a fuzzy-based methodology for an aggregative environmental risk assessment: a case study of drilling...

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Environmental Modelling & Software 20 (2005) 33e46

A fuzzy-based methodology for an aggregative environmentalrisk assessment: a case study of drilling waste

Rehan Sadiqa,), Tahir Husainb

aInstitute for Research in Construction, National Research Council, Ottawa, ON, Canada K1A 0R6bFaculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, NL, Canada

Received 26 February 2003; received in revised form 30 October 2003; accepted 16 December 2003

Abstract

The objective of this study was to develop a methodology for estimating aggregative risk of various environmental activities,pollution sources and routes in a given process. The rate of risk is defined by a product of grade of risk (r, magnitude) and grade of

importance (i, intensity). Both factors r and i are expressed by an 11-level qualitative scale which are defined by triangular fuzzynumbers to capture the vagueness in the linguistic variables. A three-stage hierarchical structure aggregative risk model wasdeveloped for grouping of risk items. For this grouping an analytical hierarchy process was used. A sensitivity analysis was alsoperformed to verify the effect of weighting schemes on the assessment of a final aggregative risk. The developed methodology is

applied to a case study of offshore drilling waste for evaluating various discharge scenarios.Crown Copyright � 2004 Published by Elsevier Ltd. All rights reserved.

Keywords: Risk; Weighting schemes; Drilling waste discharge; Qualitative assessment; Analytical hierarchy process; Fuzzy-based methodology

1. Introduction

The major objective of this study was to develop andevaluate a hierarchical model of aggregative environ-mental risk for assessing various drilling waste dischargescenarios for disposal into the marine environment. Thisstudy uses a qualitative assessment technique by incor-porating fuzzy set theory.

Generally, risk is a traditional manner of expressinguncertainty in a system’s life-cycle. In quantitativeterms, it is the probability by which the predicted goalscannot be achieved with the available resources andrefers to the joint probabilities of an occurrence of anevent and its consequences. When a complex systeminvolves various contributory risk items with uncertainsources and magnitudes, it often can not be treated withmathematical rigor during the initial or screening phaseof decision-making (Lee, 1996).

) Corresponding author. Tel.: C1-613-993-6282; fax: C1-613-954-

5984.

E-mail address: [email protected] (R. Sadiq).

1364-8152/$ - see front matter Crown Copyright � 2004 Published by Els

doi:10.1016/j.envsoft.2003.12.007

In most engineering problems, information about theprobabilities of various risk items is vaguely known. Theterm computing with words has been introduced byZadeh (1996) to capture the notion of reasoning lin-guistically rather than with numerical quantities. Suchreasoning has central importance for many emergingtechnologies related to engineering and sciences. Thisapproach has proved very useful in medical diagnosis(Lascio et al., 2002), information technology (Lee,1996), reliability analysis (Sadiq et al., 2004) and inmany other applications (Lawry, 2001), where reporteddata are either qualitative or decision-making is per-formed based on expert opinions. Belief networks (BN)are an expressive graphical approach for representinguncertain knowledge (risk) about casual and occasionalrelationships among various factors in a complex system(Attoh-Okine, 2002). In BNs a system’s risk itemsare presented as mutually dependent objects for whichprior probabilities are used to calculate posteriorprobabilities.

In evaluating risk items, decision-makers, engineers,managers, regulators and other stake-holders generallyview risk in terms of linguistic variables like very high,

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34 R. Sadiq, T. Husain / Environmental Modelling & Software 20 (2005) 33e46

Nomenclature

AX

A reciprocal square matrix used in an AHP for estimating the weightsm Membership function for fuzzy numberslmax Principal eigen valueamn or anm Elements of reciprocal matrix A

X

F(Xkj) Fuzzy assessment matrix of each item at attribute level-Ig (r, i) Rate of risk at a given grade of risk and importance (represents the centroid of fuzzy number

obtained by multiplication of two TFNs)i Grade of importance of environmental riski Risk itemj Attribute at level-Ik Attribute at level-IIl Number describing the ranking level of grade of importance or grade of riskLG(n) Centroid of qualitative scales Ln

Ln Linguistic variables (n ¼ 1e7)n Levels of linguistic variables representing various qualitative scalesn, m Representing the location (rows and columns) of an element a in the reciprocal matrix A

X

Ni TFN for grade of importanceNr TFN for grade of environmental riskr Grade of environmental riskS1(k, j, n) First stage aggregative environmental risk matrix at a given k, j; and n ¼ 1e7S2(k, n) Second stage aggregative environmental risk matrix at a given k; and n ¼ 1e7S3(n) Third stage aggregative environmental risk matrix; n ¼ 1e7W Weight matrixW1(k, j, i) Weights estimated from an AHP for risk itemsW2(k, j ) Weights estimated from an AHP for attributes at level-IW3(k) Weights estimated from an AHP for attributes at level-IIwn Elements of weight ( priority) matrix estimated through AHPx A variable representing rate of environmental riskXk Aggregative environmental risk at attribute level-IIXk j Aggregative environmental risk at attribute level-IXk ji Aggregative environmental risk for a risk itemz Power of a matrix

high, very low, low etc. Fuzzy set theory deals effectivelywith this type of uncertainty (vagueness) and linguis-tic variables can be used for approximate reasoning.Generally, triangular (TFN) or trapezoidal (ZFN) fuzzynumbers are used for representing linguistic variables(Lee, 1996).

In this paper, the term risk is defined by two distinctfactorsdgrade and importancedwhich are synonymousto joint probabilities of occurrence and consequences,where each factor is designated by TFN. A defuzzifica-tion is performed using the centroid method (Yager,1980) to determine the risk at a given grade andimportance of a risk item. A general structure modelof aggregative risk is then developed and an analyticalhierarchy process (AHP) is used to determine thepriority matrix (weights) for various risk items andattributes. Finally, aggregative risk is evaluated usinga three-stage assessment methodology. The developed

methodology is applied to a case study of drilling waste.In the end, some conclusions are drawn and recom-mendations are made for future research.

