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

2. Given feed (F). 5 dynamic control degrees of freedom (valves): L, V (Q B ), V T (Q C ), 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= p D D + p B B – p F F – p V V Constraints Purity D: For example x D, impurity · max Purity B: For example, x B, impurity · max Flow constraints: min · D, B, L etc. · max Column capacity (flooding): V · V max, etc. Pressure: 1) p given, 2) p free: p min · p · p max Feed: 1) F given 2) F free: F · F max Optimal operation: Minimize J with respect to steady-state DOFs value products cost energy (heating+ cooling) cost feed

6. Solution to optimal operation distillation Cost to be minimized J = - P where P= p D D + p B B – p F F – p V V Optimal operation: Minimize J with respect to DOFs General: Optimal solution with N DOFs:  N – N u DOFs used to satisfy “active” constraints ( · is =)  N u remaining unconstrained variables Usually: N u zero or small Distillation at steady state with given p and F: N=2 DOFs. Three cases: 1. N u =0: Two active constraints (for example, x D, impurity = max. x B, impurity = max, “TWO-POINT” CONTROL) 2. N u =1: One constraint active 3. N u =2: No constraints active very unlikely unless there are no purity specifications (e.g. byproducts or recycle)

7. Expected active constraints distillation valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% methanol + water Cost to be minimized J = - P where P= p D D + p B B – p F F – p V 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 x D, impurity = 0.5% (max.)  “Sell cheap product (water) as valuable product”  This also saves energy (because overfractionation requires larger reflux and more energy)

8. Expected active constraints distillation valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% 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 (N u =0) 2. Overpurify if energy is cheap (a) Unconstrained optimum (N u =1) : Optimal composition is determined by trade-off between energy costs and value of increased recovery, (b) Reach capacity constraint (N u =0): Loss of valuable product is minimized by operating at V=V max.  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=V max.

9. 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. (N u =0) “TWO-POINT CONTROL”  If loss (of valuable product) in “cheap end” is small 2. Operate at max. load V=V max (N u =0) “ONE-POINT CONTROL”  Maximize yield (of valuable product) if large difference in product values and energy is cheap 3. Unconstrained (N u =1) Usually “TWO-POINT” but not always  Operate at optimal trade-off between energy costs and value of improved yield (of valuable product)