Chemical Engineering Journal

Transcription

1 Chemcal Engneerng Journal 160 (2010) Contents lsts avalable at ScenceDrect Chemcal Engneerng Journal journal homepage: Enhancement of urea, ammona and carbon doxde removal from ndustral wastewater usng a cascade of hydrolyser desorber loops M.R. Rahmpour, H.R. Mottagh, M.M. Barmak Department of Chemcal Engneerng, School of Chemcal and Petroleum Engneerng, Shraz Unversty, Shraz 71345, Iran artcle nfo abstract Artcle hstory: Receved 13 October 2009 Receved n revsed form 28 March 2010 Accepted 29 March 2010 Keywords: Wastewater treatment Urea removal Ammona removal Cascadng hydrolyser desorber loop Low concentraton removal In ths study, removal of urea, ammona and carbon doxde from wastewater of conventonal urea plant n both hgh and low concentraton (ppm scale) levels usng a cascade of hydrolyser desorber loops has been nvestgated. In conventonal urea plants, wastewater treatment sectons ncludng co-current confguraton of hydrolyser were desgned accordng to the old envronmental standards. Nevertheless, the amounts of urea and ammona n outlet treated wastewater are not acceptable at present tme due to new envronmental restrctons, shortage of water sources and possblty of upgradng ths wastewater to reuse for boler feed water or coolng water. Therefore, a thermal hydrolyser desorber system s proposed to add at the end of current conventonal treatment secton n order to decrease urea and ammona contents n treated effluent to approach 0 ppm. A general model s developed for both types of thermal hydrolyser desorber loops whch n frst loop, hgh concentratons and n the second loop, low concentratons of urea and ammona are treated. The extended electrolytc UNIQUAC equaton has been used to descrbe the non-dealty of lqud phase. The proposed model ncorporates reacton rate of urea hydrolyss and takes nto account the effects of soluton non-dealty and back-mxng on the performance of hydrolyss reactors. The model was solved numercally and provdes temperature, flow rate and concentraton dstrbutons of dfferent components along the heght of reactors and desorbers. The proposed model has been valdated aganst observed data. Also the effects of key parameters on the performance of wastewater treatment process have been examned. The results of ths work show that ncrease of nlet temperature of wastewater and steam flow rate and decrease of the reflux rato mprove the urea and ammona removal effcency Elsever B.V. All rghts reserved. 1. Introducton Urea s an mportant ntrogen-based fertlzer whch s syntheszed by the reacton of ammona and carbon doxde n the range of hgh temperatures and pressures [1]. In a urea producton plant, for every ton of produced urea, 0.3 tons of water s formed. Ths water whch contans ammona, carbon doxde and urea s usually dscharged from the urea concentraton and evaporaton secton of the plant. Ths wastewater together wth the rnsng and wash effluent s collected n large storage tanks, requres treatment f t s to be reused agan. Such a stream generally contans about 2 9 wt% ammona, wt% carbon doxde and wt% urea [2,3]. Dschargng ths wastewater from urea plants have a negatve nfluence on the envronment as well as loss of urea and ammona. Urea s consdered deleterous n natural waterways that t promotes algae growth and hydrolyses slowly. Ammona s an Correspondng author. Tel.: ; fax: E-mal address: rahmpor@shrazu.ac.r (M.R. Rahmpour). extremely hazardous, toxc, and volatle materal. At hgh levels of ammona, death of anmals, brds, fsh and death or low growth rate n plant, and rrtaton and serous burn on the skn and n the mouth, throat, lungs and eyes can be observed. Therefore, treatment of urea plant wastewater s essental [4 6]. The purpose of wastewater treatment of urea plant s to remove urea, ammona and carbon doxde from the process condensate. Several processes have been suggested for treatng these ureacontanng streams due to current necesstes for envronmental protecton and possbltes to upgrade ths waste stream to valuable hgh-pressure boler feed water or coolng water. Whle n the past decade, 100 ppm of urea was consdered acceptable for plant wastewater, but today s requrements mostly call for a maxmum concentraton of 10 ppm [7]. Economcally, t s preferred to remove and recover the urea and/or ammona from the wastewater. Varous methods have been proposed to accomplsh ths, all of them bascally nvolve the steps of desorbng ammona and carbon doxde from the ureacontanng wastewater, subsequently thermal hydrolyzng the urea contaned n the wastewater, then the total or partal desorpton of the ammona and carbon doxde that are formed n the hydrolyser /$ see front matter 2010 Elsever B.V. All rghts reserved. do: /j.cej

2 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) and n the fnal step, the off-gases wll be condensed n a reflux condenser [8]. On the ndustral scale, urea thermal hydrolyss reactors operate n co-current or counter-current modes. Rahmpour and Azarpour presented varous model for studyng the urea thermal hydrolyser n hgh concentraton level n co-current mode [9 11]. Also Barmak et al. proposed a non-deal rate-based model for an ndustral urea thermal hydrolyser n hgh concentraton level n countercurrent mode [12]. In conventonal urea producton plants, thermal hydrolyss reactors are n operaton n co-current mode wth steam, nevertheless even after very long resdence tmes or hgh steam consumng n the best operatng condtons, t s not possble to acheve the urea and ammona contents less than ppm n outlet treated lqud [9,11,13]. But n modern urea plant, thermal hydrolyss reactors are based on counter-current mode. In ths manner, the ammona and urea contents of the treated stream can be reduced to a level of 1 ppm. In conventonal urea plants such as Shraz Petrochemcal Complex (SPC), outlet wastewater from treatment secton of the plant dscharges to sewage system, because of the outlet treated lqud has no enough qualty to use n utlty unt or n other unts. So n order to reuse ths wastewater, resdual urea, ammona and carbon doxde must be removed. Untl now, the publshed nformaton n lterature about smultaneous urea, ammona and carbon doxde removal n low concentraton level from ndustral wastewater of urea plants s very lttle