Optimisation and experimental veriﬁcation of startup … strategy has been used in the process...

Computers and Chemical Engineering 28 (2004) 253�/265

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Optimisation and experimental verification of startup policies fordistillation columns

Gunter Wozny, Pu Li *

Institute of Process and Plant Technology, Technical University Berlin, KWT9, 10623 Berlin, Germany

Abstract

Startup of distillation columns is one of the most difficult operations in the chemical industry. Since the startup often lasts a long

period of time, leads to off-spec products, and costs much energy, optimisation of startup operating policies for distillation columns

is of great interest. In the last few years, we have carried out both theoretical studies and experimental verifications with the purpose

of minimising the startup time of distillation columns. Model-based optimisation as well as real plant implementation is the core of

this work. The model is at first validated with experimental data and then used in the optimisation problem formulation. A rigorous

column model and a sequential dynamic optimisation approach have been applied to several pilot distillation columns.

Experimental results indicate that a significant reduction of the startup time can be achieved by implementing the developed

optimal policies. These results demonstrate the applicability of the modelling and optimisation methodology.

# 2003 Elsevier Ltd. All rights reserved.

Keywords: Startup; Distillation column; Modelling; Optimisation; Experimental verification

1. Introduction

Due to its nature of phase transition, large time delay

and strong interaction between variables, the startup of

distillation columns are one of the most difficult

operations in the chemical industry. The startup of

industrial columns lasts several to dozens of hours. Since

the process is unproductive during the startup period, it

is desired to shorten this period by optimising startup

operation policies. In spite of its importance, however,

very little previous work has been done on startup

optimisation for distillation processes, due to the

difficulties of combining the theoretical and experimen-

tal investigations. Conventionally, the so called direct

setting strategy has been used in the process industry:

the values of control variables corresponding to the

specified steady state are set to the columns for startup

and one just waits for the column running to the steady

state. A long time period is usually needed for startup by

using this strategy. Empirical startup strategies have

been proposed for single columns to improve the startup

* Corresponding author. Tel.: �/49-30-3142-3418; fax: �/49-30-

3142-6915.

E-mail address: [email protected] (P. Li).

0098-1354/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0098-1354(03)00181-9

performance. Total reflux (Ruiz, Carmeron & Gani,

1988) and zero reflux (Kruse, Fieg & Wozny, 1996)

strategies together with a large reboiler duty have been

proposed. The switching time from total or zero reflux

to values at the steady state is determined by the

criterion proposed by Yasuoka, Nakanisshi and Kunu-

gita (1987), i.e. at the time point when the difference

between the temperature at the steady state on some

trays and their measured value reaches the minimum.

Since a column startup is influenced by many factors

such as column structure, the type of trays and packing,

component properties in the mixture as well as the top

and bottom product specifications, these empirical

strategies are suitable only for some specific cases.

Therefore, systematic approaches concerning these in-

fluential factors are required to solve general startup

optimisation problems for distillation columns. This

calls for systematic methodologies of modelling and

optimisation.The essential difficulty in modelling column startup

lies in the fact that it is a quite complicated dynamic

process. In most startup models of distillation columns,

the three-phase-model proposed by Ruiz et al. (1988)

has been used. The procedure of a startup from a cold,

empty column to the required operating point consists

mailto:[email protected]

Fig. 1. A two-stage model.

G. Wozny, P. Li / Computers and Chemical Engineering 28 (2004) 253�/265254

of three phases: (1) heating the column by the rising

vapour, (2) filling the trays by the reflux and (3) running

the column to the defined steady state. The discontin-

uous phase is the time period from an empty, coldcolumn to the beginning state of equilibrium. In the

second phase, the holdup of the trays is filled from the

top to the bottom. Hangos, Hallager, Csaki and

Jorgensen (1991) studied the discontinuous phase with

a simplified non-equilibrium model. Wang, Li, Wozny

and Wang (2001) proposed a model considering the

tray-by-tray state transfer from non-equilibrium to

equilibrium for the first phase and described the secondphase by using two different weirs on the tray. Com-

pared with the first two phases (usually less than 1 h),

the third phase requires the longest time and, therefore,

possesses the potential to reduce the startup period by

developing optimal policies. In addition, hydrodynamic

properties on trays and packings in the column play an

important role in modelling startup processes and thus

should be considered. Although various startup modelshave been proposed, very few studies have been made to

utilise these models for column startup optimisation.

Based on an established model, simulation can be

made by solving the model equations to study the

startup behaviour (Ruiz, Basualdo & Scenns, 1995;

Bisowarno & Tade, 2000; Eden, Koggersbol, Hallager

& Jorgensen, 2000Wang et al., 2001). For simulation an

operating policy during startup has to be defined apriori. This means it may be neither optimal in the sense

of minimising the startup time, nor feasible in the sense

of holding the process constraints (e.g. the product

specifications at the desired steady state). Thus, a

mathematical optimisation has to be employed to search

for an optimal as well as feasible operating policy.

Optimisation approaches to solving large-scale pro-

blems have been proposed in the previous studies(Vassiliadis, Pantelides & Sargent, 1994; Cervantis &

Biegler, 1998; Li, Arellano-Garcia, Wozny & Reuter,

1998). The basic idea of these approaches is to discretise

the dynamic system into a large non-linear program-

ming (NLP) problem so that it can be solved by an NLP

solver like sequential quadratic programming (SQP).

However, although these dynamic optimisation ap-

proaches have been proved efficient in many casestudies, to the best of our knowledge, they have not

been applied to startup optimisation problems for real

distillation columns.

Derived from the above review, it can be concluded

that the theoretical studies on column startup modelling

and optimisation approaches have been well developed.

This implies that it is possible to apply these results in

real columns for startup optimisation. However, nosuccessful industrial application of these results has been

reported. This is because implementation issues have

remained a concern, primary due to the mathematical

complexity inherent in the modelling and optimisation

approaches. To convince the process industry of the

applications, verifications of these theoretical results on

real plants have to be made.

During the last few years, we have carried out asystematic study including both theoretical and experi-

mental investigations to develop optimal operating

policies for distillation columns (Kruse, Fieg & Wozny,

1996; Flender, Fieg & Wozny, 1996; Lowe, Li & Wozny,

2000; Wendt, Konigseder, Li & Wozny, 2002). The aim

of the work was to answer two questions: (1) which

model is currently suitable for column startup optimisa-

tion? (2) Which optimisation approach can be used tosolve the startup optimisation problem? Model-based

optimisation has been conducted in the work. Three

different models are used to describe the startup

behaviours of distillation columns. A detailed equili-

brium model was validated by experimental studies on

the pilot plants and used in the optimisation problem

formulation. A sequential NLP approach and the

simulated annealing (SA) algorithm were used andmodified for optimising column startup. The developed

optimal startup policies were verified on different pilot

columns. Extensive experiments were conducted to test

the optimisation results. As a result, significant reduc-

tion of the startup time can be achieved by implement-

ing the optimal operating policy.

2. Modelling column startup

In this section we present three different models used

for describing column startup operations. A simple two-

stage model is first considered to estimate the beha-

viours of startup and to gain a rough insight into the

dynamics of distillation columns. As shown in Fig. 1, the

model consists only of a total condenser and a reboiler.The dynamic component balance of the system is then:

HUdxB

dt�Fxf �DxD�BxB (1)

where F , D and B represent the molar flow rate of feed,

the distillate and bottom flow, respectively. xf , xD , xB

are the composition of these three flows. HU denotes

the total molar holdup of the system, while V and L are

the vapour as well as liquid flows inside the column. The

mass balance and equilibrium of the system can be

simply described as F�/D�/B and xD �/KxB (where K

Fig. 3. A general tray of the second model.

G. Wozny, P. Li / Computers and Chemical Engineering 28 (2004) 253�/265 255

is the phase equilibrium constant), respectively. To

study the trajectory of the reboiler composition xB

influenced by the reflux flow L , we assume HU , F , xf ,

V remain constant during startup. Then the timeconstant of the composition of the light component in

the reboiler xB will be:

t�HU

F � (K � 1)(V � L)(2)

It indicates that t will be reduced if the reflux is

decreased. Fig. 2 illustrates the reboiler compositionprofiles caused by the direct setting strategy (setting the

steady state value of reflux L�/LSP during the whole

startup period) and by the zero reflux strategy (setting

L�/0). These profiles can be received by integrating

equation (1) from an initial reboiler composition xB 0

with given value of HU , F , xf , V and the defined reflux

flow applied to the representation (2). It is noted that in

this model there should be K �/1 and V �/L . To achievean optimal startup, a proper switching point from zero

reflux to the direct setting is to be found, such that the

bottom composition will be along the arrow-pointed

trajectory from the initial composition xB 0 to the

specified product composition xBSP . The vapour flow V

represents the reboiler duty, which has the same impact

on xB but in the opposite direction. In the same way, the

influence of reflux and reboiler duty on the topcomposition xD can be analysed. As a result, the

optimal operating policy derived from this simple model

for distillation column startup is to run the column

using a maximal reboiler duty and zero reflux in a

period of time and then switch to their steady state

value. This is a qualitative result and has been used for

real implementation on a pilot packed column and an

industrial column for separating a mixture of fattyalcohols. Even using this simple strategy, the startup

time can be reduced up to 80% in comparison to the

conventional direct setting strategy (Flender, Fieg &

Wozny, 1996).

