AUTOMATIC EVOLUTION OF HEAT EXCHANGER NETWORKS WITH SIMULTANEOUS HEAT EXCHANGER DESIGN

AUTOMATIC EVOLUTION OF HEAT EXCHANGER NETWORKS WITH SIMULTANEOUS HEAT EXCHANGER DESIGN

F.S. LIPORACE ¹, F.L.P. PESSOA ¹ and E.M. QUEIROZ ¹

¹ Universidade Federal do Rio de Janeiro, Departamento de Engenharia Química, Escola de Química, Centro de Tecnologia - Bloco E - Sala 209 - CEP: 21949-900 - Cidade Universitária - Rio de Janeiro - RJ,Brazil - Phone: [phone] - Fax: [phone]

E-mail: [e-mail] / [e-mail]

(Received: June 3, 1998; Accepted: January 25, 1999)

Abstract - Recently, a new software (AtHENS) that automatically synthesizes a heat exchanger network with minima consumption of utilities was developed. This work deals with the next step, which represents the evolution of the initial network. Hence, new procedures to identify and break loops are incorporated, for which a new algorithm is proposed. Also, a heat exchanger design procedure which uses the available pressure drop to determine the film coefficient on the tube side and shell side is added, providing the utilization of more realistic heat exchangers in the network during its optimization. Results obtained from a case study point to the possibility of equipment design having a strong influence on the network synthesis.

Keywords: heat exchanger networks, loop identification, loop breaking, heat exchanger design.

INTRODUCTION

The Pinch Design Method (PDM), proposed by Linnhoff & Hindmarsh (1983), became the most popular method of heat exchanger network (HEN) synthesis because it is fast, easy and capable of interactivity. In this procedure, the main problem is divided into p+1 subproblems, with p being the number of pinch points, which are treated independently. When the results are combined, heat exchanger loops may appear. As they affect the total annual cost of the network by increasing the capital cost, they must be identified and their elimination analyzed in order to lower the total annual cost of the HEN. But, if heat exchangers are eliminated from the network while trying to maintain the same utility consumption, there could be a minimum temperature difference (MTD) violation on the hot and/or cold sides of the remaining equipment. This violation can lead to an unfeasible operation of a unit and therefore to the need of a temperature difference adjustment, orientated by economical aspects and unit design parameters, that not necessarily leads to the original MTD value. This procedure results in an increase in utilities consumption, and thus affect the operational cost. As capital and operational costs act in the total annual cost in opposite ways, a means to minimize it must be sought. In a few words, loops are broken only if the total annual cost of the after-break network is lower than the total annual cost of the before-break network. The loop is identified by matrix analysis.

A new loop break algorithm, which is based on the construction of the so-called simulation matrix, is proposed in this work. This matrix represents the network, with its heat exchangers, mixers and splitters, and allows the performance of a network steady-state simulation after each loop break in order to check some aspects, such as whether streams are still reaching their target temperature and whether there is an MTD violation.

Moreover, little work in the literature deals with the influence of heat exchanger design on the results of network synthesis. It is usual to find that some units proposed are impossible to design. This fact points to the importance of performing design and synthesis simultaneously and, of course, the use of a design procedure that is sufficiently rapid and well defined to provide results as near as possible to reality is preferred, because there is an increase on the problem complexity and computing time which vary according to the design procedure used. In addition, this kind of approach implies the need of establishing procedures to be adopted when a combination that is not recommended because the heat exchanger design is unattainable is identified.

AtHENS works in the WINDOWS-MATLAB environment. The modules of targeting and of the initial HEN synthesis with minima consumption of utilities can be found in Liporace et al. (1996, 1997). The other modules will be explained in this work.

LOOP IDENTIFICATION

The loop identification algorithm is based on the work of Pethe et al. (1989). The basic idea is that each heat exchanger can be thought of as a path by energy balance between a hot stream and a cold stream. So, the network can be represented by a (a,b) matrix, called incidence matrix, where a is the number of streams (hot and cold streams + hot and cold utilities) and b is the number of heat exchangers (process-process + heaters + coolers). When hot stream i enters heat exchanger j, element (i,j) is (+1). When stream i is cold, the value is (-1). In other cases, the setting is (0). Actually, the incidence matrix represents a linear system where the equipment is the equations and the streams are the variables. So, as the rank of the matrix is calculated, the independent and dependent equations (heat exchangers) can be determined. As each dependent equation is a linear combination of independent equations, this combination represents a loop if it is found.

The number of independent loops (IL) is given by Equation 1:

, (1)

where p_(aXb) is the rank of the incidence matrix. The loop is identified by solving Equation 2:

, (2)

where LI are the linearly independent columns, LD are the linearly dependent columns and a _i are the integer constants. A loop is formed by the LD column (heat exchanger) and the LI columns (heat exchangers) showing a _i¹ 0. The existence of more than one possibility of choosing the LI columns is common, and loop identification is dependent on that choice. The AtHENS algorithm adopts the procedure of choosing LI columns randomly.

HEAT EXCHANGER DESIGN

The heat exchanger design procedure is an extension of that proposed by Jegede and Polley (1992). In this procedure, equations are arranged in such a way that design results, such as tube and shell diameters, number of tubes, number of tube passes, number of shells, tube and shell mean flow velocities and tube length among others, are obtained directly. When shell splitting is needed, it is done by generating shells with the same heat transfer area (Oliveira, 1995).

In a simple and direct way, Equations 3 and 4 show how to calculate the tube-side (h_t) and shell-side (h_s) heat transfer coefficients from allowable tube-side (D P_t) and shell-side (D P_s) pressure drops:

and (3)

, (4)

where Kpt and Kps are constants involving the streams' thermophysical properties and heat exchanger geometrical parameters and A is the heat transfer area. Combining these equations with that which gives the heat load in the equipment generates expressions that allow calculation of h_t and h_s from the design specifications (inlet and outlet temperatures and mass flowrates of both streams, tube diameter and pressure drop). More details about this procedure can be found in Oliveira (1995).

In AtHENS, this design procedure is extended to take into account the following new aspects:

- inclusion of the header pressure drop (D P_h), which is calculated by Equation 5 (Sinnot, 1993):

, (5)

where npt is the number of tube passes; v is the mean flow velocity and r is the fluid density. Such inclusion modifies the allowable tube-side pressure drop fraction that is used in the tubes;

- utilization of an equation (Equation 6), proposed by Sinnot (1993), to calculate shell diameter (D_s) that takes into account the clearance tube bundle-shell. Oliveira et al. (1996) showed that the use of this equation leads to an improvement in the results of the heat exchanger design. This equation is:

, (6)

where N is the total number of tubes, D_o,t is the tube outer diameter and K₁ and n1 are constants which depend on the number of tube passes and on the geometrical arrangement of the tube bundle. As a consequence of this modification, constant Kpc becomes a function of D_s, imposing the inclusion of an internal loop to calculate D_s .

This design method is used simultaneously with synthesis, i.e., after the selection of a combination of a hot and a cold stream, the heat exchanger is designed. Thus, it is possible to avoid a specific combination, if the design results lead to the conclusion this is the best, and return to the synthesis step to choose another combination.

LOOP BREAKING

The simulation matrix is the proposed representation, in the form of a matrix, of the entire HEN. Its function is to facilitate the network steady-state simulation, necessary after each loop breaking, in order to verify whether streams reach their target temperature and whether there is an MTD violation in the new configuration.

Simulation Matrix Construction

Size: (n,m), where n is the number of rows, calculated as 2 x (number of hot and cold streams + number of hot and cold utilities) + 2 and m is the number of columns, determined by 4 + 2 x (number of heat exchangers + number of splitters + number of mixers) + 4.

Stream identification is an important step in the formation of the matrix since it guides the calculus algorithm. All streams in the HEN are assigned a number, and therefore are present in the matrix, but only the main streams are given integer numbers. Figure 1 shows an example of this identification process, where stream (1) is split into two branches (1.001 and 1.3) and stream 1.001 itself is also split into another two branches (1.002 and 1.301). When mixing occurs, the identification of the mixed streams must not use repeated numbers. However, if the mixing sequence leads to the recomposition of the main stream, the identification number returns to its integer value. For example, consider the set of streams being used by the program after the splits in Figure 1 (1.002; 1.3 and 1.301). The mixing of streams 1.3 and 1.301 would result in stream 1.302 (it is necessary to use a number that has not been previously assigned). The program will then work with only two streams (1.002 and 1.302) which, in the case of mixing (here, the last mixing), would result in stream 1 (the main stream). So, the stream list that would be present in the simulation matrix is: (1 1.001 1.002 1.3 1.301 and 1.302).

Figure 1:
Example of stream identification.

Inclusion of Data on Streams: The four first and last columns are used to receive all data on streams. The first and last columns show the stream identification number and a parameter that identifies stream type (1 for hot and 0 for cold). The second column is used for the specific heat of the hot streams and the next to last column (column m-1) shows this property for the cold streams. The third column and the corresponding column on the right side (column m-2) present the mass flowrates of hot and cold streams, respectively.

Finally, the fourth column is used for the inlet temperature of the hot streams and the outlet temperature of the cold streams, while the corresponding column on the right side (column m-3) has the outlet temperature of the hot streams and the inlet temperature of the cold streams. Beginning with the second line, data for each stream occupy two lines, with the main properties and operational recorded on the first line and the second used to indicate whether the stream is hot or cold. The first and last lines are used for equipment information.

For an example of this procedure, consider the heat exchanger shown in Figure 2 and Table 1, which is part of a HEN, where hot stream 1 enters at 200.0ºC and has 15.0ºC as a target temperature and cold stream 2 enters at 10.0ºC and must reach 180.0ºC. After the split, hot stream 1 reaches this particular heat exchanger at 170.0ºC and cold stream 2, also split, reaches it at 30.0ºC. The corresponding simulation matrix is shown in Figure 3, with only data on streams, which must be read from left to right for hot streams and from right to left for cold streams.

Figure 2:
A heat exchanger in an HEN.

