Improving Energy Recovery in Heat Exchanger
Networks with Intensified Heat Transfer
Ming Pan, Igor Bulatov, Robin Smith
Centre for Process Integration © 2010
Outline
1. UNIMAN activities in the project
2. Introduction
3. Modelling of shell-and-tube heat exchangers
4. Modelling of intensified heat transfer
5. Optimization of retrofitting heat exchanger
networks with intensified heat transfer
6. Conclusions and future work
Centre for Process Integration © 2010
1. UNIMAN Activities in the Project
Centre for Process Integration © 2010
UNIMAN person-months and WPs
Activity type
1
PIL
2
CALGAVIN
3
SO
DR
U
Total
4
MAKATEC
5
OIKO
S
6
UNIMAN
7
UNIBATH
8
UPB
9
UNIPAN
10
EMBAFFLE
RTD/Innovation activities
WP1
1.5
4
2.5
0
0
3
14
2
6
0
33
WP2
1.5
4
2.5
0
0
14
1
0
1
0.5
24.5
WP3
0
0
0
11
0
0
0
20
0
0
31
WP4
2
3
2.5
0
0
11
9
4
9.5
0.5
41.5
Total
Research
5
11
7.5
11
0
28
24
26
16.5
1
130
Demonstration activities
WP5
2
2
2.5
4
5
4
4
8
5
0.5
37
Total Demo
2
2
2.5
4
5
4
4
8
5
0.5
37
Consortium Management activities
Total
Management
6
6
Other activities
WP6
0
2
1.5
0
3
3
4
0
5.5
0
19
Total other
0
2
1.5
0
3
4
4
0
4
0
18.5
13
15
11.5
15
8
35
32
34
27
Total
Centre for Process Integration © 2010
1.5
192
UNIMAN in WP1
Task 1.1. Experimental fouling investigation
Collaboration with UNIBATH, CALGAVIN, PIL, UPB on kinetics of fouling
and incorporation of the data into the models being developed
Centre for Process Integration © 2010
UNIMAN in WP2
Task 2.1. Heat transfer enhancement for the tube-side of heat exchangers
Collaboration with UNIBATH, CALGAVIN on network aspects of heat
transfer intensification
Task 2.2. Heat transfer enhancement for the shell-side of heat
Collaboration with EMbaffle, UNIBATH on network aspects of heat transfer
intensification
Centre for Process Integration © 2010
UNIMAN is WP4 leader
WP
Numb
er
WP4
WP Title
Design, retrofit and control of
intensified heat recovery
networks
Type
of
activit
y
Lead
Perso
Start
End
beneficia
nmonth month
ry
month
number
s
RTD
6UNIMAN
41.5
12
24
Task 4.1. Development of a streamlined and computationally efficient
methodology for design of HENs – work started
Collaboration with UNIPAN on incorporation of P-graph and Accelerated
Branch-and-Bound algorithms for HEN retrofit
Centre for Process Integration © 2010
UNIMAN in WP6
Task 6.2. Dissemination events
PRES’11 conference presentation and Chemical Engineering Transactions
publication
Centre for Process Integration © 2010
2. Introduction
Centre for Process Integration © 2010
Heat exchanger network (HEN)
H1
H2
H3
C1
C2
C3
C4
• Models used for units in heat- exchanger network (HEN) are very simple
Q  U  A  TLM  FT
Specified overall U
Assumed as 1
No details of geometry, just overall area
• HEN design neglects the heat-exchanger details
• No account of pressure drops
Not suitable for many retrofit applications
Centre for Process Integration © 2010
HEN retrofit
Need an approach for retrofit
• Account for detailed performance of heat exchangers
• Implement intensified heat transfer techniques to
suitable heat exchangers
• Allow new heat exchanger installation
• Maximize total energy saving with less network
structure modifications
Centre for Process Integration © 2010
Research objectives
 Develop a simple but accurate model for
heat-exchanger details
 Propose correlations for heat transfer
enhancement
 Develop a design method suitable for HEN
retrofit with heat transfer enhancement
Centre for Process Integration © 2010
3. Modelling of shell-and-tube heat exchangers
Centre for Process Integration © 2010
Heat exchangers
 Double pipe (DPHEX)
two pairs of concentric pipes,
counter flow
- the simplest type
 Shell and tube (STHEX)
a bundle of tubes in a cylindrical shell,
combining parallel and counter flows
- the most widely used type in the
chemical industries
 Plate and frame (PFHEX)
metal plates are used to separate and
transfer heat between two fluids
- the common typed in the food and
pharmaceutical industries
Centre for Process Integration © 2010
Modelling requirements for STHEX
Model Input:
 Tube side
tube number (nt), tube passes (np), tube length (L), tube inner diameter (Di) …
 Shell side
tube pitch (PT), tube pattern, tube outer diameter (D0), shell inner diameter
(Ds), baffle spacing (B), baffle cut (Bc), nozzle inner diameter (Dn), shellbundle clearance (Lsb), number of baffles (nb), number of shell (Ns) …
 Stream properties
flow rate (m), density (ρ), thermal conductivity (k), specific heat (Cp),
viscosity (μ), inlet temperature (Tinlet) …
Model Output:
Heat transfer coefficients (h), pressure drops (∆P), heat transfer
area (A), stream outlet temperatures (Toutlet)
Centre for Process Integration © 2010
Main correlations of STHEX
Tube-side heat transfer coefficient (hi): (Based on Bhatti and Shah, 1987)
0.024 Re i 0 .8 Pri 0 .4
Nui  
0 .8
0 .4
0
.
023
Re
Pr
i
i

