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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Casing coupling location signals provided by the magnetic localizer in retractors are typically used to ascertain the position of casing couplings in horizontal wells. However, the casing coupling location signal is usually submerged in noise, which will result in the failure of casing coupling detection under the harsh logging environment conditions. The limitation of Shannon wavelet time entropy, in the feature extraction of casing status, is presented by analyzing its application mechanism, and a corresponding improved algorithm is subsequently proposed. On the basis of wavelet transform, two derivative algorithms, singular values decomposition and Tsallis entropy theory, are proposed and their physics meanings are researched. Meanwhile, a novel data mining approach to extract casing status features with Tsallis wavelet singularity entropy is put forward in this paper. The theoretical analysis and experiment results indicate that the proposed approach can not only extract the casing coupling features accurately, but also identify the characteristics of perforation and local corrosion in casings. The innovation of the paper is in the use of simple wavelet entropy algorithms to extract the complex nonlinear logging signal features of a horizontal well tractor.

In horizontal well production logging, it is necessary to detect casing status, including the position of casing couplings, perforations and any local corrosion [

In recent years, wavelet entropy is receiving growing attention for analyzing nonlinear signals [

In this paper, after analyzing the limitations of Shannon WTE used in casing status feature extraction, a novel data mining approach based on Tsallis wavelet singularity entropy (WSE) is proposed, and the physics meaning of the WSE derivative algorithms is researched. With the approach, the features of coupling, perforation, and local corrosion are extracted from CCL signals with noise and analyzed. Finally the results of our experimental research have been shown and are discussed.

To ascertain the speed and position of retractors creeping in horizontal well casings, a magnetic localizer including two Nd-Fe-B permanent magnets and a multi-turn induction coil are fixed in the retractor to supply the induced voltage of the CCL signal for the data acquisition module. In this paper, a 5000-turns induction coil is mounted between two magnets, its diameter and length are respectively 25.4 mm and 50.8 mm (

When the magnetic localizer passes by casing couplings, the magnetic flux changes immediately, which induces a fluctuation in the inductive-electromotive force in the induction coils (

Under realistic logging conditions, the SNR of CCL signals is very low, because there are a mass of noises caused by negative factors such as oil corrosion, multiphase flow, the compositional variety of the rock stratum and hidden flaws in well casings. Therefore the casing status feature information is sometimes submerged in noise and cannot be resolved directly as in

According to Shannon WTE definition [_{l}_{l}_{−1},_{l}_{0} < _{1} < ... < _{L}_{0} = min[_{L}_{l}_{l}

Therefore Shannon WTE under

After CCL signal in

Through the statistical calculation of data-dispersion density of _{l}_{6} to _{15} in the approximate density, therefore:
_{a}_{a}_{3} to _{5} and from _{16} to _{18} .While the tractor is passing through casing couplings, about 5∼7 percent of the total data appear in _{1}, _{2}, _{19}, and _{20}. According to

From

From

Tsallis entropy put forward by Tsallis in 1988, as nonextensive entropy, is the extension and deploitation of the extensive entropy (B-G entropy) in statistical physics [

Different from extensive entropy,

Note that _{q}

The Tsallis entropy function represents the concave nature. At the same time, Tsallis entropy function has a definite concavity for all _{q}

From

Let the wavelet coefficients (or reconstruction signals) of tested signal form _{L}_{×} _{w}_{L}_{×} _{w}_{L}_{×} _{w}_{L}_{×} _{l}_{l}_{×} _{w}_{l × l} is _{l × l} be _{i}_{1} ≥ _{2} ≥ ... ≥ _{l}_{L}_{×} _{w}

_{L}_{×} _{w}

According to singular values decomposition theory and the definition of No. 1 Tsallis WSE, we find that the similarity among {_{1}},{_{2}},...{_{L}} in the sliding-window is inversely proportional to the amount of _{i}_{i}_{i}

_{L}_{×} _{w}

According to

According to the wavelet transform principle and relative knowledge, the correlation between wavelet coefficients (or reconstruction signals) under the neighboring scales is directly proportional to the similarity in their information components. From _{i}_{i}_{i}

From the above analysis, it can be concluded that the physical meaning of the Tsallis WSE is clear, and its algorithm is flexible and concise to meet the requirement of application, therefore, Tsallis WSE is applied to extract the features of coupling, perforation, and local corrosion from CCL signals with low SNR in this paper.

We establishs a testing platform, where three casings are connected together through casing couplings, to simulate the status of horizontal well casings. When a retractor creeps in the three casings, a CCL signal is collected by the magnetic localizer and transmitted to the data terminal equipment. The creep speed of the retractor, the sampling frequency, and the total time of data acquisition are respectively fixed at 100 mm/s, 1024 Hz and 180 s, and the parameters of the three casings are shown in

As shown in

In the experiment, based on the retractor’s speed, the range of CCL signal frequencies corresponding to the casing couplings and the perforations is from 0.5 Hz to 2 Hz. If the sampling frequency is 1024 Hz and the normalized CCL signal is transformed to four scales by using the Mallat algorithm on db4, the casing coupling and perforation features in the CCL signal should exist in A4 (approximation reconstruction signal). However, during the time period of 112∼122 s, the features in A4 from

Through analyzing the mathematic structure of the Shannon WTE, we find that the relation between sliding-window width and transient signal duration is given as follows:
_{c} is transient signal duration.

