Material Selection using Multi-criteria decision making · PDF file · 2017-02-07Four main types of commercial FT reactors are ... the fluidized-bed reactor, the multi-tubular packed-bed

International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 6- April 2016

ISSN: 2231-5381 http://www.ijettjournal.org Page 273

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 packed-

bed 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

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−1

CO) [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

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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 above-

mentioned 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

(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 long-

chained 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.




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 long-

chained 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 non-

beneficial 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 SA-

106 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

Material

(A) Cost

[ ]

( )

(B)

Corrosion

rate [ ]

( )

(C)

Yield

strength

[MPa]

( )

(D)

Thermal

conductivity

[ ]

( )

(E)

Maximum

temperature

at service of

material

[ ]

( )

(F) Fracture

toughness.

[ ]

( )

(G) Thermal

expansion

[ ]

( )

(H) Specific

Heat

[ ]

( )

References

(1) AISI 316 austenitic

stainless steel 4,2 2,05 290 16,3 897,5 195 1,6 0,5 [1-5, 10, 12]

(2) AISI 430 ferritic stainless steel

3,6 2,67 513,5 24,9 842 203 1,04 0,46 [1-5, 10, 12]

(3) AISI 4140 Steel 4,3 2,67 415 42,7 845 201 1,22 0,47 [1-5, 10, 12]

(4) AISI 304 austenitic

stainless steel 5,1 2,02 215 16,2 827,5 17,3 1,73 0,5 [1-5, 10, 12]

(5) PM 2000 ODS Iron Alloy (Al 5,5%, Cr 19%,

Fe 74,5 %, Ti 0,50%,

Y2O3 0,50 %)

112,5 0,125 603 10,9 1350 34 1,5 0,48 [1-5, 10, 12]

(6) PM 1000 ODS Nickel Alloy (Al 0.3%, Cr 20%,

Fe 3,5%,Ni 75,6%, Ti

0,5%, Y2O3 0,60 %)

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]

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

weights of the criteria and to obtain more reasonable

weight coefficients. The synthesis weight for the jth

criteria is:

(1)




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).

=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

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 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 of criteria can be

obtained as:

(8)




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 criteria can be

defined as:

(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

has the complete information.

b) Gray number: ,

means insufficient and uncertain information.

c) Black number: if and

, then has no meaningful

information.

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, .

(11)

where is the interval performance value of

alternative on criterion. The value of

is determined by (the smallest value or

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).

(14)

(15)

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)




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.

(19)

Step 9: Determine the maximum relative

significance value.

(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%.

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 indicates the

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)

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):

(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)

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:




(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)

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):

(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 negative-

ideal 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

criterion respect to alternative.

Step 2: Sync the weight and the normalized

matrix , see equation (32).

(32)

Step 3: The ideal solutions ( ) and nadir

solutions ( ) are determined using (33) and (34):

(33)

(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):

(35)

(36)

Step 5: The relative closeness ( ) is computed

by equation (37).

;

(37)

The highest coefficients correspond to the best

alternatives.

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).

(38)

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




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

In Table 3 is illustrated the decision matrix

generated for the pipes of the MPBR which take into

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),

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




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 3 5 5 7

1 1 3 3 3 5 5 7

0,333 0,333 1 1 1 3 3 5

0,333 0,333 1 1 1 3 3 5

0,333 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 0,113 0,048 0,048 0,025

0,219 0,023 0,164 0,046 0,153 0,144 0,081 0,170

0,483 0,051 0,133 0,075 0,141 0,018 0,064 0,035

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 Fischer-

Tropsch 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

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.




TABLE I. DECISION MATRIX OF COPRAS-G METHOD FOR THE PIPES AND VESSEL OF THE MPBR.

Material ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 3,4 5 1,8 2,3 270 310 14,5 18,1 440 460 112 278 1,4 1,8 0,45 0,55

2 2,5 4,7 2,53 2,81 496 531 22,4 27,4 815 869 125 281 0,98 1,1 0,42 0,5

3 3,2 5,4 2,53 2,81 410 420 42,6 42,8 811 879 128 274 1,09 1,35 0,41 0,53

4 4,3 5,9 1,93 2,12 205 225 16 16,4 750 905 119 228 1,56 1,9 0,45 0,55

5 25 200 0,1 0,15 578 628 10,6 11,2 1325 1375 30 38 1,34 1,6 0,44 0,52

6 25 200 0,1 0,15 578 626 11,7 12,3 1180 1220 20 44 1,14 1,44 0,4 0,48

7 0,6 2,4 0,3 0,9 330 485 40 62 600 700 103 125 1,25 1,27 0,44 0,48

8 0,8 2,7 0,8 2 380 515 41 63 595 705 117 139 1,08 1,32 0,45 0,49

TABLE II. NORMALIZED MATRIX MADE OF GRAY NUMBERS FOR THE PIPES OF THE MPBR.

Material ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 0,00

8

0,01

1

0,00

4

0,00

5

0,01

3

0,01

5

0,00

6

0,00

7

0,00

5

0,00

5

0,00

1

0,00

3

0,00

5

0,00

6

0,00

5

0,00

6 2 0,00

6

0,01

0

0,00

6

0,00

7

0,02

3

0,02

5

0,00

9

0,01

1

0,01

0

0,01

0

0,00

1

0,00

3

0,00

3

0,00

4

0,00

4

0,00

5 3 0,00

7

0,01

2

0,00

6

0,00

0

0,01

9

0,02

0

0,01

8

0,01

8

0,01

0

0,01

0

0,00

1

0,00

3

0,00

4

0,00

5

0,00

4

0,00

6 4 0,01

0

0,01

3

0,00

4

0,00

5

0,01

0

0,01

1

0,00

7

0,00

7

0,00

9

0,01

1

0,00

1

0,00

2

0,00

5

0,00

7

0,00

5

0,00

6 5 0,05

6

0,44

4

0,00

0

0,00

0

0,02

7

0,03

0

0,00

4

0,00

5

0,01

6

0,01

6

0,00

0

0,00

0

0,00

5

0,00

6

0,00

5

0,00

6 6 0,05

6

0,44

4

0,00

0

0,00

0

0,02

7

0,03

0

0,00

5

0,00

5

0,01

4

0,01

4

0,00

0

0,00

0

0,00

4

0,00

5

0,00

4

0,00

5 7 0,00

1

0,00

5

0,00

1

0,00

2

0,01

6

0,02

3

0,01

6

0,02

6

0,00

7

0,00

8

0,00

1

0,00

1

0,00

4

0,00

4

0,00

5

0,00

5 8 0,00

2

0,00

6

0,00

2

0,00

5

0,01

8

0,02

4

0,01

7

0,02

6

0,00

7

0,00

8

0,00

1

0,00

1

0,00

4

0,00

5

0,00

5

0,00

5

TABLE III. PI, RI, QI AND UI VALUES FOR THE PIPES OF THE MPBR.

Material Pi Ri Qi Ui Rank

1 0,027 0,089 0,122 36,287 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

TABLE IV. NORMALIZED MATRIX MADE OF GRAY NUMBERS FOR THE VESSEL OF THE MPBR.