detaled and patented, especally n hydrolyssdesorpton process [3,14]. The man objectve of ths work s enhancement of urea, ammona and carbon doxde removal from outlet treated lqud of wastewater treatment loop of conventonal urea plant to obtan pure lqud that contans 1 ppm for urea and ammona and observe the new envronmental standards. In other word, n ths work removal of urea and ammona from wastewater n low concentratons (<100 ppm) s carred out whle n conventonal process, hgh concentratons (>100 ppm) of urea and ammona are removed. Changes n conventonal treatment secton s complcated and approxmately mpractcal due to dependency of dfferent equpments of plant to each other, besdes ncrease of steam flow rate and temperature of wastewater feed are shown n our prevous works [9 11]. Therefore, the new treatment system has been suggested. In ths system, the removal of mentoned components s carred out n two stages. In the frst stage, urea, ammona and carbon doxde are removed at hgh concentratons n exstng plant whle n the second stage these components are removed at low concentratons n a proposed plant. In ths work, a general model for an ntegraton of hydrolyser desorber loops ncludng conventonal and new proposed treatment sectons has been developed. Extended UNIQUAC model has been used to represent the vapor lqud equlbrum (VLE) of NH 3 CO 2 H 2 O urea system. The combned effect of chemcal reacton, lqud non-dealty and soluton backmxng was treated by a mult-stage well-mxed reactor model for thermal hydrolyser. Also the effect of dfferent parameters on the performance of hydrolyser desorber loops has been nvestgated and the desgn consequences of dfferent optons on the new proposed secton have been dscussed. 2. Process descrpton 2.1. Wastewater treatment secton of conventonal urea plant Fg. 1 shows a schematc dagram of conventonal urea, ammona and carbon doxde removal from wastewater of the urea plant n Shraz Petrochemcal Complex [8]. It manly conssts of a 1st desorber column at low pressure, whch reduces the ammona Fg. 1. Wastewater treatment loop of conventonal urea plant. and carbon doxde contents. For the next column, the hydrolyser, t s mportant that the ammona and carbon doxde concentratons at the nlet are suffcently low, n order to mantan the system far from the chemcal equlbrum. Under these condtons the hydrolyss reactons proceed towards the ammona and carbon doxde producton, reducng the urea content to approxmately less than 100 ppm. The hydrolyser s operated at relatvely medum pressures (18 bar) resultng n a temperature of about 185 C. The temperature level n the hydrolyser s mantaned by the njecton of 25 bar steam. In the 2nd desorber column agan operatng at low pressure, the ammona and carbon doxde contents are decreased to low ppm level. The strppng n the 2nd desorber s carred out by usng lfe low-pressure (LP) steam njected n the bottom and outlet vapors from ths column are used for the strppng n the 1st desorber. The vapors of the 1st desorber, whch contan ammona, carbon doxde and water, go to condenser New proposed treatment secton A schematc of cascade of hydrolyser desorber systems ncludng conventonal and new proposed treatment sectons for urea, ammona and carbon doxde removal from wastewater of urea plant s shown n Fg. 2. In ths process, the outlet lqud from 2nd desorber s heated n 2nd heat exchanger wth the clean top effluent, and t s pumped to the bottom of the new hydrolyser cocurrently wth hgh-pressure (HP 2 ) steam after passng through the 3rd heat exchanger. The heght of hydrolyser s 5 m and there are 4 trays nsde t. Urea s decomposed to ammona and carbon doxde by steam 380 C and 25 kg/cm 2. At the outlet of the hydrolyser the urea content s decreased to 1 ppm level. The ammona and carbon doxde evolvng from ths hydrolyser reacton are removed n a desorber usng low-pressure (LP 2 ) steam as strppng agent. The ammona content s also decreased to 1 ppm level. Overhead vapors from 3rd desorber contanng ammona, carbon doxde and water are condensed n a reflux condenser and rectfed to reduce the water content by returnng a reflux lqud stream to the tower and non-condensed vapors are recycled to urea producton secton. Two process process heat exchangers decrease the needed hgh-pressure steam amounts consderably. 3. Reactons The lqud phase contans physcally dssolved and chemcally combned components that are manly present as ons and molecules, namely H 2 NCONH 2 (1), H 2 O (2), NH + 4 (3), H 2NCOO (4), CO 2 (5) and NH 3 (6). The overall reacton of urea hydrolyss s as

3 596 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Fg. 2. Cascade of wastewater treatment loops. The boundares are shown for the materal balances. follows [1,15]: NH 2 CONH 2 + H 2 O 2NH 3 + CO 2 (1) The urea hydrolyss reacton occurs n two steps. The frst reacton nvolves the producton of ammonum carbamate from the combnaton of urea and water accordng to the followng: NH 2 CONH 2 (l) + H 2 O(l) H 2 NCOO + NH + 4, H 298 = 23 kj/mol Ths reacton s slghtly exothermc. Then the ammonum and carbamate ons react to yeld carbon doxde and ammona n lqud phase, whle the vapor and lqud phases are at equlbrum (endothermc reacton): H 2 NCOO + NH + 4 2NH 3(l) + CO 2 (l), H 298 = 84 kj/mol (3) It s concluded from reactons (2) and (3), the urea hydrolyss s an endothermc reacton, so for a more complete reacton, heat s needed. Reacton (2) s slow, whle reacton (3) s fast n both drectons, so t could be consdered at equlbrum under the condtons found n the ndustral hydrolyser [1,15]. Therefore reacton (2) s the rate controllng step and ts rate s consdered as the overall rate of urea hydrolyss. For chemcal reactons n thermodynamcally non-deal systems, as shown elsewhere [16 18], the rate becomes: ( R = k f a 1 a 2 1 ) a 3 a 4 =k K f [( 1 C 1 )( 2 C 2 ) 1 ] ( 3 C 3 )( 4 C 4 ) (4) 2 K 2 where k f s the forward reacton rate constant (k f = k 0 exp( E/RT)) and K 2 s the equlbrum constant of reacton (2). a, are the actvty and actvty coeffcent of speces, respectvely. C s the molar concentraton of speces. The expermental values of the pre-exponental factor and the actvaton energy n (2) the Arrhenus expresson of k f are k 0 = m 3 /(kmol h) and E = 87,780.3 kj/kmol, respectvely [19]. The equlbrum constants for reactons (2) and (3) are defned as follows: K r (T) = K X,r (X)K,r (T, X), r = 2, 3 (5) where the effects of lqud non-dealty on the reacton equlbra have been merged nto a set of parameters, K,r (T,X) whch are defned as: K,r (T, X) = 3(T, X) 4 (T, X) 1 (T, X) 2 (T, X), r = 2 (6) K,r (T, X) = 2 6 (T, X) 5(T, X) 3 (T, X) 4 (T, X), r = 3 (7) and K X,r (X) s also defned as: K X,r (X) = x 3x 4 x 1 x 2, r = 2 (8) K X,r (X) = x 5x 2 6, r = 3 (9) x 3 x 4 where X s the array of mole fractons n the lqud phase. Substtutng Eqs. (6) (9) nto Eq. (5) results: ( x3 )( x 4 3 ) (T, X) 4 (T, X) K 2 (T) =, r = 2 (10) x 1 x 2 1 (T, X) 2 (T, X) ( )( ) x5 x 2 5 (T, X) 2 (T, X) 6 6 K 3 (T) =, r = 3 (11) x 3 x 4 3 (T, X) 4 (T, X) where the actvty coeffcent of each speces n the reactng soluton can be calculated from thermodynamc model. The followng functonal form: ( U1,r ) ln K r (T) = + U 2,r ln T + U 3,r T + U 4,r (12) T

4 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Table 1 Equlbrum constant parameters [19]. Functon Parameters U 1 U U 3 U 4 ln K 2 31, ln K 3 11, was adopted to descrbe the temperature dependence of the r reacton equlbrum constant [20]. In the above equaton, U r s a constant related to reacton of number r where tabulated n Table Hydrolyser desorber loops models Overall wastewater treatment process ncludes two process loops. For smulaton of the loops, the specfcaton of streams must be obtaned. At frst, the wastewater treatment loop of conventonal secton has fve unknown streams, whch are: (1) output old of hydrolyser stream, (2) output of 1st desorber lqud stream, (3) output of 1st desorber vapor stream, (4) output of 2nd desorber lqud stream and (5) output of 2nd desorber vapor stream. Also the new proposed treatment loop has fve unknown streams, whch are: (1) output of new hydrolyser stream, (2) output of 3rd desorber lqud stream, (3) output of 3rd desorber vapor stream, (4) reflux stream and (5) outlet vapor of condenser stream. The mole fractons of all components are unknown. The reflux rato s constant and wastewater feed and steam streams values are known. Also, the content of output vapor stream of 3rd desorber s equal to total contents of the reflux and outlet vapor of condenser streams. In ths study, smulaton of the cascade of hydrolyser desorber loops was done based on the followng assumptons: Reactons of hydrolyss take place only n the lqud phase. The loops operate at steady-state condton. Each stage of hydrolyser s perfectly mxed strred-tank reactor (CSTR). Each CSTR operates adabatcally. Phase equlbrum s acheved n each stage. The volatlty of urea and ammonum carbamate s neglgble, so there are only three molecular components ncludng H 2 O, NH 3 and CO 2 n the vapor phase of desorber. Dssolved CO 2 n the lqud phase of desorber s neglgble. In fact, t could only be condensed wth ammona to form ammonum carbamate n the lqud phase Smulaton of the heat exchangers (frst, ffth and sxth boundares) There are no phase changes n the heat exchanger and t s modeled by assumng the cold stream has a temperature, T C, n the heat exchanger nlet, where heat s transferred at a rate, Q C, from the hotter tube metal at a temperature, T M (Eq. (13)): Q C = U C A C (T M T C ) (13) The hot stream has a temperature T H n the heat exchanger. Heat s transferred from the hot flow nto the tube metal at a rate, Q H : Q H = U H A H (T H T M ) (14) Fnally, each stream of the cold and hot sdes of the exchanger s descrbed by an energy balance (Eqs. (15) and (16)). (F H C PH T H ) L (F H C PH T H ) 0 Q H = 0 (15) (F C C PC T C ) L (F C C PC T C ) 0 Q C = 0 (16) where F C and F H are cold and hot stream molar flow rate, respectvely and C P s specfc heat capacty. Also subscrpts L and 0 ndcate length of heat exchanger and nlet condtons, respectvely Smulaton of the thermal hydrolyss reactors (thrd and seventh boundares) The ndustral hydrolyser s a vessel n whch the lqud resdes long enough at hgh temperature for equlbrum to be establshed. In order to ncrease the one-pass converson n the tubular hydrolyser, baffle plates are nstalled nsde the reactor to control concentraton back-mxng and to approach a plug flow pattern. Therefore, for smulaton purposes t wll be approxmated as a seres of contnuous mult-stage strred-tank reactors (CSTRs). Ths model allows sweepng of operatng condtons wth dfferent degrees of concentraton back-mxng by selectng dfferent numbers of stages. Throughout the followng dervatons, CSTRs n sequences wll be referred to as stages, numbered from bottom to top. The j subscrpt corresponds to the stage number. A stream n the CSTR sequences, and ts correspondng propertes, wll be assgned the same j subscrpt as the stage t leaves. The steady-state mass balance for speces n reacton (1) on stage j of the reactor sequence s: F,j = F,j 1 + V C R j, j = 1, 2,...,N (17) where F,j 1 and F,j are the molar flow rate of component enterng and leavng stage j n the reactor sequence, V C s the stage volume, s the stochometrc coeffcent of speces n reacton (1), R j s the overall rate of reacton (1) n stage j and N s the total number of stages. The flow rate of water to the frst stage s determned by a mass balance on the mxng pont of steam and wastewater at the nlet of column. Also, the amounts of carbamate and ammonum ons are consdered neglgble due to the fast reacton (3). Steady-state energy balance on stage j of the reactor sequence s: 6 F,j 1 C P (T j T j 1 ) + V C R j H j = 0 (18) =1 where T j 1 and T j are the temperature of the reactng flud enterng and leavng stage j n the reactor sequence and H j s the heat of reacton. The nlet temperature of the reactng mxture to the frst stage, T 0, s determned by an energy balance on the mxng pont of steam and wastewater at the nlet of the hydrolyser: 6 F n C P (T n T 0 ) m st h fg = 0 (19) =1 where m st and h fg are mass flow rate and heat of condensaton of nput steam. F n and T n are molar flow rate and temperature of component before mxng. As t s appeared n Eq. (19), ts assumed the steam s quckly condensed at the entrance of the hydrolyser. In order to calculate the actvty coeffcent of reactng materal an equlbrum-based model s used. Accordng to ths model t s assumed that both reactons (2) and (3) approaches to equlbrum [1,7]. In the lght of these assumptons, the model equatons n terms of the lqud molar flow rates are as follows: F out = F n + 2 s + 3 w (20) where F n s the nlet molar flow rate of component after mxng steam wth wastewater. F out s the molar flow rate of component n reactons (1) and (2) leavng the hydrolyser, r s the stochometrc coeffcent of speces n equlbrum reacton r (reactons

