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Dynamic models for start-up operations of batch distillation

columns with experimental validation
S. Elguea , L. Prata , M. Cabassuda,∗ , J.M. Le Lanna , J. Cézeracb
a Laboratoire de Génie Chimique, UMR 5503 CNRS/INPT/UPS, 5 rue Paulin Talabot, BP 1301, 31106 Toulouse, Cedex 1, France
b Sanofi-Synthelabo, 45 Chemin de Météline, B.P. 15, 04201 Sisteron, France

Abstract

The simulation of batch distillation columns during start-up operations is a very challenging modelling problem because of the complex
dynamic behaviour. Only few rigorous models for distillation columns start-up are available in literature and generally required a lot of
parameters related to tray or pack geometry. On an industrial viewpoint, such a complexity penalizes the achievement of a fast and reliable
estimate of start-up periods. In this paper, two “simple” mathematical models are proposed for the simulation of the dynamic behaviour
during start-up operations from an empty cold state. These mathematical models are based on a rigorous tray-by-tray description of the
column described by conservation laws, liquid–vapour equilibrium relationships and equations representative of hydrodynamics. The models
calibration and validation are studied through experiments carried out on a batch distillation pilot plant, with perforated trays, supplied by a
water methanol mixture. The proposed models are shown by comparison between simulation and experimental studies to provide accurate
and reliable representations of the dynamic behaviour of batch distillation column start-ups, in spite of the few parameters entailed.

Keywords: Dynamic simulation; Batch distillation column; Start-up operation; Experimental validation; Water–methanol

1. Introduction (Gonzalez Velasco, Castresana Pelayo, Gonzalez Marcos, &

Gutierrez Ortiz 1987; Ruiz, Cameron, & Gani, 1988; Fieg,
The simulation of batch distillation columns during start- Wozny, & Kruse, 1993; Barolo, Guarise, Rienzi, & Trotta,
up operations is a very challenging modelling problem be- 1994; Sorensen & Skogestad, 1996; Baldon, Strifezza,
cause of the inherent and complex dynamic behaviour. The Basualdo, & Ruiz,1997; Han & Park, 1997; Furlonge, 2000).
dynamic behaviour of distillation columns during start-up Although all the authors agree on the need of a reliable
operations corresponds to the time from the initial state to model in order to represent the dynamic behaviour, only
a pseudo-steady state when a defined product composition few start-up models are reported in literature (Gani, Ruiz, &
is obtained. In this way, start-up operations represent very Cameron, 1986; Albet, Le Lann, Jouila, & Koehret, 1994a,
complex transient periods because of the simultaneous drastic 1994b; Wang, Li, Wozny, & Wang, 2003). In all these differ-
changes in many state variables. As these dynamic transitions ent start-up models, distillation columns are described by a
are always considered as non-productive periods, many re- rigorous tray-by-tray modelling related to the physical prop-
searches have been performed with the objective of minimis- erties and the real geometry. The start-up behaviour is defined
ing the start-up time, the energy consumption or the amount according to a start-up sequence that describes the transi-
of waste products and present the resulting start-up policies tion on trays from a non-equilibrium a vapour–liquid equilib-
rium state. The switching conditions between the two states
∗ are determined by the bubble point temperature at operating
Corresponding author.
E-mail address: michel.cabassud@ensiacet.fr (M. Cabassud). pressure.

1
Nomenclature
ml molar
a area (m2 ) p plate wall
A heat transfer area (m2 ) tray tray
Cp specific heat (J kg−1 K−1 ) * equilibrium
e Murphree efficiency
E internal energy (J)
g universal gas constant (J mol−1 K−1 ) In industry, many configurations of distillation columns
h liquid molar enthalpy (J mol−1 ) are reported: tray columns (perforated plates, bubble-cap
H vapour molar enthalpy (J mol−1 ) plates, etc.) and packed columns. All these configurations
hw weir height (m) make difficult the set-up of start-up models which require a
K equilibrium constant lot of parameters related to geometrical characteristics. To
L liquid flow-rate (mol s−1 ) avoid this issue, we have developed two realistic but “sim-
lw weir length (m) ple” models for the simulation of batch distillation columns
m mass (kg) start-up. The purpose of the present work is then to thor-
mE model of internal energy (J) oughly study, simulate and validate the dynamic behaviour
mh model of liquid molar enthalpy (J mol−1 ) of a batch distillation column during start-up operations using
mH model of vapour molar enthalpy (J mol−1 ) these two dynamic models.
mK model of equilibrium constant Kister (1979) and Ruiz, Cameron, and Gani (1998) re-
mu model of molar hold-up (mol) ported that the start-up operation consists of three phases
m1P model of pressure losses (Pa) according to the dynamic behaviour. The first stage, called
P pressure (Pa) the discontinuous stage, is characterised by its short time
Q thermal contribution (J s−1 ) period and the discontinuous nature of all variables (hy-
R reflux ratio draulic and transfer variables). The second stage, called
t time (s) the semi-continuous stage is characterised by the non-linear
T temperature (K) transient of the variables. At the end of this stage, hy-
u molar hold-up (mol) draulic variables reach their steady state values. The third
U thermal transfer coefficient (J m−2 K−1 s−1 ) stage, called the continuous stage, is characterised by the
v volume (m−3 ) linear transient responses of all variables. At the end of
V vapour flow-rate (mol s−1 ) this stage, all variables reach their steady state values. The
x liquid molar fraction aim of this study is to develop accurate models in order to
y vapour molar fraction represent the dynamic behaviour during the discontinuous
and semi-continuous stages, operated at total reflux. In this
Greek letters way, experiments have been carried out on a batch distil-
α filling coefficient lation pilot in order to calibrate and validate the proposed
β constant related to physical characteristics of models.
tray This paper is divided into two main parts. In the first part,
1H heat of condensation (J mol−1 ) a detailed description of the developed models, their char-
ρ density (kg m−3 ) acteristics and the related dynamic behaviour is given. The
second part describes the experimental device, the different
Subscripts experiments carried out and presents the comparison between
k plate k experimental and simulated results.
1 condenser
2 plate 2
n vessel 2. General modelling
cf cooling fluid
hf heating fluid The treatment of the start-up dynamics requires to simulate
ext ambient medium a train of successive steps, related to the physical events oc-
kw plate k wall curring inside the column. Consequently, the transition from
Superscripts one step to another may lead to discontinuities in the general
i constituent i model structure. In a first part, the management procedure
b bubble point will be described then the general equations of the model will
max maximum be written. Finally, the specific adaptations for each start-up
model will be presented. Thus, a rigorous modelling may
require modifications of the general equations model, deter-

2
mined by physical switching conditions: temperature reaches
bubble point, condenser filled up, etc.
As the developed modelling is very complex, its descrip-
tion is divided in three different parts. In a first part, the man-
agement procedure of the start-up dynamics is described. In a
second part, the general equations of the model are detailed.
Finally, the specific adaptations for each start-up model are
presented.

2.1. Management procedure of the column dynamics

The management procedure of the start-up steps consists

of the following scheme: Fig. 1. Details of a tray representation.

