Numerical Microkinetic Model

Figure 4.38. Sabatier volcano-curve The limiting case of the exact numerical solution of the microkinetic Model 1.

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

The wider utilization of microkinetic models is somewhat retarded by the vast amount of information needed about interactions of chemical intermediates with complex, heterogeneous catalysts. The microkinetic approach has been applied to numerous diverse chemistries including cracking, hydrogenation, hydrogenolyis, hydrogenation, oxidation reactions and ammonia synthesis to name a few. 

The previous sections described techniques employed for parameter estimation. These thermodynamic and kinetic parameters are input to a microkinetic model that is solved numerically to describe material balances in a chemical reactor (e.g., a PFR). This section describes tools for the subsequent model analysis, which can be used in multiple ways. Initially during mechanism development, they can be used to assess which reactions and reactive intermediates are important in the model, which helps the modeler to focus on important features of the surface reaction mechanism. During this process, simulated macroscopic observables, for example, global reaction orders and apparent activation energies can be compared directly to experimental data. Then, once the model describes experimental data reasonably well, analytical tools can be used to develop further insights into the reaction mechanism, with apphcations that include catalyst design [50]. 

This converts the system of ODEs into a system of non-linear algebraic equations that can be solved with standard root-finding methods. The steady-state assumption is not strictly necessary when solving a microkinetic model numerically, but the transient start-up and shut-down behavior is typically short in comparison to steady-state operation. 

With eqns (1.52) and (1.53) there are four equations for the four unknown coverages 0q2> o, dco, and 0 and the system of nonlinear algebraic equations may be solved numerically. With currently available CPU speeds numerical solutions to microkinetic models for catalyst screening studies are generally preferred because they avoid the need to make any additional assumptions regarding the mechanism. 

We have already performed a preliminary Sabatier analysis of the CO oxidation reaction in Section 1.5.2, and derived an analytic solution under the assumption that the adsorption of CO and O2 are quasi-equilibrated in Section 1.6. Now we will formulate a numerical solution to the complete microkinetic model as a function of the descriptors AEco and AEq- We will analyze the reaction mechanism in terms of rate and catalyst control, and at the end of this section, the effect of high surface coverages on the volcano curve will also be briefly addressed. 

As discussed in Section 1.6.1 the microkinetic model may be solved as a system of ODEs or non-linear algebraic equations using the steady-state assumption. It turns out that, regardless of which approach you want to use, the function that must be passed to an ODE solver or numerical root-finding method is the same Here, the more general case of the ODE system is chosen. Note that we named the previously defined function get ratesQ. 

The numerical rate data collected in num data can then be plotted using the contourf function from matpiotiib. The full example code for solving the microkinetic model including the generation of the two-dimensional volcano graph can be found in the Appendix. 

Python Code for the numerical solution of the microkinetic model for CO oxidation and the generation of a two-dimensional volcano plot. 

The results of simulations of TWC model with microkinetics and diffusion resistance within the washcoat enable the interpretation of the dynamics of surface coverages and overal reactions and can serve for the improvement of the washcoat design. It has been found that not only multiple steady states (hysteresis) but also various types of periodic and complex spatiotemporal concentration patterns can exist in the monolith. Thorough analysis of bifurcations and transitions among existing patterns is numerically demanding task due to dimension of the problem. 

The microkinetic modehng provides us with only numerical results and is not convenient for further use in reactor design and optimization. But with the information obtained from the microkinetic analysis, a macrokinetic-based L-H model can be easily derived. In this situation, there is no need to make any assumption. The values of kinetic parameters can also be retrieved from microkinetic study. As an example, an L-H model using Eq. (2.24) as the RDS was proposed ... 

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