Step 2. Degree of freedom (DOF) analysis Nm : no. of dynamic (control) DOFs (valves) Nss = Nm- N0 : steady-state DOFs N0 : liquid levels with no steady-state effect (N0y)+ purely dynamic control DOFs (N0m) Cost J depends normally only on steady-state DOFs

Distillation column with given feed Nm = 5, N0y = 2, Nss = 5 - 2 = 3 (2 with given pressure)

Heat-integrated distillation process

Step 4. Where set production rate? Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts

Production rate set at inlet : Inventory control in direction of flow

Production rate set at outlet: Inventory control opposite flow

Production rate set inside process

Definition of bottleneck A unit (or more precisely, an extensive variable E within this unit) is a bottleneck (with respect to the flow F) if - With the flow F as a degree of freedom, the variable E is optimally at its maximum constraint (i.e., E= Emax at the optimum) - The flow F is increased by increasing this constraint (i.e., dF/dEmax > 0 at the optimum). A variable E is a dynamic( control) bottleneck if in addition - The optimal value of E is unconstrained when F is fixed at a sufficiently low value Otherwise E is a steady-state (design) bottleneck.

Heat integrated distillation process: Given feedrate with production rate set at inlet

Heat integrated distillation process: Reconfiguration required when reach bottleneck (max. cooling in column 2)

Heat integrated distillation process: Given feedrate with production rate adjusted at bottleneck (column 2) SET