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Energies 2019, 12, 469 Energies 2019, 12, x FOR PEER REVIEW 9 of 15 9 of 15 (a) FigFuirgeu5re. C5.aClcaullcauteladteadndanmdemaseuarseudreCdOCcOonccoencternatiroantiodnurdinugrinCgOCOm2emtheatnhatnioantio(fnee(dfeegdasg: a6sv: 6olv%olC%OC,O2, −1 −1 55%55H% ,Hr2e,srteNst ,Nm2, m=cat2=g2).g(a).)(rae)arcetiaocntiotenmtpemerpateurraetuvraerivaatiroiantifonr Vfor VS=TP2=2 l22h l h; (b; )(bre)sriedseindceenctiemteime 2 2cat STP ◦◦ varviatrioantioant 2a2t3223C°Coro2r32434C°C. .CCaalcluculalatitoionnbbaasseeddoonn(w(wroronngg))aasssuumppttioionntthhaattCO2 iisonllyconverted to 2 to CO via reverse watergassshiifftt((RWGSS))aannddththeennsusubbseseqquuenentltylytotommetehtahnaene(in(idnidreircetcmt mecehcahnainsmism). T).he Thelalragregeddeveviaiatitoionnoofftthe calculated CO conttenttffrroomththeemmeaesausruermemenetnsttrsotrnognlgyliyndinicdaitceasteths atthCatOCOis2 is compared to the intrinsic chemical rate; this has to be considered in the rate equation [32]. For this compared to the intrinsic chemical rate; this has to be considered in the rate equation [32]. For this purpose, the generalized Thiele modulus Φgen for an irreversible reaction with arbitrary kinetics (here purpose, the generalized Thiele modulus Φgen for an irreversible reaction with arbitrary kinetics (here dirdecirtleyctcloyncvoenrvtedrtetod mtoemtheatnhea.ne. 3.4. Influence of Pore Diffusion on the Rate of CO Methanation 3.4. Influence of Pore Diffusion on the Rate of CO Methanation A pore diffusion resistance lead to internal concentration gradients and a lower effective rate A pore diffusion resistance lead to internal concentration gradients and a lower effective rate Langmuir–Hinshelwood approach, Equation (4)), was used [33]: Langmuir–Hinshelwood approach, Equation (4)), was used [33]: is given by DKn = (dpore/3) [8RT/(π MCO)]0.5. given by DKn = (dpore/3) [8RT/(π MCO)]0.5. V rrρρ V p CO CO p pp Φgen= (10) (10) p0 Vp is the particle volume, Ap the outer surface, rco the reaction rate of CO, ρp the particle density, Φgen=AAp 2D (T)ρc p CO,eff CO cCO r It had to be considered here that the active component (Ru) is concentrated in an outer shell with It had to be considered here that the active component (Ru) is concentrated in an outer shell with a thickness dshell of 0.35 mm. In this case, Vp has to be replaced by the volume of the shell, Vshell = a thickness dshell of 0.35 mm. In this case, Vp has to be replaced by the volume of the shell, Vshell = 4/3 π 4/3 π [rp3 − (rp − dsh)3]. Hence, the rate constant kshell is higher than the measured average value k, [rp3 − (rp − dsh)3]. Hence, the rate constant kshell is higher than the measured average value k, and the ratio and the ratio can be calculated by: can be calculated by: kk mmp VVp d d shshelell p p sh = == ==1−11−− 1− kk mm VV r r 3 (b) 22 3 13−1 sh (11(1)1) mp and mshell is the mass of the catalyst and catalyst shell, respectively. The solution of Equation (10) shsehllell shellshell p p mp and mshell is the mass of the catalyst and catalyst shell, respectively. The solution of Equation (10) finally leads to: finally leads to: kρ dsh 3rp shell p Φ =1−1−d rp kshellρp b ++lnlnK(KC C+b+−b)1−−1l−nblnb gen sh Φgen= 1− 1−rp 3 3 (12) (12) The factor b is defined as b = 1 + K2 CH2O. The effectiveness factor with regard to pore diffusion is [32]: 2 dc 2 DCO,eff (T) ρ rCO dcCO CO Vp is the particle volume, Ap the outer surface, rco the reaction rate of CO, ρp the particle density, and DCO,eff the effective diffusion coefficient, DCO,eff = εp/τp [1/Dmol + 1/DKn]−1, which also considers and DCO,eff the effective diffusion coefficient, DCO,eff = εp/τp [1/Dmol + 1/DKn] −1, which also considers the the particle porosity (εp) and tortuosity (τp). The binary diffusion coefficient for CO in H2 is calculated particle porosity (εp) and tortuosity (τp). The binary diffusion coefficient for CO in H2 is calculated based on D0 for T0 = 273 K and 1 bar (0.65 cm2·s−1), Dmol = D0 (T/T0)1.75, and the Knudsen diffusivity based on D0 for T0 = 273 K and 1 bar (0.65 cm2·s−1), Dmol = D0 (T/T0)1.75, and the Knudsen diffusivity is p0 CO r p kshellkCHC b shell2 H 2D2D ρ ρ 2 1 1COCO CO,eCffO,eff p 2 2 p K CK C+b+b 1K 1CO K 1 1 COPDF Image | Selective Methanation of CO over a Ru-y-AI2O3 Catalyst in CO2 H2
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