Dynamic Modelling of Batch Distillation Columns Maria Nunes de Almeida Viseu Thesis to obtain the Master of Science Degree in Chemical Engineering Supervisors: Prof. Dr Carla Isabel Costa Pinheiro Dr Charles Brand Examination Committee Chairperson: Prof. Dr Sebastião Manuel Tavares da Silva Alves Supervisor: Prof. Dr Carla Isabel Costa Pinheiro Members of the Committee: Prof. Dr João Miguel Alves da Silva November 2014
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Dynamic Modelling of Batch Distillation Columns
Maria Nunes de Almeida Viseu
Thesis to obtain the Master of Science Degree in
Chemical Engineering
Supervisors: Prof. Dr Carla Isabel Costa Pinheiro
Dr Charles Brand
Examination Committee
Chairperson: Prof. Dr Sebastião Manuel Tavares da Silva Alves
Supervisor: Prof. Dr Carla Isabel Costa Pinheiro
Members of the Committee: Prof. Dr João Miguel Alves da Silva
November 2014
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Para os meus pais,
Com amor.
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Abstract
atch distillation is becoming increasingly important in specialty product industries in which flexibility is a
key performance factor. Because high added value chemical compounds are produced in these
industries with uncertain demands and lifetimes, mathematical models that predict separation times and
product purities thereby facilitating plant scheduling are required. The primary purpose of this study is thus to
develop a batch multi-staged distillation model based on mass and energy balances, equilibrium stages and tray
hydraulic relations. The mathematical model was implemented in gPROMS ModelBuilder®, an industry-
leading custom modelling and flowsheet environment software.
Preliminary steps were undertaken prior to implementing the dynamic multi-staged model: batch distillation
operating policies as well as modelling and tray hydraulic considerations were covered in a broad background
review; a theoretical separation example of an equimolar benzene/toluene mixture was used to validate a
simpler Rayleigh distillation model comprising only one equilibrium stage; tray hydraulic correlations
encompassing column diameter, tray holdup and tray pressure drop estimations were tested in a
methanol/water continuous separation case study.
The multi-staged batch model was validated for a methanol/water separation using literature data from an
experimental pilot plant and from theoretical results given by a model implemented in Fortran language and
by commercial simulator Batchsim of Pro/II. A sensitivity analysis was performed to evaluate the model
robustness, testing the effect of the reflux ratio and the heat duty on the separation time and methanol
recovery.
The results simulated in ModelBuilder for the batch multi-staged model reveal a 6.2% overestimation of the
experimental methanol recovery. A very good agreement is found between the ModelBuilder and Fortran
models: the methanol recovery predicted by ModelBuilder is only 2.3% lower. It is shown that the
ModelBuilder multi-staged batch model is robust with ±10% heat duty variations or ±0.5 reflux ratio
differences both affecting the total experiment time in approximately 12%. Differences of ±0.5 in the reflux
ratio are found to have a 2.2 to 6.4% absolute impact on the methanol recovery whilst this recovery is
practically not affected by 10% heat duty variations.
This work offers a tool that may be applied to the scheduling of batch chemical plants and aid industrial
1.2. State of the art .................................................................................................................................................... 2
1.3. Original contributions ....................................................................................................................................... 3
2 Literature review........................................................................................................................................................... 5
2.2.3. Two-film model .......................................................................................................................................... 11
2.2.4. Rate-based stage model ............................................................................................................................. 12
4.1. Model equations .............................................................................................................................................. 25
4.2. Model flowsheet .............................................................................................................................................. 28
4.3. Model validation .............................................................................................................................................. 30
5.1. Model assumptions ......................................................................................................................................... 36
5.2. Model equations .............................................................................................................................................. 36
6 Tray design and operation ....................................................................................................................................... 43
6.1. Case study data ................................................................................................................................................ 43
6.2. Case study results ............................................................................................................................................ 45
7.3. Total reflux ....................................................................................................................................................... 62
7.4. Model validation .............................................................................................................................................. 66
7.5.1. Total separation time ................................................................................................................................. 74
8 General conclusions and Future work ................................................................................................................. 79
8.1. General conclusions ....................................................................................................................................... 79
8.2. Future work ...................................................................................................................................................... 81
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List of figures
Figure 2.1 – The three characteristic periods in the cyclic operation of a batch distillation column [5]. ............... 7
Figure 4.3 – Instantaneous and average benzene molar fraction profiles. ............................................................... 31
Figure 4.4 – Separator and tank temperature profiles. ................................................................................................ 32
Figure 4.5 – Holdup and liquid benzene molar fraction profiles in the still. ........................................................... 32
Figure 5.1 – Countercurrent cascade of N column stages. ......................................................................................... 35
Figure 6.1 – Liquid and vapour flowrate profiles and Porter & Jenkins froth-spray prediction. ......................... 46
Table 4.1 – Required separator model specifications. ................................................................................................. 29
Table 4.2 – Benzene/toluene problem data provided by Seader et al [13]. ............................................................. 30
Table 4.3 – Required ModelBuilder inputs for the benzene/toluene separation. .................................................. 30
Table 6.1 – Case study methanol/water data. ............................................................................................................... 44
Table 7.1 – Fortran and Batchsim model specifications. ............................................................................................ 53
As previously stated the column diameter should be selected according to flooding predictions. More
specifically, the column diameter can be calculated from the vapour flooding velocity which is based on the
column net area. For this reason, the Lowenstein [18], Fair [16] and the Kister & Haas [1] flooding
correlations were implemented in this work using gPROMS ModelBuilder®. These correlations can be
consulted in the Dynamic column modelling section of this work.
18
Sinnott [18] recommends the Lowenstein correlation for maximum allowable vapour velocity calculation and
hence column area and diameter estimation. The correlation is based on the Souders and Brown equation in
which entrainment is controlled by the carry-up of liquid droplets [1]. The approximate estimate of the
diameter should be revised when the detailed plate design is undertaken.
The Fair flood correlation gives flooding gas velocities to ±10% and has been the standard of the industry for
entrainment prediction [16]. However, the correlation applies only to non-foaming systems where weir height
is less than 15% of plate spacing. The Fair correlation can be used for sieve-plate perforations with a
fractional hole area (ratio of perforation area to active area) of 0.1 or greater and when holes are 13 mm or less
in diameter. Similarly, the correlation also applies to bubble-cap and valve trays when the ratio of slot (bubble-
cap) or full valve opening (valve) area to active area is 0.1 or greater. Fair’s correlation is known to predict
most entrainment data well, although slightly conservatively.
Kister & Haas reported a recent correlation for entrainment flooding which was shown to predict a large data
of sieve and valve tray flood points to within ±20% [1]. The correlation applies to non-foaming systems with
a plate spacing, hole diameter, fractional hole area and weir height between 36-91 cm, 0.32-2.5 cm, 0.06-0.2
and 0-7.6 cm, respectively. Contrary to the Fair correlation, the Kister & Haas method provides a suitable
approximation to the effects of physical properties, operating variables and tray geometry on entrainment
flooding. The correlation was also obtained from a much larger base of industrial and laboratory-scale
columns data. However, although the Fair correlation can be used both for froth and spray entrainment flood
predictions, the Kister & Haas correlation applies exclusively to spray entrainment flood estimations.
2.3.2. Tray operation
If stage holdups are to be included in a dynamic column model, the first step is to estimate the effective liquid
holdup on the trays. The vapour holdup is then calculated considering the total tray geometry, the volume
occupied by the liquid holdup and the vapour density. Hence, in this study two correlations were added to the
dynamic multi-staged ModelBuilder model: the Bennett and the Jeronimo & Sawistowski effective clear liquid
height correlations. The Bennett clear liquid height calculation applies to froth-type regimes. This clear liquid
height calculation is based on the weir height, the liquid flow and the froth density [16]. The Jeronimo &
Sawistowski correlation has been successfully used as a building block for correlating entrainment flooding
and spray regime entrainment, strictly predicting clear liquid heights at the froth to spray transition. However,
it has been shown that the clear liquid height in the spray regime is similar to the clear liquid height at this
transition [1] and thus the correlation is applicable to spray-type regimes.
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To implement a pressure-driven dynamic system in a batch column the total pressure drop across a tray has to
be taken into consideration. Hence, in this work several tray pressure drop correlations were developed and
tested using ModelBuilder. Note that the pressure drop equations are listed in section 5.2.2.3 of this thesis.
There are two main sources of pressure loss: the pressure drop calculated for the flow of vapour through the
dry holes ℎ𝑑 and the pressure drop through the aerated mass on the plate ℎ𝑙 [18].
Vapour pressure drop in a tower is generally from 0.35 to 1.03 kPa/tray [13]. Several published correlations
are available for evaluating ℎ𝑑. In this study, three correlations were implemented in ModelBuilder: the
standard orifice equation, Liebson et al. correlation [1] and the Hughmark & O’Connell correlation [41]. The
correlation by Liebson et al. is preferred by Fair et al. and Van Winkle. Ludwig and Chase recommend the
Hughmark & O’Connell correlation [1]. The vapour velocity in the holes, the liquid and vapour densities and
the orifice coefficient are the prime variables affecting the vapour pressure drop. For both the Liebson and
the Hughmark & O’Connell correlations, the orifice discharge coefficient is a function of the ratio of tray
thickness to hole diameter and the fractional hole area. The standard orifice equation is deducted from
Bernoulli’s principle and in this case, a constant orifice discharge coefficient of 0.75 is used.
In this work, two liquid pressure drop correlations were developed in ModelBuilder: the Fair and the Bennett
aerated liquid pressure drop correlations [1].
The approach followed by Fair for pressure drop prediction uses a dimensionless tray aeration factor, 𝛽 [16].
In this context, ℎ𝑙 is determined multiplying 𝛽 by the clear liquid height of liquid on the tray, ℎ𝑐. For sieve
and valve plates, ℎ𝑐 is the sum of the weir height ℎ𝑤, the hydraulic gradient ℎℎ𝑔 and the liquid head over the
outlet weir ℎ𝑜𝑤.
The hydraulic gradient is the head of liquid necessary to overcome the frictional resistance to liquid passage
across the tray. For a significant gradient the resistance to gas flow near the liquid inlet to the tray may become
excessive, resulting in an inoperative upstream portion of the plate. The hydraulic gradient term was not
considered in this thesis since this term is negligible for sieve trays and the usual practice is to omit it from the
pressure drop calculation [16].
