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Program for North American Mobility in Higher Education
Introducing Process Integration for Environmental Control in Engineering Curricula
MODULE 12: “Heat and Mass Exchange Networks Optimization”
1
PURPOSE OF MODULE 12
What is the purpose of this module?
This module is intended to convey and illustrate the basic principles
and methodology of heat and mass networks optimization. It is
applied to chemical engineering, especially touching the petroleum
and paper industry. At the end of the module, the student should
be able to understand the main concepts of the heat and mass
exchange network and apply it to real world context.
2
STRUCTURE OF MODULE 12
What is the structure of this module?
Module 12 is divided in 3 “tiers”, each with a specific goal: Tier 1: Basic concepts Tier 2: Application examples Tier 3: Open-ended problems in a real world context
These tiers are intended to be completed in order. Students are
quizzed at various points, to measure their degree of
understanding, before proceeding.
Each tier contains a statement of intent at the beginning, and a quiz
at the end.
3
BASIC CONCEPTS
Tier I
4
TIER 1 - STATEMENT OF INTENT
The goal of Tier 1 is to provide the basic
principles and solution methods for heat and
mass exchange networks optimization with
emphasis on retrofit, heat transfer and
mass transfer analogy and optimization
techniques.
5
TIER 1 - CONTENTS
Tier 1 is broken down into three sections:
1.1 Optimization of heat exchanger networks (HEN) by Pinch Analysis
1.2 Optimization of mass exchange networks
1.3 Application of optimization techniques to heat and mass exchange networks analysis
At the end of this tier there is a short multiple
answer Quiz.
6
1.1 OPTIMIZATION OF HEAT EXCHANGER NETWORKS (HEN) BY PINCH ANALYSIS
7
1.1 OPTIMIZATION OF HEAT EXCHANGER NETWORKS (HEN) BY PINCH ANALYSIS
Principles of Pinch Analysis Methodology Special problems in heat exchangers
network design Pinch analysis and energy integration Special case of heat exchange Retrofit design Pinch software
8
INTRODUCTION
One important goal in our industry today:
Minimize the utilities consumption (fuel, steam and cooling water)
Methods based on thermodynamic analysis,
that have the objective of minimizing the
utilities consumption, are based on fundamental
concepts that help to understand the problem of
heat exchange.
9
WHAT IS PINCH TECHNOLOGY?
Pinch Technology provides a systematic
methodology for energy saving in processes
and total sites. The methodology is based on
thermodynamic principles
10
WHAT IS THE ROLE OF PINCH TECHNOLOGY IN THE OVERALL PROCESS DESIGN?
The Onion Diagram The design of the process starts with the reactors (the core)
Once feeds, products, recycle concentrations and flowrates are known, the separators (the second layer) can be designed
The basic process heat and material balance is now in place and the heat exchanger network (the third layer) can be designed
The remaining heating and cooling duties are handled by the utility systems (the fourth layer)
Pinch Analysis starts with the heat
and material balance for the process at
this boundary
Reactor
Separator
Utilities
Heat Exchanger Network
Site-wide Utilities
11
THE PHASES OF PINCH ANALYSIS
PROCESS
SIMULATION
DATA EXTRACTION
TARGETING
DESIGN OPTIMIZATION
DATA EXTRACTION OF HOT AND COLD STREAMS FROM
PROCESS FLOWSHEET
DETERMINATION OF ENERGY TARGETS
(NEEDS FOR HEATING AND COOLING)
UTILIZATION OF HEURISTICS TO
CONCEIVE A HEAT EXCHANGER NETWORK
TO REACH ENERGY TARGETS AT A MINIMUM
COST
12
DATA EXTRACTION
Extraction of information required for Pinch
Analysis from a given process flowsheet ant the relevant heat and material balance
Data extraction is THE KEY link between process and pinch analysis
The quality of data extraction has a direct influence on the quality of the final result of the analysis
13
WHAT ARE WE SEARCHING FOR?
Thermal data must be extracted from the process
This involves the identification of process heating and cooling duties
14
DEFINITIONS (1-2)
Hot streams are those that must be cooled or available to be cooled. e.g. product cooling before storage (heat sources)
Cold streams are those that must be heated. e.g. feed preheat before a reactor (heat sinks)
Utility streams are used to heat or cool process streams when heat exchange between process streams is not practical or economic (e.g cooling water, air, refrigerant)
15
DEFINITIONS (2-2)
For each hot and cold stream identified,
the following thermal data is extracted: TS : supply temperature, the temperature at
which the stream is available (oC) TT : target temperature, the temperature the
stream must be taken to (oC) ΔH : enthalpy change of streams (kW) CP: heat capacity flow rate
CP = Cp * M (kW/oC = kJ/oC kg * kg/s)16
TYPICAL STREAM DATA
STREAMNUMBER
STREAM NAMETS
(oC)TT
(oC)CP
(kW/oC)H
(kW)1 FEED 60 205 20 29002 REACTOR OUT 270 160 18 19803 PRODUCT 220 70 35 52504 RECYCLE 160 210 50 2500
17
NOTION OF ΔTmin (1-2)
ΔTmin is the minimum temperature difference, imposed in the system; under this value, heat exchange between two streams is not possible
Thus, the temperature of the hot and cold streams at any point in exchangers must always have at least a minimum temperature difference (ΔTmin)
The selection of ΔTmin value has implications for both capital and energy costs
18
NOTION OF ΔTmin (2-2)
In each temperature interval, each cold and hot stream has to be separated at least by ΔTmin. The principle of modified temperatures has to be introduced:
for a cold stream : Tmodified = T + (ΔTmin/2)
for a hot stream : Tmodified = T - (ΔTmin/2)
19
COMPOSITE CURVES
Composite curves consist of temperature-enthalpy profiles of heat availability in the process (the hot composite curve) and head demands in the process (the cold composite curve)
Composite curves allow to determine and visualize the pinch point and the energy targets (heating and cooling demands)
20
HOW TO DO IT?
- A stream with a constant CP
value is represented by a
straight line running from TS
to TT
- When there are a number of
hot and cold streams, the
construction of hot and cold
composites curves involves
the addition of the enthalpy
changes of the streams in the
respective temperature
intervals See Fig. (a), (b)
21
RESULT
Internal recuperation of heat
Cooling required
QCmin
T (oC)
H (kW)
Pinch point
Cold composite curve
Hot composite curve
TPINCH
Heating required
QHmin
22
PINCH GOLDEN RULES
Do not transfer heat across pinch
Do not use cold utilities above the pinch
Do no use hot utilities below the pinch
23
SUMMARY
The composite curves provide overall energy targets
BUT... They do not clearly indicate how much
energy is supplied by different utility levels
SOLUTION... The utility mix is determined by the Grand
Composite Curve (GCC)
24
GRAND COMPOSITE CURVE
It shows the utility requirements in both enthalpy and temperature terms
It is used to optimize the utilities network when the utilities are available at different quality levels
It is useful for integrating special equipments: cogeneration, heat pump, etc.
25
GRAND COMPOSITE CURVE
Pockets of heat recovery
ΔH
T
Heat sink
Heat source
QHmin
QCmin
Pinch point
26
DESIGN A HEAT EXCHANGER NETWORK (HEN)
Application of heuristics to design a heat exchanger network with the objectives of:
Reaching energy targets
Respecting pinch rules
27
DEVELOP A HEN FOR A MAXIMUM ENERGY RECOVERY (MER) (1-2)
Divide the problem at the pinch: above the pinch and below the pinch
Design hot-end, starting at the pinch: Pair up exchangers according to CP and
number of streams “N” constraints Immediately above the pinch, pair up streams
such that CPHOT CPCOLD , NHOT NCOLD
Add heating utilities as needed (QHmin)
28
DEVELOP A HEN FOR A MAXIMUM ENERGY RECOVERY (MER) (1-2)
Design cold-end, starting at the pinch: Pair up exchangers according to CP and
number of streams “N” constraints Immediately above the pinch, pair up streams
such that CPHOT CPCOLD , NHOT NCOLD
Add heating utilities as needed (QCmin)
29
MINIMUM NUMBER OF HEAT EXCHANGERS (Umin)The minimum number of heat exchangers in a
network is given by
Umin = Nstream + Nutilities - 1
where Nstream is the total number of streams and Nutilities the total
number of utilities in the heat exchanger network
30
SPECIAL PROBLEMS IN HEN DESIGN Introduction on a same stream of:
Splitting Mixing
Elimination of loops
More opportunities
More complexFrequently the only way of getting Umin
31
NOTION OF OPTIMAL ΔTmin
At the beginning, an arbitrary Tmin is fixed The goal is to find an optimal Tmin for a
minimum cost
The total cost is function of the utility cost and the heat exchanger cost
Utility cost = f(Qc, Qh) it is an energetic cost Heat exchanger cost = f(exchange area)
it is a capital cost
32
ESTIMATION OF THE ENERGY COST
Energy cost = (Costcold utility X Qc) + (Costhot utility X Qh)
where the cost unit is $/kW and Qc unit is kW
33
ESTIMATION OF HEN CAPITAL COST (1-3)
The capital cost of a HEN depends on 3 factors: the number of exchangers the overall network area the distribution of area between the exchangers
Capital cost = + .A
where A is the exchange area and , , are
economical and technical factors
34
ESTIMATION OF HEN CAPITAL COST (2-3)Using a temperature-enthalpy diagram and the
composite curves, the estimation of the exchange
area can be obtained by:
Amin = (1/ TLM * qj/hj)
COMPLETER.....mettre le i!
where i: enthalpy interval
j: jth stream
TLM: log mean temperature difference or LTMD
qj: enthalpy change of the jth stream in the interval i
hj: transfert coefficient of jth stream
35
ESTIMATION OF HEN CAPITAL COST (3-3)Estimation of exchange area
T (oC)
H (kW)
A1
A2
A3
A4
A5
Enthalpy intervals in the
composite curves
HEN AREAmin = A1 + A2 + A3 +...+ Ai
36
OPTIMAL ΔTmin
To arrive to an optimum Tmin, the total annual cost (the sum of total annual energy and capital cost) is plotted at varying values (see next page). Three key observations can be made:
an increase in Tmin values result in higher energy costs and lower capital costs
a decrease in Tmin values result in a lower energy costs and higher capital costs
an optimum Tmin exists where the total annual cost of energy and capital costs is minimized
37
ENERGY-CAPITAL COST TRADE OFF (OPTIMAL ΔTmin)
Tmin
An
nu
ali
zed
co
st
Optimum Tmin
Total cost
Energy cost
Capital cost
38
RETROFIT DESIGN
For a new process: the application of pinch concepts is relatively easy:
low uncertainty for data extraction low constraints in the process
For an existing process: the application of pinch concepts is more complicated:
technical, geographical and economical constraints
39
DATA EXTRACTION FOR A RETROFIT DESIGN
Data is extracted from the existing process and indeed from a simulation that has to be validated on-site
Validate a simulation is difficult: it can take up to one year! The cost is too high!
