~R
1992 ACC/WA4
A Frequency Domairn Based Dynamic Simulatioun pacika¶je I or
Continuous Distillation Urts
Ch. Durgaprasadaj Rao
Dept. of Chemiv al Engineering,
Indian Institute of Technol,ogy
Madras - CAW, 036
and
P.S.V. Nataraj
Systems & Conitrol Group
Dept. of Electrical Engg.
Indian Institute of Technology
Bombay - 400 076
ABSTRACT
this paper will dencribe the package
that computes frequency responses; the.
discussed
is
package
domain
time
elsewhere r3].
A digital simulation package for dynami c
simulation of continuous distillation
uni-ts, in the frequency domain, is
presented- The package is based on a
rigorous dynamic model that can account
for all dynamic phenomena known to be
Two
important for control studies.
industrial scale problem are taken up
tco demonstrate the developed software: a
fictitious but representative 64 tray
deisobutanizer and an actual 91 tray
Simulation
ethane-ethylene splitter.
results reveal the power of the package
in computing a wide variety of frequency
responses with sufficient accuracy.
1.
In
The paper is organized as follows.
Section 2. we list the significant
assumptions
li-near dynamic
of the
model. The dynamic simulation package
for frequency responses of distillation
units (FRODXJ) is described next in
Section 3. In Section 4, we demonstrate
the capabilities of the package on two
a
problems:
scale
industrial
hypothetical but representative 64 tray
91
actual
an
and
deisobutanizer
ethane-ethylene
tray
turbogrid
splitter- The conclusions are drawn in
Section 5.
INTRODUCTION
Despite
intensive
research
2.
investigations in distillation dynamics,
few papers describe dynamic models that
THE LI HEAR DYNAMIC MODEL
A conventional distillation unit is
shown in Figure 1.
The column is
assmed to separate a binary feed into
two liquid products and to be equipped
with a natural circulation thermosyphon
reboiler and a total condensing system.
A schtic of an ordinary stage of the
column is given in Figure 2.
all phenomena known to be
most
The
important for control.
significant contribution to this area
from the Royal Dutch/She 1l
has co
group which proposed and extensively
verified a rigorous linear dynamic model
for continuous distillation units in
1975 [1]. Though now rather dated, it
is our opinion that it still is the most
comprehensive linear model to appear in
the distillation literature. All other
linear dynamic models suffer from some
limitation or the other, and are of
limited usefulness in the synthesis of
controllers. Exactly which aspects play
a crucial role in determining the
colum's transient behavior has been
discussed elsewhere [1142]. We will
content ourselves by mentioning one such
aspect which other models lack: the
bulk
for
account
to
ability
condensation/evaporation phenomena on
every stage.
capture
2.1
Basic Assumptions of the Model
Equimlal overflow concept is
1)
appllcable.
2)
Feed is a binary mixture.
Vapor-liquid equilibrium relation
3)
is linear:
y
t
4)
Density
5)
Loading
constant.
constant.
-
E,
L
of
X
I
the
factor
(
liquid
is
7
V-<
i;
a
a
to
Resistance
6)
condensati.on
(evaporation) can be approximated as
The purpose of the present paper is to
present a digital simulation package
developed for dynamic simulation of
continuous distillation units, based on
But
the rigorous linear model of rI.
certain issues have to be resolved
before one embarks on such ventures.
There is the dilema of whether to
compute responses in the t ie or
As analysis and
frequency domain.
synthesis techniques in either domain
have their proponents, we aimed to
provide a more complete answer to the
software
undertaking
by
question
developments in both domains. However,
J
7)
=
p
Heat losses through the column
to the surroundings are negligible.
waL1l
The liquid and vapor Phases are
8)
ideally mixed.
8.8 The Model Equations
The liquid flow, pressure drop and
vapor holdup equations, together with
flow
mass
total
and
the partial
of
set
the
constitute
balances,
127
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on June 8, 2009 at 06:03 from IEEE Xplore. Restrictions apply.
equjationsi
variables-
usedi
to
find
the
stage
switch
auxiliaries, we kept these
routines separate from the rest of the
package- The advantage in doing so lies
The responses of pressure, vapor
and liquid flows, and compositions, for
a section of the column (stripping or
rectifying ), are derived by combining
the respective response equations for a
single stage.
