SPE26339 Risk Analysis Drilling AFE

Society of Petroleum Engineers

SPE 26339

Risk Analysis and Monte Carlo Simulation Applied to the Generation of Drilling APE Estimates S.K.Peterson, Marathon Oil Co., I.A.Murtha, Consultant, and F.F.Schneider, Marathon Oil Co. SPEMembers Copyright 1993, Society of Petroleum EDgioeen, IDe.

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ABSTRACT The purpose of this paper is to present a methodology for developing an APE-generating model, using a specific offshore field development case study to illustrate the technique. The model utilizes risk analysis and incorporates Monte Carlo simulation in conjunction with statistical analysis of historical drilling data to generate more accurate, risked, APE estimates. In addition to the general methodology, we present an example of an APE estimate using the presented techniques with an interpretation and statistical analysis of three years of drilling data for the North Sea.

provide a basis for future comparisons of drilling performance.! The degree of detail collected in our drilling data allowed more accurate drilling performance evaluation. For each operational phase during the drilling operations, troublefree and trouble events were recorded distinctly. As with many operators, we are evaluating the value of this data. Therefore, we have begun to question the usefulness, potential usefulness, and shortcomings of the data acquired.

Current AFE-Writing Procedures INTRODUCTION Several concurrent movements have contributed to this investigation using risk analysis and Monte Carlo simulation to generate Authorization for Expenditures (AFEs) for drilling operations: (1) the availability of historical drilling data, (2) the recognition of the inadequacies 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 for major operators to collect a variety of data relevant to drilling operations in database format. In our case, the data were gathered initially as part of a worldwide effort (1) to collect time and cost information for various operations; (2) to document drilling problems, their associated time and costs, and their solutions; and, (3) to

References and illustrations at end of paper

For many engineers, the task of writing an APE consists of artfully incorporating offset well data, engineering calculations, projections regarding operational improvements, and judgments about suitable contingencies. Fundamental to the APE estimate is an estimate of time to perform the various operations. Our attempts to analyze the first three years of drilling data highlighted that current AFE-writing procedures are inadequate. particularly if a goal is to compare actual drilling performance to predicted performance. First, it was unclear exactly how the APE time estimate was arrived at. Secondly, the APE categories recorded did not clearly coincide with the operational phases distinguished in the database. Other operators have reported on similar concerns and offered guidelines for predictive statistical methods. 2 ,3,4 Meanwhile, the desire to more wisely allocate limited drilling funds among potential projects has accentuated the need for representative APE estimates, thereby

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RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THE GENERATION OF DRILLING APE ESTIMATES

perpetuating the use of drilling "performance" evaluation based on APE estimates.

Peiformance Evaluation A popular method of quantifying drilling performance has been to look at problem time as a percentage of actual time. Drilling personnel are often held accountable for excess costs, especially those associated with problematic events commonly referred to as "trouble time." Yet in spite of painstakingly recording each trouble event during the actual drilling, few (if any) operators clearly distinguish problem-free time from problem time on the APE, thus making fair judgment in a historical context nearly impossible, except by those most intimate with the area. Occasionally the obscure "contingencies" category shows up on the APE.

In addition, at least one major company has used APEdeviation analysis as a method of drilling performance evaluation. 5 Fig. 1 illustrates the cumulative frequency of deviation of the actual dry-hole times from the APEd dryhole times. The deviation is calculated as the difference between the actual and APEd times, and is reported as a percentage of the APEd dry-hole times. A rule of thumb has been to regard the range from -10 % to + 10% as an acceptable, or desirable, range for the deviations. Wells with deviations outside this range are frequently subjected to closer scrutiny, often disregarding that given the inherent uncertainty associated with drilling, it would be expected that some APE deviations fall outside that range.

Allocation ofAvailable Drilling Funds The convention that management uses to analyze drilling performance by comparing APE costs to actual costs incorporates the philosophy that APEs should be written to ensure that just enough money is approved to drill the well, without being short of funds or leaving unspent funds "on the table." This makes good business sense, allowing operators to drill as many promising prospects as possible in a period while staying within the constraints of an approved budget. In recent years especially, restricted drilling budgets have given impetus to this philosophy which perpetuates the practice ofjudging drilling performance by comparing it to the deterministic APE. In the future, some operators will likely take a portfolio analysis approach for selecting drilling projects to more prudently allocate drilling funds.

