1- V.good Lectures.pdf

Process Integration Process Integration and Pinch Analysis for the Efficient Use of Energy

Lecture-1 PROCESS INTEGRATION Lecture – 2 PINCH TECHNOLOGY – AN OVERVIEW Lecture – 3 - 6 BASIC ELEMENTS OF PINCH TECHNOLOGY

Lecture – 7- 8 AREA TARGETING

Lecture – 9 - 11 NUMBER OF UNIT, SHELL AND COST TARGETING

Lecture – 12

PINCH DESIGN METHODS – HEURISTIC RULES

Lecture – 13 - 15 DESIGN OF HEN FOR MAXIMUM ENERGY RECOVERY, LOOP BREAKING & PATH RELAXATION

Lecturer - 16 DRIVING FORCE PLOT AND REMAINING PROBLEM ANALYSIS

Lecture-1 PROCESS INTEGRATION Department of Chemical Engineering

Process integration, a part of Process Intensification, is a fairly new term that emerged in 80’s and has been extensively used in the 90’s to describe certain systems oriented activities related primarily to process design. It has incorrectly been interpreted as Heat Integration by a lot of people, probably caused by the fact that Heat Recovery studies inspired by Pinch Concept initiated the field and is still core elements of Process Integration. It appears to be a rather dynamic field, with new method and application areas emerging constantly. The Process Integration is defined as “systematic and general methods for designing integrated production systems, ranging from individual processes to total sites, with special emphasis on the efficient use of energy and reducing environmental effects”. This definition brings Process Integration very close to Process Synthesis, which is another systems oriented technology. Process Integration and synthesis belongs to process systems engineering. Process Integration has evolved from a heat recovery methodology in the 80’s to become what a number of leading industrial companies in 90’s regarded as a “major strategic design and planning technology”. With this technology, it is possible to significantly reduce the operating cost of existing plants, while new processes often can be designed with reduction in both investment and operating costs.

1

Definition of Process Integration as per International Energy Agency (IEA) •

Process Integration is the common term used for the application of methodologies developed for System- oriented and Integrated approaches to industrial process plant design for both new and retrofit applications.

•

Process Integration refers to Optimal Design; examples of aspects are: capital investment, energy efficiency, emissions, operability, flexibility, controllability, safety and yields. Process Integration also refers to some aspects of operation and maintenance.

•

Process integration, combined with other tools such as process simulation, is a powerful approach that allows engineers to systematically analyze an industrial process and the interactions between its various parts.

Current Status of Process Integration Process Integration is a strongly growing field of Process Engineering. It is now standard curriculum for process engineers in both Chemical and Mechanical Engineering at most universities around the world, either as a separate topic or as part of a Process Design or Synthesis course. Research at UMIST has for 25 years been supported by a large number of industrial companies through a Consortium that was established in 1984. As part of the International Energy Agency (IEA) project on Process Integration, more than 50 other universities around the world involved in research in this field have been identified. From History to the Future Process Design has evolved through distinct "generations". Originally (first generation), inventions that were based on experiments in the laboratory by the chemists, were tested in pilot plants before plant construction.

2

The second generation of Process Design was based on the concept of Unit Operations, which founded Chemical Engineering as a discipline. Unit Operations acted as building blocks for the engineer in the design process. The third generation considered integration between these units; for example heat recovery between related process streams to save energy. A strong trend today (fourth generation) is to move away from Unit Operations and focus on Phenomena. Processes based on the Unit Operations concept tend to have many process units with significant and complex piping arrangements between the units. By allowing more than one phenomena (reaction, heat transfer, mass transfer, etc.) to take place within the same piece of equipment, significant savings have been observed both in investment cost and in operating cost (energy and raw materials). Different Schools of Thoughts in Process Integration The three major features of Process Integration methods are the use heuristics (insight), about design and economy, the use of thermodynamics and the use of optimization techniques. There is significant overlap between the various methods and the trend today is strongly towards methods using all three features mentioned above. The large number of structural alternatives in Process Design (and Integration) is significantly reduced by the use of insight, heuristics and thermodynamics, and it then becomes feasible to address the remaining problem and its multiple economic trade-offs with optimization techniques. Despite the merging trend mentioned above, it is still valid to say that Pinch Analysis and Exergy Analysis are methods with a particular focus on Thermodynamics. Hierarchical Analysis and Knowledge Based Systems are rule-based approaches with the ability to handle qualitative (or fuzzy) knowledge. Finally, Optimization techniques can be divided

3

into deterministic (Mathematical Programming) and non-deterministic methods (stochastic search methods such as Simulated Annealing and Genetic Algorithms). One possible classification of Process Integration methods is to use the two-dimensional (automatic vs. interactive and quantitative vs. qualitative) representation in Fig. 1. Application of Process Integration Process Integration can be applied in following fields of chemical engineering such as: 1.

Heat integration – heat exchange network

2.

Distillation column targeting

3.

Cogeneration and total site targeting

4.

Batch process targeting

5.

Emission targeting

6.

Mass exchange network (water and wastes water management & recovery of valuable materials)

7.

Hydrogen management in refineries qualitative Heuristic Rules

Knowledge Based Systems

automatic

Hierarchical Analysis

interactive

Thermodynamic Methods

Optimization Methods

quantitative Fig. 1 One possible Classification of Process Integration

4

Techniques Available for Process Integration 1.

Pinch Technology Approach

2.

MILP/MINLP Approach

3.

State-Space Approach

4.

Genetic Algorithm Approach

5.

Process Graph Theory Approach

Concept of Pinch Technology The term "Pinch Technology" was introduced by Linnhoff and Vredeveld to represent a new set of thermodynamically based methods that guarantee minimum energy levels in design of heat exchanger networks. Over the last two decades it has emerged as an unconventional development in process design and energy conservation. The term ‘Pinch Technology’ is often used to represent the application of the tools and algorithms of Pinch Technology for studying industrial processes.

The heat and material balance is at this boundary

1 2 3 4 Reactor Separator Heat exchange network

Utilities

Site-Wide Utilities Fig. 2 Onion Diagram 5

Pinch technology provides a systematic methodology for energy saving in processes and total sites. Fig. 2 illustrates the role of Pinch Technology in the overall process design. The process design hierarchy can be represented by the “onion diagram” as shown below. The design of a process starts with the reactors (in the “core” of the onion). Once feeds, products, recycle concentrations and flow rates are known, the separators (the second layer of the onion) can be designed. The network (the third layer) can be designed. The remaining heating and cooling duties are handled by the utility system (the fourth layer). The process utility system may be a part of a centralized site-wide utility system. A Pinch Analysis starts with the heat and material balance for the process. Using Pinch Technology, it is possible to identify appropriate changes in the core process conditions that can have an impact on energy savings (onion layers one and two). After the heat and material balance is established, targets for energy saving can be set prior to the design of the heat exchanger network.

6

Lecture – 2 PINCH TECHNOLOGY – AN OVERVIEW Department of Chemical Engineering One of the most practical tools to emerge in the field of process integration in the past 20 years has been pinch analysis, which may be used to improve the efficient use of energy, hydrogen and water in industrial processes. Pinch analysis is a recognized and wellproven method in each of the following industry sectors: 

Chemical



Petrochemical



Oil refinery



Pulp and paper



Steel and metallurgy



Food and drink

Over the past 20 years, pinch analysis has evolved and its techniques perfected. It provides tools that allow us to investigate the energy flows within a process, and to identify the most economical ways of maximizing heat recovery and of minimizing the demand for external utilities (e.g., steam and cooling water). The approach may be used to identify energy-saving projects within a process or utility systems. Pinch technology analyses process utilities (particularly energy and water) to find the optimum way to use them, resulting in financial savings. Pinch Technology does this by making an inventory of all producers and consumers of these utilities and then

7

systematically designing an optimal scheme of utility exchange between them. Energy & water re-use are at the heart of pinch technology. With the application of pinch technology, both capital investment and operating cost can be reduced. Emissions can be minimised and throughput maximised. The Pinch Concept Pinch analysis (or pinch technology) is a rigorous, structured approach that may be used to tackle a wide range of improvements related to process and site utility. This includes opportunities such as reducing operating costs, debottlenecking processes, improving efficiency, and reducing and planning capital investment. Major reasons for the success of pinch analysis are the simplicity of the concepts behind the approach, and the impressive results it has been obtained worldwide. It analyzes a commodity, principally energy (energy pinch) hydrogen (hydrogen pinch), or water (water pinch), in terms of its quality and quantity, recognizing the fact that the cost of using that commodity will be a function of both. In general, we are using high-value utilities in our process and rejecting waste at a low value. For example, if we consider energy, we may be burning expensive natural gas to provide the process with high temperatures heat, and are rejecting heat at low temperatures to cooling water or air. Pinch analysis now has an establishment track record in energy saving, water reduction, and hydrogen system optimization. In all cases, the fundamental principle, behind the approach is the ability to match individual demand for a commodity with suitable supply. The suitability of the match depends on the quality required and the quality offered. In the context of utility management, the commodity may be heat, with its quality measured

8

as temperature. By maximizing the match between supplies and demands, we minimize the import of purchased utilities (Fig. 1). HIGH QUALITY UTILITY

QUALITIY

Process

WASTE

QUANTITY

(a)

MINIMISE HIGH QUALITY UTILITY

Pinch

QUALITY

Process

Pinch

ENERGY: WATER: HYDROGEN

MINIMISE

WASTE

QUANTITY

Fig.1 Schematic process utility use

(b)

Pinch Technology Versus Process Engineering 

Pinch Technology is a vital subdivision of process engineering.

9



Carrying out a process engineering project without the input of a pinch study will lead to a less efficient design.



Our engineers have specialized knowledge of thermodynamics and computer analysis tools. They can communicate effectively with clients and undertake conceptual designs. This explains why we are uniquely qualified to help you get the most out of your pinch projects.

How is Pinch technology different from other energy audits? Pinch technology reveals all the possible savings and their corresponding Financial benefits. •

It defines the maximum possible savings.

