ECONOMIC PLANTWIDE CONTROL: Control structure design for complete processing plants

1
ECONOMICPLANTWIDE CONTROL Control structure
design for complete processing plants

• Sigurd Skogestad
• Department of Chemical Engineering
• Norwegian University of Science and Tecnology
  (NTNU)
• Trondheim, Norway
• Mexico, April 2012

2
Abstract and bio

• ECONOMIC PLANTWIDE CONTROL Control structure
  design for complete processing plants.
• Sigurd Skogestad , Department of Chemical
  Engineering, Norwegian University of Science and
  Technology (NTNU), Trondheim, Norway
• Abstract A chemical plant may have thousands of
  measurements and control loops. By the term
  plantwide control it is not meant the tuning and
  behavior of each of these loops, but rather the
  control philosophy of the overall plant with
  emphasis on the structural decisions. In
  practice, the control system is usually divided
  into several layers, separated by time scale
  scheduling (weeks) , site-wide optimization
  (day), local optimization (hour), supervisory
  (predictive, advanced) control (minutes) and
  regulatory control (seconds). Such a hiearchical
  (cascade) decomposition with layers operating on
  different time scale is used in the control of
  all real (complex) systems including biological
  systems and airplanes, so the issues in this
  section are not limited to process control. In
  the talk the most important issues are discussed,
  especially related to the choice of variables
  that provide the link the control layers.
• Bio Sigurd Skogestad received his Ph.D. degree
  from the California Institute of Technology,
  Pasadena, USA in 1987. He has been a full
  professor at Norwegian University of Science and
  Technology (NTNU), Trondheim, Norway since 1987
  and he was Head of the Department of Chemical
  Engineering from 1999 to 2009. He is the
  principal author, together with Prof. Ian
  Postlethwaite, of the book "Multivariable
  feedback control" published by Wiley in 1996
  (first edition) and 2005 (second edition). He
  received the Ted Peterson Award from AIChE in
  1989, the George S. Axelby Outstanding Paper
  Award from IEEE in 1990, the O. Hugo Schuck Best
  Paper Award from the American Automatic Control
  Council in 1992, and the Best Paper Award 2004
  from Computers and Chemical Engineering. He was
  an Editor of Automatica during the period
  1996-2002. His research interests include the use
  of feedback as a tool to make the system
  well-behaved (including self-optimizing control),
  limitations on performance in linear systems,
  control structure design and plantwide control,
  interactions between process design and control,
  and distillation column design, control and
  dynamics.

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Trondheim, Norway
Mexico
4
Arctic circle
North Sea
Trondheim
SWEDEN
NORWAY
Oslo
DENMARK
GERMANY
UK
5
NTNU, Trondheim
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Outline

• 1. Introduction plantwide control (control
  structure design)
• 2. Plantwide control procedure
• I Top Down
• Step 1 Define optimal operation
• Step 2 Optimize for expected disturbances
• Step 3 Select primary controlled variables cy1
  (CVs)
• Step 4 Where set the production rate? (Inventory
  control)
• II Bottom Up
• Step 5 Regulatory / stabilizing control (PID
  layer)
• What more to control (y2)?
• Pairing of inputs and outputs
• Step 6 Supervisory control (MPC layer)
• Step 7 Real-time optimization (Do we need it?)

y1
y2
MVs
Process


7
Idealized view of control(PhD control)


8
Practice Tennessee Eastman challenge problem
(Downs, 1991)(PID control)

TC
PC
LC
AC
x
SRC

Where place
??
9
How do we get from PID to PhD control?How we
design a control system for a complete chemical
plant?

• Where do we start?
• What should we control? and why?
• etc.
• etc.

10
How we design a control system for a complete
chemical plant?

• Where do we start?
• What should we control? and why?
• etc.
• etc.

11
Example Tennessee Eastman challenge problem
(Downs, 1991)

TC
PC
LC
AC
x
SRC

Where place
??
12

• Alan Foss (Critique of chemical process control
  theory, AIChE Journal,1973)
• The central issue to be resolved ... is the
  determination of control system structure. Which
  variables should be measured, which inputs should
  be manipulated and which links should be made
  between the two sets? There is more than a
  suspicion that the work of a genius is needed
  here, for without it the control configuration
  problem will likely remain in a primitive, hazily
  stated and wholly unmanageable form. The gap is
  present indeed, but contrary to the views of
  many, it is the theoretician who must close it.

