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Studies on a Novel Optimal Retrofit Strategy of Heat Exchanger Networks Applied in Crude Oil Distillation Unit Xin-Wen Liu, Xing Luo, and Stephan Kabelac Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01931 • Publication Date (Web): 13 Oct 2016 Downloaded from http://pubs.acs.org on October 15, 2016

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Industrial & Engineering Chemistry Research

Studies on a Novel Optimal Retrofit Strategy of Heat Exchanger Networks Applied in Crude Oil Distillation Unit Xin-Wen Liu1*, Xing Luo2, Stephan Kabelac2 1. School of Chemical Engineering, Ningbo University of Technology, Ningbo 315016 , PR China; 2. Institute for Thermodynamics, Gottfried Wilhelm Leibniz Universität Hannover, Hannover D-30167, Germany

ABSTRACT: A novel mathematical programming method was applied to acquire the optimal HEN retrofit in the crude oil distillation unit. The mathematical model was based on the stage-wise superstructure model with splits of streams from Yee et al. The objective function was developed into the minimum of the sum of the cost of modifications and the cost of utilities in one year with focusing on the changing heat transfer coefficients arising in the reused existing heat exchangers from stream splits. The HEN modifications included buying new heat exchangers, adding or reducing areas of the existing heat exchangers, moving the existing heat exchangers and laying pipes. It was a mixed integer nonlinear program (MINLP) problem. A hybrid genetic algorithm was used to optimize the MINLP problem. In order to reduce the total cost of modifications, the heat exchangers and the corresponding matching structures between the hot and cold streams in the existing HENs were designed as elites introduced into the hybrid genetic algorithm. The Dittus-Boelter’ correlation and kern’s correlation were used to estimate the convective heat transfer coefficients of the corresponding streams. One example was given to show the effect of the novel retrofit strategy.

1. INTRODUCTION The crude oil distillation unit (CDU) is a primary process unit of the crude oil refinery and the raw crude oil could be separated into various fractions according to the different boiling points of each fraction1. Most of the energy consumption happens in this process unit in the crude oil refinery. According to estimation, CDU could consume about 35-45% of the energy used in a refinery2. In order to save energy, many research projects were carried out to improve the energy utilization efficiency of CDUs in refineries. Bagajewicz and Ji3 presented a rigorous targeting methodology to design a multipurpose plant using a commercial simulator and acquired operating conditions for light and heavy crude oil and Bagajewicz and Soto4 dealt with the heat exchanger network design and demonstrated the associated heat exchanger networks that could handle maximum energy recovery in all scenarios. Asante N.D.K and Zhu X.X.5 described a new two-stage approach including a modification selection stage and an optimization stage for retrofit heat exchanger network design which aimed to minimize modifications to the existing HEN structure. Gu, W. et al.6 demonstrated that the selection of a vacuum distillation process and the determination of the vacuum furnace outlet temperature play a critical role in

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designing a crude oil vacuum distillation process by comparative analysis and evaluating the three process. Retrofit design appeared to be more feasible than the grassroots design in CDUs of oil refineries7. Compared to grassroots design, retrofit design was introduced as a more economical option by the adding of equipments to satisfy the new operating scenarios8. Some retrofits including a preflash implementation9 and other new techniques10 were also used to improve the distillation yield of crude oil fractionation and to improve the energy efficiency in CDUs. Other methods including the simultaneous optimization of distillation process and heat exchanger network11 and shortcut models were also developed to account for the existing HEN details within the optimization of existing refinery distillation units12. The common purpose was to find out the solution to enhance the energy efficiency and the overall performance of existing CDUs in refineries 1 . In the field of HEN retrofit, mathematical programming and pinch technology are two types of optimization methods. Tjoe and Linnhoff

13

firstly proposed the pinch concept with a two-step procedure,

namely Target and Design in the HEN retrofit. But it exist the shortcoming of evolving manually using heat loops and paths to a retrofit network as closely compatible to the existing one as possible. Asante and Zhu14 proposed a step-by-step interactive approach combining the features of pinch with mathematical programming for heat exchanger network retrofit. But this way could only identify a single topology change at a time in a sequential manner and the utmost solution was a sub-optimal solution. Li and Chang

15

and Smith et al.