Data are less reliable and the quality of the pinch analysis decreases
40
HEN IN RETROFIT DESIGN
There is already in the process violation of the golden rules
Some exchangers are already installed, used or not, have to be taken into account
important for the investment/capital cost
The geographical constraints are important for fitting of equipment in a limited space
41
OPTIMAL ΔTmin IN RETROFIT DESIGN New factors have an influence on the
determination of the optimum ΔTmin: Geographical constraints that have an impact
on the capital cost Investments already realized for the actual
network Preservation of the efficiency of the actual
network
In some cases, we can use Δtmin in the actual HEN or use a ΔTmin from similar processes
42
OPTIMAL ΔTmin IN RETROFIT DESIGN
Industrial sector Experience Tmin valuesOil refining 20 – 40 oC
Petrochemical 10 – 20 oCChemical 10 – 20 oC
Low temperatureprocesses
3 – 5 oC
43
PINCH SOFTWARES
Super Target (Linhoff March) Pinch Express (Linhoff March) Aspen Pinch (Aspentech) Hint (Angel Martin, freeware)
available on www.heatintegration.com
These softwares include the basic concepts of pinch analysis and optimization tools can be integrated
44
1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS
45
1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS
Heat transfer and mass transfer analogy Equipment configurations The three types of mass exchange
networks analysis
46
HEAT TRANSFER AND MASS TRANSFER ANALOGY
There is an analogy between the exchange potentials (temperature differences and concentration differences) and the quantities that are exchanged (enthalpy and mass)
Parameters such flux, transfer coefficient, exchange rate and other nondimensional numbers appear in the two fields, have similar roles, but the way they are expressed are sometimes really different
47
HEAT TRANSFER AND MASS TRANSFER ANALOGY
Source: Manousiouthakis, 1999
48
MASS EXCHANGE NETWORK
Mass exchange operations are important to limit or eliminate sources of industrial pollution
In process integration, mass exchange operations are used to transfer selectively some undesirable species starting from process streams (called rich streams) to mass separating agents (MSA) that act as receiving streams (called lean streams)
49
MASS EXCHANGER
Definition: a mass transfert unit by direct or indirect contact that use a MSA (lean phase) to remove selectively some compounds (for example pollutants) from a rich phase (for example a waste stream)
Mass exchangers are present in processes of absorption, adsorption, liquid-liquid extraction, desorption, etc.
50
TYPES OF EXCHANGE EQUIPMENTS (1-2)
Rich stream
Lean stream
1. Exchange by direct contact
2. Exchange by mixing of miscible phases non-redistributed
Main stream of the process
Dilution water
51
TYPES OF EXCHANGE EQUIPMENTS (2-2)
3. Exchange by direct contact of non-miscible phases
Washing water
Used water
Treated stream
Contaminated stream
52
TYPES OF MASS EXCHANGE NETWORK
Mass pinch
Water pinch
53
MASS PINCH
Optimization of the mass exchanger network by a method similar to the thermal pinch
Entity exchanged: chemical specie or group of species (e.g. contaminant or undesirable product in the stream of the main process)
The donor streams (analogues to hot streams) are the rich streams
The receiving streams (analogues to cold streams) are the lean streams
54
HOW TO DO IT?
Mass to exchange
Co
nc
en
tra
tio
n
Co
nc
en
tra
tio
n
Mass to exchange
Co
nc
en
tra
tio
n
Mass to exchange
Mass to exchange
Co
nc
en
tra
tio
n
55
RESULT
Internal exchange of materialNeed of MSA
Co
nc
en
tra
tio
n
Mass to exchange
Pinch point
Lean composite curve
Rich composite curve
Pinch
concentration
Need of MSA
56
WATER PINCH
Water pinch can be used to guide water and effluent management decisions while at the same time improving the efficiency of the processes
It is a tool for the rational analysis of the water networks to identify bottlenecks and where recycle/reuse loops should be located
57
WHAT IS THE RESULT?
The procedure enables the minimum amount of water to be determined by considering the introduction of recycle loops and reuse cascades
It highlights the operations that should be investigated for the improvement of their internal efficiencies of water management
58
LIMITING WATER PROFILE
Wastewater minimization application
Graphic of concentration (C) versus mass load (m)
59
DOMAINS OF APPLICATION (1-4)
The mass-exchange operations are necessary for pollution prevention
The realm of mass exchange includes the following applications:
Absorption : a liquid solvent is used to remove selected compounds from a gas using their preferential solubility (e.g. desulfurization of flue gases by alkaline solutions or ethanolamines, recovery of volatile-organic compounds using light oils, removal of ammonia from air using water)
see next page...
60
DOMAINS OF APPLICATION (2-4)
Adsorption : the ability of a solid adsorbent to adsorb specific component from a gaseous or a liquid solution onto its surface (e.g. activated carbon used to remove a mixture of benzene-toluene-xylene from the underground water, separation of ketones from aqueous wastes of an oil refinery, recovery of organic solvent from the exhaust gases of polymer manufacturing facilities)
Extraction : a liquid solvent is used to remove selected compounds from another liquid using their preferential solubility of the solutes in the MSA (e.g. wash oils used to remove phenol and PCBs from the aqueous wastes of synthetic-fuel plants and chlorinated hydrocarbons from organic wastewater)
61
DOMAINS OF APPLICATION (3-4)
Ion exchange : cation and/or anion resins are used to replace undesirable anionic species in liquid solutions with nonhazardous ions (e.g. cation-exchange resins contain nonhazardous, mobile, positive ions (sodium, hydrogen) which are attached to immobile acid groups (sulfonic, carboxylic); these resins are used to eliminate various species (dissolved metal, sulfides, cyanides, amines, phenols, and halides) from wastewater)
Leaching : a selective solution of specific constituents of a solid mixture is brought in contact with a liquid solvent (e.g. separating metals from solid matrices and sludge)
62
DOMAINS OF APPLICATION (4-4)
Stripping : desorption of volatile compounds from liquid or solid streams using a gaseous MSA (e.g. recovery of volatile organic compounds from aqueous wastes using air, removal of ammonia from the wastewater of fertilizer plants using steam, regeneration of activated carbon using steam or nitrogen
63
MULTI-COMPONENT EXCHANGE
Multi-component mass integration Tool to find the minimum utility cost for mass exchanger
networks with multicomponent targets The unit operations are mass-exchangers
Framework: 1st and 2nd laws of thermodynamics Infinite DimEnsional State Space (IDEAS) Conservation of mass Mass cascades from high to low chemical potential for
each component
Concepts: composition interval diagrams, mass exchange
diagrams for each component
64
1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS
65
1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS
Introduction Review of optimization techniques Mathematical programming Combinatory optimization algorithms
66
INTRODUCTION
Many problems in plant operation, design, location and scheduling involve variables that are not continuous but instead have integer values. For example, decision variables such as:
To install or not a new piece of equipment What is the optimum number of stages in a distillation
column? Should we use reactor 1 or reactor 2?
OPTIMIZATION IS NECESSARY!
67
3 DIFFERENT APPROACHES
Heuristics approach (intuition, engineering experience)
Thermodynamic approach (physical insight)
Mathematical programming approach
68
REVIEW OF OPTIMIZATION TECHNIQUES
3 groups Mathematical programming
Linear programming (LP) Non-linear programming (NLP) Mixed-integer linear programming (MILP) Mixed-integer non-linear programming (MINLP)
Combinatory optimization algorithms Branch and bound Simulated annealing Genetic algorithms
Fuzzy logic and heuristics
69
WHAT IS A MATHEMATICAL PROGRAM?A mathematical program is an optimization
problem of the form:
Maximize f(x): x in X, g(x) 0, h(x) = 0,
where X is a subset of Rn and is in the domain of the real-valued functions, f, g and h.
The relations, g(x) 0 and h(x) = 0 are called constraints, and f is called the objective function.
70
WHAT IS MATHEMATICAL PROGRAMMING ? (1-2)
Mathematical programming is the study or use of the
mathematical program. It includes any or all of the
following: Theorems about the form of a solution, including
whether one exists; Algorithms to seek a solution or ascertain that none
exists; Formulation of problems into mathematical
programs, including understanding the quality of one formulation in comparison with another;
Analysis of results, including debugging situations, such as infeasible or anomalous values;
71
WHAT IS MATHEMATICAL PROGRAMMING ? (2-2)
It includes any or all of the following:
Theorems about the model structure, including properties pertaining to feasibility, redundancy and/or implied relations (such theorems could be to support analysis of results or design of algorithms);
Theorems about approximation arising from imperfections of model forms, levels of aggregation, computational error, and other deviations;
Developments in connection with other disciplines, such as a computing environment.
