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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
Published online 18 June 2009 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.292
Research Article
Design and synthesis of separation process based on a
hybrid method
Chunshan Li,1 * Gu?nter Wozny2 and Kenzi Suzuki1
1
2
EcoTopia Science Institute, Nagoya Unviersity, Nagoya, Japan
Technische Universita?t Berlin, Berlin, Germany
Received 3 September 2008; Revised 15 February 2009; Accepted 16 February 2009
ABSTRACT: A new general hybrid methodology for separation process synthesis and design is proposed, which
considers different separation technologies by integrating mathematical modeling ? Analytical Hierarchy Process (AHP)
with heuristic approaches and thermodynamic insights. The methodology can provide suitable guidance for the initial
separation process design and energy saving. Firstly, a general separation synthesis system based on thermodynamic
insights is developed to select suitable separation techniques before sequencing, which reduces the complexity and
size of synthesis search space. Then, the pseudo-component concept is proposed and used to deal with the azeotrope
contained in the mixture, which widens the scope of the application of the proposed methodology. The AHP method is
used to make a separation sequence by pairwise comparison matrices. Lastly, the separation of the pseudo-component
will be considered, and it performs energy integration and a detailed process design. Application of the proposed
methodology is highlighted through two industrial examples: one is the separation synthesis of a light-end refinery
mixture. The other is azeotrope system, the mixture of phenol, o-cresol, p-cresol, and m-cresol. ? 2009 Curtin
University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: separation synthesis; AHP; thermodynamic insight; mathematical method
INTRODUCTION
In order to obtain products of purity, the separation parts
are crucial for every chemical process, whose capital
and operating costs will occupy from 40 to 70% of
that of the whole chemical plants. So finding suitable
synthesis methodology for separation process is urgent.
For each of the resulting separation tasks, more than
one separation technique may be feasible. Furthermore,
since more than one separation task will frequently be
required, the best sequence of separation tasks must
be established. Finally, a suitable and consistent set
of operating conditions must be determined; thus the
synthesis of separation process is a complex problem in
chemical engineering.[1]
In principle, separation process synthesis is based on
either a heuristic, thermodynamic insight or mathematical programming approaches. Heuristic method uses the
rule of thumb resulting from an engineering experience
and insights from the physics and chemistry of the separation method, which does not require any mathematical background and computational skill for the users;
*Correspondence to: Chunshan Li, EcoTopia Science Institute,
Nagoya Unviersity, Nagoya, 464-8603, Japan.
E-mail: chunshanli@gmail.com
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
thus it is easy for application.[2 ? 6] Thompson and King
(1972) proposed the use of heuristics to generate process alternatives, followed by eliminating the infeasible
separations with known constraints.[2] Nadgir (1983)
developed a simple-ordered heuristic method for the
systematic synthesis of initial sequences for multicomponent separations.[3] Barnicki and Fair (1990,1993)
provided a comprehensive set of rules for liquid and
gas/vapor separations and demonstrated how to arrive
at a design.[6] Douglas (1995) described how to consider
a wide range of separation techniques in a hierarchical
manner, emphasizing the interactions among the subsystems for gas/vapor, liquid, and solid separations.[5]
Shi(1997) put up a relative cost function replacing
the coefficient of ease of separation (CES), but which
does not fundamentally differ from the ordinary rules.[6]
Although heuristic rules to guide the order of separation sequencing have been available, many of the known
heuristic contradict or overlap others; many procedures
to resolve these conflicts have not been adequately
developed.[7,8]
Recently, Bek-Pedersen(2000, 2004) proposed a
driving-force-based approach to design and synthesize
distillation systems that were mainly based on thermodynamic insights by graphic method,[9,10] which provide a measure of the differences in chemical/physical
906
C. LI, G. WOZNY AND K. SUZUKI
properties between two co-existing phases in a separation unit. Approach based on thermodynamic insight
is often adopted by experience engineers and is easy
to use. But it is often trapped in local optimum, overlooks global optimization, and also a little difficult to
be applied in a complex system.[11]
Mathematical approach is another totally different
way, which bases on rigorous modeling; in principle it should be rigorous and infallible. For example, Grossmann (1996, 2003) put up some rigorous
algorithms for the separation synthesis,[12,13] but the
defects of these approaches are also obvious, cumbersome and overwhelming in terms of computational
time and much effort required for algorithms, especially
for a complex separation system. Thus, efforts were
made by some researches to develop combined methods, for example, Shah (2002) developed a new synthesis framework screens and examined complex distillation sequences based on knowledge and mathematical methods;[14] Zhao(2002) applied Analytical Hierarchy Process (AHP) method to determine the optimal
sequence for multicomponent distillation separation.[15]
The mathematic algorithmic methods are adopted for
modeling; the well-accepted heuristics are used to
reduce the size of the search space of the algorithmic methods for simplifying solution, which exploit
the advantages of mathematical approach and heuristic or thermodynamic method. But in these studies,
only one separation technique ? distillation was considered, although it is the most frequently used separation technique, in many industrial situations; other
techniques, e.g. extraction, absorption etc. are more economic. Therefore, more than one type of separation
technique may have to be used to separate a given
mixture economically. A ?general? separation synthesis
system should also be able to select from multiple separation techniques before sequencing. And also, most of
product mixtures contain azeotrope especially for fine
chemicals, which could not be separated by the simple common techniques, such as atmosphere distillation
and so on. From the summary of the previous research,
it can be concluded that these problems are not well
solved yet.
