Development of an expert system for underbalanced drilling using fuzzy logic

Ž .Journal of Petroleum Science and Engineering 31 2001 23–39www.elsevier.comrlocaterjpetscieng

Development of an expert system for underbalanced drillingusing fuzzy logic

Ali A. Garrouch a,), Haitham M. S. Lababidi b

a Department of Petroleum Engineering, Kuwait UniÕersity, P.O. Box 5969, Safat 13060, Kuwaitb Department of Chemical Engineering, Kuwait UniÕersity, P.O. Box 5969, Safat 13060, Kuwait

Received 17 November 2000; accepted 9 July 2001

Abstract

This paper documents the development of an expert system for screening wells that could be drilled underbalanced, andfor aiding in the preliminary selection of appropriate underbalanced drilling fluids for a given range of wellbore andreservoir conditions. This approach combines a qualitative rule-based analysis for assessing formation damage and lostcirculation potentials with quantitative analysis for assessing wellbore stability using geomechanical and petrophysical data.To make the analysis complete, a variety of other factors such as pipe sticking potential, wellbore geometry, type of fluidinflux anticipated, pore pressure value, and cost benefit are also included in the expert-system decision trees. The mainadvantage of the expert system, developed in this study, is the use of fuzzy logic for handling cases that lend themselves topartial truth. This feature makes the system a powerful tool for analyzing ambiguous drilling scenarios.

Results of compared field cases are encouraging and conformal to field practices. Allowing for human input, whenessential data are lacking, makes the system a useful tool that can help less experienced individuals function near the level ofproficient drilling engineers. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Underbalanced; Drilling; Expert systems; Fuzzy logic

1. Introduction

1.1. Scope of work

Ž .Recently, underbalanced drilling UBD has beenused with increasing frequency. The purpose of us-ing UBD is to minimize problems associated with

) Corresponding author.E-mail address: [email protected]

Ž .A.A. Garrouch .

invasive formation damage which often greatly re-duces the productivity of oil and gas reservoirsŽ .Negrao et al., 1999 . When properly designed andexecuted, UBD minimizes problems associated withthe invasion of particulate matter into the formationas well as a number of other problems such asadverse clay reactions, phase trapping, organic and

Žinorganic precipitation, and emulsification Jiao and.Sharma, 1996 . These effects may be caused by the

invasion of incompatible mud filtrates in an overbal-anced condition. Benefits of UBD result from thereduction in drilling time, greater rates of penetra-tion, increased bit life, a rapid indication of produc-

0920-4105r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0920-4105 01 00136-X

( )A.A. Garrouch, H.M.S. LababidirJournal of Petroleum Science and Engineering 31 2001 23–3924

tive reservoir zones, and the potential for dynamicflow testing while drilling; however, UBD is not asolution for all formation damage problems. Indeed,damage caused by poorly designed andror executedUBD programs can exceed that which may occurwith a well-designed conventional overbalanceddrilling program. Potential downsides and damagemechanisms associated with UBD include increasedcost and safety concerns, difficulty in maintaining acontinuously underbalanced condition, spontaneousimbibition and countercurrent imbibition effects,glazing, mashing, and mechanically induced well-

Ž .bore damage Bennion et al., 1998 .With UBD techniques, the hydrostatic pressure in

the wellbore is maintained at some pressure lowerthan the pore pressure of the target formation. Thiscondition can be generated naturally with low den-sity fluids in some situations where high naturalpressure exists in the formation. This technique iscommonly referred to as flow drilling. In other situa-tions, the underbalanced condition is generated bythe injection of some noncondensable gas with thecirculating fluid system to reduce the effective hy-drostatic column. The gas most commonly used isnitrogen because of its availability and ease of trans-portation. Underbalanced operations have also beenexecuted with air, natural gas, and reduced oxygencontent air, depending on the specific reservoir con-

Ž .ditions encountered Johnson, 1995 .UBD techniques have often been applied for hori-

zontal wells where formation damage has been ofparticular concern because of longer fluid contacttimes and a greater prevalence of open-hole comple-

Ž .tions Yan et al., 1998 . This is true because evenshallow invasive damage may significantly reducethe productivity of an open-hole horizontal well incomparison with a cased and perforated vertical well.Underbalanced technology also has applications forvertical wells; therefore, both types of operationswill be addressed in this study.

The objective of this study is to develop an expertsystem that can screen rock parameters required todesign an effective underbalanced drilling program.Once it is concluded that a particular reservoir pre-sents a good candidate for UBD technology, thesystem goes through another screening procedure toselect optimal UBD fluids. These screening proce-dures assess formation damage potential, account for

lost circulation possibilities, and assure wellbore sta-bility.

1.2. Expert system background

An expert system is an intelligent computer pro-gram that uses knowledge and inference proceduresto emulate the decision-making ability of a humanexpert. Expert systems function well in their re-stricted domain. A proof of their success is theirwidespread applications in many areas such as busi-ness, medicine, science, and engineering. The basicconcept of a knowledge-based expert system consistsof supplying facts to the expert system, and receiving

Ž .expert advice in response MacAllister et al., 1993 .Internally, the expert system consists of two maincomponents: the knowledge base and the inferenceengine. The knowledge base contains the knowledgethat is used by the inference engine to draw conclu-sions. These conclusions are the expert system’sresponses to the user’s queries for expertise.

An expert system has a number of attractivefeatures. Its expertise is readily available on anysuitable computer hardware. It is an accumulation ofthe knowledge of multiple experts. This accumula-tion may greatly exceed the expertise of a singleexpert. The expert system can explicitly explain indetail the reasoning that led to a particular conclu-sion. A human expert may be unwilling to do this allthe time. This increases the confidence level of thedecision making process. The process of developingan expert system has an indirect benefit as well.Because the knowledge is explicitly represented inthe knowledge base instead of being implicit in theexpert’s mind, it can be examined for correctness,consistency, and completeness. The knowledge maythen have to be adjusted or re-examined. This is aprocess that improves the knowledge quality.

