The analysis of data from recirculation reactors

Abstract

A critical assessment is made of a commonly used procedure for estimating the kinetic parameters in a catalytic rate model using data obtained in a recirculation reactor. Serious deficiencies in this procedure are identified, and an alternative estimation scheme is proposed.The component mass balance equations in a recirculation reactor involve no differentiation or integration, and therefore the estimation of kinetic parameters appears to be simpler than the corresponding task with integral reactor data. However, a detailed examination shows that this is not the case, and that the effort involved in correctly estimating the parameters and their covariance matrix may not be significantly different for the two reactor types. Data obtained by Boag et al(10) from the vanadia‐catalysed gas‐phase oxidation of o‐xyleue in a recirculation reactor are used to demonstrate the differences between the parameter estimation procedure in common use and the procedure recommended in this paper.

Kinetic Modelling with Multiresponse Data

“…In the chemical process example the polynomial models from the process variable study were helpful in obtaining starting values for the kinetics model. Models for rates, as discussed by Boag, Bacon and Downie (1976), are easier to handle than the more correct concentration models and may be helpful in getting starting values for use with concentrations.…”

Modelagem matematica e simulação de reatores cataliticos

“…Vanhove & Blanchard [17] Boag et ai [19,20] Os autores [19,20] observaram uma baixa seletividade para anidrido ftàlico mesmo para altas conversões e excluíram as etapas de combustão do anidrido ftàlico e da ftalida baseados no fato de que as taxas de reação associadas com estas etapas eram pequenas.…”

“…2, 195 (1957). (15),PAF (15),TEMP (15),Z( 15) DOUBLE PRECISION POX1 (15),PAF1 (15),TEMP1 (15),XX (20),W( 20 61 FORMAT(1H,3X,F5.2,3X,F8.6,3X,F8.6,3X,F8.6,3X,F8.6 WR I TE ( * , 2 4 ) Z ( J ) , POX ( J ) , PAF ( J) , TEMP ( J) (20,20),CB( 20 (20),POTA (20),PFI (20),PAF (20),TEMP (20),Z( 20…”

“…))1DENOM1 R20X = (CT(2)*CSP02*POXI*((Y(J+l)+Y(J))I2. ))1DENOM1 SUM = DELTAQ(l)*RlOX + DELTAQ(2)*R20X ALFAl = DELTAZ*PEM ALFA2 = (DELTAZ*DELTAZ*PEM*ZF)I(GAMAl*POXI) ALFA3 = DELTAZ*PEC ALFA4 = (DELTAZ*DELTAZ*PEC*ZF)ITM I F ( J • EQ • 1 ) GO TO 55 F(J) = Y ( J+l )-2*Y(J)+Y(J-1 )-ALFA1*(Y(J)-Y(J-1) )-ALFA2*RMOX F(M) = Y (M)-Y(M-1) F(J+M)=Y ( J+M+1 )-2*Y(J+M)+Y(J+M-1 )-ALFA1*(Y(J+M)-Y(J+M-1) )-ALFA2* $RMAF F(2*M) = Y(2*M)-Y(2*M-1) F ( J+2*M) =Y ( J+2*M+ 1) -2*Y ( J+2*M) +Y ( J+2*M-1) -ALFA3* ( Y ( J+2*M) -Y ( J+2*M $-1)) -ALFA4* ( GAMA2* (Y ( J+2*M) *TM-TW) -SUM) F(3*M) = Y(3*M)-Y(3*M-1) 55 F( 1) = Y ( 2)-2*Y( 1 )+YOXI-ALFA1* (Y( 1 )-YOXI )-ALFA2*RMOX F(M) = Y (M)-Y(M-1) F( 1+M)=Y ( 2+M)-2*Y( 1+M)+YAFI-ALFA1* (Y( 1+M)-YAFI )-ALFA2*RMAF F(2*M) = Y(2*M)-Y(2*M-1) F( 1+2*M) =Y( 1+2*M+1 )-2*Y( 1+2*M)+YTI-ALFA3*(Y( 1+2*M)-YTI )-ALFA4*(GA $MA2*(Y( 1+2*M)*TM-TW)-SUM) 8 (A-H,O-Z) DOUBLE PRECISION Y(50) ,F( 50) ,XX(20) ,ERR(50) ,A(50,51) DOUBLE PRECISION POX(20),POTA(20),PFI(20),PAF(20),TEMP(20),Z(20) COMMON / BLOC1 I NRE,NPC,N1 ,N2 COMMON / BLOC2 I ZF,GO,PMM,ROP,POROS,CP,U,DT,RG,CSP02 COMMON / BLOC3 I PT,TI,TM,TW,PEM,PEC,BETA1,BETA2,POXI,PAFI COMMON / BLOC4 I YOXI, YAFI, YTI COMMON / BLOC5 I S(S) ,EA(S) ,DELTAH(S) ,CA(20,20) ,CB(20*)NI,NRE,ZF,NS,EX,AMOR,TI,TW,TM,POXI,PAFI,PT READ(8,*)GO,PMM,ROP,POROS,BETA1,BETA2,RG,CP,U,…”

