Transcript Slide 1

NAMP
Program
for North American Mobility in Higher Education
PIECE
NAMP
Module 8
Introduction to Process
Integration
Tier II
Introducing
Process integration
for Integration
Environmental Control in Engineering Curricula
Module
8 – Introduction
to Process
PIECE
1
NAMP
PIECE
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Module 8 – Introduction to Process Integration
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Table of contents
Project Summary
Participating institutions
Module creators
Module Structure & Purpose
Tier II
Statement of Intent
Sections
2.1 Worked example using Data-Driven Modeling, more
specifically Multivariate Analysis
2.2 Worked example using Thermal Pinch Analysis
2.3 Worked example using Integrated Process Control and
Design, more specifically Controllability Analysis
Quiz
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Project Summary
Objectives
Create web-based modules to assist universities to address
the introduction to Process Integration into engineering
curricula
Make these modules widely available in each of the
participating countries
Participating institutions
Two universities in each of the three countries (Canada,
Mexico and the USA)
Two research institutes in different industry sectors:
petroleum (Mexico) and pulp and paper (Canada)
Each of the six universities has sponsored 7 exchange
students during the period of the grant subsidised in part by
each of the three countries’ governments
Module 8 – Introduction to Process Integration
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NAMP integration for Environmental Control in Engineering Curricula
Process
Paprican
PIECE
PIECE
École
Polytechnique de
Montréal
Universidad
Autónoma de San
Luis Potosí
University of
Ottawa
Universidad de
Guanajuato
North Carolina
State University
Instituto
Mexicano del
Petróleo
Program
forIntroduction
North American
Mobility
in Higher Education
Module
8–
to Process
Integration
University of
Texas A&M
NAMP
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Module 8
This module was created by:
Carlos Alberto Miranda Alvarez
Paul Stuart
From
Host Institution
Host director
Martin Picon-Nuñez
Jean-Martin Brault
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Structure of Module 8
What is the structure of this module?
All modules are divided into 3 tiers, each with a specific
goal:
Tier I: Background Information
Tier II: Case Study Applications
Tier III: Open-Ended Design Problem
These tiers are intended to be completed in that particular
order. Students are quizzed at various points to measure
their degree of understanding, before proceeding to the
next level. Each tier contains a statement of intent at the
beginning and a quiz at the end.
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Purpose of Module 8
What is the purpose of this module?
It is the intent of this module to cover the basic aspects
of Process Integration Methods and Tools, and to
place Process Integration into a broad perspective. It
is identified as a pre-requisite for other modules related
to the learning of Process Integration.
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Tier II
Worked Examples
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Tier II Statement of intent
The goal of this tier is to demonstrate various concepts
and tools of Process Integration using real examples.
Three examples will be given, focusing mainly on three
Process Integration tools. At the end of Tier II, the
student should have a general idea of what is:
Data-Driven Modeling - Multivariate Analysis
Thermal Pinch Analysis
Integrated Process Control and Design –
Controllability Analysis
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Tier II Contents
Tier II is broken down into three sections
2.1 Worked example using Data-Driven
Modeling, more specifically Multivariate Analysis
2.2 Worked example using Thermal Pinch
Analysis
2.3 Worked example using Integrated Process
Control and Design, more specifically
Controllability Analysis
A short multiple-choice quiz will follow at the end of this
tier.
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Tier II Outline
2.1 Worked example 1: Data-Driven Modeling –
Multivariate Analysis
2.2 Worked example 2: Thermal Pinch Analysis
2.3 Worked example 3: Integrated Process Control and
Design – Controllability Analysis
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2.1 Worked example 1: DataDriven Modeling – Multivariate
Analysis
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis – Reminder
Graphical representation of MVA
Y
Y
a
v
e
c
X1
X4
X5
Rep
1
-1
-1
-1
1
2.51
2.74
1
-1
-1
-1
2
2.36
3.22
1
-1
-1
-1
3
2.45
2.56
2
-1
2
-1
2
-1
3
-1
3
-1
3
0
1
1
2.63
3.23
0
1
2
2.55
2.47
0
1
3
2.65
2.31
1
0
1
2.45
2.67
1
0
2
2.6
2.45
-1
1
0
3
2.53
2.98
4
0
-1
1
1
3.02
3.22
4
0
-1
1
2
2.7
2.57
4
0
-1
1
3
2.97
2.63
5
0
0
0
1
2.89
3.16