Stream Number Temperature (ºC) Mass Flow (kg/s) A 1 200.0 1.0 B 1 170.0 1.0 C 1.001 170.0 0.5 D 1.3 170.0 0.5 E 1.001 50.0 0.5 F 1 110.0 1.0 G 1 15.0 1.0 H 2 10.0 1.0 I 2 30.0 1.0 J 2.001 30.0 0.5 K 2.3 30.0 0.5 L 2.001 150.0 0.5 M 2 90.0 1.0 N 2 180.0 1.0 For all streams: Cp (Specific Heat) = 1 J/kg ºC

Stream	Number	Temperature (ºC)	Mass Flow (kg/s)
A	1	200.0	1.0
B	1	170.0	1.0
C	1.001	170.0	0.5
D	1.3	170.0	0.5
E	1.001	50.0	0.5
F	1	110.0	1.0
G	1	15.0	1.0
H	2	10.0	1.0
I	2	30.0	1.0
J	2.001	30.0	0.5
K	2.3	30.0	0.5
L	2.001	150.0	0.5
M	2	90.0	1.0
N	2	180.0	1.0
For all streams: Cp (Specific Heat) = 1 J/kg ºC

Table 1: Data on streams of figure 2

Figure 3: Simulation matrix of example - data on stream.

Inclusion of Data on Heat Exchangers: Each heat exchanger is represented by two columns. The first line shows the heat exchanger identification number. The heat exchanger load is presented in the last line of the first column. The inlet and outlet temperatures of the hot stream in the equipment are shown in the first and second columns, respectively, on the line representing this hot stream. The inlet and outlet temperatures of the cold stream are presented in the second and the first columns, respectively, on the line representing this cold stream. Considering the example in Figure 2 and assuming that the heat exchanger is the third in the HEN, Figure 4 shows the simulation matrix with the addition of this heat exchanger data.

HE3

Figure 4: Simulation matrix of example - addition of data on heat exchanger.

Inclusion of Data on Splitters/Mixers: Splitters and mixers are also represented by two columns. If it is a hot stream splitter/mixer, value (-1)/(-2) must be allocated to two different positions in the first column: to the first line, indicating its existence, and to the line(s) representing the stream(s) that is (are) to be split (mixed). Value (-1)/(-2) must also be allocated to the line(s) in the second column representing the stream(s) that result(s) from the splitting (mixing). In the case of a cold stream splitter (mixer), the procedure is identical, except that it is conducted in the reverse order, namely from the second to the first column. The simulation matrix, with the addition of the two splitters and the two mixers in Figure 2, is shown in Figure 5.

Figure 5: Simulation matrix of example - addition of data on splitters and mixers.

Inclusion of Data on Heaters and Coolers: For heaters and coolers, the procedure is similar to that representing a process heat exchanger. The only change is that now the utility mass flowrate is no longer written in the third column and the corresponding column on the right, as was done in the previous procedure, but on the second line representing the utility and always in the column which the inlet temperature is allocated to (the first column, in the case of a hot utility, and the second column, in the case of a cold utility). The utility identifications are also represented by numbers. In the example in Figure 2, the cold utility could be assigned the number 3 and the hot utility, the number 4. The complete stream list used to build the simulation matrix is: (1 1.001 1.3 2 2.001 2.3 3 and 4).

Simulation Matrix Operation

Once the simulation matrix is constructed (this step is done automatically by AtHENS), it represents the actual HEN, i.e., its structure (heat exchangers, heaters, coolers, splitters and mixers) and operational conditions (inlet and outlet temperatures, mass flowrates of hot and cold streams of all heat exchangers, heaters and coolers, outlet mixing temperatures etc.). The HEN is said to be in thermal balance. As a loop is broken, by eliminating one heat exchanger from the HEN and transferring its heat load to the remaining heat exchangers in the loop, the HEN structure is changed and so are some of the operational conditions. The HEN becomes unbalanced. To rebalance it, new operational conditions must be calculated for some equipment. This is done by performing a HEN steady-state simulation, which is guided by the simulation matrix. This HEN steady-state simulation is divided into two steps: hot-stream (process streams and hot utility) steady-state simulation and cold-stream (process streams and cold utility) steady-state simulation.

Hot-Stream Steady-State Simulation: Beginning with the fifth column and ending with column (m-5), this steady-state simulation is performed by reading the first line of the odd columns in order to identify a splitter (-1), a heat exchanger (natural number) or a mixer (-2). In each one of these pieces of equipment, some procedures are necessary to add to the matrix information about inlet and outlet temperatures, in the case of process streams, and about mass flowrate, in the case of a utility.

In a splitter, a search in the first column shows the hot process stream to be split (a line with the value (-1)). In the line corresponding to this stream, the last calculated temperature is located and transferred to the splitter first column, on the same stream line. Then, the streams resulting from the splitting are identified in the second splitter column and the inlet temperature is transferred to this column, indicating the splitter outlet temperatures at the lines corresponding to the exit streams. Figure 6 shows the results of this procedure for splitter SP1 in Figure 2 (refer also to Figure 5).

Figure 6: Section of the simulation matrix in

Figure 5 - splitter procedure.

When a process-process heat exchanger is reached, its hot process stream is identified and the inlet temperature is located by a leftward search and transferred to the first heat exchanger column on the hot stream line. Then, using the heat exchanger heat load, the stream mass flowrate and the specific heat of the fluid, the outlet temperature is computed and recorded in the second heat exchanger column on the same line. This procedure is presented in Figure 7 for HE3 in the example in Figure 2. If the heat exchanger is a heater, the hot utility inlet and outlet temperatures are already known. The hot utility mass flowrate must then be calculated, which is done using those temperatures, the specific heat of the fluid and the heater heat load. The result is then transferred to the first column of the heater on the line below that corresponding to the hot utility. This procedure is shown in Figure 8 (hot utility is represented by number 3).

