Dynamic Model of Dividing Wall Column for Separation of Ternary System

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1 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta Dynamc Model of Dvdng Wall Column for Separaton of Ternary System Raeev Kumar Dohare a, Kalash Sngh a, Raesh Kumar a, Sushant Upadhyaya a, Sourabh Gupta b a Department of Chemcal Engneerng, Malavya Natonal Insttute of Technology Japur, Inda b Lurg Inda Company Prvate Lmted, New Delh. raeevdohare@gmal.com ABSTRACT Nowadays the focus s on energy-savng technologes. Several technques have been proposed n order to mprove the effcency of dstllaton process; dvdng-wall column s one of these technques. Conventonally, dstllaton columns are connected n seres to separate multcomponent mtures nto more than two product streams wth hgh purty requrements. owever, n the dvdng-wall column, mddle secton s dvded nto two sectons by nsertng a vertcal wall n the vessel at an approprate poston. Feed s ntroduced nto the prefractonator sde of the wall. A sde stream s removed from the man column. Therefore, a sngle dvdng wall column can separate a ternary mture nto three pure product streams. The sde stream s mostly the ntermedate bolng component of the ternary mture. In the present study a mathematcal model of the dvdng wall column has been developed, whch ncorporates the materal balance, energy balance, and equlbrum relatonshps. A MATLAB code and a CEMCAD model were developed to predct the composton and temperature profle of a benzene-toluene-o-ylene system. The effects of several parameters such as reflu rato, number of trays, feed composton, and splttng rato have been dscussed to fnd the optmum operatng condtons. Ths dynamc model can be further used to study the control of the column. Several authors assumed DWC model to consst of four columns n sequence and smulated n Aspen/ other software, but our work assumes a sngle column separated by a wall, whch was coded n MATLAB to study the steady state and dynamcs of the system.. Introducton Dstllaton s predomnately used n the chemcal and petroleum processng ndustres for lqud separaton technques. The huge mpact of dstllaton processes both on operaton and nvestment costs has motvated the development of varous types of fully thermally coupled dstllaton columns that can be used n savng energy and captal cost (alvorsen et al., 24). The dvdng wall column has acheved huge acceptance as an effcent means to mplement the fully thermally coupled confguraton and has thus rapdly epanded ts commercal applcatons. DWC are especally advantageous for separatng ternary mtures. The schematc dagram of the DWC s gven n Fg., whch s dvded n four sectons. Top secton of the column s known as a rectfyng secton, left secton as prefractonator, rght secton as man column, and the bottom secton as strppng secton. Feed consstng of 3% benzene, 3% toluene, and 4% o-ylene s

2 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta ntroduced at 2 th stage n the prefractonator. Almost pure toluene s wthdrawn from th stage of the man column. and o-ylene are obtaned as top and bottom products, respectvely. Rectfyng (Secton-) 8 trays Condenser Feed 3% 3% 4% o-ylene at 2 th tray Prefractonator (Secton-2) 24 trays Man column (Secton-3) 24 trays at th tray Strppng (Secton-4) 2 trays o-ylene Reboler Fg: Schematc dagram of the DWC For the separaton of the three component mture nto pure products, at least a sequence of two smple dstllaton columns s needed. Each of these columns has a rectfyng and a strppng secton. So the mnmum number of column sectons s four to receve pure products (Stupn and Lockhart, 972). If one reboler for each strppng secton and one condenser for each rectfyng secton are used, then ths leads to the conventonal dstllaton sequences: drect and ndrect splt. In the separaton of the ternary mtures, dvdng wall column (DWC) possesses a sgnfcant advantage n energy savng by avodng the remng problem that occurs n a conventonal sequental two-column system. Ths column also reduces space and nvestment requrements over conventonal dstllaton confguratons. It s a promsng energy savng alternatve for separatng mult-component mtures (Serra et al., 999). Due to the wall, whch dvdes the space n the column, the feed and the sde stream product zones are separated. Ths wall prevents contamnaton of the sde stream by the feed stream. The dvdng wall column has greater effcency than conventonal column sequence (ernadez et al., 26). The dvdng wall column prevents the lateral mng of lqud and vapour streams n the dstllaton column. eat transfer across the dvdng wall can be avoded by thermal nsulaton of the dvdng wall. Especally f very hgh purtes are needed n packed columns, nsulaton 2

