ISOTHERMAL REACTOR DESIGN (4) Marcel Lacroix Université de Sherbrooke

Transcription

1 ISOTHERML RETOR DESIGN (4) Marcel Lacroix Université de Sherbrooke

2 ISOTHERML RETOR DESIGN: OBJETIVE TO DESIGN VRIOUS TYES OF IDEL ISOTHERML RETORS USING THE FOLLOWING TOOLS: 1. MOLE BLNE OR DESIGN EQUTION: ( r, V, X ). RTE LW: r f ( ) 3. STOIHIOMETRY: g(, X, ε ) 4. OMBINTION OF THE BOVE TO DETERMINE VOLUME V OF RETOR FOR HIEVING ONVERSION X. M. Lacroix Isothermal Reactor Design

3 DESIGN STRUTURE FOR ISOTHERML RETORS 1. LY THE GENERL MOLE BLNE EQUTION. TO RRIVE T THE DESIGN EQUTION; IF THE FEED ONDITIONS RE SEIFIED (N OR F ), LL THT IS REQUIRED TO EVLUTE THE DESIGN EQUTION IS THE RTE OF RETION S FUNTION OF ONVERSION T THE SME ONDITIONS S THOSE T WHIH THE RETOR IS TO BE OERTED (TEMERTURE ND RESSURE). WHEN r f(x) IS GIVEN, ONE N DETRMINE REDILY THE TIME OR RETOR VOLUME NEESSRY TO HIEVE THE SEIFIED ONVERSION X. 3. IF THE RTE OF RETION IS NOT GIVEN EXLIITELY S FUNTION OF ONVERSION, THE RTE LW MUST BE DETERMINED (FROM REFERENES OR EXERIMENTS). M. Lacroix Isothermal Reactor Design 3

4 DESIGN STRUTURE FOR ISOTHERML RETORS 4. USE STOIHIOMETRY TOGETHER WITH THE ONDITIONS OF THE SYSTEM (i.e., ONSTNT VOLUME, ONSTNT TEMERTURE, ET.) TO EXRESS ONENTRTION S FUNTION OF ONVERSION. 5. BY OMBINING THE INFORMTION GTHERED IN THE REVIOUS STES, ONE N EXRESS THE RTE OF RETION S FUNTION OF ONVERSION. 6. IT IS NOW OSSIBLE TO DETERMINE EITHER THE TIME OR RETOR VOLUME NEESSRY TO HIEVE THE DESIRED ONVERSION BY SUBSTITUTING THE RELTIONSHIS RELTING ONVERSION ND RTE OF RETION INTO THE RORITE DESIGN EQUTION. THE DESIGN EQUTION IS THEN EVLUTED IN THE RORITE MNNER (i.e., NLYTILLY OR NUMERILLY). M. Lacroix Isothermal Reactor Design 4

5 ISOTHERML RETOR DESIGN LGORITHM 5

6 BTH OERTION: SLE-U OF DT TO THE DESIGN OF STR 1. WE SEEK TO DETERMINE THE SEIFI RETION RTE k OF LBORTORY-SLE BTH RETOR IN WHIH ONSTNT- VOLUME RETION OF KNOWN ORDER IS BEING RRIED OUT.. ND NEXT TO USE THE RETION RTE k IN THE DESIGN OF FULL-SLE STR. M. Lacroix Isothermal Reactor Design 6

