Kern Method of SHELL-AND-TUBE HEAT EXCHANGER Analysis
Mechanical Engineering Department I I T Delhi
Simplified Procedures using SemiEmpirical Correlations.….
Properties Density, kg/m3 Specific heat, kJ/kg K Viscosity iscos ity,, cPoise cPo ise Thermal conductivity, W/m.K
Crude Oil 915 2.62 0.664/0.563 0.124
Heavy gas oil 890 3.08 0.32/0.389 0.14
Properties Density, kg/m3 Specific heat, kJ/kg K Viscosity iscos ity,, cPoise cPo ise Thermal conductivity, W/m.K
Crude Oil 915 2.62 0.664/0.563 0.124
Heavy gas oil 890 3.08 0.32/0.389 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.
tube t ut Ac N t m By using above Eq. and replacing Ac by p d i2 /4, number of tubes can be calculated as
N t
tube m 2 i
t ut p d
where d i 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 PetukhovKirillov is used:
f Nutube
2
Re t Pr t
f 1.07 12.7 2
1 2
2
Pr t 3 1 2
Where f 1.58 ln Re t 3.28
Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data. Validity range: 10 4 < Ret < 5 x 10 6 and 0.5 < Pr t < 2000 with 10% error.
For laminar flow, the Sieder and Tate correlation is be used.
Nutube
Ret Pr t d i 1.86 L
1
3
1/3 > 2. is applicable for 0.48 < Pr t < 16700 and (Ret Pr t d /L) i
The heat transfer coefficient for the tube-side is expressed as follows:
ht Nut
k t d i
Thermal Analysis for Shell-Side
Tube Layout • Triangular pitch (30 o 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 < P T/do < 1.5. • When the tubes are to close to each other (P T/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.
De 4
Net Free - flow area heattransf erperimete r
Equivalent diameter for square layout:
De square
4 A flow P e
2 p 2 4 P T d O 4
Equivalent diameter for Triangular layout:
p d O
3 P 2 p 2 4 d O 8 4 T
De triangular
4 A flow P e
p d O
2
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:
Re s
sU s De s
G s De s
Re s
s m A s
De s
Shell-Side Flow Area The shell-side mass velocity is found with
A s N tc .C . B A shell
N t A pro tube CTP
D s P T p
4
A protube CL P
2 T
C . B
DS 2
C P T d o
Shell-Side Flow
Overall Heat Transfer Coefficient for the Heat Exchanger The overall heat transfer coefficient for clean surface (U c ) is given by
Considering the total fouling resistance, the heat transfer coefficient for fouled surface (U f ) 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 L M T D 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 N p passes through the heat exchanger is a multiple of the kinetic energy of the flow.
•
Therefore, the tube-side pressure drop is calculated by
2
f tube 1.58 ln Ret 3.28
Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data. Validity range: 10 4 < Ret < 5 x 10 6
Shell side Hydraulic Analysis
Where,
G s : Shell side mass velocity N b : Number of baffles
s
b w
0.14
: Variable property correction.
f s : Shell side friction factor
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
P tube
P shell
hot oil ptube m p
hot oil
crudeoil p shell m p
crudeoil
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
