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C H A P T E R

7

Heat Integration

Heating and cooling are among the most common operations in the process industries. Significant quantities of external heating and cooling utilities are used to drive reaction, induce separation, and render units and streams in desirable states of operation. To satisfy the need for heating and cooling, industrial operations require the extensive use of different forms of energy. For instance, fossil fuels are widely used as feedstocks of boilers to generate heating media (for example, steam, heating oil) or to drive power cycles that drive refrigeration systems. The excessive usage of external heating utilities incurs a substantial economic burden in the form of operating costs, depletes unsustainable energy resources (for example, fossil fuels), and generates large quantities of greenhouse gas emissions. Consequently, considerable attention has been given to the problem of conserving energy through heat integration and the synthesis of heat-exchange networks (HENs). The basic idea for heat integration is that there are process streams and units that need to be heated and other process streams and units that need to be cooled. Before using external utilities to provide the necessary heating and cooling, heat integration seeks to transfer the heat from the process hot streams and units to the process cold streams and units. The remaining heating and cooling tasks are then fulfilled using the external heating and cooling utilities. This chapter presents the key tools used in identifying rigorous targets for minimum heating and cooling utilities, selecting utilities, and synthesizing HENs that attain the desired targets.

Cold Streams In

Hot Streams In

Heat Exchange Network

Hot Streams Out

Cold Streams Out

FIGURE 7-1  Synthesis of HENs.

heated), it is desired to synthesize a cost-effective network of heat exchangers that can transfer heat from the hot streams to the cold streams. Given also are the heat capacity (flow rate x specific heat) of each process hot stream, FCP,u; its supply (inlet) temperature, Tus; and its target (outlet) temperature, Tut, where u    1, 2,…, NH. In addition, the heat capacity, fcP,v, and supply and target temperatures, tvs and tvt, are given for each process cold stream, where v    1, 2,…, NC.1 Available for service are NHU heating utilities and NCU cooling utilities whose supply and target temperatures (but not flow rates) are known. In this version of the HEN-synthesis problem statement, focus is given to hot and cold streams with changes in sensible heat. Figure 7.1 is a schematic representation of the HEN problem statement. For a given system, the synthesis of HENs entails answering several questions: Which heating/cooling utilities should be employed? What is the optimal heat load to be removed/added by each utility? l How should the hot and cold streams be matched (that is, stream pairings)? l What is the optimal system configuration (sequencing of stream and heat exchangers)? l

HEN-SYNTHESIS PROBLEM STATEMENT In defining the HEN-synthesis problem, it is useful to discuss the necessary information required to set up the heat-integration problem. The following data should be extracted from the process: Which streams and units are to be heated (the cold streams and heat sinks)? What is the heating duty required for each one? What is the temperature change associated with each cold stream and unit? l Which streams and units are to be cooled (the hot streams and heat sources)? What is the cooling duty required for each one? What is the temperature change associated with each hot stream and unit? l What are the available types of external heating and cooling utilities? What are their characteristics? l

One version of the HEN-synthesis problem can be stated as follows: Given a number NH of process hot streams (to be cooled) and a number NC of process cold streams (to be Sustainable Design Through Process Integration. © 2012 Elsevier Inc. All rights reserved.

l

Numerous methods have been developed for the synthesis of HENs. These methods have been reviewed by Foo et al. (2011), Rossiter (2010), Majozi (2010), Kemp (2009), Smith (2005), Furman and Sahinidis (2002), Shenoy (1995), Linnhoff (1993), Gundersen and Naess (1988), Douglas (1988), Linnhoff and Hindmarsh (1983), and Linnhoff et al. (1982). One of the most powerful aspects in synthesizing HENs is the identification of minimum utility targets ahead of 1

 In this version of the HEN-synthesis problem, focus is given to the exchange of sensible heat among process streams. Heat sources and sinks can be represented through surrogate streams with the flow rate*heat capacity calculated by dividing the heat duty of the unit by the difference in temperature. For cases when there is no change in temperature (for example, latent heat for streams or isothermal operation of units), an approximation may be made to allow for a small change in the temperature (for example, one-degree difference between supply and target temperatures).

147

148

Sustainable Design Through Process Integration Annualized Cost, $/yr

TABLE 7-1  Analogy between MENs and HENs

MENs

HENs

Transferred commodity: Mass

Transferred commodity: Heat

Donors: Rich streams

Donors: Hot streams

Recipient: Lean streams

Recipient: Cold streams

Rich composition: y

Hot temperature: T

Lean composition: x

Cold temperature: t

Slope of equilibrium: m

Slope of equilibrium: 1

Intercept of equilibrium: b

Intercept of equilibrium: 0

Driving force: 

Driving force: ΔTmin

Minimum Total Annualized Cost

Annual Operating Cost Annualized Fixed Cost

Minimum Annual Operating Cost

Source: El-Halwagi (2006).

designing the network. The following sections present graphical and algebraic methods of determining minimumutility targets.

MINIMUM UTILITY TARGETS VIA THE THERMAL PINCH DIAGRAM Consider a heat-exchange operation that transfers heat from a hot stream to a cold stream. An important boundary is reaching thermal equilibrium, which is simply attained when the temperatures of the hot and the cold stream are equal; that is, [7.1]

T t

where T is the temperature of the hot stream and t is the temperature of the cold stream. Thermal equilibrium requires an infinitely large heat-transfer area. For the heat exchanger to be practically feasible, a minimum heat-exchange driving force (referred to as ΔTmin) should be employed. This minimum driving force can be used to establish a one-to-one correspondence between the temperatures of the hot and the cold streams for which heat transfer is feasible; that is, [7.2]

Total Annualized Cost

T

t

∆T min

This expression ensures that the heat-transfer considerations of the second law of thermodynamics are satisfied. For a given pair of corresponding temperatures (T, t), it is thermodynamically and practically feasible to transfer heat from any hot stream whose temperature is greater than or equal to T for any cold stream whose temperature is less than or equal to t. It is worth noting the analogy between Equations 7.2 and 3.5. Thermal equilibrium is a special case of mass-exchange equilibrium with T, t, and ΔTmin corresponding to yi, xj, and j, respectively, whereas the values of mj and bj are one and zero, respectively. Table 7.1 summarizes the analogous terms in the synthesis of mass- and heat-exchange networks. Similar to the role of j in cost optimization of MENs, ΔTmin can be used to trade off capital versus operating costs in HENs as shown in Fig. 7.2. When ΔTmin approaches zero, the heattransfer area approaches infinity and, consequently, the fixed cost tends to infinity. As the heat-transfer driving

0

∆Τ optimum

∆Τ min

FIGURE 7-2  Role of minimum approach temperature.

