Kern Method of SHELL-AND-TUBE HEAT EXCHANGER Analysis

P M V SubbaraoProfessor

Mechanical Engineering DepartmentI I T Delhi

Simplified Procedures using Semi- Empirical Correlations.….

Properties Crude Oil Heavy gas oilDensity, kg/m3 915 890Specific heat, kJ/kg K 2.62 3.08Viscosity, cPoise 0.664/0.563 0.32/0.389Thermal conductivity, W/m.K

0.124 0.14

Thermal Analysis for Tube-Side

Number of Tubes • The flow rate inside the tube is a function of the density of the

fluid, the velocity of the fluid, cross-sectional flow area of the tube, and the number of tubes.

By using above Eq. and replacing Ac by di2/4, number of tubes

can be calculated as

2itt

tubet du

mN

tctttube NAum

where di is the tube inside diameter.

Tubes in Shell and Tube Hx

• The number and size of tubes in an exchanger depends on the• Fluid flow rates• Available pressure drop.• The number and size of tubes is selected such that the• Tube side velocity for water and similar liquids ranges from 0.9 to 2.4 m/s.• Shell-side velocity from 0.6 to 1.5 m/s.• The lower velocity limit corresponds to limiting the fouling,

and the• upper velocity limit corresponds to limiting the rate of

erosion.• When sand and silt are present, the velocity is kept high

enough to prevent settling.

Number of Tubes Vs Reynolds Number

Number of Tubes Vs Heat Transfer Coefficient

Tube-Side Nusselt Number

For turbulent flow, the following equation developed by Petukhov-Kirillov is used:

2

322

1

28.3Reln58.1

1Pr2

7.1207.1

PrRe2

t

t

tt

tube

fWhere

f

f

Nu

Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data.Validity range: 104 < Ret < 5 x 106 and 0.5 < Prt < 2000 with 10% error.

For laminar flow, the Sieder and Tate correlation is be used.

31

PrRe86.1

LdNu itt

tube

is applicable for 0.48 < Prt < 16700 and (Ret Prt di/L)1/3 > 2.

The heat transfer coefficient for the tube-side is expressed as follows:

i

ttt d

kNuh

Thermal Analysis for Shell-Side

Tube Layout

• Triangular pitch (30o layout) is better for heat transfer and surface area per unit length (greatest tube density.)

• Square pitch (45 & 90 layouts) is needed for mechanical cleaning.

• Note that the 30°,45° and 60° are staggered, and 90° is in line.• For the identical tube pitch and flow rates, the tube layouts in

decreasing order of shell-side heat transfer coefficient and pressure drop are: 30°,45°,60°, 90°.

• The 90° layout will have the lowest heat transfer coefficient and the lowest pressure drop.

• The square pitch (90° or 45°) is used when jet or mechanical cleaning is necessary on the shell side.

Tube Layout & Flow Scales

A Real Use of Wetted Perimeter !

Tube Pitch

• Tube pitch Pt is chosen so that the pitch ratio is 1.25 < PT/do < 1.5.

• When the tubes are to close to each other (PT/do less than 1.25), the header plate (tube sheet) becomes to weak for proper rolling of the tubes and cause leaky joints.

• Tube layout and tube locations are standardized for industrial heat exchangers.

• However, these are general rules of thumb and can be “violated” for custom heat exchanger designs.

Equivalent Counter Flow : Hydraulic or Equivalent Diameter

• The equivalent diameter is calculated along (instead of across) the long axes of the shell and therefore is taken as four times the net flow area as layout on the tube sheet (for any pitch layout) divided by the wetted perimeter.

rerperimeteheattransfDe

area flow-FreeNet 4

Equivalent diameter for square layout:

O

OT

e

flowsquaree d

dP

PA

D

22

444

Equivalent diameter for Triangular layout:

2

843

44

22

O

O

e

flowtriangulare d

dP

PA

D

T

Shell-Side Reynolds Number

Reynolds number for the shell-side is based on the equivalent diameter and the velocity on the cross flow area at the diameter of the shell:

s

e

s

ss

DAm

Re

s

es

s

esss

DGDU

Re

Shell-Side Flow Area

The shell-side mass velocity is found with

BCPDBCNA

T

stcs ... oT dPC

2

4 Stubeprot

shell DCTPAN

A

2Ttubepro PCLA

Shell-Side Flow

Overall Heat Transfer Coefficient for the Heat Exchanger

The overall heat transfer coefficient for clean surface (Uc) is given by

Considering the total fouling resistance, the heat transfer coefficient for fouled surface (Uf) can be calculated from the following expression:

Outlet Temperature Calculation and Length of the Heat Exchanger

The outlet temperature for the fluid flowing through the tube is

The surface area of the heat exchanger for the fouled condition is :

and for the clean condition

where the LMTD is always for the counter flow.

The over surface design (OS) can be calculated from :

The length of the heat exchanger is calculated by

Hydraulic Analysis for Tube-Side

• The pressure drop encountered by the fluid making Np passes through the heat exchanger is a multiple of the kinetic energy of the flow.

• Therefore, the tube-side pressure drop is calculated by

228.3Reln58.1 ttubef

Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data.Validity range: 104 < Ret < 5 x 106

Where,

baffles ofNumber :bN velocitymass side Shell :sG

.correctionproperty Variable : 14.0

w

b

s

factorfriction side Shell :sf

Shell side Hydraulic Analysis

μb is the viscosity of the shell-side fluid at bulk temperature, and μw is the viscosity of the tube-side fluid at wall temperature.

The wall temperature can be calculated as follows:

Pumping Power

oilhotp

tubeoilhottube

pmP

oilcrudep

shelloilcrudeshell

pmP

Roadmap To Increase Heat Transfer• Increase heat transfer coefficent• Tube Side

– Increase number of tubes– Decrease tube outside diameter

• Shell Side– Decrease the baffle spacing– Decrease baffle cut

• Increase surface area– Increase tube length– Increase shell diameter à increased number of tubes– Employ multiple shells in series or parallel

• Increase LMTD correction factor and heat exchanger effectiveness– Use counterflow configuration– Use multiple shell configuration

Roadmap To Reduce Pressure Drop

• Tube side– Decrease number of tube passes– Increase tube diameter– Decrease tube length and increase shell diameter and

number of tubes• Shell side

– Increase the baffle cut– Increase the baffle spacing– Increase tube pitch– Use double or triple segmental baffles

• Study the effect of baffle spacing on size of heat exchanger.

• Study the effect of baffle spacing on total pumping power.