A Novel Sensitivity Analysis Method for the Energy Consumption of

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A novel sensitivity analysis method for the energy consumption of coupled reactor and heat exchanger network system Di Zhang, Peng Wang, and Guilian Liu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b01182 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 29, 2018

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Energy & Fuels

A novel sensitivity analysis method for the energy consumption of coupled reactor and heat exchanger network system Di Zhang1, Peng Wang2, Guilian Liu1* (1 School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi Province, 710049, China; 2

Hohhoot Branch of PetroChina Pipeline Company, Hohhot, Inner Mongolia, 010000, China)

Abstract: Since the inlet feed and outlet product of the reactor generally are the cold or hot streams of the Heat Exchanger Network (HEN), it is necessary to analyze the relation between reactor parameters and the Energy Consumption (EC) of HEN based on integration. An integration-based sensitivity analysis methodology is proposed to analyze the relation among conversion, inlet/outlet temperature of Continuous Stirred Tank Reactor (CSTR) reactor, and EC of HEN. Equations are derived to show their relations, and the influence of temperature on HEN is analyzed with both positions of inlet/outlet streams and reaction's endothermic/exothermic characteristics considered. The S-Q-T-X diagram is proposed to show the relation between reactor parameters and energy consumption of HEN, and perform the sensitivity analysis of the energy consumption along conversion; the results can guide the design of reactors. Case study shows that, for the studied selective hydrogenation process from benzene to cyclohexene, the EC for producing unit product can be reduced by 34.2% with the conversion of benzene increased to 0.6.

Key words: Heat exchanger network; Reactor; Energy consumption; Sensitivity analysis; Integration

1 Introduction Energy is an important basis for the development of the world economy. With world * Corresponding author: Prof. Guilian Liu, E-mail: [email protected].

1

ACS Paragon Plus Environment

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GDP rising by 3.6% each year, the world energy consumption will increase by 56% between 2010 and 2040 1. Correspondingly, the contradiction between the demand and supply of energy will become more intense. The chemical production process consumes a lot of energy. The energy cost accounts for 20% ~ 30 % of the production cost for general chemical product, up to 70% ~ 80% for high-energy-consumption product 2. Because of this, the Energy Consumption (EC) per unit of chemical product is a critical factor impacting the production cost and has become a main indicator to measure the chemical industry. In chemical process, raw material flows through different units, including reactor, separator, mixer and Heat Exchanger Network (HEN), while the hot and cold utilities are mainly consumed by HEN. However, to reduce EC, not only the integration of HEN should be considered, but also the design of the reactor. The reason is that the reactor is the only place where raw materials are converted into products and byproducts, and its inlet feed and outlet product are generally cold streams and/or hot streams of HEN and need to be heated/cooled, as shown by Fig. 1. When the operating parameter of reactor is adjusted, the temperature and heat duty of the corresponding streams will be influenced. To decrease the chemical production cost, the parameters of reactor should be optimized based on the HEN integration. Hot/cold stream

Hot/cold stream Heat Exchanger Network

Inlet feed

Outlet product

Reactor

Utility

2


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Energy & Fuels

Fig.1 Relation between HEN and reactor

The performance of reactor is mainly reflected by its conversion and selectivity. In the design of reactor, the first step is the choice of reactor type and catalyst. After that, initial conversion of the reactor is selected to make the design to be proceeded. Based on this, feed conditions, feed ratio and other operating conditions can be chosen to achieve the selected conversion 3. However, not all these parameters directly affect the integration of HEN. The effects of some parameters (pressure, catalyst, etc.) are reflected by that of conversion and selectivity, which affect the total heat capacity (CP) of the related cold and hot streams. And, for different types of reactions, the parameters affecting HEN are different. For single reactions, the effect of reactor is directly related to temperature and conversion; while the selectivity of reactor should be considered for multiple reaction systems. In order to optimize reactor's parameters based on HEN integration, it is necessary to analyze the relation between these parameters and the EC of HEN. The EC of a HEN can be decreased through integration, and its minimum value can be targeted by pinch technology 4. Based on this method, different integration methods have been developed to target the minimum EC of HENs with different characteristics. The “plus–minus principle” 5 is put forward to identify the variation of utility along the hot and cold duties. Composite Curve (CC) 6 is proposed to manifest residual energy demands and analyze the heat recovery probability of process further. With regard to the fact that the pinch approach temperature affects the utility consumption and capital cost, Li and Motard

7

derived an equation to target its

optimal value in terms of maximizing the annual net cost saving and economic savings. A heuristic procedure was presented by Suaysompol and Wood 8 to target EC, and its application has been extended to predict the fluctuation of operating

3


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parameters 9. Yang et al.