7 LGORITHM TO ESTIMTE RETION TIMES IN BTH RETORS M. Lacroix Isothermal Reactor Design 7

8 EXMLE No. 1: DETERMINING k FROM BTH DT IT IS DESIRED TO DESIGN STR TO RODUE MILLION KG OF ETHYLENE GLYOL ER YER BY HYDROLYSING ETHYLENE OXIDE. HOWEVER, BEFORE THE DESIGN N BE RRIED OUT, IT IS NEESSRY TO ERFORM ND NLYZE BTH RETOR EXERIMENT TO DETERMINE THE SEIFI RETION RTE ONSTNT k. SINE THE RETION WILL BE RRIED OUT ISOTHERMLLY, THE SEIFI RETION RTE WILL NEED TO BE DETERMINED ONLY T THE RETION TEMERTURE OF THE STR. T HIGH TEMERTURES THERE IS SIGNIFINT BY-RODUT FORMTION, WHILE T TEMERTURES BELOW 313 K THE RETION DOES NOT ROEED T SIGNIFINT RTE. ONSEQUENTLY, TEMERTURE OF 38 K HS BEEN HOSEN. SINE WTER IS USULLY RESENT IN EXESS, ITS ONENTRTION MY BE ONSIDERED ONSTNT DURING THE OURSE OF THE RETION. THE RETION IS FIRST-ORDER IN ETHYLENE OXIDE. M. Lacroix Isothermal Reactor Design 8

9 THE RETION IS EXMLE No. : DETERMINING k FROM BTH DT ( H OH + B SO4 ) O + H O H ( H ) ( ) catalyst IN THE LBORTORY EXERIMENT, 5 ml ( kmole/m 3 ) OF ETHYLENE OXIDE IN WTER IS MIXED WITH 5 ml OF WTER ONTINING.9 wt % SULFURI ID, WHIH IS TLYST. THE TEMERTURE WS MINTINED T 38 K. THE ONENTRTION OF ETHYLENE GLYOL WS REORDED S FUNTION OF TIME. FROM THESE DT DETERMINE THE SEIFI RETION RTE T 38 K. Time (min) (kmole/m 3 ) M. Lacroix Isothermal Reactor Design 9

10 DETERMINING k WITH OLYMTH Nonlinear regression (mrqmin) 1 t; ; Model: 1 -ln()/ Variable Ini guess Value onf-inter 1,, ,41E-5 k.31min 1 M. Lacroix Isothermal Reactor Design 1

11 DESIGN OF STRs: DMKÖHLER NUMBER DESIGN EQUTION FOR STR: V F ( r X ) exit IF THE VOLUMETRI FLOW RTE ONSTNT, v v, V v ( r ) OR τ V v r FOR FIRST-ORDER IRREVERSIBLE RETION, r ND NO VOLUME HNGE DURING THE OURSE OF THE RETION (1 ), τk Da X 1+ τk 1+ Da X k Da: DMKÖHLER NUMBER. FOR Da<.1, X<1%; FOR Da>1., X>9% M. Lacroix Isothermal Reactor Design 11

12 DESIGN OF DESIGN OF STR STRs: STRs IN SERIES s: STRs IN SERIES FIRST-ORDER RETION WITH NO VOLUME HNGE, v v k +τ 1 1 ) ( k v r F F V ) )(1 ( k k k τ τ τ M. Lacroix Isothermal Reactor Design 1

13 DESIGN OF STRs: n STRs IN SERIES FOR n STRs IN SERIES, n n n (1 + τk) (1 + Da) ONVERSION FOR n RETORS IN SERIES: X 1 1 (1 +τk) n M. Lacroix Isothermal Reactor Design 13

14 DESIGN OF STRs: STRs IN RLLEL X ( r V n i V F ) i i V F X r i i i F X r F n X r i i THE ONVERSION HIEVED IN NY ONE OF THE RETORS IN RLLEL IS IDENTIL TO WHT WOULD BE HIEVED IF THE RETNT WERE FED IN ONE STREM TO ONE LRGE RETOR OF VOLUME V M. Lacroix Isothermal Reactor Design 14

15 EXMLE No. 3: DESIGN OF STR IT IS DESIRED TO RODUE 1 MILLION KG OF ETHYLENE GLYOL ER YER. THE STR IS TO BE OERTED ISOTHERMLLY..16 kmole/liter SOLUTION OF ETHYLENE OXIDE IN WTER IS FED TO THE RETOR TOGETHER WITH N EQUL VOLUMETRI SOLUTION OF WTER ONTINING.9% wt OF SULFURI ID (TLYST). IF 8% ONVERSION IS TO BE HIEVED, DETERMINE THE NEESSRY RETOR VOLUME. HOW MNY 4-liters RETORS WOULD BE REQUIRED IF THEY RE RRNGED IN RLLEL? WHT IS THE ORRESONDING ONVERSION? HOW MNY 4-liters RETORS WOULD BE REQUIRED IF THEY RE RRNGED IN SERIES? WHT IS THE ORRESONDING ONVERSION? THE SEIFI RETION RTE ONSTNT IS.311 min -1. M. Lacroix Isothermal Reactor Design 15