To determine the liquid head over the outlet weir the corrected Francis weir formula for segmental and
circular weirs was also included in ModelBuilder. For segmental weirs ℎ𝑜𝑤 may be determined as a function of
the liquid flow, the weir length and a wall correction factor. The wall correction factor is proportional to the
weir crest and considers liquid flow constriction at the approach to the weir. For circular weirs ℎ𝑜𝑤 may be
estimated using the liquid flow and the weir diameter.
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A more recent and fundamental relationship to determine the pressure loss through the aerated mass was
recommended by Bennett [1]. Indeed, Bennett developed a model of froth flow across the weir consequently
avoiding the correction of the clear liquid flow for aeration effects. In this case, the pressure drop through the
aerated liquid is the sum of two separate terms: the effective clear-liquid height ℎ𝑐 used to determine the
liquid holdup and the residual pressure drop due to surface tension ℎ𝑅. The residual pressure drop can be
interpreted as the excess pressure which bubbles must overcome due to the difference between the pressure
inside the bubble and that of the liquid.
For 302 experimental data points covering a wide range of systems the Bennett pressure drop correlation gave
an average relative error of ±0.35%. An error of approximately 5% was obtained for Fair’s correlation
considering a similar data base [16]. When an accurate pressure drop calculation is needed or when the
residual pressure drop is substantial the Bennett pressure drop correlation should be used. For example, for
sieve trays with a hole diameter lower than 0.32 cm the surface tension head loss term is significant and
should be determined using Bennett’s correlation [1]. On the contrary, estimating the residual head as a
function of the surface tension, froth density and froth height via Bennett’s correlation is an elaborate method
and its use is not justified when the surface tension head loss term is small. It should also be noted that the
Bennett pressure loss correlation is based on froth regime considerations and is not applicable to the spray
regime.
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3
Materials and methods
3.1. gPROMS platform
gPROMS® is a custom modelling platform for process industries covering process and equipment
development and design as well as optimisation of process operations [42]. gPROMS products offer several
capabilities: support for multiscale modelling, meaning that micro to full-scale phenomena can be taken into
consideration simultaneously in the same model; execution and maintenance of custom models that apply to a
wide range of equipments; process flowsheet design; steady-state and dynamic modelling implemented within
the same interface and empirical parameter estimation from laboratory or industrial scale data.
One of the main gPROMS products is gPROMS ModelBuilder® where custom modelling capabilities and
process flowsheeting environments are provided. Process model implementation, graphical development and
configuration of hierarchical flowsheets, steady-state or dynamic simulation and optimisation are key
ModelBuilder applications. Thence, all the elements of the model lifecycle are taken into account:
Building custom process models by transcribing the process equations using the library models
supplied by ModelBuilder. Features such as icons, dialogs and reports may be associated to these
models and incorporated into flowsheets;
Constructing flowsheets utilising the gPROMS equation-oriented approach, for example, by
assigning downstream values and calculating upstream values;
Validating models against experimental data using parameter estimation techniques based on
mathematical optimisation algorithms;
Simulating steady-state or dynamic models within the same framework;
Determining optimal answers using dynamic and mixed-integer optimisation;
Exporting models for implementation in other engineering software environments, using, for
instance, gPROMS objects that may be executed in Excel or VBA interfaces.
In this study ModelBuilder was used for both flowsheeting and model development purposes. For example,
the Rayleigh distillation separator was implemented specifying key inputs in a drag-and-drop type flowsheeting
22
activity. Model development was carried out by adding tray hydraulic relations encompassing column
diameter, tray holdup and tray pressure drop correlations and by implementing the dynamic MESH equations
in the ModelBuilder model libraries. Indeed, to build the pressure-driven dynamic column model validated in
Chapter 7, the ModelBuilder libraries needed to include the tray holdup and pressure drop correlations along
with the dynamic material and energy equations for equilibrium column stages.
3.2. Physical properties
The standard gPROMS physical property package is Infochem Multiflash™ supplied by KBC Advanced
Technologies [43]. Multiflash is specifically designed for equation-oriented modelling, as is gPROMS, thereby
generating tight convergence of iterations and of analytical partial derivatives with respect to temperature,
pressure and composition. The phase equilibria is determined in Multiflash for different combinations of
conditions, namely PVT, enthalpy, entropy and internal energy. Furthermore, Multiflash calculates the
fractions of any particular phase at a fixed pressure or temperature, including dew and bubble points.
The physical properties used in this work for the Rayleigh separator (Chapter 4) and the dynamic column
model (Chapter 5) are listed in Table 3.1. Each property has zero or more inputs that may be scalars, such as
the pressure 𝑃 and the temperature 𝑇, or arrays, as is the case of the liquid �⃗� and vapour �⃗� composition
fractions. Additionally, each property has a single output which may be a scalar or an array. For example, the
liquid enthalpy method returns a scalar whereas the liquid fugacity coefficient method returns an array.
Table 3.1 – Multiflash physical properties: inputs and output type.
gPROMS property name Inputs Output Type
MolecularWeight - Array
LiquidDensity 𝑇, 𝑃, �⃗� Scalar
VapourDensity 𝑇, 𝑃, �⃗� Scalar
LiquidEnthalpy 𝑇, 𝑃, �⃗� Scalar
VapourEnthalpy 𝑇, 𝑃, �⃗� Scalar
LiquidFugacityCoefficient 𝑇, 𝑃, �⃗� Array
VapourFugacityCoefficient 𝑇, 𝑃, �⃗� Array
SurfaceTension 𝑇, 𝑃, �⃗�, �⃗� Scalar
The thermodynamic properties are calculated in the Multiflash property package which contains all
commonly-used equations of state and activity coefficient thermodynamic models. Equations of state models
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include the cubic equations of state, namely the Soave-Redlich-Kwong and the Peng-Robinson equations. If
improved predictions of thermal and volumetric properties are needed the Lee-Kesler and the Benedict-Wee-
Rubin-Starling non-cubic equations of state may also be selected, for example. The Soave-Redlich-Kwong
equation of state given by Equations (3.1) to (3.7) was chosen in this study to account for intermolecular
attractive and repulsive forces occurring in the real gas, since it is adequate for fugacity calculations [44].
𝑃 = 𝑅𝑇
𝑉𝑚 − 𝑏𝑚𝑖𝑥𝑡−
𝑎𝑚𝑖𝑥𝑡(𝑇)
𝑉𝑚(𝑉𝑚 + 𝑏𝑚𝑖𝑥𝑡)
(3.1)
√𝑎𝑚𝑖𝑥𝑡(𝑇) =∑𝑦𝑖√𝑎𝑖(𝑇)
𝑁𝐶
𝑖
(3.2)
𝑏𝑚𝑖𝑥𝑡 = ∑𝑦𝑖𝑏𝑖
𝑁𝐶
𝑖
(3.3)
Note that 𝑉𝑚 is the molar volume and 𝑅 the ideal gas constant. The parameters 𝑎𝑚𝑖𝑥𝑡 and 𝑏𝑚𝑖𝑥𝑡 are
determined using the molar fractions 𝑦𝑖 and the pure component parameters 𝑎𝑖 and 𝑏𝑖 which are calculated
from the critical temperature 𝑇𝑐𝑖, the critical pressure 𝑃𝑐𝑖 and the acentric factor 𝜔𝑖.
𝑎𝑖(𝑇) =0.42747𝑅2𝑇𝑐𝑖
2
𝑃𝑐𝑖𝛼𝑖(𝑇), 𝑖 = 1,…𝑁𝐶. (3.4)
𝛼𝑖(𝑇) = [1 +𝑚𝑖 (1 − √𝑇
𝑇𝑐𝑖)]
2
, 𝑖 = 1,…𝑁𝐶. (3.5)
𝑚𝑖 = 0.48 + 1.574𝜔𝑖 − 0.176𝜔𝑖2, 𝑖 = 1,…𝑁𝐶. (3.6)
𝑏𝑖 = 0.08644𝑅𝑇𝑐𝑖𝑃𝑐𝑖
, 𝑖 = 1,…𝑁𝐶. (3.7)
A number of activity coefficient models such as the UNIQUAC, UNIFAC and NRTL models are available in
Multiflash. The NRTL activity coefficient model given by Equations (3.8) to (3.13) was selected in this work
because it may be used for vapour-liquid equilibrium calculations and it is often useful for non-ideal systems
such as the methanol-water mixtures presented in Chapters 6 and 7. The activity coefficients 𝛾1 and 𝛾2 of the
binary mixture relate to the molar fractions 𝑥 and to the binary parameters 𝐺𝑖𝑗 and 𝜏𝑖𝑗 which can be
determined using the interaction energy 𝑈𝑖𝑗 between molecular surfaces of components 𝑖 and 𝑗 and the non-
randomness parameters 𝛼12 and 𝛼21.
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𝑙𝑛𝛾1 = 𝑥22 [𝜏21(
𝐺21𝑥1 + 𝑥2𝐺21
)2 +𝜏12𝐺12
(𝑥2 + 𝑥1𝐺12)2] (3.8)
𝑙𝑛𝛾2 = 𝑥12 [𝜏12(
𝐺12𝑥2 + 𝑥1𝐺12
)2 +𝜏21𝐺21
(𝑥1 + 𝑥2𝐺21)2]
(3.9)
𝑙𝑛𝐺12 = −𝛼12𝜏12 (3.10)
𝑙𝑛𝐺21 = −𝛼21𝜏21 (3.11)
𝜏12 =𝑈12 − 𝑈22
𝑅𝑇 (3.12)
𝜏21 =𝑈21 −𝑈11
𝑅𝑇 (3.13)
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4
Rayleigh distillation he Rayleigh separation is the simplest form of a batch distillation process. A liquid mixture is charged to
a still-pot and brought to boiling. The vapour formed is assumed to be in equilibrium with perfectly
mixed liquid in the still and is continuously condensed to produce a distillate. Note that in this case no trays or
packing are provided, that is, there is only one equilibrium stage. Analysing the behavior of one equilibrium
stage dynamic unit is the first step in understanding how a multi-staged batch distillation column works. Thus,
this chapter is in fact an introduction to subsequent section 5 of this work.