In the study, one general methodology for separation process synthesis and design is proposed, which
is based on a mathematical approach, and combines
the thermodynamic insights and heuristic rules. Firstly,
the pseudo-component concept was proposed and was
used to tackle the azeotrope contained in the mixture,
which widened the scope of application of the conventional heuristic method. Then the AHP was adopted to
construct separation model and determine the optimal
separation sequence. The heuristic rules and thermodynamic insights were applied for the selection of separation techniques and operations to reduce the complexity
and size of synthesis search space. The hybrid method
is applied to two illustrative examples which have been
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
carefully selected by taking into account the importance
of practical relevance, The first example deals with a
light-end refinery mixture;[14] the second example deals
with phenol, o-cresol, p-cresol, m-cresol system containing azeotrope.
METHODOLOGY OF THE HYBRID METHOD
The analytic hierarchy process (AHP)
AHP is an approach developed by mathematician
Thomas Saaty,[16] and applied in different area,[17]
which can provide decision making that involves structuring multiple choice criteria into a hierarchy, assessing the relative importance of these criteria, comparing alternatives for each criterion, and determining an
overall ranking of the alternatives. In principle, the separation synthesis such as the selection of separation
techniques and decision of separation sequence is one
complex decision-making process, in which the final
results are usually influenced by the subjective factors
because of different designer, angle, or experience. So
AHP can be used to help capture both subjective and
objective evaluation measures for this process, provide
a useful mechanism for checking the consistency of
the evaluation measures and alternatives suggested by
the team, thus reducing bias in decision making. AHP
includes four main steps.
Decomposing
The goal is to structure the complex problem into
humanly manageable subproblems. To do so, iterating
from top (the more general) to bottom (the more specific), split the problem, which is unstructured at this
step, into submodules that will become subhierarchies.
Navigating through the hierarchy from top to bottom,
the AHP structure comprises goals (systematic branches
and nodes), criteria (evaluation parameters), and alternative ratings (measuring the adequacy of the solution
for the criterion).
Each branch is then further divided into an appropriate level of detail. At the end, the iteration process
transforms the unstructured problem into a manageable problem organized both vertically and horizontally
under the form of a hierarchy of weighted criteria.
By increasing the number of criteria, the importance
of each criterion is thus diluted, which is compensated
by assigning a weight to each criterion.
Weighing
Assign a relative weight to each criterion, based on
its importance within the node to which it belongs.
The sum of all the criteria belonging to a common
direct parent criterion in the same hierarchy level must
equal to 100% or 1. A global priority is computed,
which quantifies the relative importance of a criterion
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
SEPARATION PROCESS BY HYBRID METHOD
within the overall decision model. The detail process
for weighing will be explained in the next section.
Evaluating
Score alternatives and compare each one with others.
Using AHP, a relative score for each alternative is
assigned to each leaf within the hierarchy, then to the
branch the leaf belongs to, and so on, up to the top of
the hierarchy, where an overall score is computed.
Selecting
Compare alternatives and select the one that best fits
the requirements.
The above is the explanation in theory; details of
practical application in separation design will be shown
in the next section.
The procedure of the methodology
The hybrid method procedure is presented in Fig. 1,
which includes six main steps. Steps 1?3, thermodynamic calculation, handling azeotrope, simplifying
the scale of the mathematical problem, eliminating the
unsuitable separation technique, and selecting the suitable separation techniques based on thermodynamics,
experience, and heuristic rules. Step 4, the most important separation technique distillation, constructs the
optimal separation sequence based on the AHP method.