16 DESIGN OF FRs GS-HSE RETIONS RE RRIED OUT RIMRILY IN TUBULR RETORS SSUMING NO DISERSION ND NO RDIL GRDIENTS, WE N MODEL THE FLOW IN THE RETOR S LUG FLOW dx F r dv IN THE BSENE OF RESSURE DRO OR HET EXHNGE, THE INTEGRL FORM OF THE LUG FLOW DESIGN EQUTION IS V F X dx r r f ( ) g(, X, ε ) M. Lacroix Isothermal Reactor Design 16

17 EXMLE No.4: DESIGN OF FR IT IS DESIRED TO RODUE 15 MILLION KG OF ETHYLENE YER FROM RKING FEED STREM OF URE ETHNE USING LUG-FLOW RETOR. THE RETION IS IRREVERSIBLE ND FOLLOWS N ELEMENTRY RTE LW. WE WNT TO HIEVE 8% ONVERSION OF ETHNE, OERTING THE RETOR ISOTHERMLLY T 11 K T RESSURE OF 6 TM. THE RETION IS + H 6 H 4 H B + THE ROOSED RTE LW IS WITH 1 k.7s 8kcal / mole r k T 1 K. THE TIVTION ENERGY IS M. Lacroix Isothermal Reactor Design 17

18 RESSURE DRO IN RETORS IN LIQUID-HSE RETIONS, THE ONENTRTION OF RETNTS IS INSIGNIFINTLY FFETED BY EVEN RELTIVELY LRGE HNGES IN THE TOTL RESSURE. S RESULT, THE EFFET OF RESSURE DRO ON THE RTE OF RETION WHEN SIZING LIQUID- HSE HEMIL RETORS N BE IGNORED. IN GS-HSE RETIONS, THE ONENTRTION OF THE RETING SEIES IS ROORTIONL TO THE TOTL RESSURE ND ONSEQUENTLY, ROER OUNTING FOR THE EFFETS OF RESSURE DRO ON THE RETION SYSTEM N, IN MNY INSTNES, BE KEY FTOR IN THE SUESS OR FILURE OF THE RETOR OERTION. M. Lacroix Isothermal Reactor Design 18

19 RESSURE DRO ND THE RTE LW: EXMLE LET US ONSIDER THE SEOND-ORDER ISOMERIZTION RETION B RRIED OUT IN KED-BED RETOR. MOLE BLNE: RTE LW: r STOIHIOMETRY: (FOR GS-HSE RETIONS) OMBINTION: dx dw ' FOR ISOTHERML OERTION (TT ), F ' k dx dw k v r RIGHT-HND SIDE FUNTION OF X ND ONLY: M. Lacroix Isothermal Reactor Design 19 1 X 1+ εx (1 X ) 1+ εx T T WE NEED NOTHER EQUTION TO DETERMINE X dx dw F1 ( X, )

20 FLOW THROUGH KED BED: : ERGUN EQUTION MJORITY OF GS-HSE RETIONS RE TLYSED BY SSING THE RETNT THROUGH KED BED OF TLYST RTILES. THE EQUTION USED MOST TO LULTE THE RESSURE DRO IN KED OROUS BED IS ERGUN EQUTION : d dw α T T / (1 + εx ) α β ρ (1 φ) c c β G 1 φ 15(1 φ) µ G 3 ρ D p φ Dp M. Lacroix Isothermal Reactor Design

