European Symposum on Computer Arded Aded Process Engneerng 15 L. Pugjaner and A. Espuña (Edtors) 2005 Elsever Scence B.V. All rghts reserved. Short-Path Evaporaton for Chemcal Product Modellng, Analyss and Desgn Maurco Sales-Cruz and Rafqul Gan * CAPEC, Department of Chemcal Engneerng Techncal Unversty of Denmark, DK-2800 Lyngby, Denmark Abstract The last stage n the desgn process for a chemcal product s ts manufacture, where the purfcaton has an mportant role. Short-path evaporaton s a safe method sutable for separaton and purfcaton of thermally unstable materals. In ths work the process modellng and a systematc strategy of soluton s presented for a short-path evaporator to obtan the desred product specfcaton. The model descrbes the nfluence of the evaporator desgn and the operatonal condtons for obtanng an effcent separaton and mprovng yeld of the desred chemcal product. The model performance s llustrated wth a case study (pharmaceutcal product) usng a computer-aded modellng framework for the model analyss and soluton. Keywords: computer-aded modellng, product and process desgn, short-path evaporaton. 1. Introducton Conventonal dstllaton s one of the oldest methods to separate lqud or molten substances. However, t s not recommended for substances that can be degraded under dstllaton temperatures, such as vtamns, nsectcdes, drugs and flavours/fragrances. The short-path dstllaton s a separaton technque used as an alternatve n varous processes of the chemcal, pharmaceutcal, fragrance and food ndustry. It s a safe method sutable for separaton and purfcaton of thermally unstable materals, through a small dstance between the evaporator and the condenser, and characterzed by low temperatures, short resdence tmes of the dstlled lqud on the thermally exposed surface and suffcently low pressure n the dstllaton gap (space between evaporator and condenser). Therefore, the modellng, desgn and analyss of short-path evaporaton (or molecular dstllaton) are mportant elements n many chemcal product engneerng problems. Informaton about the flm surface temperature on the condensaton surface s mportant to determne yeld and purty of the dstlled product, as well as to defne the evaporator desgn (.e., the feed poston and the evaporator geometry). However, drect measurement on the temperature profles n the flm of the condensate s extremely dffcult, so that a key ssue s the buldng of an approprate model that can descrbe the * Author to whom correspondence should be addressed: rag@kt.dtu.dk
separaton process as a functon of the (concentraton, temperature and velocty) flm profles, and whch can be useful for operaton analyss and process desgn. Thus, the am of ths work s to present a systematc strategy for process modellng wth partcular emphass n analyss and desgn of short path dstllaton, to establsh the operatonal condtons for obtanng an effcent separaton, mprovng yeld and purty of the desred chemcal product. As startng pont, a mathematcal model s developed based on mass, heat and momentum balances for mult-component mxtures, resultng n a set of PDAEs (Partal Dfferental Algebrac Equatons). The model analyss, model soluton and model verfcaton are done usng a computer aded modellng system called ICAS-MoT. Through the model analyss, t s possble to understand how the feed concentraton, the feed temperature, the heatng surface, the system pressure and evaporator dmensons (length and gap) affect the flm temperature profle, the flm thckness, the evaporaton rate and the evaporaton yeld. As a case study, the purfcaton of an actve pharmaceutcal ngredent from a sx-component mxture s presented. 2. Short-path evaporator 2.1 Process descrpton The short-path separator conssts of a cylndrcal body surrounded by a cylnder, one of them acts as evaporaton surface and the other as condensaton surface (see Fgure 1a). The lqud materal to be dstlled s fed n the evaporaton wall. The evaporaton and condensaton surfaces are kept at constant temperatures T w1 and T w2, respectvely. Due to the low pressure nsde the separator, a fallng flm (wthout bolng) s formed and the concentraton and temperature profles (see Fgure 1b) of the most volatle compounds decrease n the axal and radal drectons. Fgure 1. (a) The short-path evaporator, (b) temperature profle and (c) velocty profle.
