DEVELOPMENT OF A DEVICE FOR MEASUREMENT AND CONTROL OF TOP

DEVELOPMENT OF A DEVICE FOR MEASUREMENT AND CONTROL OF TOP
DEVELOPMENT OF A DEVICE FOR MEASUREMENT AND CONTROL OF TOP
PRODUCT COMPOSITION IN A DISTILLATION COLUMN
KALYANA SRINIVASA CHAKRA VARTHY NANDURI
(Srinu)
A dissertation submitted in partial fu filment
of the requirements for the degree
© University of Pretoria
SYNOPSIS
NOMENCLATURE
LIST OF TABLES
LIST OF FIGURES
Chapter One: INTRODUCTION
1.1
Chapter Two: LITERATURE SURVEY
2.1
2.1
2.2
Chromatographic techniques used in
distillation column control
2.2
Infra-red spectroscopy
2.4
2.3
Refractive Index methods and density methods
2.5
2.4
Temperature-composition
2.5
Evaluation of ethanol -water composition
2.7
relations (ideal)
usmg
2.9
non-ideal temperature relations
2.6
The disadvantages of controlling composition
using temperature
2.7
Capacitance theories
using non-ideal temperature relations
2.7.1 A relation between the dielectric constant of
an ethanol-water mixture and its composition
2.8
Properties of capacitors
2.17
2.8.1
Parallel plate capacitor
2.18
2.8.2
Cylindrical capacitor
2.18
2.8.3
Comparison of the performance of
2.19
a parallel plate capacitor to a
cylindrical capacitor
2.9
2.8.3.1 Sensitivity calculations
2.20
2.8.3.2 Hold-up
2.23
calculations
Description of circuitry
2.24
(AC and D.C capacitors)
2.9.1
Description of a D.C circuit
connected to a capacitor
2.9.2
Description of an AC circuit
connected to a capacitor
Chapter THREE: Process Equipment
3.1 Description of the capacitance cell and its associated
3.1
3.1
electronics
3.1. I The capacitance cell as a sensor
3.1
3.1.2 Cell electronics
3.1
3.1.2.1 Power conditioning
3.4
3.1.2.2 Oscillator and cell
3.5
3.1.2.3 Signal level adjustment
3.6
3.1.2.4 Schmitt buffer
3.6
3.2 The laboratory distillation column setup
3.8
3.3 Data-converter cards
3.9
3.3.1 pc73 cards
3.11
3.3.2 pc30 card
3.11
3.3.3 pc66 card
3.11
Chapter FOUR: Results
4.1
4.1 Experimental planning
4.1
4.2 Calibration of the capacitance cell
4.3
4.2.1 Calibration process
4.3
4.2.2 Calibration results
4.5
4.3 Determining dynamic process parameters
4.8
for a first order after applying a step input
4.4 Cell dynamics lag testing
4.9
4.5 Determination of accuracy of the capacitance cell
4. 11
4.5.1 Methods to determine accuracy
4.11
4.5.2 Accuracy testing for temperature and capa.citance methods
4.11
4.6 Determining dynamic process parameters for the column
4.6.1 Model responses with change in the position of the
4.15
4.15
reflux valve in both the measurement systems
4.6.2 Model responses with a change in the hea1 input to the
4.18
reboiler
4.7 Closed loop control of the column based using the (:apacitance cell
4.21
Chapter FIVE : Discussion of Results
5.1 Analysis of capacitance cell readings
5.1
5.2 Accuracy ofthe capacitance cell
5.2
5.3 Dynamic responses of the column
5.3
5.4 Performance of the capacitance cell under closed
5.4
loop conditions
5.5 Dynamic lag
5.5
5.6 Ease of operation
5.5
5.7 Precautions and limitations
5.5
Chapter SIX: Conclusions and Recommendations
Appendices I-III
List of References
6.1
Development of a device for measurement and control of top product
composition in a distillation column
Master of Engineering
(Control Engineering)
Develop a capacitance measuring device that can be used for measuring composition of
ethanol-water mixtures.
Implement this measurement technique on a laboratory distillation column for top product
composition measurement and control.
Compare the results obtained in this manner with previously used inferred measurements
by temperature.
Experiments were conducted to calibrate the capacitance cell ie, to obtain a relation between
composition of an ethanol and water mixture and the output of the capacitance cell. Open loop
tests were executed on the distillation column to determine if the capacitance device had any
negative influence on measurement compared to composition measurements via temperature. Top
product composition control using the capacitance cell under dosed loop conditions was also
tested, to observe the capacitance cell's performance.
The capacitance cell gave repeatable readings during the calibration procedure. In the open loop
tests, process models were obtained for control purposes and no negative influence was observed.
The capacitance cell's closed loop responses were observed to be satisfactory. It was simple to
construct, easy to operate and proved to be a relatively inexpensive device.
In the final analysis, the capacitance cell proved to be a useful device in direct measurements of
composition of binary mixtures, and otters scope for further development in its application to the
control of top product composition in distillation columns of industrial scale.
Ontwikkeling van 'n instrument vir meting en beheer van
topproduksamestelling
in 'n distillaslekolom
Magister in Ingenieurswese
(Beheeringenieurswese)
'n kapasitansiegebaseerde meetinstrument te ontwikl<el wat gebruik kan word om
samestelling van etanol-watermengsels te meet.
hierdie meettegniek te implementeer op In laboratoriumskaal distillasiekolom vir meet en
beheer van topproduksamestelling.
die resultate op hierdie wyse verkry te vergelyk me1:metings wat deur middel van
temperatuurmetings afgelei is.
Eksperimente is uitgevoer om die kapasitansiesel te kalibreer, dws om 'n verband tussen die
samestelling van 'n etanol-watermengsel en die uitset daarvan 1everkry. Ooplus traptoetse is op
die distillasiekolom uitgevoer om vas te stel of die kapasitansiesel enige nadelige invloed het op
die dinamika van die samestellingmetingsproses in vergelyking met samestellingbepaling deur
middel van temperatuurmeting.
Die werkverrigting van die kapasitansiesel onder
geslotelustoestande is ook getoets.
Die kapasitansiesel het herhaalbare lesings gelewer tydens die kalibrasieproses. Tydens die
ooplustoetse is prosesmodelle verkry wat vir beheerderontwerpdDeleindesgebruik kan word Geen
nadelige newe-effek as gevolg van die gebruik van die kapasitansiesel in die meetlus kon
waargeneem word nie. Die geslotelusrespons van die sisteem met die kapasitansiesel was ook
bevredigend. Die sel is relatief goedkoop, eenvoudig om te vervaardig en maklik om te bedryf.
Opsommenderwys kan dit gestel word dat die kapasitansiesel 'n besonder bruikbare instrument
is vir die meting van konsentrasie in binere mengsels. Dit hou moontlikhede in vir verdere
ontwikkeling as deel van die meet en beheer van topproduksamestelling op industriele
distillasiekolomme.
11
Nomenclature
Symbol
A
Antoine constant
A.C
Alternating current
AID
Analog to Digital
A
Composition determined
a
Units
Description
[A or mAl
via measurement tee hnique
[% mass]
Inner diameter of a cylindrical
[cm or m]
capacitor
a
a constant(temperature
relations)
B
Antoine constant
B
Second Virial coefficiE~nts
B
Composition determined via
[% mass]
reference testing me1hod
b
Outer diameter of a cylindrical
[cm or m]
capacitor
C
Capacitance
[F or mF]
C
Antoine constant
c
constant( fugacity & pressure
relation)
C
Composition
DIA
Digital to analog
D.C
Direct current
[A or mAl
d
Distance between plotes of
[cm or m]
[% mass]
a parallel plate capacitor
f
Fugacity
[pa or mm Hg]
1\
Ii
Fugacity of component
solution
i in
[pa or mm Hg]
Symbol
f/
Description
Units
Fugacity of componE~nt
[pa or mm Hg]
i in standard state(STI:».
f
Frequency
[Hz]
F
Volumetric flow rate of a liquid
[m3/sec]
I/O
Input-output
K
Gain
L
Length of a cylindricCiI capacitor
L
% change in the reflux valve
[cm or m]
position
m
An input
mV
Millivolts
p
Pressure
[pa or mm Hg]
Q
Heat supplied by the thyristor
[calor kcal]
R
Gas constant
S
Surface area of a parallel plate
[cm2 or m2]
capacitor
T
Temperature
[K or Ge]
T
Time
[sec or hrs]
V
Volume of space in a capacitor
[cm3 or m3]
V
Volume of individual compounds
[cm3 or m3]
V
Voltage/Volts
[mV or V]
x
Mole-fraction
of a component
in liquid phase (ideal)
Mole-fraction
of a component
in liquid phase (non-ideal)
x
Filtered values
Symbol
y
Description
Mole-fraction
of a component
in gas phase (ideal)
Mole-fraction
of a component
in gas phase (non-idE!al)
Output of a process, olso unfiltered
output
Ethanol
Water
Characters
y
Activity coefficient
CJ)
Acentric factor
e
Permittivity
CI>
Fugacity coefficient
't
Time
a,13
Van-Laar constants
IJ
Mean
a
Standard deviation
Subscript
c
Controller coefficient
cy
Cylindrical capacitor
po
Parallel plate capaci1"or
Integral
Componenti
Pure liquid i
Pure liquid j
efh
Ethanol
waf
Water
n
Sampling interval
p
Process
p-p
peak to peak
d
Dead ( as in 'rd. ie, dHad time)
Output
Reduced{ as in reduced P or T)
Input
% change in reflux valve position
Heat added to the reboiler
Ethanol
2
Water
Superscript
sat
Saturated
o
Related to Vinal coefficient
Related to Vinal coefficient
Page no.
constant for ethanol-water
system
2.8
2.1
Antoine
2.2
Fugacity coefficients for ethanol water mixture
2.11
4.1
Statistical data of the calibration procedure
4.7
at
20 DC
4.2
Statistical data of the calibration procedure
at
30 DC
4.3
Statistical data of the calibration procedure
at
40 DC
4.4
Dynamic lag of the capacitance
4.5
Model
cell
parameters of the column after
applying a change in the reflux valve
4.6
Model
parameters of the column after
applying a change in the thyristor
4.7
Controller parameters using both the reflux valve
and thyristor as the final controller eements.
Appendix Tables
I-I
Readings obtained from 10 experime nts at
20 Dc.
Readings obtained from 10 experime nts at
30
Dc.
Readings obtained from 10 experiments at
40
Dc.
Sample data of 10 readings for a fractional
change in reflux valve position of 0,45 by
capacitance
measurements
Sample data of 10 readings for a fractional
change in reflux valve position of 0,45 by
temperature
measurements
4.10
4.16
Page no.
List of Figures
1.1
Common
configurations
for the
distillate
composition control of a simple
distillation
column:
Inferential
(a)
Feedback;
(b)
1.2
(c) Feedforward
2.1
Elementary parts of a
2.2
A relation between composition and refractive
Gas Chromat'Jgraph
2.2
2.6
index of ethanol and water mixture a",20°C.
A relation between composition and density
of ethanol and water mixture at 20 Dc.
Mole-fraction of ethanol
in liquid phase (x)
and gas phase (y) in ethanol-water
mixture at
760mm Hg.
Relation between activity coefficient~; of ethanol
and water mixture and mole fraction of ethanol
In liquid phase(x).
A relation between ethanol composition in liquid
phase and compositions obtained from ideal,
non-ideal and standard ICT data for ethanolwater mixtures.
A relation between boiling point temperatures
and mole% of ethanol and water mix~ures
for high concentrations
of ethanol.
A relation between composition of E,thanol
and water mixtures and the dielectric constant
2.9
A parallel plate capacitor
2.18
2.10
A cylindrical capacitor
2.19
2.11
(a) A parallel plate
capacitor
placed in a
cube of dimension L.
(b) A cylindrical
capacitor
placed
in
a
cube of dimension L.
An
uncharged
capacitor
beginning
to
2.20
charge up after closing the switch.
2.26
2.13
An A.C input to a capacitor.
3.1
The original electronic circuit, capacHance
3.2
The modified electronic circuit, capacitance
3.3
Block diagram
showing
electronic components
the
cell
cell
dfferent
3.2
3.3
3.4
of the capacitance
cell circuit.