Step 5 solves the pseudo-component (azeotrope) separation. Step 6 optimizes the final separation sequence.
For the final separation sequence, we only use common
column structure (one feed, two products) for the distillation separation method, not consider thermally coupled schemes such as the side-stripper, the side-rectifier,
mixture
List possible separation techniques
Step1
Calculate pure and mixture properties
Step2
containing azeotrope
No
Yes
consider the azeotrope mixture as one pseudo-component
Step3
seletion suitable method according thermodynamic analysis
distillation separation method
No
other separation methods
Yes
list all separation heurstic rules
pure product
construct the model of AHP as Fig.3
Step4
No
Yes
construct the matrix by pairwise comparisons
calculate the ordering vectors and overall ordering vectors
normalization of the ordering vectors
Step5
the optimal separation sequence
(containing pseudo-component)
select suitable separation methods for
pseudo-component(azeotrope)
Step6
Optimal flowsheet
Figure 1. The scheme of the proposed hybrid method.
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
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C. LI, G. WOZNY AND K. SUZUKI
Asia-Pacific Journal of Chemical Engineering
Table 1. Relationship between separation techniques and pure component properties.
Separation type
Distillation
Absorption
Filtration
Crystallization
Vapor?liquid separation
Gas separation
Extractive distillation
Vapor?liquid separation
Azeotropic distillation
Liquid?Liquid extraction
Liquid membranes
Vapor?liquid?liquid separation
Liquid?liquid separation
Liquid separation
Drying
Gas separation
Solid?vapor separation
Important pure component properties
Differences in volatilities(vapor pressure)
Preferential solubility
Size of solid greater than pore size of filter medium
Difference in freezing tendencies; preferential
participation in crystal structure
Vapor pressure, heat of vaporization, boiling point,
solubility parameter
Difference in volatilities
Difference in volatilities
Solubility parameter, molar volume, radius of
gyration, affinity to carrier
Solid?liquid separation
Step 1: thermodynamic data calculation
The commonly known separation techniques (distillation, extraction, crystallization, membrane separation,
adsorption, filtration, and so on) suitable for the multicomponents separation are listed in Table 1. Some
qualitative and quantitative thermodynamic properties
of pure and mixture components are calculated, which
are the base for the selection of the separation techniques. For example, the calculation results of relative
volatility and the difference of boiling point between
the two components will be the base for the decision of
distillation. If there is azeotrope in the mixture, then go
to Step 2, otherwise go to Step 3.
Step 2: pseudo-component
If two components form azeotrope (if the relative
volatility between the two components is less than
1.05, then we assume them to be azeotrope), then they
are considered and handled as one pseudo-component
until the last step, and the contents, volatility, or other
thermodynamic data will be calculated again.
Step 3: selection of separation techniques
According to the calculation result of the thermodynamic properties from Step 1, the existing experience
and heuristic, a series of tests and selection are made to
evaluate the feasibility of application of the separation
techniques.
In the past decades, a variety of new separation
methods emerged and have been applied in industry, but
the energy-driven (based on the heats of vaporization
of the components) techniques such as distillation and
evaporation are still employed by the majority The
level of application of technology and its maturity
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
are summarized by Keller,[18] and shown in Fig. 2;
it was the status 20 years ago, but it can still prove
helpful in the selection of different techniques and also
emphasized the importance of distillation separation
techniques.
Some experiences from chemical engineering are
summarized in the following. The advantages of distillation are in its simple flowsheet, low capital investment,
and low risk. If components to be separated have a
relative volatility of 1.2 or more and are thermally stable, distillation is typically the separation method of
choice.[19] The disadvantages of distillation are its low
energy efficiency and that it requires thermal stability of
compounds at their boiling points. Large energy savings
could be obtained by replacing distillation with lowenergy intensity operations. The most promising technologies for replacement of distillation include membranes, extraction, sorption (absorption and adsorption),
and hybrid systems.
Maximum
or Petlyuk column and so on, but in natural circumstances, the thermally coupled schemes are formed by
the common column structure; thus, after the optimal
separation sequence is available, by improving, a last
optimal separation sequence can also be available.
Vapor pressure, diffusivity
Industry Application Level
Separation technique
1
2
3
4
6
5
7
8
First Application
908
13
12
9
10
11
14
15
Invention
Maximum
Technical Maturity Level
Figure 2. The technology application and maturity
level.
