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

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. (TXLOLEULXPWLHOLQHIURPy locates x . H xM C (1x ) M C() T T 2 2 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 xFWxHQ F cc of their nests. The more eggs that survive in a nest the more profit is gained in that nest. Therefore, the nest in which §·QC where QHc ¨¸D is the heat removed per mole of more eggs survive will be the term that cuckoo optimization ©¹D algorithm is going to optimize. Q §·B Birds search for the most suitable nest to lay eggs to distillate in the condenser, and QHcc ¨¸W is the net ©¹W maximize their eggs survival rate. The mature cuckoos ÀRZRIKHDWSHUPROHRIUHVLGXH(TV WR UHSUHVHQW make some societies. The cuckoos immigrate toward the seven points as listed below: best habitat of all societies. Therefore, during the survival competition some of the cuckoos or their eggs die and the ªº >zQD , c@ , ªºyHnG1, , xHnLn, , xW ,Qcc , yHm1, G , surviving cuckoo societies emigrate to a better environment ¬¼n1 > @ > @ ¬¼m1 and start laying eggs. This survival effort hopefully converges ªº to a state that there is only one cuckoo society with the same xHm , L , and >zHF , F @ ¬¼m SUR¿WYDOXHV 5DMDELRXQ where >zQD , c@ and x ,Qcc are fixed. These equations > W @ 3 Results and discussion represent a set of straight lines on the H-xi,yi diagram, which passs>zQD , c@ , >xW ,Qcc @ , and >zHF , F @ known as the 3.1 Evaluation of the model upper operating point, lower operating point, and feed point The graphical model was evaluated by using the HYSYS respectively. v.3.2 simulator at the operating conditions in Table 1. The Pet.Sci.(2014)11:446-453 449

Start

Determine egg Initialize cuckoos laying radius for with eggs each cuckoo

Lay eggs in Move all cuckoos different nests toward best environment

Some of eggs are detected and killed Determine cuckoo societies

No Population is less than max value? Kill cuckoos Find nests with in worst area best survival rate Yes

Check survival of eggs in nests Let eggs grow JHWSUR¿WYDOXHV

Stop condition VDWLV¿HG" No

Yes

End

Fig. 2 Flowchart of Cuckoo optimization algorithm (Rajabioun, 2011) results are given in Table 2. It can be seen that there is good Table 2 Comparison of the results of graphical model (programmed by agreement between the results of the graphical model and the MATLAB) and HYSYS simulation values calculated with the HYSYS simulator for the assumed conditions. Given the complexity of distillation and the Items HYSYS simulation Graphical model LQÀXHQFHRIPDQ\SDUDPHWHUVLQYROYHGWKHSUHGLFWLRQIURP Minimum number of trays 10.666 9.1687 the model has proved to be very accurate. Actual number of trays 23.097 21

Table 1 Operating conditions of the distillation column Optimal feed stage 11.545 10

Items Value Condenser temperature, ºC 80.71 80.65

Lighter component benzene Reboiler temperature, ºC 110 110.09

Heavier component toluene Condenser duty, kW 1208.1 1071.7

System pressure, kPa 101.325 Reboiler duty, kW 1504.4 1405.6

Temperature of feed, ºC 25 0LQLPXPUHÀX[UDWLR 1.413 1.192

)HHGÀRZUDWHNPROHKU 100 It should be noted that, the HYSYS simulator uses the Mole fraction of lighter component in feed 0.5 McCabe-Thiele method (1925) to simulate a distillation Mole fraction of lighter component in liquid phase in condenser 0.99 column. This method is the simplest method for the analysis of binary distillation and uses the fact that the composition Mole fraction of lighter component in liquid phase in reboiler 0.01 at each tray is determined by the mole fraction of each of ȕ UHÀX[UDWLRPLQLPXPUHÀX[UDWLR 1.247 components. This method is based on the assumptions of constant molar overflow, which requires the molar heats of 450 Pet.Sci.(2014)11:446-453

