MODULE 12: “Heat and Mass Exchange Networks Optimization”

MODULE 12: “Heat and Mass Exchange Networks Optimization”
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

Tier I BASIC CONCEPTS 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
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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) Reactor Separator Utilities Heat Exchanger Network Site-wide Utilities Pinch Analysis starts with the heat and material balance for the process at this boundary 11

THE PHASES OF PINCH ANALYSIS
PROCESS SIMULATION DATA EXTRACTION TARGETING DESIGN OPTIMIZATION DATA EXTRACTION OF HOT AND COLD STREAMS FROM PROCESS FLOWSHEET UTILIZATION OF HEURISTICS TO CONCEIVE A HEAT EXCHANGER NETWORK TO REACH ENERGY TARGETS AT A MINIMUM COST DETERMINATION OF ENERGY TARGETS (NEEDS FOR HEATING AND COOLING) 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 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 T (oC) Cooling required Heating required QCmin QHmin
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 QHmin T Heat sink Pockets of heat recovery
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 complex Frequently 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

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 exchange area T (oC) H (kW) A1 A2 A3 A4 A5 Enthalpy intervals in the composite curves HEN AREAmin = A1 + A2 + A 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)
Annualized cost 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 values Oil refining 20 – 40 o C Petrochemical 10 – 20 Chemical Low temperature processes 3 – 5 43

PINCH SOFTWARES Super Target (Linhoff March)
Pinch Express (Linhoff March) Aspen Pinch (Aspentech) Hint (Angel Martin, freeware) available on These softwares include the basic concepts of pinch analysis and optimization tools can be integrated 44

1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS
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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 Concentration 55

RESULT Internal exchange of material Need of MSA Concentration
Mass to exchange Pinch point Lean composite curve Rich composite curve Pinch concentration 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

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

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

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
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Review of optimization techniques Mathematical programming
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 Number of continuous parameters to optimize 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, (available at Maia, L.O.A. et al, Synthesis of Utility Systems by Simulated Annealing, Computers Chem. Eng., Vol. 19, No. 4, 1995, pp Maréchal, F., Advanced energy: process integration and exergy analysis. 4. Heat exchangers network synthesis, Ecole Polytechnique Fédérale de Lausanne, 2002. Courses notes, GCH Process Integration Course, Ecole Polytechnique de Montréal, 2002. 94

REFERENCES Websites Pinch Analysis Mass Exchange Network
Mass Exchange Network Optimization techniques Glossary of mathematical programming: 95

07/11/2018 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

07/11/2018 Tier 2 APPLICATION EXAMPLES 97

07/11/2018 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
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EXAMPLE 1 - Data extraction
07/11/2018 EXAMPLE 1 - Data extraction The Figure 1 below shows the flowsheet of an existing process 20oC 120oC T=120oC 140oC 160oC 180oC 90oC 150oC RECYCLE A (PURE A) FLOWRATE= 50 kg/hr RECYCLE B (PURE B) FLOWRATE= 10 kg/hr REACTOR OUTLET ISOTHERMIC COLUMN 1 COLUMN 2 TO STORAGE AT AMBIENT TEMPERATURE 68.2 MJ/h 51.9 MJ/h 73.1 MJ/h 46.3 MJ/h Fig. 1 FEED A FEED B 101

07/11/2018 EXAMPLE 1 - Data extraction Additional data: 102

07/11/2018 EXAMPLE 1 - Data extraction Extract the stream data needed to perform a pinch analysis from the flowsheet given in Figure 1 103

TEMPERATURE VARIATION
07/11/2018 EXAMPLE 1 - Solution TEMPERATURE VARIATION 46.3 MJ/h 90oC RECYCLE A (PURE A) FLOWRATE= 50 kg/hr COLUMN 2 Feed A 140oC 51.9 MJ/h 73.1 MJ/h 20oC 120oC ISOTHERMIC REACTOR REACTOR OUTLET 150oC COLUMN 1 160oC TO STORAGE AT AMBIENT TEMPERATURE 20oC 120oC T=120oC Feed B 180oC RECYCLE B (PURE A) 68.2 MJ/h FLOWRATE= 10 kg/hr Identification of all the streams where there is a change in the temperature and or enthalpy 104