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
SEPARATION PROCESS BY HYBRID METHOD
Membrane permeation can generally be used only for
dilute liquid mixtures, else should be eliminated. No
bulk liquid separations are done commercially. Also,
a high-purity product will not result from membrane
permeation, and with a correspondingly low recovery rate. Thus, if high level of purity and recovery
rate are essential, membrane separation can be eliminated as a potential separation method. Feasible crystallization processes typically require 20?30 ? C differences in the freezing points of pure components. In
addition, the freezing points should be at or above
ambient temperatures if the added expense of refrigeration is to be avoided, else the crystallization process should be eliminated. The choice of other separation techniques is also based on thermodynamic
insight and experience. Jaksland recommended some
key binary parameters standard for the selection of separation techniques,[11] which are shown in Table 2. If
no information of a specific external medium is found
(or available through a knowledge base), other separation techniques (such as adsorption, filtration, prevaporation using membranes, and so on explained in
Table1) are usually eliminated and distillation will be
the best choice. If the distillation technique cannot
applied for this mixture, then go to Step 5, otherwise
Step 4.
Step 4: distillation methods
AHP in distillation. For multicomponents separation, distillation is by far the most widely used and
the first choice of separation process for mixtures. For
example, in the United States, distillation processes
constitute 90?95% of all separations in the chemicals and petroleum refining industries and account
for over 99% of the total energy associated with all
industrial separation technologies, offering the most
promising energy reduction opportunities.[19] Thu, in
Table 2. Recommended values for separation feasibility indices.
Separation process
Partial
condensation
Flash operation
Distillation
Cryogenic
distillation
Per-vaporation
Micro-filtration
Property (pj )
Boiling point
Boiling point
Vapor pressure
Boiling point
Vapor pressure
Boiling point
Vapor pressure
Molar volume
Solubility
Molecular diameter
Molecular weight
Binary ratio
value of pure
property j for
binary pair i (ri ,j )
this study, distillation technique of separation is the first
choice.
As explained the Section on The Analytic Hierarchy
Process, by reducing complex decisions to a series of
one-on-one comparisons, then synthesizing the results,
AHP not only helps decision makers arrive at the best
decision but also provides a clear rationale that it is the
best. For the multicomponents separation, the separation
sequence in nature is the decision problem, by the allside trade-off between the different separation point and
separation technique. So the separation synthesis can be
solved by the AHP. The model of AHP is shown as
Fig. 3.
A hierarchy structure shown in Fig. 3 is established
by decomposing the complex problem (mixture separation) into a hierarchy of inter-related decision elements
(the sequence of different points). This structure is the
key to interrelate and chain all decision elements of the
hierarchy from the top level down to the bottom. So
the top of the hierarchical structure is the optimal result
of all the alternative flowsheet; the lowest level of the
hierarchical structure is the feasible separation points.
For example, for the mixture ABC three-component, it
includes two possible flowsheets, A/(BC), then A/B/C
or (AB)/C, then A/B/C. So after the separation technique is decided, different thermodynamic insights or
experience rules (i.e. Rules in Fig. 3) can be calculated
based on the AHP method to decide the first separation
point (i.e. S in Fig. 3),
Prioritization and construction of the pairwise
comparison matrices. Once the hierarchical structure is established, the relative importance (weights) of
all decision elements is explicitly captured and revealed
through ratio scale approach. Pairwise comparisons of
these elements within the same hierarchical level with
respect to the parent elements in the next higher level
are established. The numerical scales ranging from 1
(equal importance) to 9 (absolute importance) (Saaty,
1980) as shown in Table 3 are used in the pairwise
comparison matrices.
The input data can be achieved by pairwise comparison. For example, for the experience rule ? ?favor easy
separation first?, we can judge this rule by the relative
2.5
1.4
15.0
1.02
1.5
1.17
2.40
4.00
2.50
3.00
2.40
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
The optimal flowsheet
Rule2
Rule1
S1
Figure 3.
process.
Rule3
S2
Rule4
S3
Rule5
S4
The model of the analytic hierarchy
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
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C. LI, G. WOZNY AND K. SUZUKI
Asia-Pacific Journal of Chemical Engineering
Table 3. Scales of relative importance.
Intensity of
importance
Definition
Explanation
1
3
Equal importance
Weak importance of one over the other
5
Essential or strong importance
7
Demonstrated importance
9
Absolute importance
2,4,6,8
Intermediate values between the two adjacent
judgments
Distillation
Two activities contribute equally to the objective
Experience and judgment strongly favor one activity
over another
Experience and judgment strongly favor one activity
over another
An activity is strongly favored and its dominance
demonstrated in practice
The evidence favoring one activity over another is of the
highest possible order of affirmation
When compromise is needed
Table 4. Problem specifications for example 1.
