** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand


 Terence Mills
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1 Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl Engineering, Ksetsrt University, mpus Box 1198, St. Louis,Missouri 63130, US ** Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd ++ Dpt. hemicl Engineering, Ksetsrt University, mpus Box 1198,St. Louis,Missouri US strct In TP Experiment, interprettion of TP trnsient response dt is crucil nd requires theoreticl development. In this pper, we develop method for estimtion of the numer of ctive sites of the ctlyst smple from the zeroth moment of the exit flow of rectnt gs for the irreversile dsorption cse. n pproximte nlyticl expression for the chnge in the zeroth moment of the gs exit flow with respect to the pulse numer is presented. The vlidity of the expression is investigted y compring with the numericl simultion results. Results otined from numericl clcultions re shown to e in good greement with the pproximte solution in wide domin of prmeters, i.e., the dsorption rte constnt nd the ctlyst numer. Key words: TP, Temporl nlysis of Products, Irreversile dsorption. 1 Introduction The TP ( Temporl nlysis of Products ) rector system [1, ] hs een recognized s powerful tool for heterogeneous kinetic studies. The experiment is performed y injecting nrrow gs pulse into n evcuted microrector contining solid ctlyst smple. t the rector exit, the gs molecules re monitored s function of time with qudruple mss spectrometer (QMS) nd produce trnsient response t the spectrometer detector. The intensity of the trnsient response is proportionl to the exit flow of the corresponding gs. The size nd shpe of the response consequently depend on the trnsport nd kinetic nd chrcteristics of the system. n importnt tsk in performing this type of experiment is the interprettion of experimentl responses. urrently, most theoreticl TP studies hve een focused on interprettion of single pulse. They involve determintion of nlyticl solutions to the equtions tht mke up mthemticl models [1,, 3, 4, 5, 6]. The solutions cn then e used to nlyze the chrcteristics of TP trnsient response curves. numer of importnt theoreticl results cn lso e otined from simultion study [, 7] re they cn e used for primry interprettion of the experimentl responses.
2 TP experiments usully involve monitoring the grdul chnges in the size nd shpe of sequentil experimentl response during numer of pulses. Those chnges ssocite with chnges in rectnt conversion nd product production rtes. The chnges cn lso ssocite with chnges in the ctlyst. This experimentl mode, the multipulse TP experiment, cn provide useful informtion on the nture of the ctlytic system. Development of multipulse TP theory will gretly utilize this type of trnsient experiments. In this pper, we focus on determintion of the numer of ctive sites of the ctlyst. n pproximte nlyticl solution for estimtion of the numer of ctive sites of the ctlyst smple from the chnge in zeroth moment of the exit flow of the rectnt gs for irreversile dsorption cse is presented nd compred with the numericl solutions. The differences of the clcultion results otined from the pproximte expression nd from the numericl simultion re quntittively chrcterized nd the domin of prmeters in which the pproximte expression works stisfctorily is reported. Irreversile dsorption Model The multipulse TP model studies in this work is the typicl irreversile dsorption model. The process of titrtion is nlogous to this process. From the mthemticl point of view, these processes re identicl. When the dsorption rte is first order in gs concentrtion nd surfce concentrtion, the mss lnce for gs nd dsored species in n isotherml TP rector uniformly pcked with nonporous ctlyst cn e descried y (1) = De Sv (1 ) k S t z S () = k S t The concentrtion of the unoccupied ctive sites, S, nd concentrtion of dspecies on the ctlyst surfce, S, re relted to frctionl surfce coverge y (3) S = s ( 1 θ ) (4) S = s θ Sustituting equtions (3) nd (4) into equtions (1) nd () gives (5) = De (1 ) (1 ) ssv k θ t z (6) θ = k ( 1 θ ) t Initil nd oundry conditions re s followed: Initil condition: (7) t = 0, = 0 (8) t = 0, θ z) = θ ( ) (, m 1 z
