Monte Carlo Simulation of Oil Fields

Abstract

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 evaluations 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 obtained 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 permeable 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 reserves 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.

Full text

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.
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