In this chapter the basic Rayleigh model equations are presented, given some insights into the phase
equilibrium of the mixture and the characteristics of the vessel where the separation is taking place. A Rayleigh
binary benzene/toluene separation example provided by Seader et al. [13] implemented in ModelBuilder will
also be shown. The validity of the Rayleigh separator model is attested by matching the obtained results with
data supplied by Seader et al.
4.1. Model equations
A flash unit of the form shown in Figure 4.1 is considered. This two-phase separator model available in the
ModelBuilder library was used to simulate a Rayleigh batch distillation, according to the following
assumptions:
The liquid outlet flowrate is set to zero by closing the associated valve (see Figure 4.2), that is, only
the vapour outlet is continuously withdrawn and condensed to produce a distillate, while the liquid
remains in the still;
The feed continuous flowrate is set to zero;
A charge is introduced at time 𝑡 = 0 in the separator according to the specified initial conditions;
The liquid and vapour phases are perfectly mixed in the separator;
The liquid and vapour are assumed to be in phase equilibrium with each other, that is, no distinction
is made between the temperatures, pressures and components chemical potentials of the two phases
in the separator;
A constant heat duty 𝑄 is provided;
T
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Adiabatic separator, i.e., there is no heat loss through the vessel;
No chemical reactions occur.
Figure 4.1 – Two-phase separator unit.
The two-phase vessel model is essentially a one-staged distillation separation. Hence, the material, equilibrium,
summation and energy balances defined by the MESH equations for a distillation section model are
applicable. A material balance on component 𝑖 yields:
𝑑𝑀𝑖𝑑𝑡
+ 𝐿𝑥𝑖 + 𝑉𝑦𝑖 = 𝐹𝑧𝑖 , 𝑖 = 1,… 𝑐. (4.1)
where 𝑀𝑖 refers to the total holdup of component 𝑖 and 𝐿, 𝑉 and 𝐹 represent the liquid, vapour and feed
molar flowrates with molar fractions 𝑥𝑖, 𝑦𝑖 and 𝑧𝑖 , respectively.
For 𝑐 components, the liquid and vapour fractions obey thermodynamic equilibrium relations of the form:
𝑦𝑖𝑥𝑖=∅̂𝑖𝐿
∅̂𝑖𝑉 , 𝑖 = 1,… 𝑐.
(4.2)
where ∅̂𝑖𝐿 and ∅̂𝑖
𝑉 represent the fugacity coefficients of species 𝑖 in the liquid and vapour phases,
respectively.
The summation equations normalise the liquid and vapour molar fractions:
∑𝑥𝑖𝑖
= 1 (4.3)
27
∑𝑦𝑖𝑖
= 1 (4.4)
The energy balance defines the energy holdup accumulation 𝑑𝑈
𝑑𝑡, as follows:
𝑑𝑈
𝑑𝑡+ 𝐿ℎ𝐿 + 𝑉ℎ𝑉 = 𝑄 + 𝐹ℎ𝐹
(4.5)
The material and energy holdups must be defined considering the total vessel volume Ѵ and the total liquid
and vapour holdups 𝑀𝐿 and 𝑀𝑉 , respectively:
𝑀𝑖 = 𝑀𝐿𝑥𝑖 +𝑀
𝑉𝑦𝑖, 𝑖 = 1,… 𝑐. (4.6)
𝑈 = 𝑀𝐿ℎ𝐿 +𝑀𝑉ℎ𝑉 − 𝑃Ѵ (4.7)
𝑀𝐿
𝜌𝑚𝐿 +
𝑀𝑉
𝜌𝑚𝑉 = Ѵ (4.8)
Note that a pressure-driven system was considered for all the Rayleigh system presented in this work. Hence,
the exit flowrate 𝑉 is a function of the pressure difference between the flash and the downstream units:
𝑉 = 𝑓(𝑃 − 𝑃𝑑𝑜𝑤𝑛) (4.9)
In addition to the above equations, the thermophysical property relations for fugacity coefficients, specific
enthalpies and densities must be considered:
∅̂𝑖𝐿= ∅̂𝑖
𝐿(𝑇, 𝑃, �⃗�), 𝑖 = 1,… 𝑐. (4.10)
∅̂𝑖𝑉= ∅̂𝑖
𝑉(𝑇, 𝑃, �⃗�), 𝑖 = 1,… 𝑐. (4.11)
ℎ𝐿 = ℎ𝐿(𝑇, 𝑃, �⃗�) (4.12)
ℎ𝑉 = ℎ𝑉(𝑇, 𝑃, �⃗�) (4.13)
𝜌𝐿 = 𝜌𝐿(𝑇, 𝑃, �⃗�) (4.14)
𝜌𝑉 = 𝜌𝑉(𝑇, 𝑃, �⃗�) (4.15)
As mentioned previously, the liquid and the vapour thermophysical properties were determined in Multiflash
using the NRTL model and the Soave-Redlich-Kwong equation of state, respectively.
28
4.2. Model flowsheet
Figure 4.2 shows the Rayleigh distillation process flowsheet implemented in ModelBuilder for the binary
benzene/toluene separation.
Figure 4.2 – Rayleigh distillation flowsheet.
The dummy source is a feed with zero flowrate. In the two-phase vessel model a feed source is required to
introduce the Multiflash physical property package, where liquid and vapour densities, specific enthalpies and
the species fugacity coefficients are determined. Note that there is also no liquid stream withdrawn in a
Rayleigh distillation scheme and thus liquid valve V-111 shown in Figure 4.2 is closed.
The feed charge is determined by specifying the following initial conditions in the still: initial pressure, vapour
fraction and holdup compositions. Hence, the total holdup is calculated using these initial conditions and the
specified volume vessel Ѵ. Note that the initial conditions may also be specified using a combination of
different variable sets, listed in Table 4.1.
29
Table 4.1 – Required separator model specifications.
The condenser cools the distillate vapour according to a required thermal specification, namely the subcooling
delta temperature ∆𝑇𝑠𝑢𝑏, outlet temperature, enthalpy, heat duty or the required vapour fraction. Additionally,
the pressure drop or alternatively the outlet pressure should be specified.
The condensed distillate accumulates in the product receiver tank. For the Rayleigh simulation analysed in this
study, an initial temperature and negligible initial component mass holdups were specified, in addition to the
receiver volume. There is no outlet stream from the receiver tank and consequently valve V-121 in Figure 4.2
is closed.
All the Rayleigh simulations were run in a pressure-driven mode and consequently the flowrates are
determined according to pressure differentials. For example, the distillate flowrate is calculated using the still
pressure and the pressure at the liquid surface of the product receiver. Thus, care must be taken when
specifying pressures for all points in the system (sources, sinks, separators, tanks, etc.).
Tab Specifications
Design
Cylindrical vessel
2 of the following geometrical variables: radius, diameter, surface area, cross-section area, length
Flat/Hemispherical heads
No other specifications required Ellipsoidal heads
Ellipsoidal radius Torispherical heads
Crown radius
Knuckle radius
Operation Adiabatic operation or specified heat duty
Initial conditions
Holdup
Composition and 1 intensive variable: pressure, temperature or specific enthalpy
Overall holdup and composition
Component holdup Thermal specification
1 of the following specifications: pressure, temperature, specific enthalpy, saturated liquid, saturated vapour, liquid level fraction, vapour fraction, subcooled liquid
∆𝑇𝑠𝑢𝑏 or superheated vapour ∆𝑇𝑠𝑢𝑝
30
4.3. Model validation
Seader et al. [13] provides a theoretical Rayleigh distillation example based on a binary benzene/toluene
separation. To validate the Rayleigh distillation model implemented in ModelBuilder, the results obtained in
the simulation were matched with the corresponding data presented by Seader et al.
The present example consists of a batch still loaded with 100 kmol of a binary 50 mol% benzene in toluene
mixture (Table 4.2). A constant boilup rate of 10 kmol/hr is assumed at a pressure of 101.3 kPa. A feed
charge of 100 kmol was obtained in ModelBuilder by specifying a vapour fraction of 0.0207 mol/mol at 1 bar
with an equimolar charge and a 158 m3 vessel (Table 4.3). Note that the simulations easily converge to the
required solution when a given vapour fraction is specified at time 𝑡 = 0. However, if vapour is present the
required vessel volume increases to maintain an initial holdup of 100 kmol. The simulations are considerably
harder to execute using a saturated liquid at 𝑡 = 0, in which case the volume vessel would significantly be
reduced. Hence, the vessel volume here is devoid of physical meaning.
Because the distillate rate and, therefore, the liquid depletion rate in the still, vary with the heat input rate, a
heat duty of 93 kW was specified to maintain the required distillate rate of 10 kmol/hr.
Table 4.2 – Benzene/toluene problem data provided by Seader et al [13].
Table 4.3 – Required ModelBuilder inputs for the benzene/toluene separation.
Feed charge (kmol)
Charge composition (mol%)
Boilup rate (kmol/hr)
Pressure (kPa)
100 Toluene – 50 Benzene - 50
10 101.3
Separator
Tank Condenser
Cylindrical vessel with flat heads
D = 4.5 m
L = 4.5 m
Cylindrical vessel with flat heads
D = 4.5 m
L = 4.5 m
Pressure specification
∆𝑃 = 0 bar
Operation
Q = 93 kW
Operation
P = 1 bar
Initial holdup
Toluene – 50 mol %
Benzene – 50 mol %
P = 1.0001 bar Initial thermal specification
Vapour fraction - 0.0207 mol/mol
Initial holdup
Toluene - 10-5 kg
Benzene - 10-5 kg Initial thermal specification
T = 75.9 °C
Thermal specification
∆𝑇𝑠𝑢𝑏 = 10 °C
31
Figure 4.3 shows the instantaneous and average vapour composition profiles obtained according to Seader et
al. and using ModelBuilder. The instantaneous composition is determined in the vapour outlet of the
separator, while the average composition is measured in the product tank receiver. Evidently, for both
simulations the composition of the lower-boiling point component benzene decreases as distillation proceeds.
As expected a sharper decrease is observed in the instantaneous vapour composition profiles, where there is
no product accumulation and prior compositions are not taken into account. In this case, during 8.9 hours the
benzene molar fraction varies from 0.73 to 0.22 and from 0.71 to 0.21 according to Seader et al. and using
ModelBuilder, respectively. After 8.9 hr, both solutions predict a similar average benzene molar fraction, that
is, 0.57 and 0.56 for Seader et al. and for ModelBuilder, respectively.
Figure 4.3 – Instantaneous and average benzene molar fraction profiles.
A comparison of the temperature in the still as predicted by the model developed and the data presented by
Seader et al. is depicted in Figure 4.4. The temperature profile in the separator provided by Seader et al. is in
agreement with the profile obtained in ModelBuilder. Indeed, the temperature increases from approximately
93°C to 105°C (ModelBuilder) or 107°C (Seader et al.) as the separation takes place and the lighter
All the initial conditions specified in this chapter refer to the initial set of inputs that are given at time 𝑡 = 0 in
the first total reflux simulation. The second simulation uses a particular split fraction based on the desired
reflux ratio. This simulation starts operating in a steady-state mode, using a saved variable set from the first
simulation, that is, all the values assigned to the variables at the end of the first simulation (when steady-state
is achieved) are saved and used to initialise the second simulation. The fact that a saved variable steady-state
set can be used to start a second simulation is an important benefit provided by the ModelBuilder tool: the
time required to run simulations is significantly reduced by saving this steady-state.
Globally the system is pressure-driven, that is, the mass flowrates are calculated in the valve model based on
pressure differentials. For this reason, valves were introduced before and after each equipment.
The input specifications for each sub-model, based on the Bonsfills experiment, are described below.
55
Figure 7.2 – Batch distillation column flowsheet.
7.2.1. Column
The input specifications for the ModelBuilder column model are listed in Table 7.2. The plate spacing of 0.25
m specified in the ModelBuilder simulations was determined by dividing the column height (3.75 m) by the
number of stages. The following input values were calculated considering suggestions given by Seader [13],
Perry [16] and Sinnott [18]: 0.8 active area fraction, 0.1 hole area fraction and 0.7 weir fraction.
56
The equilibrium stages are numbered from top (stage 1) to bottom (stage 15). Feed stage 5 is connected to a
dummy source S-111 with zero flowrate. This source was only added to introduce the Multiflash physical
property package which includes the VLE data for the methanol/water system.
The dry vapour pressure drop and the pressure drop through the aerated liquid were estimated using the
standard orifice equation with an orifice coefficient of 0.75 and the hydrostatic liquid height given by the
Francis formula for circular weirs. Note that the Francis formula defines the liquid flowrate profile in the
column as a function of the difference between the liquid level and the weir height. Thus, an adequate weir
height must be supplied. A weir height of 4.46 mm generates for all the simulations studied in this chapter an
average holdup on the plates of 0.175 moles, within a 9.2% relative error. Indeed, the average molar holdup
specified experimentally by Bonsfills is 0.175 and this value determined indirectly the weir height specified in
the ModelBuilder column model.
Table 7.2 – Column specification data.
The initial conditions specified in the total reflux simulations are listed below. Because the system is pressure-
driven, the liquid and vapour flowrates are a function of the vapour and liquid head losses. At time 𝑡 = 0, all
the mass and energy holdups must be given initial values to account for the M and H differential equations.
These mass and energy holdups were indirectly defined by specifying the set of initial conditions listed in
Table 7.2 and in Table 7.3, that is, the initial liquid level fraction, the initial pressure and the initial holdup
Tab Specifications
Column Number of stages : 15 Dummy feed stage: 5
Design
Tray type: sieve Column diameter: 50 mm Active area fraction: 0.8 Hole area fraction: 0.1 Weir fraction: 0.7 Weir height: 4.46 mm Plate spacing: 0.25 m
Pressure
Dry vapour pressure drop correlation: standard orifice equation Aerated liquid pressure drop correlation: hydrostatic Liquid height correlation: Francis formula for circular weirs
Dynamics
Mode: pressure-driven Initial liquid level fraction trays 1-15: 0.02185 Initial pressure: see Table 7.3 Initial holdup composition: see Table 7.3
Tray efficiencies Tray modelling: equilibrium
57
compositions for each tray. Note that in this case the liquid level fraction is the ratio of liquid level to plate
spacing.
Table 7.3 – Column initial pressures and holdup compositions on each tray.
7.2.2. Sump
H-119 represents the column sump, i.e., the liquid holdup that is held on the bottom of a distillation column,
below the column stages. From a modelling point of view, the sump is of significant importance. Without the
sump, the liquid would flow directly from the last stage of the column to the reboiler, with an intermediate
valve in between. Because the pressure and the flowrate of the stream leaving the column are known variables
calculated in the column model, the flowrate entering the reboiler would not be calculated in the valve model
based on the pressure differential between the last column stage and the reboiler. Both the pressure and
flowrate of the stream entering the reboiler would be known variables and therefore the system would not be
well posed. Hence, to calculate the flowrate entering the reboiler based on the pressure differentials a sump
must be introduced. In this case, the flowrate and pressure entering the sump are known variables, calculated
in the column model. The outlet sump pressure is calculated in the sump model using the hydrostatic pressure
associated to the liquid holdup. However, the flowrate of the stream leaving the sump (or likewise, entering
the reboiler) is an unknown variable and therefore may be calculated in the valve model by introducing a valve
between the sump and the reboiler.
For all the total reflux simulations analysed in this work, the sump specifications are the following:
0.1 L cylindrical vessel with flat heads and 5 cm diameter; this diameter value of 5 cm was based on
the 5 cm column diameter;
Tray Initial Pressure Initial methanol
composition (mol %)
1 1.113 80.8
2 1.121 80.2
3 1.128 80.0
4 1.136 78.7
5 1.143 77.8
6 1.151 76.8
7 1.159 75.7
8 1.166 74.1
9 1.174 71.9
10 1.182 69.0
11 1.189 64.3
12 1.197 64.3
13 1.205 64.3
14 1.213 64.3
15 1.2205 64.3
58
Initial temperature of 76.9 ºC;
0.312 and 4.440 initial molar holdups of methanol and water, respectively;
Constant liquid level fraction of 0.6.
The level controller (LC-119) and the flow controller (FC-119) input specifications are listed in Table 7.4. The
two controllers were added to maintain a constant ratio of liquid level to sump height of 0.6. Hence, during
the simulations the liquid level in the sump is maintained at a constant value of 3.1 cm.
A cascade control scheme was implemented using the level and the flow controllers. In this arrangement, the
constant liquid level in the sump is maintained by varying the sump outlet flowrate, instead of directly
changing the sump outlet valve V-117 stem position, which would be the case in a simple (non-cascade)
control scheme. In the primary loop, the level controller monitors and compares the liquid level fraction to
the specified set-point of 0.6, changing the outlet sump flowrate set-point accordingly. In the secondary loop,
the flow controller reads and compares the flowrate input value to the flowrate set-point, manipulating the
sump outlet valve stem position as necessary.
It is interesting to understand the relation between the outlet sump flowrate and the liquid level in the sump
for this particular pressure-driven system. In this case, lower liquid outlet flowrates are associated with higher
liquid levels and vice-versa. Indeed, if the outlet sump flowrate decreases, the differential pressure between the
reboiler and the sump outlet is also lower. Hence, for a given reboiler pressure, the sump outlet pressure must
also decrease. Since the inlet sump pressure is determined in a flow-driven manner (see above paragraphs), the
hydrostatic pressure, that is, the liquid level must increase to maintain a lower sump outlet pressure.
A proportional-integral type control was implemented for controllers LC-119 and FC-119. In this case, the
proportional steady-state error is avoided dynamically by adding the integral term with an integral time
constant of 0.1 s for both controllers. A maximum and minimum value for the input and output variables was
also specified for both controllers. For example, for controller LC-119 the input value (liquid level fraction) is
set between 0 and 1 and the output variable (outlet sump flowrate) is maintained between 0 and 10 kg/s.
59
Table 7.4 – Controllers LC-119 and FC-119 specifications.
7.2.3. Reboiler
Reboiler E-114 was modelled using a two-phase equilibrium stage separator, that is, using the Rayleigh set of
equations described in section 4.1. The reboiler volume, initial liquid level fraction and initial holdup
compositions were chosen according to the Bonsfills experiment. Hence, the reboiler specifications given
ModelBuilder are the following:
6 L cylindrical vessel with flat heads and 19.5 cm diameter;
Initial pressure of 1.221 bar;
Initial liquid level fraction of 0.631;
80.1 mol% and 19.9 mol% initial holdup compositions of water and methanol, respectively;
Constant heat duty specified in each simulation.
Controller Specifications
LC-119
Controller class : PI Controller action: direct Controlled variable: sump liquid level fraction Manipulated variable: sump outlet mass flowrate Proportional gain: 50 Integral time constant: 0.1 s Set-point: 0.6 Minimum input: 0 Maximum input: 1 Minimum output: 0 kg/s Maximum output: 10 kg/s
FC-119
Controller class : PI Controller action: direct Controller mode: cascade Controlled variable: sump outlet mass flowrate Manipulated variable: outlet sump valve stem position Proportional gain: 100 Integral time constant: 0.1 s Minimum input: 0 kg/s Maximum input: 10 kg/s Minimum output: 0 Maximum output: 1
60
S-116 refers to the reboiler liquid outlet sink and represents a dummy stream with zero flowrate. The
associated valve V-115 is therefore closed. The sink was added merely to comply with the mandatory material
outlet required by the reboiler separator model.
7.2.4. Condenser
The vapour distillate is condensed in total condenser E-121 where a constant sub-cooling temperature
difference of 5ºC and a negligible pressure drop are maintained. For the ModelBuilder simulations the
dynamic mode of the condenser was turned off which in practice means that a negligible holdup was assumed
in E-121.
7.2.5. Splitter
Splitter M-123 is a critical component of the dynamic system. Indeed, the splitter ensures two main functions:
defining the reflux ratio and stabilizing the system by including holdup accumulation, if such balance is
required.
It is interesting to analyse how the reflux ratio is defined in the splitter. The reflux ratio is perfectly controlled
by specifying the required split fraction and un-assigning the pump pressure increase. For a particular reflux
flowrate, reflux valve V-124 generates a given pressure drop which is perfectly compensated by pump L-126,
where the required pressure increase is established. Note that in the Bonsfills experiment the reflux ratio is
automatically controlled with an electromagnet.