• Previous work on plantwide control
• Page Buckley (1964) - Chapter on Overall process
  control (still industrial practice)
• Greg Shinskey (1967) process control systems
• Alan Foss (1973) - control system structure
• Bill Luyben et al. (1975- ) case studies
  snowball effect
• George Stephanopoulos and Manfred Morari (1980)
  synthesis of control structures for chemical
  processes
• Ruel Shinnar (1981- ) - dominant variables
• Jim Downs (1991) - Tennessee Eastman challenge
  problem
• Larsson and Skogestad (2000) Review of plantwide
  control

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Optimal operation of systems

• Example of systems we want to operate optimally
• Process plant (minimize Jcost)
• Runner (minimize Jtime)
• World Economy
• Maximize welfare (with given environmental
  impact)
• Maximize happiness (with given environmental
  impact)
• Minimize Jenvironmental impact (with given
  minimum welfare)
• General multiobjective
• Min J (scalar cost, )
• Subject to satisfying constraints (environment,
  resources)

14
Theory Optimal operation
ALLMIGHTY GOD? IDEAL COMMUNISM? PROCESS
CONTROL?
Objectives

• Theory
• Model of overall system
• Estimate present state
• Optimize all degrees of freedom
• Problems
• Model not available
• Optimization complex
• Not robust (difficult to handle uncertainty)
• Slow response time
• Process control
• Excellent candidate for centralized control

CENTRALIZED OPTIMIZER
Present state
Model of system
(Physical) Degrees of freedom
15
Practice Engineering systems

• Most (all?) large-scale engineering systems are
  controlled using hierarchies of quite simple
  controllers
• Large-scale chemical plant (refinery)
• Commercial aircraft
• 100s of loops
• Simple components
• on-off PI-control nonlinear fixes some
  feedforward

Same in biological systems
16
Practice Process control

• Practice
• Hierarchical structure

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Process control Hierarchical structure
Director
Process engineer
Operator
Logic / selectors / operator
PID control
u valves
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Dealing with complexity
Plantwide control Objectives
The controlled variables (CVs) interconnect the
layers
OBJECTIVE
Min J (economics)
RTO
cs y1s
Follow path ( look after other variables)
MPC
y2s
Stabilize avoid drift
PID

19
Translate optimal operation into simple control
objectivesWhat should we control?
20
Example Bicycle riding
y1 distance to curb (1 m)
y2 bike tilt (stabilization)
u muscles
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Control structure design procedure

• I Top Down
• Step 1 Define operational objectives (optimal
  operation)
• Cost function J (to be minimized)
• Operational constraints
• Step 2 Identify degrees of freedom (MVs) and
  optimize for
• expected disturbances
• Step 3 Select primary controlled variables cy1
  (CVs)
• Step 4 Where set the production rate? (Inventory
  control)
• II Bottom Up
• Step 5 Regulatory / stabilizing control (PID
  layer)
• What more to control (y2 local CVs)?
• Pairing of inputs and outputs
• Step 6 Supervisory control (MPC layer)
• Step 7 Real-time optimization (Do we need it?)

y1
y2
MVs
Process
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Step 1. Define optimal operation (economics)

• What are we going to use our degrees of freedom u
  (MVs) for?
• Define scalar cost function J(u,x,d)
• u degrees of freedom (usually steady-state)
• d disturbances
• x states (internal variables)
• Typical cost function
• Optimize operation with respect to u for given d
  (usually steady-state)
• minu J(u,x,d)
• subject to
• Model equations f(u,x,d) 0
• Operational constraints g(u,x,d) lt 0

J cost feed cost energy value products
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Step 2. Optimize

• Identify degrees of freedom (u)
• Optimize for expected disturbances (d)
• Identify regions of active constraints
• Need model of system
• Time consuming, but it is offline

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Example Regions of active constraints
Two distillation columns in series. 4 degrees of
freedom feedrate
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Control 2 active constraints (xA, xB) 2
selfoptimizing
5
31
40
13
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Step 3 Implementation of optimal operation

• Optimal operation for given d
• minu J(u,x,d)
• subject to
• Model equations f(u,x,d) 0
• Operational constraints g(u,x,d) lt 0

? uopt(d)
Problem Usally cannot keep uopt constant because
disturbances d change
How should we adjust the degrees of freedom (u)?
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Implementation (in practice) Local feedback
control!
y
Self-optimizing control Constant setpoints for
c gives acceptable loss
Main issue What should we control?
d
Feedforward
Optimizing control
Local feedback Control c (CV)
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Example Optimal operation of runner
Optimal operation - Runner

• Cost to be minimized, JT
• One degree of freedom (upower)
• What should we control?

