Complex distillation systems. Theory and models. Pio Aguirre - - PowerPoint PPT Presentation

Complex distillation systems. Theory and models.

Pio Aguirre INGAR Santa Fe-Argentina

1.- Introduction. 2.- Theory in simple columns design. 3.- Reversible distillation columns and sequences. 4.- Optimal synthesis distillation columns sequences.

Outline

1.- Introduction.

Mathematical models in Distillation⇒ predict values: Product composition for F (xF) Minimum energy demand Rmin Minimum number of stages Nmin Relationship R/Rmin vs N/Nmin Mathematical models for: Process optimization, design, synthesis. Process control. Process fault diagnosis. Interest in Distillation grows because of: Energy intensive process: Petrochemical, Biofuels. New processes. Complex sequences: energy intensive. Reactive distillation: equipment intensive. Reactive-extractive distillation. High improvement potentials in distillation processes.

1.- Introduction.

Different mathematical models according to their sizes: Aggregated (reduced): minimal information. Simple analytical formulae. Short cuts: few equations but require numerical solution. Rigorous: conservation laws, thermodynamics and constitutive models. Trade off: size and complexity vs. information. Limitations: Rigorous models ⇒ general purpose. Simple and reduced models ⇒ especial cases.

Fundamental concepts in distillation Models components: Mass balances V-L equilibrium Energy balances Very exact descriptions using rigorous models for distillations Concepts derived from distillation theory: Pinch points Residue curves Distillation points

1.- Introduction

2.- Theory in simple columns design.

Thermodynamic aspects V-L Equilibrium Ideal Mixtures T vs X(Y), P=cte. diagram

NC i T P P T y x K = K

i i i

... , 1 ); ( ) , , , ( = =

i i i

x T K y ) ( =

Mathematical models. Minimum energy demand. Minimum number of stages.

Simple columns. Mathematical models. Minimum energy demand. Minimum number of stages. Assumptions: Constant relative volatility and Constant difference in vaporization enthalpy ⇓ Constant Molar Overflow (CMO) ⇓ Straight operating line, decoupling mass and energy balances Y vs X diagram

2.- Theory in simple columns design.

Computing minimum energy demand. Constant molar overflow ⇒ Operating points belong to Straight lines Tray by tray calculations, equilibrium stages

Minimum energy demand. Pinch at Feed tray. The number of stages increases at the feed location.

Minimum number of stages. Total reflux = Distillation points Xk ⇒VLE ⇒ Yk

* = Xk+1 ⇒ VLE ⇒ Y* k+1 = Xk+2 …

V-L Equilibrium Non- Ideal Mixtures X vs Y ; P=cte. diagram

); ( ) , ( ) , , , ( T P T x P T y x K = K

i i i i

γ =

Constant molar overflow?.

Multicomponent systems. Adiabatic Column. Constant

• pressure. Rigorous simulation.

Liquid composition profiles

10 20 30 40 50 60 70 80 90 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

A B C Feed Stage: 42 Fraccion Molar Stages

Composition profiles (F, i = 0.33/ 0.33/ 0.34 - D, i = 0.7946/ 0.205/ 0 - B, i = 0/0.4184/0.5815 - p = 101.3 Kpa) n-pentane, n-hexane and n-heptane

Pinch points?

1

(1)

Increasing Reboil Ratio 2 3 4 5 Adiabatic Stripping Profile

(2) (3)

B

Ternary systems. Adiabatic Column. Constant pressure. Liquid composition profiles. Rigorous simulation. Specifying a liquid product composition (B) and the reboil ratio, the succession of liquid composition tray- tray profile can be computed. The liquid profile approaches a pinch point. The number of stages ⇒ ∞ at each point: 1, 2, …

1

(1)

Increasing Reboil Ratio

Reversible Profile

2 3 4 5

Adiabatic Stripping Profile

(2) (3)

B

Ternary systems. Adiabatic Column. Constant pressure. Liquid composition profiles Specifying: 1) liquid product composition (B) 2) reboil ratio value 3) equilibrium between L* and V*, a liquid composition can be computed. Changing reboil ratio⇒ different pinch point composition

L* V* F

*

B Pinch

Reversible Profile = Collection of Pinch

Reversible path for a bottom: distillative alcoholic mixture.

Reversible Profile Adiabatic Profiles

Energy Reversible Path Temperature

Reversible path for a bottom: distillative alcoholic mixture. Starting from product D (TD) and increasing reboil ratio, the profile is computed. Temperature and Energy results from the reversible profile.

Reversible path for a bottom (B): azeotropic system. Points computed with newton homotopy.

Acetone

Acetone-Chloroform Azeotrope Chloroform Benzene Benzene Reversible Profile Disjunct Arm Acetone

L* L V V* F D rev Q C rev Q H rev

*

Specifying: 1) Feed composition, 2) product compositions B and D satisfying total mass balance, 2) reboil and reflux ratios satisfying total energy balance, 3) equilibrium between L* and V* and between L and V, liquid composition profiles can be computed. PINCH CURVES, PINCH PATHS, REVERSIBLE PROFILES, REVERSIBLE PATHS, ETC. NO ASSUMPTION ON V-L EQUILIBRIUM AND ON ENTHALPY MODELS 3.- Reversible distillation columns and sequences.

s s

V = D + L

s i s D i s i s

y V = x D + x L

, , , s V s D D s L s

h V = Q h D + h L

, ,

+

) , , , (

, , s s s i s i i i

p T y x K = K

) , , (

, , , s s s i s L s L

p T x h = h ) , , (

, s s s i V V

p T y h = h

C s

p = p

s i s i s i

x K y

, , , =

Mass balances Given: XD, YD, P, TD and QD at least one liquid composition can be computed: X,s s ∈ S: set of different kinds of pinches. NO ASSUMPTION ON V-L EQUILIBRIUM AND ON ENTHALPY MODELS Equilibrium Energy balance Thermodynamic Properties Constant pressure PINCH EQUATIONS 3.- Reversible distillation columns and sequences.

Reversible Profile from D Reversible Profile from B

Pinch profiles for products B and D. Mass balance line: B-F-D Pinch points satisfying total energy balance. NO ASSUMPTION ON V-L EQUILIBRIUM AND ON MOLAR FLOWS 3.- Reversible distillation columns and sequences.

Reversible Profile from D Reversible Profile from B

Pinch profiles for products B and D. Mass balance line: B-F-D Moving F : Reversible specification NO ASSUMPTION ON V-L EQUILIBRIUM AND ON MOLAR FLOWS Reversible specification Reversible profiles intersect at feed composition

Axis – Binary Reversible Profile

Adiabatic Profiles Reversible Profile from Top Reversible Profile from Bottom

Pinch profiles for products B and D. Sharp splits. Adiabatic profiles and pinch profiles. Pinch points → critical points for the adiabatic profiles NO ASSUMPTION ON V-L EQUILIBRIUM AND ON MOLAR FLOWS Stable pinch Saddle pinch

Brev, max

(3) (2) (1) F

Drev, max

y *

Drev, max Brev, max

F

Upper Saddle Pinch Point Lower Saddle Pinch Point Double Pinch Point Q H, rev Q C, rev min

Reversible Distillation. (Sharp). For each feed composition, there exists a special, “preferred” specification. V-L equilibrium vector (Y*-X*) belongs to Mass balance line: D-F-B. NO ASSUMPTION ON V-L EQUILIBRIUM AND ON MOLAR FLOWS

Reversible distillation. For each feed composition, there exists a special “preferred” product specification set. Other product specifications ⇒ Non reversible distillation (1 col.) Are pinch points always “observable” in adiabatic columns profiles? It depends on feed and product specification and on RR. Non sharp in this figure.

D rev B rev, max B rev, max (3) (2) (1) F D rev y * F

Lower Saddle Pinch Point

Q > Q H, rev Q > Q C, rev

Adiabatic profile shape is determined by the pinch point.

Adiabatic Profiles

Reversible distillation. (Y* - X*) B-F-D ⇒ Reversible specification “Observable” pinch in adiabatic column. Double feed pinch.

Non Reversible distillation. (X* - Y*) ⊈ B-F-D Pinch topology. Specifying reflux and reboil ratios Three pinches for D→ upper triangle Three pinches for B → lower triangle Minimum reflux⇒ pinch triangles touch each other at Feed composition Note: some pinches outside: xb<0

Residue curves distillation lines Pinch profiles and Residue curves dominate distillation theory.

