INFLUENCE OF AXIAL MIXING AND PARTICLE SIZE NON-UNIFORMITY ON PERFORMANCE OF CHROMATOGRAPHIC REACTORS

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1 14 th European onference on Mxng Warszawa, 1-13 September 1 INFUENE OF XI MIXING N PRTIE SIZE NON-UNIFORMITY ON PERFORMNE OF HROMTOGRPHI RETORS Eugenusz Molga, Mchał ewak, nna Ostanewcz-ydzk Warsaw Unversty of Technology, Faculty of hemcal and Process Engneerng, ul. Warynskego 1,-645 Warszawa, Poland e.molga@chp.pw.edu.pl bstract. mathematcal model of the reactve chromatography process has been elaborated to study an nfluence of axal mxng on the reactor performance. Four seres of numercal smulatons have been executed for dfferent reactor packng. It has been found that axal mxng, ntensfed by partcle sze non-unformty, ncrease of the eluent velocty and ncrease of the packng partcle dameter, plays a sgnfcant role deteroratng the key reactant converson and the separaton of products. Useful measures to quantfy these effects have been proposed. eywords: reactve chromatography, chromatographc reactors, axal mxng, partcle sze nonunformty 1. INTROUTION Intensfcaton of processes by ntegraton of unt operatons wth chemcal reactons s now wdely nvestgated as well as employed n laboratory and ndustral practce [1]. The reactve chromatography process ntegrates the chemcal or bochemcal reacton wth smultaneous chromatographc separaton of the reacton products. Such ntegraton, due to removal of products from the reacton zone, helps to mprove the yeld of reversble reactons and smultaneously supples reacton products of hgh purty. Nevertheless, evdent advantages of process ntegraton at some conons can be mnmzed due to a reducton of freedom degree, whch s caused by the fact that operatng conons optmal for carryng out the reacton are usually dfferent than those used for separaton process []. ue to ths problem, for some cases and at some operatng conons, effcent process ntegraton s even mpossble. xal mxng of lqud flowng through the bed of chromatographc reactors can sgnfcantly deterorate the converson of reactants and the purty of obtaned products. Ths unproftable nfluence of axal mxng can be partcularly crucal n chromatographc reactors, n whch the actve bed conssts of a mxture of the adsorbent and the catalyst partcles. In such a bed the partcle sze non-unformty s dffcult to avod and augments axal dsperson ntensty [3]. In ths study an nfluence of axal mxng on effcency of the reactve chromatography has been nvestgated for processes carred out n reactors flled wth packng partcles of unform and non-unform sze, respectvely. 35

2 . RETOR MOE seres of numercal tests have been carred out to quantfy an nfluence of axal mxng on the effcency of chromatographc reactors, whch work wth lqud movng phase. To ths end the reactve chromatography process carred out n the column chromatographc reactor wth fxed bed and mpulse dosng of one reactant has been consdered. Such type of the chromatographc reactor, due to ts poor yeld, has no practcal applcatons but t s very sutable to nvestgate the process propertes. The followng reversble reacton has been chosen for tests: (1) When the acdc on exchange resn s used as the catalyst, the reacton rate equaton can be expressed as follows [4]: ' q q r k q q () ' e In the case when the reactant s used as an eluent, ts concentraton along the reactor bed remans practcally constant due to a large excess, so: c c and o q q. Therefore, the o knetc equaton () can be smplfed just ncorporatng ths constant concentraton q nto o the new constants k and e gvng: q q r k q (3) e The on exchange resn s usually used as a b-functonal packng, because due to a dfferent affnty of products to the sold phase t works smultaneously as the adsorbent. In numerous processes of reactve chromatography, due to relatvely low concentratons of reactng speces =, and, the lnear adsorpton equlbrum can be assumed, gvng: q c (4) It has been found that for the consdered process, whle a b-functonal on exchange resn s appled, ths resn works smultaneously as the catalysts and the adsorbent, adonally both, the reacton and adsorpton, take place at the outer surface of packng partcles [5]. Therefore, n the elaborated reactor model, nternal mass transfer resstances are not taken nto account and the followng stage processes have to be only consdered: - dspersve plug flow of lqud n vods between packng partcles, - mass transfer from the lqud phase to the surface of the sold phase, - adsorpton on the surface of packng grans, - catalytc reacton at the surface of packng grans. Further, from a detaled qualtatve and quanttatve analyss carred out elsewhere [6] t has been found that an nfluence of two stage processes - external mass transfer resstances and the adsorpton rate - on the entre reactve chromatography process can be neglected f packng partcles d p < [m] and ntersttal lqud velocty u < [m/s]. So, takng above nto account, n the consdered chromatographc reactor for each -th reactng speces the followng mass balance equaton can be formulated: c u x c x 1 q 1 c r t t (5) 36

