Program for North American Mobility in Higher Education Introducing Process Integration for Environmental Control in Engineering Curricula

Transcription

1 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

2 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

3 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

4 Tier I BASIC CONCEPTS 4

5 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

6 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

7 1.1 OPTIMIZATION OF HEAT EXCHANGER NETWORKS (HEN) BY PINCH ANALYSIS 7

8 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

9 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

10 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

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

12 THE PHASES OF PINCH ANALYSIS PROCESS SIMULATION DATA EXTRACTION TARGETING DATA EXTRACTION OF HOT AND COLD STREAMS FROM PROCESS FLOWSHEET DETERMINATION UTILIZATION OF OF ENERGY HEURISTICS TARGETS TO (NEEDS CONCEIVE FOR A HEATING EXCHANGER AND COOLING) NETWORK TO REACH ENERGY TARGETS AT A MINIMUM COST DESIGN OPTIMIZATION 12

13 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

14 WHAT ARE WE SEARCHING FOR? Thermal data must be extracted from the process This involves the identification of process heating and cooling duties 14

15 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

16 DEFINITIONS (2-2) For each hot and cold stream identified, the following thermal data is extracted: T S : supply temperature, the temperature at which the stream is available ( o C) T T : target temperature, the temperature the stream must be taken to ( o C) ΔH : enthalpy change of streams (kw) CP: heat capacity flow rate CP = Cp * M (kw/ o C = kj/ o Ckg * kg/s) 16

17 TYPICAL STREAM DATA STREAM NUMBER STREAM NAME T S T T CP Δ H ( o C) ( o C) (kw/ o C) (kw) 1 FEED REACTOR OUT PRODUCT RECYCLE

18 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

19 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 : T modified = T + (ΔTmin/2) for a hot stream : T modified = T - (ΔTmin/2) 19

20 COMPOSITE CURVES Composite curves consist of temperatureenthalpy 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

21 HOW TO DO IT? - A stream with a constant CP value is represented by a straight line running from T S to T T - 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

22 RESULT T ( o C) Cooling required Q Cmin Internal recuperation of heat Heating required Q Hmin Hot composite curve T PINCH Cold composite curve Pinch point H (kw) 22

23 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

24 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

25 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

26 GRAND COMPOSITE CURVE T Q Hmin Heat sink Pockets of heat recovery Pinch point Heat source Q Cmin ΔH 26

27 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

28 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 CP HOT CP COLD, N HOT N COLD Add heating utilities as needed (Q Hmin ) 28

29 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 CP HOT CP COLD, N HOT N COLD Add heating utilities as needed (Q Cmin ) 29

30 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

31 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

32 NOTION OF OPTIMAL ΔTmin At the beginning, an arbitrary ΔTmin is fixed The goal is to find an optimal ΔTmin 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

33 ESTIMATION OF THE ENERGY COST Energy cost = (Cost cold utility X Qc) + (Cost hot utility X Qh) where the cost unit is $/kw and Qc unit is kw 33

34 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 = α + β.a δ where A is the exchange area and α, β, δ are economical and technical factors 34

35 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: A min = Σ(1/ ΔT LM * Σ q j /h j ) COMPLETER...mettre le i! where i: enthalpy interval j: j th stream ΔT LM : log mean temperature difference or LTMD q j : enthalpy change of the j th stream in the interval i h j : transfert coefficient of j th stream 35

36 ESTIMATION OF HEN CAPITAL COST (3-3) Estimation of exchange area T ( o C) HEN AREA min = A 1 + A 2 + A A i Enthalpy intervals in the composite curves A1 A2 A5 A4 A3 H (kw) 36

37 OPTIMAL ΔTmin To arrive to an optimum ΔTmin, 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 ΔTmin values result in higher energy costs and lower capital costs a decrease in ΔTmin values result in a lower energy costs and higher capital costs an optimum ΔTmin exists where the total annual cost of energy and capital costs is minimized 37

