An automated method for synthesizing a multi-stream heat exchanger network based on stream pseudo-temperature

16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) © 2006 Published by Elsevier B.V.

An automated method for synthesizing a multistream heat exchanger network based on stream pseudo-temperature D o n g w e n YUAN, a Yao WANG*, a Wu XIAO, a PinNing YAO, a Xing LUO, b Wilfried R O E T Z E L b

alnstitute of Process Systems Engineering, Dalian University of Technology, Dalian 116012, P.R. China blnstitute of Thermodynamics, University of the Federal Armed Forces Hamburg, D22039 Hamburg, Germany Abstract

This paper proposes an approach for synthesizing multi-stream heat exchanger network based on the effective temperature levels of streams named "stream pseudo-temperature". Pseudo-temperature is obtained by the stream heat transfer temperature difference contribution value which is optimized with Genetic/Simulated annealing algorithm. Pinch point and utilities are presented, and a temperature-enthalpy diagram is constructed based on the stream pseudo-temperature. An automated method for multi-stream heat exchanger network synthesis using the temperature-enthalpy diagram is given. The performance of the proposed approach is demonstrated using an example and better solution is obtained compared with literatures.

Key-words: multi-stream heat exchanger network; pinch; temperature-enthalpy graph; temperature difference contribution value 1. Introduction Heat exchanger network synthesis(HENS) is a complex combinatorial problem. The conventional Pinch Design Method(PDM) employs a single allowable minimum heat transfer temperature difference (ATtain) • As ATmi, increases, the relative position of the hot and cold composite curves on the Temperature Enthalpy (T-H) diagram are apart from each other, hence all temperature differences throughout the heat exchanger system increase, resulting in a reduced heat transfer area and capital cost, while at the same time, the utility requirements and their cost increase. As A Tmi, decreases, vice versa. At a value of ATmi,, ATopt,there will be a minimum in the total cost. The optimal ATtain, ATop,Can be used to the HENS.The solution achieved through the conventional PDM is based on some assumptions: all the exchangers in the network have the same heat transfer coefficient;the same materials of construction and the uniform type; The global optimal cost network can not be reached due to these assumptions. From the industrial point of view, this paper describes an approach for multi-stream heat exchanger network (MSHEN) synthesis that uses the heat transfer temperature difference contribution values of the streams. The calculation of the heat transfer

*E-mail:

[email protected]

Supported by the Deutsche Forschungsgemeinschaft (DFG NO. RO 294/9)

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temperature difference contribution values considers the differences between streams in heat transfer coefficient and materials of construction etc..

2. Stream Pseudo-temperature To have an insight into the stream heat transfer ability level in the heat transfer process, the stream apparent temperature (indicated by thermometer) should be shifted as stream pseudo-temperature. The stream pseudo-temperature is defined as: T p = T T- AT~ (1) where, ' . . . . is for hot stream; " + " is for cold stream. TO -- stream pseudo-temperature, K; T -- stream apparent temperature, K; ATc -- stream temperature difference contribution value, K. The temperature difference between any two streams in heat exchange is expressed as the sum of two parts, either from each stream. A T m = A T h o t , c + ATcota,c (2) The suitable A Tm is used for determining the matches between hot and cold streams in a network.

2.1. Effect of the film heat transfer coefficient on TO Stream film heat transfer coefficient (h) (including film, wall and fouling contribution) is the crucial physical nature in the heat transfer process. When h-values vary significantly, the "vertical match" against the composite curves can not give the minimum area network,therefore the "non-vertical" o r " criss-crossing" match, which is more complicated, may be reasonable. Because the stream with lower h-value needs a larger heat transfer temperature difference to reduce the area requirement, a stream with a higher film heat transfer coefficient can exchange heat with smaller approach temperature. Ahmad Ill presented equation (3) to determine the stream heat transfer temperature difference contribution value:

Ar,,c:C/~r(,

~3)

Where, hi --the heat transfer film coefficient of stream i, kWom-ZoK-~. C is a constant that is adjusted until the heat recovery level obtained by using the temperature difference contributions is the same as the one using a single global minimum approach temperature.

2.2. Effect of the cost per unit heat transfer area on T° A corrosive stream that requires special materials of construction will have a greater contribution to capital cost than a non-corrosive stream. Consequently, in order to reduce the total network capital cost, the special material area from the contribution of corrosive stream must be reduced by sharing out a larger heat transfer temperature difference, and at the same time, the area from the contribution of non-corrosive stream will be forced to increase due to its heat transfer temperature difference becoming smaller. In this case, the minimum area network is not equivalent to the minimum capital cost network. In order to share out heat transfer temperature differences in a network for various streams that require mixed materials of construction for minimizing the total network capital cost, Nishimura I21 presented equation (4) which showed the relationship between the heat transfer temperature difference with the cost per unit heat transfer area. It gives the solution to minimize the heat transfer area per unit heat exchanging duty.

