Feasibility study of oil mining – a fuzzy AHP decision making approach

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Tom 24 2008 Zeszyt 4/2

A. SHAHINKAR*, K. SHAHRIAR**, A. ASADI***, A.D. AKBARI*

Feasibility study of oil mining – a fuzzy AHP decision making approach

Introduction

Increasing the oil price day by day makes trying to enhance the recovery of remained heavy oil at oilfields more attractive economically (Shahinkar et al. 2008). By using the primary production only about 19% of total oil can be recovered averagely, also after performing the secondary and tertiary methods including water flooding and gas injection, CO₂ and steam injection or polymer flooding only about 35–38% of total oil can be recovered. This means that about 65% of oil can not be recovered even after applying the mentioned methods. The oil mining method has potential to recover up to 90% of total oil (Bieniawski et al. 2007). By the reduction of light oil resources around the world and new sources exploration, and on the other hand by attention to increasing the oil price day by day and spending thousand of dollars only for slight percentage escalation in recovery factor, direct the eyes to oil mining. Due to limitation of paper length, the detailed concept of the three above methods is available in Ref 4.

Before selecting a method for recovering the remained oil, series of studies must be carried out in order to identify the advantages and disadvantages that the method offers, taking into consideration the physical and geologic characteristics of the deposit, ground conditions of the hanging wall, footwall, and ore zone, Mining and capital costs, mining rate, availability and cost of labor, environmental regulations (McCarter et al. 1992) among many

* Mining engineering department, Azad university, Science & Research Branch, Tehran, Iran.

** Mining, Metallurgical and petroleum engineering department, Amirkabir university of Technology, Tehran, Iran.

*** Mining engineering department, Azad university, Tehran South Branch, Tehran, Iran.

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other factors can be recognized. These factors are both qualitative and quantitative. For some of these attributes, we give exact assessments, while for others, we cannot. Since human judgments and preferences are often vague and complex and decision makers can not estimate their preferences with an exact scale, we can only give linguistic assessments instead of exact assessments. So fuzzy set theory introduced into Analytical hierarchy process (AHP), Fuzzy AHP is put forward to solve such uncertainty problems (Chan et al.

2007). In this paper, triangular fuzzy numbers are used to determine weights of attributes and alternatives considered in selecting method for recovering the remained oil.

In these situations, multi-attribute decision making (MADM) methods are most effective tools for making the best decision. In the hierarchical multiple attribute decision-making approaches, AHP is the well-known technique (Chan et al. 2007). This paper discussed the fuzzy integrated hierarchical decision-making approach in selection the most appropriate method to recover the remnant oil at oilfields. This approach is the combination of the hierarchical and fuzzy decision-making techniques. The process of selection waste dump site divided into two parts in this paper. The first part is based on the hierarchical representation of the problem and the fuzzy transformation of the preferences, whereas the second part includes the determination of the priority weights of the criteria, sub criteria and alternatives on the basis of the fuzzy synthetic extent values of the pair wise comparison. Finally a sensitivity analysis of the criteria and sub criteria is done to observe the effect on the most appropriate method selection with changes in the status of the individual factors.

1. Fuzzy numbers

The fuzzy set theory, introduced by Zadeh (1965), deal with vague, imprecise and uncertain problems. A fuzzy set is characterized by a membership function, which assigns to each object a grade of membership ranging between 0 and 1. In this paper, Triangular Fuzzy Numbers (TFNs) imply to illustrate the linguistic preferences of criteria and sub criteria. TFN is a special kind of fussy sets, can be denoted as N = (a, b, c). Figure 1 shows the membership function of a TFN.

The membership function of TFNs is:

u x

x a

b a a x b

c x

c b b x c

( )

,

, ,

= -

- £ £

-

- £ £

ì

í ïï ï

î ïï ï

if

if else 0

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Particularly, when a = b = c, trapezoidal fuzzy numbers become crisp numbers. So crisp numbers can be considered as a special case of fuzzy numbers (Liu et al. 2005).

