Module 04: Targeting Lecture 14: No. of units target Key Words: HEN, Subset, Loop, Separate component, MER design The fixed cost of a heat exchanger network (HEN) depends upon the number of heat exchanger it employs. Thus, there exists a possibility that a HEN with minimum no. of heat exchanger will cost less. Thus there exists a strong incentive to reduce the number of heat exchangers ( matches between hot and cold streams) in a HEN. The first step required for this process for its initiation is to identify the number of heat exchangers a HEN will require from the number of Hot, Cold and Utility streams it handles. Let us explain the problem with an example. Fig.4.23 shows the flow sheet of a palm oil refinery [1,2]. Fig. 4.23 Flow sheet of a palm oil refinery
The flow sheet uses three heat exchangers, three coolers and four heaters making 10 units in all. Now the question is whether 10 units are the minimum number of units, or a designer can reduce it without hampering the functionality of the process? The stream table for the above problem is given in Table 4.14: Table4.14 Stream data for palm oil refinery ( Fig.4.23) for T min = 10 C Stream Serial No. Stream Type CP (KW / K) Actual Temperatures Enthalpy, H T s ( 0 C) T t ( 0 C) 1 Hot 1 10.99 120 86 373.66 2 Hot 2 6.04 260 160 604 3 Hot 3 13.13 230 70 2100.8 4 Hot 4 6.56 160 50 721.6 5 Cold 1 11.83 50 97 556.01 6 Cold 2 14.89 104 124 297.8 7 Cold 3 5.69 86 230 819.36 PTA analysis of the problem shows that it is a threshold problem and needs only cooling and no. heating. The minimum cooling load required for the above system computed using PTA is 2126.89. The heat loads of different streams along with cold utility load is shown within the circles representing the streams in Fig.4.24. The predicted cold utility load is also shown similarly. Hot 1 373.66 Hot 2 604 Hot 3 2100.8 Hot 4 721.6 HX 7 HX 6 HX 5 HX 4 HX 3 HX 2 HX 1 2003.04 123.85 249.81 306.2 297.8 97.76 721.6 Cold utility 2126.89 Cold 1 556.01 Cold 2 297.8 Cold 3 819.36 Fig.4.24 Schematic matching of heat loads for stream table data, Table 4.14
Note that the complete system is in enthalpy balance (i.e. the total load of cold streams plus cold utility is equal to the total load of hot streams). If we presume that temperature constraints will allow any match to be made between hot streams and cold streams including cold utility, then we can match the whole of cold streams 3 (total 819.36 units) with Hot streams 3 & 4, leaving a residual heat load of 2003.04 units on Hot 3. Matching Hot 3 & Hot 4 with Cold 3 and maximizing the load on this match so that Cold 3 & Hot 4 is ticked off the 2003.4 residual heat available with Hot 3 is sent to cold utility which requires 2126.89 units. Cold 2 is ticked off by matching with Hot 2 leaving 306.2 units of heat in it. The remaining heat in Hot 2 along with 249.81 units of heat from Hot 1 is passed to Cold 1 to Tick it off. This leaves 123.85 units of heat with Hot 1 which is passed to cold utility. This heat along with 2003.04 units of heat from Hot 3 ticks off cold utility. So following the principle of maximizing loads, that is ticking off stream or utility loads or residuals, leads to a design with a total of seven matches (connections between streams and utilities show matches are denoted by HX with a number). This is in fact is the minimum for this problem. Notice that it is one less than the total number of streams plus utilities in the problem. Thus it can be shown that: u min = N 1.( 4.8 ) where u min = minimum number of units (including heaters and coolers) and N = total number of streams (including utilities)
In fact, it is usually possible in heat exchanger network design to find a u min solution. However, certain refinements to Eq.4.8 are required as discussed below to broaden its applicability. In Fig.4.25 (a), problem having two hot streams ( H 1 & H 2), two cold streams(c 1 & C 2), Hot utility(hu) and Cold utility (CU) is shown. In this case, HU 40 H 1 80 H 2 160 HU 40 H 1 80 H 2 160 40 50 30 90 70 40 80 90 70 C 1 90 C 2 120 CU 70 C 1 90 C 2 120 CU 70 Matches =05 (a) Matches =04 (b) HU 40 H 1 80 H 2 160 40 Y Y 50+Y 30 Y 90 70 Loop C 1 90 C 2 120 CU 70 Matches = 06 (c) Fig. 4.25 Subset and loops during matching putting matches as before by ticking off loads or residuals leads to a design with N 1 units which satisfy Eq.4.8 However, in Fig4.25(b) a design is revealed having one unit less. The justification for the fact that the number is less than minimum is not hard to find. Even as overall the problem is in enthalpy balance, the subset containing streams H 2, C 1 and CU are in enthalpy balance. Similarly HU, H 1 and C 2 are in enthalpy balance (this is a known fact as the total problem is in load balance). This means that for the given stream data set we can design two completely separate networks, employing the Eq.4.8 to each subset individually. The total number of units for the overall system is therefore (3 1) + (3 1)= 4 units, which is one less than found in Fig.4.25(a). This condition is called subset equality, this appears when for a given stream data set it is possible to identify two subsets which are separately in enthalpy balance and thus can form separate networks. Since the flowsheet designer, can control of the quantity of the heat loads in his plant to some extent, it is possible to change the heat loads so as to create subset equality and thus create an opportunity to save a unit. Finally, in Fig.4.25(c) a matching scheme is shown which requires one unit more than the scheme shown
