# Normalizing Large Scale Sensor-Based MWD Data: An Automated Method toward A Unified Database

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## Abstract

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## 1. Introduction

## 2. Material and Methods

#### 2.1. Data Source Description

#### 2.2. Applied Methodology

#### 2.2.1. Filtering Procedure in Block A

#### 2.2.2. Normalizing Procedure in Block B

#### 2.3. Generating A Unified Database

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{i}in n records at any MWD data. On the other hand, E(xi) mathematically shows the long-term average or mean (symbolized as μ), which would be expected over the long term of MWD records. Referring to the law of large numbers, the mean ($\overline{x}$) converges to the E(x) and thus to the average of the whole records as the number of repetitions approaches infinity [56,57]. Thereby, $\overline{x}$ and variance (${\sigma}_{{x}_{i}}^{2}$) can be calculated using average or a weighted average data as:

_{i}: value of observation i, n

_{i}= number of observations with value x

_{i}, N = total number of observations, $\overline{x}$: population mean, and n

_{i}/N is the weight.

_{i}statistically represents a combination of mean, mode and median of each individual component. Referring to the relation of these statistics in binomial distribution [58], due to the difference of median and mode, the mean lies in between. Therefore, for each individual record of MWD data, gated bands for both the upper and lower observed modes can be defined to cover the mean of each recorded parameter and sustain the median respectively for more efficient removal of the outliers.

**Figure A1.**Graphical plot and schemes provided to follow (

**a**) Description data removal using NIP limits and (

**b**) area analysis of the used data based on CVR for outlier elimination.

MWD Parameter | NIP-Väst Länken | NIP-CVR Väst Länken | ||||
---|---|---|---|---|---|---|

Satisfactory | Acceptable | Out of Limit | Acc. Performance | Gray Zone | Out of Limit | |

PR dm/min | 133,300 | 8126 | 2117 | 141,426 | 0 | 10,243 |

HP bar | 136,559 | 3175 | 11,935 | 136,559 | 0 | 15,110 |

FP bar | 140,450 | 3174 | 8045 | 140,450 | 0 | 11,219 |

DP bar | 104,819 | 38,844 | 8006 | 104,819 | 0 | 46,850 |

Rs r/min | 110,447 | 32,508 | 8714 | 110,447 | 0 | 41,222 |

RP bar | 103,328 | 42,012 | 6329 | 103,328 | 0 | 48,341 |

WF l/min | 129,425 | 12,672 | 9572 | 129,425 | 0 | 22,244 |

WP bar | 124,121 | 17,992 | 9572 | 124,121 | 0 | 27,548 |

MWD Parameter | NIP-FSE410 | NIP-CVR FSE410 | ||||
---|---|---|---|---|---|---|

Satisfactory | Acceptable | Out of Limit | Acc. Performance | Gray Zone | Out of Limit | |

PR dm/min | 4,137,640 | 1,111,975 | 130,073 | 4,137,640 | 0 | 1,242,048 |

HP bar | 4,337,126 | 855,113 | 187,449 | 4,337,126 | 0 | 1,042,562 |

FP bar | 3,703,051 | 1,494,882 | 181,755 | 3,703,051 | 0 | 1,866,593 |

DP bar | 3,513,095 | 1,652,843 | 213,750 | 3,513,095 | 0 | 1,866,593 |

Rs r/min | 4,642,513 | 202,275 | 534,900 | 4,642,513 | 0 | 737,175 |

RP bar | 3,760,962 | 1,389,361 | 229,365 | 3,760,962 | 0 | 1,618,726 |

WF l/min | 3,580,175 | 1,687,855 | 111,658 | 3,580,175 | 0 | 1,799,513 |

WP bar | 4,494,233 | 523,568 | 361,887 | 4,494,233 | 0 | 885,455 |

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**Figure 1.**Increasing trend of using MWD data in geoengineering application in last five decades (after [14]).

**Figure 3.**Simplified diagram of the applied automated MWD processing procedure and generating unified database.

**Figure 6.**Visualized results of the filtering procedure based on gated bands and modes of the MWD data in accordance to HP.

**Figure 7.**Rod-length checking through splitting of the merged data (checking the mode capability in splitting the high- and low-pressure values for rod 1).

**Figure 8.**Pattern identification and trend analysis between the normalized and un-normalized MWD data (hole-based).

**Figure 9.**A visualized sample of pattern identification–trend analysis between the normalized and un-normalized MWD data (peer group-based).

Normalizing Method | Preferred Interval | Note |
---|---|---|

Vector [28] | $\left[1-\frac{{a}_{ij}}{\sqrt{\sum _{i=1}^{m}{a}_{ij}^{2}}},\frac{{a}_{ij}}{\sqrt{\sum _{i=1}^{m}{a}_{ij}^{2}}}\right]$ | The ratio of values remains constant within interval [0, 1] |

Linear [25] | $\left[\frac{{maxa}_{ij-}{a}_{ij}}{{maxa}_{ij-}min{a}_{ij}},\frac{{a}_{ij}-min{a}_{ij}}{{maxa}_{ij-}min{a}_{ij}}\right]$ | The calculated values are dependent on the size of interval [maxa_{ij}, mina_{ij}] |

[24] | $\left[1-\left|\frac{min{a}_{ij}-{a}_{ij}}{{maxa}_{ij-}min{a}_{ij}}\right|,1-\left|\frac{max{a}_{ij}-{a}_{ij}}{max{a}_{ij}}\right|\right]$ | Limited to interval [0, 1] |

Nonlinear [26] | $\left[{\left(\frac{{mina}_{ij}}{{a}_{ij}}\right)}^{3},{\left(\frac{{a}_{ij}}{{maxa}_{ij}}\right)}^{2}\right]$ | The values are diminished more than when using other methods |

Logarithmic [29] | $\left[\frac{1-\frac{ln\left({a}_{ij}\right)}{ln\left(\prod _{i=1}^{n}{a}_{ij}\right)}}{n-1},\frac{ln\left({a}_{ij}\right)}{ln\left(\prod _{i=1}^{n}{a}_{ij}\right)}\right]$ | The sum of normalized criterion values is always 1 |

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## Share and Cite

**MDPI and ACS Style**

Abbaszadeh Shahri, A.; Shan, C.; Larsson, S.; Johansson, F.
Normalizing Large Scale Sensor-Based MWD Data: An Automated Method toward A Unified Database. *Sensors* **2024**, *24*, 1209.
https://doi.org/10.3390/s24041209

**AMA Style**

Abbaszadeh Shahri A, Shan C, Larsson S, Johansson F.
Normalizing Large Scale Sensor-Based MWD Data: An Automated Method toward A Unified Database. *Sensors*. 2024; 24(4):1209.
https://doi.org/10.3390/s24041209

**Chicago/Turabian Style**

Abbaszadeh Shahri, Abbas, Chunling Shan, Stefan Larsson, and Fredrik Johansson.
2024. "Normalizing Large Scale Sensor-Based MWD Data: An Automated Method toward A Unified Database" *Sensors* 24, no. 4: 1209.
https://doi.org/10.3390/s24041209