The second model we use to describe startup beha-

viours is a detailed tray-by-tray model composed of

dynamic component as well as energy balances, vapour�/

liquid equilibrium (VLE) and tray hydraulic relations.Fig. 3 shows a general tray in the column of this model,

with the variables xi ,j , yi ,j , Lj , Vj , HUj , Pj , Tj as liquid

as well as vapour component composition, liquid as well

Fig. 2. Reboiler composition profiles.

as vapour flow, holdup, pressure and temperature on

the tray. Here i (i�/1, . . ., NK ) and j (j�/1, . . ., NST )

are the indexes for components and trays, respectively.

Qj is the energy received from outside of the tray. Itcorresponds, respectively, to values of energy loss of the

trays, reboiler and condenser duty. Then the model

equations for each tray will be:

Component balance:

d(HUjxi;j)

dt�Lj�1xi;j�1�Vjyi;j�Vj�1yi;j�1�Ljxi;j

�Fjxfi;j (3)

Phase equilibrium:

yi;j �hjKi;j(xi;j; Tj; Pj)xi;j�(1�hj)yi;j�1 (4)

Summation equation:

XNK

i�1

xi;j �1;XNK

i�1

yi;j �1 (5)

Energy balance:

d(HUjHLj )

dt�Lj�1HL

j�1�Vj�1HVj�1�LjH

Lj �VjH

Vj

�FjHLf �Qj (6)

Holdup correlation:

HUj �8j(xi;j; Tj; Lj) (7)

Pressure drop equation:

Pj �Pj�1�cj(xi;j�1; yi;j; Tj; Lj�1; Vj) (8)

In addition to the equations (3)�/(8), there are

auxiliary relations to describe the vapour and liquid

enthalpy (HjV , Hj

L), phase equilibrium constant (Ki ,j),

holdup correlation (8j) and pressure drop correlation(cj ) which are functions of the state variables. Para-

meters in these correlations can be found in chemical

engineering handbooks like Reid, Prausnitz and Poling

(1987) and Gmehling, Onken and Arlt (1977). Murphree


tray efficiency (hj) is introduced to describe the non-

equilibrium behaviour. It is a parameter that can be

validated by comparing the simulation results and the

operating data. In addition, the heat loss of the column

is usually significant and should be considered in the

modelling and validated with experimental data. The

total model equations formulate a complex large-scale

differential algebraic equation (DAE) system. Using this

equilibrium model, the startup is described by the time

period from the first time point at which the phase

equilibrium is reached on all trays to the desired steady

state. The starting point corresponds to the state at

which the first drop of the liquid of the mixture reaches

the top of the column.

The third model we proposed is a hybrid model that

depicts column startup from a cold, empty state (Wang

et al., 2001), which is the extension of the second model.

Each tray is described from a non-equilibrium phase in

which only mass and energy transfer is taking place to

an equilibrium phase in which VLE is reached. The

switching point between these two phases is determined

by the bubble-point temperature at the operating

pressure. Fig. 4 illustrates the state transition of the

trays: from the empty cold state (EM)0/liquid accumu-

lation (LA)0/VLE. It describes the states of trays in the

rectifying section during startup. It differs from the

stripping section due to the downstream from the feed

flow. Using this model the simulation of startup

procedures becomes more reliable.For the purpose of optimisation of column startup, a

compromise between the model accuracy and the

problem solvability has to be made. On the one hand,

an accurate model is needed to describe startup beha-

viours, so that the optimisation results can be so credible

that they can be directly implemented on the real plants.

On the other hand, a complicated model may lead to a

complex optimisation problem, which can not be solved

with the existing solution approaches. The second model

described above can represent the largest part of the

startup period and the available optimisation ap-

Fig. 4. State transition of trays during startup.

proaches can be applied to this model. Therefore, we

use the equilibrium model formulated by (3)�/(8) to

describe distillation columns for startup optimisation in

this work.