SPE 26339

The Acceptance of Risk Analysis Methodology Risk analysis methods were articulated in the sixties6 ,7,8 and appeared to take hold in the oil and gas industry in the mid-seventies9 ,10. Both managers and technical staff, however, resisted embracing stochastic modeling until more recently as papers began to routinely appear on the subject of Monte Carlo simulation and related topics ll - 16 . Among possible explanations for the rebirth of interest are the emphasis on-quantifying alternative choices competing for limited budgets, the availability of fast, inexpensive desktop computers, and, the availability of inexpensive spreadsheet-based simulation software.

In recent drilling literature, statistical analysis of drilling data and predictions seem to be appearing more ~uently as 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 the drilling database is to improve time and cost estimates for wells in a specific area. Ideally, in an area where a company has experience, the APE would be written using the results of statistical analysis of offset data. In this way, the APE should be fully reproducible by any qualified engineer designing the well plan under the same operating parameters, and post-mortem analysis would be consistent. Rather than a deterministic estimate, a more mature view of an APE estimate might be one in which the range of possible times and costs are presented, in recognition of the inherent uncertainty associated with drilling wells. A risk analysis methodology incorporating Monte Carlo techniques using the historical data available could accomplish this goal.

THE MEmODOLOGY Monte Carlo simulation methods appear to be gaining acceptance by engineers, geoscientists, and other professionals who wish to evaluate prospects or to analyze problems that involve uncertainty. The user is required to prescribe statistical distributions for the input parameters. Selecting these distributions is guided by experience and fundamental principles, but driven by historical data. If two or more variables are dependent on one another, that dependency must be included in the model.

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

SPE 26339

S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER

are separated into inputs and outputs. Some or all of the inputs are treated as probability distributions rather than numbers. The resulting outputs are then also distributions, described in terms such as minimum, maximum, and most likely values, means and standard deviations, 90th percentile, and so on. Running a Monte Carlo simulation is customarily done using special software, either spreadsheet add-ins or compiled programs. A trial consists of selecting one value for each input parameter, according to some specified distribution, and calculating the output. A simulation is a succession of hundreds or thousands of repeated trials, during which the output values are stored. Afterwards the output values for each output are grouped into a histogram or cumulative distribution function. Monte Carlo simulation is an alternative to both single point (deterministic) estimation and the scenario approach that presents worst, most likely, and best cases.

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CASE STUDY - USING mSTORICAL DATA TO GENERATE AN AFE This example results from an analysis of drilling time and performance data on 27 wells drilled in the U.K. North Sea since 1990. For the purposes of this introductory paper, the primary focus of the model was to predict the time of the dry hole drilling operations necessary to achieve the work planned in the AFE and thereby to meet the dry-hole depth or geologic objectives. Problem time was defined in strict terms as any incident in the operation that delayed or slowed the progress of the well, even if the problem could have been reasonably anticipated or took a relatively short time to remedy. For example, problem time could range from a one-half hour delay in a bit trip due to "tight hole, " to a 20-day delay due to a well control problem resulting in stuck pipe and a sidetrack to redrill that hole interval.

1heModel Distributions and Data Presentation The cumulative distribution function (COF) is useful to illustrate how Monte Carlo sampling is accomplished, as shown in Fig. 2. First a uniformly distributed random number is selected between 0 and 1 and used to enter the vertical axis, which represents cumulative probability. Proceeding to the curve and then down to the horizontal axis, a unique value of the corresponding parameter is determined. Thus, the sampling process requires only the existence of a COF for the parameter being sampled. This is the key to using any set of historical data as a model for an input distribution. We simply construct the COF for the data, by first grouping it into classes and then calculating the cumulative relative frequency. Output distributions are most often represented with a COF as well, although some people prefer the probability density function (pOF).

Dependency One rule of Monte Carlo simulation is that the variables are assumed to be independent. In reality, many common models contain parameters that depend on each other in a cause-and-effect manner. Linear dependency can be recognized by making a "scatter plot" or "crossplot", and checking the correlation coefficient. If this type of dependency exists, it must be incorporated into the model.

In our case, the model can be described by three equations that summarize the rig time required to drill a well through the AFE dry-hole objective: (1) Total problem free time = problem free MoblDemob time + problem free drilling time + problem free evaluation 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 time

+

+ total problem

The model is initiated based on the projected depth of the well for which the AFE is to be written. The single-value input depth becomes a distribution by accounting for variations in actual depth from AFEd depth based on the historical data. Other input parameters are distributions for each of the parameters on the right-hand side of equations (1) and (2). For the purposes of this example, the three output distributions are total problem free time, total problem time, and total time.

The Input Distributions We used history-matching software called BestFit21 to match our data to the best distribution by the chi-square

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RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THE GENERATION OF DRILLING AFE ESTIMATES

"goodness of fit" criterion. We selected several candidate distributions such as normal, lognormal, triangular, beta, gamma, and exponential. Fig. 3 shows the CDF from the history match for the problem-free drilling time input parameter. Table 1 records the corresponding distributions for each of the problem-free and problem time inputs. Interestingly, many of the times were best represented by the gamma distribution. While perhaps not as familiar to petroleum engineers and geoscientists as triangular, normal, and lognormal types, the gamma distribution is quite commonly used in other disciplines and has several useful features. Based on the gamma function, which simply extends the factorial function to real numbers other than whole numbers, the gamma distribution is a generalization of both the exponential and the chi-square distributions. The beta distribution can be defined in terms of the gamma. The gamma distribution is used to revise prior probability distributions in light of experimental sample data. Dhir et al used the gamma distribution to model permeability (notoriously right skewed), reservoir pressure, and gas content in a coalbed methane volumetric model.

Dependency We checked the dependency of the nine input parameters using crossplots of the raw data, and then calculation of the rank correlation coefficients (as are customarily used in Monte Carlo simulation). Rank correlation coefficients describe relationships between parameters, without influence by either the types of underlying distributions or the magnitudes of the parameters. The only parameters that showed dependence were the problem-free and the problem drilling days, which were strongly dependent on depth, 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 the model using the bounding box method. 2 We also checked whether or not a learning curve effect was influencing the well times. Fig. 6 illustrates the lack of chronological dependence of the data. This is not surprising, since the operator has been actively drilling in this area for several years. In addition, exploration and development wells showed no important differences in drilling times (either trouble-free or trouble times) through the AFE-scope of work.

SPE 26339

Results ofMonte Carlo Simulation Two cases were run using @RISK23, a spreadsheet add-in, to prepare an AFE time estimated based on the historical data using Monte Carlo simulation results. Simulations were run for 1,000 iterations and outputs were graphed in PDF format. The first case was for a 20,090 ft well, and the second was for a 17,907 ft well. In each case the simulation results were compared to the original AFE time estimates and actual well times. 20.090 ft Well Figs. 7, 8, and 9 are the three output PDFs generated by Monte Carlo simulation for a 20,090 ft well. The PDFs illustrate the ranges of problem-free, problem, and total days for the well. The expected value for each of the output distributions is the mean of the distribution. The well was AFEd using conventional methods for 180 days dry-hole, with no specific time allotment for problem days. The Monte Carlo simulation provided an expected value time estimate of 194 days, of which 36 days were due to problem time. The well was drilled in 192 days, with 32.5 days of problem time. Table 2 shows the simulationgenerated AFE times and compares them to the conventionally-generated AFE times and the actual well times. 17.907 ft Well This well was a development well, therefore no time estimates were required for MoblDemob or P&A operations. The original well AFE called for a total dryhole time estimate of 121 days. Monte Carlo simulation yielded a total time estimate of 135 days, of which 25 days were expected to be problem time. The well was drilled in 132 days., with 19.5 days of problem time. Table 3 compares the two AFE estimates to the actual well times. For both cases, the AFEs generated using risk analysis and Monte Carlo simulation were more accurate than the conventionally-generated AFE estimates. The output PDFs helped to clarify the uncertainty associated with drilling operations based on historical data, and to quantify the contribution of problem days to total days.

CONCLUSIONS AND RECOMMENDATIONS 1. We have presented the application of Monte Carlo simulation in conjunction with statistical analysis of drilling data to generate more accurate, risked, AFE estimates.

SPE 26339

S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER

2. We have introduced a non-standard use of data collected in typical drilling databases. 3. The AFE-estimating routine presented in this paper would be applicable to any development field drilling program, although its greatest use will be in those fields with adverse and difficult drilling conditions. The advantages are the reproducibility of time estimates as they incorporate historical data, the more representative nature of the stochastic estimates instead of the traditional deterministic estimate, and the flexibility to improve as more data is obtained. 4. The two AFE estimates generated using Monte Carlo simulation were better predictors of the actual well days than the conventionally-generated AFE estimates, offered more insight of problem-free and problem days contribution to the total days, and emphasized the uncertainty associated with drilling operations. 5. The example presented is an elementary use of risk analysis and Monte Carlo simulation; the methodology has the ability, however, to be expanded as the quality of the historical drilling data permits, and to be combined with appropriate price forecasts in order to fully generate an AFE.

ACKNOWLEDGMENTS The authors would like to thank Marathon Oil Co. for permission to publish this paper. The authors offer special thanks to I.A. Turley, C.W. Truby, and J.C. Brannigan for their contributions to the original work.

REFERENCES 1. Brannigan, I. C. : "The Characterization of Drilling Operations and Their Representation in Relational Databases, " paper SPE 24429 presented at the Seventh SPE 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 Management Tool for Drilling in the 1990's," paper SPE 24559 presented at the 67th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Washington, D.C., October 4-7, 1992. 3. Shilling, K.B., and Lowe, D.E.: "Systems for Automated Drilling AFE Cost Estimating and Tracking," paper SPE 20331 presented at the Fifth SPE

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Petroleum Conference, Denver, Colorado, June 25-28, 1990. 4. Noerager, J.A. et al.: "Drilling Time Predictions From Statistical Analysis," paper SPEIIADC 16164 presented at the 1987 SPEIIADC Drilling Conference, New Orleans, LA, March 15-18, 1987. 5. Peterson, S.K. and Pearce, D.W.: "The Effect of Unplanned Operations on Drilling Performance Evaluation," ·paperSPEtIADC-25761 presented at the 1993 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 and Promise, " 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 Economic Decisions, 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 Information at Minimum Cost: A North Sea Field Development Study Using Experimental Design," paper SPE 23139 presented at the 1991 Offshore Europe Conference, Aberdeen. 13. Davies, G.G. and Whiteside, M.W.: "An Integrated Approach to Prospect Evaluation, " paper 23157 presented at the 1991 Offshore Europe Conference, Aberdeen. 14. Dhir, R., Dem, R.R. and Mavor, M.J.: "Economic and Reserve Evaluation of Coalbed Methane Reservoirs," lPT(Dec. 1991) 1424-1431. 15. Murtha, J.A.: "Infill Drilling in the Clinton: Monte Carlo Techniques Applied to the Material Balance

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RISK ANALYSIS AND MONTE CARLO SIMULATION APPLIED TO THE GENERATION OF DRILLING APE ESTIMATES Equation, " paper SPE 17068 presented at the 1987 Eastern Regional Meeting, Pittsburgh, 21-23 October.

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

16. Murtha, J.A.: "Incorporating Historical Data in Monte Carlo Simulation, paper SPE 25245 presented at the 1993 Petroleum Computer Conference, New Orleans, July 11- 14.

20. Shivers, R.M. and Domangue, R.J.: "Operational Decision Making for Stuck-Pipe Incidents in the Gulf of Mexico: A Risk Economics Approach, " SPE Drilling and Completion, (June 1993) 125-130.

17. Weakley, R.R.: "Use of Stuck Pipe Statistics To Reduce the Occurrence of Stuck Pipe, " paper SPE 20410 presented at the 65th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, 23-26 September 1990.

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

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18. Schofield, T.R., Whelehan, O.P., and Baruya, A.: "A New Fishing Equation, " paper SPE 22380 presented at the SPE International Meeting on Petroleum Engineering, Beijing, China 24-27 March 1992.

22. Murtha, J.A., Decisions Involving Uncertainty - An @RISK Tutorialfor the Petroleum Industry, Houston, 1993. 23. "@RISK - Risk Analysis and Simulation Add-in for Microsoft Excel," Release 1.1 User's Guide, Palisade Corp., Newfield, NY, 1992.

Table 1 - Input Distributions Input Parameter Depth variation Problem-free MoblDemob days Problem-free drilling; dayS Problem-free evaluation days Problem-free P&A days MoblDemob problem days Drilling problem dayS Evaluation problem dayS P&A problem days

Input Distribution Normal(-14.64,395) Gamma(5.23,0.49) Gamma(4.16,12.61) Gamma(2.97,2.92) Loe:normal(4.98,3.13) Gamma(0.97,1.34) Exp(13.99) Gamma(0.26,4.83) Gamma(0.51,2.06)

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

Problem-free days Problem days Total dayS

Actual Well 159.5 32.5 192

Conventional AFE NA NA 180

Simulation AFE 158 36 194

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

Problem-free days Problem days Total dayS

Actual Well 112.5 19.5 132

Conventional AFE NA NA 121

Simulation AFE 110 25 135

SPE 26339

S.K.PETERSON, I.A.MURTHA, AND F.F.SCHNEIDER

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SPE 26339

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