European Symposum on Computer Arded Aded Process Engneerng 15 L. Pugjaner and A. Espuña (Edtors) 2005 Elsever Scence B.V. All rghts reserved. Three-Phase Dstllaton n Packed Towers: Short-Cut Modellng and Parameter Tunng Olver Vllan *, Rchard Faber, Pu L, Jens-Uwe Repke and Günter Wozny Techncal Unversty of Berln Insttute of Process and Plant Technology and Techncal Acoustcs Sekr. KWT9, Strasse des 17. Jun 135, 10623, Germany Abstract A short-cut model s developed for the predctve smulaton of a three-phase dstllaton process n packed towers. The model s takng nto account the mass transfer resstance between the vapour phase and both lqud phases, whereas equlbrum s assumed between the two lqud phases. The development of the model was strongly connected wth a systematc expermental nvestgaton study of three-phase operated packngs. Thus, t was possble to estmate unknown parameters occurrng n the model. Therefore, a powerful parameter estmaton technque whch s able to handle a large number of expermental data sets was appled. Both the smulaton model and the parameter estmaton method are dscussed n ths contrbuton. The frst results are n good agreement wth the expermental data of the packed column. Keywords: Heterogeneous azeotropc dstllaton; packed column; Expermental nvestgaton; Parameter estmaton 1. Introducton In our own prevous study, a nonequlbrum model for three-phase dstllaton n a packed column was developed and valdated wth expermental nvestgatons (Repke et al., 2003). Thus the accuracy of the model was proved and the understandng of the mechansm governng the three-phase dstllaton wth packng was sgnfcantly mproved. But the theoretcal knowledge about three-phase dstllaton wth packng remans lmted. As a fact, predctve calculaton of the separaton effcency s stll not supported by the smulaton, and exstng models are generally not convenent for common ndustral strategc tasks. As a result, new technques for the mprovement of the desgn and the ndustral applcaton of packed towers for the three-phase dstllaton are needed. Therefore, the development of a predctve short-cut modellng method consderng the occurrence of a second lqud phase on the packng s requred. 2. Model ntroducton A model s developed for the predcton of the separaton effcency of a three-phase dstllaton process n packed towers. The model s based on the calculaton of the * Correspondng Author: olver.vllan@tu-berln.de
Heght of a Transfer Unt (HTU) of a three-phase operated packng for the multcomponent case. The method proposed n (Taylor and Krshna, 1993) s consdered for the calculaton of the multcomponent mass transfer coeffcents, whereas new methods are proposed to scale those coeffcents for one component and to take nto account the occurrence of a second lqud phase on the packng. The startng pont for the multcomponent mass transfer coeffcent calculaton s the bnary mass transfer calculaton, for example as proposed n (Bllet, 1995) and shown n equaton (1). 2 V V m V n V V a 1 V u ρ η a Ph Ph = V V V 2 ε ε h aη D ρ a L β a C D In equaton (1), the exponental parameters m and n gven n the lterature were determned for bnary mxtures n the two-phase case. Therefore, estmated values of those parameters are needed for the new short-cut method. The model presented bases on the HTU/NTU concept for bnary mxtures and for the two phase dstllaton. In the followng part of the contrbuton, the extenson of ths concept for mult-component mxtures and for the three-phase dstllaton wll be dscussed. 2.1 HTU/NTU Concept for bnary systems The basc form of the HTU/NTU-concept s relatng the packng hgh wth the separaton effcency: y,aus V dy H= HTU NTU = V * ct Aβ aph y y,en y (1) (2) where the bnary overall gas mass transfer coeffcents are calculated as follow: 1 1 c m β β β V t = + V L L ct 2.2 Defnton of a mult-component mass transfer coeffcent As an analogy to the bnary two-phase dstllaton case, the followng mult-component formulaton for the HTU/NTU concept s consdered for the next steps of the calculaton: y,aus V dy V * ct Aβ aph y y,en y H= HTU NTU = (3) (4) The detaled calculaton method of mult-component mass transfer coeffcents s gven n (Taylor and Krshna, 1993), as well as the appendng overall gas formulaton: c k k M k (5) V 1 V 1 L 1 t = + L [ ] ct
Defnton of the mult-component mass transfer coeffcent The dffuson flux of the component can be rearranged to obtan an unque mass β transfer coeffcent,, called here overall gas mult-component mass transfer coeffcent. The formulaton of ths coeffcent s gven n equaton (6). k k j k k kj + kk β = 2.3 Three-phase model (6) Fgure 1. Three-phase model percepton The man dea of the method s presented n Fg. 1: In the heterogeneous case, two vapour streams are consdered, resultng from the decomposton of the lqud on the packng surface. Thus, equaton (4) can be formulated for both lqud streams n order to obtan the outlet concentratons of both defned vapour streams. H = HTU NTU = HTU NTU (7) where,1,1,2,2 HTU = V,1 V c Aβ,1 aphfr and HTU V = c A a (1 f ),2 V β,2 Ph r wth fr, the superfcal dstrbuton of both lqud phases on the packng. Calculaton of the vapour concentraton at the packng outlet The vapour concentraton y, aus obtaned at the packng outlet results from the mxng of two vapour flows connected wth the two lqud phases (see Fg. 1). y, aus can be calculated as follows: 1 2 M1 y, aus + M 2 y, aus, aus = (9) y M (8)
3. Parameter fttng To adjust the process model for the mult-component three-phase case, the exponental parameters of equaton (1) have been adjusted based on measurement data taken from the plot plant wth model based parameter estmaton technques. Generally, f measurement errors are consdered for all varables, the sze of the parameter estmaton problem ncreases lnearly wth the number of data sets. As the parameters have been evaluated for dfferent mxtures smultaneously a large number of data sets has been used n parameter estmaton. Due to the large number of data sets used, parameter estmaton becomes a dffcult task. As measurement errors have to be consdered for dependent as well as ndependent varables the parameter estmaton problem conssts of two tasks: the parameter estmaton problem tself and a data reconclaton step to rectfy errors n the ndependent varables measurements. As the ndvdual data sets are coupled over the parameters both steps can not be solved separately. Therefore the parameter estmaton problem leads to a large scale optmzaton problem where the sze of the problem ncreases lnearly wth the number of data sets. In ths study, about 500 data sets are avalable for estmatng the exponental parameters consderng measurement errors for 5 ndependent varables for each data set. A new three stage decomposton strategy has been used for parameter estmaton (Faber et al., 2003). The developed parameter estmaton approach s able to handle large-scale systems wth multple sets of measurement data. Due to the reducton of the sze of the optmzaton problem t s possble to use standard optmzaton software. 4. Results A systematc expermental nvestgaton study of three-phase operated packng was realsed to support the model development. Addtonal expermental results from past study at our department are also avalable for the parameter estmaton. A detaled descrpton of the expermental study s gven n (Vllan et al., 2003). Fgure 2. Composton trangle of the dstllaton n packed column at total reflux for 1- propanol/1-butanol/water: experment and smulaton.
Before the ntroduced method s appled for the complex heterogeneous case, t s useful to verfy the method on the ternary homogeneous dstllaton. In Fg. 2 and Fg. 3 a comparson between experment and smulaton s shown at the example of the mxture 1-propanol/1-butanol/water. The exponents m=0.718 and n=-1.038 were used for the smulaton. These values result from a parameter estmaton run wth 15 data sets. The devaton from the values gven n (Bllet, 1995) and the valdaton of the results wll be dscussed n the lecture. Fgure 3. Separaton effcency of the dstllaton of 1-propanol/1-butanol/water at total reflux wth the packng Montzpack B1-350: experment vs. smulaton Usng the estmated parameters, the model descrbes the expermental concentraton profle and the measured separaton effcency wth a suffcent accuracy to realse desgn and plannng tasks. 5. Conclusons In ths contrbuton, a short-cut method for the predctve calculaton of the separaton effcency of the three-phase dstllaton n packed column s presented. A powerful parameter estmaton procedure s used to realse an accurate model tunng wth regard of the expermental results of a systematc nvestgaton study. In a frst step, t was possble to determne parameters fttng a range of experment wth a unque mxture and dfferent knds of packng. The frst results are n good agreement wth the expermental data of the packed column. The extenson of the use of those parameters for any combnaton of mxtures and packng wll be dscussed n the presentaton and llustrated wth examples. Symbols a total surface area per unt packed volume [m 2 /m 3 ] a Ph effectve nterfacal area per unt packed volume [m 2 /m 3 ] A free cross-sectonal area of the column [m 2 ] C packng constant to allow for mass transfer [-] c t total molar concentraton [kmol/m 3 ]
D dffuson coeffcent [m 2 /s] f r superfcal dstrbuton of both lqud phases [-] h L lqud hold-up [m 3 /m 3 ] k mult-component mass transfer coeffcent [m/s] HTU heght of a transfer unt [m] M, m slope of the equlbrum curve [-] m, n expermental determned parameters [-] NTU number of transfer unts [-] u v superfcal vapour velocty [m/s] V molar vapour stream [kmol/s] β bnary mass transfer coeffcent [m/s] ε vod fracton of packng [-] ρ mass densty [kg/m 3 ] η dynamc vscosty [kg.m -1.s -1 ] Subscrpts and Superscrpts 1, 2 ndex for frst and second lqud phase n, out nlet, outlet component L lqud phase overall gas calculaton V vapour phase * equlbrum References Repke, J.-U., Vllan, O., Wozny, G., 2003, A Nonequlbrum model for three-phase Dstllaton n a packed column: modellng and experments, ESCAPE-13, Lappeenranta, Fnland. Taylor, R.; Krshna, R., 1993, Multcomponent Mass Transfer, John Wley & Sons, nc., New York. Bllet, R., 1995, Packed Towers. VCH Verlagsgesellschaft GmbH, Wenhem. Faber, R., L, P., Wozny, G, 2003, Sequental parameter estmaton for large-scale systems wth multple data sets. Part I: Computatonal Framework. Ind. Eng. Chem. Res., 42(23), 5850-5860. Vllan, O.; Repke, J.-U.; Wozny, G.: Performance characterzaton of three-phase operated packng. AIChE annual 2003, San Francsco, 16-21 November Acknowledgements Fnancal support to ths work from the Deutsche Forschungsgemenschaft (DFG) under the project contract LI806/4-3 and the German Federaton of Industral Cooperatve Research Assocatons "Otto von Guercke" (AIF) under the project contract 13251 N s gratefully acknowledged.