Abstract
Production prediction is the most important and comprehensive index to measure the effect of oilfield development, and it is also one of the most fundamental problems in oilfield dynamic analysis. However, the recovery prediction is often affected by many factors. Usually, the recovery is predicted by core experiments, numerical simulations, and mathematical models. The main problem is accurately predicting reservoir recovery based on existing data. This paper proposes a comprehensive prediction model for the problem of recovery. First, the correlation coefficients between 14 factors and recovery were calculated based on Pearson, Spearman, gray correlation, variance selection, univariate selection method, and tree model. Second, the weights of the factors were determined using entropy weighting, CRITIC, and hierarchical analysis to clarify the degree of contribution of different factors to the recovery. Finally, a comprehensive evaluation model was established based on the results of the weighting analysis. The results indicate that the correlation coefficient and weight of porosity, permeability, oil saturation, well spacing, cluster spacing, total fluid volume, and horizontal section length are the most relevant to the recovery. The error between the comprehensive evaluation model and the actual results is less than 3%. Therefore, the method can predict the production capacity of the tight reservoirs. The research results of this paper are of guiding significance for improving the recovery of tight reservoirs.
1. Introduction
With the global exploration and development of unconventional oil and gas resources, tight oil, as an essential unconventional oil and gas resource, has received extensive attention from countries worldwide.1−3 China has made several new advances in tight oil exploration and development in Songliao, Ordos Basin, and Bohai Bay.4−6 However, the dynamic characterization of tight oil reservoir production and the prediction of recoverability are still the focus and difficulties faced by reservoir engineers.7−11 Tight oil reservoirs have geological characteristics such as complex pore structure, inconspicuous boundaries of confinement, and poor nature physical properties of reservoirs, which generally do not have or have low natural production capacity, and large-scale horizontal well technology and fracturing measures must be adopted in order to realize cost-effective mobilization and development.12−15 Compared with the development of conventional reservoirs, the production capacity and future production dynamics of tight reservoirs are affected by both reservoir quality and fracturing engineering technology.16 Due to the storage and flow space constituted by different scales of pores and fractures, tight reservoirs are characterized by the development of one well, one reservoir, which leads to the characteristics of high production and low production in the middle and late stages, so it is necessary to establish a reasonable dynamic analysis model to predict the recovery of tight reservoirs.17−20
Recovery is the material basis for oilfield development planning, an indicator of the degree of utilization of oil reserves, and the basis for evaluating the effect of oilfield development and formulating adjustment methods.21−24 With a further understanding of the current oil reservoir development situation and technical level improvement, the evaluation of recovery varies at different stages.25 Only when the recovery is accurately predicted can the oil field be reasonably developed and achieve good economic benefits. Currently, tight reservoir recovery prediction can be divided into core-scale experiment analysis and reservoir-scale water-driven post analysis, which mainly includes core repulsion, empirical formula method, water characteristic cure method, and reservoir numerical simulation calculation method.26 Chen et al. conducted core recovery calculations based on indoor physical simulation experiments, and the experimental results indicated that they were relatively reasonable due to the influence of the initiating pressure gradient considered in this experimental process.27 However, due to the influence of core size, the experimental results cannot fully reflect the vertical and planar inhomogeneity of the reservoir and the parameters of well network and well type.28 Sun et al. used indoor physical simulation to analyze the relationship between relative permeability, water saturation, and bound water saturation during core replacement.29 They determined the residual oil saturation after water driving, considering the original oil saturation of the formation, to perform recovery prediction on small-scale cores.30 Wang et al. proposed that the characteristic curve of water driving was also used for recovery prediction in volumetric fracturing of tight reservoirs, and the method was able to effectively predict the recovery change in the late stage of tight reservoir development.31 He and Shi proposed a new water-drive characteristic curve for the high-water content problem faced in the late stage of low-permeability reservoir development, which is mainly based on the change between the relative permeability of oil and water and the water saturation during the water-drive process.32 In addition, Lin and Jiang proposed the prediction of recovery variations in tight reservoirs by the declining production method, which is mainly based on scale upgrading based on indoor core results, and thus recovery prediction by numerical simulation of the reservoir.33 Xu et al. proposed the analogy method for recovery prediction in tight reservoirs.34 This quantitative model usually employs analogies with relevant data from mature or developed fields to predict new oil and gas fields’ production patterns and related parameters. However, this method generally varies in results due to differences in knowledge, experience, and ability to draw analogies.35 Xu et al. proposed combining the analog and empirical formula methods for recovery prediction, which can reduce the prediction accuracy.36 Hajizadeh et al. combined the oil–water phase infiltration curve with the exponential decreasing method. They proposed combining regression experimental data and field to predict the recovery rate through the Buckley–Leverett theory, which further improves the accuracy of the recovery rate prediction.37
