Degrees of Freedom Analysis

A simple two-product distillation column with a single feed and a total condenser has five degrees of freedom. These correspond to control valves that vary the following quantities:

• the distillate product draw rate (D);

• the reboiler duty (QR or V to denote the internal vapour rate);

• the reflux rate (L for the internal liquid rate);

The condenser and reboiler duties usually cannot be manipulated directly but the designations, QR and Qc, are used to represent the group of variables which could be used to adjust the duty in each case. For example, the control valve which is designated to regulate the condenser duty might actually manipulate the coolant flow rate (either directly or indirectly by regulating the bypass rate), the active surface area of the condenser or the rate at which vapour is withdrawn from the column. Similarly, the method of regulating the reboiler duty could be the heating medium flow rate, the reboiler exchanger area or the process flow through the reboiler.

The column pressure, the reboiler sump level and the reflux accumulator level (i.e. the column vapour and liquid inventory) must all be stabilised for the column to operate in a steady-state. The column pressure is almost always controlled via the condenser duty (Luyben, 1992) and tight control is usually achievable with a simple SISO control loop. The liquid inventory can usually also be controlled by two simple SISO controllers provided either the distillate rate or the reflux rate is used to control the reflux accumulator level and either the bottoms rate or the reboiler duty is used to control the reboiler sump level.

Therefore, two degrees of freedom remain for the control of the process objectives. If neither of these variables is used within a control loop (i.e. the process operator manipulates the control valves directly), the column is said to be operated in open-loop or manual. If only one of these variables is manipulated automatically to control a measured property, a one-point or single composition control scheme is deemed to be in use. In this case, the remaining degree of freedom is usually fixed at a constant value or manipulated only occasionally to reflect capacity constraints (e.g. maximum reboiler duty or flooding). Finally, both available degrees of freedom can be utilised within control loops. This is known as two-point or dual composition control.

Was this article helpful?

0 0

Post a comment