38 ENERGY-CAPITAL COST TRADE OFF (OPTIMAL ΔTmin) Total cost Annualized cost Energy cost Capital cost Optimum ΔTmin ΔTmin 38

39 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

40 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

41 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

42 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

43 OPTIMAL ΔTmin IN RETROFIT DESIGN Industrial sector Oil refining Petrochemical Chemical Low temperature processes Experience ΔTmin values o C o C o C 3 5 o C 43

44 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

45 1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS 45

46 1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS Heat transfer and mass transfer analogy Equipment configurations The three types of mass exchange networks analysis 46

47 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

48 HEAT TRANSFER AND MASS TRANSFER ANALOGY Source: Manousiouthakis,

49 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

50 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

51 TYPES OF EXCHANGE EQUIPMENTS (1-2) 1. Exchange by direct contact Rich stream 2. Exchange by mixing of miscible phases non-redistributed Lean stream Dilution water Main stream of the process 51

52 TYPES OF EXCHANGE EQUIPMENTS (2-2) 3. Exchange by direct contact of non-miscible phases Washing water Treated stream Used water Contaminated stream 52

53 TYPES OF MASS EXCHANGE NETWORK Mass pinch Water pinch 53

54 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

55 HOW TO DO IT? Concentration Concentration Mass to exchange Concentration Mass to exchange Mass to exchange Mass to exchange 55 Concentration

56 RESULT Need of MSA Internal exchange of material Need of MSA Concentration Rich composite curve Pinch concentration Lean composite curve Pinch point Mass to exchange 56

57 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

58 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

59 LIMITING WATER PROFILE Wastewater minimization application Graphic of concentration (C) versus mass load (m) 59

60 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

61 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-toluenexylene 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

62 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. cationexchange 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

63 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

64 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

65 1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS 65

66 1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS Introduction Review of optimization techniques Mathematical programming Combinatory optimization algorithms 66

67 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

68 3 DIFFERENT APPROACHES Heuristics approach (intuition, engineering experience) Thermodynamic approach (physical insight) Mathematical programming approach 68

69 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

70 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 R n 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

71 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

72 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

73 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

74 APPLICATION FIELDS FOR OPTIMIZATION TECHNIQUES Number of continuous parameters to optimize NLP Heuristics Exhaustive research Fuzzy logic MINLP Simulated annealing Genetic algorithms Number of discrete parameters to optimize 74

75 COMBINATORY OPTIMIZATION ALGORITHMS Branch and bound Simulated annealing Genetic algorithms 75

76 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

77 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

78 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

79 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

80 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

81 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

82 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

83 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

84 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 workstationbased 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

85 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

86 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

87 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

88 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

89 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

90 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

91 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

92 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

93 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, Edgar, T.F., Himmelblau, D.M., Optimization of Chemical Processes, McGraw-Hill, El-Halwagi, M.M, Pollution Prevention through Process Integration: Systematic Design Tools, Academic Press, San Diego, Smith, R., Chemical Process Design, McGraww-Hill, New-York,

94 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, Courses notes, GCH Process Integration Course, Ecole Polytechnique de Montréal,

95 REFERENCES Websites Pinch Analysis Mass Exchange Network _Chapter_3.pdf hakis2.ppt Optimization techniques Glossary of mathematical programming: php?page=nature.html 95

96 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

97 Tier 2 APPLICATION EXAMPLES 97

98 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

99 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

100 2.1 APPLICATION EXAMPLES FOR THERMAL PINCH ANALYSIS 100

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

102 EXAMPLE 1 - Data extraction Additional data: Feed A Feed B Reactor Outlet Product Flowrate = 100 kg/hr T Boiling Point = 90 o C H vap = kj/kg Cp liq = 2.47 kj/kg o C Cp vap = 1.07 kj/kg o C Flowrate = 50 kg/hr T Boiling Point = 180 o C H vap = kj/kg Cp liq = 4.72 kj/kg o C Cp vap = 2.36 kj/kg o C T Boiling Point = 160 o C Cp liq = kj/ o C Cp vap = kj/ o C Cp liq = kj/ o C Cp vap = kj/ o C 102

