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Operational Optimization of Ideal Internal Thermally Coupled Distillation Columns.

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Dev. Chem Eng. Mineral Process., 9(lR).pp.133-142. 2001.
Operational Optimization of Ideal Internal
Thermally Coupled Distillation Columns
Xing-Gao Liu* and Ji-Xin Qian
National Laboratoiy of Industrial Control Technology, Institute of
IndustriaI Process Control, Zhejiang University, Hangzhou 310027,
RR.China
Lack of the optimal operation parameters in operation is one of major diflculties
associated with the we of advanced mew saving distillation methods. In this paper,
the operational optimization of the ideal Internal Thermally Coupled Distillation
Column (ITCDICJ is considered. An optimization model and the related simulation
algorithm are proposed, An optimization and the related result analysis are cam'ed
out, which pave the way forfirrther design studies and its practical application.
Introduction
Distillation consumes a Iarge percentage of the energy used in the chemical process
industries. Consequently, there is a significant incentive to improve the energy
efficiency of this widely applied separation process. Thee are various methods of
reducing external energy q u t s by the effective use of heat energy in the distillation
system [I-31,such as multi-effect columns, side cooler-side heater, heat pumps and
secondary reflux and vaporization (SRV). Energy recovery by heat transfer from the
rectifying section to the stripping section is an effective method for energy savings in
distillation columns. This method, first proposed by Mah et al. [4], is called SRV
method. Since thea, there are extensive studies of SRV [5-61. ITCDIC is a distillation
column where energy savings are realized by SRV method, which has neither a
reboiler nor a condenser and possesses large potential of energy reduction [7-91.
However, one of the major difficulties associated with the use of such advanced
energy saving columns is a lack of operational optimization in operation [IO], i.e.,
how to get the optimal operation parameters. This paper will address the operational
optimization of ideal ITCDIC.
First,an optimizationmodel of ideal ITCDIC is proposed, upon which the optimal
operation parameters can be archived simultaneously guaranteeing both the product
quality and the maximumenergy savings. A related simulation algorithm is presented
The simulation and the result analysis of the steady state are carried out. Finally, the
optimization and the optimization analysis are canied out. From our current
knowledge, no one has worked in this area.
Optimization Model
Figure 1 shows the schematic diagram of the ideal ITCDIC.The rectifjmg section
~~
* Author for correspondence (e-mail: liuxinggao@263.net). Current Address: Institute
of Process Control Engineering, Department of Automation, Tsinghua University,
Beijing 1OOO84, l? R China.
133
X.-C. Liu and J.-X. Qian
and the stripping section are separated into two columns. The manipulation of internal
thermal coupling is accomplished through heat exchanger between the two sections.
In order to provide the necessary temperature driving force for the heat transferred
from the rectieing section to the stripping section, the former must be operated at a
higher pressure than the latter. To adjust the pressure, a compressor and a throttling
valve are installed between the two sections. Because of the internal t h e m 1 coupling,
a certain amount of heat is transferred from the rectifying section to the stripping
section and brings the downward reflux flow for the former and the upward vapor
flow for the latter. As a result, a condenser and a reboiler are not required and energy
savings are realized.
Figure 1. Schematic diagram of ITCDIC.
The optimization model of the ideal ITCDIC is derived by applying energy,
component, and overall material balances, and vapor-liquid equilibrium under the
following assumptions:
(1) Negligible vapor holdups, liquid molar holdups on each tray being constant;
(2) Perfect liquid and vapor mixing on each tray, the temperature and the
composition on each iray being unifonq
(3) Vapor-liquid equilibrium for streams leaving each tray;
(4) Instantaneous heat transfer from the rectifying section to the stripping section and
the transportation of liquid and vapor between trays;
( 5 ) Negligible pressure drop in each column;
(6) Negligible hydraulic delay occuniug in the liquid flows;
(7) Heat loss and heat capacity change of the separation process being negligible;
(8) No time delay in column pressure changes and feed thermal condition;
(9) Equal and constant latent heat of each component;
(1O)The relative volatility is constant;
(11)No vapor and liquid side-stream withdraw.
For a separation process, the minimum amount of thermodynamic energy required
to make a complete separation is given by the following equation:
W,, = F (AH-TAS)
For an ideal mixture, equation (1) can be expressed as:
134
(1)
Ideal Internal Thermally Coupled Distillation Columns
[X,,,
(2)
Wm,n is a thermodynamic term that is independent of any particular process. Actual
processes operate with finite driving forces, whch are irreversible and consume more
energy than the thermodynamic minimum.
