International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Material Selection using Multi-criteria
decision making methods (MCDM) for design
a multi-tubular packed-bed Fischer-Tropsch
reactor (MPBR)
Javier Martínez-Gómez#1, Ricardo A. Narváez C.*2,
1
Instituto Nacional de Eficiencia Energética y Energías Renovables (INER),
Adress: 6 de Diciembre N33-32, Quito, Ecuador. Tel +593 (0) 2 3931390 ext: 2079,
Abstract- The future of the fossil fuel supply is
uncertain. For this reason, it is necessary the
transition from a fossil based to a biobased for
greenhouse gas emissions reduction targets, and
climate change. In this regards, multi tubular
packed-bed reactor Fischer-Tropsch (MPBR)
appears has an essential technology to improve and
reduce cost of operation.
For design a MPBR, many studies has been used
CFD for detailed evaluation of reaction systems.
This research use Multi-criteria decision making
methods (MCDM) for the material selection of a
MPBR. This project focuses on the design for
selecting an alternative material which best fits the
technological requirements to make the pipes and
the vessel of a MPBR and reduce the cost of
production.
The MCMD methods implemented are complex
proportional assessment of alternatives with gray
relations (COPRAS-G), operational competitiveness
rating analysis (OCRA), a new additive ratio
assessment (ARAS) and Technique for Order of
Preference by Similarity to Ideal Solution (TOPSIS)
methods. The criteria weighting was performed by
compromised weighting method composed of AHP
(analytic hierarchy process) and Entropy methods.
The ranking results showed that ASME SA-106 and
ASME SA-106 would be the best materials for the
pipes and the vessel of a MPBR.
Keywords - Multi-criteria decision making methods,
MCDM, material selection, multi-tubular packedbed reactor Fischer-Tropsch reactor, MPBR.
I. INTRODUCTION
The future of the world‟s oil supply is at this
point uncertain. Over the last few years, a major
concern has arisen regarding the decreasing global
oil reserves, increment of fuel demand in emerging
economies and the associated increasing crude oil
price both driven by a strong world demand and by
political instabilities in oil producing regions. The
transition from a fossil based to a biobased economy
is absolutely essential in climate protection and
ISSN: 2231-5381
greenhouse gas emissions reduction targets.
Agricultural feedstock like woodchips and residual
of non-food parts of cereal crop, can be valorized
and be integrated in a second-generation Biomass to
Liquid process to synthetize liquid biofuels via the
Fischer-Tropsch (FT) synthesis [1-2].
The FT synthesis is a collection of chemical
reactions that converts a mixture of carbon
monoxide and hydrogen into liquid hydrocarbons. A
variety of synthesis-gas compositions can be used.
For iron-based catalysts promote the water-gas-shift
reaction and thus can tolerate the optimal H2:CO
ratio is around 1.2–1.5. This reactivity can be
important for synthesis gas derived from coal or
biomass, which tend to have relatively low H2:CO
ratios (<1). In addition, FT synthesis is known for its
highly exothermicity (ΔHR=–165 kJ mol−1CO) [3].
Four main types of commercial FT reactors are
commonly implemented in industrial processes: the
fluidized-bed reactor, the multi-tubular packed-bed
Fischer-Tropsch reactor (MPBR), the slurry phase
reactor (SPR) and the circulating fluidized-bed
reactor. Two operating processes have been
developed: the high-temperature FT processes (573
– 623 K, HTFT) and the low temperature FT
processes (473 – 523 K, LTFT). HTFT based on iron
catalysts yields essentially C1 to C15 hydrocarbons in
circulating fluidized-bed reactors while LTFT
processes lead mainly to linear long chain
hydrocarbons (waxes and parafins) [1], [2].
Many variables such reactant inlet temperature,
coolant flow rate, catalyst loading ratio, and space
velocity are involved in multichannel FT reactor
design [4]. In this sense, many studies used the
computational fluid dynamics (CFD) is widely used
for detailed evaluation of reaction systems [5-6].
However, when many process and coolant channels
are involved, for large-scale reactors, CFD is highly
computationally intensive and time consuming CFD
therefore may not be able to handle all the channels;
the problem is unrealistically large, because it deals
with rigorous physics such as flow patterns over the
entire domain [4-5] Other studies has been
performed by based on a kinetic model for the
conversion of syngas. The product slate is then
http://www.ijettjournal.org
Page 273
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
calculated from a simplified kinetic model to
describe the overall advancement of the reaction
followed by a distribution equations to calculate
different products in order to design a FT [6-7]. But
none of them, has been developed a previous study
of the selection of material for the Fischer Tropsch
reactor. Usually engineers and researchers use
certain materials based on experience and other
studies.
I. I. MATERIAL SELECTION FOR MCDM
The selection of the most convenient material for
a precise purpose is a crucial function in the design
and development of products. Materials selection
has become an important source at engineering
processes because of economical, technological,
environmental parameters [9-10]
Materials influence product function, the life
cycle of the product, who is going to use or produce
it, usability, product personality, environment and
costs in multiple, complex and not always
quantitative way. The improper selection of one
material could negatively affect productivity,
profitability, cost and image of an organization
because of the growing demands for extended
producer responsibility [9-10]. For this reason, the
development of products and success and
competitiveness of manufacturing organizations also
depends on the selected materials [11-12]. Material
selection carried out several research processes that
give off assessment methods to compare the
behavior of elements according to their characteristic
properties (density, yield strength, specific heat, cost,
corrosion rate, thermal diffusivity, etc.) with
efficiency indicators in order to select the best
alternative for a given engineering application [11].
Thus, efforts need to be extended to identify those
criteria that influence material selection for a given
engineering application to eliminate unsuitable
alternatives and select the most appropriate
alternative using simple and logical method [13].
Comparing candidate materials, ranking and
choosing the best material is one of most important
stages in material selection process. Multi criteria
decision making methods (MCDM) appear as an
alternative in engineering design due to its
adaptability for different applications. The MCDM
methods can be broadly divided into two categories,
as (i) multi-objective decision-making (MODM) and
(ii) multi-attribute decision-making (MADM). There
are also several methods in each of the abovementioned categories. Priority-based, outranking,
preferential ranking, distance-based and mixed
methods are some of the popular MCDM methods as
applied for evaluating and selecting the most
suitable materials for diverse engineering
applications. In most MCDM methods a certain
weight is assigned to each material requirement
ISSN: 2231-5381
(which depends on its importance to the
performance of the design). Assigning weight factor
to each material property must be done with care to
prevent bias or getting the answer you intended as
Here are some engineering applications where
MCDM have been regarded as selection tools,
performed by Jahan, Ismail, Sapuan, Mustapha [14]
“Material screening and choosing methods -A
review”, developed by [15] “Evaluating the
construction methods of cold-formed steel structures
in reconstructing the areas damaged in natural crises,
using the methods AHP and COPRAS-G”, studied
by [16] “Materials selection for lighter wagon design
with a weighted property index method”, developed
by [11] Material selection for the tool holder
working under hard milling conditions using
different multi criteria decision making methods”.
