World Academy of Science, Engineering and Technology International Journal of Materials and Metallurgical Engineering Vol:4, No:12, 2010

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1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng To Study the Parametrc Effects on Optmalty of Varous Feedng Sequences of a Multeffect Evaporators n Paper Industry usng Mathematcal Modelng and Smulaton wth MATLAB Deepak Kumar, Vvek Kumar, and V. P. Sngh Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 Abstract Ths paper descrbes a steady state model of a multple effect evaporator system for smulaton and control purposes. The model ncludes overall as well as component mass balance equatons, energy balance equatons and heat transfer rate equatons for area calculatons for all the effects. Each effect n the process s represented by a number of varables whch are related by the energy and materal balance equatons for the feed, product and vapor flow for backward, mxed and splt feed. For smulaton fsolve solver n MATLAB source code s used. The optmalty of three sequences.e. backward, mxed and splttng feed s studed by varyng the varous nput parameters. Keywords MATLAB fsolve solver, multple effect evaporators, black lquor, feedng sequences. E I. INTRODUCTION VAPORATORS are wdely used n the chemcal ndustry to concentrate weak soluton and recover solvents. It s used n ndustres lke paper, sugar and caustc soda to concentrate black lquor, sugar cane juce and caustc soda solutons respectvely. The Pulp and Paper ndustry, whch s the focus of the present nvestgaton predomnantly, uses the Kraft Process n whch black lquor s generated as spent lquor. Ths lquor s concentrated n multple effect evaporator (MEE) house for further processng. Earler, long tube vertcal (LTV) types of evaporators were employed n Inda [21]. However, wth development of flat fallng flm evaporators (FFFE), whch clam many benefts over ts counter parts LTV evaporators, most Indan paper mlls have already swtched to FFFE systems. In fact, t operates under low temperature drop (about C) across the flm and thus, more evaporators can be accommodated wthn the total temperature dfference Deepak Kumar s wth the Indan Insttute of Technology Roorkee, Saharanpur Campus, Saharanpur, Inda. (phone: ; fax: ; dkr2009@gmal.com ). Vvek Kumar s wth the Indan Insttute of Technology Roorkee, Saharanpur Campus, Saharanpur, Inda. (vvekfpt@tr.ernet.n ). V.P.Sngh s wth the Indan Insttute of Technology Roorkee, Saharanpur Campus, Saharanpur, Inda. (snghvp3@gmal.com ). avalable for evaporaton to offer hgher steam economy [23]. Reference [19] ponted out that the MEE house of Indan paper mlls alone consumes around 24 30% of the total steam requred n a large paper mll. Therefore, t calls for a thorough nvestgaton nto ts analyss and varous energy reducton schemes. The black lquor contans dssolved solds rangng from 12 to 20%. So ths lquor s concentrated to about 4 to 0%. The evaporaton for concentraton of black lquor s normally carred out n a multple effect evaporator usng low pressure steam where a seres of evaporators are operated at dfferent pressures so that the vapor from one evaporator body becomes the steam supply to the next evaporator body. Ths gves hgh steam economy. A wde varety of mathematcal models for multple effect fallng flm evaporators can be found n the lterature. Normally the man dfference among these mathematcal models s the heurstc knowledge whch s ncorporated n ther development and smulaton technque. For the analyss of MEE system mathematcal models have been reported n the lterature snce last fve decades. A few of these were developed by [1], [], [7]-[14], [17], [20], [24] and [26]-[27]. These