Kinetic Model for the Direct Conversion of CO2/CO into Light Olefins over an In2O3–ZrO2/SAPO-34 Tandem Catalyst

An original kinetic model is proposed for the direct production of light olefins by hydrogenation of CO2/CO (COx) mixtures over an In2O3–ZrO2/SAPO-34 tandem catalyst, quantifying deactivation by coke. The reaction network comprises 12 individual reactions, and deactivation is quantified with expressions dependent on the concentration of methanol (as coke precursor) and H2O and H2 (as agents attenuating coke formation). The experimental results were obtained in a fixed-bed reactor under the following conditions: In2O3–ZrO2/SAPO-34 mass ratio, 0/1–1/0; 350–425 °C; 20–50 bar; H2/COx ratio, 1–3; CO2/COx ratio, 0–1; space time, 0–10 gIn2O3–ZrO2 h molC–1, 0–20 gSAPO-34 h molC–1; time, up to 500 h; H2O and CH3OH in the feed, up to 5% vol. The utility of the model for further scale-up studies is demonstrated by its application in optimizing the process variables (temperature, pressure, and CO2/COx ratio). The model predicts an olefin yield higher than 7% (selectivity above 60%), a COx conversion of 12% and a CO2 conversion of 16% at 415 °C and 50 bar, for a CO2/COx = 0.5 in the feed. Additionally, an analysis of the effect of In2O3–ZrO2 and SAPO-34 loading in the configuration of the tandem catalyst is conducted, yielding 17% olefins and complete conversion of CO2 under full water removal conditions.


Section S3. Assessment of potential mass transfer limitation
The compliance with the Weisz-Prater criterion (eq (S1) was carried out to ascertain the absence of mass transfer constraints within the catalyst particles.The calculation was performed following the methodology suggested by García-Sánchez et al. 1    and space time 5 gcat h molC -1 .Flowrate is referred in cm 3 min -1 .

Section S4. Reaction indices
The results were quantified by calculating olefin yields, Yi (eq S2), CO2 conversion, XCO2 (eq S3), and COx conversion, XCOx (eq S4) based on the molar flows of the reactants and products in C content units as: where ni is the number of carbon atoms of each i product, Fi the molar flow rate of the i product at the outlet and    0 the total molar flow rate of COx (CO+CO2) in the feed. where and F CO 2 are the molar flow rate of CO2 at the inlet and outlet of the reactor, respectively.
where F CO x is the molar flow of (CO +CO2) at the outlet of the reactor.

Section S5. Methodology for kinetic data analysis
4][5] In summary, the calculation of the apparent kinetic constants involves fitting the results of integrating the mass conservation equations (convection-dispersion-reaction equations) for each compound (or lump) in the reaction network (eq S5) to the corresponding experimental data of concentration evolution with time on stream.
In this equation, a vector of each lumps' molar fraction yi (z,t) is considered.The equation is defined for a time value t>0 and a longitudinal position in the reactor 0<z<L (catalytic bed length).ε is the effective bed-particle porosity,  is the linear velocity, D is the effective dispersion coefficient of the gas (not relevant in this case), R the universal gas constant, T is the temperature, P the total pressure, NC is the ratio between the (carbon molar flow rate)/(total molar flow rate), ρ is the density of the catalytic bed, ri vector comprises the formation rates of each i lump and nl the number of components.
The system of parabolic partial differential equations was solved by transforming it into a system of ordinary differential equations. 6This system was integrated using an implicit Runge-Kutta method, and the kinetic parameters were calculated by minimizing the objective function vector (OF) defined in eq S6, where the first term is related to the kinetics of each j reaction step in the reaction network at t=0, and the second term is related to the deactivation kinetics.Both terms are defined as the differences between the experimental results (molar fractions at t=0 and at the given t time on stream, that is, yi,0 and yi, respectively) and the corresponding values calculated with the kinetic model.A modification of the Levenberg-Marquardt algorithm 7,8 was used for computation.The weight factors (gathered in Table S3) are calculated as the inverse of the variance of each component according to the expression defined by Constantinides and Mostoufi 9 (eq (S7)): where   2 and   2 are the variances for each distribution of experimental results of component i at each j reaction stage.
In the absence of repeated runs, no initial variances can be estimated and so, the weight factor is established to be inversely proportional to the average concentration of each component in the studied condition range (eq (S8)): Table S3.Weigh factor of the components.

Figure S1 .
Figure S1.Experimental run reproducibility for three repeated experiments at the

9 m 2 s - 1 .
and confirmed the absence of diffusional limitations to the flow of reactants within the porous structure of the catalyst.The calculated Weisz-Prater modulus (CWP) for the fastest methanol formation reaction (from CO) in the In2O3-ZrO2 catalyst accounts for 0.015.This value is in accordance with the values in the literature for Cu-Zn-Al catalysts (CWP < 0.03, for Leonzio et al. 2 ).  = (−) 2     < 1 (S1) where (-r) is the reaction rate, R is the catalyst particle radius, De is the effective diffusivity, Creactant is the concentration of the reactant.The properties of the catalysts (to calculate De) are: porosity, ε= 0.23; tortuosity, τ= 1.17; Knudsen diffusivity, Da=5 10 -Moreover, the absence of mass transfer limitations has also been experimentally proven as observed in Figures S2 (with runs carried out with different particle size, but same size for both the In2O3-ZrO2 and SAPO-34 catalysts) and S3 (with runs carried out varying the total flow rate at the reactor inlet).Figure S2 ascertains the absence of mass transfer constraints within the studied particle range.This indicates that the particle sizes employed in the kinetic modeling are appropriate (in the 125-250 µm range for the In2O3-ZrO2 catalyst and 300-400 µm range for the SAPO-34 catalyst.The distinct sizes for each catalyst were chosen to facilitate post-reaction separation and enable individual analysis of the respective catalysts).The results presented in Figure S3 highlight the absence of external diffusion constraints for the total gas flow rate used in the kinetic modeling (60 cm 3 min -1 ).

Figure S3 .
Figure S3.Evolution of products yield over time on stream for different particle size catalysts.Reaction conditions: 400 ºC; 30 bar; CO2/COx ratio in the feed, 0.5; the weight factor assigned to each component i, ξ is the number of repeated runs under the same reaction conditions, and ne,0 and ne,d denote the total number of experimental data used for calculating the first and second terms of the objective function (OF), respectively.
Figure S4.Detailed comparison of the calculated values of the molar fractions with

Figure S6 .
Figure S6.Evolution with time on stream and reactor length of activity (a), olefins

Table S2 .
Kinetic runs considered for the kinetic modeling.W and M correspond to H2O and methanol, respectively.