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Energy 34 (2009) 1097–1112

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Energy

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Modeling the time and cost to drill an offshore well

Mark J. Kaiser*

Center for Energy Studies, Louisiana State University, Energy Coast & Environment Building, Nicholson Extension Drive, Baton Rouge, LA 70803, USA

a r t i c l e i n f o

Article history:Received 11 April 2007Received in revised form24 January 2009Accepted 19 February 2009Available online 22 May 2009

Keywords:Cost estimationBenchmark performanceDrilling modelsFunctional relations

* Tel.: þ1 225 578 4554; fax: þ1 225 578 4541.E-mail address: mkaiser@lsu.edu

0360-5442/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.energy.2009.02.017

a b s t r a c t

The objective in drilling a hydrocarbon well is to make hole as quickly as possible subject to the tech-nological, operational, quality, and safety constraints associated with the process. These objectives arefrequently conflicting and depend on factors that are subject to significant private and market uncer-tainty. There is no way to identify all of the relevant characteristics of drilling operations, but through useof statistical analysis and empirical modeling, it is possible to develop relations that characterize andbenchmark drilling performance under a suitable set of assumptions. The purpose of this paper is todevelop the conceptual framework to model the time and cost to drill an offshore well and to illustratethe methodology on a test set of wells in the Gulf of Mexico. The physical characteristics of the wellboreand operational aspects of drilling, including variables such as the drilled interval, horizontal displace-ment, aspect ratio, number of casing strings, and mud weight, serve as the primary descriptive factors inthe functional relations constructed.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

To find and produce oil and gas reservoirs, holes must be drilledinto the Earth. A hole made by a drilling bit is called a well, and theprimary objective of making a well is to produce undergroundfluids such as oil and natural gas, and to study properties of geologicformations. Drilling operations are complex and labor intensive,and although many activities continue to be automated, most jobsare still performed manually, 24 h a day, seven days a week, in allweather conditions. The work is strenuous and hard, and per-formed in traditional 12 h shifts on a 2-week on/off rotation, andonly extreme weather or mechanical failure will shut downoperations.

Offshore drilling requires a floating or bottom-supported rig toconduct operations. Although offshore rigs and facilities are func-tionally similar to land operations, the remote locations, offshoreenvironment, and peculiar logistical requirements mean thatoffshore drilling costs will be higher than onshore drilling forsimilar depth wells. For example, in 2006, the average offshore welldrilled in the U.S. was about twice as deep and four times as costlyas the average onshore well [1]. Large capital expenditures arerequired to drill an offshore well, with rates to rent the drilling rigcosting anywhere from $50,000 to $500,000 per day, depending onthe rig type, water depth, market conditions and offshore basin.When the cost of labor, fuel, materials and equipment are factored

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in, the final cost to drill and equip a well is about twice the rigdayrate. A well that takes 30 days to drill with a $200,000/dayjackup, for instance, would be expected to cost about $12 million tocomplete.

Although the physics of drilling is the same everywhere in theworld, wells vary widely in complexity and type. To evaluate thedifferences that exist in drilling a well and to compare performance,it is useful to establish general functional relations of drillingtime and cost. To understand performance, it is necessary to isolatethe factors of drilling and to quantify how these factors influencethe operation. Historically, much of the work on assessing drillingperformance has focused on the identification and elimination ofnon-productive time, such as freeing stuck pipe, fishing, repairingequipment, and waiting on weather. Cost estimation and perfor-mance evaluation are not usually made outside a small subset ofwellbores because of the nature of the processes involved anduncertain operating environment, the pervasive impact of tech-nology differentials, and the many unobservable characteristicsthat influence operations.

Two methods are commonly used to benchmark drillingperformance. The first method is based on experimental design andcontrolled field studies. Typically, one or more parameters of dril-ling are varied to examine the impact of the variable on outputmeasures, such as the rate of penetration or cost per foot drilled. Asignificant amount of experimental work has been done to studyfactor effects on drilling time and cost, and a large number oftechnical studies has been performed by industry (e.g., see Ref. [2]and the references therein). The second method to study factoreffects is based on an aggregate assessment of drilling data. In this

2 Oil and gas companies are typically organized according to function, such asdrilling engineering, formation evaluation, reservoir engineering, etc. The geologicgroup usually recommends the wildcat well location, while the reservoir grouprecommends the development well locations. The drilling engineering group

M.J. Kaiser / Energy 34 (2009) 1097–11121098

method, drilling data is sampled across many different operatorsand wells, and relationships that correlate drilling parameters areestablished through empirical modeling. Both approaches havetheir advantages and disadvantages, advocates and proponents.

The purpose of this paper is to develop the analytic frameworkto construct empirical models of drilling time and cost. We providebackground material in x2–4 to orient the reader on the funda-mentals of drilling – how wells are planned, the equipment used inthe operation, the basic mechanics of making hole, and contractfundamentals – and to provide the context in which the drillingmodels are constructed. The background material is essential toprovide motivation for the model and its development. In x5,a description of the factors that influence drilling is presented,followed in x6 by the development of the cost estimation meth-odology and model formulation. In x7, drilling time and costregression models are constructed for a test set of offshore wellsdrilled in the Gulf of Mexico between 2002 and 2003. Model resultsare presented and statistical relationships derived to illustrate themethodology. Brief conclusions complete the paper. In Appendix A,a glossary of common drilling problems is provided, and inAppendix B, additional material on drilling contracts are presented.

2. Background

2.1. Purpose of drilling

Holes are drilled in the ground to search for oil and gas, toacquire information about the geologic formation, and to develophydrocarbon reservoirs. A hole made by a drilling bit is called a well.A company acquires a lease or contract area based on geological andgeophysical data and conceptual plays, and invests in additionaldata and manpower to refine their knowledge of the region. If theresults of analysis are encouraging, exploratory drilling may result.A team of geologists, geophysicists, and engineers selects the wellsite and the drilling target based on magnetic, gravity, and seismicsurveys. A well plan and a cost estimate are performed, typicallyfrom the drilling engineer, who has the responsibility for gatheringthe technical experts, letting contract, and ensuring the success ofthe operation. The well is then drilled.

Substantial resources of money and time are invested to identifythe geological target and the prognosis is confirmed or refuted onthe basis of the results of the drilled, logged,1 and tested well.During drilling, evaluation is made from the cuttings and reservoirfluids that appear at the surface and from the drilling and coringindicators. A DrillStem Test in which the pressure response of thereservoir is recorded during short production periods may be per-formed to gather additional information on the reservoir. Theresults from exploratory drilling are evaluated and may result ineither an appraisal well program or an abandonment of the pros-pect. If hydrocarbons are detected, the company will typicallyconfirm and delineate the field through additional appraisaldrilling and well testing; if the field is judged to be economic, thecompany will develop and produce the reserves in accord with itsparticular risk-reward strategy [3].

2.2. Drilling operations are complex and dynamic

The objective in drilling is to make hole as quickly as possiblesubject to the technological, operational, quality, and safetyconstraints of the process. These objectives are frequently

1 In wireline logging, a logging crew inserts a recording device into the bottom ofthe hole, and draws it upward, measuring the electrical, radioactive, and sonicproperties of the formation rocks and their fluids.

conflicting and themselves depend upon several factors (Fig. 1). Theformation geology at the site and the location of the target reservoiris a primary factor. Geologic formations vary across the world, andindeed, within the same producing basin. Hard, abrasive, andheterogeneous formations typically have low penetration rates,frequent drill string failures, and significant deviation from theplanned trajectory. Deep reservoirs are usually characterized bylow permeability, high temperature and pressure, complex fracturegrowth and stress regimes, and contaminants such as CO2 andhydrogen sulfide, which increase the complexity of the well andrequiring operators to deal with a number of issues concerningsafety and operational performance.

The drilling methods used to make hole depend upon thegeologic formation and the technology applied, the amount ofinformation known about the formation, the experience and pref-erences of the operator, available equipment, and the drillingcontractor’s experience and execution [4]. Well characteristics arespecified by the drilling plan, the location of the target reservoir,and the conditions encountered during drilling. Site characteristicssuch as water depth, operator experience in the region, and envi-ronmental conditions influence the operator’s decision regardingthe selection of the contract and rig type, which in turn, influenceperformance metrics. Exogenous events such as stuck pipe, adverseweather, and mechanical failure cannot be predicted but can havea significant impact on the time and cost of drilling.

2.3. Well construction process

The well construction process consists of four stages: design,planning, execution, and analysis. The design and planning phasesrepresent the foundation of well construction, and is usually initi-ated through the preparation of a drilling proposal by geologistsand reservoir engineers.2 The proposal provides the information bywhich the well will be designed and the drilling program prepared,and includes project team selection; well design; health, safety, andenvironmental quality; tendering, contracting, and procurement;finance and administration; operations planning; and logistics.

The drilling engineer prepares the drilling prognosis, and all theinformation that is required to safely and efficiently drill the well,including the well location and water depth, the vertical depth andtotal measured depth, the depth of the expected reservoir sands,downhole reservoir pressures, expected hydrocarbons, the pres-ence of hydrogen sulfide or CO2, evaluation needs (logging, sidewall coring, drillstem tests), special drilling problems, final dispo-sition of the well, and future sidetracking.