models are generally based on a set of lnear or nonlnear equatons and can accommodate effects of varyng physcal propertes of vapor/steam and lquor wth change n temperature and concentraton [22]. Reference [1]-[4] attempted to smulate a sextuple effect black lquor evaporator system for paper ndustry. Ths requred developng a system of nonlnear smultaneous equatons based on steady state mass and energy balances, heat transfer rate, equlbrum relatonshps and same physcochemcal/physco-thermal propertes of lquor. Numercal technques usng Newton-Raphson Jacoban matrx method and method of Gauss elmnaton are employed to solve the problem. Reference [22]-[23] developed a nonlnear model for a Sextuple effect flat fallng flm evaporator (SEFEFE) system employed for concentratng weak black lquor n an Indan Kraft Paper Mll. The system ncorporates dfferent operatng strateges such as condensate-, feed- and product-flashng, and Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 steam- and feed-splttng. Reference [18] presents the steadystate smulaton and optmzaton of a sx-effect evaporator and the provson of ts relevant software package. Reference [2] developed dfferent energy reducton schemes (ERSs) to reduce the consumpton of steam for a multple effect evaporator (MEE) system. These ERSs are condensate-, feedand product-flashng and vapor bleedng. Ths process consumes more tme and mathematcal sklls. In the present study we descrbe the steady state Mathematcal model for sx effect evaporator n the smlar manner as used by [1] wth some necessary modfcatons and used dfferent physcochemcal/physco-thermal propertes of black lquor gven by [1]. The smulated results are obtaned for the backward ( ), mxed (feed nto th effect as, ) and splt feed (equal feed n th and 6 th effects as, shown n Fg. 3) for a sextuple effect evaporator and compare wth the results of prevous workers [1], [3]-[4] respectvely. For the soluton of the system of nonlnear smultaneous equatons fsolve solver n MATLAB source code s used and the results show the good agreement wth the above researchers. To study the optmalty of the feedng sequences the effect of varous nput parameters are checked Steam (V O) Steam on the steam economy. II. DESCRIPTION OF MATHEMATICAL MODEL The flow dagrams of a sextuple effect evaporator system for backward, mxed and splt feed sequences are shown n the Fg. 1, Fg. 2 and Fg. 3 respectvely. In the backward sequence feed s ntroduced to the last effect and partly concentrated lquor flows to the ffth, fourth, thrd, second and then to the frst effect from whch the concentrated lquor s wthdrawn. Saturated steam s fed to the shell of the frst effect, and vapour generated theren flows to the shell of second effect and acts as the heatng medum there. The vapour generated n the second effect supples heat for bolng the lquor n the thrd effect. In ths manner steam generated n each effect s suppled to the next effect as shown n the Fg. 1. The steam generated n the last effect s condensed by the condenser. But n mxed sequence feed s gven n th effect and n splt sequence the feed s gven equally to both th and 6 th effects and other process s same as shown n the Fg 2 & Fg. 3 respectvely. V 1=L 2-L 1 V 2=L 3-L 2 V 3=L 4-L 3 V 4=L -L 4 V =L 6-L V 6=L F- L 2 L 3 L 4 L Product Feed (L F) C 1 C 2 C 3 C 4 C C 6 Condenser Fg. 1 Flow dagram of Sextuple backward feed evaporator ( ) V 1=L 2-L 1 V 2=L 3-L 2 V 3=L 4-L 3 V 4=L 6-L 4 V =L F- V 6=L -L 6 L 2 L 3 L 4 L L 6 Feed (L F) L 6 C Product 1 C 2 C 3 C 4 C C 6 Condenser Fg. 2 Flow dagram of Sextuple mxed feed evaporator ( ) Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng V 1=L 2-L 1 V 2=L 3-L 2 V 3=L 4-L 3 V 4=L 6+L -L 4 V = L F/2-L