3 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta mght be useful to suppress undesred wall flow of lqud. Mostly the dvdng wall s placed n the mddle, but off-centre postons of the dvdng wall are also possble. Ths mght be useful n stuatons, when the concentraton of the medum bolng component s small compared to the overhead and bottom products (Aspron and Kabel, 2). Van Dggelen et al. (2) proposed a model of DWC wth the assumptons of constant pressure, no vapor flow dynamcs, lberalzed lqud dynamcs, and neglectng energy balance and changes n enthalpy. They used ths model to compare varous control strateges. ller (2) developed a nonequlbrum stage model by assumng heat and mass transfer between the lqud and vapor phases for deal components system. Wonaroschy and Isopescu (2) used a dynamc model for mnmzng the dstllaton start-up tme for separaton of an deal benzenetoluene-ethylbenzene ternary mture and the separaton of a non-deal methanol-ethanol-- propanol mture. In ths paper, a mathematcal model of a dvdng wall column has been developed assumng non-constant volatlty. Several smulaton runs of the model have been used to nvestgate the effects of several parameters and dynamcs of the system. 2. Mathematcal Model The volume holdup of condenser/reflu drum has been assumed constant. For the rectfcaton secton, prefractonator, man column, and strppng secton: Mass balance for component, d ( M ) dt where = :n and =: n c., = V + y +, + L, V y, L, + F z, S, Summaton Equatons :, = ; y, = Energy Balance: d ( M ) L, dt = V + V + L + L V V L L + F F S L Equlbrum relatonshp: y K,,, =, where, K, γ =, P P sat, For the condenser, d Materal Balance: Energy Balance: d ( M ) dt D, ( M ) dt D = V y, + L D, = V V L, L, D D, D D q C 3

4 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta Summaton equaton: = For the reboler, Materal Balance: Energy Balance: Equlbrum Relatonshp: d d ( M ) R w, dt D, = L ( M ) n4 + dt L, n4 + n n, Vn yn w , n4 +, = Ln L n V V n n w 4,, L, n4 + 4 y n K n 4 +, = 4 +, w, Summaton Equatons: = and y = n4 +, n4 +, At the ntersecton of rectfyng secton (secton ) wth prefractonator (Secton 2) and man column (Secton 3): + q R Vapour Mng: V n = V + V () + (2) (3) V y = V y + V () () (2) (2) (3) (3) n + n +,,, y Lqud Splttng: L αl n (2) () (3) () =, L ( ) α Ln = where α s lqud splt factor. =, (2) (), n, = (3) (), n, At the ntersecton of Secton 2 and 3 wth Secton 4 (Strppng Secton): Vapour splttng: β (2) (4) V n 2 = V V n = V 2 (3) (4) + ; ( ) + β, where β s vapour splttng factor. y = y (2) (4) n2 +,, ; y = y (3) (4) n2 +,, Lqud Mng: L = L n + L (4) (2) (3) 2 n2 L + L = L (2) (2) (3) (3) (4) (4) n2 n2, n2 n2,, A MATLAB code was wrtten for ths model. These model equatons are set of ordnary dfferental equatons-ntal value problems, whch were solved by ode5s (an ODE solver n MATLAB ). 3. Results and Dscusson The data for smulaton s gven n Table. The smulaton was run by varyng several parameters such as reflu rato, feed stage, lqud splt factor, vapor splt factor, bottoms rate, sde-stream flow rate, and feed composton to nvestgate the effects of these parameters on the 4

5 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta product composton. All the varables were kept fed ecept the varable, the effect of whch was studed. Table Data used for smulaton of the model equatons Parameter Total number of trays n secton- 8 Total number of trays n secton-2 24 Total number of trays n secton-3 24 Total number of trays n secton-4 2 Feed tray locaton Sde-stream tray locaton Feed flow rate Sde-stream flow rate Bottom product flow rate Feed temperature Feed composton Pressure at top Pressure drop at each tray Value 2 th stage of prefractonator th stage of man column mols/s 296 mols/s 4 mols/s 85 o C 3% benzene, 3% toluene, 4% o-ylene Pa 689 Pa Reflu rato 2.84 Reboler duty Lqud splt factor.353 Vapor splt factor MJ/s 3. Effect of Reflu Rato In the dvdng wall column, reflu rato plays an mportant role. For a reflu rato of 2, only benzene composton s more than 9% and rest of the two products (.e. toluene and ylene) are less than 9% as shown n Fg. 2. On ncreasng reflu rato, purty of all the components ncreases up to the reflu rato of 2.84, beyond whch the composton does not mprove. Therefore, reflu rato of 2.84 s the optmum. 5