Membrane
Fraction
(mass)
Vapor
pressure
(kPa)
Relative
volatility
(relative
to Benzene)
Relative
volatility
0.091
0.169
0.176
0.019
0.030
0.177
0.112
0.226
269.70
151.31
115.71
73.63
55.41
50.62
37.44
24.30
11.10
6.23
4.76
3.03
2.28
2.08
1.61
1.00
1.78
1.31
1.57
1.33
1.09
1.35
1.54
A
A
B
C
D
E
F
G
H
B
C
D
E
F
G
H
B
B
C
B
C
D
E
F
G
C
D
D
E
F
G
E
F
E
F
G
E
F
G
H
Figure 4. The final promising design for
example 1.
Distillation
A
B
C
D
E
A
B
C
D
E
Crystallization
22-DMP
i -Pentane
n-Pentane
22-DMB
23-DMB
2-MP
n-Hexane
Benzene
Table 5. The dealing specifications for example 1.
A
Relative
volatility
Vapor
(relative
Relative
Fraction pressure/kPa to Benzene) volatility
B
C
D
C
D
E
Figure 5. The final promising design for example 2.
volatilities. For the mixture ABC, if the relative volatility of A/B is larger than B/C, then the first separation
point is A/(BC), as regards the specific scale value is 3,
5, or 6, we should trade off between all the separation
point, then decide the final value according to Table. 3
Of course, if we use only this rule to decide the separation point, the AHP method will not necessary, but if we
also consider another experience rule, for example the
experience rule ? ?favor 50/50 split?, in the same manner, the separation mixture ABC, if the mass content
of A, B, C is 10, 20, and 70 percent respectively, then
according to the rule the first separation point should
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
22-DMP
i -Pentane
n-Pentane
22-DMB
23-DMB
2-MP
n-Hexane
Benzene
0.091
0.169
0.176
0.019
0.207
0.112
0.226
269.70
151.31
115.71
73.63
55.41
50.62
37.44
24.30
11.10
6.23
4.76
3.03
2.28
1.78
1.31
1.57
1.33
1.61
1.00
1.35
1.54
be (AB)/C. Then we will find results from the two different rules to be different. To integrate the value, the
pairwise comparison matrices based on AHP will be the
best choice.
Several sets of pairwise comparison matrices of elements in the same level, which attribute to accomplishing the goals of the parent element in the next
higher level are finally obtained as in Eqn (1). The
derived pairwise comparisons of relative importance,
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
SEPARATION PROCESS BY HYBRID METHOD
Table 6. The pairwise comparison matrices and the ordering vectors for example 1.
Pairwise comparison matrices
? 1
3
5 9?
0.33 1
2 5?
AO?R = ?
0.2 0.5 1 2
0.11 0.2 0.5 1
?
AR1 ?B
1
? 0.25
? 0.5
=?
? 0.25
?
0.25
0.5
4
1
2
1
1
2
?
AR2 ?B
1 0.33
1
?3
?3
1
?
=?
2
?5
5
2
7
3
?
AR3 ?B
1 0.33
1
?3
?5
2
=?
?9
4
?
5
2
3
1
?
AR4 ?B
1
?1
?1
=?
?1
?
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0.5
1
0.5
0.5
1
4
1
2
1
1
2
4
1
2
1
1
2
Consistency check
?max = 4.033
?max = 6
[0.36,0.09,0.18,0.09,0.09,0.18]
CI = 0
RI = 0
CR = 0
?
0.14
0.33 ?
0.33 ?
?
0.5 ?
?
0.5
1
?max = 6
[0.04,0.11,0.11,0.20,0.20,0.34]
CI = 0
RI = 0
CR = 0
?
0.20 0.11 0.20 0.33
0.5 0.25 0.5
1 ?
1
0.5
1
2 ?
?
2
1
2
4 ?
?
1
0.5
1
2
0.5 0.25 0.5
1
1
1
1
1
1
1
[0.59,0.23,0.12,0.06]
CI = 0.011
RI = 0.89
CR = 0.012
?
2
0.5 ?
1 ?
?
0.5 ?
?
0.5
1
0.33 0.2 0.2
1
0.5 0.5
1
0.5 0.5
2
1
1
2
1
1
3
2
2
1
1
1
1
1
1
The total ordering vectors
?max = 6.006
[0.04,0.10,0.19,0.38,0.19,0.10]
CI = 0.001
RI = 1.86
CR = 0.001
?
1
1?
1?
?
1?
?