3. Optimisation approaches

In most cases, the aim of optimisation of column

startup is to minimise the startup time period. It leads to

a dynamic optimisation problem usually with reflux rate

and reboiler duty as the decision variables. A general

dynamic optimisation problem can be described as:

minf (x; u)

s:t: g(x; x; u)�0

h(x; x; u)]0

x(0)�x0

xmin5x5xmax

umin5u5umax (9)

where f , g and h are the objective function, vectors of

model equations and process constraints, respectively. x

and u are vectors of state and decision variables. Here g

includes all equations of the startup model and hrepresents the process restrictions and predefined steady

state specifications. An initial state x0 of the column is

required to define the state from which the optimisation

problem is considered. Approaches to solve such

dynamic optimisation problems usually use a discretisa-

tion method to transform the dynamic system into an

NLP problem. Collocation on finite elements (Finlay-

son, 1980) and multiple shooting (Bock & Plitt, 1984)are two common methods for the discretisation. The

solution approaches to such problems can be classified

into simultaneous approaches (Cervantis & Biegler,

1998), where all discretised variables are included in a

huge NLP problem, and sequential approaches (Logs-

don & Biegler, 1992; Vassiliadis et al., 1994; Feehery &

Barton, 1998), where a simulation step is adopted to

compute the dependent variables as well as theirgradients and thus only the independents are solved by

NLP. Although these approaches have been proved to

be able to solve large-scale dynamic optimisation

problems, reports on the solution of complex problems

such as startup models of distillation columns for

separating multi-component mixtures, are rarely found

in the literature.

We have applied two different approaches to solve thedynamic optimisation problem for startup optimisation.

The first one is a gradient-based sequential approach (Li

et al., 1998), which is briefly described in the following.


Using collocation on finite elements the considered time

period [t0, tf ] is discretised into time intervals (l�/1, . . .,NL ). Collocation on finite elements is used due to its

high discretisation accuracy. In each interval the vari-ables on the collocation points (i�/1, . . ., NC ) are to be

computed. With Lagrangian polynomial approximation

the state variables in (9) in interval l will be:

xl(t)�XNC

i�0

p(t)xl;i�XNC

i�0

�YNC

j�0

j"i

t � tj

ti � tj

�xl;i (10)

where ti is the time point corresponding to collocation

point i . On the collocation points:

xl(ti)�XNC

j�0

Pj(ti)xl;j �xl;i i�1; NC (11)

xl(ti)�XNC

j�0

dPj(ti)

dtxl;j i�1; NC (12)

Principally, the decision variables in (9) can also beapproximated with orthogonal polynomials. However,

for the ease of practical implementation, we consider the

form of piecewise constant controls. After this discreti-

sation, problem (9) is now transformed to (13), which

includes state variables on all time intervals and at all

collocation points in each interval. Thus it is now a

large-scale NLP problem:

minf (xl;i; ul)

s:t: gl;i(xl;i; ul)�0

hl;i(xl;i; ul)]0

x1;0�x(0)

xmin5xl;i5xmax

umin5ul 5umax (13)

To solve it with a sequential framework, the equality

constraints will be eliminated by means of an extra

simulation step, i.e. by integrating the model equations

with the Newton method. In the integration step, wetake advantage of the well-structured sparse Jacobian

matrix of the column model in the Gauss-elimination to

achieve high computation efficiency. The elimination of

the model equations (denoted as xl ,i �/8l ,i (ul )) leads to a

small optimisation problem described as (14), which

includes only the control variables and the inequality

constraints.

minf (8l;i(ul); ul)

s:t: hl;i(8l;i(ul); ul)]0

umin5ul 5umax (14)

A two-layer approach to solve this problem is

proposed: SQP is used to optimise the independent

variables in the optimisation layer, while the discretised

state variables are solved in the simulation layer. The

independent variables include the controls (which are

assumed to have a piecewise constant form in each time

interval) as well as the lengths of the time intervals. The

analytical gradients of the objective function and the

inequality constraints to the controls are computed

inside each interval. These gradients will be transferred

from an interval to the next interval through the

continuity conditions for the state variables. The sparse

structure of the related matrices is utilised in the

sensitivity computation. For details on the approach

we refer to Li et al. (1998).

In a recent study (Wendt, Li & Wozny, 2000), a

multiple time-scale strategy is proposed to modify this

approach for solving strong non-linear problems. The

number of time intervals determines the length of each

interval and the size of the optimisation problem. The

large time intervals should be long enough for the

practical realisation as well as for the reduction of the

computation time concerning the sensitivity calculation.

The small time intervals are adjusted in the simulation

layer and their length will be kept more flexible to

guarantee the accuracy and convergence in the Newton

iteration. This is also important for checking the

inequality path constraints between the collocation

points inside one time interval, such that the length of

the time interval is modified to ensure the constraints to

be satisfied at all times. This modification makes it

possible for the approach to be applied to strong non-

linear processes such as distillation of mixtures with

abnormal VLE behaviours as well as use of column

pressure as an optimisation variable. A FORTRAN

package DOSOK (dynamic optimisation with SQP and

orthogonal collocation) was developed to carry out the

computation. This package has been applied to startup

optimisation for different distillation columns described

in the next section.

