An example of a Monte Carlo simulation risk analysis model for the Oil and Gas industry

This example shows a simple use of Monte Carlo simulation to assess the uncertainty of the estimate in the oil in place in an oil formation, and the reserve estimate which is the theoretical amount of oil that can be extracted from the reserve from the natural pressure in the field.

Technical difficulty: 1

Techniques used: Monte Carlo simulation in Excel

ModelRisk functions used: VosePERT, VoseLognormal, VoseNormal VoseInput, VoseOutput

Model description

The risk analysis model is built using Excel with our Monte Carlo simulation add-in called ModelRisk. It uses the following formatting convention:

The model is simple and easy to follow:

The Point estimate column shows the calculations based on best guess estimates of the input parameters, and the Random sample column performs the same calculations where the input parameters are simulated by drawing from PERT, Lognormal and Normal statistical distributions.

The calculations follow the formulae:

where A = area, d = thickness, ϕ = porosity, Sw = water saturation, Sg = gas saturation, and B = oil formation volume factor (subscripts: i initial, a abandonment).

Results

The model takes about 2 seconds to run 5,000 samples. It is set up to directly show a number of reports within the ModelRisk ResultsViewer at the end of the simulation, which are described below.

The first tab shows a Pareto plot (combination of histogram and cumulative distributions) of the total oil reserve estimate:

This plot illustrates that it is estimated there is a 5% probability that the reserve is less than 118 MM bbl, and 5% probability it is above 250 MM bbl, and is most likely in the region of 180 MM bbl.

The second tab shows a tornado plot for the initial oil in place estimate, listing the input variables in descending order of their contribution to the total reserve uncertainty:

It illustrates, for example, that the oil in place estimate is most sensitive to oil formation volume factor at initial reservoir pressure factor. It shows that the mean oil in place estimate varies from 344 MM bbl to 456 MM bbl depending on whether this uncertainty factor is high or low. In a real problem, one would look at the most influential variables and consider how one could narrow their range and thus have a more precise estimate of the total cost.

The third tab provides the summary statistics for all the outputs:

The fourth tab shows a scatter plot of the simulated values for the oil formation factor and reserve estimate, illustrating the inverse relationship between the two:

Finally, the last tab plots the difference between the stochastic estimate and the original single-point estimate, and shows that there is a 48% probability the reserve is below the single-point estimate. The statistics to the right give a mean of 2.89 MM bbl, indicating that the mean reserve estimate is this amount higher: