Maximization of the profit and reactant conversion considering partial pressures in an ammonia synthesis reactor using a derivative-free method

In the present paper, an optimization model is proposed for the ammonia synthesis reactor. The reversible exothermic reaction has nitrogen and hydrogen as reactants, at high temperatures, and high pressures with iron catalyst. Two different single-objective optimization problems were considered, the maximization of the economic return and the maximization of the nitrogen conversion. The reaction rate model was defined as a function of partial pressures of the components. The problem was coded and solved in MATLAB using a derivative-free method after reformulating a constrained optimization problem into an unconstrained one, by penalizing the infeasibilities of the constraints in the objective functions (barrier function). The main contributions of this paper are the combination of direct-search methods in solving the optimization problem, the evaluation of the maximum ammonia production and the temperature profile. The optimal values found were better than the ones published in the literature. (author)