•

It looks at the overall site.

•

It does not bench-mark but takes into account all specific mill factors, age, location, process equipment, operating preferences, product, etc.

•

It reveals the maximum cogeneration potential.

Role of Thermodynamic Laws in Pinch Technology Pinch technology presents a simple methodology for systematically analyzing chemical processes and the surrounding utility systems with the help of the First and Second Laws of Thermodynamics. The First Law of Thermodynamics provides the energy equation for calculating the enthalpy changes (dH) in the streams passing through a heat exchanger. The Second Law determines the direction of heat flow. That is, heat energy may only flow in the direction of hot to cold. This prohibits ‘temperature crossovers’ of the hot and

10

cold stream profiles through the exchanger unit. In a heat exchanger unit neither a hot stream can be cooled below cold stream supply temperature nor a cold stream can be heated to a temperature more than the supply temperature of hot stream. In practice the hot stream can only be cooled to a temperature defined by the ‘temperature approach’ of the heat exchanger. The temperature approach is the minimum allowable temperature difference Tmin) in the stream temperature profiles, for the heat exchanger unit. The temperature level at which Tmin is observed in the process is referred to as "pinch point" or "pinch condition". The pinch defines the minimum driving force allowed in the exchanger unit. What Processes does Pinch Apply to? Pinch applies to a wide range of processes. Pinch originated in the petrochemical sector and is now widely accepted in mainstream chemical engineering. With a wealth of applications experience, benefits can now be realized in many other process industries. Wherever heating and cooling of process materials takes places there is a potential opportunity. A realistic approach addresses the practical problems specific to each and every site, leading to: •

Meaningful targets

•

Feasible projects

•

Real savings

•

Essential strategic insights

Benefits of Pinch Technology 

Pinch tells the best that can be achieved in a given system.

11



Pinch gives the practical target to aim for that is less than this theoretical maximum.



Both of the above are done before any detailed design. This target then set the basis for the design. Most importantly, it gives clear rules about how to construct a design to achieve the targets. It will also show where the inefficiency lie in the existing design.



Pinch takes a system-wide view of the problem. This allows one to see interaction that would be difficult to spot on a process flow diagram or a flow sheet of site utility system.



Pinch can work with incomplete data. One can refine the data in the areas where accuracy is most important. This is in the area around the pinch.



Pinch Technology is in contrast to other design tools, which require detailed information about geometry, flow sheet structure, etc. Pinch technology is one of the few tools that really can be used in conceptual design.

Problem Addressed by Pinch Technology Generally two types of problem are addressed: 

Creating new designs This is related to the design of HEN for a new plant, which is in design stage. The ideal time to apply pinch analysis is during the planning of process modifications that will require major investments, and before the finalization of process design. Maximum improvements in energy efficiency; along with reduced

12

investments can be obtained in a new plant design, since many plant layout and process constraints can be overcome by redesign. 

Retrofit – Revamping existing designs This is related to the retrofitting of an already existing HEN in a plant to improve its exchange efficiency. However, in retrofit projects, energy efficiency improvements usually require some capital expenditure. In this case, pinch analysis can be specifically aimed at maximizing the return of investment. Pinch analysis techniques allow us to evaluate combinations of project ideas simultaneously, in order to avoid “double – counting” savings, as well as conflicting projects. Indeed, the final investment strategy for the available opportunities will ensure that site development is consistent and synergistic.

Typical Savings •

BASF AG (Ludwigshafen, Germany), for example, has completed more than 150 retrofit using pinch technology, achieving over 25 % in energy savings site wide.

•

In natural gas sweetening, for example, The Ralph M. Parsons Co. (Pasadena, Calif.) says that pinch technology led to a 10% drop in capital costs and energy use in its amine absorption column.

•

GE plastics was faced with a requirement of invest $15 million in doubling the capacity of the wastewater handling system of its Silicones Production Facilities in Netherlands. Linnhoff March aimed to avoid this investment cost by reducing wastewater flow by 50 %.

•

The following benefits have been obtained for refinery retrofits: 13

a)

Energy reduced by 15-35 % through revamping of HENs based on paybacks of 1.5-3 years.

b)

Units debottlenecked by 10-20% without modifying fired heaters or major pumps.

c)

Lower fouling from improved understanding of the system dynamics.

d)

Improved flexibility giving the lowest cost design for different operating cases.

e) 

Reduced emissions at the source.

The potential energy and water consumption savings in major industries sectors are given in Fig. 2 & 3.

Fig. 2 Potential energy savings

14

Fig. 3 Potential water consumption savings

15

Lecture – 3 - 6 BASIC ELEMENTS OF PINCH TECHNOLOGY – PART I, II & III Department of Chemical Engineering

KEY STEPS OF PINCH TECHNOLOGY There are four key steps of pinch analysis in the design of heat recovery systems for both new and existing processes: 1)

Data Extraction, which involves collecting data for the process and the utility system.

2)

Targeting, which establishes figures for best performance in various respects.

3)

Design, where an initial Heat Exchanger Network is established.

4)

Optimization, where the initial design is simplified and improved economically.

Data Extraction The most time consuming and often most critical step is the identification of the need for heating, cooling, boiling and condensation in the process. This task is more art than science, and if not carried out properly, the final design will not be the best possible. It is quite easy to accept too many feature of the proposed flow sheet, which inevitably results in the situation where many good opportunities are excluded from the analysis. In practice, there are a number of situations where heat integration is not desirable. Examples include long distances (costly piping), safety (heat exchange between hydrocarbon streams and oxygen rich streams), product purity (potential leakage in heat exchangers), operability (start-up and shut-down), controllability and flexibility. A 16

reasonable strategy is, however, to start by including all process streams and keep the degrees of freedom open. Later, practical considerations can be used to exclude some of these streams and degrees of freedom, and the engineer will then at any time be able to establish the consequences with respect to energy consumption and total annual cost. A central part of data extraction is the identification of heating and cooling requirements in the process. The necessary data for each process stream are the following: m = mass flowrate (kg/s, tons/h, etc.) Cp = specific heat capacity (kJ/kgC) Ts = supply temperature (C) Tt = target temperature (C) Hvap = heat of vaporization for streams with a phase change (kJ/kg) Additionally, the following information must be collected on utilities and existing heat exchangers for retrofit: Existing heat exchanger area (m2) Heat transfer coefficient for cold and hot sides of heat exchangers (kW / m2 C). Utilities available in the process (water temperature, steam pressure levels, etc), Marginal utility costs, as opposed to average utility costs. Data extraction must be preformed carefully as the results strongly depend on this step. A key objective of data extraction is to recognize which parts of the flowsheet are subject to change during the analysis (e.g. possibility of making modifications to the piping, or adding new heat exchangers, possibility of making temperature changes in the process or modifying the utility that heats a given piece of equipment (MP steam instead of HP

17

steam for example), etc). If, during extraction, all features of the flowsheet are considered to be fixed, there will clearly be no scope for improvement. At the beginning of a project it is recommended that all process stream be included in the data extraction. Constraints regarding issues such as distance between operations, operability, control and safety concerns can be incorporated later on. By proceeding in such a fashion, it is possible to have an objective evaluation of the costs of imposing such constraints. PI specialists generally include some constraints form the beginning of the data extraction procedure. This can speed up the overall analysis, but a lot of experience is required to ensure that potentially interesting heat-recovery projects are not excluded. There are a lot of sector specifics for data extraction. However, heuristic rules have been developed as guidelines. The following are the most relevant: Do not mix streams at different temperatures. Direct non-isothermal mixing acts as a heat exchanger. Such mixing may involve cross-pinch heat transfer, and should not become a fixed feature of the design. For example, if the pinch is located at 70C, mixing a stream at 90C with a stream at 50C creates a cross pinch, and will increase the energy targets. The way to extract these streams is to consider them independently, i.e., one stream with a supply temperature of 50C and the required target temperature, and the other stream with a supply temperature of 90C and the required temperature. Do not include utility streams (stream, flu gas, cooling water, refrigerant, cooling air, etc.) in the process data unless they are involved directly in the process or they cannot be replaced. One of the goals of using pinch analysis is to reduce the usage of utilities. Therefore, if utility streams are extracted in a similar way to process streams, they will be considered as fixed requirements and no opportunities of reduction in utility use will be 18

identified. In some cases, utility streams can be included because it is not practical to replace them by any form of heat recovery. For example, this is often the case for stream dryers, ejectors and turbine drives. Do not consider the existing plant layout. When selecting the inlet and outlet parameters for a process stream, existing heat exchange equipment and plant topology should not be taken into account at first. True utility targets (for cooling and heating) should be set regardless of the existing plant layout. Current plant energy consumption can then be compared with minimum energy targets. In retrofit of existing facilities, once these targets have been determined, plant layout (existing heat exchangers and piping, distances, etc) needs to be taken into account in order to identify practical and costeffective projects to reach or approach these targets. Identify hard and soft constraints on temperature levels. For example, a hard constraint would be the inlet temperature of a reactor that cannot be changed in any way, while a soft constraint would be the discharged temperature of a product going to storage, for which the target temperature is often flexible. Data extraction is a complex issue, and a significant part of the pinch specialist’s expertise is related to building a good pinch model during the data extraction phase. Targeting An important feature of Process Integration is the ability to identify Performance Targets before the design step is started. For heat recovery systems with a specified value for the minimum allowable approach temperature (Tmin), targets can be established for Minimum Energy Consumption (external heating and cooling), Fewest Number of Units (process/process heat exchangers, heaters and coolers) and Minimum Total Heat Transfer 19

Area. In addition, the corresponding calculations will also identify the Heat Recovery Pinch, which acts as a bottleneck for heat recovery.

