Tuesday, October 18, 2011: 10:35 AM

205 A (Minneapolis Convention Center)

Control and operation of distillation columns has been widely studied, as

illustrated by for example Skogestad (1993). Normally, it is assumed that the

task is to control the product compositions at given setpoints (”two-point control”).

However, in many cases it may be economically optimal to overpurify

one of the products, and it is then no longer clear that two-point control is the

best.

Somewhat surprisingly, the issue of optimal economic operation of distillation

columns has been studied relatively little. The issue of active constraints

for economically optimal operation was addressed about 40 years ago by (Maarleveld

and Rijnsdorp, 1970), but they considered the extra degrees of freedom

related to column pressure and preheating, and assumed two-point composition

control. (Gordon, 1986) studied economical optimal operation and how

it relates to product purity control. He introduced the avoid product giveaway

rule, which states that it is optimal to maximize the flow of the more expensive

product by keeping the amount of impurities in that stream at the maximum

allowed (Gordon, 1986). The implication is that that one should always control

the purity of the expensive product (active constraint rule). In this paper, we

discuss this rule and point out its possible limitations.

When seeking to operate any plant in an economically optimal way, it is

often critical to know which operational constraints are optimally active. The

main focus of the paper is on showing how to identify active constraint regions

as function of disturbances, through:

• Using knowledge of the optimization problem and of the behavior of distillation

columns.

• Finding points in the disturbance space where individual constraint functions

change between active and inactive, by finding where the sum of

each constraint and its corresponding Lagrange multiplier is zero.

The second is used as an alternative to optimizing the model at a large

number of points all over the disturbance space, thus decreasing the need for

repeated optimizations.

We have identified how the active constraint set varies with the disturbances

(feed flow rate and energy cost) for a single two-product column (with fixed

product prices, case Ia) and with purity-dependent distillate price (case Ib))

and for two distillation columns in sequence (case II).

The results of this work serve to illustrate the following:

1. The complexity of the active constraint regions even for a relatively simple

problem

2. How process knowledge can be used to reduce the need for (potentially

time-consuming) optimization

3. Show when the avoid product giveaway rule is valid

For case Ia, we found that we had three distinct regions with different active

sets. In case Ib we identified five regions, and in case II we identified eight.

Only in case Ib did we find a region in which no constraints were active, which

was in keeping with the avoid product giveaway rule. We showed that the

borders between regions where only purity constraints are optimally active, are

independent of feed flow rate.

We have also explained how the avoid product giveaway rule depends on

two assumptions, of which one (one gets paid for the entire product stream, not

just the desired component) is often valid and the second (overpurification costs

energy) is always valid for realistic distillation cases.

References

Gordon, L., 1986. Simple optimization for dual composition control. Hydrocarbon

Process.;(United States) 65 (6).

Maarleveld, A., Rijnsdorp, J., 1970. Constraint control on distillation columns.

Automatica 6 (1), 51 – 58.

Skogestad, S., 1993. Dynamics and control of distillation columns – a critical

survey:. Control Engineering Practice 1 (3), 564 – 564.

**Extended Abstract:**File Not Uploaded

See more of this Session: Distillation Honors Session I: William Luyben

See more of this Group/Topical: Separations Division

See more of this Group/Topical: Separations Division