x 105 vaporization of the feed components be equal to each other, 1 (z , Q’) a mole of vapor having to be condensed for every mole of D vaporized liquid, and heat effects such as heats of solution -1 0.5 kmol DUHQHJOLJLEOH7KHVHVLPSOL¿HUDVVXPSWLRQVFDQGHFUHDVHWKH . HG (zD, HG1) H model accuracy. On the other hand, applying an optimizer L (x , H ) 0 W W (z , H ) algorithm to the HYSYS simulator for obtaining an optimum F F (zD, HD) condition for a distillation column is not possible for the users of this software. Therefore, the Ponchon-Savarit method, -0.5 which is more accurate than the McCabe-Thiele method, Molar enthalpy, kJ Molar enthalpy, was used to develop a computer program using MATLAB (x , Q”) -1 W software to simulate this distillation column and then 0 0.2 0.4 0.6 0.8 1 optimize the operating condition of this column. Mole fractions of volatile component in the liquid (x) and in the vapor (y) 3.2 Predictions from the graphical model Fig. 3 Enthalpy-concentration diagram of solved The x-y and H-xy diagrams of the graphical model for the graphical model for conditions in Table 2 conditions in Table 1 are shown in Figs. 3 and 4. As shown in 1 Figs. 5 and 6, the mole fraction of benzene in both liquid and vapor phases decreases down the distillation column, and the 0.8 temperature of solution increases from top to the bottom of y ) the column. 0.6

2SWLPXPUHÀX[UDWLR 0.4 Equilibrium line

The optimum condition for a distillation column is used in the vapor ( y=x line to achieve separation under the most profitable operating 0.2 Operating line FRQGLWLRQV6HYHUDOSDUDPHWHUV HJWKHGLDPHWHUUHÀX[UDWLR Equilibrium stage 0 and operating pressure of the column, and the temperature Mole fraction of volatile component 0 0.2 0.4 0.6 0.8 1 of the condenser and reboiler, etc.) can be adjusted to Mole fraction of volatile component in the liquid (x) optimize the total annualized cost (Talifu and Luo, 2005). The Fig. 4 Vapor-liquid equilibrium diagram of solved RSWLPL]DWLRQRIWKHUHÀX[UDWLRLVRIYLWDOLPSRUWDQFHSUR¿W graphical model for conditions in Table 2 ZLVH,QWKHSUHVHQWUHVHDUFK¿UVWDVXLWDEOHJUDSKLFDOPRGHO 1 was proposed and then this model was optimized using the y ) x Cuckoo optimization algorithm. y The cost value is a function of the number of trays and 0.8 also the total required duty (i.e. the sum of reboiler and 0.6 FRQGHQVHUGXWLHV $WWKHPLQLPXPUHÀX[UDWLRWKHFROXPQ requires an infinite number of trays, and consequently the 0.4 capital cost becomes infinite, but the energy cost would be x ) and in the vapor ( the least. As reflux ratio (R) increases, the number of trays 0.2 rapidly decreases, until it reaches a minimum. The heating and cooling requirements increase almost proportionally with 0 2 4 6 8 10 12 14 16 18 20

reflux ratio. For a stage distillation column, neglecting the in the liquid ( Mole fractions of volatile component Number of trays (N) costs of raw materials and labor, the operational costs can be Predicted mole fraction of benzene in vapor and liquid GH¿QHGDV Fig. 5 phases using the graphical model at the conditions in Table 2 Total annualized cost = Capital cost + Energy cost 115 The total annualized cost curve must therefore pass WKRXJKDPLQLPXPDWWKHRSWLPXPUHÀX[UDWLR7KHUHIRUHDQ 108

economic parameter (ĳ LVGH¿QHGDVEHORZ $EROSRXUHWDO C o 2013): 101 Energycost ($ kw11 hr ) M 94 Energycost ($ kw11 hr ) Capitalcost ($ hr 1 ) Temperature, Temperature, (18) 87 Now the reflux ratio can be optimized by minimizing the 80 total annualized cost, which is calculated by the following 5101520 equation: Number of trays (N) Fig. 6 Predicted solution temperature using the ) 365 u 24>QNtotM act (1 M )@ (19) graphical model at the conditions in Table 2 Pet.Sci.(2014)11:446-453 451

Fig. 7 shows the results of the calculated cost value at )RULQVWDQFHLIIHHGWHPSHUDWXUHLVVHWWREH&WKHHUURU each iteration of the Cuckoo optimization algorithm for the LVDERXWDQGLIxw=0.002 and zD=0.97, this value is listed parameters in Table 2 and ĳ=0.02 (Abolpour et al, DERXW 2013). In this case, the minimum value of the reflux factor (ȕ) is 1.247, which is used to compare the current model 3.4 Effects of the operating pressure and feed with the HYSYS simulator results. Fig. 7 also compares the temperature current Cuckoo algorithm with two traditional algorithms Fig. 9 shows the effects of operating pressure on (i.e. golden section search and genetic algorithm). It can be temperature of solution and mole fraction of benzene in seen that the Cuckoo optimization algorithm is faster than the liquid and vapor phases. It can be seen that with an increase golden section search and the genetic algorithm for predicting of operating pressure the temperature of solution and also the target parameter. The excellence of Cuckoo optimization the mole fraction of benzene in both liquid and vapor phases algorithm is also shown in our previous study (Kaydani and on the trays increase. Higher pressure can cause an increase Mohebbi, 2013). in the saturation temperature of the liquid. Therefore, more energy will be required for separation of these two Economic paramerer (ĳ)=0.02 components in the distillation column. From the other point 140 of view, a column with a lower pressure facilitates separation 130 Cuckoo optimization algorithm cost=62.8447, at iteration=30 Golden section search algorithm cost=62.8849, at iteration=30 and therefore less trays are required, as seen in Fig. 9 (i.e. 120 Genetic algorithm cost=62.8491, at iteration=30 at 100 kPa operating pressure, the number of equilibrium