16

applied the developed pinch-based retrofit method to retrofit HENs. Li and Chang determined the cross-pinch heat load by simple manual computation and Smith et al. developed a two-level pinching approach for the optimization of the network topology and heat transfer area respectively. However, the above retrofit methods could not ascertain exactly where the additional area was added, and how many network restructure modifications were done. Rezaei and Shafiei 17 studied HEN retrofits with considerations of the redistribution of the existing heat exchangers based on MILP model. But the model could not contain all the potential combinations and the application of the existing heat exchangers was not considered in detail. Saboo18 presented an evolutionary strategy which was based on nonlinear optimization. Their procedure generated a number of successive retrofit design alternatives without the explicit consideration of economic data. Most studies on the HEN retrofits have paid attention to the optimization of the existing HEN and the existing heat exchangers reusing. Few studies on the HEN retrofit focused on the heat transfer performance of heat exchangers. Wang et al.19 has proposed the HEN retrofit method with application of intensified heat transfer. It focused on the heat transfer enhancements in the HEN, but the fundamental structural modifications to the retrofitted HEN hasn’t been considered. In fact, when HEN retrofits were done without considering the heat transfer performance of heat exchangers, the optimal HEN retrofit schemes would be difficult to reach up to its expectation in the actual running. So in this paper, HEN retrofits in CDUs were carried out with the consideration of changing of heat transfer coefficients of the existing heat exchangers reused in the retrofitted HEN from stream splits. The

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objective function was built with the minimum of the sum of the cost of modifications and the cost of utilities in one year which could give a better trade-off between energy and capital cost. And the simultaneous optimization of HEN retrofit could be realized by applying the hybrid genetic algorithm. Comparing with the retrofit methods without considering the changing heat transfer coefficients, the scheme of HEN retrofit from this paper would be more feasible for the industrial HEN retrofits.

2. MATHEMATICAL MODEL FOR HEN RETROFIT STRATEGY The stage-wise superstructure model from Yee and Grossmann

20

was employed to show all the feasible

solutions of HEN retrofits. It was assumed that the whole HEN was divided into Ns stages ( N s = (k | k = 1,2,L, N s ) ). In each stage, the cold streams (j) and hot streams (i) were matched mutually by stream splits and the maximum matching number was Nh×Nc ( N h = (i | i = 1,2,L, N h ) , N c = ( j | j = 1,2,L, N c ) ). Heaters and coolers were placed at the ends of the cold and hot streams. 2.1. Constraints (1) Heat balance of each stream: (THin ,i − TH out,i ) ⋅ fhi = ∑∑ qijk + qCU,i k

(TCout, j − TCin, j ) ⋅ fc j = ∑∑qijk + qHU, j k

( i ∈ N h , j ∈ N c , k ∈ Ns )

j

( i ∈ Nh , j ∈ Nc , k ∈ Ns )

i

It means that the released heat of hot stream i was transferred to the cold stream j and the cold utility. And similarly, the get heat of cold stream j was from the hot stream i and the hot utility. Where qCU, i and qHU, j are the load of the cold utility and the hot utility for hot stream i and cold stream j, respectively. THin, i (thi, 0), TCin, j ( tc j , N ) are the inlet initial temperatures of the ith hot stream and the jth cold stream, and THout, i, TCout, j are s

the target temperatures of the ith hot stream and the jth cold stream, respectively. fhi and fcj are the total heat-capacity flow rates of hot stream i and cold stream j. qijk is the heat load transferring between the ith hot stream and the jth cold stream in the kth stage. (2) Heat balance of each heat exchanger:

(thi ,k − thijk ) ⋅ fhijk = (tcijk − tc j ,k +1 ) ⋅ fcijk = qijk

( i ∈ Nh , j ∈ Nc , k ∈ Ns )

It means that the released heat of the hot stream i equals the get heat of the cold stream j in the kth stage. And the transferred heat load is qijk . Where thijk and tcijk are the exit temperatures of the hot stream i and cold stream j in the kth stage after heat transfer, respectively. And the heat-capacity flow rate of the hot stream and cold stream is fhijk and fcijk, respectively. thi,k and thi,k+1 are the inlet temperature of the ith hot stream in the kth and (k+1)th stages, and tcj,k and tcj,k+1 are the exit temperature of the jth cold stream after mixing with the different -3-



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branches in the kth and (k+1)th stages. (3) Stream splits in the kth stage: Nc

∑ fhijk = fhi

( i ∈ N h , k ∈ Ns )

j =1 Nh

∑ fcijk = fc j

( j ∈ Nc , k ∈ Ns )

i =1

It means that the heat capacity of each hot (or cold) stream keeps constant in the process of heat transfer. Where the meaning of fhijk , fcijk , fhi and fcj could be found in the above. (4) The heat balance calculation of each split in the kth stage: Nc

∑ thijk ⋅ fhijk = thi,k +1 ⋅ fhi

( i ∈ Nh , k ∈ Ns )

j =1

Nh

∑ tcijk ⋅ fcijk = tc j ,k ⋅ fc j

( j ∈ N c , k ∈ Ns )

i =1

It means that the heat of the merging stream equals the sum of the heat of its each split. And the mixing of stream splits is done in non-isothermal principle. Where the meaning of each variable could be found in the above. (5) The inlet temperature of each stream: TH in,i = thi ,0

( i ∈ Nh )

TCin, j = tc j , N s

( j ∈ Nc )

(6) The feasible temperature constraints: thi ,k ≥ thijk , tc j ,k +1 ≤ tcijk , TH out ,i ≤ thi , Ns , TCout, j ≥ tc j , 0

( i ∈ N h , j ∈ N c , k ∈ Ns )

where tcj,0 is the exit temperature of the jth cold stream in the first stage. (7) The load of the cold and hot utilities: (thi , Ns − TH out,i ) ⋅ fhi = qCU,i

( i ∈ Nh )

(TC out, j − tc j , 0 ) ⋅ fc j = q HU, j

( j ∈ Nc )

where thi,Ns is the exit temperature of the ith hot stream in the Ns-th stage. (8) The minimum temperature difference constraints of heat transfer: For heat exchanger: thi ,k − tcijk ≥ dt min , thijk − tc j , k +1 ≥ dt min

( i ∈ N h , j ∈ Nc , k ∈ Ns )

For hot utilities:

thu, j ,in − TCout, j ≥ dtmin , thu, j ,out − tc j , 0 ≥ dtmin

( j ∈ Nc )

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For cold utilities:

thi , Ns − tcu,i ,out ≥ dtmin , TH out,i − t u,i ,in ≥ dtmin

( i ∈ Nh )

where thu,j,in and thu,j,out are the temperatures of the hot utility for the jth cold stream at the inlet and outlet of the heater, respectively. tcu,i,in and tcu,i,out are the temperatures of the cold utility for the ith hot stream at the inlet and outlet of the cooler, respectively. dtmin is the allowable minimum heat transfer temperature difference. (9) （0-1）constraints: The area of heat exchanger A and the heat-capacity flow rate f are continuous variables and non-negative. We use yijk, yCU,i, yHU,j as discrete 0-1 variables to show whether heat exchangers,

heaters or coolers exist or

not.

1, yijk =  0,

Aijk > 0 Aijk ≤ 0

( i ∈ N h , j ∈ N c , k ∈ Ns )

1, thi′′ − t out ,i > 0 yCU,i =  0, thi′′ − tout ,i ≤ 0

( i ∈ Nh )

1, tcout , j − tc′′j > 0 yHU, j =  0, tcout , j − tc′j′ ≤ 0

( j ∈ Nc )

in which Aijk is the area of the heat exchanger matching the ith hot stream and the jth cold stream in the kth stage.

thi′′ and thout,i are the temperature of the ith hot stream after exchanging heat with cold streams and the target temperature of the ith hot stream.

tc′′j and tcout,j are the temperature of the cold stream after exchanging heat with

hot streams and the target temperature of the jth cold stream. We further introduce a discrete 0-1 variable mijk to indicate whether the new heat exchanger should be bought or not. The discrete 0-1 variable nijk indicates whether the fixed cost of heat exchanger should be considered or not.

1, mijk =  0,

Aijk > Aijke

1, nijk =  0,

Aijke ≤ 0 Aijke > 0

Aijk ≤ Aijke

( i ∈ N h , j ∈ N c , k ∈ Ns )

( i ∈ N h , j ∈ N c , k ∈ Ns )

in which Aijk，Aeijk are the needed heat exchanger and the existing heat exchanger at the node of ijk, respectively.

zijk is also discrete 0-1 variable and means whether the corresponding stream should be split or not. And gijk is also discrete 0-1 variable and means whether the corresponding heat exchanger should be moved or not.

1, ( fhijk < fhi ) U ( fcijk < fc j ) ( i ∈ N h , j ∈ Nc , k ∈ Ns ) zijk =  0, ( fhijk = fhi ) I ( fcijk = fc j )

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e 1, (( Aijk < 0) I ( Aijke > 0)) U (( Aijk > 0) I ( Aijk < 0)) gijk =  e e 0, (( Aijk > 0) I ( Aijk > 0)) U (( Aijk < 0) I ( Aijk < 0))

( i ∈ N h , j ∈ Nc , k ∈ Ns )

(10) The area constraints:

 Aijk − Aijke ,

Aijk > Aijke

Aijke ,

Aijk ≤ Aijke

δAijk =  

( i ∈ N h , j ∈ N c , k ∈ Ns )

in which δAijk is the area of the needed added heat exchanger. The areas of the cooler (ACU,i) and heater (AHU,j) can be determined by the following equations:

 fhi (thi′′ − t out,i ) , thi′′ − t out,i > 0  ACU,i =  U CU,i ∆t m ,CU,i 0, thi′′ − t out,i ≤ 0 

AHU, j

( i ∈ Nh )

 fc j (tcout, j − tc′j′ ) , tcout, j − tc′′ > 0  =  U HU, j ∆t m,HU, j 0, tcout, j − tc′′ ≤ 0 

( j ∈ Nc )

where ∆tm ,CU,i and ∆tm,HU, j are the logarithmic mean temperature differences. UCU, i， UHU, j are the total heat transfer coefficients and are assumed to be constant. The meanings of other variables could be found in the above. For knowing the heat transfer areas Aijk and the heat-capacity flow rates fhijk and fcijk, the exit stream temperature vector T '' = [t1'' , t 2'' , Lt N'' h , t N'' h +1 , t N'' h +2 , L, t N'' h + N c ]τ is calculated by the explicit temperature solution of HENs proposed by Chen et al. ''

''

21

''

''

''

, in which t1 , t 2 , L t N h are the Nh exit stream temperatures of the hot process

''

streams and t N h +1 , t N h + 2 , L , t N h + Nc are the Nc exit stream temperatures of the cold process streams. The constraint (3) is ensured with the corrections:

fhijk =

* fhijk

• fhik

Nc

∑ fh

( i ∈ Nh , k ∈ Ns )

* ijk

j =1

fcijk =

* fcijk Nh

∑ fc

• fc jk

( j ∈ Nc , k ∈ Ns )

* ijk

i =1

in which the superscript “*” denotes that the parameters should be modified. (11) The modification of U of the reused existing heat exchangers: The correlations of tube-side Nusselt number (Nui) and shell-side Nusselt number (Nuo) in turbulent condition were given based on the Dittus-Boelter correlation22 and Kern’s equation23.

Nu i = 0 . 023 Re i0 .8 Pr i0 .4

Nu o = 0 . 36 Re 0o .55 Pr o1 / 3 ( µ / µ w ) 0 .14

( Re i ≥ 10 4 ) ( Re o = 2 × 103 ~ 10 6 )

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where µ is the viscosity of fluid and µw is the viscosity of fluid near the tube wall. And Re is the Reynolds number and Pr is the Prandtl number. Then heat transfer coefficients (h) of tube-side and shell-side could be calculated according to the correlation as follows:

h = ( k / D ) × Nu Because the structure parameters of the reused existing heat exchangers and the physical parameters of the streams keep unchangeable in the HEN retrofit, and only the stream splits result in the changing of the heat capacity flowrate of the corresponding stream. So according to the above equations, the relative correlations could be obtained as follows:

h i = ( k / D i ) × Nu i = K i ⋅ f i 0 . 8

ho = ( k / D o ) × Nu o = K o ⋅ f o0 .55 where Ki and Ko were the characteristic parameters from the heat exchangers with specific structures. In these equations, fi and fo were the heat capacity flow-rates of fluid from the tube and the shell. So the overall heat transfer coefficient (U) could be calculated with the following equation, where ktube was tube conductivity.

 D D ln( D o / D i ) 1  U = o + o +  h D 2 k h tube o   i i

−1

Otherwise, the second item in the above equation could be neglected due to its little contribution to U because the outer diameter (Do) was a little difference from the inner diameter (Di). So the relationship of U could be simplified as below.

1 1  U = +   hi h o 

−1

So the modification of U of the reused existing heat exchangers could be represented in the following equation:

λ ijk =

U ijke U ijk

( i ∈ N h , j ∈ N c , k ∈ Ns )

where λijk meant the ratio of the existing overall heat transfer coefficient ( Ueijk) and the new overall heat transfer coefficient ( Uijk).

