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Computer-aided synthesis of heat exchange network
Heat Recover)," Systems Vol. 5, No. 5, pp. 425--435, 1985 Printed in Great Britmn
0198-7593185 $3.00 + .00 Pergamon Press Ltd
COMPUTER-AIDED SYNTHESIS OF HEAT EXCHANGE NETWORK J ~ i KLEMF_~ a n d RADIM PTA~NiK Research Institute of Chemical Equipment, Trust CHEPOS, Ki'i~ikova 70, 602 00 Brno, Czechoslovakia Al~ract--Thermodynamic analysis, i.e. appreciation of the importance of the pinch point and of the composite curves has brought about a significant contribution to the heat exchange network synthesis. The actual design of a heat exchange network, however, presents some problems. To tackle them an interactive mode of computer aided synthesis has been developed. The suggested approach used for generating the network employs the information obtained by the thermodynamic analysis respecting the maximum heat recovery, together with specification of the minimum number of units. Then an optimization of shifting heat loads around loops and/or paths of individual units is applied. As a result heat exchange network with the value of the economic objective function close to the minimum is obtained. For this network a further evolution is suggested based on feasible modifications of input and/or output data. This approach is realized by a package of interactive computer programmes---HENS (Heat Exchanger Network Synthesis). Features of HENS are demonstrated on the synthesis of a preheat train in the atmospheric distillation of crude oil.
NOMENCLATURE
A A, n
b C
dQ
E,
NC Hc
NH nh nu
s~, S., U..
uL vL
Z AI,,,, 6 qJ, 0
transfer area of a heat exchanger [m2] ith unit in a path linear cost parameter exponential cost parameter investment cost of heat transfer unit [c. u. yr-t] investment cost for ith unit [c. u. yr- '] heat load change for a unit in a loop or a path [kW'] ith exchanger in a loop number of cold streams number of cold utilities number of hot streams number of hot utilities number of units amount of ith cold utilities [kg yr- J] amount ofjth hot utilities [kg yr-t] minimum number of units minimum number of units below pinch minimum number of units above pinch total annual cost [c. u. yr-t] minimum temperature approach [K] annual rate of return unit cost of ith cold utility [c. u. kg -~] unit cost ofjth hot utility [c. u. kg -~] operating hours per year 1. I N T R O D U C T I O N
A t the p r e s e n t time the p r o b l e m o f the h e a t e x c h a n g e n e t w o r k synthesis has received c o n s i d e r a b l e a t t e n t i o n . In this s t u d y synthesis m e a n s a s y s t e m a t i c g e n e r a t i n g o f the process flowsheet (i.e. t o p o l o g y a n d i n d i v i d u a l units' p a r a m e t e r s ) which w o u l d be identical with o r as m u c h as possible close to the o p t i m a l s o l u t i o n for a given objective f u n c t i o n a n d a s s u m e d m a t h e m a t i c a l m o d e l . T h e h e a t e x c h a n g e synthesis p r o b l e m is expected to p r o v i d e the process flowsheet o f the h e a t e x c h a n g e r s ( t o p o l o g y a n d size o f e x c h a n g e r s , heaters a n d coolers) which w o u l d have the lowest cost with r e g a r d to the specified objective function. A m o r e d e t a i l e d definition is given, for e x a m p l e , by L i n n h o f f [1] a n d L i n n h o f f et al. [2]. In recent y e a r s a n u m b e r o f w o r k s have been p u b l i s h e d t u r n i n g a t t e n t i o n to the t h e r m o d y n a m i c analysis which yields key p o i n t s a n d i n t e r r e l a t i o n s (the pinch p o i n t a n d the c o m p o s i t e curves) as well as the design targets ( m a x i m u m h e a t recovery, m i n i m u m n u m b e r o f units). Both theoretical f o u n d a t i o n s a n d a p p l i c a t i o n e x a m p l e s h a v e been p u b l i s h e d especially by L i n n h o f f et al. [1-3], a n d 425
426
Jffti KLEME~ a n d R A D I M P T A C N i K
550
~,00
250
I
200
~50
I00
50
0
I 25
. 50
I 75
I tOO
Q (MW)
Fig. 1. Compositecurves for a problem ELOU-AT-6 (problem data in Table 1). also by Umeda et al. [4-6]. These works are sufficiently known and in the following text we shall refer to the concepts introduced by them. A very useful graphical aid for the thermodynamic analyses of the problem appears to be the composite curves (see Fig. 1). They show the relation between the minimum utilities requirements and the minimum temperature approach Atm,, as a temperature--enthalpy function in the graph (designated T-Q or T-H graph). The curves for cold and hot streams are plotted separately. All the hot streams on this representation are merged to a one fictitious stream. The same applies to the cold streams. A more detailed description of the constructing of these composite curves is given in Linnhoff [1,2]. In the problems where the specifications can be satisfied only if both cold and hot utilities are simultaneously used one finds the location with the shortest vertical distance (in terms of temperature difference) between the composite curves--the so called pinch point. The problems which can be solved for a given value At,,~, without either coolers or heaters are not likely to be pinched. However, in these problems a value of Arm,, can be found for which they become pinched (sufficiently large, but sometimes without practical meaning). The smallest value At,,~ thus obtained is called a threshold--it is the maximum possible value of Atm,, for which the minimum energy requirements for utilities are maintained. The thermodynamic analysis represents only the first step, though very important, of the synthesis problem. The aim is to design such a heat exchange network which would in the first stage comply with the given targets but moreover with the optimum of the objective function for a real heat exchange network meeting the practical demands of design, production and operation. The presented paper is concerned with this very problem. 2. HEAT EXCHANGE NETWORK DESIGN On the base of the first step, the problem can be divided into those with and without the pinch point for the given A t e . If the problem is pinched, two independent and less extensive sub-problems (which is a great advantage) are to be solved. If the maximum heat recovery is to be achieved, two separate solutions must be found one for the sub-problem above the pinch and another for the sub-problem below the pinch [2]. The procedure of generating a heat exchange network, however, is both for these two sub-problems and for the unpinched problem the same. In many works, especially those from the period of several years ago, the possibility of solving the synthesis problem by simple hand calculation was reported [7, 8]. Nowadays, computer programs for calculation, frequently with graphical representation of values of thermodynamic analysis, are in current use. In the second step of the heat exchange network generation and designing the aid of the computer becomes even more significant. The experience of the authors of this paper as well as of literature
Computer-aided synthesis of heat exchange network
427
references confirm, that seeking an unique algorithm to design the final network is not generally useful. In spite of that, such algorithms can be advantageously used when generating the initial structures which are further developed (e.g. methods of Ponton and Donaldson [9] and Nishida et al. [7]). A good synthesis program should be an easy to use instrument capable of supplying information concerning possibilities and properties of the studied heat exchange network. The program should inform the user, as promptly and simply as possible, about changes in network performance resulting from his interactive actions. The true creator, however, directing the generating of the heat exchange networks should be a process designer who performs the synthesis employing his experience, knowledge and even intuition, who should take into account all individual requirements and differences of the particular problem (safety of operation, products quality, sensitivity to process condition changes, maximum and minimum feasible size of heat exchangers, usefulness of stream-splitting etc.). Doing this, he can not regard the heat exchanging system as an isolated problem but rather as a part integrated with the flowsheet environment. A very important factor is an appropriate choice of the objective function. It is not easy to formulate the objective function, which would incorporate in cost terms such aspects as pressure drop, utilities transport, stream splitting etc. In the literature the objective function is commonly defined as a sum of yearly return of investment of exchangers, heaters and coolers and energy cost per year. z = 6
C~, + 0 i-I
~o,Sc, \i-I
~, ~pjSn, '-I
)
(!)
