“VAPOUR LIQUID EQUILLIBRIUM MODELING USING UNIFAC GROUP CONTRIBUTION METHOD AND ITS

“VAPOUR LIQUID EQUILLIBRIUM MODELING USING UNIFAC GROUP CONTRIBUTION METHOD AND ITS
A
THESIS ON
“VAPOUR LIQUID EQUILLIBRIUM MODELING USING
UNIFAC GROUP CONTRIBUTION METHOD AND ITS
APPLICATION IN DISTILLATION COLUMN DESIGN AND
STEADY STATE SIMULATION”
A Report Submitted In Partial Fulfilment of the Requirements for the Degree Of
Bachelor of Technology (Chemical Engineering)
SUBMITTED BY
MANAGOBINDA BEHERA
Roll No. : 10600031
UNDER THE GUIDANCE OF
Prof. (Dr.) M Kundu
Department of Chemical Engineering
National Institute of Technology, Rourkela
May, 2010
National Institute of Technology
Rourkela
CERTIFICATE
This is to certify that the thesis entitled, “vapour liquid equilibrium modeling using
UNIFAC group contribution method and its application in distillation column design
and steady state simulation” submitted by Managobinda Behera in partial fulfilments for
the requirements for the award of Bachelor of Technology Degree in Chemical Engineering
at National Institute of Technology, Rourkela (Deemed University) is an authentic work
carried out by him under my supervision and guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to any
other University / Institute for the award of any Degree or Diploma.
Date:
Rourkela
[Dr. (Mrs.) Madhushree Kundu]
Dept. of Chemical Engineering,
National Institute of Technology
Rourkela - 769008, Orissa
ii
ACKNOWLEDGEMENT
I would like to make my deepest appreciation and gratitude to Dr. (Mrs) M Kundu for her
valuable guidance, constructive criticism and encouragement during every stage of this
project. I am totally indebted to her for providing me the right guidance to work on an
emerging area of chemical engineering. She was very supportive throughout the project and
was always ready to help.
Thanks to Dr. R K Singh and Dr. H M Jena for being uniformly excellent advisors. They
were always very helpful and provided broad ideas.
I owe a depth of gratitude to Prof. S. K. Agarwal, H.O.D, Department of Chemical
Engineering, for all the facilities provided during the course of my tenure.
Lastly I would like to thank my family members for their constant support, encouragement
and good wishes, without which this thesis wouldn’t have been possible.
Date:
MANAGOBINDA BEHERA
Rourkela
Dept. of Chemical Engineering,
National Institute of Technology, Rourkela – 8
iii
ABSTRACT
For efficient design of distillation equipment or any other separation processes which are
diffusional in nature requires quantitative understanding of vapour liquid equilibria. In VLE
phases are expressed through vapour phase fugacity coefficients and the liquid phase activity
coefficients. At low or modest pressures fugacity coefficient can be estimated easily for very
simple mixtures or ideal solutions, but for non-ideal mixtures, estimation of liquid phase
activity coefficient is quite difficult. Experimental mixture data are required to calculate
activity coefficient. Since the variety of chemical species is separated out in chemical process
industry and it is not necessary to every physicochemical and VLE experimental data are
available in open database. In this regard researchers developed a new ‘group contribution
model which is able to predict the VLE data. The concept of group contribution method
provide a correlation which correlate limited experimental data in such a way with
confidence of activity coefficients of those mixtures where little or experimental data are not
available. In this concept we have to know only about the each functional group of each
molecule. Each molecule is considered as the sum of the functional groups which constituent
that molecule; the thermodynamic properties of a solution are then correlated in terms of the
functional groups which comprise the mixture. The particular promising method for
calculating activity coefficient from group contributions method is provided by UNIFAC
(universal quasi chemical functional group activity coefficient model). This method is a
consequence of a model for activity coefficients called UNIQUAC (universal quasi
chemical). The word UNIFAC stands for UNIQUAC functional group activity coefficients.
The activity coefficients of binary mixtures were successfully calculated
by using UNIFAC model. And using these activity coefficients the design of distillation
column was done for the separation of these binary mixtures.
iv
CONTENTS
Topic
Page No.