However, the recovery rate of horizontal well volume fracturing and water injection in tight reservoirs is affected by various complex factors, and the above methods still cannot predict the recovery rate of tight reservoirs by considering multiple factors.38 The machine learning method can establish a reasonable prediction model for different development stages of tight reservoirs and various influencing factors and form a method suitable for predicting recovery rates in tight reservoirs.39 Belyadi and Haghighat used the gray correlation analysis to optimize the fracturing parameters of horizontal wells.40 Mohamadian et al. used gray correlation method to study the main controlling factors of residual oil in small fractured rock reservoirs.41 Jin used hierarchical analysis to optimize the oil field development scheme. Min studied the entropy weighting method based on determining the weights of various influencing factors in tight reservoirs to identify the main controlling factors.42 Layouni studied the neural network model and Bayesian method based on the machine learning method and used the method for reservoir optimization to improve the recovery rate of tight oil reservoirs.43 Cheraghi et al. proposed an efficient geometric model for predicting and analyzing production data from tight reservoirs, which achieves accuracy enhancement by variance and bias selection method.44 Al Dhaif et al. proposed recovery prediction based on the support vector machine method, a high-dimensional nonlinear machine learning method with minor error and low computational degree.45 Al-Sabaeei et al. used random forest and principal component analysis to predict the change law of production capacity in tight reservoirs and further discuss the applicability of machine learning for recovery prediction.46 Bhattacharyya and Vyas proposed a new theory based on the ANN model, which can reduce the error by the weight and bias method and improve accuracy using the genetic algorithm and ion swarm method.47 Al-Mudhafar et al. used the genetic algorithm to predict the changing pattern of the bottom-hole pressure during the production of horizontal wells. The error level was reduced to 10% compared with the measured data.48−50 Although more machine learning methods are applied to the dynamic production capacity analysis of tight reservoirs, the different methods cannot accurately predict the recovery due to the differences in evaluation indexes, data characteristics, and processing methods. There is an urgent need to propose a new model for capacity prediction that integrates multiple influencing factors to predict recovery in tight reservoirs.51−53
Aiming at the problems of a tight reservoir capacity prediction model, this paper adopts a comprehensive evaluation method to establish a new capacity prediction model based on machine learning. First, there are two indicators for tight reservoir development factors. Correlation analysis methods such as gray correlation (GRA), tree model (FCB), Spearman (SCC), Pearson (PCC), variance selection (VS) method, and univariate (UF) are used to determine the relationship between each influencing factor and recovery. On this basis, the entropy weight method (EW), CRITIC analysis method, and hierarchical analysis method (AHP) are used to determine the weight of each influencing factor and recovery. Second, to reduce the modeling error, this paper adopts the comprehensive weight analysis method to determine the main controlling factors of recovery in tight oil reservoirs. Finally, a new model for tight reservoir production capacity prediction was established using the multiple linear regression method, and the fitting results were compared with the actual data, BP neural network, support vector machine, and K-nearest-neighbor regression method to validate the reasonableness of the model further.
2. Methodology and Statistics
2.1. Influencing Factors
There are a few factors affecting the recovery factor, which should be determined by combining the actual situation of the oilfield and reservoir reconstruction technology. Considering the effect of oil field reconstruction and reservoir physical properties, the factors affecting the recovery efficiency are divided into two categories: geological factors and development factors, with a total of 14 indexes. The results are shown in Figure 1.
Figure 1.
Factors affecting recovery in tight reservoirs.
2.1.1. Geological Factors
These represent the reservoir’s physical foundation, reflecting the reservoir’s ability to supply oil to artificial fractures to a certain extent. Four indicators include reservoir thickness, porosity, permeability, and oil saturation.
2.1.2. Developing Factors
The recovery degree and capacity maintenance status after taking measures are represented, including 10 indicators, including length of horizontal well, total amount of liquid, total amount of sand, strength of sand, amount of cluster, amount of liquid per cluster, amount of sand per cluster, and strength of liquid. According to the influencing factors, the analytic hierarchy process draws the following structure.
2.2. Reservoir Characteristics
The study was conducted in a block in China that is of tight sandstone type. The rock type comprises dense clastic rocks, mainly siltstone, fine sandstone, and some medium-coarse sandstone. Disorderly matrix particles, strong heterogeneity, significant lithologic changes, complex pore-throat structure, low permeability, high water saturation, and low mobile fluid saturation characterize the reservoir. The reservoir depth in the study area is 3500–4130 m. The reservoir thickness in this block is 5–15 m, and the permeability is uneven, concentrated in 1–3 mD and 3–12 mD, and the average permeability is 6.72 mD. The cluster interval was concentrated in the range of 20–30 and 30–60 m, and the average distance was 40.2 m. The strength of sand ranges from 0.9 to 1.5 m3/m, the average length of the horizontal well ranges from 1000 to 2000 m, and the average well spacing ranges from 200 to 500 m. The original reservoir pressure is 27.49 MPa, and the geological reserves are 102 × 104 t.
2.3. Analytical Methods
2.3.1. Pearson Correlation Coefficient Method
The Pearson correlation coefficient (PCC) method is a statistical technique used to measure the linear relation between two variables. It has a range of values between −1 and 1. When the correlation coefficient is 1, it indicates a perfect positive linear relationship between the two variables, meaning that they increase in the same proportion.
When the correlation coefficient is −1, it signifies a perfect negative linear relationship between the variables, meaning that they increase in opposite proportions. When the coefficient is close to 0, it suggests that there is little to no linear relationship between the two variables.
The PCC is calculated by dividing the covariance of two variables by the product of their standard deviations. It is typically represented as r, and its formula is as follows.13
 |
1 |
In this formula, X and Y represent the values of two variables, while μX and μY represent their, respective, means or averages.
2.3.2. Gray Relational Analysis Method
The gray relational analysis (GRA) is based on gray relational degrees, and it involves comparing the geometric relationships and the similarity of geometric shapes in data sequences to analyze the degree of association among various factors within a system. The steps involved in this analysis are as follows.
Step 1: identify the feature sequences and evaluation criteria.
Comparison sequence.
 |
2 |
Evaluation criteria.
 |
3 |
Step 2: to accurately reflect the actual situation, the indicator data are dimensionless to eliminate the influence of the different units and significant differences in the numerical magnitudes of various indicators. This helps to avoid unreasonable occurrences. Typically, initial scaling and normalization are used to standardize the dimensions.
