應用數學規劃法設計冰水網路及冰水主機操作策略

(1)

國立臺灣大學工程學院化學工程學所碩士論文

Department of Chemical Engineering College of Engineering

National Taiwan University Master Thesis

A Mathematical Approach for the Design of

Refrigerated Water Network and Chiller Operating Strategy

李孟達 Meng-Da Lee

指導教授：陳誠亮博士 Advisor: Cheng-Liang Chen, Ph.D.

中華民國 100 年 7 月 July, 2011

(2)

(3)

(4)

(5)

Z & M 0 D I D K \ M N O 4 E \ 5 d M D \ c i

u v M e D G x 1 2 D a % T M P

Y n Ward Jeff 6 \ M A E

M o D a M P Y

i 2 V I = R ! I " # x D R

$ E F M P J B D 2 % & D a % T

M P Y

$ D ' l ( ) I * E M

+ O D Q D , l o - ^ . / 0 n > 1 2 3

4 5 6 I * 7 D I ! N " \ + O # _ a $ D %

& 8 9 : : 7 < = > ? @ ( A B C D e N

^ ' & d D d E M 4 F D ( M M G # I H : I J K

M N O b P Q ! M R 9 D G G d 8 9 M S Y T

) D U V W ] Y

T + D \ M # , M D \ X Y M Z $

= ! D 1 2 ! G \ D a " T ] M Y

i

(6)

ii _{@ L}

(7)

- .

1 2 3 4 5 6 7 8 9 : 5 < = 7 8 > ? @ A B C D E F G H I J K

L M N O P Q R S T U V M W X Y

Z \ ] E F ^ _ ` G a b c d ` e M 7 8 9 : f g h D 5 6 f g

h i M j ^ _ k l m n o p J q N r O D s ` t 7 8 9 : 5 < M T U

V u v w x ^ _ y z M { | R H } ~ @ J K (MINLP)H I u v D [ \

` G ] 7 8 9 : 5 < M T U V W X Y ^ _ ` H (1){ T | } 7 8 ~

D 6 ^ _ M A 3 M T U V g # D

^ _ ` H (1)M g D \ ] { ^ D c G E F ^ _ ` H (2)

{ j ^ 7 8 k l T | ' Y

[ D \ ] % E F 7 8 > ? $ f g h D 3 M 7 8 > ? @ A

D ^ _ ` H (3) { T = w @ A x 1 3 9 : g

h 6 @ A B C $ Y ' ^ _ ` H (4) 7 8 @ A N O ` G

] ^ _ ^ Y

T + \ ] ^ _ k M 7 8 9 : | x D ¡ 1 c E F $

H I ¢ z = f g h ` W X F U £ M 7 8 9 : W X 7 8 > ? @ A B

C ¤ ¥ h @ A ¦ § Y

iii

(8)

iv / 0

(9)

Abstract

This work aims to develop a mathematical model for the synthesis of refrigerated water network systems and chiller operating strategy simultaneously.

First of all, we proposed one model which includes all possible configurations of refrigerated water network system under all conditions. By setting relevant constraints up for each part of the superstructure, the design problem of refrigerated water network system is formulated as a mixed-integer nonlinear program that can be solved for optimal configuration of refrigerated water network. Objective functions 1 and 2 are considered which involving the mimnimization of refrigerated water supply and obtaining a unique network structure.

Furthermore we also proposed a superstructure for chillers’ operation, considering different operating upper and lower bounds. In this work, two objective functions are considered to minimize fixed and variable operating cost.

Finally, numerical examples are used to show that the proposed approach can provide the optimal design of refrigerated water network system and chiller operating strategy.

Key words: Optimization, Superstructure, Refrigerated Water Network Systems, Chiller,

Mixed-integer nonlinear programming (MINLP)

v

(10)

vi Abstract

(11)

ª « « !