5 598 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Table 2 The expresson for constant a k used n Eq. (23). k a k F n 6 + F n 5 + K (1) x F n 2 5 ) 5 K (1) x F nf n (F n 6 + F n 5 F n 6 F n (2) and (3)) whch s postve for products and negatve for reactants. The molar consumpton rate of urea n reacton (2) s s, and that of carbamate n reacton (3) s w. The value of water s very hgh n comparson wth the other components, so t s assumed that the value of water does not change. The expresson for mole fracton of component at the outlet of the hydrolyser s F out x = (21) F t0 + ( 2 s + 3 w) where F t0 s the total molar flow rate of the reactng mxture at the nlet of the hydrolyser. The outlet temperature s also determned by an energy balance: 6 F n C P (T out T 0 ) + s H 2 + w H 3 = 0 (22) =1 where T out s the temperature of reactng materal leavng the hydrolyser, and H 2 and H 3 are heat of reactons (2) and (3). T 0 s the temperature of reactng materal after mxng of steam and wastewater whch s determned by Eq. (22). If Eq. (21) s substtuted nto Eqs. (10) and (11), the followng nonlnear algebrac equatons are derved: a 0 s 2 + a 1 w 2 + a 2 sw + a 3 s + a 4 w + a 5 = 0 (23) b 0 s 3 + b 1 w 3 + b 2 s 2 + b 3 w 2 + b 4 s 2 w + b 5 sw 2 + b 6 sw + b 7 s + b 8 w + b 9 = 0 (24) where a k and b k are constants as a functons of F n demonstrated n Tables 2 and Smulaton of the desorbers (second, fourth and eghth boundares) and Kx r (X) as In the desorpton part, the lqud stream contanng water, ammona and carbon doxde s passed downward through the desorber column, counter-current to the hot gas or low-pressure steam enterng the column at the bottom. In ths stage, ammona and carbon doxde are transferred from the lqud stream to the gas phase. Ths provdes treated water, wth low ammona content, passng out of the column bottom. The stage equatons are the tradtonal equaton of the mass balances and energy balances n the bulk phase for each stage. For 3rd desorber, stage 1 can be a partal condenser. In the desorber column, carbamate decomposton takes place, whch can be consdered at equlbrum reacton, and then ammona and carbon doxde are strpped off from the lqud phase to the gas phase. The equlbrum-stage model that s based on rgorous thermodynamcs model has been proposed to smulate the desorber. Murphree effcency has been used for each tray. The equlbrum-stage model for the desorber s as follows (MESH equatons, for =1,..., M, j =1,..., N): M,j V j+1 y,j+1 + L j 1 x,j 1 +,3 w V j y j L j x j = 0 (25) E,j EM,j(K,j x,j y,j+1 ) (y,j y,j+1 ) 1 S x j S y j H j = 0 (26) M x,j 1 = 0 (27) M y,j 1 = 0 (28) M V,j+1 H v,j+1 + M M L,j 1 H l,j 1 V,j H v,j M L,j H l,j = 0 (29) P 1 p top p 1 = 0 (30) P j p j p j 1 p j 1 = 0 (31) where V j and L j are the vapor and lqud flow rate on the stage j, respectvely, x j and y j are the molar fracton n the lqud and vapor phases, respectvely, and,3 s the stochometrc coeffcent of speces n reacton (3) whch s postve for products and negatve for reactants. The molar consumpton rate of carbamate n reacton (3) s w and H v,j and Hl are the enthalpes of vapor and,j lqud components on the stage j, respectvely. EM,j s Murphree effcency of component on stage j, p top s the specfed pressure of the tray at the top of the desorber and p j 1 s the pressure drop per tray from stage j 1 to stage j. For the partal condenser, the enthalpy balance then has the followng form: H j M V,1 H v,1 M M V,c H v,c L,c H l,c Q c = 0 (32) where Q c s condenser duty. Also V,c and L,c are flow rate of outlet vapor and lqud component from condenser. 5. Numercal soluton Fg. 3 shows the flowchart and trend for solvng the model. The followng steps are nvolved [14,21]. Table 3 The expresson for constant b k used n Eq. (24). k b k k b k 0 K (2) x 5 K (2) x 1 4 K (2) x 6 2K (2) x F t0 2 K (2) x (F t0 + F n ) (2) K x (F t0 + 1)(F n 6 5 ) 3 K (2) x (F n 6 5 Ft n ) + 4(F n ) 8 (F )2 + 4F nf 3 4 x (F t0 (F n 6 5 ) F nf 6 5 ) 4 K (2) x 9 F n n (F 3 4 )2 K (2) x F t0 F nf 6 5

6 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Fg. 3. Flowchart for solvng the model Input data for calculaton The nput data for calculaton conssts of the specfcatons of wastewater feed, low and hgh-pressure steam streams, reflux rato, hydrolyss reactors and desorbers pressures Intal guess for unknown parameters An ntal guess s made for all unknown parameters. In ths secton, guess values for all composton, flow rates and temperatures are made by tral and error n an attempt to optmze these values Intal guess for X urea When a guess s made for urea converson n the hydrolyser, the model s solved and new values are obtaned for X urea. The purpose of the computer programmng s to reach the end, whle the dfference of new and old values of X urea approaches zero Solvng the heat exchanger model When the heat exchanger equatons are combned together, an algebrac system of equatons s obtaned. Ths nonlnear algebrac system of equatons should be solved. The Newton s method s used to solve nonlnear equatons. In ths model, the nlet temperature of the hot streams s unknown, and ths value s calculated by the 2nd desorber model for 1st heat exchanger, the 3rd desorber model for 2nd heat exchanger and the new hydrolyser model for 3rd heat exchanger later,.e., ths temperature s frstly guessed and then corrected by tral and error Soluton of the hydrolyser model The steps for soluton of hydrolyser model are as follows: Set all actvty coeffcent to 1 and guess the outlet lqud temperature. Calculate equlbrum constants usng Eqs. (6), (7), (12) and (5). Calculate s, w by Eqs. (23) and (24), outlet F, x by Eqs. (20) and (21), new actvty coeffcent by Table A.1 and outlet temperature by Eq. (22). Repeat steps 2 and 3 untl dfference between successve actvty coeffcent s suffcently small. Repeat steps 2 and 3 untl dfference between successve outlet temperature s suffcently small.

