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

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1 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December A Novel approach on entropy production rate Behnaz Jalili 1*, Cyru Aghanaafi 2*, Mohammad Khademi 3* Abtract We know diabatic ditillation with heat exchanger in all tray increae the econd law energy efficiency compared to an adiabatic ditillation. In thi paper, our main purpoe will be decribing the entropy production rate in an adiabatic experiment with Water or Ethanol in column uing thermodynamic approach and analyi. We will find out that the entropy production rate in the diabatic column i le than the entropy production in the adiabatic column. Further on, we will analyze the reflux ratio howing that thi ratio can be replaced with heat exchanger without infecting the diabatic ditillation operation pecially in the diabatic column. Index Term Diabatic, Adiabatic, Entropy, Thermodynamic analyi, Reflux ratio. 1 INTRODUCTION We undertand that ditillation i the mot important and functional proce ued in chemical indutrie, alo indutrie focuing on fluid uch a alcohol, oil, ga, petroleum etc. Typically have more than one ditillation column. With thee ditillation column, the mot important problem concerning u i the energy conumption. Therefore adiabatic column ditillation are more applicable becaue they have a re-boiler at bottom, a condener at the top tray and adiabatic tray. By adding heat exchanger to each tray, we can un-conider the adiabatic aumption, meaning a portion of the heat will be decreaed or in other word, lot. Thee ditillation column having heat exchanger a explained are known a adiabatic column. Up to now, almot all publication on thee type of ditillation have been ued on theoretical imulation auming equilibrium condition on all tray. There are two exception thou; Rivero and Rivero & Cachot & Le, whom publihed actual experimental data on diabatic ditillation of ethanol and water Behnaz Jalili,MSc.Department of chemitry,sharif univerity,tehran,iran , duman.behnaz@yahoo.com 2 Cyru Aghanaafi,Profeor Aociate.Department of mechanical Engineering,K.N.T.U.Univerity,Tehran,Iran. Aghanaafi@kntu.ac.ir 3 Mohammad Khademi,MSc.Department of Mechanical Engineering,K.N.T.U.Univerity,Tehran,Iran , M.Khademi.mech@gmail.com Alo, the ue of irreverible thermodynamic i relatively new to the tudy field of ditillation and i till under development through reearch.the importance of thi parameter i it effect on the correlation within the entropy production rate. Therefore it i well uited for procee in which econd law analyi and optimization are important. A diabatic ditillation fall in thi category, therefore irreveribility can be conidered in the tranfer of heat and ma at equilibrium tate in column. Many tudie and reearch ha been done on ditillation column, one of them being De Koeier reearch done at2003.in which they compared the entropy production in adiabatic and diabatic tate through experiment held on water and ethanol Ditillation column, holding the ame condition for both experiment. They managed to calculate the entropy production rate(with driving force?) Another approach wa done by Diego & et al which ued non equilibrium equation and tudied the econd thermodynamic efficiency in adiabatic column. Alo many reearche have been held focuing on energy optimization following ditillation column. For example Fredric tudied on the binary ditillation column, in which he teted a method to decreae the entropy production. Demirel et al. how ditillation uing heat and thermal difference i an important and applicable method. Alo he how that the work lot in eparation ytem which are baed on irreverible proce, ma and heat tranfer directly generate entropy. The main purpoe of our work i the thermodynamic analyi of adiabatic and diabatic column which Rivero and Koeier operated 2013

2 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December experimentally. Therefore in thi paper, data from adiabatic and diabatic column a publihed by Rivero and Rivero et al. will be ued. (The managed to calculate entropy uing driving force and experimentally). We alo will analyze the reflux ratio and find it effect on the diabatic column, which wan t tudied by Rivero or Koeier. 2 Experimental et up The experimental column wa a pilot-cale rectifying column and i a decribed in detail by Rivero (2003) which include a complete flowheet and detail ketche. Rivero et al (1993) contain a brief ummery on the topic. Thu only apect relevant to our tudy purpoe are mentioned in detail here. A cheme of ingle tray Fig.2 Schematic of a experimental et-up can be found in Fig.1, and the deign parameter Bearing in mind that heat exchanger vaporizing are given in Fig.2.In Fig.1 we ee that the coil are the feed i called the vaporizer; it i not a reboiler ince the ditillation column contained only hanging 2 cm above the plate. In the experiment help, forty different temperature, 14 compoition, 8 a ingle rectifying ection. preure, 13 flow and 10 valve poition were meaured and conidered. Of all thee finding, the Alo we choe two run (firt and 9 th run) of the meaured data mentioned in the table 1 i ued in total 68 held By Rivero (2003) to focu on. The firt thi paper. However the effect of heat exchanger being adiabatic and the econd adiabatic. The and vapor mole fraction could not be meaured reaon behind chooing thi lie on the imilarity directly, therefore they were calculated the molar of molar fraction and flow from the feed and it and energy balance. product which allow u to make comparion. Thu the other run were not a uitable for direct comparion. 3 Binary ditillation The imple ditillation column ha a ingle input feed, two product, a re- boiler and a condener. For the analyi of ma balance, column ditillation mut be divided in two ection: the rectifier and the tripper. The total ma balance around the ytem i hown in the Fig.3: Fig.1 Scheme of a tray 2013