hi  ki / Di  Nui
for heating
for cooling
Tube-side pressure drop (∆Pi): (Adopt existing method of Serth, 2007) 2
n p f i L i vi
0.2585
Pfi 
f i  0.4137 Re i
2 g c Di
Shell-side heat transfer coefficient (h0): (Based on Ayub, 2005)
0.765Fs k02 / 3 C p 0 0
0.6633
0.5053
Fz  0 D0vh 0 0
Fs  34.4783Fz
Bc
h0 
D0
Shell-side pressure drop (∆P0): (Develop existing method of Serth, 2007)



1/ 3

f1  0.0076  0.00653543Ds  Re 0 0.125
f 2  0.0016  2.2835 10 3 Ds Re 0 0.157
f 0  144[ f1 1.25(1 B / Ds )( f1
Pfb, 20% Bc 
f 2 )]
f 0 Ds  v
2
0 p0
2 g c De
Pf 0  Pf 0, 20% Bc ( Bc / B20% )n1
Bhatti, M. S., and R. K. Shah, Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, Chap. 4, 1987.
Serth, R. W., Process heat transfer principles and applications, Elsevier Ltd, 2007.
Ayub, Z. H., Applied Thermal Engineering, 25, 2412-2420, 2005.
Centre for Process Integration © 2010
Procedure of the new model
Input stream and geometry parameters of heat exchanger:
Thot, in, Tcold, in, Cphot, Cpcold,μhot,μcold, L, D0, ….
Calculate tubeside (∆Pi).
Plain tube
correlations
Calculate tubeside (hi).
Dittus-Boelter
correlation
Calculate shell- Calculate shell-side
side (h0).
(∆P0).
Chart
Simplified
method
Delaware method
Calculate overall heat transfer coefficient.
Assume hot stream outlet temperature (Thot, out).
Calculate cold stream outlet temperature (Tcold, out).
Calculate LMTD, LMTD correction factor (F), and heat-transfer area
based on tubes (A).
Calculate overall heat transfer area with U.
Yes
No
IA – A I ≤ ε
’
Stop
Centre for Process Integration © 2010
Examples
Ten examples are considered for model validation:
Heat exchanger geometry:
Tube: 124 ~ 3983 Tube passes: 2 ~ 6 Tube length: 2.4 m ~ 9 m
Tube diameter: 15 mm ~ 25 mm Tube pattern: 30º, 45º, 60º, 90º
Shell diameter: 0.489 m ~ 1.9 m Baffle spacing: 0.0978 m ~ 0.5 m
Baffle cut: 20% ~ 40% ……..
Stream Properties:
Specific heat (J/kg▪K): 642 ~ 4179
Thermal conductivity (W/m▪K): 0.08 ~ 0.137
Viscosity (mPa▪s): 0.17 ~ 18.93
Density (kg/m3): 635 ~ 1000
Centre for Process Integration © 2010
Details of examples
Example 1
Shell-side
Tube-side
Example 2
Shell-side
Tube-side
Example 3
Shell-side
Tube-side
Example 4
Shell-side
Example 5
Tube-side
Shell-side
Tube-side
Streams
Specific heat CP (J/kg·K)
2135
2428
4272
642
4179
4179
2470
2052
2273
2303
Thermal conductivity k (W/m·K)
0.123
0.106
0.685
0.085
0.633
0.623
0.137
0.133
0.08
0.0899
2.89
1.2
0.17
0.20
0.62
0.71
0.40
3.60
18.93
0.935
820
790
910
635
991
994
785
850
966
791
75.22
19.15
16.11
109.47
192.72
385.4
5.675
18.917
46.25
202.54
51.7
210.0
150.0
207.0
48.0
33.0
200.0
38.0
227.0
131.0
0.00035
0.00035
0.0001
0.0005
0.0007
0.0004
0.00035
0.00053
0.00176
0.00053
Viscosity μ (mPa·s)
3
Density ρ (kg/m )
Flow rate mi (kg/s)
Inlet temperature Tin (°C)
2
Fouling resistance (m ·K/W)
Geometry of heat exchanger
Tube pitch PT (m)
Number of tubes nt
Number of tube passes np
0.0254
0.032
0.025
0.03175
0.03125
528
296
3983
124
612
6
2
2
4
2
Tube length L (m)
5.422
2.4
9
4.27
6
Tube effective length Leff (m)
5.219
2.24
8.821
4.17
5.903
Tube inner diameter Di (m)
0.0148
0.02
0.015
0.0212
0.02
Tube outer diameter D0 (m)
0.0191
0.025
0.019
0.0254
0.025
Shell inner diameter Ds (m)
0.771
0.7
1.9
0.489
0.965
Number of baffles nb
18
15
16
41
25
Baffle spacing B (m)
0.2584
0.14
0.5
0.0978
0.22
Inlet baffle spacing Bin (m)
0.4132
0.14
0.66
0.127
0.3117
Outlet baffle spacing Bout (m)
0.4132
0.14
0.66
0.127
0.3117
22%
20%
25%
20%
20%
Inner diameter of tube-side inlet nozzle Di,inlet (m)
0.128
0.3
0.438
0.1023
0.336
Inner diameter of tube-side outlet nozzle Di,outlet (m)
0.128
0.3
0.438
0.1023
0.336
Inner diameter of shell-side inlet nozzle D0,inlet (m)
0.259
0.15
0.337
0.0779
0.154
Inner diameter of shell-side outlet nozzle D0,outlet (m)
0.259
0.25
0.337
0.0779
0.154
Shell-bundle diametric clearance Lsb (m)
0.074
0.074
0.023
0.059
0.069
Baffle cut Bc
Centre for Process Integration © 2010
Details of examples (continued)
Example 6
Shell-side
Tube-side
Example 7
Shell-side
Tube-side
Example 8
Shell-side
Tube-side
Example 9
Shell-side
Tube-side
Example 10
Shell-side
Tube-side
Streams
Specific heat CP (J/kg·K)
2477
2503
2505
1993
2512
2240
2555
2265
2430
4223
Thermal conductivity k (W/m·K)
0.076
0.08
0.093
0.103
0.089
0.091
0.083
0.091
0.0865
0.6749
4.53
0.67
0.26
3.76
0.33
1.1
0.5
1.05
1.8
0.296
937
748
662
846
702
801
743
798
786
957
Flow rate mi (kg/s)
32.24
130.288
71.3
202.54
76.92
405.1
17.657
202.542
60.23
23.9
Inlet temperature Tin (°C)
293.0
196.0
194.0
44.0
227.0
112.0
265.0
121.0
170.0
77.0
0.00176
0.00088
0.00053
0.00053
0.00053
0.00053
0.00053
0.00053
0.00088
0.00053
Viscosity μ (mPa·s)
3
Density ρ (kg/m )
2
Fouling resistance (m ·K/W)
Geometry of heat exchanger
Tube pitch PT (m)
Number of tubes nt
Number of tube passes np
Tube length L (m)
Tube effective length Leff (m)
0.03125
0.03125
0.03125
0.03125
0.025
538
650
1532
407
582
2
2
2
2
4
6
5.7
9
5.5
7.1
5.9
5.6
8.85
5.45
7.062
Tube inner diameter Di (m)
0.021
0.02
0.02
0.021
0.015
Tube outer diameter D0 (m)
0.025
0.025
0.025
0.025
0.019
Shell inner diameter Ds (m)
0.914
1.1
1.5
0.9
0.8
Number of baffles nb
24
14
17
29
20
Baffle spacing B (m)
0.232
0.35
0.489
0.18
0.33
Inlet baffle spacing Bin (m)
0.286
0.5227
0.539
0.205
0.4
Outlet baffle spacing Bout (m)
0.286
0.5227
0.539
0.205
0.4
Baffle cut Bc
20%
24.4%
38%
20%
40%
Inner diameter of tube-side inlet nozzle Di,inlet (m)
0.3048
0.3
0.337
0.337
0.154
Inner diameter of tube-side outlet nozzle Di,outlet (m)
0.3048
0.3
0.337
0.337
0.154
Inner diameter of shell-side inlet nozzle D0,inlet (m)
0.1541
0.3
0.255
0.102
0.203
Inner diameter of shell-side outlet nozzle D0,outlet (m)
0.1541
0.3
0.255
0.102
0.203
0.068
0.082
0.071
0.067
0.066
Shell-bundle diametric clearance Lsb (m)
Centre for Process Integration © 2010
Results – Example 1
Tube-side
Shell-side
Tube-side heat
Shell-side heat
Overall heat
Example 1
pressure drop pressure drop transfer coefficient transfer coefficient transfer coefficient
(kPa)
(kPa)
(W/(m2·K))
(W/(m2·K))
U (W/(m2·K))
Bell model (Bell, 1991)
78.8
83.6
1266.2
1260.5
375.3
Smith model (Smith, 2005)
78.7
90.6
1117.3
1215.7
354.9
Serna model (Serna, 2004)
78.8
83.6
1270.1
1372.8
385.1
New Model
87.8
92.7
1393.8
1471.1
408.7
HTRI
86.8
97.7
1470.0
1534.0
422.0
HEXTRAN
84.9
99.4
1117.2
1434.1
371.5
● Existing models give lower heat transfer coefficients and pressure drops
than HTRI®
● Good agreement between new model and HTRI ®
Bell, K. J., Process Heat Transfer Course Notes, School of Chemical Engineering, Oklahoma State University, Stillwater,
Oklahoma, 1991.
Smith, R, Chemical Process design and integration, John Wiley & Sons Ltd, 2005.
Serna, M., and Jiménez, A., An Efficient Method for the Design of Shell and Tube Heat Exchangers, Heat Transfer
Engineering, 25: 2, 5-16, 2004.
Centre for Process Integration © 2010
Results (New model vs. HTRI/HEXTRAN)
Pi (kPa)
hi (W/m2.K)
90º
tube pattern
100
8000
HTRI
HEXTRAN
HTRI
90
7000
HEXTRAN
80
Heat transfer
coefficient (hi)
Pressure drop (Pi)
HTRI / HEXTRAN
Tube-side:
HTRI / HEXTRAN
6000
5000
4000
3000
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
New m odel
5000
6000
7000
8000
0
20
40
New m odel
9000
100
100
HTRI
HEXTRAN
HTRI
8000
90
7000
80
6000
HTRI / HEXTRAN
HTRI / HEXTRAN
Heat transfer
coefficient (h0)
Pressure drop (P0)
80
P0 (kPa)
h0 (W/m2.K)
Shell-side:
60
5000
4000
3000
HEXTRAN
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
5000
New m odel
6000
7000
8000
9000
0
20
40
New m odel
60
80
100
Centre for Process Integration © 2010
Results (New model vs. HTRI/HEXTRAN)
Pi (kPa)
hi (W/m2.K)
60º
tube pattern
HEXTRAN
HTRI
90
80
5000
4000
3000
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
New m odel
5000
6000
7000
0
8000
20
40
New m odel
9000
Shell-side:
80
100
80
100
100
HTRI
HEXTRAN
HTRI
8000
90
7000
80
6000
HTRI / HEXTRAN
HTRI / HEXTRAN
60
P0 (kPa)
h0 (W/m2.K)
Heat transfer
coefficient (h0)
Pressure drop (P0)
HEXTRAN
6000
HTRI / HEXTRAN
Heat transfer
coefficient (hi)
Pressure drop (Pi)
HTRI
7000
HTRI / HEXTRAN
Tube-side:
100
8000
5000
4000
3000
HEXTRAN
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
5000
New m odel
6000
7000
8000
9000
0
20
40
New m odel
60
Centre for Process Integration © 2010
Results (New model vs. HTRI/HEXTRAN)
Pi (kPa)
hi (W/m2.K)
45º
tube pattern
HEXTRAN
HTRI
90
80
5000
4000
3000
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
New m odel
5000
6000
7000
0
8000
20
40
New m odel
9000
Shell-side:
80
100
80
100
100
HTRI
HEXTRAN
HTRI
8000
90
7000
80
6000
HTRI / HEXTRAN
HTRI / HEXTRAN
60
P0 (kPa)
h0 (W/m2.K)
Heat transfer
coefficient (h0)
Pressure drop (P0)
HEXTRAN
6000
HTRI / HEXTRAN
Heat transfer
coefficient (hi)
Pressure drop (Pi)
HTRI
7000
HTRI / HEXTRAN
Tube-side:
100
8000
5000
4000
3000
HEXTRAN
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
5000
New m odel
6000
7000
8000
9000
0
20
40
New m odel
60
Centre for Process Integration © 2010
Results (New model vs. HTRI/HEXTRAN)
Pi (kPa)
hi (W/m2.K)
30º
tube pattern
HEXTRAN
HTRI
90
80
5000
4000
3000
70
60
50
40
30
2000
20
1000
10
0
0
0
1000
2000
3000
4000
New m odel
5000
6000
7000
0
8000
20
40
New m odel
8000
Shell-side:
60
80
100
80
100
P0 (kPa)
h0 (W/m2.K)
100
HTRI
HEXTRAN
HTRI
HEXTRAN
90
7000
80
HTRI / HEXTRAN
6000
HTRI / HEXTRAN
Heat transfer
coefficient (h0)
Pressure drop (P0)
HEXTRAN
6000
HTRI / HEXTRAN
Heat transfer
coefficient (hi)
Pressure drop (Pi)
HTRI
7000
HTRI / HEXTRAN
Tube-side:
100
8000
5000
4000
3000
70
60
50
40
30
2000
20
1000
10
0
0
0
L04 – 28
1000
2000
3000
4000
New m odel
5000
6000
7000
8000
0
20
40
New m odel
Modelling of Intensified Heat Transfer for the Retrofit of Heat Exchanger Networks
60
Centre for Process Integration © 2010
Modelling of heat exchanger
The new model:
 Fewer equations and empirical factors
(compared with the existing models)
 Reliable estimation for heat transfer coefficients and pressure
drops (compared with HTRI® and HEXTRAN®)
Limits:
 No phase change
 Phase change will be considered in future work
Centre for Process Integration © 2010
4. Modelling of intensified heat transfer
Centre for Process Integration © 2010
Intensified heat transfer techniques
Tube-side:
Twisted-tape inserts, which cause
spiral flow along the tube length
to increase turbulence
Coiled wire inserts, which consist
of a helical coiled spring and
function as non-integral roughness
hiTRAN®, which consist of a wire
mesh with different densities. They
are usually used to improve the heat
transfer coefficient for the laminar
regime
Centre for Process Integration © 2010
Intensified heat transfer techniques
Shell-side:
Helical Baffles®, which reduce the
number of dead spots created by
segmented baffle design, where no
heat transfer occurs between the
tube-side and shell-side fluids
EM Baffles®, which employs
expanded metal baffles (tube
supports) made of plate material
that has been slit and expanded.
The open structure allows a
longitudinal flow pattern and results
in lower hydraulic resistance, so
that flow induced tube vibration will
not occur.
Centre for Process Integration © 2010
Modelling of twisted-tape inserts
Laminar region
Nu  4.6126.413 10

f
Re sw
9
Sw Pr
2t
 2
Di
 15.767
4t

Di

0.391 3.385
2
Nu  0.023 Re
Pr

  w 
0.8
4t
Di
2t


2
1.75
Di
0.079 
f 
4t
Re 0.25  4t

Di
Di
2t
 2
Di
4t

Di
Sw 
Re
y
y  H / Di
Re Sw  vs Di / 
6

0. 4
0.2
(1  10 Sw 2.55 )1/ 6
Turbulent region
0.8


0.2
  w 
1.25
H: 180º twist pitch of
twisted tape
t : thickness of tapes
μ: viscosity
Di: tube inner diameter
(1  2.752 / y1.29 )
Bergles A.E. and Manglik R.M. ASME Journal of Heat Transfer, 1993.
Centre for Process Integration © 2010
Modelling of coil-wire inserts
Laminar region
NuDv  1.65 tan  Re mDv Pr 0.35 (  /  w ) 0.14
f  16 / Re
Re Dv  vDv / 
0.38
Re  vDi / 
Turbulent region
Nua  0.303(e / Di )0.12 ( p / Di )
f a  9.35( p / e)
m  0.25(tan  )
1.16
Re
0.217
0.377
Re 0.72 Pr 0.37
α: insert angle
Dv: hydraulic diameter,
4x(free volume/wetted
surface)
μ: viscosity
Di: tube inner diameter
e: wire diameter
p: helical pitch
Uttarwar S.B. and Raja Rao M. ASME Journal of heat transfer, 1985.
Garcia A., Vicente P.G. and Viedma A. Experimental study of heat transfer enhancement with wire coil inserts in laminartransition-turbulent regimes at different Prandtl numbers. Elsevier Ltd, 2004.
Centre for Process Integration © 2010
Modelling of hiTRAN®
MAXHTC : heat transfer coefficient for the highest density of hiTRAN;
MINHTC : heat transfer coefficient for the lowest density of hiTRAN
Re = Di vρ / μ
MAXHTC = f1(k,Di ,Pr,Re)
Pr = Cpμ / k
MINHTC = f2 (k,Di,Pr,Re)
MAX∆P : pressure drop for the highest density of hiTRAN;
MIN∆P : pressure drop for the lowest density of hiTRAN
MAXΔP = f3 (np ,L, ρ, v,Di ,Re)
MAXΔP = f4 (np ,L,ρ, v,Di ,Re)
f1( ) , f2 ( ), f3 ( ) and f4 ( ): relative correlations for heat transfer coefficients
and pressure drops
k: conductivity, Di: tube inner diameter, v: tube-side velocity, μ: viscosity, ρ: density,
Cp: specific heat, np: tube passes, L: tube length
Centre for Process Integration © 2010
Modelling of hiTRAN®
Compared with hiTRAN.SP® (software programming supplied by Cal
Gavin Ltd.), the new correlations can predict accurate:
 Heat transfer coefficients of the highest and
lowest density of hiTRAN
 Pressure drops of the highest and lowest
density of hiTRAN
L04 – 40
Modelling of Intensified Heat Transfer for the Retrofit of Heat Exchanger Networks
Centre for Process Integration © 2010
Modelling of helical baffles
2 f s N t L s vs2
Ps 
B
hs  k / D0  Nus
Re s  uD0 / vs
Baffle type
Segmental baffles
Helical baffles, β = 20º
Helical baffles, β = 30º
Helical baffles, β = 40º
Helical baffles, β = 50º
Nus  A Re sB Prs1/ 3
A
0.706
0.275
0.365
0.455
0.326
B
0.474
0.542
0.516
0.488
0.512
C
25.1
11.0
13.5
34.7
47.9
B  2Ds tan 
f s  C Re sD
D
Deviations of Nu Deviations of fs
-0.692
6.29%
4.42%
-0.715
3.66%
4.91%
-0.774
3.65%
2.32%
-0.806
2.76%
3.63%
-0.849
1.20%
4.19%
k: conductivity, Do: tube outer diameter, Nt: number of tube rows, L: tube length,
ρ: density, Ds: shell inner diameter, β: helical angle
Zhang, J. F., Experimental performance comparison of shell-side heat transfer for shell and tube heat exchangers with
middle-overlapped helical baffles and segmental baffles. Elsevier Ltd, 2008.
Centre for Process Integration © 2010
Modelling of helical baffles
Example 1 (from Section 2):
Baffle type
Heat transfer coefficient (W/m2•K) Pressure drop (kPa)
Segmental baffles
1471.1
92.7
Helical baffles, β = 20º
1254.6
100.2
Helical baffles, β = 30º
1294.1
43.8
Helical baffles, β = 40º
1229.6
56.7
Helical baffles, β = 50º
1111.8
36.3
Helical baffles:
 High heat transfer coefficients in shell side
 Lower pressure drops in shell side
Centre for Process Integration © 2010
5. HEN retrofit with intensified heat transfer
Centre for Process Integration © 2010
Existing design methods for HEN retrofit
Limits:
 Large scale problems
 Heuristic rules
 No pressure drop restrictions
 No account of exchanger geometry modifications
 Lots of topology modifications
 Too much repiping work
Centre for Process Integration © 2010
New model for HEN retrofit (MINLP)
Energy balance:
Fh  Cph (Th Th)  Fc  Cpc (Tc Tc )
Heat transfer:
Fh  Cph (Th Th)  A  U  ln T  FT
Heat transfer coefficients:

FR , T
hi  f i h FRi , Ti ave , inserts
h0  f 0h
ave
0
0
, Bs


Pressure drops:

FR , T
Pi  f i p FRi , Ti ave ,  inserts, L
P0  f 0p
0
ave
0
, Bs , L


Overall heat transfer coefficient:
U 1  hi1  h01
……
Objective: maximizing energy saving
Fh / Fc: flow-rates of hot / cold streams,
Cph / Cpc: specific heats of hot / cold
streams,
Th / Tc: inlet temperatures of hot / cold
streams,
T’h / T’c: outlet temperatures of hot /
cold streams,
A: heat transfer area of exchanger,
U: overall heat transfer coefficient,
ln∆T: logarithmic mean temperature,
FT: ln∆T correction factor
hi: tube-side heat transfer coefficient,
h0: shell-side heat transfer coefficient,
∆Pi: tube-side pressure drop,
∆P0: shell-side pressure drop,
FRi / FR0: flow-rates in tube / shell side,
L: exchanger length,
Bs: baffle spacing,
ρinsert: density of tube inserts,
Tavei / Tave0: average temperatures in
tube / shell sides,
Centre for Process Integration © 2010
Optimization procedure
Assume an initial small value
of energy saving (QS’)
Input initial values for variables
Linearize nonlinear terms in MINLP
model
MILP model of HEN retrofit
Solve the MILP problem
If the MILP problem is
infeasible
Yes
Stop
No
Obtain new values of variables
Calculate variable differences
Replace LMTD’ex and the
initial value of variables
No
If the above differences
are small enough
Yes
Obtain the new energy saving (QS)
Gradually increase QS’ (QS’ > QS)
Centre for Process Integration © 2010
Case 1
S1
432K
540K
S2
△P
4
△P
2
1
△P
= 250 kPa
Max
△P
= 100 kPa
Max
△P
= 150 kPa
299K
S4
391K
S5
3
2
H
= 100 kPa
Max
363K
538K
Max
350K
C2
400K
= 50 kPa
C1
353K
616K
S3
Max
3
5
1
5
4
Stream specific heats: C p  A  T ave  B (kJ/kg·K)
Parameters
A
B
S1
0.020496
-3.2134
Streams
S3
0.007353
-1.09726
S2
0.005245
-0.34088
S4
0.012733
-1.45068
S5
0.011106
-1.15692
Stream flow rate (kg/s)
S1
47.6
S2
10.2
S3
21.5
S4
31.1
S5
49
Centre for Process Integration © 2010
Case 1
Tube-side heat transfer coefficients (kW/m2·K)
Without tube inserts:
Parameters
1
80.13
A
1
i
h
2
36.82
0.4
i
 A  FR
3
27.73
Exchangers
4
5
100.8 70.31
With tube inserts: hi1  A  FRi0.6  e
Parameters
1
2936
A
2
1037
3
1005
e
0.007Tiave
0.007Tiave
Exchangers
4
5
2238 2549
C1
61.24
C2
89.95
H
315
C2
2522
H
10056
1.0392
 inserts
C1
2403
Shell-side heat transfer coefficients (kW/m2·K)
1
0
h
0.35
0
 A  FR
Parameters
A
1
340.7
e
0.006T0ave
2
131.1
 Bs1.4444
3
242.3
Exchangers
4
5
105.3 148.9
C1
80.2
C2
241.3
H
8887.7
Centre for Process Integration © 2010
Case 1
Tube-side pressure drops (kPa)
Without tube inserts: Pi  A  FR
1.7415
i
Parameters
A
1
0.02958
2
0.3869
3
0.1187
e
0.003Tiave
L
Exchangers
4
5
0.6946 0.0187
C1
0.0179
C2
0.0221
H
0.052

2
With tube inserts: Pi  A  FRi1.85  e 0.003Ti  L  2072.73  33.82  inserts  inserts
ave
Parameters
-5
A (×10 )
1
1.902
2
28.455
3
6.821
Exchangers
4
5
52.579 1.068
C1
0.9791
C2
1.676

H
3.165
Shell-side pressure drops (kPa)
Pi  A  FR
1.322
i
Parameters
A
e
0.0045Tiave
1
25.855