5
0
0
0
2
2.56
3.32
5
0
0
0
3
2.52
3.26
6
0
6
6
impossible to
interpret
hundreds of columns
1
-1
1
2.44
3.1
0
1
-1
2
2.22
2.97
0
1
-1
3
2.27
2.92
thousands of rows
.
. .. .
..
. .
.
. .
s
a
n
s
Tmt
Raw Data:
Statistical Model
Module 8 – Introduction to Process Integration
Y
trends
X
(internal
to
software)
trends
trends
X
X
X
2-D Visual Outputs
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Basic Statistics
It is assumed that the student is familiar with the following basic
statistical concepts: mean, median, mode; standard deviation, variance;
normality, symmetry; degree of association, correlation coefficients; R2, Q2,
F-test; significance of differences, t-test, Chi-square; eigen values and
vectors
Statistical tests help characterize an existing dataset. They do NOT
enable you to make predictions about future data. For this we must turn
to regression techniques…
Regression
Take a set of data points, each described by a vector of values (y, x1, x2,
… x n)
Find an algebraic equation that “best expresses” the relationship
between y and the xi’s:
Y = b1x1 + b2x2 + … + bnxn + e
Data Requirements: normalized data, errors normally distributed with
mean zero and independent variables uncorrelated
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Types of MVA
1.
2.
X
Principal Component Analysis (PCA)
X’s only
In PCA, we are maximizing the variance that is explained by
the model
Projection to Latent Structures (PLS)
a.k.a. “Partial Least Squares”
X’s and Y’s
In PLS, we are maximizing the covariance
X Y
Types of MVA outputs
YObserved
MVA software generates two types of outputs: results, and diagnostics.
Results: Score Plots, Loadings Plots
240
220
Diagnostics: Plot of Residuals, Observed
200
180
vs. Predicted, and many more
IDEAL MODEL
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150 160 170 180 190 200 210 220 230 240
YPredicted
Figure 1
16
Q1
Q2
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis - PCA
Principal Component Analysis (PCA)
Consider these fish. We could
measure, for each fish, its
length and breadth.
Suppose that 50 fish were measured, a
plot like the one shown in figure 2 might
be obtained. There is an obvious
relationship between length and breadth
as longer fish tend to be broader.
Figure 2
Module 8 – Introduction to Process Integration
Reference: Manchester Metropolitan University
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis - PCA
Move the axes so that their origins are now centered on the cloud of points : this is a
change in the measurement scale. In this case the relevant means were subtracted from
each value.
Figure 3
Figure 4
In effect the major axis is a new variable, size. At its simplest, size = length + breadth
 linear combination of the two existing variables, which are given equal weighting
Suppose that we consider length to be more important than breadth in the determination
of size. In this case we could use weights or coefficients to introduce differential
contributions: size = 0.75 x length + 0.25 x breadth
For convenience, we would normally plot the graph with the X axis horizontal, this would
give the appearance of rotating the points rather than the axes.
Figure 5
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Reference: Manchester Metropolitan University
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis - PCA
A criterion for the second axis is that it should account for as much of the
remaining variation as possible. However, it must also be uncorrelated
(orthogonal) with the first.
Figure 6
Figure 7
In this example the lengths and orientations of these axes are given by the
eigen values and eigen vectors of the correlation matrix. If we retain only the
'size' variable we would retain 1.75/2.00 x 100 (87.5%) of the original variation.
Thus, if we discard the second axis we would lose 12.5% of the original
information.
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Reference: Manchester Metropolitan University
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis - PCA
Projection to Latent Structures (PLS)
PLS finds a set of orthogonal components that :
maximize the level of explanation of both X and Y
provide a predictive equation for Y in terms of the X’s
This is done by:
fitting a set of components to X (as in PCA)
similarly fitting a set of components to Y
reconciling the two sets of components so as to maximize
explanation of X and Y
Interpretation of the PLS results has all the difficulties of PCA,
plus another one: making sense of the individual components in
both X and Y space. In other words, for the results to make
sense, the first component in X must be related somehow to the
first component in Y
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Problem Statement
Let´s look at a typical integrated thermomechanical pulp (TMP) newsprint
mill in North America. The mill manager of that particular plant recognizes
