IV. Extended UNIQ UAC Model: Binary InteractionParametersi

i 1 2 3 4 5 6 7 81 -626.3 -401.5 355.6 -18.2 0.9 -118.0 -110.02 847.3 -291.4 -190.7 -41.9 335.0 -1366.7 357.13 2623.7 -610.0 836.1 825.3 -204.8 958.6 670.54 -272.8 -12.4 -65 3.6 -907.8 1476.5 -65 6.9 272.85 -2.6 844.7 -63 7.1 284.9 1158 .4 82.9 -0.96 -96.6 -62.3 -302.6 -337.2 -63 2.5 157.5 221.67 -158.7 95.6 89.1 568.6 201.1 98.0 142 .38 91.7 -532.5 269.0 -162.2 2.3 -166.2 -33.2Table V. Influence of Temperature and W o n EquilibriumConversion for L = 4; Comparison with Experimental Data

COz to urea equilib convW t ("e) exptla this model0.0 1801902002100.5 180190

2002101.0 180190200210

79.280.079.677.971.572.371.970.263.864.664.162.5

80.280.179.979.572.572.472.171.565.665.565.264.6

Calculated with the correlation of Gorlovskii and Kucheryavyi(1980) which fits experimental results from several sources.against those calculated by means of the correlation ofGorlovskii an d Kucheryavyi (1980), which is based on alarge number of experimental dat a from many independen tauthors.Fortunately, abundant plant reactor data obtainedunder different operating conditions provide an irreplace-able tool for checking both t he model performance andthe parameter quality. Agreement between plant dataand simulation results is an indication of the goodperformance of the thermodynamic model.Tables I11and IV show the m odel parameters obtainedwith the procedure explained above. Th e equilibrium da tafrom Inoue e t al. (1972) were used t o correlate the u reasynthesis reaction equilibrium con stant with the systemtemperature.Values of th e adiabatic m ixing temperature of the reactorfeed streams from pla nt m easurements and the temper-atures of allinlet and outlet streams of known ompositionwere included aspar t of the experimental da ta on whichth e parameter regression was based. Th is allowed an

90 ,

8080a 70zv,W28

L -I o L.3.50 L14.0A L.4.5o L.5.0

150 0 0 2 04 0.6 0.8

WFigure 1. Influence of HaO/COz load ratio (W) on equilibriumconversion at t = 19 0 O C and different NH$COa ratios (t).0 ,0 ,A, )Gorlovskii and Kucheryavyi (1980); (-) this model.Table VI. Influence of Ratios L an d W on EquilibriumConversion at t = 190 OC ; Comparison with E xperimentalData

COZto urea equilib convL W exptla this model

3.5 0.0 75.9 77.30.2 72.5 73.80.4 69.2 70.40.6 65.8 67.30.8 62.4 64.31.0 59.1 61.54.0 0.0 80.0 80.20.2 76.9 77.00.4 73.8 73.90.6 70.7 71.00.8 67.7 68.21.0 64.6 65.64.5 0.0 83.1 82.30.2 80.3 79.30.4 77.5 76.50.6 74.6 73.80.8 71.8 71.21.0 69.0 68.85.0 0.0 84.9 83.90.2 82.4 81.20.4 79.9 78.60.6 77.3 76.10.8 74.8 73.61.0 72.2 71.3

a Calculated with the correlation of Gorlovskii and Kucheryavyi(1980) which fits experimental resu lts from several sources.accurate prediction of the tempera ture profile along th esynthesis reactor.Figure 1 llustrates th e model performance a t predictingequilibrium conversions. It mu st be noticed th at agree-men t is bett er for initial NH3/C02 ratios closer to actualreactor operating cond itions, because of the abun dance ofpublished experimental da ta in th is region.Tables V a nd VI summarize the m odel sensitivity tochanges in the most important operating and controlvariables: temp erature, NH JC02load ratio (L),nd H2O/C02 load ratio (W). t can be noticed th at t he differencesbetween predicted a nd measured equilibrium conversionsare w ithin experimental error.Calculated bubble pressures against mole percent ofammonia fo r an NH3-CO2 initial mixtu re ar e shown in

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29 t\ \

-D t = 180"C+- =190C* =200"C

I

I

9 I I65 70 7 5 0 0 05 90 95NH, (mol %)

Figure 2. Vapor pressure of N H.q-C OrH 20 system.Figure 2. Agreement with data reported by Lemkowitz(1973) s excellent, reproducing the pressure minim um a tits exact position for each temperature. This is a re-markable result if we consider the fact th at e xperimentalpoints with zero initial H20/C02 ratio were scarce.Conclus ions

Although the m odel proposed is intended t o support a nurea reactor simulator, it was also tested a t predicting thebehavior of th e system s NH3-COz-H20 an d NH3-CO2-HzO-urea over a wide range of com position and temp er-ature. In all cases the model was able to predict vaporpressures and C02 to urea conversions satisfactorily.When used as the thermody namic support of an ureareactor simulation program (Irazoqui e t al., 1993),resultswere in excellent agreeme nt with observed plan t data . Theobserved reactor sensibility to changes in N Hd C0 2 an dH20/C02 load ratios were correctly reproduced.Acknowledgment

Financial support from Pasa P etroquimica ArgentinaS.A., Consejo Nacional de Investigaciones Cientfficas yTBcnicas, and Universidad Naciona l del Litoral is grate-fully acknowledged.N o m e n c l a t u r eA = Debye-Huckel parameterAj = th parameter in the correlation of pu re liquid referencefugacity of ammonia with temperatureai j = UNIQUAC binary interaction parameters betweencomponents i an d jBj = jt h parameter in the correlation of Henry's constant ofcarbon dioxide in water with tem peratu reb = distance of closest approach between ionsC h i =kth parameter in the correlation of the equilibriumf i 0 = pure liquid reference fugacity of component i at zerog = gas (eqs 4-6)H = molal enthalpy of the liquid mixture&= partial molal enthalpy of component iHi' molal enthalpy of componen t in the idea l gas refere nce

constant of chemical reaction j with tem peraturepressure

state

Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2669Hio = molal enthalpy of component i in the pure liquidElio = molal enthalpy of component i at infinite dilution inHij= Henry's constant of component i in solvent jKj = equilibrium constant of chemical reaction JL = NHdC02 load mole ratio1= liquid (eqs 1-14)li = see eq 22Mi = molecular weight of neutral species imi =molality of the i ionic species referred to loo0 g of mixed

solventP = pressureP v j = vapor pressure of component iqi= UNIQUAC surface parameter of com ponent iR = gas constantri= UNIQUAC volume parameter of component iT = absolute temperatureui = liquid molal volume of component iuim= liquid molal volume of com ponen t i at infinite dilutionW = H20/C02 load mole ratiox i = mole fraction of component i in the liquid phasex = array of the mole fractions in the liquid phaseyi = mole fraction of component i in the gas phasey = array of the mole fractions in the gas phasez = UNIQUAC coordination number ( z = 10)zi= charge number of a ionic species iGreek Le t te r syi = activ ity coefficient of com ponent i , rational symmetricconventionyio= activity coefficient of component , rational unsymmetricconventionyi" = limiting value of th e activity coefficient in the ra tiona lsymmetric scale taken as XI - (pure water)Bi = surface area fraction of com ponent i&= volume area fraction of com ponent iai= fugacity coefficient of com ponent i in the gas phaseS u perscr ip t sC = combinatorialDH = Debye-HuckelR = residual

reference state a t zero pressurewater reference state

L i t e r a t u r e C i t e dAnderson,T.F.;Abrams D. S.; Grens E. A. Evaluation of Param etersfor Nonlinear Thermodynamic Models. AIChE J . 1978, 4 (l),20-29.Bernardis, M.; Carvoli, G.; Delogu, P. NHs-COrHaO VLE Calcu-lations Using an Extended UNIQUAC Equation.AIChE J . 1989,Chao, G. T. Urea, ts Properties and Manufacture;Chao's Institute ,Ed.: Taipei, Taiwan, 1967.Edwards, T. J.; Maurer, G .; Newman, J.; Prausnitz, J. M. Vapor-Liquid Equilibrium in Multicomponent Aqueous Solutions ofVolatile Weak Electrolytes. AIChE J . 1978'24 (6), 6-76.Fr&jacques,M. TheoreticalBasis of the Industrial Synthesis of Urea.Chim. Znd. 1948, 0 (l), 22-35.Gillespie, P. C.; Wilding, W. V.; Wilson, G. M. Vapor-LiquidEquilibrium Measurem ents on the Ammonia-Water System from313 K to 589 K. AIChE Sy m p . Ser. 1987,83 256), 7-127.GBppert, U.; Maurer, G. Vapor-Liquid Equilibria in AqueousSolutions of Ammonia and Carbon Dioxide at TemperaturesBetween 333 and 393K and Pressures up to 7MPa. Fluid PhaseEquilib. 1988,41 (1-2), 153-185.Gorlovskii, D. M.; Kucheryavyi, V. I. Equation for Determ ination ofthe Equilibrium Degree of COz Conversion During Synth esis ofUrea. Zh. Prikl. Khim. 1980,53 (ll), 548-2551.Hatch, T. F.; Pigford, R. L. S imultaneous Absorption of CarbonDioxide and Amm onia in W ater.Znd. Eng. Chem. Fundam. 1962,I (3), 09-214.Inoue, S. ;Kasum ichi, K.; Otsuka E. Equilibrium of Urea Synthesis.1. Bull. Chem. SOC. pn. 19728,45 (5), 1339-1345.Inoue,S.; asumichi, K.; Otsuka,E. Equilibrium of Urea Synthesis.11. Bull. Chem. SOC. pn. 197213,45(6), 1616-1619.