1. Detection of an event entailing a new step (e.g. for boiler The developed modelling offers a great flexibility regard-
evaporation: temperature reaching bubble point in the ing the kind of distillation columns to simulate: tray columns
boiler). or packed columns. Packed columns can be modelled as tray
2. Resultant modifications of the mathematical model, ac- columns by the way of the height equivalent of a theoret-
cording to the occurring step (e.g. for boiler evaporation, ical plate or height of a transfer unit for a particular type
the equation describing the absence of vapour flow going of packing. For tray columns, the adopted description of a
out is substituted by an equation describing the vapour given plate (Fig. 1) allows to take into account the real ge-
flow). ometry. In fact, the constant volume of the liquid hold-up
3. Accurate and consistent initialisation of the new mathe- (assumption 4) can be defined from the real plate character-
matical model. istics for tray columns (diameter, active area, weir height)
4. Solution of the new mathematical model. or from equivalent characteristics for packed and unknown
columns. Nevertheless, the hydrodynamics of the column is
This procedure requires to test the occurrence of each not directly taken into account and so particular flow regimes
possible event at each solver step and so may be substan- (flooding, weeping, drying) cannot be rigorously represented,
tial calculation time consuming. This characteristic is how- i.e. no specific events are defined to detect flooding, weeping
ever compensated by the velocity of the solver used (DISCo: or drying conditions. A standard flow regime, limited on one
Sargousse, Le Lann, Joulia, & Jourda, 1999) thanks to the use hand by the liquid seal and on the other hand by the down-
of operator sparse and to an automatic initialisation procedure comer critical velocity (Kister, 1979) is assumed, that ensures
of the new generated DAE system. a good mixing.
The tray description (Fig. 1) involves that the liquid phase
2.2. Mathematical model held-up on a plate (k) always comes down to the plate below
(k + 1) through the downcomer (flow-rate Lk − 1 ). This liquid
The mathematical model results from the restriction to flow is assumed to be instantaneous whatever the height
distillation column of a complex dynamic model developed between plates is. The vapour phase going up from the plate
for batch processes simulation (Elgue et al., 2001). In this below (plate k + 1) is shared in two flows: one (flow-rate
framework, a tray-by-tray modelling approach of the column eVk + 1 ) is going up to the considered plate (plate k) and
has been adopted. Thus, the dynamic model is described by contributes to the plate equilibrium and the other (flow-rate
a set of differential and algebraic equations (DAE system) (1 − e)Vk − 1 ) is directly going up to the plate above (plate
written for each tray. k − 1) and by-passes the considered plate. All these vapour
Ordinary differential equations (ODE) represent energy flows are assumed to be instantaneous. The sharing constant
balances, total and component mass balances. Algebraic (e) represents the Murphree efficiency (assumption 2). It can
equations are composed of constitutive equations such as be adjusted to represent the non-ideality of the column plates.
vapour liquid equilibrium relationships, summation equa- The different plates of the column are numbered from
tions, physical property estimations, etc. In order to reduce top to bottom: plate 1 represents the condenser and plate n
the complexity of the model, the following typical assump- the boiler. The liquid reflux provided by the condenser is
tions have been adopted for each tray: introduced at the top of the column (plate 2). Thus, the reflux
1. Perfect mixing of vapour bubbles and of liquid phase. vector of plate k (Rk ) is equal to zero except for plate 2. Hence,
2. Equilibrium relationship between liquid and vapour with each plate k of the distillation column (Fig. 1), including con-
possible introduction of the Murphree efficiency. denser and boiler, is represented by the following equations.
3. Negligible vapour hold-up compared to liquid one. Total mass balance
4. Constant volume of the liquid hold-up once filling up is duk
= Vk+1 + Lk−1 − Vk − Lk + Rk L1 (1)
completed. dt

