Tier II: Case Studies

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Tier II Case Studies

• Section 2
• Heat Exchange Network Optimization by Thermal
  Pinch Analysis

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Optimization Problems

• There are many different types of optimization
  problems
• It is important to recognize that an optimization
  problem exists even if it does not immediately or
  easily lend itself to one of the previously
  described analytical methods of optimization
• Sometimes an alternative method that is more case
  specific must be used

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Optimization Problems

• A common example of one of these problems is the
  optimization of a heat exchange network
• Without knowing what the maximum possible network
  integration is, and the minimum possible heating
  and cooling utilities required, it can be very
  difficult to design an optimized heat exchange
  network

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Optimization of Utility Use in a Heat Exchange
Network

• Heating and cooling utilities consumption can be
  treated as an optimization problem
• The goal is to minimize the amount of heating and
  cooling utilities being used by optimizing the
  heat exchange network
• A different method will be used for this type of
  optimization than what was seen previously

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Constraints

• Total heating (QH) and total cooling (QC) used
  will still need to be minimized according to a
  set of constraints
• These constraints are
• The target temperature of individual streams
• The minimum approach temperature in a heat
  exchanger

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Constraints

• Objective function
• Minimize QH QC
• Constraints
• T2i ai , T1i bi
• t1i ci , t2i di
• DTmin k

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Minimum Approach Temperature
T1 hot out T2 hot in t1 cold in t2 cold
out
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Minimum Approach Temperature

• To get the outlet temperature of one stream
  closer to the inlet temperature of the other
  stream, exchanger area must be increased,
  increasing capital cost
• Decreased exchanger area means decreased capital
  cost, but increased utilities cost to make up for
  lost heat exchange capacity

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Using Minimum Approach Temperature to Tradeoff
Capital vs. Operating Costs

• This graph demonstrates the tradeoff between
  capital and operating costs a decrease in one
  is met with an increase in the other

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Minimum Approach Temperature

• The optimum exchanger size exists where the total
  annualized cost is minimized
• This typically will correspond to a minimum
  approach temperature, DTmin of about 10oC
• This DTmin 10oC is a rule of thumb it can
  change depending on the fluid service and the
  type of heat exchanger employed

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Minimum Approach Temperature

• Thermal Equilibrium
• T t
• Practical Feasibility
• T t DTmin
• This must be included in the coming analysis

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Graphical Method Thermal Pinch Analysis

• To optimize a heat exchange network, an example
  of the graphical method to determine the thermal
  pinch point will first be examined
• The same example will then be solved using the
  algebraic method for comparison

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Stream Data

• Using the stream supply and target temperatures,
  the enthalpy change of each stream must be
  calculated
• Enthalpy change
• DH FiCpi(T2i T1i) HHi
• FiCpi(t2i t1i) HCi
• FiCpi flow rate x specific heat (kW/K)

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Stream Data
Hot Stream FiCpi Supply (oC) Target (oC) Enthalpy Change
  (kW/oC) T2i T1i HHi, (kW)
H1 400 340 260 32000
H2 350 400 360 14000
H3 300 450 380 21000

Cold Stream FiCpi Supply (oC) Target (oC) Enthalpy Change
  (kW/oC) t1i t2i HCi, (kW)
C1 250 240 290 12500
C2 300 300 400 30000
C3 450 350 400 22500
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Stream Data

• Stream data is then plotted as a series of
  straight line segments in order of ascending
  temperature
• Each consecutive segment begins at the enthalpy
  level where the previous segment finished
• A hot stream is any that must be cooled, while
  a cold stream is any that must be heated,
  regardless of supply temperature

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Hot Streams
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Cold Streams
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Composite Stream Curves

• Next the composite curves of the hot and cold
  streams must be constructed
• These composite curves represent the total amount
  of heat to be removed from the hot streams and
  the total amount of heat that must be added to
  the cold streams to reach the target stream
  temperatures

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Hot Composite Stream Construction
H3
H2
H1
T11
T21
T12
T22
T13
T23
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Hot Composite Stream Construction
Hot composite stream
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Cold Composite Stream Construction
C3
C2
C1
t13
t22
t21
t11
t12
t23
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Cold Composite Stream Construction
Cold composite stream
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Optimizing the Heat Exchange Network

• The cold composite stream must now be
  superimposed over the hot composite stream to
  perform the thermal pinch analysis
• This will give the minimum amount of utilities
  required to reach the target states
• Note how the temperature axis is shifted for the
  cold composite stream to account for the minimum
  approach temperature

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No Heat Integration
Total hot utility required
Cold composite stream
QH,max 65,000 kW
Total cold utility required
Hot composite stream
QC,max 67,000 kW
QC QH 132,000 kW
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No Heat Integration

• With no heat integration, the amount of energy
  required to reach the target state is maximized
• In this case the total amounts of energy required
  are
• Cooling utility, QC 67,000 kW
• Heating utility, QH 65,000 kW
• Total utilities QC QH 132,000 kW
• Clearly there is room for optimization

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Partial Heat Integration

• By moving the cold composite stream down a bit, a
  partially integrated heat exchange network is
  graphically represented
• Some heat is transferred from hot streams to cold
  streams to approach the temperature targets

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Partial Heat Integration
Cold composite stream
Hot composite stream
QC QH 102,000 kW
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Partial Heat Integration

• This heat exchange network is only partially
  optimized and already utility consumption is
  reduced by 30,000 kW
• The utilities required are
• Cooling utility, QC 52,000 kW
• Heating utility, QH 50,000 kW
• Total utilities QC QH 102,000 kW
• Clearly further integration can provide
  significant energy savings

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Optimized Heat Integration

• To determine the optimized heat exchange network,
  the thermal pinch point must be found
• This is accomplished by moving the cold composite
  stream down just until one point on the line
  meets a point on the hot composite line
• This point is the thermal pinch point

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Optimized Heat Integration
QH,min 8,500 kW
Cold composite stream
Integrated heat exchange 56,500 kW
Pinch point
Hot composite stream
QC,min 10,500 kW
240
QC QH 19,000 kW
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Optimized Heat Integration

• The heat exchange network is now fully optimized
• Total required utilities are minimized
• Minimum cooling utility, QC,min 10,500 kW
• Minimum heating utility, QH,min 8,500 kW
• Minimum total utilities QC QH 19,000 kW
• No heat is passed through the pinch point

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Passing Heat through the Pinch Point

• To have an optimized heat exchange network, it is
  critical that no heat is passed through the
  thermal pinch point
• By passing an amount of heat, a, through the
  pinch point, an energy penalty of 2a is added to
  the total utilities requirement
• It is very important to maximize integration in a
  heat exchange network

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Passing Heat Through the Pinch Point
QH QC QH,min QC,min 2a
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Crossing the Pinch Point

• It would appear that extra energy can be saved by
  lowering the cold composite stream line further
• This does not work however because it creates a
  thermodynamically infeasible region
• For this to work, heat would have to flow from
  the cooled hot streams to the heated cold streams
  - from a cold source to a hot source

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Crossing the Pinch Point
Cold composite stream
Pinch point
Hot composite stream
Infeasible region
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Disregarding DTmin

• Another tempting error is to disregard the
  minimum approach temperature
• By disregarding a minimum approach temperature,
  the absolute minimum thermodynamically possible
  utility requirements are obtained
• Although this is thermodynamically possible, it
  is not practically feasible as it would require
  an infinitely large heat exchanger area
• This would obviously cost far more than the
  relatively small energy savings are worth

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Disregarding DTmin
QH,min thermo.
QC,min thermo.
240
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Algebraic Method

• This same problem will now be solved using the
  algebraic method
• This will involve producing a temperature
  interval diagram, tables of exchangeable heat
  loads, and cascade diagrams

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Stream Data
From before
Hot Stream FiCpi Supply (oC) Target (oC)
  (kW/oC) T2i T1i
H1 400 340 260
H2 350 400 360
H3 300 450 380

Cold Stream FiCpi Supply (oC) Target (oC)
  (kW/oC) t1i t2i
C1 250 240 290
C2 300 300 400
C3 450 350 400
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Temperature Interval Diagram

• The first step is to construct the temperature
  interval diagram
• This diagram shows the starting and finishing
  temperatures of each stream
• An interval begins at a streams starting or
  finishing temperature, and it ends where it
  encounters the next beginning or finishing
  temperature of a stream
• Draw horizontal lines across the table at each
  arrows head and tail, with the intervals lying
  between these lines
• Note how the cold stream temperature scale is
  staggered by 10 degrees

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Temperature Interval Diagram
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Table of Exchangeable Heat Loads

• The next step is to construct tables of
  exchangeable heat loads for the hot and cold
  streams
• These tables show the amount of energy that must
  be added or removed from a stream over a
  particular interval
• These energy values are calculated as
• DHj,i FCpjDTi, where DTi is the positive
  temperature difference across the interval, and j
  denotes the stream number