that there is too much data to deal with and that there is a need to estimate
the quality of their final product, i.e. paper. He decides to use Multivariate
Analysis to derive as much information as possible from the data set and try
to determine the most important variables that could have an impact on
paper quality in order to be able to classify final product quality. The mill
manager decides to first look at the refining portion of the pulping process.
Figure 8
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
X and Y Variables
X variables
Incoming chips: size
distribution, bulk density,
humidity
Refiner operating data:
throughput; energy split
between the primary and
secondary refiner; dilution
rates; levels, pressures and
temperatures in various units
immediately connected to the
refiners; voltage at chip screw
conveyors; refiner body
temperature
Season, represented by the
average monthly temperature
measured at a nearby
meteorological station
Y variables
Pulp quality data
after the latency chest
(automated, on-line
analysis of grab
samples): standard
industry parameters
including fibre length
distribution, freeness,
consistency, and
brightness
X’s
Figure 9
Y
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Results
34-months of 1 day rev . 2 (incl. c hip data) no. 2.M4 (PC A-X), Bad residuals remov ed
t [1]/ t[ 2] /t [ 3]
C olored acc ording t o class es in M4
This is the R2 and Q2 plot for the
model. The R2 values tell us that the
first component explains 32% of the
variability in the original data, the
second another 7% and the third
another 6%.
N o Class
C las s 1
C las s 2
C las s 3
C las s 4
32-months v ers ion 2.M2 (PCA-X), Ex trem e outliers remov ed R 2X(c um)
Q2(cum)
1.00
0.80
0.60
0.40
Comp No.
Figure 10
Figure 11
Module 8 – Introduction to Process Integration
Comp[3]
The
values are lower. This means
that the predictive power of the
model is around 40% when using all
three components. This may seem
low, but is normal for real process
data.
0.00
Comp[2]
Q2
Comp[1]
0.20
Autumn
Winter
Spring
Summer
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Interpretation of the results – Score Plot
Variation in this
direction appears to
occur BETWEEN
seasons
( Component 2)
34-months of 1 day rev . 2 (incl. chip data) no. 2.M4 (PCA-X), Untitled
t[1]/t[2]
Colored according to classes in M4
No Class
Class 1
Class 2
Class 3
Class 4
t[2]
5
0
-5
Autumn
Winter
Spring
Summer
-10
Module 8 – Introduction to Process Integration
0
10
t[1]
Figure 12
20
Variation in this
direction appears to
occur WITHIN a given
season
( Component 1)
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Interpretation of the results – Loadings plot
Bleach consumption
34-months of 1 day rev . 2 (incl. c hip data) no. 2.M4 (PC A-X), Bad residuals remov ed
p[1]/ p[ 2]
0.20
p[2]
0.10
0.00
-0.10
-0.20
X
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Cop>9/8
-0.20
Pulp throughput
Refining energy
Dilution flows
Steam generation
-0.10
Module 8 – Introduction to Process Integration
0.00
p[1]
Figure 13
0.10
Pulp brightness
Season
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Interpretation of the results
First Component
The first component corresponds to throughput: many process variables are related
either directly or indirectly to throughput. Remember we said that the 1st component
was something that varied within an individual season?
Second Component
The 2nd component explains only 7% of the total variability. It is therefore “messier”
than the first component, and will be less easy to interpret. It is also possible to note
that the three years were separated with respect to this second component
A major clue occurs in the prominence of two important and related tags: bleach
consumption and pulp brightness. This would suggest that perhaps the brightness of the
incoming wood chips was different from year to year, requiring more bleaching to get a
less white pulp
Note also that “Season” is prominent. This can be seen with the obvious separation of
the seasons on the score plot. This suggests that winter chips are less bright than
summer chips
Third Component
The 3rd component explains only 6% of the total variability
The 3rd component is related to the time of year. A reasonable interpretation would be
that summer chips differ from winter chips in some way other than brightness, which
was already covered by the second component. This could be, for instance, the ease
with which the wood fibres can be separated from each other
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Summary of the PCA results
SUMMER / WINTER
Using PCA, we have determined that 45% of the variability in the original 130
variables can be represented by using just 3 new variables or “components”.
These three components are orthogonal, meaning that the variation within
each one occurs independently of the others. In other words, the new