3 Boundry conditions: p (9) z = 0, De = δ ( t) z (10) z = 0, = 0 Eqution (9) indictes tht the inlet flux of gs cn e represented y delt function plced t + th t = 0 Eqution (8) indictes tht the frctionl surfce coverge fter ( m 1) pulse in the initil th conditionl for m pulse nd θ, 0 ( z) = 0. eqution (5) to (10) cn e expressed in terms of the following dimensionless prmeters: Dimensionless xil coordinte: (11) ξ = z L Dimensionless concentrtion: (1) = p / L The dimensionless concentrtion is pulseintensitynormlized gs concentrtion: Dimensionless time: tde (13) τ = L The dimensionless pprent dsorption rte constnt is defined s L (14) k = k De The pprent dsorption rte constnt, k ( s 1 ) is defined s ssv ( 1 ) k (15) k = The ctlyst numer: ssv (16) α = ( 1 )L p The ctlyst numer is the rtio of the numer of ctive sites nd the numer of gs molecules in the inlet pulse. The dimensionless from of eqution (5) cn then e written s (17) = k (1 ) θ τ ξ Eqution (6) cn e written in dimensionless from s θ (18) α = k ( 1 θ ) τ Initil nd oundry conditions, eqution (7) to (10), re written in dimensionless form s Initil conditions:
4 (19) 0 ξ 1, τ = 0, = 0 (0) 0 ξ 1, τ = 0, = 0 Boundry conditions: (1) ξ = 0, (t) ξ = δ () ξ = 1, = 0 Since the quntity tht cn e mesured in rel experiment is the gs exit flow, the solution for the dimensionless exit flow of gs is determined. The dimensionless exit flow of gs, defined y (3) (4) F cn e clculted y F F = F L = ξ 3 Results nd discussion The zeroth moment of the dimensionless exit flow of gs, ( M o ), is descried y p D ξ =1 e F,is (5) M o = F 0 dτ M o is therefore the re of the F vs. τ curve. It should e noted tht the conversion or frction of gs tht is irreversily dsored for ech pulse is equl to ( 1 M 0 ). Experimentlly, M o cn e clculted from the output response. Thy ctlyst numer cn e determined y pulsing the rectnt gs until the ctlyst smple is sturted, nd the ctlyst numer is equl to sum of the conversions of ll the pulses. It would e useful to look for simple method to estimte the ctlyst numer, nd consequently the numer of ctive sites when the numer of molecules or moles of the gs in the pulse is know, from the experimentl output response during first severl pulses other
5 Figure 1: Vlidity of the pproximte eqution within the first twenty pulse; the region on the right of ech curve represents the domin of dimensionless rte constnt ( k ) nd ctlyst numer (α ) in which the pproximte eqution is vlid ccording to the specified percentge difference, nd vice vers thn pulsing until the ctlyst is sturted. For typicl TP experiment, determined from the response of the first pulse y the simple eqution [8] k cn e 1 (6) M o = cos k tht is sed on the ssumption tht the occupied surfce coverge is very smll during the pulse nd consequently (1  θ ) is closed to until throughout the rector. It hs een expected tht the decrese of the zeroth moment of the exit flow of gs with to the pulse numer would provide informtion of the ctlyst numer. This pper focuses on determintion of the reltion etween d M o / dm nd the pulse numer (m). n eqution tht reltes d M o / dm to the ctlyst numer is derived y the perturtion method nd is given y (7) d M o 1 = dm α k tnh k (cosh 3(cosh k ) k 1)