Step 3: calculate the correlation coefficients. Calculate the correlation coefficient for each element of the compared sequence with the corresponding element of the reference sequence using the following formula.
 |
4 |
ρ is the resolution coefficient.
Step 4: calculate the correlation degree
Calculate the weighted average of the correlation coefficients for each indicator with the corresponding elements of the reference sequence to reflect the relationship, which becomes the correlation degree; it can be represented as follows.
 |
5 |
Step 5: analyze the calculation results. Establish a correlation sequence for each evaluation object based on the magnitude of the gray weighted correlation degrees. The larger the correlation degree, the more critical it indicates the evaluation object’s significance concerning the criteria.18
2.3.3. Spearman’s Rank Correlation Coefficient
Spearman’s rank correlation coefficient is a statistical method used to measure the correlation between two variables, especially when dealing with nonlinear relationships or data that do not follow a normal distribution. It is calculated based on the ranks (orderings) of the variables rather than their actual values. Spearman’s rank correlation coefficient is advantageous because it is not sensitive to outliers, can handle ordinal data, and is suitable for assessing nonlinear relationships. It is commonly used in statistical analysis and research to determine the degree of association between two variables.20
2.3.4. Feature Selection Based on Tree Models
Feature selection based on tree models is used in machine learning and data analysis to select the most essential features from a data set by leveraging tree-based models such as decision trees, random forests, or gradient-boosting trees. Feature selection based on tree models is an effective method, especially when dealing with large data sets and problems with many features. This approach allows data scientists and machine-leading practitioners to identify the most relevant features, enhancing model performance and interpretability.21
2.3.5. Variance Selection
Variance selection (VS) is a feature selection method to select features in a data set with high variance. The core idea behind this method is that features with a high variance have more information in the data, and therefore, they may contribute more significantly to modeling or analysis. VS is typically used to reduce data dimensionality, improve model efficiency, or identify the most informative features in the data. VS’s advantages include its simplicity and computational efficiency. However, it has some limitations, such as the inability to handle feature correlations as it solely considers the variance of each feature and does not account for relationships between features.23
2.3.6. Univariate Feature Selection Test
The principle of the univariate feature selection test is to calculate the scores of the input parameters in the scoring function separately and return a P-test value, which determines the correlation between the input parameters and the target parameters for feature screening. In classification problems, the χ2 test is generally used. In regression problems, the P-value is the value that rejects the original hypothesis and is usually used to judge the correlation between the input and output parameters. The smaller the P-value in a regression problem.25
The main reasons for choosing this study’s above six analysis methods include the following points: (1) the gray correlation method is suitable for assessing the degree of correlation between variables, is relatively flexible in terms of the requirements for data distribution, and applies to a wide range of data types. (2) The Spearman method has relatively low requirements for data distribution, is relatively flexible in its use, and applies to a wide range of situations and irregularly distributed data. (3) The tree model can discover the interaction between various factors, performs well on complex data, and is suitable for various types of data analysis. (4) The VS method can reduce the dimensionality of the characteristics and improve the accuracy of the model. (5) The univariate analysis method can assess the independence of each variable and has an intuitive analysis of the impact of a specific variable. (6) The Pearson analysis method can conduct correlation analysis on the data that meets the normality analysis. Through the correlation analysis of data and research methods, the above methods we proposed apply to the research in this paper, and the comprehensive consideration of multiple methods can achieve a reduction of prediction error.
3. Results and Discussion
3.1. Sensitivity Analysis
3.1.1. Correlation Analysis of Influencing Factors
3.1.1.1. PCC Method
Pearson correlation calculations are calculated in the interval −1 to 1. The size of the absolute value of the numerical result represents the degree of correlation; the more significant the absolute, the stronger the correlation, and the positive or negative value represents the conclusion’s relevance. Based on the results of Pearson’s analysis, it can be seen that the intensity of sand addition, number of clusters, fluid intake per cluster, sand intake per cluster, porosity, permeability, oil saturation, and well spacing are positively correlated with recovery, while the length of the horizontal length, the total fluid volume, the total and addition, the intensity of the fluid intake, the spacing of the clusters, and the thickness are negatively correlated with the recovery. The results are shown in Figure 2.
Figure 2.
PCC.
3.1.1.2. GRA Method
The calculation results of the gray correlation analysis method are between 0 and 1. The correlation degrees between different influencing factors and recovery rate, from high to low, are permeability, porosity, oil saturation, thickness, total fluid volume, the number of clusters, horizontal length, liquid strength, sanding strength, well spacing, cluster spacing, total amount of sand added, amount of fluid added per cluster, and amount of sand added per cluster. Among them, permeability, porosity, and oil saturation have the highest correlation and are consistent with the results obtained by other methods, which can ensure the correctness of the conclusions.28 The results are listed in Tables 1 and 2.
Table 1. Correlation Coefficient Table.
| evaluation factors | relatedness |
|---|---|
| permeability | 0.3665 |
| porosity | 0.2841 |
| oil saturation | 0.2801 |
| thicknesses | 0.2423 |
| total fluid volume | 0.2281 |
| number of clusters | 0.2277 |
Table 2. Correlation Coefficient Table.
| evaluation factors | relatedness |
|---|---|
| horizontal length | 0.2036 |
| liquid strength | 0.1989 |
| sanding strength | 0.1846 |
| well spacing | 0.1745 |
| cluster spacing | 0.1625 |
| total sand added | 0.1581 |
| liquid per cluster | 0.1287 |
| sand per cluster | 0.1136 |
3.1.1.3. Spearman’s Rank Correlation Coefficient
The results of Spearman’s analysis show that the fluid intake per cluster, number of clusters, sand addition per cluster, fluid addition intensity, oil saturation, sand addition intensity, porosity, and permeability are positively correlated with the recovery, and the length of the horizontal well, the total fluid volume, the spacing between clusters, the total sand addition, the thickness, and the distance between the wells are negatively correlated with the recovery. The results are listed in Figure 3.
