design of heat exchangers (shell tube)

1Prepared by: Kow Kien Woh

EP 315 Heat Transfer

Chapter 8: Design of heat exchangers (Shell & Tube)

2

Design principle

1. The design principle is similar with double pipe heat exchanger follows:

2. However, the overall heat transfer coefficient (U) and LMTD (∆Tlm) are heavily depending on the flow characteristics of fluids, which in turns affected by the geometry of the exchanger.

3. Thus, modifications are needed to give better estimate for both U and ∆Tlm. Such modifications are usually made using semi-empirical correlations.

Structure and terms

4

Tubes1. Tubes are available with

different wall thickness and usually defined by BWG.

2. Once the OD and BWG of tubes is known, the total flow area of tubes (at) can be calculated as:

where N = number of tubesn = number of passesat’ = flow area per tube

'

2 ft144

tt

Naa

n

Table 1: Tube size

5

E.g. 1A shell and tube heat exchanger (1S-2T) uses 32 tubes (OD = 1 inch, BWG 18). Calculate the total flow area of tubes in the exchanger.

Solution:

From the Table 1:

'232 0.639 = = 0.071 ft

144 144 2t

tNaan

' 20.639 in ta

6

Tubes3. Tube pitch (PT) is the shortest

distance from center to center between adjacent tubes.

4. The shortest distance between two adjacent tube is called clearance (C’).

5. Tubes can be arranged with square pitch or triangular pitch.

6. Since higher turbulence can cause larger heat transfer coefficient in shell side, triangular pitch is usually used to induce greater turbulence as annulus flow through the space between tubes.

Clearance

PT

Pitch

7. If pressure drop and cleanabaility is of little consequences, triangular pitch can increase the shell side heat transfer coefficient by 25% as compared with square pitch under comparable conditions.

Triangular pitch

Cleara

nce

9

Baffle

Baffle spacing, B

1. Baffle spacing (B) is the distance between baffles.

2. Baffle is used to force liquid at shell side flow at right angle to the tubes to induce more turbulence.

Baffle induced turbulence

11

Baffle3. Baffle spacing is usually not greater than the

inner diameter of shell, but not closer than 1/5 of the inner diameter of shell.

4. The closer the spacing, the greater the turbulence, and hence larger the shell side heat transfer coefficient.

5. Segmental baffle is the most common type of baffle.

Flow in segmental baffle

Disc and doughnut baffle

Flow in disc and doughnut baffle

15

Heat transfer coefficient (tube)

1. The coefficient (hi) is correlated with Re, Nu, Pr and relative viscosity as the following:

where k = thermal conductivity of fluid (Btu hr-1 ft-1 oF-1) c = specific heat capacity of fluid (Btu hr-1 oF) μ = viscosity of fluid (lb ft-1 hr-1) μw = viscosity of fluid at tube wall temperature (lb ft-1 hr-1) Gt = mass velocity (lb hr-1 ft-2) D = inner diameter of tube (ft) jH = Factor of heat transfer (dimensionless)

0.1413

iH

w

h D cjk k

Re tDGvs

16

jH - Re correlation

Heat transfer coefficient (tube)

2. Gt can be calculated from the mass flow rate Wt (lb hr-1) is known:

3. For non-viscous fluid (e.g. water) :

4. Hence, the correlation can be reduced to:

*Note: Properties such as c, μ, k and ρ are taken at the arithmetic average temperature of each fluid.

tt

t

WGa

1w

13

iH

h D cjk k

18

5. Since the outer surface of tube is used in Q = U A ∆Tlm , hi (based on ID) is corrected to hio (based on OD) as:

6. For simplicity, hi for water in tubes can be determined by water heat transfer curve, where the velocity is determined from density:

IDODio ih h

Velocity, ft/s3600

tGV

19

1. The coefficient at shell side (ho) can be determined by similar approach as tube side using:

2. However, the mass velocity (Gs) and flow area (as) are given as:

Heat transfer coefficient (shell)

0.1413

o eH

w

h D cjk k

Re e sD Gvs

2ID ' ft144s

T

C BaP

where ID = inner diameter of shell (in.) C’ = tube clearance (in.) B = baffle spacing (in.) PT = tube pitch (in.)

ss

s

WGa

20

Heat transfer coefficient (shell)

3. The equivalent diameter (De) is:

4. For square pitch: 5. For triangular pitch:

21

E.g. 220160 lb/hr of 30 wt% K3PO4 solution (shell) is to be cooled from 150oF to 90oF (tube). 41600 lb/hr of cooling water is used from 68oF to 90oF. The following shell & tube heat exchanger is used:

Shell (K3PO4 solution) Tube (Water)Baffle spacing = 2 in. Number of tubes = 52

ID = 10.02 in. Length of tubes = 16 ftPasses = 1 OD = ¾ in.

BWG = 16 Pitch (Square) = 1 in. Passes = 2

Determine the hio and ho. Given μsolution = 2.9 lb ft-1hr-1 and μwater = 2.2 lb ft-1hr-1. ksolution = 0.33 Btu hr-1 ft-1 oF-1 and ρwater = 62.5 lb ft-3.

22

E.g. 2Solution:For shell side,

2

ID '144

10.02 0.25 21 144

0.0347 ft

sT

C BaP

' OD314

0.25 in.

TC P

1 2

201600.0347578000 lb hr ft

ss

s

WGa

Alternatively, from graph,0.95 in0.95= 0.079 ft12

e

e

d

D

23

E.g. 2Solution:For shell side,

Re

0.079 5780002.9

=15750

e ss

D G

From graph,

71Hj 1

3

1 2

0.079 0.757 2.971 10.33 0.33

558 Btu hr ft F

o

oo

h

h

0.1413

o eH

w

h D cjk k

24

E.g. 2Solution:For tube side,

2' 0.302 inta

1 2

416000.0545762000 lb hr ft

tt

t

WGa

For water, the velocity is

'

2

14452 0.302=

144 2= 0.0545 ft

tt

Naa

n

Velocity, 3600

762000 3.4 ft/s3600 62.5

tGV

From water curve,1 2800 Btu hr ft Foih

1 2

IDOD

0.62800 662 Btu hr ft F0.75

io i

o

h h

25

E.g. 2Additional:The clean overall heat transfer coefficient (Uc) is:

The clean overall heat transfer coefficient (Uc) is heat transfer coefficient that does not include fouling factor.

1 2

1 1 1

1 1558 662303 Btu hr ft F

c o io

oc

U h h

U

26

Corrected LMTD1. When multi-pass is

used, part of the flow is in counter direction while the remaining is in parallel direction.

2. Hence, a correction factor (FT) is used for such conditions.

Parallel

lm,correctedQ UA T

lm TQ UA T F

Counter

27

LMTD3. For 1S-2T counter flow, FT is given as:

where

For hot fluid in shell side:

4. Alternatively, correction factor charts in P and R can be used:

2

2

2

11 ln

1 =

2 1 11 ln

2 1 1

T

XY

XYF

X Y YY

X Y Y

2 1

1 1

tT

tXt

1 2

2 1tT TY

t

2 1

1 1

co ci

hi ci

T TtXt T T

tT

1 2

2 1

hi ho

co ci

T TT TYt Tt T

28

FT charts

2 1

1 1

ttT

X Pt

1 2

2 1

T TY Rtt

29

FT charts

30

E.g.3Recall in e.g.2, 20160 lb/hr of 30 wt% K3PO4 solution is to be cooled from 150oF to 90oF. 41600 lb/hr of cooling water is used from 68oF to 90oF. The following shell & tube heat exchanger is used:

Shell (K3PO4 solution) Tube (Water)Baffle spacing = 2 in. Number of tubes = 52

ID = 10.02 in. Length of tubes = 16 ftPasses = 1 OD = ¾ in.

BWG = 16 Pitch (Square) = 1 in. Passes = 2

Determine the(a)Corrected LMTD(b)Design overall coefficient, UD

Given ch = 0.757 Btu lb-1oF-1 and cc = 1 Btu lb-1oF-1

31

E.g. 3Solution:(a)

, 90 oc oT F

, 90 oh oT F

, 150 oh iT F

, 90 oh oT F

, 68 oc iT F

, 68 oc iT F

, 150 oh iT F

, 90 oc oT F

1 60 oT F

2 22 oT F

lm60 22

60ln22

37.9 Fo

T

32

E.g. 3To find the correction factor, FT

2

2

2

11 ln

1 =

2 1 11 ln

2 1 1

T

XY

XYF

X Y YY

X Y Y

90 68 0.268150 68

co ci

hi ci

T TXT T

150 90 2.72790 68

hi ho

co ci

T TYT T

, 90 oh oT F

, 68 oc iT F

, 150 oh iT F

, 90 oc oT F

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E.g.3

2

2

2

1 0.2682.727 1 ln

1 0.268 2.727 =

2 0.268 2.727 1 2.727 12.727 1 ln

2 0.268 2.727 1 2.727 1

2.905(1) 0.80921.77971.727 ln 0.2226

TF

lm, corrected lm

37.9 0.8092

30.7 F

T

o

T T F

Alternatively, using graph

0.27P X 2.72R Y

34

E.g.3 (b) From heat balance:

To estimate UD ,

For ¾ in tube, from the table, the external surface is 0.1963 ft2 per ft of tube,

, ,

1

20160 0.757 150 90

915000 Btu hr

h h h i h ohQ m c T T

22ft52 tubes 16 ft 0.1963 163 ft

ftoA

, ,

1

41600 1 90 68

915000 Btu hr

c c c o c icQ m c T T

lm,correctedD oQ U A T

35

E.g.4 (cont.)

lm,corrected

1 2 1

915000163 30.7

183 Btu hr ft

Do

o

QUA T

F

Note: Recall in e.g., clean coefficient, Uc = 303, i.e., higher that the design coefficient UD = 183. Thus, the exchanger is capable to operate based on the temperatures requirements. In addition, it is possible to accommodate fouling with the excess of U.

36

Rating of exchanger 1. When conditions and dimensions are specified for a

heat exchanger, evaluation of suitability of an existing heat exchanger is known as rating of exchanger.

2. The maximum allowable fouling factor for the exchanger under specified conditions is given by:

3. The exchanger is suitable to be used if:

4. In addition, the allowable pressure drop for the two streams may not be exceeded.

,total allowable1 1

fD C

RU U

,total ,total allowablef fR R

Fouling factor

38

Fouling factor

39

E.g.5 Based the Uc and UD obtained in e.g. 4, calculate the total allowable fouling factor. Is the heat exchanger satisfactory for the fouling of liquids?

,total allowable

2 1

1 1

1 1= 183 3030.00216 hr ft Btu

fD C

o

RU U

F

From fouling factor table, , distilled water 0.0005fR

Since

Rf total < Rf, allowable

The heat exchanger is satisfactory for the operation.

3 4, K PO , Brine 0.001f fR R

, total 0.0005 0.001 0.0015fR

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Other considerations 1. In rating a heat exchanger, not only Uc must

exceed UD sufficiently to accommodate the fouling factor.

2. The allowable pressure drop for the two streams must also not be exceeded. Fluids may not able to circulate in shell or/and tube is the allowable pressure drop is exceeded.

3. Beside that, placement of fluid in shell or tube is usually done based on the following considerations:

(a) PressurePut a high-pressure fluid on the tube side. This usually minimizes exchanger cost. The smaller tube diameter has a higher pressure rating for the same metal thickness compared to the larger diameter shell.

41

Other considerations (b) FoulingA fluid with a tendency to foul generally should go on the tube side. Cleaning straight tubes normally is easier than cleaning the shell even if a relatively large tube pitch or a square tube pattern is used to make the shell side easier to clean. Using a fixed tubesheet mandates putting a clean fluid on the shell side; unless expected fouling is easily removed by chemical cleaning, the fixed tubesheet makes the shell side impossible to clean. In contrast, U-tubes are more difficult than straight tubes to clean.

(c) Corrosive fluidsPut a corrosive fluid on the tube side. That way, only the tubes, tubesheets, heads and channels will need expensive corrosion-resistant alloys. In contrast, a corrosive fluid on the shell side requires the entire exchanger to use the materials.

42

Other considerations (d) VaporBecause a vapor normally has a higher volume and lower heat-transfer coefficient than a liquid, allocate it to the shell side. This reduces pressure drop for a given volume and typically provides a higher heat-transfer coefficient.A condensing fluid most often goes on the shell side. If the shell-side velocity is low enough, the vapor and liquid can separate inside the exchanger

(e) Viscous fluidsA viscous fluid on the tube side tends to have high pressure drop and low heat transfer. That favors shell-side allocation. However, high pressure drop on the shell side can prompt significant flow bypassing around baffles, reducing heat transfer. A shell side with a high pressure drop also may suffer from vibration damage.

43

Design of heat exchanger

1. If a totally new heat exchanger must be designed to perform a certain service, all its geometric characteristics must be defined by the designer.

2. The heat transfer coefficients must be as high as possible because to minimize area. The obvious limitation to the increase in heat transfer coefficients is the allowable pressure drop (Δp) for both fluids.

3. As a general rule, we can say that the design will be optimal when the Δp values of both fluids are close to the maximum allowable values (because then the heat transfer coefficients also will be close to the maximum) and the heat transfer area is enough, but with little excess, to transfer the required heat duty.

4. To initially adopt the heat exchanger geometry, the following procedure is suggested:

44


Step 1:With a heat balance, the unknown process variable (flow rate or temperature) of one of the streams can be found. Then calculate LMTD.

Step 2:Based on all inlet and outlet temperatures, estimate correction factor of LMTD (FT) for various shell pass. It is recommended never to design with an FT lower than 0.75. Though counter current configuration allows FT = 1, it is avoided in case it makes the removable-bundle construction difficult, or it makes a very high tube length, or installation of shells in series necessary.

45


Step 3:Considering the type of fluids to be handled, a first guess of the overall heat transfer coefficient can be obtained using the table:

46

Typical heat transfer coefficient

47


48


49


Step 4:With the assumed U, an approximate value of the heat transfer area (A’)can be calculated as:

Step 5:A minimum fluid velocity to achieve reasonable hi is assumed (usually 1m/s is reasonable estimate to start with). The number of tubes (Ns) in single tube pass will be:

'

lmD T

QAU F T

't

St t

WNa V

50


Step 6:Select the number of tubes (N’), tube length (L), and number of tube passes (n). Here, it is necessary to find a combination of number of tubes and tube length to satisfy the value of A' calculated in step 4, which is:

At the same time, the number of tube passes must be selected in such a way that the quotient between N’ and Ns is an integer. This means that one must adopt the number of tube passes n as:

by adjusting Di , Do , L and V to get an integer. At the same time, the heat exchanger length must be reasonable.

''

oπ D LAN

'

s

NnN

51


Step 7:Selection of shell diameter. The following tables show the number of tubes that can be allocated in a certain shell diameter for different exchanger types following TEMA (Tubular Exchangers Manufacturers Association) standards. Once the number of tubes (N) has been selected with the help of these tables, it is possible to find the necessary shell diameter.

Usually the number of tubes obtained from the tables (N) will not match exactly with the number of tubes calculated in step 6. Anyway, at this stage we are only looking for a first approximation to the final design, to be verified later.

52

Shell diameter (TEMA)

53


54


55


56


Step 8:With the number of tubes determined in step 7, calculate the corrected heat transfer area as:

This is usually somewhat different from the area calculated in step 6 because we may have slightly changed the number of tubes.

Step 9:Finally, the baffle separation is selected by try to obtain a Reynolds number that gives a reasonably high shell-side heat transfer coefficient. This may require a few trial calculations using jH factor correlations. Once the heat exchanger is completely defined, we can proceed to the rating procedure explained earlier.

o π D LA N

57

Factors not considered in Kern’s method

1. The Kern method has been criticized for a number of reasons.

2. Bypass streams: The method assumes that the shell fluid flow is perpendicular to the tubes. This is not true because of bypass stream. Obviously, this flow is ineffective for the heat transfer because it by passes the tube bundle.

Bypass streamBypass stream

58

Factors not considered in Kern’s method

3. Leakage streams: Since the baffle holes crossed by the tubes are drilled with a diameter slightly larger than the tube diameter, there is a clearance between the tube and the baffle, and part of the shell fluid leaks across this clearance. There is also leakage through the free area between the baffle and the shell.

4. Tube Pattern: The equivalent diameter is defined for a flow direction parallel to the tubes, whereas the shell-side flow is mainly normal to the tubes.

5. Hence, Bell or Delaware method is used for more accurate design.

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Leakage streams

design of heat exchangers (shell tube)

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