3.3
On-Off mechanism of a Schmitt Trigg.~r
3.7
3.4
A Schematic diagram of the laboratory scale column
3.10
4.1
Experimental setup, calibration of the cell.
4.4
4.2
A
4.6
relation
between
ethanol-water
compositio'l
of
mixture and mY output.
(a) Step input to a system
4.8
(b) Firstresponse of a system
4.9
Dynamic lag of the capacitance
4.10
cell for
response time of 1,3 seconds
Comparison of composition via capacitance,
temperature
and density method for a change
in the reflux valve by 0,25 fractional units
Comparison of composition via capacitance,
temperature
and density method for a change
in the reflux valve by 0,35 fractional units
Comparison of composition via capacitance,
temperature
and density method for a change
in the reflux valve by 0,45 fractional units
(a)A change in the reflux valve position
by 0,15 fractional units.
(b)Model
response
of the column with a
change in 0,15 fractional units in the position
of the reflux valve by temperature
(c) Model
response of the column
change in 0,15 fractional
measurements.
wth
units in the
of the reflux valve by capacitance
a
position
measurements.
IX
4.10
4.19
(a)A step change in the thyrsitor by 50 % from
the operating conditions.
4.20
(b)Model response of the column with 50%
change in the thyristor by temperatur 9
l
measurements.
4.20
(c)Model response of the column w th 50 %
change in the thyristor by capacitance
measurements.
4.11
Closed loop response of the column
for a 1%
4.22
change in setpoint using the reflux val'/e as
the final control element and capad'ance
measurements.
4.11
Closed loop response of the column
for a
1%
4.22
change in setpoint using the thyristor CiS
the final control element and capadiance
measurements.
5.1
A normal distribution curve
5.1
Chapter ONE
Introduction
In
top
distillation
product
measurement
column control, accurate and reliable measurement of
composition
techniques
is a
primary requirement. There are various
in usewhich are c1asiifiedas (a) direct and (b)
inferred ,depending upon the type
of measurem'3nt. Typical examples of
direct measurement techniques are chromatographs and various
of
spectroscopic
types
analysers. They are used to measure composition
in terms of one or two key components or in terms of all the components
present in the process stream. The dominant feoture
analyzers is the
required
for
the column,
required
dead
the
time
which
sample to
plus the time
travel
can
bl~
from the
of chromatographic
quite large. The time
process
required through the column
stream
to
plus the time
by the detector at the end of the column to respond, can be quite
large. Such
large dead
times
features of
the
operational
reliability and 2) relatively high cost. Inferred measurements
composition
can
accuracy
of
the
ineffective control.
Other
analyzers stated above are 1) their low
on the other hand, use temperature to
on the
result in
infer composition and rely heavily
estimator for composition
measurement.
Thus it is understood that in practice, composition measurement techniques
have several disadvantages (Stephanopolous,1984).
In the
next
step
in column control, the measurement techniques
are applied in an appropriate control configuration, namely direct feedback,
inferential feedback
or
feedforward control, as shown below:
Control uses the
stimal:e of distillate
ompo~~ition
Compu:er
using 1, ' T2' T3
measUl'ements
estimal:es distillate
compo;,ition
Feed
Column
')
Distilillte
~
Botl:oms
Figure1.1 Common configurations for distillate composition controlof a
simple
distillation column: (a) Feedback; (b) Inferential (c)
Feedforward;(Stephanopolous,1984)
Distilate
""
The objective
of the three control configurctions mentioned above isto
keep the controlled
variable, in this case composition, at the desired value.
Feedback control configurations, as in Figure 1.1 (a) use direct measurements
of the
composition to adjust the value of the manipulated
variable, the
reflux flow rate. Inferential feedback control uses~;econdary measurements
of compositions usingtemperature to
rate. In order to calculate
values of the
Feedforward
adjust the value
composition the estimator in Figure 1.1 (b)usesthe
measured outputs, together
control,
of the reflux flow
as
in
Figure 1.1 (c)
witt1 thermodynamic relations.
uses direct measurement of
disturbance, in this case the feed composition, to adjust the value of the
manipulated variable(reflux flow rate), based on an available process model.
From the above
discussion,it follows that a direct, effective and cheaper
method of composition measurement
accurate
that
gives smaller dead times, more
measurements and a device which can easily be applied to the
above cited control configurations in a distillation column is highly desirable.
In this study it is shown that a device
that
USE~S
the principle of variation
in capacitance as a means of measuring composition in a binary mixture can
be successfullyapplied. Thiswill facilitate computerized on-line measurement
and control of composition in a distillation column a nd can also be integrated
in plant wide control.
The aim of this project is therefore:
(i)
To
study
the
basic characteristics of a capacitance cell
as
applied to direct measurement of composition of binary mixtures.
(ii)
To provide details of the development and testing of a capacitance
cell.
iii)
To use this cell for controlling the top
laboratory scale distillation column, to
product composition of a
compare
these results with
the temperature
based composition controller used previously and to
establishwhether or not the resultsobtained show an improvement
over
the other methods in use.
Thisdissertationconsistsof the following chapters:
A literature survey, in which the relation between
composition and
dielectric constant of liquid mixtures as well as the theory of capacitors and
different types of capacitors
used will be presented, specifically A.C and
D.C circuit theories in the context of choice of application of the former in
the device. A
description
of the chromatogrClphic methods and infra-
red analysers,looking at their
composition
disadvantages, followed
by
temperature-
correlations and their negative effects isalso given.
In the chapter
on process equipment a description of the capacitance
cell and its associated electronics, the laboratory scale distillation column and
data- converter cards is given.
Test
results
obtained
on the column form the contents of the
following chapter which contains the results
of ·the
calibration
and provides the experimentally derived relation between
and
capacitance.
used to obtain
Temperature
dynamic
tests. PI controllers
are
and
models for the
used
to
capacitance
process
composition
measurements are
distillation column using step
provide control action
for the top
product composition, usinga thyristor and the reflux valve as the final control
elements.
In the subsequent chapter
results will be examined, interpreted
and critically discussed.In the last chapter conclu:;ions and recommendations
are presented.
Chapter TWO
Literature Survey
Introduction:
In
this
chapter
a
detailed
survey
of
the
composition
measurement techniques, both direct and inferred which are presently in use
such as chromatographic, infra-red analysers, refrac1'iveindex and density, and
temperature methods along with their disadvantages and limitations will be
presented.
capacitance
Thiswill be followed by the theory and orinciples of the proposed
cell and its application to the measurement of composition of
ethanol and water mixtures.
Thischapter consists of the following topics:
1)Chromatographic
methods for determining composition.
2)Applications of infra-red analysers for chemical aralysis.
3) Refractive index and density methods for compo~iition determination.
4) Thermodynamic relationships between composition and temperature.
S) Evaluating ethanol and water composition using non-ideal relations.
6) Disadvantages of using temperature measurement as a means of inferring
composition measurement and control.
7) A relation between composition and dielectric constants of ethanol-water
mixtures.
8) The theory of capacitors, looking in detail at the C1dvantagesof using a
parallel plate capacitor over a cylindrical capacitor.
9)Thesignificance of using an alternating current (A.C) circuit instead of a direct
current (D.C) circuit in the measuring device.
2.1 Chromatographic techniques used in distillation column control
Gas chromatography(Schomburg,1990
technique
), is a direct
measurement
used in determining gas or liquid composition.
Their relatively limited applications in direct meosurement of composition
in a distillation column is because of their large deod times, and high costs
under typical operating conditions. The problem of their dead times is due to
liquid components
to be analysed, requiring differe'lt times of analysis. Thisis
explained by the principle of operation which is shown in Figure 2.1 below:
lI
I
I
I
I
I
I
L
----l
1
carrier gas supply
2
injector for split or splitless
3
column
4
detector
5
gas supply
( packed,
capillary
)
for Flame ionization
(a) air, (b) hydrogen,
nitrogen)
sample introduction
(c) make-up
detector
(FID),
gas ( argon or
The two elementary parts of a gas chromato~lraphic system are the
column (3), in which the separation takes place, ond the detector (4). The
carrier gas supply unit (1), has as main componE~nt, a pressure and flow
regulator connected to a gas cylinder, containing the inert carrier gas ( H2, He
, N2 or Ar). The sampling device, or injector (2), introduces the sample to be
analysed into the carrier gas against an inlet pressureof the inert gas which may
be under pressuresbetween 0,01 and 0,5 Mpa depE~nding on the type of the
carrier gas and the flow resistance. The injector isusuolly heated and operated
at a temperature which permits the volatilization of liquid samples.
The sample components are separated by dilution and mixing with the
carrier gas flow, this separation being facilitated by the fact that the column
is situated in an oven compartment. The temperature of the oven is changed
linearly to provide the temperature necessary for the optimum separation of
the components to be analysed.
The efficiency of the column isdetermined by selectivity of the stationary
phase present in the column and the sample capacity,
sample that can be separated. The sample capacity
ie the amount of
depends upon the
amount of stationary phase contained in the colum:1.
The separated
characteristic
sample
components
profile of their concentrations
enter
the
detector
with
a
within the carrier gas. The
registration system produces continuously recorded, time dependent electrical
signals. Detectors that are generally used in gas chromatography
are flame
ionization detectors (FID)and thermal conductivity detectors(TCD).
The time differences in analysis of the sample components cause major
transportation lags(dead times) in the control loop. --hiswill result in degrading
performance of the controller. Due to their delicate nature , they generally
require careful handling; they are therefore mountE~don the ground for ease
of maintenance.(Poole.S.K & Poole .C.F, 1991)
2.2 Infra-red spectroscopy
This method of analysis, ( Meehan, 1966), ( Pecksok & Shields, 1968),
(Olsen,1975) is based on the measurement of the interaction between matter
and electromagnetic
radiation in the region of 1-25
IJm. The intensity of
radiation energy absorbed or emitted due to transfE~rof electrons to and from
the characteristic energy level is measured . The absorption/ transmission
pattern is unique for any chemical compound.
The radiation source used in infra-red spectrophotometers
is one of the
following:
(i) The Nernst Bar: a hollow zirconium or yttrium oxide rod electrically heated to
1500 DC.
(ii) Globar : A silicone carbide bar heatable to 1200 DC.
Detectors used in infra-red analysers are:
In the near infra-red region ( 0.8 -3 IJm)the photo conductive cell is used. Upon
illumination with radiation of appropriate wavelength the electrons are raised
to the conducting
bands.
(Ii)In the middle and far infra-red regions the infra red (IR)photons are absorbed
and
their energies are converted
to thermal
energy. Rapid response
thermometers are therefore used as detection devices
Examples are:
Thermocouples ( gold -tellurium)
Resistance bulb thermometers
Gas thermometers
In IR devices the sample is placed before the m010chromator
monochromator
can remove unnecessary radiation emanating
so that the
from the
sample and cell before the detector isreached.
The major problem experienced during applicotion of a infrared analyser
is that it uses a narrow cell in which the sample is placed. Calculating
composition
therefore
becomes
difficult, since indices (absorption and
extinction coefficients)used in composition determination
of the analysers
require an accurate measurement of sample thicknE~ss.lnfra-redanalysers also
usewide slitwidths, the slitswhich form part of infra-rE~dspectrometers, provide
a better spectral resolution and accuracy depending on their width and are
close to 900 nM. Thiscan cause problems because ttle energy available in the
useful wavelength
range is relatively small and
a very slight shift in the
wavelength would cause a considerable change in the indices, creating a
significant error in composition.
In summary, spectroscopic analysers such as infrared analysers are to a
large extent accurate,
but expensive and requirE~careful calibration and
maintenance.
2.3 Refractive Index (R.I)Methods and Density methods.
The relation between refractive index and the composition range under
consideration (75-90%) was obtained from the International Critical Tables
(ICT,1930)and isshown in Figure 2.2. From the figure, a curvature which implies
that a single measurement indicates two different values of composition is
observed. Furthermore the refractometer that is available in the laboratory,
reads values of refractive index only up to the third decimal value. Therefore it
isonly possible to determine composition to the nearest 0,001 R.Iunits,which is
clearly not accurate enough. Refractive index methods were therefore found
to be disadvantageous.
