Back to Basics
Selecting Tube Inserts
for Shell-and-Tube
Heat Exchangers
Richard L. Shilling, P.E.
Heat Transfer Research, Inc.
A tube insert modifies flow stream characteristics to
enhance heat transfer. Here’s how to choose the
optimal insert to meet process requirements.
W
hen specifying a shell-and-tube heat exchanger,
the first steps are selecting a shell design (1) and
determining the most effective baffle arrangement
(2). After the shellside configuration has been established,
the focus shifts to tubeside heat transfer.
Tube inserts are useful tools that improve tubeside
performance in heat exchangers. Inserts are used for applications in which tubeside heat transfer is thermally limiting
and an increase in pressure drop is allowed. The best insert
type and design for a particular application depends on flow
conditions and fluid properties.
This article describes the most common types of inserts
and their principles of operation. Each insert type has one
or more means of flow modification, as well as specific
advantages and disadvantages. Often, but not always, the
benefit of an insert in two-phase flow is quite different than
the benefit obtained by the same insert in single-phase flow.
Understanding these concepts tremendously simplifies the
evaluation and selection of the proper insert for a given
application.
Tubeside flow patterns
Consider fluid flowing inside of a tube with a uniform
inlet velocity and temperature profile. At the beginning of
the flow, a lower-velocity boundary layer is initiated at the
tube wall by the no-slip boundary condition, while a highervelocity, inviscid flow region remains in the core near the
center of the tube (Figure 1). Similarly, a thermal boundary
layer forms that spans the distance from the wall to the position of the undisturbed inlet temperature (Figure 2). Eventually, both the velocity and thermal boundary layers grow and
fully displace the inviscid, isothermal core region.
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
Uniform Laminar
Velocity Profile
Hydrodynamic
Boundary Layer
Developing
Velocity Profile
Fully Developed
Hagen Poissuille
Laminar Velocity Profile
r
x
Hydrodynamic
Entry Length
Fully Developed
Hydrodynamic Flow
p Figure 1. At the start of fluid flow, a lower-velocity hydrodynamic
boundary layer forms at the tube wall.
Fully Developed
Laminar
Velocity Profile
Thermal
Boundary Layer
Uniform
Temperature
Profile
Fully Developed
Laminar Temperature Profile
Developing
Temperature Profile
r
x
Adiabatic
Starting
Length
Thermal
Entry Length
Thermally Fully
Developed Flow
p Figure 2. Likewise, a thermal boundary layer also develops at the
tube wall.
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Back to Basics
In laminar flow, where mixing is minimal, the growth of
the thermal boundary layer is limited by the fluid’s thermal
conductivity. Fluids with high thermal conductivities (such
as liquid metals) have short thermal entry lengths, and
fluids with low thermal conductivities (such as oils) have
long thermal entry lengths. Once the flow is fully thermally
developed, laminar heat transfer depends only on thermal
conductivity.
Single-phase heat transfer inserts
Inserts that augment single-phase heat transfer use one or
more of four distinct mechanisms to compensate for boundary layer effects: static mixing, boundary layer interruption,
swirl flow, and displaced flow.
Static mixing
All inserts produce some mixing when the flow stream
possesses enough kinetic energy to induce mixing due to
radial displacement in the vicinity of the insert. Static mixing, however, is the physical interchange of fluid particles to
different locations in the flow stream by mechanical (rather
than kinetic) means.
The purpose of the static mixer (Figure 3) is to transport,
by its mechanical construction, the fluid at the tube wall to
the center of the tube, to transport the fluid at the center of
the tube toward the tube wall, and to fold these transported
regions of fluid into each other. This dramat­ically improves
heat transfer, because it increases the local temperature difference between portions of the bulk (tubeside) fluid and the
tube wall. A common application for static mixing augmentation is in the cooling of highly viscous polymers where no
other method will produce acceptable results.
The effect of a static mixer is most pronounced and valu-
able when it is deployed in a flow that is laminarized (i.e.,
fully developed laminar flow). A flow becomes laminarized
when the thickness of the laminar boundary layer becomes
equal to the dimension of the flow channel and there is
no free flow stream beyond the boundary layer. In this
flow regime, static mixers are the only insert type that will
enhance heat transfer.
A useful dimensionless number for estimating the onset
of this regime is the Graetz number:
Gz = Re # Pr # `
Dh
j
L
^ 1h
where Re is the Reynolds number, Pr is the Prandtl number,
Dh is the tube’s hydraulic diameter (m), and L is the fluid
flow length from the tube’s entrance to the first boundary
layer interruption (m).
Laminarization occurs for viscous liquid flow (where
natural convection can be neglected) at Graetz numbers less
than about 20–200, depending on the shape of the flow channel. Below the Graetz number threshold, there is insufficient
energy in the flow for augmentation by any other mechanism. Heat transfer is limited by the thermal conductivity of
the liquid.
Because design calculations are based on an overall
mean temperature difference along the entire tube length, the
augmentation provided by static mixing is typically reported
in terms of an enhanced tubeside heat-transfer coefficient
instead of an increase in the local temperature difference. In
reality, the coefficient in the laminarized flow regime is constant, and all augmentation is due to temperature difference
enhancement. In some applications, a static mixing insert
can provide a sixfold improvement in heat transfer over that
in a tube without an insert.
For laminar flow in the thermal entry region, static mixer
heat-transfer equations are given in a form similar to the
Sieder-Tate equation for laminar flow (3):
Nu = 1.75` Re # Pr
Dh 0.33 c n m0.14
j
L
nw
(2)
where Nu is the Nusselt number, μ is the fluid viscosity
(N-s/m2), and μw is the fluid viscosity at the inside tube
wall’s temperature (N-s/m2). For static mixers, Eq. 2 can be
simplified to:
Nu = A^ Re # Pr hB c
p Figure 3. Static mixers augment tubeside heat transfer by mechanically
moving fluid elements to different locations in the flow stream.
20 www.aiche.org/cep September 2012 CEP
n 0.14
m
nw
^ 3h
where A is a correlation constant that includes the mixing
efficiency as a virtual boundary-layer interruption and B is
a constant that is normally equal or very close to 0.33. With
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
B set to 0.33, one measured heat-transfer data point for a
specific static mixer can be used to determine a value for A
and thus an equation that will closely predict heat transfer
performance for that mixer at other laminar flowrates.
Boundary-layer interruption
At higher Graetz numbers (often at Reynolds numbers
between 1 and 1,000), the thickness of the laminar boundary
layer can easily be reduced by boundary-layer interruption
inserts. These inserts come in a variety of shapes and sizes
(Figure 4). The key to their operation is that the interrupting portion of the insert must protrude out of the laminar
boundary layer at the tube wall. An interrupter “trips” the
boundary layer, causing it to thin to its minimum thickness,
which enhances heat transfer. After interruption, the boundary layer begins to thicken until the flow encounters the next
interruption.
Interruption inserts are commonly used for the augmentation of oil flows (such as lube oil) inside tubes when the
flow regime is laminar.
Some of these inserts can increase the heat transfer in
laminar flows by as much as five times, depending on the
fluid’s thermal conductivity. Typically, a threefold increase
can be expected for most hydrocarbon streams.
The magnitude of the heat transfer increase is inversely
proportional to the hydraulic diameter and interrupted flow
length. Equation 4 is useful for evaluating the effectiveness
of a boundary-layer interrupter relative to a bare tube and
for comparing the effectiveness of two different interrupter
inserts:
h1 = Dh2 L 2 1 3
`
j
h2
Dh1 L 1
^ 4h
where h is the heat-transfer coefficient (W/m2-K), Dh is the
tube inside hydraulic diameter (m), L is the interrupted flow
length (m), and the subscripts 1 and 2 denote the two inserts
or the bare tube and an insert.
A boundary-layer interrupter relies on a combination of
the interruption height and the spacing between interruptions. If the height/spacing combination permits the bound-
p Figure 4. Flow interrupters protrude out of the laminar boundary layer at
the tube wall, causing the boundary layer to thin.
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
ary layer to grow thicker than the interruption height, there
will be no heat-transfer augmentation, because the fluid in
the boundary layer will simply ooze around the protuberance
and continue on its path unaffected. In addition, interrupters
that are circumferentially symmetrical are more effective
than asymmetrical interrupters.
