Optimal operation of distillation columns and link to control

Distillation Course Berlin Summer 2005. Sigurd Skogestad. Part 3

Given feed (F).5 dynamic control degrees of freedom (valves): L, V (QB), VT (QC), D, B

Distillation control

First task: Stabilization and regulatory control (PID loops) Use 3 degrees of freedom for:

Control condenser holdup (stabilization) Control reboiler holdup (stabilization) Control pressure

May want to add (does not remove any degrees of freedom!) Flow controllers Temperature controller (”stabilize profile”)

Here consider second task: Use of remaining 2 degrees of freedom to achieve optimal economic operation (steady-state) Issue: Which ”primary” variables should we control?

Primary controlled variables 2 remaining degrees of freedom for control

What should we control? Often composition in both ends (”two-point control”) but not

always

Systematic approach: Define optimal operation and find optimal point To avhieve optimal operation in practice:

”Control active constraints” Control ”self-optimizing” for uncontrained degrees of freedom (if

any)

Optimal operation distillation column

Steady-state DOFs (given p and F): 2, for example L/D and V Cost to be minimized (economcs)

J = - P where P= pD D + pB B – pF F – pV V

ConstraintsPurity D: For example xD, impurity · max

Purity B: For example, xB, impurity · max

Flow constraints: min · D, B, L etc. · max

Column capacity (flooding): V · Vmax, etc.

Pressure: 1) p given, 2) p free: pmin · p · pmax

Feed: 1) F given 2) F free: F · Fmax

Optimal operation: Minimize J with respect to steady-state DOFs

value products

cost energy (heating+ cooling)

cost feed

Solution to optimal operation distillation

Cost to be minimizedJ = - P where P= pD D + pB B – pF F – pV V

Optimal operation: Minimize J with respect to DOFs General: Optimal solution with N DOFs:

N – Nu DOFs used to satisfy “active” constraints (· is =) Nu remaining unconstrained variables

Usually: Nu zero or small Distillation at steady state with given p and F:

N=2 DOFs.

Three cases:1. Nu=0: Two active constraints (for example, xD, impurity = max. xB,

impurity = max, “TWO-POINT” CONTROL)

2. Nu=1: One constraint active

3. Nu=2: No constraints activevery unlikely unless there are no purity specifications(e.g. byproducts or recycle)

Expected active constraints distillation

valuable product methanol + max. 0.5% water

cheap product(byproduct)water + max. 0.1%methanol

methanol+ water

Cost to be minimizedJ = - P where P= pD D + pB B – pF F – pV V

Amount of valuable product (D or B) should be maximized

Implication for valuable product:Avoid quality give-away (overfractionation) ) Product. spec. valuable product is always active (and should be controlled for optimal operation) Methanol + water example: Keep xD, impurity = 0.5%

(max.) “Sell cheap product (water) as valuable product” This also saves energy (because overfractionation

requires larger reflux and more energy)

Expected active constraints distillation

valuable product methanol + max. 0.5% water

cheap product(byproduct)water + max. 0.1%methanol

methanol+ water

Amount of valuable product (D or B) should be maximized

Implication for cheap product:We may reduce the loss of valuable product by over-fractionating the cheap end, but this costs more energy. Two cases:1. Keep spec. (active constraint) if energy is expensive (Nu=0)2. Overpurify if energy is cheap

(a) Unconstrained optimum (Nu=1) : Optimal composition is determined by trade-off between energy costs and value of increased recovery,

(b) Reach capacity constraint (Nu=0): Loss of valuable product is minimized by operating at V=Vmax.

Methanol + water example: Since methanol loss is anyhow low (0.1% of water), it may not be optimal to overpurify. With energy very cheap, it is probably optimal to operate at V=Vmax.

Expected active constraints distillation: Summary

Always control valuable product at purity spec. Avoid quality give-away

Remaining degree of freedom. Most common cases:

1. Control cheap product at purity spec. (Nu=0) “TWO-POINT CONTROL” If loss (of valuable product) in “cheap end” is small

2. Operate at max. load V=Vmax (Nu=0) “ONE-POINT CONTROL” Maximize yield (of valuable product) if large difference in product values and

energy is cheap

3. Unconstrained (Nu=1) Usually “TWO-POINT” but not always Operate at optimal trade-off between energy costs and value of improved yield

(of valuable product)