where Z is the annual total cost (currency unit per year), 6 the annual rate of return, CA, the investment cost for the ith unit (c. u.), 0 the operating hours in a year, Sc, the amount of the ith cold utility spent per year (kg yr-~), ~k/the operating cost oi" t h e j t h hot utility per year (c. u. kg-J), $5 the amount of the j t h hot utility spent per year (kg yr-~), ~0i the operating cost of the ith cold utility per year (c. u. kg-~), nu the number of units (exchangers, heaters, coolers), nc the number of cold utilities and nh the number of hot utilities. In a large proportion of cases the 'maximum heat recovery' part of the objective function appears to be the most decisive factor when minimizing the annual total cost. For investment cost of a unit (exchanger, cooler, heater) the frequently used expression is C = a Ab
(2)
where A is the heat transfer area (m 2) and a, b are the cost parameters. The value of exponent b is usually given as 0.6 (see [7, 9]), in some cases as 0.5 (see [8]). In these cases the investment cost is largely influenced by the number of units and it seems likely that the optimum network can be found between the topologies with the minimum number of units. Many of synthesis methods are based on the minimizing the number of process units (e.g. Linnhoff and Vredeveld [10], Jow-Lih Su and Motard [I 1]). As given by Linnhoff et al. [2] on the basis of Euler's theorem the minimum number of units (number of units can be different from number of apparatuses) equals: Urn,, = N H + N C - 1
(3)
where N H denotes number of hot streams and N C number of cold streams (including utilities). If the maximum heat recovery is a target in a pinched problem, then the minimum number of units equals Urn,, = U~,, + U~,n
(4)
where U~,, is the minimum number of units for a sub-problem above pinch point and U~, is the minimum number of units below pinch point (following [3]). It is necessary to state, that there are some problems, where the total heat exchange area is a more important factor than the minimum number of the units. For instance the heat exchange system of a furnace convection section (see [12]) has the exponent b in equation (2) equal to 1.0, which means, that the optimal solution represents the network with the minimum total area. To
428
Jl[[i KLEMF.~and R.ADIM PTA~NiK
obtain such a network the method employed by Nishida et al. [7] is suitable, but its application for more complicated problems without the help of a computer is very time consuming. The problem, by means of which some of the principles of the heat exchange network synthesis will be demonstrated in the following text, has the value of the exponent in equation (2) b = 0.88. The optimum network in this case is neither among the networks with the number of units near to the minimum nor among the networks with the total area close to the minimum possible value (this area may be calculated e.g. using the composite curves for given Arm,n). A greater value of coefficient b is caused by the considerable size of the heat exchangers in the large-scale production plant.
3. COMPUTER APPLICATION To solve the synthesis problem a programming system HENS (Heat Exchanger Network Synthesis) which can be run interactively, has been built up. Its operation when synthesizing a network proceeds through the following points: (i) Formulation of suitable synthesis model and objective function. (ii) Thermodynamic analysis of the problem (according to Linnhoff et al. [13]). Maximum heat recovery determination, pinch point identification. The available heat energy is illustrated by composite curves and grand composite curves. An estimate of the minimum total area can be made, too. Evaluation of the possible stream parameter changes in the heat exchange system (input temperatures, heat capacities flowrates) including surrounding flowsheet. Incorporating of some deviations from the idealized task (e.g. heat transfer coefficients difference). (iii) Creation of the initial design of the network. It is advisable to separate the pinched problem into sub-problems above pinch and below pinch. The initial design can be developed either interactively by defining the structure or by application of some of the programmed methods (Ponton and Donaldson [9], with several modifications [14] including the modification for multipass exchangers [15] or the Nishida et al. method [7]). By using the algorithm of Ponton and Donaldson initial networks for different values of A t u with different numbers of processing units are obtained. For sub-problems above the pinch point it is, however, useful to employ a modification of this method. The matches are created from the pinch (the design starts from the cold side of the sub-problem) and the rule 'match the streams with the highest temperatures' is replaced by the rule 'match the streams with the lowest temperatures'. (iv) Generation of the initial structure. The user is informed on the network by a grid graphic representation. The Linnhoff and Flower way [8] has been adapted to fit better the interactive computing. Hot process streams run from top to bottom, cold streams in an opposite way. The exchangers are represented by two crosses tied by a horizontal line between appropriate hot and cold stream. Coolers and heaters are represented as crosses on corresponding streams. This grid can be seen on Figs 2-4. The heat-exchangers may be specified by area, heat duty or one of the output temperatures. Similarly, the parameters of process streams and/or cost parameters can be changed interactively. (v) Heat loads optimization for the individual units by means of loops and paths--further development of the procedure mentioned by Linnhoff and Hindmarsh [3]--to obtain a procedure employing the optimization method and optimization of the stream splitting. The optimization could be also utilized for the topology changes. (vi) Detailed flowsheeting of the generated network performed on the basis of physical properties data stored in the data bank. At the present time, the synthesis program is linked with the simulation program SIPRO [16], using the data bank PHYSCO (originated from Politecnico Milano). (vii) Modification of the heat exchange network with respect to the difference between the simulation recalculation results and the values stemming from the synthesis model. Very important are especially the differences in the pinch point region.
Computer-aided synthesis of heat exchange network
429
(b) (,3)
El
E
E2 E3
E~
E4
Fig. 2. Example of the loops: (a) loop (E~, E2) the simplest case, (b) loop (EL, E:, E,, Ej).
The HENS package uses in its first section the theoretical concept published by Linnhoff et al. [2] [see above mentioned point (i)]. For the initial structure generation [see point (ii)] Ponton and Donaldson work [9] and its modifications as well as Nishida et al. method [7] have been used. To carry out the activities specified in the HENS description by points (v), (vi) and (vii) appropriate methodology had to be developed. 4. O P T I M I Z A T I O N OF HEAT LOAD ON E X C H A N G E R S A topology with minimum number of processing units essentially specifies how much of heat will be exchanged in every single unit. It is always the lower value of the heat load to be supplied to the cold stream or withdrawn from the hot one in order to reach its target temperature. A topology which has not the minimum number of units, contains always a nonzero number of so called loops. As a loop (see Fig. 2) is understood a sequence of heat exchangers (El, E : . . . E~), where each two adjoining units are located on the same .hot or cold streams. As adjoining ones are also considered units E~ and EN. Two sequences are regarded as an identical loop provided their adjoining exchangers are identical, e.g. the sequences (Et, E2, E3, E4), (E3, E4, Ej, E2) represent the same loop. If a topology contains more than one unit of cooler-heater type and simultaneously these process units are not in separately designed sub-networks (i.e. there is no exchanger transferring heat from one sub-network's hot stream to another sub-network's cold stream) then this topology involves a so called path. Under such a path (see Fig. 3) a sequence of process units (exchangers, coolers, heaters) (Aj, A 2. . . . As) is understood where every two adjoining are either of cooler-heater type or lie on the same hot, respectively cold, stream (at least one of them being heat exchanger). The first and the last process unit AI and As are considered to be adjoining, too. Further, it is assumed that the heaters are not situated on the hot streams neither are the coolers on the cold ones. Two sequences of the process units are considered as being of the same path if they share the same adjoining elements. It is obvious that the number of process units of cooler-heater type is even for each heat path. If the path is not containing the heaters or coolers then the number of process units is even. The path which involves neither heaters nor coolers is a loop. The paths and loops have the following interesting feature: If the heat loads of odd items within the sequence of process units forming a loop of path are altered by the value of dQ say and the heat loads of even ones by - d Q (where dQ must be chosen so as to guarantee that heat load of all units located in the path or around
(o ]
[b] A~ Az A3
A3 Ai
A4
A4 A~
Fig. 3. Paths examples: (a) a path (A, A2, As, A4) involving two coolers At A~ (b) a path (A I, A2, A~, A 4, As) involving I heater A z and l cooler A s. HRS
$: .~--D
430
Jx~,i KLEMF~ and RAD|M PTA~NiK
(a) Q,
Q, +clQ
Q~
Q~- clO
Q, + Og
Q. Q~
tl_
Q4
Q3
Q2- clO
Q4+clQ
Q3-dQ
(c) Q
O,+dQ O2- clQ
Q2
Q3
Q3÷aQ
Fig. 4. Heat load shift: (a) heat load shift around a loop, (b) heat load shift along a path involving 2 coolers--the heat recovery does not change. (c) heat load shift along a path involving one cooler and one heater--the heat recovery changes.
the loop would be positive or zero) then the target temperatures of all streams in the given topology will be maintained (see Fig. 4--Qi are the original values of the process units heat loads). On the other hand, for other values of heat loads the target temperatures will not be maintained. This is true with the exception of the case where the path would be formed by several segments--these being paths or loops in themselves and allowing for changes of process units' heat loads within the individual segments--paths (loops)--separately. This circumstance may be exploited when guiding the design towards the optimum parameters of the network. If a single path (loop) is chosen, then the heat loads of process units forming this path (loop) can be optimised while maintaining the parameters of the others processing units in the network unchanged. This procedure is essentially an optimum search for the function of one variable in a finite interval--thus a problem easily handled by a computer. The optimal heat loads distribution to all processing units of the network can be found for the given topology when combining the optimizations of heat loads along all the paths (loops). When optimizing the heat loads along loops and paths which do not involve coolers or heaters the heat energy supplied by utilities is preserved. On the contrary, when optimizing the paths with both coolers and heaters the amount of utilities varies. Consequently, it is possible to trade off between operating and capital cost for the problems with the pinch point. When locating the individual parameters in this way the question of appropriate Atm~ (often considered as a key point) becomes irrelevant for its value is determined in the course of optimization procedure. Using this optimization technique it can be found that certain units should be preferably left out. This is a case when a process unit transfers zero heat load (i.e. value o f d Q equal to the original heat load value of this process unit). There is one more way of applying the optimization to screen the topology. By adding a new unit into the structure (a fictitious one with zero heat load) a new loop (loops) or path 'ipaths) is
Computer-aided synthesis of heat exchange network
o,I
°,1 1
/
431
'o,+oo J J Q2-dQl t00] O-dQ
02 1
I t°,
'o,+oI l
] l O3
0
do 1
/
OI
0z
I
D
I
ol
I °1 Fig. 5. Verificationof the topology by means of the heat load distribution optimization. (a) For the paths. Testing of the suitable aiocation of a cooler. The optimal solution may be a network: (i) with the original cooler, (2) with a new cooler, (3) with both cooler. (b) For the loops. Testing of the appropriate alocation of a heat exchanger. The most satisfying may be found a network with: (I) the original exchanger, (2) with a new exchanger, (3) with both exchanger.
introduced. Optimization of this new paths may result in modification of the network by including this unit or replacing some existing in the original network (see Fig. 5). The optimization of heat loads in units forming path is so general so it is possible to consider even more detailed models o f the heat exchangers. For example, different values of the heat transfer coefficients can be attached to the particular exchanger, a functional dependance of specific heat Cp on the temperature for individual stream and even appropriate correction to the temperature difference to multipass flow arrangement within the exchanger can be assigned. These features are rather important since the so called idealized synthesis is based on purely c o u n t e r - c u r r e n t heat exchangers with m a n y simplifications (constant values of C r invariable heat transfer coefficient, etc.) 5. S Y N T H E S I S P R O B L E M IN C R U D E O I L P R E H E A T T R A I N IN T H E A T M O S P H E R I C D I S T I L L A T I O N As an example of industrial plant heat exchange network synthesis the problem o f crude oil distillation has been selected. This problem was formulated by Kafarow et al. [17]. In this system a crude oil stream is divided into two sections (before and after desalting) and heated. The heat is supplied by four process streams. In Table l the specification data for a synthesis problem are shown. F o r the given objective function
Z = 6 ~ CA, + OtpSc i-I
(simplified form of equation (l) for the given example).
(5)
Jtgti K t _ r ~
432
and R A D I M P T ~ N i K
Table 1. E L O U - A T - 6 Stream number H, H: H3 H, Cc C2
Mass flowrate Stream name
Problem data (by [17]). Input temperature
kg h - i
1. pump around . . . . . . . 2. pump around residue 230-350"C fraction
crude oil desalted crude oil
43~00
C .............
143
404000
188
316000 163000 767250 751500
340 250 30 140
c,
Target temperature C
.........
69 79 90 165 140 235
.....
k c a l k g - ' C -*
kJ k g - ' K - '
0.521 0.520
2.1813228 2.177136
0.505 0.518 0.473 0.527
2.114334 2.1687624 1.9803564 2.2064436
Overall heat transfer coefficient 2 5 0 k c a l m - 2 h - ~ : C - ' = 2 9 0 . 9 W m - " h " ~. Minimum temperature approach A t ~ = 10
where Z is the total annual cost (Rbl yr- t), 3 the annual rate of return, CA, the investment cost for ith unit (Rbl yr-1), Sc the amount of cooling water spent per year (kg yr-I), 0 the operating hours per year, ~p the unit cost of cooling water (Rbl kg-~). The solution developed by these authors represents the total cost of 118 280 Rbl per year with annualised capital cost of 56535 Rbl. The network suggested by Kararow et al. is shown in Fig. 6. The same problem was solved by Demin and Kanevec [18] who developed the network illustrated in Fig. 7 for which they reported the total annual cost amounting to 118925Rbl, the annualised investment cost rate being 57168 Rbl. It is interesting to note that if the actual data given in [17] and [18] are used the value of the objective function reads to 118054 Rbl, instead. By applying the programming system HENS on this problem several networks, both with and without splitters have been designed resulting in considerable savings if compared with the previously published solutions. The original specification of the synthesis problem is an unpinched one, the threshold temperature approach is equal to 27.46°C and located between 188°C on the hot and 160.54°C on the cold stream. The target temperature of stream C:--crude oil entering the furnace--is 235°C. The corresponding composite curves are plotted in Fig. 1. The minimum feasible area amounts to 8185 m 2 (for At,~, = 10°C). The minimum number of units equals to 6. Considering the fact that the exponent coefficient in the objective function is equal to 0.88 it is not appropriate to look for a solution among networks with the number of units close to this minimum. The minimum requirements for cold utilities are 10567 kW (the problem is unpinched and therefore hot utilities
H2
H4
I
.)
H3
G
HI
I CI
Fig. 6. The original solution o f the test problem E L O U - A T - 6 suggested in [17] (temperatures o f streams within the network arc not given).
Computer-aided synthesis of heat exchange network
433
90"
14301 Ci
30 °
~)
140°
50"87° 79"
I
140o
~
154.25°
G9 °
H3 340 C2
188° H2
140°
173./~ 235" H4
188"o~)
"
Fig. 7. Solution of the problem ELOU-AT-6-suggested by authors in
[18].
are not required). For such a problem, isolated from surrounding flowsheet, solution without splitters has been developed where the value of the objective function amounts to 115 356 Rbl per year (annualiscd investment cost 54470 Rbl). A solution with splitters has the value of the objective function of 114222 Rbl per year (annualised investment cost 53336 Rbl)--sc¢ Fig. 8. Thus, in comparison with the original solution, savings of about 5.7~ in capital cost have bccn obtained. Providing, that from the surrounding flowsheet the furnace is considered as belonging to the problem and thus the temperature of desalted crude oil C2 entering the furnace is required as high as possible, the problem remaining primarily unpinched becomes one with the pinch point. For given Atm the pinch is between temperatures 178 and 188°C. Then the input temperature to the H2
1 8 ~
I 10.4*
)
I
1 8 8 ~
CI
J
143°I 140° HI Fig. 8. Solution with the lowest annual total cost developedby systemHENS for original data. (Input temperature of crude oil to the furnaceis 235°C.)
