The Application Of The Mathematics Of Fuzzy Logic To Petrophysics Available to Purchase

Certain areas of petrophysics have benefitted from the application of the new mathematics of ?fuzzy logic?. BE? Exploration routinely uses new interpretation techniques, based on fuzzy logic, to predict permeability and litho-facies in uncored wells. Lithofacies and permeability prediction has presented a challenge to Petrophysics due to the lack of tools that measure them directly and because of the inherent errors in any measurement. Fuzzy logic is simply an application of recognized statistical techniques. Whereas conventional techniques deal with absolutes, the new methods carry the inherent error term through the calculation rather than ignoring or minimizing it. This retains the information associated with the error and gives surprisingly better results. The first application is to litho-facies determination. Litho-facies typing is used in well correlation and is important for building a 3D model of the field. The technique makes no assumptions and retains the possibility that a particular litho-facies type can give any log reading although some are more likely than others. This error or fuzziness has been measured and used to improve the facies prediction in several North Sea fields. In one study, descriptions from 10 cored wells were used to derive facies descriptions in 30 uncored wells. This technique gave near perfect differentiation between aeolian, fluvial and sabkha rock types. In addition, it went some way towards differentiating between sandy, mixed and muddy sabkhas. Using the fuzzy logic technique gives better predictions than more complicated methods. Other applications include permeability calculation, thin bed resolution and fracture prediction. Knowledge of permeability is important in determining well completion strategy and the resulting productivity. The problem with permeability prediction is derived from the fact that permeability is related more to the aperture of pore throats rather than pore size, which logging tools find difficult to measure. Determining permeability from logs is further complicated by the problem of scale; logs having a vertical resolution of typically 2 feet compared to the 2 inches of the core plug. The new techniques quantify these errors and use them, together with the measurement, to improve the prediction. In several fields in the North Sea, this new approach has given better estimates of permeability compared to conventional techniques such as multiple linear regression. In addition, the method relies on basic log data sets such as gamma-ray and porosity rather than depending on new logging technology.