This paper solves the problem of selecting the
material a MPBR using recent mathematical tools
and techniques for accurate ranking of the
alternative materials for a given engineering
application. In this paper, it has been studied the
material decision for pipes and vessel of the reactor
by four preference ranking- based MCDM methods,
i.e. COPRAS-G, OCRA, ARAS and TOPSIS
methods have been implemented. The criteria
weighting was performed by compromised
weighting method composed of AHP and Entropy
methods. For these methods, a list of all the possible
choices from the best to the worst suitable materials
is obtained, taking into account different material
selection criteria.
II. MATERIALS AND METHODS
II. I DEFINITION OF THE DECISION MAKING
PROBLEM
To optimize the material selection for a MPBR is
necessary to know the most important properties of
the design and operation. It is necessary to note, that
normally FT reactor is operated in the temperature
range of 150–300 °C [1-2]. Higher temperatures lead
to faster reactions and higher conversion rates but
also tend to favor methane production. Typical
pressures range from one to several tens of
atmospheres. Increasing the pressure leads to higher
conversion rates and also favors formation of longchained alkanes, both of which are desirable. In
addition, it is necessary the heat removal capability
that has a major impact on the products selectivity: a
temperature increase has the effect of rising methane
production as well as results in catalyst deactivation
associated to sintering and coking. In Fig. 1 is
illustrated the schema of a MPBR commercial.
http://www.ijettjournal.org
Page 274
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Figure 1.
Schema of a MPBR.
In order to meet for the material selection, it has
been identified the most important properties based
on the bibliography [1-5]. The most in one of the
most important material property is considered to be
cost ( ), the low values of which are desired in
order to provide a competitive advantage among
manufacturers. In addition, higher pressures would
be favorable, but the benefits may not justify the
additional costs of high-pressure equipment.
Furthermore, higher pressures can lead to catalyst
deactivation via coke formation. The second
property required is corrosion rates (R), the lowest
values of corrosion rate are necessary to maintain the
useful life or the reactor. A high Yield strength (Y)
and Fracture toughness (
) because it is possible
to increase the pressure which leads to higher
conversion rates and also favors formation of longchained alkanes. Thermal conductivity (λ) to transfer
heat from one part of the reactor to another very
quickly and efficiently. Maximum temperature at
service (
) which leads to higher conversion
rates. Low thermal expansion (α) is important in
order to produce low thermal stress. Finally Specific
Heat ( ) is important to the transfer of thermal
energy. Among these eight criteria, the cost,
corrosion rate and thermal expansion, are a nonbeneficial properties. Eight alternatives for the pipes
and the vessel of a MPBR were taken into
consideration: AISI 316 austenitic stainless steel,
AISI 430 ferritic stainless steel, AISI 4140 Steel,
AISI 304 austenitic stainless steel, PM 2000 ODS
Iron Alloy, PM 1000 ODS Nickel Alloy, ASME SA106 and ASME SA-516. The properties of the
materials alternatives for a MPBR with their
quantitative data are given in Table 1 and their
average values were used
Table 1. Material properties for a MPBR
(A) Cost
[ ]
Material
( )
(1) AISI 316 austenitic
stainless steel
(2) AISI 430 ferritic
stainless steel
(B)
Corrosion
rate [
]
(
)
(C)
Yield
strength
[MPa]
( )
(E)
(D)
Maximum
Thermal
temperature
conductivity at service of
[ ]
material
[ ]
( )
(
)
(F) Fracture
toughness.
[
]
(
)
(G) Thermal
expansion
[
]
(
)
(H) Specific
Heat
[ ]
(
References
)
4,2
2,05
290
16,3
897,5
195
1,6
0,5
[1-5, 10, 12]
3,6
2,67
513,5
24,9
842
203
1,04
0,46
[1-5, 10, 12]
4,3
2,67
415
42,7
845
201
1,22
0,47
[1-5, 10, 12]
5,1
2,02
215
16,2
827,5
17,3
1,73
0,5
[1-5, 10, 12]
112,5
0,125
603
10,9
1350
34
1,5
0,48
[1-5, 10, 12]
112,5
0,125
602
12
1200
32
1,29
0,44
[1-5, 10, 12]
(7) ASME SA-106
1,5
0,6
407,5
51
650
114
1,36
0,46
[1-5, 10, 12]
(8) ASME SA-516
1,75
1,4
447,5
52
650
128
1,2
0,47
[1-5, 10, 12]
(3) AISI 4140 Steel
(4) AISI 304 austenitic
stainless steel
(5) PM 2000 ODS Iron
Alloy (Al 5,5%, Cr 19%,
Fe 74,5 %, Ti 0,50%,
Y2O3 0,50 %)
(6) PM 1000 ODS Nickel
Alloy (Al 0.3%, Cr 20%,
Fe 3,5%,Ni 75,6%, Ti
0,5%, Y2O3 0,60 %)
II. II. CRITERIA WEIGHTING
The criteria weights are calculated using a
compromised weighting method, where the AHP
and Entropy methods were combined, in order to
take into account the subjective and objective
ISSN: 2231-5381
weights of the criteria and to obtain more reasonable
weight coefficients. The synthesis weight for the jth
criteria is:
http://www.ijettjournal.org
(1)
Page 275
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
where αj is the weight of jth criteria obtained via
AHP method, and βj is the weight of jth criteria
obtained through Entropy method.
II. II. I. ANALYTIC HIERARCHY PROCESS (AHP)
The AHP method was developed by [17] to
model subjective decision-making processes based
on multiple criteria in a hierarchical system. The
method composes of three principles:
a)
Structure of the model.
b)
Comparative judgment of the
alternatives and the criteria.
c)
Assessing consistency in results.
a) Structure of the model.
In order to identify the importance of every
alternative in an application, each alternative has
been assigned a value. The ranking is composed by
three levels: 1). general objective, b). criteria for
every alternative, c). alternatives to regard (Saaty,
1980).
b) Comparative
judgment
of
the
alternatives and the criteria.
The weight of criteria respect to other is set in this
section. To quantify each coefficient it is required
experience and knowledge of the application [17]
classified the importance parameters show in Table
II. The relative importance of two criteria is rated
using a scale with the digits 1, 3, 5, 7 and 9, where 1
denotes „„equally important‟‟, 3 for „„slightly more
important‟‟, 5 for „„strongly more important‟‟, 7 for
„„demonstrably more important‟‟ and 9 for
„„absolutely more important‟‟. The values 2, 4, 6 and
8 are applied to differentiate slightly differing
judgements. The comparison among n criteria is
resume in matrix A (
), the global arrange is
expressed in equation (2).
manufacturing systems. Journal of Manufacturing
Technology Management).
c) Consistency assessment
In order to ensure the consistency of the
subjective perception and the accuracy of the results
it is necessary to distinguish the importance of
alternatives among them. In equations (4) and (5) is
shown the consistency indexes required to validate
the results.
(4)
(5)
Where:
: Number of selection criteria.
: Random index.
: Consistency index.
: Consistency relationship.
Largest eigenvalue.
If
should be greater than 0,1, otherwise, the
importance coefficient (1-9) has to be set again and
recalculated [17]
II. II. II. ENTROPY METHOD
Entropy method indicates that a broad distribution
represents more uncertainty than that of a sharply
peaked one [13]. Equation (6) shows the decision
matrix A of multi-criteria problem with
alternatives and criteria:
;
;
(6)
where
=1
(2)
Afterwards, from matrix it is determined the
relative priority among properties. The eigenvector
is the weight importance and it corresponds with
the largest eigenvector (
):
(3)
The consistency of the results is resumed by the
pairwise comparison of alternatives. Matrix can
be ranked as 1 and
= n (Ozden Bayazit. Use
of AHP in decision making for flexible
ISSN: 2231-5381
is
the performance value of the
alternative to the
criteria.
The normalized decision matrix
is calculated
(ZH Zou), in order to determine the weights by the
Entropy method.
(7)
The Entropy value
obtained as:
http://www.ijettjournal.org
of
criteria can be
(8)
Page 276
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
where
is a constant that guarantees
and m is the number of alternatives.
The degree of divergence (
) of the average
information contained by each criterion can be
obtained from Eq. (9):
(9)
Thus, the weight of Entropy of
defined as:
(11)
criteria can be
where
alternative on
criterion. The value of
is determined by
(the smallest value or
(10)
II. II. III. COPRAS-G METHOD
COPRAS-G method [13] is a MCDM method that
applies gray numbers to evaluate several alternatives
of an engineering application. The gray numbers are
a section of the gray theory to confront insufficient
or incomplete information [13]. White number, gray
number and black number are the three
classifications to distinguish the uncertainty level of
information.
The uncertainty level can be expressed by three
numbers: white, gray and black.
Let the number
,
and
, where
has two real
numbers, (the lower limit of
) and (the
upper limit of
) is defined as follows [13]:
a)
White number: if
= , then
is the interval performance value of
lower limit) and
(the biggest value or upper
limit).
Step 3: Normalize the decision matrix,
using the following equations. Eq. (12) is applied for
or lower limit values, whereas, Eq. (13) is used
for
or upper limit values.
(12)
(13)
Step 4: Calculate the weights of each criterion.
Step 5: Determine the weighted normalized
decision matrix,
by mean of the equations (14)
and (15).
has the complete information.
b)
Gray number:
,
means insufficient and uncertain information.
c)
Black number: if
and
(14)
, then
information.
(15)
has no meaningful
The COPRAS-G method uses a stepwise ranking
and evaluating procedure of the alternatives in terms
of significance and utility degree. The procedure of
applying COPRAS-G method is formulated by the
following steps [13]:
Step 1: Selection of a set of the most important
criteria, describing the alternatives and develop the
initial decision matrix,
.
Step 6: The weighted mean normalized sums are
calculated for both the beneficial attributes
based
on equation (16) and non-beneficial attributes
based on equation (17) for all the alternatives.
(16)
(17)
Step 7: Determine the minimum value of
.
(18)
ISSN: 2231-5381
http://www.ijettjournal.org
Page 277
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Step 8: Determine the relative significances or
priorities of the alternatives. The priorities of the
candidate alternatives are calculated on the basis of
with equation (19). The greater the value of ,
the higher is the priority of the alternative. The
alternative with the highest relative significance
value (
) is the best choice among the feasible
candidates.
difference in performance scores for criterion ,
between
alternative and the alternative whose
score for criterion is the highest among all the
alternatives considered.
Step 2: Calculate the linear preference rating for
the input criteria ( ) using equation (23):
(23)
(19)
Step 9: Determine
significance value.
the
maximum
relative
Step 3: Compute the preference ratings with
respect to the beneficial criteria. The aggregate
performance for
alternative on all the beneficial
or output criteria is measured using the equation (24):
(20)
Step 10: Calculate the quantitative utility ( ) for
alternative through the equation (21). The
ranking is set by the .
(21)
With the increase or decrease in the value of the
relative significance for an alternative, it is observed
that its degree of utility also increases or decreases.
These utility values of the candidate alternatives
range from 0 % to 100 %. The best alternative is
assigned according to the maximum value 100%.
(24)
where
indicates the number of
beneficial attributes or output criteria and
is
calibration constant or weight importance of
output criteria. The higher an alternative‟s score for
an output criterion, the higher is the preference for
that alternative. It can be mentioned that
Step 4: Calculate the linear preference rating for
the output criteria (
) using the equation (25):
(25)
II. II. IV. OCRA METHOD
The OCRA method was developed to measure the
relative performance of a set of production units,
where resources are consumed to create value-added
outputs. OCRA uses an intuitive method for
incorporating the decision maker‟s preferences about
the relative importance of the criteria. The general
OCRA procedure is described as below [18]:
Step 1: Compute the preference ratings with
respect to the non- beneficial criteria. The aggregate
performance of
alternative with respect to all the
input criteria is calculated using the following
equation:
(i=1,2,…,m, j=1,2,…,n) (22)
where
is the measure of the relative
performance of
alternative and
is the
performance score of ith alternative with respect to
input criterion. If
alternative is preferred to
alternative with respect to
criterion, then
. Then term
ISSN: 2231-5381
indicates the
Step 5: Compute the overall preference ratings
( ) as follows in equation (26):
(26)
The alternatives are ranked according to the
values of the overall preference rating. The
alternative with the best overall preference rating
receives the first rank.
II. II. V. ARAS METHOD
The ARAS method is based on utility theory and
quantitative measurements. The steps of ARAS
method are as follows [19]:
Step 1: Determine the normalized decision matrix,
using linear normalization procedure for beneficial
attributes [19]. For non-beneficial attributes, the
normalization procedure follows two steps. At first,
the reciprocal of each criterion with respect to all the
alternatives is taken as follows:
(27)
In the second step, the normalized values are
calculated as follows:
http://www.ijettjournal.org
Page 278
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
(28)
Step 2: Determine the weighted normalized
decision matrix, D.
Step 3: Determine the optimality function ( ) for
ith alternative by means of the equation (29):
(29)
(34)
Where
and
are the index set of benefit
criteria and the index set of cost criteria, respectively.
Step 4: The distance between the ideal and nadir
solution is quantified. The two Euclidean distances
for each alternative are computed as given by
equations (35) y (36):
The optimality function
has a direct and
proportional relationship with values in the decision
matrix and criteria weights.
Step 4: Calculate the degree of the utility ( ) for
each alternative. The values of
is calculated by
means of equation (30):
(35)
(30)
The utility values of each alternative range from
0% to 100%. The alternative with the highest
is
the best choice among the material alternatives.
II. II. VI. TOPSIS METHOD
The basic idea of TOPSIS is that the best decision
should be made to be closest to the ideal and farthest
from the non-ideal [20]. Such ideal and negativeideal solutions are computed by considering the
various alternatives. The highest percentage
corresponds to the best alternative.
The TOPSIS approach is structured by the
following procedure [20]:
Step 1: Normalize the decision matrix
by is
performed using the equation 31.
(31)
Where
is the performance measure of
(36)
Step 5: The relative closeness (
by equation (37).
) is computed
;
(37)
The highest
alternatives.
coefficients correspond to the best
II. II. VII. SPEARMAN’S RANK
CORRELATION COEFFICIENT
The Spearman‟s rank correlation coefficient
measures the relation among nonlinear datasets. Its
purpose is to quantify the strength of linear
relationship between two variables. If there are no
repeated data values, a perfect Spearman correlation
of +1 or −1 occurs when each of the variables is a
perfect monotone function of the [21]. The
Spearman‟s rank correlation is computed by
equation (38).
criterion respect to
alternative.
Step 2: Sync the weight
and the normalized
matrix
(38)
, see equation (32).
(32)
Step 3: The ideal solutions (
) and nadir
solutions (
) are determined using (33) and (34):
(33)
ISSN: 2231-5381
Where:
: Spearman‟s rank coefficient
: Difference between ranks of each case
: Number of pairs of values.
III.
RESULTS
The weight of each criteria have been computed
by the AHP method and Entropy method regarding
its importance for the pipes and the vessel of a
MPBR. After the determination of the weights of
different criteria using the AHP and Entropy
methods, these weights were applied to the MCDM
http://www.ijettjournal.org
Page 279
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
methods. The results has been developed with the
methods COPRAS-G, OCRA, ARAS and TOPSIS.
The different steps involved in these methods were
discussed above. The results have been compared in
order to determine their convergence and sensibility
and ranked the best solutions.
III. I. CRITERIA WEIGHTING
The comparison among properties of every
alternative are in Table 1. The properties
identification appears under the name of each
property as ( ), ( ), ( ), (
), (Y), ( ), (λ), and
(
). The weight of each alternative was
assigned according to the AHP and Entropy methods.
The criteria weighting was firstly performed by the
AHP method to obtain the subjective weights of
different evaluation criteria. After the decision
hierarchy for the problem was designed, the criteria
was compared pairwise based on the experience of
the author using the scale given in section 3.1.1. In
Table 2 is can be showed the scale of relative
importance used in the AHP method. The
coefficients were assigned based on the
characteristic for a MPBR.
Table 2. Scale of relative importance
Definition
Intensity of importance
Equal importance
1
Moderate importance
3
Strong importance
5
Very strong importance
7
Extreme importance
9
Intermediate importance
2, 4, 6, 8
account the importance of each criteria. The most
important criteria to generate the matrix was
considered ( ); slightly more important were taken
( ), ( ), and ( ); strongly more important was
considered (
); demonstrably more important
were taken (
), ( ), (
). The results are
consistent due to the value of the consistency index
( =0,018 for pipes and
=0,019 for the vessel)
and the consistency ratio which are lower than the
limit 0,1. At the final step, the compromised weights
of the criteria ( ) were calculated using the Eq. (1).
In Table 4 the weight coefficient of every criterion
was determined for the pipes of a MPBR. The most
representative values are ( ) 54,5 % and (Y),
16,5 %. On the other hand, less than 29 % of the
overall weight is distributed in ( ), ( ), (
), ( ),
(λ), and (
).
In Table 5 is presented the decision matrix
generated for the vessel of the MPBR. The most
important criteria to generate the matrix were
considered ( ) and ( ),; slightly more important
were taken (
), ( ) and ( ); strongly more
important were considered (
) and (
);
demonstrably more important was taken (
).
The results are consistent due to the value of the
consistency index and the consistency ratio which
are lower than the limit 0,1. In Table 6 the weight
coefficient of every criterion was determined for the
vessel of the MPBR. The most representative values
are ( ) 48,3 %, ( ) 13,3 % and (
) 14,1 %. On
the other hand, less than 24,3 % of the overall
weight is distributed in ( ), ( ), (
), ( ) and (λ),
In Table 3 is illustrated the decision matrix
generated for the pipes of the MPBR which take into
Table 3. Comparison among criteria for balanced scales AHP Method for the pipes of the MPBR
(
)
(
)
( )
(
)
( )
( )
( )
( )
1
3
3
3
5
7
7
7
0,333
1
1
1
3
5
5
5
0,333
1
1
1
3
5
5
5
0,333
1
1
1
3
5
5
5
0,2
0,333
0,333
0,333
1
3
3
3
0,143
0,2
0,2
0,2
0,333
1
1
1
0,143
0,2
0,2
0,2
0,333
1
1
1
0,143
0,2
0,2
0,2
0,333
1
1
1
ISSN: 2231-5381
http://www.ijettjournal.org
Page 280
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Table 4. Criteria weighting by the AHP ( ), balanced scales entropy ( ),) and compromised weighting ( )
methods for the pipes of the MPBR.
(
)
(
)
(
( )
)
( )
( )
( )
( )
0,348
0,160
0,160
0,160
0,073
0,033
0,033
0,033
0,219
0,023
0,144
0,081
0,153
0,046
0,164
0,170
0,545
0,027
0,165
0,093
0,080
0,011
0,038
0,040
Table 5. Comparison among criteria for balanced scales AHP Method for the vessel of MPBR.
(
)
( )
( )
( )
1
1
3
3
1
1
3
0,333
0,333
0,333
0,333
(
)
(
)
( )
( )
3
5
5
7
3
3
5
5
7
1
1
1
3
3
5
0,333
1
1
1
3
3
5
0,333
1
1
1
3
3
5
0,200
0,200
0,333
0,333
0,333
1
1
3
0,200
0,200
0,333
0,333
0,333
1
1
3
0,143
0,143
0,200
0,200
0,200
0,333
0,333
1
Table 6. Criteria weighting by the AHP ( ), balanced scales entropy ( ),) and compromised weighting ( )
methods for the vessel of the MPBR.
(
)
( )
( )
( )
0,27
0,27
0,113
0,113
0,219
0,023
0,164
0,483
0,051
0,133
4.2 COPRAS-G
For application of COPRAS-G method for the
materials of the pipes of a MPBR, the related
decision matrix is first developed from the gray
numbers applied in COPRAS-G are resumed in
Table VII. Equations 16 and 17 allow to develop
decision matrix which is then weighted normalized,
as is given in Table VIII. Later, the normalized
matrix and the weight are compared by means of
equations 19 y 20. Table IX exhibits the priority
values (Qi) and quantitative utility (Ui) values for
the candidate alternatives of the pipes of FischerTropsch reactor, as calculated using equations (19)
and (21) respectively. Table X also shows the
ranking of the alternative material as 7-3-8-1-4-2-5-6.
ASME SA-106 and AISI 4140 steel, obtain the first
ISSN: 2231-5381
(
)
(
)
( )
( )
0,113
0,048
0,048
0,025
0,046
0,153
0,144
0,081
0,170
0,075
0,141
0,018
0,064
0,035
and second ranks respectively, in contrast PM 1000
ODS Nickel Alloy and PM 2000 ODS Iron Alloy
have the last rank.
For the materials of the vessel of a MPBR, the
related decision matrix is are resumed in Table VII.
In Table VIII exhibits the weight normalized
decision matrix Table IX shows the priority values
(Qi) and quantitative utility (Ui) values and ranking
alternatives for the candidate alternatives of the
vessel of a MPBR. The ranking of the alternative
material are 7-8-2-3-1-4-5-6. ASME SA-106 and
ASME SA-516, obtain the first and second ranks
respectively, in contrast PM 1000 ODS Nickel Alloy
has the last rank.
http://www.ijettjournal.org
Page 281
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
TABLE I.
Material
1
2
3
4
5
6
7
8
Material
1
2
3
4
5
6
7
8
DECISION MATRIX OF COPRAS-G METHOD FOR THE PIPES AND VESSEL OF THE MPBR.
)
278
281
274
228
38
44
125
139
(
1,8
2,53
2,53
1,93
0,1
0,1
0,3
0,8
TABLE II.
NORMALIZED MATRIX MADE OF GRAY NUMBERS FOR THE PIPES OF THE MPBR.
(
0,00
8
0,00
6
0,00
7
0,01
0
0,05
6
0,05
6
0,00
1
0,00
2
)
0,01
1
0,01
0
0,01
2
0,01
3
0,44
4
0,44
4
0,00
5
0,00
6
(
0,00
4
0,00
6
0,00
6
0,00
4
0,00
0
0,00
0
0,00
1
0,00
2
)
2,3
2,81
2,81
2,12
0,15
0,15
0,9
2
)
0,00
5
0,00
7
0,00
0
0,00
5
0,00
0
0,00
0
0,00
2
0,00
5
TABLE III.
(
270
496
410
205
578
578
330
380
TABLE IV.
(
0,00
7
0,00
5
0,00
6
0,00
8
0,04
9
0,04
9
0,00
1
0,00
2
)
0,01
0
0,00
9
0,01
1
0,01
2
0,39
3
0,39
3
0,00
5
0,00
5
)
310
531
420
225
628
626
485
515
(
14,5
22,4
42,6
16
10,6
11,7
40
41
(
1,4
0,98
1,09
1,56
1,34
1,14
1,25
1,08
(
)
(
)
( )
( )
0,01 0,01 0,00 0,00 0,00 0,00 0,00 0,00
3
5
6
7
5
5
1
3
0,02
0,02
0,00
0,01
0,01
0,01
0,00
0,00
3
5
9
1
0
0
1
3
0,01
0,02
0,01
0,01
0,01
0,01
0,00
0,00
9
0
8
8
0
0
1
3
0,01 0,01 0,00 0,00 0,00 0,01 0,00 0,00
0
1
7
7
9
1
1
2
0,02
0,03
0,00
0,00
0,01
0,01
0,00
0,00
7
0
4
5
6
6
0
0
0,02 0,03 0,00 0,00 0,01 0,01 0,00 0,00
7
0
5
5
4
4
0
0
0,01
0,02
0,01
0,02
0,00
0,00
0,00
0,00
6
3
6
6
7
8
1
1
0,01 0,02 0,01 0,02 0,00 0,00 0,00 0,00
8
4
7
6
7
8
1
1
PI, RI, QI AND UI VALUES FOR THE PIPES OF THE MPBR.
Material
Material
1
2
3
4
5
6
7
8
(
)
(
)
18,1 440 460 112
27,4 815 869 125
42,8 811 879 128
16,4 750 905 119
11,2 1325 1375 30
12,3 1180 1220 20
62 600 700 103
63 595 705 117
( )
3,4
5
2,5 4,7
3,2 5,4
4,3 5,9
25 200
25 200
0,6 2,4
0,8 2,7
1
Pi
0,027
Ri
0,089
Qi
0,122
Ui
36,287
Rank
4
2
0,034
0,112
0,110
32,772
6
3
0,035
0,058
0,181
54,123
2
4
0,024
0,089
0,119
35,375
5
5
0,024
0,138
0,086
25,575
7
6
0,024
0,137
0,085
25,479
8
7
0,030
0,028
0,335
100,000
1
8
0,033
0,059
0,174
52,009
3
)
1,8
1,1
1,35
1,9
1,6
1,44
1,27
1,32
( )
0,00 0,00
5
6
0,00
0,00
3
4
0,00
0,00
4
5
0,00 0,00
5
7
0,00
0,00
5
6
0,00 0,00
4
5
0,00
0,00
4
4
0,00 0,00
4
5
(
0,45
0,42
0,41
0,45
0,44
0,4
0,44
0,45
)
0,55
0,5
0,53
0,55
0,52
0,48
0,48
0,49
(
0,00
5
0,00
4
0,00
4
0,00
5
0,00
5
0,00
4
0,00
5
0,00
5
)
0,00
6
0,00
5
0,00
6
0,00
6
0,00
6
0,00
5
0,00
5
0,00
5
NORMALIZED MATRIX MADE OF GRAY NUMBERS FOR THE VESSEL OF THE MPBR.
(
0,00
8
0,01
1
0,01
1
0,00
8
0,00
0
0,00
0
0,00
1
0,00
4
ISSN: 2231-5381
)
0,01
0
0,01
2
0,01
2
0,00
9
0,00
1
0,00
1
0,00
4
0,00
9
(
0,01
7
0,01
2
0,01
3
0,01
9
0,01
7
0,01
4
0,01
5
0,01
3
)
0,02
2
0,01
4
0,01
7
0,02
3
0,02
0
0,01
8
0,01
6
0,01
6
(
0,00
1
0,00
2
0,00
3
0,00
1
0,00
1
0,00
1
0,00
3
0,00
3
)
0,00
1
0,00
2
0,00
3
0,00
1
0,00
1
0,00
1
0,00
4
0,00
4
(
0,01
7
0,01
6
0,01
5
0,01
7
0,01
6
0,01
5
0,01
6
0,01
7
)
0,02
1
0,01
9
0,02
0
0,02
1
0,01
9
0,01
8
0,01
8
0,01
8
http://www.ijettjournal.org
(
0,00
1
0,00
1
0,00
1
0,00
1
0,00
0
0,00
0
0,00
1
0,00
1
)
0,00
1
0,00
1
0,00
1
0,00
1
0,00
0
0,00
0
0,00
1
0,00
1
(
0,00
0
0,00
0
0,00
0
0,00
0
0,00
0
0,00
0
0,00
0
0,00
0
)
0,00
1
0,00
0
0,00
0
0,00
1
0,00
0
0,00
0
0,00
0
0,00
0
(
0,00
2
0,00
4
0,00
4
0,00
4
0,00
7
0,00
6
0,00
3
0,00
3
Page 282
)
0,00
2
0,00
4
0,00
4
0,00
5
0,00
7
0,00
6
0,00
4
0,00
4
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
PI, RI, QI AND UI VALUES FOR THE VESSEL OF THE MPBR.
TABLE V.
Material
1
Pi
0,024
Ri
0,037
Qi
0,160
Ui
60,604
Rank
5
2
0,025
0,032
0,184
69,738
3
3
0,026
0,035
0,169
64,094
4
4
0,025
0,040
0,151
57,112
6
5
0,026
0,240
0,047
17,865
7
6
0,024
0,238
0,045
17,090
8
7
0,025
0,021
0,264
100,000
1
8
0,025
0,024
0,233
88,058
2
4.3 OCRA
Firstly, the aggregate performance of each
alternative with respect to all the input criteria is
calculated with equation (22). Applying equation
(24), the aggregate performance of the alternatives
on all the beneficial or output criteria are then
determined and subsequently, the linear preference
ratings for the output criteria are calculated. Finally,
the overall preference rating for each alternative
material is determined using equation (26). The
detailed computations of this method for the pipes of
a MPBR are illustrated in Table XII. In this method,
the ranking material alternatives is obtained as 7-81-2-4-3-6-5, which suggests that ASME SA-106
attains the top rank. ASME SA-516 is the second
best choice and PM 1000 ODS Nickel Alloy has the
last rank and PM 2000 ODS Iron Alloy is the second
last rank.
In case of the vessel of the MPBR the
computation details for OCRA method for are
showed in Table XIII. For this method, the ranking
material alternatives is obtained as 7-8-1-4-2-3-6-5.
This results suggests that ASME SA-106 is and
ASME SA-516 are the best choices for the vessel of
a MPBR. On the other hand, PM 1000 ODS Nickel
Alloy and PM 2000 ODS Iron Alloy obtain the last
rank or alternative materials.
COMPUTATION DETAILS FOR OCRA METHOD FOR THE PIPES OF THE MPBR.
TABLE VI.
Material
Rank
1
40,115
39,106
0,018
0,009
39,075
3
2
39,981
38,973
0,022
0,013
38,946
4
3
39,644
38,635
0,023
0,014
38,609
6
4
39,966
38,958
0,012
0,003
38,921
5
5
1,009
0,000
0,049
0,040
0,000
8
6
1,031
0,022
0,049
0,040
0,022
7
7
41,111
40,102
0,009
0,000
40,062
1
8
40,807
39,798
0,014
0,005
39,763
2
TABLE VII.
COMPUTATION DETAILS FOR OCRA METHOD FOR THE VESSEL OF THE MPBR.
Material
Rank
1
35,420
33,366
1,457
1,448
34,774
3
2
35,343
33,289
0,022
0,013
33,262
5
3
35,003
32,949
0,023
0,014
32,923
6
4
35,908
33,854
0,012
0,003
33,817
4
5
2,054
0,000
0,049
0,040
0,000
8
6
2,104
0,050
0,049
0,040
0,050
7
7
37,078
35,024
0,009
0,000
34,984
1
8
36,617
34,563
0,014
0,005
34,527
2
ISSN: 2231-5381
http://www.ijettjournal.org
Page 283
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
best solution for the pipes of a MPBR. In contrast,
PM 1000 ODS Nickel Alloy has the last rank.
For the vessel of the reactor, the values of
and
, and the ranking achieved by the material
alternatives are illustrated in Table XVII. The
ranking material alternatives is obtained as 7-8-4-21-3-5-6. ASME SA-106 is the best choice between
the alternatives and ASME SA-516 is the second
best solution for the material of the vessel of a
MPBR. On the other hand, PM 1000 ODS Nickel
Alloy and PM 2000 ODS Iron Alloy obtain the last
rank or alternative materials.
4.4 ARAS
Weighted normalized decision matrix for ARAS
method for the pipes of a MPBR, as given in Table
XIV, and using equations (29) the optimality
function ( ) for each of the materials alternative is
calculated. Then, using the equation (30) the
corresponding values of the utility degree ( ) are
determined for all the alternatives. The values of
and
, and the ranking achieved by the material
alternatives for the pipes of the MPBR are exhibited
in Table XV. In this method, the ranking material
alternatives is obtained as 7-8-4-1-2-3-6-5. It is
revealed from this table that ASME SA-106 is the
best alternative and ASME SA-516 is the second
TABLE VIII.
WEIGHTED NORMALIZED DECISION MATRIX FOR ARAS METHOD FOR THE PIPES OF THE MPBR.
(
)
(
)
(
( )
( )
1
0,063
0,001
0,023
0,012
0,012
0,000
0,000
0,006
2
0,074
0,001
0,013
0,008
0,013
0,000
0,001
0,006
3
0,062
0,001
0,016
0,005
0,013
0,000
0,001
0,006
4
0,052
0,001
0,032
0,012
0,013
0,003
0,000
0,006
5
0,002
0,015
0,011
0,018
0,008
0,001
0,000
0,006
6
0,002
0,015
0,011
0,016
0,009
0,002
0,001
0,006
7
0,177
0,003
0,017
0,004
0,016
0,000
0,001
0,006
8
0,152
0,001
0,015
0,004
0,016
0,000
0,001
0,006
TABLE IX.
( )
SI, UI AND RANK VALUES IN ARAS METHOD FOR THE PIPES OF THE MPBR.
Material
TABLE X.
( )
)
( )
Material
Rank
1
0,118
0,525
4
2
0,115
0,514
5
3
0,103
0,459
6
4
0,118
0,528
3
5
0,063
0,279
8
6
0,063
0,279
7
7
0,224
1,000
1
8
0,196
0,872
2
WEIGHTED NORMALIZED DECISION MATRIX FOR ARAS METHOD FOR THE VESSEL OF A MPBR.
(
)
( )
( )
( )
1
0,052
0,001
0,014
0,003
2
0,061
0,001
0,021
3
0,051
0,001
4
0,043
5
0,002
6
(
)
(
)
( )
( )
0,017
0,003
0,010
0,004
0,002
0,018
0,002
0,006
0,004
0,018
0,002
0,018
0,002
0,004
0,004
0,001
0,013
0,029
0,017
0,004
0,010
0,004
0,020
0,015
0,015
0,017
0,001
0,015
0,003
0,002
0,020
0,017
0,016
0,019
0,001
0,013
0,003
7
0,146
0,004
0,016
0,004
0,018
0,002
0,003
0,006
8
0,125
0,002
0,019
0,004
0,018
0,002
0,003
0,006
Material
ISSN: 2231-5381
http://www.ijettjournal.org
Page 284
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
TABLE XI.
SI, UI AND RANK VALUES IN ARAS METHOD FOR THE VESSEL OF THE MPBR.
Material
Rank
1
0,104
0,517
5
2
0,116
0,581
4
3
0,101
0,502
6
4
0,121
0,605
3
5
0,088
0,440
8
6
0,092
0,459
7
7
0,200
1,000
1
8
0,178
0,889
2
MPBR. On the other hand, PM 1000 ODS Nickel
Alloy has the last rank.
In Table XXI is shown the weighted and
normalized decision matrix
for the vessel of the
MPBR. The ideal and nadir ideal solutions are
presented in Table XXII for the vessel of the MPBR.
The ranking of materials for the vessel of the MPBR
is illustrated in Table XXIII. The ranking of the
alternative material are 7-8-3-2-1-4-6-5. For TOPSIS
method ASME SA-106 is the best choice between
the alternatives and ASME SA-516 is the second
best choice for the material vessel of a MPBR. On
the other hand, PM 1000 ODS Nickel Alloy has the
last rank and PM 2000 ODS Iron Alloy is the second
last rank.