72
MATHEMATICAL PROGRAMMING
LP: optimization technique where constraints and objective function are expressed by linear functions in relation to continuous variables
MILP: optimization where constraints and objective function are linear in relation to mixed variables: discrete and
continuous
NLP: optimization technique where constraints and objective function are expressed by non-linear functions
MINLP: optimization technique where constraints and objective function are non-linear in relation to mixed variable:
discrete and continuous
73
APPLICATION FIELDS FOR OPTIMIZATION TECHNIQUES
Heuristics
Exhaustive research
Fuzzy logic
NLP
MINLP
Simulated annealing
Genetic algorithms
Number of discrete parameters to optimize
Nu
mb
er
of
co
nti
nu
ou
s p
ara
me
ters
to
op
tim
ize
74
COMBINATORY OPTIMIZATION ALGORITHMS
Branch and bound Simulated annealing Genetic algorithms
75
BRANCH AND BOUND
Approach developed for solving discrete and combinatorial optimization problems. Discrete optimization problems are problems in which
the decision variables assume discrete values from a specified set; when this set is a set of integers, we have an integer programming problem.
Combinatorial optimization problems, on the other hand, are problems of choosing the best combination out of all possible combinations. Most combinatorial problems can be formulated as integer programs.
76
BRANCH AND BOUND
Example: minimize a function f(x), where x is restricted to some feasible region (defined, e.g., by explicit mathematical constraints).
To apply branch and bound, one must have a means of computing a lower bound on an instance of the
optimization problem a means of dividing the feasible region of a problem to create
smaller subproblems. there must also be a way to compute an upper bound (feasible
solution) for at least some instances; for practical purposes, it should be possible to compute upper bounds for some set of nontrivial feasible regions.
77
BRANCH AND BOUND
Consider the original problem with the complete feasible region, which is called the root problem. The lower-bounding and upper-bounding procedures are applied to the
root problem. If the bounds match, then an optimal solution has been found and the
procedure terminates. Otherwise, the feasible region is divided into two or more regions, each
strict subregion of the original, which together cover the whole feasible region; ideally, these subproblems partition the feasible region.
These subproblems become children of the root search node. The algorithm is applied recursively to the subproblems, generating a tree of subproblems.
78
BRANCH AND BOUND
If an optimal solution is found to a subproblem, it is a feasible solution to the full problem, but not necessarily globally optimal. Since it is feasible, it can be used to prune the rest of the tree: if the lower bound for a node exceeds the best known feasible solution, no global optimal solution can exist in the subspace of the feasible region represented by the node. Therefore, the node can be removed from consideration. The search proceeds until all nodes have been solved or pruned, or until some specified threshold is meet between the best solution found and the lower bounds on all unsolved subproblems.
79
SIMULATED ANNEALING
Definition 1: A technique which can be applied to any minimization or learning
process based on successive update steps (either random or deterministic) where
the update step length is proportional to an arbitrary set parameter which can play
the role of a temperature. Then, in analogy with the annealing of metals, the
temperature is made high in the early stages of the process for faster minimisation
or learning, then is reduced for greater stability.
Definition 2 : An algorithm for solving hard problems, notably combinatorial
optimization, based on the metaphor of how annealing works: reach a minimum
energy state upon cooling a substance, but not too quickly in order to avoid reaching
an undesirable final state. As a heuristic search, it allows a non-improving move to a
neighbor with a probability that decreases over time. The rate of this decrease is
determined by the cooling schedule, often just a parameter used in an exponential
decay (in keeping with the thermodynamic metaphor). With some assumptions
about the cooling schedule, this will converge in probability to a global optimum.
80
GENETIC ALGORITHMS (GA)
A class of algorithms inspired by the mechanisms of genetics, which has been applied to global optimization (especially combinatorial optimization problems). It requires the specification of three operations (each is typically probabilistic) on objects, called "strings" (these could be real-valued vectors): reproduction, mutation and crossover
81
THREE OPERATIONS OF GA Reproduction - combining strings in the population to create a new string
(offspring);
Example: Taking 1st character from 1st parent + rest of string from 2nd parent:
[001001] + [111111] ===> [011111]
Mutation - spontaneous alteration of characters in a string;
Example: Just the left-most string:
[001001] ===> [101001]
Crossover - combining strings to exchange values, creating new strings in their place.
Example: With crossover location at 2:
[001001] & [111111] ===> [001111], [111001]
These can combine to form hybrid operators, and the reproduction and crossover
operations can include competition within populations.
82
GENERIC GA STRATEGY
0. Initialize population.
1. Select parents for reproduction and GA operators (reproduction, mutation and crossover).
2. Perform operations to generate intermediate population and evaluate their fitness values.
3. Select members of population to remain with new generation.
Repeat 1-3 until some stopping rule is reached.
83
FUZZY LOGIC
Problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data acquisition and control systems.
It can be implemented in hardware, software, or a combination of both.
FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL's approach to control problems mimics how a person would make decisions, only much faster.
84
HEURISTICS
The central idea of this approach is the application of empirical rules based on the experience and the “know-how” of the engineer.
The advantage of this method is the exploitation of the knowledge to simplify a problem and identify rapidly some solutions, usually good quality solutions.
The inconvenience of this method is that some heuristics rules for a given problem can enter in contradiction when used in applied problems
85
END OF TIER 1
At the end of Tier 1, you have now a global view
of the basic concepts of heat and mass exchange
networks optimization.
The next steps are the integration of all these notions in
order to solve Case Studies (Tier 2) and finally proceed to
solve real world “open Ended Problems” (Tier 3).
A short quiz and a list of bibliographic references are
completing Tier 1
86
QUIZ
Question 1
What is the objective of Pinch Analysis?
The prime objective of Pinch Analysis is to achieve financial savings in the process industries by optimizing the ways in which process utilities (particularly energy and water), are applied for a wide variety of purposes.
With the application of Pinch Analysis, savings can be achieved in both capital investment and operating cost. Emissions can be
minimized and throughput maximized.
87
QUIZ
Question 2
What is the significance of the pinch point?
The pinch point is defined as the enthalpy at which the
hot and cold composite curves are separated by the
minimum temperature difference, which corresponds with
the enthalpy of the energy cascade at which the heat flux
is zero.
88
QUIZ
Question 3
What analogy can be made between HEN and MEN?
The analogy can be made
between the exchange potentials
(temperature differences and
concentration differences) and
the quantities that are exchanged
(enthalpy and mass)
89
QUIZ
Question 4
When is it necessary to apply mass-exchange operations?
Mass-exchange operations are mainly used for pollution prevention
It is used to remove selectively some compounds (for example pollutants) from a rich phase (for example a waste stream)
Mass exchangers are present in processes of absorption, adsorption, extraction liquid-liquid, desorption, etc.
90
QUIZ
Question 5
Why do we need to optimize chemical processes?
In many plants, we are confronted to make decisions regarding the choice of operating conditions, the use of an equipment, the choice between two pieces of equipment or the determination of an optimal number of operations. Optimization is then necessary to make these decisions
91
QUIZ
Question 6
What optimization technique should you use if you have a
high number of continuous parameters and low number of
discrete parameters to optimize? Describe the chosen
technique.
NLP: optimization technique where constraints and objective function are expressed by non-linear functions
92
REFERENCES
Here is a list of the main references used to elaborate
Tier 1 Books
Douglas, J.M, Conceptual Design of Chemical Processes, McGraw-Hill, Singapore, 1988.
Edgar, T.F., Himmelblau, D.M., Optimization of Chemical Processes, McGraw-Hill, 1988.
El-Halwagi, M.M, Pollution Prevention through Process Integration: Systematic Design Tools, Academic Press, San Diego, 1997.
Smith, R., Chemical Process Design, McGraww-Hill, New-York, 1995.
93
REFERENCES
Papers Linnhoff, M., Introduction to Pinch Technology, 1998.
(available at www.linnhoffmarch.com) Maia, L.O.A. et al, Synthesis of Utility Systems by
Simulated Annealing, Computers Chem. Eng., Vol. 19, No. 4, 1995, pp. 481-488.
Maréchal, F., Advanced energy: process integration and exergy analysis. 4. Heat exchangers network synthesis, Ecole Polytechnique Fédérale de Lausanne, 2002.
Courses notes, GCH6211 - Process Integration Course, Ecole Polytechnique de Montréal, 2002.
94
REFERENCES
Websites Pinch Analysis
www.cheresources.com/pinchtech4.shtml Mass Exchange Network
http://www.eng.auburn.edu/users/edenmar/6460/6460_Chapter_3.pdf
http://www.epa.gov/ORD/NRMRL/std/mtb/Manousiouthakis2.ppt
Optimization techniques Glossary of mathematical programming:
http://carbon.cudenver.edu/~hgreenbe/glossary/index.php?page=nature.html
95
Program for North American Mobility in Higher Education
Introducing Process Integration for Environmental Control in Engineering Curricula
MODULE 12: “Heat and Mass Exchange Networks Optimization”
96
APPLICATION
EXAMPLES
Tier 2
97
TIER 2 - STATEMENT OF INTENT
The goal of Tier 2 is to demonstrate the application
of heat and mass networks optimization
techniques for a few case study examples
including thermal Pinch Analysis, mass exchange
networks analysis and optimization techniques
98
TIER 2 - CONTENTS
The tier 2 consists into three sections:
2.1 Application examples for Thermal Pinch Analysis
2.2 Application examples for Mass Exchange Network Analysis
2.3 Application examples for Optimization techniques
For each section we present example problem statements and then
the solution.
