# Prediction of Refracturing Timing of Horizontal Wells in Tight Oil Reservoirs Based on an Integrated Learning Algorithm

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}was 0.945. The established prediction method can quickly and accurately predict the refracturing time, and effectively guide refracturing practices in the tight oil test area of the Songliao basin.

## 1. Introduction

## 2. Characterization of Refracturing Timing Parameters

_{min}is the economic limit of daily oil production (t/d); I

_{D}is horizontal well drilling investment (including perforation, fracturing, etc.), 10,000 yuan/well; I

_{B}is the surface investment for horizontal wells, 10,000 yuan/well; τ

_{0}is the oil recovery rate; d

_{o}is the commodity rate of crude oil; T is the development evaluation period, year; T

_{0}is stable production period, year; P

_{o}is the selling price of crude oil, yuan/t; M is the operating cost per ton of oil, yuan/t; V

_{o}is the comprehensive tax, yuan/t; D

_{c}is the annual comprehensive decline rate of oilfield; and i is the discount interest rate, %.

## 3. Principle and Method of Refracturing Timing Prediction

#### 3.1. Sample Set Construction

^{−3}µm

^{2}were generated by a sequential Gaussian generator for model permeability. Permeability images of some geological models are shown in Figure 2. The porosity value was assigned according to the pore permeability fitting relationship of the actual reservoir. Other geological and engineering parameters were generated by calling algorithms to generate 2000 groups of random combination schemes for productivity simulation [5,33]. Finally, the geological and engineering parameters of each scheme and the corresponding refracturing time were collected and counted. On this basis, the actual statistical data of well production was added to form a learning sample set.

#### 3.2. Artificial Neural Network Algorithm

#### 3.3. Support Vector Machine Regression Algorithm

_{i}, ζ

^{*}

_{i}is the relaxation factor.

_{i},x

_{j}) is introduced to simplify the calculation process; its expression is:

#### 3.4. XGBoost Regression Algorithm

_{k}is the k

_{TH}tree model, y

_{i}is the predicted result of sample x

_{i}, and the learning process loss objective function is set as follows:

_{t}) as the regularization item, its specific form can be expressed as:

_{i}and h

_{i}are the first and second derivatives of loss function l at y

^{(t−1)}.

- According to conventional experience, a group of initial parameters was selected, and the number of decision trees was set as 50. On this basis, the depth of decision trees (max_depth) and node weights, namely, the regularization coefficient, (min_child_weight) were adjusted. The optimal parameter combination could be found by drawing a heat graph of the loss function with the tree depth and regularization coefficient.
- Adjust the gamma; this parameter determines when the loss function is split, and the smaller the parameter is, the smaller the risk of overfitting is. Therefore, under the premise of ensuring the rationality of the loss function, gamma was taken to be as small as possible.
- Adjust the sampling mode; these parameters mainly involve column sampling (colsample_bytree) and row sampling (subsample). In the same way, the best parameter combination could be found by drawing a heat map of the loss function with two parameters.
- Adjust the learning rate eta; the loss function was compared to complete the eta parameter optimization.

#### 3.5. Integrated Learning Algorithm

## 4. Algorithm Application and Analysis

#### 4.1. Application Evaluation Analysis of the Algorithm

^{2}between the predicted value and the real value of the model was 0.906. When the number of learning samples was large (1896 group), the XGBoost regression algorithm showed absolute advantages, and the correlation coefficient R

^{2}between the predicted value and the real value was 0.921. However, artificial neural networks are prone to over-fitting, so their generalization ability is poor. Under the conditions of different sample numbers, their prediction accuracy was lower than the other two algorithms, and the correlation coefficient was stable at about 0.7. Therefore, SVR and XGBoost regression are preferred as the basic models when building fusion prediction models using integrated learning algorithms.

^{1}

_{train}= (b

_{1},b

_{2},b

_{3},b

_{4},b

_{5})

^{T}and B

^{2}

_{train}= (b

_{1},b

_{2},b

_{3},b

_{4},b

_{5})

^{T}can be obtained, and the prediction results of the basic model will be fed to the secondary model for regression. In the process of regression prediction, in order to prevent the occurrence of over-fitting, a relatively simple logistics regression model was selected to process the data, and finally the prediction results of the integrated learning model were obtained (Figure 9). By comparing the predicted results of the integrated learning model and the basic model, the correlation coefficient between the real value and the predicted value of the refracturing time in the test set was calculated, as shown in Figure 10.

^{2}of the integrated learning algorithm based on a logistics regression model was the highest, up to 0.945. Compared with the prediction results of a single algorithm, the prediction accuracy of the model was further improved. The comparison curve between the real value of the refracturing time of some samples in the test set and the predicted value of the integrated learning algorithm is shown in Figure 11. It can be seen that the predicted value of the refracturing time fluctuated around the actual value with a small prediction error and a high degree of agreement with the field measurement and mathematical model data. Therefore, the established prediction method can replace the conventional numerical simulation workflow, quickly and accurately predict the refracturing time, and effectively guide field practice.