110 stages is 21 and at 300 kPa operating pressure, the number of equilibrium stages is 23). Therefore, it is clear that, high 100 operating pressure increases the total annualized cost, which 90 Cost value has no optimum value (i.e. lower pressure is better). 80 Fig. 10 shows the effects of feed temperature on the 70 temperature of solution and the mole fraction of benzene in

60 liquid and vapor phases. As one can see from Fig. 10, with 0 5 10 15 20 25 30 an increase of the feed temperature the mole fractions of Iteration benzene in both liquid and vapor phases decrease, but the Fig. 7 The Cuckoo optimization algorithm iterations temperature of the solution in the column does not change for conditions in Table 2

y ) 1 160 Fig. 8 shows the effect of economic parameter (ĳ) on the T at 300 kPa T at 100 kPa ). As one can see in Fig 8, at low 0.8 RSWLPXPUHÀX[IDFWRU ȕopt 144 C energy price or high capital cost (i.e. small value of ĳ), the o T ), RSWLPXPUHÀX[IDFWRULVKLJKDQGDWORZFDSLWDOFRVWRUKLJK 0.6 128 energy price (i.e. large value of ĳ WKHRSWLPXPUHÀX[IDFWRU 0.4 x at 100 kPa 112 is low. The fitting formulation for optimum value of reflux x ) and in the vapor ( y at 100 kPa factor would be: x at 300 kPa

0.2 y at 300 kPa 96 Temperature(

0.4422 EM 0.1068 0.6446 (20) 80 opt 0 5 10 15 20 in the liquid ( Mole fractions of volatile component Number of trays (N) This relation can be used for all the operating conditions of a benzene-toluene distillation column with negligible error. Fig. 9 Effects of operating pressure on temperature of solution and mole fraction of benzene in liquid and vapor phases

5 1 115 y ) 4.5 o ) *UDSKLFDOPRGHO T at 25, 95 and 125 C feed temperature

opt )LWWHGFXUYH 4 0.8 108 C o 3.5 T ), 0.6 101 3 x at 25 oC feed temperature 2.5 0.4 y at 25 oC feed temperature 94 x at 95 oC feed temperature