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Table of Exchangeable Heat Loads

• For the hot streams,

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Table of Exchangeable Heat Loads

• For the cold streams,

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Cascade Diagrams

• Using the information from the heat load tables,
  the cascade diagrams can now be constructed
• These diagrams will be used to determine the
  pinch point and the minimum heating and cooling
  utilities required

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Cascade Diagram

• First, the cascade diagram is drawn as it appears
  at right, with one box for each interval that
  appeared in the temperature interval diagram

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Cascade Diagram

• Next, the total values from the exchangeable heat
  load tables are added to the cascade diagram
• Hot stream loads enter on the left, cold stream
  loads exit on the right

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Cascade Diagram
0

• Now, by subtracting an intervals cold load from
  the hot load, and adding the resulting value to
  the residual from the previous stage we get the
  residual value for the subsequent stage
• ri HHi HCi ri-1

12000
7500
5500
-2500
-8500
-5500
-1500
4500
1) 12000 0 0 12000
2) 3000 7500 12000 7500
3) 13000 15000 7500 5500
5) 0 6000 -2500 -8500
6) 12000 9000 8500 -5500
8) 16000 10000 1500 4500
7) 4000 0 5500 -1500
9) 0 2500 4500 2000
4) 7000 15000 5500 -2500
2000
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Thermal Pinch Point

• The thermal pinch point occurs at the largest
  negative number

• The absolute value of this number is now added in
  at the top to cascade through

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Revised Cascade Diagram
8500
8500
8500
8500
8500
8500
8500
8500
8500
8500
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Revised Cascade Diagram
Qmin,heating

• We now have the final revised cascade diagram
• It can be seen that by adding additional energy
  at the top, it will cascade through and also be
  present at the bottom

Pinch Point
QH QC QH,min QC,min 2a !
Qmin,cooling
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Optimized Heat Integration

• The heat exchange network is now fully optimized
• Total required utilities are minimized
• Minimum cooling utility, QC,min 10,500 kW
• Minimum heating utility, QH,min 8,500 kW
• Minimum total utilities QC QH 19,000 kW
• As expected, these values are the same as
  obtained by using the graphing method

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Design Considerations

• Some design rules to optimize utility
  consumption
• Do not pass heat through the pinch point
• Do not use cooling utilities at temperatures
  above the pinch point
• Do not use heating utilities at temperatures
  below the pinch point

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Constructing the Heat Exchange Network

• Now that the pinch analysis has been performed,
  the heat exchange network can be constructed
• It is a good idea to perform the pinch analysis
  first because it sets the performance goal of an
  optimized heat exchange network
• There is no quick method of reliably determining
  the minimum number of heat exchangers, but the
  following method should help to construct the
  network

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Constructing the Heat Exchange Network

• With QC,min and QH,min known, construct a plot
  similar to the temperature interval diagram,
  except instead of arrows, use boxes that have a
  width representing FCp
• The area of these boxes corresponds to the heat
  exchanged by the stream
• Draw a horizontal line across at the pinch point
  remember, no heat is to be passed across this
  point

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Constructing the Heat Exchange Network
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Constructing the Heat Exchange Network

• Now, add QC,min to the lowest point on the
  coldest hot stream and determine the resulting T1
  and T2 for this exchange. Note that T1, T2, t1,
  and t2 now do not necessarily correspond to the
  same values as used earlier and are different for
  each exchanger
• QC,min FCp(T2 T1)
• Do the same with QH,min, adding it to the highest
  point on the hottest cold stream
• QH,min FCp(t2 t1)

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Constructing the Heat Exchange Network
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Constructing the Heat Exchange Network

• Now, working out from the pinch point, match up
  streams, remembering not to transfer heat across
  the pinch point and keeping DTmin in mind
• For each matched stream, determine the
  temperatures that exist for the inlet and outlet
  of the heat exchanger
• Qex FCp(T2 T1) FCp(t2 t1)
• Having the table of stream data including
  enthalpy change on hand may be helpful for
  determining the best way to match a stream

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Matched Streams
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Heat Exchangers

• 4 heat exchangers, plus a heater and a cooler are
  needed to meet the optimum heat exchange
  requirements of this system

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Conclusion

• There is no quick method that is guaranteed to
  give the minimum number of heat exchangers
  required every time
• However, by first performing a thermal pinch
  analysis to determine the maximum heat exchange
  possibilities, designing an optimum network
  configuration is made a lot easier

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References

• Dr. El-Halwagi lecture notes