In our package, all the
mentioned model equations are
from IlIl.
:3.
in the ease with which the user can
modify just these routines to suit his
problem, and link this compiled code
with that of the rest of the package.
The current version of FROIX deals with
vertical thermosyphon reboilers and
horizontal condensers-
above
The third level modules compute the
3
overall responses which relate {p. vi,
taken
Ii, xiI
PACKAGE DESCRIPTION
The
computing
package
frequency
responses of distillation units (FRODU)
is one of a suite of distillation
packages
developed
at
the
Indian
Institute of Technology for simulation,
analysis, and control of continuous
distillation units.
The suite is
written in FORTRAN 77 to achieve a high
degree of portability across a range of
to
access
and
cmputers,
state-of-the-art numerical subroutine
libraries.
FRDIXI can be run in a
stand-alone mode in an interactive
to
any
are
The input data required by FROT
The problem
given in Table 3.a
file
description is read from
state
the
steady
generated
by
distillation simulation program SADY
belonging to the suite of distillation
programs.
Following this, the user
responds to a series of questions to
define the respoes.
3.1 Organization of FRODU
FRTDU is organized into a three level
hierarchy of program modules, shown
schematically in Figure 3, and is
detailed below:
Output is in the form of tailor-made
the
objects convenient as inputs to
NFD toolbox 141, namely MVfR matricesFW)W also has a provision to display
the simiulation output in graphic form
l.Within the first level, all basic
function subprograms extensively used by
higher level routines are incorporated,
see Table 1I
on the screen.
3.3 Numerical Method
FIDX achieves the solution by adopting
represents
the basic
(pi, vi, 1., x., Yis
to
.P. r, f, xF. b,
ti l1b'
dL-Through qualitative arguments, some
of these pairingEs can be shown to be
inconsequential, and are ignored in
FRODLI
These Ignored transfer functions
are given in Table 2.
kId
t
3.2 Inputs and Outputs
fashion.
2 .The second level
responses: those of
Y1,
combtnation of fh. c, r, f, xF, b, di.
These together provide an additional
feature of JEIX) and permit the usr to
investigate dynamic behav'iour under
s t mu I tdaneous perturbat ions
numerical
conceptually
procedure
that
is
and
quite
simple
straightforward. We note that the model
equations basically involve the complex
variable s. To compute the frequency
responses, s is set to jo, and the
problem naturally gets transformed to
evaluation of complex expressions. For
FORTRAN to perform the required complex
algebra, we declare the appropriate
The
variables as of type CXMPLEX.
inherent feature of FORTRAN for complex
is
then
evaluation
expression
a
{Iv0
In most cases in practice, h and c are
the independent variables in place of v
and Pn, respectively.
Therefore, we
have also imbedded here routines that
facilitate
switching
independent
variables, from v to h and Pn to cThis provides the usner with further
options of obtaisning responses of (p.,
,
Y
lip xi y. . ti YIi 1dI to {h.cl
also, except for the ignored ones given
Note that the 'switch'
in Table 2.
the
routines
compute
essentially
dynamics of the column auxiliaries - the
reboiling and condensing equipment.
Keeping in mind the wide, variety in
types and arrangement of these colimn
automatically triggered to
compute frequency responses
aoothly
over
a
selected range of variation in frequency
(.3
-
We
may
nmrrical
vi
upon the alternative
strategy proposed in
11].
remark
That strategy involves inverting a 20x20
complex matrix at each frequency, and
The
all the responses are obtained.
proposed procedure avoids any matrix
the
inversion besides producing onty
desired responses4.
APPLICATIONS
128
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on June 8, 2009 at 06:03 from IEEE Xplore. Restrictions apply.