Figure 7: Section of the simulation matrix in

Figure 5 - heat exchanger procedure.

Figure 8: Section of a simulation matrix - heater procedure.

The procedure for a mixer is somewhat similar to the one for a splitter. It is identified by the value (-2) and there are two inlet temperatures in the first mixer column, which are located by a leftward search of the lines corresponding to the mixing streams. The temperature of the exit stream, recorded in the second mixer column on the stream line, is calculated by conducting an energy balance in the mixer. Figure 9 presents this procedure for mixer MI1 in Figure 2.

Figure 9: Section of the simulation matrix in

Figure 5 - mixer procedure.

Cold-Stream Steady-State Simulation: The steady-state simulation procedure for the cold process streams and for the cold utility is similar to that used for the hot process streams and hot utility, respectively, but the search in the simulation matrix is done only in the even columns from right to left, from (m-4) to the sixth column.

This steady-state simulation procedure must be followed after each loop break because in loop breaking a heat exchanger elimination occurs and, therefore, at least one heat exchanger heat load changes. The heat load of the heat exchanger that was eliminated (the heat exchanger with the lowest heat load) is transferred to the other equipment in the loop and then a new matrix is built with a new last line and without the two columns representing the eliminated heat exchanger. As this new simulation matrix is unbalanced, a new steady-state simulation must be performed in order to correct the temperatures affected by the changes introduced.

At the end of the steady-state simulation, the new simulation matrix is obtained and thermally balanced. Now, it is easy to verify whether all streams reach their target temperature and whether there is an MTD violation at both sides of all heat exchangers. If a stream does not reach its target temperature, a utility must be added. If an MTD violation occurs, a correction procedure must be implemented, i.e., utility consumption must be increased to restore the temperature difference. In both cases, if the necessary utility does not exist in the stream, a new heater or cooler is added. This procedure could be paradoxical, as the loop-breaking philosophy is to eliminate a heat exchanger, but what must be sought is a network with a total annual cost lower than that of the former, and this proposed procedure could lead to better networks by, for example, improving the heat exchanger's driving force. Again, as mentioned before, a steady-state simulation must be performed after any correction procedure adopted.

RESULTS

In this section, an example showing the utilization of the steps here discussed of AtHENS is presented. Table 2 shows the process streams with their respective inlet and outlet temperatures and heat capacity rates (Linnhoff et al., 1982). It also shows properties of the fluids that must be available for the utilization of AtHENS. Those values are selected since they are not given by Linnhoff et al. (1982). The cold utility is assumed to be water and the hot utility, engine oil. Table 3 shows the operational and capital cost data, which are specified.

Problem Table - MTD (ºC): 10; Fluid: engine oil Stream Ti To M.Cp M Cp 1 20.0 135.0 2.0 0.94 2.1 2 170.0 60.0 3.0 1.31 2.3 3 80.0 140.0 4.0 1.77 2.3 4 150.0 30.0 1.5 0.69 2.2 cold utility 5.0 10.0 ----- ----- 4.2 hot utility 330.0 250.0 ----- ----- 3.1 Stream r m k Rf D P 1 853.6 3.51 0.138 9.0 35.0 2 831.7 1.16 0.135 9.0 35.0 3 834.4 1.32 0.136 9.0 35.0 4 846.0 2.32 0.138 9.0 35.0 cold utility 1000.0 0.108 0.598 1.7 35.0 hot utility 732.0 0.066 0.119 9.0 35.0 Ti - inlet temperature (ºC); To - outlet temperature (ºC); M - mass flowrate (kg/s); Cp - specific heat at constant pressure (kJ/kg ºC); r - density (kg/m3); m - viscosity (x 10-2 N s/m2); k - thermal conductivity (J/s m ºC); Rf - fouling resistance (x 10-4 m2 s ºC/J); D P - allowable pressure drop (kN/m2); cold utility - water; hot utility -engine oil.

Problem Table - MTD (ºC): 10; Fluid: engine oil
Stream	Ti	To	M.Cp	M	Cp
1	20.0	135.0	2.0	0.94	2.1
2	170.0	60.0	3.0	1.31	2.3
3	80.0	140.0	4.0	1.77	2.3
4	150.0	30.0	1.5	0.69	2.2
cold utility	5.0	10.0	-----	-----	4.2
hot utility	330.0	250.0	-----	-----	3.1
Stream	r	m	k	Rf	D P
1	853.6	3.51	0.138	9.0	35.0
2	831.7	1.16	0.135	9.0	35.0
3	834.4	1.32	0.136	9.0	35.0
4	846.0	2.32	0.138	9.0	35.0
cold utility	1000.0	0.108	0.598	1.7	35.0
hot utility	732.0	0.066	0.119	9.0	35.0
Ti - inlet temperature (ºC); To - outlet temperature (ºC); M - mass flowrate (kg/s); Cp - specific heat at constant pressure (kJ/kg ºC); r - density (kg/m3); m - viscosity (x 10-2 N s/m2); k - thermal conductivity (J/s m ºC); Rf - fouling resistance (x 10-4 m2 s ºC/J); D P - allowable pressure drop (kN/m2); cold utility - water; hot utility -engine oil.

Table 2: Streams and properties

Hot Utility Price ($/MW year): 60,000.00 Cold Utility Price ($/MW year): 6,000.00

Hot Utility Price ($/MW year): 60,000.00	Cold Utility Price ($/MW year): 6,000.00

Table 3: Data on operational and capital cost

The initial HEN proposed by AtHENS, with minima consumption of utilities (60 kW for cold utility and 20 kW for hot utility), and its total annual cost are presented in Figure 10. The pinch point is 85ºC. In this step, AtHENS uses the synthesis algorithm proposed by Liporace et al. (1996, 1997), which adopts a modified pinch rule for synthesis near the pinch point (PP) and the Heuristic Rule of Ponton and Donaldson (Ponton and Donaldson, 1974) for synthesis far from the PP. This algorithm leads to the splitting of cold streams 1 (1A and 1B) and 3 (3A and 3B) above the PP and of hot stream 2 (2A and 2B) below the PP. Table 4 presents the combination data of this initial network. The simulation matrix will be omitted here and for the other HEN because of its large size.

Figure 10:
Initial HEN: total annual cost $24,186.80/year.

Combination 1 2 3 Hot (H) / Cold (C) 2 3B 4 1B oil 1B M (H) / M (C) (kg/s) 1.31 0.44 0.69 0.24 0.082 0.248 Ti (H) / Ti (C) (ºC) 170.0 80.0 150.0 120.0 330.0 80.0 To (H) / To (C) (ºC) 150.0 140.0 145.0 135.0 250.0 120.0 Combination 4 5 6 Hot (H) / Cold (C) 4 1A 2 3A 2A 1 M (H) / M (C) (kg/s) 0.69 0.71 1.31 1.33 0.88 0.94 Ti (H) / Ti (C) (ºC) 145.0 80.0 150.0 80.0 90.0 50.0 To (H) / To (C) (ºC) 90.0 135.0 90.0 140.0 60.0 80.0 Combination 7 8 9 Hot (H) / Cold (C) 2B 1 4 1 4 water M (H) / M (C) (kg/s) 0.44 0.94 0.69 0.94 0.69 2.87 Ti (H) / Ti (C) (ºC) 90.0 35.0 90.0 20.0 70.0 5.0 To (H) / To (C) (ºC) 60.0 50.0 70.0 35.0 30.0 10.0 H - hot stream; C - cold stream.

Combination	1		2		3
Hot (H) / Cold (C)	2	3B	4	1B	oil	1B
M (H) / M (C) (kg/s)	1.31	0.44	0.69	0.24	0.082	0.248
Ti (H) / Ti (C) (ºC)	170.0	80.0	150.0	120.0	330.0	80.0
To (H) / To (C) (ºC)	150.0	140.0	145.0	135.0	250.0	120.0
Combination	4		5		6
Hot (H) / Cold (C)	4	1A	2	3A	2A	1
M (H) / M (C) (kg/s)	0.69	0.71	1.31	1.33	0.88	0.94
Ti (H) / Ti (C) (ºC)	145.0	80.0	150.0	80.0	90.0	50.0
To (H) / To (C) (ºC)	90.0	135.0	90.0	140.0	60.0	80.0
Combination	7		8		9
Hot (H) / Cold (C)	2B	1	4	1	4	water
M (H) / M (C) (kg/s)	0.44	0.94	0.69	0.94	0.69	2.87
Ti (H) / Ti (C) (ºC)	90.0	35.0	90.0	20.0	70.0	5.0
To (H) / To (C) (ºC)	60.0	50.0	70.0	35.0	30.0	10.0
H - hot stream; C - cold stream.

Table 4: Data on initial HEN combination

Beginning the evolution of the initial network, the identification of the first loop is shown. The incidence matrix of the initial network is presented in Figure 11. It can be seen that the rank of this matrix is 5, that is, it has five LI columns. So this network has four loops. After normalizing the diagonal, a set of five LI columns is chosen to form the LI basis. One choice could be columns 2, 1, 6, 3 and 9. In this set, the LD columns are 4, 5, 7 and 8. Table 5 shows the identification of the loops, indicating the combination of each.

Figure 11: Incidence matrix - before normalization of the diagonal.

LI basis = (2,1,6,3,9) - LD = (4,5,7,8) Loop 1: => 4 - 2 Loop 3: => 7 - 6 Loop 2: => 5 - 1 Loop 4: => 8 - 2

LI basis = (2,1,6,3,9) - LD = (4,5,7,8)
Loop 1: => 4 - 2	Loop 3: => 7 - 6
Loop 2: => 5 - 1	Loop 4: => 8 - 2

Table 5: Loop identification

The algorithm assigns an order to the loops for breaking, using the following criteria: 1) totally above the PP - levels 1, 2, 3 etc. 2) totally below the PP - levels 1, 2, 3 etc. 3) crossing the PP - levels 1, 2, 3 etc. So the four loops identified are (4,2), (5,1), (7,6) and (8,2). The first, (4,2), is represented by a bold line in Figure 12. The bold dashed line indicates the heat exchanger that will be eliminated (that with the lowest heat load) from the network in order to break the loop. The network obtained after this loop breaking is shown in Figure 13. To maintain the heat balance between hot and cold streams in the network, the heat load of the eliminated heat exchanger (2) is transferred to heat exchanger (4) and then a steady-state simulation of this new network must be performed. The simulation matrix is used in this steady-state simulation, and the results make it possible to check whether all the streams reach their target temperatures and whether there is an MTD violation. In this step, none of this occurs and the correction procedure is not used. Then, a cost verification is done. As the total annual cost of the new network is lower than that of the former, this loop breaking is accepted and a new loop must be identified.

Figure 12:
First loop identification.

Figure 13: HEN after the first loop break: total annual cost $23,742.34/year.

These steps are followed until there is no loop to break which leads to a decrease in the total annual cost. The final network for this example, obtained automatically by AtHENS (average computing time of twelve seconds on a Pentium 166 MHz and 32 MB RAM), is presented in Figure 14 and in Table 6. In all the MTD restoration steps, it is used the criterion of adjusting it to its original value, but any other can be easily adopted. This final network has a hot utility consumption 37.5% higher and a cold utility consumption 12.5% higher than the initial network (Figure 10), even though the total annual cost is 7.9% lower. Note that the initial network presents the target values for utilities consumption.

Figure 14: Final HEN: total annual cost $22,278.70/year.

Combination 1 2 3 Hot (H) / Cold (C) 2 3B oil 1B 4 1A M (H) / M (C) (kg/s) 1.31 0.44 0.11 0.24 0.69 0.71 Ti (H) / Ti (C) (ºC) 170.0 80.0 330.0 65.0 150.0 65.0 To (H) / To (C) (ºC) 150.0 140.0 250.0 120.0 75.0 140.0 Combination 4 5 6 Hot (H) / Cold (C) 2 3A 2A 1 4 water M (H) / M (C) (kg/s) 1.31 1.33 0.88 0.94 0.69 3.23 Ti (H) / Ti (C) (ºC) 150.0 80.0 90.0 20.0 75.0 5.0 To (H) / To (C) (ºC) 90.0 140.0 45.0 65.0 30.0 10.0 H - hot stream; C - cold stream.

Combination	1		2		3
Hot (H) / Cold (C)	2	3B	oil	1B	4	1A
M (H) / M (C) (kg/s)	1.31	0.44	0.11	0.24	0.69	0.71
Ti (H) / Ti (C) (ºC)	170.0	80.0	330.0	65.0	150.0	65.0
To (H) / To (C) (ºC)	150.0	140.0	250.0	120.0	75.0	140.0
Combination	4		5		6
Hot (H) / Cold (C)	2	3A	2A	1	4	water
M (H) / M (C) (kg/s)	1.31	1.33	0.88	0.94	0.69	3.23
Ti (H) / Ti (C) (ºC)	150.0	80.0	90.0	20.0	75.0	5.0
To (H) / To (C) (ºC)	90.0	140.0	45.0	65.0	30.0	10.0
H - hot stream; C - cold stream.

Table 6: Data on final HEN combination

To show how design results could be used to interfere in the synthesis, Table 7 presents the results of the heat exchanger design of the initial HEN, which is done immediately after the definition of each pair combination and assumes there is a specified available pressure drop. It can be noted that some heat exchangers, 4 and 5 for example, were designed with a great number of shells. In addition, heat exchanger 4 (heater) has a very small heat transfer area. These two factors could be used to prevent those combinations. In doing so, the next step after the identification of an unfeasible unit would be to return to synthesis in order to search for a new combination, of course excluding the pair just prevented, which could be unsuccessful. If so, it indicates that a practical HEN with minima consumption of utilities could not be obtained. Another consequence of this prevention is a modification in the network structure. The design influence on synthesis can also be observed by a brief comparison among some parameters of the final HEN with design (Figure 14), the final HEN without design (specified heat transfer coefficients) and the targets.

Tube Bundle Arrangement: Triangular; Di,t = 0.01483 m. Do,t = 0.01905 m Combination 1 2 3 4 5 6 7 8 9 Tube Fluid 2 4 oil 4 2 2A 2B 4 4 D Pt (kN/m2) 28.0 26.6 23.1 30.3 30.2 29.8 28.9 26.3 29.4 D Ph (kN/m2) 7.1 8.6 11.7 4.7 4.5 5.2 6.2 8.6 5.6 ht (kJ/s m2 ºC) 0.34 0.26 1.51 0.17 0.25 0.24 0.26 0.24 0.20 Number of Shells 1 1 1 6 6 3 1 1 1 Shell Fluid 3B 1B 1B 1A 3A 1 1 1 water D Ps (kN/m2) 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 35.0 hs (kJ/s m2 ºC) 0.44 0.36 0.50 0.32 0.44 0.33 0.38 0.43 3.96 Q (kJ/s) 60.0 7.5 20.0 82.5 180.0 60.0 30.0 30.0 60.0 A (m2) 9.9 3.3 0.5 105.8 180.1 66.7 8.41 4.86 9.70 Npt 6 6 6 10 8 10 10 8 8 Ntp 9 4 1 7 12 9 4 5 6 vt (m/s) 1.07 1.16 1.46 0.67 0.74 0.71 0.77 1.01 0.82 Lt (m) 3.06 2.30 1.33 4.21 5.23 4.13 3.51 2.03 3.38 Lt/Ds 11.5 12.0 12.0 12.7 14.4 11.4 12.9 7.8 12.1 D Pt - tube pressure drop; D Ph - header pressure drop; D Ps - shell pressure drop; ht - heat transfer coefficient on tube-side; hs - heat transfer coefficient on shell-side; Di.t - tube inner diameter; Do.t - tube outer diameter; Q - heat load; A - heat transfer area; npt - number tube passes; ntp - number of tubes per pass; vt - mean tube flow velocity; Lt - tube length; Ds - shell diameter.

Tube Bundle Arrangement: Triangular; Di,t = 0.01483 m. Do,t = 0.01905 m
Combination	1	2	3	4	5	6	7	8	9
Tube Fluid	2	4	oil	4	2	2A	2B	4	4
D Pt (kN/m2)	28.0	26.6	23.1	30.3	30.2	29.8	28.9	26.3	29.4
D Ph (kN/m2)	7.1	8.6	11.7	4.7	4.5	5.2	6.2	8.6	5.6
ht (kJ/s m2 ºC)	0.34	0.26	1.51	0.17	0.25	0.24	0.26	0.24	0.20
Number of Shells	1	1	1	6	6	3	1	1	1
Shell Fluid	3B	1B	1B	1A	3A	1	1	1	water
D Ps (kN/m2)	35.0	35.0	35.0	35.0	35.0	35.0	35.0	35.0	35.0
hs (kJ/s m2 ºC)	0.44	0.36	0.50	0.32	0.44	0.33	0.38	0.43	3.96
Q (kJ/s)	60.0	7.5	20.0	82.5	180.0	60.0	30.0	30.0	60.0
A (m2)	9.9	3.3	0.5	105.8	180.1	66.7	8.41	4.86	9.70
Npt	6	6	6	10	8	10	10	8	8
Ntp	9	4	1	7	12	9	4	5	6
vt (m/s)	1.07	1.16	1.46	0.67	0.74	0.71	0.77	1.01	0.82
Lt (m)	3.06	2.30	1.33	4.21	5.23	4.13	3.51	2.03	3.38
Lt/Ds	11.5	12.0	12.0	12.7	14.4	11.4	12.9	7.8	12.1
D Pt - tube pressure drop; D Ph - header pressure drop; D Ps - shell pressure drop; ht - heat transfer coefficient on tube-side; hs - heat transfer coefficient on shell-side; Di.t - tube inner diameter; Do.t - tube outer diameter; Q - heat load; A - heat transfer area; npt - number tube passes; ntp - number of tubes per pass; vt - mean tube flow velocity; Lt - tube length; Ds - shell diameter.

Table 7: Data on heat exchanger design of the initial HEN

On the targeting stage, in order to calculate the target of minimum heat transfer area, AtHENS can use an externally specified heat transfer coefficient for each stream or estimate it considering internal flow in a 3/4(in) diameter tube, with an average fluid flow velocity of 1.5 m/s, using the well known correlation of Dittus-Boelter. In the example here shown, this is the case and the estimated values are presented in Table 8.

Table 8: Estimation of heat transfer coefficients for process streams and utilities

Stream	Estimated heat transfer coefficient (kJ/s m2 ºC)
1	0.41
2	0.37
3	0.60
4	0.27
engine oil	1.41
water	5.88

Note that this procedure leads to heat transfer coefficients values comparable with those obtained ahead with the heat exchanger design, specially for tube-side streams, as shown in Table 7. Better results are very difficult to be obtained since in the targeting stage there is no information about which stream will flow in the shell-side and what will be the effective fluid flow velocity inside the tubes, parameter that changes according to the heat exchanger.

Using the Bath formula (Townsend and Linnhoff, 1984) and the heat transfer coefficients of Table 8, the target of minimum heat transfer area is 125.5 m². The capital cost of this area, calculated with the equation on Table 3, plus the operational cost of the target utilities, leads to a target total annual cost of $12,953.20/year. The values of Table 8 can also be used to synthesize a HEN without design. In doing so, the final HEN has a total annual cost of $14,036.10/year and a structure slightly different from that of the final HEN with design (Figure 14), since the loop between streams 2 and 3 is now broken and therefore those two units become only one.

This fact demonstrates a direct influence of design on synthesis.

Finally, a comparison of the total annual cost of the final HEN without design and the target total annual cost shows a proximity between them, which was expected, since the same heat transfer coefficients values are used in both procedures and the effective temperature differences are estimated under the same assumptions, i.e., counter-current configuration. On the other hand, in the example here presented, the total annual cost of the final HEN with simultaneous design is near two times the target one, again showing the great importance of design on synthesis.