in Fig.4.25(a), the new extra unit has been introduced as the match between HU and C 2 which introduces a loop in the system. It is so because one can trace a closed path through the network starting from, say HU, the loop can be traced to C 1, from C 1 to H 1, from H 1 to C 2, and from C 2 back to HU. Though, the presence of the loop introduces an element of flexibility into the design it increases number of units in the system. Suppose the new extra match, between HU and C 2, is assigned a load of Y units, then through enthalpy balance, the load on the match between HU and C 1 has to be 40 Y, between C 1 and H 1, 50 +Y, and between H 1 and C 2, 30 Y. From Fig (c) it can be institutively said that Y can vary from 0 to a value of 30. When Y= 0 the match between HU and C 2 vanishes and when it is 30 the match between H 1 and C 2 disappears. The flexibility introduced by loops is many times useful, particularly in revamp studies and cleaning operations. The features discussed above and shown in Fig.4.25(a),(b) & (c) can be converted in to a formula to compute number of heat exchange units, using the Euler s General Network theorem applied to heat exchanger network: u min = N + L S (4.9 ) where; u = number of heat exchange units (including heaters and coolers), N = number of streams (including utilities), L = number of independent loops, and S = number of separate components Normally a designer want to avoid extra units by reducing L to zero. Unless one is lucky, there will be no subset equality in the stream data set and thus the value of s will be 1. This leads to the number of units targeting equation: u min = N 1 (4.8 ) In the design of heat exchanger networks techniques discussed above will be used to reduce the number of heat exchangers by allowing small energy penalty at various sections of the network for trading off energy against capital cost. Examples: A five stream problem is taken up compute no. of units target. Table 4.15 A five stream problem for no. of units target for T min =10 C Stream Stream Heat Capacity Source Target H, Number Type Flow Rate Temperature Temperature ( / 0 C) ( 0 C) ( 0 C) 1 HOT 1 147.74 70 10 8864.34 2 HOT 2 165.85 60 33 4478 3 COLD 1 50 57 60 150 4 COLD 2 215 41 60 4085 5 COLD 3 194.74 10 30 4479 Using PTA the minimum hot and cold utilities are computed as given below:
Hot utility(hu) Cold utility(cu) Hot Pinch Temp. Cold pinch temp. = 822.61 = 5450.95 = 60 C = 50 C From the table it appears that if the heat load of Cold 3 can be brought down to 4478 there is a chance for subset equality resulting S=2 and thereby decrease of no. of units by one. For this case: N= 7 ( including HU and CU streams); L=0 and S=2 u min = N+L S= 7+0 2 = 5 If subset equality is not created then N=7, L=0 and S=1. For this case No. of units are: u min = 7+0 1 = 6 Targeting for the minimum number of units for a MER design However if the above equation Eq.4.8 is applied to a maximum energy recovery(mer) design the results will be somewhat different. For this purpose the problem of Table 4.15 is considered. In a MER design the pinch divides the problem into two heat balanced regions. Since these balanced regions are independent, numbers of units targeting should be applied separately to each region as shown below:
Fig.4.26 shows the stream layout above and below the pinch. HU Hot Pinch = 60 C Cold Pinch = 50 C 1 70 C 10 C Above Pinch 2 Below Pinch 60 C 33 C 60 C 57 C 3 60 C 41 C 4 33 C 10 C 5 U min = 4 1 =3 U min =5 1 =4 CU Fig.4.26 Process hot and cold streams and utility stream in above and below pinch Thus total u min for the network = 3 + 4 = 7 If Pinch division is not considered then no. of streams including hot and cold utilities is = 7, S=1 and L=0. Thus, the total no. of units for non MER design = u min = 7+0 1= 6 Thus it can be proved that u min u min MER The number of units obtained in targeting for the MER design is more that u min due to the fact that streams that cross the pinch are counted twice in MER design. The conclusion is that there is a trade off between energy recovery and number of units employed in a MER design. How to reduce no. of units in a MER design will be explained when MER design will be discussed.
References 1. K.K. Trivedi, E. Fouche, K.E. Parmenter, Process Energy Efficiency: Pinch Technology in Handbook of Energy Efficiency and Renewable Energy, CRC Press, Boca Raton, 2007, pp. 15 1 15 30. 2. Sharifah R. Wan Alwi, Zainuddin A. Manan, STEP A new graphical tool for simultaneous targeting and design of a heat exchanger network, Chemical Engineering Journal 162 (2010) 106 121