7 600 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Calculate V C = V/N. Calculate F,j and T j by Eqs. (17) and (18). In the above procedure, the molar consumpton rate of urea (s) and carbamate (w) were determned by Newton Raphson algorthm Soluton of the desorber model For 1st desorber, specfcatons of nput vapor of t are unknown, whch are calculated by the 2nd desorber model later,.e., the temperature and component flow rates s frstly guessed and then corrected by tral and error. When the specfcatons of output lqud stream of old and new hydrolyss reactors are known, the calculaton relevant to 2nd and 3rd desorbers s used to obtan outlet streams flow rates, composton and temperatures, respectvely. The modelng leads to a system of algebrac equatons, whch are solved by teratve technques usng Newton s method [22]. To mprove accuracy and speed up the computaton, all of the dervatves of thermodynamc propertes n ths study are obtaned analytcally. The resultng Jacoban matrx has a block trdagonal structure. Lnear systems wth a block trdagonal coeffcent matrx can be solved qute effcently usng the Thomas algorthm [23]. Let (F(X)) = 0 (33) where X = [X 1,X 2,...,X j,...,x N ] T (34) and F = [F 1,F 2,...,F j,...,f N ] T (35) where X j s the vector of unknown varables for stage j and F j s the vector of model equatons for stage j arranged n the order. Table 4 Input specfcatons of the ndustral treatment secton of conventonal urea plant [8]. Feed specfcatons Feed wastewater HP 1 steam LP 1 steam Temperature ( C) Pressure (kg/cm 2 ) Component molar rate (kmol l/h) Water Urea CO NH Computaton of X urea At ths stage, new value for urea converson s obtaned wth Eq. (41) and compared wth the old value. X urea = F f x f (1) F e x e (1) (41) F f x f (1) 6. Model valdaton In ths work, modelng of the conventonal treatment loop was performed and ts verfcaton was carred out by comparson of the model results wth the plant data. The nput data of the treatment secton of conventonal urea plant have been summarzed n Table 4. The model results and the correspondng observed data of the plant have been presented n Table 5. It was observed that, the steady-state model performed satsfactorly well under the ndustral condtons and a good agreement was obtan between the plant data and the smulaton data whch confrm that the proposed model can be consdered sutable and relable. X j = [T j,x 1,j,x 2,j,...,x,j,...,x M,j,y 1,j,y 2,j,...,y,j,...,y M,j,L j,v j,p j,w] T (36) F j = [H j,m 1,j,M 2,j,...,M,j,...,M M,j,E 1,j,E 2,j,...,E,j,...,E M,j,S x j,sy j,p j,e c,j ] T (37) Wth ths notaton, the Newton s method becomes X (k+1) = X (k) + t X k (38) where k stands for the teraton number, and t s relaxaton factor and X s defned as: X k = [(J) 1 ] k F K (39) Also (J) 1 s the nverse Jacoban matrx of dervaton at kth teraton wth elements J,j = F X j (40) 7. Results and dscusson 7.1. Investgaton of cascade of wastewater treatment loops The desgn operatng condtons of the new proposed treatment secton are lsted n Tables 6 and 7. The smulaton results were plotted as profles of the dependent parameters versus ndependent varables. In addton, the effects of dfferent parameters on the urea and ammona removal performance were nvestgated. Table 5 Comparson of calculated results wth the observed plant data for treatment secton of conventonal urea plant. Outlet treated lqud Outlet vapor of 1st desorber Plant Calc. Error (%) Plant Calc. Error (%) Temperature ( C) Component molar rate (kmol/h) Water Urea CO NH Total (kmol/h)

8 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Table 6 Specfcatons of the steam consumpton of proposed wastewater treatment secton. LP 2 steam HP 2 steam Temperature ( C) Pressure (kg/cm 2 ) Mass flow rate (kg/h) Fg. 5. Molar flow rate of lqud products along the (a) conventonal treatment secton and (b) new proposed treatment secton where the operatng condtons are same as Tables 4 and 6. Fg. 4. (a) Molar flow rate and (b) converson of urea along the hydrolyss reactors where the operatng condtons are same as Tables 4 and 6. Fg. 4(a) and (b) presents urea flow rate and converson profles along the old and new thermal hydrolyss reactors, respectvely. Urea removal ncreases along the columns heght from bottom to top because of urea hydrolyss. These fgures demonstrate an enhancement n urea decomposton and more converson along the new hydrolyser as the hghest converson s acheved. It shows urea converson s approxmately 100%. Fg. 5(a) and (b) shows flow rate of ammona and carbon doxde n the conventonal and the new treatment process n the lqud phase, respectvely. These profles clearly show the producton of these components along the thermal hydrolyss reactors due to reactons and ther reducton n the desorbers n the lqud phase, as the two lqud and vapor streams cross each other countercurrently n the desorbers. The sudden decrease at the entrance of the 2nd desorber whch s shown n Fg. 5(a) s due to the nlet stream become two phase. In the 3rd desorber, the feed and reflux streams enter from the top of the column. Therefore a maxmum pont s observed n the ammona curve of Fg. 5(b). Fg. 6 shows flow rate of ammona and carbon doxde along the desorbers n the vapor phase. As can be seen n these fgures, the Table 7 Specfcatons of output stream of new hydrolyser and 3rd desorber. Outlet stream of hydrolyser Outlet lqud of desorber Outlet vapor of condenser Reflux stream Temperature ( C) Component mass rate (kg/h) Water 33,710 39, Urea 1 ppm 1 ppm CO NH ppm

9 602 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Fg. 6. Molar flow rate of vapor products along the desorbers where the operatng condtons are same as Tables 4 and 6. ammona and carbon doxde contents n the vapor phase ncrease from the bottom to the top of desorbers. Fg. 7(a) demonstrates the temperature profles along the hydrolyss reactors. The profle for the old hydrolyser suddenly ncreases due to the njecton of hgh-pressure steam and then has downward trend owng to the endothermc reacton and ts vara- Fg. 8. Molar flow rate of (a) urea along the hydrolyss reactors and (b) ammona along the 2nd desorber, new hydrolyser and 3rd desorber at dfferent HP 1 steam flow rates. Fg. 7. Temperature profle (a) of reactng materal along the hydrolyss reactors and (b) along the desorbers where the operatng condtons are same as Tables 4 and 6. ton s small, but the temperature profle of the new hydrolyser s constant due to low concentraton of urea. Fg. 7(b) dsplays along the desorbers, the lqud temperature ncreases from the top to the bottom of the column as the lqud flows down the desorber on nteractng wth the vapor stream. Ths fgure ndcates the temperature change along the 3rd desorber s very small because of ammona content n lqud phase s very low. Fg. 8(a) ndcates the flow rate of urea along the hydrolyss reactors at dfferent flow rates of HP 1 steam. As can be seen from ths fgure, hgher steam flow rate mantans a hgher temperature level n the reactors, so results n enhancng the urea removal. Also a change n the flow rate of the HP 1 steam has an effect on the flow rate of ammona n lqud stream. As s clearly demonstrated n Fg. 8(b), an ncrease n the HP 1 steam flow rate would result n lower ammona content n lqud phase due to temperature ncreasng. Fg. 9 shows the nfluence of low-pressure (LP 1 ) steam flow rate on the flow rate of ammona lqud along the 2nd desorber, new hydrolyser and 3rd desorber. Whle the LP 1 steam ncreases, the ammona content n the lqud phase decreases. Ths s due to hgher level of temperature and ncrease of drvng force n the desorbers.