Globally the entire flowsheet is run in a pressure-driven mode, i.e., the pressure differentials define the
system’s flowrates. However, the splitter itself is defined in a flow-driven mode. A constant pressure is
assigned to the liquid surface of product container F-140. Consequently, the splitter outlet pressure is
calculated using the liquid surface pressure and the pressure drop generated by valve V-130, placed before
product receiver F-140. Additionally, the inlet splitter pressure is also determined upstream. Because both the
inlet and outlet splitter pressures are calculated in this manner, the inlet and total outlet splitter flowrates may
also be calculated in valve models V-122 (inlet) and V-124/V-130 (outlet), by using the pressure differential
before and after the valves. Hence, both the pressure and the flowrate are well defined in the inlet and outlet
of the splitter and this is the reason why the splitter is run in a flow-driven mode.
As stated previously for a given reboiler heat duty two simulations are scheduled: a first simulation designed to
achieve steady-state conditions operating under total reflux and a second simulation where a constant reflux
ratio is assigned. From a modelling point of view having the splitter operating in a dynamic mode with a
specified volume during the total reflux simulation is beneficial. Indeed, because the splitter stabilizes the
flowrates of the system by containing a non-negligible holdup, the simulation is less likely to fail. Hence, all
61
total reflux simulations include a 1 L cylindrical splitter with flat heads and 10 cm diameter. Note that
introducing a splitter with non-negligible holdup is an artificial tool designed exclusively to help reach the
required steady-state.
In the Bonsfills experiment there is no significant mass holdup in the top portion of the separation system. In
this case, the condenser contains a small holdup and no reflux tank is included. To validate the ModelBuilder
simulations against the results provided by Bonsfills, having a splitter with negligible holdup during the finite
reflux simulations is critical. The products should not be retained in the splitter, compromising the results
validation. For this reason, at the start of the constant finite reflux simulations the splitter was re-assigned a
negligible volume. From a modelling perspective this change does not affect the steady-state conditions at the
start of the finite reflux simulations. Once steady-state is achieved the splitter’s inlet and outlet flowrates,
pressures, temperatures and compositions are identical. Consequently, if the splitter volume is re-assigned a
negligible value all the variables of the entire system remain the same, i.e., the steady-state is not modified. The
only effective change in the system is the splitter holdup which is no longer included. This modification was
taken into account by not considering any splitter holdup when calculating the steady-state molar holdup for
the system.
7.2.6. Pump
The dynamic mode was turned off for pump L-126. As stated above, the pump is working in a perfect control
mode and no characteristic curves are included. The pump pressure increase is not specified and is used to
achieve the desired reflux ratio specified by the splitter split fraction.
7.2.7. Recycle breakers
Recycle breakers are models that facilitate the initialisation procedure of simulations that contain closed loops.
The initialisation procedures help resolve the system, i.e., find a solution for time 𝑡 = 0 by defining the set of
equations that are solved as a first calculation step at time 𝑡 = 0 independently in each model.
In the present case, two recycle breakers are needed: R-128 and R-132. During initialisation all the models are
solved sequentially using the initial guesses provided by the recycle breakers. Hence, in this first step the
reboiler equations are solved first, being followed by the column section and the product receiver equations.
The following initial guesses were assigned to recycle breaker R-128:
Inlet and outlet pressure of 1.15 bar;
Temperature of 62.4 ºC;
80.9 mol% methanol and 19.1 mol% water stream.
62
An initialisation procedure starting with a zero flowrate stream was chosen for Recycle-breaker R-132. The
outlet pressure was assigned an initial guess value of 1.23 bar.
7.2.8. Product receiver
Pure methanol is withdrawn during the finite reflux simulations to product receiver F-140. For this reason, a
tank model identical to the sump model was added. In this case, the following specifications were given:
8 L cylindrical receiver with flat heads and 21.7 cm diameter;
Constant liquid surface pressure of 0.9999 bar;
Initial temperature of 66.3 ºC;
Initial negligible holdup of 3,12 × 10−4 and 5.55 × 10−4 moles of methanol and water, respectively.
Note that S-142 is the product receiver sink which is representing a dummy stream with zero flowrate. As was
the case with the reboiler outlet, the product receiver sink was added to comply with the mandatory material
outlet required by the tank model.
7.3. Total reflux
As previously stated, a first total reflux simulation is scheduled in ModelBuilder to achieve the same steady-
state conditions given by Bonsfills. Indeed, the experimental column operates under a constant heat duty of
933.3 W. After steady-state is achieved the system operates with a constant finite reflux ratio of 𝐿
𝐷= 3.
Figure 7.3 shows the temperature profile for column stages 1, 10, 12, 13, 14 and 15 obtained in the total reflux
ModelBuilder simulation for a heat duty of 933.3 W. It is interesting to note that the steady-state temperature
does not vary significantly in the upper half of the column, that is, the temperature only increases from 65.5°C
to 65.7 °C for trays 1 and 10, respectively. On the contrary, on the bottom portion of the column the steady-
state temperature varies significantly from stage to stage. Indeed, between trays 10 and 15 a temperature
difference of 7.3°C is observed. At steady-state the first nine stages of the column contain mostly methanol
which is the lightest component of the mixture. Hence, the temperature of these stages is close to the boiling
point of this component (64.7 °C).
63
Figure 7.3 – Total reflux temperature profiles for column stages 1, 10, 12, 13, 14 and 15 and Q = 933.3 W.
From Figure 7.3 it can be noted that at the beginning of the total reflux simulation a sharp decrease in
temperature is predicted for all column stages. For example, for tray 14 the temperature decreases from
75.3°C at 𝑡 = 0 to 69.3°C at 𝑡 = 1.67 min. The reason for this sharp variation can be explained by analysing
the reboiler behavior at the beginning of the simulation.
Figure 7.4 illustrates the reboiler pressure profile for the same total reflux simulation of 933.3 W heat duty. In
this case, a sharp decrease from the initial specified pressure of 1.221 bar is shown. The initial specified
pressure is significantly higher than the steady-state reboiler pressure (1.05 bar). Consequently, when the
pressure decreases sharply in the reboiler in the beginning of the simulation a significant amount of vapour is
formed, i.e., this pressure decrease is associated with a vapour fraction increase in the reboiler. During this
period of time, the reboiler vapour outlet flowrate is also markedly high (0.15 kg/s vs. 6.3 × 10−4 kg/s at
steady-state). Because a significant initial amount of vapour is sent to the column at the very beginning of the
simulation, the pressure in the column stages for times close to 𝑡 = 0 is very high, even more so than the
initial specified pressure profile listed in section 7.2.1. Consequently, the equilibrium temperature in the
column stages is also high in the beginning of the simulation. As the system stabilizes, the temperature
decrease in the column stages shown in Figure 7.3 can be noticed.
64
66
68
70
72
74
76
78
0 5 10 15 20 25 30 35 40
T(°
C)
Time (min)
Tray 1Tray 10Tray 12Tray 13Tray 14Tray 15
64
Figure 7.4 – Reboiler pressure profile for Q=933.3 W in total reflux simulation.
In the Bonsfills experiment a heat duty of 933.3 W was supplied to the reboiler. To validate the ModelBuilder
results against the experimental data, the same average distillate flowrate must be obtained for a given reflux
ratio.
Figure 7.5 shows the distillate flowrate profile obtained in the second ModelBuilder simulation set (using a
constant specified reflux ratio of 3) as well as the average distillate flowrate provided for the experiment. Note
that this second simulation starts at steady-state using the saved variables obtained at the end of the previous
total reflux simulation. In the Bonsfills experiment a heat duty of 933.3 W leads to an approximately 0.28
mol/min distillate flowrate, which is considerably lower than the 0.35 mol/min average value given by the
ModelBuilder simulation. The fact that the experimental Oldershaw column is not adiabatic may explain this
discrepancy. This means that an actually heat loss to the exterior may occur in the experiment conducted by
Bonsfills. Hence, the next step to adequately validate the ModelBuilder dynamic column model is to
determine the theoretical heat duty that generates an identical 0.28 mol/min flowrate. From Figure 7.5 it can
also be noticed that a theoretical heat duty of 736.4 W generates a 0.28 mol/min average distillate flowrate,
matching the experimental value. Hence, if a 21.1% heat loss equivalent to a 196.9 W heat loss is assumed for
the Bonsfills experiment, the distillate flowrate profiles become identical and the validity of the ModelBuilder
column model may be assessed. For this reason a heat duty of 736.4 W was used in ModelBuilder to validate
all the simulation results.
1
1.05
1.1
1.15
1.2
1.25
0 5 10 15 20 25 30 35 40
P (
bar)
Time (min)
65
Figure 7.5 – Distillate flowrate profiles for RR=3 and Q=933 W or Q=736 W.
The distillate flowrate profiles illustrated in Figure 7.5 also show that for a given heat duty the pure methanol
distillate flowrate in the first period of the simulation is higher than the pure water distillate flowrate in the
final simulation phase. This is explained by the fact that at normal pressure methanol has a lower latent heat
of vaporization than water (35.3 kJ/mol vs 40.68 kJ/mol) and consequently for the same heat duty a higher
flowrate is obtained for a pure methanol distillate, when compared to a pure water product.
In the Bonsfills methanol/water experiment an initial volume of 4L of a 20 mol% methanol and 80 mol%
water mixture was charged to a distillation still at atmospheric pressure and heated up under total reflux until
steady-state conditions were achieved. Because no product is withdrawn in the total reflux regime, the molar
holdups of methanol and water were maintained during this period at a constant value of 33.7 moles and
135.0 moles, respectively.
As stated previously, the specifications for each model in ModelBuilder are given in each total reflux
simulation for a particular reboiler heat duty 𝑄. To validate the batch dynamic model, the steady-state that is
obtained in the Bonsfills experiment must be reproduced. Hence, the specified initial conditions must
generate a steady-state with the same total holdups of methanol and water in the system, that is, 33.7 moles
and 135.0 moles, respectively.
