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Unformatted text preview: Taylor 6/13/03 10:00 AM Page 28 Reactions and Separations RealWorld
Modeling of Distillation
Ross Taylor,
Clarkson University
and University of Twente
Rajamani Krishna,
University of Amsterdam
Harry Kooijman,
Shell Global Solutions International Previously, simulations based on
nonequilibrium, or ratebased, models were
considered impractical due to their complexity.
However, with everincreasing computing
power, these simulations are not only feasible,
but in some circumstances they should be
regarded as mandatory. C HEMICAL ENGINEERS HAVE BEEN
solving their distillation problems using the
equilibrium stage model since Sorel ﬁrst used
the model for the distillation of alcohol over 100 years
ago. Seader (1) has provided an elegant history of the
ﬁrst century of equilibrium stage modeling. Real distillation and absorption processes, however, normally do
not operate at equilibrium.
In recent years, it has become more common to simulate distillation and absorption
as a masstransferratebased
A
operation, using what have beA
come known as nonequilibrium, or ratebased, models. This
article presents a brief outline
B
of nonequilibrium modeling
and provides pointers to the
growing literature in this ﬁeld. an entire column, but the most common approach is to
divide the column into a number of discrete “stages,”
as depicted in the third panel. Thus, the question to be
addressed ﬁrst is: How do we model these stages?
The equations that model equilibrium stages are
known as the MESH equations. MESH is an acronym
referring to the different types of equation that are used
in the model: C The Stage Concept A,C
V1
Stage 1 A, B, C Modeling the
oldfashioned way
To model a plant like the
one shown in Figure 1, we decompose the entire plant into
smaller units. In this case, the
plant contains a distillation column that is shown enlarged in
the center panel of the ﬁgure.
There are many ways to model 28 www.cepmagazine.org July 2003 CEP Reflux V2 L1 Vj Lj1 B I Figure 1. Decomposition of a chemical
plant into unit operations, and
decomposition of the distillation into stages. Stage j
Vj+1 Lj Taylor 6/13/03 10:00 AM Page 29 • M stands for material balances
• E stands for equilibrium relationships (to express the
assumption that the streams leaving the stage are in equilibrium with each other)
• S stands for summation equations (mole fractions are
perverse quantities and won’t sum to unity unless you
force them to)
• H stands for heat or enthalpy balances (processes conserve energy, as well as mass).
There are few mathematical models in any branch of
engineering that are as wellsuited to computer solutions
and that have prompted the development of as many different algorithms as have the MESH equations. It would not
be too far from the truth to claim that it is equilibrium
stage calculations that
brought computing into
Nomenclature
chemical engineering —
c
= number of components,
and chemical engineers
dimensionless
to computers (1).
ct = total concentration, mol/m3
The equilibrium stage
d
= driving force for mass
model is so simple in
–1
transfer, m
Di,k = MaxwellStefan diffusivity, m2/s concept, so elegant from
the mathematical viewEi,MV = Murphree tray efficiency,
point, the basis for so
dimensionless
f
= proportionality coefficient
many commercial colk
= mass transfer coefficient, m/s
umn simulation proK = vaporliquid equilibrium
grams, and been used to
constant,
simulate and design so
Ni = molar ﬂux of species i,
many real columns, that
mol/m2s
it seems almost heretical
P = pressure, Pa
to mention that the
p
= partial pressure, Pa
model is fundamentally
R = gas constant, J/molK
t
= time, s
ﬂawed. However, chemiT
= temperature, K
cal engineers have long
u
= average velocity
been aware of the fact
x
= mole fraction, dimensionless
that the streams leaving
y
= mole fraction, dimensionless
a real tray or section of a
Greek letters
packed column are not in
κ
= mass transfer coefficient of
equilibrium with each
binary pair in multicomponent
other. In fact, the separamixture, m/s
tion actually achieved
µ = Chemical potential, J/mol
depends on the rates of
η = distance along diffusion path,
mass transfer from the
dimensionless
vapor to the liquid phasSubscripts
es, and these rates dei
= component index
pend on the extent to
I
= referring to interface
which the vapor and liqj
= stage index
k
= alternative component index
uid streams are not in
m = reaction index
equilibrium with each
t
= total
other. The next question
Superscripts
is: What have we done
F = referring to feed stream
about this fundamental
I
= referring to interface
weakness?
L
= referring to liquid phase
The conventional way
V = referring to vapor phase
around this shortcoming of what is referred to frequently as the rigorous model (with
some disregard for semantic accuracy), is to employ efficiencies. Several kinds of efficiency have been used in distillation column modeling and design, including the overall,
Murphree, Hausen and vaporization efficiencies. The Murphree efficiency (2) is arguably the most widely employed
by distillation engineers and is deﬁned by:
Ei, MV = yiL − yiE
*
yiL − yiE (1) where the overbars indicate the average mole fraction in the
entering (E) and leaving (L) streams, as depicted in Figure 2.
For packed columns, we use something analogous to the V,yL L L = Liquid
V = Vapor
yE = Mole fraction in
entering stream
yL = Mole fraction in
leaving stream L
V,yE I Figure 2. Idealized ﬂow patterns on a distillation column tray.
stage efficiency called the HETP (Height Equivalent to a
Theoretical Plate). In practice, efficiencies and HETPs
often are estimated simply from past experience with similar processes. However, for new processes, this approach is
of no use whatsoever (and often fails even for old ones).
Chemical engineers have, therefore, devoted a great deal of
effort to devising methods for estimating efficiencies and
HETPs (3, 4).
These different kinds of efficiencies all attempt to represent the extent to which the real trays in a tray column (or
the entire column itself) depart from equilibrium. The
HETP is a number that is easy to use in column design.
