Introducing P rocess I ntegration for E nvironmental
C ontrol in E ngineering Curricula.
P.I.E.C.E.
Miguel Velazquez
Created at:
Texas A&M University
College Station, TX. January-May 2005

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MODULE 12. NETWORK PINCH ANALYSIS
PURPOSE
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MODULE 12. NETWORK PINCH ANALYSIS
PRE-REQUISITES
In order to achieve a better understanding of the contents of this Module, the student or reader are required to possess a background of specific areas of chemical engineering such as classic thermodynamic, mass transfer and heat transfer. These subjects are part of basic science of chemical engineering and must be contained into its curricula.
A Process Introduction Module review prior to this Module is recommended too. In such, an overview of Pinch Technology and Heat Recovery Network can be found to help you begin with the Network Pinch Analysis subject.
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MODULE 12. NETWORK PINCH ANALYSIS
AUDIENCE TARGET.
The Network Pinch Module is addressed to last year bachelor degree and MSc students in chemical engineering. Particularly it will be useful for practicing engineers and even teachers of plant design and pollution prevention courses.
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MODULE 12. NETWORK PINCH ANALYSIS
STRUCTURE:
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MODULE 12. NETWORK PINCH ANALYSIS
TIER I: FUNDAMENTALS
1.
2.
3.
4.
5.
6.
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
Heat
Recovery
Energy requirements
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MODULE 12. NETWORK PINCH ANALYSIS
1
2
4
6
Cold water
2 5 7
Steam
320
H
528.0
H
412.8
H
341.1
H
C C C
451.4 427.4 505.6
H
Heater
C
Cooler Heat exchanger
1
2
4
6
Cold water
7
1
5
2
341.1
Hot Stream
3
Steam
3
86.3
6
217.5
16.2
5
22.4
4
412.8
H
Cold Stream a) Traditional design:
Cost operating 250,838 $/year
Cost capital 4,937 $/year b) Technology Pinch approach:
Cost operating 24,077.00 $/year
Cost capital 4,180.00 $/year
Fig. 1.1 (a) The non-integrated solution, (b) The optimally integrated solution Reference.
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MODULE 12. NETWORK PINCH ANALYSIS
In addition to energy conservation studies, Pinch Technology enables process engineers to achieve the following general process improvements:
Update or Modify Process Flow Diagram : Pinch quantifies the savings available by changing the process itself. It shows where process change reduce the overall energy target, not just local energy consummation.
Conduct Process Simulation Studies : Pinch replace the old energy studies with information that can be easily updating using simulation. Such simulation studies can help avoid unnecessary capital costs by identifying energy savings with a smaller investment before the projects are implemented.
Set Practical targets: By taking in account practical constrains (difficult fluids, layout, safety, etc.), theoretical targets are modified so that they can be realistically achieved. Comparing practical with theoretical targets quantifies opportunities “lost” by constraints - a vital insight for long term development.
De-bottlenecking: Pinch analysis when specifically applied to debottlenecking studies, can lead to the following benefits compared to a conventional revamp:
– Reduction in capital costs.
– Decrease in specific energy demand giving a more competitive production facilities.
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MODULE 12. NETWORK PINCH ANALYSIS
2.
3.
4.
1.

MIN
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MODULE 12. NETWORK PINCH ANALYSIS
1 Identification of the hot, cold and utility streams in the process.
Hot streams : are those that must be cooled or are available to be cooled (T out
< T in
).
T in
T out
H1
Cold streams : are those that must be heated (T out
> T in
).
T in
T out
C1
Utility streams: are used to heat or cool process stream, when heat exchange between process stream is not practical or economic. A number of different hot utilities (steam, hot water, flue gas, etc) and cold utilities (cooling water, air, refrigerant, etc.) are used in industry.
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MODULE 12. NETWORK PINCH ANALYSIS
2 Thermal data extraction for process and utility stream.
For each hot, cold and utility stream identified, the following thermal data is extracted for the process material and heat balance flow sheet:
Supply temperature T S , the temperature which the stream is available.
Target temperature T T , the temperature the stream must be taken to.
Heat capacity flow rate (CP), the product of flow rate and specific heat.
Enthalpy change H, H = CP(T S - T T )
Stream
Number
1
2
3
4
Stream name
Feed
Reactor out
Product
Recycle
Supply
Temperature
( o
C)
Target
Temperature
( o
C)
60 205
Heat
Capacity
Flow Rate
(kW/ o
C)
20
270
220
160
160
70
210
18
35
50
Enthalpy
Change
(kW)
2900
1980
5250
2500
Table 1.1 Typical Stream Data
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MODULE 12. NETWORK PINCH ANALYSIS
3 Selection of Initial

T
MIN value.
The design of any heat transfer equipment must always adhere to the second law of thermodynamics that prohibits any temperature crossover between the hot and the cold stream I.e. a minimum heat transfer driving force must always be allowed for a feasible heat transfer design.
Thus the temperature of the hot and cold stream at the any point in the exchanger must always have a minimum temperature difference (

T
MIN
). This

T
MIN value represents the bottleneck in the heat recovery.
In mathematical terms, at any point in the exchanger
(1.1)
Hot stream temperature (T
H
) - Cold stream temperature (T
C
) =

T
MIN
The value of

T
MIN is determined by the overall heat transfer coefficient (U) and the geometry of the exchanger. In a network design, the type of heat exchanger to be used at the pinch will determine the practical

T
MIN for the network.
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MODULE 12. NETWORK PINCH ANALYSIS
For a given value of heat transfer load (Q) the selection of

T
MIN implications for both capital and energy costs.
values has

T
MIN
Area requirements rise
A few values of based Linnhoff March’s application experience are tabulated below for shell and tube heat exchangers.
No Industrial Sector
1
2
3
4
Oil Refining
Petrochemical
Chemical
Low Temperature
Process
Experience

Tmin values
20 – 40 o
C
10 – 20 o
C
10 – 20 o
C
3 – 5 o
C
Table 1.2 Typical

Tmin values .
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MODULE 12. NETWORK PINCH ANALYSIS
4 Construction of Composite Curves and Grand Composite Curve.
Composite Curves
Composite Curves consist of temperature (T) - Enthalpy (H) profiles of heat availability in the process (the Hot Composite Curve) and heat demands in the process (the Cold Composite Curve) together in a graphical representation.
In general any stream with a constant heat capacity (CP) value is represented on a diagram by a straight line running from stream supply temperature to stream target temperature. When there are a number of hot and cold composite curves simply involves the addition of the enthalpy changes of the stream in the respective temperature intervals.
An example of hot composite curves is shown in Fig. 1.2
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T
MODULE 12. NETWORK PINCH ANALYSIS
T
1000 1000
3000
1000
3000
1000 4000 1000
H H
Fig. 1.2 Temperature - Enthalpy relation used to construct Composite Curves.
A complete hot or cold composite curves consists of a series of connected straight lines, each change in slope represents a change in overall hot stream heat capacity flow rate
(CP).
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MODULE 12. NETWORK PINCH ANALYSIS
Combined Composite Curves.
Combined Composite Curves are used to predict targets for;
– Minimum energy (both hot and cold utility) required.
– Minimum network area required, and
– Minimum number of exchangers units required.
For heat exchange to occur from the hot stream to the cold stream, the hot stream cooling curve must lie above the cold stream-heating curve.
Because of the “kinked” nature of the composite curves, they approach each other most closely at one point defined as the minimum approach temperature
(

T
MIN
).

T
MIN can be measured directly from the T-H profiles as being the minimum vertical difference between the hot and cold curves.
This point of minimum temperature difference represents a bottleneck in heat recovery and is commonly referred to as the “Pinch”.
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MODULE 12. NETWORK PINCH ANALYSIS

T min and pinch Point.
The

Tmin values determine how closely the hot and cold composite curves can be “pinched” (or “squeezed) without violating the second law of Thermodynamics
(none of the heat exchangers can have a temperature crossover).
Q
H, MIN
T
“PINCH”

T
MIN
Q
C,MIN
H
Fig. 1.3 Energy targets and “the pinch” with Composite Curves.
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MODULE 12. NETWORK PINCH ANALYSIS
Hot Utilities
Q
H, MIN
Hot Composite Curve
PINCH

T
MIN
Process to process
Heat Recovery Potential
Cold Composite Curve
Q
C, MIN
Cold Utilities
Enthalpy
Fig. 1.4 Combined Composite Curves.
At a particular

T
MIN value, the overlap shows the maximum possible scope for heat recovery within the process. The hot end and cold end overshoots indicate minimum hot utility requirement (Q
H,MIN
(Q
C,MIN
), of the process for the chosen

T
) and minimum cold utility requirement
MIN
.
Thus, the energy requirement for a process is supplied via process to process heat exchange and/or exchange with several utility levels (steam levels, refrigeration levels, hot oil circuit, furnace flue gas, etc.)
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MODULE 12. NETWORK PINCH ANALYSIS
Problem Table Algorithm for minimum utility calculations .
Graphical constructions are not the most convenient means of determining energy needs. A numerical approach called “Problem Table Algorithm” PTA was developed by Linnhoff & Flower (1978) as a means of determining the utility needs of a process and the location of the process Pinch. The PTA lends itself to hand calculations of the energy targets.
For the problem data from Table 1.3 (Grid representation is shown in Fig. 1.8) streams are shown in a schematic representation with a vertical temperature scale. Temperature interval boundaries are superimposed.
The interval boundary temperatures are set at 1/2

T
MIN below hot stream temperatures and 1/2

T
MIN above
( 5 o C in this example) cold stream temperatures.
So for example in interval number 2 in Fig. 1.4, streams 2 and 4 (the hot streams) run from 150 o C to 145 o C, and stream 3 (the cold stream) from 135 o C to 140 o C.
Setting up the intervals in this way guarantees that full heat interchange within any interval is possible. Hence, each interval will have either a net surplus or net deficit of heat as dictated by enthalpy balance, but never both . This is shown in
Fig. 1.5.
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MODULE 12. NETWORK PINCH ANALYSIS
Stream
No.
And Type
(1) Cold
CP
(kW/ o
C)
2
(2) Hot
(3) Cold
3
4
(4) Hot 1.5
T
S
( o
C)
20
170
80
150
T
T
( o
C)
135
60
140
30
Table 1.3 Data for PTA example.
165 o C
1
145 o C
2
140 o C
85 o C
3
4
55 o C
5
25 o C
140
135
3
80
135
80
50
4
150
2
170
150
145
90
145
90
60
60
30
1
20
Fig. 1.4 Grid representation of hot and cold streams.
Knowing the stream population in each interval (from Fig. 1.8), enthalpy balances can easily be calculated for each according to:
(1.2)

H i
= (T i
- T i + 1
)(

CP
C
-

CP
H
)
I for any interval i .
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MODULE 12. NETWORK PINCH ANALYSIS
INTERVAL
No. i
T i
– T i +1
( o
C)

CP
Cold
-

CP
Hot
(kW/
o
C)

H
I
(kW)
SURPLUS
OR DEFICIT
T
1
= 165 o C
T
2
= 145 o C
1 20 - 3.0
- 60 SURPLUS
2 5 - 0.5
- 2.5
SURPLUS
T
3
= 140 o C
3 55 + 1.5
+ 82.5
DEFICIT
T
4
= 85 o C
4 30 - 2.5
- 75 SURPLUS
T
5
= 55 o C
5 30 + 0.5
+ 15 DEFICIT
T
6
= 25 o C
Fig. 1.5 Example for Table Problem Algorithm.
The last column in Fig. 1.5 indicates whether an interval is in heat surplus or heat deficit. It would therefore be possible to produce a feasible network design based on the assumption that all “surplus” intervals rejected heat to cold utility , and all “deficit” intervals took heat from hot utility. However, this would not be very sensible because it would involve rejecting and accepting heat at inappropriate temperatures.
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MODULE 12. NETWORK PINCH ANALYSIS
We now, however, exploit a key feature of the temperature intervals Namely, any heat available in interval i is hot enough to supply any duty in interval i +1.
This is shown in
Figure 1.6 (a), where interval 1 and 2 are used as an illustration. Instead of sending the
60 kW of surplus heat from interval 1 into cold utility, it can be sent down into interval 2.
It is therefore possible to set up a heat “cascade” as shown in the Figure 1.6 (b).
165
145
140
85
O
O
O
O c c c c
1
2
3
4
FROM HOT UTILITY
0 Kw

H = - 60 kW
60 Kw

H = - 2.5 kW
62.5 Kw

H = + 82.5 kW

H = -75 kW
- 20 kW
Q
H,MIN
55 O c
25 O c
5

55 Kw
H = + 15 kW
40 Kw
TO COLD UTILITY
(a) INFEASIBLE
1
2
FROM HOT UTILITY
20 Kw

H = - 60 kW
80 Kw

H = - 2.5 kW
3
4
5
82.5 Kw

H = + 82.5 kW
0 Kw

H = -75 kW
75 Kw

H = + 15 kW
Q
C,MIN
60 Kw
TO COLD UTILITY
(b) PINCH, Q
,H, MIN
, Q
C, MIN
Q
H,MIN and
Q
C,MIN
?
Click Here
Fig. 1.6 The heat cascade principle target prediction by “problem table” analysis.
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MODULE 12. NETWORK PINCH ANALYSIS
1
2
FROM HOT UTILITY
20 Kw

H = - 60 kW
80 Kw

H = - 2.5 kW
3
4
5
Determining Q
H,MIN
,Q
C,MIN and Pinch Point from heat “cascade”.
82.5 Kw

H = + 82.5 kW
0 Kw

H = -75 kW
75 Kw

H = + 15 kW
60 Kw
TO COLD UTILITY
Fig. 1.6 (b) (Repeat)
PINCH, Q
,H, MIN
, Q
C, MIN
Assuming that not heat is supplied to the hottest interval (1) from hot utility, then the surplus of 60 kW or surplus heat from interval 1 is cascaded into interval 2 . There it joins the 2.5 kW surplus from interval 2, making 62.5 kW to cascade into interval 3.
Interval 3 has a 82,5 kW deficit, hence after accepting the 62.5 kW it van be regarded as passing on a 20 kW deficit to interval 4.
Interval 4 has a 75 kW surplus and so passes on a 55 kW surplus to interval 5.
Finally, the 15 kW deficit in interval 5 means that 40 kW is the final cascaded energy to cold utility. This in fact is the net enthalpy balance on the whole problem.
Looking at the heat flows between intervals clearly the negative flow of 20 kW between intervals 3 and 4 is thermodynamically infeasible. To make this feasible ( I.e.
equal to zero), 20 kW of heat must be added from hot utility as shown in Figure 1.10 (b), and cascaded right through the system.
The net result of this operation is that the minimum utilities requirements have been predicted, i .e.
20 kW hot and 60 kW cold.
Further, the position of the pinch has been located. This is at the
85 0 C interval boundary temperature w here the heat flow is zero.
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MODULE 12. NETWORK PINCH ANALYSIS
Grand Composite Curve (GCC).
In selecting utilities to be used, determining utility temperatures, and deciding on utility requirements, the composite curves and PTA are not particularly useful.
The introduction of a new tool, the grand Composite Curve (GCC), was introduced in 1982 by Itoh, Shiroko and Umeda. The GCC (Figure 1.7) shows the variation of heat supply and demand within the process. Using this diagram the designer can find which utilities are to be used. The designer’s aim is to maximize the use of cheaper utility levels and minimize the use of expensive utility levels. Low-pressure steam and cooling water are preferred instead of high-pressure steam and refrigeration, respectively.
The information required for the construction of the GCC comes directly from the
Table Problem Algorithm. The method involves shifting (along the temperature
[y] axis) of the hot composite curve down by 1/2

T
MIN and that of cold composite curve up by 1/2

T
MIN
. The vertical axis on the shifted composite curves shows process interval temperature. In others words, the curves are shifted by subtracting part of the allowed temperature approach from the hot stream temperatures and adding the remaining part of the allowed temperature approach to the cold stream temperatures.
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MODULE 12. NETWORK PINCH ANALYSIS
SHIFTED
COMPOSITE CURVE
Internal Temp. = Actual
Temp. ± 1/2 
T min
+ : Cold stream
- : Hot stream
Q
H,MIN
H2
H1
GCC
T
H
1
T
H
2
T
Pinch
T
C
2
C2
Q
C,MIN
C1
T
C
1
Enthalpy
Fig. 1.7 Grand Composite Curve.
Figure 1.7 shows that it is not necessary to supply the hot utility at the top temperature level. The GCC indicates that we can supply hot utility over two temperature levels T
H
1
(HP steam) and T
H
2 (LP steam). Recall that, when placing utilities in the GCC, intervals, and not actual utility temperatures, should be used. The total minimum hot utility requirement remains the same: Q
H,MIN
T
H
2 and T
= H1 + H2. Similarly, Q
C,MIN =
C1 + C2. The points
C
2 where the H2 and C2 levels touch the GCC are called the “Utility Pinches”.
The shaded green pockets represents the process-to-process heat exchange.
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MODULE 12. NETWORK PINCH ANALYSIS
Composite curves give conceptual understanding of how energy targets can be obtained.
The Problem Table gives the same results (including the “Pinch” location) more easily.
Energy targeting is a powerful design and “process integration” aid.
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5.
6.
7.
8.

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MODULE 12. NETWORK PINCH ANALYSIS
5. Estimation of minimum energy costs.
Once the

T
MIN is chosen, minimum hot and cold utility requirements can be evaluated from the composite curves. The GCC provides information regarding the utility levels selected to meet Q
H,MIN and Q
C,MIN requirements.
If he unit cost of each utility is known, the total energy cost can be calculated using the energy equation given below
(1.3)
TOTAL ENERGY COST =

Q
U
·C
U where Q
U
C
U
= Duty of utility U, kW
= Unit Cost of utility U, $/kW, year
U = Total Number of utilities used.
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MODULE 12. NETWORK PINCH ANALYSIS
6 Estimation of Heat Exchanger Network (HEN) Capital Cost Target.
The capital cost of a heat exchanger network is dependent upon three factors:
1
2
3 the number of exchanger the overall network area the distribution of area between the exchangers
Pinch analysis enable targets for the overall heat transfer area and minimum number units of a heat exchanger network (HEN) to be predicted prior to detailed design. It is assumed that the area is evenly distributed between the units. The area distribution cannot be predicted ahead of design.
Area targeting
The calculation of surface area for a single counter-current heat exchanger requires the knowledge of the temperatures of the stream in and out (T LM I.e.
Log Mean Temperature Difference or LMTD), overall heat transfer coefficient
(U-value), and total heat transferred (Q). The area is given by the relation
Area = Q / U x T
LM
(1.4)
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MODULE 12. NETWORK PINCH ANALYSIS
The composite curves can be divided into a set of adjoining enthalpy intervals such that within each interval , the hot and cold composite do not change slope. Here the heat exchange is assumed to be “vertical” (pure counter-current heat exchange). The hot streams in any enthalpy interval, at any point, exchanges heat with the cold streams at the temperature vertically below it.
The total area of the HEN ( A
MIN
) is given by the equation following
HEN AREA
MIN
= A
1
+ A
2
+ A
3
+ ……+ A i
=

[ (1/

T
LM
)
 q j /h j ] (1.5) where i denotes the i th enthalpy and interval j i j j
LM
LMTD in the i th interval, and A
1
+ A
2
+ A
3
+ ……+ A i denotes is shown in the Figure 1.8
T Enthalpy
Intervals A
1
A
2
A
3
A
4
A
5
Fig. 1. 8 HEN Area
MIN composite curves .
estimation from
H
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MODULE 12. NETWORK PINCH ANALYSIS
The actual HEN Total Area required is generally within 10% of the area target as calculated by Eq, (1.5). With inclusion of temperature correction factors area targeting can be extended to non counter-current heat exchange as well.
Number of Units targeting.
For the minimum number of heat exchanger units ( N
MIN
) required for MER
( M inimum E nergy R equirements or M aximum E nergy R ecovery), the HEN can be evaluated prior to HEN design by using a simplified form of Euler’s graph theorem. In designing for the minimum energy requirement (MER), not heat transfer is allowed across the Pinch and so a realistic target for the minimum number of units ( N
MIN MER
) is the sum of the targets evaluated both above and below the pinch separately.
(1.6)
N
MIN, MER
= [N h
+ N
C
+ N
U
- 1]
AP
+ [N h
+ N
C
+ N
U
- 1]
BP
.
where
N
H
= Number of hot streams
N
C
= Number of cold streams
N
U
= Number of utility streams
AP / BP
: Above Pinch / Below Pinch
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MODULE 12. NETWORK PINCH ANALYSIS
HEN total capital cost targeting
.
The target for the minimum surface area (A
MIN
) and the number of units (N
MIN
) can be combined together with the heat exchanger cost law to determine the targets for HEN capital cost ( C
HEN
). The capital cost is annualized using an annualization factor that takes into account interest payments on borrowed capital. The equation used for calculation the total capital cost and exchanger cost law is given in equation 1.6.
C($)
HEN
= [N
MIN
{a + b(A
MIN
/ N
MIN
) C }]
AP
+ [N
MIN
{a + b(A
MIN
/ N
MIN
) C }]
BP
(1.7) where a,b and c are constants in exchanger cost law
Exchanger cost ($) = a + b (Area) c
For the Exchanger Cost Equation shown above, typical values for a carbon steel shell and tube exchanger would be: a = 16,000, b = 3,200 and c = 0.7 . The installed cost can be considered to be 3.5 times the purchased cost given by the Exchanger Cost equation.
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MODULE 12. NETWORK PINCH ANALYSIS
Total Cost targeting.
Used to determine the optimum level of heat recovery or the optimum

T
MIN value, by balancing energy and capital costs. Using this method it is possible to obtain an accurate estimate (within 10 - 15 %) of overall heat recovery system costs without having to design the system. The essence of the pinch approach is the speed of economic evaluation.
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MODULE 12. NETWORK PINCH ANALYSIS
7. Estimation of Optimum

T
MIN value by Energy-Capital Trade Off.
To arrive at an optimum value, the total annual cost (the sum of total annual energy and capital cost) is plotted at varying

T
MIN values (Figure 1.9). Three key
1
2
3 observation can be made from Figure 1.9:
An increase in

T values result in higher energy cost and lower capital costs.
MIN
An decrease in

T
MIN values result in lower energy costs and higher capital costs.
An optimum

T
MIN costs is minimized.
exists where the total annual cost of energy and capital
By systematically varying the temperature approach we can determine the optimum heat recovery or the