The density method, on the other hand, provides a relation between
density of the mixture and composition as shown in Figure 2.3( Perry,1987).lt is
reliable, avoiding difficulties noticed by refractive index measurements.
&frllctiue
1.364
lnilex
1.361
Composition
60
(mass 'Yo)
80
70
Figure 2.2 A relation between composition and refractive index of ethanol and water
mixture at 20 °C.(Intemational Critical Tables, 19'30)
0.86
0.85
--~----
--
-----
---
--+--- -"---_.
-----_._---
0.84
Density
,
0.83
( glml)
0.82
0.81
0.80
0.79
0.78
75
85
Composition
90
95
(% mass)
Figure 2.3 A relation between composition and density of ethanol and water mixture
at 20 °C.( Perry, 1987)
The accuracy with which density of a sample can be determined using
gravimetric analysis is
+ 0,00001g/mL(
Manahan, 1986). Although this method
is useful in determining composition, density measuring methods commercially
available
are very large in size and
operate
as a
measurement
expensive and difficult to
technique
in a
small
scale
install and
distillation
column(Svrceck,1967) .
2.4 Temperature -Composition Correlations (Ideal)
Temperature can be used as an inferred meosurement to evaluate the
composition of binary mixtures like ethanol and waterin thiscase, assuming ideal
conditions. In distillation columns, top product composition isinferred by placing
a thermocouple
in the top tray, because not only will it better reflect the
condition of the distillate but also temperature profiles at the ends of a column
tend to become flat where the products reach purity( Shinskey, 1988). The
composition inferred by temperature iscalculated usingequations which relate
the partial pressure of a component
of a mixture to its composition (in mole
fraction) in the vapour phase as derived from Dalton' slaw and the ideal gas law
( Hougen, Watson & Ragatz, 1976),Raoult's law which relates the partial pressure
of a component
of a mixture to its composition (in mole fraction) in the liquid
phase, and the Antoine equation which relates the vapour pressure of an
individual component to the prevailing temperatun3, given by Equation 2.2.
(Smith & Van Ness,1987)
= X.psat
p
1
1
1
p =y.p
1
1
Yi
P = Xi£insat
1n ( P
sat )
=
A _
B
(T+C)
Table 2.1.Antoine
&
constants for the Ethanol-Water system(Coulson,
Sinnot, 1983) (Pressure
Compounds!
Richardson
in mm Hg and Temperahll'e in Kelvin(K»
B
A
C
constants
Ethanol(1)
18,9119
3803,98
-41,86
Water(2)
18,3036
3816,44
-46,13
YI
P+
Y2P=
Xl
P Isat +
p _p
p
sat
1
_p
sat
2
sat
2
p sat
X2
2
Composition of the binary mixture of ethanol and water is a function of the
system pressure P, and
applications,
temperature
of the system. Since in
the change in system pressure issmall and within
practical
+ 1mm
of Hg, it
is assumed to be constant.
2.5 Evaluation of ethanol-water composition using non-ideal temperature
relations
Using equations 2.1- 2.3, compositions of ideal mixtures can be calculated
by the partial pressures of individual compounds. Thisishowever not possible for
ethanol(l)
and water(2) mixtures, because of their non-ideal
behaviour. This
mixture forms a minimum boiling azeotrope at higher concentration
ie at 90
mole% and 78,2°C ( Perry 1987), and therefore exhibits a positive deviation from
Raoult's law. A relation between mole-fraction
of ethanol in both the liquid and
gas phase in the mixture is given in Figure 2.4. Thl3 azeotropic
evident from the figure where at 90 mole% ethanol
behaviour is
the vapour and liquid
compositions are equal.
1
1
0.8
0.6
Ql
c;
oS
:>.
0.4
0.2
0
0
0.2
Figure 2.4 Mole fraction of ethanol in liquid phase (x) and gas phase (y) in ethanol- water mixture at
atmospheric pressure of 760 nun Hg(Intemational critical Tables,1930).
Due to its non-ideal behaviour, use of fugacity and activity coefficients
influence the final calculation of composition of ethanol and water mixtures. A
relation between fugacity (Smith & Van Ness, 1987) of a component i, and
pressureof the component is given below in equation 2.4:
c for an ideal gas isa constant, equal to 1,and for (] non-ideal gas c becomes
the fugacity coefficient which is given below:
¢Ji
= ~
1
Along with fugacity coefficients,
activity coefficients
also influence,
composition determination in non-ideal mixtures. The activity coefficient is
obtained from equation 2.6-:
A
_ h
Yi -
1 rO
XiJi
Equation 2.1 is modified for the two components 1and 2 which
<I>
incorporates
and, y as shown in equations 2.7.
1
Y I p--
YI
P
Xl
I
I
sat
<PI
I
Y2 p=
Y2
X I
2
P
<P2
2
sat
(27)
It is necessary to calculate the activity and fugacity coefficients for ethanolwater mixtures. Thiscan then be applied when evalluating the composition of
an ethanol-water
mixture using the measurement of system temperature T.
a) Calculations of fugacity coefficients for ethanol-water mixture
In equations 2.7,
<1>1
and
<1>2
are functions of temperature, pressure and
composition. In evaluating fugacity coefficients use ismade of the parameters
6° and 61 given in equations 2.8 which are the second virial coefficients for a
given gas and a function of reduced temperature only. Equation 2.9 gives the
fugacity coefficient
<I>
in which "-
= TI
Tc
and
Pr
= PI
Pc' and Pc, Tc,are the
critical pressure and temperature respectively.
BO
= 0 083 _ 0,422
,
r.r1,6
p
In(fjJ) = _r (Bo + mB])
T,.
m = -lagio ( p/at )T=O
r
Tc(K)
Pc(mm
CJ)
7
-1,000
'
T (K)
Hg)
P(mm
BO
B1
<I>
Hg)
Ethanol
516,2
63,0
0,635
351,55
656
0,073
0,138
1,02 ~1
Water
647,1
217,6
0,348
351,55
656
0,0108
0,137
1,01 ~ 1
Table 2.2 gives values that are used in determining the fugacity coefficients for
ethanol and water. Here 4>, and 4>2 show 1-2%deviation from unity and their
influence on
calculations of composition using non-ideal equations 2.7 is
negligible. Therefore they are assumed to be equal to 1.
b) Calculation of activity coefficients for ethanol-water mixtures
Yl and Y2 the activity coefficients, are independent
of pressure but
functions of temperature and liquid composition. Thesecoefficients are positive
for ethanol and water mixtures (due to positive deviation from the Raoult' slaw).
Van-Laar equations 2.11are used to determine Vl and Y2 using the composition
of ethanol and water respectively in the liquid phase, and parameters a and
r3.
Values of a and
r3
for ethanol and water mixtures are 2,203 and 0,7
respectively between 25-100DC (Sandler, 1989).
in ~2.
jJ
=
[1 +
f,.~x2 J2
a
Xl
1
In~
0.5
0
0
0.2
0.4
)(1
0.6
0.8
1
)
Figure 25 Relation between activity coefficients of ethanol and water mixture and
mole fraction of ethanol in liquid phase (x)(Sandler, 1989).
The activity
coefficients
of both the components
using equations 2.11 are
presented as their natural logarithm values given in Figure 2.5.
(c) Calculating the composition of ethanol using non-ideal equations.
In determining the composition of ethanol using non-ideal equations the
following steps were followed:
The composition
of ethanol x, obtained from equation 2.3 for ideal mixtures
was used to determine the activity coefficients y" Y2 from equations 2.12 a and
b given below( derived from equation 2.11), where )(2=1-x,.
a
r1 = e
[l+~x]l
fJx2
fJ
r2 = e
[1+~x2l
ax]
The activity coefficients calculated
as a result are then substituted in equation
2.12 c(derived from equation 2.7).
As mentioned in section 2.5(a), <1>, and <1>2 are assumed to be equal to 1.
Therefore equation 2.12c results in equation 2.12 d.
Xl _
1 -
P_y
Y
psat
2 2
psat _ y psat
1 1
2
2
Thisequation is used in calculating
the composition of ethanol
using non-ideal
relations.
d) Comparing the composition obtained by ideal and non-ideal equations to a standard
data
The calculated
values of the composition
of ethanol using both ideal
equations ( equations 2.3) and non-ideal equations (2.12 a-d) and the standard
data from International
Critical Tables (1930), at various temperatures
reference) are shown graphically in Figure 2.6. The temperature
(for
range applied
in the figure was 78-100 °c, which is the useful range for analysis.
T
(K)
360
350
o
0.8
)
Figure 26 A relation between ethanol composition in liquid phase and compositions
obtained from ideal, non-ideal T-C relations and standard ICT data for ethanol-water
mixtures
2.6 The disadvantages of controlling the composition using temperature
It is disadvantageous
to use temperature
meosurement for the purposes
of inferring composition due to the following reasons:
(a)lnferential control is used when the controlled output of a processing unit
cannot be measured directly.
In control practice, the success of this scheme depends heavily on the
availability
of a good estimator, which in turn depends
upon how well the
system, in other words description of non-ideal vapour and liquid in equilibrium,
isknown. Therefore, when the system isperfectly known, a perfect estimator can
be constructed
and consequently
a perfect control is achieved. On the other
hand, if the system is approximately
known the inferential scheme provides
control, of varying quality.
It isnow necessary to determine to what extent the long derivation to infer
composition
(non-ideal) from temperature
from figure 2.6, a difference
is inadequate.
As it can observed
upto 2.3K exists for 20 % ethanol, which is large
enough to show the difficulties in calculating
compositions making use of non-
ideal relations.
(b)
It isalso essential to show how inaccurate the calculated
temperature
is especially in the region of the azeotrope.
composition
via
Ethanol and water
system forms an azeotrope at 90% ethanol, as shown in Figure 2.4.
The temperature
range istoo narrow in this re~lion ie 0,7 K,for the change
in composition from 75%to 90% ethanol, also shown in Figure 2.6. Any slight error
in temperature
reading
will cause a major error in the desired value of
composition. Upon referring to the standard data (ICT)it isalso observed that the
relation between temperature and composition isnon-linear as the composition
increases from 75%to 100%ethanol, shown in Figure 2.7. Temperature drops from
78,7 DC to 78,2 DC for a change
in composition
from 75% to 90% ethanol
whereas it increases from 78,2 DC to 78,4 DC when the composition increases
from 90% to 100%ethanol.
It isdifficult therefore to determine the composition of the mixture at higher
concentrations
of ethanol ie between
approximated
quadratic response of a relation between higher concentrations
of ethanol and their corresponding
j
'-..\
\.
78.6
-
\.
\
l78.5
'\
]
·i
boiling point temperatures.
I
I
~
~
75-100% ethanol. The Figure 2.7 is an
..•
\,
78.4
,
:/
"
boo
.S 78.3
I
~
l:8
//
"
I
78.2
./
'\.
" "'-
,//
"'-
.......
./
-
~
.---
/'
75
Figure 27 A relation between boiling point temperatures and mole% of ethanol and
water mixtures for high concentrations of ethanol.
As such it is observed that inferential control using temperature
sensing parameter
as the
has certain limitations in its use.
2.7 Capacitance Theories
Based on the
limitations
stated
above,
investigating the feasibility of a capacitance
ethanol-water
ttlere
is definite
merit in
cell to measure composition
mixtures, with a view to its adaptability
for control of a distillation
column. The main objective isto determine whether iitwill be advantageous
use the capacitance
cell compared
of
to
to the previously discussed measurement
techniques
namely chromatographs,
infrared analyzers and temperature
measurements. Before proceeding with details of such a device, the relevant
theory of capacitors is covered in the material that follows.
2.7.1 A relation between the dielectric constant of an ethanol-water mixture and its
composition
Figure 2.8 (Akerlof, 1932) shows a relation between the dielectric constant of
ethanol-water mixtures in terms of its composition and temperature.
j---..,.
45
40
constant
I
I
-........,
Dielectric ~
~
I
!
-........
---.....
"'-..
--....,
"----..
--.,
........••
"'--.
~
----
I
~
~
I
0""
~
~0
~
I
..,
I--- ~ I---.
r--- r-I'-"'-
1
-....
---r---.....
--.