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

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

105 EXAMPLE 1 - Solution STREAM 6 HOT 46.3 MJ/h Feed A STREAM 1 COLD Cp liq = 2.47 Cp vap = o C 120 o C 20 o C STREAM 2 COLD Cp liq = 4.72 Feed B ISOTHERMIC REACTOR 120 o C T=120 o C RECYCLE A (PURE A) FLOWRATE= 50 kg/hr 140 o C REACTOR OUTLET 160 o C STREAM 3 COLD CP liq = o C RECYCLE B (PURE A) FLOWRATE= 10 kg/hr STREAM 5 HOT COLUMN MJ/h STREAM 4 COLD 68.2 MJ/h 150 o C 90 o C COLUMN MJ/h STREAM 7 HOT CP liq = TO STORAGE AT AMBIENT TEMPERATURE 105

106 EXAMPLE 1 - Solution The stream data for the process are given in the following table (streams 1 to 3). Stream T in ( 0 C) T out ( 0 C) CP kj/kg o C 1. COLD H vap = kj/kg kj/kg o C 2. COLD KJ/Kg 0 C 3. COLD Kj/ 0 C 106

107 EXAMPLE 1 - Solution The stream data for a process are given in the following table (streams 4 to 7). Stream T in ( 0 C) T out ( 0 C) Information needed for Pinch Analysis 4. Cold Vap. Heat 68.2 MJ / h 5. Hot Cond. Heat 73.1 MJ / h 6. Hot Cond. Heat 46.3 MJ / h 7. Cold Vap. Heat 51.9 MJ / h 107

108 EXAMPLE 2 - Composite curves and HEN design The stream data for a process are given in the table below Stream T in ( 0 K) T out ( 0 K) CP (kw/ 0 K) 1. Cold Cold Cold Hot Hot

109 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 Q H,min, Q C,min and the pinch temperature for ΔT min = 24 K Design a network that features the minimum number of units for maximum energy recovery 109

110 EXAMPLE 2 - Solution Step 1 - Define temperature intervals Hot stream : interval temp. = actual temp. 1/2 Δ T min Cold stream : interval temp. = actual temp. + 1/2 Δ T min Stream 1. Cold 2. Cold 3. Cold 4. Hot 5. Hot Actual temperature T S / T T ( 0 K) 311 / / / / / 339 Interval temperature T S / T T ( 0 K) 323 / / / / /

111 EXAMPLE 2 - Solution Step 2 - Interval thermal balance Interval temp Flux Interval ΔTi ( o C) ΣCpcold-ΣCphot (kw/ o C) ΔHi (kw) Surplus/deficit surplus surplus surplus deficit deficit deficit surplus deficit 1 111

112 EXAMPLE 2 - Solution Step 3 - Heat energy cascades 566 K 510 K 490 K 467 K 382 K 378 K 351 K 327 K 323 K HOT UTILITY 0 kw HOT UTILITY 0 kw COLD UTILITY COLD UTILITY Heating utility = 0 kw Pinch point at 566 K (where the energy flux between 2 intervals is 0 kw) Cooling utility = 446 kw 112

113 EXAMPLE 2 - Solution Step 4 - Composite curves 113

114 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: -CP HOT CP COLD - ΔTmin respected between streams 114

115 EXAMPLE 2 - Solution Step 5 - Network design - below the pinch point CP / ΔH / E / E / E / E / E COLD UTILITY

116 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

117 EXAMPLE 3 - Composite curves and HEN design The stream data for a process are given in the table below Stream T S ( 0 C) T T ( 0 C) CP (KW/ 0 C) 1. Hot Hot Hot Cold Cold Cold

118 EXAMPLE 3 - Composite curves and HEN design The hot utility is to be supplied by a hot oil circuit at 380 o C and the cold utility by a cooling media at 20 o C. For a ΔT min of 10 o C: Plot the composite curves and determine Q H,min, Q C,min and the pinch temperature Design a network that features the minimum number of units for maximum energy recovery, Umin MER. 118

119 EXAMPLE 3 - Solution Step 1 - Define temperature intervals Stream 1. Hot 2. Hot 3. Hot 4. Cold 5. Cold 6. Cold Actual temp. T S / T T ( 0 C) 170 / / / / / / 298 Interval temp. T S / T T ( 0 C) 165 / / / / / /

120 EXAMPLE 3 - Solution Step 2 - Interval thermal balance Interval temp Flux Interval ΣCpcold-ΣCphot ΔHi (kw) Surplus/deficit ΔTi ( o C) (kw/ o C) surplus deficit deficit deficit deficit surplus surplus surplus surplus surplus deficit 4 120

121 EXAMPLE 3 - Solution Step 3 - Heat energy cascades 349 o C HOT UTILITY 0 kw HOT UTILITY kw o C o C o C Heating utility = 153 kw 205 o C 165 o C 140 o C 135 o C 95 o C 85 o C 83 o C 35 o C Pinch point at 165 o C (where the energy flux between 2 intervals is 0 kw) Cooling utility = 85 kw COLD UTILITY COLD UTILITY 121

122 EXAMPLE 3 - Solution Step 4 - Composite curves T ( o C) ΔTmin Hpinch H (kw) 122

123 EXAMPLE 3 - Solution Step 5 - Network design H (kw) m.cp (kw/ o C) EXHAUST ALL HOT STREAMS WITH COLD STREAMS EXHAUST ALL COLD STREAMS WITH HOT STREAMS RESPECTING THE FOLLOWING RULES: -CP HOT CP COLD - ΔTmin respected between streams 123

124 EXAMPLE 3 - Solution Step 5 - Network design - above the pinch point CP/ΔH 0.2/ / E 1 2/ HOT UTILITY / E E 2 E Heating utility calculated with energy cascade = 153 kw Cooling utility calculated with energy cascade = 85 kw 124

125 EXAMPLE 3 - Solution Step 5 - Network design - below the pinch point E COLD UTILITY COLD UTILITY E COLD UTILITY E CP/ΔH 2.3/ /16 0.5/ E / E /

126 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

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

128 EXAMPLE 4 - Solution From Int. Energy Agency 128

129 EXAMPLE 5 - A complete problem The stream data for a process are given in the table below Stream T S ( 0 C) T T ( 0 C) CP (MW/ 0 C) 1. Hot Hot Hot Hot Cold Cold Cold Cold Cold

130 EXAMPLE 5 - A complete problem At the correct setting of the capital-energy trade-off, Δ T min = 26 o C Plot the composite curves for the above system and determine Q H,min, Q C,min and the pinch temperature Plot the grand composite curve of the process Design a network to achieve the target without violating Δ T min = 26 o C 130

131 EXAMPLE 5 - Solution Step 1 - Define temperature intervals Stream 1. Hot 2. Hot 3. Hot 4. Hot 5. Cold 6. Cold 7. Cold 8. Cold 9. Cold Actual temp. T S / T T ( 0 C) 327 / / / / / / / / / 300 Interval temp. T S / T T ( 0 C) 314 / / / / / / / / /

132 EXAMPLE 5 - Solution Step 2 - Interval thermal balance Interval temp Flux Interval ΔTi ( o C) 1 ΣCpcold- ΣCphot (MW/ o C) ΔHi (kw) Surplus/ deficit surplus deficit surplus deficit deficit surplus deficit deficit surplus surplus surplus surplus surplus surplus 132

133 EXAMPLE 5 - Solution Step 3 - Heat energy cascades (1 of 2) 314 o C HOT UTILITY 0 kw HOT UTILITY kw o C o C o C o C o C o C o C Heating utility = kw 133