Abstract
iv
List of figure
vii
List of table
viii
Nomenclature
ix
CHAPTER 1: INTRODUCTION 1
1
1.1 VAPOUR LIQUID EQUILLIBRIA
2
1.2 ACTIVITY COEFFICIENT
3
1.2.1 Debye-hückel equation
3
1.2.2 Davies equation
4
1.2.3 Non-random two liquid model (NRTL)
4
1.2.4 Uniquac model
5
1.2.5 UNIFAC model
CHAPTER 2: THERMODYNAMICS AND PREVIOUS WORK
2.1 ORIGIN AND RANGE OF APPLICABILITY OF THE
6
7
UNIFAC METHOD
2.2 ADVANTAGES AND DISADVANTAGES (OF UNIFAC)
7
2.3 APPLICATION OF UNIFAC GROUP CONTRIBUTION
8
METHOD
2.4 UNIFAC CORRELATION (group contribution method)
8
2.5 THE GROUP INTERACTION PARAMETERS
9
2.6 THE UNIFAC MODEL
9
CHAPTER3: VLE CALCULATION USING UNIFAC
13
3.1 CASE -1(A): diethyl ketone (1) and n-hexane(2)
14
3.2 CASE -1(B): n-hexane (1) and diethyl ketone (2)
16
3.3 COMPARISION BETWEEN EXPERIMENTAL VALUE AND
18
THEORITICAL VALUES
v
CHAPTER 4: SIMULATION OF DISTILLATIO COLUMN
19
4.1 EQUATIONS FOR DISTILLATION COLUMN DE
20
4.2 GENERAL RELATIONS WITH ENTHALPY BALANC
22
4.3 NEWTON-RAPHSON ITERATION
23
4.4 DISADVANTAGES OF NEWTON-RAPHSON METHOD
24
4.5 STEADY STATE SIMULATION OF DISTILLATION COLUMN
PROCEDURE
25
4.6 PROBLEM STATEMENT
26
4.6.1 DESIGN OF DISTILLATION COLUMN ASSUMING NO
TEMPERATURE VARIANCE
27
4.6.2 DESIGN OF DISTILLATION COLUMN ASSUMING IDEAL
CASE WITH TEMPERATURE VARIANCE
29
4.6.3 DESIGN OF DISTILLATION COLUMN ASSUMING
NON-IDEALWITH TEMPERATURE VARIANCE
CHAPTER 5: CONCLUSION AND FUTURE RECOMMENDATION
31
32
5.1 Conclusion
33
5.2 Future recommendation
33
CHAPTER 6: REFERENCES
34
vi
LIST OF FIGURES
Fig No.
3.1
Title
Page No.
Comparison between experimental and theoretical values
of activity coefficient (Diethyl ketone(1) and n-hexane(2))
3.2
18
Comparison between experimental and theoretical values
of activity coefficient (n-hexane(1) and Diethyl ketone (2))
18
4. 1
Distillation column configuration
14
4. 2
nth stage of the distillation column
15
4.3
Simple distillation column
27
vii
LIST OF TABLES
Table No.
Contents
Page No.
3.1
VLE data for di ethyl ketone (1) and n-hexane (2) at 338.15k
21
3.2
Group size (Rk)and group surface area (Qk)
22
3.3
Activity coefficient of case 1(A) using UNIFAC
22
3.4
VLE data for n-hexane (1) and di ethyl ketone (2) at 338.15k
23
3.5
Activity coefficient of case 1(B) using unifac
24
4.1
Antoine Constants for acetone and n-Pentane
27
4.2
Results for temperature independent distillation column design
29
4.3
The assumed initial values of the independent values
31
4.4
Results for ideal distillation column design
31
4.5
Results for the non ideal distillation column design
32
viii
LIST OF SYMBOLS
SYMBOLS
MEANING
H
vapour phase enthalpy
h
liquid phase enthalpy
Hf
feed enthalpy
V
total vapour flow
V
component vapour flow
L
total liquid flow
L
component liquid flow
F
total feed
f
component feed
SL
liquid side stream
SV
vapour side stream.
anm
UNIFAC binary interaction
parameter
Kn,i
equilibrium ratio of component i on
stage n
Qk
group area parameter of group k
Rk
group volume parameter of group k
xi
mole fraction of component i in
liquid phase
yi =
mole fraction of component i in vapour
phase
ix
SYMBOLS
MEANING
Activity coefficient of the component i
in the mixture
Φ
Fugacity coefficient of the component i
in the mixture
Fugacity of the pure component i
P
total pressure
p is
saturation vapour pressur of
component i
vi
molar volume liquid
T
temperature
γC
combinatorial activity coefficient of
component i
γR
residual activity coefficient of
component i
θi
molecular surface area fraction
Φi
molecular volume fraction
k(i)
number of groups of kind k in molecular
species i
ri
molecular van der waals volume
qi
molecular surface area
Vk
van der waals group volume
Ak
Γk
van der waals group surface area
group residual activity coefficient
x
SYMBOLS
MEANING
Γk(i)
the residual activity coefficient of group
k in a reference solution containing only
Molecules of type i
Xm
fraction of group m in mixture;
Ψ
UNIFAC parameter
murphee stage efficiency
ηn,i
Q group area parameter for group k
xi
CHAPTER-1
INTRODUCTION
1
INTRODUTION
1.1
Vapour Liquid Equillibria
Vapour-liquid equilibrium (VLE), is a condition where a liquid and its vapour (gas phase)
are in equilibrium with each other, a condition or state where the rate of evaporation (liquid
converting to vapour) equals the rate of condensation (vapour converting to liquid) on a
molecular level such that there is no net vapour-liquid inter-conversion. Although in theory
equilibrium takes a very long time to reach, such equilibrium is practically reached in a
relatively closed location if the liquid and its vapour are allowed to stand in contact with each
other for a while with no interference or only gradual interference from the outside.
In process design, the required phase equilibrium information is commonly expressed by
K values.
=
(1.1)
Where yi, is the mole fraction of component i in the vapour phase and xi, is the mole
fraction of component i in the liquid phase. Ki is the equilibrium constant for the component i.
Using thermodynamics
=
(1.2)
Where , is the liquid-phase activity coefficient
is the vapour-phase fugacity coefficient,
and P is the total pressure of the mixture. For condensable components as considered
here,
is the fugacity of pure liquid i at system temperature T and pressure P. It is
calculated from [Prausnitz, 1969]
=
Where, for pure liquid i,
(1.3)
is the saturation (vapour) pressure,
is the fugacity coefficient
at saturation, and vi, is the molar liquid volume, all at temperature T. Only pure- component
2
data are required to evaluate
. The fugacity coefficients
(in the mixture) and
(pure i at
saturation are found from vapour-phase volumetric properties. Normally, at the low pressures
considered here, these fugacity coefficients do not deviate much from unity. To determine K
factors,
the
most
difficult-to-estimate
quantity
is
the
activity
coefficient
.