Designing Design of Heat Exchanger Networks in various industries is primarily carried out using the now classical Pinch Design Method (Linnhoff and Hindmarsh, 1983). While the original method focused on minimum energy consumption and the fewest number of units, later graphical and numerical additions made it possible also to consider heat transfer area and total annual cost during design. The basic Pinch Design Method respects the decomposition at Process and Utility Pinch points and provides a strategy and matching rules that enable the engineer to obtain an initial network, which achieves the minimum energy target. The Pinch Design Method also indicates situations where stream splitting is required to reach the minimum energy target. Stream splitting is also important in area considerations and the optimal use of temperature driving forces. The design strategy mentioned above is simply to start design at the Pinch, where driving forces are limited and the critical matches for maximum heat recovery must be selected.

Optimization Heat exchange network for maximum energy recovery established by pinch design method, should only be regarded as initial designs and some final optimization is required. The matches in the initial network depend on pinch location and since the pinch point depends on the value of Tmin, this becomes a key parameter in the pinch design method. By repeating all calculations, for synthesis of HEN, for different values of Tmin, 20

it is possible to identify a good starting value for the level of heat recovery. This exercise of pre-optimization has been referred to as “Supertargeting”. For a typical Problem, the minimum total annual cost is obtained to be 240.42103 $/yr (Fig. 1). Thus, the optimum ΔTmin is 13 °C. 400

TAC (1000 $/yr)

350 300 250 200 150 100 50

Δ Tmin Optimum = 13 °

0 0

20

40

60

Minimum temperature difference Fig. 1 The total annualCost cost Profile profile The Total Annual

BASIC ELEMENTS OF PINCH TECHNOLOGY Grid Representation The grid is used to represent heat exchange network more conveniently. The important features of grid representations are: 

Hot streams (streams which require cooling) are drawn at the top running let to right.



Cold streams (streams which require heating) are drawn at the bottom running right to left.

21



A heat exchanger is represented by a vertical line joining two open circles on the streams being matched. The heat exchanger load can conveniently be written under the lower open circle.



Heaters (H) and coolers (C) can be represented in an open circle on the stream being heated or cooled.



Temperatures can be put on the grid as shown to allow an easy check on the terminal approach temperature for each unit.

The stream data for the typical process is shown in Table 1. The grid representation for this process, which includes two hot, H1 & H2, and two cold, C3 & C4, streams, are shown in Fig.2. Table 1 The Stream Data for the Process Ts (oC) 175 125 20 40

Stream H1 H2 C3 C4

Stream H1 H2

C3 C4

 175      125      155   112 

Tt (oC) 45 65 155 112

MCp (kW/ C) 10 40 20 15

MCp (kW/ C) 45 

3 2

 H 1400

98  85 

 

 C  1320

3 1300

65  40 20 

 40 

2 1080 Fig. 2 The grid representation of the process

22

10

20 15

Composite Curve The Composite Curves (CCs) are constructed from ‘stream data’ representing a process heat and material balance. The CCs allow the designer to predict-optimized-hot and cold utility targets ahead of design, to understand driving forces for heat transfer, and to locate the heat recovery ‘Pinch’. CCs consist of temperature-enthalpy (T-H) profiles of heat availability in the process (the “hot composite curves”) and heat demands in the process (the “cold composite curves”) together in a graphical representation. CCs also provide the minimum requirement of hot and cold utilities in the process. The construction of the hot composite curves (as shown in Fig.3) simply involves the addition of the enthalpy changes of the streams in the respective temperature intervals. The CCs for the stream data, given in Table 1, are shown in Fig.3. The QHmin and QCmin are minimum hot and cold utilities.

QHmin

200

Region of heat recovery by process to process exchange

150 T (oC) 100

Tmin Below pinch

50 QCmin

Above pinch

HCC CCC

0 0

1000

2000 3000 4000 Heat Content Q (kW)

5000

Fig. 3 The hot composite curves (HCC) and cold composite curves (CCC) respectively show the heat availability and heat requirement for the overall process.

23

Problem Table Algorithm This graphical manipulation of composite curves to generate minimum targets is time consuming and clumsy. An alternative procedure is entirely based on simply arithmetic and involves no trial and error. The procedure is known as the problem table and is broken down into three stages. 1.

Set up shifted temperature intervals from the stream supply and target temperatures by subtracting ΔTmin /2 from the hot streams and adding ΔTmin /2 to the cols streams. It is important to note that shifting the curves vertically does not alter the horizontal overlap between the curves. It therefore does not alter the amount by which the cold composite curve extends beyond the start of hot composite curve at the hot end of problem. Also, it does not alter the amount by which hot composite curve extends beyond the start of cold composite curve at the cold end.

2.

In each shifted temperature interval, calculate a simple energy balance from:

(1) Where ΔHi = heat balance for shifted temperature interval i and ΔHi is the temperature difference across it CPc = specific heat capacity of a cold stream (MW/oC) CPh = specific heat capacity of a hot stream (MW/oC). If the cold streams dominate the hot streams in a temperature interval, then the interval has a net deficit of heat, and ΔH is positive. If hot streams dominate cold streams, the interval has a net surplus of heat, and ΔH is negative. 24

3.

Now, cascade any surplus heat down the temperature scale from interval to interval. This is possible because any excess heat available from the hot streams in an interval is hot enough to supply a deficit in the cold streams in the next interval down. First, assume no heat is supplied to the first interval from hot utility. As a consequence of it some of the heat flows are negative, which is infeasible. Heat cannot be transferred up the temperature scale. To make the cascade feasible, sufficient heat must be added from hot utility to make the heat flows to be at least zero. The smallest amount of heat needed from hot utility is the largest negative heat flow.

Example The problem table algorithm is explained using the stream data of a typical process given in Table 2. The minimum approach temperature is 10 °C. The shifted temperatures for each stream are detailed in Table 3. Table 2 Stream data Heat capacity flow rate Stream

Ts (°C)

Tt (°C)

(MW/°C) Cold (C1)

0.2

20

180

Hot (H1)

0.15

250

40

Cold (C2)

0.3

140

230

Hot (H2)

0.25

200

80

25

Table 3 Stream Data with Shifted Temperature Heat capacity flow rate Stream

T*s (°C)

T*t (°C)

Cold (C1) 0.2

25

185

Hot (H1) 0.15

245

35

Cold (C2) 0.3

145

235

Hot (H2) 0.25

195

75

(MW/°C)

The shifted temperatures are arranged in decreasing order. The stream population is shown in Fig. 4 with a vertical temperature scale. The interval temperatures shown in Fig. 4 are set to ΔTmin /2 below hot stream temperatures and ΔTmin /2 above cold stream temperatures.

Fig. 4 The stream population for stream data shown in Table 2

26

Then a heat balance is carried out within each shifted temperature interval according to Eq. 1. The result is given in Fig. 5, in which some of the shifted intervals are seen to have a surplus of heat and some have a deficit.

Fig. 5 The temperature interval heat balances

Now, cascade any surplus heat down the temperature scale from interval to interval assuming no heat is supplied to the first interval from hot utility (Fig. 6). The first interval has a surplus of 1.5 MW, which is cascaded to the next interval. This second interval has a deficit of 6 MW, which leaves the heat cascaded from this interval to be -4.5 MW and so on. Some of the heat flows are negative, which is infeasible. To make the cascade feasible, largest negative heat flow from Fig. 6 that is 7.5 MW is added from hot utility to make the heat flows to be at least zero. The revised cascade is shown in Fig. 7 which gives one heat flow of just zero at an interval temperature of 145 °C.

27

More than 7.5 MW could be added from hot utility to the first interval, but the objective is to find minimum hot and cold utility. Thus, from Fig. 7 minimum hot and cold utilities are 7.5 MW and 10 MW, respectively. The point where the heat flow goes to zero at shifted temperature 145°C corresponds to the pinch. Thus, the actual hot and cold stream pinch temperatures are 150 °C and 140 °C, respectively. The composite curves are useful in providing conceptual understanding of the process but the problem table algorithm is a more convenient calculation tool.

Fig. 7 Add heat from hot utility to make all heat flows zero or positive

Fig. 6 Cascaded surplus heat from high to low temperature

28

Grand Composite Curve The grand composite curve (GCC) is a graphical representation of the heat cascade. GCC is based on the same process stream data as Composite Curves. GCCs highlight the process/utility interface. It gives clear visualization of hot and cold utility and provides an easy approach to use multiple utilities in the process. For the stream data, shown in Table 1, the GCC is represented in Fig. 8.

Hot utility Above Pinch High temperature process sink profile Low temperature process source profile

Pinch

Process to process heat exchange Below Pinch

Cold Utility

Maximum Energy Recovery The overlap between the hot and cold composite curves represents the maximum amount of heat recovery possible within the process. The source/sink characteristics of process heat exchange systems give five concepts. Targets: Once the composite curves are known, we know exactly how much external heating/cooling is required. Near-optimal processes are confirmed as such and nonoptimal processes are identified with great speed and confidence.

29

The pinch: The process needs external heating above the pinch and external cooling below the pinch. This tells us where to place furnaces, steam heaters, coolers etc. More in, more out: An inefficient process requires more than the minimum external heating and therefore more than the minimum external cooling. For every units of excess external heat in a process one has to provide heat transfer equipment twice. This insight helps us to improve both energy and capital cost. Freedom of choice: The “heat sink” and the “heat source” in Fig. 8 are separate. This constraint helps the designer to choose plant-layouts, control arrangements etc. If designer violates this constraint, he can evaluate the pinch heat flow and therefore predict what overall penalties will be involved. Trade-offs: A simple relationship exists between the number of streams (process streams plus utilities) in a problem and the minimum number of heat exchange units (i.e. heaters, coolers and interchangers). Thus if designer goes for best energy recovery, designing the “heat source” and “heat sink” section separately, he or she will incur the need for more units than if the pinch division had been ignored. Hence a new type of trade-off has been identified, between energy recovery and number of units. This insight adds to the traditional concept of a trade-off between energy and surface area.

30

Lecture – 7- 8 AREA TARGETING Department of Chemical Engineering

Area is important in determining heat exchanger network capital cost. Before explaining the complete procedure to computation of area it is necessary to discuss the principles for minimum area in heat exchanger networks. Start by considering the example in Fig. 1a, where two hot streams exchange heat against a single cold stream. If we assume the overall heat transfer coefficient U is constant for all exchangers and these exchangers are countercurrent units then the network has an area of 88 m2. Fig. 1b shows a different network with stream splitting. Its area is 84 m2. The reason is that it has better countercurrent behavior in terms of the overall network. In Fig. 1a the matches are in temperature sequence whereas in Fig. 1b the matches share more of the available temperature differences by splitting the cold stream. Fig. 1c shows that we can do better still. The network area is now 77 m2. This is the minimum area for the stream set as defined. The network has been developed by stream-splitting only where streams compete for the same driving forces by overlap in temperature. The composite curve of the data for example, shown through Fig. 1, is drawn in Fig. 2. Overall countercurrent heat exchange now appears as vertical heat transfer on the composite curves. Partitioning of the stream data to follow the temperatures of the vertical model then leads to the minimum area design for this example.

31

Fig. 1 (a) network with exchangers in temperature sequence on cold stream; (b) network with exchangers sharing temperature span of cold stream; and (c) network with exchangers showing correct distribution of temperatures for minimum area.

32

Fig. 2 Resolving temperature contention using the composite curves: (a) overall countercurrent heat exchange appears as vertical heat transfer on the composites; (b) the temperatures of enthalpy intervals show where stream-splitting will be required, (c) these temperatures can be marked on the grid; and (d) used to guide design for temperature contention.

To calculate the heat exchanger network area from composite curve, utility streams must be included with the process streams in the composite curves to obtain the balanced composite curves (BCC). The resulting BCC (Fig. 3a) should have no residual demand for utilities. The BCC are divided into vertical “enthalpy intervals”. The intervals are defined whenever a change in slope occurs in either balanced composite profile. Next, a network design is considered within each enthalpy interval, which can satisfy vertical 33

heat transfer. Fig. 3b demonstrates this for an interval, which contains two hot streams and three cold streams. Each hot stream is split into the same number of branches as the number of cold streams in that interval. Similarly, each cold stream is split into the same number of branches as the number of hot streams in that interval. Hence, each hot stream can be matched with each cold stream such that every match occurs between the corner temperatures of the enthalpy interval. The heat exchanger of these matches must therefore appear as vertical on the BCC.

Fig. 3. Example of general stream splitting and matching scheme for vertical heat transfer in an enthalpy interval of the balanced composite curves.

The minimum total area could be taken as the sum of the areas of all such exchangers from all enthalpy intervals. However, this is not necessary if U = constant. From the composite curves, the area from vertical heat transfer in interval i is simply: (1)

34

where ΔHi is the enthalpy width of interval i and ΔTLM,i

is the logarithmic mean

temperature difference of interval i. Hence, the total minimum network area is given by:

(2) This shows that in order to derive an area target based on U = constant no design is required. Different heat transfer coefficients in the model for minimum area Consider again the design in Fig. 3 for vertical heat transfer in enthalpy interval i of the composite curves. If the heat transfer coefficients differ then the total area of these exchangers is:

Where, Q13 is the duty of the match between streams 1 and 3, U13

(3) its overall heat transfer

coefficient, etc. Now,

(4) where h1 is the heat transfer coefficient of stream 1 (including film, wall and fouling resistances), etc.

35

So,

(5) But

(6) where (qj)i is the enthalpy change of stream j in enthalpy interval i. so,

(7) The argument applies in general for other enthalpy intervals. Summing up over all intervals on the composite curves gives:

(8) This simple formula incorporates stream individual heat transfer coefficients and allows a “target” for the minimum heat exchange area to be calculated from the composite curves. Further, within ith enthalpy interval, all hot streams undergo the same temperature change (dTh)i as do all the cold streams (dTc)i. As q = MCpdT, then



36

(9)

Example: Stream Data of a typical process with Tmin = 20˚ C is given in following table. Stream(s)

Ts (C)

Tt (C)

MCp (kW/ C)

h (kW/m2 C)

H1

175

45

10

0.2

C1

20

155

20

0.2

H2

125

65

40

0.2

C2

40

112

15

0.2

Steam (HU)

180

179

-

0.2

Cold Water (CU)

15

25

-

0.2

The step wise procedure is described below: Calculation of minimum hot and cold utilities Minimum hot and cold utilities are calculated by Problem Table Algorithm which are as follows: Hot utility, Qhu,min = 605 kW Cold utility, Qcu,min = 525 kW Calculation of utility flow rates The MCp values of hot utility (hu) and cold utility (cu) are given as: (MCp)hu = Qhu,min/(Tin-Tout)hu = 605/(180-179) = 605 kW/° C (MCp)cu = Qcu,min/(Tout-Tin)cu = 525/(25-15) = 52.5 kW/° C

37

Plotting the Balanced Composite Curves The procedure for plotting the Balanced Hot Composite Curve and Balanced Cold Composite Curve is the same as the Hot Composite Curve and Cold Composite Curve, except that the utilities are also considered as additional streams. Balanced Hot composite Curve (BHCC) For BHCC the temperatures of hot streams and hot utility are arranged in ascending order (Fig. 4). The sum of the MCP values of hot streams and utility present in each interval is calculated. Then this sum is multiplied by the temperature difference of each interval. After that a cumulative enthalpy is calculated using the formula: CumQhb, i = CumQhb, i-1 + Qint, hbi

(10) MCp,hb

10

Qhb

CumQhb

45 65

1

40

2

125

H2

3

175 179

4

H1

605

5

180

10

200

50

3000

3200

10

500

3700

0

3700

605

4305

0 605

200

H

Fig. 4 Data for balanced hot composite curve

Now, BHCC is obtained by plotting temperature and CumQhb as shown in Fig. 5. Similarly Balanced cold composite curve can be drawn. The two curves

are

superimposed on each other to get BCC as shown in Fig. 6. The BCC are divided into vertical “enthalpy intervals”. The intervals are defined whenever a change in slope occurs in either balanced hot composite curve (BHCC) and balanced cold composite

38

curve (BCCC) profiles. The BCC on being divided into enthalpy intervals, allow calculation of the area target based on a model of vertical heat transfer.

200 180

140 120 100 80 60 40 20 0 0

1000

2000

3000

4000

5000

Heat content Q, kW

Fig. 5 Data for balanced hot composite curve 200 180 160 140

Th,i.

120 T (C)

Temperature, Deg C

160

BHCC

100

Tc,i.

80

Th,i.-1

60 40

Interval i

BCCC

Tc,i.-1

20 0 0

500

1000

1500

2000 2500 3000 Heat Content Q (kW)

3500

4000

4500

Fig. 6 The balanced composite curve for the example

39

5000

Determination of enthalpies for intervals CumQhb and CumQcb (for BCCC) are merged by omitting cumulative enthalpies common to both values and the entries are then sorted in ascending order. This identifies all points where composite curve has a vertex (change in slope). Calculation of interval temperatures on BHCC The following formula is used for calculation of interval temperature: Th3 = Thb,row r – (CumQhb,row r- CumQ3)/MCp,hb row r Where, Thb,row r and CumQhb,row r are temperature and CumQ in the row r (in which the temperature is available), In this case, row r = 6 For CumQi = 262.5 kW,

Thi = 125˚ - (3200-262.5)/50 = 66.25˚C.

For CumQi = 200 kW, Tci = 20˚ - (262.5-200)/52.5 = 18.81˚C. Similarly other temperature intervals are found and shown in Fig. 7.

18.81 66.25 73.5 79.5 105 149.5 124.5 124.5

Fig. 7 Determination of the enthalpy intervals

Calculation of (MCp/h)h and (MCp/h)c for each interval

40

These are calculated in a manner similar to MCp,hb of Fig. 4. For example, consider first interval of Fig. 7 where only stream H1 exists, therefore (MCp/h)h = 10/0.2 = 50. Next four interval contain streams, H1 and H2, thus, (MCp/h)h = 50/0.2 = 50. These data are shown in Table 1. Calculation of (Q/h) For first interval, (Q/h) = (65˚ - 45˚)50 + (18.81˚ - 15˚)262.5 = 2000 The complete data are shown in Table 1. Calculation of log mean temperature difference, TLM This is done by the following formula:

For first interval:  

TLM, 1 = [(65-18.81)-(45-15)]/[ln(65-8.81)/(45-15) = 37.51˚ C. The complete data are shown in Table 1.

Calculation of countercurrent exchanger area in each interval This is calculated by dividing the (Q/h) by the corresponding TLM in for the interval. For first interval: A1=2000/37.51 = 53.31 m2 The complete data are shown in Table 1. Based on above calculation the minimum area is found as 1312.57 m2 for the example undertaken.

41

Table 1 Calculation of countercurrent exchanger area int

Thi

Tci

(MCp/h)h (MCp/h)c (Q/h)

TLM, i

Ai

0

45

15

0

1

65

2

0

0

0

0

18.81 50

262.5

2000

37.51

53.31

66.25

20

250

262.5

625

46.22

13.52

3

73.5

25

250

362.5

3625

47.37

76.53

4

79.5

40

250

100

3000

43.85

68.42

5

125

105

250

175

22750

28.65

794

6

149.5

112

50

175

2450

27.84

88.01

7

175

124.75 50

100

2550

43.56

58.53

8

179

124.75 0

100

0

52.22

0

9

180

155

100

6050

37.76

160.23

3025

42

Lecture – 9 - 11 NUMBER OF UNIT, SHELL AND COST TARGETING Department of Chemical Engineering Number of unit targeting The capital cost of chemical processes tends to be dominated by the number of items on the flowsheet. This is certainly true of heat exchanger networks and there is a strong incentive to reduce the number of matches between hot and cold streams. To understand the minimum number of matches or units in a heat exchanger network, Fig. 1 is considered which shows the heat loads on one hot stream and three cold streams written within the circles representing the streams. The predicted hot utility load is shown similarly. In this process only hot utility is required but no cold utility. The total system is in enthalpy balance i.e. the total hot plus utility is equal to the total cold.