The well is then drilled according to the drilling plan, usuallyunder a dayrate contract, although turnkey contracts – where thedrilling contractor drills the well for a ‘‘lump-sum’’ (fixed) price –are also employed [5]. Since the drilling budget representsa significant part of the capital expenditures for a field, usuallybetween 40 and 60% of total development cost, drilling operationsare carefully planned and closely watched, and operators maintainmeticulous and detailed records of each well drilled. In order tobetter understand the drilling operations – what worked and whatdidn’t, and why – a post-mortem analysis may be performed.

makes the preliminary well designs and cost estimates, and if the decision is madeto drill the well, the drilling group then prepares a more detailed well design andwrites the bid specification. The drilling engineer recommends the procedures todrill the well, and in many cases, the original well plan will be modified as drillingprogresses to maximize the efficiency of cutting operations.

Drillingtime and cost

Environmentalconditions

Marketconditions

Wellcharacteristics

Formationevaluation

Sitecharacteristics

Drillingcharacteristics

Geologicconditions

Water depth; distanceto shore; region/country;

soil, wave, currentconditions

Bit type, size. mudweight; casing scheme;underbalanced mode

Formation type,complexity, sequence,type; special problems

Expected and actualweather; wave, current,

eddies; frequency, durationand occurrence of

storm alerts; extreme

Supply and demand of drillingrigs; marine equipment;

operator preferences; termsof the contract

Coring; logging;testing time

Well type; total depth; verticalinterval; horizontal displacement; well geometry; well complexity;

number of casing strings; maximum angle; formation pressure;

well temperature

ExogeneouseventsProblem wells;

mechanical failure;force majeure

Fig. 1. The time and cost to drill a well is influenced by a number of variables.

M.J. Kaiser / Energy 34 (2009) 1097–1112 1099

2.4. Cost estimation

Cost estimation is performed specific to the drilling prognosis.The usual procedure is to decompose costs into general categoriesof site preparation, mobilization and rigging up, drilling, trippingoperations, formation evaluation and surveys, casing placement,well completion, and contingencies. Typically, several categoriesare specified, and the drilling engineer itemizes the expected timeand cost per category [6–9]. Each cost component is identified andcategorized into minor cost elements, and the percentage contri-bution of the total cost is computed to identify the key cost drivers.To improve the range of the estimate, the uncertainty of the costdrivers is frequently quantified [10]. This forms the framework ofthe well budget which is then sent to management for an Autho-rization for Expenditure (AFE) to drill the well.

In an AFE, intangible drilling and equipment costs, completioncosts if the well is successful, and plugging and abandonment costsif the well is dry, are listed. The AFE typically includes estimates forthe cost of the drilling rig, mud, logging, testing, cementing, casing,well stimulation, prime movers, pumps, tubing, separator, andother services and equipment required [11,12]. In joint operations,the operating agreement typically requires that the operator getapproval from the non-operators for drilling expenditures. AFEsinform non-operators as to the drilling plans, providing cost esti-mates, and obtaining necessary approvals.

2.5. Cost components

There are a number of ways in which drilling cost can beclassified, based on functional category, time or depth dependence,or variable or fixed cost classification. Cost components usually fallacross more than one category and allocation schemes arecompany-specific.

The primary time-dependent costs include the time required todrill a well, which is influenced by the well plan (e.g., intervaldepths, number of casing strings, formation evaluation require-ments), rate of penetration, and problems encountered. Rig costsand other services such as support vessels, aircraft, mud logging,and rental tools, are also time-sensitive. The costs for drilling fluids,bits, cement, logging and other consumables have a time-drivencomponent, but are mostly influenced by well depth and downholeconditions. Some consumable items such as the wellhead andcasing will be a fixed cost. Mobilization, demobilization, andpreparation are fixed costs determined by the location of the siteand the rig release location.

Functional categories may also be employed to classify costs,with groupings that include pre-spud, casing and cementing,drilling rotating cost, drilling non-rotating cost, and trouble. Thedrilling rotating cost category includes all the costs incurred whilethe drill bit is rotating such as bit and mud cost. Drilling non-rotating costs include tripping, well control, waiting, supervision,and maintenance. Drilling problems are grouped together astrouble and include stuck pipe, fish, lost circulation, hole stability,casing and cement problems. In Appendix A, a glossary of commondrilling problems is provided.

Specialized services such as perforation and cementing arecharged on the basis of a service contract, which involves both timeand volume factors. Helicopter service will have an aircraft leaserate per month, a flying charge per hour, and a fixed cost formobilization/demobilization, or may be contracted on an annualbasis. Logging operations will typically combine fixed costs formobilization/demobilization, time-dependent costs for tool rentals,and time-independent costs for tool charges.

The proportion of cost in each category will vary from well towell, but typically, the time-dependent proportion of total costvaries between 40 and 70% of the total cost. For offshore wells with

M.J. Kaiser / Energy 34 (2009) 1097–11121100

high rig and transportation costs, the proportion is toward theupper range, while for onshore wells with relatively low rig day-rates but high time-independent costs, the time-dependent vari-able cost will be toward the lower range. In the functionalcategorization, rotating drilling costs and casing/cementing areusually the dominant costs overall increasing with drilling intervaland water depth.

3. Mobile offshore drilling units

Offshore oil production began in 1947 when Kerr McGee OilIndustries drilled the first producing well beyond the sight of landin 18 feet of water, ten miles from the Louisiana coastline [13]. Some25 years later, offshore wells were being drilled in 1000 feet waterdepth, while today, drilling occurs in water depth over 10,000 feetdeep [14]. Offshore drilling operations are significantly moreexpensive, uncertain, and risky than onshore due to the harsh andunpredictable operating environment.

Oil and gas reservoirs are found in a wide variety of geographicaland geological environments, and the rig which is used to drilla particular well must have the capability to drill in the environ-ment in which it is to be used to the depth required to reach thereservoir. Exploratory drilling is most often performed froma mobile offshore drilling unit (MODU) such as a jackup, semi-submersible, or drillship. In the Gulf of Mexico, all of these types areemployed.

In shallow bays, marshes, and other protected waters whereweather conditions are not harsh, drilling rigs are mounted on steelbarges that are pushed into place and flooded to sit on the bottomof the water. These rigs are known as the ‘‘inland’’ rig fleet (orswamp barges) and typically work in 8–20 feet of water.Submersibles consist of a drilling platform mounted on verticalcolumns attached to pontoons. When water is pumped into thelower hull, the rig submerges and rests on the seabed when drilling,and when emptied, allow the rig to float and be tugged from onelocation to another. Swamp barges operate in swamp and marshareas in Louisiana, Nigeria and Indonesia.

A jackup rig is a barge with legs that can be lowered or raised(Fig. 2). Jackup rigs are the most common MODU used worldwide

Fig. 2. Mobile offshore drilling unit – jackup. Source: Pride.

and are capable of drilling on a wide variety of tracks in water depthup to 500 feet. For short distances, the platform is towed to site,while for major moves, the rig is transported as cargo on a heavy liftvessel. Once in position, the legs are lowered, hoisting the drillingplatform above the water. Jackup rigs are either ‘‘mat-supported,’’with the jacket legs attached to a submerged mat, or ‘‘independent-leg,’’ where the individual legs are driven down independently intothe ocean floor. Rig selection depends on availability and seafloorconditions. Independent-leg rigs are capable of working in deeperwater and harsher environments than mat-supported rigs. Afterpreloading the legs, the hull is raised above the sea surface toa height (called the air gap) that depends on the expected height ofthe waves or the height of the platform. A slot in the hull allows thewellhead to be positioned under the rig floor, or the rig floor andsupport structure can be extended (cantilevered) from the side of thehull to the desired drilling position. Independent-leg cantileveredrigs are usually priced at a premium over mat-supported slot rigs.

In water depths greater than 500 feet, semisubmersibles anddrillships (also called floaters) are used. Floaters require specializedtechnologies that are not used with bottom-support rigs, such asdynamic positioning systems, marine risers, and drill string motioncompensators. A semisubmersible rig (semi) is designed to float inthe water and is held in position by multiple anchors or equippedwith dynamically positioned thrusters (Fig. 3). Semisubmersibles arevery stable during high seas and winds and the most modern semiscan drill in 10,000 feet of water. Semis are normally self-propelledand supported by vertical columns on submerged pontoons. Byvarying the amount of ballast water in the pontoons, the unit can beraised or lowered. The lower the pontoons lie beneath the surface,the less they are affected by wave and current action.

A drillship has a conventional ship hull with a large apertureknown as a ‘‘moon pool’’ through which drilling takes place (Fig. 4).Drillships built before 1975 drilled in shallow waters while mooredin place, but went out of favor in the late 1980s. A new generation ofdrillships built after 1975 were dynamically positioned whichallowed drilling in water depths up to 10,000 feet.

4. Making hole

4.1. Stages of drilling

The start of drilling a well is called ‘‘spudding in’’. To spud in,a large pipe, called the conductor or foundation casing, is either

Fig. 3. Mobile offshore drilling unit – semisubmersible. Source: Transocean.

Fig. 4. Mobile offshore drilling unit – drillship. Source: Stena Drilling.

Fig. 5. Typical well configuration schematic.

M.J. Kaiser / Energy 34 (2009) 1097–1112 1101

drilled, jetted, or hammered into the seabed from 100 to 500 feet toa point below the drill floor. The conductor serves as the top part ofthe well and creates a hole for the drillstem and casing to be low-ered into.