10

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put forward a graphical method for integrating the

distillation column and heat pump with HEN. Zhang and Liu

11

analyzed the

integration between distillation column and HEN, and developed an approach for identifying the variation of utilities along the operating pressure of distillation column. Moreover, the pinch-based method has been applied to design the distillation coupled 12

with evaporation

, or investigate the integration options for clusters of chemical

production process 13. Besides the optimization of HEN introduced above, researchers also studied the integration between reactor and HEN. Glavic et al.

14

analyzed the reactor

thermodynamically and proposed its appropriate placement based on its integration with the overall process. Later, they put forward a method for matching the HEN and reactor based on the temperature-reaction heat diagram and the grand composite diagram 15. Thereafter, this method is extended to enable the simultaneous integration of all kinds of energy-active equipment and inlet streams 16. Furthermore, pinch-based methods are proposed for integrating the chemical reactor network reactors

17

and different

18

, even for integrating the exothermic/endothermic reactions with the heat

exchanger reactors, for which the energy transfer between its inlet feed and outlet product exists

18

. However, most of these methods only consider the reactors.

Although Ref. [18] considered the HEN and reactors simultaneously, the integration is only analyzed qualitatively to identify whether the integration will decrease the EC or not. These methods cannot be applied to analyze the relation between reactor parameters and the EC of HEN. Besides pinch based methods mentioned above, the mathematical programming method can also deal with such kind of problems. Chaturvedi et al. 19 present a Mixed Integer Linear Programming (MINLP) model to determine the minimal energy target

4


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Energy & Fuels

for a batch process with different reaction products. Kaiser and coworkers

20

developed a mathematical method to derive reactor-network candidates and identify the characteristics of the reaction progress. For continuously operating HENs, a method is presented for optimizing its cleaning schedule 21. In this method, a MINLP model is built and globally optimal solutions can be obtained. Besides, it can integrate the overall energy production process capture considered

22

, even with the power system

23

and CO2

24

. Compared with the pinch-based graphical method, it is more

convenient for the mathematical programming method to cope with complex HEN and identify the optimal match simultaneously. However, the mathematical programming method cannot give clear insights into the integration process as it is solved as a black-box. Based on the literature survey, there is no integration-based study on the relation between reactor parameters and EC. Since conversion is an important parameter of the reactor, its relation with the inlet temperature (T0) and outlet temperature (T) of Continuous Stirred Tank Reactor (CSTR) will be studied. On the basis of this, a sensitivity analysis method will be presented to integrate HEN with reactor, identify the variation tendency of reactor temperature and EC along the conversion, as well as EC at any given conversion. A case is analyzed to demonstrate its application.

2 Relation among the parameters of reactor The effluent temperature changes along reactor's operating parameters and inlet temperature. The relation among them is relevant to the reactor's conversion, and is different for different types of reactors. In this section, this will be studied for homogeneous CSTR reactor. 2.1 Relation between conversion and other parameters For a common reaction, components A and B reacted to produce product C, the 5


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reaction equation can be described as: ܽ‫ ܣ‬+ ܾ‫ܥܿ → ܤ‬ Where, a, b and c are the stoichiometric factors of corresponding components. Since the reaction is irreversible, the reaction rate of component A, rA, can be described by Eq. (1) and Eq. (2), respectively. − rA = FA0 X / V

(1)

−rA = kcαAcBβcνC

(2)

Where, FA0 and X denote the inlet flowrate and conversion of component A; V represents reactor volume; k denotes reaction rate constant; cA , cB and cC stand for the concentration of A, B and C, α, β and ν correspond their reaction order, respectively. Based on the definition of conversion in liquid phase, cA , cB and cC can be described by Eqs. (3) ~ (5), respectively.

cA = cA0 (1− X)

(3)

c B = c B0 − b / a ⋅ c A0 X

(4)

c C = c C0 + c / a ⋅ c A0 X

(5)