T min for the process
Total Cost
Optimum

T
MIN
Capital Cost

T
MIN
Fig. 1.9 Energy-capital cost trade off (optimum

T
MIN
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MODULE 12. NETWORK PINCH ANALYSIS
8. Estimation of Practical Targets for HEN Design.
The heat exchanger network designed on the basis of the estimated optimum

T
MIN value is not always the most appropriate design. A very small

T
MIN value, perhaps 8 o C, can lead to a very complicated network design with a large total area due to low driving forces. The designer in practice, select a higher value (15 o C) and calculates the marginal increase in utility duties and area requirements. If the marginal cost increase is small, the higher value of

T
MIN value is selected as the practical pinch point for the HEN design.
Recognizing the significance of the pinch temperature allows energy targets to be realized by design of appropriate heat recovery network.
So what is the significance of the pinch temperature?
The pinch divide the process into two separate systems each of which is in enthalpy balance with the utility. The pinch point is unique for each process.
Above the pinch, only the hot utility is required. Below the pinch, only the cold utility is required. Hence, for an optimum deign, no heat should be transferred across the pinch.
This is known as the key concept in Pinch Technology.
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MODULE 12. NETWORK PINCH ANALYSIS
The decomposition of the problem at the pinch turns out to be very useful when it comes to network design (Linnhoff and Hindmarsh, 1982).
T
Zero Flow in Pinch
Q
H,MIN
T
Heat Sink
Heat Source  T
MIN
Q
H,MIN
Q
C,MIN
H
Fig. 1.10 The Pinch decomposition into two regions.
Q
C,MIN
H
Fig. 1.11 The heat flow across the pinch is zero.
To summarize, pinch technology gives three rules that form the basis for practical network design:
1
2
3
No external heating below the pinch.
No external cooling above the pinch.
No heat transfer across the pinch.
Violations of any of the above rules results in higher energy requirements than the minimum requirements theoretically possible.
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MODULE 12. NETWORK PINCH ANALYSIS
9. Design of Heat Exchanger Network .
9.1 Network Representation.
The graphical method of representing flow streams and heat recovery matches is called “Grid Diagram”.
In order to describe this graphical method consider the simple example below.
The heat exchanger network from the flowsheet in Figure 1.12 can be represented in the “grid” form at Figure 1.13 introduced by Linnhoff and Flower (1982)
Feed
25 o C
30 o C
1
140 o C
120 o C
100 o C
Steam
200 o C
200 o C
170 o C
100 o C
30 o C
Cooling
Sep. Drum
Crude Product
Fig. 1.12 Heat exchanger network in the flowsheet representation.
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MODULE 12. NETWORK PINCH ANALYSIS
REACTOR
EFLUENT
170 o C
1
120 o C
2
100 o C
C
30 o C
200 o C
H
140 o C
1
200 o C
H
100 o C
2
25 o C FEED
30 o C RECYCLE
Fig. 1.13 Heat exchanger network in the Grid representation.
The advantage of this representation is that the heat exchange matches 1 and 2
(each represented by two circles joined by a vertical line in the grid) can be placed in either order without redrawing the stream system.
In flowsheet representation, if it were desired to match recycle against the hottest part of the reactor effluent, the stream layout would have to be redrawn. Also, the grid represent the countercurrent nature of the heat exchange, making it easier to check exchanger temperature feasibility.
Finally the pinch is easily represented in the grid, whereas it cannot be represented on the flowsheet.
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MODULE 12. NETWORK PINCH ANALYSIS
9.2 Design for the Best Energy Recovery
The data in Table 1.3 were analyzed by the Problem Table method in sub-section
4.3 with the result that the minimum utility requirements are 20 kW hot and 60 kW cold. The pinch occurs where the hot streams are at 90 o C and the cold at
80 o C. The grid structure for the problem is shown in Figure 1.14, with the pinch represented as a vertical dotted line.
Above the pinch : the hot streams are cooled from their supply temperatures to their pinch temperature, and the cold streams heated from their pinch temperatures to their target temperatures.
Below the pinch : the position is reversed with hot streams being cooled from the pinch to target temperatures and cold streams being heated from supply to pinch temperature.
2
170 o C
150 o C
4
135 o C
140 o C
90 o C
90 o C
80 o C
90 o C
90 o C
80 o C
80 o C
Q
H,MIN
= 20 kW PINCH Q
C,MIN
= 60 kW
Fig. 1.14 Example problem stream data, showing Pinch.
60 o C
CP (kW/ o C)
3.0
30 o C
1.5
20 o C
1 2.0
3 4.0
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MODULE 12. NETWORK PINCH ANALYSIS
Above the pinch all streams must be brought to pinch temperature by interchange against cold streams. We must therefore start the design at the pinch, finding matches that fulfil this condition.
DESIGN ABOVE THE PINCH.
In this example, above the pinch there are two hot streams at pinch temperature, therefore requiring two “pinch matches”. In Figure 1.15 a match between streams
2 and 1 is shown, with a T/H plot of the match shown in inset. (Note that the stream directions have been reversed so as to mirror the directions in the grid representation).
2
CP (kW/ o C)
3.0
T
4
1.5
 T
MIN
1 2.0
3 4.0
Q
H,MIN
= 20 kW
Infeasible !!
Fig. 1.15 Example problem hot end design. Infeasible.
H
Because the CP of stream 2 is grater than that of stream 1, as soon as any load is placed on the match, the

T in the exchanger becomes less than

T
MIN at its hot end.
The exchanger is clearly infeasible and therefore we must look for another match.
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MODULE 12. NETWORK PINCH ANALYSIS
In Figure 1.16, streams 2 and 3 are matched, and now the relative gradients of the T/ H plots mean that putting load on the exchanger opens up the

T.
2
CP (kW/ o C)
3.0
T
1.5
T
4
1 2.0
3 4.0
 T
MIN
H
 T
MIN
H
Q
H,MIN
= 20 kW
Fig. 1.16 Example problem hot end design. Acceptable.
This match is therefore acceptable. If it is put in as a firm design decision, then stream 4 must be brought to pinch temperature by matching against stream 1. Looking at the relatives sizes of the CPs for streams 4 and 1, the match is feasible (CP
4
< CP
1
).
There are no more streams requiring cooling to pinch temperature and so we have found a feasible pinch design because only two pinch matches are required.
In design immediately above the pinch, it is required to meet the criterion:
CP
HOT

CP
COLD
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MODULE 12. NETWORK PINCH ANALYSIS
Maximize Exchanger Loads.
Having found a feasible pinch design it is necessary to decide on the match heat loads.
The recommendation is “ maximize the heat load so as to completely satisfy one of the streams”.
This ensures minimum number of units employed.
In the example problem, since stream 2 above the pinch requires 240 kW of cooling and stream 3 above the pinch requires 240 kW of heating, co-incidentally the 2/3 match is capable of satisfying both streams.
However, the 4/1 match can only satisfy stream 4, having a load of 90 kW and therefore heating up stream 1 only as far as
125 o C. Since, both hot streams have now have been completely exhausted by these two design steps, stream 1 must be heated from 125 o C to its target temperature of 135 o C by external hot utility as shown in Figure
1. 17.
2
4
170
150 o o
C
C
90 o C
CP (kW/ o C)
3.0
90 o C
1.5
135 o C
140 o C
H
125
20 kW o C
90 kW
80 o C
240 kW
80 o C
1 2.0
3 4.0
Fig. 1.17 Example problem hot end design.
Maximizing exchanger loads.
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MODULE 12. NETWORK PINCH ANALYSIS
DESIGN BELOW THE PINCH.
The “above the pinch” section has been designed independently of the “below the pinch” section, and not using utility above the pinch. Below the pinch the design steps follow the same philosophy, only with the design criterion that mirror those for the “above the pinch” design.
Now, it is required to bring cold streams to pinch temperature by interchange with hot streams, since we do not want to use utility heating below the pinch (Figure 1.18).
In this example, only one cold stream exist below the pinch which must be matched against one of the two available hot streams. The match between streams 1 and 2 is feasible because the CP of the hot stream is greater than of the cold. The other possible match (stream 1 with stream 4) is not feasible.
T
 T
MIN
2
CP (kW/ o C)
3.0
H
4
1.5
Infeasible!!,
Why?
1 2.0
Feasible
Fig. 1.18 Example problem cold design. 2/1 Match acceptable, 2/4 match infeasible.
Immediately below the pinch, the necessary criterion is: CP
HOT inverse of the criterion for design immediately above the pinch .

CP
COLD
…. which is
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MODULE 12. NETWORK PINCH ANALYSIS
Maximize Exchanger Loads.
Maximizing the load on this match satisfies stream 2, the load being 90 kW. The heating required by stream 1 is 120 kW and therefore 30 kW of residual heating, to take stream 1 from its supply temperature of 20 o C to 35 o C, is required. Again this must come from interchange with a hot stream, the only one now available being stream 4.
Although the CP inequality does not hold for this match, the match is feasible because it is away from pinch .
That is to say, it is not a match that has to bring the cold stream up to pinch temperature. So, the match does not become infeasible
(Figure 1.19).
2
4
90 o C
90 o C 70 o C
60 o C
C
30 o C
CP (kW/ o C)
3.0
T
1.5
80 o C
90 kW
35 o C
30 kW
20 o C
1
2.0
90 o C
1
4
35 o C
Feasible
70 o C
20 o C
H
 T >  T
MIN
Fig. 1.19 Example problem cold end design.
Putting a load of 30 kW on this march leaves residual cooling of 60 kW on stream 4 which must be taken up by cold utility. This is as predicted by the Problem
Table analysis.
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9.3 Complete Design.
MODULE 12. NETWORK PINCH ANALYSIS
Putting the “hot end” and “cold end” designs together gives the completed design
(Figure 1.20). It achieves best possible energy performance for a

T
MIN of 10 o C incorporating four exchangers, one heater and one cooler. In other words, six units of heat transfer equipment in all.
2
4
170 o C
150 o C
1
2
90 o C
90 o C
3
4
70 o C
C
60 kW
135 o C
H
20 kW
140 o C
240 kW
125 o C
90 kW
80 o C
90 kW
35 o C
30 kW
CP (kW / o C)
60 o C
3.0
30 o C
1.5
20 o C
1
80 o C
3
2.0
4.0
Fig. 1.20 Example problem completed design.
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MODULE 12. NETWORK PINCH ANALYSIS
Dividing the problem at the pinch, and designing each part separately.
Starting the design at the pinch and moving away.
Immediately adjacent to the pinch, obeying the constraints:
CP
HOT

CP
COLD
(Above).
CP
HOT

CP
COLD
(Below).
Maximizing exchanger loads.
Supplying external heating only above the pinch, and external cooling only below the pinch.
These are the basic elements oh the “Pinch Design Method” of Linnhoff and Hindmarsh (1982).
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MODULE 12. NETWORK PINCH ANALYSIS
1 Identification of hot, cold and utility streams in the process.
2 Thermal data
Extraction for process and utility streams
3

MIN
4
5 Estimation of minimum energy cost targets
6 Estimation of HEN capital cost targets
7 Estimation of optimum

T
MIN value
8
9
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MODULE 12. NETWORK PINCH ANALYSIS
TIER I: FUNDAMENTALS
1.
2.
3.
4.
5.
6.
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
For an existing heat recovery network to maintain its target temperatures when changed operating conditions come into being is very significant to avoid bottlenecks at individual heat exchangers.
Typical de-bottlenecking practices for heat exchangers include modifications to surface area (overdesign) and to heat transfer coefficients (use of bypass).
If the modified operating conditions return to their original condition after a network has been de-bottlenecked, new disturbances are produced and the network has to be de-bottlenecked again in order to achieve the specified target temperatures.
A Flexible Network is one that is capable to providing an acceptable performance after being subjected to those two de-bottlenecking stages .
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MODULE 12. NETWORK PINCH ANALYSIS
During a process design the engineer fixes important parameters such as reactor feed and operating temperature, distillation column pre-heat levels, reflux ratios etc.
However, individual equipment items are often able to operate efficiently over quite a large range of conditions. For instance, in many cases a reduction in reactor operating temperature of a few degrees will have a minimal effect on conversion and selectivity.
The first step in analyzing the flexibility requirements of heat recovery networks is the specification of the process temperatures bounds, also called
“acceptable bounds”
.
These indicate the temperature range over which the process can still operate.
A heat exchanger network is supposed to have the required flexibility if its steady state response to a combination of inlet temperature and flow rate disturbances is within the acceptable bounds.
Upper Bound
Lower Bound
Upper Bound
Lower Bound time
Fig. 2.1 Acceptable Bounds
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MODULE 12. NETWORK PINCH ANALYSIS
The propagation of disturbances through heat recovery networks takes place by traveling down stream and through heat exchangers .
E3
E1
D
D
1
C Control Objective
2
D Disturbance
E4 E2
3
C
4
C
5
Fig. 2.2 propagation of disturbances through networks .
The effect of the disturbances on target temperatures can be assessed by determining the steady state response of the network. This steady state response can be used to implement retrofit strategies that will lead to flexible systems able to cater for seasonal or temporary variations in operating conditions
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MODULE 12. NETWORK PINCH ANALYSIS
Exchanger thermal effectiveness .
T
2
The response of individual exchangers to changes in flow rate and inlet temperatures can be assessed quickly and accurately by the use of the thermal effectiveness (

) relations.
T
3
Exchanger Thermal Effectiveness, represents the ratio of the actual heat load to the maximum load that is thermodynamically possible.
T
T
1
Hot
T
4
Cold
T
1
From this definition it can be shown that the exchanger thermal effectiveness can be represented by the ratio of temperature difference that the CP min stream undergoes, to the maximum temperature driving force that exists in the exchanger (Fig. 2.3).

T
1
T
1

T
2

T
3
(2.1)
T
T
2
3
T
4
H
Fig. 2.3 Temperature profiles of a heat
Exchanger Where the hot stream is the
CP min stream.
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MODULE 12. NETWORK PINCH ANALYSIS
Number of Heat transfer Units (NTU).
The number of transfer units is expressed by
NTU

UA
CP min
(2.2) where U is the overall heat transfer coefficient, and A is the exchanger surface area.
Inter-relation:

, NTU, C * and flow arrangement.
Exchanger thermal effectiveness can also be expressed as a function of C * (C * =
CP min
/CP max
), the number of heat transfer units (NTU) and the exchanger flow arrangement. For instance, the expression for a shell and tube exchanger is:
 
2

1

C
*
 
1

C
* 2
1

/ 2



1
1



1

C
* 2
1

/ e

NTU e

NTU

1

C
* 2
1

/ 2
2



(2.3)
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MODULE 12. NETWORK PINCH ANALYSIS
Exchanger variables in steady state simulation.
Single and with bypass heat exchanger variables.
E r
1.1
BP = ByPass
T
2
E
T
1
T
3 M T
1
T
3
T
4 T
4
T
2 r
1.2
T
5
(a) (b)
Fig. 2.4 Exchanger variables in steady sate simulation: (a) single heat exchanger and
(b) single heat exchanger with bypass.
Variables
Entry Temperatures
Output Temperatures
T
1
, T
3
T
2
, T
4
Variables
Entry Temperatures T
1
, T
4
Output Temperatures T
2
, T
3
(from Mixing Point, M ), T
5
Flow rate fraction (r n,j
) of each branch of the divided stream r
1.1
, r
1.2
(The number of outputs that a split generates [ j ] corresponds to the number of branches specified).
Here n =1, j = 2
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MODULE 12. NETWORK PINCH ANALYSIS
Total number of variables in a network (NV).
From the ongoing discussion it can be shown that the total number of temperature and flow fraction variables (NV) in a network can be determined by
NV

S

2 E

M

2 BP
(2.4) where S the number of process streams. For the exchanger in Fig. 2.4b
NV

2

2 ( 1 )

1

2 ( 1 )

7
Total number of equations in a network.
For a system to be fully defined, the number of variables must be equal to the number of equations. In the case of an existing heat exchanger network, the equations that can be written are: a) The thermal effectiveness equation and the heat balance equation for every heat exchanger .
From the thermal effectiveness equation Eq. (2.1), the outlet temperature of the CP min
Fig. 3.3b can be expressed as
T
2

T
1
 

T
1

T
4
 stream in the case of
(2.5)
Combining Eq. (2.5) with the heat balance equation about the exchanger, the outlet temperature of the CP max stream can be expressed as
T
5

T
4

C

( T
1

T
4
)
(2.6)
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MODULE 12. NETWORK PINCH ANALYSIS b) The mass balance equation about every mixing point.
The mass balance equation about any mixing point can be expressed as

1 j
 n , j
  n , Total
(2.7) where n is the stream number. This equation can be rewritten as j 
1 r n , j

where r is the stream branch flow fraction and
(2.8) r n , j

 n , j
 n , Total
(2.9)
T
3
T
4
For a bypass j = 2, and at least one flow fraction ( r ) is known.
M
T
2 r
1.1
Fig. 2.4b
r
1.2
BP
T
1
T
5 c) The heat balance about every mixing point.
For the exchanger in Fig. 2.4b the equation of heat balance about mixing point can be written as
H
3

H
2

H
1
(2.10)
Where H is the stream enthalpy content. For a given reference state ( T ref.
) the enthalpy content can be expressed as
H
  Cp

T

T ref

(2.11)
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d.
e.
MODULE 12. NETWORK PINCH ANALYSIS
Now the mass balance about the mixing point is

3
 
2
 
1
(2.12)
Applying Eq. (2.11) to the various streams at the mixing point, and combining with Eqs. (2.10) and (2.12) and rearranging gives
T
3
 r
1 , 1
T
1
 r
1 , 2
T
2
(2.13) where r
1,1 and r
1,2 are the flow fractions of stream 1 in branches 1 and 2.
The stream supply temperatures which are known.
The j1 flow fractions at every split point that are known.
Solution of system of equations.
In an existing network, all stream supply temperatures, mass flow rates and exchanger effectiveness are known.
The simultaneous solution of the system of equations permits the calculation of ALL
NETWORK TEMPERATURES.
Variations in supply temperatures and flow rates can be readily assessed in order to obtain the steady state response of the network.
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MODULE 12. NETWORK PINCH ANALYSIS
Simultaneous solution of system equations in a single heat exchanger
T
1
T
Taking into consideration the heat exchanger shown in the Fig.
2.4 a, it can see from effectiveness equations that outlet temperature for CPmin streams is:
T
2
T
3
H
T
4
T
1
T
4
T
2


1
  
T
1
 
T
3 and the second equations required come from heat balance about exchanger and it can written as
( T
1

T
2
) CP min

( T
4

T
3
) CP max
T
3
T
2
T
2
E
T
1
Hot
Combining two equations preceding it can obtained a equation to outlet temperature for CPmax stream (T
4
):
T
4

C

T
1

( 1

C

) T
3
T
3
T
4
Cold
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MODULE 12. NETWORK PINCH ANALYSIS
The solution of system equations for a single exchanger can be expressed into matrix form as follow
AT = B where:
T vector represents exchanger outlet and inlet temperatures
A represents outlet and inlet temperatures relation of exchanger
B represents temperatures known values.
In this case, T
1
=

1 and T
3
=

3
.
The matrix equation can be written in developed form as





( 1
1

C
0


)
0

1
0
0

0
1
( 1

C

)

0
0
0
1










T
1
T
2
T
3
 T
4














0
0
1
2





The production of a simulator for heat recovery network required of equations generation considering each one exchanger and, if there is, to mixing point existing.
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MODULE 12. NETWORK PINCH ANALYSIS
Temperature and flow fraction variables in a heat network.
T
2
T
1
1
T
6
T
5
T
4
T
3
2
3
T
7
4
T
9 r
4,1
T
8
T
10
T
12
T
13 r
4,2
T
11
Fig. 2.5 Variables in a heat exchange network
Total number of variables:
Applying Eq. 2.4: NV = S + 2E + M + 2 BP. In this example: S = 4, E = 4, M = 1 and BP = 1,
-
NV = 4 + 2(4) + 1 +2(1)
-
Equations:
The four stream supply Temperatures are known giving equations .
4
Two equations can be written for every heat exchanger: the heat balance equations .
and the thermal effectiveness giving another 8
-
-
The mass balance about the stream split gives 1 equation .
The j-1 known flow fraction gives 1 equation .
The mass balance about the mixing point gives 1 equation .
15 EQUATIONS ARE REQUIRED TO SOLVE THE SYSTEM.
The simultaneous solution of this system of equations permits the calculation of all network temperatures.
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MODULE 12. NETWORK PINCH ANALYSIS
Updating exchanger effectiveness and number of transfer units.
 The influence of temperatures variations on thermal effectiveness is negligible, thus this parameter remains constant when temperature disturbances enter the system.
 However, when flow rate variations occur, they change the stream heat coefficient that modifies the overall heat transfer coefficient which in turn affects the number of transfer units, thus causing the thermal effectiveness to change.
 In order to account for the change in exchanger effectiveness due to flow rate variations, the individual heat transfer coefficients must be updated.
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MODULE 12. NETWORK PINCH ANALYSIS
For the case of shell and tube exchangers operating in turbulent flow, the heat transfer coefficients ( h ) can be calculated from the following expressions :
Tube side
(2.14) h tube

0 .
023

Cp

G

Pr

2 / 3

Re

0 .
2 or h tube

K
T
( G )
0 .
8
(2.15) where
K
T

0 .
023

Cp
 
0 .
2 
Pr

2 / 3
D
T
0 .
2
(2.16) and G

Ac
(2.17)
For the original condition (O) and new condition (N), the tube side heat transfer coefficient is h
N 
Tube
K
T
( G
O
)
0 .
8 (2.18) h
O 
Tube
K
T
( G
N
)
0 .
8 (2.19)
The combination of Eqs. (2.18) – (2.19) gives
N h
Tube




 N m
Tube
 O m
Tube


 0 .
8
O h
Tube
(2.20)
Eq. (2.20) allows the heat transfer coefficient to be updated as the stream flow rate changes in the tube side provided turbulent flow remains.
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MODULE 12. NETWORK PINCH ANALYSIS
Shell side.
h shell
 a
 k
D
T

Re 0 .
6 
Pr 1 / 3
A similar analysis to one presented above gives the following result: h
Shell



