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The optimal design of heat exchanger networks considering heat exchanger types Georg Fieg a, Xi-Ru Hou b, Xing Luo a,b, Hu-Gen Ma b a

Institute of Process and Plant Engineering, Hamburg University of Technology, D21071 Hamburg, Germany, [email protected] b Institute of Thermal Engineering, University of Shanghai for Science and Technology, 200093 Shanghai, China, [email protected]

Abstract A hybrid genetic algorithm for the optimization of heat exchanger networks (HEN) considering the heat exchanger types is developed. The algorithm is based on an analytical solution of the stream temperatures. The heat capacity flow rates of hot and cold streams and the heat transfer parameter (the product of the correction factor of logarithmic mean temperature difference F, the overall heat transfer coefficient k and the heat transfer area A) of each heat exchanger in the HEN are taken as the decision variables to be optimized. With this method, the investment and utility costs can be calculated separately in a user subroutine where the specificities of heat exchangers can be easily taken into account. An example from literature is used to illustrate the procedure, and better optimization results are obtained. Keywords: heat exchanger network, heat recovery system, hybrid genetic algorithm, optimization

1. Introduction In the past three decades, extensive efforts have been made in the fields of energy integration and heat recovery technologies because of the steadily increasing energy cost and more rigorous CO2 discharge limitations. One of the most active subjects is the synthesis of heat exchanger networks (HENs). By the use of HEN in a heat recovery system, large amounts of hot and cold utilities as well as the investment costs can be reduced. The well known approaches to HEN synthesis are the pinch method [1], mathematical programming [2] and stochastic or heuristic algorithms such as genetic algorithm [3-4], genetic/simulated annealing algorithm [5] and tabu search procedure [6]. A review of the early work on the grassroot and retrofit design of HEN was given by Jezowski [7-8]. Recently, Chen et al. [9] developed a new hybrid genetic algorithm for HEN synthesis based on the explicit analytical solution of the stream temperatures in HENs, which ensures the feasibility of randomly produced individuals and enhances the search ability of the genetic algorithm in both structure and continuous parameters. This method can also be applied to the optimal design of HENs with multiple types of heat exchangers. The example given by Hall et al. [10] was used to test the present

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procedure. The calculations dealt with different types and materials of heat exchangers and for each case a better HEN configuration was found.

2. Mathematical model The HEN synthesis problem can be stated as follows: Given are Nh hot process streams, Nc cold process streams, hot utilities HU and cold utilities CU. Specified are heat capacity flow rates W and the supply and target temperatures of process streams. Given also are the temperature levels and costs of the hot and cold utilities, the types, costs and overall heat transfer coefficients of heat exchangers, heaters and coolers. Determine the configuration of the HEN and the values of heat transfer areas and heat capacity flow rates of each heat exchanger in the HEN which bring the total annual cost of the HEN to the minimum. The stage-wise superstructure HEN proposed by Yee et al. [11] is used in the HEN synthesis. However, the restriction of isothermal mixing used in their model is rescinded in the present model. To deal with different types of heat exchangers, we introduce the correction factor of the logarithmic mean temperature difference F into the analytical temperature solution of the HEN given by Chen et al. [9]. Then the analytic temperature solution is valid not only for counterflow heat exchangers but also for other exchanger types. the objective function of the optimization can be expressed as:

C = ¦ CE,m + ¦ C U ,n m

(1)

n

in which CE is the cost of an exchanger, which is usually a function of heat transfer area A:

CE,m = f E,m ( AE,m )

(2)

In the practical cases it could also depend on the type and material of the exchanger and design and operation restrictions. In such cases the cost function fE,m can be specified by the corresponding heat exchanger index m. CU represents the utility cost including the heaters and coolers. It can be determined by the

CU ,n

− − CHUW n (tOUT ′′ t n′′ < tOUT ,n − t n ) + f HU,n ( AHU ,n ), ,n ° − + ′′ tOUT t = ®0, < n < t OUT ,n ,n °C W (t ′′ − t + ) + f ( A ), t ′′ > t + n CU, n CU ,n OUT ,n ¯ CU n n OUT ,n

(n = 1, 2, , N h + N c )

(3)

+ − where tOUT and tOUT are the upper and lower bounds of the target stream temperatures, and CHU and CCU the hot and cold utility costs per unit duty, respectively. The costs of heaters and coolers are calculated according to the stream index n and the required heat transfer areas AHU,n and ACU,n,

AHU ,n =

− ′′ Wn (tOUT ,n − t n )

( Fk ) HU ,n Δt m HU ,n

(4)

The Optimal Design of Heat Exchanger Networks Considering Heat Exchanger Types

ACU ,n =

+ W n (t n′′ − tOUT ,n )

( Fk ) CU ,n Δt m CU ,n

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(5)

in which Δt m is the logarithmic mean temperature difference. The exit stream temperatures of the HEN (before the heaters and coolers) t n′′ are obtained by the analytic temperature solution. For a given stage-wise superstructure, they are function of Wh , m , Wc,m and (FkA)m of the heat exchangers in the HEN. Their optimal values are determined by the hybrid genetic algorithm which bring the total annual cost of the HEN (Eq. (2)) to the minimum. For a known value of (FkA), the correction factor F and overall heat transfer coefficient k can be calculated according the known heat capacity flow rates and stream temperatures as well as the heat exchanger types and design and operation restrictions. Then, the heat exchanger costs can be calculated. If the calculated temperature can not be reached by the given types of heat exchangers, the correction factor should be zero, i.e., an infinite large heat transfer area were required. The genetic algorithm will eliminate such designs automatically.

3. Example The example is taken from [10] and the problem data are listed in Table 1. The optimal design is carried out for 6 cases. It is assumed that the heat transfer coefficients are constant and do not depend on the exchanger type. In [10] it is implied that the cold utility cost depends only on the heat duty and therefore the outlet temperature of the cooling water is equal to its inlet value. It is not realistic. However, for comparison, this assumption is still used in the present design, as well as the assumption of counterflow type ( F = 1 ). Case 1: All heat exchangers including heaters and coolers are carbon-steel shell-andtube ones (CS). Hall et al. [10] used the Pinch method to optimise the problem and obtained a HEN with 14 units. According to the network configuration in Fig. 4a of [10], the total annual cost is 3.169 × 106 $/yr. Using the present genetic algorithm, we obtained a HEN with ten units and the total annual cost reduces to 3.117 × 106 $/yr, as is shown in Fig. 1. Case 2: Titanium shell-and-tube heat exchangers (TI) are used in the HEN. The optimization with the hybrid genetic algorithm yields the total annual cost of 5.864 × 106 $/yr ( 5.988 × 106 $/yr according to Fig. 4b of [10]). The HEN consists of six exchangers (H1C1a, H3aC1b, H3bC2, H4C4, H5C3, in which the subscripts a and b indicate stream splits.), three heaters for C2, C3 and C4, and two coolers for H1 and H2. Case 3: Titanium is selected for H4, H5, C1 and C2, and carbon-steel for other streams. The total annual cost of the present work is 4.148 × 106 $/yr ( 4.39 × 106 $/yr in [10]). The HEN consists of seven exchangers (TI: H5C1, H5C2a, H4C2b; CS: H1C4, H2C3, H3C3, H3C4), three heaters for C2 (TI/CS), C3 (CS) and C4 (CS), and three coolers for H1 (CS), H2 (CS) and H4 (TI/CS). Case 4: Only the plate-and-frame heat exchangers are used in the HEN. The total annual cost of the present work is 4.238 × 106 $/yr ( 4.25 × 106 $/yr according to Fig. 11 of [10]).

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Table 1. Problem data

Stream data tOUT (°C) h (kW/m2K) Stream t ′ (°C) W (kW/K) H1 120 65 50 0.50 H2 80 50 300 0.25 H3 135 110 290 0.30 H4 220 95 20 0.18 H5 135 105 260 0.25 C1 65 90 150 0.27 C2 75 200 140 0.25 C3 30 210 100 0.15 C4 60 140 50 0.45 HU (steam) 250 250 0.35 CU (cooling water) 15 15 * 0.20 Cost data Shell-and-tube, plant life = 6 yr, capital interest = 10% per annum Carbon-steel (CS) Cost ($) = 30,800 + 750 A0.81 (m2) Titanium (TI) Cost ($) = 30,800 + 4,470 A0.81 (m2) CS/TI or TI/CS Cost ($) = 30,800 + 3,349 A0.81 (m2) Plate-and-frame Cost ($) = 1,950 A0.78 (m2) Spiral Cost ($) = 19,687 A0.59 (m2) Plant life = 6 yr, capital interest = 16% per annum Annual cost of hot utility per unit duty = 120 ($/kWyr) Annual cost of cold utility per unit duty = 10 ($/kWyr) * Note: This value is estimated according to the design results of [10]. The HEN consists of seven exchangers (H1C1a, H5aC1b, H5bC3, H4C4a, H3aC4b, H3bC2, H2C3), two heaters for C2 and C3, and two coolers for H1 and H2. Case 5: Only the spiral heat exchangers are used in the HEN. The total annual cost of the present work is 6.788 × 106 $/yr ( 7.4 × 106 $/yr according to Fig. 12 of [10]). The HEN consists of five exchangers (H1C1a, H3aC1b, H3bC2, H4C4, H5C3), three heaters for C2, C3 and C4, and two coolers for H1 and H2. Case 6: Spiral heat exchangers should be used for H3 or C2, and plate-and-frame heat exchangers are used if the streams are not H3 or C2. The total annual cost of the present work is 5.021× 106 $/yr ( 5.20 × 106 $/yr in [10]). The HEN configuration is shown in Fig. 2.

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Fig. 1. Optimal heat exchanger network configurations with carbon-steel shell-and-tube heat exchangers (3,116,625$/yr).

Fig. 2. Optimal heat exchanger network configurations with spiral heat exchangers (SP) for H3 or C2 and plate-and-frame heat exchangers (PF) for other matches (5,020,606$/yr).

4. Conclusions A hybrid genetic algorithm is developed for the synthesis of HEN considering heat exchanger types. By taking the heat transfer parameter (FkA) and heat capacity flow rates W h and Wc as the decision variables in the analytical temperature solution, the costs of the heat exchangers can be calculated separately in a user subroutine, therefore, it is easy to deal with different kinds of heat exchangers in the optimization. An example taken from literature is used to illustrate the procedure and better design results are obtained.

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5. Acknowledgements The present research was supported by the Innovation Program of Shanghai Municipal Education Commission (No. 07ZZ89).

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