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2. The hierarchy of feasibility study

The hierarchy of feasibility study, as illustrated in Figure 2, can be divided into four levels: level 1 includes the primary objective of the hierarchy, which is selection the most appropriate method for oil recovery; level 2 includes the criteria or the main factors affecting the decision, in the case of feasibility of using oil mining versus other regular method such as Secondary and Tertiary techniques, the main criteria are physical & geological charac- teristics of the deposit, Ground conditions, operating and capital costs, Mining rate, avai- lability and cost of labor, environmental regulations. And sub criteria are Ore thickness (OT), Plunge (PE), Depth (DH), Grade distribution (GD), Rock substance shear strength (RS), Natural fracture and fault shear strength (NF), Orientation and location of major geologic structures (OL), Orientation, length, and spacing of joints (OS), In situ stress (IS), Hydrologic conditions (HC), Operating and Capital costs (OC), Mining rate (MR), Avai- lability and cost of labor (AC), Environmental regulations (ER) respectively. The main and sub criteria and alternatives as well as relation between them have been illustrated in the Figure 2. Some sub criteria such as plunge and grade distribution, are same for alternatives and neutral in comparison so accordingly will omit in the pair wise comparison. Level 3 includes the sub criteria and the bottom level of the hierarchy, level 4, is the decision alternatives. Three potential methods were suggested for recovering the remnant oil at oil fields. Linguistic rating variables implemented to evaluate the rating of the alternatives with respect to each criterion. In the traditional formulation of hierarchy, human judgements are represented as exact (or crisp) numbers. However, in many practical cases the human preferences model is uncertain and decision makers might be reluctant or unable to assign exact numerical values to the comparison judgments. It is more desirable for decision maker

Fig. 1. Triangular fuzzy number Rys. 1. Trójk¹tna liczba rozmyta

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to use interval or fuzzy evaluations to handle the vagueness of the data involved in the multi-criterion decision making problems (Chan et al. 2007).

Table 2 shows the triangular fuzzy scale for the linguistic preferences. Based on these preferences, the comparison matrices of criteria, sub-criteria and decision alternatives are developed.

Fig. 2. The hierarchy of feasibility study Rys. 2. Hierarchia studium wykonalnoœci

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TABLE 1 Triangular fuzzy preference measurement scale (Chan et al. 2007)

TABELA 1 Skala pomiaru trójk¹tnych preferencji rozmytych (Chan i in. 2007)

Preferences Triangular fuzzy scale Reciprocal scale

Equal (1,1,1) (1,1,1)

Moderate (2/3,1,3/2) (2/3,1,3/2)

Strange (3/2,2,5/2) (2/5,1/2,2/3)

Very strange (5/2,3,7/2) (2/7,1/3,2/5)

Extremely preferred (7/2,4,9/2) (2/9,1/4,2/7)

By carrying out a dual comparison on the sub criteria based on expert’s opinions, the priority weights of the sub criteria, on the basis of the fuzzy synthetic extent values of the pair wise comparison weighting discipline in Tables 2 to 13 have been presented.

TABLE 2 Comparison matrix for ore thickness (Shahinkar et al. 2008)

TABELA 2 Macierz porównania mi¹¿szoœci rud (Shahinkar i in. 2008)

Alternatives Oil Mining Secondary techniques Tertiary techniques

Oil Mining (1,1,1) (3/2,2,5/2) (3/2,2,5/2)

Secondary techniques (2/5,1/2,2/3) (1,1,1) (1,1,1)

Tertiary techniques (2/5,1/2,2/3) (1,1,1) (1,1,1)

TABLE 3 Comparison matrix for depth (Shahinkar et al. 2008)

TABELA 3 Macierz porównania g³êbokoœci (Shahinkar i in. 2008)

Oil Mining (1,1,1) (5/2,3,7/2) (7/2,4,9/2)

Secondary techniques (2/7,1/3,2/5) (1,1,1) (2/3,1,3/2)

Tertiary techniques (2/9,1/4,2/7) (2/3,1,3/2) (1,1,1)

TABLE 4 Comparison matrix for Rock substance shear strength (Shahinkar et al. 2008)

TABELA 4 Macierz porównania wytrzyma³oœci ska³ na œcinanie (Shahinkar i in. 2008)

Oil Mining (1,1,1) (3/2,2,5/2) (3/2,2,5/2)

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TABLE 5 Comparison matrix for Natural fracture and fault shear strength (Shahinkar et al. 2008)

TABELA 5 Macierz porównania prze³omu naturalnego i wytrzyma³oœci uskoku na œcinanie (Shahinkar i in. 2008)

Oil Mining (1,1,1) (5/2,3,7/2) (5/2,3,7/2)

TABLE 6 Comparison matrix for Orientation and location of major geologic structures (Shahinkar et al. 2008)

TABELA 6 Macierz wytrzyma³oœci dla orientacji i lokalizacji g³ównych struktur geologicznych (Shahinkar i in. 2008)

Oil Mining (1,1,1) (3/2,2,5/2) (3/2,2,5/2)

TABLE 7 Comparison matrix for Orientation, length, and spacing of joints (Shahinkar et al. 2008)

TABELA 7 Macierz porównania dla orientacji, d³ugoœci i rozstawu spoin (Shahinkar i in. 2008)

Oil Mining (1,1,1) (2/3,1,3/2) (2/3,1,3/2)

Secondary techniques (2/3,1,3/2) (1,1,1) (1,1,1)

Tertiary techniques (2/3,1,3/2) (1,1,1) (1,1,1)

TABLE 8 Comparison matrix for in situ stress (Shahinkar et al. 2008)

TABELA 8 Macierz porównania dla naprê¿eñ in situ (Shahinkar i in. 2008)

Oil Mining (1,1,1) (3/2,2,5/2) (3/2,2,5/2)

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TABLE 9 Comparison matrix for Hydrologic conditions (Shahinkar et al. 2008)

TABELA 9 Macierz porównania dla warunków hydrologicznych (Shahinkar i in. 2008)

Oil Mining (1,1,1) (2/5,1/2,2/3) (2/5,1/2,2/3)

Secondary techniques (3/2,2,5/2) (1,1,1) (2/3,1,3/2)

Tertiary techniques (3/2,2,5/2) (2/3,1,3/2) (1,1,1)

TABLE 10 Comparison matrix for operating and capital costs (Shahinkar et al. 2008)

TABELA 10 Macierz porównania dla kosztów operacyjnych i kapita³owych (Shahinkar i in. 2008)

Oil Mining (1,1,1) (2/5,1/2,2/3) (2/3,1,3/2)

Secondary techniques (3/2,2,5/2) (1,1,1) (2/3,1,3/2)

Tertiary techniques (2/3,1,3/2) (2/3,1,3/2) (1,1,1)

TABLE 11 Comparison matrix for Mining rate (Shahinkar et al. 2008)

TABELA 11 Macierz porównania dla szybkoœci wybierania (Shahinkar i in. 2008)

Oil Mining (1,1,1) (3/2,2,5/2) (5/2,3,7/2)

TABLE 12 Comparison matrix for Availability and cost of labor (Shahinkar et al. 2008)

TABELA 12 Macierz porównania dla dostêpnoœci i kosztu si³y roboczej (Shahinkar i in. 2008)

Oil Mining (1,1,1) (3/2,2,5/2) (3/2,2,5/2)

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TABLE 13 Comparison matrix for Environmental regulations (Shahinkar et al. 2008)

TABELA 13 Macierz porównania dla przepisów dotycz¹cych ochrony œrodowiska (Shahinkar i in. 2008)

Oil Mining (1,1,1) (2/3,1,3/2) (2/3,1,3/2)

Secondary techniques (2/3,1,3/2) (1,1,1) (1,1,1)

Tertiary techniques (2/3,1,3/2) (1,1,1) (1,1,1)

3. Method selection

After development the hierarchy of feasibility study and converting the linguistic preferences into TFNs, weight vectors for different decision variables should be computed.