 N m
Shell
 O m
Shell


0 .
6
O h
Shell
(2.21)
(2.22)
Whit the new values of heat transfer coefficients, the new overall heat transfer coefficient can be calculated. Once the NTU has been updated using Eq. (2.2), the new exchanger
Effectiveness can be calculated from the appropriate equation.
For instance, for a shell and tube exchanger :
 
2

1

C
*
 
1

C
* 2
1

/ 2



1
1



1

C
* 2
1

/ e

NTU e

NTU

1

C
* 2
1

/ 2
2



(2.3)
Almost any type of heat exchanger and flow arrangement can be incorporated in the analysis of
Heat recovery networks, provided the appropriate effectiveness-NTU equations are used.
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MODULE 12. NETWORK PINCH ANALYSIS
The required heat exchanger network flexibilities can be guaranteed through the implementation of a control scheme that will allow local heat exchanger duties to be increased or reduced as needed.
The simplest way of controlling target temperatures is by manipulating steam flow rates in heaters and cooling water flow rates in coolers. However, control can also achieved through the use of bypassing schemes on process to process heat exchangers. For a network to exhibit flexible operation, the implementation of bypasses must be accompanied by a given level of exchanger oversizing.
T target
T target
T target
Steam flow rate
Cooling flow rate
(b)
Over sizing
(a)
Fig. 2.6 (a) Simplest way of controlling T Target and (b) Bypassing on heat exchanger
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MODULE 12. NETWORK PINCH ANALYSIS
The basic information for the development of the simulation model of an existing structure includes the following:
1.
Network structure:
1.
Total number of hot and cold streams:
2.
3.
Number heat exchangers and
Number of mixing points.
2.
Heat exchangers: For participating streams (cold and hot) specify:
1.
2.
3.
4.
5.
Stream identification:
Branch number (for by pass and stream splitting) and CP fraction (if no stream split CP = 1):
Stream heat transfer coefficient and fouling factor.
Superficial heat transfer surface:
Type of heat exchanger and in the case of shell and tube specify stream allocation
(shell or tube).
3.
Mixing point:
1.
2.
3.
Identification number of main stream and branch number:
Inlet and outlet temperature variable in structure:
Branch CP fraction.
4.
Process streams:
1.
2.
Flow rate and supply temperature
Supply temperature annotated variable in structure.
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MODULE 12. NETWORK PINCH ANALYSIS
The simulation of the network for base case conditions and after corrective actions have been implemented facilitates the specification of the bypass fractions that will be required to operate under normal conditions.
The network simulation model can also be used to assess the performance of increased area or reduced overall heat transfer coefficient in every heat exchanger.
Cold stream
U
T
Upper
Bound
Lower
Bound
Hot stream
Reduced U t
Hot stream
A
Cold stream
Increased Area
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MODULE 12. NETWORK PINCH ANALYSIS
When various solutions to a problem are possible, the designer must choose the option that minimizes the number of exchanger modifications and minimizes the amount of additional area.
Using steady state simulation, a trial and error procedure must be established particularly in cases where modification of more than one exchanger permits the restoration of target temperatures.
The network must remain operable if operating conditions return to normal. In this case, the network is simulated with increased heat transfer areas and original flow rates and temperatures.
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MODULE 12. NETWORK PINCH ANALYSIS
Define Network Structure
Network under modified conditions
Produce equations that describe
 and heat balance about heat exchangers and mixing points
Solve the resulting set of equations
Determine the network response under modified conditions
Network continues working
Yes
Do Target
Temperatures Fall within the acceptable bounds?
No
Corrective actions must be taken
Fig. 2.7 Procedure for assessing of network response under modified conditions.
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MODULE 12. NETWORK PINCH ANALYSIS
1.
2.
3.
4.
5.
6.
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MODULE 12. NETWORK PINCH ANALYSIS
3.
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MODULE 12. NETWORK PINCH ANALYSIS
Full process design is generally undertaken for a point condition.
For instance, the basis for the design of a chemical plant may be a throughput for 100 tonnes/hour with a feedstock of specific composition being supplied at a specific temperature.
In reality, the plant will rarely operate at this point condition:
 Production demands may require a throughput of 110 tonnes/hour some weeks and 80 tonnes/hour other weeks.
 Process supply temperatures can show seasonal variations.
 Feedstoks compositions can vary.
In addition to changes in process conditions, equipment performance can vary with time, examples:
 Catalyst activity.
 Heat exchanger fouling.
Given these variations, there is a need for chemical plants to be “flexible”. They must be capable of operating efficiently under a variety of conditions.
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MODULE 12. NETWORK PINCH ANALYSIS
As mentioned early (sub-section 2.1 Introduction) disturbances propagate through heat exchanger networks by travelling downstream and through heat exchangers. These pathways are clearly shown on the ‘heat exchanger grid diagram’.
The recognition that disturbances can only be propagated ‘downstream’ has important implications for network design. If a particular stream is known to be subject to large disturbances and another stream is known to be particularly sensitive, the engineer would be advised to devise a network structure that does not have a downstream path between the two points.
In many cases the designer will have to introduce process control. This can take the form of:
 Increased utility.
 Using a Bypass to divert some flow around rather than through an exchanger.
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MODULE 12. NETWORK PINCH ANALYSIS
When dealing with the question of additional throughput the designer has the option of increasing the Number of transfer Units present in a given exchanger. This increase can be achieved either:
 through increased area or
 through the use of heat transfer enhancement.
HEAT LOAD SHIFTS. Required Load Shift.
The first step in analyzing the response of a network to imposed disturbances is obviously a comparison between the resultant target temperatures and the specified temperature bounds. The result is a picture of heat supply and demand across the network.
If a target temperature falls outside the bounds, the load to restore it to the nearest bound can be considered to be the “Required Load Shift”.
This required load shift will be given by either:
R
Heat Required
 
CP ( T

T max
) T

T max
 
CP ( T

T min
) T

T min
Surplus
Deficit
(3.1)
(3.2)
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MODULE 12. NETWORK PINCH ANALYSIS
An examination of the “ Required Shift” gives an immediate indication of what form of remedial action is required.
– If ˆ
R

Q
 on a cold stream too much heat has been added to the stream. The remedial action must be the provision of a bypass around one of the exchangers on the stream. If
ˆ
R

Q
 insufficient heat has been provided to the stream and additional area is needed on one of the exchangers.
– If ˆ
R

Q
 on a hot stream is positive: insufficient heat has been removed and additional area is necessary. If
ˆ
R

Q
 indicates the removal of too much heat and the need for a bypass.
These observations are summarized in Table 3.1.
Stream Type
Hot stream
Cold stream
Requirement Load Shift
ˆ
R
+ ve
- ve
+ ve
- ve
Action
More area
Bypass
Bypass
More area
Table 3.1. Heat load and required action
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MODULE 12. NETWORK PINCH ANALYSIS
HEAT LOAD SHIFTS. Available Shift.
If a target temperature is well within its required bounds, it has a
“required shift” of zero.
However, with such a stream there may still be scope for shifting heat down the paths by going to one of the bounds. Such heat load shifts can also generally be undertaken in either direction.
The “Available shifts” are given by:
 
CP ( T

T min
)
(3.3)
 
CP ( T

T max
)
(3.4)
Finally, it is recognized that a stream having a “required heat shift” also have an
‘available shift’. This shift is in the same direction as the ‘required shift’ and is the load that is necessary to take the stream to the furthest bound.
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MODULE 12. NETWORK PINCH ANALYSIS
Summarizing LOAD HIFTS.
Now, in summary, all streams provide two potential shifts:
– A stream that falls within its bounds does not have a ‘required shift’ but provides ‘available shifts’ in two directions.
– A stream that falls outside its bounds has a ‘required shift’ and an ‘available shift’. This available shift is in the same direction as the ‘required shift’. They are of different magnitude.
Comparison of ‘required’ and ‘available’ shifts allow us to observe:
1.
2.
3.
The stream matches that can be used to satisfy flexibility needs:
The maximum load shifts that can be employed with a given match:
A guide to structural changes that can be made in order to achieve flexibility through heat recovery rather than through the use of additional utility.
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MODULE 12. NETWORK PINCH ANALYSIS
LOAD HIFTS. EXAMPLE
By a way of illustration consider the results presented in Table 3.2.
Following a disturbance to the operating condition, it is found that streams H1 and C1 are no longer within bounds. Each requires the shifting of 20 units of heat to restore proper operation.
Examination of the Table shows that the deficit on C1 cold be supplied using any of the hot streams. The surplus on H1 could be utilized on either C1 or C2.
Hot stream Cold stream
Stream
H1
H2
H3
Required
Q
R
+20
--
--
Q +
+ 40
+ 40
+ 51
Available
Q -
--
- 10
- 15
Stream
C1
C2
C3
Required
Q
R
- 20
--
--
Q +
--
+ 30
+ 10
Available
Q -
- 45
- 20
- 10
Table 3.2 Heat demand and availability of streams after disturbed conditions.
Action required for the restoration of target temperatures.
The final choices will be based on existing paths and required additional area. As a last resort a new path (i.e. new match) could be generated.
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MODULE 12. NETWORK PINCH ANALYSIS
An examination of required and available heat shifts provides a guide as to which streams can be used to provide flexibility and it indicates the form of action to take.
However, the concept makes no consideration of temperatures field or of exchanger technology.
A shift identified in this manner may prove infeasible or extremely expensive.
In this section a single exchanger will be considered where the flow rate and inlet temperature of one of the streams changes.
An appropriate modification must be made to the unit in order to restore both outlet temperatures to their original values.
Equations relating change in exchanger outlet temperature with changes in exchanger effectiveness can be derived for each type of modification.
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MODULE 12. NETWORK PINCH ANALYSIS
Effectiveness Needs.
Referring to Figure 3.1.1, the addition of heat transfer area to an exchanger will result in the hot outlet temperature ( T ) moving to lower values and the cold outlet temperature ( t ) moving to higher values.
Consider the case in which following a disturbance the outlet temperature of the hot stream is T brought to a value
2
(N)
T
2
(O) and needs to be
.
The question that arises here is, how much area must be added to the unit to achieve this objective?
T T
1
T
2
T
1
T
2 t
1 t
2 t
1 t
2
T
:
CP min stream t
:
CP max stream
H
Fig. 3.1 Single heat exchanger
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MODULE 12. NETWORK PINCH ANALYSIS
Expressions for the exchanger outlet temperatures can be written from the definition of thermal effectiveness.
For the existing condition:
T
2
( O ) 
T
1
 
( O ) 
(3.5) and t
2
( O )  t
1

C

( O )  (3.6)
For the desired condition:
T
2
( N )

T
1
 
( N )

(3.7)
Combining equations (3.5) and (3.7) the following expression can be derived
T
2

T
2
( N ) 
T
2
( O )  

( N )  
( O )

(3.8)
Which after rearranging gives
 ˆ  
( N )  
( O )  
T
ˆ
2

(3.9)
This expression gives the change in exchanger effectiveness (

) required to bring about the desired corrective changed on T
2
.
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MODULE 12. NETWORK PINCH ANALYSIS
The same exercise can be carried out for the case where the change takes place in t
2
(O)
In such case, the new effectiveness becomes
 ˆ  
C ( N )  
( O )  t
ˆ
2
C
 (3.10)
In the above example the hot stream had the lower heat capacity flow rate. Similar equations to (3.9) and (3.10) can be derived for the case where the cold stream has the lower value. These results are:
 ˆ  
( N )  
( O )  
T
ˆ
2
C

(3.11) and
 ˆ  
( N )  
( O )   t
ˆ
2
C

(3.12)
Table 3.3 summarizes these results.
CPmin
Hot stream
Cold stream
Outlet temperature of
CPmin stream
 ˆ  
T
ˆ

 ˆ  t
ˆ

Outlet temperature of
CPmax stream
 ˆ  t
ˆ
C

 ˆ 
T
ˆ

C

Table 3.3 Corrective equations. Effectiveness needs of an exchanger
For a required temperature shift of either outlet temperature.
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MODULE 12. NETWORK PINCH ANALYSIS
Changes in effectiveness can be converted into changes in area once the type of exchanger is known.
For instance, for a pure counter-current arrangement, thermal effectiveness and
Number of transfer Units are related according to
 
1
1

 e
Ce

NTU

NTU
( 1

C )
( 1

C )
For this expression:
NTU
 ln
1

C

1

( 1

C
C )
(3.13)
(3.14)
Now, letting NTU (O) and NTU (N) be the initial and the new exchanger Number of
Transfer Units respectively, then the NTU change is given by
N T
ˆ
U
 ln

 

1
1


C

C

( N
( O )
)


1
1

 

(
( O
N
)
)




( 1

C )
(3.15)
This equation gives the required NTU increase the exchanger must undergo in order to meet the specified target temperature. The additional area can be calculated from
U
ˆ
A

N T
ˆ
U

CP min
(3.16)
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ADDITION OF HEAT TRANSFER AREA
Mass Flow Rate manipulation
Since the effectiveness of an exchanger is a function of the CP-ratio, a change to the mass flow rate of either of the streams about a single exchanger will result in a change to the thermal effectiveness of the unit. Bypass can therefore be used to achieve a desired temperature correction.
Consider manipulation of the stream exhibiting the lowest CP. The fraction of the flow of the manipulated stream actually passing through the exchanger will be represented by f .
For a bypass to be applicable the exchanger must be larger than it is actually needed for one of the operating cases. Assume that this is the base case and under this situation the bypass operates partially open and f (O) is the fraction of the flow passing through the exchanger.
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If temperature T
2 in Figure 3.1.2 needs to be reduced the bypass valve must close.
Conversely, when T
2 is to be increased the bypass valve opens. Assume the new flow fraction through the exchanger becomes f (N) .
Denoting T
2
’(O) as the initial condition of following expression can be written:
T
2
’
, the
T
2
’(O)
= T
1
-

(O)
(3.17)
A heat balance about mixing point gives
T
2
(O) = (1 – f (O) )T
1
+ f (O) T
2
’(O)
(3.18)
Combining the two equations yields
T
2
(O) = T
1
– f (O)

(O) (3.19)
When bypass valve operates T
2
’(O) and is given by becomes T
2
’(N)
T
2
’(N)
= T
1
-

(N)
(3. 20)
T
2 t
1
T
2
’ f
T
: hot stream t
: cold stream
1 - f t
2
T
1
Again, a heat balance about the mixing point gives
T
2
(N) = (1 – f (N) )T
1
+ f (N) T
2
’(N) (3. 21)
Combination of equations (3.1.20) and (3.1.21) gives
T
2
(N) = T
1
– f (N)

(N) (3. 22)
Fig. 3.2 Heat exchanger fitted with bypass.
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MODULE 12. NETWORK PINCH ANALYSIS
The total change in outlet temperature T
2 and (3.22):
T
ˆ
2
  
 f
( N can be obtained by combining equations (3.19)
)

( N )  f
( O )

( O )

(3.23)
A similar analysis performed for temperature t
2 t
ˆ
2
 
C

 f ( N gives
)

( N )
 f ( O )

( O )

(3.24)
In the case where the bypass valve operates between an initial condition of fully closed and a final condition of partially open, then f (O) = 1 and f (N) = f . Equation (3.23.) reduces to
T
ˆ
2
  
 f

( N )  
( O )

(3.25)
Similarly it can be shown that t
2
 
C

 f

( N )  
( O )

(3.26)
Equations (3.25) and (3.26) relate the required temperature change to f and new exchanger effectiveness (

(N) ).
For a given T
ˆ
2 or t
ˆ
2
, f can be calculated iteratively.
The exchanger effectiveness following a flow change can be calculated using the procedures given in sub-section “updating exchanger effectiveness and NTU” of “2.2
Response
Equations” .
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Now consider the case where one of the outlet temperatures of the exchanger (say T
2
) needs to be restored to its original value. For the case where only mass flow rate disturbances exist, it can be demonstrated that the flow fraction through the exchanger can be found from:
  base case conditions
 f

( N )
(3.27)
Specific equations like this can be derived for any combination of disturbances
(temperature and flow rate).
Summarizing:
Table 3.4 summarizes the general ‘Corrective Equations’ for flow rate manipulation.
CP min stream
Hot stream
Cold stream
MASS FLOW RATE MANIPULATION
Outlet temperature of
CP min stream
T
ˆ    ( O )
 f

( N )  
( O )
 t
ˆ   ( O )
 f

( N )  
( O )

Outlet temperature of CP max stream t
ˆ 
C
( O )  ( O )
 f

( N )  
( O )

T
ˆ  
C
( O )  ( O )
 f

( N )  
( O )

Table 3.4. Corrective Equations. Mass flow rate manipulation for the correction of outlet temperatures. Initial condition of valve: shut.
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3.
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MODULE 12. NETWORK PINCH ANALYSIS
So far only modifications to single heat exchangers have been considered. Attention must be paid to the influence of network interactions on the necessary modifications.
Network structure influences the design process in two ways:
First, it affects the order in which modifications must be considered.
Second, the network response is as important as any individual exchanger response .
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ORDER OF UNDERTAKING NETWORK MODIFICATIONS.
Consider the network problem shown in Figure 3.3 Assume temperatures T
5 been disturbed and need to be restored. Control of temperature through the provision of additional area on exchanger E 2.
T
7 by means of a bypass placed about exchanger E1 . Temperature T
5 and T
7 have can be achieved can be restored
Assume that the designer decides to look at the restoration of T
5 first.
The amount of area that needs to be added is computed on the basis of temperatures T
2
, T
4
T
5
.
and
T
T
3
4
E2
T
T
2
5

E1
T
C
1
Now the designer tackles the bypass about exchanger E1 . However, the result of this exercise is a change in temperature T
2
.
The basis of the initial modification (to
E1 ) is now prejudiced.
The designer now has to redo this modification
CP h
= CP min
T
6
T
7
Fig. 3.3 Network responses and damping.
Clearly the order in which modification are considered is important. It is also clear that upstream changes must be considered first.
C
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NETWORK RESPONSES.
Consider Figure 3.4 This shows a case in which a target temperature T x increased by an amount ( needs to be

). Assume that any of the three exchangers on the stream could be used to achieve this objective.
CP min
= CP h
E3
E1
E2

3

2

1
C
T x
Fig. 3.4 Network response and dumping.
Exchanger E1 is closet to the ‘target point’. The modification necessary to this exchanger can be calculated directly from the equations derived before for single exchangers.
Exchanger E2 is separated from the ‘target point’ by exchanger
E1 . The question that now must be asked is
‘how large is the correction that must be made to the outlet temperature?’

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MODULE 12. NETWORK PINCH ANALYSIS
A change to this outlet temperature constitutes a disturbance to the temperature of exchanger E1 . The response of E1 to this change is dependent on its effectiveness and CP ratio. In this case it can be shown that:

1
 
2
( 1

C
1

1
( O )
)
(3.28)
The important observation here, as known by experienced industrial engineers, is the presence of another exchanger between one being considered for modification and the target point dampens the effect of the proposed modification.
The damping can be determined from the steady state response developed in the subsection “Single and complex networks. Response equations” of section 3.1
Operable Network.
Starting at the exchanger furthest ‘upstream’ (
E3 ), given that the hot stream has the lower heat capacity flow rate, the response of the cold stream outlet temperature to an increase in the effectiveness of the exchanger is (from Table 3.3)

3

C
3

3

3
(3.29)
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The damping introduced by exchanger E2 is (from table XX):

2
 
3
( 1

C
2

2
( O )
) and that from exchanger E1 is:

1
 
2
( 1

C
1

1
( O )
)
So, the final effect on the ‘target point’ temperature is:

1
3 
C
3

3
 ˆ
3
( 1

C
1

2
( O ) )( 1

C
1

1
( O ) ) where superscript 3 indicates the effect after E3 .
(3.30)
(3.31)
(3.32)
Now, consider exchanger E2 . Also assume that a modification has been made to exchanger E3 . The result of the modification to exchanger E3 is a change in the temperature lift (

) of exchanger E2 . Taking this into account, the cold stream outlet temperature change resulting from a change in the effectiveness of exchanger E2 is:

2

C
2
(

2
 
3
)
 ˆ
2
(3.33)
The damping associated with the presence of exchanger E1 is:

1
2  
2
( 1

C
1

1
( O )
)
So, the final effect on the ‘target point’ temperature is:

1
2 
C
2
(

2
 
3
)
 ˆ
2
( 1

C
1

1
( O )
)
(3.34)
(3.35)
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Finally, consider a modification to exchanger E1 . The response of this exchanger to changed effectiveness occurs directly at the ‘target point’ and is:

1
1 
C
1
(

1
 
2
)
 ˆ
1
(3.36)
Knowing the structure of the ‘path’ a general equation relating the individual response with the required overall response can be written:

1
T  
3
( 1

C
2

2
( O )
)( 1

C
1

1
( O )
)
 
2
( 1

C
1

1
( O )
)
 
1
1
(3.37)
The result is a set of equations (3.2.10, 3.2.9, 3.2.3 and 3.2.2) that can be solved in order to evaluate the different combination of modifications that will provide the required result.
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COST EFFECTIVE NETWORK MODIFICATION
The cost effective modification to a network is not necessarily the one that uses the last additional area.
It is generally the one having the minimum of changes. If the required modification can be achieved using heat transfer enhancement rather than additional area this is the direction to go for it avoids the installation of a new exchanger with its associated piping, civil and instrumentation costs.
There is a hierarchy of options:
1 Use a Heat Transfer Enhancement on just one Exchanger.
2 Use of Heat Transfer Enhancement in general.
3 Installation of just one new exchanger in existing structure.
4 Installation of one new exchanger in existing structure and the use of enhancement on others.
5 Installation of more than one exchanger in existing structure.
6 New heat recovery match unless justified by energy saving rather than flexibility requirement.
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The scope for using heat transfer enhancement on any duty can easily be determined;
First, the exchanger is examined to determine the extent to which the overall heat transfer coefficient can be improved. This is then converted to a change in Number of Heat Transfer Units. Finally, the resultant change in effectiveness is obtained.
In some cases the use of heat transfer enhancement may be ruled by severe pressure drop constraints.
However, it is often possible to overcome such constraints through making judicious changes to exchanger header arrangements.
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DISTRIBUTION OF AREA BETWEEN EXCHANGERS
In some occasions it will be found that more than one exchanger will have to be modified in order to achieve a single flexibility objective. Under these circumstances the designer is interested in determining a cost effective distribution of area between the exchangers.
Again consider the network shown in Figure 3.2.2. Assume that it has been identified that in order to achieve the flexibility objective area must be added to exchangers E1 and E2.
The distribution of this area now has to be determined.
For the manipulation of two exchangers equation (3.2.10.) becomes:

T  
2
( 1

C
1

1
( O )
)
 
1
(3.38) where

1

C
1

1
 
2

1
(3.39) and 
2

C
2

2
 ˆ
2
(3.40)
The two unknowns are

1 and
 ˆ
2
.
The optimum distribution could be found through exhaustive search. Each term varies between zero and the limit given by equation (3.2.3.). For each value of of

 ˆ
1 the value necessary to achieve the objective can be calculated. Then, from these two
2 values the individual and overall increased in Number of Transfer Units can be found.
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The results of such exercises are shown in Figure 3.5 for values of individual effectiveness ranging from 0.4 to 0.9.
It is seen that the thermal effectiveness of the exchangers plays an important role in determining the cost effective area distribution.
Two regions can be observed:
Region 1.
A region in which the addition of area to exchanger 1 should be maximized. This is seen to be not only the case where E1 has the lower effectiveness but also where the adverse effects of a higher effectiveness on exchanger 1 are counteracted by its damping effect.
Region 2.
A region in which the effectiveness of E1 is much higher than that of E2 and despite the damping associated with the unit the best policy is the addition of area to E2 .
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Figure 3.5 Required NTU v.  for counter-current exchangers
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Heat exchanger networks may exhibit simple or complex structures, The latter is characterized by the presence of feedback loops in the network.
What is a FEEDBACK LOOP in a HEN?
Consider the HEN shown in Figure 3.6 and follow the path of a disturbance on stream 1 around the network.
E2
E3
Path of disturbance
E1
1
2
3
Feedback Loop
Fig. 3.6 The presence of a feedback in the network make it a Complex network.
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E1
Following the path of a disturbance on stream 1 around the network we can see that first affects the outlet temperature of exchanger 1. This form the inlet to exchanger 2 and has an effect on the cold stream leaving exchanger 2 (stream 3). This disturbance is dampened as the stream passes through exchanger 3 but some level of disturbance is still present when this stream now enters exchanger 1. Exchanger
1 which was the first unit to encounter the disturbance now encounters the downstream effects of the disturbance.
SIMPLE AND COMPLEX NETWORKS
Structures which contain cyclic elements (I.e. elements that are repeated) or overlapping loops are classified as being COMPLEX NETWORKS . In contrast with the structure shown in Figure 3.2.5 a network structure containing a loop but it does not provide feedback is classified as having a ‘SIMPLE’ STRUTURE . The Figure 3.7
shows a simple structure.
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E1
MODULE 12. NETWORK PINCH ANALYSIS
E3 E4
E2
2
1
3
4
Figure 3.7 Simple structure: loop without feedback.
The procedure for determining the response where feedback loops exist involves the derivation of a feedback factor which is a function of the network structure. This factor includes all the dampening elements that a disturbance encounters as it propagates around a loop.
Most industrial heat recovery networks are of the simple variety for they use close to the minimum number of units and only rarely contain cyclic elements or complex multiple loops.
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It is often the case that operating changes result in the need to restore more than one target temperature. It may then be found that an exchanger chosen to manipulate one target also has a downstream path to another target.
The complexity of the problem can be further increased if the remedial action proposed for one objective actually has a detrimental effect upon another objective.
Consider Figure 3.8 which shows only part of a network. Following operating disturbances it is necessary to decrease T
2 by T
ˆ
10
( C ) .
by T
ˆ
2
( C ) and T
10 is required to increase
C
T
4
T
6
E3
T
7
CP min
= CP h
T
8
E2
T
2
CP min
= CP c
T
9
E1
T
1
CP min
= CP c T
3
T
5
T
10
C
Fig. 3.8 Multiple objectives.
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It is seen that T
2 can only be restored by increasing the area of exchanger
However, it is also seen that any change to E1 also affects T
10.
can also be manipulated by changes to exchanger E3 .
E1
This temperature
.
The problem is solved by setting up and solving the following system of simultaneous equations:

3
( 1

C
2

2
)( 1
 
1
( O )
)
 
1

T
ˆ
10
(3.41)

3
( 1

C
2

2
)

( O )  
1
* 
T
ˆ
2
(3.42) where:

3
 
3
C
3

3

1
 
1


1
 
3


C
2

2
 
(3.43)
(3.44)

1
*    ˆ
1
C
1


1
 
3

1

C
2

2
 
(3.45)
Equations (3.41) and (3.42) represent the effect of the modification of exchangers E3 and E1 upon target temperatures T
10 and T
2 respectively.
Their solution together with expressions (3.43) to (3.44) yield the necessary effectiveness changes to exchangers E3 and E1.
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TIER I: FUNDAMENTALS
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A vital lesson from pinch technology has been the need to set targets. The principles is to predict what should be achieved (targeting), and to then set out to achieve it
(design).
Applications of process integration fall into two categories -grassroots design and retrofit. In retrofit is applied the same thermodynamic principles that underlie established pinch technology and the philosophy of targeting prior to design is maintained.
In the context of retrofitting, this implies the setting of targets for:
- Energy saving
- Capital cost
- Payback.
The targets recognize the specifics of the existing design.
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HOW ARE RETROFIT PROJECTS TACKLED?
Retrofit projects are tackled in three current approaches :
1.
Inspection .
Examine the plant and select a project intuitively. This approach are called
“cherry picking”. The result is never quite certain. There is usually a doubt remaining
“Could there be a better answer?”
2.
Computer search . Those who have process-synthesis computer programs may ask
“Why not generate many alternative new designs? Hopefully, one of these may be similar to the existing plant and will thus spark off a reasonable retrofit project.
” This approach can consume a lot of computation time and be very expensive. More important, it does not provide any insight into the problem and does not necessarily generate a good solution.
3.
Pinch technology . Apply pinch principles and incorporate process insight during the design. Although this approach has been used industrially with some success, it is, strictly speaking, an improvisation on methodology aimed at grassroots design. User experience is crucial for a good result.
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RETROFIT BY INSPECTION
Fig. 4.1 shows a simple heat-exchanger network in the grid representation. Let us consider an energy retrofit for this network.
Initial inspection would suggest contacting streams 1 and 5 at the cold end of the process. This would reduce the heat loads on cooler C1 and on the heater. Stream 1 is chosen in preference to stream2 because of its significantly higher heat-capacity flowrate.
However, the integration of a new heat exchanger is not completely straightforward. The new exchanger would affect the temperature in “downstream” exchangers 1 and 4 which would lead to the need for additional area here. Then if additional area were needed in exchanger 4 anyway, we should once more consider stream 2, with a view to reducing the load on cooler C2.
With this type of reasoning, a network may result as shown in Fig.2. The overall saving in energy is 2,335 kW.
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Temperatures, o C
Heat loads, kW
159
1
267
2
343
3 1
5,043
3
171
4
169
137
C1
13,695
C2
1,815
2
4,381
77
Heat-capacity flowrate
MCp, (kW/ O C)
Heat-transfer coefficient, h,
[W/( O C)(m 2 )]
228.5
400
88
20.4
300
90
53.8
250
127
265
H
17,597
175
9,230
128
73 26
4
118
5
93.3
196.1
150
500
2,000
Figure 4.1 A grid diagram, shown here for the example problem, offers a convenient method for depicting heat-exchange relationships.
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Temperatures, o C
Heat loads, kW
159
1
267
2
343
3 1 1
171
3
137
4
141
2
129
C1
11,930
C2
1,815
77
88
90
127 73
265
H
15,262
187
9,230
128
5,042
140
2,570
4,381
127
1,765
26
118
4
5
Figure 4.2 Retrofit by inspection prompts the addition of a new exchanger and revised duties.
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But why should we choose this level of energy savings? By installing more exchanger area (I.e., investing more capital) we could have saved more energy. By installing less exchanger area, we could save on capital. Although we would save less energy.
An economic analysis for various energy-recovery level is shown in Table 1. A simple calculation shows that the “set point” chosen in Fig. 2 saves significant energy
(about 13%) at a good payback (2 years).
Setpoint Investment,
£
million
1
2
3
4
0.184
0.293
0.484
0.670
Savings,
£ million/yr
0.111
0.148
0.192
0.213
Payback, yr
1.7
2.0
2.5
3.1
Table 4.1 Project economics of retrofit by inspection: higher savings, longer payback.
But how good is this result? There many be a doubt remaining. Could there be a better solution?
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SETTING RETROFIT TARGETING
Fig. 4.3 shows an energy/area plot, which relates the energy requirement with the heatexchange area used in a given process.
Point A represents a case where the composite curves are close (low

T min
), with corresponding high energy recovery but high investment in area.
Point C relates to composite curves that are more widely spaced, yielding lower energy recovery but less investment. We have a continuos curve representing networks that are all on target for both energy and area.
Point B represents the optimum tradeoff with the lowest total cost.
The area below the curve is tinted and marked “infeasible”. It is not possible for a design to be better than target..
But where would a retrofit candidate be situated? In most cases, we would expect it to be above the line, say at Point X. A design at Point X does not take best advantage of its installed area or, to put it another way, it does not recover as much energy as it should.
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A
Smaller  T
min
Optimum grassroot design
B
Infeasible
C
X
Existing network
Smaller  T
min
Energy requirement
Figure 4.3 Energy target plotted against heat-exchange-area target shows what can be achieved
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TARGETING PHILOSOPHY.
It is often assumed that good retrofits should be conducted by aiming toward the optimum new design. We can now see that this does not make sense. Who is prepared to throw away area that has already been paid for, if an optimum new design calls for less area? Our first objective must be to use the existing area more effectively.
In others words, we should try to improve on the ineffective use of area due to crisscrossing, while shifting the composite curves closer to save energy.
The ideal point to aim for from Point X in Fig. 4.3 would therefore be Point A.
here we would save as much energy as possible using the existing area. However, in practice we usually have to invest some capital to make changes to an existing network, thus increasing area. This leads to a “path” similar to that shown in Fig. 4.4
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A
Area already invested
B
Infeasible
Smaller  T
min
Likely path of retrofit
X
Existing network
Not Retrofit should not discard existing area
Optimum grassroot design
Energy requirement
Figure 4.4 A retrofit should try to reach Point A, not B, to take full advantage of the existing area
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Usually many options are available to the designer, so many paths will exist, as shown in Fig. 4.5. Clearly, the cost effectiveness of each of these curves will be different.
The lower the curve, the lower the investment for a given savings.
Assume that the best cure is that shown in Fig. 4.5. The shape of this curve is typical. Its slope increases with increasing investment. This implies that the payback period increases with investment level.
By using given costs of area and energy, the “best curve” can readily be transformed into a savings/investment relationships, as shown in Fig. 4.6. This curve relates annual energy savings to investment and payback. The project scope is usually set by one of these three criteria:
- Savings
- Investment or
- Payback period.
For example, in Fig. 4.6, for an investment of a
1
, we achieve a savings of b
1 at a 1-year payback. If we target a 2-years payback period, we can achieve a savings of b
2
.
Now we have genuine retrofit targets!.
Unfortunately, the “best curve” is difficult to determine. It is a function of plant layout and process constraints.
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Best retrofit
Existing design
Energy requirement
Fig. 4.5 many paths are possible for retrofit, but bottom curve, whose shape is typical, is the best.
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b
2
MODULE 12. NETWORK PINCH ANALYSIS
1 year
Payback period
2 years
5 years b
1 a
1 a
2
Investment
Figure 4.6 Best curve for area/energy can be translated into a savings/investment plot
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AREA EFFICIENCY
A assumption would be that the network, after retrofit, will use at least as effectively as before; if the project is good, then it is not likely to place new area in a manner that reduces the effectiveness of the area usage overall !!.
An “area efficiency” ,

, is equal to the ratio of minimum area required (target) to that actually used for a specific energy recovery:
 
A target
A existing existing energy
(4.1)
The value of
 can be expected to be less than unity in practical designs. A value of the unity would indicate “no criss-crossing”. The lower the value of 
, the poorer the use of area, and the more severe the criss-crossing.
If we assume that
 is constant over the full energy span, we would obtain the curve shown in Fig. 4.7. This curve forms a boundary for design.
We can now distinguish four distinct regions in the energy/area plot (Fig. 4.8):
- A region in which designs area infeasible (be they retrofit or new design).
- Two regions in which economic retrofits are not expected, and
- A fourth region within which good retrofits should fall.
We now have bounds within which we expected to find a good retrofit.
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A y
Target Constant

Y
A ty
A y

A tx
A x
 
A yt
A x
A tx
Existing design
E y
E x
Energy requirement
Fig.4.7 Assuming a constant area-efficiency yields a curve that serves as a boundary for design.
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Target Constant

Doubtful economics
Good projects
Infeasible Doubtful economics
Energy requirement
Figure 4.8 The best retrofits appear In a distinct region on the area/energy plot.
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From the constant-
 curve, we can determine what savings can be made for different levels of investment curve, such as in Fig. 4.6, can then drawn.
This is shown in Fig. 4.9 for the simple heat exchanger network example. The conservative target curve has been constructed, based on the data given. The economic setpoints for retrofit by inspection (Table 4.1) have also been included.
And a 2-year payback line is shown.
Figure 4.9 The economics of pinch-method retrofit markedly betters that of retrofit by inspection.
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For an investment of £ 0.29 million, retrofit by inspection yielded an energy savings of £
150,000/annum –an improvement of 28%!. This would correspond to a payback of
1.5 years, instead of 2 years. Alternatively, we would expect more than double the savings at 2years’ payback (£ 320,000 as opposed to £ 148,000).
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Having obtained targets, do not think that we can simply proceed to retrofit by inspection! What is needed is a design methodology that guarantees that the targets will be met.
Crucial design steps must be conducted correctly
A retrofit design method will be described. This method features a high degree of user interaction, rather than a mechanical “black box”.
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DESIGN PROCEDURE
The design procedure will be illustrated using the existing network shown in Fig. 4.1.
1.
Identify cross-pinch exchangers .
Draw the existing network on the grid (using

T min identified in the targeting stage) to find heat exchangers crossing the pinch. For the example, as seen in Fig. 4.10, exchangers 1, 2 and 4, and cooler C2 transfer heat across the pinch.
2
267
3
343
1
265
H
17,597
175
159 O C Pinch
4
1
169
C2
1,815
171
2
4,381

T min
= 19 o C
127
3
128
9,230
140 o C
2,000
137
C1
13,695
77
80
90
5,042
73 26
4
4,381
118
5
Figure 4.10 Network, initialized for retrofit, highlights exchangers working across the pinch.
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2. Eliminate cross-pinch exchangers. See Fig. 4.11. Exchangers 1, 2 and 4, and cooler
C2 have been removed.
Pinch
159 O C
1
2
3
267
343
3
137
C1
C2
77
80
90

T min
= 19 o C
127
265
H
175
26
4
118
5
Figure 4.11 Cross-pinch exchangers must be eliminated before network design is developed
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3.
Complete the network .
Position new exchange exchangers removed in Step 2. A possible network is shown in Fig. 4.12. Above the pinch, the heater and exchangers
1 and 4 are reused. Below the pinch, exchanger 2 is reused, but with reduced duty.
The remaining enthalpy on stream 4 is taken by exchanger 3. Cooler C2 has a reduced duty. Exchanger A is new.
159 O C Pinch
1
A
140
3
2
3
267
343
4
1
115
C2
2
1,612
C1
8,712
77
80
90

T min
= 19 o C
265
H
12,411
202
2,203
128
9,899
140 o C
4,314
127
5, 711
3,712
26
4
118
5
Figure 4.12 A preliminary design involves redeploying existing exchangers and adding new units
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4. Evolve improvements.
Improve compatibility with existing network via heat-load loops and paths. Reuse area of existing exchangers as much as possible.
A loop is a closed connection through streams and exchangers, i.e., it starts and end on the same point on the grid. Consider the corrected network shown in Fig. 4.13. An example loop is indicated by the long-dash line.
Use of loops introduces some flexibility into the design. Suppose the load of the new exchanger A is increased by X units. Then, by enthalpy balance over each, the load on exchanger 3 must be 5,711 – X, that on exchanger 2 will be 3,712 + X, and that on exchanger 1 will be 9,899 – X. This flexibility can be used to make old exchangers fit new duties.
A path also introduce flexibility. It is a connection through streams and exchangers between two utilities. In Fig. 4.13, a path can be traced from the heater through exchanger A to cooler C1 (shown as the short-dash line). Suppose we reduce the heat load on the heater by Y .
By shifting heat loads around loops and along paths, the final network as given in Fig.
4.14 is identified. In this design, the surface area of exchanger 3 is fully reused.
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MODULE 12. NETWORK PINCH ANALYSIS
2
267
343
3
4
1
159 O C Pinch
1
A
140
3

T min
= 19 o C
Path
127
5, 711
115
C2
2
1,612
C1
8,712
77
80
90
Loop
265
H
12,411
202
2,203
9,899
140 o C
4,314
3,712
26
4
118
5
Figure 4.13 Loops and paths enhance design flexibility, permitting reuse of existing exchangers
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1
159
2
267
343
3 1
4
New Exchanger
135
A
169
179
3
127
265
H
12,411
202
8,835
157
2,175
146
5,406
119
4,6471
136
4,776
115
C2
2 2
1,640
C1
8,684
77
80
90
26
118
4
5
Figure 4.14 Improved design employs all existing exchangers, and offers a 1.9-yr payback.
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State-of-the-art retrofit methodology relies on a mixture of past experience with the process, a few technical developments, and some inspired guesses.
The results are retrofit projects that range from ones that pay for themselves within a few weeks, to others that are recognized, soon after installation, to be a hindrance to further improvement.
There always seems to be an element of surprise, much more so than for grassroots design. It seems generally agreed that there is no methodology for the objective prediction of what is possible in a retrofit.
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TIER I: FUNDAMENTALS
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ROLE OF PROCESS ENGINEERS IN THE PROCESS INDUSTRIES.
Many process engineers would indicate that their responsibilities in the process industries is to design and operate industrial process and make them work:
FASTER, BETTER, CHEAPER, SAFER AND GREENER. All this tasks lead to more competitive processes with desirable profit margins and market share.
KEY DRIVERS FOR PROCESS-ENGINEERING RESEARCH .
These responsibilities may be expressed through to the seven themes identified by
Keller and Bryan 1 as the key drivers for process-engineering research, development and changes in the primary chemical process industries. These themes are:
Reduction in raw-material cost.
Reduction in capital investment.
Reduction in energy use.
Increase in process flexibility and reduction in inventory.
Ever greater emphasize on process safety.
Better environmental performance.
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FACING A TYPICAL CHALLENGING PROCESS IMPROVEMENT
PROBLEM.
The following observations may be made facing a typical challenging process improvement problem:
There are typically numerous alternatives that can solve the problem.
The optimum solution may not be intuitively obvious.
One should not focus on the symptoms of the process problem (resulting in solutions as: construct an expansion facility or ever install another one). Instead one should identify the root causes of the process deficiencies (resulting in make in plant process modifications as opposed to
“end-of-pipe” solution).
It is necessary to understand and treat the process as an integrated system.
There is a critical need to systematically extract the optimum solution from among the numerous alternatives without enumeration.
CONVENTIONAL ENGINEERING APPROACHES.
Until recently, there were three primary conventional engineering approaches to addressing process development and improvement problems:
1 Brainstorming and solution through scenarios.
2 Adopting/Evolving earlier designs.
3 Heuristics
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CONVENTIONAL APPROACHES ENGINEERING HAVE SERIOUS
LIMITATIONS.
Notwithstanding the usefulness of these approaches in providing solution that typically work, they have several serious limitations:
Cannot enumerate the infinite alternatives.
Is not guaranteed to come close to optimum solutions.
Time and money intensive.
Limited range of applicability.
Does not shed light on global insights and key characteristics of the process.
Severally limits groundbreaking and novel ideas.
These limitations can be eliminated if these two approaches are incorporated within a systematic and integrative framework
Recent advances in process design have led to the development of systematic, fundamental and generally applicable techniques can be learned and applied to overcome the aforementioned limitations and methodically address processimprovement problems. This is possible through PROCESS INTEGRATION.
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PROCESS INTEGRATION
Process Integration is a holistic approach to process design, retrofitting and operation which emphasizes the unity of the process 2 .
Process Integration involves the following activities:
1 TASK IDENTIFICATION.
2 TARGETING
3 GENERATION OF ALTERNATIVES.
4 SELECTION OF ALTERNATIVES.
5 ANALYSIS OF SELECTED ALTERNATIVES.
CLASIFICATION OF PROCESS INTEGRATION .
From the perspective of resource integration, process integration may be classified into:
ENERGY INTEGRATION
MASS INTEGRATION
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FINALLY, WHAT IS MASS INTEGRATION?
Mass Integration is a systematic methodology that provides a fundamental understanding of the global flow of mass within the process and employs this understanding in identifying performance target and optimizing the generation and routing of species throughout the process.
Mass-allocation objectives such a pollution prevention are the heart of mass integration.
Mass integration is based on fundamental principles of chemical engineering combined with systematic analysis using graphical and optimization-based tools.
The first step in conducting mass integration is the development of a global mass allocation representation of the whole process from a species viewpoint (Fig.
5.1):
Targeted species : e.g. pollutant, valuable material.
Sources: stream that carry the species (Rich streams)
Sinks : units that can accept the species (Reactors, heaters, coolers, bio-treatment facilities, and discharge media).
Mass Separating Agents (MSAs): Solvents, adsorbents, etc.
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.
.
.
prepare source streams to be acceptable to sinks within the process or to waste treatment.
Sources
Segregated
Sources
Mass-Separating
Agents in
Sources
Sinks/
Generators
(Back to
Process)
#1
MEN
.
.
.
#2
Mass-Separating
Agents out
(to Regeneration and Recycle)
N sinks
SEGREGATION
Avoid mixing of sources
RECYCLE
Direct a source in a sink
INTERCEPTION
Remove targeted species of source to make them acceptable for sinks.
Use MASs.
SINK/GENERATOR
MANIPULATION.
Involves design or unit operating changes.
Fig. 5.1 Schematic representation of process from species view point,
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EXAMPLE FOR SCHEMATIC REPRESENTATION OF PROCESS FROM SPECIES VIEW POINT
O
2
NH
3
C
3
H
6
Reactor
5.0 kg AN/s
5.1 kg H
2
O/s
+ Gases
Off-Gas
Condensate
14 ppm NH
0.4 kg AN/s
3
4.6 kg H
2
O/s
Water
6.0 kg H
2
O/s
B FW
1.2 kg H
2
O/s
Tail Gases to Disposal
Boiler
Steam
Steam-Jet
Ejector
Condensate
34 ppm NH
0.2 kg AN/s
3
1.2 kg H
2
O/s
Scrubber
18 ppm NH
4.6 kg AN/s
6.5 kg H
3
2
O/s
10 ppm NH
4.2 kg AN/s
1.0 kg H
3
2
O/s Distillation
Column
AN to
Sales
1ppm NH
3
3.9kg AN/s
0.3 kg H
2
O/s
Decanter
Source
Sinks
Aqueous
Layer
25 ppm NH
0.4 kg AN/s
3
5.5 kg H
2
O/s
Bottoms
0 ppm NH
3
0.1 kg AN/s
0.7 kg H
2
O/s
20 ppm NH
1.1 kg AN/s
3
12.0kg H
2
O/s
Wastewater to Biotreatment
Fig. 5.2a Flowsheet of Acrylonitrile (AN) production. Objective: debottlenecking the bio-treatment facilities.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE FOR SCHEMATIC REPRESENTATION OF PROCESS FROM SPECIES VIEW POINT
Air Carbon Resin
Off-Gas Condensate
Scrubber
Aqueous
Layer
Aqueous Layer
Feed to
Biotreatment
M E N
Distillation Bottoms
Ejector Condensate
Fresh Water to Scrubber
Fresh Water to Boiler
Boiler/
Ejector
Ejector
Condensate
Air to AN
Condensation
Carbon Resin
To Regeneration and Recycle
Fig. 5.2b Segregation, interception and recycle representation for the mass integration objectives in AN production
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1.- MINIMUM COST OF MSAs
Since the cost of MSAs is typically the dominant operating expenses,this target is aimed at minimizing the operating cost of the MEN,
Any design featuring the minimum cost of MSAs will be referred to as a minimum operating cost (MOC) solution.
This objective attempts to minimize indirectly the fixed cost of the network.
Minimizing the number of separators ( U) so as to reduce pipework, foundations, maintenance, and instrumentation
U = N
R
+ N
S
- N i (5.1)
N
R
= Number of Rich streams,
N
S
= Number of MSAs
Number of independent synthesis subproblems into which the original synthesis problem can be subdivided. Usually
N i = 1
In general, these two targets are incompatible. Systematic techniques will be presented to enable the identifying an MOC solution and the minimizing the number of exchangers satisfying the MOC.
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WHAT IS A MASS EXCHANGER?
Any countercurrent, Direct-contact mass-transfer operation that uses an MSA (or a
Lean phase), to selectively remove certain components (e.g. pollutants) from a
Rich phase (e.g. a waste stream).
Outlet
Composition: y i out
Rich (Waste) Stream
Flowrate:G i
Inlet Composition: y i in
Lean Stream (MSA)
Flowrate:L j
Inlet Composition: x j in
Outlet
Composition: x j out
Figure 5.3 Mass exchanger schematic representation.
ABSORPTION, DESORPTION, LIQ.-LIQ. EXTRACTION, LEACHING,
ION EXCHANGE.
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EQUILIBRIUM
MODULE 12. NETWORK PINCH ANALYSIS
Generalized description.
The composition of the Rich stream ( y i
) is a function of the composition of the Lean stream ( x j
) y i
= f * (x j
* ) (5.2)
For some applications the equilibrium function may be linearized over the operating range.
y i
= m j
·x * j
+ b j
(5.3)
For linear equilibrium the pollutant composition in the lean phase in equilibrium y i can be calculated by x
* j
 y i
 b j m j
For linear equilibrium the pollutant composition in the rich phase in equilibrium x j can be calculated by y i
*  m x j j b j
(5.4)
(5.5)
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EQUILIBRIUM
Special cases
– Raoult’s Law for absorption: y i
 p
0
( ) solute