Steam 1068

Hot 2570

1068 1165 413 Cold1 2233

992

Cold2 413

Cold3 992

Fig. 1 Illustration of minimum number of units design. Matching Steam with Cold1 and maximizing the load completely satisfies or “tick off” Steam, leaving 1165 units of heating required by Cold1. Matching Cold1 with Hot and

43

maximizing the load on this match so that it “ticks off” the 1165 residual requirement on Cold1, leaves 1405 residual heat available from Hot. So following the principle of maximizing loads, i.e. “ticking off” stream or utility loads or residuals, leads to a design with a total of four matches. This is in fact the minimum for this problem. Thus, Umin = N – 1 Where, Umin = minimum number of units (including heaters and coolers) N = total number of streams (including utilities) Another problem, Fig. 2(a) having two hot streams and two cold streams. Both hot and cold utility are required. For this problem 5 (N-1) [Where, N = 6.0] units are required which is obtained by putting the matches using ticking off loads or residuals loads to a design.

Fig. 2(a). Number of unit is one less than the number of streams included utilities

44

Fig. 2(b). Same principle for separate components – “Subset Equality”

Fig. 2(c). One unit more for every loop

Fig. 2(b) shows a design having one unit less than previous design. The subset of streams H2, C1 and CW is in enthalpy balance. Similarly, ST, H1 and C2 are in enthalpy balance (which they must be if the total problem is in balance). What this means is that for the given data set we can design two completely separate networks, with the formula Umin = N – 1 applying to each individually. The total for the overall system is therefore (3-1)+(31) = 4 units. This situation is termed “subset equality” The new unit is placed between ST and C2 as shown in Fig. 2(c). The extra units introduces what is known as a “loop” into a system. At the hot utility ST, the loop can be

45

traced through the connection to C1, from C1 to H1, from H1 to C2, and from C2 back to ST. Suppose the new match, which is between ST and C2, is given a load of X units. Then by enthalpy balance the load on the match between ST and C1 is 30-X, between C1 and H1, 10 + X, and between H1 and C2, 60-X. The features discussed above are described by a theorem from graph theory in mathematics, known as Euler’s general network theorem. This theorem translates into the terminology of HEN, states that Umin = N + L – s Where, Umin = minimum number of units (including heaters and coolers) N = total number of streams (including utilities) L = number of loops s = number of separate components. Normally we want to avoid extra units, and so design for L=0. Also, if there will be no subset equality in the data set and then minimum number of unit targets is Umin = N – 1 Since the pinch divides the problem into two thermodynamically independent regions, the targeting formula must applied to each separately. Shell Targeting The shell and tube heat exchanger (SHE) is most common type of heat transfer equipments used in heat exchanger networks (HENs) of chemical process industries. Generally multipass SHE is employed in these industries because of its following advantages: (1) the configuration gives a large surface area in a small volume, (2) good

46

mechanical layout: a good shape for pressure operation, (3) uses well established design procedures and fabrication techniques, (4) can be constructed from a wide range of materials and (5) easily cleaned. Many HEN design methods described in literature make the simplifying assumption of counter current exchanger. It has been seen that an optimal solution of the HEN problem based on purely counter current heat exchanger only will remain optimal in practice if each unit can be realized by one exchanger with single shell. However, it rarely occurs in industry as multipass construction of SHE is used here. Therefore, it is practically feasible to target number of shells than the units at the synthesis stage of HEN. FT Correction Factor In case of the simplest multipass SHE, the 1-2 type, the liquid in one tube pass flows in counter flow while in the other pass flows in parallel relative to shell fluid. To account counter and parallel flows in 1-2 SHE, a correction factor FT is introduced into the basic heat exchanger design equation, shown through Eq. 1, to take into account the above phenomena, Q = UA (Tln) FT

where 0< FT<1

(1)

Where, Q = heat exchanger duty (kW) U = overall heat transfer coefficient, (kW/m2 C) A = Heat exchanger area (m2 ) Tln = log mean temperature difference (C)

47

The FT factor is represented as the ratio of actual mean temperature difference in a 1-2 SHE to counter flow Tln for the same terminal temperatures. FT is a function of dimensionless ratios, R and P, where Heat capacity ratio, R = CPH / CPC = ((TCo – TCi ) ((THi – THo )

(2a)

and thermal effectiveness, P = (THi - THO ) / (THi – TCi )

(2b)

where THi = Hot stream inlet temperature (oC) THo = Hot stream outlet temperature (oC) TCi = cold stream inlet temperature (oC) TCo = cold stream outlet temperature (oC) Based on the value of FT, feasible design of heat exchanger is screened amongst different alternative designs. For this purpose a rule of thumb i.e. FT > 0.8 is used and each design with unacceptably low FT value is discarded. It is well known fact that for multipass exchangers heat recovery is limited by Tln correction factor, FT. If FT<0.8 one should increase the number of shells till FT becomes greater than 0.8. For a 1-2 SHE, FT falls sharply with increasing temperature cross. The ability to accommodate a temperature cross increases rapidly as the number of shell passes is increased. However, designers often encounter situations where the FT is too low or the FT slope is too large. If this happens, the designers may be forced to consider multiple shell arrangements of 1-2 type. Therefore, it is required to compute number of shells for a HEN. A method to account for design sensitivity, based on the fact that for any value of R there is a maximum asymptotic value for P, say Pmax, which is given as FT tends to – , and is evaluated by

48

Pmax 2/(R 1  R 2 1)

(3)

Practical designs will be limited to some fraction of Pmax that is: P = XP Pmax

0 < XP < 1

(4)

Where XP is a constant defined by the designer. The value of XP = 0.9 is sufficient to satisfy FT≥0.75, while also avoiding regions of steep slope and therefore assuring a more reliable design. Situations are often encountered where FT is too low (or within the present context the FT slope too steep) for a single shell. If this happens the designer may be forced to consider an arrangement of multiple shells in series. If multiple shells are required then the most common practice is to adopt a trial and error approach in which the number of shells in series is progressively increased until a satisfactory value of FT is obtained for each shell. Using the constant XP approach any need for trial and error can be eliminated since an explicit expression for the number of shells can be derived. This is done by using the following equation for N number of 1-2 shells in series. R≠1 1Y P  R Y R=1

where Y (

1RP12

)N

(5a)

1Pr2

 

P 

P12 N

(5b)

P12 N P12 1

P1-2 is the effectiveness of each single 1-2 shell (given by XP * Pmax) whereas P applies overall to the series of shells. Equations (3) and (4) which together relate P1-2 to XP and R, can then be used to eliminate P1-2 from equation (5) to give the following expressions:

49

R≠1

N = 1n ((1- RP)/(1-P))/ln W

(6a)

Where W (R 1 R2 12RX P ) /(R 1 R2 1 2X P ) R=1

N (P/(1 - P))(1 ( 2 / 2) X P ) / X p

(6b) (6c)

In terms of R, P and P1-2, the number of shells can be computed using following equations: N = ln [(1-RP)/(1-P)]ln[(1-RP12)/(1-P12)]

for R ≠ 1

(7a)

for R = 1

(7b)

And N = [P/(1-P)]/[P12/(1-P12)]

XP is chosen to satisfy the minimum allowable FT (for example, for FT ≥ 0.75, XP=0.90 is used). The application of XP is valid under the same assumptions as those of FT. Eq. 6 or 7 then evaluates explicitly the number of shells required and, at the same time, ensures that each shell in the design satisfies the required sensitivity criterion given by the specification for XP .The number of shells predicted by Eq. 6 or 7 is a real (that is, fractional or non-integer) number and the actual number of shells in practice would obviously be taken to the next largest integer. If each match enthalpy interval i requires Ni number of shells using temperatures of interval i in equation (6) then the maximum shells count for the interval is: Ni (Si – 1)

(7)

Notice the temperatures defining Ni are achieved by a minimum of (Si – 1) matches where S is the total number of streams present in ith interval.

50

The real (non-integer) number of shells target is then simply the sum of the real number of shells from all the enthalpy intervals: M

N shell N i (Si 1)

(8)

i 1

where M is the total number of enthalpy, intervals on the balanced composite curves. Furthermore, actual designs will normally observe the pinch division. Hence, Nshell should be evaluated and taken as the next largest integer for each side of the pinch. The number of shells target is then: [Nshell ] [(Nshell )abovepinch] [(Nshell )belowpinch]

(9)

Where the symbol [N] represents the next largest integer to the real number N. Example The Stream Data, shown through Table 1, is considered for this purpose. Here Tmin = 20˚ C. Table 1 Stream data for a typical process Stream

Type

Supply temp. TS (˚C)

Target temp. TT (˚C)

Heat capacity flow rate MCp (kW/ ˚C)

H1

Hot

175

45

10

H2

Hot

125

65

40

C3

Cold

20

155

20

C4

Cold

40

112

15

Hot utility inlet and outlet temperature are 180 ° C and 179 ° C. Cold utility inlet and outlet temperature are 15 ° C and 25 ° C. Calculation of P and R for an interval

51

The temperature effectiveness, P, is defined as the ratio of the temperature change in one of the streams to the maximum possible temperature difference. Pi = (Th,i. – Th,i.-1) / (Th,i. – Tc,i.-1) For i= 1,

P1 = (65˚ - 45˚) / (65˚ - 15˚) = 0.4

R is defined as the ratio of the heat capacity flow rates of the hot streams to the cold streams. Ri = (Tc,i. – Tc,i.-1) / (Th,i. – Th,i.-1) For i=1,

R1 = (18.81˚ - 15˚) / (65˚ - 45˚) = 0.1905

The complete calculation is shown in Table 2. Calculation of the temperature effectiveness of an individual 1-2 exchanger P12 = XP Pmax

where Pma 2/(R 1  x



R 2 1)

For i.=1 and XP = 0.9, P12,i.=1 = 0.9 * 2 / (0.1905+1+(0.19052+1)1/2) = 0.815 Calculation of number of 1-2 shells needed in series N = ln [(1-RP)/(1-P)]ln[(1-RP12)/(1-P12)]

for R ≠ 1

And N = [P/(1-P)]/[P12/(1-P12)]

for R = 1

For i = 1, N = ln [(1-0.1905*0.4) / ln [(1-0.1905*0.815) / (1-0.815)] = 0.2841. The complete calculation is shown in Table 3.

