# Kick Prediction Method Based on Artificial Neural Network Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Drilling Data

## 3. Data Clustering

_{min}is the minimum value of the same type of data as the prenormalization data; x

_{max}is the maximum value of the same type of data as before this normalization.

## 4. Neural Network Model

#### 4.1. Radial Basis Function Neural Network (RBFNN)

#### 4.1.1. Regularized RBFNN

_{n}is the output of the nth input layer node; C

_{i}is the center vector of the ith Gaussian function, n dimension; c

_{in}is the ith value of the center vector of the ith Gaussian function; ||X-C

_{i}|| is the Euclidean distance between the input vector X and the center vector C

_{i}of the ith Gaussian function; δ is the width of the Gaussian function; h

_{i}is the output of the ith hidden layer node.

_{i}is the output of the ith hidden layer node; w

_{ij}is the connection weight of the ith hidden layer node and the jth output layer node; m is the number of output layer nodes; k is the number of hidden layer nodes.

_{pj}is the output layer output matrix of row j of p; H

_{pi}is the hidden layer output matrix of row i of p; W

_{ij}is the output layer weight matrix of row j of i.

_{pj}is the jth output result corresponding to the pth training sample; h

_{pi}is the pth training sample corresponding to the ith output of the ith hidden layer node; w

_{ij}is the weight of the jth output layer node corresponding to the ith hidden layer node.

_{ij}. Multiplying the left and right sides of the equation by the inverse or pseudo-inverse of H

_{pi}, W

_{ij}can be obtained.

_{pi}in Equation (8) is a square matrix, and the output layer weight matrix W

_{ij}is determined by the inverse of H

_{pi}.

#### 4.1.2. Generalized RBNN

_{pi}in Equation (7) is a nonsquare matrix, and the output layer weight matrix W

_{ij}can be obtained by the pseudo-inverse of H

_{pi}.

#### 4.2. Radial Basis Function Neural Network (RBFNN)

_{j}.

_{j}is the jth output of the summation layer function G

_{j}node; q is the number of hidden layer nodes; k is the number of output layer nodes; h

_{i}is the output of the ith hidden layer node; and y

_{ij}is the jth value of the real value vector in the ith training sample.

_{j}is the output of the jth output layer node; G

_{j}is the output of the jth node of the summation layer function G

_{j}; q is the number of hidden layer nodes; A is the output of the summation layer function A node; k is the number of output layer nodes.

#### 4.3. Probabilistic Regression Neural Network (PNN)

## 5. Evaluation and Analysis of Prediction Results

#### 5.1. Prediction Results of Normalized RBFNN + k-Means Model

#### 5.2. Prediction Results of Generalized RBFNN + k-Means Model

#### 5.3. Prediction Results of GRNN + k-Means Model

#### 5.4. Prediction Results of PNN + k-Means Model

#### 5.5. Comparison of Prediction Results

## 6. Conclusions and Prospect

- (1)
- Due to the huge volume and similarity of the field data, it was important to cluster the training samples with k-means clustering to decrease data redundancy and accelerate computation speed.
- (2)
- After clustering, the data samples were applied in four ANN models, including normalized RBFNN, generalized RBFNN, GRNN, and PNN. According to the comparison and analysis, the normalized RBFNN + k-means model had the highest prediction accuracy.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Name | Working Status | No. of Normal Samples | No. of Kick Samples | Total No. of Samples |
---|---|---|---|---|

Well-1 | Normal state (0) | 20,389 | 0 | 20,389 |

Well-2 | Normal state (0) | 44,455 | 0 | 44,455 |

Well-3 | Normal state (0) | 21,927 | 0 | 21,927 |

Well-4 | Normal state (0) | 36,374 | 0 | 36,374 |

Well-5 | Normal state (0) Kick state (1) | 57,175 | 261 | 57,436 |

Well-6 | Normal state (0) | 20,970 | 0 | 20,970 |

Well-7 | Normal state (0) + Kick state (1) | 24,853 | 39 | 24,892 |

Well-8 | Normal state (0) + Kick state (1) | 40,800 | 80 | 40,880 |

Time | Well Depth | Bit Position | Vertical Pressure | String | Inlet Flow Rate | Outlet Flow Rate | Inlet Density | Oulet Density | Total Hydrocarbon | Total Pool Volume |
---|---|---|---|---|---|---|---|---|---|---|

223,209 | 5675.59 | 5674.68 | 20.52 | 1802.4 | 28.15 | 1.43 | 2.23 | 0.57157 | 37.41 | 115.71 |

223,229 | 5675.59 | 5674.71 | 21.09 | 1802.4 | 28.19 | 1.43 | 2.24 | 0.57157 | 36.41 | 115.71 |

223,249 | 5675.59 | 5674.73 | 20.6 | 1804.1 | 28.34 | 1.43 | 2.23 | 0.57157 | 35.54 | 115.72 |

223,309 | 5675.59 | 5674.76 | 20.66 | 1804.3 | 28.41 | 1.43 | 2.23 | 0.57157 | 34.48 | 115.58 |

Sample Type | No. of Clustered Sample Groups | No. of Calculations | No. of Final Cluster Sample Groups | Newly Named |
---|---|---|---|---|

Normal state (0) | 5000 | 1st time | 49 | 1 |

5000 | 2nd time | 58 | 2 | |

5000 | 3rd time | 56 | 3 | |

10,000 | 1st time | 64 | 4 | |

10,000 | 2nd time | 68 | 5 | |

10,000 | 3rd time | 64 | 6 | |

20,000 | 1st time | 76 | 7 | |

20,000 | 2nd time | 73 | 8 | |

20,000 | 3rd time | 90 | 9 |

Sample Type | No. of Clustered Sample Groups | No. of Calculations | No. of Final Cluster Sample Groups | Newly Named |
---|---|---|---|---|

Kick state (1) | 300 | 1st time | 14 | 1 |

300 | 2nd time | 10 | 2 | |

300 | 3rd time | 12 | 3 |

**Table 5.**Comparison of prediction results produced by four neural network models in overflow prediction.

Model | Regularized RBFNN + k-Means | Generalized RBFNN + k-Means | GRNN + k-Means | PNN + k-Means |
---|---|---|---|---|

Optimal cluster sample name | 8-1 | 6-2 | 4-1 | 5-2 |

Gaussian function width | 0.52 | 0.38 | 0.29 | 0.41 |

Test sample prediction accuracy (%) | 75.9 | 65.2 | 51.7 | 70.16 |

Prediction accuracy of overflow status samples in test samples (%) | 100 | 25.52 | 61.43 | 98.75 |

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**MDPI and ACS Style**

Zhao, Y.; Huang, Z.; Xin, F.; Qi, G.; Huang, H.
Kick Prediction Method Based on Artificial Neural Network Model. *Energies* **2022**, *15*, 5912.
https://doi.org/10.3390/en15165912

**AMA Style**

Zhao Y, Huang Z, Xin F, Qi G, Huang H.
Kick Prediction Method Based on Artificial Neural Network Model. *Energies*. 2022; 15(16):5912.
https://doi.org/10.3390/en15165912

**Chicago/Turabian Style**

Zhao, Yulai, Zhiqiang Huang, Fubin Xin, Guilin Qi, and Hao Huang.
2022. "Kick Prediction Method Based on Artificial Neural Network Model" *Energies* 15, no. 16: 5912.
https://doi.org/10.3390/en15165912