10 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Fg. 9. Molar flow rate of ammona along the 2nd desorber, new hydrolyser and 3rd desorber at dfferent LP 1 steam flow rates. Fg. 11. Urea concentraton n the treated effluent at dfferent HP 2 steam flow rates wth change of nlet wastewater temperature Investgaton of new proposed treatment system In the proposed desgn a questonable pont rases that wll urea removal of hydrolyser mprove, f confguraton changes from counter-current to co-current? Wth respect to endothermc overall reactons and knetc of urea hydrolyss, t s better to ncrease temperature of nlet wastewater especally f urea concentraton s so lttle. Also n ths condton such as 18 bar pressure and low concentratons of ammona and carbon doxde n hydrolyser, vapor phase does not form along t and hydrolyser s full of lqud, so counter-current confguraton concept does not mean. Therefore as exstence of especal mentoned condtons, co-current confguraton of hydrolyser s the best desgn. In ths part, the effects of dfferent parameters on the urea and ammona removal performance n new proposed treatment secton were nvestgated. Fg. 10 shows the effect of enterng LP 2 steam flow rate on the ammona concentraton n the treated effluent at dfferent reflux ratos. The ncrease of LP 2 steam flow rate mproves the desorpton performance and provdes a lower concentraton of ammona n outlet lqud. Also ncrease of ammona concentraton n treated effluent wth ncreasng of reflux rato can be observed for the reason that the reflux stream ncreases. Fg. 11 dsplays the urea concentraton n the treated effluent wth change of HP 2 steam flow rates at dfferent nlet wastewater temperatures of proposed system. Snce decomposton of urea s an endothermc reacton, ncrease of the temperature causes decrease of the urea concentraton and mproves urea removal. Also, as can be seen n Fg. 11 f flow rate of HP 2 steam ncreases, the reacton shfts to the rght and urea decomposton becomes more. The effect of LP 2 steam flow rate on ammona concentraton n treated effluent at three nlet wastewater temperature of proposed system s shown n Fg. 12. From ths fgure, lower flow rate of LP 2 steam provdes more ammona concentraton than hgher flow rate. Also the change of ammona concentraton wth alteraton of wastewater temperature s neglgble because of nlet pressure of 3rd desorber s constant. The effect of the number of new hydrolyser stages on urea concentraton wth change of flow rate of HP 2 steam s shown n Fg. 13. Increase of the number of stages enhances converson of urea, because the decomposton of urea s proportonal to the number of stages and much resdence tme that leads to more urea conver- Fg. 10. Ammona concentraton profles n treated effluent at dfferent reflux ratos wth change of LP 2 steam flow rates. Fg. 12. Ammona concentraton n treated effluent at dfferent LP 2 steam flow rates wth change of nlet wastewater temperature.

11 604 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Fg. 13. Influence of number of hydrolyser stages on urea concentraton n the treated effluent wth change of flow rate of HP 2 steam. upgrade the outlet effluent of wastewater treatment secton of conventonal urea plants whch has no qualty to reuse, s nstallaton of a new small treatment secton at end of process. In ths study, a mathematcal model was used for smulaton of cascade of hydrolyss-desorpton loops n order to remove urea, ammona and carbon doxde from wastewater of conventonal urea plant to acheve the new envronmental standard, so that all components ncludng the water can be recycled and reused n the plant. All of specfcatons of the outlet streams of the old and new hydrolyss reactors and desorbers are calculated by the model. The effects of key parameters on purty of treated effluent such as wastewater temperature, number of stages, HP and LP steam flow rates and reflux rato have been nvestgated. Generally, t was observed the postve effects on urea and ammona removal by ncrease of the temperature, steam flow rate, heght of proposed desorber column and hydrolyser. Also, decrease of reflux rato leads to better removal of urea and ammona n the treated effluent. The proposed model can be used for desgn of new ndustral wastewater treatment secton for conventonal urea plants to remove urea, ammona, urea and carbon doxde and results n decrease of envronmental polluton. Acknowledgment The authors would lke to thank Shraz Petrochemcal Complex for provdng valuable process and techncal data and fnancal support. Appendx A. Thermodynamcs equatons There are several thermodynamc models for descrbng the non-dealty of NH 3 CO 2 H 2 O urea system [1,24 28]. In ths study, the thermodynamc framework to descrbe lqud actvty coeffcents of molecular and onc speces n NH 3 CO 2 H 2 O urea system s based on the model developed by Isla et al. [1]. The volatlty of urea and ammonum carbamate s neglgble and ons cannot leave from the lqud phase to the vapor phase, so there are only three molecular components ncludng H 2 O, NH 3, and CO 2 n the vapor phase. The vapor lqud equlbrum can be expressed wth the followng relatonshps: Fg. 14. Influence of number of desorber stages on ammona concentraton n the treated effluent wth change of reflux rato. son. Also Fg. 13 shows ncreasng HP 2 steam flow rate promotes the urea removal. Fg. 14 demonstrates the effect of the number of 3rd desorber stages on ammona concentraton n treated effluent wth change of reflux rato. When the number of stages s more, the separaton s better and the purty of treated lqud becomes more whle the number of stages s fewer, the amount of ammona n lqud phase becomes more and the purty decreases. Also the role of reflux rato on the treated lqud purty s very low because of small varaton of ammona content n the treated effluent when reflux rato changes much. As clearly demonstrated n ths fgure a decrease n reflux rato would result n a hgher purty of water. 