force increases, the fixed cost decreases but the operating cost increases. Such effects lead to the nonmonotonic behavior shown by Fig. 7.2, which can be used to determine an optimal driving force. More elaborate techniques can be used by assigning a different driving force for each stream or pair of streams to trade off capital versus operating costs. To accomplish the minimum usage of heating and cooling utilities, it is necessary to maximize the heat exchange among process streams. In this context, one can use a very useful graphical technique referred to as the “thermal pinch diagram.” This technique is primarily based on the work of Linnhoff and colleagues (for example, Linnhoff and Hindmarsh, 1983) Umeda et al. (1979) and Hohmann (1971). The first step in constructing the thermal pinch diagram is creating a global representation for all the hot streams by plotting the enthalpy exchanged by each process hot stream versus its temperature.2 Hence, a hot stream losing sensible heat3 is represented as an arrow whose tail to its supply temperature and its head corresponds to its target temperature. Assuming constant heat capacity over the operating range, the slope of each arrow is equal to FuCP,u. The vertical distance between the tail and the head of each arrow represents the enthalpy lost by that hot stream according to the following expression: Heat lost from the uth hot stream HH u FuC p,u (Tus Tut ) where [7.3]

2

u  1, 2, … , N H

 In most HEN literature, the temperature is plotted versus the enthalpy. However, in this chapter, enthalpy is plotted versus temperature to draw the analogy with MEN synthesis. Furthermore, when there is a strong interaction between mass and energy objectives, the enthalpy expressions become nonlinear functions of temperature. In such cases, it is easier to represent enthalpy as a function of temperature. 3  Whenever there is a change in phase, the latent heat should also be included.

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CHAPTER 7   Heat Integration

Heat Exchanged

Heat Exchanged

H2

HH2

Hot Composite Stream

HH1 + HH2

H1

HH1

T1t

T2t

T1s

T2s

T

T1t

T2t

T1s

T2s

T

FIGURE 7-3  (a) Representing hot streams. (b) Constructing a hot composite stream using superposition. Heat Exchanged

Heat Exchanged

HC2 C1

HC1

Cold Composite Curve

HC2

C2

HC1 T

T

t1s

t2s

t1t

t2t

t=T–∆T

min

t1s

t2s

t1t

t2t

t=T–∆T min

FIGURE 7.4  (a) Representing cold streams. (b) Constructing a cold composite stream using superposition (dashed line represents composite line).

Note that any stream can be moved up or down while preserving the same vertical distance between the arrow head and tail and maintaining the same supply and target temperatures. Similar to the graphical superposition described in Chapter 4, one can create a hot composite stream using the diagonal rule. Figures 7.3a, b illustrate this concept for two hot streams (dashed line represents composite line). Next, a cold-temperature scale, t, is created in oneto-one correspondence with the hot temperature scale, T, using Eq. 7.2. The enthalpy of each cold stream is plotted versus the cold temperature scale, t. The vertical distance between the arrow head and tail for a cold stream is given by Heat gained by the vth cold stream HCv f v c p,v (t vt t vs )

Heat Exchanged

Cold Composite Stream

Hot Composite Stream T t=T–∆T min FIGURE 7-5  Placement of composite streams with no heat integration.  Source: El-Halwagi (2006).

where [7.4]

v  1, 2, … , N C

In a similar manner to constructing the hot-composite line, a cold composite stream is plotted (see Fig. 7.4a, b for an example with two cold streams). Next, both composite streams are plotted on the same diagram (Fig. 7.5). On this diagram, thermodynamic feasibility of heat exchange is guaranteed when, at any heatexchange level (which corresponds to a horizontal line), the temperature of the cold composite stream is located to the left of the hot composite stream (that is, temperature of the hot is higher than or equal to the cold temperature plus the minimum approach temperature). Hence, for a given set of corresponding temperatures, it

is thermodynamically and practically feasible to transfer heat from any hot stream to any cold stream. The cold composite stream can be moved up and down, which implies different heat-exchange decisions. For instance, if we move the cold composite stream upward in a way that leaves no horizontal overlap with the hot composite stream, then there is no integrated heat exchange between the hot composite stream and the cold composite stream as seen in Fig. 7.5. When the cold composite stream is moved downward so as to provide some horizontal overlap, some integrated heat exchange can be achieved (Fig. 7.6). However, if the cold composite stream is moved downward such that a portion of the cold is placed to the right of the hot composite stream, heat transfer from hot

150

Sustainable Design Through Process Integration Heat Exchanged

Heat Exchanged

Cold Composite Stream

Load of External Heating Utilities

Minimum Heating Utility

Heat Exchange Pinch Point

Hot Composite Stream

Load of External Cooling Utilities

Integrated Heat Exchange

Cold Composite Stream

Minimum Cooling Utility

Maximum Integrated Heat Exchange

Hot Composite Stream

T

T t=T–∆T min

FIGURE 7-6  Partial heat integration.  Source: El-Halwagi (2006).

t=T–∆T min FIGURE 7-8  The thermal pinch diagram. Heat exchanged

α Cold Composite Stream Infeasibility Region

Cold composite stream

α

Hot Composite Stream

Minimum cooling utility

T t=T–∆T min FIGURE 7-7  Infeasible heat integration.  Source: El-Halwagi (2006).

to cold becomes infeasible (Fig. 7.7). Therefore, the optimal situation is constructed when the cold composite stream is slid vertically until it touches the rich composite stream while lying completely to the left of the hot composite stream at any horizontal level. Therefore, the cold composite stream can be slid down until it touches the hot composite stream. The point where the two composite streams touch is called the “thermal pinch point.” As Fig. 7.8 shows, one can use the pinch diagram to determine the minimum heating and cooling utility requirements. Again, the cold composite line cannot be slid down any further; otherwise, portions of the cold composite stream would be to the right of the hot composite stream, causing thermodynamic infeasibility. On the other hand, if the cold composite stream is moved up (that is, passing heat through the pinch), less heat integration is possible, and

α

Minimum heating utility

Hot composite stream

Maximum integrated heat exchange

T t=T–∆T min

FIGURE 7-9  Penalties associated with passing heat through the pinch.  Source: El-Halwagi (2006).

consequently, additional heating and cooling utilities are required. Therefore, for a minimum utility usage, the following design rules must be observed: No heat should be passed through the pinch. Above the pinch, no cooling utilities should be used. l Below the pinch, no heating utilities should be used. l l

Figure 7.9 illustrates the first rule. The passage of a heat flow through the pinch (α) results in a double penalty: an increase of α in both heating utility and cooling utility. The second and third rules can be explained by noting that above the pinch there is a surplus of cooling capacity. Adding a cooling utility above the pinch will replace a load that can be removed (virtually for no operating cost) by a process cold stream. A similar argument can be made against using a heating utility below the pinch.

