An intelligent approach for reservoir quality evaluation in tight sandstone reservoir using gradient boosting decision tree algorithm

2.1 Detrital composition and rock fabric

As shown in Figure 1, the petrological properties of the Chang 7 tight sandstone reservoir of the study area were evaluated by using a large number of cast thin sections and scanning electron microscopy. It is found that the rock types of Chang 7 member of the study area are mainly lithic feldspar sandstone and feldspathic lithic sandstone.

Figure 1

The rock types of the Chang 7 member in the Ordos Basin [39].

The results of Figure 2 show that the reservoir porosity and permeability of the Chang 7 member had a medium correlation between a correlation coefficient of 0.621, which is a typical tight reservoir. The porosity is mainly distributed over 8 and 12%, and has an average value of 9.45%. The permeability is mainly distributed over 0.08 mD and 0.2 mD, and has an average of 0.154 mD. Therefore, the petrophysical characteristics of the reservoir are generally characterized by ultralow porosity and ultralow permeability.

Figure 2

Cross plot of porosity and permeability of the Chang 7 sandstone.

2.2 Diagenetic features

During the tectonic period between the mid–late Triassic and the early Jurassic, the Indosinian movement occurred in China and its surrounding areas, which had an extremely important influence on the evolution of the Ordos Basin. In the Chang 7 period, the basin lake experienced severe depressions. The corresponding sedimentary facies in this period were dominated by deep lake facies and semi-deep lake facies, forming the main oil-generating layer of the Yanchang Formation. Through casting thin section and scanning electron microscope observation, it is found that the pore types of the Chang 7 tight reservoir of the study area are mainly primary intergranular pores, dissolution pores, and intercrystalline pores, among which dissolution pores dominate. Later diagenetic reformation changed the pore structure of the reservoir. It could be seen from Figure 3 that there were enlarged quartz and feldspar cemented fillings in the pores of the reservoir rock, the pore throat morphology and the structure were dense, and the mixed matrix alteration could be seen between the grains. The residual pores of illite clay and a small amount of debris dissolution were filled with albite, and the intergranular pore throat was filled with quartz. The later diagenesis reduced the contribution rate of pores to the reservoir space, and the physical properties of the reservoir generally showed low porosity and low permeability.

Figure 3

Main diagenesis characteristics of the Chang 7 sandstone in Gucheng area. (a) Enlarged quartz and feldspar cemented filling residual intergranular pore throat morphology; (b) the structure is dense, and the hetero-base altered illite clay can be seen between the grains; (c) filling albite in the residual pores of a small amount of debris dissolution; and (d) quartz filling growth in the intergranular pore throat.

3.1 Gray correlation analysis principle

The gray system theory is proposed by Professor Deng Julong [40,41]. This method is mainly used to solve the uncertainty problems such as lack of data and poor information [42]. The purpose of applying gray relational analysis is to obtain a comprehensive method of evaluating reservoirs of multiple factors.

1. Let the reference series and the comparison series be:

   X 0 = { x 1 ( 0 ) , x 2 ( 0 ) , ⋯ , x n ( 0 ) } X j = { x 1 ( j ) , x 2 ( j ) , ⋯ , x n ( j ) } , j = 1 , 2 , 3 , ⋯ , m

2. According to the reference series and the comparison series, the following raw data can be formed:

   (1) X = x 1 ( 1 ) , x 1 ( 1 ) , x 1 ( 2 ) , ⋯ , x 1 ( m ) x 2 ( 1 ) , x 2 ( 1 ) , x 2 ( 2 ) , ⋯ , x 2 ( m ) ⋮ ⋱ ⋮ x n ( 1 ) , x n ( 1 ) , x n ( 2 ) , ⋯ , x n ( m ) .

3. Data preprocessing:

   (2) x i ′ = x i x max , i = 1 , 2 , ⋯ n .

4. Calculate the correlation coefficient

   (3) ξ i ( k ) = Δ ( min ) + ρ Δ ( max ) Δ i ( k ) + ρ Δ ( max ) , k = 1 , 2 , ⋯ m ,

   where Δ i ( k ) = ∣ x 0 ′ ( k ) − x i ′ ( k ) ∣ indicates the absolute difference between the reference series and the comparison series; Δ ( max ) = max i max k ( k ) represents the maximum absolute difference between the reference sequence and the comparison sequence; Δ ( min ) = min i min k ( k ) represents the minimum absolute difference between the reference sequence and the comparison sequence; ξ i ( k ) is the gray correlation coefficient.