1.2
Activity Coefficient
Activity coefficients may be measured experimentally or calculated theoretically, using
the Debye-Hückel equation or extensions such as Davies equation or specific ion interaction
theory (SIT) may also be used. Alternatively correlative methods such as UNIQUAC, NRTL
or UNIFAC may be employed, provided fitted component-specific or model parameters are
available.
1.2.1 Debye-Hückel equation
In order to calculate the activity of an ion in a solution, one must know the concentration and
the activity coefficient,
. The activity of some ion species C, ac, is equal to dimensionless
measure of the concentration of C, [C] multiplied by the activity coefficient of C,
[P.
Debye and E. Hückel (1923)].
ac = γ
(1.4)
[C0] represents the concentration of the chosen standard state, e.g. 1 mol/kg if we work in
molality.
3
1.2.2 Davies equation
The Davies equation is an empirical extension of the Debye–Hückel equation which can be
used to calculate activity coefficients of electrolyte solutions at relatively high concentrations.
The equation was refined by fitting to experimental data. The final form of the equation gives
the mean molal activity coefficient,
, of an electrolyte which dissociates into ions having
charges z1 and z2 as a function of ionic strength, I [Davies 1962].
-log f ± = 0.5 z1z2 (
- 0.30 I)
(1.5)
The second term, 0.30 I, goes to zero as the ionic strength goes to zero, so the equation
reduces to the Debye–Hückel equation at low concentration. However, as concentration
increases, the second term becomes increasingly important, so the Davies equation can be
used for solutions too concentrated to allow the use of the Debye–Hückel equation. For 1:1
electrolytes the difference between measured values and those calculated with this equation is
about 2% of the value for 0.1 m solutions. The calculations become less precise for
electrolytes that dissociate into ions with higher charges. Further discrepancies will arise if
there is association between the ions, with the formation of ion-pairs, such as Mg2+SO42−.
1.2.3 Non-Random Two Liquid model (NRTL)
The Non-Random Two Liquid model (NRTL model) is an activity coefficient model that
correlates the activity coefficients γi of a compound i with its mole fractions xi in the
concerning liquid phase. It is frequently applied in the field of chemical engineering to
calculate phase equilibria. The concept of NRTL is based on the hypothesis of Wilson that
the local concentration around a molecule is different from the bulk concentration. This
difference is due to a difference between the interaction energy of the central molecule with
the molecules of its own kind and that with the molecules of the other kind. The energy
difference introduces also non-randomness at the local molecular level. The NRTL model
belongs to the so-called local composition models [Renon , Prausnitz 1968].
In the case of the description of a vapour liquid equilibria it is necessary to know
which saturated vapour pressure of the pure components was used and whether the gas phases
4
was treated as an ideal or a real gas. Accurate saturated vapour pressure values are important
in the determination or the description of an azeotrope. The gas fugacity coefficients are
mostly set to unity (ideal gas assumption), but vapour-liquid equilibria at high pressures (i.e.
> 10 bar) need an equation of state to calculate the gas fugacity coefficient for a real gas
description.
1.2.4 UNIQUAC model
UNIQUAC (UNIversal QUAsiChemical) is an activity coefficient model used in description
of phase equilibria [Abrams , Prausnitz 1975]. The model is a so-called lattice model and has
been derived from a first order approximation of interacting molecule surfaces in statistical
thermodynamics. The model is however not fully thermodynamically consistent due to its
two liquid mixture approach. In this approach the local concentration around one central
molecule is assumed to be independent from the local composition around another type of
molecule.
It has been shown that while the local compositions are correlated, ignoring this correlation
gives little effect on the correlation of activity coefficients [McDermott 1976]. Today the
UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquidsolid, liquid-liquid or liquid-vapour equilibrium). The UNIQUAC model also serves as the
basis of the development of the group contribution method UNIFAC, where molecules are
subdivided in atomic groups.
1.2.5 The UNIFAC model
The UNIFAC method is a semi-empirical system for the prediction of non-electrolyte activity
estimation in non-ideal mixtures. UNIFAC uses the functional groups present on the
molecules that make up the liquid mixture to calculate activity coefficients. By utilizing
interactions for each of the functional groups present on the molecules, as well as some
binary interaction coefficients, the activity of each of the solutions can be calculated.
So, main objective of my project work is the calculation of activity coefficient of the binary
mixture using UNIFAC model.
The calculated activity coefficient is compared with experimental activity coefficient and
these calculated activity coefficient is used for steady state simulation of distillation column.
5
CHAPTER-2
THERMODYNAMICS AND
PREVIOUS WORK
6
THERMODYNAMICS OF THE MODEL
2.1
Origin And Range Of Applicability Of The UNIFAC Method
A large part of chemical engineering design is concerned with separation operations.
Many of these are diffusional operations of the phase-contacting type, and distillation,
absorption, and extraction are the most common. For rational design of such separation
processes, we require quantitative information on phase equilibria in multi-component
mixtures. Satisfactory experimental equilibrium data are only rarely available for the
particular conditions of temperature, pressure, and composition required in a particular design
problem. It is therefore necessary to interpolate or extrapolate existing mixture data or, when
suitable data are lacking, to estimate the desired equilibria from some appropriate correlation.