2. Qualitative evaluation of risk

Risk items can be divided into various qualitative orlinguistic classes. This qualitative classification systemmay induce imprecision and bias into the decision-making process, but provides useful insight into theprocess especially where quantitative information islimited or variables involve subjectivity. The qualitativeclassification describing the grade (or magnitude) of riskalone is not enough to explain risk items, however, asthe importance (intensity) of risk items is also a keyelement in determining the rate of aggregative risk ina system’s life-cycle.

35R. Sadiq, T. Husain / Environmental Modelling & Software 20 (2005) 33e46

Table 1

Linguistic classification of grades and importance of risks and their corresponding TFNs (modified after Lee, 1996)

Ranking level (l ) A qualitative explanation

for grade of risk (r)

A qualitative explanation

for importance of risk (i)

Triangular fuzzy

numbers (TFN)

1 Absolutely low Absolutely unimportant (0.0, 0.0, 0.1)

2 Extremely low Extremely unimportant (0.0, 0.1, 0.2)

3 Quite low Quite unimportant (0.1, 0.2, 0.3)

4 Low Unimportant (0.2, 0.3, 0.4)

5 Mildly low Mildly unimportant (0.3, 0.4, 0.5)

6 Ok Ok (0.4, 0.5, 0.6)

7 Mildly high Mildly important (0.5, 0.6, 0.7)

8 High Important (0.6, 0.7, 0.8)

9 Quite high Quite important (0.7, 0.8, 0.9)

10 Extremely high Extremely important (0.8, 0.9, 1.0)

11 Absolutely high Absolutely important (0.9, 1.0, 1.0)

Lee (1996) has suggested an 11-level ranking systemby which grade and importance of risk factors can beclassified. Table 1 describes this qualitative scalingsystem for grade and importance of risk items. Eachqualitative scale N ¼ 1; 2;.11 ( for both grade andimportance of risk) describing the vagueness andfuzziness in the linguistic connotation is expressed byTFNs. These definitions can be changed or modifiedbased on expert panel recommendations or conductingsurveys based on the Delphi method. The membershipfunctions of triangular fuzzy numbers for the 11-levelqualitative scales are as follows:

mN1ðxÞ¼1� 10x; 0%x! 0:1;

0; 0:1%x%1;

(

mNlðxÞ ¼

0; 0%x!l� 2

10;

10x� ðl� 2Þ; l� 2

10%x!

l� 1

10;

l� 10x;l� 1

10%x%

l

10;

0;l

10%x%1;

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð1Þ

ðl ¼ 2; 3;.10Þ and

mN11ðxÞ¼0; 0%x! 0:9;

10x� 9; 0:9%x%1:

(

considering two fuzzy numbers Nr and Ni, representinggrade and importance of risk with membership values ofmNr and mNi, respectively. To determine the risk ofa given magnitude and intensity, these two factors canbe multiplied to yield:

Risk ¼ Grade of risk!Importance of risk ð2Þ

Fuzzy mathematics is then used to determine theproduct of grade and importance values (Klir and

Yuan, 1995). The product of two TFNs is also a fuzzynumber, which is not necessarily a triangle. There arevarious techniques for defuzzification, but those mostcommonly used are the Chen (1985) ranking and theYager (1980) centroidal methods. In this paper, Yager’scentroidal method (1980) is used for defuzzification forsimplicity, which can be defined by

gðr; iÞ ¼

Z b

a

x mNr5NiðxÞ dxZ b

a

mNr5NiðxÞ dx

ð3Þ

where a and b are the lower and upper limits of theintegral, respectively. The risk contours representing thecentroid (of fuzzy numbers) for risk items are shown inFig. 1. It can be noticed that g (r, i) values are increasingfrom left to right and bottom to top with an increase ineither grade or importance of the risk either individu-ally, or simultaneously.

Fig. 1. Risk contours representing the rate of environmental risk g (r, i)

for each risk item.


3. Rate of aggregative risk

The proposed methodology follows a step-by-stepprocedure, which involves fuzzy concepts and hierar-chical analysis to determine the rate of aggregative orcumulative environmental risk at different levels. Toshow this methodology, a drilling waste example fordischarge in the marine environment is used, whichinvolves ecological and human health risks related tovarious activities and exposure routes.

3.1. Hierarchical structure

Disposal of rock cuttings and used mud con-stitutes one of the most significant waste dischargesassociated with offshore drilling. The drilling fluids, orcirculating muds, are broadly classified into threegroups: Water-based drilling fluid (WBF), oil-baseddrilling fluid (OBF) and synthetic-based drilling fluid(SBF) (US EPA, 2000a). The SBFs consist of a syn-thetic base fluid, a weighting agent (barite) and someother additives. Since 1990, the oil and gas extractionindustry has developed many synthetic and non-synthetic materials as base fluids to provide drillingperformance characteristics comparable to traditionalOBFs with the lower environmental impacts andgreater worker safety of WBFs. These characteristicshave been achieved through the lowering of SBFtoxicity, elimination of polynuclear aromatic hydro-carbons (PAHs), faster biodegradation rates and lowerbioaccumulation potential of pollutants (US EPA,2000a).

SBFs are hydrophobic in nature and tend to sink tothe bottom of a water column with little dispersion.Therefore, the main research focus of oil industry andregulators has been on determining the toxicity of SBFsin sediment as opposed to the aqueous phase. Manystudies including those by Candler and Leuterman(1997) and Rabke and Candler (1998) have reportedthe toxicity response of SBFs for different organisms. Inaddition to the toxicity of the base fluid, the drillingwaste contains organic priority pollutants and heavymetals which can adversely affect the ecology of thedrilling area (US EPA, 2000a).

Another aspect of environmental risk assessment ofdrilling waste is human exposure through consumptionof contaminated fish. Marine organisms are exposed topollutants through direct uptake and consumption oflower trophic level organisms. Bioaccumulation ofchemicals in aquatic food chains, which is the combinedeffect of the above two processes, is an important phe-nomenon in aquatic organisms and affects their pre-dators, especially humans and fish-eating wildlife. Theconsumption of contaminated organisms may pose a riskto human health.

Some additional environmental issues related tooffshore drilling waste discharges include: non-waterquality environmental impacts ( greenhouse gases andother air pollution problems); drilling fluid exposure toworkers during handling and treatment and the asso-ciated health risks; and ecological damage to local envi-ronments caused by smothering and burial of organismsby drill cuttings.

