Experimental and Modeling Studies for a Reactive Batch Distillation Column

Transcription

1 Expermental and Modelng Studes for a Reactve Batch Dstllaton Column Almıla Bahar*. Canan Özgen** Department of Chemcal Engneerng, Mddle East Techncal Unversty, Ankara, 0653, Turkey e-mal: *abahar@metu.edu.tr, **cozgen@metu.edu.tr Abstract: Modelng of esterfcaton reacton of ethanol wth acetc acd n a reactve batch dstllaton column s nvestgated. The dynamc model developed s verfed usng the data of a theoretcal study avalable n the lterature. However, the exstng models are found to be napproprate for ths system when compared wth the expermental data. Then the model s mproved usng the data obtaned from the experments performed on a lab-scale column. In the model, dfferent rate expressons and dfferent thermodynamc models ( φ φ, EOS-G ex, and γ φ methods) consderng dfferent equatons of state (EOS), mxng rules and actvty coeffcent models are used. It s found that the γ φ approach consderng van der Waals mxng rule and NRTL actvty coeffcent model gves the best ft between the dynamc model and the results of the experments for the system under study. Keywords: Reactve Dstllaton, Batch Column, Mathematcal Modelng, Dynamc Smulaton, Ethyl Acetate Producton.. INTRODUCTION Reactve dstllaton, whch s combnaton of reacton and separaton operatons n a sngle unt, has many advantages over conventonal processes. Modelng of ths process s a challengng task due to ts complex dynamcs, hghly nonlnear behavour, complex nteractons between vaporlqud equlbrum (VLE) and chemcal knetcs. The system studed n ths work s an esterfcaton reacton where ethanol (EtOH) reacts wth acetc acd (AcAc) to produce ethyl acetate (EtAc) and water (H 2 O). In ths quaternary system, azeotropes are formed between EtOH- H 2 O, EtAc-H 2 O, EtAc-EtOH, and EtAc-H 2 O-EtOH. In the lterature, most of the studes on ths reacton utlzed the numercal methods of soluton (Chang and Seader, 988; Bogack et al., 989; Smandl and Svrcek, 99) and some others worked on ts thermodynamcs for phase equlbrum (Okur and Bayramoglu, 200; Park et al., 2006) wth very smple models n smulaton. Assumptons consdered are; deal plates wth constant molar holdup, neglgble tray hydrodynamcs and steady state condton. Alejsk and Duprat (996) dealt wth the dynamc smulaton of a reactve dstllaton column for EtAc system n presence of a catalyst. Tang et al. (2003) showed that, NRTL actvty coeffcent model parameters predct the VLE data of ths system well. Both of these dynamc studes are done on contnuous column. On the other hand, unlke contnuous columns very few studes are done for modelng of reactve batch columns. Mujtaba and Macchetto (997) developed an optmzaton algorthm and Monroy-Loperena and Alvarez-Ramrez (2000) developed an output-feedback control algorthm for a reactve batch column. However, n ther studes they used very smplfed VLE models and the model s not checked wth expermental data. The objectve of ths study s to develop a dynamc mathematcal model for the esterfcaton reacton of EtOH and AcAc n a reactve batch dstllaton column (RBDC) by verfyng t wth expermental data. Thus, dfferent thermodynamc models are used for VLE calculatons n order to obtan a good ft wth the expermental data. 2. EXPERIMENTAL The batch dstllaton column (Fg. ) used n ths study (Bahar, 2007) has an nner dameter of 5 cm, a heght of 40 cm, and 8 seve plates. The overall column parameters and expermental operatng condtons are gven n Table. The column s frst operated at total reflux. After steady state s reached, reflux rato s set to a predefned value. Analyses of the collected samples are done through Gas Chromatography. Fg.. Reactve Batch Dstllaton Column.