Figure 3.
Spearman’s correlation coefficient.
3.1.1.4. Feature Selection Based on Tree Models
The results of the feature selection method of the tree model show that sand addition intensity, cluster number, fluid feed per cluster, sand addition per cluster, porosity, permeability, oil saturation, and well spacing are positively correlated with the recovery and horizontal length, total fluid volume, total sand addition, fluid feed intensity, cluster spacing, and thickness are negatively correlated with the recovery. The results are shown in Figure 4.
Figure 4.
Tree-based model correlation coefficients.
3.1.1.5. Variance Selection
The correlation results calculated by the VS method ranged from −1 to 1. Porosity, permeability, oil saturation, well spacing, the number of clusters, total sand addition, and total fluid addition positively correlate with recovery. In contrast, cluster spacing, sand addition intensity, fluid addition intensity, fluid addition per cluster, horizontal section length, and thickness negatively correlate with recovery. The results are shown in Tables 3 and 4.
Table 3. Variance Method Correlation Coefficient.
| evaluation factors | relatedness |
|---|---|
| porosity | 0.555 |
| permeability | 0.521 |
| oil saturation | 0.478 |
Table 4. Variance Method Correlation Coefficient.
| evaluation factors | relatedness |
|---|---|
| cluster spacing | –0.466 |
| sanding strength | –0.386 |
| well spacing | 0.298 |
| liquid per cluster | 0.287 |
| liquid strength | –0.272 |
| number of clusters | 0.181 |
| total fluid volume | 0.167 |
| total sand added | 0.129 |
| sand per cluster | –0.126 |
| horizontal length | –0.107 |
| thicknesses | –0.076 |
3.1.1.6. Univariate Feature Selection Test
According to the results of the correlation coefficient calculation of the univariate feature selection method, it can be seen that the results of the correlation coefficient of this method are between −1 and 1. Oil saturation, porosity, well distance, permeability, total sand addition, and total fluid volume positively correlate with recovery and the number of clusters. The amount of fluid feed per cluster, the spacing of the clusters, the strength of sand addition, the intensity of fluid addition, the sand addition per cluster, the length of the horizontal section, and the thickness are negatively correlated with recovery. The results are shown in Tables 5 and 6.
Table 5. Univariate Correlation Coefficient.
| evaluation factors | relatedness |
|---|---|
| permeability | 0.617 |
| porosity | 0.608 |
| oil saturation | 0.547 |
| well spacing | 0.487 |
| liquid per cluster | –0.458 |
| cluster spacing | –0.437 |
| number of clusters | –0.435 |
| liquid strength | –0.425 |
Table 6. Univariate Correlation Coefficient.
| evaluation factors | relatedness |
|---|---|
| sanding strength | –0.411 |
| sand per cluster | –0.352 |
| total sand added | 0.260 |
| total fluid volume | 0.258 |
| horizontal length | –0.191 |
| thickness | –0.139 |
3.1.2. Analysis of Sorting Results
The screening methods measure different indicators, and although the seven methods have many common conclusions in general, they do not all rank the results precisely the same for each factor. The ranking of the screening results by the different methods is somewhat biased, and the results of the ranking of the different parameters by each method are shown in Table 7.
Table 7. Correlation Coefficients of Different Methods.
| factor | PCC | SCC | FCB | GRA | UF | VS |
|---|---|---|---|---|---|---|
| porosity | 1 | 1 | 1 | 2 | 2 | 1 |
| permeability | 2 | 2 | 2 | 1 | 1 | 2 |
| oil saturation | 3 | 3 | 3 | 3 | 3 | 3 |
| cluster spacing | 4 | 4 | 4 | 11 | 6 | 4 |
| total fluid volume | 5 | 7 | 5 | 5 | 12 | 10 |
| well spacing | 6 | 6 | 6 | 10 | 4 | 6 |
| horizontal length | 7 | 11 | 7 | 7 | 13 | 13 |
| sand per cluster | 8 | 5 | 8 | 14 | 10 | 12 |
| total sand added | 9 | 14 | 11 | 9 | 11 | 11 |
| number of clusters | 10 | 13 | 10 | 6 | 7 | 9 |
| liquid strength | 11 | 8 | 13 | 8 | 8 | 8 |
| liquid per cluster | 12 | 12 | 12 | 12 | 5 | 7 |
| sand per cluster | 13 | 9 | 13 | 9 | 9 | 5 |
| thicknesses | 14 | 10 | 14 | 4 | 14 | 14 |
From the table, it can be found that five methods consider porosity the most important parameter and should be ranked first, and two methods consider porosity the second most important parameter and are ranked second; therefore, porosity is ranked first. Five methods considered permeability the second most important parameter, and two considered permeability the first; thus, permeability was ranked second. Six methods considered oil saturation the third most crucial parameter and one method considered oil saturation to be the third most important parameter; thus, oil saturation was ranked third. Cluster spacing was ranked fourth by four methods; two methods ranked cluster spacing as the 6th, and one method ranked cluster spacing as the 11th; thus, cluster spacing was ranked fourth. Four methods considered the total liquid volume the 5th most crucial parameter; one method ranked the total liquid volume 7th, one method ranked it 12th, and one method ranked it 10th, thus ranking the total liquid volume 5th. Based on the same analytical method, the 6th ranking is well distance, the 7th is horizontal section length, the 8th is fluid strength, and the 9th to 11th ranking is different, mainly because the role of this part of the influencing factors on the recovery is more complex. It still needs to arrive at an accurate ranking. The 12th ranked is liquid feed per cluster, and the 14th is reservoir thickness.