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Sprinter (100m)
Optimal operation - Runner

• 1. Optimal operation of Sprinter, JT
• Active constraint control
• Maximum speed (no thinking required)

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Marathon (40 km)
Optimal operation - Runner

• 2. Optimal operation of Marathon runner, JT
• Unconstrained optimum!
• Any self-optimizing variable c (to control at
  constant setpoint)?
• c1 distance to leader of race
• c2 speed
• c3 heart rate
• c4 level of lactate in muscles

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Conclusion Marathon runner
Optimal operation - Runner
select one measurement
c heart rate

• Simple and robust implementation
• Disturbances are indirectly handled by keeping a
  constant heart rate
• May have infrequent adjustment of setpoint
  (heart rate)

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Further examples

• Central bank. J welfare. cinflation rate
  (2.5)
• Cake baking. J nice taste, c Temperature
  (200C)
• Business, J profit. c Key performance
  indicator (KPI), e.g.
• Response time to order
• Energy consumption pr. kg or unit
• Number of employees
• Research spending
• Optimal values obtained by benchmarking
• Investment (portofolio management). J profit. c
  Fraction of investment in shares (50)
• Biological systems
• Self-optimizing controlled variables c have
  been found by natural selection
• Need to do reverse engineering
• Find the controlled variables used in nature
• From this identify what overall objective J the
  biological system has been attempting to optimize

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Step 3. What should we control (c)? (primary
controlled variables y1c)

• Selection of controlled variables c
• Control active constraints!
• Unconstrained variables Control self-optimizing
  variables!

33
Example active constraint Optimal operation
max. throughput (active constraint)
Want tight bottleneck control to reduce backoff!
Rule for control of hard output constraints
Squeeze and shift! Reduce variance
(Squeeze) and shift setpoint cs to reduce
backoff
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Control self-optimizing variables
Unconstrained degrees of freedom

• Old idea (Morari et al., 1980)
• We want to find a function c of the process
  variables which when held constant, leads
  automatically to the optimal adjustments of the
  manipulated variables, and with it, the optimal
  operating conditions.
• The ideal self-optimizing variable c is the
  gradient (c ? J/? u Ju)
• Keep gradient at zero for all disturbances (c
  Ju0)
• Problem no measurement of gradient

Ju
Ju0
35
H
Ideal c Ju In practise c H y. Task
Determine H!
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Systematic approach What to control?

• Define optimal operation Minimize cost function
  J
• Each candidate c Hy
• Brute force approach With constant
  setpoints cs compute loss L for expected
  disturbances d and implementation errors n
• Select variable c with smallest loss

Acceptable loss ) self-optimizing control
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Example recycle plant. 3 steady-state degrees of
freedom (u)Minimize JV (energy)
Active constraint Mr Mrmax
Self-optimizing
Active constraint xB xBmin
L/F constant Easier than two-point control
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Optimal operation
Unconstrained optimum
Cost J
Jopt
copt
Controlled variable c
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Optimal operation
Unconstrained optimum
Cost J
d
Jopt
n
copt
Controlled variable c

• Two problems
• 1. Optimum moves because of disturbances d
  copt(d)
• 2. Implementation error, c copt n

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Good candidate controlled variables c (for
self-optimizing control)

• The optimal value of c should be insensitive to
  disturbances
• Small Fc dcopt/dd
• c should be easy to measure and control
• Want flat optimum -gt The value of c should be
  sensitive to changes in the degrees of freedom
  (large gain)
• Large G dc/du HGy

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Flat optimum is same as large gain
J
Optimizer
c
cs
n
cm c n
Controller that adjusts u to keep cm cs
cscopt
u
H
y
ny
Plant
d
uopt
u
) Want c sensitive to u (large gain)
42
Optimal measurement combinations

• Optimal policy independent of disturbances
• Need model or data for optimal response to
  disturbances
• Marathon runner case
• c h1 hr h2 v
• Extension to polynomial systems
• Preheat train for energy recovery (Jäschke)
• Patent pending

43
Optimal measurement combination

• Candidate measurements (y) Include also inputs u

H
44
Optimal measurement combination Nullspace method

• Want optimal value of c independent of
  disturbances ) ? copt 0 ? d
• Find optimal solution as a function of d
  uopt(d), yopt(d)
• Linearize this relationship ?yopt F ?d
• F optimal sensitivity matrix
• Want
• To achieve this for all values of ?d (Nullspace
  method)
• Always possible if
• Comment Nullspace method is equivalent to Ju0

45
Example. Nullspace Method for Marathon runner

• u power, d slope degrees
• y1 hr beat/min, y2 v m/s
• F dyopt/dd 0.25 -0.2
• H h1 h2
• HF 0 -gt h1 f1 h2 f2 0.25 h1 0.2 h2 0
• Choose h1 1 -gt h2 0.25/0.2 1.25
• Conclusion c hr 1.25 v
• Control c constant -gt hr increases when v
  decreases (OK uphill!)

