processes
Article
Modeling/Simulation of the Dividing Wall Column
by Using the Rigorous Model
Chi Zhai 1 , Qinjun Liu 1 , Jose A. Romagnoli 2 and Wei Sun 1, *
1
2
*
Beijing Key Lab of Membrane Science and Technology, College of Chemical Engineering,
Beijing University of Chemical Technology, North Third Ring Road 15, Chaoyang District,
Beijing 100029, China; 2014400020@mail.buct.edu.cn (C.Z.); xingfuzc@163.com (Q.L.)
Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA 70803, USA;
jose@lsu.edu
Correspondence: sunwei@mail.buct.edu.cn; Tel.: +86-10-6444-5826
Received: 7 December 2018; Accepted: 29 December 2018; Published: 8 January 2019
Abstract: Dividing wall column (DWC) is an atypical distillation column with an internal, vertical
WE partition wall that effectively accommodates two conventional distillation columns into one to
improve the thermodynamic efficiency. In previous studies, different equivalent models by combining
conventional columns are adopted to approximate the DWC modeling, which may not well describe
the integration of the DWC; moreover, the computational cost increases when multiple columns are
implemented to represent one DWC. In this paper, a rigorous mathematical model is proposed based
on the mass balance, the energy and phase equilibrium of the DWC, where decision variables and
state variables are equally treated. The model was developed in the general process modeling system
(gPROMS). Based on the rigorous model, the influences of liquid split ratio and vapor split ratio are
discussed, and it is shown that the heat duty is sensitive to changes on the liquid and vapor split
ratio. Inappropriate liquid and vapor split ratio will increase the mixing effects at both ends of the
dividing wall, and adversely affect the thermodynamic efficiency. Hence, the degree of mixing is
defined to characterize the column efficiency. Furthermore, the middle component split ratio at the
top of the pre-fractionator has an optimal point for better energy saving with certain liquid and vapor
split ratios, and can be used as an indicator for the energy performance. Finally, the model was tested
and validated against literature data by using the ternary benzene–toluene–xylene mixture system as
a case study.
Keywords: rigorous DWC model; gPROMS; the benzene–toluene–xylene system
1. Introduction
Distillation column is one of the most important separation facilities in the process industry.
Distillation necessitates considerable energy investments, as it is reported that distillation can account
for more than 50% of plant operating cost [1]. There is ample scope for developing more energy
efficient distillation schemes, one of which is dividing wall column (DWC).
For the sharp separation of a multi-component mixture, one always adopts a sequence of
distillation columns. For example, at least two columns are used in either direct or indirect sequence
for the separation of a three-component mixture. Figure 1 shows an energy efficient configuration
for separating a three components mixture (Petlyuk configuration [2]). In this configuration, the
vapor and liquid streams leaving the first column are directly connected with the second column.
The first column is called the pre-fractionator and the second is the main column. In this case, a
mixture containing A, B and C (in decreasing order of volatilit) first enters the pre-fractionator, sharp
separation happens between light component A and heavy component C, while the middle component
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further separation is performed to obtain high-purity individual components at the top, middle and
Bbottom
is further
distributed
naturally
between the
top and
bottom ofindividual
the pre-fractionator
[2].at Then,
a middle
further and
of the
main
column.
separation
is performed
to obtain
high-purity
components
the top,
separation
is
performed
to
obtain
high-purity
individual
components
at
the
top,
middle
and
bottom
It is reported
thatcolumn.
the Petlyuk configuration can save up to 30% of operational cost [3], of
in
bottom
of the main
the
main It
column.
comparison
with
the
conventional
direct
or
indirect
sequencing.
The
improvement
of
is reported that the Petlyuk configuration can save up to 30% of operational cost [3], in
It is reported
that the
Petlyuk
configuration
can
upPetlyuk
tosequencing.
30%column
of operational
cost
[3], in of
thermodynamic
efficiency
from two
sources:
(1)
the
avoids
the
remixing
comparison
with
theoriginates
conventional
direct
or save
indirect
The improvement
comparison
with
the
conventional
direct
or
indirect
sequencing.
The
improvement
of
thermodynamic
of the
middle components
in the
conventional
column
sequence
andthe
(2)remixing
the
thermodynamic
efficiencyhappening
originates from
two
sources: (1) the
Petlyuk
column [4];
avoids
efficiency
originates
from
two
sources:
(1)
the
Petlyuk
column
avoids
the
remixing
of
the
middle
condenser
and
reboiler
downsize
to
one
for
a
three-component
separation
system,
which
saves
both
of the middle components happening in the conventional column sequence [4]; and (2) the
components
happening
in the
conventional
column
sequence [4];compact,
and
(2) the
andin
reboiler
energy
cost and
capital
cost.
To
make to
theone
Petlyuk
configuration
thecondenser
two
columns
Figureboth
condenser
and
reboiler
downsize
for a three-component
separation
system,
which
saves
downsize
tocost
oneand
for acapital
three-component
separation
system,
which
saves
both
energy
cost
and
capital
1 areenergy
accommodated
in
onecost.
shell,Towhich
formulates
the
DWC,
as
shown
in
Figure
2.
By
inserting
an
make the Petlyuk configuration compact, the two columns in Figure
cost.
To
make
the
Petlyuk
configuration
compact,
the
two
columns
in
Figure
1
are
accommodated
in
internal,
vertical partition
into which
the column,
the two
sections
of the in
DWC
function
as two an
1 are accommodated
in wall
one shell,
formulates
the DWC,
as shown
Figure
2. By inserting
one
shell,
which
formulates
the
DWC,
as
shown
in
Figure
2.
By
inserting
an
internal,
vertical
partition
columns
in
Figure
1,
but
one
can
easily
conjecture
that
DWC
needs
less
capital
investment
than
thetwo
internal, vertical partition wall into the column, the two sections of the DWC function as
wall
into
the
column,
the
two
sections
of
the
DWC
function
as
two
columns
in
Figure
1,
but
one
can
Petlyuk
configuration.
columns in Figure 1, but one can easily conjecture that DWC needs less capital investment than the
easily
conjecture
that DWC needs less capital investment than the Petlyuk configuration.
Petlyuk
configuration.
Figure 1. Petlyuk column configuration.
Figure 1. Petlyuk column configuration.
Figure 1. Petlyuk column configuration.
Figure 2. Scheme for the dividing wall column.
Figure 2. Scheme for the dividing wall column.
The first patent related to DWC
granted
to Wright
1949
[5], but wide acceptance of
Figurewas
2. Scheme
for the
dividing in
wall
column.
first patent
related
to DWCuntil
was the
granted
to Wright
in 1949
but wide
acceptanceofofDWC
DWC
DWCThe
in industry
did
not happen
1980s,
when the
first [5],
industrial
application
in industry
did
not
happen
until
the
1980s,
when
the
first
industrial
application
of
DWC
was
was
implemented
by
BASF
(i.e.,
Baden
Aniline
and
Soda
Factory,
a
German
chemical
company)
[6].
The first patent related to DWC was granted to Wright in 1949 [5], but wide acceptance of
DWC
implemented
BASF
Badenuntil
Aniline
Soda
Factory,
afirst
German
company)
The
The
reason
forbydelayed
recognition/acceptance
bywhen
both
academic
and chemical
industrial
communities
is was
in
industry
did
not(i.e.,
happen
theand
1980s,
the
industrial
application
of [6].
