Entropy Minimization in Design of Extractive Distillation System with Internal Heat Exchangers

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1 Entropy Minimization in Deign of Extractive Ditillation Sytem with Internal Heat Exchanger Diego F. Mendoza, Carlo.M. Riaco * Group of Proce Sytem Engineering, Department of Chemical and Environmental Engineering, Univeridad Nacional de Colombia. venida Cra. 3 No Ed. 453 Of. 3, ogotá, Colombia. camartinezri@unal.edu.co methodology for entropy production minimization in deign of extractive diabatic ditillation ytem i propoed. The feaibility of the deign i obtained by the boundary value method ued by Doherty and coworker, and the optimal deign i attained uing a genetic algorithm, thi trategy allow determine the optimal heat load ditribution, and the flow and temperature for hot and cold utilitie. For optimal deign of diabatic ditillation column it wa employed a multilevel trategy, the firt level olve the optimal adiabatic deign and the econd one determine the optimal heat load ditribution in the equential heat exchanger (), in both level the feaibility of the deign i forced by a penalty in the objective function, it conider the eparation feaibility and the energy balance conitency. The ethanol dehydration by extractive ditillation with ethylene glycol i aeed in order to how our optimal deign procedure and to compare the diabatic ditillation proce with the adiabatic one. Reult how that thi trategy allow to olve the problem, and that with, the entropy production can be reduced expreively: 4% for the recovery olvent column and 6% for the extractive one, compared to the adiabatic column.. Introduction Traditionally the external heat exchange in ditillation column i done at the top (condener) and bottom (reboiler) of the column. Neverthele, a more energy-efficient proce can be achieved when the external heat tranfer i alo allowed in the tray. better energy uage implie reduction in operational cot and carbon dioxide emiion (Suphanit, 2). The maximum econd law efficiency in diabatic column i attained with minimal temperature difference between tray and heat tranfer fluid. ut that condition can hardly be attained in a real proce plant. way to take advantage of diabatic ditillation characteritic i by uing equential heat exchanger in the tray, in thi configuration heat tranfer utility flow equentially from one tage to the next; therefore it i only neceary one fluid for heating and one for cooling. Experimental evidence how a ignificant improving on the energy efficiency when are ued (De Koeijer and Rivero, 23); the advantage of thi configuration can be exploited when a uitable heat load ditribution i found. The aim of thi work i to provide a mathematical trategy for optimal deign of both ingle and double feed column fulfilling the deign contraint, uch a product compoition and recovery of key component. The reult may be ueful for evaluating, in an early tep of deign, the advantage of uing diabatic or adiabatic ditillation.

2 2. Mathematical Model Mathematical model employed in thi work i a modification of the boundary value method (Doherty and Malone, 2), it take into account the heat tranfer in internal tage of the ditillation column. The model comprie ma and energy balance, and the vapor-liquid equilibrium. feaible deign i obtained when the operating profile from the top and the bottom interect and the overall energy balance in the column i fulfilled. detailed derivation of the equation a well a it olving methodology can be found in a previou work (Mendoza and Riaco, 2). 3. Optimization 3. Objective Function The objective function, OF, i formed by two term (Eq. ). The firt one i the entropy production in the ditillation column; the econd one i a penalty term which force the fulfillment of the contraint impoed on the deign: d 4 OF irr dt DC r r () where i a weighting factor ( = ), and r are binary variable which take the value of zero if the contraint i fulfilled and one if not. The variable conider the interection of operation profile; 2 the overall energy balance; 3 and 4 the minimum temperature approach allowed in condener and reboiler. The entropy generated in the column, (d irr /dt) DC (Mendoza and Riaco, 2) i: d dt irr DC D D F Q c DT c J q l l l F Q T M q b b b d dt irr HEDC (2) where Q c, Q, T c, T are the heat load (poitive when tranferred from the heat utility to the tage) and temperature in the condener and reboiler repectively. The ummation term repreent the heat load in internal tage of the column, l = to J are the tage of the rectifying ection and the b = to M are the tage of the tripping and extractive zone; l and b are tage dimenionle temperature ( l = T l /T c, b = T b /T ) and q l, q b are tage dimenionle heat load (q l = Q l /Q c, q b = Q b /Q ); D,, F are the molar entropie of ditillate, bottom product and feed tream. The entropy of the feed i F = (F r Fu + Fl )/(+F r ) where Fu and Fl are molar entropie of the upper and lower feed and F r i the feed ratio: F r = F u /F l. The lat term of the right hand ide in Eq. (2) i the entropy production due to heat exchange between utilitie and tage, calculated a the product of the heat flow and it thermal force (Kjeltrup et al., 2). J dirr Q Q dt T T T T l b HEDC l l f, l b b f, b M (3) where T f,l, T f,b are average temperature of the cooling and heating utilitie in the tage. The ign of the heat load enure that each term in the Eq. (3) i poitive.