However, there are several drawbacks to employing efficiencies and HETPs in a computer simulation based on the
equilibrium stage model:
• There is no consensus on which deﬁnition of efficiency is best (although many distillation experts will admit to
a preference for Murphreetype efficiencies).
• The Murphree vaporphase efficiency is not the same CEP July 2003 www.cepmagazine.org 29 6/13/03 10:00 AM Page 30 Reactions and Separations as the liquidphase efficiency on the same tray (the Hausen
efficiency does not share this property).
• The generalized Hausen efficiencies (sometimes
known as Standart efficiencies (5)) are the most fundamentally sound, but are impractically complicated to calculate
and are never used in practice.
• Vaporization efficiencies, favored by some in the past
because they are easy to include in computer programs, are
not often used today.
• Efficiencies vary from component to component, and
from tray to tray, in a multicomponent mixture. Very rarely
is this fact taken into account in a simulation model that
uses efficiencies.
• Efficiencies vary from stage to stage in a tray column.
HETPs are a function of height in a packed column. These
behaviors of efficiencies and HETPs are often not accounted for in conventional column simulation software.
These weaknesses of the standard model have been
known for a long time (6). Thus, our third question is: How
should we deal with the shortcomings of the standard model? Modeling in the real world
In recent years, a new approach to the modeling of distillation and absorption processes has become available —
the socalled nonequilibrium, or ratebased, models. These
models treat these classical separation processes as the
masstransferrategoverned processes that they really are.
The building blocks of the nonequilibrium model shown
in Figure 3 are sometimes referred to as the MERSHQ
equations, where:
• M represents material balances
• E represents energy balances
• R represents mass and heattransfer rate equations
• S represents summation equations
• H represents hydraulic equations for pressure drop
• Q represents equilibrium equations.
Some of these equations are also used in building equilibrium stage models; however, there are crucial differences
in the way in which the conservation and equilibrium equations are used in the two types of model. In a nonequilibrium model, separate balance equations are written for each
distinct phase. Figure 3 shows that the material balance for
each phase includes terms to represent the mass transferred
from one phase to the other. For the equation used in the
equilibrium stage model, the sum of the phase balances
yields the material balance for the stage as a whole. The energy balance is treated in a similar way — it is split into
two parts, one for each phase, each part containing a term
for the rate of energy transfer across the phase interface.
Modeling distillation and related operations as the ratebased processes that they really are requires us to face up to
the challenge of modeling interfacial mass and energy transfer in tray and packed columns. This is something that we do
not do in the conventional equilibrium stage model (although we face essentially the same problem if efficiencies 30 www.cepmagazine.org July 2003 CEP are to be estimated from a mathematical model (3, 4)). The
molar ﬂuxes at a vapor liquid interface may be expressed as:
NiV = ciV kiV ( yiV − yiI ) (2) NiL = ciL kiL ( xiI − xiL ) (3) where ciV and ciL are the molar densities of the superscripted phases, yiV is the mole fraction in the bulk vapor phase,
xiL is the mole fraction in the bulk liquid phase, and xiI and
yiI are the mole fractions of species i at the phase interface.
kiV and kiL are the masstransfer coefficients for the vapor
and liquid phases.
The inclusion in the model of the mass transport equations introduces the mole fractions at the interface, something we have not had to deal with so far, at least not explicitly. It is common to assume that the mole fractions at the interface are in equilibrium with each other. We may, therefore, use the very familiar equations from phase equilibrium
thermodynamics to relate the interface mole fractions:
yiI = Ki xiI (4) where the superscript I denotes the interface compositions
and Ki is the vaporliquid equilibrium ratio for component
i. These Kvalues are evaluated at the interface compositions and temperature using the same thermodynamic models used in conventional equilibrium stage simulations. The
interface composition and temperature must, therefore, be
computed during a nonequilibrium column simulation. In
equilibrium stage calculations, the equilibrium equations
are used to relate the composition of the streams leaving
the stage and the Kvalues are evaluated at the composition
of the two exiting streams and the stage temperature (usually assumed to be the same for both phases).
VL,
yL LE,
xE Vapor T Mass
Transfer
Energy
Transfer VE,
yE
LE = Liquid entering stream
LL = Liquid leaving stream
T = Temperature
VE = Vapor entering stream
VL = Vapor leaving stream Y
X Interface Taylor Vapor Liquid
Film
Film
Liquid LL,
xL
xE = Liquid mole fraction in entering stream
xL = Liquid mole fraction in leaving stream
yE = Vapor mole fraction in entering stream
yL = Vapor mole fraction in leaving stream I Figure 3. Schematic diagram of a nonequilibrium stage. Taylor 6/13/03 10:00 AM Page 31 Physical Property Requirements Activity Coefficients
Vapor Pressures
Fugacity Coefficients
Densities
Enthalpies
Diffusivities
Viscosities
Surface Tension
Thermal Conductivities Activity Coefficients
Vapor Pressures
Fugacity Coefficients
Densities
Enthalpies Model Requirements: Equations Mass Balances needs of equilibrium (right)
and nonequilibrium (left)
models. MassTransfer Coefficients
HeatTransfer Coefficients
Interfacial Areas Energy Balances Phase Energy Balances Equilibrium Eqs. Equilibrium Eqs. I Figure 4. Physical property Phase Mass Balances Summation Eqs. Summation Eqs.