CONCLUSIONS

The algorithm proposed for the automatic HEN evolution is robust, fast and easy to apply. As mentioned, the average computing time (Pentium 166 MHz, 32 MB RAM) to complete the synthesis with simultaneous design of thepresented example is less than twelve seconds. For comparison, it takes three seconds to complete the synthesis without the unit design (constant specified heat transfer coefficients). Although there is an increase by four times on the computing time, it is still a very good time considering that the heat exchangers design is done. In others processes where AtHENS was used successfully, as for example, in the Caprolactama unit of Nitrocarbono in Camaçari/BA/Brazil (thirty one process streams) and in the classical aromatic plant first presented by Linnhoff (nine process streams), the computing time has the order of a minute, using the same criteria of the example here shown.

The simulation matrix proved to be a good tool to perform a steady-state simulation and to restore the MTD in HEN

New rules for breaking loops, as well as the influence of the choice of LI basis set on loop identification and breaking, are being considered. To illustrate this influence, consider a different choice of LI set: (8,1,6,3,9) instead of (2,1,6,3,9), as in the first loop identification. The four loops identified would be different as would their ordering: (5,1), (7,6), (4,8) and (2,8). The final network would have the exact same structure as that obtained earlier (Figure 14), but with a lower total annual cost ($21,705.60/year).

Finally, in the example shown, the importance of HEN synthesis with simultaneous design could be observed, indicating that parameters to prevent heat exchanger designs and an automatic way to return to synthesis when a design is unattainable must be developed.

ACKNOWLEDGMENTS

The authors would like to acknowledgment the financial support received from CAPES.

NOMENCLATURE

D P pressure drop, kN/m² A heat transfer area, m² a number of rows in incidence matrix AtHENS Automatic Heat Exchanger Network Synthesis b number of columns in incidence matrix C cold stream Cp specific heat, kJ/kg ºC D diameter, m h heat transfer coefficient, kJ/m² s ºC H hot stream HE heat exchanger HEN heat exchanger network IL number of independent loops K1 constant, m^-1 Kps constant, kN.s^5.1 m^6.2 ºC^5.1/kJ^5.1 Kpt constant, kN s^3.5 m³ ºC^3.5/kJ^3.5 L length, m LD linearly dependent column LI linearly independent column M mass flowrate, kg/s m number of columns in simulation matrix MI mixer MTD minimum temperature difference, ºC n number of rows in simulation matrix N number of total tubes n1 constant npt number of tube passes ntp number of tubes per pass p_{(a X b)} rank of the incidence matrix PDM pinch design method PP pinch point Q heat load, kJ/s Rf fouling resistance, m² s ºC/J SP splitter T temperature, ºC v mean flow velocity, m/s

Greek Letters

a _i constant r density, kg/m³ m viscosity, N s/m² k thermal conductivity, J/s m ºC

Subscripts

H header i inlet/inner o outlet s shell t tube

REFERENCES

Jegede, F.O. and Polley, G.T., Optimum Heat Exchanger Design, Trans. I Chem E, 70 (March), Part A, pp. 133 - 141 (1992).

Linnhoff, B. et al., User Guide on Process Integration for the Efficient Use of Energy, The Institution of Chemical Engineers (1982).

Linnhoff, B. and Hindmarsh, E., The Pinch Design Method for Heat Exchanger Networks, Chem. Eng. Sci., 38 (5), pp. 745 - 763 (1983).

Liporace, F.S; Queiroz, E.M. and Pessoa, F.L.P., Generación de Redes de Intercambiadores de Calor que Involucran Corrientes Alejadas del PE, Información Tecnológica, 8 (6), pp. 187 - 196 (1997).

Liporace, F.S.; Queiroz, E.M. and Pessoa, F.L.P., Redes de Trocadores de Calor com Base no Método do Ponto de Estrangulamento Energético (MPE) - Síntese Afastada do Ponto de Estrangulamento Energético (PE), Anais do 11º Congresso Brasileiro de Engenharia Química, Rio de Janeiro (Setembro), 1, pp. 91 - 96 (1996).

Oliveira, S.G., A Influência do Projeto na Síntese de Redes de Trocadores de Calor, M.Sc. thesis (in portuguese), EQ/UFRJ, Rio de Janeiro, Brazil (1995).

Oliveira, S.G.; Costa, A.L.H.; Platt, G.M. and Queiroz, E.M., Estudo Comparativo de Métodos de Projeto de Trocadores de Calor Casco e Tubos sem Mudança de Fase, Anais do 11º Congresso Brasileiro de Engenharia Química, Rio de Janeiro (Setembro), 1, pp. 103 – 108 (1996).

Pethe, S.; Singh, R. and Knopf, F.C., A Simple Technique for Locating Loops in Heat Exchanger Networks, Comp. Chem. Eng., 13 (7), pp. 859 - 860 (1989).

Ponton, J.W. and Donaldson, R.A.B., A Fast Method for the Synthesis of Optimal Heat Exchanger Networks, Chem. Eng. Sci., 29, pp. 2375 - 2377 (1974).

Sinnot, R.K., Chemical Engineering, Vol. 6 (Design), 2nd ed., Pergamon Press, Oxford, (1993).

Townsend, D.W. and Linnhoff, B., Surface Area Targets for Heat Exchanger Networks, I Chem E 11th Annual Research Meeting on Heat Transfer, Bath (1984).

Publication Dates

• Publication in this collection
  23 Apr 1999
• Date of issue
  Mar 1999

History

• Accepted
  25 Jan 1999
• Received
  03 June 1998