10 Stage-wise Superstructure for Synthesis of Heat Exchange Networks.pdf

7/27/2019 10 Stage-wise Superstructure for Synthesis of Heat Exchange Networks.pdf

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Stage-wise Superstructure for Synthesis of

Heat Exchange Networks

Cheng-Liang Chen

PSELABORATORY

Department of Chemical EngineeringNational TAIWAN University

Chen CL 1

Heat Exchange Network Synthesis (HENS)

Given:

A set of hot process streams to be cooled, and

a set of cold process streams to be heated Available heating/cooling utilities

Inlet/outlet temperatures and

heat capacity flow rates for all streams and utilities

Area cost and fixed unit cost, utility costs

Determine: Network Configurations to

Minimize the total annual cost (TAC) Maximize operating flexibility (operating ranges ofT & F)

Chen CL 2

Heat Exchange Network Synthesis (HENS)Chen CL 3

Stage-wise Superstructure forHENSAll Possible Matches; Isothermal Mixing


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Chen CL 4

Stage-wise Superstructure for HENSOrder of Matches; Isothermal Mixing

Chen CL 5

Stage-wise Superstructure forHENSUtilities for Heating/Cooling; Isothermal Mixing

Chen CL 6

Modeling the Stage-wise SuperstructureIndices, Sets, Parameters

Indices and sets

i hot process stream

j cold process stream

k stage

hu hot utility

cu cold utility

in inlet

out outlet

Parameters

Tini , Touti , T

inj , T

outj inlet and outlet temperatures

EMAT minimum-approach tempe rature diff erence ,Tmin

F Ci, F Cj heat capacity flowrates

Uij, Ui,cu, Uhu,j overall heat transfer coefficients

Ccu, Chu per unit cost of cold and hot utility

CFij, CFi,cu, CFhu,j fixed charges for exchangers

CAij, CAi,cu, CAhu,j area cost coefficientsNOK total number of stages

upper bound for heat exchange

upper bound for temperature difference

ij, i,cu, hu,j exponent for area costs

Chen CL 7

Modeling the Stage-wise SuperstructureContinuous and Binary Variables

Positive variables

aijk , ai,cu, ahu,j areas for exchangers

tik temperature of hot streami at the temperature locationk

tjk temperature of hot streamj at the temperature location k

thijk temperature for part of hoti that is connected to cold j in stage k

tcijk temperature for part of coldj that is connected to hot i in stage k

dtijk temperature difference for match (ij)at the temperature location k

dtouti,cu temperature difference for match (i,cu)at the hot end of the heat exchanger

dtouthu,j temperature difference for match (hu,j)at the cold end of the heat exchanger

dthijk temperature difference for match (ij)at the hot end of the heat exchanger

dtcijk temperature difference for match (ij)at the cold end of the heat exchanger

qijk heat exchanged between hot steam i and cold steam j in stage k

qi,cu heat exchanged between hot steam i and cold utility

qhu,j heat exchanged between hot utility and cold steamj

rhijk split ratio of hoti that is connected to cold j in stage k

rcijk split ratio of coldj that is connected to hot i in stage k

Binary variables

zijk existence of a unit for the match(ij)in stage kzi,cu existence of a unit for the match(i,cu)

zhu,j existence of a unit for the match(hu,j)


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Chen CL 8

Modeling the Stage-wise SuperstructureOverall Heat Balance forHotStreams

jCP

kST

qijk +qi,cu = FCiTini T

outi

i HP (1)

iHP

kST qijk +qhu,j = FCj

T

out

j Tin

j j CP (2)

Chen CL 9

Modeling the Stage-wise SuperstructureOverall Heat Balance forColdStreams

jCP

kST

qijk +qi,cu = FCiTini T

outi

i HP (1)

iHP

kST qijk +qhu,j = FCj

T

out

j Tin

j j CP (2)

Chen CL 10

Modeling the Stage-wise SuperstructureStage-wise Heat Balance forHotStreams

jCP

qijk = FCi (tik ti,k+1) i HP,k ST (3)

iHP

qijk = FCj(tjk tj,k+1) j CP, k ST (4)

Chen CL 11

Modeling the Stage-wise SuperstructureStage-wise Heat Balance forColdStreams

jCP

qijk = FCi (tik ti,k+1) i HP,k ST (3)

iHP

qijk = FCj(tjk tj,k+1) j CP,k ST (4)


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Chen CL 12

Modeling the Stage-wise SuperstructureHotandColdUtility Loads

qhu,j = FCjToutj tj1

j CP (5)

qi,cu = FCi (ti,NOK+1 Touti ) i HP (6)

Chen CL 13

Modeling the Stage-wise SuperstructureAssignment of I/O Temperatures and Feasibility of Temperatures

ti1 = Tini i HP (7)

tj,NOK+1 = Tinj j CP (8)

dtini,cu = Touti T

incu i HP (9)

dtinhu,j = Tinhu T

outj j CP (10)

tik ti,k+1 i HP, k ST (11)

ti,NOK+1 Touti i HP (12)

tjk tj,k+1 j CP, k ST (13)

Toutj tj1 j CP (14)

Chen CL 14

Modeling the Stage-wise SuperstructureOther Constraints

Logical constraints

qijk zijk i HP,j CP,k ST (15)

qi,cu zi,cu i HP (16)

qhu,j zhu,j j CP (17)dtijk tik tjk + (1 zijk) i HP, j CP,k ST (18)

dtij,k+1 ti,k+1 tj,k+1+ (1 zijk) i HP,j CP,k ST (19)

dtouti,cu ti,NOK+1 Toutcu + (1 zi,cu) i HP (20)

dtouthu,j Tout

hu tj1+ (1 zhu,j) j CP (21)

Minimum approach-temperatures

dtijk EMAT i HP,j CP, k ST {NOK+ 1} (22)

dtouti,cu EMAT i HP (23)

dtouthu,j EMAT j CP (24)

Chen CL 15

Variable boundsTini tik T

outi i HP,k ST (25)

Toutj tjk Tin

j j CP,k ST (26)

qijk FCiTini T

outi

i HP,j CP, k ST (27)

qijk FCj Tout

j Tinj i HP,j CP, k ST (28)

qi,cu FCiTini Touti

i HP (29)

qhu,j FCjToutj T

inj

j CP (30)


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Chen CL 16

Modeling the Stage-wise SuperstructureObjective Function: TAC

TAC = iHP

jCP

kST

CFijzijk + iHP

CFi,cuzi,cu + jCP

CFhu,jzhu,j

+ iHP

jCP

kST

CAij(aijk)ijk +

iHP

CAi,cu (ai,cu)i,cu +

jCP

CAhu,j(ahu,j)hu,j

+ iHP

Ccuqi,cu + jCP

Chuqhu,j (31)

aijk = qijk

Uij LMTDijk(32)

LMTDijk = dtijk dtij,k+1

ln dtijk

dtij,k+1

(33)

dtijkdtij,k+1

dtijk +dtij,k+1

2

1/3(34) (Chen Approximation)

Chen CL 17

Modeling the Stage-wise SuperstructureMINLP Formulation: Isothermal Mixing

minx

TAC

x

zijk, zi,cu, zhu,j;

tik, tjk;dtijk, dtouti,cu, dt

outhu,j;

qijk, qi,cu, qhu,j

i HP,j CP,k ST

Chen CL 18

=

x

jCP

kST

qijk + qi,cu = F Ci

Tini Touti

iHP

kST

qijk + qhu,j = F Cj

Toutj T

inj

jCP

qijk = F Ci

tik ti,k+1

iHP

qijk = F Cj

tjk tj,k+1

qi,cu = F Ci

ti,NOK+1 T

outi

qhu,j = F Cj

Toutj tj1

ti1 = Tini tj,NOK+1 = T

outj

dt

in

i,cu = T

out

i

T

in

cu dt

in

hu,j = T

in

hu

T

out

jtik ti,k+1 ti,NOK+1 T

outi

tjk tj,k+1 Toutj tj1

qijk zijk , qi,cu zi,cu, qhu,j zhu,j

dtijk tik tjk + (1 zijk )

dtij,k+1 ti,k+1 tj,k+1+ (1 zijk )

dtouti,cu ti,NOK+1 Toutcu +

1 zi,cu

dtouthu,j Touthu tj1+

1 zhu,j

dtijk EMAT, dt

outi,cu, dt

outhu,j EMAT

Tini tik Touti

T

out

j tjk T

in

jqijk , qi,cu F Ci

Tini T

outi

qijk , qhu,j F Cj

Toutj T

inj

i HP,j CP,k ST

Chen CL 19

Simultaneous Optimization Model forHeat Exchanger Network SynthesisOne Problem with 2-Hot-2-ColdStreams

Stream Tin Tout FCp (kW/K) h (KW/m2K) Cost ($/KW-yr)

H1 650 370 10.0 1.0 -

H2 590 370 20.0 1.0 -

C1 410 650 15.0 1.0 -

C2 353 500 13.0 1.0 -

S1 680 680 5.0 80

W1 300 320 1.0 15

AssumeTmin= 10K, Exchanger cost= $5500 + 150A(area, m2)


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Chen CL 20

HENS: Simultaneous OptimizationOptimal Network Structure

155, 000/yr total cost

(71, 400 for utility cost and 83, 600for capital cost)

Chen CL 21

SimultaneousMINLPModel: Example

FCp (kW/K) Tin (K) Tout (K) h(kW/m2K) Cost ($/kW-yr)

H1 22. 440 350 2.0 -

C1 20. 349 430 2.0 -

C2 7.5 320 368 .67 -

S1 500 500 1.0 120

W1 300 320 1.0 20

Min recovery app temp = 1 KExchanger Cost= 6, 600 + 670(area)0.83

Chen CL 22 Chen CL 23

SimultaneousMINLP Model: SameExample with No Stream Splitting

Ch CL 24


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Chen CL 24

Thank You for Your Attention

Questions Are Welcome

10 Stage-wise Superstructure for Synthesis of Heat Exchange Networks.pdf

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