MassTransfer in
Vapor Phase I Figure 5. Equations used in
equilibrium (right) and
nonequilibrium (left) models. MassTransfer in
Liquid Phase
Energy Transfer Physical properties
Figure 4 identiﬁes the major physical property requirements. It is obvious that nonequilibrium models are more
demanding of physical property data than are equilibrium
stage models (except when trayefficiency or HETP and
equipmentdesign calculations are carried out, but those
are done after a simulation and are not needed to carry out
the column simulation). The only physical properties required for an equilibrium stage simulation are those needed
to calculate the Kvalues and enthalpies. Those same properties are needed for nonequilibrium models as well.
Masstransfer coefficients and interfacial areas must
be computed from empirical correlations or theoretical
models. There are many correlations for masstransfer
coefficients in the literature (3, 4). These coefficients
depend on the column design, as well as its method of
operation.
We do not believe that the need for additional physical properties should be a reason not to use a nonequilibrium stage model. Estimation methods are available for
these properties, although they are typically much less
accurate than methods for evaluating thermodynamic
properties (7). However, these properties are needed only
in so far as they are required to estimate masstransfer
coefficients. In fact, the sensitivity of these coefficients
to any of these properties is not that large, and the fact
that we do not always have accurate estimation methods
should not act as a deterrent to their use. Rather, it
should serve as a spur to more research and to the development of better methods for transport property prediction and estimation in much the same way as the need for
reliable phase equilibrium models has served as motivation for the development of methods to predict thermodynamic properties. Equipment design
The estimation of masstransfer coefficients and interfacial areas from empirical correlations nearly always requires us to know something about the column design. At
the very least, we need to know the diameter and type of
internal (although usually we need to know more than
that, since most empirical correlations for masstransfer
coefficients have some dependency on equipment design
parameters, such as the weir height of trays). This need for
complete equipment design details suggests that nonequilibrium models cannot be used in preliminary process design (before any actual equipment design has been carried
out). However, this is not true. Column design methods
are available in the literature, as well as in most process
simulation programs. It is straightforward to simultaneously solve equipment sizing calculations and stageequilibrium calculations (8). This does not add signiﬁcantly to
the difficulty of the calculations, and it allows nonequilibrium models to be used at all stages of process simulation,
including preliminary design, detailed plant design and
simulation, troubleshooting and retroﬁtting. In fact,
nonequilibrium models can be particularly valuable in
troubleshooting and retroﬁtting, even to the point of helping identify what particular equipment design detail might
be responsible for a column failing to do what it was designed to do.
Solving the model equations
There has been so much work done on developing computational methods for solving the equilibrium stage model
equations that we may essentially use the same approaches
to solve the nonequilibrium model equations (8). The equations required by the two kinds of model are summarized
in Figure 5. The fact that the nonequilibrium model in CEP July 2003 www.cepmagazine.org 31 6/13/03 10:00 AM Page 32 Reactions and Separations 28 Sieve Trays
p = 5.5 to 6 bar nonequilibrium model, it must be remembered, does not use efficiencies.
McCabeThiele diagrams (9) can be
constructed from the results of a
nonequilibrium simulation (Figure 8),
and are just as useful for understanding
column behavior as they are for binary
distillation. Note how the triangles do
not touch the equilibrium line. Properties:
Peng Robinson C3: 1.5
iC4: 56.5
nC4: 4.5
iC5: 1.9
1
C6: 2.9 mol s
C7: 4.9
C8: 34.3
C9: 3.9 Example 2: A notsosimple absorber. Consider the simple packed
column depicted in Figure 9. The rich
ammonia and air mixture enters at the
bottom where the ammonia is absorbed. The enthalpy of absorption is
released, causing the temperature of
the liquid to rise. As a result, water
evaporates. The mass transfer process
in the gas therefore involves three
species — ammonia, water and (essentially stagnant) air. Toward the top of
the column, the gas encounters cold
entering water. Therefore, water vapor
condenses near the top of the column,
and we now have codiffusion of ammonia and water through air. We
should not ignore water vaporization at
the bottom and condensation at the top
in the analysis. The resulting tempera C3: 1.5
iC4: 56.5
nC4: 4.5
iC5: 0.03 iC5: 1.86
C6: 2.9
C7: 4.9
C8: 34.3
C9: 3.9
Downcomer Area
10%
11%
Weir Length
1.9m
2.1m
Hole Area % of Active
12%
10% 0.6m I Figure 7. Murphree efficiency proﬁles (predicted) for the debutanizer shown in Figure 6. I Figure 6. Debutanizer adapted from Example 9.1 in Ref. 9.
The simulation program created the tray design. volves more equations is not a concern. In our experience,
the equations of both models are about equally simple (or
difficult) to solve.
Numerical solution of the nonequilibrium model equations provides the chemical engineer with all of the quantities normally associated with the conventional equilibrium stage model — temperatures, ﬂowrates, mole fractions, etc. Nonequilibriummodel calculations also provide a great deal of additional information, such as physical and transport property proﬁles, and equipment design
and operating data.
Example 1: A simple debutanizer. Consider the
simple debutanizer shown in Figure 6. The flowrate and
composition profiles do not differ to any significant extent from the results that you would obtain with a conventional equilibrium stage model (although the number
of stages and feed stage location would be different).
However, a nonequilibrium model can also provide considerable additional information, such as masstransfer
rates and predicted efficiency profiles (Figure 7). The 32 www.cepmagazine.org July 2003 CEP 1.2 Murphree Efficiency Taylor 1 0.8 0.6 0.4
5 10 15 20 25 Stage Number
Propane
Isobutane nButane
Isopentane nHexane
nHeptane nOctane
nNonane 6/13/03 10:00 AM Page 33 1 d1 = f12 x1 x 2 (u1 − u2 )
YC4 (5) where d1 is the driving force for diffusion and ui is the average velocity of species i.