“…) COMMON I BLOCl I NRE,Nl,N2 COMMON I BLOC2 I ZF,GO,PMM,ROP,POROS,CP,U,DT,RG,CSP02 COMMON I BLOC3 I PT,TI,TM,TW,PEM,PEC,CTM,CTC,ASE COMMON I BLOC4 I BETA1,BETA2,BETA3,POXI,PAFI,YOXI,YAFI,YTI COMMON I BLOCS I S(8),EA(8),DELTAH(8},CA(20,20),CB(20,20) REAL ITEMP OPEN(UNIT=7 ,FILE= 'HT3AC01.DAD' ,STATUS='OLD'} OPEN(UNIT=8,FILE='HT3AC02.DAD',STATUS='OLD'*)NI,NRE,ZF,NS,EX,AMOR,TI,TW,TM,POXI,PAFI,PT READ(8,*)GO,PMM,ROP,POROS,BETA1,BETA2,BETA3,RG,CP,U,DT,CSP02DO 15 L= 1 , NRE READ(8,*)S(L},EA(L},DELTAH(L} 15 CONTINUE READ(8,*)PEM,PEC,CTM,CTC,ASE,YOXI,YAFI,YTI,YOXSI,YAFSI,YTSI ITEMP = 1H,7X,'Z',7X,'POX',7X,'PAF',7X,'TEMP') DO 131 J=l ,N2 POX(J} = POXI*Y(J} PAF(J) = POXI*Y(J+N2) TEMP(J) = TM*Y(J+2*N2) Z(J) = ZF*XX(J) WRITE(*,22)Z(J},POX(J),PAF(J),TEMP(J) 22 FORMAT(1H,3X,F5.2,3X,F8.6,3X,F8.6,3X,F7.2ENTRADA DO REATOR IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION Y(200),F(200),CT(8),DELTAQ(8) COMMON I BLOCl I NRE,Nl,N2 COMMON I BLOC2 I ZF,GO,PMM,ROP,POROS,CP,U,DT,RG,CSP02 COMMON I BLOC3 I PT,TI,TM,TW,PEM,PEC,CTM,CTC,ASE COMMON I BLOC4 I BETA1,BETA2,BETA3,POXI,PAFI,YOXI,YAFI,YTI COMMON I BLOC5 I S(8),EA(8),DELTAH(8),CA(20,20),CB(20,20) GAMAl = GOI(PMM*PT*ROP*(l.-POROS)= S(L)*DEXP(-EA(L)I(RG*TM*Y(J+5*N2))) DELTAQ(L) = (-DELTAH(L)*ROP*(l.-POROS))I(GO*CP) 36 CONTINUE DENOM = (POXI*Y(J+3*N2)*(BETAl*CT(l)+BETA2*CT(2))+POXI*Y(J+4*N2)* $CT(3)*BETA3+CSP02) RMOX = ((CT(l)+CT(2))*CSP02*POXI*Y(J+3*N2))1DENOM RMAF = ((CT(3)*Y(J+4*N2)-CT(l)*Y(J+3*N2))*POXI*CSP02)IDENOM R10X = (CT(l)*CSP02*POXI*Y(J+3*N2))1DENOM R20X = (CT(2)*CSP02*POXI*Y(J+3*N2))1DENOM R3AF = (CT(3)*CSP02*POXI*Y(J+4*N2))1DENOM SUM = DELTAQ(l)*RlOX + DELTAQ(2)*R20X + DELTAQ(3)*R3AF F(J)=SMBOX-PEM*SMA20X-((PEM*ZF)I(POXI*GAMA1))*RMOX F(J+N2)=SMBAF-PEM*SMA2AF-((PEM*ZF)I(POXI*GAMA1))*RMAF F(J+2*N2)=SMBT-PEC*SMA2T-((PEC*ZF)ITM)*(GAMA2*(Y(J+2*N2)*TM-TW),N2 SMAJOX = SMA30X + CA(N2,I)*Y(I) SMA3AF = SMA3AF + CA(N2,I)*Y(I+N2) SMA3T = SMA3T + CA(N2,I)*Y(I+2*N2) COMMON I BLOC1 I NRE, N 1, N2 COMMON I BLOC2 I ZF,GO,PMM,ROP,POROS,CP,U,DT,RG,CSP02 COMMON I BLOC3 I PT, TI, TM, TW, PEM, PEC, CTM, CTC, ASE COMMON I BLOC4 I BETA1,BETA2,BETA3,POXI,PAFI,YOXI,YAFI,YTI COMMON I BLOC5 I S(8) ,EA(8) ,DELTAH(8) ,CA(20,20) ,CB(20,20) GAMA1 = GOI(PMM*PT*ROP*(1.-POROS)) GAMA2 = ( 4. *U) I ( GO*CP*DT) C FUNÇÕES PARA J=l ,NPC DO 34 J= 1 , NPC SMBOX = CB(J+1,1)*YOXI SMA20X = CA(J+l, 1 )*YOXI SMBAF = CB(J+1,1)*YAFI SMA2AF = CA(J+l,l)*YAFI SMBT = CB(J+l, 1 )*YTI SMA2T = CA(J+1,1)*YTI DO 35 I=l ,N1 SMBOX = SMBOX + CB(J+1,I+1)*Y(I) SMA20X = SMA20X + CA(J+1,I+1)*Y(I) SMBAF = SMBAF + CB(J+1,I+1)*Y(I+N1) SMA2AF = SMA2AF + CA(J+l,I+l)*Y(I+Nl) SMBT = SMBT + CB(J+1,I+l)*Y(I+2*Nl) SMA2T = SMA2T + CA(J+1,I+l)*Y(I+2*Nl) 35 CONTINUE DO 36 L=1 ,NRE CT(L) = S(L)*DEXP(-EA(L)I(RG*TM*Y(J+5*N1))) DELTAQ(L) = (-DELTAH(L)*ROP*(1.-POROS))I(GO*CP) 36 CONTINUE DENOM = (POXI*Y(J+3*N1)*(BETA1*CT(1)+BETA2*CT(2))+POXI*Y(J+4*N1)* $CT(3)*BETA3+CSP02) RMOX = ((CT(1)+CT(2))*CSP02*POXI*Y(J+3*N1))1DENOM RMAF = ((CT(3)*Y(J+4*Nl)-CT(l)*Y(J+3*Nl))*POXI*CSP02)1DENOM R10X = (CT(1)*CSP02*POXI*Y(J+3*Nl))IDENOM R20X = (CT(2)*CSP02*POXI*Y(J+3*Nl))IDENOM R3AF = (CT(3)*CSP02*POXI*Y(J+4*Nl))IDENOM SUM = DELTAQ(l)*RlOX + DELTAQ(2)*R20X + DELTAQ(3)*R3AF F(J)=SMBOX-PEM*SMA20X-((PEM*ZF)I(POXI*GAMA1))*RMOX F(J+N1)=SMBAF-PEM*SMA2AF-((PEM*ZF)I(POXI*GAMA1))*RMAF F(J+2*Nl)=SMBT-PEC*SMA2T-((PEC*ZF)ITM)*(GAMA2*(Y(J+2*Nl)*TM-TW)+ CA(N2,I+l)*Y(I+Nl) SMA3T = SMA3T + CA(N2,I+l)*Y(l+2*N1) 37 CONTINUE F ( N 1 ) = SMA30X F( 2*Nl) = SMA3AF F(3*Nl) = SMA3T RETURN END ======================================================================= PROGRAMA M3DRCM.FOR ======================================================================= IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION YV(200) ,YN(200) ,F(200) ,ERR(200) ,A(200,201) DOUBLE PRECI SION POX( 30), POTA( 30), PFI ( 30), PAF ( 30), T( ...…”