[ \ . . . i

+ , . . . iii

Abstract . . . . v

¯ ° ± ². . . xi

¯ ³ ± ². . . xv

1 ´ µ 1 1.1 ¶ · . . . 1

1.2 c d e f g h i j f g k l m n o p q r s j t u . . . 4

1.3 # $ % & . . . 6

1.4 . / 0 l j 1 2 . . . 8

1.5 S T U V . . . 9

2 s t u v w x y z { | } ~ 11 2.1 q t u j . . . 11

2.2 q ! " # $ . . . 17

2.3 q % & t u . . . 18

2.4 q ' ( ) * d ) + , - . j / . (Indices, Sets, Parameter, and Variables) . . . 22

2.4.1 _ k l C D (Indices) . . . 22

2.4.2 0 | C D (Sets) . . . 23 vii

(12)

viii ¸ ¹ ¹ º

2.4.3 5 < m H (Parameters) . . . 24

2.4.4 5 < w H (Variables) . . . 25

2.5 f g h i & ' ( . . . 27

2.5.1 7 8 k l ' 1 / e 1 / . . . 27

2.5.2 5 2 ( 3 ' 1 / e 1 / . . . 29

2.5.3 i 2 ( 3 ' 1 / e 1 / (Water/energy Balance) . 30 2.5.4 ) ' 2 ( 3 ' 1 / e 1 / (Water/energy Balance) . 31 2.5.5 @ ' ' $ (Upper and Lower Bounds in the Flow Rate) . . . 32

2.6 P h i Q R S 2 T U & ' ( . . . 33

2.6.1 Re-use Separate Design$ a 4 O . . . 34

2.6.2 Re-use Separate Design with Inner Mains$ a 4 O . . . . 35

2.6.3 Re-use with Inter-Plant Mains$ a 4 O . . . 36

2.6.4 Re-use with Inter/Inner-Plant Mains$ a 4 O . . . 37

2.7 _{i j k l} (Objectives) . . . 38

2.7.1 ^ _ ` H (1)' T } 7 8 ~ (To Minimize Total Re- frigerated Water) . . . 39

2.7.2 ^ _ ` H (2)' j ^ 7 8 k l T | ' (To Mini- mize Throughput of RW Units) . . . 40

3 41 3.1 q t u j . . . 41

3.2 q ! " # $ . . . 43

3.3 q % & t u . . . 44

3.4 q ' ( ) * d ) + , - . j / . (Indices, Sets, Parameter, and Variables) . . . 46

3.5 f g k l & ' ( . . . 48

3.5.1 7 8 > ? ' 1 / . . . 48

3.5.2 7 8 > ? e 1 / . . . 49

(13)

¸ ¹ ¹ º ix

3.5.3 7 8 > ? ! 4 . . . 51

3.6 1 . (Objectives) . . . 52

3.6.1 ^ _ ` H (3)' T /w @ A x 1 (To Minimize Fixed/variable Operating Cost) . . . 53

3.6.2 ^ _ ` H (4)' j ^ 7 8 > ? T | ' (To Minimize Through- put of Chillers) . . . 54

4 s t u v s t z { ! " # $ % 57 4.1 & ' ( ) * . . . 58

4.2 + , - . / 0 1 , f g 2 3 4 5 q f g h i 6 . . . 58

4.3 f g k l d q f g e f g h c d q i j (without HI) . . . 61

4.3.1 @ A 0 { 0.5D @ A 0 { 1.0 . . . 64

4.3.2 @ A 0 { 0.75D @ A 0 { 1.0 . . . 73

4.3.3 @ A 0 { 1.0D @ A 0 { 1.0 . . . 77

4.4 f g k l d q f g f g h c d q i j (with HI) . . . 81

4.4.1 @ A 0 { 0.5D @ A 0 { 1.0 . . . 81

4.4.2 @ A 0 { 0.75D @ A 0 { 1.0 . . . 81

4.4.3 @ A 0 { 1.0D @ A 0 { 1.0 . . . 83

5 " µ ! ] ^ _ ` 91 5.1 _{Q a} . . . 91

5.2 b c s k . . . 92

l m n o. . . 95

(14)

x ¸ ¹ ¹ º

(15)

" # ª !

1.1 [ X Y 7 8 5 < (Recirculating Refrigerated Water System) . . . 3

1.2 7 8 > ? X Y . . . 4

1.3 7 8 9 : M W X , - (a) . W X D (b) / . W X . . . 5

2.1 Single Plant: Parallel Design . . . 12

2.2 Single Plant: Direct Design . . . 12

2.3 Single Plant: RW Mains Design . . . 12

2.4 Single Plant: Parallel Design . . . 13

2.5 Multiple Plant: Separate Design . . . 15

2.6 Multiple Plant: Separate Design with Inner Mains . . . 15

2.7 Multiple Plant: With Inter-Plant Main . . . 16

2.8 Multiple Plant: With Inter/Inner-Plant Mains . . . 16

2.9 7 8 9 : 5 < $ f g h . . . 18

2.10 7 8 9 : $ f g h (a) Using Unit (b) Supply Main . . . 20

2.11 7 8 9 : $ f g h (c) RW Main (d) Return Main . . . 21

2.12 7 8 k l P 5 M @ ' ' e 1 / 0 P 6 . . . . 27

2.13 7 8 k l 1 = M @ ' ' e 1 / 0 P 6 . . . 28

2.14 5 2 ( 3 k l P 5 M @ ' ' e 1 / 0 P 6 . . 29

2.15 i 2 ( 3 k l P 5 M @ ' ' e 1 / 0 P 6 . . 30

2.16 ) ' 2 ( 3 k l P 5 M @ ' ' e 1 / 0 P 6 . . 31

3.1 Single Chiller: Parallel Design . . . 42

3.2 Multiple Chillers: (a) two chillers (b) three chillers . . . 42

xi

(16)

xii ½ ¾ ¸ º

3.3 7 8 > ? $ f g h . . . 45

3.4 7 8 k l P 5 M @ ' ' e 1 / 0 P 6 . . . . 48

4.1 @ A { 0.5 1.0 $ 7 8 1 6 . . . 63

4.2 @ A { 0.75 1.0 $ 7 8 1 6 . . . 63

4.3 @ A { 1.0 1.0 $ 7 8 1 6 . . . 63

4.4 Base Case7 8 9 : 7 8 > ? @ A B C W X g . . . 64

4.5 Separate Design$ 9 : 7 8 > ? @ A B C W X g . . . 65

4.6 Separate Design with Inner Mains$ 9 : 7 8 > ? @ A B C W X g . . . 67

4.7 With Inter-Plant Main$ 9 : 7 8 > ? @ A B C W X g . . . 69

4.8 With Inter/Inner-Plant Mains$ 9 : 7 8 > ? @ A B C W X g 70 4.9 Base Case7 8 9 : 7 8 > ? @ A B C W X g . . . 73

4.13 With Inter/Inner-Plant Mains$ 9 : 7 8 > ? @ A B C W X g 75 4.14 Base Case7 8 9 : 7 8 > ? @ A B C W X g . . . 77

4.18 With Inter/Inner-Plant Mains$ 9 : 7 8 > ? @ A B C W X g 79 4.19 @ A 0 { 0.5 1.0 $ ¢ g . . . 82

4.20 @ A 0 { 0.75 1.0 $ ¢ g . . . 82

4.21 Base Case7 8 9 : 7 8 > ? @ A B C W X g . . . 84

(17)

½ ¾ ¸ º xiii

4.23 Separate Design with Inner Mains$ 9 : 7 8 > ? @ A B C W X

g . . . 86 4.24 With Inter-Plant Main$ 9 : 7 8 > ? @ A B C W X g . . . 87 4.25 With Inter/Inner-Plant Mains$ 9 : 7 8 > ? @ A B C W X g 88

(18)

xiv ½ ¾ ¸ º

(19)

" $ ª !

1.1 y z A 8 À (Rosain, 1993) . . . 2

2.1 7 8 9 : _ k l C D . . . 22

2.2 7 8 9 : 5 < 0 | . . . 23

2.3 7 8 9 : 5 < m H . . . 24

2.4 7 8 9 : 7 8 w H . . . 25

2.5 7 8 9 : 0-1^{w H} . . . 26

3.1 7 8 > ? 5 < m H . . . 46

3.2 7 8 > ? 7 8 w H . . . 47

3.3 7 8 > ? 0-1^{w H} . . . 47

4.1 c 1 $ m H . . . 59

4.2 A @ A 2 ` . . . 59

4.3 @ A 0 { 0.5 1.0 $ ^ _ ` H (1) g . . . 71

4.4 @ A 0 { 0.5 1.0 $ ^ _ ` H (3) (4) g . . . . 72

4.5 @ A 0 { 0.75 1.0 $ ^ _ ` H (3) (4) g . . . 76

4.6 @ A 0 { 1.0 1.0 $ ^ _ ` H (3) (4) g . . . . 80

4.7 \ R | 8 $ g . . . 89

xv

(20)

xvi ½ Á ¸ º

(21)

1

Â Ã

1.1

Ä Å

8 D Æ Ç ( ! È É Ê Ë { ) & M Ì Í D Î Ï Ð

Ñ À " Ò Ó 70%M Ô D Õ Ö È ( × 8 D e Ø Ù , Ú d Û

M D \ ] Ü Ý S Þ D 8 2 4 } G 5 6 c Þ { ( 7 $ 8 D

$ 9 M 2 4 Y Ï : D ; < = V $ > ? D Õ , @ Æ 8

Æ B C D 6 8 8 D = E @ $ 1 \ Æ F E D c G H I M K

8 u v L L M ! " # M I $ Y

6 8 M D % ` G { & _ Ö ' @ 8 ! 8 D :

+ Ò Ö M Y ( ( < ) ! Ç ( M * + ) ! D

8 M ) & @ È , Y ! D - { . d Ë @ G = / 0 D :

1 ` G ) 2 3 D c G 4 5 r 6 i 7 ( 8 9 M ^ _ : b D : <

r 6 i ` G É Ê = > b ? V @ D Y

1

(22)

2 ß à

* 1.1 y z A 8 À (Rosain, 1993)

Purpose Description Relative usage

RW/CW system Direct contact/indirect (HEs) High

Cleaning Washing, hygiene, Medium

rinsing for product quality

Process equipment Water circulation (e.g. scrubbers) Medium General plant services Hoses (dilute/disperse spills) Medium

Pump seal water

Steam system Boiler feed water make-up Medium/low Potable/sanitary Drinking, washing, toilets Low

â 1.1 [23]{ ! 8 M H 6 B D \ ] ` G C F D E 5 < 6

R _ A M H 6 ( H £ M Y : D E 5 < F Ô D E 8 5 <

(Cooling Water System)G = 7 8 5 < (Refrigerated Water System)D D E 8 (

G H M D E 5 < # : 1 ) 7 8 D - { I G H M D E

5 < A % ( H £ M J D K * + S ) ! Y : 7 8 M L

M ( H £ e M ^ _ r 6 D A M N O ^ ` G P H Q l R S D c

G £ } x 1 L L 4 D A T 7 8 9 : M W X U L L ) & D ^

M { 8 M T V W G = T M D P : P x x 1 T | V Y

: 1 ( 5 6 7 8 9 : 5 < G = 7 8 > ? M @ A B C G H I J K

L A T U V M Y [ X Y 7 8 5 < (Recirculating Refrigerated Water System)

M @ A D 7 8 É Ê Z \ M Ì Í D : t A i j _ 7 8 k l

M \ ] $ ^ _ D P : P x ` H M Û Y

(23)

1.1 ã ä 3

) 1.1 [ X Y 7 8 5 < (Recirculating Refrigerated Water System)

C1

C2

C3

C4

C5 RW Network

Source

RW Return

Wc RW Wc

M

1

Chiller(s)

a > & F Ô & _ 5 < D b æ 1.1 '

1. 7 8 9 : 5 < (Refrigerated Water Network)

2. 7 8 > ? M @ A B C (Chiller Operating Strategy)

(24)

4 ß à

1.2

v w x y z { | } y z ~ ¡ ¢ £ } ¤ ¥

3.1c 0 D 7 8 M ) ( ( < M D ª « ¬ ? X Y c L M M D 7 (

_ > & Ö c ® x D F ¯ « ¬ ° (Compression) D ± ° (Condensation)

² ³ ´ (Expansion Valve)= µ > ° (Evaporator)Y 7 8 > ? (chiller) s { \ ¶

· (heat pump)D D ± ° M H { H 6 H D : µ > ° M H { H 6 I H D c G a r 6 ( ^ _ ` ¸ > M 4 5 (Non- Spontaneous Process)D Ü Ý 6

a r 6 A ¹ D ! e a r 6 > Y º » M I « S « ¬ ? « ¬ D

B x H « M ' \ S # a 4 D ¼ D ± ° ^ _ Ö e + B x

« ½ S # : + ² ³ ' r i D « H M ½ D ¼ ' ² ³ ´ + B

x I « I H ½ ¾ ( M D ¼ # T + D ¼ ` G ¿ µ > ° Z r 6 E

M e x { I H I « S D : 7 8 U ( a n À ) M Y

) 1.2 7 8 > ? X Y

W^c

Compressor

Expansion Valve (adiabatic)

Condenser Evaporator

CW RW

low P 2-phase high P

liquid high P

vapor low P

vapor

(25)

1.2 Á Â Ã Ä Å Æ Ç È Ä Å É Ê Ë Ì Í Î Ï Ð Ñ È Ò Ó 5

) 1.3 7 8 9 : M W X , - (a) . W X D (b) / . W X

C2 C1

Series arrangements

Return to chiller Reuse refrigerated water C2

C1

Parallel arrangements

Return to chiller

X Y 7 8 9 : i D Ô M W X ( j ^ _ k l (C1,C2) Õ Ö .

(Parallel)M W X D b æ 1.3 c 0 Y

a W X i D j ^ _ k l È × Ø M 7 8 D : j ^ k l M

M Y

{ - 5 . W X c M x M Ý O u v D Kim Smith[2] / . (Series)

M N L W X D E 8 5 < (Cooling Water System)D : \ ] ` G Ú Þ M

ß à 5 W X 7 8 5 < M 9 : g h D / . M Ó à D × Ø M 7

8 E k l ^ (C1) D á ( k l ^ (C1) F M H â I k l ã

(C2)ä M T å H (Maximum Allowable Temperature)4 D \ ] ` G k l ã (C2) [ D b æ 1.3 D k ^ æ ' & ç : 1 è é & _

k l M 1 \ D b a ^ ` G ` I 7 8 D c G / . W X M ¦ §

D \ ] ` G U I M @ A = x 1 Y

(26)

6 ß à

1.3

ê ë ì í

8 D E 8 9 : W î W X ï ð i D d I E F C L D

H I 2 " ñ ò ó D : \ ] t 5 7 8 9 : W X D a ô õ ö F <

_ 1 2 d I M 2 " D m ^ ÷ b b '

Kim» Smith[28]Z ø ù 0 L (Pinch technology) 8 9 : W î M u v D : Kim» Smith 2001 [11]$ + P ^ n t a N L ú û D E 8 9 : 5 < D : t / . (Series) M W X N O ø D E ° 9 : 5 < W

X D / . M W X N O ` G D E 8 9 : 5 < ) ' D E 8 ' T

| D : ) ' D E 8 1 H T D 9 : M ¦ § D E ; P T M @

A Û < Y 2 i % á ) ' D E ; H d T H 4 4 D & b = )

× W î D E ° 9 : Y

Kim» Smith[12]$ + > 6 ^ _ W X 9 M D E 8 9 : 5 < D H I J K L M N O D o h ^ _ { | R H M } ~ @ H I ¢ O (MINLP)P Q W X g

h M ^ ? @ P D ` I D E 8 9 : M « A D 3 4 % C

E D E ; M Û < Y

Feng , [5]5 6 D E 8 9 : 5 < E ^ _ × M W X N L D U ( D E 9 : 5 < i i 2 ( 3 (intermediate cooling-water main)M ß à D

X M D E 8 9 : i D - { F ^ _ k l F 5 M ' H Ç H

^ d w V D U I J ^ _ k l ä 5 M ¦ § D P : ) @ A

M D : 5 < . d A M @ A K @ (operational flexibility)D {