Seediscussions,stats,andauthorprofilesforthispublicationat:http://www.researchgate.net/publication/232844303

MonteCarloSimulationofOilFields

ARTICLEinENERGYSOURCES·JULY2006

ImpactFactor:0.54·DOI:10.1080/15567240500400770

READS

294

3AUTHORS,INCLUDING:

SerhatAkin

MiddleEastTechnicalUniversity

78PUBLICATIONS567CITATIONS

SEEPROFILE

Availablefrom:SerhatAkin

Retrievedon:19October2015

Energy Sources, Part B, 1:207–211, 2006Copyright © Taylor & Francis Group, LLCISSN: 1556-7249 print/1556-7257 onlineDOI: 10.1080/15567240500400770

Monte Carlo Simulation of Oil Fields

MUSTAFA VERSAN KOKEGEMEN KAYASERHAT AKIN

Department of Petroleum and Natural Gas EngineeringMiddle East Technical UniversityAnkara, Turkey

Most investments in the oil and gas industry involve considerable risk with a widerange of potential outcomes for a particular project. However, many economic eval-uations are based on the “most likely” results of variables that could be expectedwithout sufficient consideration given to other possible outcomes, and it is well knownthat initial estimates of all these variables have uncertainty. The data is usually ob-tained during drilling of the initial oil well, and the sources are geophysical (seismicsurveys) for formation depths and the areal extent of the reservoir trap, well logs forformation tops and bottoms, formation porosity, water saturation and possible perme-able strata, core analysis for porosity and saturation data, and others. The questionis how certain are the values of these variables and what is the probability of thesevalues to occur in the reservoir to evaluate the possible risks? One of the most highlyappreciable applications of the risk assessment is the estimation of volumetric re-serves of hydrocarbon reservoirs (Monte Carlo). In this study, predictions were madeabout how statistical distribution and descriptive statistics of porosity, thickness, area,water saturation, recovery factor, and oil formation volume factor affect the simulatedoriginal oil in place values of two different oil fields in Turkey, and the results arediscussed.

Keywords drill stem test, pressure, volume, temperature, formation volume factor,original oil in place

Probabilistic estimating of hydrocarbon volumes has its most important application whenassociated with major petroleum development projects. Reserves have three categories:proved, probable and possible (Yükseler, 2002). Proved reserves are estimated quantitiesof hydrocarbons and other substances that are recoverable in future years from knownreservoirs that geological and engineering data demonstrate with reasonable certainty.“Reasonable certainty” means that the average risk or confidence factor for recovering theamount estimated as proved is at least 90%. Probable reserves are estimated quantities ofhydrocarbons and other substances, in addition to proved, that geologic and engineeringdata demonstrate with reasonable probability to be recoverable in future years fromknown reservoirs. Reasonable probability means the average risk or confidence factorrecovering the amount estimated as probable will be at least 50%. Possible reservesare estimated quantities of hydrocarbons and other substances in addition to proved and

Address correspondence to Mustafa Versan Kok, Middle East Technical University, Depart-ment of Petroleum and Natural Gas Engineering, Ankara, 06531 Turkey. E-mail: kok@metu.edu.tr

207

208 M. Versan Kok

probable volumes that geologic and engineering data indicate as being reasonably possibleto be recovered in future years. Reasonable possibility means that the average risk orconfidence factor for recovering the amount estimated as proved, probable, and possiblewill exceed 5%.

The study, in which a risk analysis program was used, deals more thoroughly withgeologic structural dependency and at the same time allows for a high degree of accuracy.Data preparation is kept to a minimum, allowing seismic and other basic data to be useddirectly in calculations without the need of preparing time-consuming area-depth graphsused in more conventional methods. A further advantage is the elimination of certainarbitrary decisions related to extreme structural scenarios based on geological mappingof a very limited number of possible situations. Sensitivities related to uncertaintiesand errors are handled in an easy manner. The importance of uncertainty and risk hasbeen well recognized in the petroleum engineering literature, especially in the areas ofexploration and reserve estimation (Newendorp, 1975). Recently, petroleum engineershave also been focusing on methods for assessing the uncertainty in forecasts of primaryand enhanced oil recovery processes (Brown & Smith, 1984; Ovreberg et al., 1992). Inthese (and related) studies, Monte Carlo simulation is typically the method of choice forrelating model input-output uncertainty. The Monte Carlo simulation methodology allowsa full mapping of the uncertainty in model inputs, expressed as probability distributions,into the corresponding uncertainty in model output that is also expressed in terms of aprobability distribution (Mishra, 1998).

