Optimization of layer patterning on a plate fin heat exchanger considering abnormal operating conditions

Accepted Manuscript Research Paper Optimization of Layer Patterning on a Plate Fin Heat Exchanger Considering Abnormal Operating Conditions Du-Hyeon Cho, Seung-Kwon Seo, Chul-Jin Lee, Youngsub Lim PII: DOI: Reference:

S1359-4311(17)30892-X http://dx.doi.org/10.1016/j.applthermaleng.2017.08.084 ATE 10967

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

10 February 2017 13 June 2017 18 August 2017

Please cite this article as: D-H. Cho, S-K. Seo, C-J. Lee, Y. Lim, Optimization of Layer Patterning on a Plate Fin Heat Exchanger Considering Abnormal Operating Conditions, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.08.084

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Manuscript for Applied Thermal Engineering

Optimization of Layer Patterning on a Plate Fin Heat Exchanger Considering Abnormal Operating Conditions

Du-Hyeon Cho a, Seung-Kwon Seo b, Chul-Jin Lee b *, Youngsub Lim c,d * a

Energy System R&D Institute, Daewoo Shipbuilding & Marine Engineering Co., Ltd., 125,

Namdaemun-ro, Jung-gu, Seoul, 04521, Republic of Korea b

School of Chemical Engineering and Materials Science, Chung-Ang University, 84

Heuksuk-ro, Dongjak-gu, Seoul, 06974, Republic of Korea c

Department of Naval Architecture and Ocean Engineering, Seoul National University, 1,

Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea d

Research Institute of Marine Systems Engineering, Seoul National University, 1, Gwanak-

ro, Gwanak-gu, Seoul, 08826, Republic of Korea

Tel: +82-2-820-5941. E-mail: [email protected], [email protected]

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Abstract Cryogenic processes such as natural gas (NG) liquefaction or boil off gas (BOG) reliquefaction systems require complex heat transfer networks to achieve high thermal efficiency. A plate fin heat exchanger (PFHE) is a kind of multi-stream heat exchanger that can make a system simpler while saving space and performing the complex network functions within a single piece of equipment. However, if the layer stacking pattern that determines the PFHE cross section temperature profile is inadequately composed, the equipment can be damaged by increased thermal stress between the layers. Layer stacking patterns have mainly been determined by inefficient trial and error methods, and only considered design operating conditions. The objective of this study is to obtain a highly efficient thermal layer stacking pattern in a design condition, while also lowering thermal stress in abnormal conditions, using a Genetic Algorithm (GA). The proposed GA in this study has a checking module that reduces iteration and saves calculation time. In addition, maximum metal temperature difference is used to evaluate fitness for considering abnormal conditions. According to the proposed algorithm, PFHE metal temperature profile improved about 30% compared to trial and error methods under design condition in a single mixed refrigerant LNG liquefaction process. The optimal layer stacking pattern is determined by a fitting function that applies temperature difference between plates under abnormal and design conditions.

Keywords: Multi-stream heat exchanger; Plate fin heat exchanger; Layer patterning; Optimization; LNG liquefaction

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1. Introduction A NG liquefaction, or BOG re-liquefaction, system has to refrigerate liquefied methane (CH4) at -160°C [1]. Therefore, these systems have complex heat transfer networks to compensate for the low efficiency of cryogenic recycle systems. Multi-stream heat exchangers reduce equipment complexity and save installation space because of their heat exchange performance in a single piece of equipment compared to shell & tube heat exchangers in the same system. [2,3] A plate fin heat exchanger (PFHE) is one type of multi-stream heat exchanger that is also known as a brazed aluminum heat exchanger (BFHE). It is manufactured by brazing layers in a furnace. The layers are separated from each other by metal plates and a specified configuration of fins. [4] Also, it operates below 100 barg and from -269°C to 65°C with a maximum of 15 heat exchange streams. [5] The stacked PFHE layers are configured by changing the number of heat exchange streams, which is called a layer stacking pattern. It determines the heat exchanger thermal performance and stability. Ideally, heat is evenly exchanged between the layers allocated to the same streams. However, a metal temperature profile is generated in the horizontal cross section of a heat exchanger in actuality. Prasad suggested that if the layer stacking pattern is well designed and close to its design condition, the horizontal cross-section PFHE temperature profile is uniform [11]. If the metal temperature difference increases due to a improperly composed layer stacking pattern, not only is heat transfer efficiency reduced, but equipment can be damaged under abnormal conditions due to increased thermal stress between layers. [6] Fan discussed a basic rule for determining a layer stacking pattern called a passage segregated method, where cold and hot layers of a multi-stream heat exchanger should be

