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Optimal operation of distillation columns and link to control

Distillation Course Berlin Summer 2005. Sigurd Skogestad. Part 3. Optimal operation of distillation columns and link to control. Given feed (F). 5 dynamic control degrees of freedom (valves): L, V (Q B ), V T (Q C ), D, B. Distillation control.

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Optimal operation of distillation columns and link to control

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  1. Distillation Course Berlin Summer 2005. Sigurd Skogestad. Part 3 Optimal operation of distillation columns and link to control

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

  3. 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?

  4. 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)

  5. 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 • Constraints Purity 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 cost energy (heating+ cooling) value products cost feed

  6. Solution to optimal operation distillation • Cost to be minimized J = - 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: • Nu=0: Two active constraints (for example, xD, impurity = max. xB, impurity = max, “TWO-POINT” CONTROL) • Nu=1: One constraint active • Nu=2: No constraints active very unlikely unless there are no purity specifications (e.g. byproducts or recycle)

  7. Expected active constraints distillation • Cost to be minimized J = - 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) methanol + water valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% methanol

  8. Expected active constraints distillation • 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: • Keep spec. (active constraint) if energy is expensive (Nu=0) • 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. methanol + water valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% methanol

  9. Expected active constraints distillation: Summary • Always control valuable product at purity spec. • Avoid quality give-away • Remaining degree of freedom. Most common cases: • Control cheap product at purity spec. (Nu=0) “TWO-POINT CONTROL” • If loss (of valuable product) in “cheap end” is small • 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 • 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)

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