Quantifying the Impact of Parametric Uncertainty on Automatic Mechanism Generation for CO2 Hydrogenation on Ni(111)

Abstract

Automatic mechanism generation is used to determine mechanisms for the CO2 hydrogenation on Ni(111) in a two-stage process, while considering the uncertainty in energetic parameters systematically. In a coarse stage, all the possible chemistry is explored with gas-phase products down to the ppb level, while a refined stage discovers the core methanation submechanism. 5,000 unique mechanisms were generated, which contain minor perturbations in all parameters. Global uncertainty assessment, global sensitivity analysis, and degree of rate control analysis are performed to study the effect 1 of this parametric uncertainty on the microkinetic model predictions. Comparison of the model predictions with experimental data on a Ni/SiO2 catalyst find a feasible set of microkinetic mechanisms that are in quantitative agreement with the measured data, without relying on explicit parameter optimization. Global uncertainty and sensitivity analyses provide tools to determine the pathways and key factors that control the methanation activity within the parameter space. Together, these methods reveal that the degree of rate control approach can be misleading if parametric uncertainty is not considered. The procedure of considering uncertainties in the automated mechanism generation is not unique to CO2 methanation and can be easily extended to other challenging heterogeneously catalyzed reactions<br>

Quantifying the Impact of Parametric Uncertainty on Automatic Mechanism Generation for CO2 Hydrogenation on Ni(111)

“…The initial set of 500 generated mechanisms with the coarse settings produced considerably different microkinetic mechanisms, with large variations in overall size, possible gas-phase products and adsorbates (see Figure S15 ). All generated mechanisms along with the evaluation are made publicly available in ref ( 78 ). The number of species and reactions in the core ranged from 21 to 64 species and 20 to 450 reactions; the edge contained up to 360 more species and 1,053 different reactions.…”

“…As a simplification, no lateral interactions among the adsorbates were considered in the surface mechanism. The Python source code is available in ref ( 78 ).…”

Evaluation of the degree of rate control via automatic differentiation

“…In addition, FD requires O ( p ) rounds of function calls or forward simulations to get the derivatives of p parameters, which is time consuming for large size of parameters. For example, Bjarne et al took 300 CPU‐hours to conduct the sensitivity analysis when investigating the mechanism of CO 2 hydrogenation on Ni(111) using FD method 13 …”

“…For example, Bjarne et al took 300 CPU-hours to conduct the sensitivity analysis when investigating the mechanism of CO 2 hydrogenation on Ni(111) using FD method. 13 To avoid these issues, sensitivity analysis methods like the direct sensitivity analysis and the adjoint sensitivity analysis 14 are usually adopted by common differential equation solvers [15][16][17] to provide the derivative of the numerical solution to the parameters for differential equations. The direct sensitivity analysis converts the solution sensitivity with respect to the parameters of differential equations into n extra (number of parameters) differential equations, which are solved simultaneously with the original differential equations.…”

“…12 From a practical perspective, a simple and common way to assess the DRC is using finite difference (FD) approximations for the derivatives. 10,11,13 These are fairly straightforward to implement and only require a few more lines of code in addition to the original simulation code. Mathematically, the centered difference approximation is formulated to approximate the derivatives in…”