V 6= L F/2-L 6 Steam L 2 L 3 L 4 L L 6 C Product 1 C 2 C 3 C 4 C C 6 Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 A. Mathematcal Formulaton Fg. 3 Flow dagram of Sextuple splt feed evaporator 6 The steady state model of a multple effect evaporator system s developed by usng mass and energy balance equaton for each effect of a sextuple effect evaporator. By takng the mass and energy balances over th effect of a sextuple effect evaporator system wth backward, mxed and splt feed model s obtaned. The block dagram of the th effect evaporator s gven by Fg. 4. Overall mass balance around evaporaton secton: L = L V Overall balance around stem chest: V C - 1 = Partal mass balance for solds provdes: L X = L X = An enthalpy balance Q or = H V C hc L X f f Q = V hc + λ + Cp v * BPR C hc By usng (2) Q = V -1 Heat transfer rate λ + Cp * BPR -1 v -1 (1) (2) (3) (4) Condenser ) Hence Q = U A ( Tv -1 Tv BPR ) () Overall energy balance gves: L h Q L h V H (6) + = + + Substtutng the value of V from (1) and Q1 from (4) nto "(6) we get (7) L h + H V C hc = L h + (L - L )H Addng and subtractng L +1 h nto (7) we get L h L h + H V C hc L h + L h (L - L )H = Or t may be wrtten as L ( h h ) + H V C hc (L - L )(H h ) = (8) Steam/Vapour Inlet V -1 T -1 th Effect Steam Chest Feed (L F/2) Vapour Outlet V T Evaporaton Secton Black lquor Inlet L +1 X +1 T L+1 ( T ) eff Q = U A ( T) = Tv - Tl = eff where -1 Tl = Tv + Tv - Tv - BPR -1 BPR C T -1 L X T L Fg. 4 Block dagram of th effect evaporator Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 Now snce H = hc + λ Cp *BPR 1 +, + v h = Cp (Tv + BPR ) and hc = ATl B are enthalpes of vapor, black lquor and condensate respectvely. Puttng these values of enthalpy nto (8) we get Cp (Tv + BPR ) Cp (Tv + BPR ( hc + λ + Cp * BPR ) C hc (L - L ) -1-1 v L V (hc + λ + Cp * BPR ) Cp (T + 1 v Usng (2) and after smplfyng we get L Cp V ( λ + Cp -1-1 λ + Cp v (L - L + 1 (Tv * BPR v * BPR )(ATl Now from (4) & () gves + BPR ) Cp ) (L - L ) ) Cp (Tv + BPR ) + B) = 0 + BPR (Tv ) ) = BPR ) + (9) U A (Tv Tv BPR ) V (λ + Cp *BPR ) = 0 (10) v -1 where = 1, 2, 3, 4, & 6. Thus we have two nonlnear equatons (9) & (10) for the th effect evaporator. Hence for = 1 to 6 we have 12 nonlnear equatons for the sx effect evaporators for backward feed. To obtan the model equatons for the mxed and splt feed few changes are requred n the feedng varables. For the mxed feed n (9) for th effect.e. for =, the value L F s used n place of L 6 and the output L go nto 6 th effect and from 6 th to 4 th and from 4 th to 3 rd and up to the 1 st effect. In ths manner to obtan the model equaton for the splt feed the changes n the feedng varables are requred. For the splt feed n (9) for th and 6 th effect equal feedng L F /2 s gven and the output from th and 6 th effect go nto 4 th effect and then from 4 th to 3 rd effect and up to the frst effect. III. STEADY STATE SIMULATION For obtanng the steady state soluton of the sextuple effect evaporator system there s a need to solve the system of nonlnear smultaneous equatons. For sextuple effect evaporator (9) and (10) gve 12 nonlnear equatons as obtaned by [1]. Usng physco-chemcal propertes of black lquor from TABLEII and substtutng the values of enthalpes and heat transfer coeffcents we get the 12 nonlnear smultaneous equatons n 12 unknowns for all three feedng sequences. Data for smulaton purpose s taken from lterature. The range of operatng parameters s taken accordng to [2] and duly modfed target values are consdered accordng to Indan Paper mll evaporaton condtons. The values of the operatng parameters are presented n TABLEI. For fallng flm evaporator the range of overall heat transfer coeffcent (OHTC) s gven by varous researchers. S. No. Operatonal Parameter 1. Lquor feed flow rate, Kg/sec 2. Lquor feed TABLE I RANGE OF OPERATIONAL PARAMETERS Temperature, 0 C 3. Lquor feed concentraton Parameter s Target Value Range Steam Temperature, 0 C Last body saturaton, 0 C Lquor product concentraton 7. Heat transfer Coeffcents (KCal/hm 2 0 C) Reference [6] has suggested the value of OHTC as KCal/h m 2. 