Control of outlet concentration in distributed chemical reactors that involve strong coupling between diffusion and convection phenomena is an important subject at the interface of reactor engineering and process control. A detailed description of flow and concentration fields in a distributed chemical reactor generally requires three-dimensional in space and time-dependent computational fluid dynamic (CFD) simulations. However, a direct use of CFD models for control design or dynamic optimization involves significant computational cost. Further, application of advanced model reduction techniques to compute reduced-order models from CFD models may work well in certain cases but might require a huge amount of memory and computational cost when the CFD model consists of millions of grid points needed to accurately describe flow field behavior.

To circumvent the computational complexity brought by the high dimensionality of the dynamic system and possible irregular reactor geometry, a novel input/output approach to control of distributed chemical reactors is proposed based on the concept of residence time distribution. Initially, the residence time distribution and the cumulative residence time distribution of the chemical reactor are determined through high-fidelity CFD simulations. The output variables are then expressed as linear sums of discretized inputs or input gradients using the cumulative residence time distribution to construct an input/output model for the distributed chemical reactor. Subsequently, an optimal control is formulated and solved as a standard least square problem with inequity constraints on the basis of the derived input/output model. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous stirred tank reactor (CSTR) network and a large scale chemical reactor with complex geometry and flow behavior. In the CSTR network example for which a state space model can be easily derived, the proposed control method yields the same control trajectory as the one obtained from Linear Quadratic Regulator (LQR) theory (designed based on the state space model) when there are no input constraints present. In the distributed chemical reactor example with complex geometry and flow behavior, where a low dimensional state-space model cannot be easily derived, the proposed optimal control method computes an optimal control trajectory and is shown to be advantageous over conventional control techniques.