(507b) Experimental Design of Dynamic Temperature-Programmed Reduction (TPR) Experiments

Temperature Programmed Reduction (TPR) is a dynamic method for the characterization of metal oxide catalysts and for the estimation of reaction kinetic parameters. Hydrogen continuously flows through a small sample of the catalyst and reduces it. Temperature is increased at a constant rate from low values to several hundred °C. Due to the Arrhenius effect, reaction rates are virtually zero at first and then increase at higher temperature. The concentration of water in the outlet gas is proportional to the actual reduction rate in the sample, and is continuously measured. The result is a measured profile of the reaction rate over time. If the reduction comprises several reactions, the signals caused by each reaction are superimposed in the measured signal. The only control variable is the temperature gradient, which can be changed from run to run, but is kept constant during each experiment. The TPR data is used for two quantitative purposes: estimation of kinetic parameters (pre-exponential factor, activation energy, order of reaction) and discrimination between rivaling kinetic models. Previous works have shown that the precision of the estimated parameters and the model discrimination abilities of conventional TPR are unsatisfactory [1]. To improve the TPR method with regard to these drawbacks, the options to control the experiments must be extended. The idea is to apply non-constant temperature gradients, u(t) (nonlinear temperature profiles) such that the precision of the parameter estimation is increased. The question for the optimal temperature profile leads to a dynamic optimization problem. As an objective function, the D-optimality criterion is used. It maximizes the determinant of the predicted sensitivities of the measured output, y(t), with respect to the estimated parameters. The dynamic and algebraic state equations of the reacting system and the equations for the sensitivities are constraints to this problem. The model equations are discretized in time according to the orthogonal collocation method and solved within the software package ampl using the optimization routines CONOPT and IPOPT. As a result, optimal profiles for the temperature gradients are obtained which allow for more precise parameter estimation than linear TPR experiments. Optimal solutions for different systems with one single reaction show similar patterns (Fig. 1). This fact gives rise to the formulation of a simpler optimization problem of lower dimensionality, which can be solved quickly and reliably in a laboratory environment (Fig. 2). For systems with several reactions, the temperature profile usually separates the signals arising from different reactions, thereby reducing the covariance of the estimated parameters. Also here, a reduced problem is formulated. In a second step, the TPR is optimized with respect to its model discrimination abilities, using the T-optimality criterion as an objective function. This leads to a problem with two nested optimizations, which is solved by discretization of part of the parameter space. Optimization results show that nonlinear experiments can significantly enhance the ability of the TPR method to discriminate between different types of reaction kinetics. In this contribution, we motivate and introduce both optimization problems, present some of their solutions, and briefly touch on the reduced problems. We also show results from linear and nonlinear TPR experiments and analyze the improvements gained through the proposed nonlinear method. [1] P. Heidebrecht, V. Galvita, K. Sundmacher, ?An alternative method for parameter identification from temperature programmed reduction (TPR) data?, Chem. Eng. Sci. 63 (2008), 4776-4788.