Permeability, porosity, and oil saturation are highly correlated during the development of tight reservoirs and determine the recovery of tight reservoirs. While total fluid volume, well spacing, and horizontal section have relatively low correlations, liquid addition per cluster and reservoir thickness have the lowest influence on recovery.
3.2. Determination of Main Control Factors
In order to further determine the main controlling factors of recovery in tight reservoirs, this paper adopts five weight methods to determine the weights of different influencing factors. Based on the weighting analysis, the main controlling factors of recovery in tight reservoirs are clarified through a comprehensive evaluation method.
3.2.1. Analytic Hierarchy Process
The analytical hierarchy process (AHP) refers to the decomposition of the elements related to the overall decision into goals, guidelines, programs, and other levels. The question can be decomposed into different factors to form a multilevel fractal structure model according to the general goal. Finally, the problem can be reduced to determining the relative importance weight of the lowest level relative to the highest level or the arrangement of the relative order of the pros and cons. As shown in Table 8, the judgment matrix is constructed to judge the relative importance of each index in the hierarchy. The judgment structure is expressed by a numerical value and written as a matrix.
Table 8. Meaning of the Judgment Matrix Scale.
| standard values bij | the degree of importance between elements |
|---|---|
| 1 | factor bi and bj contribute equally |
| 3 | factor bi contributes slightly more than factor bj |
| 5 | factor bi contributes strongly more than factor bj |
| 7 | factor bi contributes very strongly more than factor bj |
| 9 | factor bi is extremely important more than factor bj |
| 2, 4, 6, 8 | the intermediate value to reflect the importance |
| reciprocal | the reverse comparison positions of above |
3.2.2. Hierarchical Single Sorting and Consistency Checking
Hierarchical single sorting is used to calculate the importance of weight related to the index of the upper level according to the judgment matrix. The judgment matrix is listed, and the eigenvalues and eigenvectors of the judgment matrix are calculated; that is, the eigenvalues and eigenvectors satisfying the following relation are calculated for the judgment matrix.8
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6 |
In the formula, λmax is the maximum eigenroot of the judgment matrix D, and V is the eigenvector corresponding to.
For the quality of the judgment matrix, it is necessary to check its consistency, and each index value in the judgment matrix should meet the following requirements.
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7 |
To investigate whether the judgment matrix applies to the AHP, it is necessary to conduct a consistency test on the judgment matrix. The consistency of the judgment matrix is tested by the following index.
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8 |
where n is the order of the judgment matrix; when the order of the matrix is less than 3, the consistency check algorithm is better. When the order of the matrix is higher, the consistency should be modified. Its operator is as follows.9
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9 |
RI is the correction factor, and its value is as follows. The results are shown in Table 9.
Table 9. Correction Factor.
| number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| RI | 0 | 0 | 0.58 | 0.9 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |
Usually, at that time, when CR < 0.1, the matrix is considered to meet the consistency requirements.
Due to the difference in experts’ knowledge structure and cognitive level, the authenticity and credibility of the judgment matrix are different, so it is necessary to determine the authority function of experts.
 |
10 |
In the formula, parameter a plays a regulating role, and in actual engineering, a = 10.
According to the following formula, the weight of experts is normalized.
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11 |
Considering the weight in the evaluation comprehensively, the final weight is
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12 |
3.2.3. Gray Correlation Component
The core of the Gray relational degree evaluation method is calculating the relational degree. The degree of correlation measures the degree of correlation between the factors of two systems that change from time to time or from different objects. It is also a method to obtain the weight. The key influencing factors are determined by looking for the primary and secondary relations of various factors in the system.
First, the initial matrix is constructed according to the actual data. There are m evaluation indicators and n evaluation objects.
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13 |
where: n, the number of candidates refracturing wells; m, influencing factors.
Because in practical problems different data generally have different dimensions, to make the quantities with different dimensions also be compared, it is necessary to eliminate the dimension of the evaluation index and then carry out the initial value processing.
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14 |
In the formula, xmaxj and xminj are, respectively, the maximum and minimum values of the JTH index Yj.
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15 |
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16 |
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17 |
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18 |
where x*j is the best fixed value of index Yj.
After the reference and sequence and comparison sequence are selected, the matrix is dimensionless utilizing averaging.
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19 |
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20 |
At the same time, to determine the interval [0.1] of the obtained data, each component of each line in the matrix should be divided by the corresponding component of the first-row vector to form the following matrix.
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21 |
Calculate the absolute values of the corresponding elements of the index sequence and reference sequence of each evaluated object one by one.
Namely, |x0(k) – xi(k)|, (k = 1,···, m, i = 1,···, n, n) the number of evaluated objects).
Computing 
and 
.
Calculate the correlation coefficient rij of the comparison between the in unit, the j index, and the reference sequence.
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22 |
The ρ is the resolution coefficient, 0 ≤ ρ ≤ 1, general ρ = 0.5; the gray correlation judgment matrix is obtained.
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23 |
It is considered that (r1j, r2j,···,rnj) is the gray correlation degree of n schemes to the JTH index. In other words, the similarity degree of the JTH factor value in the n schemes is close to that of the JTH factor value in the reference sequence, so that it can be calculated by the following equation.
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24 |
The above formula reflects the proportion of the JTH index in the whole index.