Expert systems are best suited for situations inwhich there is no efficient algorithm solution. Suchcases are called ill-structured problems, and reason-ing may offer the only hope of a good solution. Anill-structured problem would not lend itself well toan algorithm solution because there are so manypossibilities. Expert systems are, therefore, appropri-ate when the expert’s knowledge is largely heuristicand uncertain. The problem of selecting an underbal-anced drilling technique may still be regarded as an

( )A.A. Garrouch, H.M.S. LababidirJournal of Petroleum Science and Engineering 31 2001 23–39 25

ill-structured problem since it does not have a uniquesolution. Many of the reasoning tools for makingsuch a decision are still based on rules of thumb and

Ž .field experience Stone, 1995 .

2. System design

2.1. Expert system framework

The overall architecture of the expert system isdepicted in Figs. 1–3. The expert performs twoconsecutive tasks. The first one consists of analyzinggeomechanical and petrophysical data to determine

whether a particular well is a potential UBD candi-date or not. The decision tree for this task is pre-sented in Fig. 1. In screening wells for UBD, acontrolling factor is the minimum drilling density atwhich the wellbore integrity is maintained. This isverified using the stability module, discussed later inthe text. A stable rock is defined in our analysis as arock that can sustain a drilling fluid density less thanthe pore fluid density without collapse. Other well-bore and reservoir characteristics are also considered.These include the following.

Ž .a Assessing rock potential for formation damagesuch as clay swelling, and fines migration. This isaccomplished using the formation damage module.

Fig. 1. Decision tree for underbalanced candidate selection.


Ž .b Evaluating rock potential for lost circulation.This task is performed using the lost circulationmodule, discussed later in the text. In this module,we formulate a lost circulation index to assess thepotential of mud loss for a reservoir formation withknown petrographic properties.

Ž .c Assessing the well potential for stuck pipe.This opinion is generated from experience gainedwhile drilling previous wells in the area.

Ž .d Assessing rock potential for hard drilling.Hard drilling conditions are experienced whendrilling through dense formations with low perme-ability and low porosity. An increase in penetrationrates of up to 10-fold has been reported in these

Žformations when drilling underbalanced McGowen.and Medley, 2000 . The opinion about hard drilling

likelihood is also provided by the user as a valuebetween 0 and 1.

In case the UBD option was not selected, the useris left to decide the mud makeup that best fits theparticular rock properties, and minimizes serious

problems such as lost circulation and formation dam-age.

Once it has been determined that a particular wellis a potential UBD candidate, the expert continueswith the second task which consists of screening themost suitable UBD technique. Other wellbore andfluid specifics are then considered. These include:

1. The planned wellbore geometry, i.e., vertical orhorizontal trajectory.

2. The planned diameter of the wellbore.3. Evaluating the potential for penetrating water

producing zones.4. Assessing the potential for natural gas produc-

tion.5. Assessing the potential for sour gas production.6. Assessing the potential for downhole fire oc-

currence.

Once these questions are answered through inher-ent information from offset wells, mathematical

Fig. 2. Drilling fluid selection tree for UBD vertical wells.


modeling, and rule-based modules, the candidateUBD technique is selected according to the rulesderived from the decision-trees summarized in Figs.2 and 3.

2.2. Drilling fluids selection

In designing the decision trees shown in Figs. 2and 3, the following considerations were taken intoaccount. Drilling fluids are in general selected ac-cording to their ability to clean the well, preventdownhole fires, and ability to carry produced fluidsto the surface. For instance, stiff foams are preferredover unstiffened foams in our design. In foamdrilling, the efficiency of cuttings transport is ingeneral at its lowest close to the top of the bottom-hole assembly because of low annular-velocities.Since the effective viscosity of a stiff foam is higherthan that of an unstiffened foam, it is possible to drill

while having even lower annular velocities, and stillŽmaintain acceptable hole cleaning efficiency Russel,

.1993 . This makes stiff foams suitable for drillinglarge diameter holes, where the gas injection ratesrequired for other lightened drilling fluids may notbe economically feasible. This means that high-viscosity drilling fluids such as stiffened foams canbecome more attractive as the hole diameter in-creases. In our study, stiffened foams are the pre-ferred fluids for drilling holes with diameters of 17.5

Ž .in. and larger McLennan et al., 1997 with antici-pated water influx, but not significant gas influx.Stiff foams tend to be more stable than unstiffenedfoams. For this reason, they are more resistant to thegravity segregation that can lead to downhole com-

Žbustion in long, horizontal sections McLennan et.al., 1997 . Stiff foams can give better wellbore sta-

bility through poorly consolidated formations thanother lightened drilling fluids, including unstiffened

Fig. 3. Drilling fluid selection tree for UBD horizontal wells.


foams. Gas inflows can pose a problem for stiffenedfoams. Since stiff foams tend to be used at higherqualities, there is more chance for the foam structureto collapse downhole in the presence of gas influx.As a consequence, the annular velocity of the col-lapsed foam will be too low for efficient cuttingstransport. Under these circumstances, we take nitri-fied mud, or aerated mud as an alternative.

The use of dry air has been limited to verticalwellbores that are small in diameter with no sourgas, and with no downhole fires anticipated. Themain limitations of dry air drilling consist of waterinflow, downhole fires, and wellbore instability. Theflow of water into a well being drilled with dry aircan cause problems that are significant enough to

Ž .exclude dry air drilling McLennan et al., 1997 .Nitrogen is used for the same conditions suitable

for air. The major advantage over air is that mixturesof nitrogen and hydrocarbon gases are not flammable.This removes the potential of downhole fires. Circu-lating nitrogen lifts cuttings and liquid inflows thesame way that air does. The principal limitation onthe use of nitrogen for drilling operations is its cost.The following three paragraphs present various mod-ules used by the expert system in its reasoningprocess. These modules consist of routines for per-forming rock stability analysis, assessing rock im-pairment potential, and evaluating the potential forlost circulation.

2.3. Stability analysis

Wellbore stability analysis is a critical factor indetermining the appropriate drilling technique. Theneed for wellbore stability analysis during the plan-ning stage is due to the economic considerations, andthe rising use of highly deviated, extended-reach,and horizontal wells. Wellbore instability can resultin lost circulation in case rock fracturing occurs, andcaving and hole closure in case formation collapsetakes place. In some cases, hole instability can causestuck pipes and sometimes the loss of an open holesection.

The Mohr–Coulomb and the Drucker–Prager arethe two most commonly used failure criteria in ana-lyzing wellbore stability. The literature is rich inexamples that illustrate the use of these two criteria.

Ž .McLean and Addis 1990 presented a review of the

literature covering these techniques and provided anexplanation and comparison of the two criteria. It hasbeen shown that for general stress situations theMohr–Coulomb criterion underestimates rockstrength because it neglects the strengthening effectof the intermediate principal stress, while the

Ž .Drucker–Prager criterion outer circle predicts criti-cal mud weights that are less conservative than thosepredicted by the Mohr–Coulomb criterion, and that

Žare close to actual rock conditions McLean and.Addis, 1990 . In this study, we adopted an elastic

analytical approach for modeling the stress field forwells of different inclination angles in various stressregimes. The linear-elastic analysis is perhaps themost common approach due to its ease of applica-tion. On the other hand, intricate models suffer froman exhaustive list of input parameters, many ofwhich cannot be determined in practice. Appropriatemud densities for mechanically stable wells are de-termined using the Druker–Prager failure criteria. Asummary of the stress solution and coordinate sys-tem used in this study is provided in Appendix A.This module may be bypassed by the user, if hershechooses to provide the system with the collapse

Ž .density r .c

Formation pore pressure is a major factor affect-ing stability analysis, and the whole drilling opera-tion. If pore pressure is not properly evaluated, it canlead to drilling problems such as stuck pipe, holeinstability, lost circulation, blowouts and excessivecosts. In this study, the user provides the expertsystem with values of pore pressure as a function ofdepth for the formation of interest.

2.4. Assessing rock potential for impairment

Formation impairment is the term used to denotethe reduction in the permeability of the porousmedium being drilled. This impairment seems to

Žpose a greater problem for horizontal wells Bennion.et al., 1993 . This is true since the producing forma-

tion is exposed to the drilling fluid for longer periodsof time. Indeed, a greater distance is drilled throughthe pay zone at a lower penetration rates than whendrilling vertically. We have accounted for two typesof formation damage associated with drilling opera-tions. These are fines migration and clay swelling.Fines migration, especially under highly overbal-


anced conditions, occurs in the presence of a varietyof clay types such as montmorillonite, chlorite,kaolonite, and illite. Clay swelling takes place partic-ularly when drilling with fresh mud in the presenceof some clays such as montmorillonite, and vermi-culite. The ability of clays to cause permeabilityimpairment in a reservoir has been determined by

Ž .Vitthal et al. 1989 . It has been widely known that avariety of clays are sensitive to changes in the fluidpH and to the concentration of certain ions. Clayscan cause impairment by swelling, or by their releaseand migration as fines in the porous medium. Thepotential for permeability impairment in a reservoirdepends, therefore, on the clay’s morphology, itsvolume fraction, and the clay’s accessibility to invad-ing fluids. Such information on clays is obtainedfrom SEM photomicrographs, and thin-section analy-

Ž .sis Vitthal et al., 1989 .To determine the potential permeability impair-

ment caused by clay swelling and fines migration, itis assumed that the clay types, volume fractions, anddistribution are known. In this work, rules estab-

Ž .lished by Vitthal et al. 1989 for estimating potentialfor clay swelling and fines migration are used. Twodamage indices are particularly used to estimate thepotential reduction to rock permeability as a result of

Ž .clay swelling swelling index and fines migrationŽ .fines-migration index . The indices are assigned toeach clay on the basis of its distribution in the rock,

Ž .its origin authigenic or detrial , and its composition.To calculate the overall damage potential of the rock,each clay index is multiplied by its correspondingweight coefficient and its volume fraction. The over-all damage potential is the sum of these products.Tables 1 and 2 present a summary of the damageindices for various clay types, and their distribution

Table 1Ž .Damage indices for pure clays Vitthal et al., 1989

Clay component Swelling Fine-migrationŽ . Ž .index IS index IF

Montmorillonite 10 10Chlorite 1 6Kaolinite 1 6Illite 2 8Vermiculite 5 2

Table 2Ž .Distribution correction factors Vitthal et al., 1989

Clay distribution Swelling Fine-migrationŽ . Ž .factor CS factor CF

Pore lining 1.0 0.7Pore filling 1.0 1.0Pore bridging 0.5 1.0Discrete particles 0.0 0.9Thin lenses 0.5 0.0

correction factors, respectively. The overall swellingindex is, therefore, calculated as follows:

S s f IS CS . 1Ž .ÝI i i i

Ž .The swelling potential in percent is given by

SIP s100 . 2Ž .s 10

Similarly, the overall fines-migration index is givenby

F s f IF CF . 3Ž .ÝI i I i

Here f is the volume fraction of the particular clay.iŽ .The fines-migration potential in percent is given by

FIP s100 . 4Ž .F 10

The two indices P and P vary between 0% andF S

100% and are equivalent to probability values for theoccurrence of fines migration and clay swellingevents.

