SPE 26339Society of Petroleum Engineers

Risk Analysis and Monte Carlo Simulation Applied to the Generation of Drilling APEEstimatesS.K.Peterson, Marathon Oil Co., I.A.Murtha, Consultant, and F.F.Schneider, Marathon Oil Co.

SPEMembers

Copyright 1993, Society of Petroleum EDgioeen, IDe.

TbII ..... __ HIeded rar pnHIllallon It)' an SPE I'reInm CcImmI_ r...-... rm- flllDl'OI'III8lIan _ ........ ID an _..mmlled It)' the aulhar(a). Can.... fllthe ........ , .........baWl not II-. It)' the Sad" fll EnaID-- and .... aubject '" awnctIan It)' theaulhar(a). The.......u ,............ not n-ntJnIIIdany paallion flllhelladlt7 fll.........m EnaID I.. oman. ar m Papan , at SPE -mp.... aubJad '" publlalllon review It)' EdItarial CcImmI_ fllthe IladIt7 fllPelroleum En........ 1'a'mJuIan '"...". .. nelrIc:ted '" an ....._ fll not _than 381 m...-..., not be CIIpIed. Theabolnd ahould _ ..... -..,......... ""*'-\edpIenl fll ......and It)' wham the .......pnHIl..... Write LIbnrIIIIl. SPE. P.O. Box 833lIM,~TX '754IlIh1IU, U.s.A. T.... '131M SPEDAL.

ABSTRACT

The purpose of this paper is to present a methodology fordeveloping an APE-generating model, using a specificoffshore field development case study to illustrate thetechnique. The model utilizes risk analysis andincorporates Monte Carlo simulation in conjunction withstatistical analysis of historical drilling data to generatemore accurate, risked, APE estimates. In addition to thegeneral methodology, we present an example of an APEestimate using the presented techniques with aninterpretation and statistical analysis of three years ofdrilling data for the North Sea.

INTRODUCTION

Several concurrent movements have contributed to thisinvestigation using risk analysis and Monte Carlosimulation to generate Authorization for Expenditures(AFEs) for drilling operations: (1) the availability ofhistorical drilling data, (2) the recognition of theinadequacies of current AFE-writing procedures, and, (3)the acceptance of risk analysis methodology.

The Availability of Accurate Historical Data

In the past few years it bas become standard practice formajor operators to collect a variety of data relevant todrilling operations in database format. In our case, thedata were gathered initially as part of a worldwide effort(1) to collect time and cost information for variousoperations; (2) to document drilling problems, theirassociated time and costs, and their solutions; and, (3) to

References and illustrations at end of paper

provide a basis for future comparisons of drillingperformance.!

The degree of detail collected in our drilling data allowedmore accurate drilling performance evaluation. For eachoperational phase during the drilling operations, trouble­free and trouble events were recorded distinctly.

As with many operators, we are evaluating the value ofthis data. Therefore, we have begun to question theusefulness, potential usefulness, and shortcomings of thedata acquired.

Current AFE-Writing Procedures

For many engineers, the task ofwriting an APE consists ofartfully incorporating offset well data, engineeringcalculations, projections regarding operationalimprovements, and judgments about suitable contingencies.Fundamental to the APE estimate is an estimate of time toperform the various operations. Our attempts to analyzethe first three years of drilling data highlighted that currentAFE-writing procedures are inadequate. particularly if agoal is to compare actual drilling performance to predictedperformance. First, it was unclear exactly how the APEtime estimate was arrived at. Secondly, the APEcategories recorded did not clearly coincide with theoperational phases distinguished in the database. Otheroperators have reported on similar concerns and offeredguidelines for predictive statistical methods.2,3,4

Meanwhile, the desire to more wisely allocate limiteddrilling funds among potential projects has accentuated theneed for representative APE estimates, thereby

2 RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THEGENERATION OF DRILLING APE ESTIMATES

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perpetuating the use of drilling "performance" evaluationbased on APE estimates.

Peiformance Evaluation

A popular method of quantifying drilling performance hasbeen to look at problem time as a percentage of actualtime. Drilling personnel are often held accountable forexcess costs, especially those associated with problematicevents commonly referred to as "trouble time." Yet inspite of painstakingly recording each trouble event duringthe actual drilling, few (if any) operators clearlydistinguish problem-free time from problem time on theAPE, thus making fair judgment in a historical contextnearly impossible, except by those most intimate with thearea. Occasionally the obscure "contingencies" categoryshows up on the APE.