DWC
reason
for has
delayed
bythe
both
academic
industrial
communities
is that
that
DWC
more
complex
than
conventional
one,
whichchemical
leads
to company)
more design
implemented
by recognition/acceptance
BASF
(i.e.,structure
Baden Aniline
and
Soda
Factory,and
a German
[6]. The
DWC
has
more
complex
structure
than
the
conventional
one,
which
leads
to
more
design
parameters
and
makes
the
dynamics
of
the
DWC
more
difficult
to
follow.
Since
the
success
of its
reason for delayed recognition/acceptance by both academic and industrial communities
is that
parameters
andmore
makes
the dynamics
of wide
the
DWC
difficult
follow.
Since
the success
of design
its
application,
DWC
has gradually
obtained
recognition.
By 2010,toover
100
DWC
applications
were
DWC has
complex
structure
than
themore
conventional
one,
which
leads
to more
application,
DWC
has
gradually
obtained
wide
recognition.
By
2010,
over
100
DWC
applications
facilitated
worldwide
[7],
prominent
among
which
are
catalytic
product
recovery
by
a
dividing
wall
parameters and makes the dynamics of the DWC more difficult to follow. Since the success of its
wereapplication,
facilitated
worldwide
[7],i.e.,
prominent
among
which
are
catalytic
recovery
by
a dividing
debutanizer
column
[8]has
(UOP,
Universal
Oilwide
Products,
a US
chemical
company)
high-purity
DWC
gradually
obtained
recognition.
By product
2010,
over
100and
DWC
applications
wallwere
debutanizer
i.e., Universal
Products,
a USproduct
chemical
company)
and
facilitatedcolumn[8]
worldwide(UOP,
[7], prominent
amongOil
which
are catalytic
recovery
by a dividing
wall debutanizer column[8] (UOP, i.e., Universal Oil Products, a US chemical company) and
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high-purity 2-ethylhexyl-acrylate [9] and neopentyl glycol [10] preparation using the DWC
(LG
3 of 17
Chem, i.e., a Korean chemical company). In academia, DWCs are studied to conduct azeotropic,
extractive, and reactive distillation. Kiss et al. [11] proposed an innovative dimethyl ether synthesis
2-ethylhexyl-acrylate
[9] andDWC,
neopentyl
glycol
[10] preparation
using
(LG Chem,
i.e., ain
process based on a reactive
in which
a reactive
distillation
unit the
wasDWC
effectively
conducted
Korean
chemical
company).
In
academia,
DWCs
are
studied
to
conduct
azeotropic,
extractive,
and
one DWC. By their accounts, the integrated reactive DWC outperformed conventional or reactive
reactive
distillation.
et al. [11] proposed
an innovative
dimethyl
ether
process
on
distillation
schemesKiss
by significant
saving energy
of 12–58%,
reducing
COsynthesis
2 emissions
up tobased
60%, and
alowering
reactive DWC,
in which
a reactive
unit
effectively
conducted
in one
By their
total annual
costs
up to distillation
30%. Lan-Yi
et was
al. [12]
proposed
the DWC
for DWC.
heterogeneous
accounts,
thedistillation
integrated reactive
DWC outperformed
conventional
or reactive
distillationby
schemes
azeotropic
using cyclohexane
as an entrainer
for ethanol
dehydration,
which by
an
significant
saving
energyand
of 12–58%,
reducing
CO2 emissions
up towere
60%,achieved.
and lowering
totalIgnat
annual
energy saving
of 42.17%
total annual
cost reduction
of 35.18%
Kiss and
[13]
costs
up to
30%. Lan-Yi
et al.
proposed
thedehydrate
DWC for bio-ethanol
heterogeneous
azeotropic
distillation
applied
a extractive
DWC
to [12]
concentrate
and
in one
step, with
ethylene using
glycol
cyclohexane
as an entrainer
as mass separating
agent. for ethanol dehydration, by which an energy saving of 42.17% and total
annual
cost reduction
35.18% design
were achieved.
Kiss
andbeen
Ignatrather
[13] applied
DWCand
to
However,
due to of
increased
parameters,
it has
difficultatoextractive
design, model
concentrate
and
dehydrate
bio-ethanol
in
one
step,
with
ethylene
glycol
as
mass
separating
agent.
simulate DWCs. Although the MultiFrac unit of Aspen Plus can be used to model the Petlyuk
However, due
to increased
design
parameters,
has been
difficult
to design,
model
configurations,
simulation
modules
exclusively
foritDWC
are rather
still not
available
in commercial
and
simulate
DWCs.such
Although
thePlus,
MultiFrac
unit
Aspen Plus
canMoreover,
be used tothe
model
the model
Petlyukin
process
simulators
as Aspen
HYSYS,
or of
ChemCAD
[1,7].
Petlyuk
configurations,
exclusively
for DWC are
available
in commercial
process
Aspen Plus is simulation
not flexiblemodules
for customized
modification
duestill
to not
its closed
software
environment.
In
simulators
Aspen
Plus, HYSYS,
oras
ChemCAD
[1,7].
Moreover,
the Petlyuk
in Aspen
practice, a such
DWCasunit
is always
modeled
a sequence
of simple
column
sections,model
for example
the
Plus
is not flexible
for customized
modification
duemodel
to its and
closed
environment.
practice,
a
pump-around
model,
the two-column
sequence
thesoftware
four-column
sequenceInmodel
[1,7],
DWC
unit isinalways
as a sequence
of simple
columnmentioned
sections, for
example
the pump-around
as shown
Figuremodeled
3a–c, respectively.
Once
the models
above
approximate
a typical
model,
two-column
sequence model
and the
four-column
sequence
[1,7],
shown in
DWC, the
its structure
is partitioned
deliberately
and
some of the
internalmodel
relations
areasexposed
as
Figure
3a–c,
respectively.
Once
the
models
mentioned
above
approximate
a
typical
DWC,
its
structure
decision variables, which increase the number of dimensions overall and complicate the problem.
isFurthermore,
partitioned deliberately
some ofmentioned
the internalsimulators
relations are
exposed the
as decision
variables,
which
most of the and
previously
implement
sequential
modular
(SM)
increase
the which
numberadopts
of dimensions
overall and complicate the
problem.
Furthermore,
most of the
approach,
the iteration-and-convergence
solving
strategy.
Both increasing
the
previously
simulators
the sequential
modular
(SM) with
approach,
adopts
dimensionmentioned
and adopting
the SMimplement
approach cause
the simulator
to work
high which
computational
the
iteration-and-convergence solving strategy. Both increasing the dimension and adopting the SM
cost.
approach cause the simulator to work with high computational cost.
Processes 2019, 7, 26
Figure
column
model:
(a) the
model;
(b) the(b)
two-column
sequencesequence
model;
Figure3.3.Equivalent
Equivalent
column
model:
(a) pump-around
the pump-around
model;
the two-column
and
(c) the
four-column
sequencesequence
model. model.
model;
and
(c) the four-column
To
Totackle
tacklethe
theproblems
problemsabove,
above,aarigorous
rigorousDWC
DWCmodel
modelwas
wasdeveloped
developedin
inthe
thegeneral
generalprocess
process
modeling
system
(gPROMS)
environment
(Imperial
College
London,
Process
System
Enterprise
modeling system (gPROMS) environment (Imperial College London, Process System Enterprise
Ltd.,
Ltd.,
London,
UK, Version
4.0). gPROMS
software
is a flexible,
openand
source
and user-friendly
London,
UK, Version
4.0). gPROMS
software
is a flexible,
open source
user-friendly
platform,
platform,
suitable
for modeling
unconventional
or complex
as the
especiallyespecially
suitable for
modeling
unconventional
or complex
process process
systems,systems,
such as such
the catalyst
catalyst
activity
reduction
[14],
the
emulsion
polymerization
reaction
[15]
or
the
dynamics
of
activity reduction [14], the emulsion polymerization reaction [15] or the dynamics of the
the
non-equilibrium,
three-phase
separation
[16].