5. Weight coefficient

   The degree of relevance indicates the degree of relevance to the reference sequence and the comparison sequence in the corresponding time. To facilitate the overall comparison, the average value of the correlation coefficient is used to indicate the degree of correlation between the reference series and the comparison series at the corresponding time. The formula is as follows:

   (4) γ i = 1 n ∑ i n ξ i ( k ) .

3.2 Calculation of correlation degree and weight coefficient

After each parameter was standardized, the gray correlation coefficient between the reference series and the comparison series was calculated by equation (3), and then the gray correlation coefficient between the reference series and the comparison series was determined (Table 2). According to equation (4), the weighting coefficients of the six indexes of reservoir evaluation were obtained (Table 3). Add the value of each parameter multiplied by the weight coefficient to get the comprehensive score of the reservoir. The calculation formula is as follows:

According to equation (5), the standardized evaluation index and its corresponding weight coefficient were multiplied and then added to obtain the corresponding comprehensive score (Table 4). According to the evaluation factors of Table 4, the inflection point diagram could be made, where it obtained the threshold values of four types of reservoirs, namely I, II, III, and IV (Figure 4). It could be seen from the figure that the type I reservoir of a comprehensive evaluation factor greater than 0.6 was characterized by high-quality reservoirs of high porosity and permeability. The comprehensive evaluation factor of 0.5 and 0.6 was a class II reservoir, which had medium porosity and permeability and was of good quality. The comprehensive evaluation factor of 0.3 and 0.5 was class III reservoir, which had poor porosity and permeability and was of poor quality. The type IV reservoir of a comprehensive evaluation factor less than 0.3 was the reservoir of the worst porosity and permeability and the worst quality, and no industrial oil flow will occur.

Figure 4

Boundary of reservoir classification in the study.

Using the above method, the single-well reservoir classification of a certain well in the study area shown in Table 5 is obtained. The classified reservoir types were consistent with the oil field test results table. This method was used to classify the reservoir types of the remaining wells as the training sample data onto machine learning.

3.3 Research methods

3.3.1 GBDT algorithm

The GBDT algorithm was developed to ensure classification or regression by continuously reducing the residuals generated during the training process. It had been commonly used from the beginning. Many attributes of GBDT include high prediction accuracy, the ability to process data onto consistent and discrete forms, the use of certain robust loss functions, and extreme robustness to outliers [43]. The training process of the GBDT algorithm is shown in Figure 5. The GBDT algorithm used a weak classifier called the classification and regression tree (CART) in each iteration. The CART was suitable for high deviation, low variance, and sufficient depth. In the regression problem, each classifier performing the iterative process was trained based on the residual of the previous classifier, and the gradient descent technique was used to impose a negative gradient on the loss function, and then the regression tree was fitted to ensure the continuous improvement in the decision model [44].

Figure 5

Schematic diagram of training GBDT algorithm.

The main idea of GBDT is to train a new learning machine in the gradient direction to reduce the learning error rate of the previous learning machine, and the new learning machine is generated iteratively on the basis of the previous learner, and its calculation formula is as follows [45]:

(6) F m + 1 ( x ) = F m ( x ) + ρ h ( x ) , 1 ≤ m ≤ M .

The specific steps of GBDT algorithm are mainly divided into the following four steps.

Step 1: The first step is to initialize a learning machine. The initialization formula is as follows:

(7) F 0 ( x ) = arg min ρ ∑ i = 1 N L ( y i , ρ ) .

Step 2: To calculate the negative gradient value of the current loss function, the number of iterations is to calculate the fitting target of the regression tree in this iteration, and its calculation formula is:

(8) r m , i = − ∂ L ( y i , F ( x i ) ) ∂ F ( x i ) F ( x i ) = F m − 1 ( x i ) , i = 1 , 2 , 3 , ⋯ , N .

Step 3: Through the first iteration, the optimal base classifier is obtained, whose calculation formula is as follows:

(9) α m = arg min ∑ i = 1 N ( r m , i − β h ( x i ; α m ) ) .

The optimal learning rate (ρ _m ) is calculated by linear optimization method, and the next base learner is updated, whose calculation formula is:

(10) F m ( x ) = F m − 1 ( x ) + ρ m h ( x i ; a m ) .

If the iteration ends, repeat Steps 2–3, otherwise proceed to Step 4.

Step 4: Building the ultimate strong learning machine.

