Robust design of catalysts using stochastic nonlinear optimization

Computational methods for designing an optimal catalyst have recently been gaining more popularity in the fields of catalysis and reaction engineering of energy systems. However, in general, the problem in these approaches is that uncertainties present in process models should be handled correctly to achieve a robust design. To find the optimal design under these uncertainties, a stochastic optimization method can be employed. In this work, the optimal properties of a catalyst for ammonia decomposition to produce hydrogen are investigated, and uncertainties associated with the reactions and their parameters are modeled as exogenous uncertain variables which follow known probability distributions. The goal of this work is to find the optimal binding energies of the catalyst that maximize conversion of ammonia in a microreactor. Our stochastic optimization problem is nonlinear, and involves the expectation operator as well as integration in the objective function. To tackle this complex system, the expectation of conversion based on a sample average approximation (SAA) method is evaluated. However, the exponential increase in the number of samples to be considered with the number of uncertain parameters lead to severe computational problems when using all possible combinations of the uncertain parameters. To solve this, linearity analysis, together with partial least squares, is implemented to reduce the number of uncertain parameters. In the optimization step, a particle swarm optimization (PSO) is employed. The results indicate that the stochastic optimum shows higher conversion and different optimal binding energies than the deterministic optimum, and is a more robust solution.