For conventional distillation columns (CDIC), minimum energy required for the
separation process (Q,,,ln,con) is the minimumreboiler energy requirement. With the use
of the McCabe-Thiele diagram, Qm,,,con for a binary mixture can be shown to be a
function of the heat of vaporization of the bottom product, relative volatility, and feed
composition. For complete separation, when feed thermal condition q=l, there is:
Wmin = FRTqXfi
Ua-1) 5 1
(3)
The maximum thermodynamic efficiency (Em) is defined as the minimm
thermodynamic energy ( W,,,,,) divided by minimum energy required for a separation
process (Q,,,J,so for conventional distillation:
Qmmcon = Fmb,v [
Em,con=
Wmid Qmm.con
= RT4xfi
lflfi)/{ m b . v [ ll(a-1)
(4)
51 }
For the ideal ITCDIC, the energy required for the separation process (Qlcd)is
composed of the heat for preheating feed and the work of compressor ( Wcmp),that is
Qtcd = F(1-q)mjv + K o m p
(5)
We choose the compressor work as:
wcomp
= v/K/((K-~)RT,((P~/P,)(~-*~~
-1)
(6)
For gas mixture,
1/(K-1 ) = 4YJ(Kl- 1 ) )
(7)
So we achieve thermodynamic efficiency of fully ideal ITCDIC (Et&):
Etcd
=
wmd Qtcd
= FR T 4 x , 1X,M F( 1 q)mjv+ Wcomp
(8)
1
which has a profound impact on the overall cost of the separation process. Comparing
with the
the maximum thermodynamic efficiency of conventional distillation
thermodynamic efficiency of ideal ITCDIC (Etc& we can know the energy saving
effect of the ideal ITCDIC directly. The percentage of thennodynamic efficiency
enhancement of the ideal ITCDIC (XJis defined as follows:
x e = (Etcd
- ~ m , c o n/)E m , c o n
(9)
For conventional distillation, energy required for the separation process under the
minimumreflux ratio (Rmm)operation (Qmm,cm)
can be calculated by:
Qnnmcon = F ( 1 - q ) m j v +[ ( ~ r n i n + ~ ) ~ - ~ ( ~ - ~ ) I ~ b , v
(10)
where D is the top distillation product flow rate.
The percentage of energy savings of the ideal ITCDIC is defined as follows:
135
X.-G. Liu and J.-X. Qian
x,= (Qnnin.con-Qted)
(11)
1Qnninxon
which shows the energy saving effect directly.
When the stages are numbered with the top as the stage 1 and the bottom as the
stage n, the basic equations o f the ideal ITCDIC are presented as follows:
Thermal coupling [4,7,9]:
Qj
=
UA(I;-Tj+/.l)
I;. = b/( a-LnPvi
j=1,. ..,f- 1
)-c
Mass balances:
j=l,. ..,f-1
j=l,. ..,f-2
k=l
Ln
= F-Vl
Vl
= F( 1-4)
4*]= V1+Lj
J=1,.
..,f-1
j=l,. ..,f-2
k=l
Vapor-Liquid equilibrium relationships:
I;= d j / [ ( a - l v j + l ]
Component balances:
Equations (1)-(25)consist of the dynamic mathematical model o f an ideal ITCDIC.
For steady state studies, let:
&/dt = 0
(26)
the dynamic model then becomes steady state model.
The mathematical models above including the dynamic and the steady state
models provide an efficient tool for operation studes, and can be used for further
control, design and optimization studies.
We select X, as the objective function. For Merent product qualities, such as top
136
Ideal Internal Thermally Coupled Distillation Columns
product composition Y l 2 96%, bottom product composition Xnl5% or Ylr 98%,
Xn14%, there should be Merent optimizing results of energy savings. So a constraint
should be set on product qualities, such as top product composition Y1296%, bottom
product compositionXn15%.