Fig. 2 represents a hierarchical structure model ofaggregative risk involving two major attributes: ecolog-ical (X1) and human health risk (X2) at attribute Level-II. Each Level-II attribute is divided further into twoLevel-I attributes, i.e. ecological risk is divided into eco-toxicological risk (X11) and eco-physical risk (X12), andsimilarly human health risk is divided into toxicological(X21) and safety (X22) related risks. The Level-Iattributes are further divided into basic risk items, e.g.eco-toxicological risk is divided into ecological riskrelated to heavy metals (X111), PAHs (X112), and otherchemicals (X113). The eco-physical risk is divided intoburial of breeding grounds of benthic communities(X121), oxygen deficiency (X122), and particulate natureof the drilling waste which can cause respiratoryproblems in the benthic community (X123). Similarly,human health toxicity attribute at Level-I is divided intothree basic risk items: consumption of contaminated fish(X211), exposure of workers to volatile compounds at thetreatment site (X212), and non-water quality impacts dueto greenhouse gases causing global warming (X213). Thehuman health risk related to safety issues is divided intoaccidental (X221) and normal handling operations(X222). Fig. 2 illustrates the complete model structureused for determining aggregative risk assessment fordrilling waste discharges.

An expert panel, involving various stakeholders, candetermine the grade and importance of risk for each riskitem. For this example, expert judgement was used todevelop a qualitative scale ranging from 1 to 11 for bothgrade and importance of risk. With this qualitative scale,the aggregative environmental risk can then be deter-mined from the hierarchical structure model shown inFig. 2.

Let n(k) be the number of items at Level-II forattribute Xk, k ¼ 1; 2. For the drilling waste disposalexample then, nð1Þ ¼ 2 and nð2Þ ¼ 2. Weights W3(1)and W3(2) can be assigned to Level-II attributes X1 andX2. These weights are estimated using analyticalhierarchy process (AHP) described in the followingsection. For every Level-II attribute (X1 and X2),Xkj ð j ¼ 1; 2Þ; and ðk ¼ 1; 2Þ, W2(k, j ) can be denotedas the weight of attribute Level-I. Similarly, for everyrisk item Xkji ði ¼ 1; 2; ::; nðk; jÞÞ; ð j ¼ 1; 2Þ; andðk ¼ 1; 2Þ, weights W1(k, j, i) can be used, whichcan be determined using the AHP. The hierarchicalstructure for this example problem is given inTable 2.


Fig. 2. Hierarchical structure of aggregative environmental risk model for drilling waste discharges in the marine environment.

3.2. Analytical hierarchy process (AHP)

The AHP is the most widely used technique formultiple-criteria analyses (MCA). The AHP developsa linear additive model, but in its standard format, usesprocedures for deriving the weights achieved by pair-wise comparisons between criteria or attributes (Ziaraet al., 2002). The pair-wise comparisons of the attributesat each level in the hierarchy are arranged intoreciprocal matrix (Saaty, 1996). The pair-wise compar-ison of the criteria in the AHP method generates a set ofmatrices of the following form:

AX¼ amnð Þ ð4Þ

where AX¼ reciprocal matrix ðamn ¼ 1=anmÞ. There are

a number of ways to derive the vector of priorities

(weights) from matrix AX. But emphasis on consistency of

matrix leads to

AX

W ¼ n Wð Þ ð5Þ

where n is the number of attributes considered and W isthe priority vector, ðw1;w2;.;wnÞ. If a precise value of

matrix AX

is not known, the problem reduces to

AX

W ¼ lmax Wð Þ ð6Þ

where lmax is the largest or principal eigen value of AX.

The solution is obtained by raising the matrix toa sufficiently large power then summing over the rowsand normalizing to obtain the priority vector W. Theprocess is stopped when the difference between the


Table 2

A three-stage structure model of environmental risk for drilling waste discharges

Attribute level-II Attribute level-I Risk item W3(k) W2(k, j ) W1(k, j, i) r i g (r, i)

X1 W3(1)

X11 W2(1, 1)

X111 W1(1, 1, 1) r111 i111 g (r111, i111)

X112 W1(1, 1, 2) r112 i112 g (r112, i112)

X113 W1(1, 1, 3) r113 i113 g (r113, i113)

X12 W2(1, 2)

X121 W1(1, 2, 1) r121 i121 g (r121, i121)

X122 W1(1, 2, 2) r122 i122 g (r122, i122)

X123 W1(1, 2, 3) r123 i123 g (r123, i123)

X2 W3(2)

X21 W2(2, 1)

X211 W1(2, 1, 1) r211 i211 g (r211, i211)

X212 W1(2, 1, 2) r212 i212 g (r212, i212)

X213 W1(2, 1, 3) r213 i213 g (r213, i213)

X22 W2(2, 2)

X221 W1(2, 2, 1) r221 i221 g (r221, i221)

X222 W1(2, 2, 2) r222 i222 g (r222, i222)

components of the priority vector obtained at the zthpower and the ðzC1Þst power is less than somepredefined small value. The vector of priorities is thederived scale associated with the matrix of comparisons.

Saaty (2001) recommended an easy way to develop anapproximation to the priorities by normalizing thegeometric means of the rows. The results coincide withthe eigen vector for n%3. A second method to obtain anapproximation is by normalizing the elements in eachcolumn of the judgement matrix and then averagingover each row. In the drilling waste discharge example,for each attribute (at each level) either two or three sub-attributes (or risk items) exist. Therefore, the matrix canbe solved by normalizing the geometric means of therows with the same accuracy as by using the principal

eigen value method. Table 3 summarizes the weightsestimated for various items in the structure model, asshown in Fig. 2, of aggregative environmental risk ofdrilling waste disposal options.

