Sharing Reservoirs

Details Sharing Reservoirs Sharing Reservoirs

2012-04-17

arxiv.org/abs/1204.3737v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

Large reservoirs such as oil fields are typically split into exploratory blocks for different consortia. Although space demarcation at the surface level is a standard process, finding the corresponding effective extents of the shares is not simple. We introduce a theoretical framework to identify the effectively exploitable volumes and characterize their boundaries, based on the number of consortia. For three consortia, we show that in an uncorrelated medium the set of shared regions is a fractal of dimension $d_\text{tot}=1.69\pm0.02$. The subset of these shared sites spanning the entire medium has fractal dimension $d_\text{lc}=1.55\pm0.03$. The peculiar topological properties of the emerging clusters of shared sites are analyzed and the model is shown to exhibit a tricritical crossover involving also a negative exponent at criticality.

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