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crossed and arranged adjacent to layers with assigned equal stream [7]. Suessmann and Mansour found that improper layer pattern causes unbalanced heat load and declining heat transfer efficiency [8]. Also, they suggest a determining method for layer stacking pattern by evaluating each layer heat load, which changes the sign of cumulative heat load (CHL) alternatively between adjacent streams. Haseler applied this method to PFHE heat transfer in an air separation process [9]. Prasad explored a calculation method for multi-stream heat exchanger efficiency [10-15]. Prasad has made a general fin equation available to recognize the influence of layer stacking pattern on fin efficiency and PFHE performance. In this approach, the PFHE performance requires a finite difference calculation. Yuan et al. optimized passage arrangement of a multi-stream heat exchanger based on a two-step local heat load calculation [16]. Layer arrangement is determined approximately by a local balance principle in the first predict step. In the second correct step, it is adjusted by temperature distribution deducted from the difference calculation. Meanwhile, Guo et al. presented an equal temperature difference method where PFHE is considered as a two-stream heat exchanger and the layer stacking pattern is designed to a uniform temperature difference field between the streams [17]. Yanyan et al. used this method and developed a concept for a dimensionless temperature difference uniformity optimization factor to determine path arrangement for a multi-stream heat exchanger [18]. Additionally, there have been attempts to apply optimizing methods for layer stacking patterns with computer software. Sunder, Fox and Reneaume et al. developed multi-variable PFHE optimization using non-linear programming [19-21]. Picón-Núñez and López Robles used uniform heat load per passage to determine a layer stacking pattern [22]. They selected a secondary surface and fin, and considered the number of passages allocated to a given stream as directly proportional to an equal number of hot and cold passages. Their calculation method was verified by a simple steady state simulation model.

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Many different methods for optimizing layer stacking patterns have been tried recently [2326]. The common ground of these conventional methods is uniformity of behavior between cold and hot streams, and temperature difference, of the whole heat exchanger. Wang classified optimization methods as local heat load balance criterion, equal temperature difference criterion and an equal number of heat transfer unit criterion based on their control objects, which are heat load, heat transfer temperature difference and thermal conduction respectively [27]. Previous studies and commercial software can design performance and sizing results including geometry, necessary number of layers per each stream, and metal temperature profile from a determined layer stacking pattern. However, because optimization of layer stacking patterns includes a combinatorial problem, and a number of parameters, the above mentioned classical derivative based algorithms are not adequate methods. A gradient based search method is also not suitable due to inaccurate approximated derivative values. Those conventional determining layer stacking pattern methods have only depended on the experience of experts, and trial and error methods, until recently. GA based optimization has more flexibility for searching several optimal solutions compared to conventional methods. A GA is a kind of heuristic algorithm. It includes a ‘natural selection process’ that well adjusted individuals are more likely to breed, and a ‘natural evolution process’ that individuals will improve through changes during heredity. Computer simulation of these processes is calculated by selection, crossover, and mutation. This optimized algorithm can identify a chromosome that has the best fit, and they are studied actively nowadays for optimizing PFHE [28-31]. Peng and Ling optimized the weight of PFHE and the total annual cost by GA connected with the Back-Propagation Neural Network (BPNN) [33]. Mishra et al. minimized total

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annual cost of cross-flow PFHE under specified heat duty given space and flow restrictions by a GA-based optimization method [34]. Similarly, Mishra and Das computed the thermoeconomic cost of a cross-flow offset strip fin heat exchanger [35]. Luo et al. and Fieg et al. combined GA with an annealing algorithm to design a multi-stream heat exchanger network [36,37]. And Ghosh et al. used GA for optimizing the layer stacking pattern of PFHE [32]. In this method, optimization proceeded to achieve the maximum heat load of each stream, and included a checking process for cumulative heat load and temperature profile. Although they successfully used an area splitting method to rate maximum heat load, it still had drawbacks in the case where the number of each stream is limited. Recently, Zhao applied GA with a dual fitness function to software to optimize a layer stacking pattern and carried out a case study [38]. However, previous GA studies have not considered abnormal operating conditions until now. Abnormal conditions are a much greater danger for PFHE damage than design. Therefore, a developed methodology that optimizes the PFHE layer stacking pattern using GA is modified to consider abnormal operating conditions in this study. A practical case study was carried out in order to verify the methodology. Also, a abnormal state result of the case study has been compared with a design condition result for modifying the GA fitness function.