The simplest boundary-layer interruption device is a
corrugated metal strip whose width matches the tube’s inside
diameter. Another common design is a coiled wire with an
outside diameter matching the tube’s inside diameter; the
wire diameter and the pitch of the coil act as the interruption height and interruption spacing, respectively. Other
interruption inserts consist of a series of small, nested wire
loops; although the wires are small, these devices effectively
balance height and spacing.
Remember that most boundary-layer interruption inserts
Nomenclature
A
= correlation constant for static mixer heat-transfer
equation (Eq. 3)
B
= exponent for static mixer heat-transfer equation
(Eq. 3)
= specific heat, J/kg-K
Cp
D
= inside tube diameter, m
= equivalent inside tube diameter for turbulent flow
De
heat transfer, m
= inside hydraulic tube diameter, m
D h
= inside hydraulic tube diameter with Insert 1, m
Dh1
= inside hydraulic tube diameter with Insert 2, m
Dh2
G
= mass velocity of fluid, kg/s-m2
Gz
= Graetz number (Eq. 1)
= heat-transfer coefficient with core insert, W/m2-K
hcore
= heat-transfer coefficient without insert, W/m2-K
htube
= heat-transfer coefficient with Insert 1, W/m2-K
h 1
= heat-transfer coefficient with Insert 2, W/m2-K
h2
k
= thermal conductivity, W/m-K
L
= fluid flow length inside tube from entrance to first
boundary layer interruption, m
= interrupted flow length with Insert 1, m
L 1
= interrupted flow length with Insert 2, m
L 2
Nfa
= net free area inside tube with or without insert, m2
Nu = Nusselt number (Eqs. 2 and 3)
Pr
= Prandtl number = Cpμ/k
Re
= Reynolds number = ρvDh/μ
v
= velocity of the fluid, m/s
Greek Letters
μ
= fluid viscosity, N-s/m2
μw
= fluid viscosity at the inside tube wall temperature,
N-s/m2
ρ
= fluid density, kg/m3
CEP September 2012 www.aiche.org/cep 21
Back to Basics
are not considered static mixers because their only means of
redirecting flow relies on the kinetic energy of the flowing
fluid (rather than the mechanical movement imparted by
the static mixing element). At Graetz numbers below 20,
interrupters are ineffective. In addition, if the boundary layer
grows too fast for the interruption height and spacing, either
due to poor insert design or a change in fluid conditions, the
device will not augment heat transfer — it will only increase
pressure drop. Any tube insert for which there exists a lower
threshold flowrate where mixing does not occur is not a
static mixer.
Swirl flow
Swirl-flow augmentation techniques are effective with
upper-laminar flows through the transition regime — that
is, Reynolds numbers between 200 and 10,000. The most
common swirl-flow insert is the twisted tape (Figure 5). It
enhances heat transfer up to five times that of an empty tube,
depending on the flow regime in the empty tube. References
4 and 5 provide correlations for modeling twisted-tape heat
transfer under laminar flow and turbulent flow conditions,
respectively.
Contrary to popular belief, swirl flow is not a boundary-layer interruption technique. Rotational flow has two
effects. It imparts a helical flow path along the inside wall
of the tube, thereby producing a high velocity along the
tube wall that is a function of the helical flow angle. It
also imparts a combination of flow rotation and centripetal
force away from the center of the tube that, in single-phase
flow, increases mixing and turbulence at the tube wall. This
creates turbulent flows at Reynolds numbers that would be
characteristic of laminar or transition flows in tubes without
inserts. Inducing turbulence at a lower Reynolds number
enhances heat transfer.
Displaced flow
Displaced-flow inserts increase heat transfer by blocking the flow area farthest from the tube wall, which creates
higher velocities along the tube wall heat-transfer surface.
The simplest type of displaced-flow insert is a round cylinder (or core) that is supported in the center of the tube and
extends the entire length of the tube (Figure 6).
Displaced-flow inserts can effectively increase heattransfer coefficients by increasing already turbulent tubeside
flows. A very simple way to model their heat-transfer effect
in single-phase turbulent flow is to calculate a heat-transfer
equivalent diameter, De:
De =
p Figure 5. Twisted tapes are the most common type of swirl-flow insert.
4Nfa
rD
where Nfa is the net free area inside of the tube with or without an insert (m2). De will be smaller than the empty tube
diameter by an amount that depends on the diameter of the
core; the ratio of D/De is typically between 1.5 and 3.
In turbulent flow, the heat-transfer improvement due to
the core can be approximated by multiplying the plain tube
heat-transfer coefficient by D/De:
hcore = htube ` D j
De
p Figure 6. A long, cylindrical rod, or core, is the simplest type of
displaced-flow insert.
22 www.aiche.org/cep September 2012 CEP
^ 5h
^ 6h
where hcore is the heat-transfer coefficient inside a tube with
a core insert (W/m2-K) and htube is the heat-transfer coefficient inside a tube without an insert (W/m2-K).
For fluids such as water, heat transfer can be increased
by more than 2.5 times, depending on the available pressure
drop.
Although displaced-flow inserts can also enhance some
laminar flows, they are typically not as effective as the other
methods. In addition, care must be taken to avoid reducing
the hydraulic diameter to the point that the flow becomes
laminarized, which can lead to very poor heat-transfer
performance.
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
p Figure 7. A wire-wrapped core insert combines swirl-flow and
displaced-flow augmentation.
Flow regime overlap and compound enhancements
Flow regime overlap. Usually more than one type of
insert can be used to improve heat transfer. (The exception is
static mixers operating in the laminarized flow regime.) This
flow regime overlap among the various insert types is useful,
and can be extended through custom design.
For example, static mixers can be designed to augment
heat transfer in the entire laminar flow regime and beyond.
Flow interrupters can easily augment flows at Reynolds
numbers above 2,000. Swirl-flow inserts can augment flows
at Reynolds numbers below 20. However, for a given set of
fluid conditions, there is a preferred range over which each
mechanism is most efficient for heat transfer enhancement.
Compound enhancements. Every insert type enhances
heat transfer not only by the primary mechanism for which
it was designed, but also, to a lesser extent, by some of the
other mechanisms discussed earlier.
For example, although a twisted-tape insert is designed
for swirl-flow augmentation, it also provides a slight
enhancement due to displaced-flow augmentation because
the tape occupies space inside of the tube. Static mixers
are able to improve heat transfer outside of the laminarized
region because their construction provides interruption augmentation if there is sufficient kinetic energy in the flow.
Some inserts are specifically designed to take advantage of more than one kind of augmentation technique. For
instance, a wire-wrapped core insert combines displacedflow and swirl-flow augmentation. The wire-wrapped core
(Figure 7) consists of a cylindrical rod or tube around which
a smaller-diameter wire has been spirally wrapped. The core
and wire diameters are sized to increase the linear velocity
to the desired value based on the fluid flow characteristics.
The wire wrap angle is adjusted to further augment the heat
transfer by swirl flow. Under the right circumstances, it is
not uncommon to achieve a tenfold augmentation of heat
transfer over that in an empty tube.
Two-phase flow inserts
The static mixing, boundary-layer interruption, and displaced-flow mechanisms enhance two-phase flow primarily
by increased turbulence or enhanced mixing. In two-phase
flow, nonhomogeneous, poorly mixed flow is common. In
most cases, nonequilibrium two-phase flow produces lower
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
heat transfer than an equivalent flow whose phases are well
mixed.
Static mixers and interrupted-flow devices increase this
two-phase mixing and can improve heat transfer by a full
order of magnitude. However, without proper design, adding
these devices can result in an unacceptably high pressure
drop. Displaced-flow inserts will enhance two-phase flow
only as much as the resulting increased velocity will benefit
heat transfer.
In two-phase flow, the effects of swirl flow inside a tube
are different than the effects generated in single-phase flow.
Two-phase flow is usually very turbulent, and the relative
densities of the liquid and vapor phases often exceed 100:1.
Therefore, swirl flow acts as a centrifuge to concentrate the
denser liquid phase at the tube wall and the lighter vapor
phase near the tube center.
In tubeside boiling applications, the accumulation
of vapor at the wall of a tube without inserts reduces the
normally high convective boiling coefficient. Swirl flow
concentrates the liquid phase to be boiled at the tube wall,
which improves heat transfer over the entire vapor quality range. For some boiling conditions (such as horizontal
tubeside flow), swirl flow is the only means to achieve 100%
vapor quality exiting a tube. Because swirl flow is typically a
turbulent enhancement device, the pressure drop increase is
minimal for most new applications.