One
of
the
key
advantages
of
the
gPROMS
platform
non-equilibrium, three-phase separation [16]. One of the key advantages of the gPROMS platformisis
that it adopts the equation-oriented (EO) approach to solve the problem. As for the DWC case, the
Processes 2019, 7, 26
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decision variables and state variables are treated equally, which further provides high flexibility and
efficiency for solving the design and optimization problems related to the DWC design. Moreover, the
platform enables easy extrapolation to modeling more complex DWC with multiple partitioning walls.
In this paper, a rigorous DWC model is proposed based on the equilibrium stage assumption,
which may be used as a standard DWC module for further development. The rigorous DWC modeling
is detailed in Section 2. Then, the proposed model was tested and validated (against literature data) by
separation of a ternary mixture of benzene–toluene–xylene (BTX), as presented in Section 3. Based on
the case study, some of the general features about the DWC can be properly outlined and easily studied
with this rigorous DWC model. For example, the liquid and vapor split ratio are key design parameters
for the DWC, which can be studied similarly to other parameters by our proposed model, whereas, in
the “equivalent model” (as shown in Figure 3), they are exposed as decision variables, and one testing
point needs a full procedure of initial guess, iteration and convergence. Hence, we present the DWC
analysis on three key indicators for designing and assessment purposes: the liquid and vapor split
ratio, the middle component split ratio and the degree of mixing. Finally, conclusions are drawn about
the DWC based on the proposed model in Section 4.
2. Materials and Methods
As mentioned above, most existing models for the DWC are based on the combination of
conventional columns, which is only thermodynamically equivalent to the DWC. Here, a rigorous
DWC model is established based on the following assumptions:
(1)
(2)
(3)
At each stage, the vapor and liquid reach their equilibrium right after their contacting, so the
vapor and liquid leaving this stage are at equilibrium state.
The number of stages on both sides of the dividing wall is identical; hence, the pressure drop is
uniform across each stage.
The heat transfer across the dividing wall is ignored.
For modeling purpose, the DWC is considered to incorporate four main sections as shown in
Figure 4. I section is the public rectifying section, II is actually the pre-fractionator, III is the main
column, and IV is the public stripping section. A typical schematic representation of a generic stage is
shown in Figure 5. Each stage contains mass, enthalpy balance equations, phase equilibrium equations
and summary equations (MESH). The corresponding equations for the jth -stage are given below:
1. Mass balance equations
Fj + L j−1 + Vj+1 − (S j + L j ) − (Vj + Gj ) = 0
(1)
Fj zi,j + L j−1 xi,j−1 + Vj+1 yi,j+1 − (S j + L j ) xi,j − (Vj + Gj )yi,j = 0
(2)
where F is feed flow rate; L and V are the flow rates in liquid and vapor phases; S and G are the
side-draw flow rates in liquid and vapor phases; xi is liquid fraction; and yi is vapor fraction.
2. Phase equilibrium equations
yi,j = Ki,j xi,j
(3)
where K is phase equilibrium constant, which can be obtained by a suitable thermodynamic equation
of state.
3. Enthalpy balance equations
Fj HjF + L j−1 HjL−1 + Vj+1 HjV+1 − (S j + L j ) HjL − (Vj + Gj ) HjV + Q j = 0
where HF is the enthalpy of feed stream; and HV and HL are the enthalpy of vapor and liquid.
4. Summary equations
∑ xi,j = 1
(4)
(5)
F is the enthalpy
4. HSummary
equations
of feed stream; and HV and HL are the enthalpy of vapor and liquid.
where
4.
Summary equations
(5)
x = 1
x =1
(5)
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(6)
y = 1
y =stage
1 within the four sections. As shown in
(6)
y each
Equations (1)–(6) are generally suitable for
=1
(6)
i,j
i,j
i,j
i,j
i,j
∑ stage
Figure 3, the last stage of I section and the first
of IV need special consideration, because they
Equations (1)–(6) are generally suitable for each stage within the four sections. As shown in
Equations (1)–(6)
are splitting
generallyand
suitable
forofeach
stage and
within
the streams.
four sections.
As shown
in
are accompanied
with the
mixing
the liquid
vapor
As shown
in Figure
Figure 3, the last stage of I section and the first stage of IV need special consideration, because they
Figure
3, thethe
lastdividing
stage of Iwall,
section
and
the first
stage
IV need
consideration,
because
are
6a, above
the
liquid
from
I of
splits
into special
two streams,
and one
goesthey
to the
are accompanied with the splitting and mixing of the liquid and vapor streams. As shown in Figure
accompanied
with
the the
splitting
of thecolumn.
liquid and
As shown
in Figure
pre-fractionator
while
other and
goesmixing
to the main
Thevapor
vaporstreams.
leaving the
first stage
of both6a,
II
6a, above the dividing wall, the liquid from I splits into two streams, and one goes to the
above
dividing
wall,
the liquid
frominI Figure
splits into
streams,
and onewall,
goesthe
to the
pre-fractionator
and IIIthe
goes
to I and
mixes.
Similarly,
6b, two
below
the dividing
vapor
stream from
pre-fractionator while the other goes to the main column. The vapor leaving the first stage of both II
IV splits
well,goes
andtoenters
the pre-fractionator
andleaving
main column.
liquid
leaving
the
stage
while
theas
other
the main
column. The vapor
the firstThe
stage
of both
II and
IIIlast
goes
to I
and III goes to I and mixes. Similarly, in Figure 6b, below the dividing wall, the vapor stream from
of II mixes.
and III Similarly,
goes to IVinand
mixes.
and temperature
remain
unchanged
and
Figure
6b,Concentration
below the dividing
wall, the vapor
stream
from IV after
splitssplitting
as well,
IV splits as well, and enters the pre-fractionator and main column. The liquid leaving the last stage
[17] enters
for split
streams.
and
the
pre-fractionator and main column. The liquid leaving the last stage of II and III goes to
of II and III goes to IV and mixes. Concentration and temperature remain unchanged after splitting
IV and mixes. Concentration and temperature remain unchanged after splitting [17] for split streams.
[17] for split streams.
Figure 4. Four sections in dividing wall column (DWC).
Figure 4. Four sections in dividing wall column (DWC).
Figure 4. Four sections in dividing wall column (DWC).
Gj
Gj
Fj
zi ,Fj
Vj
L j −1
Vj
yi , j
L j −1
xi , j −1
yi , j
xi , j −1
± Qj
j th
j
zi , j
± Qj
j th
V j +1
xi , j
yi , j +V1 j +1
L jx i , j
yi , j +1
Lj
Sj
Sj
Figure 5. Scheme for the jth stage.
Figure 5. Scheme for the jth stage.
Figure 5. Scheme for the jth stage.