Acetone Benzene Chloroform

Distillation boundary (DB) Not possible to cross DB at total reflux

i i i Vap i Vap i

y = x K F = dt dV y F = dt x V d − − ) (

i i i Vap i i Vap i

y = x K F = dt dV x y F = dt x d V − − − ) (

Residue curves

V; X; T; P Fvap; Y; T; P

Heptane Benzene Acetone

Residue curves / distillation lines Azeotropic system with no distillation boundary

Residue curves divide the simplex in two regions. One region may be convex. Adiabatic profiles only cross residue curves to the locally convex side when going from products to feed. Ternary systems

100 200 300 1,05 1,10 1,15 1,20 rectifying section stripping section

Reduce Temperature T/298·K Cumulative Energy (KJ/s)

Cumulative energy profiles

• btained from pinch equations.

Ideal three-component mixture Improving energy distribution in Simple columns. Temperature – Energy Pinch profiles

Pinch path for 4-component mixture. # of paths into the simplex: 3

Improving energy distribution in simple columns.

Pinch path for 3-component mixture. # of paths into the simplex: 2 Which one should be used to approximate reversible profiles?

Improving energy distribution in simple columns.

A Pinch path for non ideal mixture. Tangent pinch is possible. Minimum energy determined by tangent pinch.

Improving energy distribution in simple columns.

Benzene Chloroform Acetone

Benzene

Adiabatic Profiles Reversible Profiles

Acetone

Improving energy distribution in simple columns.

Minimum energy determined by feed pinch.

Benzene Chloroform Acetone

Acetone Benzene

Adiabatic Profiles

Distillate Reversible Profile

Improving energy distribution in simple columns.

Minimum energy determined by tangent pinch.

Separations involving tangent pinch. Residue curve with inflexion points.

Improving energy distribution in simple columns.

Chloroform Acetone Benzene

Reversible Distillation Sequence Model (RDSM) What is the superstructure that most closely approximates the Reversible Distillation

• f

Multicomponent Mixtures like? Which is the optimal energy distribution in the RDSM-based sequence?

3.- Reversible distillation columns and sequences.

Theoretical model. Infinite number of stages. Continuous heat distribution along column length. Heat to and from the column is transferred at zero temperature difference. No contact of non-equilibrium streams take place in any point of the column. Only one separation task can be performed: the reversible separation. A Reversible Column

F Drev Brev

QC rev =Σ QC rev i

QH rev =Σ QH rev i F Drev Brev QC rev i QH rev i

i i

A sufficiently high number of stages must be employed. The same energy is involved in the separation with a different distribution. The same products are achieved but different composition profiles develop within each unit. RDC Adiabatic Approach

RDSM Sequence

A B C D A B C B C D C D B C D C C B C B C A B B B A A B C D B C D C D B C C A B D A A B C B C B B C

1 2 6 3 4 5 7

RDSM-based Sequence

RDSM-based Synthesis Model

Preprocessing Phase

Single Column Preprocessing Phase

Efficient Sequence Synthesis Model

Sequence Preprocessing Phase

Preprocessing Phase

Optimal Energy Distribution for

each single unit. Number of stages for each single column of the sequence. Objective functions and constraints to approach the reversible separation task.

Values to initializate variables.

Values to bound critical variables related to unit interconnection and heat loads. Parameters to formulate objective functions. Sequence Preprocessing

Reversible Products, Saddle Pinch Points and Reversible Exhausting Pinch Points Calculations

Single Column Preprocessing

Adiabatic Approximation to the Reversible Separation

Initialization

xtop i ≈ x rev

i,D

xbot i ≈ x rev

i,B

QC tot ≈ Q rev

C,

QH tot ≈ Q rev

H,

D ≈ Drev B ≈ B rev

x i, s , x*

i, s , y i, s , y* i, s

Ls , L*

s , Vs , V* s

Ts , T*

s

x xF

F i i ,

, q qF

F ,

, p pC

C

Feed Flash Model Reversible Model

hlF , hvF , yF i , TF QC rev , QH rev , x rev

i,D , x rev i,B

hD , hB , Drev , B rev

Single Column Optimization Model

Saddle Pinch Model

Ls , L*

s ,

Vs , V*

s

TD , TB F F

Initialization Initialization

Single Column Preprocessing Adiabatic Approximation to the Reversible Separation

rev

B V = L +

* *

rev B , i rev i * i *

x B y V = x L +

* * rev rev L H V B

L h Q = V h B h + +

rev B a rev D c

x x = z

, ,

min + V = D + L

rev i rev D , i rev i

y V = x D + x L

rev rev L D C V

L h + D h Q = V h +

(RM):

* F

L = F ) q ( L − + 1

* F

V = F q V +

( , , , ) 1, ...