3 ecause external mass transfer resstances can be neglected and the adsorpton equlbrum assumed, the concentratons q appearng n Eq. 5 are replaced wth use Eq. 4 gvng: c c 1 c 1 u 1 k c c c (6) x x e t Eq. 6 can be solved usng the approprate ntal and boundary conons. So, takng nto account that, at the tme moment t = the reactor column does not contan any reactng speces we have: c (,, whle at t > the anckwerts boundary conons are employed as follows: u c c t, t u c t,, and x c t, (7, 8) x Notce that for each compound the concentraton c ( t, ) n Eq. 7 s always equal to zero, except for the compound durng the njecton (dosng) tme, when for < t < t dos we have: 3 c ( t, ) c, o moldm. Solvng Eq. 6 the concentraton profles of reactng compounds along the reactor bed can be obtaned. In general case the actve packng of chromatographc reactor conssts of a mxture contanng two knds of grans: adsorbent and catalysts partcles, respectvely. So, t s dffcult to secure for the same sze of both partcle types. Partcle sze non-unformty causes n turn a decrease of the bed porosty as well as an ncrease of the axal dsperson coeffcent. oth these effects can be quanttatvely estmated wth results gven n the paper [3]. To model a performance of the chromatographc reactor flled wth a mxed packng the followng equaton can be used: c u x c x k c e c c 1 c t 1 X 1 X 1 (9) where X s the volumetrc fracton of the adsorbent partcles n the sold phase. Eq. 9 s vald wth assumptons as gven above for a b-functonal packng and can be solved wth ntal and boundary conons the same as prevously. 3. RESUTS N ISUSSION Four seres of numercal smulatons have been executed, each for the sothermal process carred out n the column reactor of nner dameter d T = [m] and length =.3 [m]. Four types of beds conssted of dfferent type of packng have been checked. Propertes of these beds are gven n Table 1. Table 1. Propertes of chromatographc reactor packng nvestgated n ths study. Seres Packng type Partcles sze d p. 1 6 [m] d cat. 1 6 [m] d F. 1 6 [m] X 1 b- functonal unform b- functonal unform b- functonal unform adsorbent-catalyst mxture nonunform [3] 37

4 c /c o c /c o c /c o c /c o ll smulatons have been carred out for the reacton knetcs descrbed wth Eq.3, where the followng values of constants have been utlzed: k =.3 [s -1 ] and e = 6. [mol dm -3 ], whle the values of adsorpton equlbrum constants appearng n Eq. 4 have been taken as: =.94, =.5 and =.7. These values of constants are characterstc for the hydrolyss reacton of esters carred out at the temperature T = 98 [5]. For the purpose of ths study, for beds conssted of unform partcle sze the axal dsperson coeffcents have been estmated wth use of the correlaton proposed by hung. 48 and Wen [7]: Pe..11Re. For the bed beng a mxture of the adsorbent and the catalyst partcles of dfferent dameters: d p and d cat, respectvely (seres see Table 1) the axal dsperson coeffcent has been calculated as:, non unform, unform, where, unform has been calculated from the hung-wen correlaton takng the volumetrc average partcle dameter d F. To take nto account an nfluence of partcle sze non-unformty on the axal dsperson coeffcent the value of correcton factor = 1.71 has been estmated from [3]. Performance of the chromatographc reactor s shown n Fg. 1, where concentraton profles of each reactng compound as measured at dfferent cross secton of the reactor bed are shown. progressve converson of the key reactant durng ts shft along the reactor column can be observed n these dagrams. Notce, that due to a dfferent affnty of the compounds and to the sold phase they are successvely separated. However, an nfluence of the axal dsperson on a spread of the peak and s also vsble.e. due to axal mxng a spread of each peak ncreases. espte of reversblty of the consdered reacton, due to removal of the product from the reacton zone, the key reactant s almost totally converted.,3,5,,3,5,,3,5, z = x/ =.33,3,5, z = x/ =.5 z = x/ = 1 z = x/ = a. x/ =.33 b. x/ =.5 c. x/ =.75 d. x/ = 1 Fgs.1a-1d. oncentraton profles for reactng compounds at dfferent cross sectons of the reactor bed as a functon of the dmensonless tme. Seres, u o =.15 m/s. n nfluence of the operatng conons, so also nfluence of the axal mxng, on a performance of the consdered chromatographc reactor can be quantfed usng statstcal moments of peaks and the followng measures are defned: 38