A very useful correlation for this purpose, UNIFAC, was recently proposed. The UNIFAC
method was originally developed by Fredenslund [Fredenslund, Gmehling, Rasmussen
(1977)]. Later the method was revised and its range of applicability considerably extended.
The UNIFAC (UNIQUAC Functional Group Activity Coefficients) group-contribution
method is a reliable and fast method for predicting liquid-phase activity coefficients in nonelectrolyte, non-polymeric mixtures at low to moderate pressures and temperatures between
300 and 425 0K .It has become widely used in practical chemical engineering applications,
most notably in phase equilibrium calculations in cases where little or no relevant
experimental information is available.
2.2
Advantages And Disadvantages (of UNIFAC)
Advantages:
1. flexibility, because UNIFAC has a well founded basis for establishing group sizes and
shapes.
2. simplicity, because UNIFAC parameters are nearly independent of temperature for
the temperature range considered here.
7
3. large range of applicability, because UNIFAC parameters are now available for
considerable number of different functional groups.
Disadvantages
1. All components must be condensable.
2. The temperature range considered is typically 30-125 0C.
3. UNIFAC method does not presently apply to mixtures containing polymers.
4. It should rarely be applied to mixtures containing components with more than ten
functional groups.
2.3
Application of UNIFAC Group Contribution Method
The UNIFAC method is most successful. It has been used in many areas, for example;
2.4
(1)
To calculate vapour-liquid equilibria (VLE).
(2)
For calculating liquid-liquid equilibria,
(3)
For calculating solid-liquid equilibria,
(4)
For determining activities in polymer solutions,
(5)
For determining vapour pressures of pure components,
(6)
For determining flash points of solvent mixtures,
(7)
For determining solubility’s of gases,
(8)
For estimation of excess enthalpies.
UNIFAC Correlation (group contribution method)
A group contribution method uses the principle that some simple aspects of the structures
of chemical components are always the same in many different molecules. The smallest
common constituents are the atoms and the bonds. All organic components for example are
built of carbon, hydrogen, oxygen, nitrogen, halogens, and maybe sulphur. Together with a
single, a double, and a triple bond there are only ten atom types and three bond types to build
thousands, of components. The next slightly more complex building blocks of components
are functional groups which are themselves built of few atoms and bonds.
8
The large advantage of a group contribution method is that it enables systematic
interpolation and extrapolation of vapor-liquid equilibrium data simultaneously for many
chemically related mixtures. Most important, it provides a reasonable method for predicting
properties of mixtures where no mixture data at all are available. For such mixtures it is not
necessary to measure the intermolecular interactions because these can be calculated
whenever appropriate group interaction parameters are known. These, however, are found
from experimental data containing not the same molecules as those in the mixture of interest,
but containing the same groups. The main advantage, then, is a form of "molecular scale-up."
While there are many thousands of liquid non-electrolyte mixtures of interest in chemical
technology, these mixtures can be constituted from a much smaller (around 50 or 100)
number of functional groups. The UNIFAC correlation attempts to break down the problem
of predicting interactions between molecules by describing molecular interactions based upon
the functional groups attached to the molecule. This is done in order to reduce the sheer
number of binary interactions that would be needed to be measured to predict the state of the
system.
UNIFAC group contribution method is quite fast and accurate. This can be seen from the
graph between the experimental and the value obtained by unifac model.
2.5
The Group Interaction Parameters
All group contribution method is necessarily approximation because any group within a
molecule is not completely independent of the other groups within that molecule. But it is
precisely this independence which is essential basis of group contribution method. Inter
dependence of groups within a molecule is allowed.
Increasing distinction of groups
however, also increases the number of group interactions that must be characterized. At last,
if we carry group distinction to the limit we recover the individual molecules. In that event,
the advantage of the group contribution method is lost. Only judgement and experience must
tell how to define functional groups so as to achieve a compromise between accuracy of
prediction and engineering utility.
9
2.6
The UNIFAC Model
UNIFAC provides a method for estimating activity coefficients in non electrolyte liquid
mixtures. To use this method, no experimental data are required for the particular mixture of
interest. In addition to the temperature and composition of the system, it is necessary only to
know the molecular structure of every component in the mixture and the necessary group
parameters. A large number of group-interaction parameters of different groups have been
calculated .
UNIFAC is an abbreviation that indicates Universal quasi-chemical Functional Group
Activity Coefficients. It is based on the quasi-chemical theory of liquid solutions.
Equations giving the activity coefficients as functions of composition and temperature are
here stated. The UNIFAC model has a combinatorial contribution to the activity coefficients,
essentially due to differences in size and shape of the molecules, and a residual contribution,
essentially due to energetic interactions.
ln
=
C
ln
Combinatorial
+
ln
R
(2.1)
residual
I. Combinatorial Part: The combinatorial contribution is
ln
C
=
=
=ln
(
+
ln
+ -
)–(
;
Pure-component parameters
(2.2)
) ; z=10
=
and
(2.3)
are respectively measures of molecular van der Waals
volumes and molecular surface areas. They are calculated as the sum of the group volume
and group-area parameters,
and
(Bondi,1968)
10
=
;
Where
and
and
=
(2.4)
, always an integer, is the number of groups of type k in molecule i. Group
parameters
area
=
are obtained from van der Waals group volumes and surface
, given by Bondi (1968)
/15.17;
=
/ (2.5*10^9)
(2.5)
II. Residual part:
The contribution from group interactions, the residual part, is assumed to be the sum of
the individual contributions of each solute group in the solution less the sum of the
individual contributions in the pure component environment.
ln
R
[ lnΓk - lnΓk(i)]
=
(2.6)
All groups
Γk is the group residual activity coefficient, and Γk(i) is the residual activity coefficient of
group k in a reference solution containing only molecules of type i.