i i i i

K = K x y T p i NC =

( , , )

L L i

h = h x T p

( , , )

V V i

h = h y T p

,

Single Column Preprocessing Adiabatic Approximation to the Reversible Separation Known values from flash calculations at Feed

rev s s

B V = L +

* *

rev rev s i s s i s

B i

x B y V = x L

,

, * , *

+

s rev s

V = D + L

s i s rev rev s i s

y V = x D + x L

D i

, ,

,

(SPM):

( , , , ) 1, ...

i i i i

K = K x y T p i NC =

( , , )

L L i

h = h x T p

( , , )

V V i

h = h y T p

,

Single Column Preprocessing Adiabatic Approximation to the Reversible Separation Known values from flash calculations at Feed

* * * * , , rev rev s L s H s V s B

L h Q = V h B h + +

, , rev rev s L s D C s i s

L h + D h Q = V h +

, , NC s NC s

x y = =

1, 1,

* *

s s

x y = =

The number of trays is selected by optimizing the condenser, reboiler and/or feed stream locations.

F D B F B D F B D

Variable feed and reboiler location

F D B F B D F B D

Variable feed and condenser location

F B D F D B F B D

Variable condenser and reboiler location

F1 Lv

2

Qctot3 PP2 PP1 PP3 F3 = S3 F2 = S2 Ll

2

Qhtot3 Qctot2 Qhtot2 Qctot1 Qhtot1

j =1 j =3 j =2

PLlj

j j +1

PLvj Qphase j < 0 Qphase j > 0 PPj

Ternary mixture. Heat Integration Superstructure

Sequence Preprocessing Reversible Products, Saddle Pinch Points and Reversible Exhausting Pinch Points Calculations

Less efficient RDSM-based superstructures:

PP3 PP1 PP2 F1

1 2 3

PP3 PP1 PP2

F1

1 3 2

Fully Thermally Coupled Scheme (Petlyuk Column) Fully Thermally Coupled Scheme with Heat Integration

ABC ABC BC AB BC A B B

Azeotrop

C B C C D A B A B C B C D A A B C D B C B C B C D

Zeotropic Mixture Azeotropic Mixture

3.- Reversible distillation columns and sequences.

PP3 PP1 PP2

Numerical Examples Models implemented and solved in GAMS employing DICOPT CONOPT.

ppl F1 Qphase Qh3 Qint Qc1 Qh1 Qc2 ppv S3 F3 S2 F2 L2

PLlj

j j +1

PLvj Qphase j < 0 Qphase j > 0 PPj

L2 L3

3.- Reversible distillation columns and sequences.

Entering stage number for Theoretical Our Model Theoretical Our Model Stream Flow rate (mol/sec) Composition Feed: n-pentane, n-hexane, n-heptane 0.3/0.5/0.2 Stages: col1 30, col2 80, col3 50 F2 F3 S2 S3 L2v L2l ppl ppv 5.34 5.36 8.16 8.08 1.05 1.15 2.45 2.29 1.88 1.77 2.49 2.4 0.67 0.60 4.33 4.42 0.6355/0.364/0 0.634/0.3652/6e-4 0/0.714/0.286 4e-3/0.71/0.2856 0.6355/0.364/0 0.634/0.3652/6e-4 0.375/0.625/0 0.373/0.6257/9e-4 0/0.864/0.1356 1e-3/0.863/0.1356 0/1/0 2e-3/0.997/7e-4 0/1/0 2e-3/0.997/7e-4 0/1/0 2e-3/0.997/7e-4 0/1/0 2e-3/0.997/7e-4 40 26 1 30 80 1

• 3.- Reversible distillation columns and sequences.

Theoretical Our Model Heat Duty Energy (KJ/sec) 107.21 114.57

• 16.63
• 18.29
• 204.3
• 203
• 1
• 50.27
• 57.81

293.4 313.78 Qctot1 Qhtot1 Qctot2 Qhtot2 Qctot3 Qhtot3 Flow rate (mol/sec) Composition Product 5.03 5e-3/0.994/3e-4 2.974 0.99/6e-5/0 1.998 0/1e-4/0.999 PP1 PP2 PP3

3.- Reversible distillation columns and sequences.

Problem specs Mixture: N-pentane/ N-hexane/ N-heptane Feed composition: 0.33/ 0.33/ 0.34 Feed: 10 moles/s Pressure: 1 atm Max no trays: 15 (each section) Min purity: 98% Ideal thermodynamics

Superestructure

NLP Model Continuous Variables 3301 Constraints 3230 MILP Model Continuous Variables 15000 Discrete Variables 96 Constraints 8000

PP1 PP2 F PP3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

M

• l

e F r a c t i

• n

n

• p

e n t a n e M

• l

e F r a c t i

• n

n

• h

e x a n e

F e e d C

• l

1 C

• l

2 C

• l

3

Initialization

4.- Optimal synthesis distillation columns sequences.

Optimal Configuration $140,880 /year

Optimal Design Annual cost ($/year) 140,880 Preprocessing(min) 2.20 Subproblems NLP (min) 6.97 Subproblems MILP (min) 2.29 Iterations 5 Total solution time (min) 11.46

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole Fraction n-pentane Mole Fraction n-hexane

Feed Col 1 (tray 1 to 14) Col 1 (tray 15 to 34) Col 2 (tray 1 al 9) Col 2 (tray 10 al 32)

PP3 98% n-heptane

36 9 32

PP2 98% n-hexane

26 19

PP1 98% n-pentane F

Qc = 52.4 kW QH = 298.8 kW 48.8 kW

1 1 1 12 14

Qc = 271.3 kW

PP3 98% n-heptane

12 23

PP2 98% n-hexane

10

PP1 98% n-pentane F

1 22

Dc1 = 0.45 m Dcrect2 = 0.6 m Dcstrip2 = 0.45 m

1 14 23 1

Dcstrip3 = 0.63 m Dcrect3 = 0.45 m

4.- Optimal synthesis distillation columns sequences.

Optimal Configuration $140,880 /año

Optimal Design Annual cost ($/year) 140,880 Preprocessing(min) 2.20 Subproblems NLP (min) 6.97 Subproblems MILP (min) 2.29 Iterations 5 Total solution time (min) 11.46

PP3 98% n-heptane

36 9 32

PP2 98% n-hexane

26 19

PP1 98% n-pentane F

Qc = 52.4 kW QH = 298.8 kW 48.8 kW

1 1 1 12 14

Qc = 271.3 kW

PP3 98% n-heptane

12 23

PP2 98% n-hexane

10

PP1 98% n-pentane F

1 22

Dc1 = 0.45 m Dcrect2 = 0.6 m Dcstrip2 = 0.45 m

1 14 23 1

Dcstrip3 = 0.63 m Dcrect3 = 0.45 m

Side-Rectifier $143,440 /year Direct Sequence $145,040 /year

4.- Optimal synthesis distillation columns sequences.

Problem specifications (Yeomans y Grossmann, 2000) Mixture: Methanol/ Ethanol/ Water Feed composition: 0.5/ 0.3/ 0.2 Feed flowrate: 10 moles/s Pressure: 1 atm Initial trays: 20 (per section) Purity specification: 90%

F methanol ethanol Azeotrope water ethanol

Superstructure

NLP Model Continuous Variables 9025 Constraints 8996 Nonlinear non-zeroes 18230 MILP Model Continuous Variables 12850 Discrete Variables 96 Constraints 18000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracción molar metanol Fracción molar de etanol

Alimentación Líquido columna 1 Líquido columna 2 Líquido columna 3 Líquido columna 4 Líquido columna 5

Initialization

4.- Optimal synthesis distillation columns sequences.

Product Specifications 95%

Optimal Configuration $318,400 /año

Optimal Solution Annual Cost ($/year) 318,400 Preprocessing (min) 6.05 Subproblems NLP (min) 36.3 Subproblems MILP (min) 3.70 Iteraciones 3 Total Solution Time (min) 46.01

F PP6 = 1.292 mole/sec 95% C PP1 = 5.158 mole/sec 95% A PP4 = 0.836 mole/sec 95% B

39 38 35

PP5 = 2.376 mole/sec Azeotrope

. . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 1 . . . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 1 .

M

• l

e F r a c t i

• n

M e t h a n

• l

M

• l

e F r a c t i

• n

E t h a n

• l

F e d d L i q . C

• l

1 L i q . C

• l

2 L i q . C

• l

3

Profiles Optimal Configuration

4.- Optimal synthesis distillation columns sequences.

Conclusions

Distillation optimization with rigorous models remains major computational challenge Optimal feed tray and number of trays problems are solvable Keys: Initialization, MINLP/GDP models Synthesis of complex columns remains non-trivial Progress with initialization, GDP, decomposition Improvements potential in distillation processes