P
Total x
* j
– Henry’s Law for striping
(5.6) y i
P
Total
Mole fraction of solute in gas
P o solute
Vapor pressure of solute at T x * j
Mole fraction of solute in liquid
Total pressure of gas y i

H j
 x
* j
(5.7) y i x * j
H j
Mole fraction of solute in gas
Mole fraction of solute in liquid
Henry’s coefficient
H j

P
Total p
0
solute
 y i solubility
(5.8) y i solubility Liquid-phase solubility of the pollutant at temperature T
– Distribution function used in solvent extraction y i
= K j
·x * j
(5.9) K j
Distribution Coefficient
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MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
EXAMPLES OF MULTISTAGES CONTACTORS
Light Phase Out
MSA
out
Waste in
Heavy Phase In
Shell
Perforated
Plate (Tray)
Weir
Downcomer
MSA
in
Light Phase In
Heavy Phase Out
Fig. 5.4 A multistage tray column
Fig. 5.5 A three-stage mixer-setter system
Waste out
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MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
A GENERIC MASS EXCHANGER
Outlet
Composition: y i out
Rich (Waste) Stream
Flowrate:G i
Inlet Composition: y i in
Lean Stream (MSA)
Flowrate:L j
Inlet Composition: x j in
Outlet
Composition: x j out
Figure 5.3 Mass exchanger schematic representation.
SCHEMATIC OF A MULTISTAGE MASS EXCHANGER y i,1
=y i out
1 y i,2
2 y i,3 y i,n n y i,n+1 y i,N-1
N-1 y i,N
N y i,N+1
=y i in x j,0
=x j in x j,1 x j,2 x j,n.1
x j,n x j,N-2 x j,N-1 x j,N
=x j ou t
Fig. 5.6 A schematic diagram of a multistage mass exchanger
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MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
OPERATING LINE (MATERIAL BALANCE)
G i
(y i in  y i out
)

L j
(x out j
 x in j
)
THE McCABE-THIELE DIAGRAM
Operating
Line y i y i in y i out
L j
/G
Equilibrium
Line x j in x j out x j
Figure 5.7 The McCabe Thiele diagram i y out y in
G
L x x in out
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MODULE 12. NETWORK PINCH ANALYSIS
MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
THE KREMSER EQUATION:
For the case of isothermal, dilute mass exchanger with linear equilibrium, the
Number of Theoretical Plates (NTP)for a mass exchanger can be determined through the Kremser equation:
NTP






 m G
L j i j

 y y i i in out

 m x j j m x in in j j

 b b j j


L j m G j i



  m G j i


L j (5.10)
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MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
OTHER FORM OF KREMSER EQUATION IS
NTP







L j m G j i

 x x j i in out

 x x out j j out
,*
,*

 m G j i
L j



 
L i m G j i

 also y i in  m x out j j
 b j
L j y i out  m x in j j
 b j m G j i


NTP where x out j
,*  y i in
 b j m j
(5.11)
(5.12)
(5.13)
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MASS EXCHANGER MODELING: MULTISTAGE CONTACTORS
NUMBER OF ACTUAL PLATES (NAP)
The overall exchanger efficiency,

0
, can be used to relate NAP and NTP as follows
NAP

NTP
 o
(5.14)
The Stage efficiency can be based on either the rich or the lean phase. If based on the rich phase the Kremser equation can rewritten as
NTP
 ln




 1
 m G
L j i j

 y y i i in out

 m x j j m x in in j j

 b b j j

 ln 1
  y



 m G j i
L j



 

1

 
 m G j i


L j
(5.15)
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MASS EXCHANGER MODELING:
DIFFERENTIAL (or CONTINUOS) CONTACTORS
Random
Packing
EXAMPLES OF DIFFERENTIALS CONTACTORS
Heavy
Phase In
Light
Phase Out
Packing Restrainer
Heavy
Phase In
Shell
Mixer
Light Phase
Out
Heavy
Phase In
Shell
Shell
Heavy-Phase
Re-Distributor
Random
Packing
Packing
Support Light
Phase in
Heavy
Phase Out
Light
Phase In
Heavy Phase
Out
Figure 5.8 Counter current packed column
Figure 5.9 A mechanically-agitated mass exchanger
Light
Phase Out
Light
Phase In
Heavy
Phase Out
5.10 A spray column
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MASS EXCHANGER MODELING
DIFFERENTIAL (or CONTINUOS) CONTACTORS
HEIGH OF A DIFFERENTIAL CONTACTOR, H .
H

HTU NTU y
H

HTU NTU x x
(5.14)
(5.15) where HTU y and HTU x are the overall height of transfer units based on the rich and the lean phases, respectively, while, NTU y and NTU x are the overall number of transfer units based on the rich and lean phases, respectively
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MASS EXCHANGER MODELING
DIFFERENTIAL (or CONTINUOS) CONTACTORS
EQUATION FOR NTU y
For the case of isothermal, dilute mass exchanger with linear equilibrium the NTU y can be theoretically estimated as follow
NTU y

y i in  y i out y i
 y i
*
log mean
(5.16) where
 y i
 y i
*
 log mean

 y i in  m x out j j
 b j
  ln

 y i out  m x in j j
 b j y i in  m x out j j
 b j y i out  m x in j j
 b j



(5.17)
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MASS EXCHANGER MODELING
DIFFERENTIAL (or CONTINUOS) CONTACTORS
EQUATION FOR NTU x
For the case of isothermal, dilute mass exchanger with linear equilibrium the
NTU x can be theoretically estimated as follow
NTU x
 x in j
( x j

 x out j x
* j
) log mean where
(5.18)
( x j
 x * j
) log mean



 x out j


 ln y i in m
 j b j













 x out j x in j







 y


 i in x m in j


 y i out m
 j j b j b j


 y i out m
 j
















 b j



(5.19)
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MASS EXCHANGER MODELING
COLUMN DIAMETER
The column diameter is normally determined by selecting a superficial velocity for one (or both) of the phases. This velocity is intended to ensure proper mixing while avoiding hydrodynamic problems such as flooding, weeping, or entrainment.
Once a superficial velocity is determined, the cross-sectional area of the column is obtained by dividing the volumetric flowrate by the velocity.
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2005
1978

.
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FIXED COST
The car itself, i.e. body, engine, tires, etc.
Old car: $ 500.00
New car: $21,000.00
ANNUAL OPERATING COST (AOC)
How much to run and maintain the car.
Old car: $ 4,000.00/year
New car: $ $ 700.00/year.
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ANNUALIZED FIXED COST (AFC)

TOTAL ANNUALIZED COST (TAC)
 
(5.20)
(5.21)
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Useful life: 2 years
Salvage value: $ 200.00
AFC = ($ 500 - $ 200)/2 yr
AFC = $ 150/yr
Useful life: 20 years
Salvage value: $ 1000
AFC = ( $ 21000 - $ 1000)/20 yr
AFC = $ 1000/yr
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TAC = $ 4,000 + $ 250 TAC = $ 1,000 + $ 700
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TOTAL ANNUALIZED COST
– Fixed Cost: Trays. Shell. Packing, etc.
– Operating Cost: Solvent makeup, pumping, heating, cooling,etc.
TAC

AOC

AFC y
Practical Feasibility Region
DRIVING FORCE
– Minimum Allowed
Composition Difference (

).
– Must stay to left of equilibrium line.
 j
(5.22)
Figure 5.11 Establishing corresponding composition scales.
 j
Equilibrium x
Line
* j
= (y - b j
)/m j
Practical Feasibility
Line x j
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MODULE 12. NETWORK PINCH ANALYSIS
DRIVING FORCE
 j y i in y i in y i y i out
Operating
Line y i
Operating
Line
 j
Equilibrium
Line
Equilibrium
Line y i out x j in x j out, max x j out, * x j
In max x j x j out, x j
Fig. 2.9. Minimum Allowable Composition Difference at the
Figure 5.12  at the rich end of a mass exchanger Figure 5.13  at the lean end of a mass exchanger
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MODULE 12. NETWORK PINCH ANALYSIS
DRIVE FORCE
 at the rich end of mass exchanger.
x out , max j
 x j out ,*   j
(5.23) but y i in  m j x out ,* j
 b j
(5.24)
Combining Eqs. (5.23) and (5.24), one obtains x out , max j
 y in  b j   j m j
(5.25)
When the minimum allowable composition difference
 j increases, then the ratio of
L/G increases.
AOC increases, due to higher MSA flow
AFC decreases, due to smaller equipment, e.g. fewer stages
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MODULE 12. NETWORK PINCH ANALYSIS
DRIVING FORCE OPTIMUM
Trade-off between reducing fixed cost and increasing operating cost
Composition driving force, becomes a optimization variable
O P
T I MU M
70,000
60,000
50,000
40,000
30,000
TAC
Annual Operating
Cost
20,000
10,000
Annualized
Fixed Cost
0
0.0000
0.0010
0.0020
0.0030
0.0040
Minimum Allowable Composition Difference,
0.0050

Fig2.13. Using Minimum Allowable Composition Difference to
Figure 5.14 Using mass transfer force to trade off fixed cost versus operating cost.
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MODULE 12. NETWORK PINCH ANALYSIS
CHEMICAL
PETROLEUM
GAS
PETROCHEMICAL
PHARMACEUTICAL
FOOD
MICROELECTRONICS
METAL
TEXTILE
FORESTRY PRODUCTS
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MODULE 12. NETWORK PINCH ANALYSIS
Figure 5.15 Schematic representation of the MEN synthesis problem
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MODULE 12. NETWORK PINCH ANALYSIS
WHAT DO WE KNOW?
A Number of N
R of waste (rich streams) sources.
A Number of Mass Separation Agents (lean streams) N
S
= N
SP
+ N
SE
:
• N
SP
Number of of process MSAs
• N
SE
Number of of external MSAs
Flowrate of of each waste stream, G i
, its supply (inlet) composition, y s i target (outlet) composition, y t i
, where i = 1, 2 ,…N
R and its
The supply and target compositions, x s j
…., N
S.
, and, x t j
, for each MSA, where j = 1, 2,
WHAT DON’T WE KNOW?
The flowrate of each MSA is unknown and is to be determined so as to minimize the network cost.
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MODULE 12. NETWORK PINCH ANALYSIS
CONSTRAINTS FOR EACH LEAN STREAM (MSAs).
Target Composition
 PHYSICAL e.g. maximum solubility of solute in solvent.
 ECONOMIC to optimize the cost of any subsequent separation of the effluent lean stream.
 TECHNICAL to avoid excessive corrosion, viscosity, or fouling.
 ENVIRONMENTAL as imposed by some environmental protection regulation.
Flowrate
 The lean process streams already exist at plant site and are bounded by availability in the plant. Can be used for pollutant removal for virtually free.
 The mass flow rate of any external MSA is flexible and should be determined according to the economic considerations of the networks synthesis.
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MODULE 12. NETWORK PINCH ANALYSIS
BASIC ASSUMPTIONS .
1 The flowrate of each stream remains essentially unchanged as it passes through network.
G in i
= G out i
(5.26)
L in j
= L out j
(5.27)
2 Within the MEN, stream recycling is not allowed.
3 In the range of composition involved, any equilibrium relation governing the distribution of a targeted species between the rich stream and the lean stream is linear and independent of the presence of othe soluble components in the rich stream.
y i
= m j
·x * j
+ b j
(5.28) where both m j and b j are assumed to be constants.
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MODULE 12. NETWORK PINCH ANALYSIS
MEN SYNTHESIS TASK .
– Which mass-exchange operations should be used (e.g. absorption, adsorption)?
– Which MSAs should be selected (e.g. which solvents, adsorbents)?
– What is the optimal flowrate of each MSA?
– How should these MSAs be matched with the waste streams (I.e., stream pairings)?
– What is the optimal system configuration (e.g., how should these mass exchangers be arranged? Is there any stream splitting and mixing?)?
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MODULE 12. NETWORK PINCH ANALYSIS
DESIGN TAGETS
Minimum Cost of MSAs
This target aims at minimizing the operating cost of the network. In many industrial applications, this target has a profound impact on the economics of the separation system.
Minimum Number of Mass Exchamger Units.
This objective attempts to minimize indirectly the fixed cost of the network since the cost of each mass exchanger is usually a cocave function of the unit size.
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MODULE 12. NETWORK PINCH ANALYSIS
THE CORRESPONDING COMPOSITION SCALES .
The concept of “corresponding composition scales” is a tool for incorporating constraints of mass exchange by establishing a one-to-one correspondence among the composition of all streams for which mass transfer is thermodynamically feasible.
This concept is based on a generalization of the notion of a “minimum allowable composition difference’, 
, presented before.
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MODULE 12. NETWORK PINCH ANALYSIS
The equilibrium relation governing the transfer of the pollutant from the waste stream,
,to the MSA, , is t given by the linear equation (5.28) y i
 m x j
  j b j which indicates that for a waste stream composition of, , the maximum theoretically attainable composition of the MSA is .
The mathematical expression relating and on the practical-feasibility line can be derived as follow y
Practical Feasibility Region combining two equations
* x j
 x j
  j
(5.29)
 j or y i
 m j

( x j
  j x j
 y i
 b j   j m j
)
 b j
(5.30)
(5.31)
 j
Equilibrium
Line x * j
= (y - b j
)/m j
Practical Feasibility
Line x j
These equations can be used to establish a one-one correspondence among all composition scales for which mass exchange is feasible.
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MODULE 12. NETWORK PINCH ANALYSIS
In order to minimize the cost of MSAs, it is necessary to make maximum use of process
MSAs before considering the application of external MSAs.
In assessing the applicability of the process MSAs to remove the pollutant, one must consider the thermodynamic limitations mass exchange. Toward this end, one may use a graphical approach referred to as the “Pinch diagram”.
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MODULE 12. NETWORK PINCH ANALYSIS
INDIVIDUAL REPRESENTATION FOR RICH STREAMS
Each rich stream is represented as as arrow whose tail corresponds to its supply composition and its head to its target composition.
The slope of each arrow is equal to the stream flowrate.
The vertical distance between the tail and the head of each arrow represents the mass of pollutant that is lost by that rich stream according to
MR i
= G i
(y s i
- y t i
) I = 1,2,…, N
R
(5.32)
The vertical scale is only relative, any stream can be moved up or down.
MR
2
R
2
MR
1
R
1 y
1 t y
2 t y
1 s y
2 s y
Figure 5.16 Representation of mass exchanged by two rich streams.
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MODULE 12. NETWORK PINCH ANALYSIS
REPRESENTATION OF RICH COMPOSITE STREAM
A Rich Composite stream represents the cumulative mass of the pollutant lost by all the rich streams.
It is obtained by applying linear superposition (by using the
“diagonal rule”) to all the rich streams.
MR
2 R
2
MR
1
R
1 y
1 t y
2 t y
1 s y
2 s y
Figure 5.17 Constructing a rich composite stream using superposition.
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MODULE 12. NETWORK PINCH ANALYSIS
INDIVIDUAL REPRESENTATION FOR LEAN STREAMS
We establish N
SP lean composition scales (one for each process MSA) that are in one-one correspondence with the rich scale.
The mass of pollutant that can be gained by each process MSA is plotted vs the composition scale of that MSA.
Each process MSA is represented as an arrow extending between supply and target composition.
The Mass of pollutant that can be gained by the j th process MSA is
MS j
= L c j
(x t j
-x s j
) j = 1, 2, …, N
SP
(5.33)
The vertical scale is only relative and any stream can be moved up or down on the diagram.
MS
2
MS
1 x
1 s x
2 s
S
1
S
2 x
1 t x
2 t x
1
 x
2
 y y
 b
1 m
1 y
 b
2
 
1
 
2 m
2
Figure 5.18 Representation mass exchanged by two process MSAs.
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MODULE 12. NETWORK PINCH ANALYSIS
REPRESENTATION OF RICH COMPOSITE STREAM
A convenient way of vertically placing each arrow is to stack the process
MSAs on top of one another starting with the MSA having the lowest supply composition.
A lean composite stream representing the cumulative mass of the pollutant gained by all the MSAs is obtained by using the diagonal rule for superposition.
MS
2
MS
1
S
1
S
2 x
1 s x
2 s x
1 t x
2 t y x
1
 x
2
 y
 b m
2
1 m
1 y
 b
2
 
1
 
2
Figure 5.19 Constructing a lean composite stream using superposition.
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MODULE 12. NETWORK PINCH ANALYSIS
CONSTRUCTING THE PINCH DIAGRAM
Both composite streams are plotted on the same diagram.
The lean composite stream can be slid down until touches the waste composite stream
The point where the two composite streams touch is called the “massexchange pinch point”: hence the name “pinch diagram”.
Lean Composite
Stream
Mass Exchange
Pinch Point
Excess capacity of Process MSAs
Load to be
Removed by
External
MSAs
Rich Composite
Stream
Integrated mass Exchanged y x
1 x
2
Figure 5.20 The mass-exchange pinch diagram.
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MODULE 12. NETWORK PINCH ANALYSIS
INTERPRETING THE PINCH DIAGRAM
INTEGRATED MASS EXCHANGE.
The vertical overlap between the two composite streams represents the maximum amount of the pollutant that can be transferred from the waste streams to the process MSAs.
EXCESS CAPACITY OF PROCESS MSAs.
It corresponds to the capacity of the process MSAs to remove pollutants that cannot be used because of thermodynamic unfeasibility.
According to the designer’s preference or to the specific circumstances of the process such excess can be eliminated from service by lowering the flowrate and/or the outlet composition of one or more of the process MSAs.
LOAD TO BE REMOVED BY EXTERNAL MSAs.
It is the vertical distance of the waste composite stream which lies below the lower end of the lean composite stream.
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The pinch point decomposes the synthesis problem into two regions .
MODULE 12. NETWORK PINCH ANALYSIS
INTERPRETING THE PINCH DIAGRAM
Rich End
Above the pinch , exchange between the rich and the lean streams takes place. External
MSAs are not required.
To minimize the cost of external
MSAs, mass should not be transferred across the Pinch .
Lean End y x
1 x
2
Figure 5.21 The pinch point decomposes the synthesis
Problem Into two regions.
Below of Pinch , both the process and the external lean streams should be used.
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MODULE 12. NETWORK PINCH ANALYSIS
RECOVERY OF BENZENE FROM GASEOUS EMISSION OF A
POLYMER PRODUCTION PROCESS.
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MODULE 12. NETWORK PINCH ANALYSIS
PROCESS DESCRIPTION.
The copolymer is produced via two-stage reaction. The monomer are first dissolved in a benzene-based solvent. The mixed-monomer mixture is fed to the first stage of reaction where a catalytic solution is added. Several additives (extending oil, inhibitors, and special additives) are mixed in a mechanically stirred column. The resulting solution is fed to the second-stage reactor, where the copolymer properties are adjusted. The stream leaving the second-stage reactor is passed to a separation system which produces four fraction: copolymer, unreacted monomers, benzene, and gaseous waste . The copolymer is fed to a coagulation and finishing section.
The unreacted monomers are recycled to the first-stage reactor, and the recovered benzene is returned to the monomer-mixing tank.
Figure 5.22 shows a simplified flowsheet of a copolymerization plant.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
FLOWSHEET PROCESS.
Inhibitors
+ Special Additives
Extending
Agent
Catalytic
Solution
( S
2
)
S
1
Additives
Mixing
Column
Gaseous
Waste (R
1
)
Monomers
Solvent
Makeup
Monomers
Mixing
Tank
First Stage
Reactor
Second Stage
Reactor
Separation
Copolymer
(to Coagulation and Finishing)
Recycled Solvent
Unreacted Monomers
Figure 5.22 A simplified flowsheet of a copolymerization process
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
RICH STREAM
The gaseous waste is the rich stream, R
1
, contains benzene as the primary pollutant that should be recovered.
Stream Description
R
1
Flowrate
G
I
, kgmol/s
Supply composition
(mole fraction), y s i
Target composition
(mole fraction), y t i
Off-gas from product separation
0.2
0.0020
0.0001
Table 5.1 Data waste stream for the benzene removal example.
LEAN STREAMS. MASS SEPARATION AGENTS (MSA).
Process MSAs : two process MSAs are considered for recovering benzene from the gaseous waste. They are the additives, S
1
, and the liquid catalytic solution, S
2
.
The use of these process MSAs offers several advantages:
– They can be used at virtually no operating cost.
– Its positive environmental impact.
– Economic incentive since it reduces the benzene makeup needed to compensate for the processing losses.
– The additives mixing column can be used as an absorption column by bubbling the gaseous waste into the additives.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
Stream
S
1
S
2
Description
Additives
Catalytic solution
Upper bound on flowrate
L
C j
kg mol/s
0.08
0.05
Supply composition of benzene
(mole fraction), x s j
0.003
0.002
Target composition of benzene
(mole fraction), x t j
Table 5.2 Data of process lean stream for the benzene removal example.
0.006
0.004
The equilibrium data for benzene in the two process MSAs are given by: where y , x
1 and respectively.
x
2 y = 0.25 x
1
(5.34) and y = 0.50 x
2
(5.35) are the mole fractions of benzene in the gaseous waste, S
1 and S
2
The minimum allowable composition difference (

) for S
1
0.001.
and S
2 should not be less than
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
External MSA : One external MSA is considered for recovering benzene. The external
MSA, S
3
, is an organic oil that can be regenerated using flash separation.
The operating cost of the oil (including pumping, makeup, and regeneration) is $ 0.05/kg mol of recirculating oil.
The equilibrium relation for transferring benzene from the gaseous waste to the oil is given by y = 0.10 x
3
(5.36)
The data for S
3 are given in the table 5.3.
Stream Description
S
3
Upper bound on flowrate
L
C j
kg mol/s
Supply composition of benzene
(mole fraction), x s j
Target composition of benzene
(mole fraction), x t j
Organic oil

0.0008
0.0100
Table 5.3 Data for the external MSA for the benzene removal example.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
DESIGN TASK.
Using the graphical pinch approach, synthesize a cost-effective Mass exchanger
Network that can be used to remove benzene from the gaseous waste, Fig. 5.22
Benzene
Oil
Makeup
Oil
S
3
Catalytic Solution
S2
Additives
(Extending Agent, Inhibitors and Special Additives)
S1
To
Atmosphere
Benzene Recovery MEN
Gaseous
Waste
R1
Monomers
Mixing
First Stage
Reactor
Second Stage
Reactor
Separation
Copolymer
( to Coagulation and Finishing)
Solvent
Makeup
Recycled Solvent
Unreacted Monomers
Figure 5.22 The copolymerization process with a benzene recovery MEN.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION.
CONSTRUCTING THE PINCH DIAGRAM .
Constructing the Rich Composite Stream.
6.0
5.0
4.0
3.0
3.8
y t
1
2.0
1.0
Rich Composite
Stream
0.0
0.0000
0.0001
0.0005
0.0010
0.0015
0.0020
0.0025
y
Figure 5.23 Rich composite stream for the benzene recovery example.
y s
1 m = G
1
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION . CONSTRUCTING THE PINCH DIAGRAM.
Constructing the Lean Composite Stream. Step 1 representation of individual lean streams.
6.0
x s
2
5.0
x t
2
4.0
3.4
3.0
S
2
Mass exchanged
2.4
2.0
S
1
1.0
0.0
0.0000
0.0001
0.0005
0.0010
0.0010
0.0030
0.0015
0.00175
0.0020
0.0050
0.006
0.0070
0.0025
y
0.0090
x
1
0.0040
x
2
0.0000
0.0010
0.0020
0.0030
Figure 5.24 Representation of the two process MSAs for the benzene recovery example.
Corresponding composition scales calculated by i x j
 j y i
 m j j b j  j
)
 j
 b j
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION.
CONSTRUCTING THE PINCH DIAGRAM.
Constructing the Lean Composite Stream. Step 2 representation of the lean composite stream curve.
6.0
5.0
4.0
3.4
3.0
S
2
2.0
1.0
0.0
0.0000
0.0001
0.0005
0.0010
S
1
0.0015
0.00175
0.0020
0.0010
0.0000
0.0030
0.0010
0.0050
0.006
0.0070
0.0020
0.0030
2.4
The lean composite stream is obtained by applying superposition to the two lean arrows
0.0025
y
0.0090
x
1
0.0040
x
2
Figure 5.25 Construction of the lean composite stream for the two process
MSAs of the benzene recovery example.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION.
CONSTRUCTING THE PINCH DIAGRAM
The pinch diagram is constructed by combining the two composite curves. The lean composite curve stream is slid vertically until it is completely above the rich composite stream.
6.0
Lean Composite
Stream
5.2
5.0
4.0
4.2
3.8
3.0
Pinch
Point
2.0
1.0
Rich
Composite
Stream
1.8
Figure 5.26 The pinch diagram for the
Benzene Recovery example
( 
1
=

2
=0.001).
0.0
0.0000
0.0001
0.0005
0.0010
0.0000
0.0010
0.0030
0.0010
0.0015
0.00175
0.0020
0.0050
0.006
0.0070
0.0020
0.0030
0.0025
y
0.0090
x
1
0.0040
x
2
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION.
INTERPRETING THE PINCH DIAGRAM .
6.0
Lean Composite
Stream
5.2
Excess capacity of process MSAs is 1.4x10
-4 kg mol/s
5.0
4.0
Excess Capacity of Process MSA’s
Pinch pint is located at:
(y, x
1
, x
2
) =
(0.0010,
0.0030,
0.10010)
3.0
Pinch
Point
2.0
1.0
Rich
Composite
Stream
0.0
0.0000
0.0001
0.0005
0.0010
0.0000
0.0010
0.0030
0.0010
4.2
3.8
Integrated
Mass
Exchange
1.8
Load to Be
Removed By
External MSA’s
0.0015
0.00175
0.0020
0.0050
0.006
0.0070
0.0020
0.0030
0.0025
y
0.0090
x
1
0.0040
x
2
1.8 x 10 -4 kg mol/s
Figure 5.27 Interpreting the pinch diagram for the benzene recovery example.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SOLUTION.
INTERPRETING THE PINCH DIAGRAM.
REMOVING EXCESS CAPACITY
The excess capacity of the process MSAs is eliminated by avoiding the use of S
2 and reducing the flowrate and/or outlet composition of S
1
.
There are infinite combinations of L
1 and x
1 out that can be used to remove the excess capacity of S
1 according to the following material balance:
S
1
= L
1
(x
1 out - x
1 s )
S
1 is benzene load above the pinch to be removed.
2 x 10 -4 = L
1
(x
1 out - 0.003)
(5.37)
(5.38)
Excess capacity
Nonetheless, since the additives-mixing column will be used for absorption, the whole flowrate of S
1
(0.08 kg/s) should be fed to the column the outlet composition of S
1 is 0.0055.
. Hence according to Eq. (5.38),
The same result can be obtained graphically as shown in Fig. 5.28.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
REMOVING EXCESS CAPACITY. Graphically
6.0
x
1 out is modified
5.0
The whole flowrate of S
1 is used
4.0
4.2
3.8
3.0
Pinch
Point
S
1
Integrated
Mass
Exchange
2.0
1.8
1.0
Rich
Composite
Stream
Load to be
Removed by
External MSA’s
0.0
0.0000
0.0001
0.0005
0.0010
0.0015
0.00175
0.0020
0.0025
y
0.0090
x
1
0.0010
0.0030
Figure 5.28 Graphical identification of x
0.0050
0.006
0.0070
0.0055
1 out .
New value of x excess capacity
1 out to remove
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
SELECTION OF THE OPTIMAL VALUE OF

.
In this example it is desired to maximize the integrated mass exchanged above the pinch. As can see on the pinch diagram when

1 increases , the x
1 axis moves to the right relative to the y axis and, consequently, the extend of integrated mass exchange decreased leading to a higher cost of external MSAs.
The increase of

1 to 0.002 results in the following mass integration values:

1
= 0.001

1
= 0.002
Load of benzene to be removed by external MSAs (kg mol/s)
Integrated mass exchanged
Excess capacity of process
MSAs
1.8 x 10
-4
2.0 x 10
-4
1.4 x 10
-4
2.3 x 10
-4
1.5 x 10
-4
1.0 x 10
-4
Thus: the optimum

1 in this example is the smallest permissible value given in the problem statement to be 0.001.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
THE PINCH DIAGRAM WHEN 
1
= 0.002
6.0
Lean
Composite
Stream
5.7
5.0
Excess Capacity of Process MSA’s
4.7
4.0
3.8
3.0
Integrated
Mass
Exchange
2.3
2.0
1.0
Rich
Composite
Stream
0.0
0.0000
0.0001
0.0005
0.0000
0.0000
Pinch
Point
0.0010
0.00125
0.0015
0.0020
0.0030
0.0040
0.0010
0.0020
Load to Be
Removed By
External MSA’s
0.0020
0.0060
0.0030
0.0025
y
0.0080
x
1
0.0040
x
2
Figure 5.29 The pinch diagram when 
1 is increased to 0.002.
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
REMAINING PROBLEM. BELOW OF PINCH
The pinch diagram demonstrates that below the pinch, the load of the waste stream has to be removed by the external MSA, S
3
.
y i out = 0.0001
Regenerated Solvent
L x j
?
j in = 0.0008
Cooler
Absorption
Column
Gaseous Waste
G y i i in
= 0.2 kgmole/s
= 0.0010
Recovered
Benzene
Flash
Column x j out ?
Heater
Optimum value of


= 1.5 x 10 -3
Optimal flowrate of S
3
S
3
= 0.0234 kg mol/s
Optimal outlet composition of S
3 x
3 out = 0.0085
Minimum TAC
$41,560/yr
Figure 5.30 Recovery of benzene from a gaseous emission.
Fig. 2.12. Recovery of Benzene from a Gaseous Emission
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MODULE 12. NETWORK PINCH ANALYSIS
EXAMPLE 1: RECOVERY OF BENZENE FROM A POLYMER PRODUCTION PROCESS
CONSTRUCTING THE SYNTHESIZED NETWORK
The previous analysis shows that the MEN comprises two units:
One above the pinch in which R
1 is matched with S
1
, and
One below the pinch in which the remainder load of R
1 is removed using S
3
.
y
1 t = 0.0001
Regenerated Solvent, S
3
L x
3
3 s
= 0.0234 kgmole/s
= 0.0008
Makeup y pinch = 0.0010
Regeneration x
3 out = 0.0085
Additives Mixture, S
1
L
1
= 0.08 kgmole/s x
1 s = 0.0030
Gaseous Waste, R
1
G y
1
1 s
= 0.2 kgmole/s
= 0.0020
x
1 out = 0.0055
Figure 5.31 Optimal MEN for the
Benzene recovery example.
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
Notwithstanding the usefulness of the pinch diagram, it is subject to the accuracy problems associated with any graphical approach. This is particularly true when there is a wide range of operating compositions for the waste and the lean streams. In such cases, an algebraic method is recommended.
This section presents an algebraic procedure which yields results that are equivalent to those provided by the graphical pinch analysis.
The algebraic method can be programmed and formulated as optimization problems.
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MODULE 12. NETWORK PINCH ANALYSIS
The CID is a useful tool for insuring thermodynamic feasibility of mass exchange.
On this diagram, N sp
+ 1 corresponding composition scales are generated:
– First, a composition scale, y , for the waste streams is established.
– Then, the equations (5.30) and (5.31) y i
 m j

( x j
  j
)
 b j
(5.30) are employed to create N sp
MSAs
, x j
 y i
 b j   j
(5.31) m j corresponding composition scales for the process
On the CID, each process stream is represented as a vertical arrow whose tail corresponds to its supply composition while its head represents its target composition.
Next, horizontal lines are drawn at the heads and tails of the arrows. These horizontal lines define a series of composition intervals.
The number of intervals is related to the number of process streams via
N int

2(N
R
+ N
SP
) - 1
(5.39)
The composition intervals are numbered from top to bottom in an ascending order.
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MODULE 12. NETWORK PINCH ANALYSIS
The index k will be used to designate an interval with k = 1 being the uppermost interval and k = N int being the lowermost interval.
Figure 5.31 provides a schematic representation of the CID.
Within any interval. It is thermodynamically feasible to transfer mass from a waste stream in an interval k to any MSA which lies an interval k* below it (i.e., k*
≥ k ).
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MODULE 12. NETWORK PINCH ANALYSIS
Interval
7
8
9
10
.
.
.
N int
3
4
1
2
5
6 y
NR t
Rich
Streams y
1 s R
1 x
1

( y
 b
1
) / m
1
 
1 x
1 t
Process MSA’s x
2

( y
 b
2
) / m
2
 
2 x
Nsp y b
Nsp
) / m
Nsp
 
Nsp x
2 t x
Nsp t y
1 t x
Nsp s
S
Nsp y
2 s R
2 y
NR s R
NR x
1 s
S
1 y
2 t x
2 s
S
2
Figure 5.31 The composition interval diagram “CID”.
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MODULE 12. NETWORK PINCH ANALYSIS
The objective of constructing a TEL is to determine the mass exchange loads of the process streams in each composition interval.
The exchangeable load of the i th waste stream which passes through the k th interval is defined as
(5.40)
W R j,k
= G i
( y k-1
- y k
) where y k-1 and y k are the waste-scale composition of the transferrable species which respectively correspond to the top and the bottom lines defining the k th interval.
The exchangeable load of the j th process MSA which passes through the k th interval is computed through the following expression
W S j,k
= L C j
( x j,k-1
- x j,k
)
(5.41) where x j,k-1 and x j,k are the composition on the j th lean composition scale which respectively correspond to the higher and lower horizontal lines bounding the k th interval.
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MODULE 12. NETWORK PINCH ANALYSIS
Clearly, if a stream does not pass through an interval, its load within that interval is zero.
The collective load of the waste streams within the k th interval is calculated by summing up the individual loads of the waste streams that pass through that interval, I.e.
W k
R  i

passes through interval k
W
R
(5.42)
The collective load of the lean streams within the k th interval is evaluated as follow:
W k
S
 j

passes through interval k
W
S (5.43)
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MODULE 12. NETWORK PINCH ANALYSIS
We are now in a position to incorporate material balance into the synthesis procedure with the objective of allocating the pinch point as well as evaluating excess capacity of process MSAs and load to be removed by external MSAs.
These aspect are assessed through the mass-exchange cascade diagram.
For the k th composition interval, one can write the following component material balance for the key pollutant:
(5.44)
W k
R   k

1

W k
S   k where
 k-1 and
 k the k th interval.
are the residual masses of the key pollutant entering and leaving
Equation (5.44) indicates that the total mass input of the key component to the k th interval is due to collective load of the waste stream in that interval as well as the residual mass of the key component leaving the interval above it,
 k-1
.
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MODULE 12. NETWORK PINCH ANALYSIS
A total mass, W S k
, of the key pollutant is transferred to the MSAs in the k th interval.
Hence, a residual mass,
 k
, of the pollutant leaving the k th interval can be calculated via Eq.( ). This output residual also constitutes the influent residual to the subsequent interval.
Fig. 5.31 illustrates the component material balance for the key pollutant around the k th composition interval.
Residual Mass from
Preceeding Interval
 k-1
W k
R
Mass Recovered from Rich
Streams
Residual Mass to
Subsequent Interval k
 k
W k
S
Mass Transferred to MSA’s
Figure 5.31 A pollutant material balance around a composition interval
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MODULE 12. NETWORK PINCH ANALYSIS

0
= 0 , It is worth pointing out that first interval.

0 is zero since no waste streams exist above the
 k
> 0, When all the
 k
’s are nonnegative Thermodynamic feasibility is insured.
 k
< 0, A negative
 k indicates that the capacity of the process lean streams at that level is greater than the load of the waste streams. The most negative
 k corresponds to the excess capacity of the process MSAs in removing the pollutant.
Therefore, this excess capacity of process MSAs should be reduced by lowering the flowrate and/or the outlet composition of one or more of the MSAs.
After removing the excess capacity of MSAs, one can construct a revised TEL in which the flowrates and/or outlet compositions of the process MSAs have been adjusted.
On the revised cascade diagram the location at which the residual mass is zero corresponds to the mass-exchange pinch composition . As expected, this location is the same as that with the most negative residual on the original cascade diagram.
Since an overall material balance for the network must be realized, the residual mass leaving the lowest composition interval of the revised cascade diagram must be removed by external MSAs.
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MODULE 12. NETWORK PINCH ANALYSIS
.
Statement problem
Create the
CID
Generate the
TEL
Construct the
Revised TEL
- The excess capacity of process MSAs is the most negative residual mass
- Adjust the excess capacity by reducing the flowrates and/or outlet compositions of the process MSAs.
- The mass-exchange pinch is located where the residual mass leaving is cero.
- The residual mass leaving the bottom interval is the amount of pollutant to be removed by external MSAs.
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MODULE 12. NETWORK PINCH ANALYSIS
PROCESS DESCRIPTION
In this process, two types of waste oil are handle: gas oil and lube oil. The two streams are first dashed and demetallized. Next, atmospheric distillation is used to obtain light gases, gas oil, and a heavy product. The heavy product is distilled under vacuum to yield lube oil. Both the gas oil and the lube oil should be further processed to attain desired properties. The gas oil is steam stripped to remove light and sulfur impurities, then hydro treated. The lube oil is dewaxed / deasphalted using solvent extraction followed by steam stripping.
The process has two main sources of waste water. These are the condensate streams from the steam stripper. The principal pollutant in both wastewater streams is phenol. Phenol is of concern primarily because of its toxicity, oxygen depletion, and turbidity. In addition, phenol can cause objectionable taste and odor in fish flesh and potable water.
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MODULE 12. NETWORK PINCH ANALYSIS
PROCESS FLOWSHEET.
Waste
Gas Oil
Deashing
and
Demetallization
Light Gases
Atmospheric
Gas
Oil
Distillation
Stripping
To regenTo phenol
To final eration & condensfinishing recycle ation
S1 S2 S3 S4 S5
R1 R1
R2
Mass
Exchange
Network
R2
Waste
Lube Oil
Deashing
and
Demetallization
Steam
Lube Oil
Vacuum
Distillation
Dewaxing
and
Deasphalting
S1
Gas
Oil
Air S5
Ion Exchange
Resin S4
Stripping
Lube Oil S2
Activated
Carbon S3
Steam
Figure 5.32 Schematic representation of an oil recycling plant.
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MODULE 12. NETWORK PINCH ANALYSIS
RICH STREAM DATA.
Stream
R
1
R
2
Description
Condensate from first stripper
Condensate from second stripper
Flowrate
G
I
, kg/s
2
1
Supply composition, y s i
0.050
0.030
Table 5.4 Data of waste stream for the dephenolization example.
Target composition, y t i
0.010
0.006
CANDIDATE MSAs.
– 2 Process MSAs:
Solvent extraction using gas oil (S
1
)
Solvent extraction using lube oil (S
2
).
– 3 external MSAs:
Adsorption using activated carbon (S
3
)
Ion exchange using polymeric resin (S
4
)
Stripping using air (S
5
)
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MODULE 12. NETWORK PINCH ANALYSIS
PROCESS MSAs DATA
Stream
S
1
S
2
Description
Gas oil
Lube oil
Upper bound on flowrate
L c j
, kg/s
5
3
Supply composition, x s j
0.005
0.010
Target composition, x t j
0.015
0.030
Table 5.5 Data of process MSAs for the Dephenolization example.
EQUILIBRIUM DATA
General equation for transferring phenol to the j th lean stream.
y
 m j
 x j m
1
= 2.00, m
2
= 1.53, m
3
= 0.02, m
4
= 0.09 and m
5
= 0.04
(5.45)
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MODULE 12. NETWORK PINCH ANALYSIS
MINIMUM ALLOWABLE COMPOSITION DIFFERENCE
 j

j = 1, 2, 3, 4, 5
(5.46)
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MODULE 12. NETWORK PINCH ANALYSIS
S O L U T I O N
1 COMPOSITION INTERVAL DIAGRAM (CID).
Interval
7
4
5
2
1
3
6
R
1
Rich Streams y
0.0500
x
1
Process MSA’s x
2
0.0240
0.0317
0.0474
0.0227
0.0300
0.0320
0.0150
0.0199
R
2 0.0300
0.0140
0.0186
0.0168
0.0074
0.0100
0.0068
S
2
0.0120
0.0050
0.0040
S
1
0.0100
0.0055
0.0060
0.0020
0.0029
Figure 5.33 The CID for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
S O L U T I O N
2 TABLE OF EXCHANGEABLE LOADS (TEL).
Interval
R
1
Load of Waste Streams kg phenol/s
R
2
R
1
+ R
2
Load of Process MSA’s kg phenol/s
S
1
S
2
S
1
+ S
2
1
2
0.0052 -
0.0308
-
0.0052 -
0.0308 -
-
0.0303 0.0303
3
0.0040 0.0040 0.0050 0.0039 0.0089
0.0264 0.0132 0.0396 0.0330 0.0258 0.0588
4
5
6
0.0096 0.0048 0.0144 0.0120 -
0.0040 0.0020 0.0060 -
0.0120
-
7
0.0040 0.0040 -
Table 5.6 The TEL for the dephenolization example.
-
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MODULE 12. NETWORK PINCH ANALYSIS
S O L U T I O N
3 MASS-EXCHANGE CASCADE DIAGRAM
0.0000
The most negative residual mass is -
0.0184 kg/s and corresponds to the excess capacity of process MSAs.
If we decide to eliminate this excess by decreasing the flowrate of S
2
, the actual flowrate of S calculated by
2 should be 2.08 kg/s
L new j

L old j

Excess x t j
 x s j
(5.47)
0.0052
0.0308
0.0040
0.0396
1
3
3
4
0.0052
0.0057
0.0008
-
0.0184
0.0000
0.0303
0.0089
0.0588
0.0144
5 0.0120
L new
2

L old
2

Excess x t
2
 x s
2
0.0184

2.08 kg/s
0.0060
6
- 0.0160
0.0000
- 0.0100
Using the adjusted flowrate of S
2
, the next step is construct the revised TEL.
0.0040
7 0.0000
- 0.0060
Figure 5.34 The cascade diagram for the
Dehenolization example
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MODULE 12. NETWORK PINCH ANALYSIS
S O L U T I O N
4 REVISED TABLE OF EXCHANGEABLE LOADS (TEL)
Interval
R
1
Load of Rich Streams kg phenol/s
R
2
R
1
+ R
2
Load of Process MSA’s kg phenol/s
S
1
S
2
S
1
+ S
2
1
2
0.0052 - 0.0052 - -
0.0308
- 0.0303
-
- 0.0210 0.0210
3
0.0040 - 0.0040 0.0050 0.0027 0.0077
0.0264 0.0132 0.0396 0.0330 0.0179 0.0509
4
5
6
0.0096 0.0048 0.0144 0.0120 - 0.0120
0.0040 0.0020 0.0060 - - -
7
- 0.0040 0.0040 - - -
Table 5.7 The revised TEL for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
S O L U T I O N
5 THE REVISED CASCADE DIAGRAM
0.0000
0.0052
On this diagram, the residual mass leaving the fourth interval is zero. Therefore, the massexchangeable pinch is located on the line separating the fourth and the fifth intervals.
This location corresponds to a set of corresponding composition scales:
0.0308
0.0040
1
0.0052
2
0.0150
3
0.0113
( y, x
1
, x
2
) = ( 0.0168, 0.0074, 0.0100
).
The residual mass leaving the bottom interval being 0.0124 kg/s is the amount of pollutant to be removed by external MSA.
0.0396
0.0144
0.0060
0.0040
0.0000
0.0210
0.0077
7
4 0.0588
0.000 (Pinch point )
5
0.0024
6 0.0000
0.0084
0.0000
0.0124
Figure 5.35 The revised cascade diagram for the dephenolization example
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
The targeting approach adopted for synthesizing MENs attempts to first minimize the cost of MSAs by identifying the flowrates and outlet compositions of MSAs which yield minimum operating cost, “MOC”. This target has been tackled into two previous sections (5.2.2 and 5.2.3).
The second stage in the synthesis procedure is to minimize the number of exchangers which can realize the MOC solution.
The minimum number of units is given by the Eq. (5.1) section 5.1.2 (Targeting):
U = N
R
+ N
S
- N i
(5.1) where N i is the number of indecent synthesis sub-problems into which the original synthesis problem can be subdivided. In most cases, there is only one indecent synthesis sub-problem.
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MODULE 12. NETWORK PINCH ANALYSIS
The Pinch point decomposes the problem into two sub-problems: one above the pinch and one below the pinch.
The minimum number of mass exchangers compatible with a MOC solution, U
MOC
, can be obtained by applying Eq. (5.1) to each sub-problem separately, I.e.
U
MOC
= U
MOC , above pinch
+ U
MOC, below pinch
(5.48) where
U
MOC, above pinch
= N
R, above pinch
+ N
S, above pinch
- N i , above pinch
(5.49) and
U
MOC, below pinch
= N
R, below pinch
+ N
S, below pinch
N i , below pinch
(5.50)
Having determined U
MOC
, we should the proceed to math the pairs of waste and lean streams.
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MODULE 12. NETWORK PINCH ANALYSIS
In order to guarantee the minimum cost of MSAs, no mass should be transferred across the pinch. The designer must start stream matching at the pinch.
At the pinch all matches feature a driving force (between operating and equilibrium lines) equal to the minimum allowable composition difference,

. Hence, since the pinch represents the most thermodynamically-constrained region for design, the number of feasible matches in this region is severely limited.
The synthesis of a MEN should start at the pinch and proceed in two directions separately: the rich and the lean ends.
Feasibility criteria identify the essential matches or topology options at the pinch (“pinch matches” or “pinch exchangers”). They will also inform the designer whether or not stream splitting is required at the pinch.
The following two feasibility criteria will be applied to the stream data:
(i) STREAM POPULATION
(ii) OPERATING LINE VERSUS EQUILIBRIUM LINE .
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MODULE 12. NETWORK PINCH ANALYSIS
Stream population Criteria.
ABOVE THE PINCH
In a MOC design, any mass exchanger immediately above the pinch operate with at the pinch side.
For each pinch match, at least one lean stream (or branch) has to exist per each waste stream. The following inequality must apply at the rich end of the pinch
N ra

N la
(5. 51a)
N ra
= Number of waste (rich) streams or branches immediately above the pinch.
N la
= Number of lean streams or branches immediately above the pinch.
If the above inequality does not hold for the stream data, one or more of the lean stream will have to be split.
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MODULE 12. NETWORK PINCH ANALYSIS
BELOW OF PINCH
Immediately below the pinch, each lean stream has to brought to its pinch composition.
At this composition, any lean stream can only operate against a waste at its pinch composition or higher.
Each lean stream immediately below the pinch will require the existence of at least one waste stream (or branch) at the pinch composition.
Therefore, immediately below the pinch, the following criteria must be satisfied:
N lb

N rb
(5.51b)
N lb
= the number of lean streams or branches immediately below the pinch
N rb
= the number of waste (rich) streams or branches immediately below the pinch.
Again, splitting of one or more of the waste streams may be necessary to realize the above inequality.
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MODULE 12. NETWORK PINCH ANALYSIS
Operating Line vs equilibrium Line Criterion.
A component material balance for the pollutant around the exchanger at the lean end immediately above the pinch (see Fig. XXX) can be written as
G i
(y i in - y i pinch ) - L j
(x j out - x j pinch )
(5.52) but at the pinch y i pinch = m j
(x j pinch +
 j
) + b j
(5.53) y i in
Mass
Exchanger x j out
In order to ensure thermodynamic feasibility at the rich end of the exchanger, the following inequality must hold y i in
 m j
(x j out +
 j
) + b j
(5.54) y i out = y i pinch x j in = x j pinch
Pinch
Point
Figure 5.36 A mass exchanger immediately above the the pinch.
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MODULE 12. NETWORK PINCH ANALYSIS
Substituting from Eqs. (5.53) and (5.54) into Eq. (5.52), one gets
G i
[ m j
( x j out +
 j
) + b j
- m j
( x j pinch +
 j
) - b j
]

L j
( x j out - x j pinch ) and hence
(5.55)
ABOVE THE PINCH
(L j
/ m j
)

G i
(5.56a) this is the feasibility criterion for matching a pair of streams ( i, j ) immediately above the pinch.
That is, in order for a match immediately above the pinch to be feasible, the slope of the operating line should be greater than or equal to the slope of the equilibrium line .
BELOW OF PINCH
On the other hand, one can similarly show that the feasibility criterion for matching a pair of streams ( i, j ) immediately below the pinch is given by
(L j
/ m j
)

G i
(5.56b)
Once again, stream splitting may be required to guarantee that criteria inequality is realized for each pinch match.
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MODULE 12. NETWORK PINCH ANALYSIS
The feasibility criteria (Eqs. 5.51 and 5.56) should be fulfilled only at the pinch. Once the pinch matches are identified, it generally becomes a simple task to complete the network design. Moreover, the designer always has the freedom to violate these feasibility criteria at the expense of increasing the cost of external MSAs beyond the
MOC requirement.
SUMMARIZING
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MODULE 12. NETWORK PINCH ANALYSIS
NETWORK REPRESENTATION
Waste streams are represented by vertical arrows running at the left of the diagram.
Compositions (expressed as weight ratios of the key component in each stream) are placed next to the corresponding arrow.
A match between two streams is indicated by placing a pair of circles on each of the streams and connecting them by a line.
Mass-transfer loads of the key component for each exchanger are noted in appropriate units (e.g. kg pollutant/s) inside the circles.
The pinch is represented by two horizontal dotted lines.
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MODULE 12. NETWORK PINCH ANALYSIS
Feasibility Criteria applied to Dephenolization Case Study.
ABOVE THE PINCH
First criterion . Above the pinch, we have two waste streams and two MSAs. Hence, minimum number of exchangers here can be calculated according to Eq. (5.49) as
U
MOC, above the pinch
= 2 + 2 - 1 = 3 exchangers
Immediately above the pinch, the number of rich streams is equal to the number of the
MSAs, thus the feasibility criterion given by Eq. (5.51) is satisfied.
Second criterion . The second feasibility (Eq. 5.56a) criterion can be checked through
Fig. 5.37. By comparing the values of L j
/m j with G i for each potential pinch match, one can readily deduce that it is feasible to match S
1 immediately above the pinch.
with either R
1 or R
2
Nonetheless, while it is possible to match S
2 immediately above the pinch.
with R
2
, it is infeasible to pair S
2 with R
1
Therefore, one can match S
1 with R
1 and S
2 with R
2 as rich end pinch exchangers.
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MODULE 12. NETWORK PINCH ANALYSIS
Matches above the pinch: criterion
L j
/m j

G i
R1
S2
S1
R2
Feasible
Feasible
Feasible
Infeasible!!
G
1
=2.00 kg/s G
2
=1.00 kg/s L
1
/m
1
=2.50 kg/s L
2
/m
2
=1.36 kg/s
Pinch
Point
Figure 5.37 Feasibility criteria above the pinch for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
Mass-transfer loads between R
1 and S
1
. When two streams are paired, the exchangeable mass is the lower of the two loads of the streams. For instance, the mass exchange loads of R
1 and S
1 are 0.0664 kg/s and 0.0380 kg/s, respectively.
Hence, the mass exchangeable from R
1 to S
1 is 0.0380 kg/s.
Owing to this match, the capacity of S
1 exhausted and S end sub-problem.
1 above the pinch has been completely may now be eliminated from any further consideration in the rich-
Mass-transfer loads between R
2 transferred from R
2 above the pinch.
to S
2 and S
2
. Similarly, 0.0132 kg/s of phenol will be thereby fulfilling the required mass-exchange duty for R
2
No mass must pass through the pinch . Both remaining loads of R
1 and S
2 above the pinch are equal (0.0284 kg/s). This is attributed to the fact that no mass is passed through the pinch.
Final design above the pinch . The two streams (R
1 and S
2
) are, therefore, matched and the synthesis sub-problem above the pinch is completed. This rich-end design is shown in Fig. 5.38.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
2.00 kg/s
0.0500
0.0284
0.0358
R
2
1.00 kg/s
0.0300
0.0132
0.0150
0.0300
0.0284
0.0164
0.0132
0.0380
0.0168
0.0380
0.0074
0.0168
5.00 kg/s
S
1
0.0100
Pinch
Point
2.08 kg/s
S
2
Figure 5.38 The rich-end design for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
Intermediate composition . The intermediate compositions can be calculated through component material balance. For instance, the composition of S
2 with R
2 leaving its match and entering is match with R
1
, x
2 intermediate , can be calculated via a material balance around the R
2
-S
2 exchanger, I.e., x
2 intermedia te 
0 .
0100

0 .
0132
2 .
08

0 .
0164 or a material balance around the R
1
-S
2 exchanger:
(5.58) x
2 intermedia te 
0 .
0300

0 .
0284
2 .
08

0 .
0164
(5.59)
Having completed the design above the pinch, we can now move to the problem below the pinch.
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MODULE 12. NETWORK PINCH ANALYSIS
Feasibility Criteria applied to Dephenolization Case Study.
BELOW THE PINCH
First criterion . Immediately below the pinch, only streams R
1
, R
2 and S
1 exist. Stream S does not reach the pinch point and, hence, will not be considered when the
3 feasibility criteria of matching streams at the pinch are applied.
Since, N rb is 2 and N lb is 1, inequality (Eq. 5.51b) is satisfied.
U
MOC, below the pinch
= 2 + 2 - 1 = 3 exchangers
Second criterion
L
1
/m
1
. As can see in Fig. Xxx S is greater than G
1 and G i cannot be matched with either R
1
2
, Hence, S
1 or R
2 since must be split into two branches: one to be matched with R
1 and the other to be paired with R
2
.
There are infinite number of ways through which L
1
(xxx) . Let us arbitrary split L
1 in the same ratio of can be split so as to satisfy Eq
G
1 to G
2
, I.e., to 3.33 and 1.67
kg/s. this split realizes the inequality (XXX) since 3.33/2 < 2 and 1.67/2 < 1.
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MODULE 12. NETWORK PINCH ANALYSIS
The remaining loads of R
1 and R
2 can now be eliminated by S
3
(activated carbon).
Several configurations can be envisioned for S
3
:
- A split design (Fig. 5.39)
- A serial design in which S
3 if first matched with R
1
(Fig. 5.40)
- A serial design in which S
3 is first matched with R
2
(Fig. 5.41).
It is worth pointing out that the number of exchangers below the pinch is four which is one more than U
MOC, below the pinch
. Once again, U
MOC, below the pinch is just a lower bound on the number of exchangers and does not have to be exactly realized.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
2.00 kg/s
0.0168
0.0080
R
2
1.00 kg/s
0.0168
0.0074
0.0074
0.0080
0.0128
0.0040
0.0040
0.0056
0.0128
0.0050
5.00 kg/s
S
1
0.1100
0.0100
0.0068
0.0068
0.0056
0.0060
0.0000
S
3
= 0.1127 kg/s
Figure 5.39 A lean-end design for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
2.00 kg/s
0.0168
0.0080
R
2
1.00 kg/s
0.0168
0.0074
0.0074
0.0080
0.0040
0.0040
0.0128
0.0128
0.0068
0.0050
5.00 kg/s
S
1
0.1100
0.0060
0.0068
0.0056
0.0497
0.0100
0.0056
0.0000
S
3
= 0.1127 kg/s
Figure 5.40 A lean-end design for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
2.00 kg/s
0.0168
0.0080
R
2
1.00 kg/s
0.0168
0.0074
0.0074
0.0080
0.0128
0.0040
0.0040
0.0056
0.0128
0.0050
5.00 kg/s
S
1
0.1100
0.0100
0.0068
0.0068
0.0497
0.0060
0.0056
0.0000
S
3
= 0.1127 kg/s
Figure 5.41 A lean-end design for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
= 2.00 kg/s
0.0500
0.0284
R
2
= 1.00 kg/s
0.0300
0.0358
0.0132
0.0380
0.0168
0.0168
0.0150
0.0380
0.0074
0.0300
0.0284
0.0164
0.0132
0.0100
0.0168
0.0074
S
2
= 2.08 kg/s
0.0168
0.0080
0.0128
0.0056
0.0040
0.0128
0.0040
0.0080
0.0500
0.0100
0.0068
0.0060
S
1
= 5.00 kg/s
0.0068
Pinch Point
0.1100
0.0056
0.0000
S
3
= 0.1127 kg/s
Figure 5.42 A complete MOC network for the dephenolization example.
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MODULE 12. NETWORK PINCH ANALYSIS
Based upon the basic principles of graphic theory, it can be shown that a minimum-utility pinched network will generally feature more than the target minimum number of exchanger units.
Any minimum-utility network will involve one unit more than the target minimum number of units. Hence, a cost-effective network design ought to include a tradeoff between the number of units (capital cost) and the external MSA’s (operating cost).
A procedure for the systematic reduction in the number of units involves the use of
“mass-load loops” and “mass-loads paths”.
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MODULE 12. NETWORK PINCH ANALYSIS
Mass-load loops
A mass-load loop is a path connection which can be traced through a network by starting from an exchanger and returning back to the same exchanger. Generally, each extra unit will correspond to the existence of one independent loop. That is, by breaking a loop, one can eliminate one exchanger from the network.
Each loop is characterized with the possibility of shifting mass-exchange loads around the loop by subtracting a load from one exchanger and adding it back to another exchanger on the same stream, and so on around the loop.
As a design heuristic, it is recommended to break the loop by eliminating the exchanger with the smallest mass-exchange load. Nonetheless, it has to be noted that it may not be always possible to apply this heuristic because of thermodynamic considerations.
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MODULE 12. NETWORK PINCH ANALYSIS
Mass-load paths
A mass-load path is a continuous which strats with an external MSA and concludes with a process MSA. By shifting the loads along a path, one can add an excess amount of external MSA to replace an equivalent amount of process MSA.
Fig. 5.43 shows a example of reducing a network after using a mass-load path.
R
1
7.00
R
2
5.10
3.10
1
2
Pinch
0.10
0.10
3
0.03
4
0.01
0.0621
0.0050
0.06
S
1
0.35
0.07
0.02
S
2
0.0006 0.0001
(a)
R
1
7.00
R
2
5.10
3.10
1
0.10
0.0621
0.06
S
1
3
0.03
4
0.01
(b)
0.12
0.11
0.02
S
2
0.0006 0.0051
Figure 5.43 Network for the removal of hydrogen sulfide from COG. (a) Minimum-utility network (b) Reduced network after using a mass-load path to shift a load of 0.0050 kg/s from S
1 to S
2
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TIER I: FUNDAMENTALS
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MODULE 12. NETWORK PINCH ANALYSIS
The synthesis of a MEN was originally only targeted on minimizing a total annualized cost. However, it is been recognized that operational aspects must be taken into in account during process design.
Notwithstanding the value of these MENs synthesis, they share a common limitation: all of them are based on designing the MEN for nominal operating conditions.
One of the most serious challenges for the design of waste-management systems is the potential variations in waste flowrate and others characteristics as inlet concentrations streams.
As it was mentioned in HENs operability analysis section, typical de-bottlenecking practices for HENs include modifications to surface area and heat transfer coefficients. Now, de-bottlenecking practices will be required for MENs when changes to normal operating conditions (as change in flowrate and/or compositions) resulting in operability problems.
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MODULE 12. NETWORK PINCH ANALYSIS
The operability analysis for Mass Exchanger Networks start from optimal design, the solution for Minimum Operational Cost (MOC).
Starting from thermal effectiveness-NTU model developed in previous sections 2 and 3 is posed in this section a similar model to operability analysis of MENs. A equivalent concept to thermal effectiveness will be used here for develop the MENs operability analysis Model. This concept is called “mass effectiveness”.
Key concepts about the similar model for MENs will be given in this section and the students have to develop the details in order to reach the operability analysis required in the Open-Ended section (Tier III)
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MODULE 12. NETWORK PINCH ANALYSIS

Exchanger Mass Effectiveness represents the ratio of the actual mass load exchanged of rich stream to the maximum load that is thermodynamically possible.
From Fig. 6.1(b) the actual mass exchanged of rich stream is
G i
L j
, y i in
, x j out
Mass
Exchanger
G
L j i
, y
, x i out j in
(a)
M
G
= G(y
1
- y
2
) and for lean stream
(6.1)
M
L
= F
L
(x j out - x j in ) (6.2) but applying the corresponding compositions scales the E. ( ) is
M
L
= L (y
4
* - y
3
* )
(6.3) where L = F
L
/m j
The maximum mass load thermodynamically possible corresponds to inlet concentrations exchanger in both streams ( y
1
, y *
3
).
The Equation for Exchanger Mass effectiveness is
G i y
1 y
2
R
1
R
1
(b)
S
1 y *
4
L j y *
3
Figure 6.1 Schematic representation of a mass exchanger

= (y
1
- y
2
)/(y
1
- y *
3
)
(6.4)
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MODULE 12. NETWORK PINCH ANALYSIS
When the value of mass effectiveness and inlet concentrations of each are given then the outlet concentration of rich stream can be known by Eq. (6.4) expressed as y
2
= y
1
-

( y
1
- y *
3
)
(6.5)
By other hand, combining the Eq. (6.5) with a mass total balance around the exchanger we can obtain an equation for outlet concentration of lean stream y *
4
= y *
3
+
 
( y
1
- y *
3
)
(6.6) where

= G/L
The Equations (6.5) and (6.6) can be used to calculate the outlet concentrations of two streams in the mass exchanger and they represent the basic equations to elaborate a mathematics model required for operability analysis of MENs.
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MODULE 12. NETWORK PINCH ANALYSIS
For a system to be fully defined, the number of variables must be equal to the number of equations. In this case of an existing mass exchanger network, the equations that can be written are
NV = S +2I where
NV = Number of variables
S = Number of streams
I = Number of mass exchangers
The exchanger in Fig. 6.1 has NV = 4 that mean four equations are required to system to be fully defined. One equation comes from mass effectiveness (Eq. 6.5) and other from total mass balance (Eq. 6.6). The other two equations are the corresponding inlet concentrations of each stream, which are known from initial data. The system equation can be represented by following matrix
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MODULE 12. NETWORK PINCH ANALYSIS
Other equation required to operability analysis of MENs as Height of differential contactor ( H ) and overall number of transfer units ( NTU ), may be taken from section
5.1.3 “Design of individual mass exchange”.
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STRUCTURE:
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MODULE 12. NETWORK PINCH ANALYSIS
The goal of this Tier is the presentation of the design experience to emphasize the inter-relationship of the foundation principles given in Tier I. This is to apply concepts and rules about Pinch Network Analysis in order to analyze and achieve improvement of industry process in saving energy and minimize operating costs.
Cases studies will be developed mainly on two subjects:
– Steady sate simulation and Operability of HENs.
– Mass Exchange Networks Operability and design of MENs.
The purpose is to teach fundamentals in Pinch Analysis over an existing network without simulation.
At the end of Tier II the student should have the basic understanding of HENs and MENs behavior and its relation to the problem of plant operability and suggest solutions.
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MODULE 12. NETWORK PINCH ANALYSIS
The worked example for the steady state response analysis has been extracted from an aromatics plant. The existing heat recovery network is described below:
– 4 hot streams
– 6 cold streams
– 3 coolers
– 2 heaters
– 9 heat exchangers
In the Grid Diagram C1, C2, and C3 represent coolers and H1 and H2 represent heaters.
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MODULE 12. NETWORK PINCH ANALYSIS
H1
E5
E-1
E-1
E4
E3
E-1
Feed H2
C1
R1
D1
F1
E-1
E2
E-1
E1
E-1
E-1
X
D2
E7
E-1
P1
E8
E-1
C2
F2
E-1
R2 H3 R3
Figure 2.1 Simplified flowsheet of Aromatic plant.
E6
E-1
E9
C3
E-1
Crude
Aromatic
Product
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MODULE 12. NETWORK PINCH ANALYSIS
T3
E2
T2
E1
C1
E3
T5
T10
C2
C3
T13
E9
E8
T9
E7
T12
T8
E6
E5
T7
E4
T14 T15
5
6
T17
T1
T4
T6
T11
T16
H1
T18
T19 T20 T21 T22
7 H2
T23 T24
8
T25 T26
9
T27 T28
10
3
4
1
2
277
Fig. 2.2 Heat Exchanger Network for Case Base.