EXAMPLE 1 - Solution Feed A Feed B 07/11/2018 STREAM 6 HOT 46.3 MJ/h
90oC RECYCLE A (PURE A) Feed A FLOWRATE= 50 kg/hr STREAM 5 HOT STREAM 1 COLD COLUMN 2 Cpliq = 2.47 Cpvap = 1.07 140oC 51.9 MJ/h 73.1 MJ/h STREAM 7 HOT 20oC 120oC ISOTHERMIC REACTOR REACTOR OUTLET 150oC CPliq = 468.3 COLUMN 1 160oC TO STORAGE AT AMBIENT TEMPERATURE 20oC 120oC T=120oC STREAM 3 COLD CPliq = 764.4 STREAM 4 COLD STREAM 2 COLD 180oC Cpliq = 4.72 Feed B RECYCLE B (PURE A) 68.2 MJ/h FLOWRATE= 10 kg/hr 105

07/11/2018 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 91 120 2.47 kJ/kgoC Hvap = kJ/kg 1.07 kJ/kgoC 2. COLD 4.72 KJ/Kg0C 3. COLD 160 764.4 Kj/0C 106

Information needed for Pinch Analysis
07/11/2018 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 46.3 MJ / h 7. Cold 149 150 51.9 MJ / h 107

EXAMPLE 2 - Composite curves and HEN design
07/11/2018 EXAMPLE 2 - Composite curves and HEN design 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 1303 4. Hot 522 394 1662 5. Hot 578 1330 108

07/11/2018 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

EXAMPLE 2 - Solution Step 1 - Define temperature intervals
07/11/2018 EXAMPLE 2 - Solution 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 / 327 110

EXAMPLE 2 - Solution Step 2 - Interval thermal balance 07/11/2018 111
5 4 1 2 3 111

EXAMPLE 2 - Solution Step 3 - Heat energy cascades
07/11/2018 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 112

07/11/2018 EXAMPLE 2 - Solution Step 4 - Composite curves 113

EXAMPLE 2 - Solution Step 5 - Network design 07/11/2018
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 Step 5 - Network design - below the pinch point
578 554 1 2 3 4 5 CP / H 11.39 / 12.92 / 13.03 / 16.62 / 13.30 / 311 339 366 478 455 522 394 E1 E3 E4 E2 E5 411 380 182.79 511 421 446.28 COLD UTILITY 115

EXAMPLE 2 - Solution Step 5 - Network design
07/11/2018 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

07/11/2018 EXAMPLE 3 - Composite curves and HEN design The stream data for a process are given in the table below Stream TS ( 0C) TT 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

07/11/2018 EXAMPLE 3 - Composite curves and HEN design The 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
07/11/2018 EXAMPLE 3 - Solution Step 1 - Define temperature intervals Stream Actual temp. TS / TT (0C) Interval temp. 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

5 4 6 120

EXAMPLE 3 - Solution Step 3 - Heat energy cascades
07/11/2018 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) 121

EXAMPLE 3 - Solution Step 4 - Composite curves 07/11/2018 122 T (oC)
H (kW) Tmin Hpinch 122

EXAMPLE 3 - Solution Step 5 - Network design 07/11/2018
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 123

EXAMPLE 3 - Solution Step 5 - Network design - above the pinch point
07/11/2018 EXAMPLE 3 - Solution Step 5 - Network design - above the pinch point 2 3 5 6 170 278 354 160 200 205 298 CP/H 0.2/21.6 0.5/92 2/90 1.8/176.4 E1 90 E2 E3 E4 152.8 HOT UTILITY 21.6 174 212 213 Heating utility calculated with energy cascade = 153 kW Cooling utility calculated with energy cascade = 85 kW 124

07/11/2018 EXAMPLE 3 - Solution Step 5 - Network design - below the pinch point 1 170 88 90 CP/H 2.3/188.6 0.2/16 2 100 0.5/35 3 130 2.0/60 5 160 30 0.9/94.5 4 135 E5 60 E6 94.5 E7 E8 E9 34.1 16 35 COLD UTILITY 144 103 125

07/11/2018 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 GCC? Using the given energy cascade, draw the
07/11/2018 EXAMPLE 4 - GCC Using the given energy cascade, draw the grand composite curve associated GCC? From Int. Energy Agency 127