0 C. Reference [16] suggested the values of OHTC nearly 1300 W/m 2 0 C. For evaporaton of black lquor [1] gave the range of OHTC for all effects for sextuple evaporator between W/m 20 C. After dscusson wth few Indan Paper Mlls, values of OHTC were taken n the range KCal/hm 2 0 C for the present study n whch concentraton rsng from 10% to 0%. The steady state soluton of the system of nonlnear equatons s obtaned by fsolve solver n MATLAB source code for the backward, mxed and splt feed sequences. The solutons of backward, mxed and splt feed are presented n TABLEIII, TABLEIV, and TABLEV respectvely. The requred steam and heat transfer area s calculated for all sequences and presented n respectve TABLES. Steam economy s also calculated by the rato of total evaporaton wth steam consumpton s also shown n respectve TABLES for each sequence. IV. RESULTS AND DISCUSSSION , 100,1100, 110, 117, 1200 The desgn and operatonal parameters (feed rate, temperature and concentraton) are equally mportant for modelng of MEE. A set of operatonal data normally employed n the paper ndustry globally, s gven n TABLE I. Wth ths data along wth the equatons for Physcochemcal/thermal propertes gven by [1] shown n TABLE II s used. The calculaton procedure structured n ths study computes desgn varables such as area (or area rato between effects), externally suppled steam rate, stages temperatures, flow rates of lqud and vapors and fnally steam economy. Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng TABLE II PHYSICO-CHEMICAL/THERMAL PROPERTISE OF BLACK LIQUOR S. No. Propertes Equatons Functon Parameters 1. Bolng Pont Rse BPR = {6.173 X X X 2 )* {1+ 0.6(Tv )/100} 2. Black Lquor Densty, Kg/m 3 Pl = ( X) { (Tl /1000) 1.94(Tl/1000) 2 } X = Sold Concentraton, Tv = Steam Temperature, 0 C Tl = Black Lquor Temp. n 0 C, X = Sold Concentraton 3. Specfc Heat Capacty, kj/kg. 0 C, Cp = 4.216(1-X) + {1.67+ (3.31Tl)/1000} Tl = Black Lquor Temp. n 0 C, *X + ( Tl/1000) (1-X) X 3 X = Sold Concentraton 4. Enthalpy of saturated water hl = α T + β, Where α = and β = ,. Enthalpy of saturated steam hv = γ T + δ, Where γ = and δ = 203.3, T = Temperature of water, 0 C T = Temperature of steam, 0 C 6. Latent Heat of Vaporzaton, kj/kg λ = T T = Temperature of steam, 0 C Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 TABLE III STEADY STATE SOLUTION OF SEXTUPLE EFFECT EVAPORATORS FOR BACKWARD FEED ( ) Effects Items I II III IV V VI Output Lquor Concentraton (kg/kg) Output Lquor Flow (kg/sec) Output Lquor Temperature (ºC) Output Steam Temperature (ºC) Output Steam Flow (kg/sec) Bolng Pont Rse (ºC) Specfc Heat (KJ/Kg. 0 C) Heat Transfer Area (m 2 ) Stream Consumpton (Kg/Sec) Total Evaporaton (Kg/Sec) TABLE IV STEADY STATE SOLUTION OF SEXTUPLE EFFECT EVAPORATORS FOR MIXED FEED ( ) Effects Items I II III IV V VI Output Lquor Concentraton (kg/kg) Output Lquor Flow (kg/sec) Output Lquor Temperature (ºC) Output Steam Temperature (ºC) Output Steam Flow (kg/sec) Bolng Pont Rse (ºC) Specfc Heat (KJ/Kg. 0 C) Heat Transfer Area (m 2 ) Stream Consumpton (Kg/Sec) Total Evaporaton (Kg/Sec) Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng TABLE V STEADY STATE SOLUTION OF SEXTUPLE EFFECT EVAPORATORS FOR SPLIT FEED ( 6 Effects ) Items I II III IV V VI Output Lquor Concentraton (kg/kg) Output Lquor Flow (kg/sec) Output Lquor Temperature (ºC) Output Steam Temperature (ºC) Output Steam Flow (kg/sec) Bolng Pont Rse (ºC) Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 Specfc Heat (KJ/Kg. 0 C) Heat Transfer Area (m 2 ) Stream Consumpton (Kg/Sec) Total Evaporaton (Kg/Sec) The results obtaned from the smulaton of models are gven n TABLE III, TABLE IV, and TABLE V for the backward, mxed and splt feed sequences respectvely. The parametrc nfluences of varous nput parameters on output parameters steam consumpton (SC), steam economy (SE) and area requrement (A) for backward, mxed and splt feed sequences were plotted n graphs gven by Fg. to Fg. 10. In ths paper the effect of varous nput parameters on steam economy (SE) only s descrbed for fndng the optmal feedng sequence. A. Effect of feed temperature on steam economy Fg. has been drawn to show that the effect of feed temperature on steam economy (SE) for backward, mxed and splt feed respectvely Mxed feed Splt feed Feed Temperature (0C) Fg. Effect of feed temperature on steam economy Wth the rse of feed temperature the SE s ncreased for all the feedng sequences. From the Fg. t s clear that the mxed feed sequence s optmal for the entre range of temperature whch s consder for the present study. Splt feed s also more economc than smple backward feed. B. Effect of steam temperature on steam economy Fg. 6 has been drawn to show that the effect of steam temperature on steam economy (SE) for backward, mxed and splt feed respectvely. Wth the rse of steam temperature the SE s decreased for all the feedng sequences. From the Fg. 6 t s clear that the mxed s the optmal sequence Mxed feed Splt feed Steam Temperature (0C) Fg. 6 Effect of steam temperature on steam economy C. Effect of feed flow rate on steam economy Fg. 7 has been drawn to show that the effect of steam temperature on steam economy (SE) for all three sequences. Wth varyng the feed flow rate from 18-2 kg/s, the SE s decreased for splt and backward feed whle the SE of the mxed feed ncreased. In ths case t s clear from the Fg. 7 that the mxed feed s more economc (optmal). Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

7 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng Mxed feed Splt feed Mxed feed Splt feed 4.8 Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/ Feed lquor (Kg/s) Fg. 7 Effect of feed flow rate on steam economy D. Effect of feed concentraton on steam economy Fg. 8 has been drawn to show that the effect of varyng feed concentraton on steam economy (SE) for all three sequences. In ths case t s clear from the Fg. 8 that the mxed feed s optmal for the entre range of feed flow rate Mxed feed Splt feed Feed Concentraton (kg/kg) Fg. 8 Effect of feed concentraton on steam economy E. Effect of product concentraton on steam economy Fg. 9 has been drawn to show that the effect of varyng product (.e. output of the frst effect) concentraton on steam economy (SE) for all three sequences. In ths case also t s clear from the Fg. 9 that the Se s ncreased and the mxed feed s optmal for the entre range of feed flow rate. F. Effect of last body temperature on steam economy Fg. 10 has been drawn to show that the effect of varyng last body (.e. output of the frst effect) temperature on steam economy (SE) for all three sequences. In ths case t s clear from the Fg. 10 that the SE s decreased for the mxed and splt feed whle the backward feed shows an ncrement n the SE for and fnally the mxed feed s optmal for the entre range of feed flow rate Product Concentraton (Kg/Kg) Fg. 9 Effect of product concentraton on steam economy Mxed feed Splt feed Last body temperature (0C) Fg. 10 Effect of last body temperature on steam economy V. CONCLUSION