components are uncorrelated with each other.
Component 3
Explains 6%
REFINER THROUGHPUT
Component 2
Explains 7%
Module 8 – Introduction to Process Integration
Component 1
Explains 32%
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2.1 Worked example 1: Data-Driven Modeling
Multivariate Analysis
Quality “reference map”
X
X
X
Figure 14
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Tier II Outline
2.1 Worked example 1: Data-Driven Modeling –
Multivariate Analysis
2.2 Worked example 2: Thermal Pinch Analysis
2.3 Worked example 3: Integrated Process Control and
Design – Controllability Analysis
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2.2 Worked example 2:
Thermal Pinch Analysis
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2.2 Worked example 2: Thermal Pinch Analysis – Reminder
What is Thermal Pinch Analysis?
Utility
Usage
HOT
Utility
COLD
Utility
Utility costs
go down
$
Internal
Exchanges
PROCESS
Trade-off
Costs related to
exchange area
go up
Trade-off
From 100% utility... ... to 100% internal exchanges
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2.2 Worked example 2: Thermal Pinch Analysis
What about an entire site ?
At least 40 streams to
heat and cool…
Example: Recovery Boiler
Obvious solution: preheat
entering fresh water with
hot condensate leaving
boiler
Figure 15
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2.2 Worked example 2: Thermal Pinch Analysis
Simulation
Data Extraction (hot
and cold streams)
with specific energy
savings objectives in
mind
Extraction
Tmin
Targeting
Use of heuristics to
design a Heat
Exchanger Network
that will reach energy
targets at lowest cost
Analysis
Targeting, i.e.
energy, design
and economical
targets
Heat Exchanger Network
Design
Plant
Module 8 – Introduction to Process Integration
Transfer of
obtained results
to plant reality
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2.2 Worked example 2: Thermal Pinch Analysis
Composite Curves
Temperature
Heating Requirement
Tmin
Pinch
point
Cooling Requirement
Enthalpy
Figure 16
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2.2 Worked example 2: Thermal Pinch Analysis
Mass Integration – Composite Curves for pollution prevention
Figure 18
Figure 17
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2.2 Worked example 2: Thermal Pinch Analysis
Problem Statement
A process engineer in a consulting firm is hired by an oil refinery to
design the Conventional Atmospheric Crude Fractionation Units section
of the refinery facility, as shown in figure 17. The main objective of this
project is to minimize the energy consumption by using Thermal Pinch
Analysis. The plant is currently using 75000 kW in hot utilities. In this
example, stress will be put on the construction of the composite curves
with the objective of identifying energy savings opportunities.
Crude Tower
Naphtha-PA
6
BPA
E2
5
E3
Kerosene
12
7
Furnace
11
1
8
2
3
L-gasoil
10
9
2
E1
Crude
E4
E5
E6
H-gasoil
4
13
Desalter
15
Figure 19
Module 8 – Introduction to Process Integration
E7
14
ATB
16
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2.2 Worked example 2: Thermal Pinch Analysis
Crude Tower
Table 2
Data Extraction
Naphtha-PA
Tmin
Industrial Sector
100º
3
150º
4
190º
180º
30º
Oil Refining
30-40ºC
Petrochemical
10-20ºC
Chemical
10-20ºC
Kerosene Low-temperature
3-5ºC
processes
270º
Crude
Feed
BPA
2
1
290º
20º
150º
150º
6
40º
Crude Pre-heat train
5
7
º
390º
350º
Desalter
Figure 20
Table 1
Process
Heat
Mass
Heat
stream capacity flow capacity
number
rate
flowrate
and type (J/kgK) (kg/s)
(kW/K)
(1)Cold 2600.00 200.00 520.00
(2)Cold 2600.00 200.00 520.00
(3)Hot
2600.00 253.00 657.80
(4)Hot
2600.00 23.00
59.80
(5)Hot
2600.00 44.00
114.40
(6)Hot
2600.00 148.00 384.80
(7)Hot
2600.00 13.00
33.80
(8)Hot
2600.00 56.00
145.60
* Fouling Factor included
30º
380º
8
Supply
temperature
Target
Temperature
(ºC)
20.00
150.00
150.00
180.00
270.00
290.00
350.00
380.00
(ºC)
150.00
390.00
100.00
30.00
40.00
190.00
30.00
50.00
Module 8 – Introduction to Process Integration
L-gasoil
50º
H-gasoil
ºC Condition
Stream Number
ATB
Stream
Heat*
Heat
Transfer
duty
coefficient
(W/m2 K)
(kW)
67600.00
170.00
124800.00
170.00
-32890.00
170.00
-8970.00
170.00
-26312.00
170.00
-38480.00
170.00
-10816.00
170.00
-48048.00
170.00
Fouling
(m2 ºC/W)
0.00147
0.00147
0.00147
0.00147
0.00147
0.00147
0.00147
0.00147
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
1. Sort in ascending order the hot streams temperatures, omitting
common temperatures
Temperatures are sorted
in ascending order,
omitting common
temperatures
Table 3
Using the data above, we form temperature intervals for the process
Interval
T
T1
T2
T3
Figure 21
Module 8 – Introduction to Process Integration
T4
1
2
3
H
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
2. Sum up the CP of every stream present in each temperature interval
CPi 