The second approach we have used is SA, which is a

stochastic search method. The advantage of this method

is that it does not require sensitivity information and

thus can be connected directly to an available simulator

(Hanke & Li, 2000; Li, Lowe, Arellano-Garcia &

Wozny, 2000). Since commercial simulation software is

widely used in industry, using SA is an easy way to

conduct startup optimisation. The shortcoming of this

method is its low computation efficiency, i.e. many runs

of simulation are needed to reach the optimal solution.

SA is applied to the startup study on a pilot column with

20 bubble-cap trays for separating a methanol-water

mixture (see Section 4.2).

Fig. 5. Measured temperature profiles of the packed column by direct

setting policy.


The reason we have used two different approaches to

solve the startup optimisation problem is as follows. We

have first implemented the startup model into a

commercial software being able to carry out dynamicsimulation. Thus the SA algorithm could be directly

connected to the simulator. The computation time for

the startup optimisation of one column (the bubble-cap

tray column described in Section 4.2) was several days

by a SUN SPARC 10 Station. It would be intolerable to

use SA for the startup optimisation of the two-column

system (described in Section 4.3). Therefore, we replaced

SA with the gradient-based approach. Using thisapproach, the CPU-time for the startup optimisation

of the two-column system was only several hours with

the same workstation.

Fig. 6. Computed optimal reflux and reboiler duty policy for the

packed column.

4. Experimental verification on different pilot plants

In this section, experimental results on three different

pilot plants are presented to verify the modelling and theoptimisation approaches for startup of distillation

columns.

4.1. A packed column

The first pilot column is a packed column (height: 6.5

m, diameter: 0.07 m) which is packed with Sulzer

packings (Sulzer Chemtech), 1.5 m BX in the rectifyingsection and 1.0 m DX in the stripping section. A total

condenser is mounted inside the column top. The

operating pressure is held with a vacuum pump. A

frequency-adjustable divider for discharge (distillate)

and return (reflux) of the condensate is employed to

manipulate the reflux ratio. The reboiler is an electrical

heat exchanger with adjustable heat duty. Several

sampling and temperature measuring points are locatedalong the column. The plant is equipped with a process

control system. A mixture of two fatty alcohols (1-

hexanol (C6) and 1-octanol (C8)) is to be separated with

the column at a specified steady state point.

To startup the column from a cold state (e.g. 25 8C), it

is reasonable that the maximum heat duty is to be used

to warm up the packing, the column wall and the feed

stream until the condensate reaches the top of thecolumn. By using the maximum heat duty (/Q/�/1 kW)

it takes about 30 min to receive the first drop of the

condensate. Since the equilibrium model is used, the

task of the optimisation is to determine the policies of

the reflux ratio and the reboiler duty after this time

point. The conventional direct setting startup procedure

used in the chemical industry simply sets the values of

the two control variables at the desired steady state(‘‘nominal’’ values). This procedure was tested on the

column and it took 7 h to reach the desired steady state.

Fig. 5 shows the measured temperature profiles along

the column resulted from this strategy. Kruse, Fieg &

Wozny (1996) modified this procedure by first switching

the heat duty to the nominal value but without reflux for

a period of time, and then switching the reflux ratio to

its nominal value. The time point of the second switch-

ing is determined by checking the summed minimum

quadratic error of the measured and desired tempera-

tures along the column. By implementing this strategy

the startup period was reduced to 2 h.

The sequential optimisation approach based on the

equilibrium model is used to develop optimal startup

policies. Corresponding to the height of the packings the

number of the theoretical trays is 28 in the rectifying

section and 22 in the stripping section. The influence of

the packing on the holdup of the internal energy is also

added to the model. The model is validated by compar-

ing the data from simulation and experiment. For the

dynamic optimisation, 40 time intervals are chosen to

discretise the dynamic system. The nominal values

corresponding to the steady state (R�/1.5, Q/�/0.7

kW) are used as the guess profiles of the two control

variables.The optimisation results are shown in Figs. 6 and 7

where t�/0 corresponds to the time of the first drop of

reaching the condenser. During the first 12 min the two

Fig. 7. Computed optimal composition profiles of the packed column.


control variables should be kept at their limiting values

(R�/0.1, Q/�/1 kW) to run the column at the maximum

speed. After this period the reflux ratio begins toincrease and at the same time the reboiler duty begins

to decrease, which slows down the run to prevent an

overshooting. By doing so the column is allowed to slide

to the desired steady state as fast as possible, because of

the improvement of the separation effect. This can be

clearly seen from Fig. 7: the distillate composition drops

in the first 12 min due to the maximum heating and the

minimum reflux, with which the bottom purity isincreased quickly. In the second period the distillate

composition returns to its specification due to the rising

reflux ratio and the decreasing reboiler duty. From the

computed results, the total startup period would be 52

min (i.e. 30 min to the first condensate plus 22 min to the

steady state). The startup time of the implementation of

the optimal policy to the pilot plant was found to be 1 h,

as shown in Fig. 8.