•...•..•. ~
I
,
I,
25
70
80
85
90
mass % ethanol-water
Figure 2.8 A relation between composition of ethanol and water mixtures
and the dielectric constant
A maximum change of 15units in dielectric constant isobserved for each
temperature in the range 70 -100 mass % ethanol-water, which is the typical
operating condition of the composition measuring device to be constructed.
Dielectric constant is only influenced
by two factors, the fractional
composition and the temperature of the solutions as shown in the figure above.
2.8 Properties of Capacitors
Thisstudy looks at the theories involving the geometries of parallel plate
and cylind~cal
capacitors.
It is necessary to
compare
properties such as
sensitivity and hold-up of the capacitors for evaluating a measurement system
for purposes of control, since instrument dynamics would affect the performance
of the control loop containing the instrument.
2.8.1 Parallel plate Capacitor:
A parallel plate capacitor (Cheng, 1989) consists of two parallel plates of
cross sectional area S separated
by a medium of uniform permittivity, e, as
shown in Figure 2.9.
+
+
- -
+
+
+
-
-
-
+
-
Figure 2.9 A Parallel Plate capacitor
The capacitance
for a parallel plate capacitor
if d is the distance between
the plates is given as:
ES
d
Charges will be uniformly distributed over the conducting
plates shown in the
figure above.
2.8.2. Cylindrical Capacitor:
A cylindrical capacitor ( Walker, 1990) as shown in Figure 2.10 comprises
of two concentric
tubes having diameters a and b respectively. The space
'\ \Lf1b'74L I
O\U4~
(0(.;,
7
between the conductors isfilled with dielectric of permittivity e. Thelength of the
capacitor is L .
- - ---- --~ -- t --.7",
I
,
I
1
;
I
',!
, .
--- __ .- -- -- _ -,--.;;",.;
Figure 2.10 A Cylindrical capacitor
The capacitance
of a cylindrical capacitor isgiven as :
c
=
21tEL
b
cy
In ( - )
a
2.8.3 Comparison oftheperfonnance
ofa parallel pla:te capacitor to a cylindrical
capacitor
As mentioned earlier, system sensitivityand
configurations should be
hold-up
of each of the
compared to evaluate the performance of both
capacitors. In the subsequent discussion, it will be shown that although
cylindrical capacitors give more sensitivereadings, smaller hold-ups in parallel
plate capacitors enable them to be better suited for use in measurement
systems.
Since dielectric constant is a function of liquid composition, one would
prefer an instrument which is sensitive enough to provide a large change in
capacitance
for a given change in e.
L
I
b=L
d
aI
ilL
(a)
(b)
Figure 2.11 (a) A parallel plate capacitor placed in a cube of dimension L; (b) A
cylindrical capacitor placed in a cube of dimension L
An example of the two capacitors placed in a cube of dimension L is
shown in Figure 2.11 given above.
The following assumptions were made to facilitate the calculations:
(a) b
= L.
(b) b-a
= 2d.
(c) (a) and (b) will also imply L -a = 2d.
(d) When the inner diameter a varies from 0 to L; d will vary from L/2 to O.
(e) The same liquid with dielectric constant e fillsthe volume between the
two capacitor configurations.
2.8.3.1 Sensitivity
Calculations
The system sensitivity of the device is determined
capacitance
by the
change
in
for a given change in the dielectric constant of fluid flowing
through the device. Geometry of the capacitor determines this property. The
sensitivities of both capacitor configurations are obtained to determine which
of the two configurations results in a more sensitive device within the given
geometrical constraints. Useof the example given in Section 2.8.3and equations
2.13 and 2.14 are made in deriving equations 2.15.
c
=
d
pa
c
cy
2
EL
d
ES
=
(2.15)
27tEL
b
In ( - )
a
27tEL
Ccy =
In(L_L
)
2d
Since it isrequired that the sensitivities of both the capacitors be compared, aCCY
/ae ,
acpo
/ae were evaluated
as equations 2.16. Reasons for using partial
derivatives is because d in the relation is a variable.
ac
aE
-2
---2::. =
The ratio of
accy!ae
to
acpa/ae
7t
L
In (L - 2 d)
L
was compared
at the two limits of d,
a and
L/2, to verify which of the capacitors gives a maximum change in capacitance
for changes in the dielectric constants of the fluid. At the lower limit, this ratio is
0/0 ie indefinite. L-Hospital's rule isapplied to this limit, which results in equations
2.17.
-Ii m ~
( 2 n: d )
d~O d(d)
Ii m ~
( In( L -2 d ) L )
d- 0 d(d)
L
lim -2n:
d- 0
.
I1m
d- 0
-2 L
L-2d
--
The relations above show that,
acCY /ae
is always greater than
ac
po
/ae
at the
lower limit. In the upper limit where d tends to L/2, the ratio of the sensitivities is
o as given
by equation 2.18:
Thisvalue of the ratio at this limit is impractical
because a sensitivity of 0
can never be useful in any measuring system. The ideal design of both types of
capacitors applies to the condition when d ~O, within practical limits. aCCY
is always larger than a
capacitor
aC
pa /
ae
/
ae
at this limit. The sensitivity of a cylindrical
is therefore greater than that of a parallel plate capacitor.
2.8.3.2 Hold-up Calculations
It is interesting to observe how system hold-up influences measurement
of a system. Hold up is defined as the time it takes to replace a given volume,
given a constant flow rate in and out of the volume. It isthe ratio of the volume
of the vessel and the volumetric flow rate of the fluid in and out of the vessel. In
control practice it is often necessary to minimise the hold up of a vessel.
Hold-up for each capacitor was calculated to determine which of the two
capacitors gave a minimum time for measurement. If the volumes of cylindrical
and parallel plate capacitors are given
by
Vcy,Vpa respectively,
then:
1t
V
cy
= -
2
d( b +a )L
A ratio of 'tpa. 'tcy,the hold up times of both the capacitors isgiven by equations
2.20.
'tcy
VcylF
't
Vpa I F
pa
1t
-d(L+a)L
---2:'. = _2
1t
't
~a
L2d
=>
-(L+a)
_2
L
»1
It is observed that hold-up in a cylindrical capacitor is larger than a
parallel plate capacitor, shown by the relation above. Thisimplies that parallel
plate capacitors give faster dynamics during measurements, explaining their
choice.
2.9. Description of the circuitry ( A.C and D.C capacitors)
The capacitor used in this investigation, usesthe variotion of dielectric constant
which isa function of composition as a means of sensingfor measurement and
control in a distillation column.
A capacitor has the ability to store electrical charge, and to increase its
charge when the voltage across its terminals risesor to discharge when the
voltage falls(Kip, 1965).In the following section, the behaviour of A.C and D.C
capacitor circuits are discussed, to observe which of the two will be more
suitable for measurement of composition.
2.9.1 Description of a D.C circuit connected to a capacitor
A D.C circuit( Kip, 1965)with individual capaciitor plates isshown in Figure
2.12 (a) , (b)& (c). The supply current isconstant bE~forethe switch isclosed as
shown in Figure 2.11 (a). With a D.C voltage source, current flows long enough
to charge the capacitor. Then as the plates gain polority and oppose additional
charge, the charging current decreases until it reoches zero at the moment
when the charge on the plates isequal to the voltoge of the D.C source.
Distribution of positive and negative charges to the upper and lower
capacitor plates respectively, will result as shown in Figures2.12 (b) & (c).
-__
-T
~~
T
==
Figure 212 An uncharged capacitor beginning to charge up after closing the switch.
(Kip, 1965)
This capacitor
behaves as an electrolytic cell with electrochemical
reactions taking place at the two plates ( ie the two electrodes) when a
dielectric fluid like ethanol-water mixture is placed between the plates. The
electrochemical
reactions can be:
(a)Cathodic
The electrode in this case isstainlesssteel (Chapter 3, Section 3.1.2.2 (b)).
Water in the mixture is subjected to a reduction reaction due to its ability to
undergo the following reduction reactions ( Stanley, 1985).
(b) Anodic
Oxidation of the ethanol-water mixture due to removal of electrons to the
electrode results in anodic reactions. Thisreaction gives hydrogen ions and
carbon dioxide in the capacitor. The reaction isgiven by equation 2.22.
The voltage
of 5V in the circuitry of the measuring device (discussed in
Chapter 3, Section 3.1.2) islarger than the individual half cell potential, sufficient
to generate electrolytic reactions in the cell. Production of carbon-dioxide
hydrogen
and
in the mixtures affect the dielectric constant in the solution, making
it impossible to obtain a consistent, representative capacitance
reading related
to the composition of the liquid mixture.
D.C capacitors
can therefore
not be used in measurement
involving liquid composition determination
systems,
of this kind.
Figure 2 .13 An A.C input to a capacitor (Kip, 1965)
Current flow in an A.C circuit across a capacitor represents continuous and
alternating charging and discharging of the capacitor
movement
plates, and no electron
takes place directly between the plates. Therefore in an A.C circuit
as shown in Figure 2.13, the voltage on a plate will vary sinusoidally from the
positive to the negative charge. No nett charge forms on any of the plates, as
a result. Electrochemical
reactions similar to those in D.C circuits will therefore
not be observed. It is therefore imperative to use an A.C circuit in any device
that makes use of capacitance
related measurements.
Chapter Three
Process Equipment
In this chapter a description of the process equipment
used in the test setup is
given as follows:
(a) The capacitance
cell prototype and its associated electronics.
(b)The laboratory distillation column.
(c) Different AID cards used in measuring voltage signals and 01A cards used
in controlling the column.
3.1 Description of the capacitance cell and its associated electronics
3.1.1. The capacitance cell as a sensor( C7, Figure 3.1)
As mentioned in the introduction, the purpose of the investigation was to
develop
and test a capacitance
composition
cell that provides direct measurement
of
of binary mixtures, in this case ethanol and water. A simple and
reliable relation exists between
the composition
and
dielectric constant of
ethanol and water mixtures at a given temperature, as shown in Figure 2.7 . The
previous chapter also provided the necessary background for using a parallel
plate capacitor
and an A.C circuit for capacitance
A prototype parallel plate capacitance
measurements.
cell was therefore fabricated
to
be used as a sensor based on the theory stated above. It isconstructed of two
rectangular stainless steel plates of dimensions 75mmX 50mm and which isused
as the capacitor.
A distance of 4mm was used between
the plates. These
dimensions were obtained from the work of Jannsen(1986).
3.1.2 Cell electronics
In order to obtain a reliable reading from the capacitor,
substantial signal
.sv
Reg
Figure 3.1 The original circuit diagram of the capacitance cell.
t:1
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~
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4
conditioning
was
required.
In
the
original
circuit
diagram
Figure
3.1(Jannsen, 1986), the oscillator and cell functions could not be divided. The
capacitors 470 pF, 220pF(which were part of the oscillator), 330pF and the cell
were connected
impedance
across the supply line and the ground, providing a low
to the oscillator. This reduced the oscillator
voltage to 0 V and
stopped its functioning. Therefore the circuit Figure 3.1 was modified as shown
in Figure 3.2 as follows:
a) The capacitors 470pF and 220pF were replaced by a tunable capacitor
C6,
and in order for the oscillator to provide the necessary oscillations, C 1 was
connected
to C6.
b) The 330 pF capacitor was then replaced by 820pF capacitor for the purpose
of stopping unwanted D.C current across the cell. Figure 3.2 shows the electronic
circuit incorporating
the capacitance
cell.
The electronic circuitry in Figure 3.2 may be divided into four sections as given in
block diagram Figure 3.3, the functions of each of these blocks isdescribed here
under:
POWER
OSCILLATOR
CONDITIONING
~I AND
CELL
SCHMITI
SIGNAL
~I
LEVEL
~I
BUFFER
ADJUSTMENT
Figure 3.3 Block diagram showing different electronic components of the
capacitance cell circuit
3.1.2.1 Power conditioning:
The power conditioning unit has the following functions:
(a) The operational voltage of the circuit in Figure 3.2 is5V and the voltage from
the D.C power source in the supply line is 15 V. The regulator U1 is used to
reduce
the
voltage
from
the
supply
line to
the
circuit's
operating
voltage(Horowitz, 1979).
(b)To provide a smooth and constant output current using a reservoir capacitor
(which has a large capacitance)
C4.
3.1.2.2 Oscillator and cell :
D.C current from the power conditioning section issupplied to thissection.
