Heat Exchanger Design Anand V P Gurumoorthy Associate Professor Chemical Engineering Division School of Mechanical & Building Sciences VIT University Vellore, India.

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Transcript Heat Exchanger Design Anand V P Gurumoorthy Associate Professor Chemical Engineering Division School of Mechanical & Building Sciences VIT University Vellore, India.

Heat Exchanger Design

Anand V P Gurumoorthy Associate Professor Chemical Engineering Division School of Mechanical & Building Sciences VIT University Vellore, India

Heat Exchanger Classification

• • • Recuperative: – Cold and hot fluid flow through the unit without mixing with each other. The transfer of heat occurs through the metal wall.

Regenerative: – Same heating surface is alternately exposed to hot and cold fluid. Heat from hot fluid is stored by packings or solids; this heat is passed over to the cold fluid.

Direct contact: – Hot and cold fluids are in direct contact and mixing occurs among them; mass transfer and heat transfer occur simultaneously.

Heat Exchanger Standards and Codes • • • British Standard BS-3274 TEMA standards are universally used.

TEMA standards cover following classes of exchangers: – Class R – designates severe requirements of petroleum and other related processing applications – Class C – moderate requirements of commercial and general process applications – Class B – specifies design and fabrication for chemical process service.

Shell and Tube Heat Exchanger

• • Most commonly used type of heat transfer equipment in the chemical and allied industries.

Advantages: – The configuration gives a large surface area in a small volume.

– Good mechanical layout: a good shape for pressure operation.

– Uses well-established fabrication techniques.

– Can be constructed from a wide range of materials.

– Easily cleaned.

– Well established design procedures.

Types of Shell and Tube Heat Exchangers • • Fixed tube design – Simplest and cheapest type.

– Tube bundle cannot be removed for cleaning.

– No provision for differential expansion of shell and tubes.

– Use of this type limited to temperature difference upto 80 0 C.

Floating head design – More versatile than fixed head exchangers.

– Suitable for higher temperature differentials.

– Bundles can be removed and cleaned (fouling liquids)

Design of Shell and Tube Heat Exchangers • • • Kern method: – Does not take into account bypass and leakage streams.

– Simple to apply and accurate enough for preliminary design calculations.

– Restricted to a fixed baffle cut (25%).

Bell-Delaware method – Most widely used.

– Takes into account: • Leakage through the gaps between tubes and baffles and the baffles and shell.

• Bypassing of flow around the gap between tube bundle and shell.

Stream Analysis method (by Tinker) – More rigorous and generic.

– Best suited for computer calculations; basis for most commercial computer codes.

Construction Details – Tube Dimensions • • • • • • Tube diameters in the range 5/8 inch (16 mm) to 2 inch (50 mm).

Smaller diameters (5/8 to 1 inch) preferred since this gives compact and cheap heat exchangers.

Larger tubes for heavily fouling fluids.

Steel tubes – BS 3606; Other tubes – BS 3274.

Preferred tube lengths are 6 ft, 8 ft, 12 ft, 16 ft, 20 ft and 24 ft; optimum tube length to shell diameter ratio ~ 5 – 10.

¾ in (19 mm) is a good starting trial tube diameter.

Construction Details – Tube Arrangements • Tubes usually arranged in equilateral triangular, square or rotated square patterns.

• Tube pitch, P t , is 1.25 times OD.

Construction Details - Shells

• • Shell should be a close fit to the tube bundle to reduce bypassing.

Shell-bundle clearance will depend on type of heat exchanger.

Construction Details - Shell-Bundle Clearance

Construction Details – Tube Count • • • • Bundle diameter depends not only on number of tubes but also number of tube passes.

D b

d

0  

N K

1

t

  1 /

n

1 N t D b D 0 is the number of tubes is the bundle diameter (mm) is tube outside diameter (mm) • n 1 and K 1 are constants

Construction Details - Baffles

• • Baffles are used: – To direct the fluid stream across the tubes – To increase the fluid velocity – To improve the rate of transfer Most commonly used baffle is the single segmental baffle.

• Optimal baffle cut ~ 20-25%

Basic Design Procedure

• General equation for heat transfer is:

Q

UA

T m

• where Q is the rate of heat transfer (duty), U is the overall heat transfer coefficient, A is the area for heat transfer ΔT m is the mean temperature difference We are not doing a mechanical design, only a thermal design.

Overall Heat Transfer Coefficient • Overall coefficient given by: 1

U

0  1

h

0  1

h od

d

0 ln  

d

0

d i

2

k w

  

d

0

d i

1

h id

d

0

d i

1

h i

h 0 (h i ) is outside (inside) film coefficient h od k w d o (h id ) is outside (inside) dirt coefficient is the tube wall conductivity (d i ) is outside (inside) tube diameters

Individual Film Coefficients

• • Magnitude of individual coefficients will depend on: – Nature of transfer processes (conduction, convection, radiation, etc.) – Physical properties of fluids – Fluid flow rates – Physical layout of heat transfer surface Physical layout cannot be determined until area is known; hence design is a trial-and-error procedure.

Typical Overall Coefficients

Typical Overall Coefficients

Fouling Factors (Dirt Coeffs)

• Difficult to predict and usually based on past experience

Mean Temperature Difference (Temperature Driving Force)

Q

UA

T m

• • To determine A, ΔT m must be estimated True counter-current flow – “logarithmic temperature difference” (LMTD)

LMTD

• LMTD is given by: 

T lm

 (

T

1  ln

t

2   )

T

1

T

2  (

T

 

t

2

t

1 2   

t

1 ) where T 1 T t 1 t 2 2 is the hot fluid temperature, inlet is the hot fluid temperature, outlet is the cold fluid temperature, inlet is the cold fluid temperature, outlet

Counter-current Flow – Temperature Proflies

1:2 Heat Exchanger – Temperature Profiles

True Temperature Difference

• Obtained from LMTD using a correction factor: 

T m

F t

T lm

• ΔT m F t is the true temperature difference is the correction factor F t is related to two dimensionless ratios:

R

 ( (

T t

1 2  

T t

1 2 ) )

S

 (

t

2 (

T

1  

t

1

t

1 ) )

Temp Correction Factor F

t Temperature correction factor, one shell pass, two or more even tube passes

Fluid Allocation: Shell or Tubes?

• • • • • • • Corrosion Fouling Fluid temperatures Operating pressures Pressure drop Viscosity Stream flow rates

Shell and Tube Fluid Velocities

• • • • High velocities give high heat-transfer coefficients but also high pressure drop.

Velocity must be high enough to prevent settling of solids, but not so high as to cause erosion.

High velocities will reduce fouling For liquids, the velocities should be as follows: – Tube side: Process liquid 1-2m/s Maximum 4m/s if required to reduce fouling Water 1.5 – 2.5 m/s – Shell side: 0.3 – 1 m/s

Pressure Drop

• • As the process fluids move through the heat exchanger there is associated pressure drop.

For liquids: viscosity < 1mNs/m 2 35kN/m 2 Viscosity 1 – 10 mNs/m 2 50-70kN/m 2

Tube-side Heat Transfer Coefficient • For turbulent flow inside conduits of uniform cross-section, Sieder Tate equation is applicable:

Nu

C

Re 0 .

8 Pr 0 .

33    

w

  0 .

14

Nu

h i d e k f

Re  

u t d e

 Pr 

C p

k f

C=0.021 for gases μ =0.023 for low viscosity liquids =0.027 for viscous liquids μ= fluid viscosity at bulk fluid temperature w =fluid viscosity at the wall

Tube-side Heat Transfer Coefficient • Butterworth equation:

St

E

Re  0 .

205 Pr  0 .

505

E

St

Nu

Re Pr 

h i

u t C p

0 .

0225 exp   0 .

0225 (ln Pr) 2  • • For laminar flow (Re<2000):

Nu

 1 .

86 (Re Pr) 0 .

33

d e L

0 .

33    

w

  0 .

14 If Nu given by above equation is less than 3.5, it should be taken as 3.5

Heat Transfer Factor, j

h • “j” factor similar to friction factor used for pressure drop:

h i d i k f

j h

Re Pr 0 .

33    

w

  0 .

14 • This equation is valid for both laminar and turbulent flows.

Tube Side Heat Transfer Factor

Heat Transfer Coefficients for Water • Many equations for h i have developed specifically for water. One such equation is:

h i

 4200 ( 1 .

