1. 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

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

3. Heat-integrated distillation process

4. 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

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

6. Production rate set at outlet: Inventory control opposite flow

7. Production rate set inside process

8. 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.

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

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

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