For total separation effect, we have:
FZy 2 V IYI
(27)
The equality constraints are equations (1)+26). The optimization goal is to find
the optimal operating parameters Pr and q so that the energy saving is maximum
compared with the energy required of CDIC under the minimum reflux ratio and the
product qualities are guaranteed simultaneously. The energy saving optimization
model of the ideal ITCDIC is derived as following:
ITCDIC min.
f (Pr,(I)= -X,
(MOPT1)
Eqs. (1-26)
Product quality constraints (such as: Y,298%, Xn s 4%)
V,YyFZ’SO
0.1013MPa S Pr 5 1.013MPa
~.t.
O l q l l
OlX*Il
o q < 1
It is a nonlinear programming (Np) constrained optimization problem. The
optimization program is programmed using the “Matlab Language”. The optimization
a l g o r i h used is the Sequential Quadratic Programming (SQP)method.
Simulation and Analysis
In following simulation and optimization,a 30-stage ideal ITCDIC is considered as an
ihstrative example, where a binary mixhue of benzene-toluene is separated. Its
detailed operation conditions are shown in Table 1.
Table I . Given operating conditionsfor the simulation.
Stage number
Feed stage
Feed flow rate
Feed composition
(Benzene)
(Toluene)
Feed thermal condition
Pressure of rectifying section
Pressure of stripping section
Heat transfer rate
Latent heat of vaporization
Relative volatility
30
16
100 Ian0l.K’
0.5
0.5
0-1
0.1013-1 .O 13MPa
0.1013MPa
9803 W K ’
30001.1 kJ.kmor’
2.317
137
X.-G. L ~ and
u J.-X. Qian
The adiabatic index number ( K ) calculation uses the heat capacity equation of an
ideal gas. The physical data used in simulation are listed in Table 2.
Table 2. Physical data used in the simulation.
Antoine constants: a
b
C
Benzene
Toluene
15.9008
2788.51
-52.36
16.0137
3096.52
-53.67
Ideal gas heat capacity equation parameters:
A
-8.101
B
1.1 33E-1
C
-7.206E-5
D
1.703E-8
-5.817
1.224E-1
-6.605E-5
1.173E-8
The simulation programs are programmed using "Matlab Language". The steady
state simulation procedure is illustrated as follows:
1. give operation condition and physical data : N J l?f i Ps. ZJ q, UA; a, b, c; A, B,
C,D ;
2. give termination criteria (E) that is a measure of the worst case precision required
of the independent variables;
3. give initial values ofX,(k).
4. calculate I;@), T&), P,~(k).Qj(k), LjF)?Q(k) from Eqs. (lW21);
from Eqs. (22)-(26);
5. calculate 4(k+l)
6. when /q(k+I)-q(k) /<E, go to step (7); if not,q(k+I)+(k,), and go to step 4;
7. calculate Qmin.con , Q r C d , X, from Eqs. (5)47), (9)4 11);
8. calculate
E,cd X,from Eqs. (
1
)
(
4
)
,
(8)-(9).
We choose PI and q as manipulated variables to inspect the system and its energy
savings. Some simulation results are shown in Table 3.For conventional distillation,
the maximum thermodynamic efficiency of the Benzene-Toluene system is 5.1 1%.
But for the ideal ITCDIC, inTable4 the minimum thermodynamic efficiency is
Table 3. Simulation results of the Benzene-Toluene system.
N
o
1
2
3
4
5
6
7
8
9
Manipulating
Parameters
4
0.25
0.25
0.25
0.5
0.5
0.5
0.75
0.75
0.75
pr
E-.cm
4.c~
Xe
0.1519
0.2532
0.3545
0.1519
0.2532
0.3545
0.1519
0.2532
0.3545
0.6373/0.0880
0.6666/0.0003
0.6667/0.oooO
0.770810.2292
0.9384/0.0616
0.9887/0.0113
0.909U0.3636
0.999710.3334
1.0000/0.3333
0.0511
0.0511
0.051 1
0.051 1
0.051I
0.05 11
0.0511
0.0511
0.0511
0.0813
0.0736
0.0692
0.1173
0.1019
0.0936
0.2103
0.1656
0.1447
59.26
44.19
35.48
129.69
99.60
83.29
311.79
224.17
183.23
Pr is m a ; Q is kWx106
138
System Characteristic
Performance Parameters
Product
quality
Yllxn
9%
Qrnin.m.