Example 7-1  Pharmaceutical facility Consider the pharmaceutical processing facility illustrated in Fig. 7.10. The feed mixture (C1) is first heated to 550 K, and then fed to an adiabatic reactor where an endothermic reaction takes place. The off-gases leaving the reactor (H1) at 520 K are cooled to 330 K prior to being forwarded to the recovery unit. The mixture leaving the bottom of the reactor is separated into a vapor fraction and a slurry fraction. The vapor fraction (H2) exits the separation unit at 380 K and is to be cooled to 300 K prior to storage. The slurry fraction is washed with a hot immiscible liquid at 380 K. The wash liquid is purified and recycled to the washing

unit. During purification, the temperature drops to 320 K. Therefore, the recycled liquid (C2) is heated to 380 K. Two utilities are available for service: HU1 and CU1. The cost of the heating and cooling utilities (in $/106 kJ) are 6 and 8, respectively. Stream data are given in Table 7.2. In the current operation, the heat exchange duties of H1, H2, C1, and C2 are fulfilled using the cooling and heating utilities. Therefore, the current annual operating cost of utilities is (Continued )

151

CHAPTER 7   Heat Integration

Example 7-1  Pharmaceutical facility (Continued)

8

120)kW 6

10

6

$ ]3600 kJ

$ (1900 400)kW kJ s $1, 501, 744/yr . 8760 yrr 10

5000

6

4000

The objective of this case study is to use heat integration via the pinch diagram to reduce this operating cost. A value of ΔTmin  10 K is used. SOLUTION Figures 7.11 through 7.13 illustrate the hot composite stream, the cold composite stream, and the pinch diagram, respectively. As can be seen from Fig. 7.13, the two composite streams touch at 310 K on the hot scale (300 K on the cold scale). The minimum heating and cooling utilities are 2620 kW and 50 kW, respectively, leading to an annual operating cost of (2620 kW 8760

6

s yr

10

6

$ kJ

50 kW

8

10

6

Heat Exchanged, kW

[(4750

3000 2300

H1

2000

1000 400 H2

0 300

340

380

420

460

500 520 540

580

T, K

FIGURE 7-11  Hot composite stream for pharmaceutical process.

$ )3600 kJ

$508, 360 /yr

5000

This is only 34 percent of the operating cost prior to heat integration. Once the minimum operating cost is determined, a network of heat exchangers can be synthesized. The network synthesis will be described later in this chapter. The trade-off between capital and operating costs can be established by iteratively varying ΔTmin until the minimum total annualized cost is attained.

4870 4750

Heat Exchanged, kw

4000

3000

C1

2000

120

C2

1000

330 K C1 300 K

550 K

Adiabatic Reactor

0 300 320 340

To Recovery

H1 520 K

380

420

460

500

540 550 580

t, K

FIGURE 7-12  Cold composite stream for pharmaceutical process. 300 K

H2 380 K

To Storage

5000

C2 320 K

4000 Heat Exchanged, kW

Separation

380 K Washing

To Finishing

Cold Composite Stream

3000

min = 2620 Heating

Q

kW

2300 2000 Hot Composite Stream

1000 Qmin = Cooling

50 kW

Purification

FIGURE 7-10  Simplified flow sheet of the pharmaceutical process.

Pinch

0

Impurities

290

310

330

370

410

450

490

280

300

320

360

400

440

480

Stream

Flow Rate   Specific Heat, kW/K

Supply Temperature, K

Target Temperature, K

Enthalpy Change, kW

H1

10

520

330

1900

H2

5

380

300

400

HU1

?

560

520

?

C1

19

300

550

4750

C2

2

320

380

120

290

300

?

?

530 520

570 T, K 550

560 t = T-10

FIGURE 7-13  Thermal pinch diagram for the pharmaceutical process.

TABLE 7-2  Stream Data for Pharmaceutical Process

CU1

520

152

Sustainable Design Through Process Integration

MINIMUM UTILITY TARGETS USING THE ALGEBRAIC CASCADE DIAGRAM Notwithstanding the insights obtained by the graphical thermal pinch diagram, in some cases, it is desirable to use an algebraic approach. Examples include problems with numerous streams with much overlapping that can render the construction of the composite curves cumbersome. Another example is the case with temperature ranges that are vastly different to the extent that they may skew the representation of certain streams. This section presents an algebraic approach referred to as the cascade diagram, which is based on the problem-table algorithm developed by Linnhoff and Flower (1978). The first step is the construction of a temperature-interval diagram (TID), which is a useful tool for ensuring thermodynamic feasibility of heat exchange. Two corresponding temperature scales are generated: hot and cold. The scale correspondence is determined using Eq. 7.2. Each stream is represented as a vertical arrow whose tail corresponds to its supply temperature, while its head represents its target temperature. Next, horizontal lines are drawn at the heads and tails of the arrows. These horizontal lines define a series of temperature intervals z    1, 2,…, nint. Within any interval, it is thermodynamically feasible to transfer heat from the hot streams to the cold streams. It is also feasible to transfer heat from a hot stream in an interval z to any cold stream that lies in an interval below it. Next, we construct a table of exchangeable heat loads (TEHL) to determine the heat-exchange loads of the process streams in each temperature interval. The exchangeable load of the uth hot stream (losing sensible heat) that passes through the zth interval is defined as [7.5]

HH u , z

FuC p,u (Tz

1

Tz )

where Tz1 and Tz are the hot-scale temperatures at the top and the bottom lines defining the zth interval. On the other hand, the exchangeable capacity of the vth cold stream (gaining sensible heat) that passes through the zth interval is computed through [7.6]

HC v, z

f v c p,v ( t z

1

[7.7]

HH zTotal 

HH u , z

Similarly, the collective cooling capacity of the cold process streams within the zth interval is evaluated as follows: [7.8]

HC zTotal 

∑

v passes through interval z and v1,2,..., N C

HC v, z

As has been mentioned earlier, within each temperature interval, it is thermodynamically as well as technically feasible to transfer heat from a hot process stream to a cold process stream. Moreover, it is feasible to pass heat from a hot process stream in an interval to any cold process stream in a lower interval. Hence, for the zth temperature interval, one can write the following heat-balance equation: [7.9]

rz

HH zTotal

HC zTotal

rz

1

where rz1 and rz are the residual heats entering and leaving the zth interval. Figure 7.14 illustrates the heat balance around the zth temperature interval. In this equation, r0 is zero, because no process streams exist above the first interval. In addition, thermodynamic feasibility is ensured when all the rzs are nonnegative. Hence, a negative rz indicates that residual heat is flowing upward, which is thermodynamically infeasible. All negative residual heats can be made nonnegative if a hot load equal to the most negative rz is added to the problem. This load is referred to as the minimum heating utility requirement, Qmin Heating. Once this hot load is added, the cascade diagram is revised. A zero residual heat designates the thermal pinch location. The load leaving the last temperature interval is the minimum cooling utility requirement, Qmin Cooling.