This expression may be derived using nothing more
complicated than Newton’s second law — the sum of the
forces acting on the molecules of a particular species is directly proportional to the rate of change of momentum
(Ref. 11 provides a more complete derivation). The rate of
change of momentum between different species is proportional to the concentrations (mole fractions) of the different
species and to their relative velocity. In Eq. 5, f12 is the coefficient of proportionality and is related to a friction factor. Eq. 5 is more often written in the form: YC4 + YC5
0.8 0.6 0.4 0.2 d1 = XC4 x1 x 2 (u1 − u2 )
D12 (6) XC4 + XC5
0
0 0.2 0.4 0.6 0.8 1 I Figure 8. McCabeThiele diagram for the debutanizer shown in Figure 6.
ture profiles along the column show a pronounced bulge
near the bottom (Figure 9). where D12 is the MS diffusion coefficient.
The MS equations are readily extended to multicomponent systems simply by adding similar terms on the righthand side to account for momentum exchanged between
each pair of differing types of molecules. For a ternary
mixture, for example, we would have two terms on the
right, one of momentum exchange between molecules of
types 1 and 2, and a second term for momentum transfer
between molecules of types 1 and 3: The MaxwellStefan approach
x x (u − u2 ) x1 x3 (u1 − u3 )
d1 = 1 2 1
−
(7)
Equations 2 and 3 are included in all basic mass transD12
D13
fer texts and chemical engineering handbooks, and are
taught to all chemical engineers in undergraduate chemiwith the equations for species 2 and 3 obtained by rotating
cal engineering degree programs. Strictly speaking, these
the subscripts.
equations are valid only for binary
systems and under conditions where
Water
the rates of mass transfer are low.
Most industrial distillation and absorption processes, however, involve more
than two different chemical species.
The most fundamentally sound way
Gas Temperature
Condensation of Water
to model mass transfer in multicompoAbsorption of Ammonia
nent systems is to use the MaxwellStefan (MS) theory (11–13). In our opinion, the MS approach to mass transfer
Liquid
should be what is taught to students,
Temperature
Evaporation of Water
but rarely is that done, even at the gradAbsorption of Ammonia
uate level; most texts give little or no
serious attention to the matter of mass
transfer in systems with more than two
20
25
30
35
components (exceptions include the
texts by Seader and Henley (9) and
Temperature, ˚C
Air Ammonia
Benitez (14)).
The MS equation for diffusion in a
I Figure 9. Ammonia absorber adapted from Example 8.8 in (10).
binary ideal gas mixture is:
Height Taylor CEP July 2003 www.cepmagazine.org 33 6/13/03 10:00 AM Page 34 Reactions and Separations The generalization of this expression to mixtures with
any number of different species is:
xi x k (ui − uk )
Dik
k =1 di = xi dµ i
RT dz (12) c (8) The difference approximation of this expression is
somewhat more involved, since we have to include the
derivative of the activity (or fugacity) coefficient (13). which is more familiar to us in the form:
x N − x k Ni
d1 = − ∑ i k
ct Dik
k =1 Example 3: The need for rigorous MaxwellStefanbased nonequilibrium models. The differences
in column composition profiles predicted by a rigorous
nonequilibrium model that incorporates the MS equations may differ significantly from those predicted by
an equilibrium stage model. Consider the experimental
work of Springer et al. (15) on the distillation of water
(1), ethanol (2) and acetone (3) carried out in a 10tray
column operated at total reflux. The residue curve map
for this system is shown in Figure 10a. This system
shows a binary minimum boiling azeotrope between
water and ethanol; an almoststraight distillation
boundary connects the azeotrope with pure acetone.
A measured composition profile, carried out in the region to the left of the distillation boundary, is shown in
Figure 10b. Simulations of the column, starting with the
vapor composition at the column top, are also shown. It is
evident that the nonequilibrium model is able to follow
the experimentally observed column trajectories much
better than the equilibrium model. The differences in the
column composition trajectories are due to differences in
the component Murphree efficiencies (Figure 10c).
Differences in component efficiencies could have a
significant impact on a column design that aims for a specific purity at either ends of the column. For example, for
the water (1), ethanol (2) and acetone (3) system operat c (9) where we have replaced the velocities with the molar ﬂuxes Ni = ciui.
For an ideal gas mixture, the driving force is the partial
pressure gradient:
d1 = 1 dpi dxi
=
P dz
dz (10) Solving the MS equations might involve the computation
of various matrices and functions thereof (11). In practice,
we most often employ a simple ﬁlm model for mass transfer
with a simple difference approximation to the MS equations:
x i N k − x k Ni
ct κ ik
k =1
c ∆xi = − ∑ (11) where xi is the average mole fraction over the ﬁlm. The MS
masstransfer coefficients κij can be estimated from existing correlations. For a nonideal ﬂuid, the driving force is
related to the chemical potential gradient:
a b 1.0
Ethanol Composition 1.0 0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0 Water Composition 0.8 0.6 0.4
0.02 0.04 0.06 Water Composition Residue Curve Lines
Azeotrope
Distillation Boundary Nonequilibrium Model
Equilibrium Model
Experimental Data Component Murphree Efficiency, Ei d1 = − ∑ Ethanol Composition Taylor c
2.0 1.5
1.0 0.5
0.0
2 4 6 8 10 Stage Number
Water
Ethanol
Acetone I Figure 10. Distillation of water (1), ethanol (2) and acetone (3) in a bubble cap tray column: (a) residue curve map; (b) experimental composition trajectory for Run 6, compared with the nonequilibrium and equilibrium simulations; and (c) component Murphree efficiencies for Run 6 (15). 34 www.cepmagazine.org July 2003 CEP 6/13/03 10:00 AM Page 35 stages are needed to reach the specified 96% ethanol purity at the top, whereas the equilibrium model indicates
that only 25 stages are needed. In this case, the nonequilibrium model takes “the scenic route” to reach the de0.8
sired top purity. Ignoring the differences in component efficiencies may lead to severe underdesign.