Normalize the above equation
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25 |
Therefore, W = (w1, w2,···wm) can be used as the weight of the indicator.
3.2.4. Criteria Importance through Intercriteria Correlation
The CRITIC method is a kind of objective weighting method, which is based on the comparative strength of the evaluation indicators and the conflict between the indicators, and comprehensively measures the objective weights of the indicators. The variability of the indicators is taken into account along with the correlation between the indicators; the larger the number, the more critical it is, and the data are used exclusively for scientific evaluation using their objective attributes. Comparative intensity refers to the size of the difference in values between the various evaluation programs for the same indicator, expressed in the form of standard deviation; the more significant the standard deviation, the greater the fluctuation, and the more significant the difference in values between the programs, the higher the weighting will be. For CRITIC, when the standard deviation is specific, the smaller the conflict between the indicators and the smaller the weight; in addition, when the degree of positive correlation between the two indicators is programmed, the smaller the conflict, which shows that there is a program similarity between the information reflected by these two indicators in the evaluation of the program. The steps are as follows.
Step 1: I factors were normalized by the number of each option.
Positive indicators.
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26 |
Negative indicators.
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27 |
Step 2: indicator variability.
Expressed as a standard deviation, Sj denotes the standard deviation of the jth indicator.
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28 |
In the CRITIC method, the standard deviation is used to indicate the fluctuation of the difference in the value of each indicator, and the more significant the standard deviation, the larger the difference in the value of the indicator, and the more it can be put to reflect more information. The strength of the evaluation of the indicator itself is also more substantial, and more weight should be assigned to the indicator.
Step 3: conflicting indicators.
Expressed in the form of correlation coefficients, rij represents the correlation coefficient between evaluation indicators i and j.
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29 |
The correlation coefficient is used to indicate the correlation between indicators; the more substantial the correlation with other indicators, the less the indicator conflicts with other indicators, the more information it reflects, the more repetitive the content of the evaluation it can reflect, and to a certain extent, the degree of evaluation of the indicator is weakened. The weight assigned to the indicator should be reduced.
Step 4: volume of information
The larger the Cj is, the greater the role of the jth evaluation indicator in the overall evaluation embodiment, and the more weight should be assigned to it.
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30 |
Step 5: weighting of the influencing factors.
Calculate the weights of the different influencing factors.
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31 |
3.2.5. Entropy Weight Method
In information theory, the entropy is a measure of uncertainty. The more significant the amount of information, the smaller the uncertainty, the smaller the entropy, the greater the uncertainty, and the greater the entropy. According to entropy characteristics, the weight of the influencing factors can be determined by calculating the entropy value.
If the system is in a variety of different states and the probability of each state is ρi (i = 1, 2,···, m), then the entropy of the system is defined as
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32 |
Obviously, when pi = 1/m (i = 1, 2,···, m), that is, the probability of occurrence of various states, the maximum entropy is
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33 |
For m projects to be evaluated and n project indicators, the original evaluation matrix R = (rij)m×n is formed; for some index rj, there is entropy of information.
 |
34 |
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35 |
Form the original data matrix R = (rij)m×n.
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36 |
rij is the evaluation value of the ith item in the JTH indicator.
The process of calculating the weight of each index value is as follows.
-
(1)
Calculate the ratio of the index value of item I of the JTH index pij.
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37 |
-
(2)
Calculate the entropy of the JTH index ej.
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38 |
-
(3)
The comprehensive weight of index j can be obtained by combining the entropy weight of index wj.
 |
39 |
3.2.5.1. Determination of Primary Control Factors
The four models can determine the weight of the factors affecting recovery efficiency. AHP weights are mainly based on experts’ and scholars’ subjective understanding and experience. The gray correlation method considers the influence of various factors on the objective function; the entropy weight method is based on the relationship between the values of each factor to determine the weight.
The CRITIC weighting method is an objective assignment method, and the idea is to use two-phase indicators, namely, contrast strength and conflictive indicators. Comparative intensity is expressed using standard deviation; if the more significant standard deviation of the data indicates that the weight fluctuates more, the higher the weight will be conflict is expressed using the correlation coefficient; if the enormous value of the correlation coefficient between the indicators indicates that the smaller the conflict, then the lower the weight will be. The CRITIC method eliminates the influence of some indicators with strong correlations and reduces the overlap of information among indicators, which is more conducive to obtaining a credible evaluation.
In order to clarify the influence of different influencing factors on recovery, this paper adopts four methods to determine the weights of the different influencing factors. Based on the weight analysis, a new comprehensive evaluation method is proposed to clarify the main controlling factors of the recovery in tight reservoirs and lay the foundation for model prediction.
The results of the comprehensive evaluation method are shown in Tables 10 and 11, which indicate that the relative importance of porosity, permeability, oil saturation, well spacing, total liquid volume, horizontal section length, and cluster spacing is higher for recovery. The relative importance of total sand addition, sand addition intensity, number of clusters, amount of fluid added per cluster, amount of sand added per cluster, intensity of liquid addition, and thickness is relatively lower for the recovery. Therefore, this article selects six factors such as porosity, permeability, oil saturation, total fluid volume, horizontal section length, and cluster spacing. The results are shown in Tables 10 and 11.
 |
40 |
Table 10. Weighting Analysis.
