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University of Calgary Chemical and Petroleum ENCH 607 - Heat Transfer
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Nashaat Nassar, Ph.D., P.Eng.
ENCH 607-Lecture-07
November 13, 2012
Heat Transfer and Heat
Transfer Equipment
ENCH 607-Dr. Nassar 2
Objectives
By the end of this lecture, students will obtain knowledge and skills on:
heat transfer mechanisms
heat transfer equipment
sizing and evaluating heat transfer equipment
performance
ENCH 607-Dr. Nassar 3
Introduction
Heat transfer is required for control of:
fluid temperature and/or its phase
rate of mass transfer between phases
rate of chemical reaction
temperature to prevent failure of equipment
The transfer of heat takes place in most equipment, but we deal
here with equipment that is designed specifically for the transfer of
heat. Heat transfer equipment can be divided into three basic types:
fluid-fluid, such as pipe in pipe, shell and tube, plate and
frame, etc
air coolers, such as fin fans, and cooling towers
fired heaters
Regardless of the type of exchanger, each makes use of the
fundamental heat transfer mechanisms.
ENCH 607-Dr. Nassar 4
Heat Transfer Mechanisms
By definition, heat is that energy transferred solely as a result of a
temperature difference that is independent of mass transfer.
There are three mechanisms, by which heat can be transferred:
conduction,
convection, and
radiation.
Heat is seldom transferred by a single mechanism, but usually by a
combination of mechanisms operating in series or parallel.
The analysis of heat transfer does not require that all parts be
solved with equal care. The engineer needs to develop the
experience to recognize the predominant mechanisms and base
calculations on these while neglecting minor effects.
ENCH 607-Dr. Nassar 5
Conduction
Conduction of heat occurs by the excitation of adjacent
molecules as opposed to overall mixing of the molecules.
Fourier’s law of heat conduction applies:
dx
dTkAQ (Eq 7-1)
Q: heat conduction in x direction (W)
k: thermal conductivity of conduction medium (W/m K)
A: cross sectional area normal to heat flow (m2)
dT/dx: temperature gradient in x direction (K/m)
The integration of Fourier’s equation provides the following
solutions for specific geometries as given in the next slide1:
ENCH 607-Dr. Nassar 6
Conduction
wdt
dTkAQ (Eq 7-2)
For perpendicular heat flow through a flat wall or very large
cylindrical tank wall.
ΔT: T1-T2 (K or oC)
tw: wall thickness (m)
For heat flow in a cylindrical shape where the heat flow is normal to
the axis, as in heat flow through a cylindrical vessel or pipe wall.
Cylindrical Shape:
Flat Surface:
)/ln(
2
io DD
TLkQ
(Eq 7-3)
ΔT: Ti -To (K or oC)
Do: outside diameter (m)
Di: inside diameter (m)
L: length of surface (m)
ENCH 607-Dr. Nassar 7
Conduction
Equation 7-3 can be multiplied by (Do-Di) in both numerator and
denominator to give:
Cylindrical Shape:
io
oi
io
io
DD
TT
DD
DDLkQ
)/ln(
)(2
(Eq 7-4)
io
oi
io
io
DD
TT
AA
AAkQ
)/ln(
)(2 (Eq 7-5)
D
TkAQ lm
2 (Eq 7-6)
Alm = is the log mean area = )/ln( io
io
AA
AA
ENCH 607-Dr. Nassar 8
Conduction
For radial heat flow through a spherical vessel
Spherical Shape:
)/1/1(
2
oi DD
TkQ
(Eq 7-7)
io
oi
DD
DDTkQ
2 (Eq 7-8)
D
TkAQ gm
2 (Eq 7-9)
Agm: is the geometric mean area = oi AA
The thermal conductivities for refractories and insulations are given in FIG 8-3 of
the GPSA Engineering Data Book. Thermal conductivities of metals can be found in
FIG 8-8 and FIG 9-8 in GPSA Engineering Data Book.
A conduction problem is shown as Example 8-1 in the GPSA Engineering Data
Book.
ENCH 607-Dr. Nassar 9
ENCH 607-Dr. Nassar 10
ENCH 607-Dr. Nassar 11
Convection is heat transfer that takes place by the physical
movement of molecules, usually a fluid passing next to a solid.
Most of the resistance to heat transfer occurs in a thin film at the
surface of the solid. This film exists even if the bulk fluid flow is very
turbulent.
Newton’s law of cooling applies in this situation:
Convection
ThAQ (Eq 7-10)
h = heat transfer coefficient (W/m2 K)
Convection can happen due to gravity and buoyant forces
(natural) or due to imposed circulation (forced).
ENCH 607-Dr. Nassar 12
Natural or free convection occurs where the only force promoting
fluid flow is a result of the temperature difference of the fluid.
For natural convection the heat transfer coefficient is governed by
the Nusselt equation.
Natural Convection
mGrCNu Pr (Eq 7-11)
where the dimensionless numbers are:
Nusselt number, k
hLNu
Grashof number, 2
23
TgDGr
Prandtl number, k
C p1000Pr
h = heat transfer coefficient (W/m2 K)
L = length of surface (m)
k = thermal conductivity of fluid (W/m K)
D = diameter (m)
ρ = fluid density (kg/m3)
g = acceleration of gravity (9.81 m/s2)
β = fluid coefficient of thermal expansion (K-1)
ΔT = temperature difference (K)
μ = fluid viscosity (Pa.s)
Cp = fluid heat capacity (kJ/kg K)
(Eq 7-12)
(Eq 7-13)
(Eq 7-14)
ENCH 607-Dr. Nassar 13
The values of C and m in equation 7-11 depend on geometry and dimensions
of the surface. Values for the coefficients for various conditions can be found
in FIG 8-4 of the GPSA Engineering Data Book.
Of most interest to us, are long horizontal cylinders (L>D) and vertical plates
or cylinders. Table 7-1 provides the coefficients.
Natural Convection
A natural convection problem is shown as Example 8-2 in the GPSA
Engineering Data Book.
Table 7-1 Vertical Plates or Cylinders (Y = Gr. Pr) C m
Y < 104 1.36 0.20
104< Y < 104 0.55 0.25
Y > 109 0.13 0.33
Horizontal Cylinder
D < 0.1 0.53 0.25
0.1 < D < 0.5 0.47 0.25
0.5 < D 0.11 0.33
Table 7-1: Heat transfer constants for vertical plates and horizontal cylinders
ENCH 607-Dr. Nassar 14
Natural Convection
ENCH 607-Dr. Nassar 15
Forced convection occurs when the fluid flow adjacent to the solid is
promoted by external forces such as pumping or agitation. This increases
the heat transfer rate.
There are two principle cases, one where viscosity effects are minimal, and
the other where viscosity is significant.
Forced Convection
Dittus-Boelter Equation
When viscosity effects are minimal
33.0PrRemCNu (Eq 7-15)
Seider-Tate Equation
When viscosity effects are important
14.0
33.0PrRe
w
bmCNu
(Eq 7-16)
μb = viscosity of fluid at bulk conditions (Pa s)
μw = viscosity of fluid at the wall conditions (Pa s)
ENCH 607-Dr. Nassar 16
The value of C and m in equations 7-15 and 7-16 depends on geometry and
dimensions of the surface. Values for the coefficients for various conditions
can be found in FIG 8-5 of the GPSA Engineering Data Book. The data
covers flat plates, flow across a cylinder, flow inside pipes, and flow on the
outside of tubes.