The individual group contributions in any environment containing groups of kinds 1,2 ...N
are assumed to be only a function of group concentrations and temperature.
lnΓk
=
[ 1- ln (
=
)–
]
;
(2.7)
(2.8)
11
is the fraction of group m in the mixture.
=exp [-(anm/T)]
(2.9)
Parameter anm characterizes the interaction between group’s n and m. For each groupgroup interaction, there are two parameters: anm ≠ amn. No ternary (or higher)
parameters are needed to describe multi-component equilibria.
PREVIOUS WORK
Jurgen Gmehling et al. (1982) Used the UNIFAC model for predicting the activity coefficient
for many non-electrolyte liquid mixtures. in his work some of the gaps in the groupinteraction parameter table have been filled, and parameters were reported for seven new
groups.
Henrik K. Hansen et al. (1991) presented the revised UNIFAC interaction parameters for 74
pairs of groups, finally they added six main groups so that UNIFAC cover the mixtures of
chlorofluorohydrocarbons, amides, glycol ethers, sulphides, morpholine and thiophenes.
Jurgen Gmehling et al. (1993) proposed a modified UNIFAC model, for increase the range of
its applicability, the temperature-dependent group interaction parameters of the modified
UNIFAC have been fitted for 45 main groups using phase equilibrium information (VLE,
HE,
LLE) stored in the Dortmund data bank. it was found that the results of other group
contribution methods confirms the high reliability of the modified UNIFAC method.
12
CHAPTER-3
VLE CALCULATION
USING UNIFAC
13
VLE CALCULATION USING UNIFAC
3.1
Case 1(A) System is Di-ethyl Ketone (1) And n-Hexane (2)
Table-3.1: VLE data for diethyl ketone (1) and n-hexane (2) at 338.15k [Smith, Van Ness,
Abbott 2005]
P/kpa
X1
Y1
ln
(Experimental)
90.15
0.0
0.0
-----
91.78
0.063
0.049
0.901
88.01
0.248
0.131
0.472
78.89
0.443
0.215
0.278
76.82
0.508
0.248
0.257
73.39
0.561
0.268
0.190
66.45
0.64
0.316
0.123
57.70
0.763
0.412
0.072
50.16
0.834
0.490
0.016
45.7
0.874
0.570
0.027
29.00
1.00
1.00
0.000
Here we have n-hexane is made up of two CH3 and four CH2 group where as di ethyl ketone
is made up of one CH2CO ,one CH3 and one CH2 groups.
14
Table 3.2 group size (RK) and group surface area (QK) [ Fredenslund, Gmehling,
Rasmussen 1977]
GROUPS
NUMBERS
Rk
Qk
CH3
1
0.9011
0.848
CH2
2
0.6744
0.540
CH2CO
3
1.4457
1.180
RESULTS:
Solving the equations of UNIFAC model in MATLAB we will get the calculated activity
coefficient.
Table 3.3 Activity Coefficient of The System Using UNIFAC
P/kpa
X1
Y1
ln
(Theoritical)
90.15
0.0
0.0
-----
91.78
0.063
0.049
0.8589
88.01
0.248
0.131
0.5394
78.89
0.443
0.215
0.3034
76.82
0.508
0.248
0.2428
73.39
0.561
0.268
0.1992
66.45
0.64
0.316
0.1430
57.70
0.763
0.412
0.0746
50.16
0.834
0.490
0.0446
45.7
0.874
0.570
0.0310
29.00
1.00
1.00
0.000
15
3.2
Case 1(B) System is n-Hexane (1) And Di-ethyl Ketone (2)
Table 3.4 VLE data for n-hexane (1) and diethyl ketone (2) at 338.15k [Smith, Van Ness,
Abbott 2005]
P/kpa
X1
Y1
ln
(Experimental)
90.15
0.0
0.0
0.000
91.78
0.063
0.049
0.033
88.01
0.248
0.131
0.121
78.89
0.443
0.215
0.210
76.82
0.508
0.248
0.264
73.39
0.561
0.268
0.306
66.45
0.64
0.316
0.337
57.70
0.763
0.412
0.462
50.16
0.834
0.490
0.536
45.7
0.874
0.570
0.548
29.00
1.00
1.00
-----
Here we have n-hexane is made up of two CH3 and four CH2 group where as diethyl ketone is
made up of one CH2CO, one CH3 and one CH2 groups. With the same values of Rk and Qk
mentioned above we can calculate the theoretical values of the activity coefficient using
UNIFAC group contribution method.
16
RESULTS:
Solving the equations of UNIFAC model in MATLAB we will get the calculated activity
coefficient.
