Fractal Location and Anomalous Diffusion Dynamics for Oil Wells from the KY Geological Survey

Abstract

Utilizing data available from the Kentucky Geonet (KYGeonet.ky.gov) the fossil fuel mining locations created by the Kentucky Geological Survey geo-locating oil and gas wells are mapped using ESRI ArcGIS in Kentucky single plain 1602 ft projection. This data was then exported into a spreadsheet showing latitude and longitude for each point to be used for modeling at different scales to determine the fractal dimension of the set. Following the porosity and diffusivity studies of Tarafdar and Roy1 we extract fractal dimensions of the fossil fuel mining locations and search for evidence of scaling laws for the set of deposits. The Levy index is used to determine a match to a statistical mechanically motivated generalized probability function for the wells. This probability distribution corresponds to a solution of a dynamical anomalous diffusion equation of fractional order that describes the Levy paths which can be solved in the diffusion limit by the Fox H function ansatz.