Monte Carlo Simulation Example 3

Oil industry example: Estimating hydrocarbon reserves

Introduction

This example shows how oil and gas exploration and production companies estimate the recoverable volumes of oil and gas trapped in geological structures two kilometres or more underground.

The volume of recoverable gas depends on many input values including the volume of rock containing the gas, the porosity and permeability of the rock and the properties of the gas.

These input values are estimated using seismic data to detect the depth and shape of the geological structure and well intersections to sample the rock and gas properties within the structure.

The input values are not known exactly but probability distributions can be defined using the available data. Triangular distributions are often used for simple but adequate models.
In this example the gas resource estimation random variables are defined as:

Name Distribution Units Min Max Peak
Gross Rock Volume Triangular Million Cubic Metres 5000 15000 10000
Net to Gross Triangular Factor 0.4 0.7 0.6
Porosity Triangular Factor 0.13 0.16 0.15
Gas Saturation Triangular Factor 0.5 0.85 0.75
Gas Volume Factor Triangular Factor 230 250 240
Condensate Ratio Triangular bbl/MMscf 20 80 50
Gas Recovery Factor Triangular Factor 0.6 0.8 0.7
Condensate RF Triangular Factor 0.5 0.7 0.6


Step 1 - Enter the Random Variable Probability Distributions into the Monte Carlo Model

Triangular probability distributions can be used for simple models.
Other distributions may be used for more refined models.

Probability Distribution Input Figure


Step 2 - Define any Correlations Between the Random Variables

A correlation matrix is used to specify the correlation factors between random variables.
A correlation coefficient of 0.7 is defined between the Porosity and Gas Recovery Factor variables.


Correlation Input Figure


Step 3 - Simulate Values of Each Random Variable for a Number of Trials

The Monte Carlo software generates reservoir rock and gas property values for the specified number of trials.
10,000 trials were run in this example.
Some of these values are shown in the table below.


Simulate Input Values Figure


Step 4 - Correlate the Random Variables Using a Correlation Matrix

Gas recovery factors tend to be correlated to the rock porosity.
Reservoir simulations and experience provide a guide to suitable correlation coefficients.
A coefficient of 0.7 is used in this example.
More refined models will define correlations between other random variables.

Apply the Correlation Matrix Figure


Step 5 - Define the Calculations to be Performed on the Random Variable Values

A calculation tree is defined to read the reservoir and gas properties from the table, perform calculations for gas in place and recoverable gas then write these calculated values back to the table.


Calculation Tree Figure


Step 6 - Generate the Calculated Values for Each Trial

The Monte Carlo software generates the specified calculated values for the number of trials used in the model.
In this model, the Gas In Place and Gas Resource volumes are calculated.
This completes the simulation.
Some of calculated volumes are shown in the table below.


Calculated Values Figure


Step 7 - Analyse the Results

The cumulative probability and probability density charts shown below show the simulated Gas Resource probability distribution graphically.


Simulation Results Figure

The Monte Carlo simulation shows that the calculated gas resource volume has a mean value of 3,453 billion cubic feet (bcf).
Reverse cumulative distribution functions are used to display resource volume distributions. The P90 value of 2,294 bcf means the gas resource volume has a 90 percent chance of being 2,294 bcf or larger.
Resource development companies usually require the P90 volumes to be profitable before proceeding with the cost of a development project.



Introduction   Deterministic Vs Probabilistic   Overview   Example 1   Example 2   Example 3