Wells are drilled in stages:

� The bit and drill string is inserted into the hole and drills toa certain depth.� The drill string is removed from the hole.� Casing is put into the hole to line it, and in most cases, is

cemented to the wall of the hole.� The bit reenters the hole and the process is repeated until the

target is reached.

The drill string and bit represent the business end of drilling,and all the equipment on the surface and subsurface is used tosupport drilling with the bit. Wells are drilled ‘‘open hole’’ until it isnecessary to run and cement casing to protect the integrity of thewell. Wellbore stability can be a mechanical problem, where weakformations exist, or it can be a chemically based problem, whereclays in the shales and other formations are weakened whenexposed to the drilling fluid. The amount of open hole limits howlong an interval can be and how long it may be safe to expose theformations to the drilling fluids.

A well penetrates many different types of rock formations(zones) until total depth is achieved, and as drilling continuesdeeper into the earth, the operating environment becomes morehostile and drilling becomes more difficult: temperatures andpressures increase,3 formations become more abrasive and harder,complex stress regimes and fracture growth develop, and the timeand cost of drilling increases, often substantially.

A well is usually spudded with a 3600, 3000, or 2600 casing, and asthe hole deepens the casing becomes progressively narrower,

3 High temperature problems are most frequently associated with the instru-mentation used to measure and control the drilling direction and with loggingequipment. A negative temperature gradient runs from the waterline to seafloor,which turns positive below the mudline and increases with the pressure approxi-mately linearly with distance. The average temperature increase is 2 �F/100 feetbelow the mudline, but it can vary between 0.5� and 5.0 �F/100 feet depending onlocation [11]. Fluid pressure depends on the density of the overlying water andaverages 45 psi/100 feet In the GOM coastline, the normal pressure gradient is 46.5 psi/100 feet A ‘‘typical’’ 10,000 feet well should therefore have a temperature ofabout 200 �F and reservoir pressure 4500 psi. Deep shelf prospects may havetemperatures as high as 450 �F and formation pressures in excess of 30,000 psi.

perhaps finishing with 73800

or 95800

diameter at target (Fig. 5). Surfacecasing protects freshwater acquifers, anchors the blowout preven-tion equipment, and protects the hole from potentially hazardousshallow formations. Intermediate casing protects holes fromabnormally pressured zones and poor formations such as salt andsloughing shale. Most casing is thin-wall, 30 feet sections ofseamless steel pipe and the space between the casing and theborehole is cemented to support the casing and to prevent the flowof underground fluids to the surface and/or into freshwater zones.The number of casing strings needed to drill a well depends on theformation and often varies from 3 to 8 strings. Troublesomeformations such as high pressure zones, sloughing shale, andshallow water flows require more intermediate casing. A narrowpore pressure–fracture gradient will also require more casingstrings, and because of the time involved to trip out the hole and setcasing pipe, the cost of drilling increases with the number of casingstrings.

The drill bit is attached to 30 feet joints of steel pipe screwed orjoined together as they go downhole. The drill pipe may be pre-racked into double and triple joints depending on the capability ofthe drilling rig. The pieces of formation which are cut away is calledcuttings, and during the drilling process, drilling fluid (i.e., mud) iscirculated down the drill string, through the nozzles in the bit, andthen back to the surface through the annulus between the drill

4 Some E&P companies participate in joint ventures with drilling contractors tofinance, design, build, and operate deepwater rigs.

M.J. Kaiser / Energy 34 (2009) 1097–11121102

string and the borehole walls. At the surface, the drill cuttings, silt,and sand are removed from the drilling fluid before it is returneddownhole through the drill string.

4.2. The role of mud

Drilling fluids, also referred to as mud, play a number ofimportant functions in drilling: to control the pressures that exist inthe wellbore at different depths, to carry the cuttings out of thehole, to lubricate the drill string, and stabilize the wellbore. Drillingmud consists of four basic parts: (1) base fluids – water, oil,synthetic material, or varying combinations – which classify themud; (2) active solids – the viscosity building part of the system,often bentonite clays; (3) inert solids – the density building part ofthe system, such as barite; and (4) other additives – to control thechemical, physical, and biological properties of the mud, such aspolymers, starches, and various other chemicals.

Mud is classified into three general categories: water-based mud(WBM), oil-based mud (OBM), and synthetic-based mud (SBM)[15]. WBM is made with fresh or saline water and is used for mosttypes of drilling, often consisting of dissolved salts, additives,polymers, clays, and weight material such as barite. OBMs arewater-in-oil emulsions with dispersed clay and weighting material.In SBM, the oil is substituted with long-chain esters, ethers, acetyls,and synthetic hydrocarbons. OBM and SBM have special opera-tional advantages over WBM due to their low friction, goodtemperature tolerance, and inertness to formation clays. SBM weredeveloped in response to the requirements for drilling fluids withperformance comparable to OBM but without the adverse envi-ronmental implications. SBM and OBM are not generally used forthe entire depth of the well; typically, WBM are used for the upperportion with a change to SBM below the 1600 or 1300 casing point ata depth of 5000 feet or more. Each mud program is well specific.

Formation pressure can be unpredictable, and therefore,potentially hazardous. If the drill bit penetrates a high pressurezone unexpectedly, oil or gas, or a mixture of both, may rush intoand up the wellbore, dilute the mud, and reduce its pressure. This iscalled a ‘‘kick,’’ and it can lead – if unchecked – to an uncontrollablegusher at the wellhead (a blowout). Drilling fluid and the experi-ence of the drill team is the first line of defense to prevent thisoccurrence. The last line of defense situated below the wellheadcontrol valves is the emergency blowout preventer (BOP); indeepwater, BOPs may be situated on the seabed. Kicks and blow-outs can be detected by monitoring the density, viscosity, and otherproperties of the drilling mud. A drilling problem may requirechemical additives (‘‘pill’’) to be injected into the mud, or heavymud (‘‘kill mud’’) to circulate the kick out of the well.

The density of the mud depends on the formation pressuresanticipated or encountered, which in turn impacts the rate of bitpenetration. Heavy mud retards bit penetration and can cause stuckpipe and skin damage. Light muds are used if the well is plannedand drilled in underbalanced mode, where the pressure of the fluidcolumn is designed to be less than that of the formation pressure.Drilling is usually performed underbalanced in non-permeablezones and overbalanced in permeable zones. In development dril-ling, the local pressure regime is usually known, while in wildcats,it is uncertain since the local geology has not yet been explored.

4.3. Generalized dayrate contracts

The operator writes a drilling prognosis – which essentially isthe recipe book for the well, and includes equipment and proce-dures that the operator will require, together with a well descrip-tion, bid specifications, and drilling contract – and then the drillingsuperintendent will choose a group of companies with rigs that

meet the demands of the project and which are in the generalvicinity of the well to be drilled. The terms of the contract can be forone or more wells over a short- or long-term basis on eithera ‘‘dayrate’’ or ‘‘turnkey’’ contract (see Appendix B for furtherdetails on contract terms). After the contractors submit their formalbids, the drilling superintendent and his team select the rig thatthey believe will drill the well in the most cost effective and safestway. The operator selects the best bid according to price, avail-ability, reputation, past experience, and other factors. The contractwinner is not necessarily the lowest bid contractor.

Drilling contracts are complex instruments because in additionto covering the financial, legal, environmental and health andsafety aspects of the job, they must also accommodate the uncer-tainties inherent in the operation, so that neither party is undulypenalized for unforeseeable events [16]. Offshore contracts origi-nated from their land-based counterparts and developed over theyears with increased sophistication, but there is still little stan-dardization. The American Petroleum Institute, the InternationalAssociation of Drilling Contractors, the American Association ofDrilling Contractors, the United Kingdom Cost Reduction Network,and other organizations all have their own draft drilling contractforms. Operators also maintain forms [17] which are designed toavoid problems encountered in their particular experience.

A drilling contract is a service contract in which a companyagrees to perform certain services for a monetary payment. Thepayment terms under a dayrate contract are usually decomposed interms of four basic subrates: mobilization rate, operating rate,reduced rate, and special rate.

The mobilization rate is used during the time the rig is mobi-lized/demobilized between well locations or shore, and covers portfees, towing cost, fuel and other expenses incurred by thecontractor to arrive at site. Mobilization/demobilization may alsobe specified on a lump sum basis.

The operating rate governs the cost during drilling and coversthe rig rental, crew and consumables. The dayrate is primarilydetermined by water depth and rig capabilities, the supply/demandconditions that exist in the region at the time the contract iswritten, and the duration of the contract. Most shallow water rigsare relatively non-specific assets, capable of drilling on a widevariety of tracts. Deepwater rigs are more capital intensive andsometimes firm-specific.4 The drilling business is highly competi-tive and dayrates typically follow utilization levels.

The reduced or standby rate covers conditions when the rig isnot drilling, such as during moves, logging or testing, whilespecial rates are used when drilling is interrupted by adverse seaor weather conditions, mechanical failure, force majeure, or theconcession holder’s inability to obtain the required permits orauthorization.

The total drilling cost under a standard dayrate contract isdetermined thus

DHC ¼X4

i¼1

TiRi;

where DHC¼ total drilling cost ($), T1¼ total amount of time rigmobilized and anchored (h), T2¼ total amount of drilling time(day), T3¼ total amount of time spent moving, logging, or testing(h), and T4¼ total amount of downtime spent on equipment failureor waiting on weather (h), R1¼mobilization rate ($/h),R2¼ operating rate ($/day), R3¼ reduced rate ($/h), and R4¼ specialrate ($/h).