The steady-state molar holdups obtained in the total reflux ModelBuilder simulation using a heat duty of 736.4
W are listed in Table 7.5. In the steady-state regime the holdups in the system are split between the reboiler,
the 15 column stages and the sump. The Bonsfills experiment yields an average steady-state molar holdup of
0.175 per column stage which is approximately the value obtained in the ModelBuilder simulation, within a
9.2% error. The required total steady-state molar holdups are obtained for the ModelBuilder simulation with a
relative error of 0.25%. The methanol and water holdup errors are presented in Table 7.5, translating the
relative deviations between the ModelBuilder steady-state holdups and the steady-state holdups of 33.7 moles
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 1 2 3 4 5 6 7 8 9
Dis
till
ate
flo
wra
te (
mo
l/m
in)
Time (hr)
Experimental (average)
ModelBuilder Q=933.3 W
0.2
0.25
0.3
0.35
0.4
0.45
0 1 2 3 4 5 6 7 8 9
Dis
till
ate
flo
wra
te (
mo
l/m
in)
Time (min)
Experimental (average)
ModelBuilder Q=736 W
66
of methanol and 135.0 moles of water given by Bonsfills. Because the required steady-state is reached in the
total reflux ModelBuilder simulation, the results may now be validated against the data given by Bonsfills.
Table 7.5 - Reboiler, column and sump steady-state holdups for Q=736.4 W.
7.4. Model validation
In this section the batch multi-staged ModelBuilder model is validated against temperature and composition
profiles provided by Bonsfills for the distillate, for plate 5 and for the reboiler. The Bonsfills experimental data
is compared with the ModelBuilder, Fortran and Batchsim theoretical results and the discrepancies are
explained by analysing the theoretical simplifications assumed for the models.
7.4.1. Column section
The left-hand side of Figure 7.6 shows the molar methanol fraction profile in the distillate for a ModelBuilder
simulation with a constant reflux ratio 𝑅𝑅 = 3 and a reboiler heat duty of 736.4 W. The same profile is also
illustrated for the Bonsfills experiment, Fortran model and the Batchsim model for a reflux ratio of 3 and for
the heat duty required to generate an average distillate flowrate of 0.28 mol/min. Note that at time 𝑡 = 0 the
system is operating under steady-state conditions.
Globally three distinct time periods can be noted: a first period where a plateau occurs for a molar methanol
fraction of 1; a second phase where the methanol molar fraction decreases and a final period where pure water
is withdrawn from the column.
During the first period pure methanol is withdrawn from the column and collected in the product receiver. In
this work, the first plateau duration is defined by the methanol purity, i.e., the first plateau ends when the
methanol purity falls below 0.99. The estimated duration of this first plateau is 94 min for the ModelBuilder
model, 105 min for the Fortran model and 112 min for the Batchsim model. Because Bonsfills obtained an
experimental plateau time of 80 min, ModelBuilder gives the closest estimation to this value, with an error of
17.2%. The methanol plateau duration is directly related to the distillate flowrate profile since higher distillate
Reboiler Column Sump Total Holdup error (%)
Methanol 30.2 moles 0.180 moles
per plate 1.017 moles 33.9 moles 0.59
Water 134.2 moles 0.0108 moles
per plate 0.807 moles 135.2 moles 0.15
Methanol+water holdup
164.4 moles 0.191 moles
per plate 9.2 % error
1.824 moles 169.1 moles 0.25
67
flowrates in this period mean that more pure methanol is being withdrawn per unit of time and consequently
shorter first plateau durations are obtained. This fact explains why the ModelBuilder estimation gives the
closest approximation to the experimental methanol plateau duration: both the experimental setting and the
ModelBuilder model use a constant heat duty; because methanol has a lower heat of vaporization than water,
to maintain an average distillate flowrate of 0.28 mol/min, the experimental and ModelBuilder distillate
flowrate profiles must reveal higher flowrates in the pure methanol withdrawal period (>0.28 mol/min) when
compared to the pure water withdrawal period (<0.28 mol/min) and thus shorter methanol periods are to be
expected in these cases. Both the Fortran and Batchsim models assume a constant distillate flowrate of 0.28
mol/min and thus the pure methanol withdrawal period lasts longer.
The second phase of the distillation process generates off-cuts, impure methanol/water mixtures that in an
industrial set context would be collected separately and recycled to a next batch. The off-cut duration refers to
the period where impure methanol/water products are obtained, i.e., where 0.01 < 𝑦𝑚𝑒𝑡ℎ𝑎𝑛𝑜𝑙 < 0.99. To
satisfactorily compare the off-cut periods, each one of the four profiles on the left-hand side of Figure 7.6 was
shifted in the xx axis by a time equal to the first plateau duration, thereby eliminating this first plateau (see
Figure 7.6- right-hand side). The shifted transformations show that the ModelBuilder and the Batchsim slopes
are close and almost parallel in this second time period, predicting very sharp decreases in the methanol
composition, i.e., efficient separations linked to short off-cut periods. The models used to determine the VLE
data might explain the off-cut slopes: both the ModelBuilder and the Batchsim models use the NRTL
equations to determine the activity coefficients of the liquid phase. A simpler assumption of constant relative
volatility is given in the Fortran model, explaining why the off-cut slope is shallower than the remaining
theoretical models.
The Bonsfills experiment gives a significantly longer off-cut period (>174 min). Unlike the models, in an
experimental setting the liquid and vapour phases leaving each stage are not in thermal, mechanical and
thermodynamic equilibrium primarily due to insufficient contact time between the two phases and deficient
mixing [23]. The assumption of equilibrium stages for all the models may have affected the distillate profiles
generating optimistic (short) off-cut periods and efficient separations. Indeed, the three models predict a
higher methanol recovery when compared to the experimental value of 79.7%: 85.4% for ModelBuilder,
86.7% for Fortran and 92.7% for Batchsim (see Table 7.6). Hence, a future model improvement would be to
possibly implement rate-based equations thereby considering mass and heat transfer limitations.
68
Figure 7.6 - Distillate methanol composition profiles with RR=3 and �̅� = 0.28 mol/min. The right-hand side figure represents the same profiles with an xx axis shift for each of the 3 functions to G(X) = F(X+T1
stplateau).
Finally, in the last phase the distillate is in the form of pure water. This is shown in the profiles illustrated in
Figure 7.6, where the methanol molar fraction decreases to approximately 0 during the last period.
Table 7.6 summarizes the information described above by listing the 1st plateau and off-cut period durations,
as well as the experimental, ModelBuilder, Fortran and Batchsim methanol recoveries.
Table 7.6 – 1st plateau and off-cut durations and methanol recoveries. The first plateau ends when the methanol purity
falls below 0.99. The off-cut duration refers to the period where 0.01 < 𝑦𝑚𝑒𝑡ℎ𝑎𝑛𝑜𝑙 < 0.99.
Figure 7.7 compares the distillate temperature profile obtained in ModelBuilder with the Fortran model for
the same simulation (RR=3 and D̅= 0.28 mol/min). In this case, the same three time periods can be noted. In
the first plateau pure methanol is distilled and the temperature given by both simulations is 65.3 °C, which is
close to the component’s boiling point (64.7 °C). The temperature increases and the second phase ends when
the distillate temperature reaches 100 °C, when the process of withdrawing pure water from the column starts.
A sharper increase in temperature during the second phase is given by ModelBuilder, more so than the
shallower slope obtained in Fortran. This sharp increase in temperature is in agreement with the shorter off-
cut time estimated in Figure 7.6 for the ModelBuilder simulation.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
y m
eth
an
ol
(mo
l fr
ac)
Time (hr)
Fortran
ModelBuilder
Batchsim
Experimental
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
y m
eth
an
ol
(mo
l fr
ac)
Time (hr)
Fortran
ModelBuilder
Batchsim
Experimental
Experimental
ModelBuilder
Fortran Batchsim
1st plateau duration (min)
80 94 105 112
Off-cut duration (min)
>174 78 174 84
Methanol recovery (%)
79.7 85.4 86.7 92.7
69
Figure 7.7 - Distillate temperature with RR=3 and �̅� = 0.28 mol/min.
Now that the behavior of the ModelBuilder simulations has been analysed and validated for the distillate
stream, let us consider an intermediate column plate 5. Figure 7.8 shows the ModelBuilder, Fortran and
Batchsim liquid outlet stream composition profiles for plate 5. It can be noticed that the three time periods
analysed for the distillate profile are still very clearly defined for plate 5. Pure methanol (xmethanol ≥ 0.99) is
obtained on plate 5 during 81 min for the ModelBuilder simulation, 86 min for Fortran and 103 min
according to Batchsim. The liquid composition profiles simulated by the three models are very similar for this
plate, with the only significant difference being in fact the duration of this first plateau.
As expected, the period where pure methanol is obtained in the distillate is longer than for plate 5. However,
for plate 5 the duration of the period where pure water is obtained increases. Evidently, as the stage column
number increases the methanol is held during shorter times while the water is retained for longer periods. This
fact is clearly illustrated in Figure 7.9 where the methanol holdup profiles (i.e., the sum of the vapour and
liquid tray holdups) are shown for column stages 1, 5 and 10-15 for the ModelBuilder simulation. Not only
does the first plateau last longer for the upper column stages, but the total molar methanol holdup is also
higher. For example, tray 1 starts with a 0.186 moles methanol holdup while on stage 15 the methanol molar
holdup is only 0.127 at time 𝑡 = 0. From stages 12 to 15 the first plateau ceases to exist and the methanol
holdup decreases immediately at the start of the simulation.
40
50
60
70
80
90
100
110
0 1 2 3 4 5 6 7 8 9 10 11
Tem
pera
ture
(°)
Time (hr)
FortranModelBuilder
70
Figure 7.8 - Methanol composition for plate 5 with RR=3 and �̅� = 0.28 mol/min.
Figure 7.9 – Methanol holdup profiles for column trays with RR=3 and �̅� = 0.28 mol/min (ModelBuilder).
As shown in Figure 7.10, the temperature profiles for plate 5 generated by the theoretical models
(ModelBuilder, Fortran and Batchsim) are quite similar. However, the experimental temperatures given by
Bonsfills for plate 5 in the first plateau are higher than predicted by all theoretical models. For example, an
average experimental temperature of 71.3 °C is given for the first plateau, which is significantly higher than
the average temperature predicted by ModelBuilder.