2 x ) and in the vapor ( y at 95 oC feed temperature 0.2 x at 125 oC feed temperature 87 1.5 ( Temperature y at 125 oC feed temperature 1 2SWLPXPUHÀX[IDFWRU ȕ 0 80 2 4 6 8 101214161820 0 0.02 0.04 0.06 0.08 0.1 in the liquid ( Mole fractions of volatile component Number of trays (N) (FRQRPLFSDUDPHWHU ĳ) Fig. 10 Effects of feed temperature on temperature of solution and Fig. 8 Effect of economic parameter (ĳ RQWKHRSWLPXPUHÀX[IDFWRU ȕopt) mole fraction of benzene in liquid and vapor phases 452 Pet.Sci.(2014)11:446-453 significantly. The temperature of the feed supplies some of * -1 H G Molar enthalpy of Q1-ÂPRO the required energy for distillation. It should be noted that, n1 Molar enthalpy of residue product at the bottom of H -1 WKHIHHGFRQGLWLRQV LHVXEFROGOLTXLGDW&WZRSKDVHV W FROXPQ-ÂPRO DW&DQGVXSHUKHDWHGYDSRUDW&IRUWKHVROXWLRQRI -1 benzene-toluene) affect the x-y and H-xy (Fig. 3) diagrams. L /LTXLGÀRZUDWHNPROÂKU 7KHÀRZUDWHRIH[LWHGOLTXLGIURPWKHWUD\QXPEHUm This parameter (feed temperature) affects the required number /P -1 of trays in the column. An increase of the feed temperature RIVWULSSLQJVHFWLRQRIWKHFROXPQNPROÂKU Ln 7KHÀRZUDWHRIH[LWHGOLTXLGIURPWKHWUD\QXPEHUn will decrease the total annualized cost. The optimum value of -1 feed temperature is a function of the initial conditions of the RIHQULFKLQJVHFWLRQRIWKHFROXPQNPROÂKU -1 available feed. L0 ([WHUQDOUHÀX[UDWHNPROÂKU M 0ROHFXODUZHLJKWJÂPRO-1 4 Conclusions Nact Actual number of trays A graphical model for the operating profit of benzene- Q Heat added in the reboiler, kW toluene stage distillation columns was developed to optimize B the operating reflux ratio of the column by the Cuckoo QC Heat removed in the condenser, kW optimization algorithm. The model was then evaluated with Q Total duty, kW the HYSYS simulator and it was observed that the results tot from the model agree well with simulator results. Finally a R 5HÀX[UDWLR ¿WWLQJUHODWLRQZDVLQWURGXFHGWRFDOFXODWHWKHRSWLPXPUHÀX[ T 6ROXWLRQWHPSHUDWXUH& ratio of the distillation column. The optimum reflux factor -1 ZDVGH¿QHGDVDIXQFWLRQRIHQHUJ\SULFHDQGFDSLWDOFRVW,W W 5HVLGXHUDWHNPROÂKU was concluded that at low energy price or high capital cost, x Mole fraction of volatile component in the liquid WKHRSWLPXPUHÀX[IDFWRULVKLJKZKHUHDVDWORZFDSLWDOFRVW x Mole fraction of volatile component in L RUKLJKHQHUJ\SULFHWKHRSWLPXPUHÀX[IDFWRULVORZ 0 0 For more accuracy, the Ponchon-Savarit graphical method xm Mole fraction of volatile component in the exited OLTXLGÀRZIURPWKHWUD\QXPEHUPRIVWULSSLQJVHFWLRQ was used to model this distillation column. This shows that of the column the Cuckoo optimization algorithm is fast enough to optimize xn Mole fraction of volatile component in the exited this column. This column also could be optimized to obtain OLTXLGÀRZIURPWKHWUD\QXPEHUQRIHQULFKLQJVHFWLRQ optimum values of the all of operating parameters such as of the column operating pressure and feed temperature, but other parameters xW Mole fraction of volatile component in the residue except reflux ratio, have no significant effects on the total product at the bottom of column annualized cost for optimization. y Mole fraction of volatile component in the vapor

List of symbols y1 Mole fraction of volatile component in G1

ym+1 Mole fraction of volatile component in the exited gas C +HDWFDSDFLW\DWFRQVWDQWSUHVVXUH-ÂJ-1 ÀRZIURPWKHWUD\QXPEHUm+1 of stripping section of P the column D 'LVWLOODWHUDWHNPROÂKU-1 yn+1 Mole fraction of volatile component in the exited gas F )HHGUDWHNPROÂKU-1 ÀRZIURPWKHWUD\QXPEHUn+1 of enriching section of the column -1 G 9DSRUÀRZUDWHNPROÂKU z Average mole fraction of volatile component in the 7KHÀRZUDWHRIH[LWHGYDSRUIURPWRSRIWKHFROXPQ mixture of liquid and vapor phases G1 -1 NPROÂKU zD Average mole fraction of volatile component in the mixture of liquid and vapor of distillate product at the * P1 The flow rate of exited vapor from the tray number -1 top of column mRIVWULSSLQJVHFWLRQRIWKHFROXPQNPROÂKU The flow rate of exited vapor from the tray number zF Average mole fraction of volatile component in the *Q1 nRIHQULFKLQJVHFWLRQRIWKHFROXPQNPROÂKU-1 IHHGÀRZ H 0RODUHQWKDOS\-ÂPRO-1 ȕ 5HÀX[IDFWRU ȕ 2SWLPXPUHÀX[IDFWRU HD Molar enthalpy of distillate product at the top of opt -1 FROXPQ-ÂPRO Ȝ /DWHQWKHDWRIYDSRUL]DWLRQ-ÂJ-1 H 0RODUHQWKDOS\RIIHHGÀRZ-ÂPRO-1 F ĳ Economic parameter -1 H Molar enthalpy of G -ÂPRO -1 G1 1 ĭ 7RWDODQQXDOL]HGFRVWSDUDPHWHUÂ\HDU -1 HL0 Molar enthalpy of L0-ÂPRO -1 References HLm Molar enthalpy of /P -ÂPRO Abo lpour B, Abolpour R, Shamseddini A, et al. Optimization of the H Molar enthalpy of L -ÂPRO-1 Ln n UHÀX[UDWLRIRUPHWKDQROZDWHUVWDJHGLVWLOODWLRQFROXPQ5HVHDUFK -1 H Molar enthalpy of * P1-ÂPRO on Chemical Intermediates. 2013. 39(2): 681-692 Gm1 Pet.Sci.(2014)11:446-453 453

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