General remarks

Experimental studies

The experimental studies, conducted as part of this dissertation are described in Chapter 4 and supplementary data concerning the experimental setup and prepared catalysts are given in Appendices A and B, respectively. The experimental part of the research was divided into two primal sections. Firstly, the methodology of preparation catalytic materials for methane/steam the reforming process was designed. The different types of powders (Ni/NiO) and dispersion agents were tested; furthermore parameters such as sintering curve, binder agent, mixing and crushing time were adjusted to follow the laboratory and industrial processes of preparing the SOFC anodes. Then, the prepared catalytic materials were tested experimentally in the plug-flow reactors. The studies were conducted on the crushed catalyst in order to avoid the influence of mass transfer in the porous material, which can disturb the results of investigation focused on catalytic properties. The experimental conditions relevant for the proposed numerical algorithms were designed with respect to the specific requirements of each mathematical technique introduced in Chapter 3. Additionally, the correlation between the Gas Space Hourly Velocity and the predicted conversion rate of methane were delivered and discussed in the context of delivering the correct kinetic equation.

Classical analysis of methane steam reforming – comparison of approach

Chapter 5 is divided into two parts. Firstly, the classical approaches to modelling and investigating the methane/steam reforming process were applied to the experimental studies on nickel cermet catalyst with volumetric composition of Ni equalled 60%. The standard and modified methods popularly adopted in the literature were compared. An improvement in the modified method for the simultaneous calculation was proposed: the appropriate reaction order was selected in terms of giving the smallest sum of the relative standard deviation found in the reaction constant for all of the temperatures simultaneously. The influence of the experimental data set for every calculated algorithm was discussed. Finally the activation energy and pre-exponential factor were derived from the Arrhenius plot. The proposed equation was used to simulate the reforming process and compare numerical and experimental results. The influence of the temperature and steam-to-carbon ratio for the outlet gas composition and the conversion rate of methane were discussed. Good agreement was found for the results characterized by the conversion rates lower than 60%. In this context, the change in the experimental conditions and the increase of Gas Space Hourly Velocity are

The updated experimental conditions were applied to the analyses in the second part of Chapter 5. The influence of the volumetric composition of nickel cermet catalyst was experimentally investigated. The reaction order rates for various catalytic material were provided and compared with Mogensen and Iwai' research findings, who investigated SOFC dedicated materials. The results were found to be convergent and independent on the volumetric composition in terms of reaction orders.

Application of Generalized Least Squares Algorithm

The Generalized Least Squares (GLS) method is known as a data reconciliation methodology.

The reconciled data are more precise in general than the corresponding set of measurements.

By the application of the GLS algorithm, the mass and energy balances as well as the physical constraints describing the measurement system are closed and the model is coherent. The application of the GLS method results in an improvement in the quality of the obtained solution by decreasing the uncertainties of the model. In Chapter 6 a novel approach to evaluate the reaction kinetics of the methane/steam reforming process by adopting an Orthogonal Least Squares method was introduced. The advantages of such an approach enables a more general analysis of the problem and provides more precise information about obtained results, which includes their uncertainty. The Generalized Least Square (GLS) method was applied to the calculation of the empirical parameters of the methane/steam reforming reaction on a Ni/YSZ SOFC anode cermet catalyst: the pre-exponential factor of A, the activation energy E, the reaction orders with respect to CH4 and H2O, a and b, and therefore to the estimation of the reaction rate and the methane conversion rate of the steam reforming process.

The application of the GLS algorithm is divided into three main phases: the experimental investigation of the methane/steam reforming process over a fine powder catalyst of NiO/YSZ, the numerical analysis of collected data which aimed to find the initial approximations of empirical parameters describing the process, and finally the definition and application of the operators of the GLS algorithm.

In Chapter 6 all elements of the GLS algorithm were precisely defined. The introduced mathematical model has been based only on the fundamental physical equations describing the chemical process, and it can be noted that it does not contain any additional assumptions

provides for greater versatility of the proposed methodology in comparison with approaches used in the previous studies. The experimental measurements and process unknowns were introduced to the variables vector x. In the standard approach to the calculation of the reforming reaction kinetic, different series of experimental measurements are used to calculate the reaction rates and different experimental conditions are required to determine the activation energy and Arrhenius constant. On the other hand, one of the requirements in the proposed GLS model is that all of the experimental results are subjected to all of the model equations, and they have to fulfil all the constraints imposed on the problem. Then, because of the large redundancy in the model definition, an increase in the security of the final solution is observed; it is significant especially when the measurements are influenced by process variability and experimental inaccuracies.

It was proven that the proposed GLS method not only allows for obtaining the most probable values of the estimated parameters but also makes possible the a posteriori evaluation of the errors of the directly measured variables and unknown parameters. It was demonstrated that the GLS method is useful in securing higher accuracy of measured data and decreasing the value of the residuum of the constraint equations. The present results primarily proved an applicability of the GLS methodology into the investigation of a chemical reaction process for deriving its reaction kinetics.

Critical Comparison with literature data

A critical comparison of the obtained results with the literature data and discussion on the possible reasons for the essential discrepancies between various studies are presented in Chapter 7. The considerations were focused on the literature studies on methane/steam reforming over nickel cermet catalyst. The multiplicity of the derived modelling equations was listed. The chosen equations were later compared with the results derived in Chapter 6. In order to give a meaningful comparison, the unification of pre-exponential factors had to be conducted, as this parameter is most fragile for individual properties of material and many authors do not provide enough information to identify the investigated catalyst unambiguously. The highest correlation between experimental data and a modelling equation was obtained for the model derived by the GLS algorithm in Chapter 6.

Validation of models for reforming process

The GLS method has the potential to provide objective criteria for the formal evaluation and falsification of different mathematical models of the methane reforming process. The studies in Chapter 8 particularly focused on the importance of the mathematical expressions, of the physical phenomena occurring in the chemical reforming system. The analysis was conducted in the light of improving the precise quantification of uncertainties found in the evaluation of the chemical reaction process and providing a reliable reaction rate equation. The analysis of the volume of covariance ellipsoid provides information about the importance and influence of separated constraints on the final results. The various models of the reforming process analysed in Chapter 8 proved a significant decrease in the uncertainty of the model with increased numbers of modelling equation. The increased security was observed for both:

measurements and unknown variables. It was pointed out, that not all constraints are equally valuable, from the point of view of increasing security of the model: the balances of the elements in the system had a critical influence, while the linear Arrhenius correlation slightly changed the result and volume of the covariance ellipsoid. The variations in the volume of the covariance ellipsoid were explained in intuitive projections on three and two-dimensional variable spaces.