Residual Heat From Preceding Interval

tz )

where tz1 and tz are the cold-scale temperatures at the top and the bottom lines defining the zth interval. Having determined the individual heating loads and cooling capacities of all process streams for all temperature intervals, one can also obtain the collective loads (capacities) of the hot (cold) process streams. The collective load of hot process streams within the zth interval is calculated by summing up the individual loads of the hot process streams that pass through that interval; that is,

∑

u passes through interval z where u 1,2,..., N H

rz–1

Total Heat Added HHz By Process Hot Streams

HCzTotal Heat Removed By Process Cold Streams

Z rz Residual Heat To Subsequent Interval

FIGURE 7-14  Heat balance around a temperature interval.

CHAPTER 7   Heat Integration

153

Example 7-2  Revisiting the case study on the pharmaceutical facility using the algebraic cascade diagram We now solve the pharmaceutical case study described earlier using the algebraic cascade diagram. The first step is the construction of the TID (Fig. 7.15). Next, the TEHLs for the process hot and cold streams are developed (Tables 7.3 and 7.4). Figures 7.16 and 7.17 show the cascade diagram calculations. The results obtained from the revised cascade diagram are identical to those obtained using the graphical pinch approach.

0 0

760

1 –760

1300

2

2470

–1930 Interval

Hot Streams

t

T

5 6

520

510

390

380

380

370

330

320

310

300

300

290

–2340

100

5 –2620

50

C2

1050

4

f2Cp2 =2

F2Cp2 = 5

4

H2

–2040 750

f1Cp1=19

3

F1Cp1 = 10

2

H1

210

3

550

560

1

100

Cold Streams

5

C1

380

0

–2570

FIGURE 7-15  Temperature interval diagram for pharmaceutical case study.

FIGURE 7-16  Cascade diagram for the pharmaceutical case study.

TABLE 7-3  TEHL for Process Hot Streams

Interval

Load of H1 (kW)

Load of H2 (kW)

Total Load (kW)

1

–

–

–

2

1300

–

1300

min QHeating = 2620 kW

0

3

100

–

100

4

  500

250

750

5

–

100

100

6

–

50

50

1300

760

1 1860 2

2470

690 100

210

3 580

750 TABLE 7-4  TEHL for Process Cold Streams

Interval

Capacity of C1 (kW)

Capacity of C2 (kW)

Total Capacity (kW)

1

760

–

760

2

2470

–

2470

3

190

20

210

4

950

100

1050

380

–

5 6

–

–

100

50

1050

4 280 5

6

380

0 Thermal-Pinch Location 0

min Qcooling = 50kW

380 –

FIGURE 7-17  Revised cascade diagram for the pharmaceutical case study. (Continued )

154

Sustainable Design Through Process Integration

Example 7-2  Revisiting the case study on the pharmaceutical facility using the algebraic cascade diagram (Continued) extra

Heating Utility = 2620 + QHeating 0 0

760

1

extra

1300

1860 + QHeating 2470

2

As mentioned earlier, for minimum utility usage, no heat should be passed through the pinch. Let us illustrate this point using the cascade diagram. Suppose that we use Qextra Heating kW more than the minimum heating utility. As can be seen from Fig. 7.18, this additional heating utility passes down through the cascade diagram in the form of an increased residual heat load. At the pinch, the residual load becomes Qextra Heating. The net effect is not only an increase in the heating utility load, but also an equivalent increase in the cooling utility load.

extra

100

750

100

690 + QHeating 210

3

4

5

extra 580 + QHeating 1050 extra 280 + QHeating 380 extra

50

QHeating 0

6

extra

Cooling Utility = 50 + QHeating FIGURE 7-18  Consequences of passing heat through the pinch.

SCREENING OF MULTIPLE UTILITIES USING THE GRAND COMPOSITE REPRESENTATION The aforementioned graphical thermal pinch diagram and its numerical analog, the cascade diagram, identify the minimum heating and cooling utilities. These targets are determined without specifying the type of utilities to be used or whether several heating or cooling utilities are needed. In many cases, multiple utilities are available for service. These utilities must be screened so as to determine which one(s) should be used and the task of each utility. To minimize the cost of utilities, it may be necessary to stage the use of utilities such that at each level the use of the cheapest utility ($/kJ) is maximized while ensuring its feasibility. A convenient way of screening multiple utilities is the grand composite curve (GCC). The GCC may be directly constructed from the cascade diagram (Linnhoff et al., 1982). To illustrate the procedure for constructing the GCC, let us consider the cascade diagram shown in Fig. 7.19a. The residual heat loads are shown leaving the temperature intervals. Suppose that r4 is the most negative residual. As mentioned previously, this infeasibility and all other infeasibilities are removed by adding the absolute value of r4 to the top of the cascade diagram. This value is also the minimum heating utility. The residual loads are recalculated with the load leaving the last temperature interval being the minimum cold utility as illustrated by Fig. 7.19b.

Each residual heat corresponds to a hot temperature and a cold temperature. To have a single-temperature representation, we use an adjusted temperature scale that is calculated as the arithmetic average of the hot and the cold temperature; that is, [7.10]

T

Adjusted temperature

t 2

Given the relationship between the hot and cold temperature (described by Eq. 7.2), we get: [7.11a]

[7.11b]

Adjusted temperature

=t+

T

∆T min 2

∆T min 2

Next, we represent the adjusted temperature versus the residual enthalpy as shown in Fig. 7.20a. This representation is the GCC. The pinch point corresponds to the zero-residual point. Additionally, the top and bottom residuals represent the minimum heating and cooling utilities. The question is how to distribute these loads over the multiple utilities. Any time, the enthalpy representation is given by a line drawn from left to right; it corresponds to a surplus of heat in that interval. Conversely,

155

CHAPTER 7   Heat Integration (T+t)/2

1

r1 2

r2 3

r3 Pinch Point

4

r4(supposedly most negative number)

5

0

r5

Qcmin

d5

d2

d3 Qhmin

d1

Enthalpy

FIGURE 7-20A  Construction of the GCC.

6

r6 FIGURE. 7-19A  Cascade diagram.