CPj  stream
i  interval, j  stream
j  stream
Table 4
CP1  CP4 H  CP7 H  59.8  33.8  93.6
We then obtain the Composite CP for each temperature interval
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
3. Calculate the net enthalpy for each temperature interval
Qi  CPi * (Ti  Ti 1 )
Table 5
Q1  CP1 * (T1  T0 )  93.6 * (313 303)  936kW
We obtain the enthalpy for each temperature interval, as shown in
the column Qint,h
Module 8 – Introduction to Process Integration
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
4. Obtain the accumulated enthalpy for each temperature interval
SumQi  SumQi 1  Qi
Table 6
SumQ1  SumQ0  Q1  0  936  936
Module 8 – Introduction to Process Integration
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
5. Plot temperature on the Y axis versus accumulated enthalpy on the X axis
Hot Composite Curve
700
653
623
600
T (K)
563
543
500
463
453
423
400
373
323
313
303
300
0
50000
100000
H (kW)
150000
200000
Figure 22
Module 8 – Introduction to Process Integration
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
The construction of the Cold Composite Curve is similar to that of the Hot
Composite Curve.
Table 7
Cold Composite Curve
T(K)
700
650
663
600
550
500
450
400
350
423
300
250
293
0
50000
100000
Module 8 – Introduction to Process Integration
150000
H (kW)
Figure 23
200000
250000
43
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2.2 Worked example 2: Thermal Pinch Analysis – Composite Curves
Application Composite Curves
QHmin
Internal Heat Recovery
700
600
Tmin= 40K
T (K)
500
Minimum
Cooling
Requirement
400
300
QCmin
200
Minimum
Heating
Requirement
100
Cold composite curve
Hot composite curve
0
0
50000
100000
150000
H (kW)
200000
250000
Figure 24
This representation reduces the entire process into one combined hot and cold stream
The heat recovery between the composite curves can be increased until we reach DTmin.
Composite curves, just like individual streams can be shifted horizontally on the T-H diagram
without causing changes to the process because H is a state function
This sets the minimum hot (QHmin) and cold (QCmin) utilities requirements for the entire
process and the maximum possible process-process heat recovery
Module 8 – Introduction to Process Integration
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2.2 Worked example 2: Thermal Pinch Analysis
Summary of results
As seen in the previous slides, from the temperature-enthalpy plot, we
can determine three useful pieces of information:
Amount of possible process-process heat recovery represented by the
area between the two composites curves
Hot Utility requirement or target = 57668 kW
Cold Utility requirement or target = 30784 kW
Composite curves are excellent tools for learning the methods and
understanding the overall energy situation, but minimum energy
consumption and the heat recovery Pinch are more often obtained by
numerical procedures. This method is called the Problem Table
Algorithm. Typically, it is based on notions of Heat Cascade.
Module 8 – Introduction to Process Integration
Q5
45
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Tier II Outline
2.1 Worked example 1: Data-Driven Modeling –
Multivariate Analysis
2.2 Worked example 2: Thermal Pinch Analysis
2.3 Worked example 3: Integrated Process Control and
Design – Controllability Analysis
Module 8 – Introduction to Process Integration
46
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2.3 Worked example 3:
Integrated Process Control –
Controllability Analysis
Module 8 – Introduction to Process Integration
47
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis – Reminder
Fundamentals
PROCESS RESILIENCY
Input
Variables
Control Loop
Disturbances
sensor
Input Variables
(manipulated)
Internal interactions
Process
PROCESS FLEXIBILITY
Uncertainties
Output
Variables
(controlled and
measured)
Figure 25
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Water: F1,C1
CC
C, F
Pulp: F2,C2
INPUTS
(manipulated variables or
disturbances)
FC
Figure 26
Module 8 – Introduction to Process Integration
EFFECTS
OUTPUTS
(Best Selection by
Controllability analysis)
49
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
+
_
C1
y1sp
u1
F11
y1
+
+
y1
F21
F12
y2sp
+
_
C2
u2
F22
y2
+
+
y2
Figure 27
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Experiment 1: Step Change in u1 with all loops open
u1
ss
u1
+
F11
+ y1
F21
F12
u2
F22
+
+
y2
Figure 28
Main Effect:
y1
 K11 , (OL gain, u1 - y1 )
u1
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Experiment 2: Step Change in u1 with all loops closed
u1
u1
ss
+
F11
+
y1
F21
F12
y2sp
e2
+ _
u2
C2
F22
+
+
y2
Figure 29
Total Effect:
CL
11
K
K
OL
11
Module 8 – Introduction to Process Integration
 y1r
Main Effect
Interactive Effect
52
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Relative Gain and Relative Gain Array (RGA)
CL
OL
 y1r
K11
K11
Main Effect (1st Experiment)
11
K11OL
 CL
K11
Total Effect (2nd Experiment)
11
ij
Relative Gain
y1
u1
Relative Gain Array
yi
uj
Module 8 – Introduction to Process Integration
11 : measure of the
extent of steady state
interaction in using u1 to
control y1, while using u2
to control y2
 yi 