#### 4.2. Field Implementation Effect

^{3}, and fracturing sand addition of 460 m

^{3}. The initial average production after pressure was up to 30 t/d. Up to now, the average daily oil production was 3.07 t/d, close to the economic limit of daily production. By inputting geological and engineering parameters into the established prediction model, the predicted value of the time of repeated fracturing was 712 d, which is highly consistent with the actual value of 649 d.

^{3}/min. The dual-packer and single-clip staged fracturing technology was used to complete the construction, and the refracturing process was smooth. To the whole well was added 56 m

^{3}ceramsite, 748 m

^{3}quartz sand and 7673 m

^{3}Guar gum fracturing fluid. After refracturing, the daily fluid level recovered to 31 t/d, and the daily oil level recovered to 10.2 t/d. The daily oil output reached 71.2% of that of the initial fracturing, and the cumulative oil increase was 3171.4 t, showing an obvious stimulation effect (Figure 12).

## 5. Conclusions

- Based on the increased production of horizontal wells with refracturing measures as the evaluation index, the law of the influence of refracturing timing on the stimulation effect was analyzed. Combined with the economic limit of tight oil horizontal wells, the economic limit daily production of horizontal wells was calculated, and the reasonable refracturing timing was quantitatively characterized.
- Using machine learning techniques to measure the geologic and engineering parameters of horizontal wells, with a total of 11 variables as input, the refracturing time as output, the comprehensive field measurements and a large number of numerical simulation data to construct the learning sample set, and noise reduction processing on the sample set, three kinds of modeling and prediction effect comparisons of machine learning algorithms were chosen; the results showed that the support vector machine and XGBoost regression algorithm of artificial neural network algorithm showed better generalization.
- Through integrated study of the depth of the stacking method, SVR and XGBoost were combined to build the dense oil refracturing horizontal well, based on the integrated study time prediction method. Using 257 groups to build a prediction model in a test set forecast result analysis, it was shown that, compared with a single algorithm model, the prediction accuracy was higher, and the actual and estimated values of the correlation coefficient R
^{2}were 0.945—alternative numerical simulation processes quickly predicted refracturing timing. The prediction model was used to predict the refracturing time of the X34-P6 well in the target reservoir, and the predicted results were in great agreement with the actual value. - Having a high predictive accuracy, the integrated learning model can serve as a reliable tool for predicting refracturing time. It has high potential for being applied in macro decision making of horizontal well repeated fracturing.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Comparison of production capacity at different refracturing timings: (

**a**) Daily production curve at different refracturing times; (

**b**) Oil increments at different refracturing times.

**Figure 3.**Comparison of Distribution before and after logarithmic transformation of refracturing timing.

**Figure 6.**XGBoost regression algorithm to optimize the parameter adjustment process: (

**a**) eta and gamma parameter optimization; (

**b**) max_depth and min_child_weight parameter optimization; (

**c**) colsample_bytree and subsample parameter optimization.

**Figure 8.**Comparison of algorithm prediction accuracy under different learning sample numbers: (

**a**) n = 800; (

**b**) n = 1896.

**Figure 10.**Intersection diagram of simulation data and verification data: (

**a**) SVR; (

**b**) XGBoost; (

**c**) integrated learning algorithm.

Input | Output | |
---|---|---|

Geological properties | Matrix permeability | Refracturing timing |

Matrix porosity | ||

Reservoir pressure | ||

Effective reservoir thickness | ||

Oil saturation | ||

Engineering properties | Fracture half-length | |

Fracture conductivity | ||

Fracture spacing | ||

Fracturing fluid consumption | ||

Footage of horizontal well | ||

Bottom hole pressure |

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**MDPI and ACS Style**

Zhang, X.; Ren, J.; Feng, Q.; Wang, X.; Wang, W.
Prediction of Refracturing Timing of Horizontal Wells in Tight Oil Reservoirs Based on an Integrated Learning Algorithm. *Energies* **2021**, *14*, 6524.
https://doi.org/10.3390/en14206524

**AMA Style**

Zhang X, Ren J, Feng Q, Wang X, Wang W.
Prediction of Refracturing Timing of Horizontal Wells in Tight Oil Reservoirs Based on an Integrated Learning Algorithm. *Energies*. 2021; 14(20):6524.
https://doi.org/10.3390/en14206524

**Chicago/Turabian Style**

Zhang, Xianmin, Jiawei Ren, Qihong Feng, Xianjun Wang, and Wei Wang.
2021. "Prediction of Refracturing Timing of Horizontal Wells in Tight Oil Reservoirs Based on an Integrated Learning Algorithm" *Energies* 14, no. 20: 6524.
https://doi.org/10.3390/en14206524