(T+t)/2 QHHT (e.g., HP steam)

Qhmin = |r4|

QHLT (e.g., LP steam)

1

d1 = r1+Qhmin 2

d2 = r2+Qhmin 3

Pinch point CU Enthalpy

d3 = r3+Qhmin

FIGURE 7-20B  Representation of the GCC with integrated pockets and optimal placement of utilities.

4

d4 = 0 (pinch location) 5

d5 = r5+Qhmin 6

Qcmin = r6+Qhmin FIGURE 7-19B  Revised cascade diagram.

when an enthalpy line is drawn from right to left, it corresponds to deficiency in heat in that interval. A heat surplus may be used to satisfy a heat residual below it. Therefore, the shaded regions (referred to as “pockets”)

shown in Fig. 7.20b are fully integrated by transferring heat from process hot streams to process cold streams. Then, we represent each utility based on its temperature. The adjusted temperature of a heating utility is given by Eq. 7.11a whereas that for a cooling utility is given by Eq. 7.11b. We start with the cheapest utility and maximize its use by filling the enthalpy gap (deficiency) at that level. Then, we move up for heating utilities and down for cooling utilities and continue to fill the enthalpy gaps by the cheapest utility at that level. Figure 7.20b is an illustration of this concept by screening low- and high-pressure steam where the low-pressure steam is cheaper ($/kJ) than the high-pressure steam. It is worth noting that the sum of the heating loads of the low- and high-pressure steams is equal to the minimum heating utility (the value of the top heat residual).

156

Sustainable Design Through Process Integration

Example 7-3  Using the GCC for utility selection (El-Halwagi, 2006) TABLE 7-5  Stream Data for Example 7.3

Stream

Flow Rate   Specific Heat MMBtu/hr, °F

Supply Temperature, °F

Target Temperature, °F

Enthalpy Change MMBtu/hr

H1

0.5

650

150

250.0

H2

2.0

550

500

100.0

C1

0.9

490

640

135.0

C2

1.5

360

490

195.0

Source: El-Halwagi (2006).

T

40 MM Btu/hr of VHP steam

t (T+t)/2

2.0

0.5

650

640

550

540

500

490

645

545

0.9

495 50 MM Btu/hr of HP steam 445 365

370

360

150

140

1.5

145

FIGURE 7-21  The temperature interval diagram for Example 7.3.  Source: El-Halwagi (2006). Qcmin = 90 50

90

1

50

125

2

50

45

125

195

65

110

3

–90 0 4 20

45

2

40 65

3

130 195 0

110

4

0

50

90

110 130

FIGURE 7-23  The GCC for Example 7.3.  Source: El-Halwagi (2006).

90

1

–40

110 MM Btu/hr of Cooling Utility

0 Qcmin = 110

Consider the stream data given in Table 7.5. Available for service are two heating utilities: a high-pressure (HP) steam and a very high-pressure (VHP) steam whose temperatures are 450°F and 660°F, respectively. The VHP steam is more expensive than the HP steam. Also available for service is a cooling utility whose temperature is 100°F. The minimum approach temperature is taken as 10°F. Figures 7.21 through 7.23 represent the temperature-interval diagram, cascade diagram, and the GCC. As can be seen from Fig. 7.22, the minimum heating requirement is 90 MM Btu/hr. To maximize the use of the HP steam, we represent the HP on the GCC (a horizontal line at 450  (10/2)  445°F). The deficit below this line is 50 MM Btu/hr. Therefore, the duty of the HP steam is 50 MM Btu/hr, and the rest of the heating requirement (40 MM Btu/hr) will be provided by the VHP steam.

Original Cascade Adding Heating Utility Diagram (with negative residulas) at the Highest Level

FIGURE 7-22  The cascade and revised cascade diagrams for Example 7.3.  Source: El-Halwagi (2006).

STREAM MATCHING AND THE SYNTHESIS OF HEAT-EXCHANGE NETWORKS This section presents a systematic method for the matching of hot and cold streams to synthesize a network of heat exchangers that satisfy the identified targets for minimum heating and cooling utilities (the minimum

operating cost “MOC”). It is worth recalling the analogy between MENs and HENs, including the matching rules for MENs described in Chapter 5. For HENs featuring minimum-utility usage, there is no heat flow across the pinch. Therefore, it is possible to decompose the synthesis task into two subproblems: one above the pinch and one below the pinch. The target for the minimum

157

CHAPTER 7   Heat Integration

number of heat exchangers satisfying the MOC is given by (Hohmann, 1971; Linnhoff et al., 1982): [7.12] U MOC

U MOC ,above pinch

tvout

Tuin

U MOC ,below pinch

Heat Exchanger

where [7.12b]

U MOC,above pinch N C,above pinch

N H,above pinch N i,above pinch

Tuout =T pinch

tv in =t pinch

and [7.12c]

Pinch

U MOC,below pinch N C,below pinch

N H,below pinch N i,below pinch .

where UMOC, above pinch is the number of MOC units above the pinch, NH,above pinch is the number of hot streams (including heating utilities) above the pinch, NC,above pinch is the number of cold streams (including cooling utilities) below the pinch, Ni,above pinch is the number of independent problems above the pinch, UMOC,below pinch is the number of MOC units below the pinch, NH,below pinch is the number of hot streams below the pinch, NC,below pinch is the number of cold streams below the pinch, and Ni,below pinch is the number of independent problems below the pinch. The number of independent problems (above or below the pinch) includes cases such as when a hot and a cold stream have exactly the same load and, therefore, only one heat exchanger is needed to match the two streams. To determine the specific matches satisfying these targets, the design is started at the pinch and moved away according to the following rules (Linnhoff and Hindmarsh, 1983):

STREAM POPULATION RULES FOR MATCHING Let us first consider the case above the pinch. In an MOC design, any heat exchanger immediately above the pinch will operate with the minimum temperature driving force ΔTmin (because the two composites touch at the pinch, then all pinch matches have the minimum driving force at the pinch). Therefore, for each pinch match, at least one cold stream (or branch) has to exist per each hot stream to be able to cool the hot stream down to the pinch temperature (on the hot scale). In other words, for an MOC design, the following inequality must apply at the hot end of the pinch (that is, immediately above the pinch): [7.13a]

FIGURE 7-24  A heat exchanger immediately above the pinch.

transfer of heat across the pinch, each cold stream immediately below the pinch will require the existence of at least one hot stream (or branch) at the pinch. Therefore, immediately below the pinch, the following criterion must be satisfied:

where Ncb is the number of cold streams or branches immediately below the pinch, and Nhb is the number of hot streams or branches immediately below the pinch. Splitting of one or more of the hot streams may be necessary to realize this inequality.