3
Component mass balances to physical phenomena (boiling, tray filling up) and concern-
ing hydrodynamic relationship and vapour–liquid constraint.
d(uk xki ) i
= Vk+1 yk+1 i
+ Lk−1 xk−1 − Vk yki − Lk xki Therefore, the formulations of Eqs. (7) and (8) vary according
dt to the considered start-up step.
+Rk L1 x1i (2) Correlations (Dream, 1999) are used to determine heat
transfer coefficients. A complete physical property estima-
Energy balance tion system with associated data bank (Prophy® ; Le Lann,
d(uk hk ) Joulia, & Kohret, 1988) is also used for models determina-
= Vk+1 Hk+1 + Lk−1 hk−1 − Vk Hk − Lk hk tion: physical properties models, hydrodynamic relationship
dt
and, pressure drop. Physical properties (density, specific heat,
+Rk L1 h1 + Qk (3)
enthalpies, molar volume, bubble point and vapour–liquid
Vapour–liquid equilibrium relationships equilibrium constant) are estimated from typical laws: equa-
tion of state and activity coefficient models (UNIFAC or
yki − yk+1
i
(1 − ek ) − ek Kki xki = 0 (4) NRTL). Formulations of the other models are given in Eqs.
Vapour enthalpy balance (16)–(19). It has to be noted that different formulations can
be adopted for each model, according to the desired level of
ek Hk∗ + (1 − ek )Hk+1 − Hk = 0 (5) complexity. For instance, hydrodynamic relationship can be
Summation equation defined by a simple volume constraint (Eq. (19)) or by typical
X formulations such as Francis formula (Eq. (20)).
(xki − yki ) = 0 (6) Hold-up model
i tray
ak hwk
Hydrodynamic relationship muk = simple formulation (16)
vml
k
Lk = 0 or uk − muk (Tk , Pk , xki ) = 0 (7)
"  2/3 #
Liquid–vapour constraint ρk tray L k mk
muk = a hwk + 1.41 √
mk k gρk lwk
Vk = 0 or Tk − Tkb = 0 (8)
Francis formula (17)
Liquid enthalpy model
Pressure drop model
hk − mhk (Tk , Pk , xki ) = 0 (9)
m1P = constant simple formulation (18)
Vapour enthalpy model
Hk − mHk (Tkb , Pk , yki ) = 0 (10) m1P = βtray Vk 2 formulation related to tray geometry
Equilibrium constant model (19)
Kki − mKik (Tkb , Pk , xki , yki ) = 0 (11) DISCo (Sargousse et al., 1999), a general solver of DAE
Pressure model system based on the Gear method (Gear, 1971) allows to
obtain the numerical solution of the developed mathematical
Pk+1 − Pk − m1Pk = 0 (12) model. Besides its accuracy and numerical robustness, DISCo
allows to develop a complex management procedure of the
The thermal contributions of the different parts of the column
column dynamic from its event detection facilities and its
are the following:
consistent initial condition calculations.
For condenser
Q1 = U1,cf A1,cf (Tcf − T1 ) − V2 (H2 − 1H1 ) (13) 2.3. Start-up models
For boiler The aim of the present work is to represent the dynamic
Qn = Un,hf An,hf (Thf − Tn ) + Un,ext An,ext (Text − Tn ) (14) behaviour of batch distillation columns during start-up op-
erations, particularly during the period described by Ruiz,
For column plate Cameron, and Gani (1988) as the discontinuous stage. During
Qk = Uk,ext Ak,ext (Text − Tk ) (15) this period, important changes (large dynamics) of thermo-
dynamic variables take place inside the column. Two models
During start-up, the transition from one step to another may describing the dynamic behaviour of start-up have been de-
lead to modification of the equation models. The general veloped. The second model is more realistic and complex
modelling then entails a hybrid model including equations than the first one. Consequently, it is called “realistic model”
discontinuities determined by switching conditions related by opposition to the first one, called “simple model”. These