3.3. Evaluation of aggregative risk

The evaluation of aggregative risk of drilling wastedisposal was carried out using a three-step procedure.The criteria ratings of risk were linguistic variables L1,L2, L3, L4, L5, L6, and L7. These linguistic variables weredefined as extremely low, quite low, low, OK, high, quitehigh and extremely high, respectively. These linguisticvariables were then defined by TFNs with membershipfunctions as follows:

Table 3

Weights estimated through the analytical hierarchy process (AHP) from priority vectors

Definition W3(k) W2(k, j ) W1(k, j, i) Values

Ecological risk W3(1) 0.333

Eco-toxicological risk W2(1, 1) 0.600

Heavy metals W1(1, 1, 1) 0.416

PAHs W1(1, 1, 2) 0.458

Other chemicals W1(1, 1, 3) 0.126

Eco-physical risk W2(1, 2) 0.400

Burial W1(1, 2, 1) 0.498

Oxygen deficiency W1(1, 2, 2) 0.285

Particulates causing respiration problems W1(1, 2, 3) 0.218

Human health risk W3(2) 0.667

Human health toxicological effects W2(2, 1) 0.600

Contaminated fish W1(2, 1, 1) 0.498

Exposure at the rig W1(2, 1, 2) 0.285

Non water quality impacts W1(2, 1, 3) 0.217

Safety related human health dangers W2(2, 2) 0.400

Accidents W1(2, 2, 1) 0.333

During normal handling operations W1(2, 2, 2) 0.667


L1 ¼ ð0; 0; 1=6Þ mL1ðxÞ ¼

1� 6x; 0%x!1

6;

0; 0:1%x%1;

8><>:

Ln ¼ ððn� 2Þ=6; ðn� 1Þ=6; n=6Þ mLnðxÞ ¼

0; 0%x!n� 2

6;

6x� ðn� 2Þ; n� 2

6%x!

n� 1

6;

n� 6x;n� 1

6%x%

n

6;

0;n

6%x%1;

ð7Þ

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ðn ¼ 2; 3; 4; 5; 6Þ and

L7 ¼ ð5=6; 1; 1Þ mN7ðxÞ ¼0; 0%x%

5

6

6x� 55

6%x%1:

8>><>>:

The centers of mass (centroids) of the above sevenqualitative scales in ascending order are LG ð1Þ ¼0:056; LG ð2Þ ¼ 0:167; LG ð3Þ ¼ 0:333; LG ð4Þ ¼ 0:500;LG ð5Þ ¼ 0:667; LG ð6Þ ¼ 0:834; and LG ð7Þ ¼ 0:944,respectively. Let Ln ¼ fL1; L2; L3; L4; L5; L6; andL7g be the set of the criteria rating of risk for eachitem. The fuzzy assessment matrix for risk items ofattribute Level-I can be established for X11, X12, X21

and X22 individually. For example, for Xkj ¼ X11, therisk items involved are X111, X112 and X113 and thecorresponding rates of risk are g(r111, i111), g(r112, i112),and g(r113, i113), respectively (see Table 2). The value ofeach g(rkji, ikji) was estimated from Fig. 1, and then usedin Eq. (7) to estimate the L(rkji, ikji, n) (wheren ¼ 1; 2; ::7). Thus a fuzzy assessment matrix F(X11)can be formed as follows:

FðX11Þ¼Lðr111; i111; 1Þ Lðr111; i111; 2Þ : : : : Lðr111; i111; 7Þ

Lðr112; i112; 1Þ Lðr112; i112; 2Þ : : : : Lðr112; i112; 7Þ

Lðr113; i113; 1Þ Lðr113; i113; 2Þ : : : : Lðr113; i113; 7Þ

X111

X112

X113

��

��(8)

Similarly, the fuzzy assessment matrices for F(X12),F(X21) and F(X22) can be formed for the correspondingattributes X12, X21 and X22, respectively. Now the firststage aggregative assessment of environmental risk canbe evaluated for attribute X11 as follows:

½Sð1; 1; 1Þ;.;Sð1; 1; 7Þ�1!7

¼ ½W1ð1; 1; 1Þ; W1ð1; 1; 2Þ; W1ð1; 1; 3Þ�1!3

!FðX11Þ3!7 ð9Þ

where

Sð1; 1; nÞ ¼X3

i¼1

W1ð1; 1; iÞ!Lðr11i; i11i; nÞ for n

¼ 1; 2;.; 7: ð10Þ

Therefore, S1ð1; 1Þ ¼ ½Sð1; 1; 1Þ; Sð1; 1; 2Þ; ::;Sð1; 1; 7Þ�can be denoted as the vector of first stage aggregativeenvironmental risk for attribute X11. Similarly, S1(1,2),S1(2,1), and S1(2,2) are the vectors of the first stageaggregative risk for the Level-1 attributes, X12, X21 andX22, respectively.

The second stage assessment ( for X1) is carried out asfollows:

½Sð1; 1Þ; Sð1; 2Þ; :::;Sð1; 7Þ�1!7

¼ ½W2ð1; 1Þ; W2ð1; 2Þ�1!25S1ð1; 1Þ

S1ð1; 2Þ

" #2!7

ð11Þ

where

S2ð1Þ ¼ ½Sð1; 1Þ; Sð1; 2Þ; ::;Sð1; 7Þ� and

S2ð1; nÞ ¼X2

j¼1

W2ð1; jÞ!S2ð1; j; nÞ for n ¼ 1; 2; ::; 7:

Similarly, for X2

½Sð2; 1Þ;Sð2; 2Þ; :::;Sð2; 7Þ�1!7

¼ ½W2ð2; 1Þ;W2ð2; 2Þ�1!25S1ð2; 1Þ

S1ð2; 2Þ

" #2!7

ð12Þ


where

S2ð2Þ ¼ ½Sð2; 1Þ;Sð2; 2Þ; ::;Sð2; 7Þ� and

S2ð2; nÞ ¼X2

j¼1

W2ð2; jÞ!S2ð2; j; nÞ for n ¼ 1; 2; :::; 7:

The third stage assessment for X is as follows:

½Sð1Þ;Sð2Þ; :::;Sð7Þ�1!7

¼ ½W3ð1Þ;W3ð2Þ�1!25S2ð1Þ

S2ð2Þ

" #2!7

ð13Þ

where

S3ðnÞ ¼ ½Sð1Þ;Sð2Þ;.;Sð7Þ�

The rate of final aggregative environmental risk (X ) canbe defuzzified using Eq. (3) by the centroid method(Yager, 1980) as:

Final aggregative risk ¼ R ¼X7

n¼1

LGðnÞ!S3ðnÞ ð14Þ

4. An application of the proposed methodology

Due to possible adverse environmental impacts,prohibition of the discharge of rock cuttings into theNorth Sea has been implemented. As a result, all drillcuttings must be either re-injected downhole, or shippedto shore for treatment and disposal. The regulatoryauthorities in Newfoundland, Canada have advocatedfor treating the drilling waste to a level of 6.9% (on wetcuttings) before discharge if the re-injection of waste isnot possible (it is assumed that all contaminantsincluding PAH, metals decrease proportionately). Asthe best available economically achievable technology(BAT) can reduce SBFs to the neighbourhood of 5e7%on wet cuttings, therefore the CNOPB (2002) recom-mended value of 6.9% SBFs on wet cuttings is aneconomically achievable goal.