Where, superscript 0 represent the corresponding inlet parameters. Based on Eq. (1) ~ Eq. (5), Eq. (6) is deduced to show the relation between k and X. k = FA0 c A0 −α / V ⋅ X ⋅ (1 − X )

−α

⋅ ( cB0 − b / a ⋅ c A0 X )

−β

⋅ ( cC0 + c / a ⋅ c 0A X )

−ν

(6)

Besides, k is also related to the reaction temperature and the activation energy, E, as shown by Eq. (7). With Eq. (6) and Eq. (7) combined, Eq. (8) is obtained to show the relation among reaction temperature (T), conversion (X) and activation energy (E). For gas phase reaction, the relation can be deduced by the same method. Note, strictly 6


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Energy & Fuels

speaking, activation energy is affected by temperature. For a specific catalyst and in a small temperature interval, it can be taken as a constant with the influence of temperature ignored. The derivation of Eq. (8) is based on this assumption.

k = Aexp ( −E / RT )

(7)

{

}

−β −ν −α T = − E / R ⋅ ln  FA0cA0 −α / ( A ⋅V ) ⋅ X ⋅ (1 − X ) ⋅ ( cB0 − b / a ⋅ cA0 X ) ⋅ ( cC0 + c / a ⋅ cA0 X )    (8)

Where, A is the pre-exponential factor. According to the energy balance of reactor, its outlet temperature is affected not merely by its operating parameters, but also its inlet temperature and energy supplied to it. For a CSTR reactor with n species and operated at a steady state, their relation could be deduced based on its energy conservation, which is displayed by Eq. (9). n

o Q − WS − FA0 ∑ Fi 0 / FA0 ⋅ Cpi (T − Ti 0 ) − ∆H Rx (TR ) + ∆Cp (T − TR ) FA0 X = 0

(9)

i =1

Where, Q is the heat flow into the system; WS denotes the reactor's inlet work; Fi 0 o and Cpi stand for the inlet flowrate and heat capacity of species i; ∆HRx (TR ) is the

reaction heat at reference temperature TR; ∆Cp is the difference between the heat-capacities of feed and product. In most systems, reactants enter the reactor at the same temperature, T0, i.e. Ti 0 = T 0

(10)

M = ∑ Fi 0 / FA0Cpi = CpA + FB0 / FA0 ⋅ CpB + FC0 / FA0 ⋅ CpC

(11)

N = ∆ C p = c / a ⋅ C pC − b / a ⋅ C p B − C p A

(12)

Define

According to these two equations, it can be known that M and N are constant as long as the inlet feed of the reactor is given. 7


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According to Eqs. (10)~(12), Eq. (9) can be simplified into Eq. (13). o Q − W S − FA0 M (T − T0 ) −  ∆ H Rx (TR ) + N ⋅ (T − TR )  FA0 X = 0

(13)

For system operated with no work inlet, WS=0, Eq. (13) can be rewritten into Eq. (14), which clearly demonstrate the relationship among X, T, T0 and Q.

{

}

o T0 = T − Q − FA0 X  ∆ H RX (TR ) + N (T − TR ) / FA0 M

(14)

2.2 Graphic representation of the relationship among T, T0 and X The variation of T, T0 and Q along X can be derived with Eq. (8) and Eq. (14) combined, and the corresponding curves can be plotted. Since the shape of these curves is affected by the reaction types, exothermic reactions and endothermic reactions are studied, respectively, with either T0 or Q kept unchanged.

T0 is kept unchanged For exothermic reactions, T00, point D' should move rightward to D" by ∆CP × (T '− TE ) , and point C' need to be shifted with the same distance to C' '. If not,

they should be shifted leftward. Note, TE represents the TT of SRp.

∆CP = FA0 N ( X ′ − X )

(15)

Where, X' is the conversion of the reactor when ST of SRp increases to T'. Consequently, in Fig. 7, C"D"DEFPG is the new HCC; C"C indicates the increment of energy provided by hot streams (∆H1), which can be calculated by Eq. (16).