8. Conclusons Nowadays, the envronmental polluton s so mportant, especally water polluton whch wll become vtal subject n future. The lqud waste polluton control problem of a urea plant can be solved usng a treatment wastewater secton whch ncludes two man equpments, urea thermal hydrolyser to decrease urea content and desorber to decrease ammona and carbon doxde contents. Results of study showed one of the best methods to NH 3 (l) NH 3 (g) CO 2 (l) CO 2 (g) H 2 O(l) H 2 O(g) (A.1) (A.2) (A.3) As follows n Table A.1, the extended UNIQUAC equaton conssts of three tems [1,25 28]. The volume and surface factors, r and q, are tabulated n Table A.2. All of the bnary nteracton parameters are lsted n Table A.3. For water and ammona, the phase equlbrum equatons are represented as follows: x f 0 ( v l exp P RT ) = Py (A.4) where f 0 s defned as the standard fugacty under the system temperature and zero pressure. Whle for carbon doxde, Henry s law s applcable, and vapor lqud equlbrum equaton s represented as Eq. (A.5), whle H CO2 s the Henry s constant of CO 2 under the system temperature. ( ) v l x H CO2 exp (P Ps 2 ) = Py RT (A.5) The temperature dependence of the pure lqud reference fugacty at zero pressure for ammona, and Henry s constant for carbon

12 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) Table A.1 Parameters of extended UNIQUAC model [1]. Appendx B. Nomenclature Parameter Expresson (T, x) C (X) RE (T, X) v v = q X ln (T, x) = ln C (X) + ln RE (T, X) + ln DH (X, T) ln C (X) = ln( ) + Z X 2 q ln v + l X X j l j ln RE (T, X) = q [1 ln q j X j j = r X r j X j j ( l l = Z 2 ( r q ) ( r 1) j j = exp( aj ),a T = a jj = 0 DH (T, X) DH (T, X) ln DH (T, X) = ln DH I I = ( 1 2 (T, X) = z 2 ) m j z 2 j m j=1 v j j ) ( ) 2A M b 3 [1 + bi 1/2 AI 1/2 1+BI 1/2 Z Z = T T 2 Table A.2 Pure component parameters of extended UNIQUAC model [1]. j m j=1 v j j m v k kj k=1 ] ] 1 2 ln(1 + 1+bI 1/2 bi1/2 ) Component q r Unts H 2NCONH ( ) H 2O ( ) NH ( ) H 2NCOO ( ) CO ( ) NH ( ) Table A.3 Bnary nteracton parameters of extended UNIQUAC model [1]. j doxde are modeled as ln f 0 NH 3 (T) = A 1 T + A 2 ln T + A 3 T + A 4 (A.6) ln H CO2 (T) = B 1 T + B 2 ln T + B 3 T + B 4 q 5 5,2 (A.7) where q 5 and 5,2 are obtaned from Table A.1. All parameters of ammona fugacty and carbon doxde Henry s constant are represented n Table A.4. Table A.4 Ammona fugacty and carbon doxde Henry s constant parameters. Functon Parameters 10 2 A A A 3 10A 4 ln f 0 NH Functon Parameters 10 2 B B B 3 10B 4 ln H CO A j jth parameter n the correlaton of pure lqud reference fugacty of ammona wth temperature a k, b k constants of Eqs. (23) and (24) B j jth parameter n the correlaton of Henry s constant of carbon doxde n water wth temperature C concentraton of component (kmol/m 3 ) C P heat capacty of flud (kj/(kmol K)) E actvaton energy (kj/kmol) E c,j resdual functon for chemcal equlbrum relaton for carbamate on the jth tray E,j resdual functon for phase equlbrum relaton for component on the jth tray EM,j Murphree tray effcency for component on the jth tray f fugacty of component (kpa) F matrx of functons F e molar flow rate of hydrolyser effluent (kmol/h) F f molar flow rate of hydrolyser feed (kmol/h) F,j molar flow rate of component leavng stage j n the reactor (kmol/h) F n molar flow rate of component before mxng at the entrance of reactor (kmol/h) F t0 total molar flow rate at the nlet of hydrolyser (kmol/h) h fg heat of condensaton of nput steam to the hydrolyser (kj/kg) H v,j enthalpy of component n vapor phase on stage j (kj/kmol) H l,j enthalpy of component n lqud phase on stage j (kj/kmol) H heat of reacton (kj/kmol) H j resdual functon for total heat balance on the jth tray H CO2 Henry s constant of component n solvent j I onc power n Table A.1 J Jacoban matrx (matrx of blocks of partal dervatves of all functons wth respect to all the output varables) K,j the equlbrum constant K 0 pre-exponental factor of urea hydrolyss rate constant (m 3 /(kmol h)) K f the forward reacton rate constant (m 3 /(kmol h)) K x,r equlbrum constant of reacton r dependent on temperature and mole fracton K,r equlbrum constant of reacton r dependent on mole fracton K r equlbrum constant of reacton r dependent on temperature L j mole flow rate of lqud on stage j (kmol/h) L,j lqud mole flow rate of component on stage j (kmol/h) l parameter of UNIQUAC equaton n Table A.1 m st mass flow rate of nput steam to the hydrolyser (kg/h) M number of components M,j resdual functon for materal balance for component on the jth tray m molalty of the onc speces referred to 1000 g of mxed solvent (kg/(kg soln)) N number of stages P j pressure of stage j (kpa) P j pressure drop (kpa) p top pressure at the top of the column (kpa) q UNIQUAC surface parameter of component Q c condenser duty (kj/h) Q heat transfer n the heat (kj/h) r UNIQUAC volume parameter of component R unversal gas constant (kj/(kmol K))