Forced Convection
ENCH 607-Dr. Nassar 17
Additional work has been done to fine tune the
predictions of the equations 7-15, and 7-16. Rearranging
the equations, we can write
Forced Convection
nm
D
kCh PrRe
(Eq 7-17)
with the values of C, m and n for various configurations given in Table 7-2.
ENCH 607-Dr. Nassar 18
Forced Convection
Table 7-2
ENCH 607-Dr. Nassar 19
Heat transfer in concentric pipes is often encountered. The heat transfer
coefficient of the fluid in the annular space can be predicted from equations
similar to those which apply for circular pipes; however the equivalent
diameter must be used. For the annular space
Convection in Noncircular Conduits
ioeq DDD (Eq 7-18)
Weigand has proposed the following for the turbulent flow heat transfer
coefficient on the outer wall of the inner pipe
45.04.08.01000023.0
i
opeq
eq D
D
k
CvD
D
kh
(Eq 7-19)
A forced convection problem is shown as Example 8-3 in the GPSA
Engineering Data Book.
ENCH 607-Dr. Nassar 20
Eq 7-17 and Table 7-2 can be used to estimate the heat transfer coefficient
for a bank of tubes.
The following equation is applied to gases.
Convection Normal to a Bank of Circular Tubes
n
DGC
k
hD
max (Eq 7-20)
Where Gmax is the product of density times velocity at the minimum cross
section. Gas properties are evaluated at the arithmetic mean of the gas and the
tube wall temperature.
The coefficients for tube banks 10 or more rows deep are given in Table 7-3
C n
Triangular pitch, centre to centre = 2 D 0.482 0.556
Square pitch, centre to centre = 2 D 0.229 0.632
Table 7-3: Coefficients for Grimison Equation
ENCH 607-Dr. Nassar 21
For liquids, Grimison’s equation is:
Convection Normal to a Bank of Circular Tubes
33.0
max1000
1.1
k
CDGC
k
hD p
n
(Eq 7-21)
For banks of tubes less than 10 rows deep, equation 7-20 can be used and
the heat transfer coefficient adjusted using the ratio in Table 7-4.
N 1 2 3 4 5 6 7 8 9 10
Triangular 1.0 1.10 1.22 1.31 1.35 1.40 1.42 1.44 1.46 1.47
Square 1.0 1.25 1.36 1.41 1.44 1.47 1.50 1.53 1.55 1.56
Table 7-4: Ratio of Mean Heat Transfer Coefficients for a Bank of Tubes N rows
Deep to the Coefficient for Tubes in a Single Row
ENCH 607-Dr. Nassar 22
Convection from a sphere can be described by an equation attributed to
Froessling.
Convection from Spheres
5.033.01000
6.00.2
Dv
k
C
k
hD p (Eq 7-22)
Convection Between a Fluid and a Packed Bed
Ranz developed a model to determine the heat transfer between a fluid
and a packed bed. Although the model assumes spherical particles, and
perfect rhombohedral packing, it provides a good approximation for most
packed beds. The equation for the heat transfer coefficient is
rhombohedral packing
Porosity: 26%
67.05.01000
)1(82.26
k
CDvCvh
psps
(Eq 7-23)
ENCH 607-Dr. Nassar 23
Radiation is the process whereby a body emits heat waves that may be absorbed, reflected,
or transmitted through a colder body.
A hot body emits a whole spectrum of wavelengths. Heat is transmitted through the full wave
length, infrared, visible, ultraviolet. An estimate of the radiant heat flux between two surfaces
is:
Radiation
111
21
4
2
4
1
TTF
A
Q (Eq 7-24)
σ = Stefan-Boltzmann constant (5.67 x 10-8 W/m2 K)
F = view factor (dimensionless)
T1 = temperature of hot surface (K)
T2 = temperature of cold surface (K)
ε1 = emissivity of hot surface
ε2 = emissivity of cold surface
The geometry or shape factor, F, is the fraction of the surface area that is
exposed to and absorbs radiant heat. The value of F must be determined by
an analysis of the geometry and should normally be greater than 0.67.
The emissivities of common materials are given in FIG 8-9 of the GPSA
Engineering Data Book. The emissivities of gases are more complex, as it
depends on the partial pressure of the gas and the path length. Gas
emissivities are given in FIG 8-12.
A radiation problem is shown as Example 8-6 in the GPSA Engineering Data
Book.
ENCH 607-Dr. Nassar 24
ENCH 607-Dr. Nassar 25
Heat is seldom transferred by only one mechanism and often heat is
transferred through a series of different materials. When this is true, the heat
transfer from each component must be consistent with the overall heat
transfer.
Overall Heat Transfer
Coefficients
Conduction through a series of materials must satisfy the overall
conduction equation as well as the individual conduction equations.
Series Conduction Through a Flat Surface
For conduction through a series of flat materials, such as a boiler wall
shown in Figure 7-1, the conduction equations are:
Series Conduction
Figure 7-1 Conduction
Through a Flat Wall
ENCH 607-Dr. Nassar 26
Overall Heat Transfer
Coefficients
Ak
xQTT
a
a 21
(Eq 7-25)
Ak
xQTT
b
b 32
(Eq 7-26)
Ak
xQTT
c
c 43
(Eq 7-27)
Ak
x
Ak
x
Ak
xQTT
c
c
b
b
a
a41
(Eq 7-28)
Adding these equations gives
and therefore
Ak
x
Ak
x
Ak
x
TTQ
c
c
b
b
a
a
41
(Eq 7-29)
This is equivalent to Ohm’s law for electricity, and the denominator is the overall
resistance to heat transfer. Since Q/A is the same for all layers, the temperature
gradient, ΔT/Δx, is inversely proportional to the thermal conductivity of the layer.
ENCH 607-Dr. Nassar 27
Overall Heat Transfer
Coefficients
lmcc
c
lmbb
b
lmaa
a
Ak
D
Ak
D
Ak
D
TTQ
2
1
41
(Eq 7-30)
Series Conduction Through a Cylinder
If conduction takes place through a cylinder, such as an insulated pipe, as
shown in Figure 7-2,
Where:
1
2
121
lnA
A
AAAlm
(Eq 7-31)
LDA ii (Eq 7-32)
Figure 7-2 Conduction Through Cylinders
ENCH 607-Dr. Nassar 28
Overall Heat Transfer
Coefficients
Series Conduction Through a Sphere
Similarly, for a sphere it can be shown that:
gmcc
c
gmbb
b
gmaa
a
Ak
D
Ak
D
Ak
D
TTQ
2
1
41
(Eq 7-32)
where the area term is now the geometric mean area, 21AAAgm
ENCH 607-Dr. Nassar 29
Finned Tubes
Gas side heat transfer coefficients are usually much less than liquid side
coefficients, and fins on the gas side are often used to increase the heat
transfer.
For tubes used in combustion gases, typical fins are 1.25 – 3.0 mm thick,
12.5 – 40 mm length, with a linear density of 80 - 240 fins/m.
The total external fin area and the cross flow area per linear meter are then
given by:
6
22
102
.
1000
.1
1000
ofoo
ddntndA
(Eq 7-34)
610
).(.
