Optimization of a catalytic reactor subject to temperature constraints

The optimal design for maximum yield of SO₃ in the oxidation of SO₂ over a commercial vanadium pentoxide catalyst is considered. The control variables are the wall heat flux and the reactor radius, both as functions of axial distance. The volume and length of the reactor are both specified, as well as the maximum radial-average temperature. The problem is attacked by a partial averaging technique, whereby the full set of state partial differential equations are integrated forward, but a set of ordinary functional-differential adjoint equations are integrated on the backward pass in order to determine the new estimate of the optimal control. It is found that the optimal design consists of two approximately constant-radius adiabatic sections separated by a small intercooler, which is fairly close to existing commercial designs.