The United States Environmental Protection Agency(US EPA) has identified different options to reduce thedischarge of drilling waste into the marine environment.Current industry practice for managing and treatingSBF-cuttings before discharge is to process the cuttingsthrough solids separation equipment, which consists ofprimary and secondary shale shakers and occasionallya centrifuge. Based on current industry data, theefficiency of solids separation equipment results ina long-term average of 10.2% (by dry weight) retentionof SBF on cuttings. However, using new treatmenttechnology, the retention of SBF can be reduced toapproximately 4% (US EPA, 2000a, 2000b). Sadiq

(2001) and Sadiq et al. (2003) have evaluated fivedischarge scenarios; 4%, 5.5%, 7%, 85% and 10% SBFretention on drilling solids, for risk management ofdrilling wastes off the Newfoundland coast. Based onvarious regulatory regimes, in this study three dischargescenarios were selectedd4%, 7% and 10% SBF re-tention on drilling solidsdto generate an estimation ofaggregative environmental risk. A step-by-step method-ology for estimating the rate of aggregative risk is shownin the flow chart in Fig. 3.

4.1. First stage assessment

In the first stage assessment, an alternative (dischargescenario) is selected. A hierarchical structure of anaggregative environmental risk model is developed andthe grade of risk and grade of importance are decidedupon based on either expert panel recommendations orby conducting a survey through telephone interviews orquestionnaires (Fig. 3). A Delphi-type method can beutilized to reach a consensus. After deciding the r andi values for each risk item, the rate of aggregative riskg (r, i) is evaluated from Fig. 1. The results (risk items)of the three discharge scenarios selected for this casestudy are summarized in Table 4.

For each g (r, i), the membership mLi (x) for linguisticvariables (L1 to L7) can be estimated, e.g. in the case ofthe 4% discharge scenario for the risk item X112, theaggregative risk is g (3,6), which is equal to 0.105. Thememberships mLi (x) of linguistic variables areL1 ¼ 0:37;L2 ¼ 0:63 and L3 to L7 ¼ 0:00 as shown inFig. 4. The same procedure is repeated for X111 andX113.Therefore, the F(X11) matrix can be formed as:Similarly, assessment matrices F(X12), F(X21), andF(X22) can be formed as follows:

FðX11Þ¼

0:49 0:51 0:00 0:00 0:00 0:00 0:00

0:37 0:63 0:00 0:00 0:00 0:00 0:00

0:92 0:08 0:00 0:00 0:00 0:00 0:00

2664

3775X111

X112

X113

ð15Þ

FðX12Þ¼

0:49 0:51 0:00 0:00 0:00 0:00 0:00

0:85 0:15 0:00 0:00 0:00 0:00 0:00

0:91 0:09 0:00 0:00 0:00 0:00 0:00

2664

3775

X121

X122

X123

;

FðX21Þ¼

0:61 0:39 0:00 0:00 0:00 0:00 0:00

0:25 0:75 0:00 0:00 0:00 0:00 0:00

0:73 0:27 0:00 0:00 0:00 0:00 0:00

2664

3775

X211

X212

X213

; and

FðX22Þ¼0:61 0:39 0:00 0:00 0:00 0:00 0:00

0:25 0:75 0:00 0:00 0:00 0:00 0:00

" #X221

X222

ð16Þ


Fig. 3. Methodology for estimating aggregative rate of environmental risk for drilling waste discharges.

Now the F(Xkj) matrix can be multiplied by W1(k, j, n)to determine the items for attribute Level-I as:

S1 ð1; 1; nÞ¼ 0:416 0:458 0:126½ �1!35½FðX11Þ�3!7

S1 ð1; 1; nÞ¼ ½0:49 0:51 0:00 0:00 0:00 0:00 0:00 �1!7

ð17Þ

Similarly the following can be calculated:

S1 ð1; 2; nÞ¼ 0:68 0:32 0:00 0:00 0:00 0:00 0:00½ �1!7;S1 2; 1; nð Þ¼ 0:53 0:47 0:00 0:00 0:00 0:00 0:00½ �1!7;S1 2; 2; nð Þ¼ 0:61 0:39 0:00 0:00 0:00 0:00 0:00½ �1!7:

ð18Þ

This first stage aggregative risk can then be used for theassessment of the second stage aggregative risk.

4.2. Second stage assessment

The second stage assessment follows similar steps asthe first stage, but now the matrix W2(k, n) is multipliedby S1(k, j, n) to determine the items for attribute Level-II:

S2 1; nð Þ¼ 0:60 0:40½ �1!2

50:49 0:51 0:00 0:00 0:00 0:00 0:00

0:68 0:32 0:00 0:00 0:00 0:00 0:00

" #2!7

S2 1; nð Þ¼ 0:57 0:43 0:00 0:00 0:00 0:00 0:00½ �1!7

ð19Þ

Similarly,


Table 4

A complete data set of environmental risk items for three drilling waste discharge scenarios

