Heat Exchange Network Optimization by Thermal Pinch Analysis Tier II: Case Studies Section 2: Heat Exchange Network Optimization by Thermal Pinch Analysis

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

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

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

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

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

Minimum Approach Temperature T1 – hot out T2 – hot in t1 – cold in t2 – cold out oC T1 t2 T2 t1 Minimum approach temperature

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

Using Minimum Approach Temperature to Tradeoff Capital vs 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

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

Minimum Approach Temperature Thermal Equilibrium T = t Practical Feasibility T = t + DTmin This must be included in the coming analysis

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

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)

Stream Data Hot Stream FiCpi Supply (oC) Target (oC) Enthalpy Change   (kW/oC) T2i T1i HHi, (kW) H1 400 340 260 32000 H2 350 360 14000 H3 300 450 380 21000 Cold Stream t1i t2i HCi, (kW) C1 250 240 290 12500 C2 30000 C3 22500

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

Hot Streams

Cold Streams

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

Hot Composite Stream Construction

Hot Composite Stream Construction

Cold Composite Stream Construction

Cold Composite Stream Construction

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

No Heat Integration Cold composite stream Hot composite stream 240 Cold composite stream Total hot utility required QH,max = 65,000 kW Total cold utility required Hot composite stream QC,max = 67,000 kW QC + QH = 132,000 kW

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

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

Partial Heat Integration QC = 52,000 kW QH = 50,000 kW Integrated heat exchange 15,000 kW Total hot utility required Total cold utility required Cold composite stream Hot composite stream QC + QH = 102,000 kW

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

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

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

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

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

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

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

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

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

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

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

Stream Data From before: Hot Stream FiCpi Supply (oC) Target (oC)   (kW/oC) T2i T1i H1 400 340 260 H2 350 360 H3 300 450 380 Cold Stream t1i t2i C1 250 240 290 C2 C3

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 stream’s 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 arrow’s head and tail, with the intervals lying between these lines Note how the cold stream temperature scale is staggered by 10 degrees

Temperature Interval Diagram

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

Table of Exchangeable Heat Loads For the hot streams,

Table of Exchangeable Heat Loads For the cold streams,

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

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

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

Cascade Diagram Now, by subtracting an interval’s 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 7) 4000 – 0 – 5500 = -1500 9) 0 – 2500 + 4500 = 2000 4) 7000 – 15000 + 5500 = -2500 8) 16000 – 10000 – 1500 = 4500 6) 12000 – 9000 – 8500 = -5500 2) 3000 – 7500 + 12000 = 7500 3) 13000 – 15000 + 7500 = 5500 5) 0 – 6000 -2500 = -8500 1) 12000 – 0 + 0 = 12000 2000

Thermal Pinch Point The thermal pinch point occurs at the largest negative number Pinch Point The absolute value of this number is now added in at the top to cascade through

Revised Cascade Diagram 8500 + 8500 + 8500 + 8500 + 8500 + 8500 + 8500 + 8500 + 8500 + 8500

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 =

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

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

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

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

Constructing the Heat Exchange Network

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)

Constructing the Heat Exchange Network

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

Matched Streams

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

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

References Dr. El-Halwagi lecture notes