Table 3.5 Activity Coefficient of the System Using UNIFAC
P/kpa
X1
Y1
ln
(calculated)
90.15
0.0
0.0
0.000
91.78
0.063
0.049
0.0044
88.01
0.248
0.131
0.2139
78.89
0.443
0.215
0.2239
76.82
0.508
0.248
0.2636
73.39
0.561
0.268
0.2959
66.45
0.64
0.316
0.3714
57.70
0.763
0.412
0.4728
50.16
0.834
0.490
0.5434
45.7
0.874
0.570
0.5808
29.00
1.00
1.00
-----
17
3.3
Comparison Between Experimental Value And Theoretical Values:
Case 1(A): System Is Di-ethyl Ketone (1) And n-Hexane (2) At 650c
FIGURE 3.1 comparisons between the theoretical and experimental activity coefficient for
case1 (a)
Case 1(B): System Is n-Hexane(1) And Di-ethyl Ketone (2) At 650c
FIGURE 3.2 comparisons between the theoretical and experimental activity coefficient for
Case 1(b)
18
CHAPTER-4
SIMULATION OF
DISTILLATION
COLUMN
19
SIMULATION OF DISTILLATION COLUMN
4.1
Equations for Distillation Column Design
FIGURE 4.1 Distillation Column Configurations
Distillation columns with up to 50 (actual) stages, up to ten components, a partial
condenser, and any number of feed- and side streams may be considered. In our “operating
column analysis”, the user must specify: (a) the number of actual stages, (b) stage
efficiencies, (c) feed- and side stream locations, (d) feed compositions, flow rates, and
thermal states, (e) distillate flow rate, (f) side stream phase conditions and flow rates, (g)
reflux ratio, and (h) column pressure. The nomenclature for an arbitrary stage n, which
includes the possibility of feed- and side streams, is given below [Naphtali and Sandholm
(1971)].
20
FIGURE 4.2 nTH Stage of The Distillation Column
Subscript n: flow from stage n, n = 1, 2. . . N;
Subscript i: component i, i = 1, 2. . . M;
21
4.2
General Relations with Enthalpy Balances
For stage n one obtains the following set of dependent relationships (test functions F1
(n,i))
which must be satisfied.
Component Balances. (Total: N X M relations)
F1(n,i)= (1+ )
+ (1+ )
-
-
-
=0
(4.1)
Enthalpy Balances. (Total: N relations)
F2(n)= (1+ )
+ (1+ )
-
-
-
=0
(4.2)
Equilibrium Conditions with Murphree Stage Efficiencies: (Total: N xM relations).
F3 (n,i)= ηn,i Kn,i Vn ln,i / Ln -
Kn,i = (
)n =(
+ (1-ηn,i )
Vn / Vn-1 = 0
(4.3)
)n
The above relationships comprise a vector of test functions
(4.4)
This contains N X (2M + 1) elements, and which may be solved for equally many unknowns.
(4.5)
Where the vector 1 contains all the elements ln,i, v all elements vn,i and T all elements Ti.
Once all ln,i , vn,i & Ti are known, the product compositions and product flow rates and the
concentration- and temperature profiles in the column follow readily.
22
4.3
Newton-Raphson Iteration
Solving equation 4(B) or 9(B) means finding the set of values of the independent variables, x,
which makes the set of test functions become equal to zero
F(x) = 0
In Newton-Raphson iterations, a new set of values of the test functions F(new), regenerate from
a previous estimate in the following fashion
F(new)(x(new))=F(old)(x(old))+( )x=x(old) (x(new)-x(old))=0
(4.6)
This equation is used to estimate x (new) .When (x (new) - x (old)) is sufficiently small, the correct
set of values of x has been found, and the iteration stops.
The variation between subsequent iterations is arbitrarily limited as follows:
(1) Negative component molar flow rates are equated to zero,
(2) Component flow rates exceeding Ln are equated to Ln,
(3) The maximum change in the temperature at each stage, Tn is 10K.
The initial geuss values for the independent variables, x0 must be supplied by the user. Wild
initial guesses can make the Newton-Raphson linearization approximation invalid to such an
extent that the method fails to convergence characteristics far from the correct solution.
23
4.4
Disadvantages of Newton-Raphson Method
Newton's method is an extremely powerful technique—in general the convergence is
quadratic: the error is essentially squared (the number of accurate digits roughly doubles) at
each step. However, there are some difficulties with the method.
1. Newton's method requires that the derivative be calculated directly. In most practical
problems, the function in question may be given by a long and complicated formula,
and hence an analytical expression for the derivative may not be easily obtainable. In
these situations, it may be appropriate to approximate the derivative by using the
slope of a line through two points on the function. In this case, the Secant method
results. This has slightly slower convergence than Newton's method but does not
require the existence of derivatives.
2. If the initial value is too far from the true zero, Newton's method may fail to
converge. For this reason, Newton's method is often referred to as a local technique.
Most practical implementations of Newton's method put an upper limit on the number
of iterations and perhaps on the size of the iterates.
3. If the derivative of the function is not continuous the method may fail to converge.
4. It is clear from the formula for Newton's method that it will fail in cases where the
derivative is zero. Similarly, when the derivative is close to zero, the tangent line is
nearly horizontal and hence may overshoot the desired root.
5. If the root being sought has multiplicity greater than one, the convergence rate is
merely linear (errors reduced by a constant factor at each step) unless special steps are
taken. When there are two or more roots that are close together then it may take many
iterations before the iterates get close enough to one of them for the quadratic
convergence to be apparent.
6. Newton's method works best for functions with low curvature. For linear function
with zero curvature, Newton's method will find the root after a single iteration.