07/11/2018 EXAMPLE 4 - Solution From Int. Energy Agency 128

EXAMPLE 5 - A complete problem
07/11/2018 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 60 1.8 4. Hot 45 12.0 5. Cold 100 300 6. Cold 35 164 2.1 7. Cold 85 138 10.5 8. Cold 170 9. Cold 140 6.0 129

EXAMPLE 5 - A complete problem
07/11/2018 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
07/11/2018 EXAMPLE 5 - Solution Step 1 - Define temperature intervals Stream Actual temp. TS / TT (0C) Interval temp. 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

4 5 6 7 8 9 132

EXAMPLE 5 - Solution Step 3 - Heat energy cascades (1 of 2)
07/11/2018 EXAMPLE 5 - Solution Step 3 - Heat energy cascades (1 of 2) Heating utility = kW 133

EXAMPLE 5 - Solution Step 3 - Heat energy cascades (2 of 2)
07/11/2018 EXAMPLE 5 - Solution Step 3 - Heat energy cascades (2 of 2) Cooling utility = kW Pinch point at 113oC (where the energy flux between 2 intervals is 0 kW) 134

07/11/2018 EXAMPLE 5 - Solution Step 4 - Composite curves ΔΤmin 135

07/11/2018 EXAMPLE 5 - Solution Step 5 - Grand composite curve 136

EXAMPLE 5 - Solution Step 6 - Network design 07/11/2018 137 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 - Solution Step 6 - Network design - above the pinch point
07/11/2018 EXAMPLE 5 - Solution Step 6 - Network design - above the pinch point CP/H 327 126 3000 / 1 E3 220 160 4800 / 2 E2 220 126 1800 / 3 E6 E5 160 126 / 4 E4 E1 300 224.4 168 134 100 3000 / H1 5 226800 169200 102000 102000 164 100 2100 / H2 6 134400 138 127.4 100 / H3 7 111000 288000 170 100 1800 / H4 8 126000 300 274.5 174 140 6000 / H5 9 153000 603000 204000 138

07/11/2018 EXAMPLE 5 - Solution Step 6 - Network design - below the pinch point 1 40 126 3 60 4 45 6 35 7 85 8 CP/H 3000 / 1800 / / 2100 / / 1800 / 100 102 72 000 E2 E1 E3 C1 C2 C3 COLD UTILITY 113 101.5 139

07/11/2018 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
07/11/2018 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

07/11/2018 EXAMPLE 1 COPOLYMERIZATION PROCESS WITH A BENZENE RECOVERY MEN Monomers Mixing Tank Recycled Solvent Second Stage Reactor Additive Mixing Column Separation First Stage Reactor Unreacted Monomers Catalytic Solution (S2) Monomers Solvent Makeup Inhibitors + Special Additives Extending Agent Copolymer (to Coagulation and Finishing) S1 Gaseous Waste (R1) 143

EXAMPLE 1 Data of rich stream for the benzene removal example
07/11/2018 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 144

EXAMPLE 1 Data of process lean streams for the benzene removal example
07/11/2018 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 145

07/11/2018 EXAMPLE 1 SIMPLIFIED FLOWSHEET OF THE COPOLYMERIZATION PROCESS Monomers Mixing Tank Recycled Solvent Second Stage Reactor Separation First Stage Reactor Unreacted Monomers Catalytic Solution S2 Monomers Solvent Makeup Copolymer (to Coagulation and Finishing) Gaseous Waste R1 Benzene Recovery MEN Regeneration To atmosphere Benzene Oil Makeup Oil S3 Additive (Extending Agent, Inhibitors and Special Additives S1 146

EXAMPLE 1 Construct the pinch diagram of this process
07/11/2018 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)
07/11/2018 EXAMPLE 1 - SOLUTION 1. Construct the pinch diagram (1 of 4) 148

07/11/2018 EXAMPLE 1 - SOLUTION 1. Construct the pinch diagram (2 of 4) Representation of the two process MSA’s 149

EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram
07/11/2018 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, , ) 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
07/11/2018 EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram (2 of 3) There are infinite combination of L1 and x1out 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(x1out - x1S) i.e 2.4X10-4 = L1(x1out ) 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 153

07/11/2018 EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram (3 of 3) Graphical identification of x1out 154