21 FLOW THROUGH KED BED: : DEFINITIONS φ D p µ z VOLUME _ VOID TOTL _ BED _ VOLUME RESSURE (N/m ); INLET RESSURE (N/m ); OROSITY( ) OR DIMETER OF RTILE IN BED (m) VISOSITY OF GS SSING THROUGH BED (N/sm ) LENGTH DOWN THE KED BED OF IE (m) u SUERFIIL VELOITYVOLUMETRI FLOW OVER ρ ROSS SETIONL RE OF IE (m/s) GS DENSITY (kg/m 3 ); INLET GS DENSITY; ρ c SOLID DENSITY (kg/m 3 ); G ρu ( total _ mass _ flow _ rate) / (kg/m s) c TEMERTURE (K); INLET TEMERTURE (K) T FT F T c TOTL MOLR FLOW RTE (moles/s); INLET RTE ROSS SETIONL RE (m ) W MSS OF TLYST (kg) T ρ VOLUME _ OF _ SOLID ( 1 φ) TOTL _ BED _ VOLUME M. Lacroix Isothermal Reactor Design 1

22 FLOW THROUGH KED BED: : SEIL SE FOR ISOTHERML OERTION, WE HVE TWO EQUTIONS FOR TWO UNKNOWNS: X ND d dw F ( X, ) ND dx dw ε εx << 1 F ( X, 1 SEIL SE: OR, WE OBTIN N NLYTIL SOLUTION FOR THE RESSURE FOR ISOTHERML OERTION: ( 1 αw ) 1 ) M. Lacroix Isothermal Reactor Design

23 EXMLE No. 5: FLOW THROUGH KED BED LULTE THE TLYST MSS W NEESSRY TO HIEVE ONVERSION X WHEN ETHYLENE OXIDE IS TO BE MDE BY THE VOR-HSE TLYTI OXIDTION OF ETHYLENE WITH IR: H 4 +1/ O H H O + 1/ B ETHYLENE ND OXYGEN RE FED IN STOIHIOMETRI ROORTIONS TO KED-BED RETOR OERTED ISOTHERMLLY T 533K. ETHYLENE IS FED T RTE OF.136 kmole/s T RESSURE OF 1 atm. IT IS ROOSED TO USE 1 BNKS OF 1 TUBES ER BNK KED WITH TLYST. ONSEQUENTLY, THE MOLR FLOW RTE TO EH TUBE IS.136/1 kmoles/s. THE ROSS SETIONL RE OF EH TUBE IS.1313 m. THE ROERTIES OF THE RETING FLUID RE TO BE ONSIDERED IDENTIL TO THOSE OF IR T THIS TEMERTURE ND RESSURE. THE DENSITY OF THE.635 cm TLYST RTILES IS 19 kg/m 3 ND THE BED VOID IS.45. M. Lacroix Isothermal Reactor Design 3

24 FLOW THROUGH KED BED: : MODEL 1. MOLE BLNE: F. ROOSED RTE LW : dx dw r ' r k ' B 3. IDEL GS LW: j j RT 4. F (1 X ) STOIHIOMETRY: ; v 1+ εx 5. dx (1 X ) OMBINING: F.63k dw (1 + εx ) 6. RESSURE LOSS: d α (1 + εx ) dw / B F v B ( θ B X 1+ εx / ) 7. SOLUTION OF (5) ND (6) FOR X ND VERSUS W; INITIL ONDITIONS: T W, X ND M. Lacroix Isothermal Reactor Design 4

25 ODE Report (RKF45) FLOW THROUGH KED BED: OLYMTH OMUTER ROGRM Differential equations as entered by the user [1] d(x)/d(w) rate/fa [] d(y)/d(w) -alpha*(1+eps*x)//y Explicit equations as entered by the user [1] fa 49e- [] alpha 366e-4 [3] eps -15e- [4] kprime 66e-4 [5] f (1+eps*x)/y [6] rate kprime*((1-x)/(1+eps*x))*y Independent variable variable name : w initial value : final value : 5 5

26 FLOW THROUGH KED BED: : SOLUTION 6

27 FLOW THROUGH KED BED: : SOLUTION 7