2. Methodology Normally, GA consists of three different steps: initialize population, fitness, and reproduction. First, the algorithm initializes population by randomly generating and allocating layer types (i.e., chromosomes) to each layer pattern (i.e., population). After that, in the fitness step, the most suitable population for the operating heat exchanger is selected as

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an elite value. The previous research for obtaining elite value has the objective function that maximizes total heat duty of the heat exchanger [32] or minimizes deviation of cumulative heat load along the layer stacking direction [38]. However, because thermal stress of PFHE is directly affected by the temperature difference between each layer, the objective function in the fitness step should be changed to minimize deviation of the metal temperature profile between the layers if the stability of PFHE is considered under an abnormal condition. Ghosh et al. suggested an area splitting method to calculate metal temperature profile [39]. In this method, PFHE was divided by i-th sub-exchangers and k-th nodes as seen on Fig. 1. The temperature profile of each sub-exchanger can be obtained by heat transfer calculation with energy balance using appropriate formulas. The procedure of this calculation was used as an iteration algorithm for tolerance of error. However, in this study, commercial software was used for calculating the temperature profile of PFHE to avoid complexity. 2.1. Optimization procedure Some commercial software can be used to design PFHE such as: Exchanger Design and Rating – Plate Fin from the Aspentech corp. (Aspen EDR-PFIN), Xchanger Suite – Xpfe from the HTRI corp. and Unisim Heat Exchangers – Plate Fin Exchanger Model from Honeywell [27]. Among those, Aspen EDR-PFIN and HYSYS were used for heat exchanger design and process simulation. A layer stacking pattern can be created on the basis of PFHE sizing and rating results from the Aspen EDR-PFIN. After that, GA generates layer stacking patterns through the Visual Basic for Application (VBA). Aspen EDR-PFIN calculates the metal temperature profile of each generated layer stacking pattern and sends the result back to VBA. The population is ranked in an ascending order of maximum metal temperature difference (

) to sort out layer stacking pattern achieving objective function.

is

the maximum wall temperature range value of the points in PFHE along the length direction in the Aspen EDR-PFIN. This interworking process is depicted by the concept map in Fig. 2. 7

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2.2. Encoding chromosomes The structure of a layer stacking pattern is very similar to a gene sequence as shown in Fig. 3. In this study, a layer is viewed as a single chromosome and the algorithm for calculating an optimal pattern is organized by changing the layer type on each pattern, which is expressed as a character string,

, where,

Also, each layer type ( different way,

and

in the VBA.

) is classified into a hot or cold stream and represented in a .

2.3. Proposed optimization algorithm The algorithm iterates reproduction and evaluating fitness after the initialize population step until termination criteria is met, either maximum generation or number of iterations. Essential information involving thermal performance and temperature profile can be obtained from Aspen EDR-PFIN during iteration. 2.3.1. Initialize population The initial generation was made by 10% ordinary random generation and 90% by Fan’s passage segregated method to achieve maximum efficiency with minimum iterations. As Fan’s segregated random generation (SR) ratio increases in the initialize step, initial elite has high possibility of having better maximum metal temperature difference compared with lower SR ratio (see Fig. S1). However, the ordinary random generation is still set to occupy 10% in the initial population because it can enhance to preserve diversity of population in a next generation. Those two random generations allocate chromosomes keeping the number of each necessary layer type as well as the number of hot and cold layers. However, population from a segregated random generation is quite differently arranged to satisfy alternation of hot and cold streams. For example, the following relations:

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(1)

2.3.2. Evaluate fitness Layer patterns generated from the initialize population or reproduction step are given by , where

and

denote generation number and population number respectively. Each

has

is calculated from the Aspen EDR-PFIN. Then, the Evaluate Fitness

function conducts the following process. ① Obtain

for =1 to

② Rank the population

in ascending order of

their

values.

③ Rerecord population number

according to the rank.

④ Select first and second ranked value

and

as elite 1 and 2.

2.3.3. Reproduction Then, the elite 1 and 2 values (i.e., parent 1, 2) are used to reproduce new layer stacking patterns (i.e., child values) by crossover, gene position swap and mutation process. The crossover process inserts part of elite values into the child value according to the order-1crossover rule. Similarly, each elite value exchanges location of their layer types through a gene position swap process. Those two reproduction methods randomly determine parent 1, their gene position and the number of exchange. Fig. 4 shows an example of the order-1crossover and gene position swap. Maximum number of chromosome to be crossover or swap is restricted 1/3 and 1/5 of whole length of layer stacking pattern respectively because its

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maximum metal temperature difference can drastically differ from parent value above those ratios. On the other hand, a mutation process randomly generates layer stacking patterns in two ways that are the same as ordinary random generation (i.e., mutation) and passage segregated method based random generation (i.e., segregated mutation). The proportion of the mutation process should be a high value initially to maintain diversity of population. Meanwhile, the proportion of the crossover and gene position swap processes increased gradually as calculation proceeds on until maximum generation. This reproduction ratio dependent on iteration time is user defined and determined by the number of populations created from each reproduction method,

, which can be expressed as (2)

where, subscript and

means crossover, gene position swap, mutation or segregated mutation,

is a user defined reproduction ratio at start time and

is at the end time.

2.3.4. Checking module It is necessary to add a checking module for execution time reduction. The checking module finds and removes values that have a large cumulative heat load difference with the previous generation and removes duplications with previous elite values. The cumulative heat load per layer is calculated through the local heat load balance criterion from Fig. 1 and following equations. (3)

,

(4)

,

(5)

,

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Local heat load, mass flow rate, heat capacity at constant pressure and total number of layers of hot stream

are represented by

to the k-th node ( and

,

and

, while inlet temperature of

) and outlet temperature are represented by

. Cold stream

is also represented the same way. Then, the heat load of each layer

) in the

can be obtained. In other words, the local heat load of a single

type ( layer in

,

can be expressed by

calculated and

values in the same

. Therefore, CHL per layer in the create set

) is

as Eq. (6).

If layer pattern has a large average CHL value ( CHL deviation values (

value (

) calculated from maximum

) obtained by Eq. (7), the checking module returns the

layer pattern to the reproduction step without evaluating fitness. The criterion for returning is comparison with

to the elite value in the previous generation. These calculations

are shown as follows, (6) (7) (8)

(9) where the criterion (

) is defined 110% of the minimum value among the average

CHL values of elite 1 and 2 in the previous generation, and

means total number of nodes. In

summary, the optimizing process by GA is shown in Fig. 5. 2.4. Modification of the algorithm for considering abnormal condition

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The causes of thermal stress are abnormal operation conditions as follows. ① Start-up / Shut down ② Idle mode (= Standby mode) ③ Inadequate plant control system The idle mode is a state where the refrigeration cycle keeps driving without inflow to cool. For instance, this could occur when the PFHE is cooled down at initial start-up in a LNG liquefaction process, or only the refrigerant loop operates without treated gas stream (i.e., when the gas treatment system is malfunctioning). The idle mode operation would make parting sheet temperature difference maximize and result in thermal stress as well as one of the most unbalanced heat loads between streams. Therefore, it would be the worst abnormal operating condition. ALPEMA Standard [5] suggested that maximum metal temperature difference between streams is below 50°C and 30°C at the single and two phase flow system respectively. Maximum metal temperature difference in the idle mode (

) should be reflected by the

evaluation function to adjust the ALPEMA criterion as Fig. 6. The layer stacking patterns are ranked in ascending order considering both design and abnormal conditions of maximum metal temperature difference. In fact, a weighted average method is applied to combine the two conditions because PFHE are operated in design condition longer than abnormal condition. The weight averaged maximum metal temperature difference between design and abnormal condition,

, is given by (10)

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where

and

denotes the maximum metal temperature difference at

design and abnormal condition respectively. The weighted value, (design : abnormal =

)

4:1, 3:1, 2:1, was used for case study. 3. Case Study: SMR Process It is easier to confirm the performance and horizontal cross-sectional metal temperature difference between the parting sheets when the heat exchange process involves phase change, than when the only sensitive heat exchanges occurs only in the single phase. That is why the phase change results in unbalanced temperature change on overall intervals in the heat exchanger. For this reason, the case study focused on a single mixed refrigerant process in LNG liquefaction. 3.1. Process Description and Design Data SMR process is based on reverse Rankine cycle and takes cryogenic refrigerant through cooling condensation and expansion to produce atmospheric LNG (-161°C). The composition of the refrigerant in the SMR process is a mixture of hydrocarbons such as methane, ethane or ethylene, propane and iso-pentane. Cooling condensation of the high pressure refrigerant is achieved by multi-stream heat exchange between low and high pressure refrigerants in a PFHE. Fig. 7(a) shows the SMR process with detailed operating condition obtained from Aspen HYSYS in Table 1. The SMR process is modified in case of idle mode as seen in Fig. 7 (b); not supplied treated gas to be cooled. It means that flow rate of natural gas feed (stream 5) has almost close to 0. The abnormal operating conditions of SMR case including pressure, temperature and flow rate of the other streams are same with design condition except for natural gas feed flow rate which is set to 1 % of design condition instead of 0 % due to simulation

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convergence. The stream physical property data are tabulated in Table S1 and Table S2. Also, the Evaluate Fitness function of GA reflected maximum metal temperature difference at this state and parameters for calculating GA are given in Table 2. 3.2. Results and Discussion Among the GA parameters, selection of generation and population size depends on the user. Fig. S2 shows the change of

of elite 1, 2 and average

of whole population

during the 50 population and 80 generation sized GA optimization in the SMR case. The minimum value of average

is 38.78°C at the 29th generation and

of elite 1, 2

scarcely decrease after the 31st generation. Therefore, the enough size for searching solution near the optimum in SMR case can be presumed as the number of population accumulated to the 32nd generation, 1650. In other words, 40 population and 40 generation size is enough to examine GA optimization for the SMR case study. The reproduction ratio of crossover (C), gene position swap (S), mutation (R) and segregated mutation (SR) are set to be increased from 15, 15, 20, 50 to 20, 65, 5, 10 respectively, as the number of generation increases. Results in Table S3 are obtained when the optimization of 40 population and 100 generation size is carried out in the SMR case only considering design condition. If all reproduction ratios are equal to 25 % regardless of their type and calculation progress, reproduction type of the top 10 ranked layer stacking patterns of whole generation are distributed by 18.1% (C), 56.6% (S), 9.0% (R) and 16.3% (SR). Therefore, the set value of the increasing C and S reproduction ratio is appropriate to reflect GA property that elite layer stacking patterns are likely to be from gene position swap or crossover as calculation proceeds. However, R and SR ratio should be kept relatively high during early GA calculation because elite values are far away from the optimum in that time.

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Fig. 8 shows the configuration of core sizing results including length, width, height, In/Out nozzle location and streams connection using the Aspen EDR-PFIN Design Mode. It needs to manufacture 14 parallel connected cores per PFHE with 95 layers of 5 streams in order to satisfy the SMR process condition. Table 3 presents the results of the number of layers, fin type, height, thickness and frequency required of each stream in a core. At the same time, the GA optimized layer stacking pattern, with an assumed 5 sets of pattern, are layered repeatedly. One set of patterns consists of 19 layers which is obtained from dividing the number of each layer by a least common multiple; see Table 4. That is because the temperature distribution of the whole PFHE is regular only if a minimal layer unit with the same patterns has evenly distributed temperature. The graph in Fig. S3 shows the cumulative number of layer stacking patterns removed by checking module when the optimization of SMR case is performed with fitness function only considering design condition. The cumulative number of duplicated layer patterns and having large cumulative heat load (

) compared with previous generations are 59,662 and

217,938 at the 40th generation. In fact, the most time-consuming procedure during the optimization is evaluating fitness which calculates

of selected layer stacking patterns.

However, the total 277,600 evaluating fitness calculations can be skipped by checking module in SMR case study. In other words, checking module reduces 99.43% dispensable layer stacking patterns created by GA (1600 population size) and saves an enormous amount of time. Fig. 9 shows that all layer stacking patterns generated from GA population marked maximum metal temperature difference at design (x-axis) and abnormal condition (y-axis) respectively. It shows a trend that maximum metal temperature difference at abnormal condition (i.e., idle mode operation) is proportional to that at design condition. In spite of this

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trend, distribution of dots is meaningfully dispersed, therefore, it should be considered to apply abnormal condition to determining layer stacking pattern for better result. The best 4 layer stacking patterns in Fig. 9 was chosen in order to investigate effects of the Evaluate Fitness function on determining layer stacking pattern (Pattern 2 – 5). The results are tabulated in Table 5. Pattern 1 is obtained by conventional method based on the equal temperature difference criterion, and the others are calculated from the GA. Especially, Pattern 5 is the result of optimal layer stacking pattern at design condition. The maximum metal temperature difference of pattern 1 was 11.95 °C in the overall interval. On the other hand, the GA calculated the layer stacking pattern at design condition as pattern 5 with a maximum metal temperature difference of 8.30 °C, which improves about 30% compared to the conventional method. However, the optimal layer stacking pattern is changed when Evaluate Fitness function considers abnormal operating condition. The weighted average rank in Table 5 is obtained by ascending order of fitness function value with given weight average ratio. Weight average ratio should reflect frequency of abnormal operating occurrence and structure reinforcement resulted from thermal stress as cost factors. Determining (

) ratio based on total annual

cost analysis is not described in the present work. However, since though rank of patterns is changed by a weight average ratio, pattern 2 is always first ranked, the results demonstrate that the pattern 2 is the most optimal layer stacking pattern in the SMR case for 1:1 to 4:1 ratios. Fig. 10 also shows which pattern is the best when the weight ratio of design condition ( ) changes from 0 to 10 with fixed weight ratio of abnormal condition ( ) by 1. The pattern 2 has the lowest fitness function value until

becomes 4. It means the optimal layer stacking

pattern in Table 5 is pattern 2 because fitness function values are almost same after than 4.

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Fig. 11(a) and (b) compare the distribution of metal temperature difference range (i.e., maximum – minimum metal temperature) inside a PFHE core for each of the four patterns at design and abnormal condition respectively. The peaks of the four patterns have similar shape and location because metal temperature profile significantly changes at back and forth of distributors location which are start or end points of inlet and outlet streams. It implies that stable metal temperature profile can be formed regardless of metal temperature distribution if the layer stacking pattern has minimum peak size. Therefore, pattern 2 is the optimal layer stacking pattern in the SMR case study considering abnormal condition and has relatively uniform difference between maximum and minimum of each point inside a PFHE core at both of design and abnormal condition as seen in Fig. S4. 4. Conclusion Layer stacking pattern is important to assure thermal stability in a PFHE. GA can successfully provide optimal results for evaluation of maximum metal temperature difference. In this study, the SMR case study was conducted and verified the effect of GA through commercial software. The algorithm used in this study suggested a heuristic rule which prevents reproduction of duplicated solutions and removes irrelevant solutions during calculation of cumulative heat load. This checking module requires less time to calculate the maximum metal temperature difference. The effects of checking module are confirmed by 1600 population size of the proposed GA optimization in SMR case study, which removes dispensable solutions usually occupied 99.43 % of whole generated population. As a result, maximum metal temperature difference of the optimal layer stacking pattern calculated from GA is 8.30 °C. The improvement of GA is 30% compared to a conventional method (11.95 °C) if design condition is only considered. Also, optimal layer stacking pattern was determined by applying a weighted average method to the Evaluate Fitness function in the GA, which has 9.17 °C of maximum metal temperature difference. Therefore, definitive 17

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improvement of GA considering abnormal operating condition is 23 % compared to a conventional method. This result reduces the risk of thermal stress at abnormal condition as well as provides better heat transfer performance at normal state. However, it does not include the basis of weight average ratio. It is recommended to investigate the relationship between cost impact and weight average ratio and to find a new solution by analysis of economic results in future works. Acknowledgments This research was supported by a grant (17CTAP-C129846-01#) from Infrastructure and transportation technology promotion research Program Funded by Ministry of Land, Infrastructure and Transport of Korean government and Program of University Specialized for Offshore Plant Engineering funded by Ministry of Trade, Industry and Energy, Republic of Korea. References [1] Li Q, Flamant G, Yuan X, et al. Compact heat exchangers: a review and future applications for a new generation of high temperature solar receivers. Renew Sustain Energy Rev 2011;15(9):4855–75. [2] Manjunath K, Kaushik SC. Second law thermodynamic study of heat exchangers: a review. Renew Sustain Energy Rev 2014;40:348–74. [3] Das PK, Ghosh I. Thermal design of multistream plate fin heat exchangers—a state-ofthe-art review. Heat Transf Eng 2012;33(4–5):284–300. [4] Thulukkanan K, Heat exchanger design handbook, 2nd ed, CRC Press. New York, 2013 [5] ALPEMA, The standards of the brazed aluminum plate-fin heat exchanger manufacturers association. 2nd ed. [6] Weimer RF, Hartzog DG. Effects of maldistribution on the performance of multistream, multipassage heat exchangers. Adv Cryogen Eng 1973;Springer US:52–64 [7] Fan YN, How to design plate fin heat exchangers. Hydrocarbon Process 1966;45:211–17 [8] Suessmann W, Mansour W. Passage arrangements in plate-fin heat exchanger, in: Proc. of 15th International Congress of Refrigeration 1979;Venice:421–9.

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[26] Guo J, Cui G, Lv Y, et al. Passage arrangement optimization of multi-stream heat exchanger based on structure performance continuity principle. J Eng Thermophys 2009;8(30):1379–82. [27] Wang Z, Li Y. Layer pattern thermal design and optimization for multistream plate-fin heat exchangers-A review. Renew Sust Energ Rev 2016;53:500–14 [28] Holland J, Adaptation in natural and artificial system. University of Michigan Press, Ann Arbor 1975. [29] Deb K, Optimization for engineering design; algorithms and examples. Prentice-Hall of India Pvt. Ltd. 1995. [30] Mitchell M. An introduction to genetic algorithm. Prentice Hall of India Pvt. Ltd. 1998. [31] Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman, Inc. 2000. [32] Ghosh S, et al. Optimum stacking pattern for multi-stream plate-fin heat exchanger through a genetic algorithm. International Journal of Thermal Sciences 2011;50:214–24 [33] Peng H, Ling X. Optimal design approach for the plate-fin heat exchangers using neural networks cooperated with genetic algorithms, Appl Thermal Eng. 2008;28:642–50. [34] Mishra M, Das PK, Sarangi S. Optimum design of crossflow plate-fin heat exchangers through genetic algorithm. Int J Heat Exchangers 2004;5:379–401. [35] Mishra M, Das PK. Thermoeconomic design-optimization of crossflow plate fin heat exchanger using genetic algorithm. Int J Energy, 2009;6(6):837–52 [36] Luo X, Yao P, Wei G, Roetzel W. Study on multi-stream heat exchanger network synthesis with parallel genetic/simulated annealing algorithm. Chin J Chem Eng 2004;12:66– 77. [37] Fieg G, Luo X, Jeżowskic J. A monogenetic algorithm for optimal design of large-scale heat exchanger. Networks 2009;48:1506–16. [38] Zhao M, Li Y, An effective layer pattern optimization model for multi-stream plate-fin heat exchanger using genetic algorithm. Int J Heat Mass Tran 2013;60:480–89 [39] Ghosh I, Sarangi SK, Das PK, An alternate algorithm for the analysis of multistream plate fin heat exchangers. Int J Heat Mass Tran 2006;49:2889–902.

Nomenclature reproduction ratio at start point reproduction ratio at the end point j-th cold type layer specific heat at constant pressure, (J/kg K) number of generations i-th hot type layer total number of layers in pattern number of iterations

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making integer function by round the number down mass flow rate of stream, (kg/s) select maximum value of a set of elements select minimum value of a set of elements total number of cold type layer from 1 to j total number of hot type layer from 1 to i k-th node number of population heat load per layer, (W) cumulative heat load from stream 1 to i, (W) inlet temperature, (K) outlet temperature, (K) a set of cumulative heat load of each layer in the k-th node i-th stacked layer total number of nodes Greek symbols weight average ratio of design condition weight average ratio of abnormal condition average maximum deviation of cumulative heat load, (W) criterion value for checking cumulative heat load, (W) maximum deviation of cumulative heat load in the k-th node, (W) maximum metal temperature difference, (K) Subscripts C max min R S SR

crossover maximum value minimum value mutation gene position swap mutation based on the Fan’s passage segregated method

Superscripts abn abnormal condition avg average deg design condition

Figures

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Fig. 1. Configuration of area splitting method for calculating temperature profile suggested by Ghosh et al.

Fig. 2. Optimization procedure.

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Fig. 3. Comparison of gene sequence and layer stacking pattern.

Fig. 4. Example of reproduction methods

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Fig. 5. Proposed optimization algorithm

Fig. 6. Modified Evaluate Fitness function for considering abnormal condition

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(a)

(b) Fig. 7. Single mixed refrigerant process schematic diagram: (a) design condition operation; (b) idle mode operation.

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Fig. 8. Heat exchanger diagram and geometry information from Aspen EDR-PFIN.

Fig. 9. Distribution of maximum metal temperature difference of whole population generated by GA: x axis; at design condition, y axis; at abnormal condition.

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Fig. 10. Fitness function value of the patterns in Table 5 with weight average ratio from 0:1 to 10:1.

(a)

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(b) Fig. 11. Metal temperature range distribution of the patterns in Table 5 along the distance from end A in a PFHE core: (a) design condition; (b) abnormal condition.

Tables Table 1. The operating temperature and pressure of each in/out Stream in the SMR process. Direction

①→②

③→④

⑤→⑥

⑦→⑧

⑨→⑩

Description

MR Liquid

MR Liquid Return

MR Vapor

MR Vapor Return

Natural Gas

Hot /Cold

Hot

Cold

Hot

Cold

Hot

P [bar]

43.5

4.1

43.5

4.1

60

T[℃]

33.73

-83.17

33.73

-159.85

30

P [bar]

43

3.6

43

3.6

59.5

T[℃]

-80

25

-155

25

-155

Inlet

Outlet Mass Flow [kg/s]

84.1

93.4

36.3 (design) 0.363 (abnormal)

Table 2. Setting parameters of the genetic algorithm for the case study. Item

Value

Maximum number of generation

40

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Population size

40

Total number of nodes

10

Percentage of reproduction by crossover at start point

15

Percentage of reproduction by gene position swap at start point

15

Percentage of reproduction by mutation at start point

20

Percentage of reproduction by segregated mutation at start point

50

Percentage of reproduction by crossover at the end point

20

Percentage of reproduction by gene position swap at the end point

65

Percentage of reproduction by mutation at the end point

5

Percentage of reproduction by segregated mutation at the end point

10

Maximum number of

to perform crossover in a single layer pattern

1/3

Maximum number of

to perform gene position swap in a single layer pattern

1/5

Table 3. Sizing results of PFHE in the SMR process. No. of parallel Exchangers

14

Layer

A

B

C

D

E

Stream number in Fig.8

1&5

2

3

4

5

No. of Layers / Exchanger

10

20

15

25

25

Fin type

Serrated

Perforated

Serrated

Perforated

Plain

Fin height [mm]

6.4

6.4

6.4

6.4

6.4

Fin thickness [mm]

0.41

0.3

0.51

0.61

0.61

Fin frequency [No./m]

787

787

709

590

590

Inlet [mm]

314.24

4650.82

502.88

6181.39

977.31

Outlet [mm]

4569.64

634.8

6181.39

634.8

6181.39

Distributor (from End A)

Table 4. The number of layers required to design and optimizing pattern. Layer

A

B

C

D

E

Total

No. of Layers / Exchanger

10

20

15

25

25

95

No. of Layers / Set (5sets / Exchanger)

2

4

3

5

5

19

Table 5. Rank of conventional result and the best four patterns in Fig. 9 evaluated by weighted average. Case

Pattern 29

Weighted average rank

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1 2 3 4 5

EDCBEDABCDEBADEBCDE ABDECDBECDBEAEDBCDE ABEDCDBECDBEEADBCDE BCDEADBECDEBEDAEDCB EBADCDEBEDCEBDCDABE

Design

Abnormal

11.95 9.17 8.62 8.96 8.30

27.54 32.49 36.97 36.02 37.90

Design 4:1 3:1 2:1 Only → Conventional method 4 1 1 1 2 3 3 3 3 4 4 2 1 2 2 4

Supplements

Fig. S 1. Maximum metal temperature difference in the initial population by 0% to 100% of Fan’s segregated random generation (SR) ratio. (GA parameters and process data correspond to the SMR case study)

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Fig. S 2. The change of maximum metal temperature difference during the 50 population and 80 generation sized GA optimization: x axis; the number of generation, y axis; maximum metal temperature difference, only considered design condition.

Fig. S 3. The cumulative number of layer stacking patterns removed by checking module in the SMR case (40 population, 40 generation and total 1600 population): x axis; generation, y axis; cumulative number of removed layer stacking patterns.

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(a)

(b) Fig. S 4. Metal temperature difference of Pattern 2 along the distance from end A in a PFHE core: (a) design condition; (b) abnormal condition.

Table S 1. The physical property data of inlet stream in the SMR case. ①→②

Inlet stream Temperature

③→④

⑤→⑥

⑦→⑧

⑨→⑩

(℃)

33.73

-83.17

33.73

-159.85

30

(kg/m3)

461.61

632.82

461.61

606.83

(-)

(kJ/kg K)

2.959

1.947

2.959

2.141

(-)

Liquid viscosity

(mPa s)

0.0817

0.3291

0.0817

0.4302

(-)

Liquid thermal conductivity

(W/(m K))

0.0814

0.1449

0.0814

0.1941

(-)

(N/m)

0.0054

0.0196

0.0054

0.0215

(-)

Liquid density Liquid specific heat

Liquid surface tension

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Liquid molecular weight

(kg/kmol)

42.867

44.549

42.866

28.121

(-)

(kJ/kg)

270.2

0

676.3

0

794.7

(-)

1.526 10-6

0.03294

1

0.09

1

(kg/m3)

62.09

5.47

62.09

12.32

48.14

(kJ/kg K)

2.337

1.701

2.337

1.191

2.624

Vapor viscosity

(mPa s)

0.0131

0.0081

0.0131

0.0072

0.0129

Vapor thermal conductivity

(W/(m K))

0.0308

0.0179

0.0308

0.0112

0.039

Vapor molecular weight

(kg/kmol)

27.945

20.333

27.945

26.276

17.5653

③→④

⑤→⑥

⑦→⑧

⑨→⑩

Specific enthalpy Vapor mass fraction Vapor density Vapor specific heat

Table S 2. The physical property data of outlet stream in the SMR case. ①→②

Outlet stream Temperature

(℃)

-80

25

-155

25

-155

(kg/m3)

623.95

598.06

612.1

(-)

449.02

(kJ/kg K)

1.979

2.335

2.121

(-)

3.149

Liquid viscosity

(mPa s)

0.2883

0.1875

0.3358

(-)

0.1237

Liquid thermal conductivity

(W/(m K))

0.1371

0.1016

0.179

(-)

0.1858

(N/m)

0.018

0.0131

0.0189

(-)

0.0121

(kg/kmol)

42.867

64.681

27.9448

(-)

17.5653

(kJ/kg)

0

536.2

0

725.2

0

(-)

0

0.8582

0

1

0

(kg/m3)

(-)

7.13

(-)

4.73

(-)

(kJ/kg K)

(-)

1.773

(-)

1.776

(-)

Vapor viscosity

(mPa s)

(-)

0.009

(-)

0.0109

(-)

Vapor thermal conductivity

(W/(m K))

(-)

0.0199

(-)

0.0252

(-)

Vapor molecular weight

(kg/kmol)

(-)

40.605

(-)

27.945

(-)

Liquid density Liquid specific heat

Liquid surface tension Liquid molecular weight Specific enthalpy Vapor mass fraction Vapor density Vapor specific heat

Table S 3. The top 10 ranked distribution of reproduction types when 40 population and 100 generation sized GA optimization is carried out in the SMR case. (generation 1 ~ 100, total 4000 layer stacking patterns are examined.) Reproduction type

Number

Elite value same with previous generation

192

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Reproduction ratio (%)

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Reproduction

Crossover

146

18.1

Gene position swap

457

56.6

Mutation

73

9.0

Segregated mutation

132

16.3

1000

100

Total

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