4.2. A bubble-cap tray column

The second pilot column we used for experimental

verification is a tray-by-tray column. The column has a

diameter of 100 mm and 20 bubble-cap trays with a

Fig. 8. Measured temperature profiles of the packed column by the

optimal policy.

central downcomer. Isolation coat is mounted to pre-

vent the heat loss from the column wall. The boilup is

provided by an electrical reboiler with a maximum duty

of 30 kW. The condensation is carried out by a total

condenser with cooling water. The plant is equipped

with temperature, pressure, level and flow rate measure-

ments and electrical valves for the flow control. All

input/output signals are treated by a process control

system. Several control loops have been configured and

implemented on the plant. The control system is

connected to the local area network to manage experi-

mental data. The composition of the feed stream,

distillate and bottom product is measured off-line with

a gas chromatograph. We consider the separation of a

mixture of water and methanol by this plant. The

startup of the column to the steady state with a purity

of 99.5 mol% for both methanol and water was studied.

SA is used for the startup of this plant and the

equilibrium model is used in the problem formulation.

The model was implemented in the software SPEEDUP as

a simulator, which is called by a file of the SA algorithm.

The problem definition is the minimisation of the time

period from an initial state of the column to the desired

steady state. Fig. 9 shows the computed optimal

operation policy and Fig. 10 shows the corresponding

product purity profiles. It is interesting to note the

difference between the optimal policies of the packed

column (Fig. 6) and the tray column (Fig. 9). Unlike the

operating policy for the packed column shown in Fig. 6,

both the reflux rate and reboiler duty shown in Fig. 9 for

this tray column should be high in the first period and

should be decreased to the steady state nominal value in

the second period. Figs. 10 and 11 shows the measured

bottom and top temperature profiles by different startup

policies: (a) direct setting; (b) zero reflux; (c) optimal

policy. All three experiments had the same feed condi-

tion (composition: 29 mol% of methanol, flow rate: 15 l/

h, temperature: 60 8C). It can be seen that the time taken

for reaching both bottom and top temperature at steady

state was 220, 170 and 120 min by the three different

policies, respectively, as shown in Fig. 12.

Fig. 9. Computed optimal policy for the bubble tray column.

Fig. 10. Computed optimal purity profiles for the bubble tray column.

Fig. 11. Measured bottom temperature profiles of the bubble tray

column.

Fig. 12. Measured top temperature profiles of the bubble tray column.

Fig. 13. The heat-integrated column system.


4.3. A heat-integrated column system

As shown in Fig. 13, the third pilot plant considered is

a heat-integrated column system consisting of a high

pressure (HP) and a low pressure (LP) column, with 28

and 20 bubble-cap trays, respectively. The vapour from

HP is introduced as the heating medium to the reboiler

of LP. Due to the heat-integration startup of the plant

becomes complicated. The end of the startup period is

defined as the time when both columns have arrived at

the desired steady state. The startup time can be defined

as the objective function subject to the steady state

conditions. Since this kind of formulation may cause

numerical expenses, the following formulation is used asan alternative to describe this optimisation problem:

min gtf

t0

[(xHPD �xD�)2�(xLP

D �xD�)2�(xHPB �xB�)2

�(xLPB �xB�)2]dt (15)

where xD � and xB � are the distillate and bottom

product specifications, respectively, for the light com-

ponent. t0 is the initial time point and tf is the final time

point. The pilot plant with the parallel arrangement to

separate a mixture of methanol and water is considered.

The total feed flow is splitted into two parallel flows to

the two columns and both columns have top and bottomproduct. This arrangement represents a typical opera-

tion case of such processes in the chemical industry. The

input constraints are the limitations of the control

variables, i.e. the reflux flow of both HP and LP and

the reboiler duty of HP:

05LHP(t)5LHPmax (16)

05LLP(t)5LLPmax (17)

05QHP(t)5QHPmax

Fig. 15. Computed optimal composition profiles during startup.

Fig. 16. Computed optimal temperature profiles during startup.