Since this section performs a very important role in generating an A.C current to
the cell it can be described as the heart of the circuit. It has the following
components:
a) L-C Colpitt's Oscillator.
b) The Cell, C7.
(a) L-C Colpitf's oscillator
It is the function of an oscillator (Rhea,1990) to produce a sinusoidal A.C
current from the D.C supply current. Thiscurrent isthen supplied to the parallel
plates to provide an effective capacitor for measurement purposes.
The configuration comprising of components Q2, L1, R8,C!, C6, C2 and
R5is the L-C Colpitt's oscillator. Since it is possible to tune a capacitor whereas
an inductor cannot be tuned, its advantage in electronic circuit applications
over the other type of oscillator, the Hartley's oscillator, is due to its two
capacitors and one inductor configuration in comparison to the two inductors
and one capacitor
of the latter. This provides a better tuned circuit for
measurement purposes.
(b) The cell prototype
Thishas already been described in section 3.1.1.
3.1.2.3 Signal level adjustment:
It is important
components
to isolate the operation
of the oscillator, because
of
like the Schmitt trigger {IC 1, in Figure 3.1} and frequency dividers
IC2,IC3 which draw a certain amount of current from the circuit. Thisresults in an
unwanted drop in the voltage in the output signal. It is also necessary that the
oscillator's output
difference
of 12 mV p_p
{
voltage
- peak to peak, referring to the
in maximum and minimum voltage in an A.C sinusoidal signal} be
amplified to 3 Vp_p because this enables switching on digital components
as the Schmitt Trigger and
components
require
frequency
dividers down the signal path. These
higher voltages
operation. The combination
such
in
the range
of 1.5 - 4 V p_p for their
of the transistor Q 1 and the resistor R6is used for the
dual purpose of acting as a buffer that protects the operation of the oscillator,
and for magnifying of voltage output from the oscillator. Transistor Q1 will be a
common collector with a high impedance
input.
The A.C current in the output may not be influenced by any D.C current
in the circuit. Resistor C3, the blocking resistor, blocks any D.C current resulting
from the transistor Q 1.
The Schmitt Trigger IC1, operates around a threshold voltage{ described
in the next section}. Transistor Q3 and resistorsR2, R4 and R3will tune the output
from the oscillator to adjust the level of the voltage
to a threshold voltage.
3.1.2.4 Schmitt buffer
In the operation of the circuit a noisy output is produced which should be
filtered out. A Schmitt trigger {Young, 1968} ,IC1, is employed
for purposes of
filtering this noise. After the resistor R3 has provided a threshold voltage, V as
shown in Figure 3.4 the trigger will function as an on-off mechanism. Voltage
values below this threshold are interpreted as 'off', and those above will be 'on'.
The 12 MHz output is a square wave and isanolysed based on the width
of its pulses.The width gives an indication of the frequency or period via the
well-known relation 3.1 :
1
f=T
A shorter period which is a higher frequency will indicate lower concentrations
of ethanol
while a longer period or lower frequency
will show higher
concentrations of ethanol.
The analogue-to-digital
converter cards used in the laboratory, Eagle
PC30 cards, cannot handle such high input frequEmcies and can read only
voltage signals. Frequency dividers IC2, IC3 are therefore used to reduce the
frequency output by a factor of 256 and frequency conversion to voltage is
done
using
by a frequency-voltage
converter( LM131standard National
Semiconductors device) to provide an input to this cord. Turbo-Pascal was used
as the interface programming language.
V
O"hreshold voltage)
3.2 Laboratory distillation
column
The column given by Figure 3.5 and obtained from Van Niekerk (1995) has
ten plates. Each plate is made of copper and has three bubble cap trays. The
reboiler of the column of 20 litre capacity,
consists of three, 2 kW electrical
elements in parallel. Bottom product (B)tapped out of the reboiler and cooled
by a heat exchanger flows into the collection drum, while the top product(D)
flows into the reflux drum of 10 litre capacity.
Liquid in the collection
drum is
pumped to the feed drum from where it is used as the feed to plate four of the
column. The temperature
in this drum is maintained
constant using a single 2,3
kW heating element.
The liquid in the column is ethanol-water.
It is cheap,
non-toxic, non-
corrosive and the boiling point can easily be reac1hed in the laboratory. The
azeotrope isreached at 90 mole % of ethanol at atmospheric pressure of 87 kPa.
The following legend would describe the various components
of the distillation
column setup:
Tl
: Feed drum
TC/l :Temperature controller of the feed drum.
Tl/I2 : Temperature indicator of the feed drum.
E3
: Heating element in the feed drum.
FIll
: Feed flow rate (to the column)indicator
FC/l
: Feed flow rate (to the column)controller
KI
: Feed stream valve
F
: Feed
Cl
: The column
CC/2: composition controller cascaded to the thyristor(in the reboiler).
...-------$
I
_---...,jc...I
t"'V
-
Figure 3.5 A schematic diagram of the distillation column setup.
E4
: Heating elements in the reboiler(The thyristor).
D
: Distillate
R
Reflux
11 1-11: Temperature indicators or thermocouples in the plates of the column.
CC/l
composition controller cascaded to the reflux valve.
C/l
: composition analyser
K2
: The reflux valve
T2
: The reflux drum.
E2
: The condenser connecting top of the column to the reflux drum.
P1
: pump connecting the reflux drum to the top of the column via K2.
PIll & PI/2: Liquid level indicators of the reflux drum.
LC/2
level controller of the reflux drum.
K3
distillate valve.
T3
: The collection drum.
P2
: pump connecting the collection drum to the feed drum.
LI/l
liquid level indicator of the reboiler.
LC/l
liquid level controller of the reboiler.
K4
: Valve connected to the level controller of the reboiler.
El
condenser connecting reboiler and the collection drum.
B
Bottom product
3.3 Data - converter cards
Reading of the analogue signals from the distillation column and the cell
equipment
was done by two types of cards namely the pc73 and the pc30
(Eagle Electric ,1992). The former reads temperatures from the column based
on mVreadings obtained from thermocouples,
voltage signals.
while the pc30 cards measure
Control signals to the column are provided using a pc66 card. The cards and the
interface are calibrated
to the correct limits. A brief discussion of the cards is
given below.
3.3.1 pc66 card
The 01A conversions which are used for controlling the control valves and
heat input to the reboiler by means of a thyristor were done by means of a pc66
card. Thiscard has 12 output channels and a 12 bit accuracy.
3.3.2 pc73 cards
The two pc73 cards used in the equipment
in the distillation column using thermocouples
accuracy of
+ 0,5 °C. Eleven
obtain temperature
which are
such thermocouples
cards.
The pc73
compensation
cards
are
equipped
K-type and have an
are placed, one each in the
10 plates and one in the reboiler of the distillation column
and provide mV- signals which are converted
shown in Figure 3.4
to temperature
with
readings
a cold
readings by the
junction,
enabling
of a reading due to variations in the ambient temperature.
Each
card has 8 channels with a 12 bit accuracy. The maximum rate at which the AID
conversion is done is 30 Hz.
3.3.3 pc30 card
The AID conversions are done through 16analogue single-ended input or
8 double-ended
input the maximum throughput being 30 kHz. Apart from this,
the card has two 12 bit 01A outputs and two 8 bit 01A outputs and 24 digital 1/0
lines for 01A conversions, which are not used. The input range of this card is
0- 10 V. It is used to measure the flow rates of feed, distillate, bottom product
reflux, thyristor heat input to the reboiler, and the capacitance
cell output.
Chapter FOUR
Planning and execution of Experiments and Results
4.1 Experimental planning
Experiments were planned using the capacitance
cell to achieve the
following goals:
.To obtain a relation between the output from the capacitance cell and the
composition of ethanol and water mixtures by calibration
and to verify
if the relation between the dielectric property and composition holds good
for the chosen range of composition and temperature .
• To determine the dynamic lag of the capacitance cell. Thiswas done by first
studying the responsesobtained from a first order process, in the context of
its application on the column and the cell dynamic responses.
• To test the accuracy of the composition measurements on the column via
capacitance
cell readings and temperature measurements by
comparison with the density method as reference for composition.
·To apply the capacitance
cell on the column under both open-loop and
closed loop conditions and study the effect of the capacitance
cellon the
dynamics of the column.
Experimentswere conducted in the following manner:
An experimental setup was devised to obtain the relation between
composition of an ethanol and water mixture and the
output from the
capacitance
cell. It consisted of a circulating pump and a beaker containing the
test mixture which was placed in a constant temperature bath and connected
to the capacitance
cell. Ten experiments at each of the following compositions,
75%, 85% and 90% were
performed and the average of the corresponding
voltage outputs were taken to obtain a final relation.
To determine the dynamic lag of the capacitance
cell, five experiments
were performed by changing the composition of the mixture flowing through the
capacitance
cell from 75 mass % to 85 mass%ethanol.
Thisexperiment was
performed making useof the beaker setup of the previous experiment except that
heating was not required. The dynamic lag obtained by these experiments would
then be compared with the actual responsesfrom the column to determine the
effect of the capacitance
The capacitance
conveniently
cell dynamics on the column dynamics.
cell was compact in sizeand therefore could be placed
between the accumulator
and condenser for providing in-line
measurements to test the cell's behaviour on the column.
The steady state operating conditions of the column were:
(a) 50 % of ethanol-water in the feed, the feed temperature being 19-22 DC.
However it was not possible to observe any difference in composition due to this
small range of temperature variation. The fractional valve opening of the feed
stream valve was 0,6 and feed flow rate was172,9 ml/sec.
(b) The fractional valve opening of the reflux valve was 0,5.
(c) Thyristorheat input to the reboiler: 50 % of its maximum power of 6 kW,ie 3kW.
(d) The steady -state composition of the ethanol-water mixture in the top product
was 76.2 %.
The following experiments were performed on the column:
Accuracy testing involved changing the fractional opening of reflux valve
by 0,25 , 0,35 and 0,45 from the steady state operating conditions. In this
procedure, the density method was used as the reference to determine the
accuracy
of
capacitance
the measurements obtained
by
both temperature
and
methods.
A series of experiments were performed
measurement
of composition
to determine whether the
via capacitance
detrimental effect, ie, more dead time and lag,
measurement
had
any
on the dynamic relation
between top product composition from the column and an input change. At the
same time, these measurements were compared to composition measurement
via temperature to observe whether there was any substantial difference in the
dynamics of these two techniques.
A seriesof experiments was also executed under closed loop conditions to
confirm the capacitance cell performance.
4.2 Calibration of the capacitance cell
4.2.1 Calibration Process
Experimentswere planned to calibrate the capacitance cell to determine
a reliable relation between the output from the capacitance
composition
of the ethanol
and water
cell, and the
mixture at a chosen operating
temperature. The experimental setup is shown in Figure 4.1. In this setup, a
constant temperature
containing
the
bath equipped with a heating coil and a beaker
ethanol-water
mixture were
used. A high
speed
pump
circulated solutionsat temperatures between 20-70°C through the capacitance
cell. PVC tubing was used to connect the various elements in this arrangement.
Three different compositions 75,85 and 90 in mass%ethanol and water mixture
were prepared usingvolumetric flasks.Theaccuracy with which mixturescan be
o
Cell
~
Figure 4.1 Experimental setup, calibration of the cell.
made
up
using volumetric
manufacturers specification
flasks of
100ml solution
is
+ 0,5%(
Standard
1107,South African Bureau of Standards). Taking into
account that the specific gravity of 100%ethanol is0,79 and that of water is0,998
at 20 DC, the following mixtures were prepared.
75 mass% ethanol-water: 475 ml ethanol and 125 ml water.
85 mass% ethanol-water: 538 ml ethanol and 75 ml water.
90 mass% ethanol-water: 570 ml ethanol and 50 ml water.
The output was in millivolts (mV)
obtained
as result of
voltage conversion, the frequency signal from the capacitance
frequency-to-
cell which in turn
was a function of ethanol composition (also explained in section 3.1.2.4). The mV
output was measured using a pc30 card, and the chosen operating temperature
maintained by monitoring temperature reading through a thermocouple
placed
close to the cell (position 1 in Figure 4.1) in the flow stream, the reading obtained
from a pc73 card.
