Simulating the Spatial Distribution of Undiscovered Petroleum Accumulations
Authors: Chen Z. , Osadetz K.G. 
Published: March 2010

Abstract
There are two major problems in the construction of a stochastic model that describes quantitatively the spatial distribution of undiscovered petroleum accumulations: a) available exploration results are biased; and, b) information associated with the locations of accumulations is incomplete. Studies in the Western Canada Sedimentary Basin (WCSB) and elsewhere indicate that the spatial characteristics of petroleum accumulations are fractal. In this paper, we propose the use of these fractal characteristics to calibrate sampling bias, thus deriving an unbiased spatial correlation (covariance function) for the stochastic modelling. The uncertainty in the modelled locations of undiscovered accumulations resulting from insufficient information is captured by equal-probable realizations of the simulation and these are subsequently converted to a probability map of petroleum occurrence. In the example, a pre-1994 exploratory data set for the Rainbow gas play in WCSB was used to derive simulation parameters. A comparison of the simulated results to post-1993 gas discoveries in the same play shows that most of the post-1993 discoveries are located in areas with high predicted probability values.

Introduction
Spatial characteristics of undiscovered oil and gas accumulations are important for both better natural resource management and improved exploration efficiency. There are two major obstacles associated with the construction of a stochastic model for describing the spatial distribution of undiscovered petroleum accumulations. The first is that the available information is biased with respect to exploration results. The second is that information associated with the locations of petroleum accumulations is incomplete unless all accumulations are discovered. It is well known that the data associated with the discovery of petroleum accumulations in an exploration program is biased. Larger features are generally tested with higher priority(1,2). This sampling bias prohibits the use of conventional methods to estimate stochastic model parameters. Barton et al.(3) and La Pointe(4) studied the data from well-explored petroleum basins in the United States and concluded that the spatial distribution of hydrocarbon accumulations is fractal. Our studies in the WCSB also indicate that the spatial distribution of petroleum accumulations exhibits a similar characteristic. Figure 1 shows the box counting results for the Rainbow gas play in the WCSB. The linear relation between box size and the number of boxes containing gas pools (on a logarithmic scale) indicates fractal geometry of the spatial distribution of gas accumulations. The scaling property of the spatial objects means that spatial characteristics of large objects of petroleum accumulations could be used to infer the spatial characteristics for the smaller ones, which are underrepresented in the data set. Thus, an unbiased spatial structure of petroleum accumulations could be inferred from the biased observations. By transforming the spatial information of discovered hydrocarbon accumulations into a frequency domain using a fast Fourier transform (FFT), it results in an amplitude map and a phase map. The amplitude map contains information associated with spatial correlation, while the phase map contains location specific information. When both the location-specific information in the phase map and the spatial correlation in the amplitude map are complete, the true spatial locations of petroleum accumulation can be inferred.