2.5. Assessing lost circulation potential

Lost circulation is defined as the partial or totalloss of drilling fluids to the formation being pene-trated. It occurs when natural, or induced formationopenings are large enough to allow mud to passthrough, and when the pressure applied by the mudcolumn exceeds formation pore pressure. The sever-ity of these losses varies from minor seepage lossesto a complete loss of returns. These losses can occurin unconsolidated or highly permeable formations, innaturally fractured formations, or formations withinduced fractures, and in cavernous formations.

To determine the lost circulation potential, weassume that the user has a quantitative estimates of

Ž . Ž .both permeability k and porosity f , and a quali-


tative petrographic description of the reservoir beingdrilled such as the presence of natural or inducedfractures and the presence of vugs. The presence of

Ž .fractures is assigned an index FI that takes thevalue of 10 for highly fractured formations, and thevalue of 1 for unfractured formations. Similarly, the

Ž .presence of vugs is assigned an index VI that takesthe value of 10 for vuggy rocks, and the value of 1for rocks that do not display any vugs. A numberbetween 1 and 10 for both indices may be selected,pending on the user judgment. The geological eventsthat resulted in the makeup of the rock petrographicproperties such as permeability, porosity, presence ofvugs and fractures are considered in this analysis tobe independent events. As a consequence, the lost

Ž .circulation index LCI , which is the resultant effectof these four variables, is defined in our study as theproduct of the likelihood of the independent occur-rence of these events. We therefore formulate thelost circulation index as follows:

k f FI VILCIs 5Ž .

4000 0.4 10 10

Here, k is in md, and f is a fraction. The LCI indexis calculated based on a maximum permeability valueof 4000 md encountered in oil and gas fields, and amaximum porosity value of 40%. Table 3 gives asummary of extreme cases studied with known lostcirculation outcomes. Based on these results, thefollowing guidelines are considered by the expertsystem:

LCIG5% Have severe lost circulationproblems.

LCI-0.1% No lost circulation problemsencountered.

0.1%FLCI-5% Have some loss. Use fuzzylogic to decide on lostcirculation severity. Thefollowing paragraph presentsthe methodology used forimplementing fuzzy logic intothe expert system.

2.6. Introducing fuzzy logic in the expert system

There are various ways to represent knowledgefor the expert system. Perhaps the most common

Table 3General lost circulation case studies

Ž . Ž .k md f FI VI LCI % Outcome

4000 0.4 10 10 100 severe loss4000 0.4 10 1 10 severe loss100 0.2 1 1 0.0125 no loss200 0.2 10 1 0.25 some loss200 0.3 1 1 0.0375 no loss

way is to form it into natural language expressions ofŽ .the type: IF condition hypothesis, antecedent ,

Ž .THEN conclusion consequent . This expression iscommonly referred to as the IF–THEN rule-basedform. It typically expresses an inference such that if

Žwe know a fact the condition, hypothesis, or an-.tecedent , then we can infer, or derive, another fact

Ž .called a conclusion consequent . Since the reasoningprocess is based on knowledge that can cover manyaspects of a problem, it may conclude several possi-ble recommendations in the same way human ex-perts would. Hence, the system should be able tohandle rules which state that an answer is possible,but not definitely true. Then, the multiple recommen-dations would be arranged in order of likelihoodbased on the certainty by which the condition-partsof the rules are satisfied. The inference engine car-ries out this process using a predefined confidencemode. The confidence mode defines the mechanismused in calculating the overall confidence of thecondition-part of the rule, inferring the confidence ofthe conclusion part, as well as combining the confi-dences of multiple conclusions.

Selecting the appropriate confidence mode is quiteimportant, and highly dependent on the nature ofthe domain of application. The simplest mode is

Ž .AYESrNOB or 0r1 system which is good forselecting among groups of items that can be defi-nitely identified. Majority of the systems reported inthe literature use statistical confidence modes based

Žon specifying a continuous range 0 to 1 or y100 to.100 . This offers more precision in the confidence

values. In this work, fuzzy logic is implemented asthe confidence mode. Expert systems using fuzzylogic as a confidence mode are termed as fuzzyexpert systems.

Ž .Zadeh 1965 suggested that set membership wasthe key to decision making when faced with uncer-


tainty. He introduced the notion of a fuzzy set whichprovided a convenient point of departure from theordinary crisp sets. For crisp sets, an element x inthe universe X is either a member of some crisp setA, or is not. This can be written as

1 x g Ax x s 6Ž . Ž .A ½ 0 xfA

Ž .In this notation x x gives the indication of anA

unambiguous membership of element x in set A.Fuzzy sets extended the notion of binary member-

ship to accommodate various degrees of membershipw xon the real continuous interval 0,1 , where the end-

points of 0 and 1 conform to no membership and fullmembership, respectively. This is similar to the indi-cator-function behavior with crisp sets, but withinfinite number of values in-between the end pointsrepresenting various degrees of membership for anelement x in a given set of the universe. Hence,fuzzy sets are always functions mathematically rep-

Ž . w x Ž .resented as m x g 0,1 . Here m x is the degreeA A

of membership of element x in the fuzzy set A. To

Ž . Ž . Ž .Fig. 4. Membership functions for linguistic variables: a lost circulation, b clay swelling, and fines migration, c hard drilling, costbenefit and stuck pipe potentials.


illustrate the difference between the crisp sets andfuzzy sets, consider the Aclay swellingB parameterŽ .Fig. 4b . In crisp notation, Aclay swellingB is eithersignificant, or insignificant. On the other hand, byfuzzifying this parameter, we are able to say that fora clay swelling potential of 15% for instance, clayswelling is insignificant with m s0.6, and at thePS

same time significant with m s0.4.PS

Our fuzzy expert system, therefore, takes the formof linguistic models containing a set of rules, formu-lated as IFrTHEN statements. It allows the use ofvariables whose values are specified as linguistic

Ž .terms e.g. high, medium, low, very low . For exam-ple, consider the statement:

IF the reservoir rock is stableAND the formation is susceptible for lost circula-tionAND the reservoir is highly susceptible for dam-ageTHEN UBD technique is most likely to be effec-tive

This rule might form part of a linguistic model of aUBD drilling technique. The IFrTHEN statementinvolves some linguistic variables such as ‘suscepti-ble for damage’, ‘susceptible for lost circulation’ and‘UBD technique’, and the linguistic terms ‘highly’and ‘most likely’. Variables are fuzzified by assign-

Ž .ing membership functions m x defining the confi-A

dence of the linguistic terms. Hence, the confidencewith which a particular parametric value belongs to agiven set is defined as a linguistic term to a certaindegree of confidence. Degrees of confidence arederived from membership functions which are de-fined for each linguistic variable. This presents agreat advantage because the rules would be firedgradually taking into account a wider range of thedecision variables, rather than suddenly switching ata threshold value. In effect, this would resolve theAgray areaB experienced by human experts in yesrnodecisions.

Fuzzified variables are stored as facts againstwhich condition-parts of the rules are matched. Whenthe IF part consists of more than one condition, thecombined confidence is calculated using the follow-ing formula:

C sC qC) 1yC ts1, . . . , I 7Ž . Ž .t ty1 i ty1

In this notation, C is the combined confidence upty1

to condition i, and C is the confidence of thei

current condition. This formula guarantees that thecombined confidence never exceeds a value of 1.0,and each positive confidence increases the finaloverall confidence. When a rule fires, the conclu-sions are inferred with confidence determined bymultiplying the combined IF confidence with thespecific condition confidence. After processing allthe rules in the knowledge base, the conclusionlinguistic variables are defuzzified and returned bythe system as final results and recommendations.

3. Discussion

3.1. System implementation

Ž .ReSolver MultiLogic, 1997 was used in devel-oping the expert system for selecting a candidate

ŽUBD technique. ReSolver previously known as.Exsys is a knowledge base development tool that

consists of various utilities for developing and main-taining the rules, and implementing inference mecha-nisms. The principal attractive feature of ReSolver isthat it supports fuzzy logic among other confidencemodes. The main inference mechanism adopted forthis work was backward chaining, in which goal-driven rules were automatically tested to see if therewere another rule in the knowledge base that wouldsupply the necessary information. The expert systemis menu-driven, all menus being context-dependent,only displaying options that are valid at that time.

The first stage in constructing the current expertsystem was knowledge acquisition in which domainknowledge was extracted, refined and structured sothat it could be used by the reasoning process. Inpractice, this was built up progressively through aseries of consultation sessions between the expertand the artificial intelligence specialist, the knowl-edge engineer. Extracted knowledge was then ar-

Ž .ranged in hierarchical tree forms as shown in Figs.1–3. The next step before converting the elicitedknowledge to the IF–THEN format was to formulatethe fuzzy model that would be used in the reasoningprocess. The decision variables were first selected,and the linguistic terms and membership functionsfor each of these variables were then formulated.


Membership functions were defined to assist theexpert system in making decisions when the decisionvariables fall in a Agray areaB. Fig. 4 displays mem-bership functions defined for variables such as lostcirculation, clay swelling, fines migration, harddrilling potentials, cost benefit and stuck pipe poten-

Ž .tial. The lost circulation index Fig. 4a is fuzzifiedusing two linguistic terms AsevereB and Anot severeB.The lost circulation index is calculated as discussedpreviously. For flexibility, the user is given theoption to bypass the lost circulation calculations andenter the likelihood of this event. As shown in Fig.4b, clay swelling and fines migration indices arefuzzified using the linguistic terms AsignificantB andAinsignificantB. Another type of membership func-tions is shown in Fig. 4c where the user is allowed touse hisrher own judgment in specifying the likeli-hood of hard drilling, cost benefit, or stuck pipe. Themembership functions for these variables are as-sumed to be linear in our analysis. Similar member-ship functions are defined for the potentials of fire,water and gas influx, and sour gas production. Thesevariables are used in deciding the type of drillingfluid. The rock stability variable is allowed crispŽ .YesrNo values. If the ratio of pore fluid density tothe minimum drilling fluid density, required to pre-vent collapse, is greater than 1, the rock is consid-ered stable; otherwise the rock is considered unsta-ble. The minimum fluid density to prevent collapseis calculated using the stability module, detailed inAppendix A.

In evaluating the feasibility of candidate drillingtechniques, a controlling factor is the range of antici-pated borehole pressures which will be required foreach zone to be drilled. The upper limit for underbal-anced conditions is the pore pressure. The lowerlimit is generally regulated by the lowest pressure atwhich wellbore stability is ensured. When the finaloutcome consists of a set of drilling fluids ratherthan a single one, these drilling fluids options areeven screened further by the expert system to assurethat the UBD fluid density is adequate within thepressure window. If the expert system still recom-mends more than a single drilling fluid option, aconfidence level is given with each option. The useris left to make hisrher own decision based on theconfidence levels and other factors such as economicincentives and environmental restrictions.