∆H1 = CPSRP (T ′ − T ) + ∆CP (T ′ − TE )

12


(16)

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Energy & Fuels

∆H1

T C C′ C′′ D′ D′′

TC T′ T TE TH TI T0′ T0

D E

H

H′

I I′

F J′ J P

∆H2

K L H′′

G M

∆QHmin

∆QCmin

H Fig. 7 Variation of CC when the temperature of SRp and SKq increases (exothermic reaction)

If T0 increases, the variation of CCC can be identified by the similar analysis. H′I′J′JKLM is new CCC when the TT of SKq increases from T0 to T0′; the length of H′H represents the increment of the energy demanded by all cold streams, and is denoted as ∆H2, which also equals to that of SKq. Hence, the variation of hot utility, ∆H, is ∆ H = ∆ H 2 − ∆ H 1 = CPSK q (T0 ′ − T0 ) − CPSRP (T ′ − T ) − ∆ CP (T ′ − TE )

(17)

In the HEN, it is convinced that the inlet temperature is always the target temperature while the outlet temperature is the supply temperature, no matter the corresponding stream is a cold or hot. However, the location of this pair of hot and/or cold streams might be different. Assume the pinch position is unchanged and reaction is exothermic, the variation of hot and cold utilities can be determined by this approach when the two streams have different properties and different locations, and the results are shown by Table 1. Same as before, ∆H1 and ∆H2 in this table are the energy increment of the inlet stream and outlet stream, respectively. With the same approach, the variation of the 13


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utilities for endothermic reactions can be also determined and listed in Table 2. Table 1 Variation of utilities for inlet and outlet streams with different positions (exothermic reactions) Position

Above the pinch

Type of streams Inlet Outlet Hot Hot Hot Cold Cold Hot Cold Cold

Variation Hot utility Cold utility ∆H2-∆H1

Unchanged

Below the pinch

Hot Hot Cold Cold

Hot Cold Hot Cold

Unchanged

∆H1-∆H2

Across the pinch

Hot Hot Cold Cold

Hot Cold Hot Cold

-∆H1

-∆H2

Table 2 Variation of utilities for inlet and outlet streams with different positions (endothermic reactions) Position

Variation

Type of streams Inlet

Outlet

Hot utility

Cold utility

Above the pinch

Hot Hot Cold Cold

Hot Cold Hot Cold

∆H1-∆H2

Unchanged

Below the pinch

Hot Hot Cold Cold

Hot Cold Hot Cold

Unchanged

∆H2-∆H1

Hot

Hot

Hot

Cold

Cold

Hot

∆H1

∆H2

Cold

Cold

Across the pinch

However, for some cases, the pinch position varies accordingly when the inlet and

14


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Energy & Fuels

outlet temperatures change, and CCs should be shifted to meet the minimum temperature approach. The translation of CCs increases the complexity of analyzing the HEN and will be discussed in the future work.

4 The sensitivity analysis of conversion In order to evaluate the effect of conversion on the EC of the whole process, sensitivity analysis should be conducted. When the conversion changes, the product flowrate of reactor varies correspondingly. To evaluate the sensitivity with both the variation of EC and that of product flowrate considered, the Energy Consumption of Unit Product Produced (ECUPP) will be used. The ECUPP, S, is defined by Eq. (18). In this equation, h, l and g are the translation factor of cold utility, hot utility and the energy supplied to reactor, respectively, and could be applied to transform the energy measured by kW into that by standard coal.

S = h QC min + l ( QH min + ∆H ) + g Q  / XFA0

(18)

According to Eq. (8), Eq. (14) and Eq. (18), the S-Q-X diagram, such as Fig. 8, can be plotted to illustrate the variation relation of S, hot and cold utility consumption along conversion. S |Q|

0

0

X

Fig. 8 S-Q-X diagram 15


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Since both EC and reactor temperature change along X, S-Q-T-X diagram can be constructed with curves shown in Fig. 2 and Fig. 8 plotted together. Hence, the variation tendency of EC and temperatures along the conversion in different conversion intervals can be revealed clearly. Based on this, the sensitivity analysis of these parameters along X can be performed. Fig. 9 illustrates a S-Q-T-X diagram for the exothermic reaction with inlet temperature of reactor fixed. In this figure, ECUPP decreases rapidly in conversion interval (0, XC], and decreases slowly in [XC, XD]. The increment of the conversion in interval (0, XC] can significantly decrease the EC of this system. As long as X is given, the corresponding T0 and T to achieve this conversion can be distinguished. For example, when the reactor is operated at conversion XC, a vertical line across point (XC, 0) can be plotted and intersects these curves at point C1, C2, C3, C4, C5 and C6, respectively. These points correspond the outlet and inlet temperatures (T and T0), hot (QHmin) and cold utility (QCmin), ECUPP (S), and heat flow into the reactor (Q) in turn, and can be used to guide the design of the reactor. Note, in the derivation of the energy increment shown in Table 1, the pinch is assumed to be kept unchanged. Although this is general, checking whether this assumption is true or not is still necessary. If the pinch change, the EC should be corrected with the new pinch and adjustment of the EC determined by the method introduced in Section 3.2. Above all, the procedure for integrating the HEN with reactor and analyzing the effect of conversion is summarized and given in Fig. 10.