It is important to analyse the differences between the theoretical models and the pilot plant experiment. In an
experimental setting, systematic or random experimental errors may affect the results. In the Bonsfils
experimet, for example, the distillate flowrate is measured by weighing the distillate weight in a scale with time,
Figure 7.12 – Reboiler temperature profile with RR=3 and �̅� = 0.28 mol/min.
The reboiler molar holdup and vapour fraction profiles are illustrated in Figure 7.13 for the ModelBuilder
simulation. As expected, the reboiler holdup profiles clearly indicate two distinct phases: a methanol
withdrawal period and a water removal phase. Indeed, the methanol holdup decreases from 30 to
approximately 0 moles during the first two hours whereas the water holdup which is 4.5 times higher is
removed during the following 7.7 hours. For almost the entire simulation the reboiler contains a saturated
liquid mixture. However, at time 𝑡 = 9 hours a dramatic rise in the vapour fraction is observed as the reboiler
is run dry.
Figure 7.13 – Reboiler holdup and vapour fraction profiles for RR=3 and �̅�=0.28 mol/min (ModelBuilder).
60
65
70
75
80
85
90
95
100
105
0 25 50 75 100 125 150 175 200 225 250
Tem
pera
ture
(°C
)
Time (min)
BatchsimFortranModelBuilder
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5 6 7 8 9 10 11
Ho
ldu
p (
mo
l)
Time (hr)
Water
Methanol
0
0.04
0.08
0.12
0.16
0.2
0 1 2 3 4 5 6 7 8 9 10 11
Vap
ou
r fr
acti
on
(m
ol/
mo
l)
Time (hr)
74
7.5. Sensitivity analysis
The relative importance of key operating conditions is now assessed by performing a sensitivity analysis. The
effect of the reflux ratio and the heat duty on the total separation time and on the methanol recovery was
analysed in a total of 9 simulations with ±0.5 reflux ratio differences and ±10% heat duty relative variations
starting from the base case scenario with a reflux ratio of 3 and 736 W heat duty. Hence, the simulations were
carried out combining reflux ratios of 2.5, 3 and 3.5 with heat duties of 663 W, 736 W and 810 W.
7.5.1. Total separation time
The distillate flowrate profiles obtained for reflux ratios of 2.5, 3 and 3.5 with a fixed 736 W heat duty are
represented in Figure 7.14 – a). As can be seen, the behavior of these profiles is similar. A pure methanol
withdrawal period where the distillate flowrate increases up to a maximum can be noticed, followed by an off-
cut removal phase with an associated distillate flowrate decrease and a final pure water withdrawal period
where the distillate flowrate remains approximately at a constant relative minimum. As previously stated,
because at normal pressure methanol has a lower latent heat of vaporization than water (35.3 kJ/mol vs 40.68
kJ/mol), for the same heat duty the pure methanol distillate flowrate in the first period of the simulation is
necessarily higher than the pure water distillate flowrate in the final simulation phase. Figure 7.14 – a) also
shows that for all simulation times the distillate flowrate increases with a reflux ratio decrease, which should
evidently be expected since less reflux is returned to the top of the column and more product is withdrawn
per unit of time. From Figure 7.14 – b) it can also be noticed that for a fixed reflux ratio of 3, a heat duty
increase generates higher distillate flowrates throughout the entire simulation runs.
Figure 7.14 – a) Distillate flowrate profiles for a fixed Q = 736 W and RR = 2.5, 3 and 3.5. b) Distillate flowrate profiles for a fixed RR = 3 and Q = 663 W, 736 W and 810 W.
Figure 7.15 shows the average distillate flowrate (ADF) and the total separation time (TST) for all simulations.
The total separation time starts in the steady-state regime and ends when the reboiler is run dry, i.e., it is the
0.20
0.24
0.28
0.32
0.36
0.40
0 1 2 3 4 5 6
Dis
till
ate
flo
wra
te (
mo
l/m
in)
Time (hr) a)
RR=3
RR=2.5
RR=3.5
0.20
0.24
0.28
0.32
0.36
0.40
0 1 2 3 4 5 6
Dis
till
ate
flo
wra
te (
mo
l/m
in)
Time (hr) b)
Q=736 W
Q=810 W
Q=663 W
75
period of time where a constant finite reflux separation is established. As can be seen from Figure 7.15, the
highest average distillate flowrate of 0.35 mol/min is obtained combining the lowest reflux ratio of 2.5 with
the highest heat duty of 810 W. On the contrary, the lowest average distillate flowrate of 0.22 mol/min is
given for the highest reflux ratio and the lowest heat duty combination (3.5 and 663 W, respectively).
Evidently, higher distillate flowrates generate a shorter total separation time since more product is withdrawn
per unit of time. Consequently, the shortest total separation time of 7.8 hours is given by the 2.5 RR – 810 W
simulation whereas the longest total separation time of 12.1 hours is predicted by the 3.5 RR – 663 W
simulation.
Figure 7.15 – ADF and TST for Q = 663 W, 736 W and 810 W and RR = 2.5, 3 and 3.5.
The average distillate flowrate (ADF) and the total separation time (TST) variations based on the base case 3
RR – 736 W simulation are listed in Table 7.7. As expected, for a particular reflux ratio and heat duty the ADF
and the TST relative variations present similar symmetrical values. For instance, a 1.8% increase in the average
distillate flowrate generates a 1.8% reduction in the total separation time for the 2.5 RR – 663 W simulation.
Another conclusion that may be drawn from Table 7.7 is that ±10% heat duty variations with fixed reflux
ratios and ±0.5 reflux ratio differences with fixed heat duties affect the total experiment time approximately
12%. For example, when maintaining a constant heat duty of 736 W the total separation time varies -12.3%
for a reflux ratio of 2.5 and +12.8% for a reflux ratio of 3.5. Similarly, when fixing a reflux ratio of 3 the total
separation time varies 12% and -8.4% for the 663 W and the 810 W simulations, respectively.
Table 7.7 – ADF and TST relative variations. Base simulation: 736 W with RR = 3.
0.20 0.25 0.30 0.35 0.40
Q=663 W
Q=736 W
Q=810 W
ADF (mol/min)
RR=3.5
RR=3
RR=2.5
6 8 10 12 14
Q=663 W
Q=736 W
Q=810 W
TST (hr)
RR=3.5
RR=3
RR=2.5
ADF variation (%) 663 W 736 W 810 W TST variation (%) 663 W 736 W 810 W
RR = 2.5 1.8 14.0 24.2 RR = 2.5 -1.8 -12.3 -19.7
RR = 3 -11.2 0.0 8.6 RR = 3 12.0 0 -8.4
RR = 3.5 -20.2 -11.6 -2.9 RR = 3.5 25.3 12.8 2.7
76
7.5.2. Methanol recovery
The distillate methanol composition profiles are represented in Figure 7.16 for a constant heat duty of 736 W
and reflux ratios of 2.5, 3 and 3.5. Here, two main aspects should be noted: firstly, the pure methanol
withdrawal duration is in agreement with the distillate flowrate profiles given in the section above, i.e., the
duration of the first plateau increases for higher reflux ratios due to an associated decrease in the distillate
flowrate (see Table 7.8); secondly, during the off-cut phases the profiles are relatively dissimilar directly
affecting the separation efficiency and therefore the product recovery. To satisfactorily compare the off-cut
periods, each one of the three profiles was shifted in the xx axis by a time equal to the first plateau duration,
thereby eliminating this first plateau (see Figure 7.16 - right-hand side). The shifted transformations show that
the separation is not as sharp for lower reflux ratios, where the off-cut slope is shallower and the off-cut
duration is longer.
Figure 7.16 – Distillate methanol composition profiles for a fixed Q = 736 W and RR = 2.5, 3 and 3.5. The right-hand side figure represents the same profiles with an xx axis shift for each of the 3 functions to G(X) = F(X+T1
stplateau).
Figure 7.17 shows the distillate methanol composition profiles for a fixed reflux ratio of 3 and heat duties of
663 W, 736 W and 810 W. Once again, the 1st plateau durations are in agreement with the distillate flowrate
profiles analysed in the previous section since higher heat duties generate higher distillate flowrates and thus a
shorter first plateau duration (Table 7.8). The off-cut periods can be conveniently compared using the xx axis
transformation mentioned above, generating the profiles shown in the right-hand side of Figure 7.17. In this
case, the off-cut slopes do not vary significantly for different heat duties and the expected separation
efficiency should be quite similar.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.0 1.5 2.0 2.5 3.0 3.5 4.0
y m
eth
an
ol (m
ol fr
ac)
Time (hr)
RR=2.5
RR=3
RR=3.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.2 0.4 0.6 0.8 1.0
y m
eth
an
ol (m
ol fr
ac)
Time (hr)
RR=2.5
RR=3
RR=3.5
77
Figure 7.17 - Distillate methanol composition profiles for a fixed RR=3 and Q = 663 W, 736 W and 810 W. The right-hand side figure represents the same profiles with an xx axis shift for each of the 3 functions to G(X) = F(X+T1
stplateau).
Table 7.8 – 1st plateau duration for Q = 663 W, 736 W and 810 W and RR = 2.5, 3 and 3.5. The first plateau duration is defined by the methanol purity, i.e., the first plateau ends when the methanol purity falls below 0.99.
1st plateau duration (min) 663 W 736 W 810 W
RR = 2.5 85.5 75.5 68.7
RR = 3 102.3 94 83.9
RR = 3.5 120.2 107 98.6
It is interesting to note that the off-cut profiles analysed above are in agreement with the methanol recoveries
listed in Table 7.9. The methanol recoveries are affected by ±0.5 differences in the reflux ratio, fact that
should be expected considering the above-mentioned differences in the off-cut profiles, namely the off-cut
slopes. For instance, a 6.8% relative decrease and a 2.6% relative increase in the methanol recovery is obtained
using the 2.5 RR – 736 W and the 3.5 RR – 736 W simulations, respectively, when compared to the base case
3.0 RR – 736 W simulation. Correspondingly, a ±10% heat duty variation practically does not modify the
methanol recovery since the off-cut period profiles are almost identical, i.e., the off-cut slopes are not altered
and hence the separation efficiency is maintained. This fact is demonstrated, for example, in the fixed RR = 3
simulations where a negligible methanol recovery relative variation of -0.7% is given for the 3.0 RR – 663 W
simulation and of -0.1% for the 3.0 RR – 810 W simulation. In conclusion, the methanol recovery varies
between 2.2 and 6.4% in absolute values when fixing the heat duties and modifying the reflux ratio in ±0.5
increments; on the contrary, a maximum absolute change of only 1.2% is observed in the methanol recovery
when the reflux ratio is maintained and the heat duties are varied ±10%.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.0 1.5 2.0 2.5 3.0 3.5 4.0
xm
eth
an
ol
(mo
l fr
ac)
Time (hr)
Q=736 W
Q=663 W
Q=810 W
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
xm
eth
an
ol
(mo
l fr
ac)
Time (hr)
Q=736 W
Q=663 W
Q=810 W
78
Table 7.9 – Methanol recovery and associated relative variation. Base simulation: 736 W with RR = 3.