1
1
?max = 6
[0.17, 0.17, 0.17, 0.17, 0.17, 0.17]
CI = 0
RI = 0
CR = 0
Table 7. The total ordering vectors of the pairwise comparison matrices for example 1.
The total ordering matrices
? 0.36 0.09 0.18 0.09
? 0.04 0.11 0.11 0.20
0.04 0.10 0.19 0.38
0.17 0.17 0.17 0.17
0.09
0.20
0.19
0.17
Consistency check
The total ordering vectors
CI = 0.012
[0.24, 0.10, 0.16, 0.15, 0.13, 0.21]
0.18 ?
0.34 ?
0.10
0.17
RI = 0.90
CR = 0.013
aij = wi /wj , for all decision elements and their reciprocals, aji = 1/aij , are inserted into a reciprocal square
matrix A = {aij } as shown in Eqn (1). The analytical
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
solution of Eqn (2) then provides the relative weights
for each decision element. According to the eigenvalue method, the normalized right eigenvector (W =
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
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C. LI, G. WOZNY AND K. SUZUKI
Asia-Pacific Journal of Chemical Engineering
{w1 , w2 , . . . , wn }T ) associated with the largest eigenvalue (?max ) of the square matrix A provides the weighting values for all decision elements.
?
1
? w2 /w1
A=?
? ...
wn /w1
AW = ?max W
w1 /w2
1
..
.
wn /w2
?
и и и w1 /wn
и и и w2 /wn ?
?
?
иии
иии
(1)
1
(2)
In this step, the final pairwise comparison matrices will be under the influence of subjective factors
on some degree and, as far as we know, has seldom
been addressed in the literature before. The AHP uses
a principal eigenvalue method to derive priority vectors, Following Saaty,[15] the priority vector has two
meanings: ?The first is a numerical ranking of the alternatives, which indicates an order of preference among
them. The other is that the ordering should also reflect
intensity or cardinal preference as indicated by the ratios
of the numerical values.? This second meaning requires,
in our view, that these ratios preserve, whenever possible, the order of the respective preference intensities,
which is not always the case for AHP priority vectors;
this can be considered as a basic drawback of the AHP.
But for our application in this study, the construction
of pairwise comparison matrices will bases on the thermodynamic and experience, and the drawback will be
weaken to some extent.
The distillation separation sequence. In the
step, the ordering vectors of the pairwise comparison
matrices (A shown in Eqn (1)) and the final ordering
vectors (W shown in Eqn (2)) are calculated. Normalize
these vectors and gain the initial separation sequence.
Step 5. Separation pseudo-component
For the pseudo-component separation, it belongs to the
research field of azeotrope separation synthesis, and lots
of synthesis methods are published,[15,16] which need
special information from the forgoing experience, and
also based on the factual industrialization application.
For this topic, making concrete analysis of concrete
problems is the best method.
Step 6. Optimize the final separation sequence
In this step, the final separation sequence is optimized
by the simulation tool, and the final operation parameters can be available. An energy saving methodology
also can be applied in this step. But the detailed simulation results from the integrated approach are not
provided in this study. They can be obtained from the
authors.
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
APPLICATION EXAMPLES
Example 1: separation of a light-end refinery
mixture
The first example deals with a light-end refinery mixture
which is separated into eight products.[9,14] The vapor
pressure and relative volatility of the components are
calculated The data is presented in Table 4. From the
calculating results, the relative volatility of 23-DMB
and 2-MP is close to 1. According to the proposed
method, if two components form azeotrope, the two
components are considered as one pseudo-component
which is separated in the last step. After this, the new
calculation results are listed as in Table 5.
From Table 5, it can be seen that the relative volatility
of all the mixture are larger than 1.2. So based on pure
component and mixture properties analysis, the crystallization and membrane separation and other separation
techniques are eliminated. The distillation technique is
preferred. Thus we can start from Step 4 of our proposed procedure. The rules selected for the separation
point are according to the examples; different examples
can use different rules. The rules[3] used in the example
are listed in the following.
Rule 1. Favor easy separations first. Specifically,
arrange the components separately according to their
relative volatilities as separation factors in the ordered
components in the feed vary widely. Sequence the splits
in the order of decreasing adjacent relative volatility.
Rule 2. Remove the most plentiful component first.