Practical considerations when using tube inserts
Pressure drop. In the design of new heat exchangers, where the flow length is adjusted based on the duty
achieved, most inserts (operating in their optimum regime)
can be designed to produce the same tubeside pressure drop
that would be experienced by a much longer plain tube. If an
insert is added to an existing heat exchanger, pressure drop
may significantly increase if the system was designed for
plain-tube conditions. In these cases, for the same flows, the
pressure drop can be two to six times the plain-tube pressure
drop, which sometimes makes a retrofit impractical.
Upset conditions. The system design must take into
account upset conditions that can change the tubeside
operating characteristics. Many inserts are attached to the
faces of the tubesheets to permit removal and/or replacement
during maintenance. The insert attachment can be designed
to withstand a substantial upset pressure drop if the supplier knows what upset conditions might be experienced.
An attachment design based on the steady-state pressure
drop with a small margin for condition changes may not be
able to withstand a substantially higher load (as produced
in an upset). For example, inserts have been found embedded in a downstream pump when upset conditions were not
accounted for.
Transient operation. Be certain to advise the designer if
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Back to Basics
transient operation is anticipated. Inserts can tremendously
augment heat transfer in laminar flows, but if the fluid flow
stops and is allowed to cool to ambient, the start-up pressure
drop with the inserts can approach 100 times the pressure
drop at normal operating conditions. In these cases, to prevent problems at start-up, it is important to heat the tubeside fluid to the approximate operating temperature before
attempting to reach the design flowrate.
Materials compatibility. Make sure that the insert material is compatible with the tube material and the fluid. For
example, carbon steel inserts in a water service tend to
“weld” themselves to the tube wall over a few months of
operation, sometimes requiring scrapping of the entire tube
bundle to replace them. The use of stainless steel and other
corrosion-resistant metallurgies is often the best way to
avoid this problem.
Fluid condition. Be aware of the conditions of the tubeside fluid. For example, when augmenting a laminar flow,
the fluid should be relatively free of particulates to prevent
tube plugging. In laminar flow, an interrupter can act as a
particulate dam, and a swirl-flow device may not produce
enough turbulence to carry the particles up and around each
helical rotation, so these designs should not be used in laminar flow containing particulates.
Anticipated fouling. It is important to evaluate the extent
and types of fouling expected and determine whether it will
be possible to remove the insert for maintenance. If hard,
crusty fouling (such as from polymerization) is expected
inside the tube, the fouling layer may fuse the insert to the
tube wall. Some inserts are strong enough that they can be
removed without damage (and draw a great deal of fouling
out of the tubes upon removal as well). If the insert is not
robust enough to be withdrawn from the tube without breaking, the fouling layer will need to be chemically dissolved to
allow withdrawal of the insert.
Typical application
A process stream is preheated using waste heat recovered
during the cooling of a light polymer. The polymer stream
requires Type 316 stainless steel, whereas carbon steel with
a 3-mm corrosion allowance is sufficient for the process
stream.
Maximum energy recovery involves a temperature cross
(i.e., the outlet temperature of the cold stream is higher than
the inlet temperature of the hot stream). The required tubular
heat exchanger must be either a single counterflow heat
exchanger or multiple shells in series. For the same reason,
the normal practice of increasing the number of tube passes
RichaRD L. ShiLLing, P.e., is Senior Engineering Consultant at Heat
Transfer Research, Inc. (HTRI; www.htri.net), where he provides
technical expertise and research, software, and engineering services
for various projects. Previously, he worked for more than 25 years for
Koch Heat Transfer Co. (formerly Brown Fin Tube Corp.) in Houston,
TX, where as Vice President of Engineering, he directed and managed
engineering research projects and oversaw engineering software
development. He has developed new heat exchanger enhancement
devices and techniques for equipment designs, and is experienced in
troubleshooting exchanger problems in a refinery. Shilling holds a BS
in mathematics from Grove City College in Pennsylvania and a BEng in
mechanical engineering from Youngstown State Univ. in Ohio. He chairs
the HTRI Exchanger Design Margin Task Force (EDMTF) and is the editor
of the heat transfer equipment section of Perry’s Chemical Engineers’
Handbook. A member of ASME, he is a licensed professional engineer
in Texas.