16


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Energy & Fuels

T

S |Q| Energy consumption of unit product produced

C3 Hot utility C1 T

C2

Inlet temperature

T0

C6 QC C5

SC Q

C4 Cold utility

0

0

XB

XC

Fig. 9 S-Q-T-X diagram

17


XD

X

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Identify the reactions

Establish the material balance equation between the X and T of the reactor according to Eq. (8)

Establish the relation among the Q, T and T0 according to Eq. (9)

T0 is unchanged

Q is unchanged

Construct the Q-T-X diagram

Calculate the variation of hot and cold utility according to Table 1 or Table 2

Calculate S according to Eq. (18)

Construct the S-Q-T-X diagram

Analysis the relation among reactor's T/T0 and X, and S; identify the optimal conversion.

Fig. 10 Procedure for integrating the HEN with reactor and analyzing the effect of conversion

5 Case study As an important industrial chemical, cyclohexene (HE) is widely produced from benzene (BZ) by selective hydrogenation. To verify the application of introduced 18


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Energy & Fuels

approach, a cyclohexene production process, illustrated by Fig.11, will be studied in this section. In this process, the inlet flowrate of benzene is 980 mol·min-1.

E111

E112

The raw benzene Discharge D102

E101

E113 R101

E114 R102

Discharge

D201

Hydrogen

E102

T200 E115

Discharge

E103 Cooling water

D101

Purified process

E111

E402

E201

E311

E211

R401 T400 T301

E202

R301

E301

T203 E302

E303

R101 - Benzene pretreatment reactor R102 - Hydrogenation reactor R301 - Hydration reactor R401 - Impurity hydrogenation reactor T200 - Dehydration column T201 - Benzene separation Column T202 - Benzene recovery column T203 - Cyclohexene separation Column T301 - NOL separation column

T202

T201 E401

Raw cyclohexane

Separators – D101 D102 D201

T403

Heat exchangers – E101 E102 E103 E111 E112 E113 E114 E115 E201 E202 E211 E301 E302 E303E311 E401 E402 E403 E801 E802 (Not shown)

Purified cyclohexane

E403

Fig. 11 Selective hydrogenation flowsheet for producing cyclohexene from benzene

Cyclohexene is produced in CSTR reactor, R102, according to reaction:

BZ + 2H2  → HE Besides this primary reaction, some of the cyclohexene undergoes a secondary reaction in series to an unwanted byproduct, cyclohexane (HA), according to the following reaction:

HE + H 2  → HA Since the reaction rate of the primary reaction is about 30 times faster than that of the secondary reaction, only the former is considered in this section

19


25

. When R102 is

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operated at high pressure (>3.0 MPa) and high temperature (>383 K), the reaction rate (r) can be represented by Eq. (19)

26

.

−rBZ = kcBZ

(19)

Where, cBZ represents benzene’s outlet concentration. When the catalyst of hydrogenation is Ru-M-B/ZrO2

27

, and the operating

temperature and the pressure are 403.15 K and 5 MPa, respectively, the active energy, E, equals 32,630 kJ·mol-1, and k can be calculated by Eq. (20).

k = 734.95(min −1 ) exp  −32, 630(kJ⋅ mol -1 ) / RT 

(20)

In R102, the inlet hydrogen is in gas phase and dispersed at the bottom of CSTR; benzene and cyclohexane only exist in liquid-phase. Since r is not affected by the pressure of hydrogen when the pressure (>3.0 MPa) and temperature (>383 K) are high enough 25, the reaction is taken as processed in a homogeneous liquid. According to the general definition of conversion, Eq. (21) can be obtained to describe the concentration of benzene. 0 cBZ = cBZ ⋅ (1− X )

(21)