7.6. Conclusion
In this chapter a multi-staged batch dynamic distillation model based on an experimental pilot plant assembled
by Bonsfills [45] was successfully implemented in ModelBuilder for a methanol/water mixture.
Model validation was also successfully carried out by comparing the ModelBuilder simulations with
experimental data and theoretical results given by Bonsfills for a Fortran model and for simulator Batchsim of
Pro/II for a reflux ratio of 3 and an average distillate flowrate of 0.28 mol/min. The assumption of constant
heat duty vs. constant distillate flowrate created differences in the duration of the pure methanol withdrawal
period. It was also found that the assumption of equilibrium stages generated for all models a non-negligible
overestimation of the separation efficiency and thus the methanol recovery.
The robustness of the dynamic ModelBuilder model was attested by performing a sensitivity analysis with
10% heat duty variations for the reflux ratios of 2.5, 3 and 3.5. As expected, shorter separation times were
obtained for lower reflux ratios and higher heat duties whereas higher reflux ratios and lower heat duties led to
longer separation times. The positive impact on the methanol recovery generated by using higher reflux ratios
was also analysed.
Methanol recovery (%)
663 W 736 W 810 W Methanol recovery
variation (%) 663 W 736 W 810 W
RR = 2.5 80.4 79.6 78.9 RR = 2.5 -5.9 -6.8 -7.6
RR = 3 84.8 85.4 85.4 RR = 3 -0.7 0.0 -0.1
RR = 3.5 88.7 87.6 88.8 RR = 3.5 3.9 2.6 4.0
79
8
General conclusions
and Future work
8.1. General conclusions
The background research presented in this work provided a broad overview on the field of batch distillation.
In particular, the literature review focused on introducing batch distillation with regard to operating policies
and modelling approaches, the latter comprising a general explanation of equilibrium and rate-based models as
well as tray hydraulic modelling issues. Because the demand for productivity in the fine chemical industry is
increasing, robust models that can predict separation performance indicators such as operation time and
component purity are required. Thence, the main contribution of this study has been the implementation of a
dynamic multi-staged distillation model in gPROMS ModelBuilder® based on equilibrium stages and
including the effects of non-negligible tray holdup and of tray pressure drop.
Preliminary steps were undertaken prior to implementing the dynamic multi-staged model. A one equilibrium
stage separator ModelBuilder model was successfully validated against a base case benzene/toluene separation
supplied by Seader et al. [13]. The composition, temperature and holdup profiles simulated in ModelBuilder
were overall in agreement with the data given by Seader et al. Indeed, the average benzene molar fraction in
the distillate predicted by ModelBuilder after 8.9 hours was found to be only 1.8% lower, being coupled with a
1.9% lower still temperature estimation. The thermodynamic models used to predict equilibrium data in both
cases should explain the noted divergences: a constant relative volatility was assumed by Seader et al. whereas
in ModelBuilder the more accurate NRTL and Soave-Redlich-Kwong equations accounted for the liquid and
the vapour non-idealities, respectively.
Tray holdup and pressure drop equations should be incorporated when developing a rigorous dynamic multi-
staged model in which the flowrates are pressure-driven and where non-negligible tray holdups are considered.
Thus, in this work several tray holdup and pressure drop correlations were added to the multi-staged column
80
model. Furthermore, column diameter correlations based on flooding limit estimations were also included as
preliminary design options.
To ensure model convergence, supplying accurate tray geometrical specifications when applying these
correlations is of significant importance. In this work, a methanol/water continuous distillation case study
with suitable geometrical specifications was used to preliminarily test the implemented hydraulic correlations.
Here, the type of flow regime was found to significantly affect the liquid holdup, dry vapour head loss and
aerated liquid head loss profiles. This fact was clearly illustrated considering that in the rectifying section
operating under a spray regime, Jeronimo & Sawistowski was found to be applicable, giving a liquid holdup of
approximately 977 moles; this value increased to 2517 moles for the froth-type stripping section where the
Bennett holdup correlation was found to be applicable.
Another noteworthy aspect relates to the importance of pondering the accuracy gain with a non-desirable
complexity increase when applying a more rigorous hydraulic correlation. In the dry vapour head loss case the
more complex Hughmark & O’Connell and Liebson equations predicted maximum absolute differences
relative to the simpler standard orifice equation of only 4.0% and 2.1%, respectively. On the contrary, for the
case study in question using a more complex column diameter equation was compensated by the accuracy
gain: the estimated column diameter was found to be 18% higher for the simpler Lowenstein correlation
compared to the more complex Fair correlation. In essence, all the implemented hydraulic correlations were
successfully simulated in ModelBuilder generating appropriate values if taken into account the occurring flow
regime and the complexity of each correlation.
After testing the one-staged equilibrium separator model and the hydraulic relations for the methanol/water
continuous distillation case study, a multi-staged dynamic distillation model based on an experimental pilot
plant assembled by Bonsfills [45] was implemented in ModelBuilder for a methanol/water mixture. As
expected, the distillate profiles highlighted three distinct phases: two pure methanol and pure water
withdrawal periods and an intermediate phase where impure mixtures were obtained.
Model validation was carried out by comparing the ModelBuilder simulations with experimental data and
theoretical results given by Bonsfills for a Fortran model and for simulator Batchsim of Pro/II for a reflux
ratio of 3 and an average distillate flowrate of 0.28 mol/min. The distillate flowrate profile was found to
significantly affect the duration of the pure methanol withdrawal period. A constant heat duty was supplied
experimentally. The ModelBuilder model assumed a constant heat duty profile, unlike the Fortran and
Batchsim models where a constant distillate flowrate was given. Regarding the duration of the methanol
withdrawal period, ModelBuilder predicted a closer agreement to the experimental data (94 vs. 80 min) than
the Fortran and Batchsim simulators where longer first plateau durations of 105 and 112 min were estimated,
respectively. This fact illustrates the non-negligible effect generated when assuming a constant distillate
81
flowrate profile adapting the heat duty accordingly, rather than providing a constant heat duty obtaining the
corresponding distillate flowrate profile. It was also found that the assumption of equilibrium stages generated
for all models a non-negligible overestimation of the separation efficiency and thus the methanol recovery.
The experimental methanol recovery of 80% was thereby lower than the ModelBuilder prediction of 85%, the
87% Fortran estimation and the Batchsim 93% methanol recovery. Nevertheless, the dynamic ModelBuilder
model was successfully validated simulating the expected composition, temperature and flowrate profiles with
occasional divergences from the experimental data being explained by the factors described above.
The robustness of the dynamic ModelBuilder model was attested by performing a sensitivity analysis with
10% heat duty variations for the reflux ratios of 2.5, 3 and 3.5. It was shown that ±10% heat duty variations
with a fixed reflux ratio and ±0.5 reflux ratio differences with a fixed heat duty affect the total experiment
time in approximately 12%. Furthermore, ±0.5 variations in the reflux ratio were found to have an absolute
impact of 2.2 to 6.4% on the methanol recovery. On the contrary, this recovery was practically not affected by
the 10% heat duty variation.
The main objective of this work was accomplished: a dynamic multi-staged batch distillation model enhanced
with tray hydraulic relations was successfully implemented in ModelBuilder. This tool may be applied, for
example, to the scheduling of chemical plants thereby facilitating industrial management at the scheduling
level. Future model improvements are discussed in the section presented below.
8.2. Future work
Future work is suggested for further development of the dynamic model presented in this thesis. A first
direction for future work involves further model improvement in the following aspects: simulation time and
convergence. If the initial conditions specified in the total reflux simulations are very far from steady-state, the
simulation time is long. This issue could be improved by appropriately scaling the model equations,
maintaining all the terms between 10−3 and 103. In the finite reflux period there are two phases where the
model is more likely to fail: at the beginning of the simulation, when defining the reflux ratio in the splitter
and during the first moments of off-cut mixtures removal from the column. In most cases the issue is solved
by temporarily increasing the heat duty to keep the system in the vapour-liquid phase equilibria region, since a
bubble point limit is impeding model convergence.
A second direction for future work would be to further validate both the Rayleigh separator and the batch
column model with mixtures comprising three or more components. The need for experimental data must
also be highlighted here since there is a lack of batch experiments available in the open literature, with only a
82
few research works being validated experimentally. In addition, an interesting possibility would be to describe
the vapour-liquid equilibrium differently by choosing other thermodynamic models for the Rayleigh
benzene/toluene separation presented in Chapter 4 and for the batch multi-staged methanol/water distillation
shown in Chapter 7 (e.g., Peng-Robinson equation of state for the vapour phase and the UNIQUAC model
for the liquid phase).
The extension of the dynamic equations to model mass and heat transfer processes could be another
consideration for future work. A rate-based model of this sort would be useful to simulate mixtures exhibiting
liquid non-idealities or to model reactive separations. In the methanol/water multi-staged distillation
presented in this work, the existence of a rate-based model would allow an accuracy reassessment in the
predicted methanol recoveries and off-cut durations. However, the increase in accuracy should be measured
against the additional complexity level and the availability of parameters such as mass and heat transfer
coefficients.
83
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Engineering - Optimization of Batch Reactive Distillation Process: Production of Lactic Acid, Elsevier
B.V., 2010.
[3] Diwekar, "Unified approach to solving optimal design-control problems in batch distillation," vol. 38,
1992.
[4] M. Noda, A. Kato, T. Chida, S. Hasebe and I. Hashimoto, "Optimal structure and on-line optimal
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