2.2. Objective Function In order to obtain the target HEN with the optimal structure matches and the least consumption of utilities, the objective function was designed to include the cost of cold utilities, hot utilities in one year and the cost of

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heater and cooler and the cost of new heat exchangers and the cost of newly added area of heat exchangers and the cost of re-piping and the cost of reassigning the existing heat exchangers. The cost of calculating the heat exchangers is as follows:

C f + C ⋅ AB The first item Cf is the fixed cost of heat exchanger and the second item is the area cost of heat exchanger. C, A,

B is the coefficient of area cost of heat exchangers, area of heat exchanger and the exponent of area cost,

C CU ,C HU

respectively. Otherwise,

is respectively the cost of unit cold utility and hot utility in one year.

And Cp is the cost of re-piping a single stream. Cm is reassigning an existing heat exchanger. So the object function is as follows.

 min  ∑  i +

∑ ∑ ((

∑ ( (C

j

f

+ C ⋅ AHU, j

j

+

j

B

)

) ⋅ y ijk

B

) ⋅ y HU j )+ ∑ C CU i

∑ ∑ ∑ (C i

C f ⋅ n ijk + C ⋅ δ Aijk

k

⋅ m ijk + ∑

f

+ C ⋅ ACU, i

B

) ⋅ y CU, i )

⋅ q CU, i ⋅ y CU, i + ∑ C HU ⋅ q HU, j ⋅ y HU, j j

) ∑ ∑ ∑ (C

⋅ z ijk + C ⋅ Aijk ⋅ ( λ ijk − 1) B ⋅ z ijk + B

p

(C

(

i

k

i

j

k

m

 ⋅ g ijk ) 

The retrofit of the existing HEN is carried out in this paper based on the above mathematical model.

3. RETROFIT OF HEAT EXCHANGER NETWORKS As you know, the mathematical model for HEN retrofit was a mixed integer nonlinear programming (MINLP) problem. So the hybrid genetic algorithm was applied to optimize the mathematical model of HEN retrofit. The optimization variables were the area of each heat exchanger ( Aijk), the heat-capacity flow rate of each hot stream (fhijk) and the heat-capacity flow rate of each cold stream ( fcijk). As genes, the three variables constituted an individual of HGA. In order to realize the local optimization, the Simulated Annealing (SA) was adopted in the hybrid genetic algorithm. The operation steps and diagram of hybrid genetic algorithm was given in detail in the reference

24

. The full utilization of the existing heat exchangers and structure was designed as a constraint for

the optimal HEN retrofit strategy. The HEN retrofit could be described as follows. Firstly, the heat exchangers in the existing HEN were numbered in sequence and the areas of the corresponding heat exchangers were listed in the table. Secondly, the stage of the existing HEN was determined according to the stepwise superstructure. That was to say, in each stage, a cold (hot) stream could not be matched by more than one hot (cold) stream directly but by stream splits. And the maximum stage number is Ns. The stage of HEN was numbered from the left to right in sequence. Thirdly, determining the location of each existing heat exchanger with the area of Aeijk in the stepwise superstructure by ijk was done according to the following equation. Here,

ijk = ( k − 1 ) × N

h

× N

c

+ ( i − 1) × N

-8-


c

+ j

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The ijk value could show the different heat exchangers matching the hot stream i with the cold stream j in the stage k. Fourthly, the HGA was run and the existing heat exchangers as elites were introduced by ijk. And the new heat exchanger (when Aeijk =0) or the new area (when Aeijk >0) wasn’t bought until the introduced new Aijk was more than Aeijk. That was to say, mijk=0. If the introduced new Aijk was more than Aeijk, mijk=1. And the needed added area was equal to δAijk. At the same time, if Aeijk existed, nijk=0 and the fixed cost of heat exchanger was not calculated. Otherwise, nijk=1 and the fixed cost of heat exchanger needed to be calculated. Fifthly, if stream splits exist (zijk=1), the heat transfer coefficients of the existing heat exchangers applied in the retrofitted HEN should be estimated again. And the fixed cost of re-piping was represented with the symbol Cp in this paper, which included the fixed cost of piping support structure, valves, flow control stations et al. Sixthly, if the relocation of the existing heat exchangers existed (gijk=1), the cost of moving the corresponding heat exchanger should be added and was represented with symbol Cm. Other costs such as the installation of new piping, insulation and instrumentation are represented with the fixed cost of heat exchanger Cf in this paper. Finally, the total cost of modifications and the utilities is calculated. The steps were repeated till the optimal retrofitted HEN with the full use of the existing heat exchangers and structures could be obtained. The diagram of HEN retrofit was given as Fig. 1.

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Numbering the existing heat exchangers Determining the stage of existing HEN (Ns) Determining the location of the existing heat exchanger in the stepwise superstructure (ijk)

Running HGA and introducing the new individuals Yes

mijk=0

Aeijk≥Aijk? No mijk=1

δAijk = Aijk − Aijke Yes nijk=0

Aeijk> 0? No nijk=1

zijk=1

Yes λijk Aijk → Aijk

Split?

zijk=1

No

zijk=0

gijk=1

Yes

zijk=1

Move? No

gijk=0

Cost calculation

No Satisfied? Yes Output

Fig. 1 Diagram of HEN retrofit

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4. CASE STUDY AND DISCUSSIONS The existing HEN in CDU included seven hot streams and three cold streams and one group of hot and cold utilities25. The flow sheet of the crude oil distillation unit was shown in Fig.2. The hot streams (H1~H7) and cold streams (C1~C3) have been identified in the flow sheet. The initial and target temperatures of hot streams and cold streams, the coefficients of heat exchanging and the heat capacity flow rates in the existing HEN were listed in Table 1. The relative cost data was referred in Table 2. H1 H2

H3

H4

H5 T5

T5 H6 Steam

H7

Steam

T3 T2

T4 Steam Steam

T1

Steam Salt water

Steam C3

C2

C1

Crude Oil

Notes: T1: Desalter T2: Primary distillation column T3: Atmospheric distillation column T4: Stripping column T5: Buffer unit

Fig. 2 The flow sheet of the crude oil distillation unit Table 1 Stream Data for Case Stream

Fcp（kW/℃）

Tin（℃）

Tout（℃）

h（ kW/m2℃）

H1

470.00

140

40

0.8

Utility Cost in one year （$/kW） -

H2

825.00

160

120

0.8

-

H3

42.42

210

45

0.8

-

H4

100.00

260

60

0.8

-

H5

357.14

280

210

0.8

-

H6

50.00

350

170

0.8

-

H7

136.36

380

160

0.8

-

C1

826.09

270

385

0.8

-

C2

500.00

130

270

0.8

-

C3

363.64

20

130

0.8

-

HU

500

499

0.8

60

CU

20

40

0.8

5

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Table 2 Relative cost data in case Item

Cost function（$）

Cost of area for a new heat exchanger

300A

Cost of area for an existing heat exchanger

300X

The fixed cost for a new heat exchanger

0

The cost of reassigning an existing heat exchanger

300

Cost of re-piping a single stream

50

(From reference (17)) 47000

H1 H2 H3 H4 H5 H6 H7

C

33000 7000

9800

10200

C

25000 9000

9200

20800

C

95000

C1 C2 C3

H H 5000

Fig. 3 The existing structure of HEN Table 3 Matching of the existing heat exchangers in Case Heat exchanger number

Heat exchangers matches

Q（ kW）

Area of heat exchanger（ m2）

1#

H7C2

20,800

1.21×103

2#

H5C2

25,000

1.23×103

3#

H4C2

10,200

6.92×102

4#

H6C2

9,000

2.25×102

5#

H2C3

33,000

1.61×103

6#

H3C3

7,000

2.31×102

7#

H1CU

47,000

2.36×103

8#

H4CU

9,800

3.39×102

9#

H7CU

9,200

1.41×102

10#

HUC1

95,000

1.44×103

11#

HUC2

5,000

0.53×102

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 4 Total heat transfer coefficient and area distribution of corresponding match in retrofitted HEN U （kW/(m2·℃)）

The modification area （m2）

New heat exchanger area （m2）

Newly added Utilization extent area of the of existing area existing heat (%) 2 exchangers（m ）

Match（stage）

Q（kW）

Match of the existing heat exchangers

H6C1（1）

1,181

New

0.4

77.5

77.5

-

-

2.33×104

H6C2（1）

3,222

New

0.4

165.7

165.7

-

-

4.97×104

H7C2（1）

19,607.1

1#

0.38

1,176.7

-

-

97.25%

0

H5C2（2）

22,637.5

2#

0.4

1,230

-

-

100%

0

H4C2（3）

9,012

3#

0.4

692

-

-

100%

0

H6C2（4）

4,597

4#

0.4

238.2

-

13.2

100%

3.96×103

H2C3（5）

33,000

5#

0.4

1,610

-

-

100%

0

H3C3（6）

6,999.3

6#

0.4

231

-

-

100%

0

H5C2（7）

2,362.3

New

0.4

81.5

81.5

-

-

2.44×104

H7C2（7）

8,562.1

New

0.4

347.7

347.7

-

-

1.04×105

H1CU

47,000

7#

0.4

2,360

-

-

100%

0

H4CU

10,988

8#

0.4

360

-

21

100%

6.30×103

H7CU

1,830

9#

0.4

33.5

-

-

23.76%

0

HUC1

93,819.35

10#

0.4

1422.1

-

-

98.76%

0

Note: “-“ represents no item.

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Cost（$）


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 19

Table 5 The contrasts of different HEN retrofit strategies

Item

Strategy from this paper

Strategy from Ahmad25

Total added area（m2）

689.5

2818.8 5

6.89×10

Strategy from Adam27 2694.4

5

6.85×105

Total utilities saving（$/yr）

4.02×10

Total modification cost（$）

2.07×105

8.46×105

8.08×105

Payback period（yr）

0.53

1.23

1.18

Return on investment（%）

194.2

81.4

84.8

The existing HEN structure was shown in Fig. 3. It included six matching units of cold and hot streams and the area distribution of heat exchangers was listed in Table 3. The numbers presented in Fig. 3. were the heat loads of the corresponding heat exchangers. The total areas of the heat exchangers including 1# ~ 6# were 5.20×103m2. The areas of all the coolers were 2.84×103 m2. And the areas of all the heaters were 1.49×103 m2. 1.0×105kW steam and 6.6×104 kW cooling water were needed in the existing HEN and the cost of utilities was $ 6.33×106 yr -1. The result of the HEN retrofit demonstrated that the new structure of HEN contained sixteen matching units and the retrofitted HEN structure was shown in Fig. 4. In this figure, the numbers above lines were the heat loads of the corresponding heat exchangers and the numbers under lines or in brackets were the heat capacity flow-rates of the corresponding streams. The matches of H6C1 and H6C2 in the 1st stage, H7C2 and H5C2 in the 7th stage were the newly added heat exchanging units (Table 4). And the areas of the newly added heat exchangers were 6.72×102m2 . And the cost of the newly added heat exchangers and re-piping was $ 2.02×105. The total areas of heat exchangers including H6C1(1st stage), H6C2(1st stage), H7C2(1st stage), H5C2(2st stage), H4C2(3st stage), H6C2(4st stage), H2C3(5st stage), H3C3(6st stage), H5C2(7st stage), H7C2(7st stage) were 5.85×103m2 . The areas of all the coolers were 2.76×103 m2. And the areas of all the heaters were 1.42×103m2. The areas of H4CU ranged from 339 m2 to 360 m2. And its cost was $ 6,300. Compared with the existing HEN, the areas of the heat exchangers in the retrofitted HEN were increased by 12.5%, the areas of coolers were reduced by 2.81% and the areas of heater were reduced by 4.70% because the existing HEN structure was optimized in this paper. At the same time, the existing heat exchangers and structure full application in situ in this optimal retrofit strategy including the existing heat exchangers (1# ~ 6#), the coolers, the heaters and their areas were all reused in situ in the retrofit HEN. So the total modification cost was only $2.12×105 . And 9.38×104 kW steam and 5.98×104 kW cooling water were needed in the optimal retrofitted HEN and the cost of utilities could reach $5.93×106yr-1. The cost of utilities could be saved $ 4.02×105 yr-1. According to the energy saving cost conversion, the retrofitted HEN could save more energy by 6.35%. But due to the stream splits, the heat transfer coefficients of streams would be changed. So in this paper, the changing of heat transfer coefficients from stream splits was considered. Here, only when the splits of - 14 -


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streams went through the reused existing heat exchangers, the changing of heat transfer coefficients was studied. Of course, other cases were also studied in the same method proposed in this paper. So only the total heat transfer coefficient of 1# heat exchanger changed from 0.4 kW·m-2·℃-1 to 0.38 kW·m-2·℃ -1 and the heat transfer areas were increased by 5.25%. The payback period was about 0.53 years. 47000

H1

C 33000 (825)

H2 6999.3 (42.42)

H3 9012 (100)

10988

H4

C 2362.3 (357.14)

22637.5 (357.14)

H5

4597 (50)

1181 (18.08)

H6 19607.1 (136.36)

H7

8562.1 (136.36)

3222 (31.92)

1830

C 93819.35

C1

H

(826.09)

(421.79)

(500)

(500)

(500)

(388.48)

C2

(111.52)

(78.21)

C3 (363.64) (363.64)

Fig.4 The retrofitted structure of HEN Compared with the retrofitting strategy from the reference26, the existing heat exchangers and the existing structures were both used up to 100% (Calculating according to the number of nodes) due to adopting the existing heat exchangers and structures full application in situ in two kinds of HEN retrofit strategies. Because of considering the constraint of the changing heat transfer coefficients in this paper, the number of stream splits with the existing heat exchangers reused was decreased by 50% in the same example. However, the total modification cost was also reduced by 37%. And the energy saving was reduced from 8.53% to 6.35% according to the energy saving cost conversion. As far as the payback periods, the two strategies were almost the same. Ahmad et al

25

and Adam et al

27

have also studied the HEN retrofit of the same example based on the

pinch technology. According to the retrofit strategy from Ahmad et al, the payback period was 1.23 years without considering the cost of moving heat exchangers and re-piping. And the payback period from Adam et al was 1.18 years. As far as the return on investment is concerned, the retrofit strategy in this paper is better than the others from Ahmad et al

25

and Adam et al 27. Compared with the retrofit strategy studied in this paper, the

HEN retrofit strategies based on the pinch technology could save much more energy, but they had the longer payback periods (Table 5).

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5. CONCLUSIONS The novel mathematical model for the retrofit of HENs in CDUs has been proposed in this paper. The mathematical model was built based on the stage-wise superstructure with the stream splits. The object function was the minimum of the total cost of modifications and utilities with focusing on the changing heat transfer coefficients arising in the reused existing heat exchangers from stream splits. The HEN modifications included buying new heat exchangers, adding or reducing areas of the existing heat exchangers, moving the existing heat exchangers and laying pipes. The stream splits increased the matching probability of cold and hot streams from the stream splits, but the total heat transfer coefficients may also decreased. The hybrid genetic algorithm was used to solve the MINLP problem. The existing heat exchangers and their structures were designed as elites introduced into the HGA and reused in situ completely. The Dittus-Boelter’ correlation and kern’s correlation were used to estimate the convective heat transfer coefficients of the corresponding streams. One example was studied to show the effect of the novel HEN retrofit. Compared with the existing HEN, the areas of the heat exchangers in the retrofitted HEN were increased by 12.5%, the areas of coolers were reduced by 2.81% and the areas of heater were reduced by 4.70%. And the existing heat exchangers and structure full application in situ in this optimal retrofit strategy. The total modification cost was $2.12×105. The cost of utilities could reach $5.93×106 yr-1. The cost of utilities could be saved $ 4.02×105 yr -1. According to the energy saving cost conversion, the retrofitted HEN could save more energy by 6.35%. And due to the stream splits, the heat transfer coefficients of streams would be changed. And the heat transfer areas were increased by 5.25%. The payback period was about 0.53 years. Compared with the retrofitting strategy from the reference 26, because of considering the constraint of the changing heat transfer coefficients in this paper, the number of stream splits with the existing heat exchangers reused was decreased by 50%. The total modification cost was also reduced by 37%. And the energy saving was reduced from 8.53% to 6.35% comparing with the existing HEN from the reference26 according to the energy saving cost conversion. As far as the payback periods, the two strategies were almost the same. Compared with the pinch method from Ahmad et al

25

and Adam et al

27

,

the HEN retrofit strategies based on the pinch technology could save much more energy, but they had the longer payback periods and the worse return on investment. In order to acquire the steady optimal HEN, the online optimal control strategy and improving the capacity of resisting disturbances would be our research interest in the future work.

AUTHOR INFORMATION Corresponding author *Tel.:+86 574 87081240; fax: +86 574 87081240. E-mail address:

[email protected]

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ACKNOWLEDGMENTS Part of this project was supported by the Zhejiang Provincial Education Office Project (Grant No. Y201431687) and Startup Fund for Doctor of Ningbo University of Technology.

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