A product composing a large fraction of the feed should
Table 8. Problem specifications for example 2.
phenol
o-cresol
m-cresol
p-cresol
2,4 -xylenol
Fraction
Vapor
pressure
(kPa)
Relative
volatility
(relative to
2,4 -xylenol)
Relative
volatility
0.35
0.20
0.15
0.15
0.10
0.1690
0.1317
0.0834
0.0833
0.0545
3.10
2.42
1.53
1.53
1
1.28
1.58
1.00
1.53
Table 9. the dealing specifications for example 2.
phenol
o-cresol
m-cresol
p-cresol
2,4 -xylenol
Fraction
Vapor
pressure
(kPa)
Relative
volatility
(relative to
2,4 -xylenol)
Relative
volatility
0.35
0.20
0.30
0.1690
0.1317
0.0833
3.10
2.42
1.53
1.28
1.58
0.15
0.0545
1
1.53
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
SEPARATION PROCESS BY HYBRID METHOD
Table 10. The pairwise comparison matrices and the ordering vectors for example 2.
Pairwise comparison matrices
? 1
3
5
9?
0.33 1
2
5?
AO?R = ?
0.2 0.5
1
3
0.11 0.2 0.33 1
AR1 ?B =
AR2 ?B =
AR3 ?B =
AR4 ?B =
1
5
4
0.20 0.25
1
2
0.5
1
1
2
0.5
1
0.2 0.33
5
3
1
1
0.5
2
1
0.2 0.14
5
7
1
1
5
0.2
1
0.11 0.33
Consistency check
The ordering vectors
?max = 4.026
[0.59, 0.23, 0.13, 0.05]
CI = 0.003
RI = 0.89
CR = 0.003
?max = 3.04
[0.10, 0.57, 0.33]
CI = 0.02
RI = 0.58
CR = 0.03
?max = 3.02
[0.58, 0.31, 0.11]
CI = 0.01
RI = 0.58
CR = 0.02
?max = 3.05
9
3
1
[0.33, 0.59, 0.08]
CI 0.03
RI 0.58
CR = 0.05
?max = 3.032
[0.75, 0.18, 0.07]
CI = 0.016
RI = 0.58
CR = 0.03
Table 11. The total ordering vectors of the pairwise comparison matrices for example 2.
The total ordering matrices
? 0.10 0.57 0.33 ?
? 0.58 0.31 0.11 ?
0.33 0.59 0.08
0.75 0.18 0.07
Consistency check
CI = 0.043
The total ordering vectors
W = [0.28, 0.49, 0.23]
RI = 1.47
CR = 0.03
be separated first, provided that the separation factor or
relative volatility is reasonable for the separation.
Rule 3. Favor 50/50 split. If component compositions
do not vary widely, sequences which give a more nearly
50/50 or equimolar split of the feed between distillate
(D) and bottom (B) products should be favored, provided that the separation factor or relative volatility is
reasonable for the split.
Rule 4. Direct sequence rule. During distillation
neither the relative volatility nor the molar percentage
in the feed varies widely. Remove the components one
by one as distillate products. The resulting sequence is
commonly known as the direct sequence, in which the
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
optimum operation pressure tends to be highest in the
first separator and reduces in each subsequent separator.
Based on Rules 1?4, construct the AHP model as
Fig. 3; in this model, the top level is the optimal
flowsheet (final results), the middle level is rules; for
this study, there are only four rules. And the bottom
level is separation points, totally six.
The constructed pairwise comparison matrices and
the calculated ordering vectors of the pairwise comparison matrices are listed in Table 6. We take Rule 1 as a
sample to explain how to construct the matrices AR1?B .
First, according to the calculation results of relative
volatilities, we evaluate the relative importance for the
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
913
914
C. LI, G. WOZNY AND K. SUZUKI
Asia-Pacific Journal of Chemical Engineering
Table 12. Energy consumption of different separation sequence for example 2.