Columns operating close to the distillation boundary
0.6
may experience much more exotic differences in the column composition trajectories predicted by the nonequilibrium and equilibrium models. For operation with the
0.4
Nonequilibrium Model
same water, ethanol and acetone system, Figure 12a
Equilibrium Model +
shows that the experiments cross the straightline distil60% Efficiency
lation boundary (15), something that is forbidden by the
0.2
equilibrium model (16). The nonequilibrium model is
NEQ = 39 Stages
able to retrace this boundarycrossing trajectory, whereas
EQ, 60% Efficiency = 25 Stages
the equilibrium model remains on one side of the distil0.0
lation boundary. The nonequilibrium model predicts that
0.00
0.04
0.08
the column gets progressively richer in water as we proWater Composition
ceed down the column to the reboiler, whereas the equilibrium model anticipates that the column gets enriched
I Figure 11. Comparison of nonequilibrium and equilibrium models for
in ethanol as the reboiler is approached. The root cause
distillation of water (1), ethanol (2) and acetone (3) in a bubble cap tray colof this behavior lies with the differences in the efficienumn with the objective of reaching 96% ethanol purity at the top.
cies of the individual species (Figure 12b); the component efficiency of ethanol varies siga
b
nificantly from tray to tray. Comparing the component efficiency values
1.0
1.4
in Figures 10c and 12b reveals that
Water
even though the mass transfer paramEthanol
1.2
Acetone
eters used in the nonequilibrium
0.8
1.0
model are identical for these two runs,
0.8
the calculated component efficiency
0.6
values bear no resemblance to one an0.6
EthanolWater
other. This underlines the difficulty of
Binary Azeotrope
0.4
0.4
trying to emulate the performance of
0.2
the nonequilibrium model by fudging
0.2
component efficiency values. There is
0.0
0.0
0.1
0.2
2
4
6
8
10
no way that this can be achieved.
Component Murphree Efficiency, Ei Ethanol Composition 1.0 Ethanol Composition Taylor Water Composition Stage Number Nonequilibrium Model
Experimental Data
Distillation Boundaries
Equilibrium Model I Figure 12. Distillation of water (1), ethanol (2) and acetone (3) in a bubble
cap tray column: (a) experimental composition trajectory for Run 26, compared with the nonequilibrium and equilibrium simulations; and (b) Component Murphree efficiencies for Run 26 (15). ing in the region to the left of the distillation boundary,
let us demand a purity of 96% ethanol at the top of the
column. For a specified feed composition and reflux
ratio, the column composition trajectories for the
nonequilibrium model and the equilibrium model (assuming 60% efficiencies for all components) are presented in
Figure 11. The nonequilibrium model suggests that 39 Other applications
The principles outlined above are
applicable to a wide range of related
processes. Below, we very briefly
consider some of these applications.
Threephase distillation. Threephase distillation remains relatively poorly understood
compared to conventional distillation operations involving just a single liquid phase. Simulation methods currently in use for threephase systems employ the equilibrium stage model (16). It is important to be able to
correctly predict the location of the stages where a second liquid phase can form (to determine the appropriate
location for a sidestream decanter, for example). The
limited experimental data available suggest that efficiencies can be low and highly variable. Clearly, a
model based on the assumption of equilibrium on every CEP July 2003 www.cepmagazine.org 35 6/13/03 10:00 AM Page 36 Reactions and Separations Heterogenous
Ternary Azeotrope
0.6 Vapor Liquid l
Transfer Transfer Transfer
Liquid ll I Figure 13. Schematic representation of a threephase nonequilibrium stage.
stage cannot predict column performance. Springer and
others (17) stress the limitations of simulation models
assuming equal Murphree efficiencies for all components in the mixture.
It is straightforward in principle to extend the ideas
that underlie nonequilibrium models to systems with
more than two phases, as first shown by Lao and Taylor (18). A complete nonequilibrium model for the system depicted in Figure 13 contains three phase balances, each of which contains terms for mass transfer
to or from both of the other two phases. In addition,
the model contains up to six sets of the MS equations,
two for each phase boundary (vapor–liquid I,
vapor–liquid II, and liquid I–liquid II). Three sets of
equilibrium equations, one for each possible interface,
complete the model. In practice, it is quite likely that
the vapor phase and a dispersed liquid phase see only a
continuous liquid phase, thereby considerably simplifying the model (17).
Example 4. Heterogeneous azeotropic system.
Sometimes the curvature of the distillation boundary is
such that its crossing by the equilibrium stage model is
allowable (16). This is illustrated in Figure 14 for the
water (1), cyclohexane (2) and ethanol (3) system. For a
column operating at total reflux with the top composition corresponding to the heterogenous ternary
azeotrope, the equilibrium model has no difficulty
crossing the curved distillation boundary from the convex side, moving in the direction of high water compositions and proceeding down the column. However, the
experimental data of Springer et al. (17) show that the
boundary is not crossed in practice and the column composition trajectories are anticipated very well by a
nonequilibrium model.