During initial experiments, the readings from the capacitance
cell were not
repeatable. A trouble-shooting exercise revealed the following:
(a)Bubbles started forming at temperatures over 40°C, due to the onset of boiling
and generation of
vapour bubbles ( Smith & Van Ness, 1987). The bubble
formation caused a variation of the dielectric constant of the solution. The output
from the capacitance
cell was never consistent because of this.Thisproblem was
solved by ensuring that the feed temperature of the liquid to the cell is in the
range of 20-40°C.
(b)Formation of a white precipitate was observed during the initial test runs and
thiswas attributed to the presence of plasticiserson the PVC that were extracted
by ethanol at high temperatures. PVC tUbing was therefore replaced by silicon
tubing.
(c)The high speed pump was replaced by a low speed circulating pump after it
was observed that the cell needed smooth running conditions in order to provide
accurate results.
(d)A drift in the output readings from the cell was observed due to the
components of the cell electronics, which were temperature sensitive. An air
conditioner used in the laboratory provided a constant external temperature in
the range of 20-21°Cand solved this problem.
(e)The cell electronics required a certain amount of time to reach steady state
after switching on, to be able to give consistent readings. Thistime was found to
be approximately 4-5 hours.
4.2.2 Calibration results
After overcoming the difficulties stated above
the output was consistent.
Ten experiments were performed at three different temperatures 20°C, 30 °c ,
40°C, for each composition, 75 %, 85 %, 90 %. An average of the mV output of
-----------.--------
40 ..-
I
-- .....
--~---
I
..
_----------
I
I
20
74
88
Mass % Ethanol ------)
Figure 4.2 A relation between composition of ethanol and water mixture and mV
output
A spreadsheet was used to obtain a linear regression of mV readings as a
function of temperature and composition. The least squares method was applied
and the relation is given as equation 4.1. The correlation coefficient for this curve
fit was 0,999.
mV := -2,128 C + 209,83+0,24(T)
(4.1)
Rewriting equation 4.1 to obtain an expression for composition as function of mV
output and temperature
as shown below.
c:= -0,47mV +0,113 (T)+ 98,62
Thisexpression will be useful to calculate
(4.2)
the unknown composition of a sample
of ethanol and water mixture, when the readings of the mVand temperature
are
known.
Using equation 4.2, the derived values of composition obtained from the
10 experiments iscalculated and presented in appendix I for temperatures of 20
°C,30 °c °C,40 °c respectively.
Tables 4.1-4.3 show the mean value and the confidence
limits or the
standard deviation of the derived composition from these experiments. A
confidence limit is defined as the range in which the mean of an experimental
data is accurate, and the standard deviation gives the confidence limits of a
certain set of data(Manahan,
1989). From Tables 4.1-4.3 it is observed that the
confidence limitsare within ±O,55which isgood enough for all practical purposes.
Composition
Mean
Standard Deviation
75%
75,03
± 0,542
85%
84,9
±0,383
90%
90,07
±0,53
Standard Deviation
Composition
Mean
75%
75,22
±O,542
85%
85,09
±O,542
90%
89,79
±O,55
Table 4.3 Statistical data of the calibration
Composition
procedure at 40 °c
Mean
Standard Deviation
75%
74.94
t 0,52
85%
85,75
to,55
90%
90,02
to,53
4.3 Detennining dynamic process parameters for a first order process after
providing a step input.
Response of a first order process after providing a step change in the input
as shown in Figure 4.3 (a), resembles Figure 4.3 (b).
In the response curve Figure 4.3 (b), y is the output,
"t"p
represents the time
constant of the process for the column for the change, 'td the process dead time,
Kp the process gain which gives the ratio of the change in the magnitude of the
output(Kr) to the change in the magnitude of the input(Ksl
Therefore Kp = Kr /Ks • Since the response isassumed to be that of a first order
process, at 0,632 Ksonthe y-axis, the corresponding reading on the x-axis gives the
time constant for the process,
"t"p.
~
The approxi~at~d~esponse~
~
-
--
The actual response
-- - - -
.....•
Kr
~
point of disturbance
4.4 Cell dynamics lag testing
Dynamic lag for the capacitance
capacitance
cell gives an indication of how quickly the
cell reacts for a change in composition.
Thisexperiment was performed by taking two beakers one containing 75%
ethanol and the other containing 85% ethanol. Then using the arrangement
Figure 4.1 and removing the heating equipment(
in
heating is not required for this
experiment), solution from the beaker containing 75%ethanol ispumped through
the capacitance
cell. After this the tube was placed in the beaker containing the
85% ethanol solution and the response reached its new steady state value within
±5%.The response time of the cell was determined using a sampling interval of 0, 1
second.
Five such experiments were performed and the time for the change in the
composition isgiven in Table 4.4 below. The largest response time for the change
in composition was 1,3 seconds and the response of the capacitance
cell was
observed at this value, as shown in Figure 4.4. Thisresponse was assumed to be
first order because
the capacitance
cell acted
as the only single medium
between the pumped solution and the reading obtained (Stephanopoulos, 1984).
The corresponding
dynamic lag was therefore obtained
similar to Figure 4.3(b)
and was 0,4 seconds, also shown in Figure 4.4.
Table 4.4. Dynamic lag of the capacitance cell
Expt1
Expt2
Expt 3
Expt4
Expt5
1 see
1,2 see
1,3 see
1,2 see
1,1 see
0,2 see
0,3 see
0,4 see
0,3see
0,2 see
Response Time
(see)
Dynamie ('t'pJ
Lag
5
~
..... _ .....
V
I
I
I
.
7'iii
o
~p
,
_--
.'-'---
4.5 Determination of the accuracy of the capacitance cell.
4.5.1. Methods to determine accuracy.
It was planned to test the
capacitance
cell for accuracy by using a
reliable reference and comparing the readings obtained by the capacitance
measurement technique.
Accuracy may be expressed by the following expression
% Accuracy of a measurement technique=10o- {A-B}/ {B},. 100
(4.3)
where A= composition determined via the new measurement technique.
B=composition determined via the reference testing method.
Density determination was used as the reference
method for confirming the
accuracy of readings of the capacitance cell. Therelation between density of the
mixture and composition is shown in Figure 2.3( Perry,1987). The accuracy of
determining density of a sample is + 0,00001g/mL using the gravimetric analysis
(Manahan.S.E,1986).
In the following paragraphs, resultsof accuracy testing are presented.
4.5.2 Accuracy testing for temperature and capacitance methods.
In order to compare readings via the two available techniques, ie via
temperature measurement and via capacitance
obtained were compared
measurement, the values so
with composition obtained by means of density
measurement. From these readings it was desired to obtain the accuracy of the
capacitance
cell readings as installed, compared with that of temperature
measurements. The temperature measurements were performed by placing a
thermocouple on the top tray due to reasonsmentioned in section 2.4. Equations
2.1 -2.13 were used to obtain
composition
measurements by means of
temperature, while equation 4.2 was used to obtain composition readings by
means of capacitance
measurements. These equations were introduced in an
algorithm for determining composition of ethanol and water mixture. Density
measurements involved the weighing of a sample of the top product in constant
volume flasks, then obtaining the corresponding composition reading based on
the density value and using of Figure 2.3.
The pc30 and pc73 cards were used to obtain
capacitance
measurements
using a
temperature
and
sampling interval of one second.
Composition was obtained by density measurements using 10ml constant volume
flasks,the accuracy being ± 1%. The top product sample was taken at 20°C and
weighed using a mass balance, the accuracy of these measurements being ±
0,001% ( Standard manufacturers specification 1107, South African Bureau of
Standards). Density was calculated at 20°C and composition of the sample was
obtained from Figure 2.3.
Todetermine the accuracy of the capacitance
and temperature methods
step disturbances to the reflux valve( refer to Figure 3.2) of magnitudes 0,25, 0,35
and 0,45 was applied. The density and capacitance
measurements were
performed after the vapour of the top product iscooled down by the condenser,
therefore lag between these measurements was nil. Since the temperature
measurements were performed
on the top plate
measurement between temperature and capacitance
there is a time lag in
methods. The lag was
between these two methods was found to be 7 seconds for 0,25 change, 6.5 sec
for 0,35 and 6 seconds for 0,45 changes in the reflux valve positions. These lags
were compensated
for in calculating
the accuracy
of the measurement
techniques.
After obtaining the raw data, the average of readings of both temperature
and capacitance
measurements in a 50 second interval were determined while
at the same time taking a sample of the distillate in thisinterval. Byperforming this,
it was intended to use the average deviation from the actual value for the
capacitance
and temperature methods for purposes of determining accuracy
of these techniques.
Figures4.5, 4.6 and 4.7 show the results obtained by the three reflux valve
changes. Each composition point isrepresented by the average value obtained
in a 50 second
interval.
It can
measurements from the capacitance
be observed from the figures that
the
cell are closer to the density method. NB.
In this investigation, the responsesfrom the column are given as a deviation from
the steady state composition ( ie 76,2%ethanol).
14
12 ------10
%
deviation
of
cOIWposition
8
6
42
o
-2
200
400
I: Capacitance
II: Density
600
II: Temperature
Time (see)
Figure 4.5 Comparison of composition via capacitance, temperature and density
measurements for a change in the reflux valve by 0,25 units
12
10
%
deviation
of
8
co_position
6
4
2
o
-2
o
( I: Capacnance
II: Density IH: Temperature)
Time (see)
Figure 4.6 Comparison of composition via capacitance, temperature and density
measurements for a change in the reflux valve by 0,35units
12
10
8
%
devu.tlon
co~~
4
2
o
-2
o
100
200
( l~ C'P'Cit"M'>Ca
Time (.ec)
1&
~
o~
300
11II ~ ..-~
400
•••.•••.
.,.,
Figure 4.7 Comparison of composition via capacitance, temperature and density
measurements for a change in the reflux valve by 0,45units
4.6 Detennining dynamic process parameters for the column
In order to control the top product composition of the distillation column,
dynamic models relating process outputs to various inputs were obtained from the
column. Thiswas done by means of step tests. The dynamic model parameters ie
steady state gains, process time constants and dead times were determined from
the response curves. Two important disturbances were used namely, change in the
power supplied to the reboiler and change in the position of the reflux valve. The
responses obtained as a result of the changes were assumed to be first order. This
is because in applying the change from the thyristor for example, each plate of
the column can be assumed to add a lag, resulting in a
higher
order
system
(definitely greater than a second order system). Thishigher order system can in turn
be considered as a first order system with dead time.
4.6.1 Model responses with change in the position of the reflux valve in both the
measurement systems.
0.7
Position of
refluxvalve
0.6
0.5 -t---------'
0.41----o
100
-----1
200
Time (seconds)
300
A reflux valve change of 15 % was applied, as shown in Figure 4.8 (a) to
obtain a dynamic model for the effect of this on top product composition.
responses were assumed to be first order by both temperature
The
and capacitance
measurements, as shown in Figures4.8(b) and 4.8(c). The first order discrete models
using regression analysis( Stephanoupoulos,
1984)for both the methods were:
Temperature method( Figure 4.8 (b)): Yn = 0,96* Yn-l +0, 12* mn-1
Capacitance
method( Figure 4.8 (c)): Yn = 0,96* Yn-l +0, 13* mn-1
These responses were filtered in Matlab (procedure isdescribed in appendix
III) using single exponential smoothing (Seborg , Edgar &Mellichamp, 1989). In this
method the equation 4.4 was used:
Yn
= a * xn + ( J -
a)
* Y n- J
The values of afor the filtered values of both temperature and capacitance
methods were 0,105 and 0,109 respectively, the correlation coefficients between
the filtered and unfiltered readings were 0,982, and 0,981 respectively.
Since the responses were assumed to be first order, Figures 4.3(a) and (b) are
used to obtain the dynamic model parameters. The responses indicated a change
in the composition of 4,2 and 4,7 respectively, besides different time constants and
dead times, also shown in Table 4.5.
Table 4.5 Model parameters of the column
after applying a change in the reflux valve
position
Temperature
measurements
Capacitance
Measurements
Kp = 28 mass %/
'tp=
55 see
'td
=17see
'td
= 25see
fractional valve opening
Kp = 31,33 mass
%/ fractional valve
opening
'tp
=70see
%
DtNiation
in
3
composition
'li8
temper8ture2
methods
• =55sec
200
300
Figure 4.8 (b) Model response of top product composition with a change in 0,15units in
the position of the reflux valve by temperature measurements.
%
4
Deviation in
composition
0
via
3
capacitance
I· = "78 see
20(Y
300
Figure 4.8 (c) Model response of top product composition with a change in 0,15units in
the position of the reflux valve by capacitance measurements.
The gain of the process was obtained as follows using the method described in
section 4.3:
Kp= 4,2/0,15= 28 %mass
1 fractional
Kp= 4,7/0,15= 31,33 %mass/Fractional
valve opening (Temperature
measurements)
valve opening (Capacitance
measurements)
4.6.2 Model Responses with change in the heat input to the reboiler.
Step changes to the reboiler by applying a 50%increase in the heat input
as shown in Figure 4.9 (a), resulted in first order responsesgiven in Figure 4.9(b) and
Figure 4.9(c) by the respective measuring methods.
The composition
capacitance
changes
in the top
product
by temperature
and
methods were -1,25 and -1,37 and the corresponding process time
constants and dead times are shown in Figures4.9 (b) and 4.9(c) and Table 4.7.
The first order discrete models given by regression analysis( Stephanoupoulos,
1984)forboth methods are as follows:
= 0,98* Yn-l +0,001* mn-1
Yn = 0,97* Yn-l +0,001* mn-J
Temperature method: Yn
Capacitance
method:
Theseresponseswere filtered in Matlab (procedure isdescribed in appendix
III) using single exponential smoothing(Seborg, Edgar &Mellichamp,
method makes use of equation 4.4. The values of a used to obtain
of temperature and capacitance
1989). This
filtered values
methods were 0,2and 0,23respectively, and the
correlation coefficients between the filtered and unfiltered readings were 0,983
and 0,986 respectively.
Change
in the
thyrsitoT 511"
heat
input
100
Time (seconds)
~ = -1,25/50 *100 = -2,5 %mass/%thyristor input( Temperature measurement)
~ = -1,37/50 *100 = -2,75 % mass /
Temperature
measurements
% thyristor input( Capacitance measurement)
~=-2,5mass
'tp
=30 see
'td
= 12 see
'tp
= 35 see
'td
= 14 see
% / % thyristor heat
input
Capacitance
Measurements
~= -2,9 mass
% / % thyristor heat
input
% deviation in
0
composition
'lia
temp8l"ature
measurements
-1.5
'f
o
=
38 see
p
100
Figure 4.9 (b) Model response of top product composition with 50 % change in the
thyristor by temperature measurements.
%
deviation in
composition
0
via
capacitance
-0.5
'1
= '14
ee
'1 =35sec
50
p
100
Figure 4.9 (c)Model response of top product composition with 50 % change in the
thyristor by capacitance measurements.
4.7 Closed-loop control of the column using the capacitance cell.
Experiments with
were
conducted
closed loop
control
of top
on the column usingthe capacitance
these experiments being to confirm whether
satisfactorily
under
closed
controllers were tuned
composition
the
product composition
and
the capacitance
loop conditions. In
a 1% change
cell, the purpose of
cell works
order to confirm this,
in the setpoint ie changing the
from
76,2%to 77,2%, was applied. The reflux valve was used as
manipulated
variable in one series of experiments and the the boil-up
rate( thyrsitor) as the manipulated variable in another seriesof experiments and
the responseswere monitored. The parameters of the controller by using the
reflux valve and the thyristorin separate setsof experiments are given below in
Table 4.8:
Table 4.8 Controller parameters using both Reflux valve position and thyristor as final
control elements.
Reflux valve position
Kc = 0,05755 fractional valve
opening/
Thyristor
% thyristor input/
manipulated
action
= 109,821sec
% mass
~= -0,8055
A PI controller
"t"r
"t"r
=47,346sec
% mass
was applied and the responses for both the
variables, are shown in Figures4.10 and 4.11.
% deviation
in
composition
Figure 4.10. Closed loop Response of the column for 1 % change in the setpoint of the top product
composition using the reflux valve as the final control element and capacitance measurements.
J
dlNlation
in
Composition
Figure 4.11. Closed loop Response of the column for 1 % change in the setpoint of the top product
composition using the thyristor as the final control element and capacitance measurements.
Chapter FIVE
Discussion of Results
The resultspresented in chapter four will be discussed with regard to the
repeatability, accuracy, and reliability of measurements of the capacitance cell
5.1 Analysis of the capacitance cell readings
The capacitance
90% ethanol
and
cell was calibrated using compositions of 75%,85%,and
water. Each experiment was repeated
particular composition,
at three different temperatures
40°C. The mV readings obtained
from
10 times with a
namely 20°C, 30 °c,
10 experiments were converted to
composition using equation 4.2 and the data is presented in appendix I, Tables
1,2,3.
In
order to ascertain the
repeatability
of the results obtained from
the calibration process use of the theory of normal distribution was made.
Figure5.1 shows a typical
normal distribution curve. According to this theory,
there isabout 70 % probability that data lies between
1l-0
and IJ+0.
Similarly there
is
95 % chance that data lies between 1J-2a and 1J+2a
(Kirkup.L1994). Thismethod is very usefulin analyzing experimental data, in as
much as the smaller the
standard
deviation,
the better the repeatability of
a reading.
The calculated
experimental data
three
values
have
of
mean
and
standard
deviation
of the
been presented in Tables 4.1-4.3.It follows that for the
compositions 75%, 85%and 90%, at
the three given temperatures the
maximum value of standard deviation is0,55which isa good enough indication
of repeatability for all practical purposes.
5.2. Accuracy of the capacitance cell
The capacitance cell should provide accurate readings that can be used
for effective control of the column.
Therefore to check the accuracy,
position were applied
from the steady state
several changes in the reflux valve
namely 0,25,0,35and 0,45 (fractional valve opening),
operating
conditions of the column
and
values of
composition were obtained for temperature, capacitance and density method.
Figures4.5-4.7 showed the resultsof these tests. From the data obtained for the
reflux valve position of 0,45 for example and using equation 4.3, accuracy is
calculated
in respect of capacitance
details of which
temperature
methods the
are given in appendix II.
The above stated tables
standard
and
deviation
show a statistically calculated
of 98,57 and
mean and
0,795 respectively, for accuracy of the
capacitance derived compositions, whereas the corresponding figures of the
temperature derived
composition is 98,121 and 1,21 respectively. The mean
in the capacitance derived 'methods is closer to 100%accuracy of the density
method, and also the standard deviation
is smaller for capacitance
derived
composition compared to temperature methods, confirming that the capacitance method has given more accurate readings.
5.3. Dynamic responses of the column
To
determine
whether the measurement
capacitance cell had any negative
between top product composition
influence
and
of composition
via the
upon the dynamic relation
an input change, step disturbances
in both the position of the reflux valve ( magnitude of 0,15, fractional
opening) and
input)
were
valve
heat added to the reboiler, (magnitude of 50 %, thyristor heat
applied
to determine the dynamic
Measurements with both temperature and
models for the column.
capacitance
techniques
were
used, and the response of the column for these disturbances was observed as
shown in Figures 4.8(a,b,c)- 4.9 (a,b,c) and the process constants are given in
Tables 4.5 and 4.6.
The two techniques provided nearly the same dynamic data. The temperature measurements were performed in the top plate
of the distillation column
due to reasons explained in section 2.4. and the capacitance
cell measurements
between the accumulator and the condenser. The capacitance
cell
provided
an accurately enough reading at the point of measurement since in the installed
position the reading which has already been shown, is accurate.
Models for both the measurement techniques are provided in equations
5.1 and 5.2 below. Thesemodels
the process ie response of top
be useful in obtaining
composition.
will not only determine
product
controller
composition
the behaviour of
over time
but also will
parameters in controlling the top product
In either case the sensingelement isalways in contact with the
medium for which the composition is being measured.
28e-17s
Fractional
55s+1
(:~)
-25e, 12s
=
[
valve Opening]
%Thyristor
input
.
30s+1
Models obtained by capacitance measurements:
31.33e-17s
.
(:~)
=
Fractional
70s+ 1
ge-12s
-2 ,
[
valve Opening]
% Thyristor
input
35s+ 1
Closed loop control was performed on the column using the capacitance
cell, in conjunction with the reflux valve and thyristor as final control elements to
control
top
product
change in setpoint of
composition. A PI controller was tuned and
a 1%
top product composition was applied. The response was
monitored using the two final control elements in separate set of experiments,
also given in Figures4.10-4.11.
5.5 Dynamic lag
The dynamics
the larger the
time
of a
measuring device plays a major role on the process,
constant
or the time required for it to respond the slower is
the controlling action. The dynamic lag was tested by five experiments in which
composition of the feed to the capacitance
cell was changed
from 75% to 85 %
ethanol. The response times for the five experiments were also given in Table 4.5.
The largest
response
time was 1,3 seconds.
The dynamic lag obtained
corresponding to this value was 0,4 seconds, as shown in Figure 4.4 and is
expressed by the transfer function 5.3
1
G(s)=-O,4s+ 1
The effect that the dynamic lag has on the process is 0,4/70*100
is the time constant for reflux valve change)
= 0,57 (35 seconds
and 0,4/35* 100 = 1,4 % ( 70 seconds is
the time constant for thyristor heat input change ),which is negligible, showing that
the capacitance
cell does not significantly affect the process dynamics.
5.6 Ease of Operation
The capacitance
measuring device
is a cheap
and simple piece of
equipment, which is easy to fabricate, install and operate in conjunction with the
electronic circuitry of which it forms part. It is also convenient for use on the
column.
5.7Precautions and limitations
Effect of contamination:
There is a possibility of suspended particles in the flow stream to form a
deposit on the capacitor
plates which may cause variation from the
original settings. Thismay be eliminated by incorporating
microfilters before the inlet to the capacitance
temperature
suitable
cell. In case of
method the sensor is a thermocouple
tray of the column, and it is unlikely to be affected
placed in the top
by contamination
in the fluid.
Calibration:
Like in any instrumentation capacitance
cell involves calibration.
Although it appears lengthy during the initial stages, the process of
calibration is easy and straightforward.
Dielectric property:
The capacitance
cell can be used to determine composition of only
dielectric fluids and cannot be used to determine the composition of
reactive mixtures.
Multicomponent
mixtures:
The capacitance
cell can be used in determining composition of
multi-component
mixtures, provided that while compositions of two
components
remain fixed.
vary, the composition of the other components
should
Chapter Six
Chapter SIX
Conclusions and Recommendations
Thisinvestigation was intended to develop and test a capacitance cell for
top product
composition measurement and control in a distillation column and
to compare its performance with the presently used composition measurement
techniques
such
as
chromatographs,
infrared
analyzers and inferred
measurements by temperature. Likein any other measurement technique it was
necessary to
observe
the repeatability, accuracy and performance of the
capacitance cellon column control.
The capacitance
cell
was tested for repeatable readings during the
calibration procedure. Resultsobtained in a seriesof ten experiments were found
to
be normally distributed with a mean and the standard deviation as shown
in Tables 4.1-4.3.The standard deviation values as observed from the tables
were not greater than 0,55 which isa good enough indication for all practical
purposes,confirming that the capacitance cell gave good repeatability.
Test results to determine the accuracy of capacitance and temperature
methods on the column
more accurate
showed
that
the
capacitance
measurements of composition
cell
provided
than those obtained via
temperature method, suggesting its advantageous use on the column.
Open
loop
tests were
measurements by temperature
conducted
and
influence the capacitance cell has on
on the column to compare the
capacitance
the
relation
and also to observe the
between
top product
composition and an input change. These experiments showed that although
the capacitance cell readings deviated from temperature measurements due
to its positioning on the column, measurements via capacitance were found to
be advantageous due to their direct and accurate measurements.
During
the
closed
loop tests,it was observed that the capacitance
6.2
Chapter Six
cell proved to be effective
in
measuring
and
controlling the top product
composition.
The capacitance
binary
cell can be used for measuring composition of any
fluid mixture that has dielectric
properties but cannot
measuring compositions of reactive mixtures.It can
be used for
be used in determining
composition of multi-component mixtures,provided that while compositions of
two components vary the other components would remain fixed.