Table 14 represents fuzzy comparison matrix of main criteria with respect to the final objective (FO), which is selection the most appropriate method for oil recovery. Since plunge and grade distribution are same for all suggested alternatives, they are omitted from pair wise comparison.

The fuzzy comparison matrix in Table 14 is constructed by the pair-wise comparison of the different criteria relevant to the overall objective. The fuzzy synthetic extent value with respect to each criterion is calculated applying the following equation (Chan et al. 2007):

F_i N_oi^j N_oi^j

j m

i n

j

= m Äé

ë êê

ù û úú

=

-

å å å

1 1 1

1

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The first part of equation 2 can be found using equation 3

N_oi^j n n n

j m

j j j

j m

= = = =

å

⁼^æ

å å å

è çç

ö ø

÷÷

1

1 2 3

1 1 1

, , (3)

The second part can be obtained by performing the fuzzy additional operation of N_oi^j (j = 1, 2, …, m) such that:

N_oi^j n n n

j m

j j j

i n

= = = =

=

å å å å

å

⁼^æ

è çç

ö ø

÷÷

1

1 2 3

1 1 1 1

, , (4)

The second part of equation 2 can be calculated by the inverse of equation 4 as follow:

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N

n n n

oi j j

m

i n

i i

n

i i

n

i i

=

-

= =

å

å å å

é ë êê

ù û úú =

1 1

1

3 1

2 1

1

1 1 1

, ,

å

=

æ

è çç çç ç

ö

ø

÷÷

1 ÷

n (5)

In all above equations N_oi^j (j = 1, 2, …, m) are TFNs.

Applying the TFNs in Table 14 and using equations 2 through 5, the different values of fuzzy synthetic extent of the 12 different criteria (Fi (i = 1, … 12)) calculated (Shahinkar et al. 2008).

F1 = (5.5, 7, 9.27) Ä (141.82, 179.66, 232.41)^–1= (0.024, 0.039, 0.065);

F2 = (21.17, 26, 31.5) Ä (141.82, 179.66, 232.41)^–1= (0.091, 0.145, 0.222);

F3 = (5.5, 7, 9.27) Ä (141.82, 179.66, 232.41)^–1= (0.024, 0.039, 0.065);

F4= (6.8, 9.17, 12.8)Ä (141.82, 179.66, 232.41)^–1= (0.029, 0.051, 0.090);

F5 = (8.8, 11.8, 15.9) Ä (141.82, 179.66, 232.41)^–1= (0.038, 0.066, 0. 112);

F6 = (12.6, 16.5, 21.7) Ä (141.82, 179.66, 232.41)^–1= (0.054, 0.092, 0.153);

F7 = (11.6, 15.3, 20.4) Ä (141.82, 179.66, 232.41)^–1= (0.050, 0.085, 0.144);

F8 = (13.4, 17.5, 22.7) Ä (141.82, 179.66, 232.41)^–1= (0.058, 0.097, 0.160);

F9 = (24.8, 30, 35.5) Ä (141.82, 179.66, 232.41)^–1= (0.107, 0.167, 0.250);

F10 = (7.6, 10.7, 15.3) Ä (141.82, 179.66, 232.41)^–1= (0.033, 0.060, 0.108);

F11 = (12.2, 16.5, 21.7) Ä (141.82, 179.66, 232.41)^–1= (0.052, 0.092, 0.153);

F12 = (8.9, 12.2, 16.5) Ä (141.82, 179.66, 232.41)^–1= (0.038, 0.068, 0.116).

If F₁and F₂are two TFNs represented by (f₁₁, f₁₂, f₁₃) and (f₂₁, f₂₂, f₂₃) respectively, then corresponding values of (f₁₁, f₂₁), (f₁₂, f₂₂) and (f₁₃, f₂₃) denote the smallest possible, most promising and larger possible values of F₁ and F₂ respectively.

