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Optimization of the Reflux Ratio of Benzene Toluene Stage Distillation Columns by the Cuckoo Algorithm

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Optimization of the Reflux Ratio of Benzene Toluene Stage Distillation Columns by the Cuckoo Algorithm 446 Pet.Sci.(2014)11:446-453 DOI 10.1007/s12182-014-0360-3 2SWLPL]DWLRQRIWKHUHÀX[UDWLRRIEHQ]HQHWROXHQH stage distillation columns by the Cuckoo algorithm Bahador Abolpour and Ali Mohebbi Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran © China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg 2014 Abstract: In this study, an enthalpy-concentration method was applied in order to model a steady state continuous benzene-toluene mixture distillation column. For a distillation tower such as the benzene- toluene splitter, there are relatively few degrees of freedom that can be manipulated in order to minimize the total annualized cost. The reflux ratio can influence the steady-state operating point and therefore LQÀXHQFHWKHWRWDODQQXDOL]HGFRVW7KHWUDGHRIIVEHWZHHQUHÀX[UDWLRVDQGWRWDODQQXDOL]HGFRVWZHUH discussed. The Cuckoo optimization algorithm was applied to obtain a correlation for the optimum value RIWKHUHÀX[UDWLRDVDSRZHUIXQFWLRQRIWKHHFRQRPLFSDUDPHWHUVRIHQHUJ\SULFHDQGFDSLWDOFRVW7KH UHVXOWVVKRZWKDWDWORZHQHUJ\SULFHRUKLJKFDSLWDOFRVWWKHRSWLPXPUHÀX[IDFWRULVKLJK Key words: Benzene-toluene mixture, distillation column, Cuckoo optimization algorithm, optimized UHÀX[UDWLRWRWDODQQXDOL]HGFRVW 1 Introduction As an important part of most chemical plants, distillation RISUHVVXUHDQGUHÀX[UDWLRZDVIRXQGWRPLQLPL]HWKHHQHUJ\ remains as the most important separation technique in consumption in the reboiler and to obtain the required product chemical process industries (Luyben, 1990) and is a complex purity. process for modeling and controlling (Balchen and Mumme, Fazlali et al (2009) optimized operating conditions 1988; Luyben, 1992; Shinskey, 1984). About 95 percent of petroleum refinery distillation columns by means of a of the separation processes in the chemical industries use simulator with the aim to reduce energy consumption. In the distillation columns (Enagandula and Riggs, 2006), and close next step the optimization results from the simulator were control is necessary to achieve the desired product purity at applied in the real unit. Chen and Lin (2001) studied the minimum cost. Achieving control of an integrated distillation RSWLPL]DWLRQRIGLVWLOODWLRQFROXPQUHÀX[UDWLRVLQSHWUROHXP column is difficult due to the nonlinearities of the process, refining. In their work, they explored the optimum reflux multivariable interaction, non-stationary behavior and severe UDWLRVRIWZRGLVWLOODWLRQFROXPQVXVHGLQSHWUROHXPUH¿QLQJ disturbances inside the column (Hurowitz et al, 2003). one was a propylene splitter, and another was a debutanizer Moreover, continuous distillation may show more dynamic XVHGLQDÀXLGFDWDO\WLFFUDFNLQJSODQW behaviors during the process. The basis of distillation is Economic calculations are important in industrial designs. vapor-liquid equilibrium. Distillation is applicable in the In our previous study, a simple method was developed for separation of chemical components, where concentrations in optimizing a methanol-water distillation column (Abolpour et both phases differ from each other. al, 2013). In that study, the operating cost of each operating Diwekar et al (1989) studied the optimization of multi- FRQGLWLRQVZDVFDOFXODWHGLQDUDQJHRIUHÀX[UDWLRIURPWR component distillation columns, and presented formulation LQVWHSVRI7KHQWKHYDOXHRIWKHUHÀX[UDWLRZKLFK for single-fraction and multi-fraction batch distillation will result in the minimum operating cost was selected as FROXPQVXQGHUFRQVWDQWDQGYDULDEOHUHÀX[UDWLRV5HQHWDO WKHRSWLPXPUHÀX[UDWLRIRUWKDWRSHUDWLQJFRQGLWLRQ,QWKLV (2010) established a model for a stage distillation column. study, the Cuckoo optimization algorithm was used to model ,QRUGHUWRRSWLPL]HWKHUHÀX[UDWLRE\VROYLQJWKHQRQOLQHDU a steady state continuous benzene-toluene mixture distillation objective function, an improved particle swarm algorithm FROXPQ$FRUUHODWLRQIRUWKHRSWLPXPYDOXHRIUHÀX[UDWLR was developed for improving the searching ability of the was obtained. basic particle swarm algorithm. Optimization of propylene- propane distillation was carried out by Mauhar et al (2004) 2 Modeling using Aspen Plus simulation engine. A suitable combination 2.1 Principles *Corresponding author. email: [email protected] Received March 26, 2013 The degradation of heat can drive the chemical separation Pet.Sci.(2014)11:446-453 447 in the distillation process (Henley and Seader, 1981; King, products. 