FLOW RATE*SPECIFIC HEAT RULES FOR MATCHING Consider the heat exchanger shown in Fig. 7.19. The cold end of this exchanger is immediately above the pinch. A heat balance around the exchanger can be written as: [7.14] FuC p,u (Tuin

T Pinch )

f v c p,v (t vout

t Pinch )

where the symbols for the inlet and outlet temperatures are shown on Fig. 7.24. At the pinch: [7.15]

T Pinch

t Pinch

∆T min

Substituting from Eq. 7.15 into Eq. 7.14, we get: [7.16]

N ha  N ca

where Nha is the number of hot streams or branches immediately above the pinch, and Nca is the number of cold streams or branches immediately above the pinch. If this inequality does not hold for the stream data, one or more of the cold streams will have to be split to maintain the branch(s) of the cold stream(s) at the pinch temperature at the cold inlet of the pinch exchangers. Conversely, immediately below the pinch, each cold stream must be heated to reach the pinch temperature (on the cold scale). To reach this temperature, there has to be at least one hot stream (or a branch of a hot stream) at the pinch. Because an MOC design does not permit the

N cb  N hb

[7.13b]

FuC p,u (Tuin t Pinch ∆T min ) f v c p,v (t vout t Pinch )

For the feasibility of heat transfer at the hot end of the exchanger, the following condition must apply to maintain a minimum temperature driving force: [7.17]

Tuin

t vout

∆T min

Combining Equations 7.16 and 7.17, we obtain the following inequality: FuC p,u (t vout ∆T min t Pinch f v c p,v (t vout t Pinch )

∆T min )

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Sustainable Design Through Process Integration

or

[7.19] f v c p,v ≤ FuC p,u Immediately below the pinch

[7.18] FuC p,u  f v c p,v Immediately above the pinch Inequality 7.18 indicates that a required feasibility condition for the match of a hot stream and a cold stream immediately above the pinch is that the product of the flow rate*specific heat for the hot stream (or a branch of a hot stream) must be less than or equal to that for the matched cold stream (or branch of cold stream). If this condition is not satisfied, splitting a hot stream is used to reduce the flow rate of the matched branch of the cold stream so as to meet the feasibility criterion. Conversely, immediately below the pinch, the following condition can be derived:

Example 7-4

Splitting of the cold stream can be used to satisfy this feasibility criterion. Matching the streams is started at the pinch (immediately above and immediately below). Once the pinch matches are identified, it generally becomes a simple task to complete the network design. Moreover, designers always have the freedom to violate these feasibility criteria at the expense of increasing the cost of heating and cooling utilities beyond the MOC requirement. When some of the heat exchangers already exist, retrofitting techniques can be used to include these units in the synthesis procedure (for example, Al-Thubaiti et al., 2008).

Network synthesis of a heat-exchanger network in a specialty chemical plant

Consider the specialty chemical processing facility shown in Fig. 7.25. The process has two adiabatic reactors. The intermediate product leaving the first reactor (C1) is heated from 450 K to 510 K before being fed to the second reactor. The gaseous stream leaving the second reactor (H1) at 520 K is cooled to 380 K and then sent to a disposal unit. The stream leaving the bottom of the second reactor is fed to a separation network. The product stream leaving the finishing, recovery, and separation network (H2) is cooled from 490 K to 460 K prior to sales. Table 7.6 gives the stream data. SOLUTION First, the minimum utility targets are identified through the algebraic approach. The TID, the cascade diagram, and the revised cascade diagram are shown by Figures 7.26, 7.27, and 7.28, respectively. Therefore, the minimum heating and cooling utilities are 15,000 and 11,000 kW, respectively. To synthesize the HEN that attains the identified utility targets, the problem is decomposed into two subproblems: one above the pinch and one below the

pinch. Figure 7.29 shows the streams above the pinch. The number of hot streams immediately above the pinch (H1 and H2) is greater than the number of cold streams immediately above the pinch (C1). Therefore, according to Inequality 7.13a, the cold stream C1 should be split into two portions: one to be matched with H1 and another to be matched with H2. There are numerous ways to split the two portions of C1 that satisfy Inequality 7.18. Figure 7.30 shows a particularly effective split where a portion of flow rate*specific heat of stream C1 is taken as 200 kW/K to match that of hot stream (H1) above the pinch. Hence, this portion and H1 above the pinch have the same heat load, which can be transferred in a single heat exchanger. The remaining flow rate*specific heat of stream C1 (400 kW/K) is matched to H2 above the pinch to exchange 9000 kW. The following representation will be used to illustrate the network structure graphically. Vertical arrows running at the left of the diagram represent hot streams. Temperatures are placed next to each arrow. A match between two streams is indicated by placing an ellipse on each of the streams and connecting

Solvent H1 520 K

Feed

Reactor I

C1 450 K

510 K

Reactor II

380 K

Scrubber

To Gas Disposal

Spent Solvent (to regeneration) By-products

Finishing, Recovery, and Separation System C2 300 K

H2 490 K

Product (to sales) 460K

350K Separation

Waste FIGURE 7-25  Simplified flow sheet for the specialty chemical processing facility. (Continued )

159

CHAPTER 7   Heat Integration

Example 7-4  Network synthesis of a heat-exchanger network in a specialty chemical plant (Continued) them by a line. Heat-transfer rates are noted in appropriate units (for example, kW) inside the ellipses. The pinch is represented by two horizontal dotted lines. When two streams are paired, the exchangeable rate of heat transfer is the lower of the two heat loads of the streams. For instance, the heat-exchange rate of H2 and C1 matched above the pinch are 300*(490  460)  9000 kW and 400* (480  450)  12,000 kW. Therefore, the exchangeable load between H2 and C1 is 9000 kW. The temperature of the C1 branch leaving the match with H2 is calculated through heat balance; that is,

0 6000

15,000

2

[7.20] 450 472.5 K

–12,000 18,000 –15,000

6000

Temperature of the C1 branch leaving the match with H2

18,000

1

9000 400

0

3 –9000

10,000

0

4 1000

The rest of the matches are similarly carried out, and Fig. 7.31 shows the results. There are no cold streams immediately below the pinch. Therefore, the matches are relatively simple. Matching H1 with C2 below the pinch entails transferring the lower of the two heat-transfer rates: 200*(460  380)  16,000 kW and 100*(350  300)  5000 kW. Hence, 5000 kW should be transferred from H1 to C2. The remaining load of H1 (16,000  5000  11,000 kW) is transferred to the cooling utility as shown by Fig. 7.32. Other configurations are also possible. For instance, H1 below the pinch can be split into two streams in parallel and matched with C2 and the cooling utility (compared to the serial structure shown by Fig. 7.32). It is also worth noting that the calculated heating and cooling utilities are consistent with the values determined from the targeting approach.

0

1000 0

FIGURE 7-27  The cascade diagram for the specialty chemical processing facility. min QHeating = 15,000kW

15,000

Hot Streams

1

4 5

520

510

490

480

460

450

430

420

380

370

360

350

330

Cold Streams

300

6000

10,000

18,000

1 3000 2

3

18,000

0 Thermal-Pinch Location 0 6000 0

4

C1

16,000 0

0

5 16,000

f2Cp2 = 100

6

F2Cp2 = 300

3

F1Cp1 = 200

2

H2

t

f1Cp1 = 600

H1

T

5000

6 –4000

6000

Interval

0

5

0

5

5000

C2

FIGURE 7-26  The TID for the specialty chemical processing facility.

min QCooling = 11,000kW

FIGURE 7-28  The revised cascade diagram for the specialty chemical processing facility. TABLE 7-6  Stream Data for the Specialty Chemical Process

Stream

Flow Rate   Specific Heat kW/K

Supply Temperature, K

Target Temperature, K

Enthalpy Change kW

H1

200

520

380

28,000

H2

300

490

460

9000

C1

600

450

510

36,000

C2

100

300

350

5000 (Continued )

160

Sustainable Design Through Process Integration

Example 7-4  Network synthesis of a heat-exchanger network in a specialty chemical plant (Continued) C1

H1

C1

HU

510 K f1Cp1=600

F2Cp2=300

F1Cp1=200

H2

510 K

12,000

472.5K

12,000

H2

490 K 9000

9000 fCp

450 K

=400

460 K

fCp

=200

460 K

C1

F2Cp2 =300

=200

F1Cp1

FIGURE 7-29  Examining the feasibility criteria above the pinch for the specialty chemical example. H1

15,000

C1

520 K Pinch

C1

15,000

H1

450K Pinch

FIGURE 7-31  Stream matching above the pinch for the specialty chemical example. Note: HU is heating utility. fCp=400

H1

Pinch

460K

5000

FIGURE 7-30  Hot stream splitting above the pinch for the specialty chemical example.

435K 11,000 380K

Pinch F2Cp2 = 100

F1Cp1 = 200

fCp=200

F2Cp2=300

F1Cp1=200

H2

420K

5000 C2

350K 11,000 CU

FIGURE 7-32  Stream matching below the pinch for the specialty chemical example. Note: CU is cooling utility.

TABLE 7-7  Stream Data for Problem 7.1

Stream

Flow Rate   Specific Heat (Btu/hr °F)

Supply Temperature (°F)

Target Temperature (°F)

Enthalpy Change (103 Btu/hr)

H1

1000

250

120

130

H2

4000

200

100

400

HU1

?

280

250

?

C1

3000

90

150

180

C2

6000

130

190

360

CU1

?

60

80

?

Source: Douglas (1988).

HOMEWORK PROBLEMS 7.1. A plant has two process hot streams (H1 and H2), two process cold streams (C1 and C2), a heating utility (HU1), and a cooling utility (CU1). The problem data are given in Table 7.7. A value of ΔTmin  10°F is used. Using graphical and algebraic techniques, determine the minimum heating and cooling requirements for the problem. Also, develop an HEN implementation matching the hot and the cold streams to achieve the minimum utility targets.

7.2. Consider a process that has two process hot streams (H1 and H2), two process cold streams (C1 and C2), a heating utility (HU1, which is a saturated vapor that loses its latent heat of condensation), and a cooling utility (CU1). The problem data are given in Table 7.8. The cost of the heating utility is $6/106 kJ added, and the cost of the coolant is $4/106 kJ. A value of ΔTmin    10 K is used. Determine the minimum heating and cooling requirements for the process and synthesize a network of heat exchangers that meets the targets.

CHAPTER 7   Heat Integration

161

TABLE 7-8  Stream Data for Problem 7.2

Stream

Flow Rate   Specific Heat, kW/°C

Supply Temperature, °C

Target Temperature, °C

H1

10.55

249

H2

  8.79

160

138 93

HU1

?

270

270

C1

  7.62

60

160

C2

  6.08

116

260

CU1

?

38

82

Source: Papoulias and Grossmann (1983).

Solvent H1 460 K

Feed

Reactor I

C1 420 K

490 K

Reactor II

350 K

Scrubber

Off-Gas (to gas treatment)

Spent Solvent (to regeneration) Byproducts H2 400 K

300 K Product (to sales)

Separation Network

C2 320 K

390 K

Flash Column

Wastewater

FIGURE 7-33  Simplified flow sheet for the chemical processing facility.  Source: El-Halwagi (2006).

7.3. Consider the chemical processing facility illustrated in Fig. 7.33 (El-Halwagi, 2006). The process has two adiabatic reactors. The intermediate product leaving the first reactor (C1) is heated from 420 K to 490 K before being fed to the second reactor. The off-gases leaving the reactor (H1) at 460 K are cooled to 350 K prior to being forwarded to the gas-treatment unit. The product leaving the bottom of the reactor is fed to a separation network. The product stream leaving the separation network (H2) is cooled from 400 K to 300 K prior to sales. A by-product stream (C2) is heated from 320 K to 390 K before being fed to a flash column. Stream data are given in Table 7.9. In the current operation, the heat exchange duties of H1, H2, C1, and C2 are fulfilled using the cooling and heating utilities. Therefore, the current usage of cooling and heating utilities are 83,000 and 56,000 kW, respectively. The objective of this problem is to identify the target for minimum heating and cooling utilities and to

synthesize a network of heat exchangers that achieves the utility targets. A value of ΔTmin  10 K is used. 7.4. A plant has one process hot stream (H1) and two process cold streams (C1 and C2). Two heating utilities (HU1 and HU2) are available for service, as well as a cooling utility. The two heating utilities are condensing steams whose costs are 5 and 7 ($/106 Btu), respectively. A minimum driving force of 10°F is required for any heat-exchange duty. Table 7.10 provides the data for the process. Determine the optimal usage of the two heating utilities and the cooling utility. Synthesize a network of minimum number of heat exchangers satisfying the minimum utility targets. 7.5. Consider the formic acid process shown by Fig. 7.34 (Tora and El-Halwagi, 2010). Methanol and carbon monoxide are reacted to produce methyl formate, which is later distilled. The bottom stream of the methyl formate column (C1) enters the reboiler where it is heated to create the boil-up vapor that is returned

162

Sustainable Design Through Process Integration

TABLE 7-9  Stream Data for the Chemical Process

Stream

Flow Rate   Specific Heat, kW/K

Supply Temperature, K

Target Temperature, K

Enthalpy Change, kW

H1

300

460

350

33,000

H2

500

400

300

50,000

C1

600

420

490

42,000

C2

200

320

390

14,000

Source: El-Halwagi (2006).