Since F₁ and F₂ are convex fuzzy numbers, for the comparison of F₁ and F₂, both V (F₁³ F2) and V (F₂³ F1) are required:

V F( ₁³F₂)=1 if f₁₁³ f₂₁ (6)

V F F f f

f f f f

( )

( ) ( )

2 1 11 23

22 23 12 11

³ = -

- - -

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Whenever the nominator becomes positive, i.e. (f₁₁– f₂₃) > 0, in calculation of the fuzzy synthetic extent value, the elements of the matrix should be normalized and the same process should be repeated again.

The degree of possibility of superiority of Fi over Fj (i ¹ j) can be calculated employing equations 6 and 7.

The degree of possibility of the superiority of each fuzzy synthetic extended value in comparison with one another is represented in Table 15.

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TABLE14 Fuzzycomparisonmatrixofmaincriteriaoffeasibilitystudy(Shahinkaretal.2008) TABELA14 Rozmytamacierzporównaniag³ównychkryteriówstudiumwykonalnoœci(Shahinkariin.2008) FOOTDHRSNFOLOSISHCOCMRACER OT(1,1,1)(2/9,1/4,2/7)(2/3,1,3/2)(2/3,1,3/2)(2/5,1/2,2/3)(2/7,1/3,2/5)(2/7,1/3,2/5)(2/7,1/3,2/5)(2/9,1/4,2/7)(2/3,1,3/2)(2/5,1/2,2/3)(2/5,1/2,2/3) DH(7/2,4,9/2)(1,1,1)(7/2,4,9/2)(5/2,3,7/2)(3/2,2,5/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(5/2,3,7/2)(3/2,2,5/2)(5/2,3,7/2) RS(2/3,1,3/2)(2/9,1/4,2/7)(1,1,1)(2/3,1,3/2)(2/5,1/2,2/3)(2/7,1/3,2/5)(2/7,1/3,2/5)(2/7,1/3,2/5)(2/9,1/4,2/7)(2/3,1,3/2)(2/5,1/2,2/3)(2/5,1/2,2/3) NF(2/3,1,3/2)(2/7,1/3,2/5)(2/3,1,3/2)(1,1,1)(2/3,1,3/2)(2/5,1/2,2/3)(2/3,1,3/2)(2/5,1/2,2/3)(2/7,1/3,2/5)(2/3,1,3/2)(2/5,1/2,2/3)(2/3,1,3/2) OL(3/2,2,5/2)(2/5,1/2,2/3)(3/2,2,5/2)(2/3,1,3/2)(1,1,1)(2/3,1,3/2)(2/3,1,3/2)(2/5,1/2,2/3)(2/7,1/3,2/5)(2/3,1,3/2)(2/5,1/2,2/3)(2/3,1,3/2) OS(5/2,3,7/2)(2/3,1,3/2)(5/2,3,7/2)(3/2,2,5/2)(2/3,1,3/2)(1,1,1)(2/3,1,3/2)(2/3,1,3/2)(2/5,1/2,2/3)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2) IS(5/2,3,7/2)(2/3,1,3/2)(5/2,3,7/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(1,1,1)(2/3,1,3/2)(2/7,1/3,2/5)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2) HC(5/2,3,7/2)(2/3,1,3/2)(5/2,3,7/2)(3/2,2,5/2)(3/2,2,5/2)(2/3,1,3/2)(2/3,1,3/2)(1,1,1)(2/5,1/2,2/3)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2) OC(7/2,4,9/2)(2/3,1,3/2)(7/2,4,9/2)(5/2,3,7/2)(5/2,3,7/2)(3/2,2,5/2)(5/2,3,7/2)(3/2,2,5/2)(1,1,1)(5/2,3,7/2)(2/3,1,3/2)(5/2,3,7/2) MR(2/3,1,3/2)(2/7,1/3,2/5)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/7,1/3,2/5)(1,1,1)(2/3,1,3/2)(2/3,1,3/2) AC(3/2,2,5/2)(2/5,1/2,2/3)(3/2,2,5/2)(3/2,2,5/2)(3/2,2,5/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(1,1,1)(3/2,2,5/2) ER(3/2,2,5/2)(2/7,1/3,2/5)(3/2,2,5/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/3,1,3/2)(2/7,1/3,2/5)(2/3,1,3/2)(2/5,1/2,2/3)(1,1,1)