The feed condition (flow, composition and tempera-

ture) is determined through experiment such that it will

lead to a proper vapour and liquid load for the two

columns. With the equilibrium model, we assume the

starting state for the optimisation at the time point when

the pressure of HP reaches 2.5 bar, at which both

columns just approach VLE and the heat-integration

takes place. The state variables at this initial state can be

computed with the help of the measured data in the past

experiment. Moreover, the profile of the pressure rising

in the HP has to be estimated (Wendt et al., 2002).

Furthermore, to deal with the time-optimal problem, a

sufficiently large time horizon has to be chosen, in order

to ensure the plant to reach the steady state. The final

optimisation results of the optimal trajectories of the

reboiler duty for HP and the reflux flow for both

columns are shown in Fig. 14. The corresponding

product composition and temperature profiles are

shown in Figs. 15 and 16, respectively.As shown in Fig. 14, the optimisation results illustrate

that at the beginning a high value of the reboiler duty

should be chosen, since it is necessary to increase

especially the bottom temperatures and thus the purity

of the bottom products. With a slight time delay, the

two refluxes need to be increased in order for the two

columns to approach the desired purity of both top and

bottom products as fast as possible, as shown in Figs. 15

and 16. However, as soon as the column system reaches

close to the steady state, the controls need to be step by

step decreased down to their steady state level. It should

be noted that the optimisation results are developed

based on the model. The model reflects the steady state

points of the pilot plant fairly well and also depicts

roughly the shape of the experimentally measured

profiles, but there is still a large model-mismatch

concerning the time delay.

From the optimisation results, a startup rule for

practical purpose can be obtained. It can be seen in

Fig. 14 that there is one certain time point at which the

control parameters have to be decreased drastically.

Fig. 14. Computed optimal trajecto

When this decrease for the reboiler duty has to be made,

the temperature of the bottom in the LP has reached the

value of approximately 98 8C. Since this temperature is

the major concern for startup operation of this plant,

this value can be used as a switching criterion. To

transfer the optimisation results to a practical operation

policy, an easy-implementing strategy can be derived,

which means that the plant is first operated with the

maximum value for all control parameters until the

bottom of the LP reaches its switching temperature and

then all the control parameters are switched to their

steady state values.

ries of the control variables.


For comparison of startup time, different operating

policies were implemented in different startup runs for

the experimental verification. A feed flow of a

methanol�/water mixture (F�/34.5 l/h, xf �/0.3 mol/

mol, Tf �/60 8C) was to be separated. The feed flows

of the two columns are set as constant with their steady

state value (F1�/19 l/h, F2�/15.5 l/h). The feed tray is

set at 10th tray for HP and 6th tray for LP. The

operating pressure at steady state is 4.7 bar for HP and

atmospheric for LP. The startup of the pilot plant from

a cold, empty state (at atmospheric temperature and

pressure) to the desired steady state (xD ��/0.99, xB ��/

0.01 mol/mol for both columns) was considered. Based

on simulation as well as experimental results, the bottom

and top temperatures of the two columns corresponding

to the steady state purity specifications are TBssHP �/

144 8C, TTssHP �/108 8C and TBss

LP �/99 8C, TTssLP �/65 8C,

respectively. And the corresponding values of the

control variables at this steady state are QssHP �/9.54

kW, LssHP �/26 l/h, Lss

LP �/11.2 l/h. During startup, the

level and flow control loops shown in Fig. 13 are active,

while the temperature control loops (except for the

cooling water temperature control) are set to open loop

in order to manually implement the startup policies.

The direct setting strategy was first implemented for

startup. Fig. 17 shows the measured temperature

profiles of the two columns. It can be seen that there

is a time delay of about 50 min for the top temperature

of LP (TTLP) to begin to increase after the top tempera-

ture of HP (TTHP ) rises. This is because the driving force

of LP is from the latent heat of the vapour from HP.

However, despite of the delay, TTLP first reached its

steady state value. It took 465 min for all temperatures

to approach their steady state. Moreover, it is shown

that the warm-up time of the two columns (i.e. the

Fig. 17. Measured temperature pro

discontinuous phase) was about 10 and 20 min, respec-

tively.