Steady state smulaton s done successfully by usng fsolve solver n MATLAB source code for three feedng sequences backward, mxed and splttng. The effect of varaton of varous nput parameters on steam economy s studed. It may be concluded that mxed feed s always optmal for entre range of each parameters. The mathematcal models developed and the soluton technque employed n ths present nvestgaton can precsely evaluate data for any sequence of any MEE set up. The computatonal developed helps to generate large body of data and can handle many varables and the nteractons and nterdependence wth each other. In today s context t s extremely essental to use ths software for the beneft of ndustry, paper mll n partcular. The desgn procedure developed can brng accuracy n assessng the performance of an exstng evaporator system or can help n desgnng a new system for a Greenfeld pulp and paper mll. Internatonal Scholarly and Scentfc Research & Innovaton 4(12)

8 World Academy of Scence, Engneerng and Technology Internatonal Journal of Materals and Metallurgcal Engneerng Dgtal Open Scence Index, Materals and Metallurgcal Engneerng waset.org/publcaton/6691 A Shell area, m 2 BPR Bolng pont rse, ºC C Cp Condensate flow rate TABLE VI NOMENCLATURE Specfc heat of water at constant pressure, KJ/Kg h Enthalpy, KJ/Kg ºC H Enthalpy of saturated steam/vapour, KJ/Kg ºC Q λ t Heat transfer rate, KJ Latent heat of vaporzaton, KJ/Kg Tme, sec T Temperature, ºC U L Overall Heat Transfer Coeffcent (OHTC), KJ/sec.m 2 0 C Mass flow rate, Kg/s X Sold content, % V c l v f Lve steam/vapour flow rate, Kg/s Subscrpts Condensate Lquor Effect number Vapor feed REFERENCES [1] A.K. Ray and Ptam. Sngh, Smulaton of Multple Effect Evaporator for black Lquor Concentraton, IPPTA, vol. 12(3), pp. 3-4, (2000). [2] A.R. Gupta, Mathematcal Modelng g and analyss of pulp washng problems, Ph.D Thess, Indan Insttute of Technology Roorkee. (2001). [3] A.K. Ray, N.K. Sharma and Ptam. Sngh, Estmaton of Energy Gans through Modellng and Smulaton of Multple Effect Evaporator System n a Paper Mll, IPPTA, vol. 16(2), pp. 3-4, (2004). [4] A.K. Ray and N.K. Sharma, Smulaton of Mult-Effect Evaporator for Paper Mll-Effect of Flash and Product Utlzaton for Mxed Feeds Sequences, IPPTA, vol. 16(4), pp. -64, (2004). [] A.O.S. Costa, and E.L. Enrque, Modelng of an ndustral multple effect evaporator system, In Proceedngs of the 3th Congresso e Exposcao Anual de Celulose e Papel [6] B.K. Dutta, Heat transfer Prcples and Applcatons. Prentce Hall of Inda Pvt.Ltd, New Delh. (200). [7] C. D. Holland, Fundamentals and modellng of separaton processes Englewood clffs, NJ: Prentce Hall Inc [8] C.H. Runyon, T.R. Rumsey and K.L. McCarthy, Dynamc smulaton of a non-lnear model of a double effect evaporator, Journal of Food Engneerng, vol. 14, pp , [9] C. Cadet, Y. Toure, G. Glles and J.P. Chabrat, Knowledge modellng and non-lnear predctve control of evaporators n cane sugar producton plants, Journal of Food Engneerng, vol. 40(1/2), pp.9 70, [10] C. Rverol, and V. Napoltano, Non-lnear Control of an evaporator usng an error trajectory technque, Journal of Chemcal Technology and Botechnology, vol. 7, pp , [11] D.Q. Kern, Process heat transfer. McGraw Hll, 190. [12] H. Nshtan and E. Kunugta, The optmal flow pattern of multple effect evaporator systems Computers and Chemcal Engneerng, vol. 3,pp , [13] H.T. El-Dessouky, I. Alatq, S. Bngulac and H. Ettouney, Steady state analyss of the multple effect evaporaton desalnaton process. Chemcal Engneerng Technology, 21, [14] H.T. El-Dessouky, H.M. Ettouney and F. Al-Juwayhel, Multple effect evaporaton-vapor compresson desalnaton processes, Transactons of IChemE, vol. 78(Part A), pp , [1] J. Gullchsen and C.J. Fogelholm, Chemcal Pulpng, Paper Makng Scence and Technology a seres of 19 books, 6B, B18-20, [16] J. Algehed, & T. Berntsson Evaporaton of black lquor and wastewater usng medum-pressure steam:smulaton and economc evaluaton of novel desgns, Appled Thermal Engneerng, 23, , [17] L.R. Radovc, A.Z Tasc, D.K. Grozanc, B.D. Djordjevc and V.J. Valent, Computer desgn and analyss of operaton of a multple effect evaporator system n the sugar ndustry, Industral and Engneerng Chemstry Process Desgn and Development, vol. 18, pp , [18] M.H. Khadem, M.R. Rahmpour, and A. Jahanmr, Smulaton and optmzaton of a sx-effect evaporator n a desalnaton process, Chemcal Engneerng and Processng, vol. 48, pp , (2009). [19] N.J. Rao, and R. Kumar, Energy conservaton approaches n a paper mll wth specal reference to the evaporator plant. In Proceedngs of the IPPTA nternatonal (198). [20] R.N. Lambert, D.D. Joye and F.W. Koko, Desgn calculatons for multple effect evaporators. I. Lnear methods, Industral Engneerng Chemstry Research, vol. 26, pp , [21] R. Bhargava, Smulaton of flat fallng flm evaporator network, PhD dssertaton, Department of Chemcal Engneerng, Indan Insttute of Technology Roorkee, Inda, [22] R.Bhargava, S.Khanam., B.Mohanty and A. K. Ray, Selecton of optmal feed flow sequence for a multple effect evaporator system, Computers and Chemcal Engneerng, vol. 32, pp , 2008a. [23] R.Bhargava, S.Khanam., B.Mohanty and A. K. Ray, Smulaton of flat fallnf flm evaporator system for concentraton black lquor, Computers and Chemcal Engneerng, vol. 32, pp , 2008b. [24] S. Itahara and L.I. Stel, Optmal desgn of multple effect evaporators by dynamc programmng, Industral and Engneerng Chemstry Process Desgn and Development, vol., pp. 309, [2] S. Khanam and B.Mohanty, Energy reducton schemes for multple effect evaporator systems, Appled Energy, vol. 87, pp , (2010). [26] V.K. Agarwal, M.S. Alam. and S.C. Gupta. Mathematcal model for exstng multple effect evaporator systems, Chemcal Engneerng World, vol.39, pp [27] V. Mranda and R. Smpson, Modellng and smulaton of an ndustral multple effect evaporator: Tomato concentrate, Journal of Food Engneerng, vol. 66, pp , 200. Deepak Kumar receved the Bachelor s and Mater s degree from M. J. P. Rohlkhand Unversty, Barelly, Inda n Mathematcs n 2000 and 2002 respectvely. He s pursung Ph.D degree n Industral Mathematcs from the Indan Insttute of Technology Roorkee. He s workng on Mathematcal Modellng and Smulaton n Pulp mll Operatons. He has publshed 6 research papers n whch 4 are n nternatonal Journals of peer revew. Vvek kumar receved the Bachelor of Engneerng (Pulp and Paper Engneerng) from Unversty of Roorkee, Inda n 1992, Master n Engneerng n Chemcal Engneerng from Unversty of Roorkee (now, Indan Insttute of Technology Roorkee), n 1994 and Ph.D degrees n Envronmental Management from Indan Insttute of Technology Delh Inda, n Dr. Vvek Kumar s currently wth Indan Insttute of Technology Roorkee, Inda, where he s an Assstant Professor n the Department of Paper Technology. Hs specal felds of nterests nclude mathematcal modelng and smulaton and Envronmental & Energy Management. V.P. Sngh receved the Bachelor s degree from Meerut Unversty, Inda n 1970, Master s and Ph.D degrees n Appled Mathematcs from the Unversty of Roorkee (now, Indan Insttute of Technology Roorkee), Inda, n 1972 and 1978, respectvely. Dr. V.P. Sngh s currently wth Indan Insttute of Technology Roorkee, Inda, where he s a Professor n the Department of Paper Technology. Hs specal felds of nterests nclude appled and ndustral mathematcs, mathematcal modelng of pulp washng problems. Internatonal Scholarly and Scentfc Research & Innovaton 4(12)