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An Automated Method for Synthesizing a Multi-Stream Heat Exchanger Network

(4) Where, the temperature of hot stream i, K; t -- temperature of cold stream, K; ai -- capital cost per unit area of heat exchanger, $.m-2; Ui -- the heat transfer film coefficient, KW.m-Z.K -1. Ti-

2.3. Effect o f the stream thermodynamic mean temperature on I p

In the energy balance, work and heat are counted the same. In the exergy balance, work and heat are not counted the same. All work input increases the exergy of streams flowing through the process. As to the heat, only a portion of the heat transferred into a system is available to increase the exergy of flowing streams. The heat is degraded by a coefficient 1-(To/T), where To and T refer to environment and heat source temperature (K) respectively. Consider a steady state heat transfer between the high-and lowtemperature reservoirs in Fig.1

Fig.1 Heat exchange between two reservoirs The loss of exergy(lost work, Lw) is determined as following: Lw

- (1-)Q

+ (1-)(-Q)

- Q(

T°) - Q T0 (

) - Q T0 (

) (5)

and then the approach temperature A T = LW " T~ " T 2 = L w I"1(T1 - A T ) = Q'To Q'To

or,

AT =

Lw Q To T2 (T2 + A T ) = •

Lw

L w (T2_1,1 . A T ) (6_a) Q'To

(T22 + T2 •A T ) (6-b)

Q.Vo

In general, T ~ - A T < < T12 , T2 • A T << T2 (rough treatment here). Hence, A T =

Lw T,2 or A T -

Q Vo

Lw

T22(7)

Q.To

It can be seen that, for a given rate of heat transfer Q and a given rate of exergy loss(Lw),the approach temperature(AT) increases almost proportionally with the increase in the square of the temperature level(T1 or T2 ). This explains the necessity to use a very small approach temperature, on the order of 1 °C in the cold boxes of cryogenic process. If the AT is not reduced, there would be a large increase in the energy required to operate the process. According to the discussion above, the heat transfer temperature difference contribution value of a stream can approximately be expressed as: T c - C . h -1/2 • a 1/2 • T 2 (8) dTc - - heat transfer temperature difference contribution value, K;

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C - - the coefficient obtained by regression technique; h --the heat transfer film coefficient,KWom-ZoK-1; a - - capital cost per unit area of heat exchanger, $°m-2; T - - the thermodynamic mean temperature of each stream, K. After selecting a set of suitable heat exchanger data which reflect the effects of h, a, and T on ATc, adequately, the value of coefficient C in equation (8) is obtained by using regression technique. The value of ATe obtained by equation (8) is rude because the error of reference streams data are not avoidable, so A Tc should span an indefinite interval, [ATc-ATk, ATc+ATk], for example, substituting 0.2ATc for ATk. Given any group of ATc-values in this interval, Corresponding network can always be attained by relying on the strategy represented as follows. The annual cost is regarded as an objective function and A Tc-values are taken as decision variables simultaneously. The optimization of A Tcvalues is a complex combinatorial problem which can be solved by Genetic/simulated annealing algorithm (GA/SA). Optimum A Tc-values attained by GA/SA mean the corresponding network is the cost-optimum solution.

3. Automatic Generation Strategy of MSHEN Stream pseudo-temperature is calculated by using equation (8) and (1). Construct hot and cold composite curves on the basis of the pseudo-temperature problem table algorithm. The pinch point is located and utilities are determined. Divide the hot and cold composite curves into several blocks by cutting vertically at every point where the composite curves bend (kink). Namely, wherever a change in slope occurs in either composite curve. The segments that require hot or cold utilities in both composite curves are left out in Fig. 2. Given an adjustable constant K which is a parameter dependent on the engineer's experiences, the interval whose heat load is less than K is regarded as a small block (block 2, 6, 7 in Fig.2 ), which needs to be merged into a big one in order to prevent some small-duty exchangers. With that conjoin all the proximate small blocks (block 6 and 7 become a new one in Fig.2) until the left of small blocks are all independent. If the new block from 6 and 7 also belong to the small-duty, put it into the only neighbour block because it is terminal (put 6+7 into 5 in Fig.2). If the small-duty block has two neighbours (block 2 in Fig.2), put it into the one which has the larger mean heat transfer temperature difference to prevent the inverse heat transfer when the exit temperature of cold stream is larger than the inlet temperature of hot stream (put block 2 into blockl in Fig.2). The pseudo-temperature of each stream is reverted to type. Two stream heat exchangers network are obtained from the first enthalpy interval to the last. The matches between hot and cold streams follow the heuristic guidelines E31.In each interval the amount of heat load of hot streams and the heat load of cold streams are balanceable, and the heat transfer temperature difference is not less than the allowable values. Several branches of a stream in the same enthalpy interval merged into a multi-stream heat exchanger. Each interval corresponds to several multi-stream or two stream heat exchangers. A group of multi-stream heat exchangers in series is obtained. The procedure is presented as follows: Step 1: Given stream data, calculate ATc for each stream according to the equation (8) Step 2: Set the indefinite interval [ATc-ATk, ATc+ATk] for each ~Tc, select a ATc from individual randomly Step 3: Determine the pseudo-temperature for each stream using equation (1)