5 - converson of the key reactant x c ( t, 1 (1) c ( t,) - resoluton of the products and R 1, ( 1, ( ( (11) ( ( ( ) ( ( ( ), 1,,, - effectveness factor for the demanded product t o QE c t, t1 (1) P where t 1 and t n the ntegral of Eq. 1 are tme borders lmtng the peak zone, for whch a purty of the collected product s not lower than the requested one, whle P o s a number of moles of the key reactant added nto the reactor. For each -th reactng compound the approprate n-order statstcal moment appearng n Eq.11 can be estmated as follows: n t c ( t, ( (13) n, c ( t, comparson of the and values obtaned for packng conssted of unform and nonunform partcles, respectvely are shown n Fgs. a-b. Ths comparson ndcates that, ndependently on the partcle sze unformty, at low eluent veloctes u o almost complete converson of the key reactant s always observed. Whle at that low veloctes a dstnct nfluence of partcle sze non-unformty on the effectveness factor can be observed due to more ntensve axal mxng n such non-unform packng. 1, 1, 1,9,8 1,8,6,4 3,7,, u o [m/s], 1E-5 1E-4 1E-3,1 u o [m/s] a. b. Fgs.a-b. omparson of the converson and the effectveness factor obtaned n the reactor flled wth the packng of unform partcle sze (Seres 1-3) and non-unform one (Seres ). s t s shown n Fgs. a, at very low eluent velocty u o almost complete converson of the key reactant s observed, whle ncreasng u o the converson decreases due to a decrease of the reacton (resdence) tme. In Fg. a, a dstnct nfluence of partcle sze nonunformty - so more ntensve axal mxng - on the converson s also vsble. It s clear 39

6 that to lmt an nfluence of the axal mxng, the packng bed of the chromatographc reactor should consst of partcles of the same sze. decrease of eluent velocty n the reactor bed has two opposte effects: t helps to deterorate a sgnfcance of axal dsperson, so mprove separaton of products, but smultaneously t decreases the productvty. To take above nto account the effectveness factor has been defned as n Eq. 1. Values of ths factor vs. the eluent velocty obtaned for all nvestgated reactor packngs are plotted n Fg. b. lso a dstnctve nfluence of the axal mxng can be observed. 4. SUMMRY n nfluence of the axal mxng on effectve operaton of chromatographc reactors has been quanttatvely studed. For ths purpose, a useful model based approach has been proposed as well as four seres of numercal smulatons executed. The obtaned results ndcate that an nfluence of the axal mxng - ntensfed by ncrease of the eleunt flow velocty, partcle sze and/or partcle sze non-unformty on the reactor performance s sgnfcant. The elaborated method can be used to optmze the reactve chromatography process. 5. NOMENTURE c - concentraton of the -th speces n the sold phase, mol dm -3 d p - dameter of adsorbent partcles, m d F - average dameter of packng, m d cat - dameter of catalyst partcles, m - axal dsperson coeffcent, m s -1 k - reacton rate constant (Eq. ), dm 3 mol -1 s -1 k - reacton rate constant (Eq.3), s -1 e - chemcal equlbrum constant (Eq.), - e - chemcal equlbrum constant (Eq.3), mol dm -3 - adsorpton equlbrum constant, - q - concentraton of the -th compound per unt volume of the sold phase, mol dm -3 Q E - volumetrc flow rate of the eluent, dm 3 s -1 r - reacton rate per unt volume of the sold catalyst, mol dm -3 s -1 u - ntersttal lqud velocty, m s -1 u o - supersttal lqud velocty, m s -1 t - tme, s X - volume fracton of the adsorbent partcles n the sold phase, - - bed porosty,- 6. REFERENES [1] Sundmacher., enle., Sedel-Morgenstern, 5, Integrated hemcal Processes, Wley-VH Verlag GmbH & o.ga, Wenhem. [] Schembecker G., Tlatlk S., 3. Process synthess for reactve separaton, hem. Eng. Process., 4, [3] Wrońsk S., Molga E., xal dsperson n packed beds: the effect of partcle sze non-unformtes, hem. Eng. Process.,, [4] Yu W., Hdajat. and Ray.., 4. etermnaton of adsorpton and knetc parameters for methyl acetate esterfcaton and hydrolyss reacton catalyzed by mberlyst 15, ppl. atalyss : General, 6, [5] ach M., 9. Integraton of chemcal processes n chromatographc reactors, Ph Thess, Warsaw Unversty of Technology, Warsaw. [6] Molga E., 8. Modellng of reactve adsorpton processes, hem. Proc. Eng., 9, [7] hung S.F., Wen.Y., ongtudal dsperson of lqud flowng through fxed and fludzed beds, IhE Journal,,