3.2. System testing

We have tested the expert system with a numberof hypothetical cases. These cases were generated byexploring the combinations of all branches of thedecision-trees shown in Figs. 1–3. The expert systemresponses were systematically consistent with thefinal decisions shown in Fig. 1, regarding UBDrno-UBD options. In case UBD options were selected,the expert system resumed the reasoning process toconclude the drilling fluid options following thepaths of the decision trees shown in Figs. 2 and 3.Table 4 displays the input data and the expert-system

Table 4Hypothetical cases for testing the first flow chart of the expert system

Cases r Lost circulation Reservoir Stuck Hard Cost UBD candidate confidencecŽ . Ž .lbmrgal index damage pipe drilling benefit level %

1 1 6% 0.50 0.50 0.50 0.50 63% recommended25% not recommended

2 1 6% 0.25 – – 0.25 19% recommended81% not recommended

3 1 6% 0.75 – – – 100% recommended4 1 0.09% – 0.10 0.00 – 100% not recommended5 1 0.09% – 0.50 0.90 1 75% recommended6 1 0.09% – 0.90 – 1 100% recommended7 1 0.09% – 0.00 0.10 – 100% not recommended8 1 0.09% – 0.00 0.50 1 50% recommended

50% not recommended9 1 0.09% – 0.00 0.90 1 100% recommended


results pertaining to cases that focused on testing thefirst flow-chart shown in Fig. 1, for formations withnormal pore pressure. The system was provided witha mix of firm and fuzzy data to decide whether todrill underbalanced, or overbalanced. The systemresults came in the form of statements to eitherrecommend UBD, or not recommend it, or both.Each statement is associated with a confidence levelthat reflects the uncertainty inherent in the input

Ž .variables. For case 1 Table 4 , for instance, the lostcirculation index was 6% implying severe lost circu-lation potential. On the other hand, the reservoirdamage, stuck pipe, hard drilling, and cost benefitlikelihoods were all fixed at 50%. For these condi-tions, the system favored the UBD option with amarginal confidence level of 63% while yielding aconfidence level for not recommending UBD of25%.

It is important to clarify the meaning of theconfidence levels and how they may be used in

analyzing the outcomes of the expert system. Deci-sions made by the expert system are the results of aninference process. During this process uncertaintiesassociated with variables and rules are accumulated,

Ž .using Eq. 7 , to yield the final confidence assignedto the reasoning outcome. Hence, a confidence levelof 63% means that the ambiguity and vagueness inderiving this decision is 37%. Decisions in our anal-ysis are ranked according to their confidence level;i.e., the system reasoning leads to the best decision,second best decision, and so forth. Hence, confi-dence levels are specific to the decisions and do notadd up to 100%.

For those cases that favored the UBD options,additional parameters were entered to decide on thedrilling fluid type. These included the likelihood ofwater influx, gas influx, sour gas production, firesparks, and the borehole diameter. As shown inTable 5, the presence of more than 10% gas influxlikelihood tends to disqualify the stiffened foam

Table 5Hypothetical vertical well cases

Ž .Cases Hole diameter in. Water influx Gas influx H S influx Fire potential UBD techniques,2Ž .confidence level %

1 5.875 0.5 0.50 0.50 0.50 Stiff foam, 10%Aerated mud, 10%Nitrified mud, 62.4%Nitrogen, 40%

2 5.875 0.5 0.5 0.0 0.1 Nitrified mud, 64%Nitrogen, 40%Aerated mud, 19%Dry air, 10%Mist, 10%Stiff foam, 10%

3 5.875 0.0 0.5 1.0 – Nitrogen, 84%Nitrified mud, 84%

4 – – – – – UBD not recommended5 5.875 0.0 0.0 0.00 0.00 Dry air, 100%

Mist, 100%Aerated mud, 100%

6 16 0.5 0.1 0.1 0.1 Aerated mud, 82%Stiff foam, 79%Dry air, 15%Mist, 15%

7 – – – – – UBD not recommended8 16 1 0.0 – – Aerated mud, 83%

Stiff foam, 83%9 16 0.0 1 – – Nitrified mud, 83%

Nitrogen, 30%


option. On the other hand, the presence of sour gasproduction adds more weight to the nitrified mudoption. The smaller the value of fire potential proba-bility, the more weight was accorded to the dry airalternative. These conclusions are in agreement withengineering practices.

To test the system with horizontal well cases, weprovided firm data sets that yielded the UBD option.Table 6 shows the system outcomes, for each casewhich recommended UBD, in terms of the appropri-ate drilling fluids ranked according to their confi-dence levels. To test Agray areaB cases, we variedthe water and gas influx potentials between 0 and 1.When the input data was approximately firm, theexpert-system decision was also firm suggesting aset of UBD fluids with a 100% confidence level.

Ž .This is true for case 7 Table 6 . Neither the lowŽ .gas-influx probability of 1% case 4 in Table 6 , norŽ .its high probability of 90% case 5 in Table 6

altered the confidence level of the expert-systemdecision. However, the high gas influx potential of

Ž .90% case 5, Table 6 has eliminated the stiff foamoption. This is consistent with engineering practicesince gas abundance tends to break the stiffenedfoam. When water and gas influx potentials were

Ž .equally varied such as in cases 1, 2, and 6 Table 6 ,

the expert-system decision came in the form of adistribution of UBD techniques options with varyingconfidence levels. For a gas-influx potential of 50%,the stiff-foam option had the smallest confidencelevel, making it the least likely to be adopted as aUBD fluid for these cases.

It is important to note that the term AmudB in thisexpert-system terminology stands for a given Adrill-ing fluidB. Therefore, if the final expert-system rec-ommendation is to use a nitrified mud for instance, itis left to the operator to decide the AmudB systemthat fits the pore pressure conditions, and gas injec-tion rates for efficient hole cleaning. For highlydepleted formations, the term Anitrified mudB maybe equivalent to Anitrified brineB.

3.3. Field cases

The expert performance is tested here with acouple of field cases. The first one is the drilling of a1067 ft horizontal section in the R3 sandstone of awell that is 11,765 ft deep in the Oficina formation,

Žin Acema-200 field in Eastern Venezuela Vieira et.al., 1999 . Even though the formation was highly

depleted with 4.0 ppg pore fluid density, it contained

Table 6Hypothetical horizontal wells, and field cases for testing the expert system

Cases Pore-fluid Collapse Lost Reservoir Hole Water Gas Extended Drilling Drilling fluid,Ž .density density circulation damage diameter influx influx reach option confidence level %

Ž . Ž . Ž .ppg ppg index in.