134 EXAMPLE 5 - Solution Step 3 - Heat energy cascades (2 of 2) 147 o C 113 o C 98 o C 73 o C 48 o C 47 o C 32 o C 27 o C COLD UTILITY COLD UTILITY Pinch point at 113 o C (where the energy flux between 2 intervals is 0 kw) Cooling utility = kw 134

135 EXAMPLE 5 - Solution Step 4 - Composite curves ΔΤ min 135

136 EXAMPLE 5 - Solution Step 5 - Grand composite curve 136

137 EXAMPLE 5 - Solution Step 6 - Network design H (kw) m.cp (kw/ o C) EXHAUST ALL HOT STREAMS WITH COLD STREAMS EXHAUST ALL COLD STREAMS WITH HOT STREAMS RESPECTING THE FOLLOWING RULES: -CP HOT CP COLD - ΔTmin respected between streams 137

138 EXAMPLE 5 - Solution Step 6 - Network design - above the pinch point CP/ΔH 3000 / E / E / E 6 E / E / / / / / H H H H H E

139 EXAMPLE 5 - Solution Step 6 - Network design - below the pinch point C COLD UTILITY 40 CP/ΔH 3000 / C COLD UTILITY 60 C COLD UTILITY / / E E E / / /

140 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

141 2.2 APPLICATION EXAMPLE FOR MASS EXCHANGE NETWORK ANALYSIS 141

142 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

143 EXAMPLE 1 COPOLYMERIZATION PROCESS WITH A BENZENE RECOVERY MEN Inhibitors + Special Additives Extending Agent Catalytic Solution (S 2 ) S 1 Additive Mixing Column Gaseous Waste (R 1 ) Monomers Solvent Makeup Monomers Mixing Tank First Stage Reactor Recycled Solvent Second Stage Reactor Separation Copolymer (to Coagulation and Finishing) Unreacted Monomers 143

144 EXAMPLE 1 Data of rich stream for the benzene removal example Stream Description Flowrate G i, kg mol/s Supply composition (mole fraction) y s i Target composition (mole fraction) y t i R 1 Off-gas from product separation Candidate MSA s : Two process MSA s and one external MSA Process MSA s : Additives (S 1 ) : The additives mixing column can be used as a absorption column by bubbling the gaseous waste into the additives Liquid catalytic solution (S 2 ) : The equilibrium data for benzene in the two process MSA s are given by: y 1 = 0.25x 1 y 1 = 0.50x 2 For control purpose, the minimum allowable composition difference for S 1 and S 2 should not be less than

145 EXAMPLE 1 Data of process lean streams for the benzene removal example Stream Description Upper bound on flowrate L c j kg mol/s Supply composition of benzene (mole fraction) x s j Target composition of benzene (mole fraction) x t j S 1 Additives S 2 Catalytic solution The external MSA, S 3, 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: y 1 = 0.10x 3 Data for the external MSA for the benzene removal example Stream Description Upper bound on flowrate L c j kg mol/s Supply composition of benzene (mole fraction) x s j Target composition of benzene (mole fraction) x t j S 3 Organic oil infinite

146 EXAMPLE 1 SIMPLIFIED FLOWSHEET OF THE COPOLYMERIZATION PROCESS Benzene Oil Makeup Oil S 3 Catalytic Solution S 2 Additive (Extending Agent, Inhibitors and Special Additives S 1 Regeneration To atmos phere Benzene Recovery MEN Gaseous Waste R 1 Monomers Solvent Makeup Monomers Mixing Tank First Stage Reactor Recycled Solvent Second Stage Reactor Separation Copolymer (to Coagulation and Finishing) Unreacted Monomers 146

147 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 additivesmixing column (S1) 147

148 EXAMPLE 1 - SOLUTION 1. Construct the pinch diagram (1 of 4) 148

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

150 EXAMPLE 1 - SOLUTION 1. Construct the pinch diagram (3 of 4) 150

151 EXAMPLE 1 - SOLUTION 1. Construct the pinch diagram (4 of 4) 151

152 EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram (1 of 3) Pinch is located at the corresponding mole fractions (y, x 1, x 2 ) = (0.0010, , ) The excess capacity of the process MSA s is 1.4X10-4 kgmole benzene/s 152