Risk items r4% i4% g (r, i)4% r7% i7% g (r, i) 7% r10% i10% g (r, i) 10%

X111 3 5 0.0850 4 5 0.1250 7 5 0.2450

X112 3 6 0.1050 4 6 0.1550 5 6 0.2050

X113 1 4 0.0128 2 4 0.0350 3 4 0.0650

X121 3 5 0.0850 4 5 0.1250 6 5 0.2050

X122 2 3 0.0250 3 3 0.0450 4 3 0.0650

X123 2 2 0.0150 4 2 0.0350 4 2 0.0350

X211 2 7 0.0650 3 7 0.1250 5 7 0.2450

X212 3 7 0.1250 4 7 0.0450 6 7 0.3050

X213 2 5 0.0450 3 5 0.0350 4 7 0.1850

X221 3 6 0.1050 5 6 0.2050 6 6 0.2550

X222 2 5 0.0450 4 5 0.1250 6 5 0.2050

S2 2; nð Þ¼ 0:60 0:40½ �1!2

50:53 0:47 0:00 0:00 0:00 0:00 0:00

0:61 0:39 0:00 0:00 0:00 0:00 0:00

" #2!7

S2 2; nð Þ¼ 0:56 0:44 0:00 0:00 0:00 0:00 0:00½ �1!7

ð20Þ

The second stage aggregative risk is now used for theassessment of the third stage aggregative risk.

4.3. Third stage assessment

In the third stage assessment, the matrix W3(n) ismultiplied by S2(k, n) to obtain the aggregative matrixS3(n) as follows:

S3 nð Þ¼ 0:333 0:667½ �1!2

50:57 0:43 0:00 0:00 0:00 0:00 0:00

0:56 0:44 0:00 0:00 0:00 0:00 0:00

" #2!7

S3 nð Þ¼ 0:57 0:43 0:00 0:00 0:00 0:00 0:00½ �1!7

ð21Þ

To determine the final aggregative risk in the case of the4% SBF retention discharge option, LG(x) is multipliedby S3(n) (using Eq. (14)) to yield:

Aggregative risk for 4% discharge option ¼ R4%

R4% ¼ ½ð0:056!0:57ÞCð0:167!0:43ÞCð0:333!0:00ÞCð0:500!0:00ÞCð0:667!0:00ÞCð0:834!0:00ÞCð0:944!0:00Þ� ¼ 0:104 ð22Þ

The same methodology is repeated for the 7% and 10%discharge options, and the following aggregative riskvalues were obtained:

R7% ¼ 0:130; andR10% ¼ 0:220

Tables 5e7 show the detailed calculations for the 4%,7% and 10% SBF retention on drilling waste solidsdischarge options, respectively. Fig. 5 shows the riskcontours for three discharge options. It is evident fromFig. 5 that approximately 40% decrease in aggregativeenvironmental risk is expected when the 7% SBFretention discharge option is selected instead of the10% SBF retention discharge option. This reduction

Fig. 4. Membership functions of the set of criteria ratings of environmental risk associated with drilling waste disposal.


Table 5

Estimation of the rate of aggregative environmental risk for the 4% drilling waste discharge scenario

Risk item Items g (r, i)4% W1() L1 L2 L3 L4 L5 L6 L7

X111 F(X111) 0.0850 0.416 0.49 0.51 0.00 0.00 0.00 0.00 0.00

X112 F(X112) 0.1050 0.458 0.37 0.63 0.00 0.00 0.00 0.00 0.00

X113 F(X113) 0.0128 0.126 0.92 0.08 0.00 0.00 0.00 0.00 0.00

X121 F(X121) 0.0850 0.498 0.49 0.51 0.00 0.00 0.00 0.00 0.00

X122 F(X122) 0.0250 0.285 0.85 0.15 0.00 0.00 0.00 0.00 0.00

X123 F(X123) 0.0150 0.218 0.91 0.09 0.00 0.00 0.00 0.00 0.00

X211 F(X211) 0.0650 0.498 0.61 0.39 0.00 0.00 0.00 0.00 0.00

X212 F(X212) 0.1250 0.285 0.25 0.75 0.00 0.00 0.00 0.00 0.00

X213 F(X213) 0.0450 0.217 0.73 0.27 0.00 0.00 0.00 0.00 0.00

X221 F(X221) 0.1050 0.333 0.37 0.63 0.23 0.00 0.00 0.00 0.00

X222 F(X222) 0.0450 0.667 0.73 0.27 0.00 0.00 0.00 0.00 0.00

Attribute Level-I Items W2() S1(k, j, 1) S1(k, j, 2) S1(k, j, 3) S1(k, j, 4) S1(k, j, 5) S1(k, j, 6) S1(k, j, 7)

X11 S1(1, 1, n) 0.600 0.49 0.51 0.00 0.00 0.00 0.00 0.00

X12 S1(1, 2, n) 0.400 0.68 0.32 0.00 0.00 0.00 0.00 0.00

X21 S1(2, 1, n) 0.600 0.53 0.47 0.00 0.00 0.00 0.00 0.00

X22 S1(2, 3, n) 0.400 0.61 0.39 0.00 0.00 0.00 0.00 0.00

Attribute Level-II Items W3() S2(k, 1) S2(k, 2) S2(k, 3) S2(k, 4) S2(k, 5) S2(k, 6) S2(k, 7)

X1 S2(1, n) 0.333 0.57 0.43 0.00 0.00 0.00 0.00 0.00

X2 S2(2, n) 0.667 0.56 0.44 0.00 0.00 0.00 0.00 0.00

Aggregative risk Items S3(1) S3(2) S3(3) S3(4) S3(5) S3(6) S3(7)

X S3(n) 0.57 0.43 0.00 0.00 0.00 0.00 0.00

Centroid LG(n) 0.056 0.167 0.333 0.500 0.667 0.833 0.944

Risk R4% 0.104

W1ðÞ ¼ W1ðk; j; iÞ;W2ðÞ ¼ W2ðk; jÞ;W3ðÞ ¼ W1ðkÞ:

Table 6

Estimation of the rate of aggregative environmental risk for the 7% drilling waste discharge scenario