The second strategy studied was the total distillate

strategy. In a beginning period the condensed liquidfrom both columns was pulled out as distillate (zero

reflux) and then the operation was switched to the reflux

flow for the steady state value. The reboiler duty

remained constant during startup. This total distillate

strategy has the advantage to accelerate the rise of the

bottom temperature of both columns. The switching

point from zero reflux to the nominal reflux value was

decided by the minimum point of the following function:

MT �XN

i�1

½Ti�Tss;i½ (19)

which is the sum of discrepancies of measured tempera-tures on all trays (there is a temperature sensor on each

tray for the pilot plant) and their desired values at the

steady state. The value of this function was on-line

computed and observed, through which the switching

time point can be determined. Fig. 18 shows the

measured temperature profiles caused by the total

distillate strategy. Due to zero reflux before the switch-

ing, the temperature increased with a fast speed. Anover-shooting of the top temperature of both columns

was observed. Because of the heat-integration, the

bottom temperature of LP is stagnated and thus without

over-shooting. Switching the reflux flow to their steady

state value led to a decrease of the top temperature of

both columns. The total startup time for all tempera-

tures to reach their steady state value was reduced to 403

min.The optimal strategy developed by the optimisation

was implemented in the third experimental run. From

the optimisation results shown in Fig. 14, the control

files by direct setting strategy.

Fig. 18. Measured temperature profiles by total distillate strategy.


variables (the reflux flow for both columns and the

reboiler duty for HP) should be first set at an optimised

maximal value for a time period and then decreased

gradually to their steady state value. From the practical

point of view, it is desired to implement a simple startup

policy. Therefore, we simply tailored the numerically

optimised operating policy shown in Fig. 14 into a two-

stage strategy. The optimised maximal values of the

control variables (QoptHP �/11.14 kW, Lopt

HP �/29 l/h,

LoptLP �/13.5 l/h) were taken in the first period and the

steady state values were set in the second period to the

pilot plant. The switching time point was chosen at the

time when the bottom temperature of LP reaches 98 8Cthat is almost approaching its steady state value.

Fig. 19. Measured temperature p

Fig. 19 shows the top and bottom temperature

profiles of both columns by the optimal strategy. With

the enhanced values of the control variables, TBHP , TT

HP

and TBLP rose fast to their steady state value before the

switching. After the switching the two columns con-

tinued running to the desired steady state. It can be seen

that HP ran a little bit over the steady state before the

switching in order to provide enough energy to LP, so

that both columns could approach the desired steady

state as quickly as possible. Compared with the results

of the other startup strategies (Figs. 17 and 18), the

optimal strategy really resulted in the best startup

performance and thus took the shortest startup time.

With the optimal strategy, the total startup time was

rofiles by optimal strategy.


about 300 min, which is 64% of the time needed by the

direct setting strategy.

5. Conclusions

The theoretical work on dynamic process modelling,

simulation and optimisation has been well-developed in

the last two decades. However, very few studies on the

validation and implementation of such results to real

plants for column startup have been made in the past.

Although there exist profit incentives, no industrial

application has been reported on realisation of dynamicoptimisation results. Extensive and intensive work on

practical verification needs to be conducted to bridge the

theoretical development and the industrial application,

so as to convince the process industry to apply the

theoretical results. To this end, beside the theoretical

work of modelling, simulation and optimisation, prac-

tical issues including plant and equipment engineering

should be considered.In this work, we have considered the startup optimi-

sation problem, which represents one of the most

complicated dynamic operations in chemical industry.

Dozens of hours are needed in industrial practice for

column startup and it results in large amount of off-spec

products. Many factors have impacts on the perfor-

mance of startup operations. There exist no general

rules of startup strategies for all kinds of distillationcolumns. We used a systematic approach including

modelling, model validation, optimisation and imple-

mentation on the real pants to address this problem.

Model-based optimisation for searching time-optimal

policies for column startup was the core of this work. A

detailed equilibrium model was chosen for the base of

optimisation. The model was at first validated (e.g. tray

efficiency, tray holdup, column heat loss etc.) and thenused for startup policy development. Reflux and reboiler

duty policies for startup were searched for and verified

on different pilot plants. The temperature profiles on

trays of the column were measured as signals to observe

the performances by different startup strategies. Sig-

nificant reduction of startup time was achieved by

implementing the optimal policies, in comparison to

the conventional startup strategy. The experimentalresults demonstrated the applicability of the modelling

and optimisation results, showing that they can be

applied to start up industrial columns.

An extension of this work will be the optimisation of

column startup based on the non-equilibrium model, so

as to include the time period from the cold, empty state

to the equilibrium state into the problem formulation.

Moreover, heuristics for column startup is to be devel-oped. These heuristics may depend on the properties of

equipment (packings, tray-internals), the features of

mixtures to be separated, as well as the requirement of

the desired steady state. Moreover, the startup of some

distillation columns with special characteristics such as

reactive distillation and three-phase distillation is also a

future challenge.

Acknowledgements

We thank Deutsche Forschungsgemeinschaft (DFG)

for the financial support in this work under the contract

WO565/6-3 and WO565/10-3.

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