An Automated Method for Synthesizing a Multi-Stream Heat Exchanger Network

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Step 4: Locate the pinch and construct the T--H diagram Step 5: Divide the hot and cold composite curves into enthalpy intervals Step 6: Determine a two-stream heat exchanger network on the T--H diagram Step 7: Construct multi-stream heat exchangers from two stream heat exchangers Step 8: Calculate the annual cost of the gotten network in step (6) Step 9: Go to step 3.Regenerate a set of ATc in their individual intervals with GA/SA to optimize A Tc-values until the best solution 260

hot composite curve

240 220

200 18o 160 140 120 100 10'00

15100

2000

u ~

25'00

30100

~5'00

Fig.2 Combination of small interval 4. Example This example is taken from Ciric M. It involves a system of four hot streams and three cold streams, with heating and cooling utilities provided by steam and cooling water. Problem data is shown in Table 1. The synthesis results are shown in Fig.3 and Table2. Results attained by superstructure in literatures are also shown in table 2 for comparison. The figure underlined in Fig.3 is not the load of a stream but a heat exchanger. Table 1 Stream data Stream

T~.( [] )

Tout( [] )

Fcp(kW-[]-1)

C o s t ( $ . k W - 1. a- 1)

H1 H2

160 249

110 138

7.032 8.44

---

H3

227

106

11.816

--

H4

271

146

7.0

--

C1

96

160

9.144

--

C2

115

217

7.296

--

C3

140

250

18

--

S

300

300

--

80

CW

70

90

--

20

The spaghetti design in this paper cuts the streams into several segment, the number of enthalpy intervals is larger than the number of stages of superstructure. Hence a larger number of exchangers are required in this paper. In Ciric or Wei's superstructure, ATmg, is a crucial factor. When ATtain becomes smaller, the recovery energy increases sharply correspondingly, as a result, heat transfer area increases inevitably, however, there is inferior limit determined by feasibility.The stream temperature difference contribution value proposed in this paper guarantees that the temperature differences are large enough between two streams exchanging heat within any exchanger, and as a

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result, the total area of the whole network is smaller compared with the Ciric or Wei's model. Furthermore, the Pinch Design Method has much more recovery energy, so the total annual cost is less. Table 2 Comparison of the solution with literature results Total area

(m2)

Number of units (number)

Equipment cost* ( $ .a "1)

Utility cost ( $ "a-1)

Total annual cost ( $ *a"1)

Ciric I41

281

12

91104

23356

114460

Wei [51

301

7

75678

23846

99524

This paper

241

12

86183

11998

98180

Item

Equipment cost: 1300[area(pa2)] °6 $.a-1; Annual cost = Equipment cost+ Utility cost 434.598 HI

1030.28 H2 249"C

242. 584

......

°i

[~

7:~16°ck~ 150"6: i

l o

1t4 271"C Cl 160"C

i 158.Ol

C2 217"C ~347.13 C3 250"C ~

194.17

279.03

~ 149168"c~

160"C

......

l ....... ° c @ ...... °c

534. 20 151.21°C

.~ 110"C = 138"C = 106"C

53.19 15',360°C . (~ = 146"C

14a.53~c@

96"C

141.61"c

115"C

I

°C

124.50 152.75°C

)

140"C

Fig.3 Synthesis result 5. Conclusion In this paper, an automatic generation strategy for synthesizing multi-stream heat exchanger network based on stream pseudo-temperature is proposed. The automatic procedure is used to obtain a family of multi-stream heat exchangers in serial. This method is more feasible and effective than mathematical model. References [ 1] Ahmad S., 1985, Heat exchanger networks: cost trade-offs in energy and capital, Ph. D Thesis, University of Manchester Inst. of Sci. and Technol. [2] Nishimula H., 1980, A theory for the optimum synthesis of heat exchange systems,J. Optimization Theory Applic., 30,423-450 [3] PinNing Yao, 1995, Total Process Energy Integration.Dalian, Dalian University of Technology Press, 46-53 [4] Ciric A. R. and Floudas C. A., 1991, Heat exchanger networks synthesis without decomposition, Computers and Chemical Engineering, 15, 10, 385-396 [5] Guanfeng Wei,Pingjing Yao,Xing Luo, Wilfried Roetzel,2004,Study on multistream heat exchanger network synthesis with parallel Genetic/simulated Annealing algorithm, Chinese J.Chem.Eng., 12,1,66-77