X111 F(X111) 0.1250 0.416 0.25 0.75 0.00 0.00 0.00 0.00 0.00

X112 F(X112) 0.1550 0.458 0.07 0.93 0.00 0.00 0.00 0.00 0.00

X113 F(X113) 0.0350 0.126 0.79 0.21 0.00 0.00 0.00 0.00 0.00

X121 F(X121) 0.1250 0.498 0.25 0.75 0.00 0.00 0.00 0.00 0.00

X122 F(X122) 0.0450 0.285 0.73 0.27 0.00 0.00 0.00 0.00 0.00

X123 F(X123) 0.0350 0.218 0.79 0.21 0.00 0.00 0.00 0.00 0.00

X211 F(X211) 0.1250 0.498 0.25 0.75 0.00 0.00 0.00 0.00 0.00

X212 F(X212) 0.0450 0.285 0.73 0.27 0.00 0.00 0.00 0.00 0.00

X213 F(X213) 0.0350 0.217 0.79 0.21 0.00 0.00 0.00 0.00 0.00

X221 F(X221) 0.2050 0.333 0.00 0.77 0.23 0.00 0.00 0.00 0.00

X222 F(X222) 0.1250 0.667 0.25 0.75 0.00 0.00 0.00 0.00 0.00


X12 S1(1, 2, n) 0.400 0.50 0.50 0.00 0.00 0.00 0.00 0.00

X21 S1(2, 1, n) 0.600 0.50 0.50 0.00 0.00 0.00 0.00 0.00

X22 S1(2, 3, n) 0.400 0.17 0.76 0.08 0.00 0.00 0.00 0.00


X1 S2(1, n) 0.333 0.34 0.66 0.00 0.00 0.00 0.00 0.00

X2 S2(2, n) 0.667 0.37 0.60 0.03 0.00 0.00 0.00 0.00


X S3(n) 0.36 0.62 0.02 0.00 0.00 0.00 0.00

Centroid LG(n) 0.056 0.167 0.333 0.500 0.667 0.833 0.944

Risk R7% 0.130



Table 7

Estimation of the rate of environmental aggregative risk for the 10% drilling waste discharge scenario


X111 F(X111) 0.2450 0.416 0.00 0.53 0.47 0.00 0.00 0.00 0.00

X112 F(X112) 0.2050 0.458 0.00 0.77 0.23 0.00 0.00 0.00 0.00

X113 F(X113) 0.0650 0.126 0.61 0.39 0.00 0.00 0.00 0.00 0.00

X121 F(X121) 0.2050 0.498 0.00 0.77 0.23 0.00 0.00 0.00 0.00

X122 F(X122) 0.0650 0.285 0.61 0.39 0.00 0.00 0.00 0.00 0.00

X123 F(X123) 0.0350 0.218 0.79 0.21 0.00 0.00 0.00 0.00 0.00

X211 F(X211) 0.2450 0.498 0.00 0.53 0.47 0.00 0.00 0.00 0.00

X212 F(X212) 0.3050 0.285 0.00 0.17 0.83 0.00 0.00 0.00 0.00

X213 F(X213) 0.1850 0.217 0.00 0.89 0.11 0.00 0.00 0.00 0.00

X221 F(X221) 0.2550 0.333 0.00 0.47 0.53 0.00 0.00 0.00 0.00

X222 F(X222) 0.2050 0.667 0.00 0.77 0.23 0.00 0.00 0.00 0.00


X11 S1(1, 1, n) 0.600 0.08 0.62 0.30 0.00 0.00 0.00 0.00

X12 S1(1, 2, n) 0.400 0.35 0.54 0.11 0.00 0.00 0.00 0.00

X21 S1(2, 1, n) 0.600 0.00 0.51 0.49 0.00 0.00 0.00 0.00

X22 S1(2, 3, n) 0.400 0.00 0.67 0.33 0.00 0.00 0.00 0.00


X1 S2(1, n) 0.333 0.18 0.59 0.23 0.00 0.00 0.00 0.00

X2 S2(2, n) 0.667 0.0 0.57 0.43 0.00 0.00 0.00 0.00


Centroid LG(n) 0.056 0.167 0.333 0.500 0.667 0.833 0.944

Risk R10% 0.220


increases to 53% when the 4% SBF retention dischargeoption is considered instead of the 10% SBF retentiondischarge option. These results imply a non-linearrelationship between risk and treatment provided tothe drilling waste before discharge into the marineenvironment. Cost can become a limiting factor in thiscase as the reduction in risk after a certain level isachieved only at a very high treatment cost. Similar

Fig. 5. Comparison of aggregative environmental risk values for three

drilling waste discharge scenarios.

conclusions were reported by Sadiq (2001) and Sadiqet al. (2003) in a drilling waste discharge study for theeast coast of Canada.

4.4. Sensitivity analysis

The process of ranking alternatives involved assump-tions and human judgment for assigning weights andqualitative scales to various risk items and attributes. Toconfirm the aggregative risk values obtained in theprevious section, a sensitivity analysis was performed inwhich various weighting schemes were employed and theentire procedure was repeated. Table 8 summarizes fourtrials in which new weights were assigned at attributeLevels I and II. The results of the first trial have alreadybeen discussed in the previous section in which atattribute Level-II, the human health risk, was givenmore weight than ecological risk described in attributeLevel-I. The second trial represented the case in whichecological and human health both were assigned equalweights. Similarly, in the third and the fourth trials, theweights were varied at attribute Level-I and aggregativerisks for three discharge scenarios were re-evaluated. Itcan be seen that the estimated aggregative risks were notvery sensitive to weighting schemes. Rather, the selec-tion of the grade of risk (r) and grade of importance (i)were found to be the most important factors in affectingthe outcome of the aggregative environmental riskmodel, as indicated by the results of the three dischargescenarios generated in each trial risk assessment.