Material ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 0,00

7

0,01

0

0,00

8

0,01

0

0,01

7

0,02

2

0,00

1

0,00

1

0,01

7

0,02

1

0,00

1

0,00

1

0,00

0

0,00

1

0,00

2

0,00

2 2 0,00

5

0,00

9

0,01

1

0,01

2

0,01

2

0,01

4

0,00

2

0,00

2

0,01

6

0,01

9

0,00

1

0,00

1

0,00

0

0,00

0

0,00

4

0,00

4 3 0,00

6

0,01

1

0,01

1

0,01

2

0,01

3

0,01

7

0,00

3

0,00

3

0,01

5

0,02

0

0,00

1

0,00

1

0,00

0

0,00

0

0,00

4

0,00

4 4 0,00

8

0,01

2

0,00

8

0,00

9

0,01

9

0,02

3

0,00

1

0,00

1

0,01

7

0,02

1

0,00

1

0,00

1

0,00

0

0,00

1

0,00

4

0,00

5 5 0,04

9

0,39

3

0,00

0

0,00

1

0,01

7

0,02

0

0,00

1

0,00

1

0,01

6

0,01

9

0,00

0

0,00

0

0,00

0

0,00

0

0,00

7

0,00

7 6 0,04

9

0,39

3

0,00

0

0,00

1

0,01

4

0,01

8

0,00

1

0,00

1

0,01

5

0,01

8

0,00

0

0,00

0

0,00

0

0,00

0

0,00

6

0,00

6 7 0,00

1

0,00

5

0,00

1

0,00

4

0,01

5

0,01

6

0,00

3

0,00

4

0,01

6

0,01

8

0,00

1

0,00

1

0,00

0

0,00

0

0,00

3

0,00

4 8 0,00

2

0,00

5

0,00

4

0,00

9

0,01

3

0,01

6

0,00

3

0,00

4

0,01

7

0,01

8

0,00

1

0,00

1

0,00

0

0,00

0

0,00

3

0,00

4




TABLE V. PI, RI, QI AND UI VALUES FOR THE VESSEL OF THE MPBR.

Material Pi Ri Qi Ui Rank

1 0,024 0,037 0,160 60,604 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 7-8-

1-2-4-3-6-5, 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.

TABLE VI. COMPUTATION DETAILS FOR OCRA METHOD FOR THE PIPES OF THE MPBR.

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




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

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 7-8-4-2-

1-3-5-6. 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.

TABLE VIII. WEIGHTED NORMALIZED DECISION MATRIX FOR ARAS METHOD FOR THE PIPES OF THE MPBR.

Material ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

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

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

TABLE X. WEIGHTED NORMALIZED DECISION MATRIX FOR ARAS METHOD FOR THE VESSEL OF A MPBR.

Material ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 0,052 0,001 0,014 0,003 0,017 0,003 0,010 0,004

2 0,061 0,001 0,021 0,002 0,018 0,002 0,006 0,004

3 0,051 0,001 0,018 0,002 0,018 0,002 0,004 0,004

4 0,043 0,001 0,013 0,029 0,017 0,004 0,010 0,004

5 0,002 0,020 0,015 0,015 0,017 0,001 0,015 0,003

6 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




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

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

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.

TABLE XII. W

EIGHTED AND NORMALIZED DECISION MATRIX, OF TOPSIS METHOD FOR THE PIPES OF THE MPBR.

Mate

rial ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 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. T

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




TABLE XIV. C

OMPUTATION DETAILS FOR TOPSIS METHOD FOR THE PIPES OF THE MPBR.

Material

Rank

1 0,040 0,399 0,909 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. W

EIGHTED AND NORMALIZED DECISION MATRIX, OF TOPSIS METHOD FOR THE VESSEL OF MPBR.

Materia

l ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 0,02

6 0,411 0,40

9 0,501 0,225 0,374 0,176 0,339

2 0,02

3 0,535 0,26

6 0,522 0,399 0,344 0,269 0,318

3 0,02

7 0,535 0,31

2 0,516 0,322 0,351 0,462 0,319

4 0,03

2 0,405 0,44

2 0,044 0,167 0,374 0,175 0,312

5 0,70

6 0,025 0,38

3 0,087 0,468 0,359 0,118 0,509

6 0,70

6 0,025 0,33

0 0,082 0,467 0,329 0,130 0,453

7 0,00

9 0,120 0,34

7 0,293 0,316 0,344 0,552 0,245

8 0,01

1 0,281 0,30

7 0,329 0,347 0,351 0,563 0,245

TABLE XVI. T

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. C

OMPUTATION DETAILS FOR TOPSIS METHOD FOR THE VESSEL OF THE MPBR.

Material

Rank

1 0,330 0,039 0,895 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

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 COPRAS-

G, ARAS and TOPIS methods, the Spearman‟s

correlation coefficients exceeds 0,7.




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

OCRA ARAS TOPSIS

COPRA

S

0,571 0,702 0,810

OCRA - 0,893 0,810

ARAS - - 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.

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.

Figure 2. Rank materilas vs. alternative materials for the pipes of the MPBR




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

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

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[2] Krishna, R., & Sie, S. T. 2000. Design and scale-up of the

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[3] Dry, M. E. 1996. Practical and theoretical aspects of the

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Material Selection using Multi-criteria decision making · PDF file · 2017-02-07Four main types of commercial FT reactors are ... the fluidized-bed reactor, the multi-tubular packed-bed