4
models, with their advantages and drawbacks, are detailed in 7. The bottom plate is completely filled up. Discontinuous
the following sections. stage ends.
Simplicity is the main advantage of this model. In fact,
2.3.1. Simple model
apart from the typical characteristics of the column, only one
This model is based on an improved version of the start-
parameter (the filling ratio) allows to describe the dynamic
up model developed by Albet Le Lann, Joulia, and Koehret
behaviour. According to the initial conditions of the column,
(1994a,b). The introduction of one additional parameter, the
this ratio varies in the range from 0 to 1. The filling coefficient
plate filling ratio, constitutes the main difference. During the
tends towards 1 or 0 for start-ups, respectively, from cold state
column start-up, all the vapour flow going up from the lower
or hot state.
plate is assumed to instantaneously condense on the consid-
However, this model appears not able to represent the cases
ered plate, originally cold. As vapour continue to come from
of trays filled up, with liquid falling down the downcomers
the plate below through the plate holes, the liquid is held-up
before filling up of the condenser and reflux flow introduced
on the plate. Thus, the liquid hold-up on the plate increases.
inside the column. Such sequence may occur in the case of
Moreover, as fast as it fills up, the plate heats up. At the be-
start-ups from cold state of columns with a high thermal in-
ginning of the filling up, the plate is assumed too cold to
ertia and/or high thermal losses. This drawback leads us to
generate vapour flow. The filling ratio represents the value
develop another more realistic model, suitable with the real
of the liquid hold-up from which the plate is hot enough to
physical behaviour of the column.
generate vapour flow that goes up to the plate above. In the
present paper, this event is called local vapour generation
event (LVGE). Consequently, the following steps sequence 2.3.2. Realistic model
composes the modelling of the dynamic behaviour: This model is partly based on the previous one. A new
definition of the LVGE occurrence constitutes the main dif-
1. Heat is introduced into the boiler. ference. In this model, the vapour going up from the lower
2. The boiler temperature reaches bubble point. Vapour starts plate is assumed to condense on the wall of the considered
going up and condensing on the upper plate which begins plate (which heats up) before falling down. The falling liq-
to fill up. uid is assumed without under-cooling (i.e. liquid at its bub-
Event : Tn = Tnb ble point temperature) and to hold-up on the plate below.
Thus, as fast as the plate wall heats up, the plate below fills
Modification of Eq. (8) :
up. Once the plate wall temperature reaches the liquid bub-
Vn = 0 replaced by Tn − Tnb = 0 ble point temperature, the vapour goes up through the plate
and starts to condense on the plate wall above, before falling
3. Liquid hold-up reaches the filling ratio (α) in plate n − 1.
down to the plate which starts to fill up. In this way, ac-
Vapour starts to go up from the plate and to condense on
cording to its thermal and geometrical characteristics, a plate
the upper plate.
may supply vapour to the plate above before or after the
Event : vn−1 − α vmax n−1 = 0 plate below is completely filled up. The dynamic behaviour
Modification of Eq. (8) : of the start-up is then represented by the following step
b
sequence:
Vn−1 = 0 replaced by Tn−1 − Tn−1 =0
1. Heat is introduced into the boiler.
4. From plate to plate, vapour reaches the top of the column. 2. The boiler temperature reaches bubble point. Vapour starts
When the top tray generates a vapour flow, the condenser to go up and to condense on the upper plate wall which is
starts to fill up. heated.
5. The condenser is completely filled up. Total reflux or fixed
Event : Tn − Tnb = 0
reflux is introduced into the column. The top tray ends to
fill up, for a (1 − α) fraction. Modification of Eq. (8) :
Event : v1 − vmax 1 =0
Vn = 0 replaced by Tn − Tnb = 0
Modification of Eq. (7) :
L1 = 0 replaced by u1 − mu1 (T1 , P1 , x1i ) = 0 Modification of Eq. (7) :
6. The top tray is completely filled up. Liquid starts falling Ln−1 = 0 replaced by Ln−1 = Vn
down the downcomer to the lower plate. In this way, step-
by-step plates ends to fill up. 3. The plate wall reaches the liquid bubble point temperature.
Event : vk − vmax =0 Vapour goes up and starts to heat the upper plate. The
k
resultant condensation phenomenon starts to fill up the
Modification of Eq. (7) : plate.
p
Lk = 0 replaced by uk − muk (Tk , Pk , xki ) = 0 Event : Tn−1 = Tnb

5
 Modification of Eq. (8) :
b
Vn−1 = 0 replaced by Tn−1 − Tn−1 =0

Modification of Eq. (7) :