434
JIAi KLEMF.~ and RADIM PT.~.'qjK 165 ° F
165o
165"
140"
250
252.46*
'88* 188" 90*
90.
I
f
I
H2 152..5"
30°
140"
78.6*
69*
143"
Fig. 9. Design with the lowest total cost at the maximum heat recovery. Input temperature of crude oil to the furnace (for At=i. 10cC) increased to 252.46°C.
furnace can be raised up to 252.46°C. At the same time the requirements for cold utilities are reduced to 2521 kW. In this case the rise of the input temperature to the furnace makes it possible, according to the data given [17], to economise 22116 tons of fuel per year, that means to save 145000 Rbl per year (the constant capital cost of the furnace is assumed, e.g. in case of reconstruction, otherwise savings would be even higher). Two networks have been designed to solve this problem one without stream splitting where the value of the objective function reaches 113453 Rbl per year and another with stream splitting where the value of the objective function amounts to 110605 Rbl per year (see Fig. 9). This solution brings savings of 7449 Rbl per year in comparison with the original figure in [17], apart from reduction of fuel consumed in the furnace. Admitting the possibility of violating the value At,,,, = 10°C then (theoretically) all the heat of the four process streams can be used. The corresponding value At,,,, is 4.54°C and the input temperature to the furnace could be increased up to 257.93°C. When integrating the heat exchange network with the surrounding flowsheet, some recommendations from the composite curves can be put forward, which would lead to the improved heat recovery of the heat supplied by the process streams for the given Atm,,, or perhaps reduction of the overall heat exchange area for the given network's structure. These modifications are aimed at favourable changing of the conditions around the pinch where the network design appears to be most sensitive with respect to the objective function. Inspecting the composite curves (Fig. I) implies that the most important region from this point of view is between 143 and 188°C. The analysis of the composite curves shows that it is possible to reach higher heat recovery. Increasing the temperature of crude oil entering the furnace (for given Attar,) could be obtained by increasing heat capacity of hot streams (i.e. their input temperature or mass flowrate) which are above the pinch only (streams H4, H~ in presented problem). On the other hand in streams Ht, H2, which are below the pinch, it would be useful to reduce heat capacity. This leads to the saving of necessary amount of cold utilities. There are some modifications of surrounding flowsheet which could be discussed. It could be seen from the composite curves that it is useful to open them more for the same heat recovery (the required heat exchange area could be reduced), or to shift the curve of cold streams and the curve of hot streams in direction of horizontal axis. So they would more overlap and thus the target value for minimum utilities would be reduced.
Computer-aided synthesis of heat exchange network
435
In the studied p r o b l e m these suggestions c o u l d be reflected, e.g. in shifting up the t e m p e r a t u r e s o f the stream H2, i.e. rising b o t h the i n p u t (188°C) a n d target t e m p e r a t u r e (79°C) by 5°C (for Atm,n = 10°C). This m o d i f i c a t i o n w o u l d represent a r e d u c t i o n o f the energy s u p p l y to the furnace by 760,122 kcal h - t = 884.4 k W a n d s i m u l t a n e o u s l y the r e q u i r e m e n t for the c o l d utility w o u l d be r e d u c e d by the s a m e a m o u n t o f heat. This i m p r o v e m e n t w o u l d be caused by the shift o f the pinch. CONCLUSION T h e objective o f the p r e s e n t s t u d y is to d e m o n s t r a t e new possibilities in designing an i m p o r t a n t p a r t o f a chemical p r o c e s s - - t h e h e a t e x c h a n g e n e t w o r k . It is s h o w n that the suitable usage o f an interactive p r o g r a m m i n g system, which is b a s e d o n t h e r m o d y n a m i c analysis followed by optim i z a t i o n p r o c e d u r e t o g e t h e r with a m a n - m a c h i n e d i a l o g u e f o u n d e d on a p p r o p r i a t e user-friendly r e p r e s e n t a t i o n , brings significant energy saving a s s o c i a t e d with the c a p i t a l cost reduction. A l t h o u g h this t o p i c has been studied b y a n u m b e r o f a u t h o r s , it can be seen, t h a t especially an a p p l i c a t i o n o f the o p t i m i z a t i o n a p p r o a c h yields b o t h m o r e effective p r o g r e s s as well as m o r e f a v o u r a b l e results. REFERENCES 1. B. Linnhoff, Ph.D. Thesis, University of Leeds (1979). 2. B. Linnhoff, B. W. Townsend, D. Boland, G. F. Hewitt, B. E. A. Thomas, A. R. Guy and R. H. Marsland, A User Guide on Process Integration for the Efficient Use of Energy. Institute of Chemical Engineers, Rugby (1982). 3. B. Linnhoff and E. Hindmarsch, The pinch design method for heat exchanger networks. Chem. Engng Sci. 5, 745-763 (1983). 4. T. Umeda, K. Niida and K. Shiroko, A thermodynamic approach to heat integration in distillation systems, AICHE J. 25, 423--429 (1979). 5. T. Umeda, T. Harada and K. Shiroko, A Thermodynamic Approach to the Synthesis of Heat Integration Systems in Chemical Processes. Comput. Chem. Enginng 3 (I--4), 273-282 (1979). 6. M. Nishio, J. Itch, K. Shiroko and T. Umeda, A thermodynamic approach to steam-power system design, Ind. Eng. Chem. Process Des. Dev. 19, 306 (1980). 7. N, Nishida, Y. A. Liu and L. Lapidus, Studies in chemical process design and synthesis: III. A simple and practical approach to the optimal synthesis of heat exchanger networks. AICHE J. 23, 77-93 (1977). 8. B. Linnhoff and J. R. Flower, Synthesis of heat exchanger networks. AICHE J. 23, 333-354 (1978). 9. J. W. Ponton and R. A. B. Donaldson, Fast method for the synthesis of optimal heat exchanger networks. Chem. Engng Sci. 29, 2375-2377 (1974). 10. B. Linnhoff and D. R. Vrcdeveld, AICHE Diamond Jubilee Meeting, Washington (1983). 1I. Jow-Lih Su and R. L. Motard, Evolutionary synthesis of heat-exchanger networks. Comput. Chem. Engng $ (2), 67-80 (1984). 12. J. Klemeg and R. Pt~i~nik, Methods of optimal synthesis for heat energy calculation of steam reforming process. Research Report, Research Institute of Chemical Equipment (in Czech). CHEPOS, Brno (1983). 13. D. W. Townsend and B. Linnhoff, AICHE J. 29, 742-771 (1983). 14. J. R. Flower, Ph.D. Thesis, Computer program HXSJF. University of Leeds (1977). 15. J. Zachoval and Z. Konetn~, 15th European Syrup. on Use of Computers in the Chemical Engineering, Antwerp (1982). 16. V. Vagek and J. Kleme~, Simulation programming system SlPRO--Version for desk-top computer Compucorp 625 in Basic language. Comput. Chem. Engng 7, 175-182 (1983). 17. V. V. Kafarov, V. P. Meshalkin and V. L. Perov, Mathematical Bases of Automatized Design of Chemical Plants (in Russian). Khimia, Moscow (1979). 18. A. A. Detain and G. E. Kanevec, Decomposition--modular method of synthesis of heat exchange systems (in Russian). Chem. TechnoL 4, 42-44 (1982).
0198-7593185 $3.00 + .00 Pergamon Press Ltd
COMPUTER-AIDED SYNTHESIS OF HEAT EXCHANGE NETWORK J ~ i KLEMF_~ a n d RADIM PTA~NiK Research Institute of Chemical Equipment, Trust CHEPOS, Ki'i~ikova 70, 602 00 Brno, Czechoslovakia Al~ract--Thermodynamic analysis, i.e. appreciation of the importance of the pinch point and of the composite curves has brought about a significant contribution to the heat exchange network synthesis. The actual design of a heat exchange network, however, presents some problems. To tackle them an interactive mode of computer aided synthesis has been developed. The suggested approach used for generating the network employs the information obtained by the thermodynamic analysis respecting the maximum heat recovery, together with specification of the minimum number of units. Then an optimization of shifting heat loads around loops and/or paths of individual units is applied. As a result heat exchange network with the value of the economic objective function close to the minimum is obtained. For this network a further evolution is suggested based on feasible modifications of input and/or output data. This approach is realized by a package of interactive computer programmes---HENS (Heat Exchanger Network Synthesis). Features of HENS are demonstrated on the synthesis of a preheat train in the atmospheric distillation of crude oil.
NOMENCLATURE
A A, n
b C
dQ
E,
NC Hc
NH nh nu
s~, S., U..
uL vL
Z AI,,,, 6 qJ, 0
transfer area of a heat exchanger [m2] ith unit in a path linear cost parameter exponential cost parameter investment cost of heat transfer unit [c. u. yr-t] investment cost for ith unit [c. u. yr- '] heat load change for a unit in a loop or a path [kW'] ith exchanger in a loop number of cold streams number of cold utilities number of hot streams number of hot utilities number of units amount of ith cold utilities [kg yr- J] amount ofjth hot utilities [kg yr-t] minimum number of units minimum number of units below pinch minimum number of units above pinch total annual cost [c. u. yr-t] minimum temperature approach [K] annual rate of return unit cost of ith cold utility [c. u. kg -~] unit cost ofjth hot utility [c. u. kg -~] operating hours per year 1. I N T R O D U C T I O N
A t the p r e s e n t time the p r o b l e m o f the h e a t e x c h a n g e n e t w o r k synthesis has received c o n s i d e r a b l e a t t e n t i o n . In this s t u d y synthesis m e a n s a s y s t e m a t i c g e n e r a t i n g o f the process flowsheet (i.e. t o p o l o g y a n d i n d i v i d u a l units' p a r a m e t e r s ) which w o u l d be identical with o r as m u c h as possible close to the o p t i m a l s o l u t i o n for a given objective f u n c t i o n a n d a s s u m e d m a t h e m a t i c a l m o d e l . T h e h e a t e x c h a n g e synthesis p r o b l e m is expected to p r o v i d e the process flowsheet o f the h e a t e x c h a n g e r s ( t o p o l o g y a n d size o f e x c h a n g e r s , heaters a n d coolers) which w o u l d have the lowest cost with r e g a r d to the specified objective function. A m o r e d e t a i l e d definition is given, for e x a m p l e , by L i n n h o f f [1] a n d L i n n h o f f et al. [2]. In recent y e a r s a n u m b e r o f w o r k s have been p u b l i s h e d t u r n i n g a t t e n t i o n to the t h e r m o d y n a m i c analysis which yields key p o i n t s a n d i n t e r r e l a t i o n s (the pinch p o i n t a n d the c o m p o s i t e curves) as well as the design targets ( m a x i m u m h e a t recovery, m i n i m u m n u m b e r o f units). Both theoretical f o u n d a t i o n s a n d a p p l i c a t i o n e x a m p l e s h a v e been p u b l i s h e d especially by L i n n h o f f et al. [1-3], a n d 425
426
Jffti KLEME~ a n d R A D I M P T A C N i K
550
~,00
250
I
200
~50
I00
50
0
I 25
. 50
I 75
I tOO
Q (MW)
Fig. 1. Compositecurves for a problem ELOU-AT-6 (problem data in Table 1). also by Umeda et al. [4-6]. These works are sufficiently known and in the following text we shall refer to the concepts introduced by them. A very useful graphical aid for the thermodynamic analyses of the problem appears to be the composite curves (see Fig. 1). They show the relation between the minimum utilities requirements and the minimum temperature approach Atm,, as a temperature--enthalpy function in the graph (designated T-Q or T-H graph). The curves for cold and hot streams are plotted separately. All the hot streams on this representation are merged to a one fictitious stream. The same applies to the cold streams. A more detailed description of the constructing of these composite curves is given in Linnhoff [1,2]. In the problems where the specifications can be satisfied only if both cold and hot utilities are simultaneously used one finds the location with the shortest vertical distance (in terms of temperature difference) between the composite curves--the so called pinch point. The problems which can be solved for a given value At,,~, without either coolers or heaters are not likely to be pinched. However, in these problems a value of Arm,, can be found for which they become pinched (sufficiently large, but sometimes without practical meaning). The smallest value At,,~ thus obtained is called a threshold--it is the maximum possible value of Atm,, for which the minimum energy requirements for utilities are maintained. The thermodynamic analysis represents only the first step, though very important, of the synthesis problem. The aim is to design such a heat exchange network which would in the first stage comply with the given targets but moreover with the optimum of the objective function for a real heat exchange network meeting the practical demands of design, production and operation. The presented paper is concerned with this very problem. 2. HEAT EXCHANGE NETWORK DESIGN On the base of the first step, the problem can be divided into those with and without the pinch point for the given A t e . If the problem is pinched, two independent and less extensive sub-problems (which is a great advantage) are to be solved. If the maximum heat recovery is to be achieved, two separate solutions must be found one for the sub-problem above the pinch and another for the sub-problem below the pinch [2]. The procedure of generating a heat exchange network, however, is both for these two sub-problems and for the unpinched problem the same. In many works, especially those from the period of several years ago, the possibility of solving the synthesis problem by simple hand calculation was reported [7, 8]. Nowadays, computer programs for calculation, frequently with graphical representation of values of thermodynamic analysis, are in current use. In the second step of the heat exchange network generation and designing the aid of the computer becomes even more significant. The experience of the authors of this paper as well as of literature
Computer-aided synthesis of heat exchange network
427
references confirm, that seeking an unique algorithm to design the final network is not generally useful. In spite of that, such algorithms can be advantageously used when generating the initial structures which are further developed (e.g. methods of Ponton and Donaldson [9] and Nishida et al. [7]). A good synthesis program should be an easy to use instrument capable of supplying information concerning possibilities and properties of the studied heat exchange network. The program should inform the user, as promptly and simply as possible, about changes in network performance resulting from his interactive actions. The true creator, however, directing the generating of the heat exchange networks should be a process designer who performs the synthesis employing his experience, knowledge and even intuition, who should take into account all individual requirements and differences of the particular problem (safety of operation, products quality, sensitivity to process condition changes, maximum and minimum feasible size of heat exchangers, usefulness of stream-splitting etc.). Doing this, he can not regard the heat exchanging system as an isolated problem but rather as a part integrated with the flowsheet environment. A very important factor is an appropriate choice of the objective function. It is not easy to formulate the objective function, which would incorporate in cost terms such aspects as pressure drop, utilities transport, stream splitting etc. In the literature the objective function is commonly defined as a sum of yearly return of investment of exchangers, heaters and coolers and energy cost per year. z = 6
C~, + 0 i-I
~o,Sc, \i-I
~, ~pjSn, '-I
)
(!)