DrillingFactors

Observable

Unobservable

Physical characteristicsof the well, geology, and

drilling process

Operator experience,well quality, operator

characteristics

Well planning and execution,comunication, team

dynamics, leadership,project management

Measurable(Direct)

Measurable(Indirect)

Fig. 6. Drilling factors are classified into observable and unobservable categories.

M.J. Kaiser / Energy 34 (2009) 1097–1112 1103

Contract terms are proprietary, but dayrates are widely reportedand tracked by industry. The time for the rig to mobilize and anchordepends on the type of rig and the distance from its current loca-tion to the new site. The total amount of time spent coring, logging,and testing depends upon the well type, well design, and thesuccess of drilling. The amount of time spent moving the rig orwaiting on weather is a stochastic function depending on the regionand time of the operation. Downtime spent on equipment failure orproblem wells may be attributable to geologic conditions, operatorand contractor experience, and a random forcing function.

5. Model factors

Drilling operations are complex and uncertain, and many factorsinfluence the time and cost to drill a well. These factors aremultidimensional, often interdependent, and usually stochastic;the factors can be classified as either observable or unobservable(Fig. 6). Measurable factors include the physical characteristics ofthe well, geology, and drill parameters; while indirect character-istics, such as wellbore design, contractor experience and holequality, need to be proxied through other variables if they are to beincorporated in analysis. Factors such as communication, leader-ship, and project management skills will also impact drillingperformance, sometimes significantly, but to capture and identifythe influence of these (unobservable) variables is usually beyondthe scope of analysis and the reporting capabilities of operators. Theamount of data required to construct a reasonable representation ofdrilling operations depends in part on the nature of the data set andthe system characteristics.

5 Because the bit is being turned clockwise during drilling, the wellbore tends to‘‘walk to the right’’ with a clockwise corkscrew pattern as it goes down. Drillingcontracts often have a clause stipulating that the well can change in deviation nomore than 3� per 100 feet anywhere along the wellbore and must end up in a conewith a maximum angle of 5� . This is commonly referred to as a ‘‘straight’’ hole, butother definitions exist [11].

5.1. Well characteristics

5.1.1. Well typeThere are many ways to classify wells. The most common

distinction is between exploratory and development wells. Wellsthat are drilled in an unproved area to add reserves are exploratorywells, while wells drilled in the known extent of a field to produceknown reserves are development wells.

Exploratory wells are drilled to find oil and gas, and theirprimary purpose is to gather information on subterranean condi-tions and confirm whether geological formations contain hydro-carbons. Most exploratory wells are drilled as straight as possible,5

but in special circumstances, may be drilled at an angle or evenhorizontally. Development wells are drilled as part of a productionplan. Usually only the first development well is vertical; subsequentwells are drilled vertical to a certain depth and then kicked off ina ‘‘J-shaped’’ or ‘‘S-shaped’’ pattern to total depth. A plannedmultilateral will involve sidetracking out of the well from a zoneshallower than the original leg of the wellbore to reach a newsection of the formation.

The first exploration well in an area will be drilled very carefullybecause the geologic formations are untested and the risk ofoverpressure may result in a blowout, but after a few wells thestratigraphic layers where overpressures can be expected areknown, and drilling can often proceed at a faster rate. The time andcosts to drill a development well is expected to be smaller thanexploration wells because information gathered from exploration isapplied in drilling. Learning economies are also well documented indevelopment drilling [18].

Well status describes if the well hit ‘‘pay dirt’’ (successful) or wasa ‘‘duster’’ (dry hole). An unsuccessful well will often lead to side-tracking to test a different section or zone. Dry wells will be pluggedwith cement and abandoned, and the extra time and cost of thisoperation suggest that dry hole cost will exceed, if all other thingsare equal, the cost to drill a successful well. This is generally true foronshore wells as reported by American Petroleum Institute drillingcost data [1,19], but in an offshore environment, the extra cost toplug and abandon a well is usually a small part of the total drillingcost and is not easily distinguished. Offshore, wildcats that find

7 Liners are casing string that are suspended from the bottom of the next largestcasing string. The principal advantage of a liner is its lower cost, since it does not

M.J. Kaiser / Energy 34 (2009) 1097–11121104

a commercial pay zone may be temporarily plugged and aban-doned until the field is developed or permanently plugged if thelocation is not optimal from which to produce the field.

5.1.2. Well geometryA wellbore is a three-dimensional object which can be described

in geometric terms with respect to the length, diameter, andcurvature of the hole trajectory. The depth of a well measured fromthe rotary table in the XY-plane along the length of the wellbore iscalled total depth (or total measured depth) and denoted by TD,while the (true) vertical depth VD is the distance from the rotarytable measured in a vertical plane to TD. Spud depth SD is thedistance from the rotary table to the seabed. The drilled interval DIis the difference between the total depth and the spud depth,DI¼ TD� SD; the vertical interval is defined as VI¼ VD� SD.The horizontal displacement HD is the distance in plan view6 fromthe rotary table to TD. Water depth WD is the distance from thewaterline to the seabed.

The problems, costs, and hazards of drilling increase with waterdepth and drilled interval. Water depth is an important factor in alloffshore operations because as water depth increases, rig specifi-cations also need to increase. Drilling operations with floatersrequire even more specialized technology which adds significantlyto dayrates. The deeper the hole the more time is lost in round tripsto replace worn bits and to run casing, tests, and logs. The numberof formations encountered will typically increase along with thenumber of casing strings required to maintain well control. As thenumber of casings increase, the trip time, installation, cement, andcementing time will also increase.

The direct cost of the additional strings has an effect, but thereare also costs that occur because of well-diameter constraints. Theability to handle larger casing requires more expensive rigs, tools,pumps, compressors, and wellhead control equipment. Increasingthe number of casing strings from 3 to 4 may result in a 10–20%increase in well cost; increasing the number of strings from 4 to 5may increase cost by 20–30%; and so on. Offshore drilling mud is anexpensive chemical preparation, and the deeper the hole, the moremud is needed. Beyond a certain depth below mudline(15,000 feet), technical complications and the opportunity forproblems increase significantly. In many deepwater wells, thepercentage of total well cost as a fraction of total depth is such thatas much as 50% of the total cost can be spent on drilling the last 10–20% of the well.

A well is composed of segments of casing string Si oriented at anangle A(Si) relative to a reference coordinate system. The maximumangle of the wellbore is computed as MA ¼ max

iAðSiÞ. If MA� 85�

the well is classified as a horizontal well using the indicator variableHW:

HW ¼�

1;MA � 85�

0; otherwise:

If L(Si) denotes the length of well section Si, then the total lengthof the horizontal section of a well is denoted as HL:

HL ¼(Xl

i¼1

LðSiÞ��AðSiÞ � 85

�; i ¼ 1;.; l

):

Oil and gas wells are drilled horizontally for a variety of reasons,but primarily to improve production and reach reserves thatotherwise might not be developed. Horizontal drilling is less stablethan drilling vertically, more difficult to log and complete, and often

6 Looking down from above as if the well path is straight.

between 2 and 3 times the cost of a similar length vertical borehole.Directional wells with long horizontal departure are calledextended reach wells and are often defined as wells with TD/VD> 2.0.

5.1.3. Casing geometryCasing serves several important functions in drilling and

completing a well, and is one of the most expensive parts ofa drilling program, ranging from 10 to 20% of the total cost ofa completed well [20]. Casing prevents collapse of the boreholeduring drilling and isolates the wellbore fluids from the subsurfaceformations. Casing also provides a flow conduit for the drilling fluidand permits the safe control of formation pressure. A well that doesnot encounter abnormal formation pore pressure gradients, lostcirculation zones, or salt sections usually require only conductorand surface casing to drill to target. Deeper wells that penetrateabnormally pressured formations, lost circulation zones, unstableshale sections, or salt sections generally will require one or morestrings of intermediate casing to protect formations and to preventproblems [21,22].

Each casing section has a diameter Di¼D(Si), radius Ri¼ R(Si),and length Li¼ L(Si) measured from the rotary table. If k¼NSrepresents the number of strings associated with the well, thena finished well is characterized by the vectors D¼ (D1, D2,., Dk) andL¼ (L1, L2,., Lk). The number of casing strings provides an indirectmeasure of well complexity, since complex wells are frequentlyassociated with multiple strings and narrow margins between porepressure and fracture gradients. The incremental well casing lengthis denoted by L* ¼ ðL*

1; L*2;.; L*

kÞ, where L*i ¼ Li � Li�1, for i¼ 1,.,

k, and L*0 ¼ 0. If hole sections can be drilled without setting

intermediate strings or liners,7 then drilling can proceed quickly.Operators generally prefer the production casing to be as large

as possible to maximize production, but large production casingrequires a large wellbore, which is more complicated and expensiveto drill, since the rig has to be higher spec and more rock volumehas to be removed. Average hole size and removed rock volume arenumerical measures that characterize the geometry of the finaldrilled well. The average hole size HS is determined by theweighted average diameter of the casing string along the wellbore:

HS ¼Pk

i¼0 DiL*iPk

i¼0 L*i

;

while the rock volume removed VR from the wellbore withoutwashout is defined as

VR ¼ pXk

i¼0

R2i L*

i :

The cost of drilling should be larger the greater the average holesize and volume removed from the wellbore.