Ln−2 = 0 replaced by Ln−2 = Vn−1 ,
Ln−1 = Vn replaced by Ln−1 = 0
4. Vapour gradually reaches the top of the column. When the
LVGE occurs at the top, the condenser starts to fill up.
5. The condenser is completely filled up. Total reflux is in-
troduced inside the column. The top tray finishes to fill up
(except if it has already been done).
Event : v1 − vmax 1 =0
Modification of Eq. (7) :
L1 = 0 replaced by u1 − mu1 (T1 , P1 , x1i ) = 0
6. The top tray is completely filled up. Liquid starts to fall
down through the downcomer to the lower plate. In this
way, plates end to fill up step-by-step (except if it has
already been done). Fig. 2. Batch distillation pilot plant.
Event : vk − vmaxk =0
it allows to simulate complex sequences of start-ups from
Modification of Eq. (7) :
cold and empty state. Moreover, the thermal inertia due to
Lk = 0 replaced by uk − muk (Tk , Pk , xki ) = 0 vapour condensation on the column wall between two plates
can also be considered, through a modification of the plate
7. The bottom plate is completely filled up. Discontinuous wall energy model.
stage ends.
In consequence of this specific modelling, two new equa-
tions with the associated variables have been added to the 3. Experimental device
model (Eqs. (20) and (21)). The plate wall internal energy is
estimated from the tray geometry by Eq. (22). For the purpose of the present study, a batch distillation
Plate wall energy balance column, composed of two glass elements of 1 m height and
p 100 mm diameter, has been used (Fig. 2). Each element is
dEk
= Vk+1 Hk+1 − Lk hk packed with 10 glass perforated plates of Oldershaw type.
dt Oldershaw plate is provided with circular, vertically disposed
p
+ Ukw,ext Akw,ext (Text − Tk ) (20) holes. The vapour rising through these holes prevent the con-
densate to pass through in the opposite direction. A weir and
Plate wall internal energy model overflow pipe, mounted in the centre of the plate, keeps a
p p p constant low level of liquid on the plate and ensures a good
Ek − mEk (Tk ) = 0 (21)
internal reflux distribution. Temperatures inside the column
Plate wall internal energy are recorded every other plate. Samples of the liquid hold-up
p
mEk = mk Cpk Tk
p p p
(22) can be withdrawn on every plate.
The bottom of the column is composed of a glass ves-
In comparison to the previous one, this model is more com- sel (volume: 50 l, diameter 400 mm) connected to a ther-
plex and needs additional data: the plate wall mass (related to mosiphon. The heat transfer area of the thermosiphon is
the plate geometry) and the plate wall specific heat. In return, 0.18 m2 . Thermosiphon is supplied by a heat transfer fluid

Table 1
Details of experiments carried out
Experiment Heat transfer fluid flow-rate (m3 h−1 ) Initial vessel volume (l) Initial column temperature (◦ C) Room temperature (◦ C)
1 1.5 39.0 27 27
2 1.2 38.5 30 30
3 0.9 37.5 25 25

6
(Gilotherm) circulating in a boiler at about 160 ◦ C. A control Table 2
valve, between the boiler and the thermosiphon, regulates the NRTL parameters of water–methanol mixture
heat transfer fluid flow-rate. The temperature of the medium A12 −243.55
inside the vessel is also recorded. A21 872.81
α12 0.2994
The condenser is located 2.5 m up from the column bot-
tom. It is composed of a spiral coil heat exchanger (0.75 m2
heat transfer area) provided with cooling water. The flow-
rate, input and output temperatures (around 20 ◦ C) of the
cooling water are recorded. A control valve allows to control
the water flow-rate. The condenser is operated as a total con-
denser with the vapour condensing at the top of the column
and flowing back to a reflux divider located below. An ad-
justable timer controls periodic switching between distillate
tanks and reflux to the column. A full SIEMENS numerical
system (DCS) allows to record all pertinent information.
As plates are numbered from top to bottom, the different
parts of the pilot column are indexed as follows (Fig. 2):