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LΙN1 −1
VNΙ1
Ι
N1
L
V1ΙΙ
LΙΙ0
LΙΙΙ
0
L
L1ΙΙ
L1ΙΙΙ
VNΙΙΙ3
VNΙΙΙ3 −1
V1ΙΙΙ
ΙΙ
N2
V2ΙΙ
VNΙΙ2
LΙΙN2 −1
VNΙΙ2 +1
VNΙΙΙ3 +1
LΙΙΙ
N3
ΙV
1
V
V2ΙΙΙ
V2ΙV
L1ΙV
Figure 6. The liquid and vapor splitting and mixing at the specific wall: (a) the structure at the top of
the column, and (b) the structure at the bottom of the column.
Figure 6. The liquid and vapor splitting and mixing at the specific wall : (a) the structure at the top
Above
the dividing
the liquid
from
the of
last
of I is splits into two streams, one enters
of
the column,
and (b) wall,
the structure
at the
bottom
thestage
column.
the pre-fractionator, while the other going to the main column. That means,
Above the dividing wall, the liquid from the last stage of I is splits into two streams, one enters
I
= main
LII
LIII
(7)
the pre-fractionator, while the other going L
toNthe
That means,
0 + column.
0
1
III
LN1 =theL0last
+ Lstage
(7)
where LIN1 represents the total liquid flow from
of I, and LII
0
0 and L0 represent the liquid
streams which enter the first stage of II (pre-fractionator) and III (main column), respectively. The
II
III
LIN1 represents
the total
liquid flow
where
liquid split
ratio is defined
accordingly
as: from the last stage of I, and L0 and L0 represent the
I
II
III
liquid streams which enter the first stage of II (pre-fractionator)
and III (main column), respectively.
LII
0
The liquid split ratio is defined accordingly as:
βL = I
(8)
L N1
LII
LN1 column.
goes to the pre-fractionator, and the other enters the main
0
β Lfrom
= Ithe
Below the dividing wall, the vapor stream
first stage of IV splits into two streams, (8)
one
Below the dividing wall, the vapor stream
from the first stage of IV splits into two streams, one
V IV = V II2 +1 + VNIII3 +1
(9)
goes to the pre-fractionator, and the other1 entersNthe
main column.
V1IV = VNII2 +1 + VNIII3 +1
(9)
Processes 2019, 7, 26
7 of 17
where V1IV represents the total vapor stream from the first stage of IV, and VNII2 +1 and VNIII3 +1 represent
the vapor streams which enter the last stage of II and III, respectively. Here, the vapor split ratio is
defined as:
VNII2 +1
βV =
(10)
V1IV
As the vapor streams from both sides of the dividing wall are mixed, the material and enthalpy
balance equations of the last stage of I are different from other stages, and can be described as follows,
V1II + V1III + LIN1 −1 − VNI 1 − LIN1 = 0
(11)
II
III
I
I
I
V1II HV,1
+ V1III HV,1
+ LIN1 −1 HL,N
− VNI 1 HV,N
− LIN1 HL,N
=0
1
1
1 −1
(12)
where L and V are the flow rates in liquid and vapor phases, and HV and HL are the enthalpy of vapor
and liquid.
As the liquid streams from both ends of the dividing wall are mixed, the material and enthalpy
balance equations of the first stage of Section IV are different from other stages and can be described
as follows,
IV
IV
IV
LIIN2 + LIII
(13)
N3 + V2 − L1 − V1 = 0
II
III
IV IV
IV IV
IV IV
LIIN2 HL,N
+ LIII
N3 HL,N3 + V2 HV,2 − L1 HL,1 − V1 HV,1 = 0
2
(14)
It is interesting to investigate how each component moves through the column sections towards
the products. According to the Mueller and Kenig [18], another important parameter RB,top , the middle
component split ratio at the top of the pre-fractionator, is defined as:
R B,top =
Vout,top .yout,top,B − Lin,top .xin,top,B
Fz B
(15)
Accordingly, the middle component split ratio at the bottom of the pre-fractionator is defined as:
R B,botm =
Lout,botm .xout,botm,B − Vin,botm .yin,botm,B
Fz B
(16)
As shown in Figure 7, Vout,top and Lin,top represent the outlet vapor flowrate and inlet liquid
flowrate at the top of the pre-fractionator; yout,top,B and xout,top,B represent the middle component
mole fractions of the corresponding streams; Lout,botm and Vin,botm represent the outlet liquid and inlet
vapor flowrate at the bottom of the pre-fractionator, respectively; xout,botm,B and yin,botm,B represent
the middle component mole fractions of the corresponding streams. From Equations (15) and (16),
parameters R B,top and R B,botm are related to the liquid and vapor split ratio. Note that the summation
of R B,top and R B,botm is 1. Thus, if one parameter is known, the other can be readily determined.
Processes
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26 PEER REVIEW
Processes
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6, x7,FOR
of 17
8 of8 18
Vout , top
Lin ,top
Vin,botm
Lout,botm
Figure 7. Material balance in Equations (15) and (16).
Figure 7. Material balance in Equations (15) and (16).
Mixing streams with different compositions, which occurs at stages of I and IV right next to the
Mixing
streams
with
different
compositions,
which occurs
atcomponent
stages of I and
IV II
right
to the
dividing wall,
means
changes
of the
monotonic property
of each
within
andnext
III (typically,
dividing
wall,
means
changes
of
the
monotonic
property
of
each
component
within
II
and
III
a weighted average of that from both sides). This inevitably accompanies with an increase in entropy,
(typically,
weighted
ofthermodynamic
that from both sides).
This inevitably
accompanies
with
an increase
which is aan
intrinsicaverage
source of
inefficiency
of the separation
process
occurring
in the
in DWC
entropy,
which
is
an
intrinsic
source
of
thermodynamic
inefficiency
of
the
separation
process
[1,7,19]. To measure the mixing effect at both ends of the dividing wall, the liquid and vapor
occurring
in the need
DWCto[1,7,19].
To measure
the mixing
effect
both ends
of the
dividing
the
mixing degree
be assessed.
In this paper,
we define
theatdegree
of liquid
mixing
as thewall,
quadratic
liquid
vaporconcentration
mixing degree
need to for
be assessed.
In this paper,atwe
the
of liquid
sum and
of liquid
difference
the three components
thedefine
bottom
ofdegree
the dividing
wall,
mixing
as
the
quadratic
sum
of
liquid
concentration
difference
for
the
three
components
at the
and similarly the degree of vapor mixing is defined as the quadratic sum of the vapor concentration
bottom
of the
and similarly
of vapor
mixing is defined as the quadratic
difference
fordividing
the threewall,
components
at the the
top degree
of the wall
indicates,
sum of the vapor concentration difference for the three components at the top of the wall indicates,
2
Degree o f liquid mixing = ( x
)2 + ( xC,pre f rac − x2C,main )2 (17)
2
f rac − x A,main2 ) + ( x B,pre f rac − x B,main
Degree of liquid mixing = ( xA,pre
−
x
)
+
(
x
−
x
)
+
(
xC , prefrac − xC ,main )
(17)
A, prefrac
A, main
B , prefrac
B , main
2
2
2
Degree of
o f vapor
)2 + (yC,pre f rac − yC,main
)2 (18)
f rac − y A,main2 ) + ( y B,pre f rac − y B,main
Degree
vapormixing
mixing== ((yyA,pre
(18)
A, prefrac − y A, main ) + ( y B , prefrac − y B , main ) + ( yC , prefrac − yC , main )
The solution of the rigorous model of the DWC described in previous section (Equations (1)–(14))
The solution of the rigorous model of the DWC described in previous section (Equations
requires definition of a number of parameters: the number of stages in the four different sections of
(1)–(14)) requires definition of a number of parameters: the number of stages in the four different
the column, the locations of the feed and side-draw, feed condition and the position of the dividing
sections of the column, the locations of the feed and side-draw, feed condition and the position of the
wall [19].
dividing wall [19].