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MODULE 12. NETWORK PINCH ANALYSIS
The throughput of the plant is to be increased by 20%.
It is desired to de-bottleneck the process to maintain feasible operation under new campaign.
It is also required that operation for the base case conditions must be feasible as an alternative option.
It is assumed that during the new campaign, the inlet temperature of stream 1 is set to 365 o C.
Limitations on installed utility capacity dictate that the critical target temperatures under new conditions are:
For T
3
; 42

T
3
< 51 o C.
For T
5
For T
10
: T
5
= 303
; 85

T
10 o C.
< 107 o C.
For T
For T
26
28
; 145

T
26
; 82

T
28
< 173 o C.
< 128 o C.
During normal operation the conditions for Temperature target of stream 5 is

256 o C
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5
MODULE 12. NETWORK PINCH ANALYSIS
68

T
13
< 74 o C
85

T
10
< 95 o C
C1
T10
C2
C3
T13
E9
T14
E8
T9
E7
T
5
= 303 o C
T5
E5
T7
E4
T3
42

T
3
< 51 o C
E2
T2
E1
E3
T12
T8
E6
T15
290

T
16
< 300 p C
T17
T1
T4
T6
T11
T16
H1
T18
3
4
1
2
6
T19 T20 T21 T22
7
8
9
T23
T25 T26
T24
87

T
24
< 107 p C
H2
111

T
16
< 127 p C
380

T
22
< 468 p C
10
T27 T28
145

T
26
< 173 p C
82

T
28
< 128
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MODULE 12. NETWORK PINCH ANALYSIS
Stream No.
Flow rate (kg/s)
Supply Temperature ( o C)
1 2 3 4 5 6 7 8
40.64
60 53.8
33.3
48.5
31.2
89.5
34.3
9
27.
7
10
45.9
T1 T4 T6 T11 T14 T17 T19 T23 T25 T27
327 495 220 222 102 35
Table 2.1 Stream data for base case
140 80 59 85
E1
E2
E3
E4
E5
E6
E7
E8
E9
Exchanger
Area
(m 2 )
1207.4
1237.6
928.46
1276.9
143.34
186.12
346.3
649.7
1501.4
Stream
Cp
(J/kg o C)
Tube side
Heat transfer
Coefficient
(W/m 2 o C)
Fouling factor
(m 2 o C/W)
Stream
7
3
5
1
6
4
8
2600
2600
1706
2600
2600
2600
2600
608
812
774
998
1046
934
610
0.000492
0.000366
0.000450
0.000379
0.000096
0.000214
0.000165
10 2600
9 2600
906
852
0.000109
0.000118
3
4
Table 2.2 Heat exchanger data.
2
7
3
5
1
7
3
Cp
(J/kg o C)
Shell side
Heat transfer
Coefficient
(W/m 2 o C)
2490
3141
2600
2167
3744
2600
4455
4217
2329
608
812
774
998
1046
934
610
906
852
Fouling factor
(m 2 o C/W)
0.000495
0.000366
0.000450
0.000379
0.000096
0.000214
0.000165
0.000109
0.000118
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MODULE 12. NETWORK PINCH ANALYSIS
Variables and equations .
Applying Eq. (2.4) of Tier I to the network of Fig. 2.2, the number of variables we have is
(NV),
NV

S

2 E

M

2 BP (2.4)
In this case: S = 10, E = 9 M = 0 and BP = 0.
Therefore NV = 28 Variables.
Now the knows equations are: o All supply temperatures are known, there are 10 streams so 10 equations.
o Two equations (effectiveness and heat balance) by each heat exchanger: 2x9 =
18. 18 equations.
o Mass balance about each stream split: in this case there is not split stream and we have zero equations here.
o The j – 1 known flow fraction gives one equation: in this case we have zero equations here.
o Mass balance about each mixing point gives one equation: in this case we have no mixing points and also we have zero equations here.
Finally we have 28 equations .
Our system of equations is contains 28 variables (10 known and 18 unknown) and 28 equations (10 equations from inlet temperatures known and 18 will be generated for each heat exchanger).
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MODULE 12. NETWORK PINCH ANALYSIS
Generation of equations .
The equations are generated as described in the section 2.2
“Response Equations”. In order to show the procedure, the equations of only four heat exchangers will be developed.
E1: HEAT EXCHANGER 1.
From Effectiveness equation:
T
2
= (1 -

)T
1
+

T
15
From heat balance about heat exchanger
T
16
= C

T
1
+ (1-C

)T
15
5
T
2
E1
T
1
1
T
15
T
16
E4: HEAT EXCHANGER 4.
From Effectiveness equation:
T
7
= (1 -

)T
6
+

T
20
From heat balance about heat exchanger
T
21
= C

T
6
+ (1-C

)T
20
7
T
7
E4
T
6
3
T
20
T
21
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MODULE 12. NETWORK PINCH ANALYSIS
E6: HEAT EXCHANGER 6.
From Effectiveness equation:
T
12
= (1 -

)T
11
+

T
19
From heat balance about heat exchanger
T
20
= C

T
11
+ (1-C

)T
19
7
T
12
E6
T
11
4
T
19
T
20
E8: HEAT EXCHANGER 8 .
From Effectiveness equation:
T
10
= (1 -

)T
9
+

T
27
From heat balance about heat exchanger
T
28
= C

T
9
+ (1-C

)T
27
10
T
10
E8
T
9
3
T
27
T
28
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MODULE 12. NETWORK PINCH ANALYSIS
T
1
2 T
2
3 T
3
= 327
= (1 -

)T
1
= (1 -

)T
2
+

T
15
+

T
17
4 T
4
5 T
5
= 495
= (1 -

)T
4
+

T
21
6 T
6
= 220
7 T
8 T
7
8
= (1 -

)T
6
= (1 -

)T
7
+

T
20
+

T
14
9 T
9
10 T
10
= (1 -

)T
8
= (1 -

)T
9
+

T
23
+

T
27
11 T
11
12 T
12
13 T
13
= 222
= (1 -

)T
11
= (1 -

)T
12
+

T
19
+

T
25
14 T
14
= 102
15 T
15
16 T
16
= C

T
7
= C

T
1
+ (1 - C

)T
14
+ (1 - C

)T
15
17 T
17
18 T
18
= 35
= C

T
2
+ (1 - C

)T
17
19 T
19
20 T
20
21 T
21
22 T
22
= 140
= C

T
11
= C

T
6
= C

T
4
+ (1 - C

)T
+ (1 - C

)T
20
+ (1 - C

)T
21
19
23 T
23
24 T
24
= 80
= C

T
8
+ (1 - C

)T
23
25 T
25
26 T
26
= 59
= C

T
12
+ (1 - C

)T
25
27 T
27
28 T
28
= 85
= C

T
9
+ (1 - C

)T
27
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MODULE 12. NETWORK PINCH ANALYSIS
The network temperatures for the base case which have been calculated solving the system of equations are shown in Table 2.3.
T
1
= 327 T
8
= 142 T
15
= 117 T
22
= 383
T
2
= 167 T
9
= 104 T
16
= 257 T
23
= 80
T
3
= 45 T
10
= 89 T
17
= 35 T
24
= 94
T
4
= 495 T
11
= 222 T
18
= 113 T
25
= 59
T
5
= 303 T
12
= 179 T
19
= 140 T
26
= 161
T
6
= 220 T
13
= 69 T
20
= 156 T
27
= 85
T
7
= 166 T
14
= 102 T
21
= 195 T
28
= 93
Table 2.3 Heat exchanger network temperatures for base case conditions.
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MODULE 12. NETWORK PINCH ANALYSIS
The network response is simulated after modification of flow rates and the inlet temperature of stream 1. With the flow rates modification, the effectiveness must be up date by the equation 2.3 Tier I and the results for network supply and target temperatures for new operating conditions are shown in Table 2.4
Stream No.
1
2
3
4
5
6
7
8
9
10
Supply temperature
T
1
= 365
T
4
= 495
T
6
= 220
T
11
= 222
T
14
= 102
T
17
= 35
T
19
= 140
T
23
= 80
T
25
= 59
T
27
= 85
Target temperature
T
3
= 49
T
5
= 308
T
10
= 91
T
13
= 71
T
16
= 277
T
18
= 118
T
22
= 376
T
24
= 94
T
26
= 162
T
28
= 95
Temperature requirements
42

T
3
< 51
T
5
= 303
85

T
10
< 95
68

T
13
< 74
290

T
16
< 300
111

T
18
< 127
380

T
22
< 468
87

T
24
< 107
145

T
26
< 173
82

T
28
< 128
Table 2.4. Network supply and target temperatures for new operating conditions .
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MODULE 12. NETWORK PINCH ANALYSIS
The temperature response analysis will show what temperatures values are within acceptable bounds. Figure 2.3 shows the streams that fall outside bounds.
T ( o C)
Upper
Bound
51
T
5
= 308
303
49
Lower
Bound
42 303
95
91
85
T t outside
1 acceptable bound
2
T
5
T t within acceptable bound is 5 o C above T t
3
74 300 127 468 107 173
71
118
68 290 111
T
22
380
= 376
94
87
T
16
= 277
4 5
T
16 is 13 o C below T t
6 7
T
22 is 4 o C below T t
8
162
145
Fig. 2.3 Target temperatures on acceptable bounds review.
128
95
82
9 10
Stream No
.
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MODULE 12. NETWORK PINCH ANALYSIS
Streams 2 and 7.
Stream 2 matches with stream 7 by Exchanger 3 (E3). In each stream its target temperatures is outside of acceptable bounds.
This is the case of a hot stream falling above the upper bound. The way to restore the target temperature of stream 2 is by increasing the heat exchanger area of E3.
This action also benefits stream 7. However, for the target temperature of stream 7 to be acceptable, more heat is needed. Exchanger E6 is chosen and more area added.
Stream 5.
Stream 5 enters exchanger E5 first and E1 afterward. After E1 stream temperature (T
16 is 13 o C below the target temperature required by the process.
)
This is the case of a cold stream falling below the lower bound. The solution is to increase the heat exchanger area.
Increasing area on exchangers E1 and E5 restores the target temperature of stream 5.
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MODULE 12. NETWORK PINCH ANALYSIS
The solution results for additional surface area and network temperatures after the exchangers have been modified are presented in Tables 2.4 and 2.5 respectively.
Exchanger No. Additional area
(m
2
)
E1
E3
E5
E6
1534
1002.6
291.3
239.6
Table 2.5 Heat transfer area requirements on exchangers E1, E3 and E6.
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MODULE 12. NETWORK PINCH ANALYSIS
Stream No.
1
2
3
4
5
6
7
8
9
10
Supply temperature
T
1
= 365
T
4
= 495
T
6
= 220
T
11
= 222
T
14
= 102
T
17
= 35
T
19
= 140
T
23
= 80
T
25
= 59
T
27
= 85
T
3
T
T
T
T
T
T
T
T temperature
5
10
13
T
16
18
22
24
26
28
Target
= 48
= 303.3
= 89.4
= 70.4
= 290.9
= 115
= 381.7
= 91.2
= 156.6
= 92.4
Temperature requirements
42

T
3
< 51
T
5
= 303
85

T
10
< 95
68

T
13
< 74
290

T
16
< 300
111

T
18
< 127
380

T
22
< 468
87

T
24
< 107
145

T
26
< 173
82

T
28
< 128
Table 2.6 Stream supply and target temperatures for new operating
Conditions and increasing area on exchangers E1, E3, E5 and E6.
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MODULE 12. NETWORK PINCH ANALYSIS
Solution results for additional surface are and network temperatures after the exchangers have been modified.
T ( o C)
Upper
Bound
51
303.3
303
48
95
Lower
Bound 42 303
89.4
85
74 300 127 468 107 173 128
70.4
68
290.9
290
115
111
381.7
380
91.2
87
156.6
145
92.2
82
1 2 3 4 5 6 7 8 9 10
t
Stream No
.
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MODULE 12. NETWORK PINCH ANALYSIS
Stream 7.
The restoration of target temperature of stream 7 can be accomplished by modification of exchangers E3, E4 and E6.
Heat exchangers with a high thermal effectiveness require larger amount of additional surface area to achieve a certain response on outlet temperatures whereas low effectiveness exchangers achieve the same response with less additional area. In this case, the thermal effectiveness of exchangers E3, E4 and E6 for the base case are 0.64, 0.84 and 0.52 respectively.
Therefore, the designer should start his analysis by considering the exchangers with the lower thermal effectiveness that in this case are E3 and E6.
Another element that needs to be considered in the solution of cases like this, is that the interaction between exchangers call for a strategic order of modifications. This is, if target temperature of stream 7 is to be restored, E6 must be analyzed first, followed by E4 and then E3.
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MODULE 12. NETWORK PINCH ANALYSIS
From the results shown in Table 2.6, the only target temperature that is now out of specification is T
5
, the outlet temperature of stream 2.
Analyzing structure it is clear that the restoration of this controlled variable can be achieved by reducing the heat load of E3. So, a bypass must be implemented here.
It is found that by allowing 10 % of the flow rate of stream 2 through the bypass, temperature T
5 reaches the required condition.
The simulation results are shown in Table 2.7.
BP = ByPass
T
5 M
BP
E3 r
2.1
= 0.10
T
4
2 r
2.2
= 0.90
T
21
T
22
Fig. 2.5 Heat exchanger 3 with bypass.
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MODULE 12. NETWORK PINCH ANALYSIS
Stream No.
1
2
3
4
5
6
7
8
9
10
Supply temperature
T
1
= 327
T
4
= 495
T
6
= 220
T
11
= 222
T
14
= 102
T
17
= 35
T
19
= 140
T
23
= 80
T
25
= 59
T
27
= 85
T
T
T
T
T
T
T
3
5
10
13
16
18
22
T
28
Target temperature
= 44.3
= 303
= 87.9
= 68.5
= 268.2
= 111.2
= 391.1
T
24
= 91.2
T
26
= 155.3
= 91.2
Temperature requirements
42

T
3
< 51
T
5
= 303
85

T
10
< 95
68

T
13
< 74
T
16

256
111

T
18
< 127
380

T
22
< 468
87

T
24
< 107
145

T
26
< 173
82

T
28
< 128
Table 2.7 Stream supply and target temperatures with increased area on E1, E3, E5 and E6 and restored original operating conditions.
Bypass on exchanger E3.
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MODULE 12. NETWORK PINCH ANALYSIS
The response analysis shows that all target temperatures are within acceptable bounds after corrective actions have been taken.
T ( o C)
Upper
Bound
51
48
303 95 74 300 127 468 107 173 128
89.4
Lower
Bound
42
303
303 85
70.4
68
209.9
290
115
111
381.7
380
91.2
87
156.6
145
92.2
82
1 2 3
T t within acceptable bound
4 5 6 7 8 9 10
Stream No
.
Fig. 2.4 Target temperatures are all within acceptable bounds after correctives actions.
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MODULE 12. NETWORK PINCH ANALYSIS
The model for the steady state simulation of a single phase heat recovery networks is based on the development of a system of steady state linear equations: these include the thermal effectiveness and the heat balance of every exchanger, the heat balance about the mixing points and the mass balance about stream split points present in the network.
In this case study it is shown how to retrofit an existing heat exchanger network to operate under conditions different from the original design and deliver target temperatures that meet the process requirements. The final network is said to be
FLEXIBLE and OPERABLE. The retrofit of the existing network to achieved by the incorporation of additional surface area and the use of bypasses.
The method includes the assessment of the network response to modified ( hA ).
This is done by updating the heat transfer coefficient to variations in stream flow rate.
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-Problem description
MODULE 12. NETWORK PINCH ANALYSIS
-Grid Diagram
EXISTING HEAT RECOVERY NETWORK
--Flow sheet
-- Stream and heat exchanger dataset
MODEL
T UNKNOWN CALCULATION
System of Equations
NEW REQUIREMENTS
Solution of equation system
SIMULATION
-Increased Area
-- Bypass
All T t streams are within acceptable bounds?
Yes
NETWORK SIMULATION RESTORED
ORIGINAL OPERATING CONDITIONS
No
TAKE CORRECTIVE
ACTIONS
-Increased Area
-- Bypass
All T t streams are within acceptable bounds?
Yes
HEAT RECOVERY NETWORK
OPERABLE AND FLEXIBLE
No
TAKE CORRECTIVE
ACTIONS
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MODULE 12. NETWORK PINCH ANALYSIS
STRUCTURE:
298

OPEN ENDED
PROBLEM

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MODULE 12. NETWORK PINCH ANALYSIS
The goal of this Tier is for students to solve to exercise their ability to integrate methods and technologies about operability analysis in existing heat exchange networks and mass exchange networks that have been taught from Fundamentals (Tier I) and Study Cases (Tier II) sections in this Module.
The solution of open ended problems involves to reaching several or many correct answers, and several ways to the correct answer(s) depending of approach used. It is important not only to show final results, but also to explain how students got their answers or why they chose the method they did.
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MODULE 12. NETWORK PINCH ANALYSIS
1 Operability analysis for a Heat Exchange Network
2 Operability analysis for a Mass Exchange Network
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
The open ended problem for the HEN operability analysis is about the same aromatics plant worked in the Study Cases (Tier II) section. The existing heat recovery network requires to be retrofitted for 120 % throughput (relative to existing capacity) and reach new target temperatures in some streams. These new target temperatures are:
– Inlet temperature to exchanger X which must be kept at 307 o C (Stream 2)
– Inlet temperature to Reactor R1 (Stream 5)
– Feed to distillation column D1 whose minimum allowable bound is 164 o C (Stream 6)
– Inlet temperature to Reactor R2 (stream 7)
– Feed to distillation column D2 whose minimum allowable bound is 152 o C (Stream 9)
Another constraint that adds to the problem is that furnaces H1 and H2 have maximum firing capacities that must be observed. These are:
– H1, 8 300 kW
– H2, 19 400 kW
In the Figures 3.1 and 3.2 are shown the flowsheet and grid diagram respectively of aromatic plant that will be worked for operability analysis.
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MODULE 12. NETWORK PINCH ANALYSIS
H1
E5
Treated
Naphta
Feed
E-1
E-1
E4
E3
E-1
H2
C1
R1
D1
F1
E-1
E2
E-1
E1
E-1
E-1
X
D2
E7
E-1
P1
E8
E-1
C2
F2
E-1
R2 H3 R3
Figure 3.1 Simplified flowsheet of Aromatic plant.
E6
E-1
E9
C3
E-1
Crude
Aromatic
Product
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MODULE 12. NETWORK PINCH ANALYSIS
T4
C1
Inlet to exchanger X
E8
T10
E7
T14
T9
E6
E5
T8
E4
T3
T6
E3
E2
T2
E1
T7
T1
1
T5
2
Outlet from
Exchanger X
3
T13
4
5
T12
C2
T11
T16
C3
T15
E9
T17
T21
6
T23
7
T28
8
T30
9
T32
10
T31
T33
T24
T29
T18
T25
T22
T26
T19
H1
T20
H2
T27
305
Fig. 3.2 Grid representation of exchanger network of aromatic plant.

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MODULE 12. NETWORK PINCH ANALYSIS
Solve operability problem for exposed process through finding critical exchangers within network and apply the appropriate corrective actions (additional area or bypass) to ensure that all network temperatures are within acceptable bounds.
Develop different strategies to reach the required operability with new requirement and under normal operating conditions based on basics given into parts 2 and 3 of Tier I and methodology developed into Tier II.
Additional information about stream data for base case and heat exchanger data for solving this problem must be taken of the same process developed in Case Studies
(Tier II)
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MODULE 12. NETWORK PINCH ANALYSIS
The following steps may help you to the identification of strategies to achieve the operability analysis task:
– Specify all stream temperature bounds
– Determine the steady state response of the network to imposed disturbances.
– Produce the Heat Load Shift Table
– Devise the strategy for the shifting of heat within the network. This is done in conjunction with the actual network structure.
– Determine order in which modifications should be undertaken
– Apply corrective equations to calculate additional area (or, bypass) for the various exchangers involved.
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MODULE 12. NETWORK PINCH ANALYSIS
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MODULE 12. NETWORK PINCH ANALYSIS
OPEN ENDED PROBLEM FOR THE DEPHENOLIZATION PROBLEM.
The open ended problem for MENs operability analysis is for a network resulting of example problem worked in section 5.2.4
“Design to Minimum Number of Mass
Exchanger units” of Tier I.
The network for operability analysis is shown in Fig. 3.3. It has two rich streams, one lean stream (external MSA), and two mass exchanger. New operating conditions are required to flowrate and stream composition. This disturbance will affect target composition.
Using fundamentals given in Tier I and methodology developed to study case in Tier II for HENs operability analysis develop in a similar way different solutions strategies to reach operability condition required for new operating condition in network given.
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MODULE 12. NETWORK PINCH ANALYSIS
R
1
2.00 kg/s
R
2
1.00 kg/s
0.0500
0.0300
0.0800
0.0100
0.0240
0.0060
0.1100
0.0240
0.0800
0.0000
S
3
= 0.9455 kg/s
Figure 3.3 Network for the dephenolization open ended problem
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MODULE 12. NETWORK PINCH ANALYSIS
311