• plate 1: condenser,
• plate 2: top of the column,
Fig. 3. Variations of vessel temperature for experiment 1.
• plate 21: bottom of the column,
• plate 22: thermosiphon.
ical properties of the water–methanol mixture. The NRTL
numerical parameters used, according to DECHEMA data,
4. Application results are given in Table 2.
Considering the simulation calibration and validation, two
The purpose of this experimental study is to obtain an points appear particularly critical: the column behaviour and
accurate measurement of the dynamic behaviour during the the thermosiphon representation. Consequently, in order to
start-up of the column and particularly during the discon- highlight the benefits of the developed models, the vessel
tinuous stage. In this way, only the total reflux period has temperature variations on one hand and the temperature vari-
been studied. In order to increase the time of the dynamic ations of the different column plates on the other hand are
behaviour, experiments have been carried out from cold state presented.
and at atmospheric pressure.
The vessel is fed with approximately 40 l of 4.1. Thermosiphon simulation
water–methanol mixture, with a composition of around
82% molar of water. The exact composition is determined With regard to the thermosiphon representation, the tem-
before each experiment by gas chromatography. This perature measured inside the vessel is directly compared to
well-known binary mixture has been chosen in order to the simulation results, as shown in Figs. 3–5 for experiments
avoid sample taking in the column during experiments. In
fact, temperature measurements allow to know the exact tray
composition by the way of the vapour–liquid equilibrium
diagram. A water–methanol mixture has also been chosen
for the volatility variations it presents. Furthermore, this
binary mixture is in agreement with assumption 3 of the
mathematical model set-up (vapour density is negligible
compared to the liquid density).
The column start-up has been studied through three ex-
periments, with different heating powers and hence different
dynamic behaviour. Therefore, three different flow-rates of
the heat transfer fluid have been supplied to the thermosiphon
by the way of the control valve. Table 1 gathers theses flow-
rates and the other operating conditions of each experiment.
The three different experiments carried out have been sim-
ulated. In order to verify the accuracy of the developed mod-
els, experimental results are compared to the associated sim-
ulations. NRTL model has been chosen to estimate the phys- Fig. 4. Variations of vessel temperature for experiment 2.

7
 1–3, respectively. As can be seen, simulations show a good
agreement with experiments. Nevertheless, experimentally at
the beginning of the start-up, the thermosiphon heat supply
presents an oscillatory behaviour. This behaviour is directly
related to the thermosiphon technology. In fact, the liquid
heated by the thermosiphon only flows to the vessel when
its temperature is high enough. Therefore, the heat internal
reflux inside the vessel shows an oscillatory behaviour, de-
creasing until the vessel mixture reaches bubble point. As the
aim of this study is not to obtain an accurate representation
of thermosiphons, this oscillatory behaviour has not been in-
tegrated in the mathematical model and then does not appear
in simulations.
Fig. 5. Variations of vessel temperature for experiment 3.

Fig. 6. Analysis of tray dynamics.

Fig. 7. Temperature profiles, experiment 1 conditions, simple model.

8
 Fig. 8. Temperature profiles, experiment 1 conditions, realistic model.

4.2. Start-up simulation bubble points, filling up of plates and condenser, total start-up
period, etc.
The study of the temperature profiles inside the column With regard to the column start-up, the validation approach
appears as a good way to validate the developed start-up mod- differs from the thermosiphon study. In a first part, using
els. In fact, temperature sensors are easy to implement and experiment 1 results, the specific parameters of each model
offer a fast and reliable records. Measurements of hydrody- have been estimated from temperature profiles:
namic variables (such as liquid flow-rate, liquid level or pres-
• the filling ratio (α), for the simple model,
sure drop) are very difficult to set-up and cannot offer stable
• the mass added to each plate wall to represent the thermal
records because of the constant local variations on plates.
inertia of the column, for the realistic model.
Moreover, temperature measurements represent the standard
measurement in industry. Finally, the analysis of the temper- In a second part, experiments 2 and 3 have been simulated
ature records offers dynamic information about both hydro- with the same parameters value in order to exemplify the
dynamic and thermodynamic variables, as shown in Fig. 6: models accuracy.

Fig. 9. Temperature profiles, experiment 2 conditions, simple model.

9
 Fig. 10. Temperature profiles, experiment 2 conditions, realistic model.

For the simple model, experiment 1 allows to evaluate the mass addition represents the thermal environment of each
filling ratio. Initially, the column is cold, and so the filling plate. In this way, the addition depends of the plate position
coefficient is set to a value close to 1, equal to 0.95 (Fig. 7). inside the column, the more a plate is high, the less thermal
In order to simplify its determination, the filling coefficient inertia is felt (Fig. 8).
is assumed to be constant all along the column (i.e. equal for Figs. 7 and 8 emphasize a limitation peculiar to our model.
each plate of the column). Experimentally, bottom plates (particularly plates 21 and 20)
For the realistic model, the thermal characteristics of each appear to heat up from the beginning of the start-up. In fact,
plate have been defined from the plate geometry: specific heat even before temperature reaches bubble point, a slight vapour
and mass of the plate wall. In order to take into account the flow, due to the thermosiphon heat, escapes from the vessel
thermal inertia, due to the cold wall of the column, a mass and begins to heat bottom plates. In our model, vapour flows
addition has been defined in the internal energy model. This are only generated when bubble point is reached. Therefore,

Fig. 11. Temperature profiles, experiment 3 conditions, simple model.