4.1 GBDT model construction and data analysis

According to the reservoir evaluation standard of Figure 5, the reservoirs of the study area were divided into four types, and effective porosity (POR), gamma-ray (GR), acoustic curve (AC), spontaneous potential (SP), resistivity (RT), characterizing the physical and electrical characteristics of the core, as well as 7 logging curves of water saturation (SW), and shale content (SH) were taken as input parameters. The sampling interval was 0.125 m, and a total of 5,515 data points were recorded, and the relationship between each data point and reservoir type is shown in Figure 6.

Figure 6

The relationship between data points and reservoir types based on normalized logging curves.

The construction model was divided into the following two parts:

Step 1: Divide the dataset into the training set and test set according to 8:2 through the train_test_split module. Select feature subset D and divide it into training set D_train and test set D_test;

Step 2: Establish the GBDT model. The GridSearchCV module was used to perform grid search and cross-validation to find the most accurate parameter within the specified parameter range. According to the final selected hyperparameters, 300 iterations are performed in Boosting, the maximum depth of each learner was set to 3, the minimum number of classification samples was set to 2, the learning rate is set to 0.01, and the loss function was the cross-entropy loss function. After determining the dataset, the training of GBDT could be launched [20,21].

4.2 Model training results

The results of GBDT model training and testing are shown in Table 8. The accuracy of the model training set and test set was 100% and 95%, and the corresponding F-scores were 1.00% and 93.7%, respectively. From the GBDT model test set confusion matrix (Figure 7), it was found that the model predicted 90, 92, 90, and 98% accuracy for Class I, II, III, and IV reservoirs, respectively. In comparison, the model had low accuracy in predicting Type I and Type III reservoirs. From the overall point of view of the model prediction results, good results had been achieved, and the prediction accuracy of the model was sufficient to provide reliable results. In addition, Figure 8 shows the original and predicted reservoir quality logging curves for the coring wells. It could be seen that the accuracy of type I and III thin interbeds was slightly worse than that of type IV, thus confirming the conclusion of confusion matrix analysis. Finally, it could be inferred that the proposed GBDT algorithm was suitable for dense sandstone reservoir quality evaluation.

Figure 7

Confusion matrix diagram of GBDT model test set.

Figure 8

Evaluation results of the A88 well.

4.3 Feature importance

When the dataset was large, the amount of calculation required by the classifier would increase, thereby increasing the running time. We used machine learning algorithms before we selected the parameters with larger correlation characteristics between input data and output data to improve the effectiveness of the analysis. The relative importance of each feature parameter in the GBDT model are shown in Figure 9. It could be seen from the figure that AC was considered the most important feature (>0.3), followed by POR (0.2), compared with SP and SH (0.027 and 0.052, respectively), whose importance were low. When five important characteristic parameters (AC, RT, SW, POR, and GR) were selected, the discrimination accuracy of the GBDT model was 88%. However, the accuracy of class I, II, and III reservoirs decreased by 67, 57, and 75, with a 35% decrease in class II (Figure 10). Therefore, the input parameters SP and SH are retained here to ensure the prediction accuracy of the GBDT model.

Figure 9

The feature importance of the datasets.

Figure 10

Confusion matrix plot of the GBDT model with five features.

5.1 Prediction performance comparison

At present, the common methods of identifying reservoir types by logging curves mainly include Bayesian discriminant analysis and machine learning methods. The following is a comparison of the prediction results of the typical algorithms of these two methods with that of the GBDT algorithm proposed to this article.

5.1.1 Bayesian discriminant analysis

This study used Python software to analyze the applicability of the Bayesian algorithm to reservoir quality of seven logging curves. The Bayesian discriminant accuracy rate was 69%, and the Micro F1-score was 70%. It could be seen from the confusion matrix of Bayesian discriminant analysis in Figure 11 that the effectiveness of Bayesian discriminant analysis was relatively weak. The recognition accuracy of type II and type III reservoirs was poor, especially the recognition accuracy rate of type II is only 20%. In contrast, the recognition of type IV reservoir is better.

Figure 11

Confusion matrix diagram of Bayesian discriminant analysis.

5.1.2 Machine learning approach

This part discusses the accuracy of random forest algorithm and support vector machine for reservoir quality identification.

1. Random forest

   This is a supervised algorithm of machine learning, a classifier that uses multiple trees to train and predict samples. This study uses Python software to compile a random forest algorithm to analyze the recognition of reservoir quality by seven logging curves. The accuracy of random forest discrimination is 87%, and the Micro F1-score is 87%. According to the confusion matrix of random forest test set in Figure 12, it could be seen that the identification accuracy of class I, class II, and class III reservoirs is 56, 61, and 69%. In contrast, the recognition accuracy of Type IV reservoir is 97%, but the overall recognition accuracy of the random forest was lower than that of the GBDT model.

2. Support vector machine

   Support vector machine is currently a more popular machine learning model. It is a two-classification model. When it dealt with multi-classification problems, it was necessary to construct a suitable multi-classifier. This study used Python software to compile a support vector machine algorithm to analyze the recognition of reservoir quality by seven logging curves. The discrimination accuracy of the support vector machine was 82%, and the Micro F1-score was 82%. From the discriminant analysis confusion matrix in Figure 13, it could be seen that the model had the highest recognition accuracy for type IV reservoirs, followed by type I, and the recognition accuracy for type II reservoirs was 0. Therefore, support vector machines were not suitable for reservoir quality evaluation based on logging data.

Figure 12

Confusion matrix diagram of random forest discriminant analysis.

Figure 13

Confusion matrix diagram of support vector machine discriminant analysis.

5.1.3 ANN

ANN is a very important computing model in the current artificial intelligence (AI) field. This study used Python software to compile ANN algorithms to analyze the recognition of reservoir quality by seven logging curves. The discrimination accuracy of the model was 83%, and the Micro F1-score was 83%. As could be seen from the confusion matrix of ANN discriminant analysis in Figure 14, the recognition accuracy of class I, class II, and class III reservoirs was 56, 47, and 66%, respectively. By comparison, class IV was identified with 94% accuracy. The ANN was not suitable for reservoir quality evaluation based on logging data because of its poor recognition of reservoir types.

Figure 14

Confusion matrix diagram of the discriminant analysis of artificial neural network.

The results of the reservoir quality evaluation of Well A88 in the study area using the above methods are shown in Figure 15. It can be seen from the figure that the prediction result of GBDT is the closest to the original conclusion, and the error is the smallest compared with other methods. Therefore, it can be inferred that the GBDT algorithm is the most suitable for the quality evaluation of tight sandstone reservoirs. According to the geological background of Chang 7 reservoir of Yanchang Formation in Ordos Basin, the rock types of the reservoir are mainly lithic feldspar sandstone and feldspar lithic sandstone, and there are enlarged quartz and feldspar cemented filling residual grains in the rock pores. The shape and structure of the intergranular pore throats are dense, and the intergranular altered illite clay can be seen between the grains, a small amount of debris dissolving the residual pores are filled with albite, and the intergranular pore throats are filled with quartz. The pore types are dominated by primary intergranular pores, dissolution pores, and intercrystalline pores. The contribution rate of pores in the later diagenesis to the reservoir space of the reservoir is reduced, resulting in the general characteristics of low porosity and low permeability in the physical properties of the reservoir rock. The reservoir types of this characteristic are mostly type IV, followed by types III, II, and I, decreasing in order. When the amount of data on each type of reservoir is completely unbalanced, the accuracy of conventional reservoir identification methods is generally low. The GBDT algorithm proposed to this article is an algorithm designed for the imbalance of data volume. It has unique advantages in dealing with the problem of uneven data volume and can be well applied for actual production.

Figure 15

Evaluation results of four models in Well A88.

5.2 Distribution of the reservoir quality

The above results show that the GBDT model was effective against tight sandstone reservoir evaluation. Therefore, this article evaluates the reservoir quality distribution of the remaining 30 wells. In addition, it was verified through the oil field test data, and the relationship between the reservoir quality type and the test oil production (t/d.m) as shown in Figure 16. It can be seen from the figure that there was a positive correlation between the reservoir type determined by GBDT and the daily production per meter of a single well. It shows that the machine learning model selected in this study was effective against identifying tight reservoir quality. Finally, the quality of reservoirs of the 6th and 7th members of the 51 wells in the target area were identified and statistically calculated, and the reservoir quality distribution was predicted basis of difference prediction and facies control. Figure 17 shows a section of part of the well-connected well reservoir. It could be seen from the figure that the high-quality reservoirs are distributed over obvious bands of the Chang 7 member. In addition, the Chang 6 reservoir is a key area for the future development of reservoir porosity and permeability.

Figure 16

Relationship between reservoir quality categories and production materials.

Figure 17

Interwell reservoir profile of the study area.