 u 
j  OL
ij  
 yi 


 u 
 j
CL
 11 12 




 21 22 
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Selection of Loops using RGA – How to select the configuration
with minimum interaction
Table 8
ij  1
ij  0
0  ij  1
Implication
Loop i not subject to interactive action
from other loops
uj has no direct influence on yi
- Loops are interacting
- below 0.5, interactive effect > main effect
ij  1
- Loops are interacting
- interactive effect acts in opposition to the main
effect
ij  0
- Loops are interacting
- interactive effect not only acts in opposition to
the main effect, it is also more dominant
Recommendation
Pair :
yi  u j
yi  u j
Do not pair :
Avoid:
yi  u j
Avoidat high ij :
Do not pair :
yi  u j
yi  u j
yi : Controlled variable
uj : Manipulated variable
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Other Controllability Indexes
Niederlinski (NI) : system stability index
Condition Number (CN) and Disturbance Condition
Number (DCN) : sensibility measure
Relative Disturbance Gain (RDG) : index that gives an
idea of the influence of internal interactions on the
effect of disturbances
Others: Singular Value Decomposition (SVD)
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Problem Statement
In this case-study, a process control engineer is asked to create a model of the
thermomechanical pulping process to find the best process control selection
and variable pairing for a plant that has not been built yet. Consider the
simplified newsprint paper machine short loop configuration shown in figure
30. Variable pairing techniques will be applied as well as the use of
controllability indexes.
F4
401.885 l/min
18 %
13924 lt/min
1.00382 %
3.51707 %
595.592 lt/min
495.588 lt/min
16
11069.6 lt/min
Broke
2
Tank
Mixing
13
Chest
2.96551 %
13287.5 lt/min
2.79214 %
12
3.02375 %
249.355 lt/min
100 lt/min
Machine
Chest3
14
32
31
5
2.94705 %
3157.18 lt/min
12628.8 lt/min
15
11565.2 lt/min
10
Module 8 – Introduction to Process Integration
11814.6 lt/min
Figure 30
0.4 %
15786 lt/min
3.78427 %
24
11958.7 lt/min
11144.5 lt/min
6300 lt/min
Broke (18 %)
5961.63 lt/min
62610 lt/min
1.92733 %
CUV P A T E
CUV P A T E 1
4
S
47494 lt/min
21
F3
10299.6 lt/min
2.99513 %
20
23
F2
814.218 lt/min
Pulp
1
Tank
F5
2.03148 %
1.81 %
4000 lt/min
Wet web
F6
48686 lt/min
2.19041 %
S
11
22
Fresh Pulp (7 %)
F1
4769.6 lt/min
2264.4 lt/min
F7
Fresh water
Base Case: TMP Newsprint Mill
Steady State Simulation
WW
Tank
F8
6
56
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
controlled
Problem Statement
Table 9
manipulated
disturbances
INPUTS
Name
Fresh Pulp
Broke
Fresh water
OUTPUTS
ID stream
1
3
63
Flow(lt/min) Cons. (%)
Temp (°C)
Fines (%)
TDS (ppm) Flow(TN/d)
4000.0
7.0
67.0
20.7
6049
5791.3
100.0
18.0
54.0
29.0
4063
151.3
2264.4
0.0
55.0
0.0
0
3214.1
Pfin = % Fines retained
Name
ID stream
Flow(lt/min) Cons. (%)
Temp (°C)
Fines (%)
TDS (ppm) Flow(TN/d)
Wet Web
62
401.9
18.00
61.5
30.06
4063
605.8
Dilution 1
32
6300.0
0.40
61.5
98.80
3270
8937.2
Dilution 2
6
495.6
0.40
61.5
98.80
3270
703.0
Dilution 3
22
249.4
0.40
61.5
98.80
3270
353.7
Dilution 4
16
814.2
0.40
61.5
98.80
3270
1155.1
Dilution of Rejects Screen
41
4769.6
0.40
61.5
98.80
3270
6766.2
Ww drained from forming zone
61
15786.0
0.40
61.5
98.80
3270
22394.1
Ww Short Loop
40
3157.2
0.40
61.5
98.80
3270
4478.8
Pulp to Headbox
34
13924.0
1.00
62.6
61.06
3826
19786.0
Pulp to Screen
25
62610.0
1.93
62.6
10.07
3826
89243.4
Diluted Broke entering Mixing Chest
30
595.6
3.52
60.3
35.53
3389
854.4
Diluted Pulp entering Mixing Chest
33
10299.6
3.00
63.6
27.03
4317
14728.5
Pulp leaving Mixing Chest
12
10895.2
3.02
63.4
27.57
4267
15582.9
Pulp leaving Machine Chest
24
12473.3
2.95
63.4
27.85
4237
17835.7
Rejects (Screening system)
52
5961.6
3.78
62.5
18.24
3776
8551.0
Accepts (Hydrocyclone)
36
47493.9
1.81
62.5
1.61
3776
67672.6
Pulp entering Machine Chest
23
11144.5
2.97
63.4
27.78
4244
15936.6
Pulp entering Stock
CuvierChest
de pâte
43
13287.5
2.79
63.3
28.47
4176
18990.7
Ww Long Loop
15
12628.8
0.40
61.5
98.80
3270
17915.2
Ww Short Loop after accepts
46
50651.1
1.72
62.4
3.01
3744
72151.4
Broke Ratio, %
5.5
Retention, %
54.9
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
2264.4 lt/min
Fresh water
Base Case: TMP Newsprint Mill
Steady State Simulation
Pfin
Disturbances
13924 lt/min
1.00382 %
C
Fines
Fresh Pulp (7 %)
401.885 l/min
18 %
11
Wet web
Ret
22
48686 lt/min
2.19041 %
23
2.03148 %
100 lt/min
16
11069.6 lt/min
495.588 lt/min
S
Broke
2
Tank
Manipulated
Mixing
13
Chest
2.96551 %
13287.5 lt/min
2.79214 %
12
3.02375 %
Machine
Chest3
14
0.4 %
1.81 %
11958.7 lt/min
3.51707 %
595.592 lt/min
249.355 lt/min
Broke (18 %)
11144.5 lt/min
6300 lt/min
15786 lt/min
4
24
3.78427 %
BR
62610 lt/min
1.92733 %
CUV P A T E
CUV P A T E 1
10299.6 lt/min
2.99513 %
5961.63 lt/min
21
Controlled
20
47494 lt/min
Pulp
1
Tank
S
814.218 lt/min
4769.6 lt/min
4000 lt/min
32
31
5
2.94705 %
3157.18 lt/min
WW
Tank
12628.8 lt/min
15
11565.2 lt/min
10
11814.6 lt/min
6
Figure 31
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Process Gain Matrices and Steady-State Controllability
 C33 
C 
 30 
 C 23 


C
 43 
 BR 


C
 34 
 Re t 


=
  0.031
 0.002

  0.029

 0.027
  0.065

 0.002
  0.114

 0.028
 0.404 0.001
0.001
0.024
0.005  0.038
 0.020  0.011 0.001
0.036
0.004  0.029

 0.018  0.010  0.016 0.036
0.004  0.030
0.775
0.000
0.000
3.340
0.000
0.000 

0.001
0.001
0.001
0.049
0.004  0.025
 0.077  0.042  0.068  0.608  0.265 4.020 
0.001
0.001
0.001
Gp
Controlled
RGA
=
0.004
 F32 
F 
 6
 F22 
 
 F16 
 F3 
 
 F40 
P 
 fin 
+

Disturbances
F6
F22
F16
F3
F40
Pfin
 0.942

 0.001
0.001

 0.000
 0.010

 0.039
 0.010

0.000
1.009
0.000
0.000
0.013
0.003
0.001
0.047
0.004
0.947
0.000
0.000
0.001
0.000
0.000
0.000
0.053
0.941
0.000
0.005
0.001
0.011
0.014
0.000
0.000
1.003
0.006
0.000
0.038
0.047
0.000
0.058
0.000
1.566
0.615
0.016

0.020 
0.000 

0.001 
0.000

0.608
1.603 
Module 8 – Introduction to Process Integration
0.518 0.056 
0.052 0.076 


0.483 0.058 

 C1 
0
.
455
0
.
060

  
0.000 0.000   f1 


0.164 0.079 
0.075  4.597


Gd
Manipulated
F
32
 C33 
C 
 30 
 C 23 


 C 43 
 BR 


 C34 
 Re t 


0.018
59
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
2264.4 lt/min
Fresh water
Base Case: TMP Newsprint Mill
Steady State Simulation
Pfin
13924 lt/min
1.00382 %
401.885 l/min
18 %
11
Wet web
Ret
22
Fresh Pulp (7 %)
48686 lt/min
2.19041 %
23
2.03148 %
100 lt/min
495.588 lt/min
16
11069.6 lt/min
S
Broke
2
Tank
Mixing
13
Chest
2.96551 %
13287.5 lt/min
2.79214 %
12
3.02375 %
Machine
Chest3
14
0.4 %
1.81 %
11958.7 lt/min
3.51707 %
595.592 lt/min
249.355 lt/min
Broke (18 %)
11144.5 lt/min
6300 lt/min
15786 lt/min
4
24
3.78427 %
BR
62610 lt/min
1.92733 %
CUV P A T E
CUV P A T E 1
5961.63 lt/min
21
10299.6 lt/min
2.99513 %
20
47494 lt/min
Pulp
1
Tank
S
814.218 lt/min
4769.6 lt/min
4000 lt/min
32
31
5
2.94705 %
3157.18 lt/min
WW
Tank
12628.8 lt/min
15
11565.2 lt/min
10
11814.6 lt/min
6
Figure 32
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Controllability Indexes (1)
Niederlinski Index (NI)  Stability considerations
NI < 0. System will be unstable under closed-loop conditions
NI > 0. System is stabilizable (function of controller parameters)
NI=0.73
Condition number (CN)  Sensitivity to model uncertainty
CN ~< 2. Multivariable effects of uncertainty are not likely to be
serious
CN ~> 10. ILL-CONDITIONED process
CN=713
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Controllability Indexes (2)
Disturbance Condition Number (DCN)  Is the action taken by the
manipulated variable large or small?
1≤ DCN ≤ CN
DCN for %Cfresh pulp = 9.2
DCN for %finesfresh pulp = 4.6
 It is harder to reject a sudden change in fresh pulp consistency
Relative Disturbance Gain (RDG)  Internal interaction among the
loops is favorable or unfavorable to reject disturbances?
RDG ~<2 . Internal interactions reduce the effect of the
disturbance
The effect of both disturbances, %C and %fines in FRESH
PULP, is reduced by internal interactions. All RDG’s are ~<2
Module 8 – Introduction to Process Integration
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2.3 Worked example 3: Integrated Process Control and Design –
Controllability Analysis
Conclusion
Control structure configuration: RGA results
confirmed current implementation in newsprint mills
Internal interactions of the aforementioned
configuration reduce the effect of disturbances on
output variables
The process is ill-conditioned. Model uncertainty
may be highly amplified
Resiliency Indexes, DCN and RDG, can be used to
account for disturbance rejection in newsprint
processes
Module 8 – Introduction to Process Integration
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End of Tier II
This is the end of Tier II. At this point, we assume that you have done all the
reading. You should have a pretty good idea of what Process Integration is as
well as basic knowledge in regards to Multivariate Analysis, Thermal Pinch
Analysis and Controllability Analysis. For further information on the tools
presented in Tier II as well as on other Process Integration tools introduced in
Tier I, please consult the references slides in Tiers I and II.
Prior to advancing to Tier III, a short multiple choice quiz will follow.
Module 8 – Introduction to Process Integration
64
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QUIZ
Module 8 – Introduction to Process Integration
65
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Tier II - Quiz
Question 1
What is Principal Components Analysis used for?
1. Understand relations between the variables of a system
2. Identify the components having an influence on one or many outputs
3. Predict certain outputs
4. Maximize the covariance of a set of variables
2 and 3
1 and 3
1
3
1 and 2
1,2 and 3
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Question 2
Associate each Multivariate Analysis output with the kind of information it
provides the user with.
1. Residuals plot
A. Shows all the original data points in a
new set of coordinates or components
2. Score plot
B. Shows the distance between each real
observation in the initial dataset and the
predicted value based on the model
3. Observed vs. Predicted
C. Shows the accuracy of prediction
4. Loadings plot
D. Shows how strongly each variable is
associated with each new component
1B, 2A, 3C, 4D
1D, 2B, 3A, 4C
1C, 2D, 3A, 4B
1B, 2C, 3D, 4A
1A, 2D, 3B, 4C
1B, 2D, 3C, 4A
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Question 3
The lengths and orientations of the axes obtained with a PCA are given by
the eigen values and eigen vectors of the correlation matrix. Let's say the
length and breadth variables have a lower correlation coefficient than in
the example given in slide 13 and that we obtain the eigen values shown in
the figure below. If we discard the second axis, what percentage of the
original information would we lose?
12,5%
75%
25%
62,5%
37,5%
0%
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Question 4
In the context of a Thermal Pinch Analysis, what is a hot stream?
1. A process stream that needs to be heated
2. A process stream with a very high temperature
3. A process stream that is used to generate steam
4. A process stream that needs to be cooled
1
3
2
4
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Question 5
A Thermal Pinch Analysis has been performed at a plant and the Tmin was
set at 40ºC. If another plant was to be built with a lower Tmin, how would
the corresponding energy costs be in comparison to the first plant?
Higher
Lower
Would stay the same
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Tier II - Quiz
Question 6
Which of the following statements are true?
1. Minimum energy consumption and the heat recovery Pinch are more
often obtained by Composite Curves
2. Composite curves, just like individual streams, can be shifted
horizontally on the T-H diagram without causing changes to the
process
3. Heat can sometimes be transferred across the Pinch
4. With the help of Tmin and the thermal data, Pinch Analysis provides a
target for the minimum energy consumption
2 and 3
2 and 4
1 and 3
3 and 4
1 and 2
All of the above
Module 8 – Introduction to Process Integration
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PIECE
Tier II - Quiz
Question 7
Associate each controllability tool or index with the kind of information it
provides the user with.
1. Niederlinski Index
A. Shows the importance of interactions in
a system
2. Relative Disturbance Gain
B. Estimates the sensitivity of the
problem's answer to error in the input
3. Condition Number
C. Includes disturbances in interactions
analysis
4. Relative Gain Array
D. Discusses the stability of a closed-loop
control configuration
1B, 2A, 3C, 4D
1D, 2B, 3A, 4C
1C, 2D, 3A, 4B
1B, 2C, 3D, 4A
1A, 2D, 3B, 4C
1D, 2C, 3B, 4A
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Question 8
In the Relative Gain Array shown in slide 54, what do the values 1.566 and
1.603 for the pairing of F40 and C34, and Pfin and Ret, tell you?
1. There is no interaction with other control loops
2. The interactive effect is more important than the main effect
3. The manipulated input has no effect on output
4. The interactions from the other loops are opposite in direction but
smaller in magnitude than the effect of the main loop
5. Pairing is recommended
6. Pairing is not recommended
1 and 5
4 and 5
3 and 6
2 and 5
2 and 6
4 and 6
Module 8 – Introduction to Process Integration
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PIECE
Tier II - Quiz
Question 9
Which of the following statements are false?
1. Feedforward control compensates for immeasurable disturbances
2. Feedback control compensates for measurable disturbances
3. Resiliency is the degree to which a processing system can meet its
design objectives despite uncertainties in its design parameters
4. Flexibility is the degree to which a processing system can meet its
design objectives despite external disturbances
2 and 3
2 and 4
1 and 3
3 and 4
1 and 2
All of the above
Module 8 – Introduction to Process Integration
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Tier II - Quiz
Answers
Question 1
1 and 2
Question 2
1B, 2A, 3C, 4D
Question 3
37,5%
Question 4
4
Question 5
Lower
Question 6
2 and 4
Question 7
1D, 2C, 3B, 4A
Question 8
4 and 5
Question 9
All of the above
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