Separation process
Distillation
Crystallization
A
I
A
B
C
D
E
B
B
C
D
E
1
C
D
E
2
II
1
A
B
C
D
E
1
Top/bottom
Column pressure (atm)
Trays
Top/bottom
1 ??1
60
182/199
?0.0577/0.0654
2 ??1
40
190/204
?0.0433/0.0434
3 ??1
40
202/211
?0.0511/0.0510
E
?0.1521/0.1598
Crystallization
A
B
A
B
2
C
D
E
C
C
D
1 ??1
40
184/204
?0.0312/0.0388
2 ??1
60
182/190
?0.0659/0.0660
3 ??1
40
201/211
?0.0415/0.0415
D
E
3
Distillation
III
D
Heat duty (MMkcal/h)
3
Distillation
A
B
C
D
E
C
C
D
Temperature (? C)
?0.1386/1463
Crystallization
1 ??1
40
190/210
?0.1052/0.1127
2 ??1
60
182/197
?0.0659/0.0661
3 ??1
40
190/202
?0.0330/0.0330
A
A
B
C
D
B
B
C
D
E
2
C
D
3
?0.2039/0.2118
Distillation
IV
A
B
C
D
E
1
A
B
C
D
E
2
A
B
1 ??1
40
190/210
?0.1052/0.1127
B
2 ??1
40
184/202
?0.0998/0.0998
C
3 ??1
60
182/190
?0.0659/0.0660
A
3
C
D
D
Crystallization
six separation points by pairwise comparison and give
the value respectively, but in the same matrices all the
value should have consistency, for example, if B and
C are two and four times for A, then C should be two
times for B during pairwise comparison process. In this
procedure, it will include some subject factors whose
influence in the whole process is small in relation to
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
?0.2709/0.2785
other methods. After all, the pairwise comparison matrices are decided and the total ordering vectors of the
pairwise comparison matrices are calculated by Eqn (2)
and listed in Table 7.
According to the total ordering vectors of the pairwise
comparison matrices, from the result of consistency
checking (C .R.total < 0.1) we can conclude that the
Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
results have a good consistency. From the final vectors,
we can construct the initial separation sequence from
the larger values to smaller values.
Lastly, for the separation of the pseudo-component
(23-DMB, 2-MP), thermodynamic analysis, crystallization, or membrane[20] are all possible separation techniques; by trading-off, it is the second choice. The final
promising design for Example 1 is shown in Fig 4,
which is a little different from the result of the BekPedersen[9] and Shah,[14] It is because they did not
consider azeotrope.
Example 2: separation of phenolic mixture
The second example deals with the mixture which
contains phenol(A), o-cresol(B), p-cresol(C), and mcresol(D), which come in oil or fine chemical process.
The vapor pressure and relative volatility of the
components are calculated. The original data is presented in Table 8. From the calculated results, the relative volatility of m-cresol and p-cresol is close to 1,
so the two components are considered as one pseudocomponent which is separated in the last step. The data
are listed in Table 9.
Based on Rules 1?4, construct the AHP model as
Fig. 3; the constructed pairwise comparison matrices
and the calculated ordering vectors of the pairwise
comparison matrices are listed in Table 10. The total
ordering vectors of the pairwise comparison matrices
are listed in Table 11. From the result of consistency
checking (C .R.total < 0.1) we can conclude that the
results have a good consistency.
For the pseudo-component (m-cresol and p-cresol),
based on thermodynamic analysis according to the
proposed method of Li,[21] crystallization is selected
as the separation technique, so the final promising
design for the Example 2 is shown as Fig 5. We also
carried out a simple simulation (without optimization)
for the different promising designs of the sample; the
results were shown in Table. 12 The purities of all the
products are above 98%. The energy consumption for
the separation of C/D by crystallization method was not
considered, which will not influence the final results. It
can be found that the final promising design based on
our proposed method has low energy consumption.
It should be mentioned that the results of examples
1 and 2 are only relevant for the analyses. For another
mixture including the same kinds of components, the
results may be different even if the components are the
same.
? 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
SEPARATION PROCESS BY HYBRID METHOD
CONCLUSION
A hybrid method integrating the AHP with heuristic
approaches and thermodynamic insights for separation
synthesis is proposed. The AHP method is used to
decide the initial separation sequence and help capture
both subjective and objective evaluation measures for
this process. Useful rules and thermodynamic calculation are used to reduce the size of the search space of the
algorithmic methods and construct the AHP model. The
hybrid method is applied to two illustrative examples, a
light-end refinery mixture and phenol system containing
phenol, o-cresol, p-cresol, m-cresol. The results show
that the methodology can prove as a guide for the initial
separation process design and it can be easily applied.
REFERENCES
[1] J.L. Humphrey, G.E. Keller. Separation Process Technology,
McGraw-Hill: New York, 1997; pp.50?101.
[2] R.W. Thompson, C.J. King. AIChE J., 1972; 18, 491?496.
[3] V.M. Nadgir, Y.A. Liu. AIChE J., 1983; 29(6), 926?934.
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Wiley: New York, 1987; pp.210?260.
[19] Oak Ridge National Laboratory, DOE-EERE-Industrial Technologies Program (ITP)-Materials for Separation Technologies: Energy and Emission Reduction Opportunities. 2005.5.4.
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Asia-Pac. J. Chem. Eng. 2009; 4: 905?915
DOI: 10.1002/apj
915
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