2 Table. Expermental Column Parameters and Operatng Condtons Total fresh feed, mol 3.67 Feed composton (EtAc, EtOH, H 2 O, 0.0, 0.5, 0.0, 0.5 AcAc), mole fracton Column holdup, mol condenser+drum nternal plates Reboler heat duty, J/h 2.06x0 6 Column pressure, bar.03 Coolng water flow rate, lt/mn.0 3. RBDC MODELING The unsteady state model of RBDC s based on model of Yıldız et al. (2005). The assumptons employed are neglgble vapour holdup, constant volume of tray lqud holdup, constant lqud molar holdup n the reflux drum, total condenser, neglgble flud dynamc lags, lnear pressure drop profle, Murphree tray effcency, approxmated enthalpy dervatves and adabatc operaton. The balance equatons for column reboler, trays and reflux-drum-condenser system are gven as follows: Reboler: j =,,NC dm/ dt = L2 V () dmx ( )/ dt= Lx Vy + ε RM (2) j 2 2j j j d( Mh)/ dt = L2h2 VH+ Q (3) where the reboler holdup, M, s as gven n (4) where s the molar amount of feed ntally charged to the column. NT + 2 t 0 = f n n= 2 0 M M M D( τ) d τ (4) Trays: = 2,,N T+ ; j =,,NC dm dt = L + V L V (5) / + j + +, j, j j j j 0 M f dmx ( )/ dt= L x + V y Lx Vy + ε RM (6) dmh ( )/ dt= L+ h+ + V H Lh VH (7) avg avg where M = ( ρ / Mw ) v s the molar holdups on trays where ρ avg s the average densty of the mxture on the th avg tray, Mw s the average molecular weght of the mxture on the th tray, v s the volume of the lqud tray holdup. Reflux-drum-condenser system: j =,,NC dm NT + 2 / dt = VNT + LNT + 2 D (8) dm ( NT + 2xNT + 2, j ) = VNT + ynt +, j LNT + 2xNT + 2, j DxNT + 2, j + ε jrnt + 2M (9) NT + 2 dt dm ( NT + 2hNT + 2) = VNT + HNT + 2 LNT + 2hNT + 2 DhNT + 2 Q (0) NT + 2 dt where R s the reacton rate at th stage n mol/h and can be expressed as gven n () and the rate expresson, r, wthout catalyst s expressed as r = kx2x4 k2x3x. The forward and backward reacton rate constants n lt/gmol.mn are k =2900exp(-790/T(K)) and k 2 =7380exp(-790/T(K)), respectvely (Alejsk and Duprat, 996). R = rρ / MW for =,,N T+2 () The reflux rato s defned as R = L / NT + 2 D. The subscrpts and j are for stage and component numbers, respectvely. = for reboler, =2,.,N T+ for trays and =N T+2 for reflux-drumcondenser unt. The components are numbered n the subscrpts as follows: EtAc-, EtOH-2, H 2 O-3, and AcAc-4. In energy balance equatons, no addtonal term for the heat of reacton s ncluded because, the enthalpes are referred to ther elemental state for whch the heat of reacton s accounted automatcally and thus, no separate term s needed (Mujtaba and Macchetto, 997). The lnear pressure drop profle s gven as P = P ( P PNT+ 2)/ NT where P s the pressure n th tray, P, the pressure n the reboler and P NT+2, the pressure n the reflux drum. 4. MODELS FOR VAPOR-LIQUID EQUILIBRIUM In modelng of batch dstllaton column, the selecton of proper thermodynamc model affects the estmaton of compostons hghly and therefore s very crucal. In smulaton studes, four dfferent models are used for phase equlbrum and these models are explaned below n detal. 4. Model-I:Phase Equlbrum Usng VLE data n Lterature VLE data for EtAc-EtOH-H 2 O-AcAc system gven n Table 2 s taken from lterature (Suzuk et al., 97). Ths data s utlzed n the smulaton as a prelmnary check. Table 2. Vapor Lqud Equlbrum Data. EtAc log K = -2.3 x 0 3 /T EtOH log K = -2.3 x 0 3 /T H 2 O log K = -2.3 x 0 3 /T AcAc K = (2.25 x 0-2 )/T K = 0.00 for T K for T > K 4.2 Model-II: Phase Equlbrum Usng φ φ Approach In ths approach, Peng Robnson EOS (PR) wth van der Waals one-flud mxng rule s used to calculate the fugacty of speces for both lqud and vapor phases. The bnary nteracton parameters are gven n Table 3 (Burgos- Solorzano, 2004). Table 3. Bnary nteracton parameters, k j. k j EtAc EtOH H 2 O AcAc EtAc EtOH H 2 O AcAc Model-III: Phase Equlbrum Usng Combnaton of EOS wth Excess Free Energy Models (EOS-G ex Approach) In ths method, actvty coeffcent models are ncorporated nto EOS. NRTL, Wlson, and UNIQUAC models are used

3 and performances for the system under consderaton are compared. The parameters for these models are obtaned from Tang et al. (2003), Okur and Bayramo lu (200), and Kang et al., (992). In ths study, as EOS; PR and Peng-Robnson-Stryjek-Vera (PRSV) (Stryjek and Vera, 986) are used. κ parameters for components are gven n Table 4 (Stryjek and Vera, 986). As the mxng rule, van der Waals one-flud mxng rule, Huron-Vdal (Orgnal) Mxng Rule (HVO), and Orbey- Sandler modfcaton of the Huron-Vdal mxng rule (HVOS) are used. Table 4. PRSV EOS parameters, κ. (a) Components κ EtAc EtOH H 2 O AcAc Model-IV: Phase Equlbrum Usng γ φ Approach In VLE descrptons wth the γ φ approach, an actvty coeffcent model can be used for the lqud phase and an EOS s used for the vapor phase. 5. RESULTS AND DISCUSSION Ths study s done n three phases. In frst phase, modelng studes are done and then checked wth a smulaton study found from the lterature whch has the same reactve system. In second phase, expermental studes are done and data s collected for total and dfferent reflux ratos. In thrd phase, the expermental fndngs and the smulaton results are compared and the dynamc model s fnalzed by selectng the approprate thermodynamc model for VLE calculatons. The propertes of the column whch s used n smulaton are gven n Table 5. Monroy-Loperena and Alvarez-Ramrez (2000) used the VLE data of Model-I and temperature ndependent rate constants wth k of 4.76x0-4 lt/(gmol.mn) and k 2 of.63x0-4 lt/(gmol.mn). The comparson of dynamc model usng same rate expresson at total reflux s gven n Fg. 2. As can be seen, the results are almost the same. Ths ndcates that the developed dynamc model s qute satsfactory to represent ths non-lnear and complex problem of RBDC behavour. Table 5. RBDC Specfcatons No. of stages (ncludng reboler and 0 total condenser) Total fresh feed, kmol 5.0 Feed composton (EtAc, EtOH, H 2 O, 0.0, 0.45, 0., 0.45 AcAc), mole fracton Column holdup, kmol condenser 0. nternal plates Condenser vapor load, kmol/h 2.5 Column pressure, bar.03 (b) Fg. 2. Dstllate compostons at total reflux. (a) Results from lterature (b) Results from the smulaton n ths study. After obtanng smlar results wth lterature, experments are performed n order to mprove the model. Column s frst operated at total reflux untl the steady state s reached. Then t s operated wth arbtrary reflux ratos and data for dstllate and reboler compostons are collected wth respect to tme. 5. Dynamc Analyss of the Results of Expermental and Smulaton Studes There s a dfference n ntalzaton of the experments and smulaton program. Therefore, although the trends of the profles of compostons are smlar, they cannot be compared up to steady state pont. Consequently, f the two results match at total reflux steady state, then comparsons of dynamc response can be done. Thus, for each model explaned n Secton 4, the expermental data collected s checked wth the smulaton results. Model-I: In Table 6, smulaton result of Model-I and experments at total reflux steady state are gven. It can be seen that, when steady state values are compared, they are too dfferent from each other and there s no need to check the dynamc behavour. More accurate VLE model s needed. Table 6. Total Reflux Steady State Composton Values Comp. Dstllate Reboler Exp. Sm. Exp. Sm. EtAc EtOH H 2 O AcAc x

4 Model-II: The results of smulaton that uses Model-II and experments are gven n Fg. 3. It s found that total reflux steady state values are better compared to Model-I. The comparson s further contnued dynamcally for a constant reflux rato of The tme at total reflux steady state s shown as zero. It can be seen that there are great dfferences n the dstllate and reboler lqud composton trends wth respect to tme. model for ths system, snce t gves slghtly better results than Wlson model, and wll be used also n Model-IV. Fg. 4. Results wth Model-III-A Fg. 3. Results wth Model-II Model-III: In Model-III, frst of all PR wth HVO mxng rule and NRTL actvty coeffcent model (Model-III-A) s tested. It can be seen from Fg. 4 that the results are somewhat mproved compared to Model-II, especally for the reboler compostons. However, the results for dstllate compostons are not satsfactory. Therefore, EOS s changed to PRSV wth same mxng rule and actvty coeffcent model; the performance of the system wth ths model (Model-III-B) s gven n Fg. 5. Dstllate compostons are much better than that of Model-III-A. However, reboler compostons become worse and therefore ths result s also found to be not satsfactory. As a further step, mxng rule s changed to HVOS and t s used together wth PRSV and NRTL actvty coeffcent model (Model-III-C). The results are gven n Fg. 6. The results for both dstllate and reboler compostons are mproved sgnfcantly wth ths thermodynamc model. In order to see the effects of dfferent actvty coeffcent models, Wlson and UNIQUAC models are used n EOS-G ex approach. The dstllate and reboler lqud compostons wth Wlson model (Model-III-D) and UNIQUAC model (Model- III-E) are gven n Fg. 7 and Fg. 8, respectvely. It can be seen from the fgures that, whle NRTL and Wlson models gve smlar results, UNIQUAC performs poorly. NRTL model s selected to be the most proper actvty coeffcent Fg. 5. Results wth Model-III-B