where Z is the annual total cost (currency unit per year), 6 the annual rate of return, CA, the investment cost for the ith unit (c. u.), 0 the operating hours in a year, Sc, the amount of the ith cold utility spent per year (kg yr-~), ~k/the operating cost oi" t h e j t h hot utility per year (c. u. kg-J), $5 the amount of the j t h hot utility spent per year (kg yr-~), ~0i the operating cost of the ith cold utility per year (c. u. kg-~), nu the number of units (exchangers, heaters, coolers), nc the number of cold utilities and nh the number of hot utilities. In a large proportion of cases the 'maximum heat recovery' part of the objective function appears to be the most decisive factor when minimizing the annual total cost. For investment cost of a unit (exchanger, cooler, heater) the frequently used expression is C = a Ab
(2)
where A is the heat transfer area (m 2) and a, b are the cost parameters. The value of exponent b is usually given as 0.6 (see [7, 9]), in some cases as 0.5 (see [8]). In these cases the investment cost is largely influenced by the number of units and it seems likely that the optimum network can be found between the topologies with the minimum number of units. Many of synthesis methods are based on the minimizing the number of process units (e.g. Linnhoff and Vredeveld [10], Jow-Lih Su and Motard [I 1]). As given by Linnhoff et al. [2] on the basis of Euler's theorem the minimum number of units (number of units can be different from number of apparatuses) equals: Urn,, = N H + N C - 1
(3)
where N H denotes number of hot streams and N C number of cold streams (including utilities). If the maximum heat recovery is a target in a pinched problem, then the minimum number of units equals Urn,, = U~,, + U~,n
(4)
where U~,, is the minimum number of units for a sub-problem above pinch point and U~, is the minimum number of units below pinch point (following [3]). It is necessary to state, that there are some problems, where the total heat exchange area is a more important factor than the minimum number of the units. For instance the heat exchange system of a furnace convection section (see [12]) has the exponent b in equation (2) equal to 1.0, which means, that the optimal solution represents the network with the minimum total area. To
428
Jl[[i KLEMF.~and R.ADIM PTA~NiK
obtain such a network the method employed by Nishida et al. [7] is suitable, but its application for more complicated problems without the help of a computer is very time consuming. The problem, by means of which some of the principles of the heat exchange network synthesis will be demonstrated in the following text, has the value of the exponent in equation (2) b = 0.88. The optimum network in this case is neither among the networks with the number of units near to the minimum nor among the networks with the total area close to the minimum possible value (this area may be calculated e.g. using the composite curves for given Arm,n). A greater value of coefficient b is caused by the considerable size of the heat exchangers in the large-scale production plant.
3. COMPUTER APPLICATION To solve the synthesis problem a programming system HENS (Heat Exchanger Network Synthesis) which can be run interactively, has been built up. Its operation when synthesizing a network proceeds through the following points: (i) Formulation of suitable synthesis model and objective function. (ii) Thermodynamic analysis of the problem (according to Linnhoff et al. [13]). Maximum heat recovery determination, pinch point identification. The available heat energy is illustrated by composite curves and grand composite curves. An estimate of the minimum total area can be made, too. Evaluation of the possible stream parameter changes in the heat exchange system (input temperatures, heat capacities flowrates) including surrounding flowsheet. Incorporating of some deviations from the idealized task (e.g. heat transfer coefficients difference). (iii) Creation of the initial design of the network. It is advisable to separate the pinched problem into sub-problems above pinch and below pinch. The initial design can be developed either interactively by defining the structure or by application of some of the programmed methods (Ponton and Donaldson [9], with several modifications [14] including the modification for multipass exchangers [15] or the Nishida et al. method [7]). By using the algorithm of Ponton and Donaldson initial networks for different values of A t u with different numbers of processing units are obtained. For sub-problems above the pinch point it is, however, useful to employ a modification of this method. The matches are created from the pinch (the design starts from the cold side of the sub-problem) and the rule 'match the streams with the highest temperatures' is replaced by the rule 'match the streams with the lowest temperatures'. (iv) Generation of the initial structure. The user is informed on the network by a grid graphic representation. The Linnhoff and Flower way [8] has been adapted to fit better the interactive computing. Hot process streams run from top to bottom, cold streams in an opposite way. The exchangers are represented by two crosses tied by a horizontal line between appropriate hot and cold stream. Coolers and heaters are represented as crosses on corresponding streams. This grid can be seen on Figs 2-4. The heat-exchangers may be specified by area, heat duty or one of the output temperatures. Similarly, the parameters of process streams and/or cost parameters can be changed interactively. (v) Heat loads optimization for the individual units by means of loops and paths--further development of the procedure mentioned by Linnhoff and Hindmarsh [3]--to obtain a procedure employing the optimization method and optimization of the stream splitting. The optimization could be also utilized for the topology changes. (vi) Detailed flowsheeting of the generated network performed on the basis of physical properties data stored in the data bank. At the present time, the synthesis program is linked with the simulation program SIPRO [16], using the data bank PHYSCO (originated from Politecnico Milano). (vii) Modification of the heat exchange network with respect to the difference between the simulation recalculation results and the values stemming from the synthesis model. Very important are especially the differences in the pinch point region.
Computer-aided synthesis of heat exchange network
429
(b) (,3)
El
E
E2 E3
E~
E4
Fig. 2. Example of the loops: (a) loop (E~, E2) the simplest case, (b) loop (EL, E:, E,, Ej).
The HENS package uses in its first section the theoretical concept published by Linnhoff et al. [2] [see above mentioned point (i)]. For the initial structure generation [see point (ii)] Ponton and Donaldson work [9] and its modifications as well as Nishida et al. method [7] have been used. To carry out the activities specified in the HENS description by points (v), (vi) and (vii) appropriate methodology had to be developed. 4. O P T I M I Z A T I O N OF HEAT LOAD ON E X C H A N G E R S A topology with minimum number of processing units essentially specifies how much of heat will be exchanged in every single unit. It is always the lower value of the heat load to be supplied to the cold stream or withdrawn from the hot one in order to reach its target temperature. A topology which has not the minimum number of units, contains always a nonzero number of so called loops. As a loop (see Fig. 2) is understood a sequence of heat exchangers (El, E : . . . E~), where each two adjoining units are located on the same .hot or cold streams. As adjoining ones are also considered units E~ and EN. Two sequences are regarded as an identical loop provided their adjoining exchangers are identical, e.g. the sequences (Et, E2, E3, E4), (E3, E4, Ej, E2) represent the same loop. If a topology contains more than one unit of cooler-heater type and simultaneously these process units are not in separately designed sub-networks (i.e. there is no exchanger transferring heat from one sub-network's hot stream to another sub-network's cold stream) then this topology involves a so called path. Under such a path (see Fig. 3) a sequence of process units (exchangers, coolers, heaters) (Aj, A 2. . . . As) is understood where every two adjoining are either of cooler-heater type or lie on the same hot, respectively cold, stream (at least one of them being heat exchanger). The first and the last process unit AI and As are considered to be adjoining, too. Further, it is assumed that the heaters are not situated on the hot streams neither are the coolers on the cold ones. Two sequences of the process units are considered as being of the same path if they share the same adjoining elements. It is obvious that the number of process units of cooler-heater type is even for each heat path. If the path is not containing the heaters or coolers then the number of process units is even. The path which involves neither heaters nor coolers is a loop. The paths and loops have the following interesting feature: If the heat loads of odd items within the sequence of process units forming a loop of path are altered by the value of dQ say and the heat loads of even ones by - d Q (where dQ must be chosen so as to guarantee that heat load of all units located in the path or around
(o ]
[b] A~ Az A3
A3 Ai
A4
A4 A~
Fig. 3. Paths examples: (a) a path (A, A2, As, A4) involving two coolers At A~ (b) a path (A I, A2, A~, A 4, As) involving I heater A z and l cooler A s. HRS
$: .~--D
430
Jx~,i KLEMF~ and RAD|M PTA~NiK
(a) Q,
Q, +clQ
Q~
Q~- clO
Q, + Og
Q. Q~
tl_
Q4
Q3
Q2- clO
Q4+clQ
Q3-dQ
(c) Q
O,+dQ O2- clQ
Q2
Q3
Q3÷aQ
Fig. 4. Heat load shift: (a) heat load shift around a loop, (b) heat load shift along a path involving 2 coolers--the heat recovery does not change. (c) heat load shift along a path involving one cooler and one heater--the heat recovery changes.