99
2.1 APPLICATION EXAMPLES FOR THERMAL PINCH ANALYSIS
100
EXAMPLE 1 - Data extraction
The Figure 1 below shows the flowsheet of an existing
process
20oC
20oC 120oC
120oC T=120oC
140oC
160oC
180oC
90oC
150oC
RECYCLE A (PURE A)FLOWRATE= 50 kg/hr
RECYCLE B (PURE B)FLOWRATE= 10 kg/hr
REACTOROUTLET
ISOTHERMIC
REACTORCOLUMN 1
COLUMN 2
TO STORAGE AT AMBIENT TEMPERATURE
68.2 MJ/h
51.9 MJ/h73.1 MJ/h
46.3 MJ/h
Fig. 1
FEED A
FEED B
101
EXAMPLE 1 - Data extraction
Additional data:
Flowrate = 100 kg/hrTBoiling Point = 90 oCHvap = 184.2 kJ/kg
Cpliq = 2.47 kJ/kgoC
Feed A
Cpvap = 1.07 kJ/kgoCFlowrate = 50 kg/hrTBoiling Point = 180 oCHvap = 317.1 kJ/kg
Cpliq = 4.72 kJ/kgoC
Feed B
Cpvap = 2.36 kJ/kgoCTBoiling Point = 160 oCCpliq = 764.4 kJ/oC
Reactor Outlet
Cpvap = 451.6 kJ/oCCpliq = 468.3 kJ/oCProductCpvap = 279.5 kJ/oC
102
EXAMPLE 1 - Data extraction
Extract the stream data needed to perform a pinch
analysis from the flowsheet given in Figure 1
103
EXAMPLE 1 - Solution
20oC
20oC 120oC
120oC T=120oC
140oC
160oC
180oC
90oC
150oC
RECYCLE A (PURE A)FLOWRATE= 50 kg/hr
RECYCLE B (PURE A)FLOWRATE= 10 kg/hr
REACTOROUTLET
ISOTHERMIC
REACTORCOLUMN 1
COLUMN 2
TO STORAGE AT AMBIENT TEMPERATURE
68.2 MJ/h
51.9 MJ/h73.1 MJ/h
46.3 MJ/hTEMPERATURE VARIATION
Identification of all the streams where there is a change in the temperatureand or enthalpy
Feed A
Feed B
104
EXAMPLE 1 - Solution
20oC
20oC 120oC
120oC T=120oC
140oC
160oC
180oC
90oC
150oC
RECYCLE A (PURE A)FLOWRATE= 50 kg/hr
RECYCLE B (PURE A)FLOWRATE= 10 kg/hr
REACTOROUTLET
ISOTHERMIC
REACTORCOLUMN 1
COLUMN 2
TO STORAGE AT AMBIENT TEMPERATURE
68.2 MJ/h
51.9 MJ/h73.1 MJ/h
46.3 MJ/h
Cpvap = 1.07Cpliq = 2.47
Cpliq = 4.72
CPliq = 764.4
STREAM 1COLD
STREAM 2COLD
STREAM 3COLD
STREAM 7HOT
CPliq = 468.3
STREAM 4COLD
STREAM 5HOT
STREAM 6HOT
Feed A
Feed B
105
EXAMPLE 1 - Solution
The stream data for the process are given in the following table
(streams 1 to 3).
Stream Tin
(0C)
Tout (0C) CP
1. COLD
20
90
91
90
91
120
2.47 kJ/kgoC
Hvap = 184.2 kJ/kg
1.07 kJ/kgoC
2. COLD 20 120 4.72 KJ/Kg0C
3. COLD 120 160 764.4 Kj/0C
106
EXAMPLE 1 - Solution
The stream data for a process are given in the following table
(streams 4 to 7).
Stream Tin ( 0C) Tout ( 0C) Information needed for Pinch Analysis
4. Cold 179 180 Vap. Heat
68.2 MJ / h
5. Hot 140 139 Cond. Heat
73.1 MJ / h
6. Hot 90 89 Cond. Heat
46.3 MJ / h
7. Cold 149 150 Vap. Heat
51.9 MJ / h
107
The stream data for a process are given in the table
below
Stream Tin ( 0K) Tout ( 0K) CP (kW/ 0K)
1. Cold 311 478 1139
2. Cold 339 455 1292
3. Cold 366 478 1303
4. Hot 522 394 1662
5. Hot 578 339 1330
EXAMPLE 2 - Composite curves and HEN design
108
EXAMPLE 2 - Composite curves and HEN design
The hot utility is steam at 509 K and the cold utility is
water at 311 K Plot the composite curves for the above system
and determine QH,min, QC,min and the pinch temperature for Tmin = 24 K
Design a network that features the minimum number of units for maximum energy recovery
109
Step 1 - Define temperature intervals Hot stream :
interval temp. = actual temp. – 1/2 Tmin
Cold stream :
interval temp. = actual temp. + 1/2 Tmin
Stream Actual temperature TS / TT ( 0K)
Interval temperature TS / TT ( 0K)
1. Cold 311 / 478 323 / 490
2. Cold 339 / 455 351 / 467
3. Cold 366 / 478 478 / 490
4. Hot 522 / 394 510 / 382
5. Hot 578 / 339 566 / 327
EXAMPLE 2 - Solution
110
EXAMPLE 2 - Solution
Step 2 - Interval thermal balance
Interval temp Flux IntervalTi (oC)
Cpcold-Cphot(kW/ oC)
Hi (kW) Surplus/deficit
566 ---510 56 -13.3 -744.8 surplus490 20 -29.92 -598.4 surplus467 23 -5.5 -126.5 surplus382 85 7.42 630.7 deficit378 4 24.04 96.16 deficit351 27 11.01 297.27 deficit327 24 -1.91 -45.84 surplus323 4 11.39 45.56 deficit
5
4
1
2
3
111
EXAMPLE 2 - Solution
Step 3 - Heat energy cascades
Heating utility = 0 kW
Pinch point at 566 K (where the energy flux between 2 intervals is 0 kW)
Cooling utility = 446 kW
HOT UTILITY 0 kW HOT UTILITY 0 kW566 K
-744.8 744.8 -744.8 744.8
510 K
-598.4 1343.2 -598.4 1343.2
490 K
-126.5 1469.7 -126.5 1469.7
467 K
630.7 839 630.7 839
382 K
96.16 742.84 96.16 742.84
378 K
297.27 445.57 297.27 445.57
351 K
-45.84 491.41 -45.84 491.41
327 K
45.56 445.85 45.56 445.85
323 K
COLDUTILITY
COLDUTILITY
112
EXAMPLE 2 - Solution
Step 4 - Composite curves
113
EXAMPLE 2 - Solution
Step 5 - Network design
EXHAUST ALL HOT STREAMS WITH COLD STREAMS
EXHAUST ALL COLD STREAMS WITH HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT CPCOLD
- ΔTmin respected between streams
114
EXAMPLE 2 - Solution
578554
1
2
3
4
5
CP / H
11.39 / 1902.13
12.92 / 1498.72
13.03 / 1459.36
16.62 / 2127.36
13.30 / 3178.7
311
339
366
478
455
478
522
578339
394
E1
E3
E4
E2
E5
1902.13
1285.57
411
380
182.79
511
1498.72
421
446.28
578554COLD UTILITY
Step 5 - Network design - below the pinch point
115
EXAMPLE 2 - Solution
Step 5 - Network design
Above the pinch point, 0 heat exchanger are necessary
Below the pinch point, 5 heat exchangers are necessary
In total, 5 heat exchangers are necessary for this network
Min Number of HX for MER = Umin MER = Umin above + Umin below
Umin above = 0 Umin below = N – 1 = 6 – 1 = 5 where N is the total number of
streams including utilities
116
EXAMPLE 3 - Composite curves and HEN design
The stream data for a process are given in the table below
Stream TS
( 0C)
TT
( 0C)
CP
(KW/ 0C)
1. Hot 170 88 2.3
2. Hot 278 90 0.2
3. Hot 354 100 0.5
4. Cold 30 135 0.9
5. Cold 130 205 2.0
6. Cold 200 298 1.8
117
EXAMPLE 3 - Composite curves and HEN designThe hot utility is to be supplied by a hot oil circuit at 380oC
and the cold utility by a cooling media at 20oC. For a Tmin
of 10oC: Plot the composite curves and determine QH,min,
QC,min and the pinch temperature Design a network that features the minimum
number of units for maximum energy recovery, Umin MER.
118
EXAMPLE 3 - Solution
Step 1 - Define temperature intervals
Stream Actual temp.
TS / TT (0C)
Interval temp.
TS / TT (0C)
1. Hot 170 / 88 165 / 83
2. Hot 278 / 90 273 / 85
3. Hot 354 / 100 349 / 95
4. Cold 30 / 135 35 / 140
5. Cold 130 / 205 135 / 210
6. Cold 200 / 298 205 / 303
119
EXAMPLE 3 - Solution
Step 2 - Interval thermal balance
Interval temp Flux IntervalTi (oC)
Cpcold-Cphot(kW/ oC)
Hi (kW) Surplus/deficit
349 ---303 46 -0.5 -23 surplus273 30 1.3 39 deficit210 63 1.1 69.3 deficit205 5 3.1 15.5 deficit165 40 1.3 52 deficit140 25 -1 -25 surplus135 5 -0.1 -0.5 surplus95 40 -2.1 -84 surplus85 10 -1.6 -16 surplus
83 2 -1.4 -2.8 surplus35 48 0.9 43.2 deficit
1
2
3
5
4
6
120
EXAMPLE 3 - Solution
Step 3 - Heat energy cascades
Heating utility = 153 kW
Cooling utility = 85 kW
Pinch point at 165oC (where the energy flux between 2 intervals is 0 kW)
HOT UTILITY 0 kW HOT UTILITY 152.8 kW349oC
-23 23 -23 175.8
303 oC
39 -16 39 136.8
273 oC
69.3 -85.3 69.3 67.5
210 oC
15.5 -100.8 15.5 52
205 oC
52 -152.8 52 0
165 oC
-25 -127.8 -25 25
140 oC
-0.5 -127.3 -0.5 25.5
135 oC
-84 -43.3 -84 109.5
95 oC
-16 -27.3 -16 125.5
85 oC
-2.8 -24.5 -2.8 128.3
83 oC
43.2 -67.7 43.2 85.10
35 oC
COLDUTILITY
COLDUTILITY
121
EXAMPLE 3 - Solution
Step 4 - Composite curvesT (oC)
H (kW)
Tmin
Hpinch
122
EXAMPLE 3 - Solution
Step 5 - Network designH (kW) m.cp (kW/oC)
EXHAUST ALL HOT STREAMS WITH COLD STREAMS
EXHAUST ALL COLD STREAMS WITH HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT CPCOLD
- ΔTmin respected between streams
123
EXAMPLE 3 - Solution
Step 5 - Network design - above the pinch point
Heating utility calculated with energy cascade = 153 kW
Cooling utility calculated with energy cascade = 85 kW
2
3
5
6
170278
354 170
160
200
205
298
CP/H
0.2/21.6
0.5/92
2/90
1.8/176.4
E1
90
E2 E3E4
152.8
HOT UTILITY
2
21.6
174
212213
124
EXAMPLE 3 - Solution
Step 5 - Network design - below the pinch point
1170 88
90
CP/H
2.3/188.6
0.2/162 170
100 0.5/353 170
130 2.0/605160
30 0.9/94.54135
E5
60
E6
94.5
E7
E8
E9
34.1
16
35
COLD UTILITY
COLD UTILITY
COLD UTILITY
144 103
125
EXAMPLE 3 - Solution
Step 5 - Network design
Above the pinch point, 4 heat exchangers are necessary
Below the pinch point, 5 heat exchangers are necessary
In total, 9 heat exchangers are necessary for this network
Min Number of HX for MER = Umin MER = Umin above + Umin below
Umin above = N – 1 = 5 – 1 = 4 Umin below = N – 1 = 6 – 1 = 5 where N is the total number of
streams including utilities
126
EXAMPLE 4 - GCC
Using the given energy
cascade, draw the
grand composite
curve associated
GCC?