According to Eq. (8), the relation between reaction temperature and conversion can be written as Eq. (22). 0 −1 T = −3,924.7 / ln  FBZ0 ⋅ cBZ / ( 734.95 ⋅V ) ⋅ X ⋅ (1 − X )  (22)   Besides, the space time of benzene in R102 equals 15 min. According to its definition −1

shown by Eq. (23), Eq. (22) can be transformed into Eq. (24). 0 τ = V ⋅ cBZ / FBZ0

{

(23)

}

T = −3, 924.7 / ln X / 11, 024.25 (1 − X ) 

(24)

At 403 K and 5 MPa, the reaction heat is -95,000 J·mol-1 27, and the value of M and N calculated by Eq. (11) and Eq. (12) are 123.8 J·mol-1·K-1 and -24.91J·mol-1·K-1,

20


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Energy & Fuels

respectively. When the energy sent to R102, Q, is -500 kW, the expression of the inlet temperature (T0), Eq. (25), is obtained according to Eq. (14) and Eq. (24). This equation shows the relationship between T and X, while Eq. (24) illustrates that between T0 and X.

{

}

T0 = − 3, 924.7 (1 − 0.12 X ) / ln X / 11, 024.25 (1 − X )  − 405 X + 141

(25)

In this process, 9 cold streams and 12 hot streams compose a HEN. When X in terms of BZ equals 0.40, data of these streams are listed in Table 3. H1 and H2 are a pair of streams related to R102, the former is its inlet stream, while the latter is its effluent. When ∆Tmin is taken as 10 K, the HCC and CCC are shown by Fig. 12. It is made out that the consumptions of cold and hot utilities are 2,730.57 kW and 7,165.04 kW (exclude Q), respectively; the pinch corresponds point P and its average temperature is 380 K. Note, the cold utility is cooling water, while the hot utility is steam; the reaction heat (Q) is taken out from reactor by cooling water.

Fig. 12 Composite curves when benzene’s conversion equals 0.4

21


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Table 3 Process stream data Streams

Heat exchanger

ST, K

TT, K

∆H, kW

CP, kW·K -1

H1

E101, E103

411.65

365.15

1,323.93

28.38

H2

E111

403.15

305.15

359.88

3.67

H3

E112

305.15

288.15

62.39

3.67

H4

E113

394.95

313.15

827.18

10.11

H5

E302, E201, E202

431.15

337.85

2,982.40

31.97

H6

E115

360.85

324.15

285.8

7.79

H7

E211

369.65

343.15

1,021.21

38.54

H8

E114

313.15

288.15

4.38

0.18

H9

E303, E311

438.35

369.95

1,286.34

18.81

H10

E401

310.45

310.15

0.19

0.63

H11

E403

363.95

313.15

45.79

0.9

H12

E801, E802

344.35

325.15

116.68

6.08

C1

E101, E102

305.15

423.15

574.44

4.87

C2

E201

318.15

391.65

856.71

11.66

C3

E115

306.95

333.15

156.83

5.99

C4

E311

353.85

384.75

1,286.34

41.63

C5

E402

287.15

356.15

45.64

0.66

C6

E303

375.15

400.65

1,227.15

48.12

C7

E302

375.15

401.55

1,651.33

62.55

C8

E301

375.15

377.15

6,849.11

3,424.55

C9

E801

311.65

320.85

50.57

5.5

In Fig. 12, point E corresponds the ST of H2, while point I corresponds the TT of H1, these two points locate on the pinch’s different sides. In the light of Table 1, it is identified that the decrement of hot and cold utilities are ∆H1 and ∆H2, and can be calculated according to Eqs. (26) and (27), respectively.

∆H1 = CPH2 (T '− 403.15) + ∆CP(T '− 305.15)

(26)

∆H2 = CPH1 (T0 '− 365.15)

(27)

According to these two equations and Eq. (18), Eq. (28) is obtained to calculate ECUPP. S =  h ( 8, 598 − 3.83T '− 0.41XT + 125 X ) + l (13, 765.1 − 28.38T0 ' )  / 16.33 X

22


(28)