6 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta 3.2 Effect of Feed Stage Selecton of feed stage s an mportant factor for product purty, the effect of whch s shown n Fg. 3. The poston of the feed stage has mnmal effect on product purty yet as the feed stage n the prefractonator s lowered, the o-ylene purty ncreases, however, toluene purty decreases. mole fracton also decreases for the feed stage lower than 2. Therefore, stage number 2 s almost the optmum feed stage, at whch all the product compostons are almost 99% pure..9 Product Composton Reflu Rato Fg. 2: Effect of reflu rato n dvdng wall column.995 Product Composton Feed Stages Fg. 3: Effect of feed stage locaton 6

7 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta 3.3 Effect of Lqud Splt factor The lqud splt factor n the dvdng wall column decdes how much quantty of the lqud wll enter the prefractonator from the rectfyng secton. As we are supplyng the feed n the prefractonator column, the fracton of lqud to be dstrbuted comng from the rectfyng secton should be less n comparson wth the man column to mantan the lqud hold up n both sectons. Increasng the lqud splt rato from.3 to.4, the purty of toluene and o-ylene decreases from 99.8% to 94.6% and 99.7% to 96%, respectvely as shown n Fg. 4, however, benzene purty s not affected much..99 Product Composton Lqud Splt 3.4 Effect of Vapour Splt factor Fg. 4: Effect of Lqud Splttng on Product Composton The vapour splt factor n the dvdng wall column decdes how much quantty of the vapour wll enter n the prefractonator from strppng secton. Increasng the vapour splt rato from.575 to.675, the purty of all the products ncreases, however, benzene becomes almost constant at 98.9% after a gradual ncrease up to a splt rato of.62 as shown n Fg Effect of Bottoms Rate The bottoms rate drectly affects the purty of all the components as shown n Fg. 6. As we ncrease the bottom flow rate, purty of the bottom product wll decrease as other components wll also enter nto the bottoms. At.325 kmol/sec of bottoms rate, ylene s almost 98% and 7

8 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta rest two components are below 8%. On contnuously ncreasng the bottoms rate up to.4 kmol/sec, compostons of benzene and toluene get mproved, however, ylene remans almost constant. Furthermore, on ncreasng the bottoms rate beyond.4 kmol/s, toluene and ylene purtes decrease, however, benzene becomes almost constant. Therefore, bottoms rate of.4 kmol/s s almost optmum..99 Product Composton Vapour Splt Fg. 5: Effect of vapour splttng on product composton Product Composton Bottom Rate (kmol/s) Fg. 6: Effect of bottoms rate on product composton 8

9 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta 3.6 Effect of Sde Stage Sde stream stage poston decdes the purty of the ntermedate component,.e., toluene. The effect of changng the sde stage locaton s shown n Fg. 7. There s apprecable drop n toluene and o-ylene purty on lowerng down the sde stage locaton from 9 to, after whch there s a slght ncrease n the purty. owever, benzene purty does not vary much. Therefore, sde product wthdrawal stage should be below th stage downwards. Product Composton Sde Stage poston Fg. 7: Effect of sde stage locaton n dvdng wall dstllaton column 3.7 Effect of Composton n Feed The effect of benzene composton n feed s as shown n Fg 8. Whle changng the benzene composton, the other two components were assumed to be n the same proporton. At 3 mole% benzene n the feed, all the product purtes are nearly 98%, but as ts composton ncreases up to 3.7% all the product have more than 99% purty. owever, there s a decreasng trend afterwards. 3.8 Effect of Composton n Feed The effect of o-ylene composton s shown n Fg. 9. Whle changng the o-ylene composton, the other two components were assumed to be n the same proporton. Purty of benzene s constant up to 4% o-ylenen the feed after whch, t suddenly decreases. Moreover, ylene purty n the product ncreases up to 4% and then t becomes constant on further ncreasng ylene composton. purty ncreases wth the ylene composton up to 4% after whch t starts decreasng. 9

10 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta.998 Product Composton Composton Fg. 8: Effect of benzene composton n feed.9.8 Products Composton o-ylene composton Fg. 9: Effect of o-ylene composton n feed