| number | factors | EW | AHP | CRITIC | GRA | comprehensive weight |
|---|---|---|---|---|---|---|
| 1 | horizontal length | 0.069 | 0.061 | 0.065 | 0.03 | 0.0110 |
| 2 | total fluid volume | 0.006 | 0.15 | 0.091 | 0.112 | 0.0122 |
| 3 | sum amount of sand | 0.021 | 0.003 | 0.053 | 0.07 | 0.0003 |
| 4 | the intensity of sand | 0.056 | 0.001 | 0.074 | 0.08 | 0.0004 |
| 5 | number of clusters | 0.049 | 0.03 | 0.0212 | 0.07 | 0.0029 |
| 6 | cluster spacing | 0.012 | 0.056 | 0.107 | 0.084 | 0.0081 |
| 7 | liquid per cluster | 0.077 | 0.005 | 0.017 | 0.095 | 0.0008 |
| 8 | sand per cluster | 0.054 | 0.064 | 0.012 | 0.132 | 0.0073 |
| 9 | porosity | 0.115 | 0.162 | 0.12 | 0.081 | 0.2433 |
| 10 | permeability | 0.12 | 0.128 | 0.15 | 0.07 | 0.2167 |
Table 11. Weighting Analysis.
| number | factors | EW | AHP | CRITIC | GRA | comprehensive weight |
|---|---|---|---|---|---|---|
| 11 | oil saturation | 0.16 | 0.151 | 0.137 | 0.04 | 0.1779 |
| 12 | charging strength | 0.125 | 0.033 | 0.0035 | 0.04 | 0.0007 |
| 13 | reservoir thickness | 0.006 | 0.04 | 0.0093 | 0.04 | 0.0001 |
| 14 | well spacing | 0.13 | 0.116 | 0.14 | 0.056 | 0.1588 |
3.3. Modeling of Production Capacity
3.3.1. Recovery Modeling
According to the comprehensive weighting method, it can be seen that seven influencing factors, such as porosity, permeability, oil saturation, cluster spacing, total fluid volume, well spacing, and horizontal section length, have a high correlation with recovery. In contrast, other influencing factors are analyzed to have no apparent relationship with the recovery. Therefore, seven influencing factors, such as porosity, permeability, oil saturation, cluster spacing, total fluid volume, well distance, and horizontal section length, were selected for multiple linear regression fitting to derive a new model for predicting the production capacity of tight reservoirs. In order to determine the correctness of the capacity prediction model, the capacity prediction was conducted using actual data, and the fitting results are shown in Figure 5. The model was fitted with less than 5% using 61 sets of experimental data, indicating that the model can be used for a tight reservoir capacity prediction.
 |
41 |
Figure 5.
Recovery factor analysis and comparison.
3.3.2. Model Validation and Method Comparison
In order to verify the accuracy of the established capacity prediction model of tight reservoirs, this paper utilized the BP neural network model algorithm, support vector machine algorithm, and K nearest neighbor algorithm for recovery prediction and compared it with the recovery of the established capacity model (the results are shown in Tables 15 and 16). The results indicate that the average error in 61 sets of capacity prediction results of BP neural network model algorithm is 4%, the average error in capacity prediction of support vector machine algorithm is 4.5%, the average error in capacity prediction of K nearest neighbor algorithm is 3.8%, and the average error between the capacity prediction model established in this paper and the actual production capacity is 2.3%, which fully illustrates the accuracy of the model. It can be used for capacity prediction of tight oil reservoirs. The results show that the capacity prediction model established in this paper can effectively reduce the prediction error and improve the recovery accuracy. The main reason for this is that (1) the study in this paper adopts multiple methods for correlation coefficient analysis and comprehensively evaluates the relationship between each factor and the recovery rate. (2) Four weighting methods are used to determine the weights of the influencing factors, and the comprehensive weighting method is used to do further analysis, which reduces the modeling error. Therefore, the model can be applied to tight reservoir production capacity prediction. The basic parameters of the predicted data are shown in Tables 12–14.
Table 15. Comparison of Recovery Rates by Different Methods.
| no | actual recovery (%) | BP | SVM | KNN | prediction (%) |
|---|---|---|---|---|---|
| 1 | 13.15274 | 15.17689 | 8.6503 | 14.4176 | 9.2577 |
| 2 | 20.34116 | 14.08744 | 7.0487 | 15.1446 | 14.0992 |
| 3 | 19.6097 | 15.53438 | 5.1447 | 13.8531 | 14.4516 |
| 4 | 24.93584 | 16.51668 | 10.799 | 15.8445 | 11.2314 |
| 5 | 20.22535 | 18.94315 | 7.6222 | 17.96 | 14.4516 |
| 6 | 11.23145 | 13.12484 | 4.6439 | 14.74 | 11.2314 |
| 7 | 10.51063 | 10.86121 | 21.724 | 8.6 | 10.3447 |
| 8 | 11.46009 | 14.89977 | 5.7481 | 15.15 | 11.2314 |
| 9 | 10.41717 | 13.88708 | 12.885 | 16.56 | 10.4172 |
| 10 | 15.65195 | 11.72949 | 13.546 | 9.52 | 10.5106 |
| 11 | 15.04114 | 15.58366 | 12.882 | 15.47 | 14.8905 |
| 12 | 17.65599 | 14.80337 | 14.383 | 16.37 | 13.4148 |
| 13 | 19.66495 | 17.74201 | 9.912 | 16.58 | 12.318 |
| 14 | 12.36441 | 14.76217 | 11.625 | 16.34 | 12.3644 |
| 15 | 11.51572 | 12.71824 | 19.185 | 13.04 | 11.5157 |
| 16 | 16.73024 | 14.78791 | 15.173 | 13.76 | 9.6751 |
| 17 | 14.89054 | 19.40383 | 20.892 | 14.4 | 14.8905 |
| 18 | 12.00111 | 11.96234 | 18.257 | 13.44 | 11.5157 |
| 19 | 8.450471 | 12.54036 | 4.6168 | 12.76 | 8.4505 |
| 20 | 9.25771 | 14.26149 | 5.1261 | 15.2 | 9.2577 |
| 21 | 8.764613 | 11.37634 | 6.7594 | 12.03 | 8.7646 |
| 22 | 14.00175 | 11.88945 | 6.7649 | 13.67 | 8.4505 |
| 23 | 14.09916 | 13.24734 | 8.9375 | 13.21 | 12.3644 |
| 24 | 13.41485 | 12.3194 | 16.121 | 14.46 | 13.4148 |
| 25 | 14.45165 | 19.59576 | 7.8255 | 18.57 | 14.4516 |
Table 16. Comparison of Recovery Rates by Different Methods.