 L  0.179  0.041 Bs  Bs2
2
14.622
3
5.183
Exchangers
4
5
83.426 5.638

C1
8.31
C2
63.9
H
125.5
Centre for Process Integration © 2010
Case 1
Initial HEN:
S1
432K
419.1K
5
540K
S2
439.3K
4
616K
S3
449.2K
1
Total
△P
3
△P
= 20.1 kPa
= 67.0 kPa
538K 478.7K
H
13053 kW
4
Fx = 0.6276
2
411.9K
1
9441 kW 350K
Total
C1
1420 kW 353K
Total
C2
△P
= 101.5 kPa
△P
= 73.6 kPa
△P
= 48.1 kPa
363K
2
400K
Total
3
394.9K
5
Total
299K
S4
391K
S5
Fx = 0.1817
Retrofitted HEN:
6054 kW 350K
S1
Total △P = 233.0 kPa
C1
3
5
1268 kW 353K
540K
432 K
Total △P = 91.0 kPa
S2
C2
4
By pass (Fx) = 0.3056
616K
432.1K
363K
S3
1
Total △P = 111.1 kPa
2
Fx = 0.6811
299K
3
400K
S4
2
391K
538K 495.6K
427K
H
S5
5
1
4
Fx = 0.1819
9521 kW
Centre for Process Integration © 2010
432K
EX
Enhanced
exchangers
Total
△P
= 34.7 kPa
Total
△P
= 64.9 kPa
408.8K
379.8K
Case 1
Initial HEN:
L
EXs
(m)
1 4.97
2 2.08
3 2.73
4 2.91
5 3.90
np
1(n)
1(n)
1(n)
1(n)
4(n)
ρinserts
(%)
0
0
0
0
0
Bs
(m)
0.43
0.23
0.19
0.30
0.42
FRi
(kg/s)
40.095
11.582
19.518
8.905
49
h-1i
(m2·K/kW)
0.811
1.198
0.731
1.857
0.892
FR0
△Pi
(kg/s)
(kPa)
23.9 21.5
20.1 21.5
20.1 47.6
23.9 10.2
19.2 47.6
h-10
(m2·K/kW)
1.390
0.475
0.484
0.426
0.859
△P0
(kPa)
10.1
38.0
56.7
59.8
10.2
U
(kW/ m2·K)
0.454
0.598
0.823
0.438
0.571
Area
Q
LMTD Ns FT
(m2)
(kW)
289.8 76.8 1
10110
103.8 56.4 1
3499
151.6 47.5 1
5922
124.8 41.8 1
2287
270.1 23.9 1 0.916 3373
Bs
(m)
0.18
0.41
0.33
0.15
0.18
FRi
(kg/s)
40.073
9.819
21.183
8.732
49
h-1i
(m ·K/kW)
0.462
1.313
0.228
0.571
0.386
FR0
△Pi
(kPa) (kg/s)
37.2 21.5
17.3 14.93
11.6 47.6
37.2 10.2
4.13 47.6
h-10
(m ·K/kW)
0.428
1.463
1.171
0.163
0.249
△P0
(kPa)
99.4
5.88
28.0
77.5
59.6
U
2
(kW/ m ·K)
1.123
0.360
0.715
1.363
1.573
Area
Q
LMTD Ns FT
2
(m )
(kW)
267.6 36.3 1
10900
118.3 31.8 2
2711
125.6 27.2 3 0.915 6711
101.2 17.6 1
2432
188.7 10.1 2
5972
Retrofitted HEN:
EXs
1
2
3
4
5
L
(m)
4.59
2.37
2.26
2.36
2.73
np
1(e)
1(n)
2(e)
1(e)
1(e)
ρinserts
(%)
24.3
0
34.7
36.6
70.9
2
2
np: tube passes, 1(n): one tube pass without inserts, 1(e): one tube pass with inserts;
L: exchanger length; ρinserts : percentage of inserts density; Bs: baffle spacing;
FRi: tube-side flow rate; hi: tube-side heat transfer coefficient;
△Pi: tube-side pressure drop; FR0: shell-side flow rate;
h0: shell-side heat transfer coefficient; △P0: shell-side pressure drop;
U: overall heat transfer coefficient; Ns: shell passes; Q: duty.
Centre for Process Integration © 2010
Case 1
Conclusions:
 Heat transfer coefficients of exchangers increase through:
tube-side enhancement: increasing tube passes, implementing tube
inserts
shell-side enhancement: increasing baffle spacing
 Pressure drops restrictions are satisfied through:
adjusting tube passes, baffle spacing, exchanger length, stream flow
rates and shell passes
 No topology modifications for HEN
 No many geometry modifications for exchangers, heat transfer
area can change with exchanger length
 Based on the new approach, 27% reduction of heat duty is
achieved (13 MW to 9.5 MW)
Centre for Process Integration © 2010
Case 2
12 6
13
1
5
C1
3
21
20
18
17
C2
16
30
29
28
27 26 24
4
23
H1
22
C3
17
H2
15
24 20
H3
32
16
26
2
H4
5
22 12
H5
7
1
H6
3
8
9
H7
31
H8
29
28
H9
H10
25
4
18
H11
19
23
H12
HU
14
13
27
21
10
6
11
30
2
Hot stream: H
Hot utility: HU
Cold stream:
C
25 32 19 15 14
Cold utility:
7
11
10 8
9
31
CU
CU
Centre for Process Integration © 2010
Case 2
Stream data without utilities
Stream
C1
C2
C3
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
H12
F
(kg/s)
125.91
160.23
153.69
6.39
73.11
40.63
9.27
9.27
16.21
20.12
11.64
63.45
9.28
9.58
25.05
T
Maximum Pressure drop
(°C)
(kPa)
33.5 → 95.6
600
91.4 → 157.3
500
151.1 → 351.9
900
335.4 → 69.4
200
253.2 → 116.1
300
293.7 → 130.
300
212.4 → 156.1
100
212.7 → 61.7
400
174.4 → 43.3
300
134.5 → 74.2
100
364.3 → 65.6
400
290.4 → 210.9
200
