Monte Carlo Methods - Estimation and Measurement

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Monte Carlo Methods - Measurement. Determining the volume of oil that can be recovered from an underground reservoir requires several measurements to be combined. Running 3D seismic surveys may cost $50,000/day and exploratory wells between $1m and $20m, thus an estimate of reserves is based the combination of data elements from a limited number of sample points. For example the porosity determined from the discovery well may not be representative of the field as a whole. Thus whilst a core sample may have porosity of 10%, a geologist with experience of an area may treat this value as a triangular distribution with a minimum value of 2.5%, a modal value of 7.5% and a maximum value of 20%, giving a mean value of 10%. The same principle can be applied to the area of the field, its thickness and recovery factor all of which are combined using the formula:

Where:

V is the volume of oil which will be recovered from the reservoir

A is the area of the reservoir

T is the thickness of the reservoir

P is the porosity of the reservoir, this is the %age of the reservoir's rock volume which is void space. For example, if a reservoir has a porosity of 10%, the void space in 1 cubic meter of rock which might contain fluid is 0.1 cubic meter.

R is the recovery factor. Not all the oil from the reservoir will be recovered, the recovery factor is an estimate of the %age that can be extracted economically from the reservoir.

Using the Monte Carlo technique we can derive an estimate of the recoverable reserves in the form of a distribution. The choice of distribution for each parameter depends on the nature of the parameter and the amount of data available to estimate them. In this example, we'll use a triangular distribution for all the independent variables. An alternative would be a lognormal distribution.

Parameter Units Minimum Mode Maximum

Area KM2 1.5 4.0 10.0

Thickness M 2.5 10.0 30.0

Porosity % 2.5 7.5 20.0

Recovery % 5.0 10.0 30.0

Evaluating the reserves formula 1 million times and sorting the results so that they can be plotted on a probability density curve, yields the highly left skewed plot shown below.

Whilst frequency curves and probability density graphs give a good visual indication of skewness and kurtosis, the cumulative probability curve has the advantage that probabilities can be visually extracted.

The spread of reserves of our hypothetical oilfield in cubic meters is:

5% 194,000

50% (Median) 839,000

95% 2,286,000

Mode 400,000

The example was intended to show the use of the technique. In practice, the models used to estimate recoverable reserves include many more factors and are often integrated with economic software which attempts to determine what development scenario will give the highest rate of return.

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