From Int. Energy Agency
127
EXAMPLE 4 - Solution
From Int. Energy Agency
128
EXAMPLE 5 - A complete problem
The stream data for a process are given in the table below
Stream TS (0C) TT (0C) CP (MW/0C)
1. Hot 327 40 3.0
2. Hot 220 160 4.8
3. Hot 220 60 1.8
4. Hot 160 45 12.0
5. Cold 100 300 3.0
6. Cold 35 164 2.1
7. Cold 85 138 10.5
8. Cold 60 170 1.8
9. Cold 140 300 6.0
129
EXAMPLE 5 - A complete problem
At the correct setting of the capital-energy trade-off,
Tmin = 26oC Plot the composite curves for the above system
and determine QH,min, QC,min and the pinch temperature
Plot the grand composite curve of the process Design a network to achieve the target without
violating Tmin = 26oC
130
EXAMPLE 5 - Solution
Step 1 - Define temperature intervals
Stream Actual temp.
TS / TT (0C)
Interval temp.
TS / TT (0C)
1. Hot 327 / 40 314 / 27
2. Hot 220 / 160 207 / 147
3. Hot 220 / 60 207 / 47
4. Hot 160 / 45 147 / 32
5. Cold 100 / 300 113 / 313
6. Cold 35 / 164 48 / 177
7. Cold 85 / 138 98 / 151
8. Cold 60 / 170 73 / 183
9. Cold 140 / 300 153 / 313
131
EXAMPLE 5 - Solution
Step 2 - Interval thermal balanceInterval temp Flux Interval
Ti (oC)
Cpcold-Cphot
(MW/ oC)
Hi(kW)
Surplus/deficit
314 ---313 1 -3 -3000 surplus207 106 6 636 000 deficit183 24 -0.6 -14 400 surplus177 6 1.2 7200 deficit153 24 3.3 79 200 deficit151 2 -2.7 -5400 surplus147 4 7.8 31 200 deficit113 34 0.6 20 400 deficit98 15 -2.4 -36 000 surplus
73 25 -12.5 -322 500 surplus48 25 -14.7 -367 500 surplus47 1 -16.8 -16 800 surplus32 15 -15 -225 000 surplus27 5 -3 -15 000 surplus
2
1
3
4
5
6
7
8
9
132
EXAMPLE 5 - Solution
Step 3 - Heat energy cascades (1 of 2)
Heating utility = 751 200 kWHOT UTILITY 0 kW HOT UTILITY 751 200 kW314 oC
-3000 3000 -3000 742 200
313 oC
636 000 -633 000 636 000 118 200
207 oC
-14 400 -618 600 -14 400 132 600
183 oC
7200 -625 800 7200 125 400
177 oC
79 200 -705 000 79 200 46 200
153 oC
-5400 -699 600 -5400 51 400
151 oC
31 200 -730 800 31 200 20 400
147 oC
20 400 -751 200 20 400 0
133
EXAMPLE 5 - Solution
Step 3 - Heat energy cascades (2 of 2)
Cooling utility = 982 800 kW
Pinch point at 113oC (where the energy flux between 2 intervals is 0 kW)
147 oC
20 400 -751 200 20 400 0
113 oC
-36 000 -715 200 -36 000 36 000
98 oC
-322 500 -392 700 -322 500 358 500
73 oC
-367 500 -25 200 -367 500 726 000
48 oC
-16 800 -8400 -16 800 742 800
47 oC
-225 000 216 600 -225 000 967 800
32 oC
-15 000 231 600 -15 000 982 800
27 oC
COLDUTILITY
COLDUTILITY
134
EXAMPLE 5 - Solution
Step 4 - Composite curves
ΔΤmin
135
EXAMPLE 5 - Solution
Step 5 - Grand composite curve
136
EXAMPLE 5 - Solution
Step 6 - Network design
H (kW) m.cp (kW/oC)
EXHAUST ALL HOT STREAMS WITH COLD STREAMS
EXHAUST ALL COLD STREAMS WITH HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT CPCOLD
- ΔTmin respected between streams
137
EXAMPLE 5 - SolutionStep 6 - Network design - above the pinch point
1126327
CP/H
3000 / 603 000
2160220
4800 / 288 000
3126220
1800 / 169 200
4126160
12 000 / 408 000
5100300
3000 / 600 000
6100
2100 / 134 400
7100
10 500 / 399 000
8100
1800 / 126 000
9140
6000 / 960 000
164
138
170
300
E3
288000
E6
E2
603000 204000
274.5
127.4
168
102000
111000
134224.4
E4
H1
H2
H3
226800
134400
153000
174
E1
E5
102000169200
H4
H5
126000
138
EXAMPLE 5 - Solution
Step 6 - Network design - below the pinch point
140126
360126
445126
635
785
860
CP/H
3000 / 258 000
1800 / 118 800
12 000 / 972 000
2100 / 136 500
10 500 / 157 500
1800 / 72 000
100
100
100
102
72 000
E2
157 500E1
E3
C1
C2
C3
COLD UTILITY
COLD UTILITY
COLD UTILITY
186 000
118 000
136 500
294 000
113 101.5
139
EXAMPLE 5 - Solution
Step 6 - Network design
Above the pinch point, 11 heat exchangers are necessary
Below the pinch point, 6 heat exchangers are necessary
In total, 17 heat exchangers are necessary for this network
Min Number of HX for MER = Umin MER = Umin above + Umin below
Umin above = N – 1 = 12 – 1 = 11 Umin below = N – 1 = 7 – 1 = 6
where N is the total number of streams including utilities
140
2.2 APPLICATION EXAMPLE FOR MASS EXCHANGE NETWORK ANALYSIS
141
EXAMPLE 1
Recovery of benzene from gaseous emission of
a polymer production facility (Source: Pollution
prevention through process integration, El
Halwagi, M.M)
A simplified flowsheet of the copolymerization
process can be found next
142
EXAMPLE 1
Monomers Mixing Tank
Recycled Solvent
Second Stage Reactor
Additive Mixing Column
SeparationFirst Stage Reactor
Unreacted Monomers
Catalytic Solution
(S2)
Monomers
Solvent Makeup
Inhibitors + Special Additives
Extending Agent
Copolymer (to
Coagulation and
Finishing)
S1Gaseous
Waste (R1)
COPOLYMERIZATION PROCESS WITH A BENZENE RECOVERY MEN
143
EXAMPLE 1
Data of rich stream for the benzene removal example
Candidate MSA’s :
Two process MSA’s and one external MSA Process MSA’s :
Additives (S1) : The additives mixing column can be used as a absorption column by bubbling the gaseous waste into the additives
Liquid catalytic solution (S2) : The equilibrium data for benzene in the two process MSA’s are given by:
y1 = 0.25x1
y1 = 0.50x2
For control purpose, the minimum allowable composition difference for S1 and S2 should not be less than 0.001.
Stream Description FlowrateGi, kg mol/s
Supply composition(mole fraction) ys
i
Target composition(mole fraction) yt
i
R1 Off-gas fromproduct separation
0.2 0.0020 0.0001
144
EXAMPLE 1
Data of process lean streams for the benzene removal example
The external MSA, S3, is an organic oil which can be regenerated using flash separation. The operating cost of the oil (including pumping, makeup and regeneration) is $0.05/kgmole of recirculating oil
The equilibrium relation for transferring benzene from the gaseous waste to the oil is given by:
y1 = 0.10x3
Data for the external MSA for the benzene removal example
Stream Description Upper bound onflowrate Lc
j
kg mol/s
Supply compositionof benzene (mole
fraction) xsj
Target compositionof benzene (mole
fraction) xtj
S1 Additives 0.08 0.003 0.006S2 Catalytic solution 0.05 0.002 0.004
Stream Description Upper bound onflowrate Lc
j
kg mol/s
Supply compositionof benzene (mole
fraction) xsj
Target compositionof benzene (mole
fraction) xtj
S3 Organic oil infinite 0.0008 0.0100
145
EXAMPLE 1 SIMPLIFIED FLOWSHEET OF THE COPOLYMERIZATION PROCESS
Monomers Mixing Tank
Recycled Solvent
Second Stage Reactor
SeparationFirst Stage Reactor
Unreacted Monomers
Catalytic Solution S2
Monomers
Solvent Makeup
Copolymer (to
Coagulation and
Finishing)
Gaseous Waste R1Benzene Recovery MEN
Re
ge
ne
ratio
n
To atmosphere
Benzene
Oil Makeup
OilS3
Additive (Extending Agent, Inhibitors and Special Additives S1
146
EXAMPLE 1
Construct the pinch diagram of this process Find where the pinch point is located and
what is the excess capacity of the process MSA’s
Find the outlet composition of the additives-mixing column (S1)
147
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (1 of 4)
148
EXAMPLE 1 - SOLUTION
Representation of the two process MSA’s
1. Construct the pinch diagram (2 of 4)
149
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (3 of 4)
150
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (4 of 4)
151
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram
(1 of 3)
Pinch is located at the corresponding mole fractions (y, x1, x2) = (0.0010, 0.0030, 0.0010)
The excess capacity of the process MSA’s is 1.4X10-4 kgmole benzene/s
152
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram
(2 of 3) There are infinite combination of L1 and x1
out that can be used to remove the excess capacity of S1 according to the following mass balance:
Benzene load above the pinch to be remove by S1=L1(x1
out - x1S) i.e 2.4X10-4 = L1(x1
out - 0.003)
Since the additives-mixing column will be used for absorption, the whole flowrate S1 (0.08 kgmole/s) should be fed to the column. The outlet composition of S1 is 0.0055.