the loop would be positive or zero) then the target temperatures of all streams in the given topology will be maintained (see Fig. 4--Qi are the original values of the process units heat loads). On the other hand, for other values of heat loads the target temperatures will not be maintained. This is true with the exception of the case where the path would be formed by several segments--these being paths or loops in themselves and allowing for changes of process units' heat loads within the individual segments--paths (loops)--separately. This circumstance may be exploited when guiding the design towards the optimum parameters of the network. If a single path (loop) is chosen, then the heat loads of process units forming this path (loop) can be optimised while maintaining the parameters of the others processing units in the network unchanged. This procedure is essentially an optimum search for the function of one variable in a finite interval--thus a problem easily handled by a computer. The optimal heat loads distribution to all processing units of the network can be found for the given topology when combining the optimizations of heat loads along all the paths (loops). When optimizing the heat loads along loops and paths which do not involve coolers or heaters the heat energy supplied by utilities is preserved. On the contrary, when optimizing the paths with both coolers and heaters the amount of utilities varies. Consequently, it is possible to trade off between operating and capital cost for the problems with the pinch point. When locating the individual parameters in this way the question of appropriate Atm~ (often considered as a key point) becomes irrelevant for its value is determined in the course of optimization procedure. Using this optimization technique it can be found that certain units should be preferably left out. This is a case when a process unit transfers zero heat load (i.e. value o f d Q equal to the original heat load value of this process unit). There is one more way of applying the optimization to screen the topology. By adding a new unit into the structure (a fictitious one with zero heat load) a new loop (loops) or path 'ipaths) is
Computer-aided synthesis of heat exchange network
o,I
°,1 1
/
431
'o,+oo J J Q2-dQl t00] O-dQ
02 1
I t°,
'o,+oI l
] l O3
0
do 1
/
OI
0z
I
D
I
ol
I °1 Fig. 5. Verificationof the topology by means of the heat load distribution optimization. (a) For the paths. Testing of the suitable aiocation of a cooler. The optimal solution may be a network: (i) with the original cooler, (2) with a new cooler, (3) with both cooler. (b) For the loops. Testing of the appropriate alocation of a heat exchanger. The most satisfying may be found a network with: (I) the original exchanger, (2) with a new exchanger, (3) with both exchanger.
introduced. Optimization of this new paths may result in modification of the network by including this unit or replacing some existing in the original network (see Fig. 5). The optimization of heat loads in units forming path is so general so it is possible to consider even more detailed models o f the heat exchangers. For example, different values of the heat transfer coefficients can be attached to the particular exchanger, a functional dependance of specific heat Cp on the temperature for individual stream and even appropriate correction to the temperature difference to multipass flow arrangement within the exchanger can be assigned. These features are rather important since the so called idealized synthesis is based on purely c o u n t e r - c u r r e n t heat exchangers with m a n y simplifications (constant values of C r invariable heat transfer coefficient, etc.) 5. S Y N T H E S I S P R O B L E M IN C R U D E O I L P R E H E A T T R A I N IN T H E A T M O S P H E R I C D I S T I L L A T I O N As an example of industrial plant heat exchange network synthesis the problem o f crude oil distillation has been selected. This problem was formulated by Kafarow et al. [17]. In this system a crude oil stream is divided into two sections (before and after desalting) and heated. The heat is supplied by four process streams. In Table l the specification data for a synthesis problem are shown. F o r the given objective function
Z = 6 ~ CA, + OtpSc i-I
(simplified form of equation (l) for the given example).
(5)
Jtgti K t _ r ~
432
and R A D I M P T ~ N i K
Table 1. E L O U - A T - 6 Stream number H, H: H3 H, Cc C2
Mass flowrate Stream name
Problem data (by [17]). Input temperature
kg h - i
1. pump around . . . . . . . 2. pump around residue 230-350"C fraction
crude oil desalted crude oil
43~00
C .............
143
404000
188
316000 163000 767250 751500
340 250 30 140
c,
Target temperature C
.........
69 79 90 165 140 235
.....
k c a l k g - ' C -*
kJ k g - ' K - '
0.521 0.520
2.1813228 2.177136
0.505 0.518 0.473 0.527
2.114334 2.1687624 1.9803564 2.2064436
Overall heat transfer coefficient 2 5 0 k c a l m - 2 h - ~ : C - ' = 2 9 0 . 9 W m - " h " ~. Minimum temperature approach A t ~ = 10
where Z is the total annual cost (Rbl yr- t), 3 the annual rate of return, CA, the investment cost for ith unit (Rbl yr-1), Sc the amount of cooling water spent per year (kg yr-I), 0 the operating hours per year, ~p the unit cost of cooling water (Rbl kg-~). The solution developed by these authors represents the total cost of 118 280 Rbl per year with annualised capital cost of 56535 Rbl. The network suggested by Kararow et al. is shown in Fig. 6. The same problem was solved by Demin and Kanevec [18] who developed the network illustrated in Fig. 7 for which they reported the total annual cost amounting to 118925Rbl, the annualised investment cost rate being 57168 Rbl. It is interesting to note that if the actual data given in [17] and [18] are used the value of the objective function reads to 118054 Rbl, instead. By applying the programming system HENS on this problem several networks, both with and without splitters have been designed resulting in considerable savings if compared with the previously published solutions. The original specification of the synthesis problem is an unpinched one, the threshold temperature approach is equal to 27.46°C and located between 188°C on the hot and 160.54°C on the cold stream. The target temperature of stream C:--crude oil entering the furnace--is 235°C. The corresponding composite curves are plotted in Fig. 1. The minimum feasible area amounts to 8185 m 2 (for At,~, = 10°C). The minimum number of units equals to 6. Considering the fact that the exponent coefficient in the objective function is equal to 0.88 it is not appropriate to look for a solution among networks with the number of units close to this minimum. The minimum requirements for cold utilities are 10567 kW (the problem is unpinched and therefore hot utilities
H2
H4
I
.)
H3
G
HI
I CI
Fig. 6. The original solution o f the test problem E L O U - A T - 6 suggested in [17] (temperatures o f streams within the network arc not given).
Computer-aided synthesis of heat exchange network
433
90"
14301 Ci
30 °
~)
140°
50"87° 79"
I
140o
~
154.25°
G9 °
H3 340 C2
188° H2
140°
173./~ 235" H4
188"o~)
"
Fig. 7. Solution of the problem ELOU-AT-6-suggested by authors in
[18].
are not required). For such a problem, isolated from surrounding flowsheet, solution without splitters has been developed where the value of the objective function amounts to 115 356 Rbl per year (annualiscd investment cost 54470 Rbl). A solution with splitters has the value of the objective function of 114222 Rbl per year (annualised investment cost 53336 Rbl)--sc¢ Fig. 8. Thus, in comparison with the original solution, savings of about 5.7~ in capital cost have bccn obtained. Providing, that from the surrounding flowsheet the furnace is considered as belonging to the problem and thus the temperature of desalted crude oil C2 entering the furnace is required as high as possible, the problem remaining primarily unpinched becomes one with the pinch point. For given Atm the pinch is between temperatures 178 and 188°C. Then the input temperature to the H2
1 8 ~
I 10.4*
)
I
1 8 8 ~
CI
J
143°I 140° HI Fig. 8. Solution with the lowest annual total cost developedby systemHENS for original data. (Input temperature of crude oil to the furnaceis 235°C.)