Reactive distillation. The design and operation issues 36 www.cepmagazine.org July 2003 CEP Cyclohexane Composition Taylor LiquidLiquid
Phase
Splitting 0.4 0.2 0.0
0.04 0.08 0.12 0.16 Water Composition
EthanolWater
Nonequilibrium Model
Binary Azeotrope
Experimental Data
Distillation Boundaries
Equilibrium Model I Figure 14. Distillation of water (1), cyclohexane (2), ethanol (3) and acetone (3) in a bubble cap tray column: experimental composition trajectory,
compared with the nonequilibrium and equilibrium simulations (17). for reactive distillation processes are considerably more
complex than those of either conventional reactors or
conventional distillation columns. The introduction of
an in situ separation function within the reaction zone
leads to complex interactions between vaporliquid
equilibrium, vaporliquid mass transfer, intracatalyst
diffusion (for heterogeneously catalyzed processes) and
chemical kinetics. For such systems, the chemical reaction influences the efficiencies to such an extent that the
concept loses its meaning (19).
Building a nonequilibrium model of a reactive separation process is not as straightforward as building an
equilibrium stage model, in which we simply add a
term to account for reaction to the liquidphase material
balances. It must be recognized that no single nonequilibrium model can deal with all possible situations.
Separate models are needed depending on whether the
reaction takes place within only the liquid phase or if a
solid phase is present to catalyze the reaction. Refer to
Refs. 16, 19 and 20 for further discussion.
Gas absorption. Efficiencies in gas absorption tend
to be much lower than in distillation, sometimes as low
as 5%. In addition, many important gas absorption processes involve chemical reactions. It does not seem to Taylor 6/13/03 10:00 AM Page 37 Tray
Section Cell Liquid Packed
Section I Figure 15. The nonequilibrium cell model.
make a great deal of sense to employ an equilibrium
stage model for systems so far removed from equilibrium. In fact, although equilibrium stage models for
such systems are used, it has long been more common
to use masstransferratebased models to design gas
absorption processes (21). Nonequilibrium models
apply more or less unchanged in principle to gas absorption (with or without reaction). The only differences between the models are the inclusion of different
submodels for the reaction kinetics and thermodynamic properties. Many absorption processes involve dilute
mixtures, and the rate relationships in Eqs. 2 and 3 suffice (the latter modified by the inclusion of an enhancement factor to account for any chemical reaction in the liquid phase). Models of this sort
have been used with some success in
the modeling of aminebased gas treating processes (22).
Distillation column dynamics. One
of the key points of this article is that
nonequilibrium models should be used
when efficiencies are unknown, cannot
be reliably predicted, and are low
and/or highly variable. Efficiencies in
any process depend strongly on the
properties of the mixture, whether or
not chemical reactions are involved,
and (last, but by no means least in importance) the type of column employed
and the way in which it is operated. If a
column is not at steady state, then efficiencies vary with time as a result of
changes to flowrates and composition.
Thus, equilibrium stage models with efVapor
ficiencies should not be used to model
the dynamic behavior of distillation and
absorption columns. Nonequilibrium
models for column dynamics are described in Refs. 23–25.
Nonequilibrium cell model. An issue
that is not adequately addressed by most
models is that of vapor and liquid flow
patterns on distillation trays or maldistribution in packed columns. Since reaction rates and chemical equilibrium constants depend on the local concentrations and temperature, they may vary
along the flow path of liquid on a tray,
or from side to side in a packed column.
For such systems, the residence time
distribution could be very important.
To deal with this shortcoming of earlier models, nonequilibrium cell models
have been developed (26–28). The distinguishing feature of this model is that the stages are
divided into a number of contacting cells (Figure 15).
These cells describe just a small section of the tray or
packing, and by choosing an appropriate set of cell connections, one can very easily study the influence of flow
patterns on the distillation process.
Flow patterns on distillation trays are modeled by
choosing an appropriate number of cells in each flow
direction. A column of cells can model plug flow in the
vapor phase, and multiple columns of cells can model
plug flow in the liquid phase as depicted in Figure 15.
Backmixing may also be taken into account by using
an appropriate number of cells. Flow patterns in
packed columns are evaluated by means of a cell flow
model (27). CEP July 2003 www.cepmagazine.org 37 Taylor 6/13/03 10:00 AM Page 38 Reactions and Separations Available software
AspenTech developed RateFrac, in collaboration with
Koch Engineering, Inc. This implementation is based largely on the nonequilibrium model described in the original
papers by Krishnamurthy and Taylor (29, 30), with the important additional capability of being able to handle systems with chemical reactions. The inﬂuence of reaction on
mass transfer is modeled by means of enhancement factors.
RateFrac has one masstransfer coefficient model for each
type of column internal, but it has the facilities to add user
models for the calculation of transfer coefficients, pressure drop and interfacial area. RateFrac can use any of the thermodynamic packages that exist within AspenPlus, and can
model columns with sidestreams, interstage heaters/coolers
and pumparounds. Complex speciﬁcations can designated
for product purity or internal streams. RateFrac is especially
useful for modeling columns with chemical reactions that
inﬂuence the separation. Illustrations of the use of RateFrac
are described in Seader and Henley (9). For more information, visit www.aspentech.com/includes/product.cfm?IndustryID=0&ProductID=110
CHEMCAD from Chemstations, Inc. (www.chemsta Literature Cited
1. Seader, J. D., “The B. C. (before computers) and A. D. of EquilibriumStage Operations,” Chem. Eng. Educ., 19 (2), pp. 88–103
(Spring 1985).
2. Murphree, E. V., “Rectifying Column Calculations with Particular
Reference to ncomponent Mixtures,” Ind. Eng. Chem., 17, pp.
747–750 (1925).