5.1.4. Well complexityA wide variety of well types and configurations exist, along with

several notions of what constitutes a ‘‘complex’’ well, and it isunlikely that a single definition will ever be widely accepted sincepractices, opinions, and experiences among drilling contractors

run the length of the well, but problems may arise in production and workoversfrom hanger seals and cement leakage. The decision to use strings or linersrepresents a trade-off between the cost savings realized by using less casing versuspotential future problems caused by hangers and leakage.

M.J. Kaiser / Energy 34 (2009) 1097–1112 1105

vary significantly. Complex wells arise from geologic formations,target depth and the size of the reservoir sands, wellbore trajectory,the experience of the contractor and application of technology, aswell as numerous other factors. Conditions that create a complexwell are often proxied through a description of the physical char-acteristics of the well, such as the water depth, vertical depth,maximum angle, and number of casing strings.

High-pressure/high temperature HP/HT wells begin to exhibithigh temperatures at depths around 18,000–20,000 feet, althoughin areas with geothermal activity, hot drilling conditions can occurat shallower depths. HP/HT wells are usually planned and drilledusing significantly less formation data than shallower and coolerwells. The trajectory of a well, G, can also be used to describecomplex wells. A well is often considered complex if its formationpressure FP exceeds 10,000 psi or temperature T is greater than300 �F anywhere along the wellbore. A complexity index is used toidentify complex drilling environments if any of these conditionsoccur:

CI ¼�

1; FP > 10;000 psi; T > 300 �F; or G complex0; otherwise:

The ratio of the horizontal length to the total footage drilleddescribes the percentage of the well’s footage drilled under hori-zontal conditions:

HR ¼ HLDI

;

e.g., for most exploratory wells HRz0, while for development andextended reach wells, 0<HR� 1. The aspect ratio AR,

AR ¼ HDVI;

measures the aggregate curvature of the well trajectory, and theextended reach ratio, ER, is defined as the ratio of total depth tototal vertical depth:

ER ¼ TDVD

:

All three ratios provide metrics that quantify the wellboretrajectory.

5.2. Site characteristics

The well site is characterized by its geographic location deter-mined through its latitude/longitude coordinates, the distancefrom the well to the nearest onshore service station, and the waterdepth. Water depth and environmental conditions expected to beencountered are primary determinants in the selection of the rigrequired for drilling. As water depth increases, larger and morerobust rigs are required, with extra hoisting capacity, mud circu-lation systems, mooring systems, etc. The region and country inwhich a well is located is an important consideration in obtaininggovernment regulations and permits. The maturity of the infra-structure support services can play a significant role in determiningdrilling cost, and the knowledge and experience of the contractor,say as measured by the number of wells drilled in the region, can beimportant factors.

5.3. Operator preference

5.3.1. Contract typeThe operator decides not only where to drill, but also how to

drill, and the manner in which to let the contract. The contract type

(dayrate, turnkey), job specification (one well, multiple wells),market rate, and negotiating strategies are important factors indetermining drilling time and cost.

5.3.2. Rig selectionMany different rigs can be used to drill an offshore well. Rig

selection depends upon factors such as the type of well being drilled,water depth and environmental criteria, the type and density ofthe seabed, expected drilling depth, load capacity, frequency ofmoves, ability to operate without support and availability.

Before selecting a rig, a detailed site assessment is completed toidentify water depth and bottom conditions, and expected weather,wind, tides, wave heights and current speeds. Water depth is animportant factor since the rig must be rated to work in the depthrequired; e.g., a jackup must be able to jack up on location andwithstand the normal environmental forces encountered. Seabedconditions determine if an independent-leg or mat-supportedjackup can be employed. Independent-leg jackups are employed infirm soil, coral, or uneven seabeds; mat-supported jackups requirelow soil shear values and a flat seabed. The decision to use ananchored or dynamically positioned rig depends on the nature ofthe seafloor, the size of the rig, and the expected operating condi-tions. Deepwaters characterized by strong currents create a needfor high specification rigs capable of maintaining station, and insome instances, suppressing vortex induced vibrations.

If weather and environmental conditions are expected to bea problem, then sophisticated all-weather semis can be used tohedge against weather downtime. The increase in availability isachieved through the higher capital cost of the equipment; which inturn is passed to the operator in higher dayrates. Jackups arecheaper but are more prone to weather delay. The choice is up to theoperator: the trade-off is between drilling availability and dayrate.

Rig availability also plays a role in the selection process, since ifthe regional demand exceeds supply, market rates will rise. In thepast, dayrates were based on investment and depreciation sched-ules, but when a market has a capacity shortage, dayrates will bedetermined primarily by demand rather than cost recovery. Ifregional utilization rates are low, drillers may stack jackups andcontract large rigs to shallow water projects to maintain the utili-zation of high cost equipment.

5.4. Drilling characteristics

5.4.1. Bit size and typeDifferent types and sizes of bits are used according to the

hardness of formations, pressure regime, and drilling plan. Bits areclassified as roller bits, such as steel tooth and insert bits, and fixedcutter bits, such as polycrystalline diamond compact (PDC), ther-mally stable polycrystalline (TSP) and natural diamond bits. Forhard and abrasive drilling conditions in deep wells drilled withmud, tricone bits are commonly used, but their susceptibility towear and bearing failure limits their drilling time. In deep holesections, where tripping times are longer, polycrystalline or naturaldiamond bits are competitive with the tricone bit [23]. The final bitsize employed in the well is denoted FBS.

5.4.2. Drilling fluidDrilling mud is applied to control the pressures that exist in the

wellbore at different depths. Synthetic-based muds have downholeperformance similar to OBMs and offer advantages over WBMs incertain circumstances; e.g., SBM have higher lubricity compared toWBM and can endure more hostile downhole conditions. The use ofSBM is likely to enjoy faster penetration rates and is also less likelythan WBM to interact with the production horizons becausetheir physical and chemical makeup is similar to the hydrocarbon

M.J. Kaiser / Energy 34 (2009) 1097–11121106

bearing zone. Other fluid-related issues involved in the choice ofdrilling fluid system include hole cleaning, lubricity, stability, baritesag, and fluid stability. In horizontal, multilateral and extendedreach applications, fluid-related issues become more complicated,and the more complex the mud program, the greater the expectedcost of drilling.

5.4.3. Mud weightHeavy mud is typically used to create an overbalance to prevent

fluids from entering the well. The greater the hole pressure, theheavier the mud, and the slower the drilling. Mud weights varyover each well section. If the mud weight applied to drill out wellsection Li*, i¼ 1,., k, is denoted MW(Li*), then the average mudweight employed in the drilling program is defined by

MWA ¼Pk

i¼0 MW�

L*i

�L*

iPki¼0 L*

i

:

Mud weight at TD is denoted MWTD. The maximum mud weightused over the wellbore is determined as

MWMX ¼ maxi¼1;.;k

MW�

L*i

�:

To the extent that high pressure wells are more complex to drill,MWA, MWTD, and MWMX serve to proxy well complexity [24].

5.5. Formation evaluation

Formation evaluation is a critical step in exploration since it isthe stage in which information about the presence/absence ofhydrocarbon bearing reservoirs is acquired. It is important toremember, however, that time spent coring, logging, reaming, andtesting is ‘‘flat’’ time, and so for wells that require extensiveformation evaluation data, normalization is required prior toperformance comparison.

Cutting a core requires separate round trips to install andremove the coring assembly, and because coring is slower thandrilling, if the well is deep and the interval is large, coring can incura significant amount of rig time. The number of days spent drillingout core samples, or trying to core, the well in any hole section isdenoted by CD. The number of days spent logging, or trying to log,before or after total depth is reached, but excluding logging whiledrilling or formation evaluation drilling, is denoted LD. Coring andlogging days include interrupt time and waiting on weather time.

5.6. Exogenous events

Exogenous events cannot be predicted with any degree ofaccuracy, but their impact and duration needs to be considered tonormalize for conditions beyond the control of the contractor.

5.6.1. WeatherOffshore drilling may be subject to significant delays caused by

the weather, and weather downtime can play an important factor inthe total costs of the operation. Weather downtime can impactdrilling operations in various ways; e.g., weather too severe foroperations involving supply boats may lead to delay if stock levelson the rig decline to a critical level; weather may impact anchoringup and moving time; weather may be too severe for drilling tooccur; and extreme weather may result in damaged or lost drillstrings and risers. If operating limits are exceeded because waveheights, ocean currents, or eddies are too strong, drilling operationswill be temporarily abandoned and resumed when conditions fallwithin the operating capabilities of the equipment [25]. Waiting on

weather WOW time needs to be considered separate from thedrilling time and cost metrics.

5.6.2. Interrupt timeMany problems can occur during drilling requiring suspension

of the activity. Most contracts specify a certain amount of ‘‘free’’downtime (24 h per month is typical), but outside this allowance,the contractor does not receive payment for the time the rig wasinactive. Other delays that may occur not directly accountable tothe driller are usually charged at a reduced rate.