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Energy & Fuels

When l and h are taken as 3.41×10-5 kg standard coal·kJ-1 and 3.42×10-6 kg standard coal·kJ-1 28, respectively, S-X curve is plotted on the basis of Eq. (28). Besides, the outlet temperature versus conversion curve is determined by Eq. (24); the inlet temperature versus conversion curve is plotted according to Eq. (25); the hot and cold utility is the sum of the utilities at present operating condition and the variation calculated according to equations shown in Table 1, Eq. (26) and (27). As Q is kept to be 500 kW, the Q versus conversion curve is a horizontal line. With all these curves combined, Fig. 13 is obtained and can be used to perform the sensitivity analysis. With X given, the corresponding T0, T and EC can be targeted according to this figure. When X equals 0.4, the corresponding T0, T, QHmin and QCmin correspond point A1, A2, A3 and A4, respectively, and are 403 K, 365 K, 7,165 kW, and 2,730 kW. A5 lies on the S-X curve; its vertical coordinate, 0.038 kg standard coal·mol-1, is the corresponding ECUPP. A6 stands for the energy provided to reactor, Q, and equals 500 kW. Furthermore, based on this diagram and the sensitivity analysis, some features can be acquired: (1) When the conversion of R-102 is less than 0.32, T0 > T. The reason is that the total reaction heat is less than the energy transferred to the cold utility. (2) T0 of R102 should be increased to achieve a higher conversion, while T should be decreased simultaneously. (3) Cold utility consumption increases fast along the conversion, while that of hot utility decreases slowly. (4) When the energy transferred from the reactor to the cold utility is fixed, the

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difference between T and T0 increases along conversion. (5) The ECUPP decreases sharply in conversion interval [0.1, 0.3] and decreases rapidly in interval [0.3, 0.6], and finally tends to be stable when the conversion is greater than 0.6.

Fig. 13 The S-Q-T-X diagram

Based on the sensitivity analysis, it can be identified that it is necessary to increase the conversion of R102 into 0.6, so that ECUPP can be decreased significantly. When the conversion increases from 0.4 to 0.6, the ECUPP will decrease by 34.2% to 0.025 kg standard coal·mol-1, and the cold and hot utility consumptions are 4,320 kW (excluded Q) and 7,020 kW, respectively. To achieve this conversion, the corresponding outlet temperature will increase to 440 K and the inlet temperature should decrease to 309 K. Besides, Fig. 13 shows that when the hot utility decreases slowly and the cold one increases fast along X, ECUPP decreases. The reason is that, in this case, the energy transformation factor of hot utility is ten times greater than that of cold utility, and the increment of the product flowrate is greater than that of EC. Consequently, the 24


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Energy & Fuels

ECUPP decreases along the conversion. When X equals 0.844, there are extremums on the curves of inlet temperature and cold utility, as shown by Fig. 13. The inlet temperature to achieve the corresponding conversion is determined by the mass balance and energy balance of the reactor. The reason why the cold utility consumption reaches the minimum is that the inlet energy of reactor R-104 reaches minimum when the conversion equals 0.844, as well as the difference between its inlet and outlet energy. As both the inlet stream and outlet stream of this reactor are hot streams, and the data of other hot and cold streams are kept to be unchanged, this will cause the cold utility reaches the minimum. In Fig. 14, the inlet energy versus conversion curve, the outlet energy versus conversion curve, and the energy difference versus conversion curve are plotted. Note, the inlet energy includes the enthalpy of the inlet stream and the reaction heat, the outlet energy includes the enthalpy of the outlet stream and Q, and the energy difference refers that between the inlet and outlet energy of the reactor.

Fig. 14 Energy versus conversion diagram of R-104

To check whether the assumption that the pinch does not change is true or not, and

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verify the accuracy of the proposed method, the CCs corresponding conversion 0.6 are plotted, as shown by Fig. 15. From this diagram, the target for cold utility, hot utility and the average pinch temperature are distinguished to be 4,319.67 kW, 7,022.84 kW and 380 K, respectively, same with that identified from Fig. 13. Therefore, the assumption that the pinch does not change is true; energy target identified from S-Q-T-X diagram is accurate, and the proposed method is efficient and accurate in identifying the EC and reactor's inlet and outlet temperatures, and their variation tendency. In the design stage, the effect of reactors on the HEN can be analyzed based on the proposed method, and the suitable conversion can be further identified. Since the conversion of a reactor is affected by multiple factors, including the operating temperature, pressure (vapor phase reaction), concentration, reactor size, catalyst and its activity, etc, its variation can be achieved with these parameters adjusted. For example, for a reactor of an established process, the catalyst activity will decrease from the SOR (Start of Run) stage to EOR (End of Run) stage, the conversion of reactants will decrease correspondingly. To compensate for deactivation of the catalyst and maintain the conversion of reactants, the inlet and operating temperatures of the reactor are generally increased. For the studied case, reactor R102 has been established. The conversion can be improved with the operating temperature, or the concentration of some reactants increased.