The capacitance
cell iscompact and portable which enables it to be
very convenient to incorporate in the control system.The probability of having
suspended particles
in the
flow stream to form a deposit on the capacitor
plates is likely to cause variation of calibration values from the original settings.
This may be eliminated by incorporating suitable microfilters before the inlet to
the capacitance cell.
As is common
needs accurate
practice
calibration.
stages, the process of
in
instrumentation the
capacitance cell
Although it appears lengthy during the initial
calibration
is easy
and
straightforward and
does not pose any problem.
While
that
the
recommending
electronics
improvements to the device it issuggested
on
to compensate for ambient
the
instrument
temperature changes. The improvements should
take thisinto account and provide for temperature
temperature
dependent
be redesigned to be able
components
compensation of typically
such as transistorsand oscillatorsthat
deviate under different ambient conditions.
The capacitance
controlling
choice
top
than
cell
proved to be a useful device in measuring and
product composition in distillation column, and makes a better
other methods. It also offers scope for further development and
applications in industrialscale plants.
Appendix-I
C
Exptl
Expt2
Expt3
Expt4
Expt5
Expt6
Expt7
Expt8
Expt9
ExptlO
75%
75,03
75,03
74,56
74,09
75,5
75,97
74,56
75,5
75,03
75,03
85%
84,9
84,43
84,9
85,37
85,37
84,43
84,9
85,37
84,9
84,43
90%
90,07
89,6
90,07
90,54
89,6
90,07
90,54
90,07
91,01
89,13
C
Exptl
Expt2
Expt3
Expt4
Expt5
Expt6
Expt7
Expt8
Expt9
ExptlO
75%
75,22
75,69
75,22
74,75
75,69
74.75
75.22
74,28
75,22
76,16
85%
85,09
85,56
84,62
85,09
85,56
84,62
85,09
84,15
86,03
85,09
90%
89,79
90,73
90,26
88,85
89,32
89,79
89,79
89,32
90,26
89,79
C
Exptl
Expt2
Expt3
Expt4
Expt5
Expt6
Expt7
Expt8
Expt9
ExptlO
75%
75,41
75,47
74,94
74,94
74,47
75,41
75,88
74
74,94
74,94
85%
84.81
84,34
85,75
85,28
84,87
85,75
85,28
84,81
84,34
84,87
90%
89,98
90,45
89,98
90,45
89,51
89,98
90,02
89,51
89,04
89,98
Appendix-n
Table 1. Sample data of 10 readings for a fractional change in reflux valve position of
0,45 by capacitance measurements.
0
50
100
150
200
250
300
350
400
450
500
77,2
76.2
78,4
79,7
81
82,1
83,2
83,7
84,9
85,9
88,2
C(density)
76,2
76,2
77,6
79,4
80,3
81,4
81,8
82,4
83,2
83,8
85,8
Ac%
98,03
100
98,97
99,62
99,13
99,14
98,29
98,42
97,96
97,45
97,2
Time
(see)
C(capacitance)
Table 2. Sample data of 10 readings for a fractional change in reflux valve position of
0,45 by temperature measurements.
Time (see)
0
50
100
150
200
250
300
350
400
450
500
C(temper-
76
76,1
75,3
76,9
77,6
79,2
79,3
81
82,2
82,S
85,3
C(density)
76,2
76,2
77,6
79,4
80,3
81,4
81,8
82,4
83,2
83,8
85,8
Ac%
99,73
99,86
97,03
96,85
96,63
97,3
98,95
98,3
98,8
98,45
99,41
ature)
Appendix-m
Commissioning
and use of the capacitance cell on the column .
. Ensurethat the computer and the interface between the computer and
the
column are switched off (Gericke,1992), (Van Niekerk, 1995).
. Ensurethat
1.The liquid level in the heating unit isaligned with the heating
element.
2. The liquid level in the supply drum isaligned with the heating
element.
If not - Do
not
switch the trip switch of the heating element on at the
control panel. Firstuse the control/master/executive
program and the
pumps to bring the liquids to the desired levels.
Ensurethat - There isenough liquid in the storage drum. If not use the pressure
release pipe
on the top of the storage
more ethanol.
Remember
water also evaporates
to
drum
periodically
and
add
plastic
pipe to add
water, because
the
from the system, but not at the same rate as the
ethanol.
Switch on all the switches on the control panel.
Switch on thyristor and push the <START>
button.
Turn the
air pressuresupply tap on and then turn on the air pressureto the
supply drum( NB-inthis order and not the reverse)
Turnon the cooling
tap
and do so until the
tap stops making a noise.
Switch the computer on.
Begin the program BEHEER.
Switch the interface on .
Set the valves to O.( use the F3 (valves) option on the menu of the program)
Set the thyristor to 100 %.
After 20 minutes the liquids on all the plates will start to bubble and the
vapour will flow to the condenser drum.
Lock the
single loop controllers which control the levels in the reboiler and
the reflux and the feedflowcontrol
( use F1 (control loop) option on the
menu of the program).
Use the steady
Chapter
state operating
conditions of the column (mentioned in
four, Section 4.1).
Wait for the system to reach
steady
state.( It is expected to take
+ 70
minutes)
Ensurethat - The liquid circulates between the storage drum and the feed
drum. if not, Switch the pump off after 30 seconds so that the air bubbles
which have formed
can
be expelled.
Usage of Program
.TheProgram on the hard drive
.Thecontrol program BEHEER
isin C:\DISTILor C:\SRINU
.Thedata isstored in C:\DISTIL\DATASTOR.
.The control loop
parameters can be adjusted by changing the file
C:\DISTIL\SETUP.oAT
.Thevalues of the composition filter can be altered by changing the file
FILTER.oAT.
Application of the Capacitance
.The capacitance
condenser
the
is placed
between
the
accumulator
and the
of the column .
.Readings of the
and
cell
cell
computer
capacitance
cell can obtained as soon as the interface
is switched on. A red light isobserved on the top of
the cell, indicating that it isready for operation .
.Program on the hard drive that is used to obtain composition readings from
the capacitance
cell isc:\Srinu\capa.pas.
From the Turbo Pascal program procedure
. Take the mV readings from the capacitance
cell. Thesereadings
are taken from channell 0 of the pc30 card .
.Takes the
capacitance
temperature
readings in
cell. This is obtained
the
from
flow stream
through the
the thermocouple 3 of the pc73
card .
.Composition is obtained from the main program relation between
the
mV and temperature readings.
.Open loop tests are conducted using the capacitance
cell as follows:
.Set up the column to its operating conditions,
.Settingsof the
reflux valve
and
the thyristor are changed in
c:\Srinu\beheer.
.Composition readings are obtained from c:\srinu\capa.pas
based
on these changes .
.Closed loop control on the column using the capacitance
cell isachieved
as follows:
. Forthe reflux valve as the final control element the program
C:\Srinu\capal.pas
is used.
Thisprogram consistsof
.C:\Srinu\pc66.pas
as a Turbo
Pascal unit in which
the reflux valve
settings are specified .
.C:\Srinu\capa.pas as a Turbo
Pascal
unit
in
which
composition
readings from the capacitance cell are obtained.
A PIcontroller algorithm
as a main program relating composition and
reflux valve position. This program makes use of the above mentioned
Turbo Pascal units. In it also given the controller parameters, ie controller
gain and integral time
.From thyristor as the final control element the
program
C:\Srinu\capa2.pas is used.
Thisprogram consistsof
.C:\Srinu\pc66.pas
as the
Turbo Pascal unit in which
the
thyristor
settings are specified .
. C:\Srinu\capa.pas
readings
is used as a Turbo Pascal unit in which composition
from the
capacitance
cell
are
obtained .
.A PIcontroller algorithm as a main program relating composition and
thyristor. This program
makes use of the
above mentioned turbo
pascal units. In it also given the controller parameters, ie controller gain
and integral time
Filtering Data in Matlab
The following procedure is undertaken using Matlab to filter an unfiltered data.
· Run the program Matlab.
· load the unfiltered data from C:\Srinu\unfiltered.dat
.
· Activate "Simulink" in Matlab.
· Three blocks are chosen in this program
.Thefirst block usesisa "workspace" in which the unfiltered.dat issaved
as unfiltered.mat
.Thesecond block contains the "filter", where the filtering parameter a is
appropriately adjusted .
.The third block is the output block in which the filtered values are
obtained.
· The filtered data then obtained will be analyzed.
Shutdown procedure of the experimental apparatus
Switch off all the switches on the control panel.
Switch off thyristor and push the <STOP>button.
Turn off the air pressure to the
supply tap.
Turn off the cooling tap.
Switch the interface off.
Exitthe program BEHEER.
Switch the computer off.
supply drum and turn off the air pressure
List of References
1. Akerlof, G. (1932), "Dielectric
American
2.Cheng,
Chemical
D. (1989)
constants
of
liquid
mixtures",
Society,
V 54 (11). pp - 4130-4131
Field and
Wave Electromagnetics,
Publishing Company.
Journal
of
Addison - Wesley
pp 123-125
3. Coulson, J.M, Richardson,
J.F & Sinnot, R.K (1983) Chemical Engineering
Design (Volume 6). Pergomom.
4. Eagle Electric (1992) UsermanualforPC73,
PC30, & PC66, Cape Town, South
Africa.
5. Gericke.J.(1992)"
beheersisteem
Die
implementering
op "n distillasieKolom
en evaluering
van "n gevorgerde
", M Eng dissertation,
University of
Pretoria.
6. International Critical Tablesof Numerical Data
for
PHYSICS,
CHEMISTRY
AND TECHNOLOGY(1930),Vol VII, Mc- Graw Hill Company.
7.Jannsen,
P.W.M. (1986), "Bilinear
Thesis in Chemical
Christchurch,
Identification
& Process Engineering,
of a distillation
column",Ph.D.
University of Canterbury,
New Zealand.
8. Kip, A. F. (1965) Fundamentals of Electricity and Magnetism, Second
Mc Graw Hill, New York. pp 47-48
Edition,
10. Hougen, O.A, Watson, K.M, Ragatz, R.A (1958) Chemical Process Principles,
John Wiley and sons, Inc.pp 56- 59
11. Horowitz ,M. ( 1989), The Art of Electronics, Second edition. W Cambridge
University Press.pp 297-298, pp 231-232.
12. Manahan, S.E.(1986) Quantitative Chemical Analysis, Brookes/Cole
publishing company.
15. Pecksok, R.C. & Shields L.D. (1986) Modem Methods of Chemical
Analysis,
John Wiley and Sons.
16. Poole, C.F &Poole, S.K.( 1991) Chromatography Today, Elsevier Science
Publishers.
17. Rhea, R.E.( 1990), Oscillator Design and Computer Simulation Prentice Hall, INC. pp 23-155
18. Perry, R.H & Green, G. (1987) Chemical Engineers Handbook, Me-Grow-Hill
International.
20. Sandler,S.1.(1989) Chemical
and Engineering thermodynamics, Second
edition, Wiley series in chemical engineering,
pp 321-337.
22. Shinskey, F.G.(1988) Processcontrol systems- Application
design and tuning,
Mc- Grow Hill Inc. pp 431-445
23. Smith, J.M. and
Van
Ness. H.C. (1987) Introduction
to Chemical
Engineering thermodynamics, fourth edition, Mc Grow Hill, New York.
24. Stanley, B. H. (1985) Experimentsin Electric Circuits,Second edition, Bell
and Howell Company. pp 129-180
25. Stanton, BD.(1986)"
towers";
Designing
Front-end
control
schemes
for distillation
Chemical Engineering, Vol.24/November /pp. 87-92.
26. Stephanopoulos.G
(1984) Chemical
Process control, An introduction to
theory and practise, Prentice-Hall International, Inc.
27. Svrceck/W.Y. (1967) "Dynamic response of a binary distillation column "/ PhD
Thesis,Department
of Chemical and Petroleum Engineering, University of
Alberta, Edmonton. pp 57-67.
28. Swan ,T.(1988), Mastering TurboPascal 4.0 / Second edition, Hayden
Books.
29. Van
Niekerk. F.J. ( 1995) "Die
internemodelbeheerer
implementering
van
In Multiverranderlike
op In distillasiekolom", MEng dissertation, University of
Pretoria.
30. Walker ,C.S.(1990) Capacitance,
House. pp 15-17
Inductance,
Cross Talk Analysis,Artech
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