24
4.5
Steady State Simulation of Distillation Column Procedure
The calculation procedure may be outlined as follows:
(1) Input value was taken (pure-component data, thermodynamic data for the mixture, and
detailed column specifications such as feed plates, reflux ratio, etc)
(2) Initial temperature and component flow profiles was guessed.
(3) Then all K-factors, stream enthalpies, and their derivatives with respect to temperature
and composition were determined.
(4) The discrepancy functions F(x) was set.
(5) The elements of the jacobian matrix were determined and the block tri-diagonal system of
equations was solved.
(6) The correlations to the temperature and component vapour and liquid flow profiles were
determined. New profiles were determined.
(7) Check, whether the correlated value is smaller than a specified value.
If no, go to step (3) with the newly determined profiles.
If yes, go to step (8)
(8) Print final output and stop.
25
4.6
Problem Statement
FIG 4.3. DISTILLATION COLUMN
MIXTURE: Binary mixture of n-pentane (1) and Acetone (2)
Table 4.1 Antoine Constants for acetone and n-Pentane
COMPONENTS
A
B
C
Acetone
6.8
1064.63
232
n-Pentane
7.23
1277.03
237.23
26
4.6.1
Design of Distillation Column Assuming No Temperature Variance:
Number of plates: 10 (including the reboiler and condenser)
Feed plate: 5
Feed flow rate: 100 moles/hr
Mole fraction of n-pentane xf : 0.5
Column pressure: 101kpa
The top temperature: 323.4 K
The bottom temperature: 303.3 K
The reflux ratio =2.5
There is no side stream taken.
SOLUTION:
The boiling point of n-pentane is less than that of the acetone so n-pentane is more volatile
than acetone. The top product will be n-pentane and the bottom product will be acetone.
Taking the average temperature in the column T = (303.3+323.4)/2 = 313.50K
Calculating the saturation pressure of both of the components using Antoine equation
Psat acetone = 105.9 kpa
Psat n-pentane=82.5 kpa
Calculating the activity coefficient at the average temperature for both of the components
using UNIFAC group contribution method in MATLAB
Activity coefficient γ n-pentane = 1.2192
Activity coefficient γ acetone = 1.7259
27
RESULTS:
Solving the mass, energy and equilibrium equations in MATLAB, we get the results as
follows:
Table 4.2 Results for temperature independent distillation column design
No. of Plates
Liq. Flow Rate
Liq. Flow Rate of Mole Fraction of
Of n-pentane
Acetone(moles/hr)
n-pentane
(moles/hr)
1
16.5071
0.1949
0.988
2
35.2652
0.7856
0.978
3
56.5813
2.5754
0.956
4
80.8040
7.999
0.91
5
108.3299
24.4346
0.815
6
139.60
74.2392
0.65
7
118.33
73.647
0.61
8
94.1615
71.8524
0.56
9
66.69
66.4146
0.501
10
35.47
49.9357
0.41
28
4.6.2
Design of Distillation Column Assuming Ideal Case with Temperature Variance
Number of plates: 5 (including the reboiler and condenser)
Feed plate: 3
Feed flow rate: 100 moles/hr
Mole fraction of n-pentane xf : 0.5
Column pressure: 101kpa
The top temperature: 323.4 K
The bottom temperature: 303.3 K
The reflux ratio =2.5
There is no side stream taken.
For the ideal case the activity coefficient γ = 1 for both the components.
SOLUTION:
For solving the mass, energy, and equilibrium relation equations by Newton-Raphson method
we have to assume the initial values of the independent variables.
Here the variables are component liquid flow rates, component vapour flow rates and
temperature.
The top and the bottom temperature are known so
we can assume the intermediate
temperatures. Similarly from the top and bottom liquid and vapour flow rates we can assume
the intermediate flow rates.
The condenser is counted as the number one plate and the boiler is the 5th plate. The
condenser is partial one.
29
Table 4.3 The assumed initial values of the independent values
NO. OF PLATES
TEMPERATURE
TOTAL LIQ. FLOW
TOTAL VAPOUR
RATES
FLOW RATES
( moles/hr)
(moles/hr)
( 0C)
1
303.3
44
110
2
308.32
74.25
99
3
313.35
104.5
88
4
318.37
134.75
77
5
323.4
165
66
Now using these initial guess values of the variables and forming the jacobian matrix and
solving the mass, energy and equilibrium relation by Newton-Raphson method, the results
will come like this
Table 4.4 Results for ideal distillation column design
No. of Plates
Temperature
Component
Component
Component
(0C)
Liq. Flow
Liq.
Rates (l1)
Rates
(moles/hr)
(moles/hr)
(moles/hr)
Component
Flow Vapour Flow Vapour Flow
(l2) Rates
(v1)
Rates
(v2)
(moles/hr)
1
278.7
163.02
1.98
65.99
0.000142
2
288.8
128.8
5.95
76.99
0.0025
3
298.71
85.16
19.33
87.94
0.0554
4
308.6
41.58
32.67
98.62
0.38
5
318.1724
18
25.96
109.25
0.7464
30
4.6.3 Design of Distillation Column Assuming Non-Ideal Case with Temperature
Variance
Number of plates: 5 (including the reboiler and condenser)
Feed plate: 3
Feed flow rate: 100 moles/hr
Mole fraction of n-pentane xf : 0.5
Column pressure: 101kpa
The top temperature: 323.4 K
The bottom temperature: 303.3 K
The reflux ratio =2.5
There is no side stream taken.