1 7.0 2.1 8% 1 5.900 0.5 0.5 1 UBD 1. Aerated mud, 19%2. Stiff foam, 19%3. Nitrified mud, 64%

2 4.0 1.0 8% 1 5.875 0.5 0.5 1 UBD 1. Aerated mud, 19%2. Stiff foam, 19%3. Nitrified mud, 64%

3 4.0 1.0 8% 1 5.875 0 0.5 1 UBD 1. Aerated mud, 20%2. Stiff foam, 20%3. Nitrified mud, 80%

4 4.0 1.0 8% 1 5.875 0 0.01 1 UBD 1. Aerated mud, 100%2. Stiff foam, 100%

5 4.0 1.0 8% 1 5.875 0 0.9 1 UBD 1. Nitrified mud, 100%6 4.0 1.0 8% 1 16.50 0.5 0.5 1 UBD 1. Aerated mud, 34%

2. Nitrified mud, 34%7 12.0 7.0 8% 1 5.875 0 1 0 UBD 1. Nitrified mud, 100%Ž .8 R3 4.0 1.4 5% 1 5.875 1 1 1 UBD 1. Nitrified mud, 100%

9 ARUN 1.8 1.2 11% 1 6.250 1 1 1 UBD 1. Nitrified mud, 100%


large volumes of recoverable oil. Productivity ofvertical and directional wells in this reservoir waslow. Pressure restoration tests showed skin factorsbetween 60 and 100, implying severe formationdamage. A comprehensive geomechanical study wasperformed to estimate the principal stresses magni-tude and directions, compressive strength, Poisson’sratio and the Mohr–Coulomb failure envelope pa-rameters. A detailed list of the geomechanical data isprovided in Table 7. A horizontal well was decidedto be drilled in a thin sandstone layer, with anazimuth angle with respect to the maximum horizon-tal stress axis of 2708, and with an azimuth anglewith respect to north of 908. Based on this data, thestability module predicted a collapse density of 1.4ppg. The expert system was provided with this dataŽ .case 8, Table 6 and recommended the use ofnitrified mud, with a confidence level of 100%. Thishorizontal section was ultimately drilled with nitri-fied mud with a density of 4.3 ppg. No wellboreinstability problems were reported. The applicationof this near-balanced drilling technique increasedconsiderably the rate of penetration and the effectivebit life. An average rate of penetration of 20 ftrhwas attained while drilling this horizontal section.This is seven times higher than previous penetrationrates experienced while drilling horizontal sectionsin the same sand using conventional drilling tech-

Ž .niques Vieira et al., 1999 . Although the reservoirwas 8 ft thick, a 5 7r8-in. hole was maintainedinside the proposed window of this long horizontalsection without leaving the sand. Only two polycrys-talline diamond bits were used to drill the wholesection in a sand known for its high abrasivity andhigh unconfined compressive strength.

The second field case consists of drilling a 1000-fthorizontal section in a fractured and vuggy limestonereservoir at a depth of 10,000 ft in the Arun field in

Ž .Indonesia Frink et al., 1999 , with an azimuth angle

with respect to the maximum horizontal stress axisof 908, and with an azimuth angle with respect tonorth of 358. The Arun field has been producing aslightly sour gasrcondensate blend since 1978 witha current pore pressure of 930 psi corresponding toan equivalent density of 1.8 ppg. In addition, theproduced fluids contain 15% CO , and water. Using2

an average porosity value of 25%, an average perme-ability value of 700 md for this field which is knownto be highly fractured and vuggy, we obtained a lostcirculation index value of approximately 11% whichimplied severe lost circulation. Indeed, conventionaloverbalanced drilling in this reservoir resulted inlarge fluid losses, increased risk of pipe stickingcaused by inefficient hole cleaning, and the inabilityto achieve desired horizontal length. Significant for-mation damage has therefore resulted as a conse-quence of mud invasion. This effect reduced theproductivity of these wells drilled overbalanced.Table 7 presents the geomechanical data for thisfield. Based on this data, the stability module re-sulted in a collapse density of 1.2 ppg. Presented

Ž .with this information case 9, Table 6 , the expertsystem recommended the use of Anitrified mudB witha confidence level of 100%. In agreement with theexpert-system decision, the operator considered in-jecting nitrified brine, or gasified brine. Since naturalgas was produced from the reservoir itself, it wasused instead because of its abundance only. Theinjection of gasified brine resulted in a bottom holepressure of 925 psi which is a little less than the porepressure value of 930 psi. Due to this underbalancedcondition, lost circulation was not detected, only onetrip was needed compared to eight trips needed inthe past, and hole cleaning was adequate since nostuck pipe situations were reported. After cleaningthe well, a stabilized gas production rate of 42MMscfrday was obtained. This rate was twice thepredicted rate. This well also yielded a condensation

Table 7Geomechanical properties for field cases tested in this study

Ž . Ž .Formation S psi f deg y s s s Depth Tensile Poreo v H hŽ . Ž . Ž . Ž .psirft psirft psirft ft strength pressure

Ž . Ž .psi psi

R3 sandstone 9200 32.0 0.23 1.0 0.86 0.70 11,765 340 2420Arun limestone 2050 43.5 0.16 1.0 0.89 0.72 10,000 450 936


rate of 57 bblsrMMscf of gas which was the highestrate reported in this field. This is probably due to theelimination of formation damage caused by the un-derbalanced conditions.

4. Summary

This paper presents the development of an expertsystem for deciding whether to drill underbalancedor overbalanced, and for making a preliminary selec-tion of adequate UBD fluids. The expert systemscreens rock parameters required to design an effec-tive underbalanced or overbalanced drilling program.Once it is concluded that a particular reservoir pre-sents a good candidate for underbalanced drilling

Ž .technology UBD , a reasoning procedure is thenfollowed to select optimal UBD techniques. Thisreasoning procedure is put in an interactive advisorsystem that accounts for rock formation damage, andwellbore stability. We developed a lost circulationindex that was adopted by the expert system to studythe rock potential for fluid losses. A linear-elasticconstitutive model was used in conjunction with theDrucker–Prager failure criterion to determine thedrilling fluid density that guaranteed wellbore stabil-ity and prevented collapse.

The expert system features the use of fuzzy logicwhich is implemented to handle the concept of par-tial truth associated with some of the rules. Theexpert system decision for these cases comes as adrilling fluid option associated with a confidencelevel. As a consequence, this expert system enablesthe user to decide on an infinite number of cases thatmay be ambiguous for a human expert.

NomenclatureCS swelling factorCF fine-migration factorCt combined confidenceFI fracture indexFI overall fines-migration indexh takes on values of 1 and 0 when in under-

balanced and overbalanced, respectivelyŽassuming the development of an imperme-

.able mud cakeIF fines-migration index

IS clay-swelling indexk rock permeabilityLCI lost circulation indexP formation pore pressurePS swelling potentialPF fines-migration potentialSI overall swelling indexSO rock cohesive strengthVI vugs index

Greek Lettersa the angle between s and the projection ofH

the borehole axis onto the horizontal planeaO Biot porelastic constantb the angle between the borehole axis and the

vertical directionDP Žexcess fluid pressure in the borehole i.e.,

mud pressure less pore pressure in the for-.mation

f rock porosityŽ .m xA membership function of element x in a

fuzzy set A.u polar angle in the borehole cylindrical coor-

dinate systemf friction anglesH effective major horizontal principal stresssh effective minor horizontal principal stresss , s , s X , s X , s , s Xr u z u z ru r z stress tensor in the bore-

hole cylindrical coordinate systemsv effective vertical stresss , s , s , s , s , sx y z x y x z y z stress tensor in the bore-

hole cartesian coordinate systems1 effective maximum principal stress in the

borehole cylindrical coordinate systems2 effective intermediate principal stress in the

borehole cylindrical coordinate systems3 effective minimum principal stress in the

borehole cylindrical coordinate systemrc collapse densityy Poisson’s ratio

Ž .x XA membership of element x in a crisp set A

Acknowledgements

The authors wish to thank Kuwait University forfunding project EP 03r00.


Appendix A. Stress solution

For an arbitrarily oriented borehole as shown inFig. 5, the mapping of the stress tensor from theglobal in situ coordinate system into the boreholecoordinate system is given by solving the followingsystem of six equations for the six unknowns s , s ,x y

Ž .s , t , t , and t Zhou et al., 1996 :z x y x z y z

s 2 2 2 2 2° ¶x sin b cos bcos a cos b sin a° ¶s 2 2y 0 sin a cos a

2 2 2 2 2s cos b sin bcos a sin b sin az~ • ~ •st 0 ysinacosa sinb sinacosa sinby z

2 2ysinbcosb sinbcosbcos a sinbcosb sin atx z ¢ ß¢ ßt 0 ysinacosacosb sinacosacosbx y

=

sÕ

A-1s Ž .H½ 5sh

In this notation, s , s , and s are the effectivev H h

vertical stress, effective major horizontal principalstress, and effective minor horizontal principal stress,respectively. The solution of the above system isused to estimate the stress field at the wall of theborehold as follows:

s sDP A-2Ž .r

s ss qs y2 s ys cos2uy4t sin2uŽ .u x y x y x y

h 1y2yŽ .yDP 1y A-3Ž .

1yy

s Xss y2y s ys cos2uy4yt sin2uŽ .z z x y x y

h 1y2y DPŽ .q A-4Ž .

1yy

t Xs2 yt sinuqt cosu A-5Ž .Ž .u z x z y z

t s0 A-6Ž .ru

t Xs0 A-7Ž .r z

Based on the above equations, the effective principalŽstresses on the borehole wall which are orthogonal

Fig. 5. Borehole orientation and coordinate system used in thisstudy.

.to each other in the local borehold coordinate sys-tem can be expressed by

1 1 2 2X X X(s s s qs q s ys q4t A-8Ž . Ž . Ž .1 u z u z u z2 2

1 1 2 2X X X(s s s qs y s ys q4t A-9Ž . Ž . Ž .2 u z u z u z2 2

s ss . A-10Ž .3 r

Now that the stresses at the wellbore wall have beenestimated, it is necessary to use them with somefailure criterion to determine whether the wellborewill collapse or not. The Drucker–Prager criterion isof the form:

2 2 2s ys q s ys q s ysŽ . Ž . Ž .1 2 2 3 3 1

2F AqB s qs qs , A-11Ž . Ž .1 2 3

where A and B are a combination of rock propertiesand pore pressure, and are given by

3 S ya P tanfŽ .o oAs A-12Ž .

2(9q12tan f

tanfBs A-13Ž .

2(9q12tan f

In this notation, a is the Biot poroelastic con-o

stant and P is the pore pressure. Collapse failure


Ž .will not occur when Eq. A-11 is satisfied. Bycomputing the stresses at points around the circum-

Ž . Ž .ference of the wellbore using Eqs. A-1 – A-10 ,Žand comparing them with the failure criterion Eq.

Ž .. Ž .A-11 , we determine the drilling fluid density rc

at which collapse failure is initiated. The collapsedensity is obtained by converting the hydrostaticcolumn from the DP term to a density. The angle u

is varied through 3608 to determine the most criticalstress point around the circumference of the wellborewall.

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Development of an expert system for underbalanced drilling using fuzzy logic