153
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram (3 of 3)
Graphical identification of x1
out
154
2.3 APPLICATION EXAMPLES FOR OPTIMIZATION TECHNIQUES
155
A process consists of the following set of hot and coldprocess streams:
Stream Tin( 0C) Tout( 0C) F Cp (kW 0C-1)
H1 95 75 5
H2 80 75 50
C1 30 90 10
C2 60 70 12.5
Example taken from Floudas and Ciric (1989)
This example features constant flow rate heat capacities, one hot and one cold utility being steam and cooling water, respectively.
EXAMPLE 1 - Linear programming (LP)
156
Assumption: the costs of hot utility i (Ci) and cold utility j (Cj) are equal to 1, for the minimum utility consumption.
Formulate the linear programming (LP) transshipment model, and solve it to determine the minimum utility cost.
EXAMPLE 1 - Linear programming (LP)
157
The temperature interval partitioning along with the transshipment representation is shown in Figure 1.
Figure 1.
(120) (90)
(95) (65)
TI - 1
TI - 2
(90) (60)
TI - 3
(80) (50)
(60) (30)
TI - 4
QS
R1
R2
R3
QW
H2
H1
C2
C1
25
50
25
250
250
50
100200
62.5
62.5
EXAMPLE 1 - SOLUTION
158
Then, the LP transshipment model for minimum utility consumption takes the form:
min QS + QW
s.t. R1 – QS = -312.5
R2 – R1 = -87.5
R3 – R2 = -50
QW – R3 = 75
QS, QW, R1, R2, R3 ≥ 0
EXAMPLE 1 - SOLUTION
159
This model features four equalities, five variables and has linear objective function constraints. Its solution obtained via GAMS/MINOS (General Algebraic Modeling System / Modular Incore Nonlinear Optimization System) is:
QS = 450
QW = 75
R1 = 137.5
R2 = 50
R3 = 0
EXAMPLE 1 - SOLUTION
160
Since R3 =0, there is a pinch point between TI – 3 and TI - 4. hence, the problem can be decomposed into two independent subnetworks, one above the pinch and one below the pinch point.
Remind that when we have one hot and one cold utility, it is possible to solve the LP transshipment model by hand. This can be done by solving the energy balances of TI – 1 for R1, TI – 2 for R2, TI – 3 for R3, and TI – 4 for QW which become
EXAMPLE 1 - SOLUTION
161
Since R1, R2, R3, R4 ≥ 0 we have
QS ≥ 312.5
QS ≥ 400
QS ≥ 450
QS ≥ 375
EXAMPLE 1 - SOLUTION
R1 = QS – 312.5
R2 = R1 – 87.5 = QS – 400
R3 = R2 – 50 = QS – 450
QW = R3 + 75 = QS – 375
162
The objective function to be minimized becomes
QS + QW = 2*QS – 375
Then, we seek the minimum QS that satisfies all the above four inequalities. This is
QS = 450
EXAMPLE 1 - SOLUTION
163
Etching of copper is achieved through ammoniacal solution and etching efficiency is higher for copper concentrations in the ammoniacal solution between 10 - 13 w/w%. To maintain the desired copper concentration in the solution, copper must be continuously removed. Copper must also be removed from the rinse water, with which the etched printed circuits are washed out, for environmental and economic reasons.
EXAMPLE 2
164
Thus, two rich streams in copper must be purified up to concentrations dictated by environmental regulations and process economics. Mass flow rate data and concentration specifications are given in table I.
Stream No.
Description Mass flow rateGi (Kg/s)
Initial concentration
Yis
Targetconcentration
yit
R1 Ammoniacal solution 0.25 0.13 0.10
R2 Rinse water 0.10 0.06 0.02Table I. Rich streams of copper recovery problem
EXAMPLE 2
165
A simplified representation of the etching process is illustrated in Fig 1.
Etching Line
Rinse Bath
MassExchangeNetwork
To solventRegeneration
S1
S2
R2
R1
R2
EtchantEtchantMakeup
Printed CircuitBoards
Spent Echant
RinseWater
Makeup
Rinse Water
Etched Boards
Treated Rinse Water
Regenerated Etchant
Fig. 1. Recovery of streams of copper in an etching plant.
EXAMPLE 2
166
Two extractants are proposed for copper recovery, LIX63 (an aliphatic α- hydroxyoxime, S1) and P1 (an aromatic β-hydroxyoxime, S2). The initial concentrations in copper of the available lean streams, an upper bound on their final concentration and their costs are given in table II.
Stream Description Initial concentration
xjs
Maximum outlet concentration
xjT, up
Cost (US$/Kg)
Ann. Cost (US$/Kg)
S1 L1X63 0.030 0.07 0.010 88,020
S2 P1 0.001 0.02 0.120 1,056,240
Table II. Lean streams of copper recovery problem
EXAMPLE 2
167
Within the ranges of copper concentrations of interest, the copper transfer between the given rich and lean streams is governed by the following linear equilibrium relations (Henry equation):
R1 - S1 : y1* = 0.734 x1
* + 0.001
R2 - S1 : y2* = 0.734 x1
* + 0.001
R1 - S2 : y1* = 0.111 x2
* + 0.008
R2 - S2 : y2* = 0.148 x2
* + 0.013
EXAMPLE 2 - SOLUTION
168
Two types of contactors are considered:
• a perforated plate column for S1 (LIX63)
• a packed tower for S2 (P1)
Where y1*, y2* and x1*, x2* are the copper concentrations of R1, R2 and S1, S2, respectively, at equilibrium.
EXAMPLE 2 - SOLUTION
169
LmG
LmG
bmxybxmy
LmG
Ninout
inin
St
ln
1ln
The annualized investment cost of a plate-column is based on the number of plates NSt which is determined through Kremser equation.
x )( * RRTotal
yOR NHH
yyK
GH
EXAMPLE 2 - SOLUTION
The cost of packed tower is based on the overall height of the column:
170
The annualized investment costs are given in table III
Cost of plate column 4 552 NSt $ / Yr
Cost of packed column 4 245 H $ / Yr
Table III. Capital cost data for copper recovery problem
(Papalexandri et al., 1994)
EXAMPLE 2 - SOLUTION
171
The obtained mass exchange network for copper recovery is illustrated in Fig 2. the model was solved in 3GBD (Generalized benders decomposition) iterations.
1
1 1R2
R1
S1 S2
N2 = 4 N3 = 1
N1 = 1
xs = 0.0300.278 kg/s
xs = 0.0010.019 kg/s
ys = 0.0600.100 kg/s
ys = 0.1300.250 kg/s
xT = 0.070
xT = 0.020
yT = 0.100
yT = 0.020
Fig 2.
EXAMPLE 2 - SOLUTION
172
It features 3 mass exchangers in series and a total annualized cost of $15,933/yr, with $52,591/yr corresponding to operating cost.
A flexibility analysis (Grossmann and Floudas, 1987) of the proposed MEN reveals that it is flexible to operate in the whole uncertainty range of GR.
EXAMPLE 2 - SOLUTION
173
System closure in pulp and paper mills
One can formulate the problem as having two types of white water streams:
•Sources: white water streams that are produced in different operations and are available to be used in other operations. They are characterized by fiber, fine and contaminant concentrations and by flow rate.
•Demands: white water streams that are required by operations, and on which limiting concentrations in fibers, fines and, contaminants are imposed.
EXAMPLE 3 Problem statement & solution structure
174
The objective is to establish a white water network configuration such that all demands are satisfied and yet optimization goals such as minimized fresh water consumption, fiber loss degree of contamination are met. The method consists of encoding structure elements in the general framework of a genetic algorithm problem and relating network characteristics to linear programming problem. A superstructure is formed by respecting the following rules:
EXAMPLE 3 Problem statement & solution structure
175
•Each source stream and fresh water enters a splitter in which it can be divided into several streams that are directed to various demands while the excess is sent to the waste water effluent.
•Before each demand there is a mixer, which gathers all the streams coming from the different sources; wastewater effluents are also collected into a single stream.
EXAMPLE 3 Problem statement & solution structure
176
This form of superstructure is encoded as follows. Each individual configuration of the superstructure is characterized by chromosome in which each gene represents a potential connection between a splitter and a mixer. The value of a gene is one or zero indicating the existence or absence of connection. All possible configurations for a given set of sources and demands can thus be represented by a set of chromosomes in a unique one-to-one correspondence. Figure 1 shows an example of a structure and corresponding code.
EXAMPLE 3 Problem statement & solution structure
177
S1
D2
D1
D3
Waste Fresh Water
S4
S3
S2
Splitters Mixers
1 0 01 1 1 11 1 0 01 0 1 00
Figure 1: example of coding for a system of 4 sources and 3 demands
EXAMPLE 3 Problem statement & solution structure
178
Knowing the number of sources and demands the number of genes and hence, the length of chromosomes is determined. For example if there are m sources and n demands, the number of genes will be (m+1)(n+1). This includes the genes needed to take into account fresh water as a source stream and the effluent stream as a demand.
Overall and component material balances are written for each splitter and mixer for any structure considered.
EXAMPLE 3 Problem statement & solution structure
179
The balance equations constitute constraints of the optimization problem with specified objective function. A linear or non-linear programming problem is thus formed and is solved to give the value of the objective function for the given structure. The optimization of the network is treated a two levels; at the master problem level a set of feasible structures is proposed by GA and at slave problem level the proposed structures are optimized by mathematical programming methods to obtain the optimal value of the objective function.
EXAMPLE 3 Problem statement & solution structure
180
This value in turn is passed to the master problem by means of an adaptation index to be used in the generation of new structures. At the end of the iterative procedure a set of structures is available that have near optimal objective function values.
EXAMPLE 3 Problem statement & solution structure
181
Genetic algorithm procedure (GA)
The GA implemented follows the classical iterative procedure introduced by Goldberg (1989):
Generation of the initial population
Evaluation of the fitness of the initial population
Iteration of the following sequence until total number of generations is reached
EXAMPLE 3 Problem statement & solution structure
182
Generation of the offspring population
Selection of surviving individuals
Synthesis of offspring obtained by cross-over
Mutation of individuals
End of search
The initial population consists of 20 structures that have been created randomly by assigning to the genes.
EXAMPLE 3 Problem statement & solution structure
183
For each generation subsequently generated, a fixed fraction is conserved in the offspring generation and the rest of the population is created by crossover of randomly selected pairs of individuals (Figure 2). In crossover the chromosomes are cut and recombined at a randomly selected crossover point (CP)
EXAMPLE 3 Problem statement & solution structure
184
The individuals interchange chromosome sections and two new individuals are thus created. In mutation one gene is selected randomly and its value is changed.
1 01 11 0
1 01 1 1 1
Crossover
P1
E2E1
P2
CPCP
Mutation
Before mutation
After mutation
Muted Gene
Figure 2. Crossover and mutation operations
EXAMPLE 3 Problem statement & solution structure
185
Each interesting solution given by the program in the final population is compared with the base case of the mill by PS. The necessary changes to be made are extracted from the solution and a scenario is formulated. This scenario is executed in the mill simulation and the changes in concentration of the different species in important points of the process are determined. Figure 3 shows the flow of information at different stages of the overall procedure.
EXAMPLE 3 Problem statement & solution structure
186
Figure 3.General structure of procedure
Superstructure Mass
Balance
ProcessSimulation
Demand Constraints
ObjectiveFunction
Master problemGenetic Algorithm
Superstructure
Retained Solutions
AdaptationIndex
Feasibility Engineering
OPTIMIZATION
IMPLEMENTATION
PROBLEM DEFINITION
EXAMPLE 3 Problem statement & solution structure
187
In this process four sources of water and three demands are identified. The specification of the sources and demands are given on table I
Sources Available flow- rate (L/min)
Fines concentration (%)
Contaminant concentration (ppm)
S 1 500 0.3 100
S 2 2000 0.1 110
S 3 400 0.5 110
S 4 300 0.5 60
Demands Required flow- rate (L/min)
Limiting fines concentration (%)
Limiting contaminant concentration (ppm)
D 1 1200 0.5 120
D 2 800 0.4 105
D 3 500 0.1 80Table I
EXAMPLE 3 Problem statement & solution structure
188
The initial configuration of the process is given on figure I, the demands D2 and D3 are satisfied by fresh water and all the sources are sewered except a fraction of source 2, used to satisfy demand 1. The goal is to find the optimal configuration of the water network, minimizing the fresh water consumption.
EXAMPLE 3 Problem statement & solution structure
189
D1
S1S2
D2
S3
D3
S4
Pulp Pulp
Fresh Water Fresh Water800 5001200
waste waste waste500 400 300
waste800
Flow sheet general diagram
EXAMPLE 3 Problem statement & solution structure
190
800
1200
2000
500
500
2000
400
300
1300
S1
D2
D1
D3
SewerFreshWater
S4
S3
S2
Splitters Mixers
Superstructure
EXAMPLE 3 - Solution (GA)
191
The initial solution of the process is given on table II. The fresh water consumption is 122 L/min, it is 90% reduced from the initial data (1300 L/min)
D1 D2 D3 Waste
S1 500
S2 540 290 348 822
S3 390 10
S4 270 30
Fresh water
122
800
1200
822
500
500
2000
400
300
122
S1
D2
D1
D3
WasteFreshWater
S4
S3
S2
Splitters Mixers
First solution
Table II
EXAMPLE 3 – Solution (GA)
192
The second solution of the process is given on table III. The fresh water consumption is 172 L/min.
D1 D2 D3 Waste
S1 500
S2 764 364 872
S3 400
S4 300
Fresh water
36 136
800
1200
872
500
500
2000
400
300
172
S1
D2
D1
D3
WasteFreshWater
S4
S3
S2
Splitters Mixers
Second solution
Table III
EXAMPLE 3 – Solution (GA)
193
On table IV are compared the first and second solutions of the process using a Genetic Algorithms
Water consumption
(L/min)
Fibers Waste
g/min
GA1 122 0.822
GA2 172 0.872
Table IV
EXAMPLE 3 – Solution (GA)
194
•El-Halwagi, MM and Manousiouthakis, V., “Synthesis of Mass Exchange Networks”, AIChE Journal, 35,(8), 1233-1244, (1989)
•El-Halwagi, MM and Manousiouthakis, V., “Simultaneuos Synthesis of Mass Exchange and Regeneration Networks, AIChE Journal, 36,(8), 1209, (1990a)
•Floudas C. A. and Paules IV G. E. “A mixed-integer non linear programming formulation for the synthesis of heat-integrated distillation sequences”, Comp. Chem. Eng., 12, 259-372, (1998)
REFERENCES
195
•Garrard A., Fraga E. S., “Mass exchange network synthesis using genetic algorithms” Computers and Chemical Engineering, 22, (12), 1837-1850, (1998).
•Goldberg D.E., “Genetic Algorithms in Search, Optimization, and Machine Learning” Ed. Addison Wesley, (1997).
•Jacob, J., H. Kaipe, F. Couderc and J.Paris, “Water network analysis in pulp and paper processes by pinch and linear programming techniques”, Chem. Eng. Communication, 189, (2), 184-206 (2002b).
REFERENCES
196
•Shafiei S., Domenech S., Koteles R., Paris J., “System Closure in Pulp and Paper Mills: Network Analysis by Genetic Algorithm” Pulp and Paper Canada (soumis).
REFERENCES
197
Program for North American Mobility in Higher Education
Introducing Process Integration for Environmental Control in Engineering Curricula
MODULE 12: “Heat and Mass Exchange Networks Optimization”
198
OPEN-ENDED PROBLEMS IN A REAL WORLD CONTEXT
Tier 3
199
TIER 3 - STATEMENT OF INTENT
The goal of Tier 3 is to present an open-ended problem to
solve an industrial case study of actual heat or mass
exchange network optimization in which the student must
interpret results and evaluate a range of potential
solutions. The problem involves defining objective
functions, generating solutions, evaluating their technical
and economical feasibilities. Problem will be drawn from
actual cases in the petroleum and pulp and paper
industries.
200
TIER 3 - CONTENTS
The tier 3 is broken down into two sections:
3.1 Design of a heat and mass exchange network for the efficient management of energy, water and hydrogen in a selected oil refinery process.
3.2 Design of a whitewater network in an integrated thermomecanical pulp and newsprint mill for minimum fresh water consumption and minimum fiber loss
201
3.1 PETROLEUM OPEN-ENDED PROBLEM
202
PROBLEM DEFINITION
A mill is designed to eliminate the sulfuric compounds
present in a feed stream of diesel and light oil.
The mill is divided in 7 sections: Reaction and load section Gaz separation Hydrogen purification Diesel stabilization Product cooling Treatment with DEA Compression of recirculated hydrogen
PROBLEM DEFINITION
A mill is designed to eliminate the sulfuric compounds
present in a feed stream of diesel and light oil.
The mill is divided in 7 sections: Reaction and load section Gaz separation Hydrogen purification Diesel stabilization Product cooling Treatment with DEA Compression of recirculated hydrogen
203
REACTION AND LOADSECTION The objective of this section is to eliminate the
sulfur components and nitrogen, throught the hydrogenation reaction in a fixed bed catalytic reactor.
First, a stream of diesel and a stream of oil are mixted together (MX-801***). The resultant mix is then heated and transported to the decantation tank (FA-801) where the aqueous phase is remove.
The water-free mix is then heated in the three heat exchangers (EA-802, EA-803, EA-804)
The mix is then sent to a heater to reach the temperature of 346oC.
204
REACTION AND LOADSECTION The vapor mix or charge is then transported to the
reactor (DC-801) where the reactions of hydrogenation and the transformation of the nitrogen and oxygen compounds are done.
The reactor effluent is then passed another time in the three heat exchangers (EA-802, EA-803, EA-804)
*** The identification equipment numbers can be founded on the process diagram following the present description of the process
205
GAS SEPARATION SECTION
The vapor and liquid mix is separated in a liquid phase and a gaseous in the FA-802 tank.
The gaseous phase is cooled and a water stream is then injected to eliminate the last impurities.
The resultant mix is then cooled in the aerocooler EC-801
The aqueous phase is separated from the gaseous phase rich in sulfur compounds in the separator FC-803.
The aqueous phase is sent to the stabilization section
The gaseous phase is sent to the DEA treatment section
206
HYDROGEN PURIFICATION SECTION The hydrogen from the reformation plant is sent to a
separator (FA-805) to remove heavy compounds. The hydrogen pass through three steps of compression
(GB-802, GB-803, GB-804) Between each compression, the hydrogen is cooled (EC-
803, EC-804) and is entering a separator (FA-806, FA-807) to remove the heavy compounds from the hydrogen stream.
After the third compression, the hydrogen is at the conditions of pressure and temperature necessary to be utilized in the process.
207
DIESEL STABILIZATION SECTION The liquid phase resulting from the separation in FA-
802 is sent to heat exchanger EA-806. The preheated phase is then sent to the stabilization tower DA-801
The liquid phase resulting from the separation in FA-803 is also sent to the stabilization tower DA-801
The stabilization tower is used to separate the lightweight hydrocarbures from the heavyweight ones.
At the top of the tower, vapor containing sulfur compounds exit and are condensated in EC-805. The separation is done in FA-808.