6 Eqution (7) cn e used to estimte the ctlyst numer from the chnge in the zeroth moment with respect to pulse numer during the first severl pulses in multipulse TP experiment. However, since it ws derived y the perturtion method, it is good for lrge ctlyst numer (or smll 1/α ). Eqution (7) ws therefore investigted y compring with the numericl simultion results in order to determine the domin of α in which eqution (7) works stisfctorily. It ws found tht the percentge differences etween d M o / dm clculted y eqution (7) nd d M o / dm from numericl simultion increses with k nd pulse numer (m). Figure 1 shows three curves for three percentge differences. Ech curve divides the domin of k nd α into two regions; the region on the right of ech curve represents the domin of k nd α in which eqution (7) grees with the numericl simultion results within the percentge difference specified for ech curve, nd vice vers. Figure 1 is good for m up to 0. The vlue of k equl to 100 corresponds to conversion of percent. In typicl multipulse TP experiment, α is not lrger thn onclusion n pproximte expression for the chnge in the zeroth moment of the gs flow with respect to the pulse numer for irreversile dsorption cse in multipulse TP experiment is presented. The vlidity of the expression is nlyzed y compring with the numericl simultion results. The expression is shown to e vlid in wide domin of the dsorption rte constnt nd the ctlyst numer. This simple expression is useful for estimtion of the ctlyst numer, nd, consequently, ctive sites of the ctlyst smple when the numer of moles of the rectnt gs in the inlet pulse is known. 5 cknowledgment We re grteful to the Thilnd Reserch Found nd the Ksetsrt University Reserch nd Development Institute for their finncil support. We lso cknowledgment Prof. Gregory S. Ylonsky for mny fruitful discussions. 6 omenclture s Surfce concentrtion of the ctive sites (mol / cm of ctlyst ) ross sectionl of the ed ( cm ) oncentrtion of gs (mol / cm 3 ) S oncentrtion of the unoccupied ctive site (mol / cm of ctlyst ) S oncentrtion of dspecies (mol / cm 3 of ctlyst )
7 Dimensionless concentrtion, defined y eqution (1 ) D e Effective Knudsen diffusivity of gs F Exit flow of gs (mol / s) F Dimensionless exit flow of gs defined y eqution (3) k dsorption rte constnt (cm 3 of gs/mols) k Dimensionless pprent dsorption rte constnt, defined y eqution (14) k pprent dsorption rte constnt defined y eqution (15) (s 1 ) L Rector length (cm) m Pulse numer M o Zeroth moment of the dimensionless exit flow of gs defined y eqution (5) p umer of moles of the rectnt gs in the inlet pulse (mol) S v Surfce re of the ctlyst per volume of ctlyst (cm 1 ) t Time (s) z xil coordinte of the rector (cm) α tlyst numer, the rdio of the numer of ctive sites nd numer of gs molecules in the inlet pulse δ () t Delt function plced t t = 0 + Frctionl voidge of the ed θ Frctionl surfce coverge of the dspecies θ, m 1( z) Frctionl surfce coverge of dspecies fter ( m 1) pulse ( θ, 0 ( z) = 0 ) τ Dimensionless time defined y eqution (13) ξ Dimensionless xil coordinte, defined y eqution (11) References [1] J.T. Gleves, J.R. Ener, nd T.. Kuechler, Temporl nlysis of Products (TP) unique ctlyst evlution system with sumillisecond time resolution, tl. Rev. Sci., 30 (1988), pp [] J.T. Gleves, G.S. Ylonskii, P. Phnwdee, nd Y. Schuurmn, TP: n interrogtive kinetics pproch, pplied tlyst : Generl, 160 (1997), pp [3] J.P. Huinink, J.H.B.J. Hoelink, nd G.B. Mrin, Pulse experiment over ctlyst eds; window of mesurle rection rte coefficient, n. J. hem. Eng.74 (1996), pp [4] G.S. Ylonskii, I.. Ktz, P. Phnwdee, nd J.T. Gleves, Symmetricl cylindricl model for TP pulse response experiments nd vlidity of the onedimensionl model, Ind. Eng. hem. Res., 36 (1997),
8 [5] G.S. Ylonskii, S.O. Shekhtmn, S. hen, nd J.T. Gleves, Moment sed nlysis of trnsient response ctlytic studies (TP experiment), Ind. Eng. hem.res., 37 (1998), pp [6] P. Phnwdee, G.S. Ylonsky, P. Preechsnongkit, nd K. Somp, new correltion for determintion of the effective Knudsen diffusivity of gs in TP rector, Ind. hem. Res., 38 (1999), pp [7] M. Rothemel, nd M. Berns, Modeling nd simultion of trnsient dsorption nd rection in vcuum using the Temporl nlysis of Products rector, Ind. Eng. hem.res., 35 (1996), pp [8] G.D. Svood, Fundmentl trnsportkinetic models for interprettion of TP rector response dt with ppliction to rective systems, Doctorl Disserttion, Wshington University, 1993.
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