Application of Fractal Analysis of Time Series in Oil and Gas Production

Abstract

The peculiarities of fractal characteristics' calculations for time series are described in this article. It was suggested an algorithm for calculation of fractal dimension for time series. This method differs from the covering method, considering only the Y coordinate and possessing high accuracy and rapidity of convergence on a limited number of measurements, compared to the method of covering. The criteria of early diagnosis for changes in the condition of hydrodynamic processes that do not vary by fractal dimension have been recommended.

The presented method is applicable for practical engineering calculations with self-affine, chaotic data, usually with a relatively limited number of measurements. It is quite a simple method for calculation of fractal dimensions and the algorithm can be easily realized. The applicability of the proposed algorithm for fractal dimension calculation and early diagnosis criteria of qualitative changes in the behavior of various dynamic systems has been tested both on simulated as well as practical examples of oil and gas production.

Keywords:

• diagnosis
• distribution
• fractal dimension
• oil and gas wells
• pressure fluctuations
• time series

ACKNOWLEDGEMENTS

We would like to express our acknowledgements to Arzu H. Hajizada for helping to prepare this manuscript.