208
DIESEL STABILIZATION SECTION At the bottom of the tower, the stream containing
mainly heavyweight hydrocarbures is divided in two streams. The first stream is sent to the heater BA-802 where it acquire the heat necessary to be injected in the stabilization tower another time. The second stream is sent to the heat exchanger EA-806. The hydrodesulfurized and stabilized diesel is sent to the vapor generator EA-807, and then the diesel at a temperature of 215oC is transported to the preheater EA-801.
209
PRODUCT COOLING SECTION
The diesel from the heatexchanger EA-801 is sent to the heat exchanger EA-808 where it is cooled until 153oC.
The cooled stream enters the aerocooler EC-802 and the watercooler EA-809.
After these two steps, the diesel is at the conditions necessary to be stock.
210
TREATMENT WITH DEA SECTION The gaseous phase rich in sulfur compounds from
the separator FA-803 is feeded the last tray of the absorption column DA-802. A stream of DEA (dietanolamine) in aqueous phase is sent to the first tray to absorb the sulphuridric acid contained in the feed stream.
The gas obtained at the top of the column is transported to the recirculated gas compression section.
The amine obtained at the bottom of the column, rich in H2S, is sent to the amine recuperation plant.
211
RECIRCULATED HYDROGENCOMPRESSION SECTION The gas free of H2S and rich in hydrogen is feeded
to the separator FA-804 where traces of amine can be totally eliminated.
The gaseous phase is sent to the hydrogen compressor GB-801 to increase its pressure
The compressed gas obtained is either mixted with the hydrogen coming from the gas purification section, or directly sent to the hydrodesulfurized reactor DC-801.
212
PROCESS FLOWSHEET AND DATA The process flowsheet can be found at the
following link: ProcessFlowsheet _PetroleumProb.pdf
The process data can be found at the following link:
ProcessData_PetroleumProb.xls
213
WHAT YOU HAVE TO DO?
Perform a complete pinch analysis using the following
steps
a) Extract the hot and cold streams from the process
flowsheet and extract all the data necessary from the
data flowsheet (flowrate, temperature, enthalpy or Cp)
b) Determine QH,min, QC,min , the minimum consumption of
external utilities (energy targets)
214
WHAT YOU HAVE TO DO?
c) Propose a ΔTmin using Introduction to Pinch
Technology, 1998.of Linnhoff, M., (disponible atwww.linnhoffmarch.com) or using the experience ΔTmin
presented in the first tier - basic concepts.
d) Propose a heat exchanger network for the chosen
ΔTmin and respecting the energy targets.
e) Design a network that features the minimum number
of units for maximum energy recovery
215
3.2 PULP & PAPER OPEN-ENDED PROBLEM
216
PROBLEM DEFINITION
An integrated newsprint mill is located in Canada. The nominal production of the mill is 1230 odt/d (oven dried tons per day) of paper with a feedstock of 1060 odt/d of thermomechanical pulp (TMP) and 170 odt/d of deinked pulp (DIP) also produced on site.
A simplified process flow diagram focusing on steam and fresh water requirements is given in Fig.1.
217
PROBLEM DEFINITION
Fig. 1. Simplified reference process flow diagram. Abbreviations: CPH: chips pre-heather, HRU: heat recovery unit, OM: old magazines, ONP: old newsprint, PM: paper machine.
218
PROBLEM DEFINITION
High pressure steam (16.5 bar, 540 K) is produced by boilers burning biomass( wood residues) and natural gas (NG). It is in part directly used to meet some mill needs and in part depressurised through turbines and headers to three lower pressure levels: MP (4.5 bar, 421 K), LP (3.4 bar, 415 K) and VLP (1.7 bar, 408K).
As indicated on Fig. 2, steam is then directed to the TMP, DIP, paper making plants and other miscellaneous operations. Steam is also exported to an adjoining saw mill. The turbines produce 2 MWe of electricity, while the mill purchases 125 MWe.
219
PROBLEM DEFINITION
Fig. 2. Reference steam distribution system. Abbreviations, NG: natural gas, WM: water make-up.
220
PROBLEM DEFINITION
The two most important operations from the energy standpoint are wood chips refining and paper drying.
Refining consists in disintegrating wood into individual fibres by forcing the chips between two grooved disks rotating at very high speed. In the mill analysed, the refiners consume 83.7 MWe or 6820 kJ/odt. The mechanical energy supplied to the refiners is largely dissipated into heat, which evaporates whitewater injected with the chips.
221
PROBLEM DEFINITION
The heat content of this medium steam is recovered through heat exchanges with fresh water in the heat recovery unit (Fig.1) since it contains wood contaminants and cannot be reused directly. The steam from the primary refiners is released at medium pressure (MP) but is subsequently depressurised to low pressure (LP). The steam from the secondary refiners (1 bar, 273 and 1.4 bar, 282 K) is not recovered currently.
Paper is dried in the end section of the paper machine by passing the sheet of paper over a series of steam-heated steel rolls.
222
PROBLEM DEFINITION
High-pressure steam is used at the beginning and MP in the intermediate zone.
In the follwowing sections are refer types of operation in the paper mill and the thermodynamic requirements.
Preheating by steam injection
The chip washing operation and the three main whitewater chests are heated by direct contact with steam (Fig. 1). This steam must be treated as loss by the utility network since it is not returned to the boilers as condensate.
223
PROBLEM DEFINITION
The thermodynamic requirement is defined by two cold streams in order to separate mass exchange from heat exchange. The first represents the heat required to raise the temperature of the process stream to tank mixing conditions. The second cold stream represents the heat required to raise the liquid water makeup that completes the mass balance from ambient (i.e. the water inlet temperature) to the reservoir mixing conditions. Data are given on Fig. 3 for the wood chip washing operation. In the thermodynamic representation isothermal mixing is assumed, all the process streams entering the mixer having first been heated to the mixing temperature.
224
PROBLEM DEFINITION
Fig. 3. Thermodynamic (reference case)
Stream Comp. T (K) P (bar) m (kg/s)
1 WW 278 2 3.6
2 Steam 351 1 3.6
3 Steam 351 1 3057.3
4 Chips 278 1 15.7
5 WW 350 1 3040
Exchanger
Q (kW)
EX 1 1086
EX 2 2243
EX 3 6390
225
PROBLEM DEFINITION
Paper machine drying
There are two thermodynamic requirements for the drying section of the paper machine: preheating the humid sheet, and evaporating its water content which is reduced from 58% at the inlet of the drying section to 8% in the exiting paper.
Primary and secondary refiners
Since the steam produced by evaporation of the white water in the refiners is not returned in the steam network, the thermodynamic requirements are identically defined as a hot stream to be condensed and cooled to the ambient temperature. 226
PROBLEM DEFINITION
Table 1 gives the characteristics of the hot and cold streams for thermodynamic requirements of each of the major energy consuming operations in the process shown on Fig.1. Steam consumption for soot blowing and general heating has been assimilated to process requirements and the consumption for deaeration is treated as part of the steam network model. The secondary refiner steam will be recovered.
227
TABLE 1
Representation Stream type Tin (K) Tout (K) m Cp (kW/K) Q (MW) P (bar)
Wood chip washing
Thermo. (chips) Cold 278 351 31 2.2 –
Thermo. (WW) Cold 350 351 13,595 6.4 –
Thermo. (makeup) Cold 278 351 15 1.1 –
Preheat before primary refiners
Thermo. 351 388 251 9.4 –
Preheat before secondary refiners
Thermo. (makeup) Cold 278 362 116 9.8 –
Thermo. (pulp) Cold 324 362 60 2.3 –
TMP whitewater tank
Thermo. (FW) Cold 278 321 591 25.7 –
Thermo. (makeup) Cold 278 321 32 1.4 –
Thermo. (WW) Hot 324 321 2576 6.5 –
228
TABLE 1 (CONTINUED)
Representation Stream type Tin (K) Tout (K) m Cp (kW/K) Q (MW) P (bar)
Deinking whitewater tank
Thermo. (FW) Cold 308 313 70 0.3 –
Thermo. (WW) Cold 313 313 950 0.2 –
Thermo. (makeup) Cold 278 313 1 0.03 –
Paper machine whitewater
Thermo. (FW) Cold 288 308 1004 20.2 –
Thermo. (makeup) Cold 278 308 23 0.7 –
Thermo. (WW) Hot 309 308 4768 5.8 –
Drying section
Thermo. (heating) Cold 309 363 42 25.7 –
Thermo. (drying) Cold 309 373 Water 1.4 –
229
TABLE 1 (CONTINUED)
Representation Stream type Tin (K) Tout (K) m Cp (kW/K) Q (MW) P (bar)
Conventional representation
Primary refiners Cold 421 298 Water 73.7 4.46
Secondary refiners Cold 373 298 Water 14.3 1.00
Secondary refiners Hot 388 298 Water 7.5 1.70
Heating Cold 323 417 Water 30.1 3.43
Soot blowing Cold 278 540 Water 6.0 16.52
Effluent treatment Cold 278 417 Water 1.5 3.43
Saw mill Cold 278 417 Water 5.1 3.43
Boilers Cold 323 417 Water 8.3 3.43
Deareator Cold 323 408 Water 3.8 1.70
LP level Cold 323 417 Water 47.6 3.43
MP level Cold 323 421 Water 8.7 4.46
HP level Cold 323 540 Water 10.7 16.52
LP level Hot 394 323 Water 10.2 2.03
MP level Hot 407 323 Water 2.3 3.06
HP level Hot 472 323 Water 3.5 15.12
230
WHAT YOU HAVE TO DO?
Perform a complete Thermal Pinch Analysis
Using the hot and cold streams from the process flowsheet reported in the table 1, determine QH,min, QC,min , the minimum consumption of external utilities (energy targets), and construct the grand composite curves.
Propose a ΔTmin using Introduction to Pinch Technology, 1998.of Linnhoff, M., (disponible at www.linnhoffmarch.com) or using the experience ΔTmin presented in the first tier - basic concepts.
Propose a heat exchanger network for the chosen ΔTmin and respecting the energy targets.
231