52

Table 2 Determination of P and R for non countercurrent flow Int. i.

Col. A Th,i

Col. B Tc,i

Col. A P

Col. B R

0 1 2 3 4 5 6 7 8 9

45 65 66.25 73.5 79.5 125 149.5 175 179 180

15 18.81 20 25 40 105 112 124.75 124.75 155

0.4000 0.0263 0.1355 0.1101 0.5353 0.5506 0.4048 0.0000 0.0181

0.1905 0.9524 0.6897 2.5000 1.4286 0.2857 0.5000 0.0000 30.250

Table 3 Determination of number of Shells for each enthalpy interval Int. i.

Col. A Th,i

Col. B Tc,i

Col. A Pi

Col. B Ri

Col. C P12, i

Col. D Ni

0 1 2 3 4 5 6 7 8 9

45 65 66.25 73.5 79.5 125 149.5 175 179 180

15 18.81 20 25 40 105 112 124.75 124.75 155

0.4000 0.0263 0.1355 0.1101 0.5353 0.5506 0.4048 0.0000 0.0181

0.1905 0.9524 0.6897 2.5000 1.4286 0.2857 0.5000 0.0000 30.250

0.8150 0.5400 0.6197 0.2907 0.4314 0.7740 0.6875 0.0000 0.0293

0.2841 0.0237 0.1160 0.2152 1.7304 0.5081 0.3944 0.0000 0.3630

Calculation of number of shells in an interval (Ni[Si – 1]) The minimum number of shells in an enthalpy interval, i, is Ni(Si – 1). For i. = 3,

Ni(Si – 1) = 0.0237*2 = 0.0474.

The complete calculation is shown in Table 4.

53

Table 4 Number of Shell for present problem

0.0237

Calculation of estimate of shells targets The pinch occurs at 125 ˚ C/105 ˚ C. So, Shells below pinch = 0.2841+0.0474+0.3481+0.4305+5.1912 = 6.3013, (rounded off to 7) Shells above pinch = 1.0163+0.3944+0.3630 = 1.7737 (rounded off to 2). Thus total number of shells required is 9. Cost Targeting The cost of the network basically comprises the operating cost and capital cost. Operating cost The operating cost is the function of energy requirements and is given by: OC = Chu * Qhu,min + Ccu * Qcu, min

(10)

Where Chu & Ccu are the costs of minimum loads of hot and cold utility respectively and Qhu,min and Q cu,min are the minimum requirements of hot and cold utilities respectively. 54

Capital cost A simple linear cost law for individual heat exchanges is CC = a + b Ak

(11)

The capital cost of a network can then be predicted on the basis of targets for the number of units for maximum energy recovery (Umin,MER ) and minimum network area (Amin ). Thus: Umin MER

CCnetwork 

CC

k

aU min,MER b

k

Umin MER

 A

k

aU min .MER bAmin .

(12)

k

Most often, the cost law for individual exchangers takes the nonlinear form as: CCk = a + b Akc

(13)

If nonlinear cost law is used in targeting, we assume the areas of individual units are all identical: Amin Ak  U min,,MER

(14)

This leads to the network capital cost given by: CCnetwork

  Amin U min a b( c  ) U min,MER  



(15)

Total annual cost (TAC) TAC is given by: TAC = OC + CCnetwork * Af

(16)

Where Af = (1 + r)t /t Where Af is the annualization factor, r, is the rate of return of capital interest and t is the expected plant life.

55

Lecture – 12 PINCH DESIGN METHODS – HEURISTIC RULES Department of Chemical Engineering

The pinch design method incorporates two fundamentally important features. First, it realizes the pinch is the most temperature constrained region. The design is started at the pinch and developed moving away. Second, it allows the designer to choose between options.

Feasibility Criteria at the Pinch The identification of essential matches at the pinch, of a available design options and of the need to split streams, is achieved by applying three feasibility criteria to the stream data at the pinch. In developing these feasibility criteria reference is made to "pinch exchangers" (sometimes called "pinch matches").

A pinch match

56

Exchanger 2 is not a pinch match

Exchanger 3 is not a pinch match

The number of process streams and branches The first feasibility criterion concerns the stream population at the pinch. The population of hot and cold streams has to be such that it will allow an arrangement of exchangers compatible with minimum utility usage. Consider a hot end design as in Fig. 1(a). Utility cooling above the pinch would violate the minimum utility objective. Therefore, each hot stream has to be cooled to the pinch temperature by process exchange. This is attempted in Fig. 1(a) by placing pinch matches between hot stream No. 2 and cold stream No. 4 and hot stream No. 3 and cold stream No. 5. Notice, however that having made these matches hot stream No. 1 cannot be matched with either cold stream without violating the Tmin constraint. Utility cooling

57

would now be required above the pinch to cool stream No. 1 to the pinch temperature. In such circumstances we say the original stream data at the pinch is not compatible with a minimum utility design. When this incompatibility occurs the streams at the pinch need "correcting" by stream splitting (see Fig. 1(b)). By splitting a cold stream an extra cold "branch" is created, allowing a pinch match with hot stream No. 1. To summarize, the hot end stream population at the pinch is compatible with a minimum utility design only if a pinch match can be found for each hot stream. For this to occur inequality (1a) must apply NH NC

(1a)

Where NH is the number of hot streams or branches and NC is the number of cold streams or branches. Stream splitting may be needed to ensure that the inequality is fulfilled.

Fig. 1. (a) An infeasible hot end design at the pinch. (b) Stream splitting at the pinch 58

The converse arguments apply below the pinch. To avoid utility heating each cold stream must be brought to the pinch temperature by process exchange. As a result, a pinch match is required for each cold stream at the pinch and this is possible only if inequality (1b) holds NH NC

(1b)

Once again stream splitting may be necessary to ensure that the inequality is fulfilled.

The CP inequality for individual matches The second feasibility criterion is concerned with temperature feasibility. As shown in Fig. 2, temperature driving force in a pinch match cannot decrease away from the pinch. For this condition to be fulfilled the following CP inequalities must apply in every pinch match Hot end pinch match CPH CPC

(2a)

Cold end pinch match CPH CPC

(2b)

Where CPH is the heat capacity flowrate of a hot stream or stream branch and CPC is the heat capacity flowrate of a cold stream or stream branch. If an arrangement of matches fulfilling these inequalities is not possible then it is necessary to change one or more CPs by stream splitting. It should be noted that inequalities (2a) and (2b) only apply at the pinch. Away from the pinch, temperature driving forces may have increased sufficiently to allow matches in which the CP's of the streams matched violate the inequalities.

59

Fig. 2 (a) A feasible pinch exchanger above the pinch (b) A feasible pinch exchanger below the pinch The CP difference To understand the third feasibility criterion at the pinch it is convenient to define the "CP difference". It can be understood by Fig. 3a, 3b and 3c. For a hot end pinch match CP difference = CPC-CPH

(3a)

For a cold end pinch match CP difference = CPH - CPC

(3b)

Similar equations can be written for differences in the overall sum of hot stream CPs and cold stream CPs at the pinch. Immediately above the pinch Overall CP difference =

NC

NH

1

1

CPC CPH 60

(4a)

Immediately below the pinch Overall CP difference =

NH

NC

1

1

CPH CPC

(4b)

Fig. 3a The sum of the match CP differences equals the overall difference. All stream at the pinch are involved in pinch exchangers.

Fig. 3b The sum of the match CP differences amount to less than the total. In this case not all streams at the pinch are involved in pinch match.

Fig. 3c The sum of the match CP differences exceeds the total. The pinch match shown is feasible by itself as it fulfills CP inequality criterion but it is incompatible with overall CP difference. (the pinch match has a CP difference of 6 whereas the total available is only 4.) Thus, it is not possible to complete this design.

61

Lecture – 13 - 15 DESIGN OF HEN FOR MAXIMUM ENERGY RECOVERY, LOOP BREAKING & PATH RELAXATION Department of Chemical Engineering

Design of HEN for Maximum Energy Recovery The pinch represents the most constrained region of a design; after all, Tmin exists between all hot and cold streams at the pinch. As a result the number of feasible matches in this region is severely restricted. Quite often there is a crucial or "essential" match. If this match is not made, this will result in heat transfer across the pinch and thus in increased hot and cold utility usage. The pinch design method, therefore * recognizes the pinch division * starts the design at the pinch developing it separately into two remaining problems. This approach is completely different from the normal intuitive approach of starting the design at the hot side and developing it towards the cold. When a design is started at the hot side, initial design decisions may later necessitate follow-up decisions which violate the pinch. On the other hand, when a design is started at the pinch, initial design decisions are made in the most constrained part of the problem and are less likely to lead to difficulties later. Thus, commencing a design at the pinch has the distinct advantage of allowing the designer to identify essential matches or topology options in the most constrained region of the design, which are in keeping with minimum utility usage or maximum energy

62

recovery (MER). Basic element for Design of HEN The CP table Fig. 1(a) and 1(b) show a step-by-step procedure for applying the feasibility criteria such as: number of process streams & branches, CP inequality for individual matches and CP difference. By following the sequence, the designer can

* identify essential matches at the pinch. * identify available match options at the pinch. * identify the need to split streams and generate stream splitting options at the pinch.

The procedure is aided by the use of another new concept, the "CP table". CP tables for the hot and cold ends of a typical problem are shown in Figs. 2 and 3 respectively. In these tables hot and cold stream CPs at the pinch are separately listed in numerical order. The appropriate feasibility criteria are noted at the top of the table and the CPs representing streams, which have to be involved in process exchange at the pinch, are boxed for emphasis. A pinch match is represented in the table by pairing the CPs of a hot and a cold stream. Stream splits are represented by writing the separate branch flowrate CPs adjacent to the original CP (see Fig. 3(C)). The step by step procedure from Fig. 1 is easily followed in the CP table.