2.1. Case Description
2.1. Case Description
A ternary feed mixture of Benzene (A), Toluene (B) and p-Xylene (C) was used as the case study.
ternary was
feedset
mixture
of Benzene
Toluene as
(B)358
and
(C) was used
the30:30:40
case
TheAflowrate
as 1 kmol/s,
feeding(A),
temperature
K, p-Xylene
and the composition
ratioaswas
study.
setwas
as 1 implemented
kmol/s, feeding
asthe
358three
K, and
the composition
ratio purity
was
mol%The
forflowrate
A:B:C. Awas
DWC
fortemperature
separation of
components
with molar
30:30:40
mol%
for
A:B:C.
A
DWC
was
implemented
for
separation
of
the
three
components
with
up to 99 mol% by each.
molar purity
up toto99Luyben
mol% by
each.
According
[20],
there are four sections in the DWC (as shown in Figure 4), 12 stages
According
to
Luyben
[20],
there
are four
sections
the DWC
(as shown in
4), of
12 II
stages
for I and IV, and 24 stages for II and
III. The
feed in
steam
was introduced
at Figure
Stage 12
in the
forpre-fractionator,
I and IV, and the
24 stages
for
II
and
III.
The
feed
steam
was
introduced
at
Stage
12
of
II
the
middle component was extracted from the main column at the side-draw in
of Stage
pre-fractionator,
middle
was extracted from the main column at the side-draw of
11 in III, and thethe
reflux
ratiocomponent
was set as 2.62.
Stage 11 in III, and the reflux ratio was set as 2.62.
2.2. Model Validation
2.2. Model Validation
Based on the configuration described above, the DWC model proposed in this paper was adopted
Based
onthe
theternary
configuration
above,
theand
DWC
model with
proposed
in this
paperpurities.
was
to separate
mixturedescribed
of benzene,
toluene
o-xylene,
99 mol%
product
adopted
separate
ternary mixture
of benzene,
toluene with
and o-xylene,
with 99[20].
mol% product
Table 1 to
presents
thethe
simulation
results, which
are compared
those of Luyben
purities. Table 1 presents the simulation results, which are compared with those of Luyben [20].
Processes 2019, 7, 26
9 of 17
Table 1. Results comparison between this paper and Luyben [20].
This work
Luyben
Tcon #
/K
Treb
/K
D
/kmol·s−1
S
/kmol·s−1
B
/kmol·s−1
Qreb
/MW
Qcon
/MW
LP
/kmol·s−1
VP
/kmol·s−1
323
322
396.8
403.7
0.3027
0.303
0.296
0.296
0.4013
0.401
42.597
39.15
34.698
36.46
0.303
0.208
0.651
0.612
Tcon # and Treb are condenser temperature and reboiler temperature; D, S and B are molar flow rate of distillate,
side-draw and bottoms; Qreb and Qcon are heat duty of condenser and reboiler; Lp is liquid stream going to the first
stage of II (prefractionator); Vp is vapor stream going to the last stage of II.
As shown in Table 1, the simulation result by our model shows an excellent agreement with those
of Luyben [20]. We also cross-validated the simulation results with other process simulation platform,
e.g., Aspen Plus (Version 7.1, Aspen Technology, Inc., Burlington, MA, USA, 2009). After a few tests
on different thermodynamic models or other ternary species separation cases, we rendered that the
model we developed is mathematically correct in describing the DWC process, and further analysis
based on this model is presented in the next section.
3. Results and Discussion
The DWC has the prominent feature of energy saving compared to the conventional columns,
which makes it a problem for the assessment of its energy efficiency. The rigorous DWC model
developed in this paper enables implementing the assessment procedure simply. Based on the
case study introduced previously, three key indicators, the liquid and vapor split ratio, the middle
component split ratio and the degree of mixing, are discussed in detail as follows. Note that not all
indicators are mandatory for a specific DWC application. We incorporated all of them to both test our
DWC model and outline the general properties of a DWC at different angles.
3.1. The Effect of Liquid and Vapor Split Ratio
As defined in Section 2, vapor split ratio is the vapor flowrate entering the pre-fractionator against
the total vapor flowrate, and the liquid split ratio is the liquid flowrate entering the pre-fractionator
against the total liquid flowrate. The split and mix of liquid and vapor flows from both sides of the
dividing wall take place at both ends of the wall, which can be adjusted by proper positioning of the
dividing wall, or by shifting the capacity from one side to the other.
The liquid and vapor split ratio affects the separation performance and energy efficiency of a
DWC. If the liquid or vapor split ratio is too low, it means that large amount of vapor flow or liquid
flow enters the main column. If the liquid or vapor split ratio is too high, it means that large amount of
vapor flow or liquid flow enters the pre-fractionator. As these cases are similar with the separation of
three components in a conventional distillation, the split ratios considered were within the range from
0.35 to 0.66.
For specified separation requirement and DWC configuration, the performance depends on its
energy consumption at the steady state, i.e., heat duties of reboiler and condenser (neglects energy
loses elsewhere). Figures 8 and 9 illustrate the reboiler and condenser heat duties under different
liquid and vapor split ratios.
Processes 2018, 6, x FOR 250
PEER REVIEW
Reboiler heat duty
/kW heat duty /kW
Reboiler
Processes 2019, 7, 26
β V = 0.56
10 of 18
β V = 0.58
10 of 17
β V = 0.6
200
β V = 0.62
ββV =
= 0.56
0.64
V
ββV =
0.58
= 0.66
250
150
V
β V = 0.6
200
100
β V = 0.62
β V = 0.64
150
50
1000.30
β V = 0.66
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
βL
50
0.35
0.40split0.45
0.55 heat
0.60
0.65the case
0.70study.
Figure 8. 0.30
The effect
of liquid
ratio on0.50
the reboiler
duty for
βL
Figure 8. The effect of liquid split ratio on the reboiler heat duty for the case study.
Figure 8. The effect of liquid split ratio on the reboiler heat duty for the case study.
βV = 0.56
250
Condenser heat
duty /kWheat duty /kW
Condenser
βV = 0.58
βV = 0.6
200
150
0.62
ββVV == 0.56
0.64
ββV == 0.58
200
0.66
ββVV == 0.6
100
βV = 0.62
150
βV = 0.64
50
βV = 0.66
250
100
0.30
V
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
βL
Figure 9. 50
The effect of liquid split ratio on the condenser heat duty for the case study.
For a specified vapor
ratio β0.40
heat duty
varies0.60
with the
change
of the liquid split
0.30 split
0.35
0.45
0.50
0.55
0.65
0.70
V , the reboiler
Figure 9. The effect of liquid split ratio on the condenser heat duty for the case study.
ratio βL , i.e., when the vapor split ratio βV is 0.56 in βFigure 8, the heat duty of the reboiler decreases
L
first, and then increases with the increase of βL after reaching its minimum value of 0.43. Hence, an
For a specified vapor split ratio βV, the reboiler heat duty varies with the change of the liquid
optimal liquid split ratio exists to reduce the reboiler duty to minimum when the vapor split ratio
split ratio βL, i.e., when the vapor split ratio βV is 0.56 in Figure 8, the heat duty of the reboiler
is specified. In accordance with the result in Figure 8, for a given vapor split ratio βV , the heat duty
decreases first, and then increases with the increase of βL after reaching its minimum value of 0.43.
of condenserFigure
decreases
first
and
the
increaseheat
of liquid
split
βL , as shown in
9. The
effect
of then
liquidincreases
split ratiowith
on the
condenser
duty for
the ratio
case study.