1000
ofoCS
ddtndA
(Eq 7-35)
Ao = outside fin area (m2)
Acs = cross sectional area of flow (m2)
do = outside pipe diameter (mm)
df = outside fin diameter (mm)
n = fin density (fin/m)
t = fin thickness (mm)
ENCH 607-Dr. Nassar 30
Finned Tubes
The surface area of the fin is not as efficient as the external pipe surface, so there is
an efficiency adjustment that is determined by using FIG 8-6 in the GPSA
Engineering Data Book. The fin efficiency is then applied to the total heat transfer
area.
In order to calculate the fin efficiency, from FIG 8-6, two parameters must be
determined as follows:
o
fo
o
f
d
Hd
d
d 2
(Eq 7-36)
Hf = fin height (mm)
ho = outside heat transfer coefficient (W/m2 oC)
kf = thermal conductivity of fin (W/m oC)
t = fin thickness (mm)
do = pipe diameter (mm)
df = fin diameter = do + 2Hf (mm)
(Eq 7-37)
Fin tip temperature must be considered if the tube is in the hot convection zone of a
furnace. The fin tip temperature can be determined from FIG 8-7 in the GPSA .
The maximum recommended fin tip temperature for various materials, and the
material thermal conductivities are given in FIG 8-8.
A fin efficiency problem is shown as Example 8-5 in the GPSA Engineering Data Book.
5.0
0405.0
tk
hHX
f
of
ENCH 607-Dr. Nassar 31
ENCH 607-Dr. Nassar 32
ENCH 607-Dr. Nassar 33
ENCH 607-Dr. Nassar 34
Overall Heat Transfer Coefficient
We have seen convective and conductive heat transfer in separate equations. When
heat is transferred from a fluid, through a pipe and into another pipe, convective and
conductive heat transfer are taking place in series.
It is customary to show the total heat transferred in terms of an overall heat transfer
coefficient, U. The overall heat transfer coefficient must be based on some specific
area, and it is common to use the outside area of the tube and write the heat transfer
equation as:
lmoo TAUQ
hi = inside pipe convective heat transfer coefficient (W/m2 K)
hfi = inside pipe fouling factor (W/m2 K)
tw = pipe wall thickness (m)
kw = pipe thermal conductivity (W/m K)
hfo = outside pipe fouling factor (W/m2 K)
ho = outside pipe convective heat transfer coefficient (W/m2 K)
Ao = outside tube area (m2)
Ai = inside tube area (m2)
(Eq 7-38)
For a tube:
ofolmw
ow
ifi
o
ii
oo
hhAk
At
Ah
A
Ah
AU
11
1
(Eq 7-39)
ENCH 607-Dr. Nassar 35
Overall Heat Transfer Coefficient
Note that the areas referred to above are the surface area of the pipe, and not
the cross sectional area available for flow.
The fouling resistances are often just provided as ri and ro:
fo
o
ifi
oi
hr
Ah
Ar
1
(Eq 7-40)
Typical range for fouling resistances is from 0.0001-0.0005 m2 oC/W.
The values of the inside and outside heat transfer coefficients can be calculated
from the Dittus-Boelter equation or the Seider-Tate equation. Typical values for
individual heat transfer coefficients are:
W/m2 oC
Gases (natural convection) 5-25
Gases (forced convection) 10-250
Liquids 100-10,000
Liquid metals 5000-250,000
Boiling 1000-250,000
Condensation 1000-25,000
Typical values for the overall heat transfer coefficients and fouling resistances are
given in FIG 9-9 of the GPSA Engineering Data Book. Values can also be found in
the literature.
ENCH 607-Dr. Nassar 36
Overall Heat Transfer Coefficient
ENCH 607-Dr. Nassar 37
Heat transfer theory is put into practice by construction
equipment to transfer heat between two streams without
physically mixing the streams themselves.
There are a variety of different heat exchangers to transfer
heat from one process fluid to another. The most common
types are pipe-in-pipe, shell and tube, spiral, and plate and
frame.
Special exchanger types include brazed aluminum, printed
circuit, and coil wound exchangers.
Before looking at the various exchangers, it is worthwhile to
look at Figure 7-3 showing the temperature profiles that can
be expected.
Heat Exchangers
ENCH 607-Dr. Nassar 38
Heat Exchangers
Figure 7-3 Exchanger Temperature Profiles
ENCH 607-Dr. Nassar 39
The lines shown in the previous figure represent fluids that have a constant heat
capacity. In actual fluids, the heat capacity is a function of temperature so the
cooling curves tend to be slightly curved.
For each side of the exchanger, the heat transferred into or out of the fluid must be
equal.
Heat Exchangers
111 )( outinP TTCmQ (Eq 7-41)
222 )( outinP TTCmQ (Eq 7-42)
22 vapHmQ (Eq 7-43)
If there is sensible heat and heat of vapourization on one side, then the Q
calculation will have to include a term to capture each region in the exchanger.
In addition, the exchanger must follow the overall heat transfer equation.
lmoo TFAUQ (Eq 7-44)
1
2
12
lnT
T
TTTlm (Eq 7-45)
ENCH 607-Dr. Nassar 40
The factor F has been added here to account for the
geometry of the exchanger. For counter-current flow, F = 1.0.
Most exchangers however use cross flow in the way they are
configured and the value of F is less than 1.0. The value of F
can be determined from FIG 9-4 through 9-7 in the GPSA
Engineering Data Book.
Again, if there is a phase change, then the exchanger may
have to be segmented and the calculation of Q will involve
multiple terms.
Heat Exchangers
ENCH 607-Dr. Nassar 41
ENCH 607-Dr. Nassar 42
There are a variety of heat exchanger calculations that can be
done.
The first calculations are related to the process design. The
engineer is interested in the amount of heat transferred and the
temperatures in the incoming and outgoing streams. At this point
the process engineer may also indicate the type of exchanger that
should be used, the allowable pressure drop through the
exchanger, and an estimate of the product UoAo.
The next step is the determination of the mechanical design of the
exchanger. This involves the physical layout of the exchanger,
determination of dimensions, number of tubes, required wall
thickness, and other design requirements in order to meet the
process specifications. We will focus on the process aspects, but
address some of the mechanical considerations.
When looking at the process aspects of an exchanger, there are
three types of calculations that can be performed.
Heat Exchanger Calculations
ENCH 607-Dr. Nassar 43
In design calculations, the two flow rates, and three temperatures will be known.
The objective is to determine the quantity of heat transferred, the unknown
temperature, and the product of UoAo. The solution proceeds as follows:
Q is calculated using one of the flow rates and the inlet and outlet
temperatures for that side of the exchanger,
The fourth temperature is calculated using the other fluid flow rate and the
third temperature (inlet or outlet for that side of the exchanger),
UA is determined from the overall heat transfer equation and an assumption
about the type of exchanger,
Details of U and A are then calculated iteratively along with allowable pressure
drops
The number, size, and pitch layout of tubes are assumed
Ao is calculated based on the tube data
Flow velocities are calculated, and inside and outside heat transfer
coefficients are calculated (hi and ho) from fluid properties, geometry, and
the Dittus-Boelter or Sider-Tate equations.
Uo is calculated from all of the individual heat transfer coefficients,
The calculated values of Ao and Uo are used to see if the overall duty, Q
can be met.
Pressure drop calculations are performed to see if the hydraulic
constraints are met.