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Energy & Fuels

Fig. 15 Composite curves when X equals 0.6

6 Conclusions Based on the integration of the HEN and CSTR reactor, a pinch-based sensitivity analysis methodology is proposed to analyze the relation among T0/T and X of the reactor, and the energy consumption of HEN. For a HEN, the influence of reactor’s feed and product on its energy consumption can be identified based on the analysis of composite curves. Equations derived on the basis of material and energy conservation can show the relation among the temperatures of reactor's feed and product, conversion and energy consumption. Furthermore, the proposed S-Q-T-X diagram can give clear insight into their relationship. It could be applied to perform the sensitivity analysis of energy consumption along conversion, and identify the corresponding variation tendency, which can guide the design of reactors. The case study of the benzene to cyclohexene process shows that the energy consumption can be reduced by 34.2 % when the conversion increases to 0.6; the

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proposed approach is simple and efficient for analyzing the integration between HEN and reactor. In the design stage of a process, the proposed method can be used to optimize the energy consumption. For a mature technique of chemical process or practical production process, the proposed method can be used to analyze the effect of practical problems, such as the effect of the catalyst deactivation. In this work, only the CSTR reactor with single irreversible reaction is studied. However, for PFR reactors, batch reactors and reactors with complex multiple-reactions, secondary reactions and selectivity should be taken into account. The relation among the reactor parameters and heat exchanger networks will be more complex. And the position of the pinch also influence the hot and cold utilities. Although the equations derived in this work cannot be applied directly, the analysis method of this work can be further extended to deal with this kind of complex problems. The study of this manuscript shows the energy consumption of unit product decreases along conversion. However, the conversion cannot be increased randomly, as the capital cost of the reactor will increase correspondingly. To identify the optimal conversion, economic analysis should be taken into account. The integration between other types of reactors/reaction systems and heat exchanger networks as well as the changed pinch position, and the identification of the optimal conversion based on the economic analysis will be investigated in our future work.

Acknowledgement Financial supports provided by the National Natural Science Foundation of China (21736008) and (U1662126) are gratefully acknowledged.

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Energy & Fuels

Nomenclature A

Pre-exponential factor, min-1

a, b, c

Stoichiometric coefficient of reaction

c

Concentration, mol·L-1

Cp

Heat capacity, J·mol-1·K-1

CP

Heat capacity flowrate, kJ·min-1·K-1

∆Cp

Difference of heat-capacity between the inlet and outlet stream, J·mol-1·K-1

E

Activity energy, J

F

Molar flowrate , kmol·min-1

h, l, g

Energy translation factor, kg standard coal·kJ-1

0 ∆H RX

Reaction heat, J·mol-1

∆H1

Energy increment of inlet stream, kW

∆H2

Energy increment of outlet stream, kW

k

Reaction rate constant, min-1

Q

Heat added to reactor, kW

QC

Cold utility, kW

QH

Hot utility, kW

r

Reaction rate, mol·L-1·min-1

S

Energy consumption of unit product produced, kg standard coal·mol-1

T

Outlet temperature of reactor, K

T0

Inlet temperature of reactor, K

TR

Reference temperature, K

V

Volume of the reactor, L

WS

Work inlet into the reactor, kW

X

Conversion of species A

α, β, γ

Reaction order

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Subscript i

Species i in the reaction system

SKq

Cold stream corresponding to the inlet/outlet stream of reactor

SRp

Hot stream corresponding to the inlet/outlet stream of reactor

min

Minimum value

Superscript 0

Condition at inlet of reactor

'

Condition after adjusting parameters of reactor

Abbreviation BZ

Benzene

CC

Composite curve

CCC

Cold composite curve

EC

Energy Consumption

ECUPP

Energy Consumption of Unit Product Produced

HA

Cyclohexane

HCC

Hot Composite Curve

HE

Cyclohexene

ST

Supply temperature of stream

TT

Target temperature of stream

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A Novel Sensitivity Analysis Method for the Energy Consumption of

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