63

Fig. 1. (a) Hot end pinch design procedure. (b) Cold end pinch design procedure.

Fig. 2. (a) The CP table for a typical problem hot end. (b) & (c) Feasible pinch matches identified in the CP table 64

Fig. 3(a) The CP table for a typical process cold end. (b) Infeasible pinch topologies. (c) Feasible pinch topology with two stream splits. (d) Feasible pinch topology with one stream split The "tick-off" heuristic Once a pinch topology has been chosen, the design of both hot and cold ends must be continued in such a manner as to keep capital costs at a minimum, i.e. the final designs ought to be steered towards the minimum number of units. This can be achieved by employing a "tick-off" heuristic to identify the heat loads on the pinch exchangers. The targeting equation for the minimum number of units is satisfied if every match brings one stream to its target temperature or exhausts a utility. In this case, the match is said to "tick-off" the stream or utility, i.e. the stream or utility need no longer be considered part of the remaining design task. The pinch exchangers can usually be made to tick-off streams by choosing each 65

exchanger load to equal the smaller heat load of the two streams matched. The CP inequalities will guarantee the possibility of choosing pinch exchanger loads by tickingoff streams as long as the stream CP remains constant with varying temperature and as long as cold and hot stream temperature overlaps do not require an excessive number of shells for a single pinch match. The tick-off heuristic is a "heuristic" as it can occasionally penalize the design by introducing the need for increased utility usage. Temperature driving force, essential elsewhere, may be used up excessively in pinch exchangers that are extended too far into the remaining problem. In such cases the designer can choose either to * reduce the load on the offending pinch match and run the risk of needing more than the minimum number of units. *

use another pinch topology in which the tick-off heuristic does not cause essential

driving force to be used up. Design method summary The pinch design method incorporates five important stages. These are: 1.

The HEN problem is divided at the pinch into separate problems.

2.

The design for these separate problems is started at the pinch and developed

moving away from the pinch. At the pinch essential matches, match options and stream splitting requirements are identified by applying the feasibility criteria. 3.

When options exist at the pinch, the engineer is free to base his selection to suit

the process requirements. 4.

The heat loads of exchangers at the pinch are determined using the stream "tick-

off" heuristic. In case of difficulty (increased utility usage) a different exchanger

66

topology at the pinch can be chosen or the load on the offending match can be reduced. 5.

Away from the pinch there is generally a "free choice" of matches. The procedure

does not insist on particular matches but allows the designer to discriminate between matches based on his judgment and process knowledge. Example The stream data is shown below. For this problem Tmin = 10 °C and the hot and cold utility requirements are 7.5 MW and 10 MW. Hot and cold pinch temperatures are 150 and 140 °C, respectively. Number of units required, including heaters and coolers, are 7 (4 above the pinch and 3 below the pinch). The grid representation of this data is shown in Fig. 4. Stream

Type

TS (°C)

TT (°C)

H (MW)

CP (MW °C-1)

1

Cold

20

180

32

0.2

2

Hot

250

40

- 31.5

0.15

3

Cold

140

230

27

0.3

4

Hot

200

80

- 30

0.25

Fig. 4 The grid diagram

67

Design above the pinch Fig. 5a shows the grid diagram with CP-table for design above the pinch. Cold utility must not be used above the pinch, which means that hot streams must be cooled to pinch temperature by heat recovery. Hot utility can be used, if necessary, on the cold streams above the pinch. Thus, it is essential to match hot streams above the pinch with a cold partner. In addition, if the hot stream is at pinch conditions, the cold stream it is to be matched with must also be at pinch conditions, otherwise the Tmin constraint will be violated. Fig. 5a shows a feasible design arrangement above the pinch that does not use temperature differences smaller than Tmin. Note again that the CP inequality only applies when a match is made between two streams that are both at the pinch. Away from the pinch, temperature differences increase, and it is no longer essential to obey the CP inequalities. NHNC

NHNC

(b) (a) Fig. 5 The CP table for the designs above and below the pinch

68

Design below the pinch Fig. 5b shows the grid diagram with CP-table for the design below the pinch. Hot utility must not be used below the pinch, which means that cold streams must be heated to pinch temperature by heat recovery. Cold utility can be used, if necessary, on the hot streams below the pinch. Thus, it is essential to match cold streams below the pinch with a hot partner. In addition, if the cold stream is at pinch conditions, the hot stream it is to be matched with must also be at pinch conditions, otherwise the Tmin constraint will be violated. Fig. 5b shows a design arrangement below the pinch that does not use temperature differences smaller than Tmin. Sizing the units above the pinch using the tick-off heuristic Once the matches around the pinch have been chosen to satisfy the criteria for minimum energy, the design should be continued in such a manner as to keep capital costs to a minimum. One important criterion in the capital cost is the number of units (there are others, of course, which shall be addressed later). Keeping the number of units to a minimum can be achieved using the tick-off heuristic. To tick off a stream, individual units are made as large as possible, that is, the smaller of the two heat duties on the streams being matched. Fig. 6a shows the matches around the pinch from Fig. 5a with their duties maximized to tick off streams. It should be emphasized that the tick-off heuristic is only a heuristic and can occasionally penalize the design. Methods will be developed later, which allow such penalties to be identified as the design proceeds. The design in Fig. 6a can now be completed by satisfying the heating and cooling duties away from the pinch. Cooling water must not be used above the pinch. Therefore, if there

69

are hot streams above the pinch for which the pinch matches do not satisfy the duties, additional process-to-process heat recovery is required. Fig. 6b shows an additional match to satisfy the residual cooling of the hot streams above the pinch. Again, the duty on the unit is maximized. Finally, above the pinch, the residual heating duty on the cold streams must be satisfied. Since there are no hot streams left above the pinch, hot utility must be used as shown in Fig. 6c. Similarly sizing of units below the pinch can be done as shown in Fig. 7.

Fig. 6 Sizing of units above the pinch

Fig. 7 Sizing of units below the pinch The complete HEN design for MER The final design shown in Fig. 8 amalgamates the hot end design from Fig. 6c and cold end design from Fig. 7c. The duty on hot utility of 7.5 MW agrees with QHmin and the duty on cold utility of 10.0 MW agrees with QCmin predicted by the composite curves and the problem table algorithm. 70

Note one further point from Fig. 8 that the number of units is 7 in total (including the heater and cooler) which is equal to the targeted value. It therefore appears that there was something in the procedure that naturally steered the design to achieve the target for the minimum number of units.

Fig. 8 The completed design for the stream data undertaken Design of HEN with Stream Splitting The pinch design method developed earlier followed several rules and guidelines to allow design for minimum utility (or maximum energy recovery) in the minimum number of units. Occasionally, it appears not to be possible to create the appropriate matches because one or other of the design criteria cannot be satisfied. In such cases stream splitting is done. The algorithm of stream splitting is shown in Fig. 9.

71

Stream data at pinch Yes

CpH CpC for Yes pinch match

NH NC ? No

No

Split cold stream Split hot stream

(a) Stream splitting above pinch Place match

Stream data at pinch

Yes

CpHCpC for pinch match

Yes

NH NC ? No

No

Split hot stream Split cold stream

(b) Stream splitting below pinch Place match

Fig. 9 Stream splitting algorithm Example The grid representation for a high temperature process is shown in Fig. 10a where

Tmin=20 C. The process requires 9.2 MW of hot utility, 6.4 MW of cold utility and the pinch is located at 520 C for hot streams and 500 C for cold streams.

72

Fig. 10b shows the CP tables for the above- and below-pinch designs. Following the algorithms in Fig. 9, a hot stream must be split above the pinch to satisfy the CP inequality, as shown in Fig. 10b.

The grid diagram

The splitting of hot stream

73

Fig. 10 Maximum energy recovery design with stream splitting

Identification of Loops & Paths and Loop Breaking and Path Relaxation There will generally be scope to simplify minimum utility designs by a controlled reduction in the number of units. By transferring heat across the pinch and therefore increasing the utility usage the number of capital items can be reduced. There is a tradeoff between units (capital cost) and the utility usage (energy cost). In order to explore the scope for a controlled reduction in the number of units it is important to understand the concepts of heat load loops and heat load paths. Heat Load Loops A loop is a set of connections that can be traced through a network (via streams and units) that starts at one exchanger and returns to the same exchanger. Whenever a design features more than the target minimum number of units for the whole problem, ignoring the pinch, it is due to the existence of heat load loops. There will be one loop for each extra unit. As an example, the minimum utility design for a typical

74

problem has two more units than the definite minimum according to Fig. 11. Hence there must be two loops in the design. Figs. 12(a) and (b) show these loops. An important feature of every loop is that heat loads can be shifted around the loop from one unit to another. The load is subtracted from the next and so on around the loop. This load shift always maintains the correct stream heat loads but the exchanger duties are changed and may cause a violation of Tmin. However, driving forces can be "restored" using heat load paths.

Fig 11. (a) The number of units for maximum energy recovery. (b) The overall minimum number of units.

(b)

75

Heat Load Paths A path is a continuous connection in the grid between a heater, heat exchangers and a cooler. Fig. 14 shows the simplest form of a path. Load shifts along paths follow equivalent rules to load shifts around a loop. Load is added to a heater, subtracted from an exchanger, added to the next exchanger in the path, subtracted from the next, and so on along the path until it is finally added to a cooler. Stream enthalpy balance is maintained but exchanger loads and operating temperatures are changed. This last feature means that a path can be used to restore driving forces. Loop Breaking and Path Relaxation We will now illustrate the use of heat load loops and paths to reduce the number of units of the design in Fig. 12a from seven to six.

