Chemical Engineering December 2014 - 35

Department Editor: Scott Jenkins
Distillation Column
Modeling
rocess simulation methods are used
to evaluate the performance of
proposed distillation systems and
improve the performance of existing
ones. The most common approaches for
modeling distillation processes can be
broadly divided into equilibrium and nonequilibrium
methods. This article provides
information about the differences between
the two approaches and outlines
their advantages and disadvantages.
Due to the limitations in the assumptions
used to derive each model and in the
data required to accurately perform the
calculations, neither model can be assumed
to work best in all situations.
P
Table 2. PhysiCal ProPerTy
requireMenTs for DisTillaTion
MoDeling
Equilibrium
models
Activity coefficients
Vapor pressures
Enthalpies
Non-equilibrium
models
Activity coefficients
Vapor pressures
Fugacity coefficients Fugacity coefficients
Densities
Densities
Enthalpies
Diffusivities
Viscosities
Surface tensions
Thermal
Equilibrium models
The longest-used (over a century) method
for modeling a full distillation column is
the equilibrium method, where the vapor
and liquid phases are assumed to be in
a state of thermodynamic equilibrium.
Models based on ideal equilibrium
stages are widely used to help determine
the configuration of proposed columns.
The approach is to divide the column
into discrete stages and use computer
programs to solve so-called MESH equations.
The acronym MESH stands for material
balances, equilibrium relationships,
summation equations and heat (enthalpy)
balances (Table 1). Since the 1950s,
many algorithms have been developed to
solve the MESH equations.
The equilibrium-stage approach offers
a practical and efficient method for
simulating an existing column for which
data exist. The main disadvantage of
the equilibrium-stage is that ideal stages
are used to model real trays and packing
depths. Determining what packing
height corresponds to an equilibrium
stage, for example, is not necessarily
simple and straightforward.
Engineers have been aware for
decades that vapor and liquid streams
leaving a real column tray or section of
Table 1. equaTions useD for
DisTillaTion MoDeling
Equilibrium
models
Mass balances
Energy balances
Equilibrium
equations
Summation
equations:
Non-equilibrium
models
Phase mass balances
Phase energy
balances
Equilibrium equations
Summation equations
Mass-transfer in vapor
phase
Mass transfer in liquid
phase
Energy transfer
conductivities
Mass-transfer
coefficients
Heat-transfer
coefficients
Interfacial areas
column packing are rarely, if ever, in
equilibrium with each other. The actual
separation achieved depends on the
rates of mass transfer from the vapor
to the liquid phases, and these rates
depend on the extent to which vapor and
liquid streams are not in equilibrium with
each other.
Efficiencies
To get around the fact that real columns
are not in equilibrium, modeling engineers
have used various efficiencies for
equilibrium-stage modeling. Murphree
tray efficiencies and Hausen efficiencies
are examples. Understanding efficiencies
is important in the design and
performance evaluation of distillation
columns. Many approaches to estimating
overall column efficiencies are also
available. Efficiencies are often used
in equilibrium-stage models to fit actual
column operating data, and are said
to represent the extent to which the real
column departs from equilibrium. There
are several limitations to using efficiencies
in computer simulations, but most
important is that they are a function of
column conditions, and can vary from
substance to substance and from stage to
stage. Therefore, extrapolating to other
conditions is difficult.
Non-equilibrium models
Predictions of non-equilibrium and equilibrium
models often differ considerably.
Although equilibrium-stage models can
be useful as engineers determine initial
column configurations, non-equilibrium
(rate-based) models are said to offer
a more realistic modeling approach.
Non-equilibrium simulation methods can
provide a more accurate way of checking
final column designs and simulating
existing columns to seek optimal separation
performance.
Non-equilibrium models forego the use
of efficiencies and strive to calculate the
actual rates of interphase mass and heat
transfer in the column. Modeling distillation
as rate-based processes requires the
modeling of interfacial mass and energy
transfer in tray and packed columns,
which is something that is not done in
conventional equilibrium stage models.
Rate-based models are fundamentally
more rigorous, but they require that more
parameters be known or estimated (Table
2). Also, they generally require more
computing power to run the algorithms.
In the past, non-equilibrium models
were sometimes considered impractical
due to their complexity, but ever-growing
computer power has greatly increased
their feasibility. Building blocks of the
non-equilibrium models are the MERSHQ
equations (material balances, energy balances,
mass- and heat-transfer rates, summation
equations, hydraulic equations
for pressure drop, equilibrium equations).
In a non-equilibrium model, separate
balance equations are written for each
distinct phase.
Numerical solutions of non-equilibrium
model equations provide engineers with
all of the quantitites normally associated
with the conventional equilibrium model
(temperatures, flowrates, mole fractions,
and so on), but non-equilibrium-model
calculations also provide a great deal of
additional information, such as physical
and transport property profiles, and
equipment design and operating data. ■
References
1. Luyben, W.L., " Distillation Design and Control
Using Aspen Simulation, " 2nd ed., John Wiley
& Sons, Inc., Hoboken, N.J., 2013.
2. Petlyuk, F.B., " Distillation Theory and its Application
to Optimal Design of Separation Units, "
Cambridge University Press, Cambridge, U.K.,
2004.
3. Strigle, R.F., " Random Packings and Packed
Towers: Design and Applications, " Gulf Publishing
Co., Houston, 1987.
4. Taylor, R. and others, Real-World Modeling of
Distillation, Chemical Engineering Progress,
July 2003, pp. 28-39.
5. Graf, K., Determining Packing Height With
Accuracy, Chem. Eng., October 2011, pp.
55-63.
6. Skowlund, C. and others, Comparison of ideal
stage and mass-transfer models for separation
processes with and without chemical reactions,
Bryan Research & Engineering Inc., Technical
papers, www.bre.com, accessed Nov. 1,
2014.
Editor's note: Tables 1 and 2 are adapted from
graphics in Ref. 4.
http://www.bre.com
Chemical Engineering December 2014

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