I dea l ly,
val idation of distillation
models should be done on industrial
problems. Successful simulations
(o
such problems enhances the confidernce of
indistry in the softWare and encourages
in
control
usage
subsequent
anid
endeavours.
automation
related
Considering industrial scale problems,
A
we focus specially on two examples.
deisobutanizer and an ethane -ethylene
splitter. Some details of these columns
are given in Table 4
For further
details of the column, see [1].
two industrial scale ccoluimn:sz;*nd the
results illustrate the versatili ty of
FRODU in computing a wide variety of
It is
responses
fairly accuratelyemphasized that FROXDJ possesses certain
unique features as it is based on the
most comprehensive linear model existing
in literature and that ;hese features
are crucial for obtaining results that
allow meaningful anaiysis and controller
arc,
Such
features
synthesis.
necessarily absent in other packages (lue
to the inherent deficiencies of the
Another
models they are based on.
noteworthy feature, i3 that the package
simulates responses quickly. easily an.:
accurately in the form of MVFR matriecs
that can serve directly as inputs to the
--based Multivariable frequency
MATLAB
domain toolbox for subsequent analysis,
and controller synthesis.
4.1 Deiscobutarazer Exanqpl e
Though fictitious, this deisobutanizer
had been devised very carefully in [1-1
so as to be representative of a range of
pressure
industrial
columns.
high
Basically, one of the main obstacles for
a potential user of simulation software
for industrial problems seems to be the
difficulty in collecting key physical,
chemical, and stage data. Fortunately,
in this case, all the required principal
data are given in [1], together with an
extensive analysis of this example
As
through
analog
simulation.
anticipated, this case turned out to be
a good diagnostic exercise, prompting us
make
effective
a
time
to
many
alterations or remove difficult bugs in
the program routines.
Ref erences
O Rademaker, J..E.
I.
Rijnsdorp and
nc
Orr
A.Maarleveld, Dyn-.-wanc
Ltr7t-. E
t
oa
Cort trinuats
Amsterdam: Elsevier, 1975.
2.
P.S.V.Nataraj and Ch.Durgaprasada
model of
Rao, "A rigorous nonlinear
control
for
suitable
distillation
for publication.
studies", Submitted
3.
P.S.V.Natarai and Ch.Durgaprasada
dynamic
Rao, "A time domain based
for
distillation
simulation package
for publication.
units", Submitted
An extensive series of simulations were
performed to test the effectiveness of
the package.A typical response is shown
in Figure 4. 4.2 Ethane-Ethylene Splitter Example
M.P.Ford, J.M.Maciejowski and J.M.
L.
L
ar t abLe Fr equenc y
Do.¢ a L
Boyle, .Nth
Us er- ' s
Too L box
Cambridge:
Guwt de.
and
Ltd.
GEC
Control
Cambridge
Engineering Research Centre, 1988.
4.
Unlike the deisobutanizer, the splitter
is an actual industrial column.
Its
dynamic behaviour has been extensively
investigated to verify the theory behind
the linear model of E1]. Our simulation
study is somewhat hampered by the fact
that little principal data are provided
in the reference, and has to therefore
be guestimated.
Table of Symbols
Only selected symbols
For others, see El].
A mall selection of results obtained
using FRODIJ for the splitter is shown in
Figures 5 and 6. In these figures, the
experiemental
data given in [11] are
Considering
represented as circles.
that key data were guest imated, the
simulations are validated, i.e. FRQDU
has succeeded in the simulation quite
well.
Similar performance trends were
observed for other responses (omitted to
save space)
B
C
D
E
F
H
L
'3.
N
n
p
R
R
Lb
Ld
NF
CONCLUSIONS
We have presented a powerful digital
simulation package FRODU for computing
the open loop frequiency responses of
continuous distillation units.
Th-e
package has been successfully opplied to
p
T
V
are
listed below.
Bottom product rate
Cooling water rate
Top product rate
Stripping factor
Feed rate
Heating medium (reboiler) rate
Flow rate of liquid
Level in the column bottom
Level in the accumulator
Location of feed stage
Number of actual stages
Number of theoretical stages
Pressure
Ref lux rate
Interphase resistance to bulk
condensation/evaporation
Temperature
Vapor rate
129
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on June 8, 2009 at 06:03 from IEEE Xplore. Restrictions apply.
.w =S
Rate of condensation
Concentration of liquid
Concentration of vapor
Ve
X
Y
Table 2E
Transfer Functions Ignored in ROiKAO
Pressure
flow
Deviation from steady state value
Suhacrinta
b
d
Column bottom
Accumulator
Feed tray
At stage i
F
i
1
Liquid
phase
e
p iF
/x ,
v
p./d
v./b
Liquid
It'.
l
.x.,
Ii
I /d
!
Table 1:
Some Quantities Calculated at Level 1
i xl/d
.-I/P
d/Pn
I
|
describing vapor/liquid flow
and concentration respoeses
IbFd
1~~~~/d
tue
(bottom)i
Ib"o'
ld//V
/b
Roots of characteristic eqns.
Modified
Level
Level
(top)
Composition
Steady state value
Equilibriua value
V
flow
v/d
rsc.r±ptn
-
flow
Top of the column
Vapor phase
n
v
Liquid
Vapor
constant
id/XF
ib/ZFI
1d Fs
/
of
51
composition responsesShort and long, pressure and
vapor flow functions.
C",C.It Frequency dependent effective
p
p-A
vapor capacity of stage andi
its heating term
0
dependent time const.
v
of vapor f low and pressure
Tabl e 3
Typical Input Data for FROIJ
From the Steady State
Operating Data
Frequieny
I~~ ~~~~~~~~sw.._ __
Des igni
Program
Data
and
Coefficients
__,
responses-
tcPtH
Transfer fns of condenser
FI
and reboiler, respectively,
with constant process side
temperatures
Admittance of the column
L
1'
L_
1.
Ethane-
Ethylene
splitter
__
No.
of actual.
aT
3.
Iocation of
feed tray
Feed !'low rat
(Ko Is)
e
4. Feed
Composition
91
64
33
32
0.G1%-5
0.1e0T
5.
6.
47/5i3
Ref lux rate
(KmoI/s)
0.00of
c
~~~~c
.
Miscellaneous
i
T
User- Suppl ied
*
of stages at which the
frequency responz3es ire- t be
comp-utecd.
Number
The stages at which the
responses
50/50
*
'
*
(%)
Column pressure 25-6
(atm)
vr
Deisobutanizer
stage s
2.
Md3Q
Thermedynamic
Tabl e 4
Some Principal Data for Columns Simulated
Variable
'EMb
0.426
are
to
which frequency
computed?
which frequency
frequency
te computed.
responses to
responses
saved in files (as MVVRZ
130
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on June 8, 2009 at 06:03 from IEEE Xplore. Restrictions apply.
to
mnLr
be,
be
e.
10
Ti
!~!!
0
m
.........
-10
-201
..... ..........
....
Feed Tray NF
Feed
F , XF
..........
_-nn
-qn
10-3
First Tray
Boa. ..
Vapor V0_
FREQUENCY
Heatir
di1
Fig 4
:Response of
deisobutanizer
Reboiler
Bottomi
for
12/v
)-2 L
Prodct
B,
0o-1
10-2
r
.-
XB
0
9-
Fig
'a4 10-31
1: Schematic of a conventional
dis1tillation colun
Li
I1
-t- - ------ t
I~~
,
0 \\
-J
0.
4
-^~ ~ ~ ~ ~ ~ ~
14
0 \
0 \
1
--.....
------
I
I
A
_
Li
,
Vi1il Yi_i
Xi
3
1
a
A
I
1
I
LI
FREQUENCY cls
: Response of P
spliter
Fig- 5
Fig. 2 : Schmtic of an ordinary stage.
TEVETL
b
-
L-
Vi Y.
, itt
_
0
1
_-1
10
for E-E
10 1
hverall Respo Routinesj
lVtL-2
0
PIIVi,*LiX
Yi v,T
V0to
H
Phto
c
|
Routines
I
I
N
N
N,."N
0
-1
10
1e
Fig. 6
Problem Description
J
~~~
0
1~0N' 119
1~~~~~
...................
USERK
N
.
~
stage
.Basic stage
Coefficients-
Reust<
-
4t
rpara_tersModified
0
-
I
LEVEL1
1
LEVEL
_-
'a
Q.
Basic
10°
:
ido
10
FREQUENCY c/s
Response of t./r
spliter
Steady
I Distillation
state
Si..
ProgramI
Fig 3 : Organizational Structure Of FROLAE
131
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on June 8, 2009 at 06:03 from IEEE Xplore. Restrictions apply.
X 1
for
E-E