2.2 Mathematcal Model Let consder the lqud flms on the evaporaton and condensaton walls are much thnner than the correspondng cylnder dameters then rectangular coordnates can be used. The mathematcal model for the short-path evaporator under steady state comes from momentum, energy and mass balances for both evaporaton and condensaton flms as follows (Lutšan et al, 2002). 2.2.1 Momentum balance In most cases of short-path evaporaton, the evaporatng lqud s hghly vscous and hence the Reynolds numbers are small. The Naver-Stokes equaton (at steady state) for lamnar regmen descrbes the velocty profle (see Fgure 1c) of fallng flm 2 v y, z vz 2 y g Ths has the followng boundary condtons max v 0, z 0, v y, z v (2) Where v s the velocty, g s the gravty constant, and y and z s the radal and axal coordnates respectvely. 2.2.2 Energy balance The temperature (T) profle n the fallng flm s gven by the equaton v y, z, 2, 2, T y z T y z T y z 2 2 (3) z Cp y z Wth boundary condtons 1 T y,0 TF, T 0, z Tw, T y z y, vap yh1 H Where,,C p, H vap are the thermal conductvty, densty, thermal capacty and heat of evaporaton of the multcomponent mxture respectvely. 2.2.3 Mass balances The composton (C ) profles for each component are calculated from the dffuson equaton, 2, 2, C y z C y z C y z vy, z D N 2 2, 1,, z y z Where D s the (constant) dffuson coeffcent for the -th component. The boundary condtons for Eq. (5) are,0, C y C, o C 0, z y 0, k C y, z D y yh1 2.2.3 Rate of evaporaton The flow rate I for each component s descrbe by the contnuty equaton (1) (4) (5) I z (6)
I z z 2 Rk, 1,, N (7) Where the effectve rate of evaporaton (k ) s calculated through a modfed Langmur- Knudsen equaton (Kawala and Stephan, 1989) z vap p n Ts z P h k 11F1 e, 1,, 2 RMT P N (8) g s ref It contans a factor (P/P ref ) for correctng the vacuum pressure, as well as a correcton that takes nto account the ansotropc propertes of the vapour, where s the mean path of vapour molecule, h s the dstllaton gap, n s the number of ntermolecular collson, F s the surface rato and s the ansotropy of the vapour phase gven by Ak F A A k V 4, log 0.2F 1.38 f 0.1 (9) A k and A v are the condensaton and evaporaton areas, respectvely. The effectve rate of evaporaton [Eq. (7)] also depends on some mxture propertes (the vapour pressure p vap and molecular weght M of each compound) as well as on desgn parameters (the radus of the evaporator nsde cylnder R and the surface temperature T s ). 2.2.4 Thckness flm Fnally, an mportant varable of nterest s the thckness flm (h 1 ) along the evaporator heght that s calculated as follows (Kawala and Stephan, 1989) N N 3 h 3 1 z Iz, Iz I z, c C z (10) 2 R g c 1 1 where s the knematc vscosty of the multcomponent mxture. 3. Strategy of Soluton 3.1 Computer-aded modellng framework It s useful to take advantage of Computer-Aded Modellng Systems (CAMS) and tools for ntegrated process analyss, to reduce the tme to market and nvestment costs, and to acheve a successful ntegrated product and process desgn through n a fast, relable and effcent way. In partcular, ICAS-MoT s used n ths work that s an ntegrated modellng envronment to buld, analyse, manpulate, solve and vsualse mathematcal models. An mportant feature of ICAS-MoT s that the model developer does not need to wrte any programmng codes to enter the model equatons. Models are entered (mported) as text-fles or XML-fles, whch are then nternally translated. In model analyss step ICAS-MoT orders the equatons nto lower trangular form (f feasble), generates the ncdence matrx, verfes the degrees of freedom, and checks for sngularty. After ths nteractve model analyss, the approprate solver for the model equatons s selected together wth a correspondng strategy of soluton. As solver optons, ICAS-MoT provdes several solvers for AEs (algebrac equatons), DAEs (dfferental algebrac equatons) and numercal optmsaton methods. More detals can be found n Sales-Cruz and Gan (2003).