4.9122
4.9122
4.9122
4.4928
4.4928
4.4928
4.1562
4.1562
4.1562
Qtcd
2.6042
2.8764
3.0613
1.8057
2.0779
2.2628
1.0072
1.2794
1.4643
Xs ,%
46.99
41.44
37.68
59.81
53.75
49.64
75.71
69.22
64.77
Ideal Internal Thermally Coupled Distillation Columns
Table 4. Optimization results of the Benzene-Toluene system.
Product quality constrains
Y,2
XnS
Achieved optimal operation Pc MPa
parameters
9
System characteristics under Yl
optimal operation parameters Xn
Qmin.con. l 0 k W
1 0 % ~
elc,+
Maximum energy savings
X,, %
96%
5%
0.2826
0.5111
0.9705
0.0500
4.3933
2.0803
52.65
98%
4%
0.3006
0.5107
0.9800
0.0400
4.4768
2.1375
52.25
6.92%, enhancing 35.48%, and the related energy saving percentage is 37.68%; the
maximum thermodynamic efficiency is 2 1.03%, enhancing 3 11.79%, and the related
energy saving percentage is 75.77%. Obviously, the ideal ITCDIC can save more
energy than conventional distillation, and the effect of energy savings is marked.
When the feed thermal condhon, q, is 0.25, 0.5, 0.75 and pressure of rectifying
section, Pr, is 0.15 19MPa, 0.2532MPa, 0.3545MPaYrespectively, the product qualities
change from 63.73% to 100.00% for Yl, and from 0.00% to 36.36% for Xn. The
performance parameter ElCdchanges from 6.92% to 2 1.03%; X, changes from 35.48%
to 311.79%; and X, changes from 37.68% to 75.77%. It shows that there are very
complicated relations and very large changes among energy saving, X,,manipulation
parameters, h,q, and product quality, Xn, Y,. Hence, there should be an optimization
between operation parameters and system characteristics.
Optimization Result and Discussion
The optimization results of operation variables of the ideal ITCDIC are shown in
Table 4. For the Benzene-Toluene system, when top product composition Y, 2
98%, bottom product composition Xn I4%, the optimal operation variables and
the maximum energy savings are achieved. The rectifying section pressure Pr,
0.3006MPa, the feed thermal condition q, 0.5107, the other operation conditions
are the same as in Table 2. Under the above operation conditions, the percentage
of energy savings of ideal ITCDIC is 52.25%. Table 5 lists other study results.
Comparing the results of Table 5 with those of Table 4, it is seen that the ideal
ITCDIC method saves more energy. Energy recovery by heat transfer from the
Table 5. Results of other studies.
Author
Energy
savings
Studied system
ethyl benzene/ dimethyl benzene
non-ideal mixtureof
Li [12], 1995
33.14%
ethanol, ether etc.
ethylend ethane etc.
Mah [4], 1977
54%*
Finn 1131, 1993
16%
i-butand n-butane
*Indicate relative steam consumption
Yang [ I l l , 1990
50%
Column
construction
Compared with
petlyuk
actual CDlC
petlyuk
actual CDlC
SRV.
actual CDlC
direct sequence rectifier
side rectifier
139
X.-G.Liu and J. -X.Qian
rectifying section to the stripping section is an effective method for energy savings in
distillation columns.
Figure 2 shows the operating line contrast figure of the ideal ITCDIC under one of
the optimal operating conditions, Pr, 0.2826MPa and q, 0.5111. For a conventional
distillation column under the minimum operating reflux ratio, product quality
requirements are the same as those of the ideal ITCDIC. Other parameters are the
same as those in Table 1.
0
02
04
0.6
lqud mnpostmnX
08
Figure 2. Operating line contrast figure, P ~ 0 . 2 8 2 6q=O.5111.
,
Owing to the internal thermal coupllng between the rectifying and stripping
sections where the operating line is very close to the equilibrium line. Especially, near
the top and the bottom stage number, the driving forces of mass and heat transfer of
ITCDIC have been significantly reduced compared with the conventional distillation
columns (even under minimum reflux operation). Hence the process irreversibilityhas
been sigmfkantly reduced. From the viewpoint of thermodynamics, large energy
losses for the separation process usually occur due to the irreversibility of processes.
The result is that either fewer stages are needed to accomplish the same separation, or
better separation effect is obtained with the same number of stages at the same energy
consumption, and energy savings occur in the ideal ITCDIC process.
Conclusions
This paper gives an effective method to obtain the optimal operation
parameters of the
'
ideal ITCDIC. The illustrative example shows its validity.