35  0 .

02

t

)

u t

0 .

8

d i

0 .

2 where h i is the inside coefficient (W/m t is the water temperature ( 0 C) 2 0 C) u t d t is water velocity (m/s) is tube inside diameter (mm)

Tube-side Pressure Drop

P t

N p

   8

j f

 

L d i

     

w

  

m

 2 .

5    

u t

2 2 where ΔP is tube-side pressure drop (N/m 2 ) N u t L is the length of one tube m is 0.25 for laminar and 0.14 for turbulent j f p is number of tube-side passes is tube-side velocity (m/s) is dimensionless friction factor for heat exchanger tubes

Tube Side Friction Factor

Shell-side Heat Transfer and Pressure Drop • • Kern’s method Bell’s method

Procedure for Kern’s Method

• • Calculate area for cross-flow A of tubes in the shell equator.

s for the hypothetical row p t d 0 D s l B

A s

 (

p t

d

0 )

D s

b p t

is the tube pitch is the tube outside diameter is the shell inside diameter is the baffle spacing, m. Calculate shell-side mass velocity G u s .

G s

W A s s u s

G

s

s and linear velocity, where W s is the fluid mass flow rate in the shell in kg/s

Procedure for Kern’s Method

• Calculate the shell side equivalent diameter (hydraulic diameter).

– For a square pitch arrangement:  4 

p t

2  

d

2 0    4

d e

d

0 – For a triangular pitch arrangement

d e

  4 

p t

2  0 .

87

p t

 1 2  

d

0 2

d

0 2 4  

Shell-side Reynolds Number

• • The shell-side Reynolds number is given by: Re 

G s

d e

u s d

e

 The coefficient h s is given by: where j h

Nu

h s d e k f

j h

Re Pr 1 / 3    

w

  0 .

14 is given by the following chart

Shell Side Heat Transfer Factor

Shell-side Pressure Drop

• The shell-side pressure drop is given by: 

P s

 8

j f

 

D s d e

   

L

B

  

u s

2 2    

w

   0 .

14 where j f is the friction factor given by following chart.

Shell Side Friction Factor

(Figure 8 in notes)

R

 (

T

(

t

2 1  

T

2

t

1 ) )

S

 (

t

2 (

T

1 

t

1 ) 

t

1 )

(Figure 4 in notes) (Figure 2)

Q

UA

T m D b

d

0  

N K

1

t

  1 /

n

1

h i

 4200 ( 1 .

35 

d i

0 .

2 0 .

02

t

)

u t

0 .

8

(Figure 9 in notes)

A s

 (

p t

d

0 )

D s

b p t d e

  4 

p t

2  0 .

87

p t

d

0 2  1 2 

d

2 0 4  

(Table 3 in notes) (Figure 10 in notes) 1

U

0  1

h

0  1

h od

d

0 ln  

d

0

d i

2

k w

  

d

0

d i

1

h id

d

0

d i

1

h i

(Figure 12 in notes) 

P t

N p

   8

j f

 

L d i

     

w

  

m

 2 .

5    

u t

2 2 

P s

 8

j f

 

D s d e

   

L

B

  

u s

2 2    

w

   0 .

14

Bell’s Method

• • In Bell’s method, the heat transfer coefficient and pressure drop are estimated from correlations for flow over ideal tube banks. The effects of leakage, by-passing, and flow in the window zone are allowed for by applying correction factors.

Bell’s Method – Shell-side Heat Transfer Coefficient

h s

h oc F n F w F b F L

where h oc is heat transfer coeff for cross flow over ideal tube banks F n is correction factor to allow for no. of vertical tube rows F w F b F L is window effect correction factor is bypass stream correction factor is leakage correction factor

Bell’s Method – Ideal Cross Flow Coefficient • • The Re for cross-flow through the tube bank is given by: G s Re 

G s

d

0 

u s

d

 0 is the mass flow rate per unit area d 0 is tube OD Heat transfer coefficient is given by:

h oc d

0

k f

j h

Re Pr 1 / 3    

w

  0 .

14

Bell’s Method – Tube Row Correction Factor • For Re>2100, F of N cv n is obtained as a function (no. of tubes between baffle tips) from the chart below: • • For Re 100

For Re<100,

F n

 (

N

'

c

)  0 .