3 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December Fig.4 Operation line plot in the rectifier Fig.3 Total ma balance around the ytem Total ma balance i: V n+1 = L n +D (1) Ma balance for each partial molar in the tripper i : L m x m,i = V m+1 y m+1,i + B x B,i (6) With the aumption of L m = L and V m+1 = V can be written : Ma balance for each partial molar in the rectifier i: L = V+ B (7) Y m+1 = L v xn,i - B xb,i (8) V n+1 y n+1,i =L n x n, I V + D x D,i (2) Equation (8) i plotted ame a the following V&L are conecutively vapor and liquid. Figure. The lop line i L V With the aumption of L n = L and V n+1 it can be written: V=L+D (3) Reflux ratio i written by (4): R = L D (4) The equation (3) and (4) ubtitute in (2) can be written a : Y n+1,i = R 1+R xn,i + 1 xd,i (5) 1+R Equation (5) can be plotted ame a the following R Figure. The lope of the line i 1+R Fig.5 Operation line plot in the tripper Reflux ration concept: An important factor in each ditillation column i the reflux ratio, o important that the ditillation column cannot be analyzed without it. Thu the preence of thi parameter i highlighted a extremely important. We know that the feed i uually inected to the ditillation column from beneath. The ditillation being done, lighter part are lifted to the top of the 2013

4 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December column. The reflux ratio i the ection in the column which i tranferred and cooled in the condener and retuned back to the column. The reflux phenomena help where there are ubtance within the vapor which aren t ditillated. Thi work a the fluid i being lifted to the top of the column, the unwanted ubtance inide the are returned to the lower tray of the ditillation column. It good to mention that in a diabatic ditillation column R i zero. entropy generation and the econd meaning energy lot, making it MESHEE. Fig.6 how the total equilibrium of a ditillation tower. Thi can be ued for deign purpoe of ditillation column. In which a vapor tream flow from the bottom tray and a liquid phae fluid flow from the top tray into each part. Thee operation are held in each tray. Feed can be alo been entered and the heat withdrawn in needed. There are 4 different approach method for olving thi cae of problem: 1) The adiabatic column i analyzed uing the temperature, preure, feed and the condener information at hand. With the condition mentioned, R will be equal to 0.5 which ha a great contrat with the adiabatic aumption in ditillation column. 2) If the reflux ratio i mall enough to be neglected o that there will be on reflux flow within the column. Thi i the aumption held in the diabatic ditillation column. In the cae, R i taken to be ) In order to decreae the heat from the condener and to decreae the ditillation rate, Fig.6 Total equilibrium part of the ditillation tower more heat i taken from the firt tray. 4) The ide team method can be a uitable L 1x 1+ V+ 1 yi, FZ i, ( L+ V) xi, ( V+ W) y (9) i, approach, however it i lightly difficult. Becaue in order for it to be done correctly, we yi, Ki, xi, = 0 (10) have to enure the equilibrium tate i held in all tray. The analyi of the diabatic column and calculation of the entropy production and xi, 1= 0& yi, 1= 0 (11) energy lot ha been done uing the econd L V F L V method. L 1H 1+ V+ 1H + 1+ FH ( L + V) H ( V + W) H Q = 0 (12) 4 The thermodynamic analyi Q V L L V F S gen, = ( V + W) S + ( L + U) S L 1 V + 1 FS + All equation ued for teady tate operation of the T0 (13) ditillation column are MESH equation. 5 Dicuion and reult MESH abbreviate for the following word: 5-1 Experimental reult M: Ma equilibrium equation E: Equilibrium equation that include dew point and bubble point S: Summation of toichiometric equation H: Heat tranfer equation In thi paper, we added two other word to the above lit. We added two E, firt meaning In the table 1 hown below, experimental reult from Rivero paper (2003) are hown. It can be een from thee reult that the operation of adiabatic and diabatic column i ditillation doen t differ much. However there i a ditinction between them, the abence of reflux ratio and le entropy production inide the diabatic column in comparion to the preence of the reflux ration and higher entropy production in adiabatic column. Another focu point for our tudy wa the 2013