In

Taking the approximation reconstruction signal A4 in

From

To explain the reason why the improved Shannon WTE failed to extract the features of the No. 2 and No. 3 perforation, we do the following: first of all, we get the A4 signal shown in _{e}_{noise}_{e}_{e}

Through researching Tsallis WSE in Section 4, it is found that the No. 1 algorithm of the Tsallis WSE is better suited for extracting low-energy featurees for signals with low SNR. In order to keep the integrity of feature information and reduce calculative complexity, the range of

According to _{c}_{max} ≈ 0.075 s. As

In order to further compare the difference between the improved Shannon WTE and Tsallis WSE in terms of feature extraction of the perforations, the magnetic localizer of the retractor is used to collect CCL signals of casings with perforations with different degrees of corrosion in

The ROC plot is used to reflect the difference between two methods in perforation feature extraction ability. We calculate the TPR and FPR of the two feature extraction methods and draw ROC plots as shown in

Under the condition of

For the above mentioned research and experiment evidence, the main conclusions are as follows:

Dividing the data dispersion range mechanically results in a declined sensitivity of the Shannon WTE to the feature information hidden in the original signals. When CCL signals under low SNR are taken as the analysis object, the casing status features cannot be extracted using the Shannon WTE algorithm. Although the capability to extract features is improved, the improved Shannon WTE algorithm still has some disadvantages in feature extraction in the strong noisy background.

Tsallis WSE, as the composition of wavelet transform, singular values decomposition and Tsallis entropy, inherits the advantages of wavelet transform and Tsallis entropy. The singular features of low SNR signals can be extracted using its derivate algorithm. As the complexity of Tsallis WSE algorithm and improved Shannon WTE are at the same level, the feature extraction effect of the Tsallis WSE algorithm is better than that of the improved Shannon WTE.

Using Tsallis WSE to complete data mining of CCL signals, we successfully extracted the feature information corresponding to casing couplings, perforations and extent of local corrosion. Consequently, the casing status detection process is simplified and can supply valid data for horizontal well production logging.

The financial support received from the National Natural Science Foundation of China (Grant No. 51074056) is gratefully acknowledged.

The authors declare no conflict of interest.

Magnetic localizer and its inner structure.

The creeping retractor in casings and the generation of an ideal CCL signal.

CCL signal with low SNR.

The Shannon WTE curve.

Relation between entropy with

Sliding-window and matrix structure in No. 1 Tsallis singular values decomposition.

Sliding-window and matrix structure in No. 2 Tsallis singular values decomposition.

CCL signal from the magnetic localizer in the retractor.

Reconstruction signals of the db4 wavelet transform.

(

The statistics results of the uneven data distribution method.

Feature extraction of casing couplings and perforations with the No. 1 Tsallis WSE.

A testing casing with perforations showing different degrees of corrosion.

ROC plots of the two methods.

Feature extraction of local casing corrosion with No. 2 Tsallis WSE.

Parameters of casings on the testing platform.

No. 1 | slight | 8000 | 140 | 0 | / | / |

No. 2 | serious | 8000 | 140 | 6 | 7 | 100 |

No. 3 | serious | 8000 | 140 | 0 | / | / |

Statistical results for feature extraction of perforations based on the two approaches.

100 | Improved Shannon WTE | 120 | 0 | 0 | 60 | 60 | 0 |

Tsallis WSE | 120 | 0 | 0 | 60 | 60 | 0 | |

95 | Improved Shannon WTE | 120 | 40 | 1 | 20 | 59 | 82.5 |

Tsallis WSE | 120 | 47 | 0 | 13 | 60 | 89.2 | |

85 | Improved Shannon WTE | 120 | 43 | 3 | 17 | 57 | 83.3 |

Tsallis WSE | 120 | 52 | 1 | 8 | 59 | 92.5 | |

75 | Improved Shannon WTE | 120 | 47 | 6 | 13 | 54 | 84.2 |

Tsallis WSE | 120 | 54 | 2 | 6 | 58 | 93.3 | |

70 | Improved Shannon WTE | 120 | 50 | 10 | 10 | 50 | 83.3 |

Tsallis WSE | 120 | 56 | 3 | 4 | 57 | 94.2 | |

60 | Improved Shannon WTE | 120 | 51 | 16 | 9 | 44 | 79.2 |

Tsallis WSE | 120 | 58 | 5 | 2 | 55 | 94.2 |