One of the most common problems in drilling a hole is thatsomething breaks inside the well, such as a piece of bit or drillstring, or something falls down into the wellbore, such as wrenchesor other tools (see Appendix A). These pieces of metal are called‘‘fish’’ or ‘‘junk,’’ and because the bit cannot drill through them,drilling must be suspended until they can be retrieved by ‘‘fishing’’tools leased from a service company. The use of fishing tools costthe operation extra money and time spent fishing is flat time. Iffishing is unsuccessful, the hole will either be sidetracked orwhipstocked (drilled around the obstacle), and in the worst case,a new hole may need to be spudded. Rig equipment failure, lostcirculation and stuck pipe are the main causes of downtime in theGulf of Mexico, and in some cases have been reported to account fornearly 25% of drilling budgets [26]. Interrupt time cannot be pre-dicted with any degree of accuracy, and so an upper limit exists onthe expected reliability of any cost prediction tool.

5.6.3. Oil and gas pricesThere is a correlation between hydrocarbon prices and drilling

costs. When the price of crude oil increases, there is generally anincrease in exploration and drilling activity, and a decrease in rigavailability. Supply-and-demand lead to an increase in the costs ofrig rental rates, material costs, and services. Natural gas pricesimpact rigs drilling for gas on a regional basis.

5.7. Unobservable variables

Many variables which influence drilling performance, such aswell planning and preparation, project management, and technologyare difficult (if not impossible) to quantify, and since the manner inwhich these variables impact the drilling program are essentiallyunobservable, it is usually not possible to directly incorporate thesefactors into modeling. The importance of these factors to perfor-mance cannot be overstated, however, and is commonly recognizedas playing an important role in operations [27].

5.7.1. Well planningThe first step in planning any well is to design the wellbore path

to intersect a given target. Were adequate time and resources givento the operational team to develop an efficient and best practicewell design, or was too little given too late for the team to succeed?Careful planning and evaluation are required to successfullycomplete a project whether drilling easy, normal pressure wells, inshallow water, shallow target, benign environments; or difficultwells with a complex geometry that have a combination of hightemperature, high pressure, narrow pressure/formation gradientwindows, salt, rafted shale, high angle, shallow hazards, deepwater,contaminated environments. A multi-disciplinary operational teamis usually the most efficient to deal with drilling/well constructionissues and objectives [28–30].

5.7.2. Project management and leadershipComprehensive, forward looking, integrated engineering plan-

ning, coordination, execution and management, including definedcontingencies and options, helps the drilling program to be

M.J. Kaiser / Energy 34 (2009) 1097–1112 1107

executed in the shortest possible time [31–34]. What was theexperience of the project management team and how was projectmanagement executed? Was leadership shown in decision makingand planning goals?

5.7.3. Well qualityThe timely delivery of logged, tested, and producible boreholes

is important to the profitability of the field [35–37]. What was thequality of the final wellbore? Was there skin damage?

5.7.4. TechnologyThe impact of technology on drilling performance is pervasive

but difficult to isolate. Technology may be ‘‘enabling’’ or ‘‘enhancing’’or both, and will normally shift from enabling to enhancing overtime. New technology is expensive, both in terms of cost andlearning, but if the technology reduces drilling time or improves theefficiency or safety of the operation and becomes widely adopted,costs decline and the performance efficiencies will improve andbecome absorbed within the process. Trade-offs between competingtechnologies and processes are common,8 but quantifying thedifferences in impact remains notoriously difficult to evaluate.

6. Model formulation

Associated with every well w is a vector of dependent variables,4(w), and a matrix of observations of independent variables, X(w).The dependent variable set includes both reported and derivedmeasures. The matrix of observations is used to explain thedependent variables and is selected based on the underlyingengineering and mechanical processes associated with drilling, thechoice of dependent variable, data availability, level of aggregation,and other factors.

6.1. Methodology

A large number of parameters influence drilling operations andinteract in a complex and dynamic manner. Regression analysisprovides a standard and transparent analytic framework to estab-lish relationships among the drilling variables. The approachfollows four basic steps:

Step 1. Select descriptor variables of the drilling process X1, .,Xp.

Step 2. Aggregate the descriptor variables as a component vectoraccording to category U,

U ¼��

X1;.;Xp�jAi� Xi� Bi

;

where the values of Ai and Bi, i¼ 1,., p, are user-defined.

Step 3. Construct a regression model for given dependent variablesbased on the sample data and aggregation category U,

4ðUÞ ¼ a00 þXp

a0iXi;

i¼1

8 For example, underbalanced drilling accelerates drill time and may improvewellbore quality but requires specialized equipment and training for safe opera-tions; 5th generation drilling rigs offer dual derrick capability to maximize drillingefficiency but charge a higher rig rate; the use of specialized drilling fluids costmore but can improve drilling efficiencies; the presence of shallow hazards can beidentified with special processing of seismic data but the extra cost of a directionalwell may not offset the delay of the hazard.

and test the model coefficients ða00;a01;.;a0pÞ for statisticalsignificance.

Step 4. Maintain the significant variables and other factors ofinterest, re-estimate the model specification,

4ðUÞ ¼ a0 þXq<p

i¼1

aiXi

and report the final model results.Linear models are selected for ease in presentation and fix the

functional form. If linear models do not provide adequate response,more complex nonlinear models can be adopted. Because a numberof (unobservable) variables were omitted that may affect the timeand cost of drilling, such as management efforts, well quality,technology and weather conditions, it is possible that omittingthese variables may result in biased estimates if they are correlatedwith other independent variables.9 We could use a fixed effectsmodel to address the omitted variable concern by including loca-tion, time, and developer fixed effects, and if the sample is large andsufficiently robust, this would be reasonable to investigate.

6.2. Dependent variables

The dependent variables of the model include the time to drilla well described by the number of dry hole days, DHD, the numberof days from the spud date to TD, plus any time spent batch setting,pre-installing or pre-setting casings. Dry hole days are normallydefined to include interrupt and weather time, time spent ontechnical/mechanical sidetracking, and the operational time to seta whipstock in multilateral wells. The total number of days from therig arrival on location until the rig is released is the total site days,TWD. This time includes the time for mooring and demooring,where applicable, completion and testing, suspension and plug andabandonment activities.

The cost of operations during the dry hole day period plus thecasing batch set, pre-set period is denoted DHC. The definition ofDHC will vary with the operator, but will normally include the costof operations, plus overhead, base operations, incentive payments,logging, transport, materials supply, marine vessel support, marinesupply base, port facility, and warehousing. The costs for comple-tion and well test operations, production strings/liners, trees,completion equipment, long-term daily rental of completionsequipment, well design and programming, site survey and prepa-ration, rig mobilization and demobilization, well suspension andre-entry cost, and plug and abandonment are usually not includedin DHC. Total well cost TWC is dry hole costs plus all cost that werespecifically excluded.

6.3. Source data

The database employed in this study consists of 73 wells drilledin the Gulf of Mexico between 2002 and 2003. Well costs are notnormally made public by companies, and are considered confi-dential and proprietary. Data was compiled from two domesticindependents and one major who provided a representativesample of their drilling program. Full data submission would bepreferable, of course, since it would avoid selection bias, but theeffort involved to collect and process ‘‘complete’’ data was outside

9 For example, if management efforts are expected to be positively correlatedwith drilling exploratory wells, the coefficient associated with well type will beunderestimated.

M.J. Kaiser / Energy 34 (2009) 1097–11121108

the scope of the study. The collected data is meant to be illustrative,rather than representative, and no claims regarding the generalityof the statistical relations to the GOM drilling environment shouldbe inferred. If more comprehensive data was available, however,general models are readily established. All costs are reported innominal dollars and are not inflation-adjusted.

The technical characteristics of each well, such as drilledinterval, water depth, and casing sizes, and the data related tooperational times is considered reliable, since these are well-defined and frequently utilized industry measures. Data related tointerrupt times and cost is more subjective, due to the differentways in which operators may define and calculate these values. Weconsider measurement errors to be randomly distributed. Anattempt was made to ensure that all output metrics were properlynormalized, but again, constraints implicit in the data collectionplace inherent limitations on the sample set.

The restricted time window minimizes the impact of changes inreporting requirements, inflation, technological improvements,and volatility in the market rates of rigs. Only project data repre-senting actual cost was processed, and to minimize the influence ofscale effects, batch and campaign drilling operations were excludedfrom consideration. Only ‘‘new’’ wells are considered; sidetracks,slot recovery/enhancement, and multilateral wells were excludedfrom the sample.

All the wells in the sample set were drilled using dayratecontracts with water/synthetic fluids, and none of the wells werehorizontal or drilled in an underbalanced mode. Potentially usefulcharacteristics such as hole size, volume removed, well status,maximum angle, and average mud weight were not available foranalysis.

6.4. Model specification

The initial model

4ðUÞ ¼ a00 þX10

i¼1

a0iXi;

is constructed for each of the dependent variables

4ðUÞ ¼ fDHDðUÞ;DHCðUÞ; TWCðUÞg;

for the input vector set,

ðX1;.;X10Þ ¼ ðWT; WD; DI; HD; VD; AR; ER; FBS; NS; MXMWÞ:

All the variables are numeric except well type which is cate-gorical (WT¼ 1, exploratory well; WT¼ 0, development well). Thequantitative factors include water depth (WD, in 100 m), drilledinterval (DI, in 100 m), horizontal displacement (HD, in 100 m),vertical depth (VD, in 100 m), aspect ratio (AR, unitless), extendedreach ratio (ER, unitless), final bit size (FBS, in inches), number ofcasing strings (NS, integer valued), and maximum mud weight(MXMW, in specific gravity).

Ideally, the input variables would be available for all aspects ofwell construction in a consistent and comparable format, but forpractical purposes, we were selective in variable inclusionbecause of data integrity and consistency issues. The coefficientsða00;a01;.;a010Þ are estimated for each output measure. After theinitial model is computed and the statistical significance of thevariables determined, the variable set is refined and the modelre-estimated. Usually, only variables with p-values< 0.05 aremaintained, but other criteria may also be applied. The final re-estimated model is specified with all the regression coefficientsreported.

Functional relations evaluated at the component vector for wellw in category U are denoted as DHD(wjU), DHC(wjU), andTWC(wjU). Performance metrics such as the rate of penetration ROP,dry hole cost per day CPD, dry hole cost per meter DHCPM, and totalwell cost per meter TWCPM, are derived from these measures. Forinstance,

ROPðwjUÞ ¼ DIDHDðwjUÞ; CPDðwjUÞ ¼ DHCðwjUÞ

DHDðwjUÞ;

DHCPMðwjUÞ ¼ DHCðwjUÞDI

; TWCPMðwjUÞ ¼ TWCðwjUÞDI

:

6.5. Expected signs

The expected signs of the model coefficients are easy to ascer-tain in most instances and provides a first check on the veracity ofthe results. If the signs of the coefficients do not follow the expectedpattern and the variables are statistically significant, additionalstructural issues may need to be investigated.

Exploratory wells are expected to take more time to drillbecause of the potential risk involved, and since greater waterdepth means additional complexity, technical and environmentalcomplications, the water depth coefficient is also expected to bepositive. The drilled interval is the length of the wellbore, and allthings being equal, it is clear that the greater the drilled interval thelonger the time and the greater the cost of drilling. The drilledinterval is expected to be a primary explanatory variable across allmodel types. The vertical interval is expected to be correlated to thedrilled interval for exploratory wells, but for horizontal wells, thecorrespondence is expected to be weaker.

The sign of the horizontal displacement, aspect ratio, andextended reach ratio is uncertain. The aspect ratio and extendedreach ratio describe the geometry of the wellbore trajectory,and since they are strongly correlated, only one of the variablesshould be included in the regression model. The coefficient of thefinal bit size is expected to be positive since a large wellbore shouldtake more time to drill and cost more than a small wellbore. Thenumber of casing strings is a direct indicator of the complexity ofthe well and the maximum mud weight is positively correlatedwith the pressure profile. Increasing the number of casing strings orapplying greater mud weight is expected to be associated withslower drilling time and greater costs.

7. Drilling time and cost functionals

7.1. Statistical analysis

Half of the drilled wells in the sample were exploratory and theother half development. Ideally, we would prefer to perform anal-ysis on each class separately, but the small sample size precludedseparate assessments. There was significant variation among thewater depth and well trajectory characteristics, and most wellsrequired between 3 and 5 casing strings, which is typical in theshallow waters of the GOM (Table 1). Most of the wells were drilleddirectionally which is common in development programs. Thedrilled interval for the sample set ranged between 2000 and4400 m. The average final bit size and maximum mud weightparameters are common in GOM shelf operations.

Additional sample statistics presented in Table 1 include waterdepth, drilled interval, horizontal displacement, vertical distance,aspect ratio and extended reach ratio. Most factors exhibitedsignificant variability and a low level of correlation. The extendedreach and aspect ratio measures provide roughly the same

Table 1Wellbore statistics for Gulf of Mexico sample set (2002–2003).

Metric (unit) Mean Std. deviation Min Max

WT 0.51 0.50 0 1WD (m) 1041 590 5 2432DI (m) 3254 1219 1118 7027HD (m) 823 789 0 2752VD (m) 3916 1365 1619 7758AR 0.36 0.39 0 1.5ER 1.1 0.2 1 1.7HL (m) 416 675 0 4540FBS (in) 10.6 2.1 6 14.8NS 4.1 0.9 2 6MXMW (s.g.) 1.5 0.2 1.1 2.0

Based on 73 wells collected from 3 companies.

Table 3Drilling time and cost model results.

4ðUÞ ¼ a0 þ a1WT þ a2WDþ a3DI þ a4HDþ a5ARþ a6NS

DHD DHC TWC

a0 �26.3 (�3.8) �13.9 (�4.7) �10.99 (�3.0)a1 1.79 (1.2)a2 0.19 (1.1) 0.46 (4.4) 0.60 (4.6)a3 0.99 (7.6) 0.29 (4.7) 0.31 (4.1)a4 �0.86 (�1.8) �0.28 (�1.3) �0.22 (*)a5 13.43 (1.4) 6.54 (1.5) 4.62 (1.8)a6 6.16 (3.7) 2.32 (3.1) 2.01 (2.1)R2 0.66 0.59 0.48n 73 73 73

t-Statistics reported in parenthesis. (*) indicates t-statistic <1.

M.J. Kaiser / Energy 34 (2009) 1097–1112 1109

information about well geometry and should not both be incor-porated in the model.

The average dry hole days, dry hole cost, and total well cost forthe sample set are depicted in Table 2. Derived measures such asthe rate of penetration (ROP), dry hole cost per day (CPD), and dryhole and total cost per meter (DHCPM, TWCPM) are also depicted.The average dry hole days per well was 31 and the average dry holecost was $9.8 million per well. The average rate of penetration overthe drilling cycle was nearly 100 m/d. Observe that the standarddeviation of the performance statistics is in most cases only slightlyless than the average values, indicating that the data spread issignificant. Total well cost is nearly $1000/m more than the dry holedrilling cost. The dry hole and total well cost data are stronglycorrelated, r(DHC, TWC)¼ 0.93, with weaker but still significantcorrelations between dry hole days and cost: r(DHD, DHC)¼ 0.75,r(DHD, TWC)¼ 0.72.

7.2. Model results

Functional relations for DHD, DHC, and TWC are shown inTable 3. The average dry hole days, dry hole cost, and total wellcost are estimated as:

DHD ¼ �26:3þ 0:2 WDþ 1:0 DI � 0:9 HDþ 13:4 ARþ 6:2 NS;

DHC ¼ �13:9þ 1:8 WT þ 0:46 WDþ 0:3 DI � 0:28 HDþ 6:5AR

þ 2:3NS;

TWC ¼ �11:0þ 0:6 WDþ 0:3 DI � 2:0 HDþ 4:6 ARþ 0:2 NS:

Most of the variables are statistically significant and of theexpected sign, and the most significant variables for DHD includedrilled interval and number of strings; and for DHC and TWC, waterdepth, drilled interval, and number of strings. Drilled interval isa primary variable in all three models. The statistical significance of

Table 2Performance statistics for Gulf of Mexico sample set (2002–2003).

Metric (unit) Mean Std. deviation

DHD (days) 31.1 17.2DHC ($ million) 9.8 6.1TWC ($ million) 12.4 9.9ROP (m/d) 99.3 66.8CPD ($1000/d) 285.1 94.1DHCPM ($/m) 3097.8 1674.5TWCPM ($/m) 4014.2 2545.3

DHC/DHD ($1000/d) 315.1 121.2TWC/DHC 1.27 0.41

Based on 73 wells collected from 3 companies.

the variables and model fits appear reasonable considering the sizeof the data set.

7.3. Example

The average time and cost to drill an exploratory well (WT¼ 1)in the Gulf of Mexico in 220 m of water (WD¼ 2.2) with a 1500-mdrilling interval (DI¼ 15), 250 m horizontal displacement(HD¼ 2.5), 0.2 aspect ratio (AR¼ 0.2) and four strings (NS¼ 4) isestimated using the functional relations presented previously asfollows: DHD¼ 16.4 days, DHC¼ $3.07 million, and TWC¼ $3.68million.

7.4. Time and cost relationships

The number of dry hole days to reach total depth is a primarydeterminant of the dry hole cost, and similarly, the total well cost ispositively correlated with the dry hole cost. This relation shouldhold across all levels of aggregation, and if one quantity can bepredicted, then a functional relation could be used to derive theother quantity values.

The functional relation can be a simple multiplier, such as

kðUÞ ¼ DHCDHD

;

lðUÞ ¼ TWCDHC

;

so that if the DHC(wjU) functional is established, then estimates forDHC(wjU) and TWC(wjU) follow from

DHCðwjUÞ ¼ kðUÞDHDðwjUÞ;

TWCðwjUÞ ¼ lðUÞDHCðwjUÞ:

Functional relations can also be derived directly, such as

DHCðUÞ ¼ a0 þ a1DHDðUÞ;

TWCðUÞ ¼ a0 þ a1DHDðUÞ:

Functional relations between dry hole cost and total well costare depicted in Table 4. A positive and strong correlation existsbetween cost and drilling days.

7.5. Example

Consider a well that is expected to take 55 days to reach totaldepth. From Table 4, the average dry hole and total well cost areestimated to be DHC¼ $16.8 million, TWC¼ 2.02þ 0.33(55)¼ $20.2million.

Table 4Dry hole cost and total well cost functional relations.

DHC (U)¼ a0þ a1DHD (U) TWC (U)¼ a0þ a1DHD (U)

a0 0.29 (*) 2.02 (1.5)a1 0.30 (9.4) 0.33 (8.6)R2 0.56 0.57n 73 73

t-Statistics reported in parenthesis. (*) indicates t-statistic <1.

M.J. Kaiser / Energy 34 (2009) 1097–11121110

8. Conclusions

Drilling operations are complex and many factors influence thetime and cost to drill a well. In this paper, we described the factorsthat impact drilling performance, and outlined a general approachto understand how the factors of drilling can be quantified ina predictive model. The advantages and limitations of this approachwere described as issues were encountered. We do not have perfectknowledge of the system and may miss important elements orinteractions. The analytic tools introduce uncertainties, and sincecomputational capabilities are limited, trade-offs and approxima-tions are necessary. Models also cannot anticipate the inherentvariability associated with the human aspects of decision making.The model quantifies the nature of the drilling process and thephysical characteristics of the drilled well. It does not take intoaccount estimates of the time or material costs for actions related todrilling.

It is not possible to identify all of the relevant characteristics ofdrilling, especially when data sets are diverse and incomplete, butthrough the use of statistical analysis and empirical modeling, it ispossible to develop relatively robust relations that characterizedrilling performance through the specification of the primaryphysical characteristics of the wellbore. Operators maintainmeticulous and detailed records of each well drilled, and by creatingan analytic framework that incorporates the main components ofdrilling, it is possible to quantify the influence of individual factorsand interaction terms. This generalized functional approachrepresents a stylized framework to understand the drilling processand is the best way to quantify performance evaluation. The basicstructure of the analytic framework was illustrated using a smallsample set which precluded detailed and generalized analysis.

Appendix A. Drilling problem glossary

General categories of drilling problems include:

� Fish or junk. Material that breaks (e.g., drill string, bit cone) orfalls (e.g., pipe wrench) into the well.� Stuck pipe. Drill string stuck in a well, frequently by doglegs or

an inappropriate mud program.� Sloughing shale. Shale that adsorbs water from the drilling

mud and expands when contracted by drilling mud, sloughing(falling) into the hole.� Lost circulation. Excessive amount of mud lost during drilling,

usually occurring in a porous or highly fractured zone. Thesudden loss of fluid return causes the cuttings to be suspendedin the annulus and/or fall back down the well, clogging the drillpipe.� Formation (skin) damage. Mud filtrate which decreases the

permeability of a reservoir rock near the wellbore.� Embrittlement. Corrosive gas such as CO2 and H2S which

weakens the steel casing and drill string.� Abnormal high pressure. Hole pressure higher than the

expected hydrostatic pressure for that depth.

Appendix B. Drilling contract fundamentals

Drilling contractors

The oil and gas industry is composed of operating companies,drilling contractors, and service and supply companies. In the U.S.,operating companies are classified as independents and majors.Majors (e.g., ExxonMobil, Shell, Chevron) are ‘‘integrated’’ in thesense that they produce, transport, refine, and sell petroleumproducts along the entire hydrocarbon supply chain. Independents(e.g., Kerr McGee, Anadarko, Devon) are more specialized in thesense that they only explore and produce (E&P) oil and gas. Inde-pendents can range in size from just a few employees to severalthousand, comparable to the majors. Outside the U.S., national oilcompanies play a prominent role in exploration and production andare owned to varying degrees by the state.

Majors and independents do not own the rigs that carry outdrilling. In the past, they use to, but because of efficiencies,contractors who own and maintain a fleet of drilling rigs andemploy and train the personnel required to operate these rigs arehired by an operating company. There are many drilling contractorsin the Gulf of Mexico, such as Pride International, DiamondOffshore, ENSCO International, Global SantaFe, TODCO, Transocean,Noble, and Hercules Offshore. No drilling contractor is diverseenough to perform all the work required to drill a well, and bothcontractors and operators rely heavily on other companies toprovide equipment, supplies and services. Service companies offerspecial support to the drilling operation such as mud logging, welllogging, completion, cementing, and catering.

Contract type

A footage contract is common onshore, where the contractorreceives a specified amount of compensation for each foot of holedrilled to a specified depth. A dayrate contract is common offshore,where the contractor charges on a dayrate basis until the well isdrilled. Combination contracts apply a footage rate to a certaindepth and a dayrate below is sometimes used onshore. In a turnkeycontract, a contractor agrees to drill a well for a fixed price to beearned only when a specified depth is reached. Optional work afterturnkey depth such as logging, plug and abandonment operations,and other services are usually performed on a dayrate basis. Arelatively new construct, incentive-based contracts, allow a rig’sdayrate to increase when it performs faster than the historicaverage drilling curve. The basic idea is that an agreed upon norm isused to determine expected time and cost for the operation. Dril-ling slower than the average time yields a financial penalty, whileperformance that beats the average results in a financial reward.

Contract durations can range from a few weeks, in the case ofa single well, to as long as three to five years, for a series of deep-water wells. Drilling contracts in shallow water tend to be writtenon a per well basis, while in the deepwater, contracts are writtenover a longer period of time. Turnkey contracts are used in the Gulfof Mexico in about 10% of wells drilled, and are significantly lesscommon in other basins.

Dayrate contracts

There are significant differences between dayrate and turnkeycontracts with respect to risk allocation and insurance. Undera dayrate contract, the E&P company pays the drilling contractora fixed fee per day worked. The responsibilities of the operator andcontractor are specified in the drilling contract, but typically, theoperator is responsible for: (1) rig relocation cost; (2) well designand decisions regarding the drilling process, including total vertical

M.J. Kaiser / Energy 34 (2009) 1097–1112 1111

depth, mud type, mud weight, hole diameter, bit type, number ofcasing strings, etc.; (3) coordinating supply purchases and delivery;and (4) contracting for specialty services.

The contractor is responsible for (1) rig, including activities suchas tripping of drill pipe, running and retrieving riser, runningcasing, and testing blowout preventer and surface equipment; (2)fully staffed crew, which include the toolpusher, driller, derrick-man, several roughnecks and roustabouts, and other specialistsdepending on the contract specification; (3) repair and mainte-nance of the rig and equipment; and (4) specified materials andsupplies. Circulating systems, horizontal displacement, weight onbit, and pump rate may be managed by the operator and contractor.

The E&P company has one or more personnel stationed on-siteto direct and supervise the drilling operation and provide supportservices. Support personnel typically includes the company man,drilling engineer, mud engineer, geologist, and logger. Support andcoordination tasks for the purchase and delivery of all othermaterials required for drilling, supplies, and equipment is borne bythe E&P company. Logging, core tests, drilling mud, drill pipe, bits,casing and well equipment are typically supplied by the operator.The E&P company is also responsible for back-up services, trans-portation, and tugs during operations.

The contractor owns the rig and is responsible for its mainte-nance, crew training, and management. The driller gives the ordersin running the rig, but decisions on how the hole is to be drilledare made by the E&P company. Drilling activities are monitored bythe company man, rig-based support personnel, and in some cases,the headquarters staff. Well data is analyzed, geophysical condi-tions evaluated, and decisions are made as to the type of bit toemploy, its orientation, the weight and pressure of the mud,drilling tests, logs, cores to be performed, etc.

Turnkey contracts

In a turnkey contract, the drilling contractor designs the well,purchases all the consumables, establishes contracts for thetransport and support services, drills the well, and charges the E&Pcompany a fixed sum of money for the operation. The role of theoperator in this case is to specify the drilling targets and evaluationrequirements, and to specify the configuration of the completedwellbore. Under a turnkey contract, the E&P company is selling theproject risk to a contractor who is paid a fixed fee in return fordrilling a well of given specification. The contractor assumes allresponsibility and is in total charge of drilling and completionoperations. The E&P company normally retains the risk for extremeweather events and specific geologic formations, but if thecontractor expects the E&P company is letting the contract ona ‘‘lemon’’ (i.e., extremely risky, difficult, and/or complex well), thecontractor will price at a premium in a way that reflects higherexpected cost. The ability to price a turnkey drilling contract tomake a profit requires extensive experience, tight cost controls anda balanced portfolio of projects to spread the risk.

Negotiation and risk allocation

In a tight market, where rig utilization and dayrates are high,contractors are able to negotiate favorable terms, while in a softmarket, operators are often able to reshape contracts in their favor.Thus, contractors tend to enjoy high rates, high utilization, andfavorable contract terms in good markets, and low rates, poorutilization, and unfavorable contracts in soft markets.

Under a dayrate contract, the dayrate charged and servicesperformed are the negotiating factors, while under a turnkey,drillers compete on the price of the total job. The turnkey option isused primarily as a risk management tool. Marginal well economics

often demand a known drilling cost in order to justify projectapproval, and co-ventures may want the operating partner to fix orguarantee the well cost. Although underbidding a project wouldallow a contractor to keep its rigs working in a downturn, if thecontractor bid a price that did not cover its cost, significant losseswould be realized. Turnkey contracts offer strong incentives tofinish the job early since the contractor retains the full cost savingsof early completion. Turnkey bids can also be used as a way ofbenchmarking the performance of the drilling staff, since thereusually does not exist a way to properly validate a drilling AFE.

The main purpose of risk allocation in the offshore industry isto create a clear delineation of risk to enable each party tomeasure the risk exposure it will absorb or insure. Risks aregenerally allocated without regard to cause, with the customarypractice for the contractor to bear the risks of personal injury ordeath of its personnel and assume liability for rig and associatedcontractor equipment loss or damage. The operator normallyaccepts liability for its own personnel and property, and in dayratecontracts, assumes responsibility for well related risks (includingpollution, wild well control, well damage or loss) and reservoirdamage.

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