Hence, an optimal liquid split ratio exists to reduce the reboiler duty to minimum when
the vapor
Figure 9. Consequently, there also exists an optimal βL that minimize the heat duty of the condenser.
split ratio is specified. In accordance with the result in Figure 8, for a given vapor split ratio βV, the
specified
, theoptimal
reboilervalue,
heat duty
varies withand
thereboiler
change heat
of theduties
liquid
WhenFor
the aliquid
splitvapor
ratio split
is lessratio
thanβVthe
the condenser
heat duty of condenser decreases first and then increases with the increase of liquid split ratio βL, as
split
ratio
β
L
,
i.e.,
when
the
vapor
split
ratio
β
V
is
0.56
in
Figure
8,
the
heat
duty
of
the
reboiler
increase with the increase of vapor split ratio and vice versa. Therefore, there is always an optimal
shown in Figure 9. Consequently, there also exists an optimal βL that minimize the heat duty of the
decreases
then
increases
with the
increase
ofheat
βL after
reaching
its minimum
value
0.43.
liquid
split first,
ratio and
where
both
the condenser
and
reboiler
duties
reach minimum
when
the of
vapor
Hence,
liquid split ratio exists to reduce the reboiler duty to minimum when the vapor
split
ratioan
is optimal
specified.
split ratio is specified. In accordance with the result in Figure 8, for a given vapor split ratio βV, the
heat duty of condenser decreases first and then increases with the increase of liquid split ratio βL, as
shown in Figure 9. Consequently, there also exists an optimal βL that minimize the heat duty of the
condenser. When the liquid split ratio is less than the optimal value, the condenser and reboiler heat
duties increase with the increase of vapor split ratio and vice versa. Therefore, there is always an
optimal liquid split ratio where both the condenser and reboiler heat duties reach minimum when
the vapor split ratio is specified.
Processes 2019, 7, 26
11 of 17
3.2. The Middle Component Split Ratio
In Section 2, we define the middle component split ratio at the top and bottom of the
3.2.
The Middle Component
Split
Ratio
pre-fractionator
(Equations
(15)
and (16)). According to the definition, the middle component split
ratioInis Section
determined
by
the
liquid
vapor
streams entering
the at
pre-fractionator,
which directly
2, we define the and
middle
component
split ratio
the top and bottom
of the
affects the overall
heat duty
the(16)).
DWC.
In practice,
thedefinition,
ratio of liquid
refluxcomponent
to feed (L/F)
pre-fractionator
(Equations
(15)ofand
According
to the
the middle
splitis
commonly
used.
Figures
10
and
11
show
the
behavior
of
the
middle
component
split
ratio
at
the
top
ratio is determined by the liquid and vapor streams entering the pre-fractionator, which directly affects
of pre-fractionator
the corresponding
L/Fratio
under
different
liquid
and(L/F)
vaporissplit
ratios. used.
the
overall heat dutyagainst
of the DWC.
In practice, the
of liquid
reflux
to feed
commonly
Figures 10 and 11 show the behavior of the middle component split ratio at the top of pre-fractionator
against the corresponding L/F under different liquid and vapor split ratios.
Reboiler heat duty /kW
70
βV = 0.56
65
βV = 0.58
60
βV = 0.62
βV = 0.6
βV = 0.64
βV = 0.66
55
50
45
40
0.0
0.1
0.2
0.3
0.4
1.6
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
βV = 0.56
1.5
βV = 0.58
1.4
L/F
0.5
βV = 0.6
1.3
βV = 0.62
1.2
βV = 0.64
1.1
βV = 0.66
1.0
0.9
0.8
0.7
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Middle component split ratio
Figure 10. The middle component split ratio at the top of pre-fractionator versus corresponding L/F
and the heat duty of reboiler.
Figure 10. The middle component split ratio at the top of pre-fractionator versus corresponding L/F
and the heat duty of reboiler.
Processes 2019, 7, 26
Processes 2018, 6, x FOR PEER REVIEW
12 of 17
12 of 18
65
βL = 0.43
βL = 0.45
Reboiler heat duty /kW
60
βL = 0.47
βL = 0.49
βL = 0.51
55
βL = 0.53
βL = 0.55
50
45
40
0.0
1.5
0.1
0.2
0.3
0.4
0.6
1.4
βL = 0.43
1.3
βL = 0.47
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
βL = 0.45
βL = 0.49
1.2
L/F
0.5
βL = 0.51
βL = 0.53
1.1
βL = 0.55
1.0
0.9
0.8
0.7
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Middle component split ratio
Figure 11. The middle component split ratio at the top of column versus L/F and the heat duty
of reboiler.
Figure 11. The middle component split ratio at the top of column versus L/F and the heat duty of
Figures 12 and 13 shows how both the reboiler and condenser heat duties vary with changes of
reboiler.
the vapor split ratio. For a given liquid split ratio βL , an optimal vapor split ratio can minimize the heat
duty of both the reboiler and condenser. The results show that the separation performance is almost
Figures 12 and 13 shows how both the reboiler and condenser heat duties vary with changes of
the same as that in the single distillation column, but the heat duty of the DWC increases dramatically.
the vapor split ratio. For a given liquid split ratio βL, an optimal vapor split ratio can minimize the
Figure 14 shows the total heat duty under different liquid and vapor split ratios. Total heat duty
heat duty of both the reboiler and condenser. The results show that the separation performance is
is the sum of condenser heat duty and reboiler heat duty. We can see that the minimum total heat duty
almost the same as that in the single distillation column, but the heat duty of the DWC increases
is 77.557 kW when liquid split ratio is 0.45 and vapor split ratio is 0.58. Based on the above analysis,
dramatically.
the liquid and vapor split ratios strongly affect the heat duty of the DWC. Hence, it is necessary to
Figure 14 shows the total heat duty under different liquid and vapor split ratios. Total heat duty
decide the liquid and vapor split ratio appropriately to design a good DWC.
is the sum of condenser heat duty and reboiler heat duty. We can see that the minimum total heat
For specified vapor and liquid split ratio, when the middle component split ratio increases, heat
duty is 77.557 kW when liquid split ratio is 0.45 and vapor split ratio is 0.58. Based on the above
duty decreases first, and then reaches the minimum before increasing. The trend of L/F is consistent
analysis, the liquid and vapor split ratios strongly affect the heat duty of the DWC. Hence, it is
with that of the heat duty, i.e., there is a minimum L/F for a given separation requirement, which
necessary to decide the liquid and vapor split ratio appropriately to design a good DWC.
means the minimum energy consumption. In practice, we cannot control the middle component split
For specified vapor and liquid split ratio, when the middle component split ratio increases,
heat duty decreases first, and then reaches the minimum before increasing. The trend of L/F is
consistent with that of the heat duty, i.e., there is a minimum L/F for a given separation
requirement, which means the minimum energy consumption. In practice, we cannot control the
middle component split ratio. Instead, the liquid reflux rate (L) and feed rate (F) are controlled.