In addition, at least one major company has used APE­deviation analysis as a method of drilling performanceevaluation.5 Fig. 1 illustrates the cumulative frequency ofdeviation of the actual dry-hole times from the APEd dry­hole times. The deviation is calculated as the differencebetween the actual and APEd times, and is reported as apercentage of the APEd dry-hole times. A rule of thumbhas been to regard the range from -10 % to +10% as anacceptable, or desirable, range for the deviations. Wellswith deviations outside this range are frequently subjectedto closer scrutiny, often disregarding that given theinherent uncertainty associated with drilling, it would beexpected that some APE deviations fall outside that range.

Allocation ofAvailable Drilling Funds

The convention that management uses to analyze drillingperformance by comparing APE costs to actual costsincorporates the philosophy that APEs should be written toensure that just enough money is approved to drill thewell, without being short of funds or leaving unspent funds"on the table." This makes good business sense, allowingoperators to drill as many promising prospects as possiblein a period while staying within the constraints of anapproved budget. In recent years especially, restricteddrilling budgets have given impetus to this philosophywhich perpetuates the practice ofjudging drillingperformance by comparing it to the deterministic APE. Inthe future, some operators will likely take a portfolioanalysis approach for selecting drilling projects to moreprudently allocate drilling funds.

The Acceptance of Risk Analysis Methodology

Risk analysis methods were articulated in the sixties6,7,8and appeared to take hold in the oil and gas industry in themid-seventies9,10. Both managers and technical staff,however, resisted embracing stochastic modeling untilmore recently as papers began to routinely appear on thesubject of Monte Carlo simulation and related topicsll-16.Among possible explanations for the rebirth of interest arethe emphasis on-quantifying alternative choices competingfor limited budgets, the availability of fast, inexpensivedesktop computers, and, the availability of inexpensivespreadsheet-based simulation software.

In recent drilling literature, statistical analysis of drillingdata and predictions seem to be appearing more ~uentlyas well, particularly with regard to stuck pipe.l7-2

Using Risk Analysis with the Historical Data

A natural use of the historical data available from thedrilling database is to improve time and cost estimates forwells in a specific area. Ideally, in an area where acompany has experience, the APE would be written usingthe results of statistical analysis of offset data. In this way,the APE should be fully reproducible by any qualifiedengineer designing the well plan under the same operatingparameters, and post-mortem analysis would be consistent.Rather than a deterministic estimate, a more mature viewof an APE estimate might be one in which the range ofpossible times and costs are presented, in recognition ofthe inherent uncertainty associated with drilling wells. Arisk analysis methodology incorporating Monte Carlotechniques using the historical data available couldaccomplish this goal.

THE MEmODOLOGY

Monte Carlo simulation methods appear to be gainingacceptance by engineers, geoscientists, and otherprofessionals who wish to evaluate prospects or to analyzeproblems that involve uncertainty. The user is required toprescribe statistical distributions for the input parameters.Selecting these distributions is guided by experience andfundamental principles, but driven by historical data. Iftwo or more variables are dependent on one another, thatdependency must be included in the model.

Monte Carlo Simulation

A Monte Carlo simulation begins with a model in the formof one or more equations. The variables of the equations

SPE 26339 S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER 3

are separated into inputs and outputs. Some or all of theinputs are treated as probability distributions rather thannumbers. The resulting outputs are then also distributions,described in terms such as minimum, maximum, and mostlikely values, means and standard deviations, 90thpercentile, and so on.

Running a Monte Carlo simulation is customarily doneusing special software, either spreadsheet add-ins orcompiled programs. A trial consists of selecting one valuefor each input parameter, according to some specifieddistribution, and calculating the output. A simulation is asuccession of hundreds or thousands of repeated trials,during which the output values are stored. Afterwards theoutput values for each output are grouped into a histogramor cumulative distribution function.

Monte Carlo simulation is an alternative to both singlepoint (deterministic) estimation and the scenario approachthat presents worst, most likely, and best cases.

Distributions and Data Presentation

The cumulative distribution function (COF) is useful toillustrate how Monte Carlo sampling is accomplished, asshown in Fig. 2. First a uniformly distributed randomnumber is selected between 0 and 1 and used to enter thevertical axis, which represents cumulative probability.Proceeding to the curve and then down to the horizontalaxis, a unique value of the corresponding parameter isdetermined. Thus, the sampling process requires only theexistence of a COF for the parameter being sampled. Thisis the key to using any set of historical data as a model foran input distribution. We simply construct the COF forthe data, by first grouping it into classes and thencalculating the cumulative relative frequency.

Output distributions are most often represented with a COFas well, although some people prefer the probabilitydensity function (pOF).

Dependency

One rule of Monte Carlo simulation is that the variablesare assumed to be independent. In reality, many commonmodels contain parameters that depend on each other in acause-and-effect manner. Linear dependency can berecognized by making a "scatter plot" or "crossplot", andchecking the correlation coefficient. If this type ofdependency exists, it must be incorporated into the model.

CASE STUDY - USING mSTORICAL DATA TOGENERATE AN AFE

This example results from an analysis of drilling time andperformance data on 27 wells drilled in the U.K. North Seasince 1990. For the purposes of this introductory paper,the primary focus of the model was to predict the time ofthe dry hole drilling operations necessary to achieve thework planned in the AFE and thereby to meet the dry-holedepth or geologic objectives.

Problem time was defined in strict terms as any incident inthe operation that delayed or slowed the progress of thewell, even if the problem could have been reasonablyanticipated or took a relatively short time to remedy. Forexample, problem time could range from a one-half hourdelay in a bit trip due to "tight hole, " to a 20-day delaydue to a well control problem resulting in stuck pipe and asidetrack to redrill that hole interval.

1heModel

In our case, the model can be described by three equationsthat summarize the rig time required to drill a well throughthe AFE dry-hole objective:

(1) Total problem free time = problem free MoblDemobtime + problem free drilling time + problem freeevaluation time + problem free P&A time

(2) Total problem time = problem MoblDemob time +problem drilling time + problem evaluation time +problem P&A time

(3) Total time = total problem free time + total problemtime

The model is initiated based on the projected depth of thewell for which the AFE is to be written. The single-valueinput depth becomes a distribution by accounting forvariations in actual depth from AFEd depth based on thehistorical data. Other input parameters are distributionsfor each of the parameters on the right-hand side ofequations (1) and (2).

For the purposes of this example, the three outputdistributions are total problem free time, total problemtime, and total time.

The Input Distributions

We used history-matching software called BestFit21 tomatch our data to the best distribution by the chi-square

4 RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THEGENERATION OF DRILLING AFE ESTIMATES

SPE 26339

"goodness of fit" criterion. We selected several candidatedistributions such as normal, lognormal, triangular, beta,gamma, and exponential. Fig. 3 shows the CDF from thehistory match for the problem-free drilling time inputparameter. Table 1 records the corresponding distributionsfor each of the problem-free and problem time inputs.Interestingly, many of the times were best represented bythe gamma distribution.

While perhaps not as familiar to petroleum engineers andgeoscientists as triangular, normal, and lognormal types,the gamma distribution is quite commonly used in otherdisciplines and has several useful features. Based on thegamma function, which simply extends the factorialfunction to real numbers other than whole numbers, thegamma distribution is a generalization of both theexponential and the chi-square distributions. The betadistribution can be defined in terms of the gamma. Thegamma distribution is used to revise prior probabilitydistributions in light of experimental sample data. Dhir etal used the gamma distribution to model permeability(notoriously right skewed), reservoir pressure, and gascontent in a coalbed methane volumetric model.

Dependency

We checked the dependency of the nine input parametersusing crossplots of the raw data, and then calculation of therank correlation coefficients (as are customarily used inMonte Carlo simulation). Rank correlation coefficientsdescribe relationships between parameters, withoutinfluence by either the types of underlying distributions orthe magnitudes of the parameters. The only parametersthat showed dependence were the problem-free and theproblem drilling days, which were strongly dependent ondepth, as expected. Figs. 4 and 5 show the crossplots.The rank correlation coefficients were 0.82 and 0.62,respectively. The dependency was inco~rated into themodel using the bounding box method.2

We also checked whether or not a learning curve effect wasinfluencing the well times. Fig. 6 illustrates the lack ofchronological dependence of the data. This is notsurprising, since the operator has been actively drilling inthis area for several years. In addition, exploration anddevelopment wells showed no important differences indrilling times (either trouble-free or trouble times) throughthe AFE-scope of work.

Results ofMonte Carlo Simulation

Two cases were run using @RISK23, a spreadsheet add-in,to prepare an AFE time estimated based on the historicaldata using Monte Carlo simulation results. Simulationswere run for 1,000 iterations and outputs were graphed inPDF format. The first case was for a 20,090 ft well, andthe second was for a 17,907 ft well. In each case thesimulation results were compared to the original AFE timeestimates and actual well times.

20.090 ft Well

Figs. 7, 8, and 9 are the three output PDFs generated byMonte Carlo simulation for a 20,090 ft well. The PDFsillustrate the ranges of problem-free, problem, and totaldays for the well. The expected value for each of theoutput distributions is the mean of the distribution. Thewell was AFEd using conventional methods for 180 daysdry-hole, with no specific time allotment for problem days.The Monte Carlo simulation provided an expected valuetime estimate of 194 days, of which 36 days were due toproblem time. The well was drilled in 192 days, with 32.5days of problem time. Table 2 shows the simulation­generated AFE times and compares them to theconventionally-generated AFE times and the actual welltimes.

17.907 ft Well

This well was a development well, therefore no timeestimates were required for MoblDemob or P&Aoperations. The original well AFE called for a total dry­hole time estimate of 121 days. Monte Carlo simulationyielded a total time estimate of 135 days, of which 25 dayswere expected to be problem time. The well was drilled in132 days., with 19.5 days of problem time. Table 3compares the two AFE estimates to the actual well times.

For both cases, the AFEs generated using risk analysis andMonte Carlo simulation were more accurate than theconventionally-generated AFE estimates. The outputPDFs helped to clarify the uncertainty associated withdrilling operations based on historical data, and to quantifythe contribution of problem days to total days.

CONCLUSIONS AND RECOMMENDATIONS

1. We have presented the application of Monte Carlosimulation in conjunction with statistical analysis ofdrilling data to generate more accurate, risked, AFEestimates.

SPE 26339 S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER 5

2. We have introduced a non-standard use of datacollected in typical drilling databases.

3. The AFE-estimating routine presented in this paperwould be applicable to any development field drillingprogram, although its greatest use will be in those fieldswith adverse and difficult drilling conditions. Theadvantages are the reproducibility of time estimates as theyincorporate historical data, the more representative natureof the stochastic estimates instead of the traditionaldeterministic estimate, and the flexibility to improve asmore data is obtained.

4. The two AFE estimates generated using Monte Carlosimulation were better predictors of the actual well daysthan the conventionally-generated AFE estimates, offeredmore insight of problem-free and problem dayscontribution to the total days, and emphasized theuncertainty associated with drilling operations.

5. The example presented is an elementary use of riskanalysis and Monte Carlo simulation; the methodology hasthe ability, however, to be expanded as the quality of thehistorical drilling data permits, and to be combined withappropriate price forecasts in order to fully generate anAFE.

ACKNOWLEDGMENTS

The authors would like to thank Marathon Oil Co. forpermission to publish this paper. The authors offer specialthanks to I.A. Turley, C.W. Truby, and J.C. Branniganfor their contributions to the original work.

REFERENCES

1. Brannigan, I.C. : "The Characterization of DrillingOperations and Their Representation in RelationalDatabases, " paper SPE 24429 presented at the SeventhSPE Petroleum Computer Conference, Houston, TX,July 19-22, 1992.

2. Kadaster, A.G., Townsend, C.W., and Albaugh, E.K.:"Drilling Time Analysis: A Total Quality ManagementTool for Drilling in the 1990's," paper SPE 24559presented at the 67th Annual Technical Conference andExhibition of the Society of Petroleum Engineers,Washington, D.C., October 4-7, 1992.

3. Shilling, K.B., and Lowe, D.E.: "Systems forAutomated Drilling AFE Cost Estimating andTracking," paper SPE 20331 presented at the Fifth SPE

Petroleum Conference, Denver, Colorado, June 25-28,1990.

4. Noerager, J.A. et al.: "Drilling Time PredictionsFrom Statistical Analysis," paper SPEIIADC 16164presented at the 1987 SPEIIADC Drilling Conference,New Orleans, LA, March 15-18, 1987.

5. Peterson, S.K. and Pearce, D.W.: "The Effect ofUnplanned Operations on Drilling PerformanceEvaluation," ·paperSPEtIADC-25761 presented at the1993 SPEIIADC Drilling Conference, Amsterdam,February 23-25, 1993.

6. Hertz, D.B.: "Risk Analysis in Capital Investments,"Harvard Business Review, Jan. - Feb. 1964, p. 95-106.

7. Howard, R.A.: "Decision Analysis: Practice andPromise, " Management Science, 34, p.679-695.

8. Walstrom, J.E., Mueller, T.D., and McFarlane, R.C.:"Evaluating Uncertainty in Engineering Calculations, "lPT (Dec. 1967) 1595.

9. McCray, A.W:, Petroleum Evaluations and EconomicDecisions, Prentice-Hall, Inc. Englewood Cliffs, NJ,1975.

10. Megill, R.E., An Introduction to Risk Analysis,Petroleum Publishing Co., Tulsa, 1977.

11. Cronquist, C.: "Reserves and Probabilities­Synergism or Anachronism?, lPT (Oct. 1991) 1258­1264.

12. Damsleth, E. and Hage, A.: "Maximum Informationat Minimum Cost: A North Sea Field DevelopmentStudy Using Experimental Design," paper SPE 23139presented at the 1991 Offshore Europe Conference,Aberdeen.

13. Davies, G.G. and Whiteside, M.W.: "An IntegratedApproach to Prospect Evaluation, " paper 23157presented at the 1991 Offshore Europe Conference,Aberdeen.

14. Dhir, R., Dem, R.R. and Mavor, M.J.: "Economicand Reserve Evaluation of Coalbed MethaneReservoirs," lPT(Dec. 1991) 1424-1431.

15. Murtha, J.A.: "Infill Drilling in the Clinton: MonteCarlo Techniques Applied to the Material Balance

6 RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THEGENERATION OF DRILLING APE ESTIMATES

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Equation, " paper SPE 17068 presented at the 1987Eastern Regional Meeting, Pittsburgh, 21-23 October.

16. Murtha, J.A.: "Incorporating Historical Data inMonte Carlo Simulation, If paper SPE 25245 presentedat the 1993 Petroleum Computer Conference, NewOrleans, July 11- 14.

17. Weakley, R.R.: "Use of Stuck Pipe Statistics ToReduce the Occurrence of Stuck Pipe, " paper SPE20410 presented at the 65th Annual TechnicalConference and Exhibition of the Society of PetroleumEngineers, New Orleans, 23-26 September 1990.

18. Schofield, T.R., Whelehan, O.P., and Baruya, A.:"A New Fishing Equation, " paper SPE 22380presented at the SPE International Meeting onPetroleum Engineering, Beijing, China 24-27 March1992.

19. Harrison, C.G.:" "Fishing Decisions UnderUncertainty, " lPT (Feb. 1992) 299-300.

20. Shivers, R.M. and Domangue, R.J.: "OperationalDecision Making for Stuck-Pipe Incidents in the Gulfof Mexico: A Risk Economics Approach, " SPEDrilling and Completion, (June 1993) 125-130.

21. "BestFit - Distribution Fitting Software forWindows, " Beta Release 1.0,Palisade·Corp.,Newfield, NY, 1993.

22. Murtha, J.A., Decisions Involving Uncertainty - An@RISK Tutorialfor the Petroleum Industry, Houston,1993.

23. "@RISK - Risk Analysis and Simulation Add-in forMicrosoft Excel," Release 1.1 User's Guide, PalisadeCorp., Newfield, NY, 1992.

Table 1 - Input Distributions

Input Parameter Input DistributionDepth variation Normal(-14.64,395)

Problem-free MoblDemob days Gamma(5.23,0.49)Problem-free drilling; dayS Gamma(4.16,12.61)

Problem-free evaluation days Gamma(2.97,2.92)Problem-free P&A days Loe:normal(4.98,3.13)

MoblDemob problem days Gamma(0.97,1.34)Drilling problem dayS Exp(13.99)

Evaluation problem dayS Gamma(0.26,4.83)P&A problem days Gamma(0.51,2.06)

Table 2 - AFE to Actual Comparison for 20,090 ft Well

Actual Well Conventional AFE Simulation AFEProblem-free days 159.5 NA 158

Problem days 32.5 NA 36Total dayS 192 180 194

Table 3 - AFE to Actual Comparison for 17,907 ft Well

Actual Well Conventional AFE Simulation AFEProblem-free days 112.5 NA 110

Problem days 19.5 NA 25Total dayS 132 121 135

SPE 26339 S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER 7

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8 RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THEGENERATION OF DRILLING AFE ESTIMATES

SPE26339

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SPE 26339 S.K..PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER 9

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