46
Example CO2 refrigeration cycle
pH
J Ws (work supplied) DOF u (valve opening,
z) Main disturbances d1 TH d2 TCs
(setpoint) d3 UAloss What should we
control?
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CO2 refrigeration cycle

• Step 1. One (remaining) degree of freedom (uz)
• Step 2. Objective function. J Ws (compressor
  work)
• Step 3. Optimize operation for disturbances
  (d1TC, d2TH, d3UA)
• Optimum always unconstrained
• Step 4. Implementation of optimal operation
• No good single measurements (all give large
  losses)
• ph, Th, z,
• Nullspace method Need to combine nund134
  measurements to have zero disturbance loss
• Simpler Try combining two measurements. Exact
  local method
• c h1 ph h2 Th ph k Th k -8.53 bar/K
• Nonlinear evaluation of loss OK!

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CO2 cycle Maximum gain rule
49
Refrigeration cycle Proposed control structure
Control c temperature-corrected high pressure.
k -8.5 bar/K
50
With measurement noise
Optimal measurement combination, c Hy
0 in nullspace method (no noise)
Minimize in Maximum gain rule ( maximize S1 G
Juu-1/2 , GHGy )
Scaling S1


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Case study
Control structure design using self-optimizing
control for economically optimal CO2 recovery
Step S1. Objective function J energy cost
cost (tax) of released CO2 to air

• 4 equality and 2 inequality constraints
• stripper top pressure
• condenser temperature
• pump pressure of recycle amine
• cooler temperature
• CO2 recovery 80
• Reboiler duty lt 1393 kW (nominal 20)

Step S2. (a) 10 degrees of freedom 8 valves 2
pumps
4 levels without steady state effect absorber
1,stripper 2,make up tank 1
Disturbances flue gas flowrate, CO2 composition
in flue gas active constraints
(b) Optimization using Unisim steady-state
simulator. Region I (nominal feedrate) No
inequality constraints active 2 unconstrained
degrees of freedom 10-4-4
Step S3 (Identify CVs). 1. Control the 4 equality
constraints 2. Identify 2 self-optimizing CVs.
Use Exact Local method and select CV set with
minimum loss.
M. Panahi and S. Skogestad, Economically
efficient operation of CO2 capturing process,
part I Self-optimizing procedure for selecting
the best controlled variables'', Chemical
Engineering and Processing, 50, 247-253 (2011).
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Proposed control structure with given feed
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Step 4. Where set production rate?

• Where locale the TPM (throughput manipulator)?
• The gas pedal of the process
• Very important!
• Determines structure of remaining inventory
  (level) control system
• Set production rate at (dynamic) bottleneck
• Link between Top-down and Bottom-up parts

54
Production rate set at inlet Inventory control
in direction of flow
TPM
Required to get local-consistent inventory
controlC
55
Production rate set at outletInventory control
opposite flow
TPM
56
Production rate set inside process
TPM
Radiating inventory control around TPM (Georgakis
et al.)
57
LOCATE TPM?

• Conventional choice Feedrate
• Consider moving if there is an important active
  constraint that could otherwise not be well
  controlled
• Good choice Locate at bottleneck

58
Step 5. Regulatory control layer

• Purpose Stabilize the plant using a simple
  control configuration (usually local SISO PID
  controllers simple cascades)
• Enable manual operation (by operators)
• Main structural decisions
• What more should we control? (secondary CVs, y2,
  use of extra measurements)
• Pairing with manipulated variables (MVs u2)

59
Degrees of freedom for optimization (usually
steady-state DOFs), MVopt CV1s Degrees of
freedom for supervisory control, MV1CV2s
unused valves Physical degrees of freedom for
stabilizing control, MV2 valves (dynamic
process inputs)
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Main objectives control system

1. Implementation of acceptable (near-optimal)
   operation
2. Stabilization

• ARE THESE OBJECTIVES CONFLICTING?
• Usually NOT
• Different time scales
• Stabilization fast time scale
• Stabilization doesnt use up any degrees of
  freedom
• Reference value (setpoint) available for layer
  above
• But it uses up part of the time window
  (frequency range)