5 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December temperature of each tray hown in Fig3. Table 2 and 3 how ome parameter in the adiabatic and diabatic column, the condener being the firt tray in them. Table 1.Meaurement reult of the adiabatic and diabatic column Diabatic Adiabatic 296 6) Feed Ditillation (mol/) Bottom(mol/) Feed mole fraction ethanol Ditillate mole fraction ethanol B mole fraction ethanol bottom 999 Top preure (10^ Pa) Bottom preure (10^5 Pa ) Water flow into the condener and heat exchanger (mol/) Oil flow into the vaporizer (Kg/) Meaurement error in temperature (K) Meaurement error in mole Table 2. Calculate reult of the adiabatic column Tray Tempera Pre Heat Liquid Vapor 99 num ber ture (K) ure (K.Pa ) duty (Watt ) flow (mol/ ec) flow (mol/ ec) Tray num ber Table 3 Calculate reult of the diabatic column Tempera ture (K) Pre ure (K.Pa ) Heat duty (Watt ) Liquid flow (mol/ ec) 4.27* 10^(- Vapor flow (mol/ ec) Heat load analyi in the diabatic column We know there i a heat exchanger in each tray of the adiabatic column. Analytical reult are hown in table 3. For more accurate analyi of adiabatic column, a re-boiler mut be conidered. A hown, in Fig. 3.The fluid flow enter the re-boiler, later exiting to the tray. Thi can have an effect on the operation of the column. It i clear that no ingle tray can have two different temperature at the ame time, becaue of thi aumption to implify the condition and reduce the error the heat load of the final two tray are added together and conidered a the lat tray temperature. It i mot uited in our analyi that the condener i located in the firt tray. 2013

6 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December Entropy production analyi The mot important analyi in the diabatic and adiabatic column i the entropy production analyi. In the Rivero and Koeier paper, the focu only on the ma and heat tranfer. Therefore the preure and mixing effect were never conidered. Fig.1 give a cheme of tray N with the variable including numbering. The enlargement of the bubble i hown and alo the three flow through the interface cauing the entropy production are diplayed. Jw and Je are the number of mole of water and ethanol repectively tranferred per econd, from the liquid into the vapor. Ma tranfer rate through the interface. Jp i the correponding meaure (or fourier tray) of heat flow through the interface, or alternatively the heat tranfer rate. The entropy production caued by the heat and ma tranfer to the Nth tray through the interface are decribed by three flow-force production: ds dt n qn, qn, wn, wn, en, en, (15) T 2 Tn+ 1 Tn 1 = J X + J X + J X (14) In thi equation the J are the flow (or integrated flux or tranfer rate) and the X are the average driving force between inlet and outlet of tray. X qn, = = For an equilibrium column eparating and ideal mixture, Eq.14 can be implified to a ingle forceflow product. The decription for the entropy production rate i: ds y y y n = = dt y y y ν,, + 1, ( J wn, ynjen, ) X n J wn, R. Ln wn wn wn en, en, + 1 wn, + 1 (16) Thi equation contain only a ingle force-flow product, which i in agreement with the ingle thermodynamic degree of freedom in a column with equilibrium tate condition on all tray. Fig.7 and Fig.8 how the entropy production rate in the two column uing the thermodynamic analyi and equation (13).Fig.(9) and Fig.10 how the entropy production rate that Rivero & Koeier meaured uing equation (14) and it expanion. Comparing Fig 8&9 and Fig10&11 we can find indication of entropy production rate uing thermodynamic analyi which have acceptable reult. Fig.7 Tray number from condener : reult Eq. 14 and 16 (diabatic column) (a) Fig.8 Tray number from condener : reult Eq. 14 and 16 (diabatic column) (b) Fig.9 Tray number from condener : reult of Eq. 14 and 16 (adiabatic column) Fig.10 Tray number from condener : reult Eq. 14 and 16 (diabatic column) 2013

7 International Journal of Scientific & Engineering Reearch, Volume 4, Iue 12, December The role of heat exchanger in the diabatic column i extremely important. The main improvement by adding heat exchanger diabatiation, wa on the temperature of the cooling water. In the adiabatic column, water exited at a temperature of 340K which i conider uele (in the hape, the water outlet are hown by down facing arrow, howing their direction). However in the diabatic column, water exited at 370K. Thi mean an elevated 30K temperature difference, which give it a potential uefulne. The cooling water output are ued for heating other part in the plant, reulting in reduced energy loe and therefore aving energy. 6 Concluion Our firt concluion in thi tudy i that the entropy production rate calculated by thermodynamic analyi in the diabatic column i le than the entropy production rate in the adiabatic column. Thi i caued by the heat exchanger of the diabatic column, becaue the heat exchanger can withdraw more heat from the column cooling it down. Alo thi heat taken, could be ued omewhere ele to heat another part, aving dramatically in energy. The econd concluion taken from thi tudy i that the reflux phenomena can be replaced by heat exchanger in the diabatic column without great effect on the operation of the column. In fact, heat exchanger can execute the exact benefit of the reflux phenomena, with a greater entropy production rate. Notation B d dt D F bottom, m/ entropy production rate, J K ditillation rate, J K feed, mol H enthalpy, J mol J K L flow through interface, mol or J contant, dimenionle liquid flow, mol Q R R S T V X x y duty, J reflux ratio, mol (ut in equ22,r i ga contant, J ) mol. K entropy, J mol. K temperature,k vapor flow, mol force, J mol. K liquid mole function, dimenionle vapor mole function, dimenionle y dimenionle Z mole partial of the feed, mol Super-and ub-cript e ethanol F i L n m V w feed average Gibb-Duhem vapor mole function, component i liquid tray number n tray number m tray number vapor water Reference [1] A. Ahrafizadeh,R. Mehdipour,C. Aghanaafi A hybrid optimization algorithm for the thermal deign of radiant paint cure oven. Applied Thermal Engineering 40 (2012)

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