5 an acceptable range. Unlke Model-III, PR also gves smlar results wth PRSV n Model-IV as can be seen n Fg. 0. Fg. 6. Results wth Model-III-C Fg. 8. Results wth Model-III-E Fg. 7. Results wth Model-III-D Model-IV: In Model-IV, NRTL actvty coeffcent model s used for lqud phase, PRSV (Model-IV-A) and PR (Model- IV-B) wth van der Waals mxng rule s used for vapor phase. It can be seen from Fg. 9 that the dstllate compostons are mproved compared to Model-III. Although the reboler compostons become a lttle worse, they are n Fg. 9. Results wth Model-IV-A

6 score. Thus, both methods are suggested to be used n the smulaton of EtOH esterfcaton reacton wth AcAc n a RBDC system. Fg. 0. Results wth Model-IV-B Table 7. Summary of Thermodynamc Models. IAE Scores Model Descrpton Dstllate Reboler Overall Model-I VLE data from lterature Model- φ φ method II (PR+van der Waals) III-A (PR + HVO + NRTL) III-B (PRSV + HVO + NRTL) III-C (PRSV+HVOS+NRTL) III-D (PRSV+HVOS+Wlson) III-E (PRSV+HVOS+UNIQUAC) Model- IV-A Model- IV-B γ γ φ method (PRSV+van der Waals+NRTL) φ method (PR+van der Waals+NRTL) CONCLUSIONS A summary of results for dfferent thermodynamc models are gven n Table 7 wth Integral Absolute Error (IAE) scores of response curves. Model-IV-A, whch uses tradtonal γ φ approach wth NRTL actvty coeffcent model for lqud phase and PRSV for vapor phase gves the smallest IAE score for the quaternary EtOH-AcAc-EtAc-H 2 O system. Nevertheless, Model-IV-B whch uses the tradtonal approach wth NRTL actvty coeffcent model for the lqud phase and the PR-EOS for the vapor phase, whch s smple to use also gves smlar result wth a slghtly hgher IAE REFERENCES Alejsk, K., Duprat, F. (996). Dynamc Smulaton of the Multcomponent Reactve Dstllaton. Chem Eng Sc, 5 (8), Bahar, A. (2007). Modelng and Control Studes for a Reactve Batch Dstllaton Column, n Ph.D. Thess, Chemcal Engneerng Department, Mddle East Techncal Unversty, Ankara. Bogack, M.B., Alejsk, K., Szymanowsk, J. (989). The Fast Method of the Soluton of a Reactng Dstllaton Problem. Comput Chem Eng, 3 (9), Burgos-Solorzano, G.I., Brennecke, J.F., Stadtherr, M.A. (2004). Valdated Computng Approach for Hgh- Pressure Chemcal and Multphase Equlbrum. Flud Phase Equlbr, 29 (2), Chang, Y.A., Seader, J.D. (988). Smulaton of Contnuous Reactve Dstllaton by a Homotopy-Contnuaton Method. Comput Chem Eng, 2 (2), Kang, Y. W., Lee, Y. Y., Lee, W. K. (992). Vapor-Lqud Equlbra wth Chemcal Reacton Equlbrum - Systems Contanng Acetc Acd, Ethly Alcohol, Water, and Ethyl Acetate. J Chem Eng Jpn, 25 (6), Monroy-Loperena R., Alvarez-Ramrez, J. (2000), Output- Feedback Control of Reactve Batch Dstllaton Columns. Ind Eng Chem Res, 39, Mujtaba, I.M., Macchetto, S. (997). Effcent Optmzaton of Batch Dstllaton wth Chemcal Reacton Usng Polynomal Curve Fttng Technques. Ind Eng Chem Res, 36, Okur, H. and Bayramoglu, M. (200), The Effect of the Lqud-Phase Actvty Model on the Smulaton of Ethyl Acetate Producton by Reactve Dstllaton. Ind Eng Chem Res, 40, Park J., Lee, N., Park, S., Cho, J. (2006). Expermental and Smulaton Study on the Reactve Dstllaton Process for the Producton of Ethyl Acetate. J Ind Eng Chem, 2(4), Smandl, J. Svrcek, W.Y. (99). Extenson of the Smultaneous-Soluton and Insde-Outsde Algorthms to Dstllaton wth Chemcal Reactons. Comput Chem Eng, 5 (5), Stryjek R., Vera J.H. (986). An Improved Peng-Robnson Equaton of State for Pure Compounds and Mxtures, 64 (2), Suzuk, I., Yag, H., Komatsu, H., Hrata. M. (97). Calculaton of Mult-component Dstllaton Accompaned by a Chemcal Reacton. J Chem Eng Jpn, 4 (), Tang, Y. T., Huang, H., Chen, I. (2003). Desgn of a Complete Ethyl Acetate Reactve Dstllaton System. J Chem Eng Jpn, 36 (), Yıldız, U., Gürkan, U.A., Özgen, C., Leblebco lu, K. (2005), State Estmator Desgn for Multcomponent Batch Dstllaton Columns. Chem Eng Res Des, 83(A5), -2.