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 Fig. 12. Temperature profiles, experiment 3 conditions, realistic model.

in the period before the water–methanol mixture reaches bub- mances. In fact, the specific parameters of each model
ble point (the first 40 min), experiment and simulation tem- require to be adjusted to the configuration of the con-
peratures of bottom plates differ. sidered batch distillation column. Once this preliminary
The set of estimated parameters has been used for simu- tuning phase has been performed, the results show that
lation of experiments 2 and 3. Figs. 9–12 show, for exper- the models offer accurate and reliable representations of
iments 2 and 3, the temperature variations inside the col- column start-ups, as can be seen on the different com-
umn, respectively, for the simple and the realistic model. In parison realised between experimental and simulated re-
Figs. 10 and 12, the realistic model appears more accurate sults.
than the simple one. Nevertheless, the good agreement be- Hydrodynamic variables are significant of start-up mod-
tween experimental and simulated results in both cases allows elling since they dictate the transition states of the trays. To
to validate the two models of column start-up. emphasize the changes involved by the developed models,
The developed start-up models need a preliminary tun- the liquid hold-up variations occurring on trays 10 and 20 are
ing phase in order to obtain fully satisfactory perfor- reported in Figs. 13 and 14. These figures allow to assess the

Fig. 13. Flow-rate profiles, experiment 1 conditions, simple model.

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 Fig. 14. Flow-rate profiles, experiment 1 conditions, realistic model.

modelling sequences defined to represent the column start-up plate, packed, etc. On an industrial viewpoint, such simplicity
and to highlight the models differences. and flexibility appear as significant features.
In the field of column optimisation, a correct estimation
of the period from empty and cold state to steady state is
5. Conclusion of prime necessity. In this way, the developed models offer
significant improvements compared to the traditional mod-
Two models have been developed for the representation elling based on an initial state derived from a steady state at
of start-up operations of batch distillation columns: a simple total reflux. Therefore, in the case of optimisation problems
model and a realistic model. The proposed models are defined including time-dependant objective function, the accurate es-
by a succession of steps based on the real behaviour. There- timation of start-up times provided by the proposed models
fore, two start-up sequences are proposed, starting from an appears very interesting. Perspectives are not only focused
empty cold state. The train of steps is determined by switch- on the optimisation of batch distillation start-up policy but
ing conditions related to physical phenomena, that leads to an also on optimisation of global processes integrating batch
hybrid formulation of the model equations. On a resolution distillation. In this way, the developed modelling has been
viewpoint, a specific solver is used to clear up event detection, satisfactory used for the optimisation of the solvent changing
system initialisation and calculation time issues. policy of a batch pharmaceutical application (Elgue et al.,
The two mathematical models have been successfully ap- 2001).
plied for the simulation of a batch distillation column start-up.
Three application cases allow to emphasize the advantages
and drawbacks of each model. Thus, the used of one model Acknowledgements
rather than the other depends on the desired representation.
The simple model allows, with only one adjustable param- We gratefully acknowledge Professor J.S. Condoret, man-
eter, a fast and reliable representation. The realistic model ager of the AIGEP (Atelier Inter-universitaire de Génie des
gives a more accurate representation but needs more parame- Procédés de Toulouse) located at ENSIACET (ex ENSIGCT)
ters and entails additional tuning efforts and so further tuning before the AZF blast explosion on 21 September 2001, for
time. its permission to use the batch distillation pilot plant.
The proposed models offer a simple but realistic tray-by-
tray description of the start-up. In fact, only one specific pa-
rameter per tray for the simple model and two for the realistic References
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