434
JIAi KLEMF.~ and RADIM PT.~.'qjK 165 ° F
165o
165"
140"
250
252.46*
'88* 188" 90*
90.
I
f
I
H2 152..5"
30°
140"
78.6*
69*
143"
Fig. 9. Design with the lowest total cost at the maximum heat recovery. Input temperature of crude oil to the furnace (for At=i. 10cC) increased to 252.46°C.
furnace can be raised up to 252.46°C. At the same time the requirements for cold utilities are reduced to 2521 kW. In this case the rise of the input temperature to the furnace makes it possible, according to the data given [17], to economise 22116 tons of fuel per year, that means to save 145000 Rbl per year (the constant capital cost of the furnace is assumed, e.g. in case of reconstruction, otherwise savings would be even higher). Two networks have been designed to solve this problem one without stream splitting where the value of the objective function reaches 113453 Rbl per year and another with stream splitting where the value of the objective function amounts to 110605 Rbl per year (see Fig. 9). This solution brings savings of 7449 Rbl per year in comparison with the original figure in [17], apart from reduction of fuel consumed in the furnace. Admitting the possibility of violating the value At,,,, = 10°C then (theoretically) all the heat of the four process streams can be used. The corresponding value At,,,, is 4.54°C and the input temperature to the furnace could be increased up to 257.93°C. When integrating the heat exchange network with the surrounding flowsheet, some recommendations from the composite curves can be put forward, which would lead to the improved heat recovery of the heat supplied by the process streams for the given Atm,,, or perhaps reduction of the overall heat exchange area for the given network's structure. These modifications are aimed at favourable changing of the conditions around the pinch where the network design appears to be most sensitive with respect to the objective function. Inspecting the composite curves (Fig. I) implies that the most important region from this point of view is between 143 and 188°C. The analysis of the composite curves shows that it is possible to reach higher heat recovery. Increasing the temperature of crude oil entering the furnace (for given Attar,) could be obtained by increasing heat capacity of hot streams (i.e. their input temperature or mass flowrate) which are above the pinch only (streams H4, H~ in presented problem). On the other hand in streams Ht, H2, which are below the pinch, it would be useful to reduce heat capacity. This leads to the saving of necessary amount of cold utilities. There are some modifications of surrounding flowsheet which could be discussed. It could be seen from the composite curves that it is useful to open them more for the same heat recovery (the required heat exchange area could be reduced), or to shift the curve of cold streams and the curve of hot streams in direction of horizontal axis. So they would more overlap and thus the target value for minimum utilities would be reduced.
Computer-aided synthesis of heat exchange network
435
In the studied p r o b l e m these suggestions c o u l d be reflected, e.g. in shifting up the t e m p e r a t u r e s o f the stream H2, i.e. rising b o t h the i n p u t (188°C) a n d target t e m p e r a t u r e (79°C) by 5°C (for Atm,n = 10°C). This m o d i f i c a t i o n w o u l d represent a r e d u c t i o n o f the energy s u p p l y to the furnace by 760,122 kcal h - t = 884.4 k W a n d s i m u l t a n e o u s l y the r e q u i r e m e n t for the c o l d utility w o u l d be r e d u c e d by the s a m e a m o u n t o f heat. This i m p r o v e m e n t w o u l d be caused by the shift o f the pinch. CONCLUSION T h e objective o f the p r e s e n t s t u d y is to d e m o n s t r a t e new possibilities in designing an i m p o r t a n t p a r t o f a chemical p r o c e s s - - t h e h e a t e x c h a n g e n e t w o r k . It is s h o w n that the suitable usage o f an interactive p r o g r a m m i n g system, which is b a s e d o n t h e r m o d y n a m i c analysis followed by optim i z a t i o n p r o c e d u r e t o g e t h e r with a m a n - m a c h i n e d i a l o g u e f o u n d e d on a p p r o p r i a t e user-friendly r e p r e s e n t a t i o n , brings significant energy saving a s s o c i a t e d with the c a p i t a l cost reduction. A l t h o u g h this t o p i c has been studied b y a n u m b e r o f a u t h o r s , it can be seen, t h a t especially an a p p l i c a t i o n o f the o p t i m i z a t i o n a p p r o a c h yields b o t h m o r e effective p r o g r e s s as well as m o r e f a v o u r a b l e results. REFERENCES 1. B. Linnhoff, Ph.D. Thesis, University of Leeds (1979). 2. B. Linnhoff, B. W. Townsend, D. Boland, G. F. Hewitt, B. E. A. Thomas, A. R. Guy and R. H. Marsland, A User Guide on Process Integration for the Efficient Use of Energy. Institute of Chemical Engineers, Rugby (1982). 3. B. Linnhoff and E. Hindmarsch, The pinch design method for heat exchanger networks. Chem. Engng Sci. 5, 745-763 (1983). 4. T. Umeda, K. Niida and K. Shiroko, A thermodynamic approach to heat integration in distillation systems, AICHE J. 25, 423--429 (1979). 5. T. Umeda, T. Harada and K. Shiroko, A Thermodynamic Approach to the Synthesis of Heat Integration Systems in Chemical Processes. Comput. Chem. Enginng 3 (I--4), 273-282 (1979). 6. M. Nishio, J. Itch, K. Shiroko and T. Umeda, A thermodynamic approach to steam-power system design, Ind. Eng. Chem. Process Des. Dev. 19, 306 (1980). 7. N, Nishida, Y. A. Liu and L. Lapidus, Studies in chemical process design and synthesis: III. A simple and practical approach to the optimal synthesis of heat exchanger networks. AICHE J. 23, 77-93 (1977). 8. B. Linnhoff and J. R. Flower, Synthesis of heat exchanger networks. AICHE J. 23, 333-354 (1978). 9. J. W. Ponton and R. A. B. Donaldson, Fast method for the synthesis of optimal heat exchanger networks. Chem. Engng Sci. 29, 2375-2377 (1974). 10. B. Linnhoff and D. R. Vrcdeveld, AICHE Diamond Jubilee Meeting, Washington (1983). 1I. Jow-Lih Su and R. L. Motard, Evolutionary synthesis of heat-exchanger networks. Comput. Chem. Engng $ (2), 67-80 (1984). 12. J. Klemeg and R. Pt~i~nik, Methods of optimal synthesis for heat energy calculation of steam reforming process. Research Report, Research Institute of Chemical Equipment (in Czech). CHEPOS, Brno (1983). 13. D. W. Townsend and B. Linnhoff, AICHE J. 29, 742-771 (1983). 14. J. R. Flower, Ph.D. Thesis, Computer program HXSJF. University of Leeds (1977). 15. J. Zachoval and Z. Konetn~, 15th European Syrup. on Use of Computers in the Chemical Engineering, Antwerp (1982). 16. V. Vagek and J. Kleme~, Simulation programming system SlPRO--Version for desk-top computer Compucorp 625 in Basic language. Comput. Chem. Engng 7, 175-182 (1983). 17. V. V. Kafarov, V. P. Meshalkin and V. L. Perov, Mathematical Bases of Automatized Design of Chemical Plants (in Russian). Khimia, Moscow (1979). 18. A. A. Detain and G. E. Kanevec, Decomposition--modular method of synthesis of heat exchange systems (in Russian). Chem. TechnoL 4, 42-44 (1982).