Table 8

Results of a sensitivity analysis performed for the drilling waste disposal risk assessment example

Trials W2(k, j ) W3(k) Aggregative risk for various discharge scenarios

4% 7% 10%

1 (Human health is given

more weight)

X11 (0.600) X1 (0.333) 0.1041 0.1301 0.2200

X12 (0.400)

X21 (0.600) X2 (0.667)

X22 (0.400)

2 (Human and ecological

health are given equal

weights)

X11 (0.600) X1 (0.500) 0.1038 0.1297 0.2110

X12 (0.400)

X21 (0.600) X2 (0.500)

X22 (0.400)

3 (Weights are changed at

attribute level-I)

X11 (0.500) X1 (0.333) 0.1026 0.1324 0.2162

X12 (0.500)

X21 (0.500) X2 (0.667)

X22 (0.500)

4 (Weights are changed at

attribute level-I)

X11 (0.500) X1 (0.500) 0.1023 0.1307 0.2066

X12 (0.500)

X21 (0.500) X2 (0.500)

X22 (0.500)

5. Summary and conclusions

The purpose of this study was to develop a method-ology for determining the aggregative risk of varioussources and routes of exposure for a given process. Therate of risk was defined by the product of grade of risk(r, magnitude) and grade of importance (i, intensity).Risk factors r and i were expressed by a multiple level,qualitative scaling scheme increasing in value from 1 to11. The qualitative scales were expressed by triangularfuzzy numbers to capture the vagueness in the linguisticsubjectivity of risk definitions. A hierarchical structuremodel was developed for various environmental riskitems at three stages to determine the final aggregativerisk. During grouping of attributes or risk items, ananalytical hierarchy process is used for estimating thepriority matrix (weights).

The developed methodology was applied to evaluatevarious scenarios of drilling waste discharge in themarine environment. Three discharge scenarios selectedwere 4%, 7% and 10% SBF attached to dry drillcuttings. The estimated aggregative environmental riskfor three discharge scenarios were 0.10, 0.13 and 0.22,respectively. Approximately a 40% decrease in aggre-gative risk was obtained for the 7% SBF retentiondischarge option as compared to the 10% SBF retentiondischarge option. This reduction was increased to 53%with the 4% SBF retention discharge option. Thisindicates that a non-linear trend prevailed between riskand treatment provided for the drilling waste. Asensitivity analysis revealed that that the aggregativeenvironmental risks were not sensitive to weightingschemes, rather the selection of the grade of risk andgrade of importance were found to be the mostimportant factors affecting overall aggregative risk.

Cost can often become a limiting factor in theselection of risk reduction alternatives as was indicatedby this case study where the reduction in risk aftera certain level is achieved only at a very high treatmentcost. In this example, only environmental (ecologicaland human health) risks were used to evaluate variousdischarge scenarios. To perform a more detailed multi-criteria analysis, financial, technical, and/or socio-political risks can be incorporated into the hierarchicalstructure of the aggregative risk model presented in thispaper for the optimal selection of the ‘‘best’’ dischargescenario based on a diverse set of decision criteria.

References

Attoh-Okine, N.O., 2002. Probabilistic analysis of factors affecting

highway construction costs: a belief network approach. Canadian

Journal of Civil Engineering 29, 369e374.

Candler, J.R., Leuterman, A.J.J., 1997. Effectiveness of a 10-Days

Amphipod Sediment Test to Screen Drilling Mud Base Fluids for

Benthic Toxicity. Society of Petroleum Engineers SPE 37890.

Chen, S.H., 1985. Ranking fuzzy numbers with maximising set and

minimising set. Fuzzy Set Systems 17 (2), 113e129.

CNOPB 2002. Offshore waste treatment guidelines, CanadaeNewfoundland Offshore Petroleum Board, http://www.cnopb.

nfnet.com.

Klir, G.J., Yuan, B., 1995. Fuzzy Sets and Fuzzy LogicdTheory and

Applications. Prentice-Hall, Englewood Cliffs, NJ, USA.

Lascio, L.D., Gisolfi, A., Albunia, A., Galardi, G., Moschi, F., 2002.

A fuzzy-based methodology for the analysis of diabetic neuropa-

thy. Fuzzy Sets and Systems 129, 203e228.Lawry, J., 2001. A methodology for computing with words. In-

ternational Journal of Approximate Reasoning 28, 51e89.

Lee, H.M., 1996. Applying fuzzy set theory to evaluate the rate of

aggregative risk in software development. Fuzzy Sets and Systems

79, 323e336.

Rabke, S., Candler, J., 1998. Development of acute benthic toxicity

for monitoring synthetic-based muds discharged offshore. IBC

http://www.cnopb.nfnet.com

http://www.cnopb.nfnet.com


Conference on Minimising the Environmental Effects of Offshore

Drilling, Houston, Texas.

Saaty, T.L., 1996. Decision Making with Dependence and Feedback:

The Analytic Hierarchy Process. RWS, Pittsburgh.

Saaty, T.L., 2001. How to make a decision? Chapter 1. In: Satay, T.L.,

Vargas, L.G. (Eds.), Models, Methods, Concepts and Applications

of the Analytic Hierarchy Process. Kluwer International.

Sadiq, R. 2001. Drilling waste discharges in the marine environ-

ment: a risk based decision methodology, PhD dissertation,

Memorial University of Newfoundland, St. John’s, NL,

Canada.

Sadiq, R., Husain, T., Veitch, B., Bose, N., 2003. Risk management of

drilling waste disposal in the marine environmentda holistic

approach. Oceanic Engineering International 7 (1), 1e22.

Sadiq, R., Rajani, B., Kleiner, Y. 2004. A fuzzy-based method to

evaluate soil corrosivity for prediction of water main deterioration,

ASCE Journal of Infrastructure Systems (submitted).

US EPA 2000a. Development document for final effluent limitations

guidelines and standards for synthetic-based drilling fluids and

other non-aqueous drilling fluids in the oil and gas extraction point

source category, US Environmental Protection Agency, Washing-

ton DC, EPA-821-00-013.

U.S. EPA 2000b. Environmental assessment of final effluent limi-

tations guidelines and standards for synthetic-based drilling fluids

and other non-aqueous drilling fluids in the oil and gas extraction

point source category, US Environmental Protection Agency,

Washington DC, EPA-821-00-014.

Yager, R.R., 1980. A general class of fuzzy connectives. Fuzzy Sets

and Systems 4, 235e242.Zadeh, L.A., 1996. Fuzzy logic computing with words. IEEE Trans-

actions, Fuzzy Systems 4 (2), 103e111.

Ziara, M., Nigim, K., Enshassi, A., Ayyub, B.M., 2002. Strategic

implementation of infrastructure priority projects: case study in

Palestine. ASCE, Journal of Infrastructure Systems 8 (1), 2e11.

a fuzzy-based methodology for an aggregative environmental risk assessment: a case study of drilling...

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