11 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta 3.9 Dynamc Response of Dvdng Wall Column A step change was gven n lqud splt factor to study the response of the composton of all the three products. Fgure (a) and (b) show the results for +% and -%, respectvely. The composton of all the three products drop wth ncrease n the lqud splt factor, however, they rse for the decrease n the lqud splt factor. As can be observed, the dynamcs of toluene composton s the fastest because of the change n the lqud flow rate n the man column; however t s the slowest for o-ylene due to the farthest dstance from the locaton of change. Composton Tme(Sec) (a) Composton Tme(Sec) (b) Fg.: Dynamcs of DWC for step change of (a) +% (b) -% n lqud splt factor 4. Conclusons A mathematcal model has been developed for a dvdng wall column, whch has been used to nvestgate the parametrc effects of several parameters such as reflu rato, feed stage, lqud splt factor, vapor splt factor, bottoms rate, sde stage locaton, and the feed composton. On ncreasng reflu rato, there s mprovement n the purty of all the three products up to a reflu rato of 2.84, beyond whch there s no sgnfcant mprovement. There s no maor effect of feed stage locaton on the product purty on varyng the feed stage locaton from th stage to 4 th stage. The effect of lqud splt factor s not so much on benzene purty, however, toluene and o-ylene purtes decrease on ncreasng the lqud splt factor. All the three product purtes are senstve to the vapor-splt factor; they ncrease on ncreasng the vapor-splt factor. The optmum bottoms rate comes out to be.4 kmol/s. Sde-product locaton should be th stage downwards. The product purtes are senstve to feed composton and therefore may adversely affect the process, whch may requre re-adustng the product flow-rates.

12 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta Notaton M Total lqud hold on th stage, moles, Mole fracton of th components n lqud phase at th stage V L Vapour flow rate from th stage, mole/s Lqud flow rate from th stage, mole/s y, Mole fracton of th components n vapour phase at th stage F Feed flow rate on th stage, mole/s Z, Mole fracton of th component n feed at th stage S Sde stream flow rate at th stage, mole/s n k Number of stages n k th secton (k=,2, 3, and 4) n c Number of component=3 L Lqud enthalpy on th stage, oule/mole Vapour enthalpy on th stage, oule/mole V sat P, Saturaton pressure of th component at th stage, pa P M D, L D Pressure on th stage, pa Lqud holdup n condenser, moles Mole fracton of th component n dstllate Reflu rate, mole/s Dstllate rate, mole/s D Lqud enthalpy of dstllate, oule/mol q C M R Condenser duty, oule/s Lqud holdup n reboler, mole 2

13 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta w, w Mole fracton of th component n bottom product Bottom product flow rate, mole/s Greek symbols α Lqud splt factor β Vapour splt factor γ, Actvty coeffcent of th component n lqud phase at th stage References ASPRION, N. & KAIBEL, G. (2) Dvdng wall columns: Fundamentals and recent advances. Chemcal Engneerng and Processng: Process Intensfcaton, 49, GLINOS, K. & MALONE, M. F. (988) Optmalty regons for comple column alternatves n dstllaton systems. Chemcal Engneerng Research & Desgn, 66, ALVORSEN, I. J. & SKOGESTAD, S. (24) Shortcut analyss of optmal operaton of Petlyuk dstllaton. Industral & Engneerng Chemstry Research, 43, ERNÁNDEZ, S. & GABRIEL, S.. (26) Thermodynamcally equvalent dstllaton schemes to the Petlyuk column for ternary mtures. Energy, 3, ILLER, C., BUCK, C., ELERS, C., & FIEG, G. (2) Nonequlbrum stage modellng of dvdng wall columns and epermental valdaton. eat & Mass Transfer, 46, KAIBEL, G. (987) Dstllaton columns wth vertcal parttons. Chemcal Engneerng & Technology,, SERRA, M., ESPUNA, A. & PUIGJANER, L. (999) Control and optmzaton of the dvded wall column. Chemcal Engneerng and Processng, 38, STUPIN, W. J. & LOCKART, F. J. (972) Thermally coupled dstllaton-a case hstory. Chem. Eng. Prog, 68, VAN DIGGELEN, R.C., KISS, A.A., & EEMINK, A.W. (2) Comparson of Control Strateges for Dvdng-Wall Columns. Industral & Engneerng Chemstry Research, 49, WOINAROSCY, A. & ISOPESCU. R. (2) Tme-optmal control of dvdng-wall dstllaton columns. Industral & Engneerng Chemstry Research, 49,

14 R. K. Dohare, K. Sngh, R. Kumar, S. Upadhyaya, S. Gupta Bography of Presenter Raeev Kumar Dohare has a B.E from NIT Surat n 22 and M.Tech from Algarh Muslm Unversty, Algarh, Inda n 26 wth frst class. Now he s workng as Assstant Professor n the Department of Chemcal Engneerng at Malavya Natonal Insttute of Technology Japur. e s also currently pursung Ph.D. on Dvdng wall Column from the same nsttute. s Research areas are process modelng, smulaton and control, sold waste management, flud mechancs, and processes optmzaton. 4