Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon Polymerzaon Technology Laboraory Course Resdence Tme Dsrbuon of Chemcal Reacors If molecules or elemens of a flud are akng dfferen roues hrough he volume of a connuous operaed reacor, hey wll spend dfferen mes whn such a reacor. The dsrbuon of hese holdng mes s called he resdence me dsrbuon (RTD) of he flud. The RTD can affec he performance of a reacor and may also have a srong npu on he selecvy of a chemcal reacon. In case of polymerzaon reacons he RTD can have an effec on he molecular wegh dsrbuon of he polymer formed. Ths wll be manly he case when he mean lfe me of he acve speces of he polymerzaon reacon s n he same order of magnude lke he mean resdence me of he reacor. In hs case polymers wh a narrow molecular wegh dsrbuon can only be formed n a reacor wh narrow RTD. The RTD n case of polymerzaon reacons can also play a major role f he reacon mxure s a segregaed sysem. Segregaon n he reacon mxure can easly occur f he reacon mxure s of hgh vscosy or heerogeneous naure wh elemens whch ac as ndvdual mcro reacors whou exchange of mass. The RTD of a polymerzaon reacor s herefore an mporan parameer whch may affec he performance of he reacor bu also he properes of he polymer formed.. Expermenal mehods for deermnaon of RTD Mos mporan for deermnaon of he RTD of a reacor s he applcaon of a suable racer. A suable racer should be easy o deec and he oal amoun of njeced racer should be deecable a he ex of reacor. The mos mporan mehods for he deermnaon of he RTD are he so called pulse and sep expermens. They are easy o perform and nerpre. The pulse expermens In hs case a ceran amoun of a racer s added pulse wse o he flud enerng he reacor and he concenraon-me relaon of he racer a he ex of reacor s recorded. Ths s shown schemacally n Fg.. From he balance of maeral for he reacor he mean me of he concenraon-me dsrbuon can be found. Mean me (holdng me): 0 = Cd Cd 0 C = C [s] Resdence Tme Dsrbuon (SS 2007) See /8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon nroduced amoun of racer, M [kg] Tracer concenraon [kg/m 3 ] Area = Cd = 0 C me [s ] Tracer pulse npu Reacor Tracer pulse oupu Flow rae, v [m 3 /s] V [m 3 ] Fg. : Tracer concenraon-me correlaon of a pulse expermen To fnd he RTD whch s also called he ex age dsrbuon E concenraon-me dsrbuon has o be normalzed n such a way ha he area under he dsrbuon curve s uny. For dong hs he concenraon readngs have o be dvded by he area under he concenraon curve. Ths s shown n Fg. 2. The relaonshp beween C and E curves only hold s exacly for reacors wh so called closed boundary condons. Ths means ha he flud only eners and only leaves he reacor one me. No dsperson of racer a he boundares of reacor should happen. Very ofen s convenen o use a dmensonless E θ curve for reasons of comparson of reacors. In hs case me s measured n erms of mean resdence me E = θ = /. Then E θ. C [kg/m 3 ] v E=C M [/s] Area = M/v Area = me [s] me [s] Fg. 2: Transformng he expermenal concenraon curve no he ex age curve Resdence Tme Dsrbuon (SS 2007) See 2/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon The sep expermen In hs case he racer s no nroduced pulse wse no he flud enerng he reacor bu s nroduced n a connuous way by njecng a consan sde sream of racer o he flud enerng he reacor and measurng he oule racer concenraon C versus me as shown n Fg. 3. The mean resdence me s gven by followng equaon: = C max dc Cmax 0 = dc max Cmax 0 dc C 0 Fg. 3: Tracer concenraon-me correlaon of a sep expermen The dmensonless form of he concenraon curve s called F curve or ranson funcon. Here he racer concenraon s rsng from zero o uny wh me (see Fg. 4). Fg. 4: Transformng he expermenal racer concenraon curve no he F curve (ranson funcon) Resdence Tme Dsrbuon (SS 2007) See 3/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon 2. RTD of plug flow and mxed flow reacors Fg. 5 s showng he resdence me dsrbuon of a plug flow ubular reacor, a sngle well mxed srred ank reacor and of a cascade of N equal sze well mxed srred ank reacors whch are conneced o each oher n seres. The mos narrow dsrbuon s shown by he plug flow ubular reacor and he cascade of srred ank reacors wh an nfne number of vessels. The broades RTD resuls n case of a sngle srred ank reacor. The RTD of equal szed srred ank reacors wh mxed flow s gven by he followng equaons: E = N N N ( N )! e N wh = N (N = number of reacors). F = e N + N + 2! N 2 +... + N N ( N )! ) plug flow mxed flow 2 N mxed flow n seres N= 5 5 5 θ Fg. 5: RTD of dfferen deal reacors: PFTR, HCSTR and Cascade of HCSTRs (from Levenspel) Resdence Tme Dsrbuon (SS 2007) See 4/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon 3. RTD of reacors wh non-deal flow paern In realy he flow paern of reacors devae from plug or mxed flow paerns. Ths s especally he case for polymerzaon reacors n whch a polymer soluon or dsperson wh hgh vscosy s flowng hrough he volume of reacor causng a non-deal flow paern. Non-deal flow paerns can resul for example f he reacor volume conans so called dead or sagnan regons or f bypass or recycle flow s presen nex o he acve flow hrough reacor regons of plug and mxed flow. If hese non-deal flow paerns are presen n a gven reacor hey can be seen easly by lookng a he correspondng expermenal RTD. The followng models can be used o descrbe he measured RTD of real reacors wh devaon from deal flow: Comparmen Model Dsperson Model Tanks-In-Seres Model Convecon Model (for lamnar flow) In Fg. 6 comparmen flow models are gven for a ubular and a srred ank reacor whch are characerzed by he presence of dead zones and bypass. The dsperson and anks-n-seres E E E E Fg. 6: Comparmen models for ubular and srred ank reacor wh dead zone and bypass (from Levenspel) Resdence Tme Dsrbuon (SS 2007) See 5/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon model s used n general when small devaons from plug flow are expeced. They are one parameer models. A dsperson number s used n case of he dsperson model whereas he number of srred anks s used n case of he anks-n-seres model. In Fg. 7 he correlaon beween dsperson and hydrodynamcs of dfferen lquds flowng n ppes are gven. waer Dsperson number Reynolds number Fg. 7: Correlaon beween dsperson number and Reynolds number of hree dfferen lquds flowng n ppes. Dsperson number: D ax ul, Reynolds number: ud ρ η, Schmd number: η ρd The convecon model s used f a vscous lqud s pumped hrough a ubular reacor. In general he flow s of lamnar characersc wh a parabolc velocy profle. Thus he spread n resdence mes s caused only by velocy varaons. The velocy profle of a lamnar flow s shown ogeher wh he correspondng RTD n Fg. 8. Resdence Tme Dsrbuon (SS 2007) See 6/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon L d u max = 2u 4 E θ 3 2 0 0,5,5 θ = Fg. 8: Parabolc flow velocy profle and resdence me dsrbuon of lamnar flow n ppe 4. Expermenal RTD of ubular reacor and connuous srred ank reacor 4. Pulse expermens n ubular reacor Pu selecor valve of laboraory se o ubular reacor poson Swch on conducmeer. Pu selecor swch for es daa o Srömungsrohr. Sengs of conducmeer: Temp.: 20 C Coeff%K-: Sengs of recorder: Speed: 200 mm/mn Range: 20 mv Zero lne o 90 % scales on he paper 3 measuremens a varous flow raes: 50 l/h wh,5 ml KMnO4/KCl soluon for markng 80 l/h wh,0 ml KMnO4/KCl soluon for markng 05 l/h wh 0,6 ml KMnO4/KCl soluon for markng (see dagram for flow raes). Markng soluon wh 2,5% KCl Resdence Tme Dsrbuon (SS 2007) See 7/8
Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon Before sarng each measuremen check he flow rae a he roameer and wa for consance of he zero lne. Injec he markng soluon quckly and mark he sarng pon on he recorder paper. Measuremen s fnshed a consan conducvy. 4.2 Pulse expermens n srred ank reacor: Close waer cock!!! Pu selecor valve o srred ank reacor poson Flow rae a he roameer: 60 l/h When he srrng ank s flled wh waer, swch on he srrer. Srrer: 50 and 600 RPM Reacor volume: 400 ml Sengs of recorder: Speed: 50 mm/mn Range: 20 mv Zero lne o 90 % scales on he paper 2 measuremens a each srrng rae wh and whou dead waer zone (00ml) for each expermen use 2,0 ml of he KMnO 4 /KCl soluon for markng. Markng soluon wh 25% KCl 4.3 Sep expermens n srred ank reacor: Flow rae a he roameer: 60 l/h Srrer: 200 RPM Reacor volume: 400 ml Sengs of recorder: lke 2 2 measuremens wh and whou dead waer zone (00ml ppee) for each expermen use 25% KCl soluon and he flexble-ube pump for markng. 4.4 Repor: Esmae E and F curves for all pulse and sep expermens Compare hydrodynamc resdence me ( V / V& R ) wh expermenal resdence me (mean me). Deermne nfluence of srrer speed, dead waer zone and flow rae on resdence me dsrbuon and dscuss exensve all resuls Resdence Tme Dsrbuon (SS 2007) See 8/8