2.3 APPLICATION EXAMPLES FOR OPTIMIZATION TECHNIQUES
155

EXAMPLE 1 - Linear programming (LP)
07/11/2018 EXAMPLE 1 - Linear programming (LP) A process consists of the following set of hot and cold process streams: Stream Tin( 0C) Tout( 0C) F Cp (kW 0C-1) H1 95 75 5 H2 80 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. 156

EXAMPLE 1 - Linear programming (LP)
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. 157

EXAMPLE 1 - SOLUTION The temperature interval partitioning along with the transshipment representation is shown in Figure 1. (120) (90) (95) (65) TI - 1 TI - 2 (60) TI - 3 (80) (50) (30) TI - 4 QS R1 R2 R3 QW H2 H1 C2 C1 25 50 250 100 200 62.5 Figure 1. 158

EXAMPLE 1 - SOLUTION Then, the LP transshipment model for minimum utility consumption takes the form: min QS + QW s.t. R1 – QS = R2 – R1 = -87.5 R3 – R2 = -50 QW – R3 = 75 QS, QW, R1, R2, R3 ≥ 0 159

EXAMPLE 1 - SOLUTION 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 = 0 160

EXAMPLE 1 - SOLUTION 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 161

EXAMPLE 1 - SOLUTION Since R1, R2, R3, R4 ≥ 0 we have R1 = QS – 312.5
R2 = R1 – 87.5 = QS – 400 R3 = R2 – 50 = QS – 450 QW = R = QS – 375 Since R1, R2, R3, R4 ≥ 0 we have QS ≥ 312.5 QS ≥ 400 QS ≥ 450 QS ≥ 375 162

EXAMPLE 1 - SOLUTION 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 = 450 163

EXAMPLE 2 Etching of copper is achieved through ammoniacal solution and etching efficiency is higher for copper concentrations in the ammoniacal solution between 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. 164

Table I. Rich streams of copper recovery problem
EXAMPLE 2 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 rate Gi (Kg/s) Initial concentration Yis Target yit R1 Ammoniacal solution 0.25 0.13 0.10 R2 Rinse water 0.06 0.02 Table I. Rich streams of copper recovery problem 165

Fig. 1. Recovery of streams of copper in an etching plant.
EXAMPLE 2 A simplified representation of the etching process is illustrated in Fig 1. Etching Line Rinse Bath Mass Exchange Network To solvent Regeneration S1 S2 R2 R1 Etchant Makeup Printed Circuit Boards Spent Echant Water Rinse Water Etched Boards Treated Rinse Water Regenerated Etchant Fig. 1. Recovery of streams of copper in an etching plant. 166

EXAMPLE 2 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 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 167

EXAMPLE 2 - SOLUTION 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* = x1* R2 - S1 : y2* = x1* R1 - S2 : y1* = x2* R2 - S2 : y2* = x2* 168

EXAMPLE 2 - SOLUTION 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. 169

EXAMPLE 2 - SOLUTION The annualized investment cost of a plate-column is based on the number of plates NSt which is determined through Kremser equation. The cost of packed tower is based on the overall height of the column: 170

Table III. Capital cost data for copper recovery problem
EXAMPLE 2 - SOLUTION 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) 171

EXAMPLE 2 - SOLUTION The obtained mass exchange network for copper recovery is illustrated in Fig 2. the model was solved in 3GBD (Generalized benders decomposition) iterations. 1 R2 R1 S1 S2 N2 = 4 N3 = 1 N1 = 1 xs = 0.030 0.278 kg/s xs = 0.001 0.019 kg/s ys = 0.060 0.100 kg/s ys = 0.130 0.250 kg/s xT = 0.070 xT = 0.020 yT = 0.100 yT = 0.020 Fig 2. 172

EXAMPLE 2 - SOLUTION 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. 173

EXAMPLE 3 Problem statement & solution structure
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. 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: 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. 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. 177

Figure 1: example of coding for a system of 4 sources and 3 demands
EXAMPLE 3 Problem statement & solution structure S1 D2 D1 D3 Waste Fresh Water S4 S3 S2 Splitters Mixers 1 Figure 1: example of coding for a system of 4 sources and 3 demands 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. 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. 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. 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 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. 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) 184

Figure 2. Crossover and mutation operations
EXAMPLE 3 Problem statement & solution structure 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 Crossover P1 E2 E1 P2 CP Mutation Before mutation After mutation Muted Gene Figure 2. Crossover and mutation operations 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. 186