TABLE 7-10  Stream Data for the Hot and Cold Streams of Problem 7.4

Stream

Flow Rate   Specific Heat, Btu/°F . hr

Supply Temperature, °F

Target Temperature, °F

H1

20,000

300

100

HU1

?

300

300

HU2

?

500

500

C1

20,000

190

290

C2

40,000

190

390

CU1

?

30

40

H2 H1

Purge Gas Water Recycled Water

C2

Hydrolysis Reactor

Methyl Formate Column

Makeup Methanol and Catalyst

Carbonylation Reactor

Carbon Monoxide

Recycled Methyl Formate and Methanol H3

Recycled Methyl Formate and Methanol

H4

Recycle Column

Recycled Methanol and Catalyst

Flash Column

C1

H5

Formic Acid Column

C3

H6 C4 FIGURE 7-34  Formic acid process.  Source: Tora and El-Halwagi (2010).

Formic Acid

CHAPTER 7   Heat Integration

TABLE 7-11  Data for the Process Hot and Cold Streams for

the Formic Acid Process

Stream

Supply Temperature, K

Target Temperature, K

Rate of Enthalpy Change, MW

H1

338

333

5.3

H2

333

288

0.3

H3

330

288

1.4

H4

310

308

2.7

H5

393

308

4.3

H6

423

308

0.2

C1

368

370

5.8

C2

333

393

0.8

C3

368

383

2.9

C4

423

430

4.7

Source: Tora and El-Halwagi (2010).

to the column. The vapor product (H1) from the top of the methyl formate column is cooled and partially condensed. The remaining vapor (H2) is further condensed using a refrigerant in a partial condenser. The noncondensed gases are purged and incinerated. Methyl formate is heated (C2) then hydrolyzed to produce formic acid and regenerate methanol. A flash column is used to recover methyl formate and methanol, which are cooled (H3) and recycled to the hydrolysis reactor. The liquid stream leaving the bottom of the flash unit is separate in a distillation column for further recovery of methyl formate and methanol. The overhead condenser requires cooling (H4), and the reboiler requires heating (C3). An additional distillation column is used to recover formic acid. The overhead condenser requires cooling (H5), and the reboiler requires heating (C4). The concentrated formic acid (H6) is cooled prior to storage. The stream data are given in Table 7.11. Two cooling utilities are available for service. Cooling water can cool the hot streams down to 308 K and a refrigeration system can be used to cool the hot streams to 288 K. A minimum driving force (ΔTmin) value of 10 K is required. a. Using the GCC, determine the optimal targets for the two cooling utilities and for a heating utility. b. Synthesize a network of heat exchangers that meets the utility targets.

NOMENCLATURE CP,u cP,v f F HCv,z HHu,z MOC NC

specific heat of hot stream u [kJ/(kg K)] specific heat of cold stream v [kJ/(kg K)] flow rate of cold stream (kg/s) flow rate of hot stream (kg/s) cold load in interval z hot load in interval z minimum operating cost number of process cold streams

163

Nca number of cold streams immediately above the pinch Ncb number of cold streams immediately below the pinch NCU number of cooling utilities NH number of process hot streams Nha number of hot streams immediately above the pinch Nhb number of hot streams immediately below the pinch NHU number of process cold streams Qmin minimum cooling utility Cooling Qmin minimum heating utility Heating rz residual heat leaving interval z t temperature of cold stream (K) tvs supply temperature of cold stream v (K) tvt target temperature of cold stream v (K) Tus supply temperature of hot stream u (K) Tut target temperature of hot stream u (K) T temperature of hot stream (K) u index for hot streams UMOC minimum number of heat-exchange units satisfying the minimum operating cost v index for cold streams z temperature interval

GREEK LETTER ΔTmin

minimum approach temperature (K)

REFERENCES Al-Thubaiti M, Al-Azri N, El-Halwagi M: Optimize heat transfer networks: an innovative method applies heat integration to cost effectively retrofit bottlenecks in utility systems, Hydrocarbon Process:109–115, March 2008. Douglas JM: Conceptual design of chemical processes, New York, McGraw Hill, 1988. El-Halwagi MM: Process integration, Amsterdam, Academic Press/Elsevier, 2006. Foo DCY, El-Halwagi MM, Tan RR, editors: Recent advances in sustainable process design and optimization, Series on Advances in Process Systems Engineering, World Scientific Publishing Company, 2011. Furman KC, Sahinidis NV: A critical review and annotated bibliography for heat exchanger network synthesis in the 20th century, Ind Eng Chem Res 41(10):2335–2370, 2002. Gundersen T, Naess L: The synthesis of cost optimal heat exchanger networks: an industrial review of the state of the art, Comp Chem Eng 12(6):503–530, 1988. Hohmann EC: Optimum networks for heat exchange, PhD Thesis, California, Los Angeles, University of Southern, 1971. Kemp I: Pinch analysis and process integration: a user guide on process integration for the efficient use of energy, ed 2, Butterworth-Heinemann, 2009. Linnhoff B: Pinch analysis: a state of the art overview, Trans Inst Chem Eng 71(A5):503–522, 1993. Linnhoff B, Flower JR: Synthesis of heat exchanger networks: I. Systematic generation of energy optimal networks, AIChE J 24(4):633–642, 1978. Linnhoff B, Hindmarsh E: The pinch design method for heat exchanger networks, Chem Eng Sci 38(5):745–763, 1983. Linnhoff B, Townsend DW, Boland D, Hewitt GF, Thomas BEA, Guy AR, Marsland RH: A user guide on process integration for the efficient use of energy, UK, IChemE, 1982. Majozi T: Batch chemical process integration: analysis, synthesis, and optimization, Heidelberg, Springer, 2010. Papoulias SA, Grossmann IE: A structural optimization approach in process synthesis. II. Heat recovery networks, Comput Chem Eng 7(6):707–721, 1983. Rossiter AP: Improve energy efficiency via heat integration, Chem Eng Prog 106(12):33–42, 2010. Shenoy UV: Heat exchange network synthesis: process optimization by energy and resource analysis, Houston, Texas, Gulf Publ. Co, 1995. Smith R: Chemical process design and integration, New York, Wiley, 2005. Tora EA, El-Halwagi MM: Integration of solar energy into absorption refrigerators and industrial processes, Chem Eng Technol 33(9):1495–1505, 2010. Umeda T, Itoh J, Shiroko K: A thermodynamic approach to the synthesis of heat integration systems in chemical processes, Comput Chem Eng 3:273–282, 1979.