Table 1. Tube inserts augment heat transfer, and require a shorter tube length than a system that uses no inserts.
Design
No.
Description*
No. of Tube
Passes
h-shellside†,
W/m2K
h-tubeside‡,
W/m2K
dP-tubeside#,
kPa
Area¶,
m2
MTD**, K
1
(1)-12420 AFU, No Inserts
2
452.7
90.52
1.03
79.9
24.4
2
(1)-12228 AFU, Twisted-Tape Inserts
2
451.3
188.5
2.34
43.8
24.4
3
(1)-12144 AFU, Wire-Wrapped Cores
2
450.0
395.1
12.5
27.9
24.4
4
(1)-08240 AFU, Wire-Wrapped Cores
2
620.4
564.1
72.7
19.1
24.4
5
(2)-12180 AEU, No Inserts
8
332.8
202.3
61.0
52.5
21.2
*The number in parentheses is the number of shells. The first two digits after the dash indicate the shell inside diameter in inches,
and the final three digits represent the straight tube length in inches. The letters used in the heat exchanger descriptions are based
on the Tubular Exchanger Manufacturers Association (TEMA) nomenclature standards; A designates a removable front channel with
cover, F a shell with an axial baffle in the center that creates two shell passes, E a one-pass shell, and U a U-tube bundle.
†h-shellside
is the heat-transfer coefficient of the fluid flowing on the outside surface of the tubes.
‡h-tubeside
is the heat-transfer coefficient of the fluid flowing on the inside surface of the tubes.
#dP-tubeside
¶Area
is the total pressure drop, from inlet to outlet, of the fluid flowing inside the tubes.
is the total surface area of all the tubes in the bundle calculated based on the tube outside diameter.
**MTD is the mean temperature difference between the fluids flowing outside and inside the tubes.
24
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September 2012
CEP
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
to augment the tubeside heat-transfer coefficient requires
multiple shells in series.
Table 1 summarizes key parameters for five alternative
designs. Adding twisted-tape (Design 2) or wire-wrapped
core inserts (Design 3) to the tubes reduces the required
flow length while increasing the tubeside heat transfer.
This allows for a more compact design than the plain
tube exchanger (Design 1). Reducing the shell diameter
(Design 4) increases heat transfer, but with a significant
pressure drop penalty. Changing from a single two-pass shell
to two single-pass shells and increasing the number of tube
passes from two to eight, without adding inserts (Design 5),
increases tubeside heat transfer, but noticeably reduces
shellside heat transfer and increases pressure drop.
2. Bouhairie, S., “Selecting Baffles for Shell-and-Tube Heat
Exchangers,” Chem. Eng. Progress, 108 (2), pp. 27–33
(Feb. 2012).
3. Sieder, E. N., and G. E. Tate, “Heat Transfer and Pressure Drop
of Liquids in Tubes,” Industrial & Engineering Chemistry, 28,
pp. 1429–1435 (1936).
4. Manglik, R. M., and A. E. Bergles, “Heat Transfer and Pressure
Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes:
Part I — Laminar Flow,” ASME Journal of Heat Transfer,
115 (4), pp. 881–889 (1993).
5. Manglik, R. M., and A. E. Bergles, “Heat Transfer and Pressure
Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes:
Part II — Transition and Turbulent Flows,” ASME Journal of
Heat Transfer, 115 (4), pp. 890–896 (1993).
Additional Reading
Sununu, J. H., “Heat Transfer with Static Mixer Systems,” Kenics
Corp., Danvers, MA (1970).
www.aiche.org/cep or Circle No.118
Closing thoughts
Of the four inserts types, the best design for a particular
application will depend mainly on the specific space and
pressure drop limits. The decisions on the use of tube inserts
must be balanced with the proper selection of shell type
and baffle type in order to design the most efficient heat
CEP
exchanger for the required conditions.
Literature Cited
1. Lestina, T. G., “Selecting a Heat Exchanger Shell,” Chem. Eng.
Progress, 107 (6), pp. 34–38 (June 2011).
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
CEP September 2012 www.aiche.org/cep 25