Large-scale DAE-constrained optimization applied to a modified spouted bed reactor for ethylene production from methane

In this paper, a modified spouted bed reactor is proposed to enhance the yield of the oxidative coupling of methane (OCM). Optimization techniques are used to carry out a theoretical analysis of ethylene production via OCM and define some optimal operating conditions of the reacting system. A model-based DAE-constrained optimization strategy is proposed and applied to the OCM process to illustrate the computational capability of the proposed formulation, and the theoretical feasibility of the proposed reactor. The model developed for the reactor is a one-dimensional model composed of material, energy, and momentum balances. This model along with the kinetic model constitute a non-linear and differential-algebraic system, which is discretized using orthogonal collocation on finite elements with continuous profiles approximated by Lagrange polynomials. The resulting algebraic collocation equations are written as equality constraints in the optimization problem, which is solved with the IPOPT solver within the optimization-modeling platform. An initialization routine based on simulations was carried out to guarantee convergence in optimizations. Results from simulations and optimizations showed the potential of combining different reactor concepts to improve the ethylene production from natural gas via oxidative coupling of methane.