Fig. 12 (a,b) A minimum utility design for a typical problem showing the two heat load loops

76

It is apparent that load shifts around loops can form the basic mechanism for the reduction in the number of units. When the load shift around a loop leads to a reduction in the heat load of a unit, which equals the load on that unit, then the unit is removed from the design and the number of units is reduced by one. Consider Fig. 12(a), which shows a minimum utility design with seven units. A good choice of exchanger to remove is exchanger No. 4 as it has the smallest load and forms part of the simplest loop. Fig. 13 shows the topology and temperatures after the load of match No. 4 has been transferred to exchanger No. 1. The heat loads of all other units in the design are unchanged as they were not part of the original loop. There is now a small violation in Tmin as reflected by the difference in temperatures T1 and T2.

Fig. 13 A six unit topology that is a result of breaking Loop 1 (Fig. 12a).

However, Tmin can be restored using the heat load path shown in Fig. 14. It is apparent that T1 is fixed at 62C. It is therefore T2 which must be changed to restore Tmin. Requiring T2 to equal 82C, the heat load of individual units can now be changed while the stream heat loads are maintained by using the path through exchanger No. 1. It is a trivial task to calculate the hot and cold utility increase x required. This load is 4 kW. In other words, by supplying a further 4 kW of utility heating and cooling and by reducing the heat load on exchanger No. 1 by 4 kW, the solution is brought back in line with the Tmin. 77

Fig. 14 Identifying a path

The summary of this section is as follows 

There is generally scope to reduce the number of units in a pinched problem starting from a minimum utility design.



This reduction in the number of units can be achieved in a controlled manner. By this we mean that the utility penalty incurred in reducing the number of units is minimized.



Not all units exist in a suitable loop or along a suitable path. Thus, the procedure would not be applicable to the "removal" of such units.

78

Lecturer - 16 DRIVING FORCE PLOT AND REMAINING PROBLEM ANALYSIS Department of Chemical Engineering

The Driving Force Plot Fig. 1 shows two networks having the same CP-ratios for the pinch match. However, network 2A comes to within 16% of the above pinch area target, while network 2B requires 108% more area than target. Why is there such a large discrepancy? Examining the Composite Curves, we suspect network 2B makes poor use of driving forces away from the pinch. To take this further the concept of “Driving Force Plot” is used.

Fig. 1 Both networks have identical CP-ratios for pinch matches. There is, however, significant difference in network areas

79

The area target is based on the vertical temperature differences along the whole balanced composite curves. Ideally, we need to measure the temperature differences of individual matches against the vertical driving forces available on the composites. A simple way of expressing this is firstly to draw the vertical temperature difference T between the composites as it changes with the temperature of say the cold composite Tcold (Fig. 2). Equivalently, T=f(Thot) or Thot=f(Tcold) may also be used. The diagram is called the "Driving force Plot" (Fig. 2).

Fig. 2 Construction of Driving Force Plot

Next, individual matches are shown in these coordinates (Fig. 3). Matches displaying vertical heat transfer on the composites fit the Driving force Plot exactly, such as the match shown in Fig. 3. Matches which are not vertical (or which criss-cross) on the composites show a blatant misfit (Fig. 4, 5). Matches using excessive temperature differences have less area than if they had been vertical, but cause other (subsequently placed) matches to have smaller temperature differences. The net result overall is increased heat exchange area for the network.

80

Fig. 3 The match with “vertical heat transfer”

Fig. 4 The match with “excessive driving force”

Fig. 5 The match under-utilizing driving force

The Driving Force Plot provides a rapid and easy way to use guideline for designing networks, which are close to minimum area. However, it is only a guideline and does not provide quantitative information.

81

Networks 2A and 2B are displayed against their Driving Force Plot in Fig. 6. The pinch matches placed according to the CP-rules follow well the slope of the Driving Force Plot near the pinch. Away from the pinch, however, network 2B shows a poorer overall fit to the plot. Its pinch matches are too large to duty and under-utilize driving forces away from the pinch. These duties were established using the “tick-off’ heuristic for obtaining minimum number of units in the design.

Fig. 6 Networks 2A & 2B compared on the Driving Force Plot. Network 2B shows a much poorer overall fit to the plot than network 2A. The plot shows the tick-off heuristic is inappropriate here for achieving low network area. Violation of the tick-off rule usually means additional units above target, as in network 2A. The significantly improved area performance in this example gives lower overall capital cost. Designs achieving a good fit to the Driving Force Plot in minimum number 82

of units or within 10% of this (to the nearest integer number of units) are usually within 10% of the area target. Remaining Problem Analysis Suppose a design obtains a good fit to the Driving Force Plot but the final network area is appreciably above target. Such an occurrence is infrequent considering the plot steers design towards vertical heat transfer and minimum area. Fig. 7, however, demonstrates the plot may not always be sufficient for minimum area. Networks 3A and 3B appear remarkably similar in use of driving forces, but 3B has an area 22% in excess of the above-pinch target whereas 3A is only 10% above this target.

Fig. 7 Both networks show very similar fit to the Driving Force Plot but differ appreciably in area 83

The Driving Force Plot works in temperatures only, neglecting the effect of duty on heat exchanger area. It is possible for matches to appear identical in Driving Force coordinates, yet have very different duties. Generally, good utilization of driving forces for matches of large duty is required in regions of small temperature difference. When a match is placed, the duty needs to be chosen with some quantitative assessment of the match in the context of the whole network, without having to complete the network. This can be done by exploiting the powers of targeting using a technique known as Remaining Problem Analysis. Consider the design for minimum energy in a more complex problem. If a problem table analysis (PTA) is performed on the stream data, QHmin and QCmin can be calculated. When the network is designed and a match is placed, it would be useful to assess whether there will be any energy penalty caused by some feature of the match without having to complete the design. This penalty can be determined by performing a PTA on the remaining problem. The PTA is simply repeated on the stream data, leaving out those parts of the hot and cold stream satisfied by the match. One of the two results would then occur: 1.

The algorithm may calculate QHmin and QCmin to be unchanged. In this case, the designer knows that the match will not penalize the design in terms of increased utility usage.

2.

The algorithm may calculate an increase in QHmin and QCmin. This means that the match is transferring heat across the pinch or that there is some feature of the design that will cause cross-pinch heat transfer if the design was completed. If the

84

match is not transferring heat across the pinch directly, then the increase in utility will result from the match being too big as a result of the tick-off heuristic. The remaining problem analysis (RPA) technique can be applied to any feature of the network that can be targeted, such as a minimum area. RPA can be used to approach the area target, as closely as a practical design permits, using a minimum (or near minimum) number of units. Suppose a match is placed, then its area requirement can be calculated. A RPA can be carried out by calculating the area satisfied by the match. The area of the match is now added to the area target for the remaining problem. Subtraction of original area target for the whole-stream data gives the area penalty incurred. Targets for number of shells, capital cost and total cost also can be set. Thus, RPA can be used on these design parameters also. The “Remaining Problem Analysis” is explained in Fig. 8. Suppose the minimum total area possible for a design completed after accepting a match M is Atotal. M. This is the sum of the match area aM and the area target for the remaining stream data Ar, M. Subtraction of the original area target for the whole stream data Amin gives the minimum area penalty incurred. The analysis can quantify both surplus and deficit use of driving forces. A large T match incurs area penalty from the small T caused in the remaining problem. A small T match incurs area penalty from the match itself.

85

Fig. 8 Remaining Problem Analysis for area

Fig. 9 the Remaining Problem Analysis for match 4 in network 38 shows significant penalty in area for the network. 86

The Remaining Problem Analyses for networks 3A and 3B are shown in Fig. 9. It is now clear that match 4 in network 3B is not as good as the rest. Surprisingly, it looks similar on the Driving Force Plot (Fig. 7) to matches 4 and 5 in network 3A, which return much lower area penalties. The Remaining Problem Analysis improves on the Driving Force Plot. At present, it is the only known method for quantifying approach to the targets during design development. The Remaining Problem Analysis discussed so far treats each match in isolation of the others when several matches exist at any stage of design (as in Fig. 9). In other words, the remaining problem is defined as the full stream data excluding only the hot and cold stream sections of the match being analyzed.

87

REFERENCES 1.

Linnhoff, B.; Dunford; H.; and Smit, R.; “Heat Integration of Distillation Columns into Overall Process”; Chem. Engg. Science; Vol.38; No.8; pp-11751189, (1983).

2.

Robin Smith, “Chemical Process Design”, McGraw Hill, 1995.

3.

Linnhoff B, Townsend D W, Boland D, Hewitt G F, Thomas B E A, Guy A R & Marsland R H, “User guide on process integration for the efficient use of energy”, (The Institution of Chemical Engineers, Rugby, U.K.; available in the U.S. through Pergamon Press, Inc. Elmsord, N.Y.), 1982.

4.

Ahmad S and R .Smith, “Targets and design for minimum number of shell in heat exchangers networks”, Chem. Eng. Res. Des., Vol. 67, Sep 1989, pp 481-494.

5.

Linnhoff B. and S. Ahmad, “Cost optimal heat exchanger networks I Minimum energy and capital cost using simple models for capital cost , Comp Chem Engg., Vol. 14, No. 7 1990, pp 729-767.

6.

Linnhoff B. and E. Hindmarsh, “The pinch design methods for heat exchanger networks”, Chem Engg. Sci, Vol. 38, No. 5 1983, pp 745-763.

7.

Linnhoff B., “Pinch Analysis-A state-of-the- art overview”, Trans IchemE, Vol. 71, Part A, Sep 1993, pp 503-522.

8.

Linnhoff B. and J. R. Flower, “Synthesis of heat exchanger networks”, AIChE J, Vol. 24, July 1978, pp 633-642.

9.

Smith G. and A. Patel, “Step by step through pinch”, The Chem. Eng., Nov 1987, pp 26-31.

10.

Linnhoff B. and D. R. Vredeveld, “Pinch Technology has come of age”, CEP, July 1984, pp 33-39.

11.

Uday V. Shenoy, “Heat Exchange Network Synthesis”, Gulf Publishing Company, 1995. 88