Consequently, liquid split ratio and the minimum L/F need to be decided to keep the energy
Processes 2018, 6, x FOR PEER REVIEW
13 of 18
consumption at the optimal value.
means the minimum energy consumption. In practice, we cannot control
13 of the
17
middle component split ratio. Instead, the liquid reflux rate (L) and feed rate (F) are controlled.
140
Consequently, liquid split ratio
and the minimum L/F need to be decided to keep the energy
βL = 0.43
ratio.
Instead, the
liquid
refluxvalue.
rate
(L) and feed rate (F) are controlled. Consequently, liquid split ratio
consumption
at the
optimal
βL = 0.45
and the minimum L/F
decided to keep the energy consumption at the optimal value.
120 need to be
βL = 0.47
140
βL = 0.49
βL = 0.43
100
βL = 0.51
βL = 0.45
βL =0.53
120
βL = 0.47
βL = 0.55
80
βL = 0.49
100
βL = 0.51
60
β =0.53
Reboiler heat Reboiler
duty /kWheat duty /kW
requirement,
Processes
2019, 7, 26which
L
βL = 0.55
80
40
60
0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70
βV
40
0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70
Figure 12. The effect of vapor split ratio on
β reboiler heat duty for the case study.
V
Figure 12. The effect of vapor split ratio on reboiler heat duty for the case study.
Condenser heat
duty /kWheat duty /kW
Condenser
= 0.43
Figure
of vapor split ratio on reboiler heat duty for the case study.
L
120 12. Theβeffect
βL =0.45
100
120
80
100
60
80
40
60
20
0.50
40
βL = 0.47
βL = 0.49
ββL ==0.43
0.51
L
ββL =0.45
= 0.53
L
ββL =
= 0.47
0.55
L
βL = 0.49
βL = 0.51
βL = 0.53
βL = 0.55
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
βV
Figure 13. The effect of vapor split ratio on condenser heat duty for the case study.
20
0.50
0.52effect
0.54
0.56split0.58
0.60
0.62 heat
0.64duty
0.66
0.68
0.70
Figure
13. The
of vapor
ratio on
condenser
for the
case study.
βV
Figure 13. The effect of vapor split ratio on condenser heat duty for the case study.
Processes 2018, 6, x FOR PEER REVIEW
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Processes 2019, 7, 26
14 of 17
240
ty
Total heat du
/kW
280
200
160
120
80
4
2
0.
54
tio
ra
0.
5
pli
rs
0
.5
0
lit
sp
0.5
Va
po
8
.4
id
qu
Li
0.6
0
0 .5
8
4
tr
ati
o
0. 6
2
6
0.4
0
0.4
0.6
6
0.6
6
Figure 14. The total heat duty versus liquid and vapor split ratios for the case study.
3.3. The Effect of Mixing
Figure 14. The total heat duty versus liquid and vapor split ratios for the case study.
We define the degree of mixing above (Equations (17) and (18)). Figures 15 and 16 illustrate the
effect of mixing under different liquid split ratios and vapor split ratios. We can see in Figure 15
that, for a specified vapor split ratio, heat duty decreases first and then increases with the increase of
3.3. split
The Effect
Mixingheat duties are obtained when the degree of liquid mixing or the degree of
liquid
ratio.ofHigher
vapor mixing
is high,
same above
time, higher
or lower
splitFigures
ratio will
to increased
We define
thewhile,
degreeatofthe
mixing
(Equations
(17) liquid
and (18)).
15 lead
and 16
illustrate the
degree
ofof
mixing.
thedifferent
separation
conducted
within
generally
the 15
effect
mixingSince
under
liquid
split ratios
anda distillation
vapor split column
ratios. We
can seefollows
in Figure
monotonic
component
change
along
the
stages
in
both
directions,
the
interruption
of
the
monotonic
that, for a specified vapor split ratio, heat duty decreases first and then increases with the increase of
property
the mixing
which
is obtained
hinders separation.
However,
whenmixing
the liquid
or degree
vapor of
liquid causes
split ratio.
Higher effect,
heat duties
are
when the degree
of liquid
or the
from
bothmixing
sub-columns
at the
endsame
of dividing
wall, or
thelower
monotonic
interrupted
is
vapor
is high,meet
while,
at the
time, higher
liquidproperty
split ratiobeing
will lead
to increased
inevitable.
Hence,
the
degree
of
mixing
can
be
assessed
to
evaluate
the
energy
efficiency
of
the
DWC.
degree of mixing. Since the separation conducted within a distillation column generally follows the
monotonic component change along the stages in both directions, the interruption of the monotonic
property causes the mixing effect, which is hinders separation. However, when the liquid or vapor
from both sub-columns meet at the end of dividing wall, the monotonic property being interrupted
is inevitable. Hence, the degree of mixing can be assessed to evaluate the energy efficiency of the
DWC.
Processes 2018, 6, x FOR PEER REVIEW
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Processes 2019, 7, 26
15 of 17
0.12
βV = 0.56
80
0.08
72
Q
reb
64
0.04
56
0.02
48
0.00
40
0.35
0.40
0.45
0.50
0.55
56
0.06
0.04
L
V
0.02
Q
reb
44
0.40
0.44
0.48
L
V
0.02
48
Q
reb
44
The degree of mixing
The degree of mixing
0.04
52
βL
0.56
0.60
βV = 0.62
0.04
55
0.02
50
45
0.45
0.48
Q
reb
65
60
0.04
55
0.02
50
0.00
45
0.60
0.64
The degree of mixing
The degree of mixing
0.54
0.57
40
0.63
0.60
βL
100
βV = 0.66
0.08
90
L
V
Q
reb
0.06
80
70
0.04
60
0.02
50
0.00
0.45
Heat duty/kW
70
0.06
0.56
0.51
0.10
Heat duty/kW
0.08
65
60
0.42
L
V
70
Q
reb
(d)
βV = 0.64
(e) βL
40
0.06
0.64
75
0.52
L
V
0.08
(c)
0.48
0.64
0.00
0.00
0.44
0.60
Heat duty/kW
56
Heat duty/kW
0.06
0.10
0.56
75
0.10
60
0.52
0.52
L
64
0.48
48
(b) β
βV = 0.6
0.44
52
0.00
0.60
0.10
0.40
60
0.08
(a) βL
0.08
64
βV = 0.58
0.10
Heat duty/kW
0.06
L
V
The degree of mixing
0.10
88
Heat duty/kW
The degree of mixing
0.12
40
0.48
0.51
0.54
(f) β
0.57
0.60
0.63
0.66
L
15. The
Theeffects
effectsofofmixing
mixing
and
heat
duty
of reboiler
versus
liquid
ratio under
different
Figure 15.
and
heat
duty
of reboiler
versus
liquid
split split
ratio under
different
vapor
vaporratios.
split ratios.
L, the liquid
at the bottom
of the dividing
V, the mixing
vapor mixing
split
L, the liquid
mixingmixing
effects effects
at the bottom
of the dividing
wall; V,wall;
the vapor
effects
, theduty
heatofduty
the reboiler:
βV is fixed
at (b)
0.56;
βV is fixed
at
effects
at the
topwall;
of theQwall;
Qreb
at
the top
of the
heat
the of
reboiler:
(a) βV (a)
is fixed
at 0.56;
βV(b)
is fixed
at 0.58;
reb , the
V is fixed
at 0.60;
β
V
is
fixed
at
0.62;
(e)
β
V
is
fixed
at
0.64;
(f)
β
V
is
fixed
at
0.66.