RESULTS:
Solving the mass, energy and equilibrium equations using Newton-Raphson method in
MATLAB, we get the results as follows:
Table 4.5 Results for the non ideal distillation column design
30.53
Vapour
Acetone
Flow Rate
(moles/hr)
9.6377
Liquid NPentane Flow
Rate
(moles/hr)
7.522
Vapour N Pentane
Flow Rate
(moles/hr)
2.37
253.8115
114.93
36.282
38.05
12.01
3
242.06
135.79
77.08
122.45
38.65
4
270.24
93.31
63.59
93.31
29.45
5
321.28
42.478
47.62
50.58
15.96
Plate
Temperature(k)
Liquid Acetone
Flow Rate
(moles/hr)
1
267.67
2
No.
31
CHAPTER-5
CONCLUSION AND
FUTURE
RECOMMENDATION
32
CONCLUSION
The average percentage of error in determining the activity coefficient by UNIFAC group
contribution method varies from 9- 15% with respect to the experimental values. So with this
much percentage of error the VLE data generated by UNIFAC can be successfully
implemented in designing separation processes. UNIFAC model is a thermodynamic
framework to describe the non-linearity in vapour-liquid equilibrium prediction. Presently
UNIFAC model cannot apply to all type of mixtures containing polymers. Future study and
research are required so that this method can be applied to all types of mixtures. The steady
state simulation of binary distillation (n-pentane + acetone) column (10 plates, including
reboiler and condenser) has been done assuming temperature independence. The temperature
dependent simulation could not reach convergence.
FUTURE RECOMMENDATION
•
The temperature dependent steady state simulation of the distillation column is to be
done.
•
The VLE data can be generated for ternary or quaternary mixtures using UNIFAC
model,
•
And steady state simulation for the multi component mixtures is to be done and the
results should be compared with the other models.
33
References
34
REFERENCE
1- Fredenslund A, Gmehling J, Rasmussen P, “vapour liquid equilibria using UNIFAC”
Elsevier, Amsterdam, 1977.
2- Fredenslund, A., Jones, R. L., Prausnitz, J. M., AIChE J., 21, 1086 (1975).
3- Abrams. D. S., Prausnitz, J. M., AIChE J., 21, 116 (1975). Bondi, A., "Physical
Properties of Molecular Crystals, Liquids, and Glasses",
4- Christiansen, L. J., Fredenslund, A, AIChE J., 21, 49 (1975).
5- Prausnitz, J. M., "Molecular Thermodynamics of Fluid-Phase Equilibria", PrenticeHall, Englewood Cliffs, New Jersey, 1969.
6- Napthali, L.M, Sandholm, D.P, AIchE J., 17 , 148 (1971).
7- http://en.wikipedia.org/wiki/Group_contribution_method.
8- Guggenheim,E.A., “mixtures” clarendon press , oxford , 1952.
9- Gmehling, J., Onken, U., “vapour liquid equilibrium data collection”DECHEMA
chemistry data series, Frankfurt am Main, 1977.
10- Hayden , J.G.,O’ Connell, J.P., Ind. Eng. Chem., Process Des Dev.,14,209 (1975).
11- King,C.J., “separation processes”, McGraw-Hill, new York , N.Y.,1971.
12- Langmuir,I., “ the distribution and orientation of molecules”, Third colloid
symposium Monograph, The chemical catalog co., Inc.,New York,N.Y.,1925.
13- Smith “design of equilibrium stage processes”, pp 424-428, McGraw-Hill, new York,
N.Y.,1963.
14- Bondi A, physical prosperities of molecular crystals, liquids, and glasses, wiley, New
York, 1968.
15- Davies, C.W. (1962). Ion Association. London: Butterworths. 37–53.
16- P. Debye and E. Hückel (1923). "The theory of electrolytes. I. Lowering of freezing
point and related phenomena". Physikalische Zeitschrift 24: 185–206.
17- Renon H., Prausnitz J. M., "Local Compositions in Thermodynamic Excess
Functions for Liquid Mixtures", AIChE J., 14(1), S.135-144, 1968.
18- Abrams D.S., Prausnitz J.M., “Statistical Thermodynamics of Liquid Mixtures: A
New Expression for the Excess Gibbs Energy of Partly or Completely Miscible
Systems”, AIChE J., 21(1), 116-128, 1975.
19- McDermott
(Fluid
Phase
Equilibrium
(Coll.Czech.Chem.Comm., 41(1976)3347)
35
1(1977)33)
and
Flemr
20- Smith J. M., Van Ness H. C., Abbott M M, “Introduction to Chemical Engineering
Thermodynmics”, Mc Graw Hill, 2005.
21- Gmehling J., Rasmussen P., Fredensfund A., “vapour liquid equilibria by UNIFAC
group contribution. Revision and extension.2” Ind. Eng. Chem. Process Des. Dev.
1982, 21, 118-127.
22- Hansen H. K., Rasmussen P., Fredenslund A., “vapour liquid equilibria by UNIFAC
group contribution. Revision and extension.5”, Ind. Eng. Chem. Res. 1991, 30, 23522355.
23- Gmehling J., Li J.,Schiller M., “ A modified UNIFAC model. 2. Present parameter
matrix and results for different thermodynamic properties” Ind. Eng. Chem. Res.
1993, 32,178-193.
36
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement