3.1

Data set acquisition and preprocessing

Engineering geological parameters and fracturing construction data were collected from the field and used to construct the structured dataset. The original dataset cannot be directly used to train the model, and a series of preprocessing operations are required. In the original dataset, when the missing data in the feature variable is greater than the safety threshold of 5%, it will not be considered in the modeling. The original data needs to be normalized as different units may affect the results¹⁰. The Z-Score method is an ideal solution and is often used in data normalization. It represents how many standard deviations the measurement data deviates from the mean of the data population, and its expression is:

where z is the standardized dimensionless data; σ is the sample standard deviation; x is the original value of a sample; μ is the mean value of the sample. Assuming the dataset D contains n learning samples, each sample has m feature parameters and a feature label, namely:

3.2

Feature optimization

There are many methods for feature optimization. Commonly used methods include multiple regression method, gray correlation method, Lasso method, covariance and so on¹¹. The Pearson correlation coefficient characterizes the similarity between variables, and its output ranges from -1 to +1, among them, 0 means that the vectors are independent of each other, and the closer the absolute value is to 1, the stronger the correlation¹². The formula for calculating the Pearson correlation coefficient is as follows:

where cov is the covariance and σ is the standard deviation. Compared with covariance, Pearson’s correlation coefficient removes the effect of variable dimension.

This study uses the Grey Relation Analysis (GRA) method to study the influence of the selected features, and the grey relational analysis of the main controlling factors helps to enhance the interpretability of the model. The GRA method is a multivariate statistical analysis research tool. Simply put, in a gray system, we want to know how strongly a variable is affected by other variables or factors¹³. Grey relational degree analysis has low requirements on data and calculation, and its calculation formula is as follows:

where i is the serial number of a sample; k represents the serial number of a feature; ρ is the resolution coefficient, ranging from 0 to 1. The smaller the ρ, the more obvious the difference between samples, and usually ρ is taken as 0.5. x₀(k) is selected by user and regarded as the reference sequence. According to the calculated correlation coefficient, the influence of each factor on the production can be analyzed. The correlation order can be further calculated based on the correlation coefficient, and the formula is:

The degree of influence of each factor can be obtained by sorting the correlation degree.

3.3

Data set division

The original dataset is usually divided using the set-out method and setting a ratio. When the amount of data is relatively small, a ratio of 7:3 to 9:1 can usually be used to divide training data and test data. Commonly used partitioning methods for datasets include hand-out method and cross-validation method. The hand-out method is to use a portion of the total samples as test set. The proportion is usually 10%-30%, and generally the capacity of the test set is at least more than 30.

To ensure that the model’s predictions are reliable, this study performed 300 samplings, divided the training and test sets, and trained and evaluated the selected machine learning models accordingly¹⁴.

3.4

Intelligent algorithm model selection

Commonly used intelligent algorithms are compared in this study, including gradient boosting, random forests, support vectors, and neural networks. The training set data is used to train the intelligent model, and the performance of the model is evaluated by using the test set^15-17.

For regression problems, commonly model prediction evaluation indicators include mean square error, root mean square error, mean absolute error, coefficient of determination, etc. In this study, RMSE (Root Mean Square Error) is used as a key indicator to compare the performance of different models, and its expression is as follows:

Accuracy is also used as a key indicator to compare the performance of different models, and its expression is as follows:

4.1

Data collection and preprocessing

This paper takes the W tight gas reservoir in Alberta, Canada as a case study. The depth of the W reservoir is 2000 meters. The research target is located in the RT21 block, with an area of 2500 km² and an average reservoir thickness of 200 meters. The samples of 1091 wells in the study area were de-noised, cleaned and screened, and there were 1071 available data sample wells, and each sample contained 12 dimension features and 1 set of production label. After missing vale pre-processing, the feature dimension of the model is changed from 12 to 10.

4.2

Feature optimization

If the feature parameters of the model input are strongly correlated, it will not only increase the model training time, but also affect the interpretability of the model. Figure 1 shows the Pearson correlation coefficient matrix of the characteristic variables. Total Proppant Pumped dose has a strong linear positive correlation with Proppant Pumped Per Stimulated Length (Pearson’s coefficient is 0.92). Total Fluid also has a strong linear positive correlation with Fluid Per Stimulated Length (Pearson’s coefficient is 0.86). After removing the linear correlation variables Proppant Pumped Per Stimulated Length and Fluid Per Stimulated Length, the dimension of the feature variable is reduced from 10 dimensions to 8 dimensions.

Figure 1.

Variable correlation analysis matrix.

The grey correlation method can be used to calculate the correlation between the 8 control factors and the production. As shown in figure 2, it can be seen that Fluid Per Stage has the greatest impact on the Production and Total Proppant Pumped has the least impact on the production.

Figure 2.

Tornado chart of controlling factors by grey correlation method.

4.3

AI model optimization and analysis

In order to select the optimal model, this study evaluates gradient boosting, decision tree, random forest, support vector machine and neural network respectively. The evaluation results are shown in table 1 below.

Table 1.

Intelligent model predictive evaluation.

From the table 1, we can acknowledge that the performance of the random forest model is the best, the test set accuracy can reach more than 85%, and the model training time is about 12.63 s, which is relatively short. Therefore, the random forest is chosen as the intelligence model in this research area.