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The degree of possibility of a convex fuzzy number being greater than k convex fuzzy numbers Ni (i = 1, 2,…, k) can be defined as (Wang et al. 2008):

V(N³ N1,N₂,...,N_k) = V(N³ N1) and V(N³ N2) and ... and V(N³ Nk) = min V(N³ Ni) i = 1,2,…, K

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If m(P_i) = min V(F_i³ Fk) for k = 1, 2, …, n; k¹ i, then the weight vector is given by:

W_P= (m(P₁), m(P₂), …, m(P_n))^T (9)

Where P_i(i = 1, 2, …, n) are n elements. After normalizing W_P, the normalized weight vector will be obtained:

W_P= (W(P₁), W(P₂), …, W(P_n))^T (10)

TABLE 15 Degree of the superiority of each criterion in feasibility study (Shahinkar et al. 2008)

TABELA 15 Stopieñ nadrzêdnoœci ka¿dego kryterium w studium wykonalnoœci (Shahinkar i in. 2008)

Criterion OT DH RS NF OL OS IS HC OC MR AC ER

V F( _i³F_j) F₁ F₂ F₃ F₄ F₅ F₆ F₇ F₈ F₉ F₁₀ F₁₁ F₁₂ V F( ₁³F_j) - 0.325 1 0.750 0.500 0.172 0.246 0.108 0.488 0.604 0.197 0.482

V F( ₂³F_j) 1 - 1 1 1 1 1 1 0.840 1 1 1

V F( ₃³F_j) 1 0.312 - 0.750 0.500 0.172 0.246 0.108 0.488 0.603 0.197 0.482 V F( ₄³F_j) 1 0.011 1 - 0.776 0.467 0.540 0.410 0.172 0.864 0.481 0.754

V F( ₅³F_j) 1 0.210 1 1 - 0.690 0.765 0.635 0.047 1 0.697 1

V F( ₆³F_j) 1 0.539 1 1 1 - 1 0.950 0.380 1 1 1

V F( ₇³F_j) 1 0.469 1 1 1 0.928 - 0.877 0.310 1 0.929 1

V F( ₈³F_j) 1 0.590 1 1 1 1 1 - 0.430 1 1 1

V F( ₉³F_j) 1 1 1 1 1 1 1 1 - 1 1 1

V F( ₁₀³F_j) 1 0.167 1 1 0.921 0.628 0.699 0.574 0.009 - 0.636 0.897

V F( ₁₁³F_j) 1 0.539 1 1 1 1 1 0.950 0.380 1 - 1

V F( ₁₂³F_j) 1 0.245 1 1 1 0.720 0.795 0.667 0.084 1 0.727 -

Where W is a non-fuzzy number and gives the priority weights of one criterion over another. With the help of equation 9, it is possible to obtain the weight vector, which is given as:

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W_C= (0.108, 0.84, 0.108, 0.011, 0.047, 0.38, 0.31, 0.43, 1, 0.009, 0.38, 0.084)^T The normalized value of this vector decides the priority weights of each criterion over another. The normalized weight vector is calculated as:

W_O= (0.029, 0.227, 0.029, 0.003, 0.013, 0.103, 0.084, 0.116, 0.270, 0.002, 0.103, 0.023) All suggested methods for oil recovery are analyzed under the board heading of the twelve main criteria. In this study, the preferences of the three potential methods are decided based on the triangular fuzzy preference measurement scale (Tab. 1). The fuzzy evaluation matrices of the three preferred methods with respect to criteria are computed. The corresponding weights are noted down in Table 16. The priority weights of the decision alternatives with respect to each criterion are also illustrated in Table 16. This is basically the summation of the combined weights of the criteria and decision alternatives.