13 606 M.R. Rahmpour et al. / Chemcal Engneerng Journal 160 (2010) R j rate of reacton (2) on the jth tray (kmol/(m 3 h)) S x j resdual functon for summaton relaton n lqud phase on the jth tray S y j resdual functon for summaton relaton n lqud phase on the jth tray t relaxaton factor T temperature (K) T n temperature of component before mxng at the entrance of the hydrolyser (K) T M metal temperature n heat exchanger (K) T 0 nlet temperature of the reactng mxture to the frst stage n the hydrolyser (K) U constant (Eq. (12)) U overall heat transfer coeffcent n heat exchanger (kj/(h m 2 K)) V C stage volume of hydrolyser (m 3 ) V j mole flow rate of vapor on stage j (kmol/h) V,j vapor mole flow rate of component on stage j (kmol/h) v l lqud molal volume of component v lqud molal volume of component at nfnte dluton w consumpton molar flow rate of carbamate n reacton (3) (kmol/h) x e mole fracton of component n hydrolyser effluent x f mole fracton of component n hydrolyser feed x,j mole fracton of component n lqud phase on the jth tray X matrx of output varables X urea urea converson y,j mole fracton of component n vapor phase on the jth tray Z UNIQUAC coordnaton number (Z = 10) n Table A.1 Greek letters,2 stochometrc coeffcent of speces n reacton (2),3 stochometrc coeffcent of speces n reacton (3) a j parameter of UNIQUAC equaton (kj/mol) n Table A.1 actvty coeffcent of component n Table A.1 stochometrc coeffcent of speces n reacton (1) v surface area fracton of component n Table A.1 volume area fracton of component n Table A.1 j parameter of UNIQUAC equaton n Table A.1 reduced densty n equaton state Subscrpts 0 nlet condtons component number j stage number k counter of constants a and b n Eqs. (23) and (24) L length of heat exchanger r reacton number t total Superscrpts C combnatoral DH Debye Huckel n out RE References nlet of hydrolyser outlet of hydrolyser resdual [1] M.A. Isla, H.A. Irazoqu, C.M. Genoud, Smulaton of a urea synthess reactor. Part 1. Thermodynamc framework, Ind. Eng. Chem. Res. 32 (1993) [2] V. Lagana, US Patent 5,399,755 (1995). [3] H. van Baal, The envronmental mpact of a Stamcarbon 2000 mtd urea plant, n: Proceedngs of Eghth Stamcarbon Urea Symposum, Amsterdam, The Netherlands, 1996, pp [4] Norrs, J. Lands, US Patent 4,341,640 (1982). [5] J.N. Sahu, K. Mahalk, A.V. Patwardhan, B.C. Mekap, Equlbrum and knetc studes on the hydrolyss of urea for ammona generaton n a batch reactor, Ind. Eng. Chem. Res. 47 (14) (2008) [6] M.R. Rahmpour, A. Asgar, Modelng and smulaton of ammona removal from purge gases of ammona plants usng a catalytc Pd Ag membrane reactor, J. Hazard. Mater. 153 (2007) [7] J. Mehnen, C. Verweel, Experence to date wth the Stamcarbon desorber hydrolyser system, n: Proceedng of Stamcarbon s Seventh Urea Symposum, Maastrkht, The Netherlands, 1987, pp (Paper 9). [8] Shraz Petrochemcal Complex, Urea Plant, Operatng Data of Urea Thermal Hydrolyss Process, [9] M.R. Rahmpour, A. Azarpour, Smulaton of a urea thermal hydrolyss reactor, Chem. Eng. Commun. 192 (2005) [10] M.R. Rahmpour, A. Azarpour, A multstage well-mxed model for urea removal from ndustral wastewater, Eng. Lfe Sc. 3 (2003) [11] M.R. Rahmpour, A non-deal rate-based model for ndustral urea thermal hydrolyser, Chem. Eng. Process. 43 (2004) [12] M.M. Barmak, M.R. Rahmpour, A. Jahanmr, Treatment of wastewater polluted wth urea by counter-current thermal hydrolyss n an ndustral urea plant, Sep. Purf. Technol. 66 (2009) [13] A.M. Douwes, US Patent 4,652,678 (1987). [14] M.R. Rahmpour, H.R. Mottagh, Smultaneous removal of urea, ammona, and carbon doxde from ndustral wastewater usng a thermal hydrolyzer separator loop, Ind. Eng. Chem. Res. 48 (2009) [15] B. Claudel, E. Brousse, G. Shehadeh, Novel thermodynamc and knetc nvestgaton of ammonum carbamate decomposton nto urea, Thermochm. Acta 102 (1986) [16] M. Boudart, Knetcs of Chemcal Processes, Prentce-Hall, New Jersey, [17] H. Eyrng, E.M. Eyrng, Modern Chemcal Knetcs, Renhold, New York, [18] J.B. Butt, Reacton Knetcs and Reactor Desgn, second ed., Marcel Dekker, New York, [19] H. Aok, T. Fujwara, Y. Morozum, T. Mura, Proceedngs of the Ffth Internatonal Conference on Technologes and Combuston for a Clean Envronment, Lsbon, 1999, pp [20] T.F. Anderson, D.S. Abrams, E.A. Grens, Evaluaton of parameters for nonlnear thermodynamcs models, AIChE J. 24 (1978) [21] P. Parvas, M.R. Rahmpour, A. Jahanmr, Incorporaton of dynamc flexblty n the desgn of a methanol synthess loop n the presence of catalyst deactvaton, Chem. Eng. Technol. 31 (2008) [22] A.L. Myers, W.D. Seder, Introducton to Chemcal Engneerng and Computer Calculaton, Prentce-Hall, [23] J.D. Seader, E.J. Henley, Separaton Process Prncples, Wley, New York, [24] M. Bernards, G. Carvol, M. Santn, Urea NH 3 CO 2 H 2O: VLE calculatons usng an extended UNIQUAC equaton, Flud Phase Equlb. 53 (1989) [25] E.A. Kotula, A VLE model of the NH 3 CO 2 H 2O urea system at elevated pressure, J. Chem. Technol. Botechnol. 31 (1981) [26] B. Sander, A. Fredenslund, P. Rasmussen, Calculaton of vapour lqud equlbra n mxed solvent/salt systems usng an extended UNIQUAC equaton, Chem. Eng. Sc. 41 (1986) [27] B. Sander, P. Rasmussen, A. Fredenslund, Calculaton of vapor lqud equlbrum n ntrc acd water ntrate salt systems usng an extended UNIQUAC equaton, Chem. Eng. Sc. 41 (1986) [28] B. Sander, P. Rasmussen, A. Fredenslund, Calculaton of sold lqud equlbra n aqueous solutons of ntrate salts usng an extended UNIQUAC equaton, Chem. Eng. Sc. 41 (1986)