For other systems, such as non-ideal mixture separation, the optimization model
can be also applied, the only thing needed is to change the given conditions, physical
data and vapor-liquid equilibrium relationships. Based on the study in h s paper, we
have developed the relative s o h a r e "ENORM", which is very useful for future
research on ITCDIC and its practical application. Further investigation is underway to
study the control and design of ITCDIC.
I40
Ideal Internal Thermally Coupled Distillation Columns
Acknowledgment
The authors thank the National Environmental Protect Bureau of P. R. China (HuanKe-Ke, 1997, No. 006, Project 14) for financial support.
Nomenclature
Thermodynamic efficiency
Percent energy saving
Percent thermodynamic efficiency enhancement
x
e
Feed
F
Stage holdups
H
Adiabatic index number of gas
K
Liquid flow rate
L
Number of total stages
n
Vapor saturation pressure
Atp
Pressure of rectifying sectiona
pr
Pressure of stripping section
Ps
Representation of either Pr or Ps
P
Feed thermal condition
4
Energy require
Q
General gas constant
R
Minimum reflux ratio
Rmin
Time
t
Absolute temperature
T
Heat transfer rate
UA
Vapor flow rate
V
Thermodynamic work
W
Mole fraction of liquid
X
Mole fraction of vapor
Y
Mole
fiaction of feed
5
Change
in enthalpy and entropy
AH,ds
Relative
volatility
a
latent
heat.
A
E
4
(kJ/lanol)
Subscripts
b
Bottom
comp
Compressor
con
Conventional distillation column
f
Feed stage
1
Component
j
Stage number
maX
Maximum amount
min
Minimum amount
rmin
Minimumrefluxratio
tcd
The ideal ITCDIC
V
Vaporization
I41
X.-G. Liu and J.-X. Qian
References
Lang, L. 1996. Dynamic Behavior and Operational Aspects of Heat-Integrated Distillation Processes.
Chem. Eng. Tech., 19,498-497.
2. Umeda, T., Niida, K., and Shiroko, K. 1979. A Thermodynamic Approach to Heat Integration in
Distillation Systems. AlChE J., 25(3), 423-429.
3. Linnhoff, B. 1993. Pinch Analysis - A State of the Art Review. Trans. IChemE., 71A, 503-51 1.
4. Mah, R.S.H.,Nicholas, J.J., and Wodnik, RB. 1977. Distillation with Secondary Reflux and
Vaporization: A Comparative Evaluation. AlChE J., 23(5), 651-658.
5. Shimizu, K., Holt, B.R., et al. 1985. Assessment of Control Structures for Binary Distillation Columns
with Secondary Reflux and Vaporization. Ind. Eng. Chem. Pro. Des.Dev., 24,852-858.
6. Fitmwrris, RE., and Mah, R.S.H. 1980. Improving Distillation Columns Design Using
ThermodynamicAvailability Analysis. AIChE J., 26(2), 265-273.
7. Humg, K.J., Qian, Ji-Xin, et al. 1997. Steady-state operation analysis of an ideal heat integrated
distillation column. Chinese J. Chem. Eng., 5(4), 325-336.
8. Lueprasitsakul, V., Hasebe, S., et al. 1990. Analyses of the characteristics of a binary packed
distillation column with internal heat integration. J. Chem. Eng. Japan, 23(6), 686-691.
9. Lestak, F., Smith, R., and Dhole, V.R 1994. Heat Transfer Across the Wall of Dividing Wall Columns.
Trans.IChemE., 72(A9), 639-644.
10. Glinos, K., and Malone, M.F. 1988. Optimality regions for complex column alternatives in distillation
systems. Chem. h g . R ~ s D~s.,
.
66,229-240.
11. Yang, Y. Q. 1990. Simulation Study of Operational Performance of Thermally Coupled Distillation. J.
Chern. Ind Eng. (Chinese), 41(4), 491-497.
12. Li, F. H.,Fan, X. S., and Yao,P. J. 1995. Study on the Feasibility of Employing Thermally Coupled
Distillation Tower to Save Energy. Shi You Hua Gong (Chinese), 24(1 I), 783-798.
13. Finn, A.J. 1993. Consider Thermally Coupled Distillation. Chem. Eng. Pro., Oct., 41-45
1.
Received: 28 October 1999; Accepted afier revision: 24 May 2000.
I42
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