1. Design Calculations
ENCH 607-Dr. Nassar 44
For performance calculations the exchanger is existing, so all of the geometry is
known, and Ao is known. The following process data should be available:
Four temperatures and two flow rates (best)
Three temperatures and two flow rates (better)
Four temperatures and one flow rate (good)
The above data is used to calculate Q. In the first case you can calculate Q with
two sets of data, and the results will likely be different. Engineering judgment
should be applied to determine if one calculated value is more reliable than the
other, or if the two Q values should be averaged. For the other two data sets, the
missing piece of data must be calculated and there is no check available for data
quality.
Once Q is determined, Uo can be calculated from the heat transfer equation and
the known exchanger geometry. The calculated value of Uo can be compared to
the design value of Uo. Individual components of the overall Uo; hi, ho, the
conduction term and the total fouling resistance are determined. The inside and
outside fouling resistances cannot be separated. The results indicate if the
exchanger is fouled more than its design fouling and if cleaning is required.
2. Performance Calculations
ENCH 607-Dr. Nassar 45
Often, the performance of an existing exchanger under new operating
conditions is desired. For this case, two flow rates are available, and two
inlet temperatures are available. The exchanger geometry and area, Ao is
known, but Uo must be determined based on the new flow rates and fluid
physical properties.
Multiple calculations of Uo may be required if the fluid physical properties
change appreciably, but often one calculation is sufficiently accurate. The
performance calculation is however a trial and error solution, as ΔTlm must
be determined. The solution proceeds as follows:
Assume one outlet temperature and calculate Q1
Using Q1, determine the other outlet temperature
Calculate Uo from hi, ho, tube data, and fouling resistances
Calculate ΔTlm
Determine Q2 from the heat transfer equation
If Q1 = Q2, then converged, else assume new outlet temperature and
repeat.
3. Performance Prediction
ENCH 607-Dr. Nassar 46
This type of exchanger is good for small heat loads where one stream is a
gas or viscous liquid, or for relatively small exchangers operating at high
pressure.
In these exchangers a piece of pipe serves as the shell. The internals
may be a single concentric pipe or a group of pipes. The internal pipes
have a U-tube design. The process diagram is shown in Figure 7-4.
Pipe-in-Pipe Exchangers
Shell side
Tube side
Counter current flow
Figure 7-4: Pipe in Pipe Exchanger (Brown Fin Tube)
ENCH 607-Dr. Nassar 47
Note that the configuration allows for true counter-current flow. It is
possible to enhance the heat exchanger by adding fins to the outside of
the inner tube, by twisting the inner tubes, or by adding turbulators to the
inside of the inner tube. A cutaway of a multi-tube pipe-in-pipe exchanger
is shown in Figure 7-5.
Pipe-in-Pipe Exchangers
Figure 7-5 Cutaway View of Pipe in Pipe Exchanger
ENCH 607-Dr. Nassar 48
Double pipe exchangers are intended for small duties, where surface
areas of 10-20 m2 are required.
They are usually assembled in 12, 15, or 20 ft sections, as longer lengths
result in sagging of the inner tube and poor flow distribution.
Standard sizes are:
Pipe-in-Pipe Exchangers
Outer Pipe (NPS) Inner Pipe (NPS)
2 1¼
2½ 1¼
3 2
4 3
ENCH 607-Dr. Nassar 49
The design equations are used to calculate duty, pipe diameter, wall thickness,
pressure drop, and heat transfer coefficient. Some iteration may be required given
the interaction of the variables.
The exchanger duty is calculated based on the flow, heat capacity, and
temperature change of one of the fluids. The other fluid flow rate or temperature
change is then determined.
A trial pipe diameter is selected based on a velocity of 1-3 m/s. Higher flow rates
will provide better heat transfer.
Wall thick can then be determined based on the operating pressure and the trial
pipe diameter. If the high pressure is in the annulus, a calculation for external
pressure will have to be done.
The heat transfer calculation is performed next. The inside and outside heat
transfer coefficients can be calculated using the Seider-Tate or the Dittus-Boelter
equations. For the inside heat transfer coefficient, the diameter to use is the inner
diameter of the inside tube.
For the outside heat transfer coefficient, the equivalent diameter for heat transfer
must be used. Similar to the equivalent diameter of pressure drop, the equivalent
diameter is defined as the ratio
Flow area/wetted perimeter
Pipe-in-Pipe Exchangers:
Design Equations
ENCH 607-Dr. Nassar 50
For heat transfer, the wetted perimeter is only the outside of the inner pipe. The
equivalent diameter for heat transfer is then
Pipe-in-Pipe Exchangers:
Design Equations
1
2
1
2
2
1
2
1
2
2
4
4
D
DD
D
DDDe
(Eq 7-46)
It is customary to use the outside area of the inner tube for the heat transfer
equation, so the overall heat transfer coefficient is given by
o
o
lmw
owi
ii
oo
hr
Ak
Atr
Ah
AU
1
1
(Eq 7-47)
The required surface area is now found using
lmo
oTU
QA (Eq 7-48)
ENCH 607-Dr. Nassar 51
Based on the required area and the inner pipe outer wall
diameter, the length of pipe is determined. In some cases,
two or three units can be connected together to provide the
required surface.
Pressure drop calculation can now be performed on the inner
pipe and the annular space using the methods in Lecture 5.
If the pressure drop is too high, then a larger diameter pipe is
required, and the calculation is repeated.
Pipe-in-Pipe Exchangers:
Design Equations
ENCH 607-Dr. Nassar 52
Shell and tube heat exchangers
are the most common heat
exchange device in plants.
The major manufactures have a
trade association (Tubular
Exchanger Manufacturers
Association, TEMA), which has a
set of standards.
Exchangers can be designed to
Class R, C, or B. Class R is the
most stringent and is generally
used for oil and gas applications.
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 53
Shell and Tube Exchangers
TEMA Type
Shell and tube exchangers can be made with different end closures
and different shell designs. These are designated in TEMA by a three
letter designation indicating front end, shell type, and rear end. Thus,
each exchanger is given three letter designation
A description of the types and their letter designation can be found in
FIG 9-23 in the GPSA Engineering Data Book. A shell and tube
exchanger selection guide is provided in FIG 9-24 to help select the
type of exchanger configuration.
Shell Front end
stationary head
type
Rear end
head type
ENCH 607-Dr. Nassar 54
Courtesy of
TEMA
ENCH 607-Dr. Nassar 55
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 56
Tubes
Exchanger tubes must be designed to withstand the differential
pressure across the tube, but should be checked to ensure that
they can handle the internal or external pressure if the start-up can
pressure up one side prior to the other.
Tubes come in various outside diameters, OD, and different wall
thickness. OD is usually specified in inches, and wall thickness in
Birmingham Wire Gauge, BWG. Tubing characteristics are
provided in FIG 9-25 of the GPSA Engineering Data Book.
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 57
Shells
The surface area required in an exchanger must be placed
inside a shell. The number of tubes that can fit into a circular
cross section depends on the tube OD, and the tube pitch.
Pitch refers to the distance between tube centres, as well as
the geometry of the layout.
Shell diameter can be estimated using FIG 9-26 through 9-28
in the GPSA Data Book.
An example calculation is provided as Example 9-3.
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 58
Typically, 1 in tubes on a
1.25 in pitch or 0.75 in
tubes on a 1 in pitch
Triangular layouts give
more tubes in a given shell
Square layouts give
cleaning lanes with close
pitch
Tube layout patterns
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 59
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 60
Design Tips
The tube length is often taken as 20 feet (about 6 m) as this is a common
length of tube that can be purchased. Other lengths are of course
available. The following general guidelines are useful:
Shell side
viscous fluid to increase the value of U
fluid with the lower flow rate
condensing or boiling fluid
fluid for which pressure drop is critical
if one fluid is a gas
Tube side
toxic fluid to minimize leakage
corrosive fluid
fouling fluid, higher velocity and easier to clean
high temperature fluids requiring alloy pipe
high pressure fluid to minimize cost
cool water
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 61
Should outside tube surface cleaning be required, square pitch is
preferred to triangular pitch.
The shell of the exchanger is often designed to 10/13th of the
design pressure of the tubes. This allows for the rupture of a tube,
and the pressuring up of the shell.
During the hydrotest, the shell would have been pressured up to
130% of its design pressure, so for a tube rupture case it has
already been proven that the shell can withstand this pressure.
Although there are exceptions, most tubes are 15-25 mm (5/8-1.0
in.) diameter, with 19 mm (3/4 in.) being the most common. The
minimum tube pitch is 1.25 times the tube OD.
Triangular pitch gives the best heat transfer coefficient and allows
more tubes to be placed in a shell.
Square pitch allows for easier cleaning of the outside of the tubes.
The tubes are supported in the shell by baffles.
The baffles also serve to force the fluid to flow across the tubes as
it flows down the shell, thus increasing the heat transfer coefficient.
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 62
Baffle Design
The most common type of baffle is the single
segmented baffle.
Baffles can be placed vertically or horizontally.
The baffle cut (Figure 7-6) sets the open area
for flow around the baffle. It is expressed as a
fraction of the inside shell diameter. Typical
baffle cuts are 0.20 – 0.35, and the opening in
the baffle should provide roughly the same
area as the crossflow area between the
baffles.
The distance between the baffles is termed
the baffle pitch, and typically ranges from 20-
100% of the shell diameter.
The baffle pitch and cut are the primary
factors affecting shell side pressure drop and
heat transfer coefficient.
The bundle in Figure 7-7 shows a very low
baffle cut and a very low baffle pitch, not the
typical values.
Shell and Tube Exchangers
Figure 7-6 Baffle Cut
ENCH 607-Dr. Nassar 63
Shell and Tube Exchangers
Figure 7-7 Shell and Tube Exchanger
ENCH 607-Dr. Nassar 64
Types of Baffles
ENCH 607-Dr. Nassar 65
Effect of small and large baffle cut
ENCH 607-Dr. Nassar 66
Shell and Tube Exchanger Thermal Design
The factor F in the heat transfer (Eq 7-44) equation is 1.0 in pipe-in-
pipe exchangers and in counter flow shell and tube exchangers with an
equal number of shell and tube passes.
If the number of shell and tube passes differ, or if the exchanger is a
crossflow type (TEMA X or J), then F will be less than 1.0.
As a general rule, one should not pick a configuration where F is less
than 0.8. The value of F can be determined by referring to FIG 9-4
through 9-7 in the GPSA Engineering Data Book. The figures provide F
values for various shell and tube configurations based on inlet and
outlet temperatures. The parameters on the charts are calculated using
equations 7-49 and 7-50.
Figure 7-8 shows the temperature variables, and Figure 7-9 shows a
typical F factor Plot.
Shell and Tube Exchangers
ENCH 607-Dr. Nassar 67
Shell and Tube Exchangers
Figure 7-8 Configuration for F Factor Calculation
11
12
tT
ttP
(Eq 7-49)
12
21
tt
TTR
(Eq 7-50)
T1 = shell side fluid inlet temperature
T2 = shell side fluid outlet temperature
t1 = tube side fluid inlet temperature
t2 = tube side fluid outlet temperature
The effectiveness of heat exchanger:
The capacity ratio in a heat exchanger:
ENCH 607-Dr. Nassar 68
Shell and Tube Exchangers
Figure 7-9 LMTD Correction Factor Chart
ENCH 607-Dr. Nassar 69
Shell and Tube Exchangers
The curves on Figure 7-9 can be calculated using
112
1121
1
1ln1
2
2
2
RRP
RRPR
RP
PR
FT (Eq 7-51)
When all four temperatures are known, as in a design case, the values of
P and R are calculated and then a configuration is selected. If the value
of F is less than 0.8, then increase the number of shell passes.
ENCH 607-Dr. Nassar 70
In order to determine the area required for an
exchanger, the overall heat transfer coefficient needs
to be determined.
Values of typical overall heat transfer coefficient and
typical fouling factors are given in FIG 9-9 in the
GPSA Engineering Data Book.
The TEMA standard contains more data for typical U
values. For detailed analysis, the overall heat transfer
coefficient is calculated using the individual film
coefficients.
Overall Heat Transfer Coefficients
ENCH 607-Dr. Nassar 71
Fluid Film Coefficients
Tube side and shell side film coefficients are calculated based on the
Dittus-Boelter or Siedler-Tate equations. Once film coefficients are
estimated, the overall heat transfer coefficient is calculated using Eq 7-47.
Calculation of the inside film coefficient is straight forward.
Calculation of the shell side coefficient is more complicated. The tube
bundle baffles provide cross flow and turbulence resulting in higher film
coefficients than for undisturbed flow along the tube axis. Flow across the
tubes also results in increased turbulence, and the velocity is not constant
across the bundle.
Triangular pitch provides more turbulence than square pitch, and film
coefficients are about 25% for triangular pitch.
Clearly, the same equation cannot be used to calculate the tube side and
the shell side film coefficients. The form of the equation however has been
retained, with special definitions used for the mass velocity and the
equivalent diameter.
ENCH 607-Dr. Nassar 72
Fluid Film Coefficients
For values of the Reynolds number from 2000 to 1,000,000, the following equation
applies
14.033.055.01000
36.0
w
pseseso
k
CGD
k
Dh
(Eq 7-52)
ENCH 607-Dr. Nassar 73
Fluid Film Coefficients
Calculation of the mass velocity is based on the maximum flow area of the
hypothetical tube row at the centre of the shell.
The length of the flow area is taken as the baffle spacing. There is usually no
row of tubes at the centre, but rather two equal maximum rows on either side,
having fewer tubes than computed for the centre. This difference is negligible.
The flowing area is then given by
T
ss
P
BCDa
'
(Eq 7-53)
s
sa
WG (Eq 7-54)
Ds = shell inside diameter (m)
C’ = clearance between tubes (mm)
B = baffle spacing (m)
PT = tube pitch (mm)
as = flow area (m2)
W = flow rate kg/s
and the mass velocity is
ENCH 607-Dr. Nassar 74
Fluid Film Coefficients
Reference to Figure 7-10 shows the tube spacing measurements.
Figure 7-10 Exchanger Tube Pitch
Tube pitch and clearance are related to the tube diameter as
oT dPC ' (Eq 7-55)
And the equivalent diameters for use in the Reynolds number are
o
oTes
d
dPD
1000
4 22 for square pitch (Eq 7-56)
o
oTes
d
dPD
1000
25.044.3 22 for triangular pitch (Eq 7-57)
ENCH 607-Dr. Nassar 75
For Shell and tube heat exchangers one needs to calculate
the pressure drops on both sides. Again, the tube side
pressure drop is easier to calculate because of the simpler
geometry. For the tube side, the pressure drop consists of
three components:
ΔPf = pressure drop due to friction in tubes (Pa)
ΔPN = pressure drop due to nozzles (Pa)
ΔPe = pressure drop due to tube entrance and exits (Pa)
In the absence of a phase change, the pressure drop in the
tubes is given by Darcy’s equation
Pressure Drop
Dg
LGfP
c
f
f
22 (Eq 7-58)
ENCH 607-Dr. Nassar 76
Chopey and Hicks20 provide a simple relationship for the
Fanning friction factor for the tubes
Pressure Drop
Re/16ff (Eq 7-59) Re < 2100
Re ≥ 2100 2.0Re/054.0ff (Eq 7-60)
Chopey and Hicks also provide a pressure drop
correlation for exit and entry losses for the nozzles on
the heads and the head to tube connections.
Nozzle 2/2
nN vKP (Eq 7-61)
Tube entrance and exit
2/2
tte vKNP (Eq 7-62)
vn = velocity in the shell nozzle (m/s)
vt = velocity in the tubes (m/s)
ρ = density (kg/m3)
Nt = number of tube passes
K = 0, head-nozzle fluid entrance loss
1.25, head-nozzle fluid exit loss
1.80, tube entrance and exit
ENCH 607-Dr. Nassar 77
The shell side pressure drop has a similar form with
Pressure Drop
e
Bsss
D
NDfGP
2
)1(2 (Eq 7-63)
Details of the friction factor, equivalent diameter, and effects of baffle
spacing can be found in the TEMA handbook.
Pressure drops in an exchanger depend on the system operating
pressure. Typical pressure drops are as follows:
Vacuum 5-10% of absolute system pressure
101-170 kPa 3.5-34.5 kPa
>170 kPa 45 kPa up to 50% of gauge pressure
For high pressure drop systems, tube velocity might limit due to erosion
concerns. Liquid velocity greater than 5 m/s may cause erosion.
ENCH 607-Dr. Nassar 78
Re-rating Existing Exchangers
It is often required to predict the performance of an
exchanger in a new service, or for a different flow rate.
FIG 9-10 and 9-11 in the GPSA Engineering Data Book
can be used for this purpose.
The figures are based on the fact that the performance at
the new condition, 2, can be prorated from the previous
condition, 1.
FIG 9-10 shows the relationship amongst the variables.
FIG 9-11 provides a base exchanger design that serves as
case 1 for various fluids.
An example calculations for a given exchanger data sheet
is given as Example 9-1.
ENCH 607-Dr. Nassar 79
Re-rating Existing Exchangers
ENCH 607-Dr. Nassar 80
Re-rating Existing Exchangers
ENCH 607-Dr. Nassar 81
Re-rating Existing Exchangers
ENCH 607-Dr. Nassar 82
A spiral exchanger is a true counter-
current exchanger that separates the two
fluids by a single plate.
Cold fluid enters the outside shell and
exits the center of the exchanger. Hot fluid
enters the centre of the exchanger and
circulates to the outside as shown in
Figure 7-11.
The surface area is increased by
increasing the width of the exchanger.
A gasketed plate covers and seals the
channels and can be removed for
cleaning.
The units are compact, have low pressure
drop, and a tight approach temperature.
They are ideal for handling sludge.
Capacities up to about 2000 kW are
available.
Spiral Exchangers
Figure 7-11 Spiral Exchanger
ENCH 607-Dr. Nassar 83
Plate and Frame Exchangers
Where applicable, the plate and frame exchanger has become a viable alternative to
other sorts of exchangers.
The advantages are the small footprint, light weight, lower cost and good heat transfer
performance.
The unit is limited by a maximum pressure of about 1600 - 2000 kPa.
A cut away view of a plate and frame exchanger is shown as Figure 7-12. The unit
consists of a number of corrugated plates that are held in a frame by bolts that pass
through the end plate. Each plate is gasketed to prevent leakage. There are four entry
ports on each plate that can be arranged in a number of ways to form different flow
patterns.
The plates normally have chevron type grooves that can have different angles. High
theta plates provide better heat transfer at the expense of additional pressure drop. The
plates can be mixed and matched to provide more efficient heat transfer.
Stainless steel is a common plate material, but titanium, Monel, nickel, Incoloy, and other
materials can also be used.
Plate thickness ranges from 0.5-3.0 mm with an average gap between plates of 1.5-5.0
mm. Most plates have an area of less than 1.5 m2, but as many as 600 plates can be
installed in one frame.
Temperature is limited by metallurgy and gasket material. Temperatures up to 250 oC
have been used, but 150 oC gives much better gasket life.
Plate sets can be purchased where one side is welded, which eliminates one set of
gaskets. This is a popular configuration for the rich amine side in a gas processing plant.
ENCH 607-Dr. Nassar 84
Plate and Frame Exchangers
Figure 7-12 Plate and Frame Exchanger
ENCH 607-Dr. Nassar 85
Plate and Frame Exchangers
The theta factor is also called the NTU (number of transfer units). Theta is
stated in terms of the required duty of one or both fluids.
A consistent set of units must be used to make theta dimensionless.
Theta is calculated as:
Theta Factor
Plm
oi
Cm
UA
T
tt
(Eq 7-64)
ti = inlet temperature to fluid channel
to = outlet temperature from fluid channel
ΔTlm = log mean temperature difference
U = overall heat transfer coefficient (W/m2 K)
A = total area of thermal plates (m2)
m = mass flow rate of fluid (kg/s)
CP = specific heat of fluid (kJ/kg K)
ENCH 607-Dr. Nassar 86
Plate and Frame Exchangers
4.065.0
10002536.0
k
CGd
d
kh Pe
e
(Eq 7-65)
The film coefficients for plate and frame exchangers may be estimated as:
Heat Transfer Coefficients
Turbulent flow11
Laminar flow12 14.067.062.0
1000742.0
w
PeP
k
CGdWCh
(Eq 7-66)
de = effective diameter (4Wb)/(2W+2b) (m)
W = plate width (m)
b = mean distance between plates (m)
G = mass velocity between plates (kg/m2 s)
μ = fluid viscosity (kg/m s)
CP = specific heat (kJ/kg K)
μw = fluid viscosity at the wall (kg/m s)
k = thermal conductivity (W/m K)
The overall heat transfer coefficient is then given as
21
21
111rr
hk
t
hU w
(Eq 7-67)
t = plate thickness (m)
kw = thermal conductivity of plate (W/m K)
ENCH 607-Dr. Nassar 87
Plate and Frame Exchangers
LMTD and F
The LMTD is calculated as for any other exchanger. F is a function of θ and the
plate arrangement.
For low values of θ and for equal passes of hot and cold fluid, F approaches
1.0. The factor F decreases rapidly as the number of passes of hot and cold
fluid become unequal. The passes may become unequal if there is a large
difference in the flow rates of the hot and cold fluids. If this is the case, a plate
and frame exchanger may not be the best choice.
Table 7-3 provides some typical F factors.
7-3
ENCH 607-Dr. Nassar 88
Plate and Frame Exchangers
The pressure drop depends on:
plate design,
flow rate, and
flow pattern.
Pressure drop is usually less than in a comparable shell and
tube unit.
High pressure drop increases the shear stress in the
exchanger and tends to keep the exchanger cleaner.
Pressure drop calculations are best done by the vendor.
Pressure Drop
ENCH 607-Dr. Nassar 89
Compablock Exchangers
The Compablock exchanger, as
shown in Figure 7-13, is a
variation of the plate and frame
units.
In a Compablock, the plates are
completely welded together and
there are no gaskets between the
plates.
There are four gaskets on the
cover plates.
The unit can be used for liquid-
liquid exchange, and as a
reboiler or a condenser.
The units are compact and
robust.
Figure 7-13 Compablock Exchanger
ENCH 607-Dr. Nassar 90
Compablock Exchangers
ENCH 607-Dr. Nassar 91
Compablock Exchangers
ENCH 607-Dr. Nassar 92
Brazed Aluminum Exchangers
Brazed aluminum exchangers have been employed in cryogenic gas processing
facilities since the 1950s.
Brazed aluminum exchangers are composed of alternating layers of corrugated fins
and flat separator sheets called parting sheets.
The number of layers, type of fins, stacking arrangements, and stream circuiting will
vary depending on the exchanger service and duty.
A cut away view (FIG 9-34) and a good description of terms are provided in the
GPSA Engineering Data Book.
Brazed aluminum exchangers are compact and light weight and can operate at
pressures up to 9500 kPa. The surface area to volume ratio for a brazed aluminum
exchanger is 6-8 times greater than for a shell and tube unit. A brazed aluminum
exchanger has a density of 30-35% of a shell and tube unit. This means that about
25 times more surface per kilogram of exchanger is possible.
Because of the compact design, temperature approaches of 1.5 oC are possible on
single-phase fluids, and 2.75 oC on two-phase fluids.
Brazed aluminum exchangers should be used with clean fluids. Upstream filters may
be used to keep fine particles out.
Brazed aluminum exchangers must be protected from elemental mercury and
caustic, as both are extremely corrosive to aluminum. Hydrogen sulphide and carbon
dioxide are not a concern as long as water does not condense out of the stream.
ENCH 607-Dr. Nassar 93
ENCH 607-Dr. Nassar 94
Printed Circuit Exchangers (PCHE)
Printed circuit exchangers are highly compact, corrosion resistant heat
exchangers capable of operating at pressures up to 50,000 kPa and
temperatures from cryogenic to several hundred degrees Celsius.
PCHEs are constructed from flat plates into which flow channels have been
chemically milled or etched. The plates are stacked and diffusion bonded
together to form a core. Fluid heads and nozzles are attached to the core to
direct fluids to the appropriate channels. Two or more fluids can be
accommodated in a core, and virtually any arrangement of passes or flow
combinations is possible.
Passages are typically 2 mm semicircles, see Figure 7-14, so the fluids need to
be relatively clean or blockage of the passages will take place.
Materials of construction include stainless steels, titanium, nickel, and nickel
alloys.
The diffusion bonding process ensures that the surfaces are sealed, and these
units are well suited to high pressure gas operations.
Vapourization and condensation of fluids is readily accommodated.
The major drawback is that failures have occurred due to thermal cycling. This
type of exchanger should not be used in situations where the feed streams have
large changes in flow rates or temperatures. A complete PCHE is shown in
Figure 7-15.
ENCH 607-Dr. Nassar 95
Printed Circuit Exchangers (PCHE)
Figure 7-15 A Complete PCHE
Figure 7-14 PCHE Internals
ENCH 607-Dr. Nassar 96
Coil Wound Exchangers
Spiral wound exchangers are used in natural gas
liquefaction plants as the main cryogenic exchanger (MCE).
Thousands of small diameter aluminum tubes are wrapped
around a core and encased in a shell.
These units are the heart of the liquefaction process.
Figure 7-16 shows a spiral wound exchanger.
ENCH 607-Dr. Nassar 97
Coil Wound Exchangers
Figure 7-16 Coil Wound Exchanger
ENCH 607-Dr. Nassar 98
Aerial Coolers
Aerial coolers or air-cooled exchangers are used to cool
fluids with ambient air.
Aerial coolers are relatively simple, but in cold climates, the
addition of freeze protection measures makes them
somewhat more complex.
The advantage of cooling with air is that it is plentiful and
cheap.
The temperature achievable with aerial cooling is however
about 15 oC above the ambient temperature and significant
extra cost is incurred to reduce this approach temperature.
ENCH 607-Dr. Nassar 99
Mechanical Arrangements
Aerial coolers typically come as forced draft units or induced draft units. Forced
draft units have the tube section on the discharge side of the fan, while induced
draft units have the tubes on the suction side of the fan.
A diagram showing typical layouts is shown in FIG 10-2 of the GPSA Engineering
Data Book. More than one tube bundle can be included in a unit, and more than
one fan bay can be included in a unit as shown in FIG 10-3.
Advantages and disadvantages of each layout are described in the GPSA. For
process fluids above 175 oC, forced draft units should be used to keep the fan
components from becoming too hot.
Fan sizes range from 0.9 – 8.5 m, but units of 4.3-4.9 m diameter are the most
common.
Drivers are usually electric and a speed reducer is required to match motor speed
to fan speed. A fan tip speed of 3650 m/min or less is common. V-belt drives are
used up to about 22 kW and gear drives are used for higher power. Maximum
motor size is limited to 37 kW.
The tube bundle is fabricated with multiple rows (3-8) of finned tubes and may
have one pass or two passes. Tube diameters are 16-38 mm, fin heights are 12.7
mm to 25.4 mm, and fin densities range from 276 – 433 fins/metre.
Tubes in gas processing services are usually carbon steel, but stainless steel may
also be used in some services.
For low pressure service, header boxes are built with a cover plate. For higher
pressure service the end plate must be thicker, and then the header will have plugs
for access to the tubes. FIG 10-5 illustrates the two types of header boxes.
ENCH 607-Dr. Nassar 100
The outlet temperature of the process stream is controlled, but if the process fluid becomes
viscous or freezes when cooled, the air temperature may also have to be controlled. When the
ambient temperature is low, recirculation of warm air is often required to keep the bottom row of
tubes from becoming too cold.
The two control schemes must work together. Refer to FIG 10-7 in the GPSA Engineering Data
Book to see the arrangement of air control louvers on a typical cooler.
Temperature control of the process stream is usually accomplished by changing the amount of air
that flows past the coil. The top louver can be adjusted to change the back pressure on the fan and
change the air flow rate. In addition, fan drivers often have two speed motors or completely
variable speed motors. In addition, in multi-fan units, one of more of the fans can be shut off. Some
older units had variable pitch fans, but these were generally high maintenance units and have
mostly been replaced by variable speed drives.
The cooler is designed to provide sufficient cooling when the ambient temperature is high. In
Alberta, a typical design air temperature is 28 - 30 oC. In the Middle East, the air design temperature
can be as high as 50 oC. The process temperature that can usually be achieved is 12 - 15 oC higher
than the air temperature. As the ambient temperature falls below design, less air is required to
provide the process duty, and the fans will slow down or stop to reduce the air flow. As the ambient
temperature gets colder, the operators will close the manual louvers, to limit the intake of cold air.
At some point, the top louvers will start to close to reduce the air flow even more. If this does not
keep the inlet air warm enough, the recirculation louvers will open to allow warm air to mix with the
incoming air. Since the cooler is designed for an inlet air temperature of 28 – 30 oC, there is no
problem with making the process temperature if the blended air temperature is 10 –15 oC. If the
inlet air temperature is allowed to get too cold, the bottom row of tubes can freeze.
Process Control
ENCH 607-Dr. Nassar 101
Thermal Design
Thermal design of an aerial cooler is done in much the same manner as for any
other exchanger. The basic design equations are:
21 TTmCQ P (Eq 7-68)
12 ttCmQ Paa (Eq 7-69)
LMTDFAUQ (Eq 7-70)
The temperature correction factor, F in the heat transfer equation can be found
from FIG 10-8 or 10-9 in the GPSA Engineering Data Book. The factor is based
on values of P and R as follows:
11
12
tT
ttP
(Eq 7-71)
12
21
tt
TTR
(Eq 7-72)
ENCH 607-Dr. Nassar 102
Thermal Design
t1 = inlet air temperature (oC)
t2 = outlet air temperature (oC)
T1 = inlet process temperature (oC)
T2 = outlet process temperature (oC)
U = overall heat transfer coefficient (W/m2 K)
Normally Q is known, U and LMTD are calculated and the
equation is solved for the required area, A.
The procedure is complicated by the fact that the air flow
is not known, and hence the air outlet temperature is not
known.
The design is thus iterative with regard to air flow, which
depends on the type of coil, number of tube rows, fin type
etc.
ENCH 607-Dr. Nassar 103
ENCH 607-Dr. Nassar 104
ENCH 607-Dr. Nassar 105
Preliminary Design Calculations
For preliminary calculations for gases, the overall heat transfer coefficients in
Table 7-4, based on bare tube area may be used:
7-4
ENCH 607-Dr. Nassar 106
Preliminary Design Calculations
For preliminary calculations for liquids, the overall heat transfer coefficients in
Table 7-5, based on bare tube area may be used:
7-5
ENCH 607-Dr. Nassar 107
Preliminary Design Calculations
For preliminary calculations for condensing fluids, the overall heat transfer
coefficients in Table 7-6, based on bare tube area may be used.
7-6
ENCH 607-Dr. Nassar 108
Preliminary Design Calculations
The optimum air temperature rise across the tubes may be estimated
using
1
1212
2..00088.0 t
TTUCFtt
(Eq 7-73)
210025.089.0 TTCF (Eq 7-74)
The above equations will allow the calculation of the value of maCpa
required for the air flow. The Cpa value for the air must consider the relative
humidity of the air.
Cpa = molar heat capacity of air (kJ/kmol K)
RH = relative humidity (%)
Pvpw = vapour pressure of water at air temperature T1 (kPa)
P = air pressure (kPa)
P
PRH
PPRH
C
vpwvpw
pa
100
1.29100
5.33 (Eq 7-75)
ENCH 607-Dr. Nassar 109
Preliminary Design Calculations
The ambient air pressure is a function of plant elevation in metres, h, and is
given by:
128.29exp325.101
t
hP (Eq 7-76)
Once Cpa is determined, the molar flow of air, ma, is found.
The molecular mass of the air is determined, considering the relative humidity.
P
PRH
PPRH
MW
vpwvpw
a
100
29100
18 (Eq 7-77)
With the MW of the air and the ambient air conditions, the density of the inlet air
can be determined.
1Rt
PMWa (Eq 7-78)
ENCH 607-Dr. Nassar 110
Preliminary Design Calculations
P
Rtmq a
a1 (Eq 7-79)
With the molar flow rate of air and the ambient conditions, the volumetric
flow of air is found.
With the volumetric air flow rate determined, the fan power requirements
can be estimated using
aaqP
kW
(Eq 7-80)
ΔPa = air side pressure drop (kPa)
qa = actual air flow rate (m3/s)
η = fan efficiency (0.4 - 0.75: 0.70 for planning)
For planning purposes, the pressure drop per tube row is 25 - 35 Pa,
and a typical cooler has 3 - 6 tube rows.
ENCH 607-Dr. Nassar 111
Rigorous Design Calculations
Rigorous design calculations are best done with a
computer program such as HTRI. This program will
calculate:
heat transfer coefficients,
air flow rate,
pressure drops and
duty based on coil design parameters.
Most EPC firms should have the program available.
The GPSA Engineering Data Book provides an example
of a more rigorous hand calculation. The procedure is
basically to assume a design, and then prove that it is
correct.
The procedure is detailed in Example 10-1.
ENCH 607-Dr. Nassar 112
Performance Testing
Performance testing of an aerial cooler is complicated by the
fact that the air flow rate must be determined. This is done by
measuring the air velocity in a number of locations just under
the fan.
The ambient air temperature is available, so the air outlet can
be determined from the value of Q. Q is determined from the
process side conditions.
One can now calculate the overall heat transfer coefficient, the
individual heat transfer coefficients for both the air side and
process side, and then determine the overall fouling factor. If
the overall fouling factor is larger than the design value, the
cooler is fouled and may benefit from cleaning.
Both the inside of the tubes and the fins may need to be
cleaned.
ENCH 607-Dr. Nassar 113
1. Bennett, C.O., and J.E. Myers, Momentum, Heat, and Mass Transfer, McGraw Hill, 1974.
2. Seider, E.N. and G.E. Tate, Ind. & Eng. Chem., 28, (1936), p. 1429.
3. Colburn, A.P., Trans. AIChE, 29, (1933), p. 174.
4. Marriott, J., “Where and How to Use Plate Heat Exchangers”, Chem. Eng., April 5, 1971, p. 127.
5. API Standard 661, “Air Cooled heat Exchanges for General Refinery Service”.
6. Steinmeyer, D., “Understanding ΔP and ΔT in Turbulent Flow Heat Exchangers”, Chem. Eng. Prog.,
(June 1996), p. 49.
7. Poddar, T.K. and G.T. Polley, “Optimize Shell and Tube Heat Exchanger Design”, CEP (Sept. 2000),
p.41.
8. Standard of the Tubular Exchanger Mft. Assoc., 6th Edition, New York, 1978.
9. Chen, C.C., Chem. Eng., (Mar. 1984), p. 155
10. Bell, K.J., Oil and Gas J., (Dec. 4,1978), p.59.
11. Buonopane, R.A. et al., Chem. Eng. Prog., Vol. 59, No. 7, (1963), p. 185.
12. Jackson, B.W., and R.A. Troup, Chem. Eng. Prog., Vol. 60, No. 7, (1964), p. 62.
13. Burn, J., A.M. Johnston, N.M. Johnston, “Experience With Printed Circuit Heat Exchangers”,
European GPA Continental Meeting, Budapest, (1999).
14. Rorschach, R.L., Oil and Gas J., (June 13, 1966), p.90.
15. Brown, R., Chem. Eng.,(Mar. 27,1978), p. 108.
16. Glass, J., Chem. Eng.,(Mar. 27,1978), p. 120.
17. Baker, W.J., Hydr. Proc. (May 1980), p.173.
18. Ganapathy, V., Oil and Gas J., (Dec. 3,1979), p.74.
19. Rubin, F.C., Hydr. Proc. (Dec. 1980), p.147.
20. Chopey, N. P., Hicks, T. G., Handbook of Chemical Engineering Calculations, McGraw-Hill, 1984, pp.7-
86.
References Read Section 9 of the GPSA Engineering Data Book – Heat Exchangers
Read Section 10 of the GPSA Engineering Data Book – Air-Cooled Exchangers