3. Kister, H. Z., “Distillation Design,” McGrawHill, New York (1992).
4. Lockett, M. J., “Distillation Tray Fundamentals,” Cambridge University Press, Cambridge, MA (1986).
5. Standart, G., “Distillation. V. Generalized Deﬁnition of Theoretical
Plate or Stage of Contacting Equipment,” Chem. Eng. Sci., 20, pp.
611–622 (1965).
6. Seader, J. D., “The RateBased Approach for Modeling Staged Separations,” Chem. Eng. Prog., 85, pp. 41–49 (1989).
7. Poling, B. E., et al., “The Properties of Gases and Liquids,” 5th Edition, McGrawHill, New York (2001).
8. Taylor, R., et al., “A 2nd Generation Nonequilibrium Model for
ComputerSimulation of Multicomponent Separation Processes,”
Comput. Chem. Eng., 18, pp. 205–217 (1994).
9. Seader, J. D., and E. J. Henley, “Separation Process Principles,”
John Wiley, New York, NY (1998).
10. Treybal, R. E., “MassTransfer Operations,” 3rd Edition, McGrawHill, New York, NY (1980).
11. Taylor, R., and R. Krishna, “Multicomponent Mass Transfer,” John
Wiley, New York, NY (1993).
12. Krishna, R., and J. A. Wesselingh, “The MaxwellStefan Approach
to Mass Transfer,” Chem. Eng. Sci., 52, pp. 861–911 (1997).
13. Wesselingh, J. A., and R. Krishna, “Mass Transfer in Multicomponent Mixtures,” Delft University Press, Delft (2000).
14. Benitez, J., “Principles and Modern Applications of Mass Transfer
Operations,” John Wiley, New York, NY (2002).
15. Springer, P. A. M., et al., “Crossing of the Distillation Boundary in
Homogeneous Azeotropic Distillation: Inﬂuence of Interphase Mass
Transfer,” Ind. Eng. Chem. Res., 41, pp. 1621–1631 (2002).
16. Doherty, M. F., and M. F. Malone, “Conceptual Design of Distillation Systems,” McGrawHill, New York, NY (2001).
17. Springer, P. A. M., et al., “Composition Trajectories for Heterogeneous Azeotropic Distillation in a Bubblecap Tray Column: Inﬂuence of Mass Transfer,” Chem. Eng. Res. Des., 81, pp. 413–426
(2003).
18. Lao, M. Z., and R. Taylor, “Modeling MassTransfer in 3Phase
Distillation,” Ind. Eng. Chem. Res., 33, pp. 2637–2650 (1994).
19. Taylor, R., and R. Krishna, “Modeling Reactive Distillation,”
Chem. Eng. Sci., 55, pp. 5183–5229 (2000).
20. Sundmacher, K., and A. Kienle, “Reactive Distillation. Status and
Future Directions,” WileyVCH Verlag, Weinheim, Germany (2003). 38 www.cepmagazine.org July 2003 CEP 21. Cornelisse, R., et al., “Numerical Calculation of Simultaneous
Mass Transfer of Two Gases Accompanied by Complex Reversible
Reactions,” Chem. Eng. Sci., 35, pp. 1245–1260 (1980).
22. Pacheco, M. A., and G. T. Rochelle, “RateBased Modeling of Reactive Absorption of CO2 and H2S into Aqueous
Methyldiethanolamine,” Ind. Eng. Chem. Res., 37, pp. 4107–4117
(1998).
23. Kooijman, H. A., and R. Taylor, “A Nonequilibrium Model for
Dynamic Simulation of Tray DistillationColumns,” AIChE Journal,
41, pp. 1852–1863 (1995).
24. Baur, R., et al., “Dynamic Behaviour of Reactive Distillation
Columns Described by a Nonequilibrium Stage Model,” Chem. Eng.
Sci., 56, pp. 2085–2102 (2001).
25. Gunaseelan, P., and P. C. Wankat, “Transient Pressure and Flow
Predictions for Concentrated Packed Absorbers Using a Dynamic
Nonequilibrium Model,” Ind. Eng. Chem. Res., 41, pp. 5775–5788
(2002).
26. Higler, A., et al., “Nonequilibrium Cell Model for Multicomponent
(Reactive) Separation Processes,” AIChE Journal, 45, pp.
2357–2370 (1999).
27. Higler, A , et al., “Nonequilibrium Cell Model for Packed Distillation Columns — The Inﬂuence of Maldistribution,” Ind. Eng. Chem.
Res., 38, pp. 3988–3999 (1999).
28. Baur, R., et al., “Dynamic Behaviour of Reactive Distillation Tray
Columns Described with a Nonequilibrium Cell Model,” Chem.
Eng. Sci., 56, pp. 1721–1729 (2001).
29. Krishnamurthy, R., and R. Taylor, “A Nonequilibrium Stage
Model of Multicomponent Separation Processes. Part I: Model Description and Method of Solution,” AIChE Journal, 31, pp. 449–456
(1985).
30. Krishnamurthy, R., and R. Taylor, “A Nonequilibrium Stage
Model of Multicomponent Separation Processes. Part III: The Inﬂuence of Unequal Component Efficiencies in Process Design Problems,” AIChE Journal, 31, pp. 1973–1985 (1985).
31. Kooijman, H. A., and R. Taylor, “The ChemSep Book,” Books on
Demand, Norderstedt, Germany (2001).
32. Lewis, W. K., and K. C. Chang, “Distillation. III. The Mechanism
of Rectiﬁcation,” Trans. Am. Inst. Chem. Eng., 21, pp. 127–138
(1928).
33. Krishna, R., “A Uniﬁed Theory of Separation Processes Based on Irreversible Thermodynamics,” Chem. Eng. Commun., 59, pp.3364 (1987). Further Reading
For further reading, visit www.chemsep.org/publications Taylor 6/13/03 10:00 AM Page 39 tions.net) contains a nonequilibrium model for both steadystate and dynamic simulation.