3 3.2 Optimization Strategy The trategy for optimal deign conider two level: the firt level olve the optimal adiabatic deign and the econd one determine the optimal heat load ditribution with equential heat exchanger (). The tage for the optimal deign of adiabatic column conider:. Etimate the minimum reflux ratio of the ditillation column, which generate the leat entropy production for the eparation tak in the adiabatic column. 2. Define the operational reflux ratio, which et up the number of tage of the ditillation column, the operational reflux i found baed on economic criteria. 3. Entropy production of the adiabatic column i calculated after the number of tage and the inlet temperature of the heat utilitie are defined. The optimal heat load ditribution uing i achieved allowing heat tranfer in the internal tage of the ditillation column, and minimizing the entropy production in the column. The maximum heat tranfer area i defined knowing the available pace given by the column diameter and the tray layout. 4. Cae Studie The methodology wa applied on the column that compoe an extractive ditillation ytem for ethanol dehydration with ethylene glycol. The firt column i an extractive (double feed) column fed with.278 mol - of water/ethanol (W/E) mixture, 85% mol E and 5% mol W, it i dehydrated to obtain high-purity ethanol in the ditillate (99.8% mol). The upper feed i a water/ethylene glycol (W/EG) mixture,.% mol W and 99.9 % mol EG. Fractional recovery of ethanol in the column i 99.99%. The E/W mixture enter at bubble point wherea the upper feed temperature i 35 K. The econd column (ingle feed) i fed with the bottom product from the firt one, at bubble point, and dehydrate the mixture obtaining EG at 99.9% mol in the bottom tream. Fractional recovery of EG i %. oth column operate at a total preure of atm, and no preure drop i aumed; the minima temperature approach in all heat exchanger i K. Reflux ratio of ingle and double feed adiabatic column were RR =.32 and RR2 =.65; thee value correpond to.3 and.5 time the minimum reflux of the eparation tak carried out in the ingle and double feed column repectively, and they are within the value recommended (Seader and Henley, 998). The feed ratio in the double feed column wa et to Fr =.5, baed on the economic optimization done by Knight and Doherty (989). 4. Optimization Variable The optimization variable of diabatic column were the flow of heating and cooling utilitie (m H and m C ), the reflux and the reboil ratio and the total heat tranfer capacity in tage ( U tage.2 kw K - ). The total heat tranfer capacity wa etimated from experimental data (Kaeer and Pritchard, 25). 4.2 Thermodynamic Propertie and Computational Method In liquid phae the activity coefficient a well a the enthalpie and entropie of mixing were calculated uing the NRTL model (Seader and Henley, 998), wherea vapor phae are decribed by the ideal ga law. Liquid and vapor heat capacitie and heat of vaporization were taken from Poling et al. (28). The heat capacity of heating utility, Dowtherm T, can be found in the Dow' web page (Dow, 24). The model wa programmed in Matlab uing a genetic algorithm to optimize the model.

4 Q / W T / K Table : Flow and temperature of heat utilitie, and total energy tranferred. Double feed adiabatic Double feed Single feed adiabatic Single feed m c (mol - ) in T C (K) out T C (K) m H (mol - ) in T H (K) out T H (K) Q added (kw) Q removed (kw) Reult and Dicuion The principal reult of optimal deign for adiabatic and no-adiabatic column are in Table. From energetic efficiency comparion: the entropy generated in the ingle feed and adiabatic column were.3 and.52 W K - repectively, and the entropy production in the double feed column were 2.55 W K - in the adiabatic one and.5 W K - in the one. The reduction achieved in the ingle and double column were 3.8% and 6.2% compared with the adiabatic column. Entropy production profile (Fig. and 2) how the reduction are given mainly by the heat load ditribution in the tripping zone of the ditillation column. Vapor and liquid profile in the tripping zone of the column differ from the adiabatic one becaue in adiabatic one the external upply of heat i located only in Flow / mol L L V V d irr /dt / W K C D Figure : Single feed ditillation column.. Flow.. Temperature. C. Entropy production. D Heat load profile. L and V are vapor and liquid flow for the diabatic column (); L and V are liquid and vapor flow for adiabatic one ().

5 Q / W T / K the reboiler, wherea in column, a part of the external heat upply i ditributed in internal tage obtaining moother change in compoition and temperature. The heat load input i approximately the ame in both type of ditillation column, with a maximum difference of 2.6% in the ingle feed column (ee Table ). Neverthele, the column diminih the energy degradation in the proce; thi fact i reflected by the reduction of the flow of the heating (62.% ingle feed, and 87.5% double feed) and cooling utilitie (8.9% ingle feed, and 5.4% double feed) with repect to the flow required by the adiabatic column (Table ), the flow reduction mean that the column leen the demand of high quality energy reource (i.e. the heating flow at the temperature of 432 K and 49 K). nother apect related with entropy production aving in column i the outlet temperature of heat tranfer utilitie: the equential heat exchanger allow the heat removal, in the rectifying ection, at higher temperature and the heat addition, in the tripping ection, at lower temperature. The gaining in the outlet temperature of the cooling utility in the i relevant if it can be ued in a further heat tranfer before it come back to the cooling tower, imilarly the lower outlet temperature of the heating utility i advantageou if a part of the heat needed to upgrading it temperature can be obtained from a low temperature heat ource. Flow / mol V V L L d irr /dt / W K C x 4 D Figure 2: Double feed ditillation column.. Flow.. Temperature. C. Entropy production. D Heat load profile. L and V are vapor and liquid flow for diabatic () column; L and V are liquid and vapor flow for adiabatic () one. If the inlet temperature of the heating utility would have been an optimization variable the aving in entropy would be reflected in a lower inlet temperature of the heating utility than the required in the adiabatic cae (ee Kjeltrup et al., 2). Nonethele, the lower limit of the heating utility mut be greater than the temperature in the reboiler. Uing the inlet temperature of the heating utility a an optimization variable depend on the availability of a heat ource uitable for upgrading the temperature of the heating

6 utility; ele it i more adviable to ue the inlet temperature a optimization variable. In the preent work the reduction in the entropy production due to diabatization wa lower than the experimental value of 39% reported by De Koeijer and Rivero (23). They worked with a rectifying column eparating water and ethanol, the difference can be explained becaue of the ytem conidered and their thermodynamic behavior and the contraint impoed over the ditillation column. In that work, adiabatic and ditillation column with the ame number of tage were analyzed, but the eparation tak carried out by the column wa lightly different, in the preent work the entropy production wa minimized taking into account column not only with the ame number of tage, but alo, with the ame eparation tak; which contraint the optimal deign. 6. Concluion and Outlook methodology for optimal deign of ingle and double feed ditillation column with equential heat exchanger wa preented, and it wa proven that thi kind of column can be conidered a a good alternative to the claical (adiabatic) ditillation column becaue the entropy production aving obtained by ditillation column leen the amount of fuel required in the proce and the carbon dioxide emiion. The column can contribute ignificantly to an energy-efficient chemical indutry ince ditillation i the major eparation operation in the chemical indutry. There i a need for more experimental information about the heat and ma tranfer characteritic of the ditillation column in order to generate more accurate deign. Reference De Koeijer G. and Rivero R., 23, Entropy Production and Exergy Lo in Experimental Ditillation Column, Chemical Engineering Science, 58, Doherty M.F. and Malone, M.F., 2, Conceptual Deign of Ditillation Sytem, McGraw-Hill, Singapore. Dow, 24, Dowtherm T <dow.com>, acceed Kaeer M. and Pritchard C., 25, Heat Tranfer at the Surface of Sieve Tray, Chemical Engineering Reearch and Deign, 83, Kjeltrup S., edeaux D., Johanneen E. and Gro J., 2, Non-Equilibrium Thermodynamic for Engineer, World Scientific, Singapore. Knight J. and Doherty M, 989, Optimal Deign and Synthei of Homogeneou zeotropic Ditillation Sequence, Indutrial & Engineering Chemitry Reearch 28, Mendoza D. and Riaco C., 2, Deign and Optimization of Single and Double feed Diabatic Ditillation Column with Sequential Heat Exchanger. Proceeding of EngOpt2 <lemac.dem.it.utl.pt/engopt2/ook_and_cd/paper_cd_final_ Verion/html/paper.html>, acceed Poling.E., Thomon G.H., Friend D.G., Rowley R.L. and Wilding W.V., 28, Perry Chemical Engineer Handbook, 8th ed., McGraw-Hill, New York, United State of merica. Seader J. and Henley E., 998, Separation Proce Principle, John Wiley, New York, United State of merica. Suphanit,., 2, Deign of Internally Heat-Integrated Ditillation Column (HIDiC): Uniform Heat Tranfer rea Veru Uniform Heat Ditribution, Energy, 35,

International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December ISSN

International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December-2013 180 A Novel approach on entropy production rate Behnaz Jalili 1*, Cyru Aghanaafi 2*, Mohammad Khademi 3* Abtract