Choosing optimal control policies using the attainable region approach

Previously, the attainable region has been constructed for systems where th e rate vector is uniquely defined. In this paper we extend the attainable r egion approach to situations where the rate vector depends on a control par ameter, such as temperature. In these cases, the rate vector can take on a range of values, depending on the value of the control parameter. Arguments based on the geometry of the boundary of the attainable region are used to derive equations that describe the optimal control policies. These conditi ons are applied to various examples and both the optimal reactor structures as well as optimal operating and control policies are derived by looking a t the structures that make up the boundary of the attainable region. In par ticular, an example is given where the optimal reactor structure has a reac tor with simultaneous side stream addition and temperature control.