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Energy Sources, Part B, 1:207–211, 2006

Copyright © Taylor & Francis Group, LLC

ISSN: 1556-7249 print/1556-7257 online

DOI: 10.1080/15567240500400770

Monte Carlo Simulation of Oil Fields

MUSTAFA VERSAN KOK

EGEMEN KAYA

SERHAT AKIN

Department of Petroleum and Natural Gas Engineering

Middle East Technical University

Ankara, Turkey

Most investments in the oil and gas industry involve considerable risk with a wide

range of potential outcomes for a particular project. However, many economic eval-

uations are based on the “most likely” results of variables that could be expected

without sufﬁcient consideration given to other possible outcomes, and it is well known

that 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 (seismic

surveys) for formation depths and the areal extent of the reservoir trap, well logs for

formation tops and bottoms, formation porosity, water saturation and possible perme-

able strata, core analysis for porosity and saturation data, and others. The question

is how certain are the values of these variables and what is the probability of these

values to occur in the reservoir to evaluate the possible risks? One of the most highly

appreciable applications of the risk assessment is the estimation of volumetric re-

serves of hydrocarbon reservoirs (Monte Carlo). In this study, predictions were made

about how statistical distribution and descriptive statistics of porosity, thickness, area,

water saturation, recovery factor, and oil formation volume factor affect the simulated

original oil in place values of two different oil ﬁelds in Turkey, and the results are

discussed.

Keywords drill stem test, pressure, volume, temperature, formation volume factor,

original oil in place

Probabilistic estimating of hydrocarbon volumes has its most important application when

associated with major petroleum development projects. Reserves have three categories:

proved, probable and possible (Yükseler, 2002). Proved reserves are estimated quantities

of hydrocarbons and other substances that are recoverable in future years from known

reservoirs that geological and engineering data demonstrate with reasonable certainty.

“Reasonable certainty” means that the average risk or conﬁdence factor for recovering the

amount estimated as proved is at least 90%. Probable reserves are estimated quantities of

hydrocarbons and other substances, in addition to proved, that geologic and engineering

data demonstrate with reasonable probability to be recoverable in future years from

known reservoirs. Reasonable probability means the average risk or conﬁdence factor

recovering the amount estimated as probable will be at least 50%. Possible reserves

are 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 possible

to be recovered in future years. Reasonable possibility means that the average risk or

conﬁdence factor for recovering the amount estimated as proved, probable, and possible

will exceed 5%.

The study, in which a risk analysis program was used, deals more thoroughly with

geologic 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 used

directly in calculations without the need of preparing time-consuming area-depth graphs

used in more conventional methods. A further advantage is the elimination of certain

arbitrary decisions related to extreme structural scenarios based on geological mapping

of a very limited number of possible situations. Sensitivities related to uncertainties

and errors are handled in an easy manner. The importance of uncertainty and risk has

been well recognized in the petroleum engineering literature, especially in the areas of

exploration and reserve estimation (Newendorp, 1975). Recently, petroleum engineers

have also been focusing on methods for assessing the uncertainty in forecasts of primary

and enhanced oil recovery processes (Brown & Smith, 1984; Ovreberg et al., 1992). In

these (and related) studies, Monte Carlo simulation is typically the method of choice for

relating model input-output uncertainty. The Monte Carlo simulation methodology allows

a 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 a

probability distribution (Mishra, 1998).

In a research made by Galli and colleagues (1999), three methods of evaluating oil

projects were compared. Option pricing, decision trees, and Monte Carlo simulations are

three 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 research

and games theory neglect the time variations in prices but concentrate on estimating the

probabilities 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 parameters

appearing 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 using

a Monte Carlo Simulation technique, and the results are discussed in detail.

Monte Carlo Simulation

AMonte 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 a

net present value and return on investment. Nowadays, Monte Carlo simulation is getting

more applied in the major investment to better evaluate the appraisal of the projects,

among which the economic evaluation of the petroleum industry applications forms the

majority. Probabilistic reserves estimating using a generalized Monte Carlo approach

have many advantages over simpler deterministic or other probabilistic methods.

AMonte 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 the

distribution’s shape. The distribution of values calculated for the model outcome therefore

reﬂects the probability of values that could occur.

AMonte Carlo simulation begins with a model (i.e., one or more questions, together

with assumptions and logic relating the parameters in the equations). In this model, each

of 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 data

preparation may be very time consuming, it is an important step in obtaining realistic

results. One may ﬁrst consider factors, which determine the type of distribution, which

should be most appropriately used in describing a particular variable. The overriding

factor 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 be

simplicity and ease of handling of a particular distribution, especially if one were to

manipulate distributions analytically. When a Monte Carlo approach is taken, original

frequency distributions may be employed directly. Finally, when experience dictates the

likelihood of a particular distribution in the presence of a sparse data set, sensitivity

calculations for a number of possible distributions may be beneﬁcial. A Monte Carlo

simulation therefore provides results that are also far more realistic than those that are

produced by “what if” scenarios.

In this study, an estimation of reserves of two Turkish oil ﬁelds is performed by

using a Monte Carlo simulation technique. Field data is evaluated by a risk analysis and

decision-making software package known as Design of Experiments (DOE). The ﬁnal

results 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 usual

manner, the hydrocarbon initially in place is the product of the ﬁrst ﬁve quantities while

recoverable hydrocarbons also include the recovery factor.

In the content of this research, estimation of the reserves of two Turkish oil ﬁelds

is performed by using a Monte Carlo simulation technique. Field Ahas an anticlinal

structure, and the lithology is limestone. The entrapment is structural. Water oil contact

is at −1470 m, and porosity and water saturation cuts are 7% and 45%, respectively.

On the other hand, Field Bhas an anticlinal structure, and the lithology is dolomite and

limestone. The entrapment is structural. Water oil contact is at −1230 m, and porosity

and water saturation cuts are 7% and 45%, respectively. Input data for both ﬁelds are

given 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 was

calculated using different thicknesses to obtain minimum, likely, and maximum values

of volume. From 15 m minimum thickness to 40 m maximum thickness, bulk volumes

were calculated. The results are given in Table 2.

In the next step, a sensitivity analysis was conducted. The error percentages for

Fields Aand Bare calculated as 0.4% and 0.03%, respectively. Low percentages show

that 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 used

are 1.74% for Field A and 1.3% for Field B. The results mean that increasing sampling

numbers decreases the error percentage. Thus, an optimum number, 3,000, was taken as

the sampling (or iteration) number.

210 M. Versan Kok

Table 1

Input data for Fields Aand B

Field A

Distribution Min. Likely Max. Mean Std. Dev.

Volume (acre-ft) Triangular 4,100 4,175 4,250

N/G Triangular 0.5 0.6 0.7

Porosity (%) Normal 0.14 0.042

(1-Sw) (%) Normal 0.75 0.103

FVF (bbl/STB) Constant 1.03

RF (%) Triangular 15 25 35

Field B

Distribution Min. Likely Max. Mean Std. Dev.

Volume (acre-ft) Triangular 26,672 33,300 50,710

N/G Triangular 0.2 0.5 0.7

Porosity (%) Normal 0.16 0.026

(1-Sw) (%) Normal 0.71 0.076

FVF (bbl/STB) Constant 1.03

RF (%) Triangular 15 25 35

FVF: formation volume factor.

RF: recovery factor.

Table 2

Output data for Fields Aand B

Field A

Sampling # 2500 3000

Minimum, STB 0.3276E+7 0.2070E+9

Maximum, STB 0.1408E+9 0.1346E+9

Mean, STB 0.4953E+8 0.4952E+8

Median, STB 0.4733E+8 0.4752E+8

Ave. Dev., STB 0.1497E+8 0.1479E+8

Variance, STB 0.3614E+15 0.3539E+15

Skewness 0.6491 0.5828

Kurtosis 0.7598 0.4598

Field B

Sampling # 2500 3000

Minimum, STB 0.8550E+8 0.6649E+8

Maximum, STB 0.9883E+9 0.1044E+10

Mean, STB 0.3682E+9 0.3680E+9

Median, STB 0.3492E+9 0.3493E+9

Ave. Dev., STB 0.1083E+9 0.1061E+9

Variance, STB 0.1862E+17 0.1842E+17

Skewness 0.7504 0.8192

Kurtosis 0.5929 1.001

Monte Carlo Simulation of Oil Fields 211

Conclusions

Reserve estimation in the petroleum industry is important for reservoir evaluation and

investment 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 DOE

software 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 related

to gross rock volumes of a structure.

•When the number of samples increases, the error percentage decreases, and error

percentage is negligible between 2,500 samples and 3,000 samples. An optimum

number, 3,000, was taken as the sampling (or iteration) number.

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

References

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prediction, SPE Paper 13237. SPE Annual Technical Conference and Exhibition, Houston,

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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. Hydrocarbon

Economics and Evaluation Symposium, Dallas, Texas: Society of Petroleum Engineers.

Mishra, S. 1998. Alternatives to Monte Carlo simulation for probabilistic reserves estimation and

production forecasting, SPE Paper 49313. SPE Annual Technical Conference and Exhibition,

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Newendorp, P. D. 1975. Decision analysis for petroleum exploration. Tulsa, OK: Pennwell Books.

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