153 EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram (2 of 3) There are infinite combination of L 1 and x 1 out that can be used to remove the excess capacity of S 1 according to the following mass balance: Benzene load above the pinch to be remove by S 1 =L1(x out 1 -x 1S ) i.e 2.4X10-4 = L1(x out ) 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 S 1 is

154 EXAMPLE 1 - SOLUTION 2. Interpret de results of the pinch diagram (3 of 3) Graphical identification of x 1 out 154

155 2.3 APPLICATION EXAMPLES FOR OPTIMIZATION TECHNIQUES 155

156 EXAMPLE 1 - Linear programming (LP) A process consists of the following set of hot and cold process streams: Stream T in ( 0 C) T out ( 0 C) F Cp (kw 0 C -1 ) H H C C 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

157 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

158 EXAMPLE 1 - SOLUTION The temperature interval partitioning along with the transshipment representation is shown in Figure 1. QS (120) (90) 250 TI C 1 H (95) (65) TI - 2 (90) (60) TI - 3 R 1 R H (80) (50) TI - 4 R C 2 (60) (30) QW Figure

159 EXAMPLE 1 - SOLUTION Then, the LP transshipment model for minimum utility consumption takes the form: min QS + QW s.t. R 1 QS = R 2 R 1 = R 3 R 2 = -50 QW R 3 = 75 QS, QW, R 1, R 2, R

160 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 R 1 = R 2 = 50 R 3 = 0 160

161 EXAMPLE 1 - SOLUTION Since R 3 =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 R 1, TI 2 for R 2, TI 3 for R 3, and TI 4 for QW which become 161

162 EXAMPLE 1 - SOLUTION R 1 = QS R 2 = R = QS 400 R 3 = R 2 50 = QS 450 QW = R = QS 375 Since R1, R2, R3, R4 0 we have QS QS 400 QS 450 QS

163 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 =

164 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

165 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 G i (Kg/s) Initial concentration Y i s Target concentration y i t R 1 Ammoniacal solution R 2 Rinse water Table I. Rich streams of copper recovery problem 165

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

167 EXAMPLE 2 Two extractants are proposed for copper recovery, LIX63 (an aliphatic α- hydroxyoxime, S 1 ) and P1 (an aromatic β-hydroxyoxime, S 2 ). 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 x j s Maximum outlet concentration x j T, up Cost (US$/Kg) Ann. Cost (US$/Kg) S 1 L1X ,020 S 2 P ,056,240 Table II. Lean streams of copper recovery problem 167

168 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): R 1 -S 1 : y 1* = x 1* R 2 -S 1 : y 2* = x 1* R 1 -S 2 : y 1* = x 2* R 2 -S 2 : y 2* = x 2*

169 EXAMPLE 2 - SOLUTION Two types of contactors are considered: a perforated plate column for S 1 (LIX63) a packed tower for S 2 (P1) Where y 1 *, y 2 * and x 1 *, x 2 * are the copper concentrations of R 1, R 2 and S 1, S 2, respectively, at equilibrium. 169

170 EXAMPLE 2 - SOLUTION The annualized investment cost of a plate-column is based on the number of plates N St which is determined through Kremser equation. N St mg ln 1 L = y in in ( y mx b) out in ( y mx mg ln L mg + L The cost of packed tower is based on the overall height of the column: G H OR = HTotal = H K α( y y ) x N * R R 170

171 EXAMPLE 2 - SOLUTION The annualized investment costs are given in table III Cost of plate column Cost of packed column N St $ / Yr H $ / Yr Table III. Capital cost data for copper recovery problem (Papalexandri et al., 1994) 171