1971; Robinson and Gilliland, 1950). To perform a separation Fig. 1 shows the purification of the feed flow. The by distillation a minimum quantity of internally circulating distillate (D) and bottoms (W) are enriched with the more fluid is needed. The vapor-liquid countercurrent flows can volatile and less volatile components respectively. Fig. 1 EHHVWDEOLVKHGE\DFRQWLQXRXVUHÀX[LQGLVWLOODWLRQ$OLTXLG shows six valves available to control the column, with which ÀRZ L LVPDLQWDLQHGDWLWVERLOLQJSRLQWDQGYDSRUÀRZ G) the valves 2 and 3 control the reflux ratio (Abolpour et al, is circulated between stages to purify a feed flow (F) into 2013). Top 1 product G1 y1 H G1 QC L0 x0 H L0 2 Tray 1 3 n L D n G z x n+ 1 D n y H H n+ 1 D Ln H 4 Gn+ 1 F m Feed zF Lm Gm+ 1 HF xm y H m+ 1 Lm H Gm+ 1 Reboiler N 5 QB 6 W xW Bottom HW product Fig. 1 Schematic of a distillation column (Abolpour et al, 2013) (4) 2.2 Governing equations GDR1 1 7KHOLTXLGDQGYDSRUÀRZVGRQRWFKDQJHLQDVHFWLRQRI distillation column without heat exchangers or side-stream Gy11 DzD Lx00 (5) LQSXWVRURXWSXWV$VVXPLQJFRQVWDQWÀRZVDQGFRQVLGHULQJ QDRH ªº1 RHH (6) mass balance obtains linear relations (i.e. operating lines, CG¬¼ 10LD Eqs. (8) and (11)) for the component concentrations in the flow streams passing between adjacent stages. Equilibrium Mole and enthalpy balances for the section of the column conditions limit the concentrations of flow streams leaving above the feed point (i.e. enriching section) would be as DVWDJH7KHUHIRUHWKHFRQFHQWUDWLRQGLIIHUHQFHVLQWKHÀRZ follows: streams at a point of column are bounded by the operating (7) lines and the equilibrium curve. In the mentioned isolated GLDnn1 column, heat losses are assumed to be negligible. Therefore, Gy LxDz mole and enthalpy (H) balances can be written as the nn11 nn D (8) following equations: GH LHDHQ (9) nG1 n1 nn D C FDW (1) Also mole and enthalpy balances for the section of the FzDzWxFDW (2) column below the feed point (i.e. stripping section) are: QDHWHFHQB DWFC (3) Lmm GW1 (10) The product may be liquid, vapor, or a mixture of both, L0 L xGy Wx (11) EXWWKHUHÀX[VKRXOGEHOLTXLG7KHUHÀX[UDWLR R ) is mm m11 m W D WKHPRODUUDWLRRIUHÀX[WRZLWKGUDZQGLVWLOODWH8VLQJPROH LmmHGH m1 G WHQWB (12) and enthalpy balances over the condenser we have: m1 448 Pet.Sci.(2014)11:446-453 Eqs. (1) to (12) are fundamental equations to define 2.4 Methodology the problem and their solutions give information about the A computer program was written using MATLAB v.7.6 distillation column. software. Matrix operation facilities were used to reduce 2.3 Graphical solution method computation time. The solution procedure is described as below and more descriptions on the dimensionless The Ponchon-Savarit graphical method was used to mathematical model are presented in literature (Treybal, investigate the relationship between tray numbers, liquid/ 1981). vapor ratios, and product compositions (Treybal, 1981). The (TXLOLEULXPWLHOLQHIURPy1 (where y1= xD) locates x1. liquid enthalpy can be obtained by the following equation: c x1 connected to >zQD , @ locates y2. (TXLOLEULXPWLHOLQHIURPy2 locates x2. H xM C (1x ) M C() T T LP ªº¬¼Benzene ,Benzene TolueneP ,Toluene ref c x2 connected to >zQD , @ locates y3. (13) c $QGVRRQDVyn connected to >zQD , @ locates xn. This trend continues up to a point where the tie-line where CP is the heat capacity of pure liquid (Perry and Green, passes z namely the feed composition. 1999), and TrefLVWKHUHIHUHQFHWHPSHUDWXUH & ,W F, is assumed that the unmixed liquids are first heated to the In this way the equilibrium stages are determined (i.e. bubble point of the liquid (TD), and then vaporized at this each tie line represent an equilibrium stage). WHPSHUDWXUHDQG¿QDOO\WKHYDSRUVDUHPL[HG7KHUHIRUHWKH Locate xw at intersection of x=xw and the bubble point gas enthalpy can be obtained by the following equation: curve. The reboiler is taken as an equilibrium stage; hence xw and yN+1 are in equilibrium with each other. The tie lie from xw HyMCGPD Benzene¬¼ªº ,Benzene () TTrefO Benzene (14) locates yN+1. 1()yMªº C T T Toluene¬¼PD ,Toluene ref O Toluene Straight line connecting yN+1 to the lower operating point x ,Qcc >@W locates xN on the saturated liquid bubble point curve. where Ȝ is the latent heat of evaporation of the pure substance xN locates yN with the equilibrium tie line equation. at T (Perry and Green, 1999). Combining Eq. (1) to Eq. (12) D Straight line connecting yN to the operating point yields the following equations: >@xW ,Qcc locates xN+1. And so on, using tie line and operating point relations for zy QHc G number of equilibrium stages until x is reached or crossed by Dn1 n1 (15) F yxHH a tie line. nnG1 nn1 L 2.5 Cuckoo optimization algorithm yx HQG cc mW1 m1 (16) )LJVKRZVDÀRZFKDUWRIWKHSURSRVHGDOJRULWKP7KLV yxHH mm1 Gm1 Lm algorithm starts with an initial population (i.e. mature cuckoos and eggs). These initial cuckoos lay some eggs in some host birds’ nests. Some of these eggs that are similar to the host x xQHc bird’s eggs grow up and become a mature cuckoo. Other eggs D FF (17) are killed by host birds. The grown eggs reveal the suitability
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