TABLE 16 Summary combination of the overall priority weights (Shahinkar et al. 2008)

TABELA 16 Podsumowanie po³¹czenia ogólnego wag priorytetów (Shahinkar i in. 2008)

Weight Method

OT DH RS NF OL OS IS HC OC MR AC ER Priority

Weight (0.029) (0.227) (0.029) (0.003) (0.013) (0.103) (0.084) (0.116) (0.27) (0.002) (0.103) (0.023) Secondary

methods 0.45 0.38 0.55 0.55 0.45 0.75 0.45 0.95 0.8 0.55 0.65 0.3 0.639 Tertiary

methods 0.45 0.38 0.55 0.55 0.5 0.75 0.45 0.95 0.6 0.4 0.65 0.3 0.585 Oil mining 0.6 0.95 0.75 0.8 0.75 0.85 0.6 0.8 0.5 0.8 0.85 0.4 0.731

Based on the priority weights calculated in Table 16, the highest score of the decision alternatives gives an idea of the most appropriate method for oil recovery. The priority score of Oil Mining is the highest, so it is selected as the most preferred method. Secondary method is the second preferred and Tertiary method is the last.

4. Discussion

The results of fuzzy AHP integrated approach selects Oil Mining as the most appropriate method for oil recovery among others. Sensitivity analysis of three suggested methods, with respect to main criteria is carried out to illustrate the consequences of changes in the priority weights of the criteria over methods.

Figure 3 shows thatTertiary and Secondary Methods preferred well in terms of Hydro- logic conditions and Operating and Capital costs; whereas Oil Mining has better per- formance in terms of other criteria, specially in terms of Depth (shallow) and Mining Rate, regardless the higher Operating and Capital costs, So Oil Mining becomes the superior among the other alternatives.

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Conclusion

Today, by increasing oil price, improving the overall recovery factor from 35–38% to 90% will be a thaumaturge and may cause a mutation in internal and external diplomacies of the countries. But using oil mining is limited to shallow oilfields, on the other hand sensitivity analysis shows that against depth limitation and higher operating and capital costs, preference in other criteria, as well as the considerable cumulative operating and capital costs of secondary and tertiary methods versus the operating and capital costs of oil mining, make it more desirable option in feasibility study.

In this paper, a fuzzy integrated hierarchical decision making approach implemented to find the most appropriate method for oil recovery. During this feasibility study over 360 factors have been obtained and the results show that oil mining with the less constraint in Availability and cost of labor, Hydrologic conditions, in-situ stress, Orientation, length, and spacing of joints, Orientation and location of major geologic structures, Natural fracture and fault shear strength, Rock substance shear strength, Ore thickness, mining rate and En- vironmental regulations against limitation of depth and higher Operating and Capital costs is the superior method for oil recovery.

In comparison with the traditional AHP method, fuzzy-based approach seems more robust because of its ability to map the decision maker’s perceptions to fuzzy numbers instead of exact numbers. The fuzzy model discussed in this paper is simple and has less computational expenses compared with other multi-objective programming techniques. This method can also be easily implemented on more complex cases having a greater number of decision alternatives and criteria.

0 0.2 0.4 0.6 0.8 1 1.2 1.4

OT DH RS NF OL OS IS HC OC MR AC ER

Criteria

PriorityWeights

Secondary Methods Tertiary Methods Oil Mining

Fig. 3. Sensitivity analysis of the main criteria (Shahinkar et al. 2008) Rys. 3. Analiza wra¿liwoœci g³ównych kryteriów (Shahinkar i in. 2008)

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REFERENCES

[1] B i e n i a w s k i Z.T., 1987 – Strata control in mineral engineering. New York: Wiley.

[2] C h a n F.T., K u m a r N., C h o l y K.L., 2007 – Decision-making approach for the distribution center location problem in the supply chain network using fuzzy-based hierarchical concept. Engineering Manufacture vol. 221, Part B: J., pp. 725–739.