4.5 TOPSIS
The decision matrix given in Table I was
normalized using equation (32) for the application of
the TOPSIS method and this was multiplied by the
compromised weights obtained. In Table XVIII is
shown the weighted and normalized decision matrix
for the pipes of the MPBR. The ideal and nadir
ideal solutions, determined by equations (33) and
(34), are presented in Table XIX for the pipes of the
Fischer-Tropsch reactor. The distances from the
ideal ( ) and nadir ideal solutions ( ) and the
relative closeness to the ideal solution ( ) are
measured using equations (35)–(37). The materials
for the pipes of the MPBR could be ranked by the
relative degree of approximation and the ranking is
shown in Table XX. The ranking of the alternative
material are 7-8-3-1-4-2-5-6. For TOPSIS method
ASME SA-106 is the best alternative and ASME
SA-516 is the second best choice for the pipes of a
TABLE XII.
EIGHTED AND NORMALIZED DECISION MATRIX,
Mate
rial
1
OF TOPSIS METHOD FOR THE PIPES OF THE MPBR.
(
)
(
)
(
( )
0,026
0,411
0,225
0,176
0,339
0,501
0,409
0,374
2
0,023
0,535
0,399
0,269
0,318
0,522
0,266
0,344
3
0,027
0,535
0,322
0,462
0,319
0,516
0,312
0,351
4
0,032
0,405
0,167
0,175
0,312
0,044
0,442
0,374
5
0,706
0,025
0,468
0,118
0,509
0,087
0,383
0,359
6
0,706
0,025
0,467
0,130
0,453
0,082
0,330
0,329
7
0,009
0,120
0,316
0,552
0,245
0,293
0,347
0,344
8
0,011
0,281
0,347
0,563
0,245
0,329
0,307
0,351
( )
( )
( )
)
( )
TABLE XIII.
HE IDEAL AND NADIR IDEAL SOLUTIONS OF TOPSIS METHOD FOR THE PIPES OF THE MPBR.
(
)
(
)
)
( )
( )
( )
0,006
0,001
0,023
0,044
0,051
0,004
0,002
0,018
0,413
0,021
0,065
0,009
0,024
0,000
0,001
0,016
ISSN: 2231-5381
http://www.ijettjournal.org
( )
(
( )
Page 285
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
TABLE XIV.
OMPUTATION DETAILS FOR TOPSIS METHOD FOR THE PIPES OF THE MPBR.
Material
1
0,040
0,399
0,909
Rank
4
2
0,049
0,400
0,892
6
3
0,037
0,399
0,915
3
4
0,041
0,397
0,906
5
5
0,411
0,033
0,074
7
6
0,411
0,029
0,065
8
7
0,034
0,410
0,924
1
8
0,038
0,409
0,915
2
TABLE XV.
EIGHTED AND NORMALIZED DECISION MATRIX,
Materia
l
1
2
3
4
5
6
7
8
( )
0,02
6
0,02
( )
0,411
3
0,02
7
0,03
0,535
0,535
0,405
2
0,70
6
0,70
0,025
6
0,00
9
0,01
0,120
0,025
0,281
1
( )
0,40
9
0,26
(
OF TOPSIS METHOD FOR THE VESSEL OF MPBR.
)
(
)
( ) (
( )
)
0,501
0,225
0,374
0,176
0,339
0,522
0,399
0,344
0,269
0,318
6
0,31
2
0,44
0,516
0,322
0,351
0,462
0,319
0,044
0,167
0,374
0,175
0,312
2
0,38
3
0,33
0,087
0,468
0,359
0,118
0,509
0,082
0,467
0,329
0,130
0,453
0
0,34
7
0,30
0,293
0,316
0,344
0,552
0,245
0,329
0,347
0,351
0,563
0,245
7
TABLE XVI.
HE IDEAL AND NADIR IDEAL SOLUTIONS OF TOPSIS METHOD FOR THE VESSEL OF THE MPBR.
( )
( )
( )
(
)
(
)
( )
( )
(
0,005
0,001
0,035
0,039
0,053
0,008
0,036
0,018
0,341
0,027
0,059
0,003
0,046
0,003
0,008
0,009
TABLE XVII.
OMPUTATION DETAILS FOR TOPSIS METHOD FOR THE VESSEL OF THE MPBR.
Material
1
0,330
0,039
0,895
Rank
5
2
0,333
0,034
0,908
4
3
0,331
0,030
0,917
3
4
0,326
0,055
0,855
6
5
0,030
0,339
0,081
8
6
0,032
0,339
0,085
7
7
0,339
0,023
0,935
1
8
0,338
0,023
0,937
2
III. VI SPEARMAN’S CORRELATION COEFFICIENTS
In Table 24 and Table 25 is shown the
Spearman‟s correlation coefficients for the pipes and
the vessel of the MPBR. These represent the mutual
correspondence among MCDM methods. The
ISSN: 2231-5381
magnitude of this parameter for the pipes of the
MPBR exceeds 0,57 for the relation between all the
methods. In case of the relation between COPRASG, ARAS and TOPIS methods, the Spearman‟s
correlation coefficients exceeds 0,7.
http://www.ijettjournal.org
Page 286
)
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Table 24. Spearman‟s correlation indexes for the
pipes of the MPBR
OCRA
ARAS
TOPSIS
COPRAS
0,571
0,571
0,952
OCRA
-
0,893
0,702
ARAS
-
-
0,702
Table 25. Spearman‟s correlation indexes for the
vessel of the MPBR
COPRA
S
OCRA
ARAS
OCRA
0,571
-
ARAS
0,702
0,893
-
TOPSIS
0,810
0,810
0,952
The Spearman‟s correlation coefficients for the
vessel of the MPBR exceeds 0,57 for the relation of
all the cases. In case of the relation between
COPRAS-G, ARAS and TOPIS methods, the
Spearman‟s correlation coefficients exceeds 0,81.
IV DISCUSSION
For design a MPBR, many studies has been used
CFD for detailed evaluation of reaction systems [5]
However, for this design usually engineers use
certain materials based on experience and other
studies, but they do not make a preliminary selection.
The MCDM are an important tool to recognize
and identify the best material alternative in a bunch
of several of them. These methods can adapt to
different sort of environments and conditions that
would affect the final result and that is why these
approaches are applied in different areas of science,
engineering and management.
Figure 2.
ISSN: 2231-5381
In this case, we take advantage of MCDM
methods in order know the best alternative for the
pipes and the vessel of the MPBR. In Fig. 2 is
resumed the overall rank of each MCDM method for
the pipes of the MPBR. It has been observed than in
all the cases, the best alternative and second best
alternative correspond with ASME SA-106 and
ASME SA-516 because it low cost and good ( ). In
addition, PM 1000 ODS Nickel Alloy and PM 2000
ODS Iron Alloy are presented on the last rank
alternatives in all the MCDM methods considered.
On the other hand In Fig. 3 is illustrated the overall
rank of each MCDM method for the vessel of the
MPBR. It has been observed than in all the best
alternative and second best alternative correspond
with ASME SA-106 and ASME SA-516 because it
low cost and good ( ) and PM 1000 ODS Nickel
Alloy and PM 2000 ODS Iron Alloy appear on the
last rank alternatives in the most of the MCDM
analyzed too. The method validation was correlated
by Spearman‟s coefficients. The magnitude of this
parameter for the pipes and the vessel of the MPBR
exceeds 0,57 for the relation between all the
methods.
The results show that make a MPBR with ASME
SA-106 and ASME SA-516 could reduce the
manufacturing cost with a good corrosion rate, yield
strength and fracture toughness. This properties
should improve the life at service of the MPBR. In
addition, it should take into account that the
maximum temperature at service it is around 650°C.
In case of the maximum temperature at service
overpass this value it should choose other alloy.
Finally, the high thermal conductivity of this alloys
suggest to control the outer surface of the MPBR.
Rank materilas vs. alternative materials for the pipes of the MPBR
http://www.ijettjournal.org
Page 287
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
Figure 3 Rank materilas vs. alternative materials for the vessel of an MPBR
V CONCLUSIONS
Use of bioenergy energy produced from organic
matter or biomass has the potential to increase
energy security, promote economic development,
and decrease global warming pollution. For this
reason, it is necessary to improve the design of the
technology to produce bioenergy in an efficiency
way.
In this paper the material selection problem for a
MPBR has been solved utilizing a decision model.
The alternative materials were successfully
evaluated using all the considered methods. Ranking
scores which were used to rank the alternative
materials were obtained as results of the methods.
The model includes the COPRAS-G, OCRA, ARAS
and TOPSIS methods for the ranking of the
alternative materials according to determined criteria.
The weighting of the material properties was
performed using the compromised weighting method
composes of the AHP and Entropy methods
According to the results, ASME SA-106 would be
the best material for the pipes and the vessel of a
MPBR and ASME SA-516 the second best choice.
The main contribution to the field of this results is to
obtain a material with an adequate corrosion rate and
mechanical properties with the lowest cost. In
contrast, it is necessary to take into account that the
maximum temperature at service is 650 °C for these
alloy and control the outer surface of the MPBR.
It was validated that the MCDM approach is a
viable tool in solving the complex material selection
decision problems. Spearman‟s rank correlation
coefficient was found to be very useful in
assessment of the correlation between all the ranking
methods. The model which was developed for the
material selection for the pipes and the vessel of a
ISSN: 2231-5381
MPBR can be applied on other mechanical
components for material selection problems. The
materials analyzed in this paper are used in industrial
applications and their workability are reasonable. In
this way they could be used in industrial applications
and for build a MPBR.
ACKNOWLEDGEMENTS
The authors of this research acknowledge to the
Secretaría Nacional de Planificación y Desarrollo
(SENPLADES) for financing the execution of the
present research. This work was sponsored by the
Prometeo project of the Secretaria de Educación
Superior, Ciencia, Tecnología e Innovación
(SENESCYT) held in the Republic of Ecuador. The
information necessary to complete this work was
given by the Ministerio de Electricidad y Energía
Renovable (MEER) of Ecuador
REFERENCES
[1] Iglesia, E. 1997. Design, synthesis, and use of cobalt-based
Fischer-Tropsch synthesis catalysts. Applied Catalysis A:
General, 161(1), 59-78.
[2] Krishna, R., & Sie, S. T. 2000. Design and scale-up of the
Fischer–Tropsch bubble column slurry reactor. Fuel Processing
Technology, 64(1), 73-105.
[3] Dry, M. E. 1996. Practical and theoretical aspects of the
catalytic Fischer-Tropsch process. Applied Catalysis A: General,
138(2), 319-344.
[4] Park, S., Jung, I., Lee, U., Na, J., Kshetrimayum, K. S.,
Lee, Y., & Han, C. 2015. Design and modeling of large-scale
cross-current multichannel Fischer–Tropsch reactor using channel
decomposition and cell-coupling method. Chemical Engineering
Science, 134, 448-456.
[5] Arzamendi, G., Diéguez, P. M., Montes, M., Odriozola, J.
A., Sousa-Aguiar, E. F., & Gandía, L. 2009. M. Methane steam
reforming in a microchannel reactor for GTL intensification: A
computational fluid dynamics simulation study. Chemical
Engineering Journal, 154(1), 168-173.
[6] Mohammadi, M., Jovanovic, G. N., & Sharp, K. V. 2013.
Numerical study of flow uniformity and pressure characteristics
http://www.ijettjournal.org
Page 288
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016
within a microchannel array with triangular manifolds. Computers
& Chemical Engineering, 52, 134-144.
[7] Almeida, L. C., Sanz, O., Merino, D., Arzamendi, G.,
Gandía, L. M., & Montes, M. 2013. Kinetic analysis and
microstructured reactors modeling for the Fischer–Tropsch
synthesis over a Co–Re/Al 2 O 3 catalyst. Catalysis Today, 215,
103-111.
[8] Ellepola, J., Thijssen, N., Grievink, J., Baak, G., Avhale,
A., & van Schijndel, J. 2012. Development of a synthesis tool for
Gas-To-Liquid complexes. Computers & Chemical Engineering,
42, 2-14.
[9] Tawancy, H. M., Ul-Hamid, A., Mohammed, A. I., &
Abbas, N. M. 2007. Effect of materials selection and design on
the performance of an engineering product–An example from
petrochemical industry. Materials & design, 28(2), 686-703.
[10] Alibaba Available from: http://www.alibaba.com/
[11] Ashby, M. F., Brechet, Y. J. M., Cebon, D., & Salvo, L.
2004. Selection strategies for materials and processes. Materials
& Design, 25(1), 51-67.
[12]Matweb Available from: http://www.matweb.com/
[13] Chatterjee, P., Athawale, V. M., & Chakraborty, S. 2011.
Materials selection using complex proportional assessment and
evaluation of mixed data methods. Materials & Design, 32(2),
851-860.
[14] Jahan, A., Ismail, M. Y., Sapuan, S. M., & Mustapha, F.
2010. Material screening and choosing methods–a review.
Materials & Design, 31(2), 696-705.
[15] Findik, F., & Turan, K. 2012. Materials selection for
lighter wagon design with a weighted property index method.
Materials & Design, 37, 470-477.
[16] Bitarafan, M., Zolfani, S. H., Arefi, S. L., & Zavadskas,
E. K. 2012.Evaluating the construction methods of cold-formed
steel structures in reconstructing the areas damaged in natural
crises, using the methods AHP and COPRAS-G. Archives of
Civil and Mechanical Engineering, 12(3), 360-367.
[17] Saaty, T. L. How to make a decision: the analytic
hierarchy process. European journal of operational research,
48(1), 9-26.
[18] Parkan, C., & Wu, M. L. 1980. Measurement of the
performance of an investment bank using the operational
competitiveness rating procedure. Omega, 1999. 27(2), 201-217.
[19] Turskis, Z., & Zavadskas, E.K. 2010. A novel method for
multiple criteria analysis: Grey additive ratio assessment (ARASG) method. Informatica, 21(4), 597-610.
[20] Khorshidi J. and Hassani, A. 2013. Comparative analysis
between TOPSIS and PSI methods of materials selection to
achieve a desirable combination of strength and workability in
Al/SiC composite, Mater. Des., vol. 52, pp. 999–1010.
[21] Borradaile, G. J. 2013. Statistics of earth science data:
their distribution in time, space and orientation. Springer Science
& Business Media.
ISSN: 2231-5381
http://www.ijettjournal.org
Page 289