284.2 → 65.6
300
240.1 → 57.8
200
178.7 → 69.3
300
Centre for Process Integration © 2010
Case 2
Exchanger data without utilities
Exchanger
U
Max enhanced U
2
2
Area
2
ΔTln
Th
Tc
Cph
Cpc
Tube-side
Shell-side
(J/kg·K) (J/kg·K) Max ∆P (kPa) Max ∆P (kPa)
(kW/m ·K)
(kW/m ·K)
(m )
(°C)
(°C)
(°C)
1
139.75
209.63
167.6
48.3
117.2 → 61.7
33.5 → 40.8
2197.4
2450.1
100
100
3
626.92
940.38
89.9
73.1 174.4 → 76.7
33.5 → 59.9
2598.2
2474.6
100
100
4
184.78
277.17
153.1
74.4 284.2 → 203.2
2831.6
2413.4
100
100
5
571.56
857.34
50.5 → 68.2
2598.2
2531.3
100
100
6
203.56
305.34
635.1
46.9 175.4 → 89.0
68.2 → 86.6
2813.4
2623.8
100
100
12
84.2
126.30
225.4
46.8 157.2 → 117.2
86.6 → 89.2
2397.3
2681.6
100
100
13
62.81
94.22
380.8
89.6 226.7 → 147.2
33.5 → 95.6
2316.9
2681.6
100
100
16
673.27
1009.91
113.1 110.3 262.8 → 189.6
91.4 → 139.5
2824.1
2184.8
100
100
17
128.37
192.56
191.1 121.8 335.4 → 147.2
91.4 → 108.9
2483.8
2134.3
100
100
18
187.66
281.49
188.9
39.2 203.2 → 141.6 124.4 → 128.4
2483.8
2189.3
100
100
20
321.4
482.10 1336.3
24.3 200.1 → 140.3 128.4 → 156.6
2390.4
2310.0
100
100
21
52.71
79.07
220.2
20.1 178.7 → 175.4 156.6 → 157.3
2831.6
2344.4
100
100
22
75.18
112.77
768.5
23.1 212.7 → 157.2 151.1 → 154.8
2596.9
2343.3
100
100
23
143.03
214.55
390.9
35.7 240.1 → 166.6 154.8 → 160.2
2831.6
2368.1
100
100
24
219.1
328.65 1004.7
166 → 192.9
2601.4
2444.1
100
100
26
169.8
254.70
272.4
80.2 293.7 → 262.8 192.9 → 202.4
2965.2
2525.8
100
100
27
182.95
274.43
223.5
46.9 287.8 → 226.7 202.4 → 207.2
2577.3
2525.8
100
100
28
211.1
316.65 1003.3
44.1 290.4 → 238.4 207.2 → 230.4
2831.3
2608.7
100
100
29
126.44
189.66
87.8 364.3 → 287.8 230.4 → 236.7
2832.4
2633.6
100
100
79.5 123.9 212.4 → 156.1
227.1
46 253.2 → 200.1
160.2 →166
Objective - Maximize overall energy saving in HEN!
Centre for Process Integration © 2010
Case 2
Optimal solution when N exchangers can be enhanced
N
Enhanced exchanger:
EX (U: W/m2·K)
EX16 (849.67), EX20 (457.68), EX24 (328.53), EX28 (316.65)
EX16 (1009.9), EX20 (468.73), EX24 (321.74), EX26 (253.15), EX28 (304.08),
EX29 (189.64),
8 EX4 (277.00), EX6 (211.13), EX16 (1009.56), EX20 (434.28), EX24 (328.65),
EX26 (254.53), EX28 (316.65), EX29 (189.65)
All EX4 (272.97), EX6 (219.63), EX16 (1009.88), EX18 (190.20), EX20 (406.29),
EX22 (82.19), EX23 (207.29), EX24 (328.65), EX26 (254.68), EX27 (257.87),
EX28 (316.65), EX29 (189.65)
4
6
Energy
saving
(kW)
4250
Energy
saving
(%)
6.51
5500
8.43
6100
9.35
6400
9.81
Enhancing eight exchangers can obtain almost maximum energy saving!
Centre for Process Integration © 2010
Case 2
Conclusions:
 Overall heat transfer coefficients of enhanced
exchangers increase
 Pressure drops restrictions and target temperatures
are satisfied
 No topology modifications for HEN
 Based on the new model, up to 9.81% reduction of
heat duty is achieved (65.27 MW to 58.87 MW)
Centre for Process Integration © 2010
6. Conclusions and future work
Centre for Process Integration © 2010
Conclusions
• New model of heat exchanger
 Tube-side heat transfer coefficients and pressure drops
 Shell-side heat transfer coefficients and pressure drops
• New correlations of heat transfer enhancement
 Heat transfer coefficients
 Pressure drops
• Retrofit of HEN with heat transfer enhancement
 Increase over heat transfer coefficients of enhanced exchangers
 Satisfy pressure drop constraints
 Increase energy saving
Centre for Process Integration © 2010
Future works
 Developing correlations for heat transfer enhancement
 Tube-side (twisted-tape, coiled wire)
 Shell-side (helical baffles, EM baffles)
 Improving optimal model for HEN retrofit
 Large scale problems
 Minimizing retrofitting costs
 Build up optimal model for HEN design
 Exchanger geometry details
 Pressure drop constraints
 Maximizing total profit
Centre for Process Integration © 2010