0.58;
(c)
βV(c)
is βfixed
at 0.60;
(d) β(d)
is
fixed
at
0.62;
(e)
β
is
fixed
at
0.64;
(f)
β
is
fixed
at
0.66.
V
V
V
Accordingly,
16 16
areare
similar
to those
in Figure
15. Based
on the on
above
Accordingly, the
theresults
resultsininFigure
Figure
similar
to those
in Figure
15. Based
the results,
above
it
can beitconcluded
that suitable
split
ratiosplit
and ratio
vaporand
split
ratiosplit
can reduce
thereduce
degreethe
of mixing,
results,
can be concluded
that liquid
suitable
liquid
vapor
ratio can
degree
hence
increase
theincrease
separation
efficiency. efficiency.
of mixing,
hence
the separation
To summarize,
three
indicators
are discussed through the rigorous
rigorous DWC
DWC model
model in
in this
this section.
section.
summarize,
The first
areare
for design
purposes,
and the
lastthe
reveals
intrinsic
thatreasons
cause unnecessary
firsttwo
two
for design
purposes,
and
last the
reveals
thereasons
intrinsic
that cause
energy
loss
in
a
DWC
configuration.
It
is
obvious
that
the
three
indicators
are
intercorrelated,
and their
unnecessary energy loss in a DWC configuration. It is obvious that the three indicators
are
analysis
aids
DWC
design
and
evaluation.
intercorrelated, and their analysis aids DWC design and evaluation.
Processes 2018, 6, x FOR PEER REVIEW
Processes 2019, 7, 26
16 of 17
βL = 0.45
65
60
0.04
55
0.02
50
0.08
Degree of mixing
0.06
Q
reb
70
0.56
0.58
0.60
0.62
0.64
60
0.02
50
0.00
40
40
0.56
0.58
0.60
0.62
0.04
51
48
0.02
68
64
L
V
Degree of mixing
54
0.68
0.06
Heat duty/kW
57
Q
reb
0.66
βL = 0.51
0.08
60
L
V
Heat duty/kW
Degree of mixing
0.64
(b)
0.10
63
0.06
80
70
βV
βL = 0.49
Q
reb
0.04
(a)βV
0.08
90
0.06
45
0.00
L
V
Heat duty/kW
L
V
βL = 0.47
0.10
Heat duty/kW
0.08
0.54
100
75
0.10
Degree of mixing
16 of 18
60
Q
reb
56
0.04
52
0.02
48
45
0.00
0.56
0.58
0.60
(c )
βL = 0.53
0.62
0.64
0.66
0.08
0.12
57
0.10
54
Q
reb
0.06
60
51
0.04
48
0.02
0.56
0.58
0.60
βV
0.62
0.64
0.66
0.68
(d)
60
βL = 0.55
58
0.08
L
V
56
Q
reb
54
0.06
52
0.04
50
48
0.02
46
45
0.00
0.54
0.00
0.56
0.58
0.60
(e)
βV
0.62
0.64
0.66
0.68
Heat duty/kW
L
V
44
0.54
Heat duty/kW
Degree of mixing
0.10
βV
0.00
Degree of mixing
0.54
42
0.54
0.56
0.58
0.60
βV
0.62
0.64
0.66
0.68
44
0.70
(f )
Figure 16. The effects of mixing and heat duty of reboiler versus vapor split ratio under different liquid
split
ratios,16.
where
L is theof
liquid
mixing
at the
the dividing
wall,ratio
V is under
the vapor
mixing
Figure
The effects
mixing
and effects
heat duty
of bottom
reboilerof
versus
vapor split
different
effects
at split
the top
of the
wallL and
Qreb
is the
heat duty
(a)the
βL is
fixed atwall,
0.45;V(b)
βL is
liquid
ratios,
where
is the
liquid
mixing
effectsofatthe
thereboiler:
bottom of
dividing
is the
fixed
at
0.47;
(c)
β
is
fixed
at
0.49;
(d)
β
is
fixed
at
0.51;
(e)
β
is
fixed
at
0.53;
(f)
β
is
fixed
at
0.55.
L
L
L
L
vapor mixing effects at the top of the wall and Qreb is the heat duty of the reboiler: (a) βL is fixed at
0.45; (b) βL is fixed at 0.47; (c) βL is fixed at 0.49; (d) βL is fixed at 0.51; (e) βL is fixed at 0.53; (f) βL is
fixed at 0.55.
4. Conclusions
In this paper, a rigorous mathematical model is proposed based on the mass balance, the energy
Conclusions
and4.phase
equilibrium of the DWC, where decision variables and state variables are treated equally,
and thisInmodel
has thea potential
be a standard
DWC
onbased
the gPROMS
platform.
Based
this paper,
rigorous to
mathematical
model
is module
proposed
on the mass
balance,
theon
theenergy
rigorous
model,
the
influences
of
liquid
split
ratio
and
vapor
split
ratio
are
discussed,
and
it is
and phase equilibrium of the DWC, where decision variables and state variables are treated
shown
that
the
heat
duty
is
sensitive
to
changes
in
the
liquid
and
vapor
split
ratio.
Inappropriate
equally, and this model has the potential to be a standard DWC module on the gPROMS platform.
liquid
and
split ratio
willthe
increase
the of
mixing
at both
ends of
theratio
dividing
wall, and
Based
onvapor
the rigorous
model,
influences
liquid effects
split ratio
and vapor
split
are discussed,
and it is
shown
the heat duty
is sensitive
to changes
in of
themixing
liquidisand
vapor
ratio.
adversely
affect
the that
thermodynamic
efficiency.
Hence,
the degree
defined
to split
characterize
Inappropriate
liquid
and
vapor
split
ratio
will
increase
the
mixing
effects
at
both
ends
of
the
the column efficiency. Furthermore, the middle component split ratio at the top of the pre-fractionator
wall,point
and adversely
thesaving
thermodynamic
efficiency.
the degree
of mixing
hasdividing
an optimal
for betteraffect
energy
with certain
liquid Hence,
and vapor
split ratios,
and is
can
thethe
column
efficiency.
Furthermore,
the middle
component
split ratio at
the
be defined
used astoancharacterize
indicator for
energy
performance.
The model
was tested
and validated
against
top of the
has benzene–toluene–xylene
an optimal point for better
energysystem
savingas
with
certain
liquid
and of
literature
datapre-fractionator
using the ternary
mixture
a case
study.
Instead
vapor
split
ratios,
and
can
be
used
as
an
indicator
for
the
energy
performance.
The
model
was
constructing thermodynamically equivalent models by combining conventional columns, the rigorous
model developed in this paper could provide better design and assessment of DWC processes.
Processes 2019, 7, 26
17 of 17
Author Contributions: C.Z. and Q.L. conceived and designed the case-study; Q.L. performed the simulation and
analysis; C.Z. and W.S. conceived and analyzed the solution methods; J.A.R. contributed analysis tools paper
conception; C.Z. and Q.L. wrote and revised the paper.
Funding: The authors gratefully acknowledge the following institutions for support: The National Natural Science
Foundation of China (Grant No. 2157015); and the National Basic Research Program of China, 973 Program
(Grant No. 2013CB733600).
Conflicts of Interest: The authors declare no conflict of interest.
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