Fractal analysis of time series in oil and gas production

The peculiarities of fractal characteristics' calculations for time series are described in this article. An algorithm for calculation of fractal dimension is suggested. it has been proved that the suggested method possesses high accuracy and the rapidity of convergence on the limited number of measurements compared to the methods of covering. The criteria of early diagnosis for changes in the condition of hydrodynamic processes, which 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 relatively limited number of measurements. It is quite a simple method for calculation of fractal dimension, algorithm can be easily realized and it should be useful for engineers. The applicability of the proposed algorithm for fractal dimension calculation and early diagnosis criteria of qualitative changes in the behaviour of various dynamic systems has been tested both on simulated as well as practical examples of oil and gas production. (C) 2008 Elsevier Ltd. All rights reserved.