18

Bell’s Method – Window Correction Factor • F w , the window correction factor is obtained from the where R w is the ratio of bundle cross-sectional area in (obtained from simple formulae).

Bell’s Method – Bypass Correction Factor • Clearance area between the bundle and the shell

A b

 

B

(

D s

D b

) • For the case of no sealing strips, F b function of A b /A s following chart as a can be obtained from the

Bell’s Method – Bypass Correction Factor • For sealing strips, for N s

F b

 exp     

A A b s

  1    2

N s N cv

  1 / 3      where α=1.5 for Re<100 and α=1.35 for Re>100.

Bell’s Method – Leakage Correction Factor • • • Tube-baffle clearance area A tb

A tb

 0 .

8  2

d

0 is given by: (

N t

N w

) Shell-baffle clearance area A sb

A sb

C s D s

2 is given by: ( 2   

b

) where C s chord is baffle to shell clearance and θ A L =A tb +A sb

F L

 1  

L

  (

A tb

A L

2

A sb

) b   is the angle subtended by baffle where β L is a factor obtained from following chart

Coefficient for F

L

, Heat Transfer

Shell-side Pressure Drop

• Involves three components: – Pressure drop in cross-flow zone – Pressure drop in window zone – Pressure drop in end zone

Pressure Drop in Cross Flow Zone 

P c

 

P i F b

'

F L

' where ΔP i pressure drop calculated for an equivalent ideal tube bank F b ’ is bypass correction factor F L ’ is leakage correction factor 

P i

 8

j f N cv

u

2

s

2    

w

   0 .

14 where j f N cv u s is given by the following chart is number of tube rows crossed is shell-side velocity

Friction Factor for Cross Flow Banks

Bell’s Method – Bypass Correction Factor for Pressure Drop

F b

'  exp     

A b A s

  1    2

N s N cv

  1 / 3      α is 5.0 for laminar flow, Re<100 4.0 for transitional and turbulent flow, Re>100 A b N s is the clearance area between the bundle and shell is the number of sealing strips encountered by bypass stream N cv is the number of tube rows encountered in the cross flow section

Bell’s Method – Leakage Factor for Pressure Drop

F L

'  1  

L

'   (

A tb

A L

2

A sb

)   where A tb A sb is the tube to baffle clearance area is the shell to baffle clearance area A L is total leakage area = A tb +A sb β L ’ is factor obtained from following chart

Coefficient for F

L

Pressure Drop in Window Zones 

P w

F L

' ( 2 .

0  0 .

6

N wv

) 

u z

2 2 where u s is the geometric mean velocity

u z

u w u s

u w is the velocity in the window zone

u w

W s A w

 W s N wv is the shell-side fluid mass flow is number of restrictions for cross-flow in window zone, approximately equal to the number of tube rows.

Pressure Drop in End Zones

• • 

P e

 

P i

  (

N wv

N cv N cv

)  

F b

' N cv is the number of tube rows encountered in the cross-flow section N wv is number of restrictions for cross-flow in window zone, approximately equal to the number of tube rows.

Bell’s Method – Total Shell-side Pressure Drop 

P s

 2

end

N b zones window

 (

N b zones

 1 )

crossflow zones

P s

 2 

P e

 (

N b

 1 ) 

P c

N b

P w

Effect of Fouling

• Above calculation assumes clean tubes • Effect of fouling on pressure drop is given by table above

Condensers

• Construction of a condenser is similar to other shell and tube heat exchangers, but with a wider baffle spacing

l B

D s

• • Four condenser configurations: – Horizontal, with condensation in the shell – Horizontal, with condensation in the tubes – Vertical, with condensation in the shell – Vertical, with condensation in the tubes Horizontal shell-side and vertical tube-side are the most commonly used types of condenser.

Heat Transfer Mechanisms

• • • • • Filmwise condensation – Normal mechanism for heat transfer in commercial condensers Dropwise condensation – Will give higher heat transfer coefficients but is unpredictable – Not yet considered a practical proposition for the design of condensers In the Nusselt model of condensation laminar flow is assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film.

Nusselt model strictly applied only at low liquid and vapor rates when the film is undisturbed.

At higher rates, turbulence is induced in the liquid film increasing the rate of heat transfer over that predicted by Nusselt model.

