This paper investigates application of SQP optimization algorithms to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs. full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.

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In this work, a two-dimensional model for a conventional packed-bed membrane reactor (CPBMR) is developed for the oxidative coupling of methane, which uses a nonselective porous membrane to continuously feed oxygen to the catalytic bed. The model incorporates radial diffusion and thermal conduction and assumes convective transport for the axial direction. In addition, two 10 cm long cooling segments for the CPBMR were implemented based on the idea of a fixed cooling temperature outside the reactor shell. The resulting model is discretized using two-dimensional orthogonal collocation on finite elements with a combination of Hermite polynomials for the radial and Lagrangian polynomials for the axial coordinate. The simulation study shows that it is necessary to make all transport coefficients dependent on local temperatures and compositions. This leads to a simulation with roughly 130,000 variables, which is then used to generate initial points for the optimization of the CPBMR stand-alone operation. In addition, inequality constraints and variable bounds are introduced so as to avoid potentially hazardous mixtures of methane and oxygen in both shell and tube as well as to keep the temperatures below levels stressing reactor materials (< 1,100 °C). Moreover, membrane thickness, feed compositions, temperatures at the reactor inlet and for the cooling segments, diameters of tube and shell, and finally the amount of inert packing in the reactor are considered as decision variables. The optimization procedure uses IPOPT as a solver. Afterwards, the 2D model is integrated into a membrane reactor network (MRN) proposed by H. Godin, 2010 which is simulated. Finally, attempts are made to optimize its operation