[3] M c C a r t e r M.K., 1992 – Open pit mining in SME mining engineering handbook. Ed: H.L. Hartman. PP 2051–2057, published by SME, Colorado, USA.

[4] S h a h i n k a r A., 2008 – Feasibility Study of oil mining. MSc thesis, University of Azad, Science & Research Branch, Iran, pp. 10–111.

[5] W a n g Ying-Ming, 2008 – On the extent analysis method for fuzzy AHP and its applications. European journal of Operational Research, 186, pp. 735–747.

[6] Z a d e h L.A., 1968 – Probability measures of fuzzy sets. Math, Anal., And Appl. Vol. 23, pp. 421–427.

STUDIUM WYKONALNOŒCI WYDOBYCIA ROPY NAFTOWEJ – PODEJŒCIE Z WYKORZYSTANIEM ROZMYTEGO AHP W PODEJMOWANIU DECYZJI

S ³ o w a k l u c z o w e

Wydobycie ropy naftowej, AHP, logika rozmyta, podejmowanie decyzji, studium wykonalnoœci

S t r e s z c z e n i e

Nies³ychany dot¹d wzrost cen ropy naftowej do 115 $/bbl, jak równie¿ stosowanie nowych technologii, przy równoczesnym zmniejszaniu siê œwiatowych zasobów ropy, uczyni³y odzyskiwanie ciê¿kich frakcji ropy bardzo atrakcyjnym ekonomicznie. Odzyskiwanie ciê¿kich frakcji ropy na polach naftowych po g³ównej produkcji (tryskanie ropy pod w³asnym ciœnieniem lub pompowanie) obejmuje dwa etapy: Produkcja wtórna, zawieraj¹ca technologie takie jak zawadnianie i wtrysk gazu przy wspó³czynniku wydobycia oko³o 15–33% i Produkcja Trzeciego Rzêdu, zawieraj¹ca technologie takie jak wtrysk CO₂i pary wodnej lub zalewanie polimerem przy wspó³czynniku wydobycia oko³o 35–38%. Oznacza to, ¿e oko³o 65% ropy naftowej nie mo¿na odzyskaæ nawet po zastosowaniu wymienionych technologii. Ropa górnicza jest czwartym rodzajem technologii odzyskiwania ropy, który mo¿e prowadziæ do produkcji do 90% ropy niewydobywalnej. Literatura zawiera ostatnie oceny sprzed dwudziestu lat, dlatego w niniejszym opracowaniu przeprowadzono wszechstronne studium wykonalnoœci za pomoc¹ nowego podejœcia Rozmytego AHP. Dokonano równie¿ analizy wra¿liwoœci kryteriów i subkryteriów dla zaobserwowania wp³ywu na metodê odzysku ostatecznego ze zmianami sytuacji poszczególnych czynników.

FEASIBILITY STUDY OF OIL MINING – A FUZZY AHP DECISION MAKING APPROACH

K e y w o r d s Oil mining, AHP, fuzzy logic, decision making, feasibility study

A b s t r a c t

Today, unheard increasing oil price up to 115 $/bbl as well as using new technologies, concurrent with decreasing the World’s light oil resources, made enhanced heavy oil recovery very economically attractive.

Recovering the remained heavy oil at oil fields after primary production (oil gushing under it’s own pressure or being pumped) involves two stages, called Secondary production including technologies such as water flooding and gas injection by enhanced recovery factor about 15–33% and Tertiary production including technologies such

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as CO₂and steam injection or polymer flooding by enhanced recovery factor about 35–38% respectively. This means that about 65% of oil can not be recovered even after applying the mentioned technologies. Mining oil is the fourth order of oil recovery technology which may result in the economic production of up to 90% of the oil remaining in the unrecoverable reservoirs. Last evaluations in the literatures returns in two decades, so in this paper a comprehensive feasibility study has done by using a new Fuzzy AHP approach. Finally a sensitivity analysis of the criteria and sub criteria is done to observe the effects on the final recovery method with changes in the status of the individual factors.

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