Figure 3.General structure of procedure
EXAMPLE 3 Problem statement & solution structure Figure 3.General structure of procedure Superstructure Mass Balance Process Simulation Demand Constraints Objective Function Master problem Genetic Algorithm Retained Solutions Adaptation Index Feasibility Engineering OPTIMIZATION IMPLEMENTATION PROBLEM DEFINITION 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 flowrate (L/min) Fines concentration (%) Contaminant concentration (ppm) S 1 500 0.3 100 S 2 2000 0.1 110 S 3 400 0.5 S 4 300 60 Demands Required flowrate (L/min) Limiting fines concentration (%) Limiting contaminant concentration (ppm) D 1 1200 120 D 2 800 0.4 105 D 3 80 Table I 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. 189

Flow sheet general diagram
EXAMPLE 3 Problem statement & solution structure D1 S1 S2 D2 S3 D3 S4 Pulp Fresh Water 800 500 1200 waste 400 300 Flow sheet general diagram 190

EXAMPLE 3 - Solution (GA)
800 1200 2000 500 400 300 1300 S1 D2 D1 D3 Sewer Fresh Water S4 S3 S2 Splitters Mixers Superstructure 191

EXAMPLE 3 – Solution (GA)
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) 800 1200 822 500 2000 400 300 122 S1 D2 D1 D3 Waste Fresh Water S4 S3 S2 Splitters Mixers D1 D2 D3 Waste S1 500 S2 540 290 348 822 S3 390 10 S4 270 30 Fresh water 122 Table II First solution 192

The second solution of the process is given on table III. The fresh water consumption is 172 L/min. 800 1200 872 500 2000 400 300 172 S1 D2 D1 D3 Waste Fresh Water S4 S3 S2 Splitters Mixers Second solution D1 D2 D3 Waste S1 500 S2 764 364 872 S3 400 S4 300 Fresh water 36 136 Table III 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 194

REFERENCES El-Halwagi, MM and Manousiouthakis, V., “Synthesis of Mass Exchange Networks”, AIChE Journal, 35,(8), , (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, , (1998) 195

REFERENCES Garrard A., Fraga E. S., “Mass exchange network synthesis using genetic algorithms” Computers and Chemical Engineering, 22, (12), , (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), (2002b). 196

REFERENCES 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). 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 OPEN-ENDED PROBLEMS IN A REAL WORLD CONTEXT 199

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 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 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 LOAD SECTION
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 LOAD SECTION
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 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 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 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 HYDROGEN COMPRESSION 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 at 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

Fig. 3. Thermodynamic (reference case)
PROBLEM DEFINITION Stream Comp. T (K) P (bar) m (kg/s) 1 WW 278 2 3.6 Steam 351 3 3057.3 4 Chips 15.7 5 350 3040 Exchanger Q (kW) EX 1 1086 EX 2 2243 EX 3 6390 Fig. 3. Thermodynamic (reference case) 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 1 228 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) 350 13,595 6.4 Thermo. (makeup) 15 1.1 Preheat before primary refiners Thermo. 388 251 9.4 Preheat before secondary refiners 362 116 9.8 Thermo. (pulp) 324 60 2.3 TMP whitewater tank Thermo. (FW) 321 591 25.7 32 1.4 Hot 2576 6.5 228

TABLE 1 (CONTINUED) 229 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) 950 0.2 Thermo. (makeup) 278 1 0.03 Paper machine whitewater 288 1004 20.2 23 0.7 Hot 309 4768 5.8 Drying section Thermo. (heating) 363 42 25.7 Thermo. (drying) 373 Water 1.4 229

TABLE 1 (CONTINUED) 230 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 373 14.3 1.00 Hot 388 7.5 1.70 Heating 323 417 30.1 3.43 Soot blowing 278 540 6.0 16.52 Effluent treatment 1.5 Saw mill 5.1 Boilers 8.3 Deareator 408 3.8 LP level 47.6 MP level 8.7 HP level 10.7 394 10.2 2.03 407 2.3 3.06 472 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 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

MODULE 12: “Heat and Mass Exchange Networks Optimization”

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MODULE 12: “Heat and Mass Exchange Networks Optimization”

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