In a research made by Galli and colleagues (1999), three methods of evaluating oilprojects were compared. Option pricing, decision trees, and Monte Carlo simulations arethree methods for evaluating oil projects that seem at first radically different. Option pric-ing comes from the world of finance. Decision trees that come from operations researchand games theory neglect the time variations in prices but concentrate on estimating theprobabilities of possible values of the project. In their simplest form, Monte Carlo sim-ulations merely require the user to specify the marginal distributions of all parametersappearing in the equation for the net present value of the project.

In this study, an estimation of reserves of two Turkish oil fields is estimated by usinga Monte Carlo Simulation technique, and the results are discussed in detail.

Monte Carlo Simulation

A Monte Carlo simulation is a statistics-based analysis tool that yields probability vs.value relationship for parameters, including oil and gas reserves, and investments such as anet present value and return on investment. Nowadays, Monte Carlo simulation is gettingmore applied in the major investment to better evaluate the appraisal of the projects,among which the economic evaluation of the petroleum industry applications forms themajority. Probabilistic reserves estimating using a generalized Monte Carlo approachhave many advantages over simpler deterministic or other probabilistic methods.

A Monte Carlo simulation technique involves the random sampling of each proba-bility distribution within the model to produce hundreds or even thousands of scenarios(Vose, 1996). Each probability distribution is sampled in a manner that reproduces thedistribution’s shape. The distribution of values calculated for the model outcome thereforereflects the probability of values that could occur.

A Monte Carlo simulation begins with a model (i.e., one or more questions, togetherwith assumptions and logic relating the parameters in the equations). In this model, eachof the parameters entering the calculations has to be described by a probability distri-

Monte Carlo Simulation of Oil Fields 209

bution, representative of the original data (frequency distribution). Although such datapreparation may be very time consuming, it is an important step in obtaining realisticresults. One may first consider factors, which determine the type of distribution, whichshould be most appropriately used in describing a particular variable. The overridingfactor would be data availability, which is in many situations only the most likely range(extreme values) of that parameter may be known; in other cases, a very detailed fre-quency distribution may exist as part of the data set. A second consideration would besimplicity and ease of handling of a particular distribution, especially if one were tomanipulate distributions analytically. When a Monte Carlo approach is taken, originalfrequency distributions may be employed directly. Finally, when experience dictates thelikelihood of a particular distribution in the presence of a sparse data set, sensitivitycalculations for a number of possible distributions may be beneficial. A Monte Carlosimulation therefore provides results that are also far more realistic than those that areproduced by “what if” scenarios.

In this study, an estimation of reserves of two Turkish oil fields is performed byusing a Monte Carlo simulation technique. Field data is evaluated by a risk analysis anddecision-making software package known as Design of Experiments (DOE). The finalresults of the software are statistical analysis (the minimum, maximum, mean, skewness,kurtosis, etc.), probability density distributions, and cumulative distributions.

Results and Discussion

The minimum data requirement for probabilistic reserves calculations involves the follow-ing basic quantities: area and net pay or gross rock volume, net to gross rock thickness,porosity, hydrocarbon saturation, volumetric factor, and recovery factor. In the usualmanner, the hydrocarbon initially in place is the product of the first five quantities whilerecoverable hydrocarbons also include the recovery factor.

In the content of this research, estimation of the reserves of two Turkish oil fieldsis performed by using a Monte Carlo simulation technique. Field A has an anticlinalstructure, and the lithology is limestone. The entrapment is structural. Water oil contactis at −1470 m, and porosity and water saturation cuts are 7% and 45%, respectively.On the other hand, Field B has an anticlinal structure, and the lithology is dolomite andlimestone. The entrapment is structural. Water oil contact is at −1230 m, and porosityand water saturation cuts are 7% and 45%, respectively. Input data for both fields aregiven in Table 1.

In the calculation process, areas of reservoirs were calculated using a planimeter.After calculating the area, gross rock volume is obtained from the area vs. depth graph.For both fields, porosity and saturation cuts are taken at 7% and 45%, respectively,due to company policies. After area calculations, the bulk volume of the reservoir wascalculated using different thicknesses to obtain minimum, likely, and maximum valuesof volume. From 15 m minimum thickness to 40 m maximum thickness, bulk volumeswere calculated. The results are given in Table 2.

In the next step, a sensitivity analysis was conducted. The error percentages forFields A and B are calculated as 0.4% and 0.03%, respectively. Low percentages showthat there is a negligible difference between results of 2,500 sampling and 3,000 sampling.The error percentages for two fields when 2,000 and 2,500 sampling numbers are usedare 1.74% for Field A and 1.3% for Field B. The results mean that increasing samplingnumbers decreases the error percentage. Thus, an optimum number, 3,000, was taken asthe sampling (or iteration) number.

210 M. Versan Kok

Table 1Input data for Fields A and B

Field A

Distribution Min. Likely Max. Mean Std. Dev.

Volume (acre-ft) Triangular 4,100 4,175 4,250N/G Triangular 0.5 0.6 0.7Porosity (%) Normal 0.14 0.042(1-Sw) (%) Normal 0.75 0.103FVF (bbl/STB) Constant 1.03RF (%) Triangular 15 25 35

Field B

Distribution Min. Likely Max. Mean Std. Dev.

Volume (acre-ft) Triangular 26,672 33,300 50,710N/G Triangular 0.2 0.5 0.7Porosity (%) Normal 0.16 0.026(1-Sw) (%) Normal 0.71 0.076FVF (bbl/STB) Constant 1.03RF (%) Triangular 15 25 35

FVF: formation volume factor.RF: recovery factor.

Table 2Output data for Fields A and B

Field A

Sampling # 2500 3000

Minimum, STB 0.3276E+7 0.2070E+9Maximum, STB 0.1408E+9 0.1346E+9Mean, STB 0.4953E+8 0.4952E+8Median, STB 0.4733E+8 0.4752E+8Ave. Dev., STB 0.1497E+8 0.1479E+8Variance, STB 0.3614E+15 0.3539E+15Skewness 0.6491 0.5828Kurtosis 0.7598 0.4598

Field B

Sampling # 2500 3000

Minimum, STB 0.8550E+8 0.6649E+8Maximum, STB 0.9883E+9 0.1044E+10Mean, STB 0.3682E+9 0.3680E+9Median, STB 0.3492E+9 0.3493E+9Ave. Dev., STB 0.1083E+9 0.1061E+9Variance, STB 0.1862E+17 0.1842E+17Skewness 0.7504 0.8192Kurtosis 0.5929 1.001

Monte Carlo Simulation of Oil Fields 211

Conclusions

Reserve estimation in the petroleum industry is important for reservoir evaluation andinvestment projects. In this study, a systematic procedure for risk assessment and uncer-tainty analysis has been presented, and two Turkish oil fields were revaluated by DOEsoftware using a Monte Carlo Simulation. The conclusions derived from the study follow.

• Probabilistic methods are useful for the estimation of hydrocarbon reserves par-ticularly when they are related to large projects-contracted deliveries.

• Monte Carlo methods provide more proper handling of partial dependencies relatedto gross rock volumes of a structure.

• When the number of samples increases, the error percentage decreases, and errorpercentage is negligible between 2,500 samples and 3,000 samples. An optimumnumber, 3,000, was taken as the sampling (or iteration) number.

• No correlation exists between porosity and saturation values for both of the fields.

References

Brown, C. E., and Smith, P. J. 1984. The evaluation of uncertainty in surfactant EOR performanceprediction, SPE Paper 13237. SPE Annual Technical Conference and Exhibition, Houston,Texas: Society of Petroleum Engineers.

Galli, A., Armstrong, M., and Jehl, B. 1999. Comparing three methods for evaluating oil projects:Option pricing, decision trees, and Monte Carlo simulations, SPE Paper 52949. HydrocarbonEconomics and Evaluation Symposium, Dallas, Texas: Society of Petroleum Engineers.

Mishra, S. 1998. Alternatives to Monte Carlo simulation for probabilistic reserves estimation andproduction forecasting, SPE Paper 49313. SPE Annual Technical Conference and Exhibition,New Orleans, Louisiana: Society of Petroleum Engineers.

Newendorp, P. D. 1975. Decision analysis for petroleum exploration. Tulsa, OK: Pennwell Books.Ovreberg, O., Damsleth, E., and Haldosen, H. 1992. Putting error bars on reservoir engineering

forecasts. J. of Petroleum Technology 4:732–739.Vose, D. 1996. Quantitative risk analysis: A guide to Monte Carlo simulation modeling. London,

England: Wiley & Sons.Yükseler, U. 2002. Reserve estimation using stochastic approach and risk analysis. MSc Thesis,

Middle East Technical University, Ankara, Turkey.