61
Example Exothermic reactor (unstable)
Active constraints (economics)Product
composition c level (max)

• u cooling flow (q)
• y1 composition (c)
• y2 temperature (T)

feed
Lsmax
LC
product
u
cooling


62
Step 5 Regulatory control layer

• Step 5. Choose structure of regulatory
  (stabilizing) layer
• (a) Identify stabilizing CV2s (levels,
  pressures, reactor temperature,one temperature in
  each column, etc.).
• In addition, active constraints (CV1) that
  require tight control (small backoff) may be
  assigned to the regulatory layer.
• (Comment usually not necessary with tight
  control of unconstrained CVs because optimum is
  usually relatively flat)
• (b) Identify pairings (MVs to be used to control
  CV2), taking into account
• Want local consistency for the inventory
  control
• Want tight control of important active
  constraints
• Avoid MVs that may saturate in the regulatory
  layer, because this would require either
• reassigning the regulatory loop (complication
  penalty), or
• requiring back-off for the MV variable (economic
  penalty)
• Preferably, the same regulatory layer should be
  used for all operating regions without the need
  for reassigning inputs or outputs.

63
Example Distillation

• Primary controlled variable y1 c xD, xB
  (compositions top, bottom)
• BUT Delay in measurement of x unreliable
• Regulatory control For stabilization need
  control of (y2)
• Liquid level condenser (MD)
• Liquid level reboiler (MB)
• Pressure (p)
• Holdup of light component in column
• (temperature profile)

Unstable (Integrating) No steady-state effect
Variations in p disturb other loops
Almost unstable (integrating)
Ts
TC
64
Why simplified configurations?Why control
layers?Why not one big multivariable
controller?

• Fundamental Save on modelling effort
• Other
• easy to understand
• easy to tune and retune
• insensitive to model uncertainty
• possible to design for failure tolerance
• fewer links
• reduced computation load

65
Advanced control STEP 6. SUPERVISORY LAYER

• Objectives of supervisory layer
• 1. Switch control structures (CV1) depending on
  operating region
• Active constraints
• self-optimizing variables
• 2. Perform advanced economic/coordination
  control tasks.
• Control primary variables CV1 at setpoint using
  as degrees of freedom (MV)
• Setpoints to the regulatory layer (CV2s)
• unused degrees of freedom (valves)
• Keep an eye on stabilizing layer
• Avoid saturation in stabilizing layer
• Feedforward from disturbances
• If helpful
• Make use of extra inputs
• Make use of extra measurements
• Implementation
• Alternative 1 Advanced control based on simple
  elements
• Alternative 2 MPC

66
Summary. Systematic procedure for plantwide
control

• Start top-down with economics
• Step 1 Define operational objectives and
  identify degrees of freeedom
• Step 2 Optimize steady-state operation.
• Step 3A Identify active constraints primary
  CVs c. Should controlled to maximize profit)
• Step 3B For remaining unconstrained degrees of
  freedom Select CVs c based on self-optimizing
  control.
• Step 4 Where to set the throughput (usually
  feed)
• Regulatory control I Decide on how to move mass
  through the plant
• Step 5A Propose local-consistent inventory
  (level) control structure.
• Regulatory control II Bottom-up stabilization
  of the plant
• Step 5B Control variables to stop drift
  (sensitive temperatures, pressures, ....)
• Pair variables to avoid interaction and
  saturation
• Finally make link between top-down and bottom
  up.
• Step 6 Advanced/supervisory control system
  (MPC)
• CVs Active constraints and self-optimizing
  economic variables
• look after variables in layer below (e.g.,
  avoid saturation)
• MVs Setpoints to regulatory control layer.
• Coordinates within units and possibly between
  units

cs
http//www.nt.ntnu.no/users/skoge/plantwide
67
Summary and references

• The following paper summarizes the procedure
• S. Skogestad, Control structure design for
  complete chemical plants'', Computers and
  Chemical Engineering, 28 (1-2), 219-234 (2004).
• There are many approaches to plantwide control as
  discussed in the following review paper
• T. Larsson and S. Skogestad, Plantwide control
  A review and a new design procedure'' Modeling,
  Identification and Control, 21, 209-240 (2000).
• The following paper updates the procedure
• S. Skogestad, Economic plantwide control,
  Book chapter in V. Kariwala and V.P. Rangaiah
  (Eds), Plant-Wide Control Recent Developments
  and Applications, Wiley (2012).
• More information

http//www.nt.ntnu.no/users/skoge/plantwide
68

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  AIChE J., 54 (1), 150-162 (2008). DOI
  10.1002/aic.11366