ChemSep (31) incorporates some of the most recent developments in nonequilibrium modeling. Many correlations for the masstransfer coefficients, interfacial area and
ﬂow models are built into ChemSep. It also contains a variety of thermodynamic and physical property models.
ChemSep can also provide a detailed design of the equipment selected for the simulation. This allows the program
to simulate columns for preliminary design purposes. It has
a limited component library but allows the user to add
components with a databank manager. ChemSep is available through CACHE (www.cache.org) for educational use
only. Applications of ChemSep are discussed in Refs. 9,
14, 31. For more information, visit www.chemsep.org.
Many other models have been implemented primarily
for research purposes and are not available to others. Conclusion
Within the last two decades, a new way of simulating
multicomponent distillation operations has come of age.
These nonequilibrium, or ratebased, models abandon the
idea that the vapor and liquid streams in a distillation column ever are in equilibrium with each other. The idea of
modeling distillation as a masstransferratebased operation is hardly new. Equations 2 and 3 (albeit in different
units) actually appear in the classic paper by E.V. Murphree (2) that introduced us to efficiencies. Murphree went
so far as to say: “the use of the general [masstransfer]
equation in rectifying column problems would cause the
calculations to become very much involved, and it is therefore not considered feasible for practical purposes.” Nowadays, such calculations not only are feasible, there are circumstances where they should be regarded as mandatory.
Of course, models based on equilibrium stage concepts
will not be abandoned, nor is there any need for us to do
so. For design of new columns in which the column conﬁguration is not ﬁxed, it is best to start with the equilibrium model to determine the conﬁguration, optimum reﬂux
,etc. (16). The ﬁnal design should be checked against the
nonequilibrium model because, as we have seen, it is possible for the predictions of the nonequilibrium model to
differ considerably from those of the equilibrium model.
Nonequilibrium models are of great value in simulating
existing columns. No longer is it necessary to guess the
number of equilibrium stages, the location of the feed and
any intermediate product streams, and the individual component efficiencies in order to try and model a column that
no longer is performing as intended.
Reactive distillation is an emerging application that has
introduced additional complications. Here it is not uncommon to assume equilibrium with regard to mass transfer,
but allow for ﬁnite reaction rates. This is ﬁne for conceptual design. But for equipment sizing, the problem of determining column heights remains. For reactive distillation, HETPs and efficiencies have no physical meaning, as these
are also inﬂuenced by reaction.
Rigorous nonequilibrium models require the use of
the MS equations to properly describe mass transfer in
multicomponent systems. These equations have, in fact,
been with us for much longer than has the equilibrium
stage model (see Ref. 11 for original citations). The application of the MS equations to modeling mass transfer
in distillation is also not all that recent. Lewis and Chang
(32), in a remarkably prescient paper that appears to
have been largely ignored, used the MS equations to investigate the mechanism of rectification. They wrote:
“engineers generally are unfamiliar with them” — a situation that has persisted until relatively recent times. Not
only do the MS equations allow us to model mass transfer in conventional operations like distillation, absorption and extraction, they also describe transport in many
less common separation processes, such as membrane
processes. Indeed, the MS formulation of mass transfer
provides a rational basis for unifying the treatment of
CEP
separation processes (33). ROSS TAYLOR is the Kodak Distinguished Professor of Chemical Engineering
at Clarkson Univ. in Potsdam, New York (taylor@clarkson.edu), where he
has been since 1980. He currently serves as chair of the Dept. of Chemical
Engineering. He received his PhD degree from the Univ. of Manchester
Institute of Science and Technology in England. His research interests are
in the areas of separation process modeling, multicomponent mass
transfer, thermodynamics, and developing applications of computer
algebra to process engineering (and cartography). He is a coauthor (with
Krishna) of the textbook “Multicomponent Mass Transfer” (Wiley, 1993).
He also holds a joint appointment as Professor of Reactive Separations in
the Dept. of Chemical Technology at the Univ. of Twente in The
Netherlands, and is a trustee of The CACHE Corp.
R. KRISHNA is a professor at the Univ. of Amsterdam (krishna@science.uva.nl).
He graduated in chemical engineering from the Univ. of Bombay and was
awarded a PhD in 1975 from the Univ. of Manchester. He then joined the
Royal Dutch Shell Laboratory in Amsterdam, where he was engaged in
research, development and design of separation and reaction equipment.
After nine years of industrial experience, he returned to India to take over
the Directorship of the Indian Institute of Petroleum. Since 1990, he
occupies the position of Professor of Chemical Reactor Engineering at the
Univ. of Amsterdam. His current research interests range from molecular
modeling, bubble and particle dynamics, and reactor scaleup to process
synthesis. Krishna has coauthored three textbooks. His research
contributions have won him the Conrad Premie of the Royal Dutch
Institution of Engineers in 1981, and the AkzoNobel prize in 1997.
HARRY KOOIJMAN is a research distillation specialist at the Amsterdam
laboratory of Shell Global Solutions International BV, The Netherlands
(kooijman@chemsep.org). He graduated from Delft Univ. of Technology
and received his PhD in 1995 from Clarkson Univ. He joined the BOC Group
in 1996 as a senior research engineer, where he was involved with the
development of structured packing for cryogenic distillation. In 1999, he
moved to Germany where he worked at science+computing as a consultant
in highperformance computing. He joined Shell Global Solutions in 2002,
where he focuses on the development of distillation tray technology and
separation equipment. CEP July 2003 www.cepmagazine.org 39 ...
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