3.2 Model dscretsaton In order to solve the evaporator model that nvolves PDAEs [Eqs. (1)-(10)], method of lnes usng centered fnte dfference s appled consderng an M-pont dscretsaton scheme for the radal coordnate y as shown n Fgure 2 (Cvengroš et al, 2000). Good performances can be acheved wth a mnmum value of M = 10. Afterwards, the resultng DAE system s solved through ICAS-MoT usng the Backward Dfference Formula method. One partcular advantage of the ntegrated ICAS s that all physcochemcal propertes are recalled from modules that can be easly ntegrated to the short-path evaporator model. Therefore a large number of chemcal products can be studed very fast and wth mnmum effort. 4. Model evaluaton 4.1 Case study: a pharmaceutcal mxture Consder the process producton of a drug where after the reacton stage, the actve molecule of the actve pharmaceutcal ngredent (API) s formed. Then the resultng lqud mxture composed of sx heat senstve compounds (that are called A, B, C, D, E and F for confdentally reasons) needs to be purfed. A s the lghtest and more volatle compound and F s the one wth the hghest bolng pont. The role of the short-path evaporator s to separate the actve molecule (form manly by C, D and E) together wth the nert component F from the feed multcomponent mxture comng from the reactor. 4.2 Model analyss The classfcaton of varables and model equatons was done through ICAS-MoT as follows: (a) there are 128 equatons sorted as 17 ODEs, 1 mplct and 110 explct AEs, and (b) 306 varables sorted as 17 dependent, 1 unknown, 4 known, 174 parameters, and 110 explct. Afterwards, the ncdence matrx, degrees of freedom and non-sngularty were verfed to ensure that the problem was not ll-posed before gong to the soluton step. 4.3 Smulaton results The feed flows as well as expermental and calculated flows of the dstllate and resdual are reported n Table 1, where t can be seen that the model s able to predct qute satsfactory the ext flow rates. Table 1. Expermental and calculated flow rates of dstllate and resdual. Compound Expermental flows (kmole/h) Calculated flows (kmole/h) Feed I 0 Resdual I R Dstllate I D Resdual I R Dstllate I D A 6.11x10-5 0.0 6.11x10-5 0.0 6.11 x10-5 B 1.22x10-5 0.0 1.22x10-5 0.0 1.22 x10-5 C 4.72x10-2 4.46x10-2 2.61x10-3 4.46x10-2 2.61 x10-3 D 1.90x10-4 1.88x10-4 2.09x10-6 1.87x10-4 3.07 x10-6 E 2.17x10-3 2.16x10-3 6.79x10-6 2.14x10-3 2.46 x10-5 F 6.66x10-4 6.66x10-4 0.0 6.66x10-4 0.0
As the chemcal product (C, D, E and F) s obtaned as the resdual n the short-path evaporator, then the surface velocty, temperature, thckness and some flow rates are shown for the evaporatng flm n Fgures 2. The rse n temperature (Fgure 2a) s related to the evaporaton of compounds A and B as can be seen n Fgure 2b. In fact, A and B are the man compounds that are evaporated from the mxture and are obtaned as dstllate product. The surface velocty (Fgure 2a) has a rapd ncrease at the frst part of the evaporator axal poston achevng a maxmum pont, and then decreasng slghtly due to the decrease of the total evaporaton rate. Fgure 2b also shows the dependence of the flm thckness throughout evaporator cylnder axs. Flm thckness decreases wth the ncreasng surface temperature due to evaporaton. Both flm surface temperature and flm thckness turn asymptotc as soon as a constant flm thckness has formed. 0.080 405 126 20 Surface velocty v (m/s) 0.079 0.078 0.077 0.076 0.075 0.00 0.02 0.04 0.06 0.08 0.10 Axal poston z (m) 400 395 390 385 Surface temperature T s (K) Flm thckness h 1 (m) x 10-6 124 122 120 118 116 0.00 0.02 0.04 0.06 0.08 0.10 Axal poston z (m) compound B compound A 15 10 5 0 Flow rate, I R, (mol/s) x 10-6 Fgure 2. (a) Surface velocty and temperature, (b) Flm thckness and flow rate for compound A. 5. Conclusons A short-path evaporator model has been presented for the purfcaton of multcomponent mxtures. The modellng methodology presented llustrates how the desgn and analyss aspects of a short-path evaporator are related to the purty and stablty of the chemcal product and the correspondng condtons of operaton. The process flexblty allows desgnng the separator n such way that the mxture to be separated can be fed ether n the cylndrcal body or n the outsde cylnder wall, dependng on whether the chemcal product need to be recovered as a dstlled product or concentrated as the heavy resdue. On the other hand, the results also hghlght the mportance of a general-purpose and easy to use modellng toolbox for computer-aded desgn and analyss of complex process operatons. References Cvengroš J., J. Lutšan and M. Mcova, 2000, Feed temperature nfluence on the effcency of a molecular evaporator, Chemcal Engneerng Journal, 78, 61 67. Lutšan J., J. Cvengroš and M. Mcov, 2002, Heat and mass transfer n the evaporatng flm of a molecular evaporator, Chemcal Engneerng Journal, 85, 225 234. Kawala Z. and K. Stephan, 1989, Evaporaton Rate and Separaton Factor of Molecular Dstllaton n a Fallng Flm Apparatus, Chem. Eng. Technology, 12, 406-413. Sales-Cruz, M. and R. Gan, 2003, Computer-Aded Chemcal Engneerng, vol. 16: Dynamc Model Development, Eds. S.P. Asprey and S. Macchetto, Elsever, Amsterdam.