Condensation Outside Horizontal Tubes (

h c

) 1  0 .

95

k L

  

L

(  

L

L

 

v

)

g

  1 / 3 • where (h k L c ) 1 is the mean condensation film coefficient, for a single tube is the condensate thermal conductivity ρ L ρ v is the condensate density is the vapour density μ L is the condensate viscosity g is the gravitational acceleration Γ is the tube loading, the condensate flow per unit length of tube.

If there are N r tubes in a vertical row and the condensate is assumed to film coefficient is given by: (

h c

)

N r

 (

h c

) 1

N r

 1 / 4

Condensation Outside Horizontal Tubes • • In practice, condensate will not flow smoothly from tube to tube.

Kern’s estimate of mean coefficient for a tube bundle is given by: (

h c

)

b

 0 .

95

k L

  

L

(  

L L

 

h

v

)

g

  1 / 3

N r

 1 / 6 

h

W c LN t

• L is the tube length W c is the total condensate flow N N r t is the total number of tubes in the bundle is the average number of tubes in a vertical tube row For low-viscosity condensates the correction for the number of tube rows is generally ignored.

Condensation Inside and Outside Vertical Tubes • • • • For condensation inside and outside vertical tubes the Nusselt model gives: (

h c

)

v

 0 .

926

L

  

L

(  

L L

 

v

v

)

g

  1 / 3 where (h c ) v Γ v perimeter is the mean condensation coefficient is the vertical tube loading, condensate per unit tube Above equation applicable for Re<30 For higher Re the above equation gives a conservative (safe) estimate.

For Re>2000, turbulent flow; situation analyzed by Colburn and results in following chart.

Colburn’s Results

Boyko-Kruzhilin Correlation

• • • A correlation for shear-controlled condensation in tubes; simple to use.

The correlation gives mean coefficient between two points at which vapor quality, x, (mass fraction of vapour) is known.

(

h c

)

BK

h

i

 

J

1 / 1 2  2

J

1 / 2 2  

where J

 1    

L

 

v

v

 

x

1,2 refer to inlet and outlet conditions respectively

h i

  0 .

021  

k L d i

  Re 0 .

8 Pr 0 .

43 In a condenser, the inlet stream will normally be saturated vapour and vapour will be totally condensed. For these conditions: (

h c

)

BK

h

i

     1   2

L

v

     • For design of condensers with condensation inside the tubes and downward vapor flow, coefficient should be evaluated using Colburn’s method and Boyko-Kruzhilin correlation and the higher value selected.

Flooding in Vertical Tubes

• • • When the vapor flows up the tube, tubes should not flood.

Flooding should not occur if the following condition is satisfied: where u v 

u v

1 / 2 liquid and d i  1 /

v

4  and u L

u

1

L

/ 2  1

L

/ 4   is in metres.

0 .

6 

gd i

( 

L

 

v

)  1 / 4 are velocities of vapor and The critical condition will occur at the bottom of the tube, so vapor and liquid velocities should be evaluated at this point.

Condensation Inside Horizontal Tubes • When condensation occurs, the heat transfer coefficient at any point along the tube will depend on the flow pattern at that point.

• No general satisfactory method exists that will give accurate predictions over a wide flow range.

Two Flow Models

• Two flow models: – Stratified flow • Limiting condition at low condensate and vapor rates – Annular flow • Limiting condition at high vapor and low condensate rates – – – For stratified flow, the condensate film coefficient can be estimated as: (

h c

)

s

 0 .

76

k L

  

L

(  

L L

 

h

v

)

g

  1 / 3 For annular flow, the Boyko-Kruzhilin equation can be used For condenser design, both annular and stratified flow should be considered and the higher value of mean coefficient should be selected.

• Condensation of steam – For air-free steam a coefficient of 8000 W/m 2 0 C should be used.

• Mean Temperature Difference – A pure, saturated, vapor will condense at a constant temperature, at constant pressure.

– For an isothermal process such as this, the LMTD is given by: 

T lm

 ln   (

t

2

T T

sa t sa t t

1 ) 

t

1 

t

2   where T sat is saturation temperature of vapor t 1 (t 2 ) is the inlet (outlet) coolant temperature – No correction factor for multiple passes is needed.