172 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. S 1 S kg/s x s = kg/s x s = R kg/s y s = N 2 = 4 N 3 = y T = R kg/s y s = N 1 = 1 y T = x T = x T = Fig

173 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 G R. 173

174 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

175 EXAMPLE 3 Problem statement & solution structure 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

176 EXAMPLE 3 Problem statement & solution structure 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

177 EXAMPLE 3 Problem statement & solution structure 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

178 EXAMPLE 3 Problem statement & solution structure Splitters Mixers S 1 D 1 S 2 D 2 S 3 D 3 S 4 Fresh Water Waste Figure 1: example of coding for a system of 4 sources and 3 demands 178

179 EXAMPLE 3 Problem statement & solution structure 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

180 EXAMPLE 3 Problem statement & solution structure 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

181 EXAMPLE 3 Problem statement & solution structure 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

182 EXAMPLE 3 Problem statement & solution structure 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

183 EXAMPLE 3 Problem statement & solution structure 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

184 EXAMPLE 3 Problem statement & solution structure 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

185 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. CP CP Muted Gene P 1 P 2 Before mutation E 1 E 2 After mutation Crossover Mutation Figure 2. Crossover and mutation operations 185

186 EXAMPLE 3 Problem statement & solution structure 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

187 EXAMPLE 3 Problem statement & solution structure Process Simulation PROBLEM DEFINITION Superstructure Mass Balance Demand Constraints Objective Function Master problem Genetic Algorithm OPTIMIZATION Superstructure Retained Solutions Adaptation Index Feasibility IMPLEMENTATION Engineering Figure 3.General structure of procedure 187

188 EXAMPLE 3 Problem statement & solution structure 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 S S S S Demands Available flowrate (L/min) Required flowrate (L/min) Fines concentration (%) Limiting fines concentration (%) Contaminant concentration (ppm) Limiting contaminant concentration (ppm) D D D Table I 188

189 EXAMPLE 3 Problem statement & solution structure The initial configuration of the process is given on figure I, the demands D 2 and D 3 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

190 EXAMPLE 3 Problem statement & solution structure 1200 Fresh Water Fresh Water Pulp D 1 D 2 D 3 Pulp S 1 S 2 S 3 S 4 waste waste waste waste Flow sheet general diagram 190

191 EXAMPLE 3 - Solution (GA) Splitters Mixers S D 1 S D S D 3 S 4 Fresh Water Sewer Superstructure 191

192 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) D 1 D 2 D S S S S Fresh 122 water Table II Waste S 1 S 2 S 3 S Fresh122 Water Splitters First solution Mixers D 1 D 2 D 3 Waste 192

193 EXAMPLE 3 Solution (GA) The second solution of the process is given on table III. The fresh water consumption is 172 L/min. D 1 D 2 D S S S S Fresh water Table III Waste S 1 S 2 S 3 S 4 Splitters Fresh 172 Water Mixers D 1 D 2 D 3 Waste Second solution 193

194 EXAMPLE 3 Solution (GA) 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 GA GA Table IV 194

195 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

196 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

197 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

198 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

199 Tier 3 OPEN-ENDED PROBLEMS IN A REAL WORLD CONTEXT 199

200 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

201 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

202 3.1 PETROLEUM OPEN- ENDED PROBLEM 202

203 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

204 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 346 o C. 204

205 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

206 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

207 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

208 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

209 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 The hydrodesulfurized and stabilized diesel is sent to the vapor generator EA-807, and then the diesel at a temperature of 215 o C is transported to the preheater EA

210 PRODUCT COOLING SECTION The diesel from the heatexchanger EA-801 is sent to the heat exchanger EA-808 where it is cooled until 153 o C. 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

211 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

212 RECIRCULATED HYDROGEN COMPRESSION SECTION The gas free of H 2 S 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

213 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

214 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 Q H,min, Q C,min, the minimum consumption of external utilities (energy targets) 214

215 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

216 3.2 PULP & PAPER OPEN- ENDED PROBLEM 216

217 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

218 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