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2670 Ind.Eng.C h e m . Res., Vol. 32,No. 11,1993Irazoqui, H. A.; Isla, M. A.; Genoud, C. M. Simulation of a UreaSynthesis Reactor. 2.Reactor Model.Znd. Eng. C hem. Res., 1993,following paper in this issue.Kawasumi,S.Equilibrium of the C O2-NHs-urea-HzOSystem underHigh Temperature a nd Pressure. 11. Liquid-Vapor Equilibriumin the Loading Mole R atio of 2" to COz. Bull. Chem. SOC. p n.1952,25 (4), 27-238.Kawasumi,S. quilibrium of the COz-N H3-urea-H20 System und erHigh Temperature and Pressure. 111.Effect of Water Added onLiquid-Vapor Equilibrium. Bull. Chem. SOC. pn . 1953a, 26 (5),Kawasumi,S.Equilibrium of th e COkNHB-urea-HZO System und er

High Tempe rature a nd Pressure. IV. Effect of Loading NH3-COzMole Ratio on Equilibrium Pressure an d Vapor Composition.Bull.Chem. SO C. pn . 1953b, 26 (5), 222-227.Kawasumi,S.Equilibrium of the COz-N Hs-urea-H20System underHigh Temperature and P ressure. V. Liquid-Vapor Equilibrium inthe Presence of E xcess Ammonia an d Carbon Dioxide.Bull.Chem.SOC . pn. 1954,27 (5), 254-259.Kawazuishi, K.; Pra usnitz, J. M. Correlation of Vapor-LiquidEquilibria for the System Amm onia-Carbon Dioxide-Water.Znd.Eng. Chem. Res. 19 87,26 (7), 1482-1485.Kotula, E. A Vapor-Liquid Equilibrium Model of the NHs-COz-HzO- Urea System at Elevated Pressure. J . Chem. Technol.Biotechnol. 1981,31, 103-110.Kuc heryavyi, V. I.; Go rbushenk ov, V. A. Kinetic Equation for UreaSynthesis from Amm onia and Carbon D ioxide in a Flow ColumnUnder Pressure. Zh.Prikl. Khim. 197 0,43 (9), 102-2104.Kumm el, R.; Kilgler, L.; Bendel, H.; Jasche, K. Research on theKinetics of the Urea Formation R eaction. Chem. Tech. 1981,33(9), 63-465.Lemkowitz, S.M.; de Cooker, M. G. R.; van den Berg, P. J. AnEmpiricalThermodynamicModel for the A mmonia-Water-CarbonDioxide System a t Urea Synthesis Conditions. J . Appl. Chem.Biotechnol. 1973,23 ,63-76 .Mavrovic, I. Find Equilibrium Urea Yield. Hydrocarbon Process.1971, April, 161-162.

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Nakamura, R., Breedveld, G.J. F.; Prausnitz, J. M. ThermodynamicProperties of Gas Mixtures Containing Common Polar andNonpolar Components. Znd. Eng. Che m. Process Des. De v. 197 6,Pawlikowsky,E. M.; Newman, J.; Prausnitz, J. M. Phase Equilibriafor Aqueous Solutions of A mmo nia and Carb on Dioxide.Znd. Eng .Chem. Process Des. De v. 1982,21 (4), 64-770.Pelkie,J.E.; oncannon,P. J.; Man ley, D. B.; Poling, B. E. Prod uctDistributions in the COz-NHs-HzO System from L iquid Conduc-tivity Measurements. Znd. Eng. Chem . Res. 1992, 31 (9), 2209-2215.Prausnitz, J. M.; Anderson,T. F.; Grens, E. A.; Ecke rt, C. A,; Hsieh ,

R.; O'Connell, J.P. Computer Calculations fo r MulticomponentVapor-Liquid and Liquid-Liquid E quilibria;Prentice-Hall: En-glewood Cliffs, NJ , 1980.Sander, B.; Fredenslund, A.; Rasmussen P. Calculation of Vapor-Liquid Equilibria in Mixed Solvent/Salt Systems Using anExtended UNIQUAC Equation. Chem. Eng. S ci. 1 986a, 41 (5),Sander, B.; Fredenslund, A,; Rasmussen, P. Calculation of Vapor-Liquid Equilibria in Nitric Acid-W ater-NitrateSalt SystemsUsingan E xtended UNIQUAC Equation. Chem . Eng. Sc i. 1986 b, 41 (5),1185-1195.Stamicarbon Staff. Stamicarbon Carbon Dioxide Stripping UreaProcess. n Handbook of ChemicalsProductionRocesses;Meyers,R. A., Ed.; McGraw-Hill: New York, 1986; ection 3.11.Uchino, H. Toyo Urea Process-Advanced Process for Cost andEnergy Savings. In Handbook of Chemicals ProductionProcesses;Me yers, R. A,, Ed.; McGraw -Hill: New York, 1986;Section 3.12.

Received for review February 8 , 1993Revised manuscript received J u l y 7, 1993Accepted Ju ly 14, 1993.

15 (4), 57-564.

1171-1183.

Abstract published in Advance ACS Abstracts, October 1,1993.