| no | actual recovery (%) | BP | SVM | KNN | prediction (%) |
|---|---|---|---|---|---|
| 26 | 24.12556 | 17.33868 | 11.668 | 16.37 | 17.1159 |
| 27 | 12.11246 | 16.32205 | 11.086 | 15.17 | 9.2577 |
| 28 | 11.06613 | 11.61875 | 10.231 | 14.43 | 9.6751 |
| 29 | 18.25758 | 15.6519 | 5.4267 | 16.41 | 14.4516 |
| 30 | 9.714831 | 16.86478 | 15.864 | 13.62 | 9.6751 |
| 31 | 16.27227 | 15.68809 | 21.076 | 16.42 | 12.2909 |
| 32 | 14.74324 | 16.89696 | 27.068 | 14.49 | 10.0251 |
| 33 | 12.62966 | 14.31432 | 23.559 | 12.85 | 12.6297 |
| 34 | 10.02507 | 13.30587 | 20.868 | 11.74 | 10.0251 |
| 35 | 14.35193 | 12.28226 | 17.034 | 16.17 | 10.0251 |
| 36 | 14.28657 | 12.20784 | 16.878 | 16.08 | 13.4148 |
| 37 | 15.14657 | 9.525231 | 26.909 | 12.34 | 7.3905 |
| 38 | 12.26478 | 11.04962 | 15.566 | 13.28 | 11.4014 |
| 39 | 10.91266 | 11.36525 | 23.225 | 14.1 | 10.9127 |
| 40 | 12.38952 | 10.04302 | 13.062 | 13.17 | 10.3447 |
| 41 | 11.66493 | 8.656634 | 12.515 | 10.97 | 11.6649 |
| 42 | 15.03237 | 12.44685 | 21.423 | 14.05 | 11.6649 |
| 43 | 14.41164 | 16.19768 | 19.607 | 13.97 | 13.4148 |
| 44 | 10.21024 | 11.65758 | 19.85 | 13.27 | 7.3905 |
| 45 | 15.01676 | 13.78475 | 9.505 | 15.22 | 14.8905 |
| 46 | 12.67652 | 9.340231 | 16.431 | 10.92 | 10.9127 |
| 47 | 12.30483 | 13.23006 | 15.985 | 13.45 | 10.3447 |
| 48 | 13.70483 | 8.915915 | 21.702 | 14.48 | 7.3905 |
| 49 | 14.26222 | 11.71356 | 19.236 | 15.33 | 11.6649 |
| 50 | 10.36304 | 10.51657 | 16.359 | 12.31 | 10.363 |
| 51 | 17.11594 | 12.22991 | 6.0893 | 14.6 | 12.1125 |
| 52 | 12.29093 | 9.936084 | 20.758 | 14.18 | 12.2909 |
| 53 | 11.19343 | 10.62529 | 13.69 | 15.65 | 8.7646 |
| 54 | 12.31801 | 8.691246 | 9.9428 | 15.03 | 12.318 |
| 55 | 13.15792 | 10.93439 | 13.333 | 14.82 | 12.3895 |
| 56 | 13.93521 | 13.04077 | 11.987 | 14.32 | 11.5157 |
| 57 | 12.7964 | 7.401625 | 19.918 | 12.88 | 12.2909 |
| 58 | 7.39052 | 9.033691 | 21.952 | 9.42 | 7.3905 |
| 59 | 11.40136 | 9.264675 | 14.487 | 10.99 | 10.363 |
| 60 | 12.5322 | 9.8826 | 15.221 | 10.72 | 12.3421 |
| 61 | 11.0371 | 8.1720 | 14.312 | 9.71 | 11.0911 |
Table 12. Parameters Underlying the Recovery Prediction.
| no | length (m) | total fluid volume | cluster spacing | porosity (%) | permeability (mD) | saturation (%) | well spacing |
|---|---|---|---|---|---|---|---|
| 1 | 994.0 | 18565.0 | 30.12 | 11.56 | 3.06 | 55.56 | 400 |
| 2 | 1149.0 | 19840.8 | 28.02 | 10.877 | 2.245 | 58.4 | 250 |
| 3 | 904.0 | 12954.5 | 21.02 | 11.02 | 1.37 | 54.37 | 400 |
| 4 | 1212.0 | 18083.7 | 31.08 | 10.77 | 1.77 | 59.01 | 400 |
| 5 | 1107 | 16557.4 | 27.00 | 13.38 | 5.19 | 56.42 | 250 |
| 6 | 1000 | 18296.7 | 21.28 | 10.381 | 1.954 | 55.653 | 300 |
| 7 | 2000.5 | 26877.0 | 64.53 | 9.167 | 1.143 | 55.08 | 300 |
| 8 | 986 | 18140.6 | 20.12 | 9.92 | 2.071 | 57.48 | 400 |
| 9 | 1400 | 23191.3 | 35.00 | 9.472 | 2.154 | 57.458 | 400 |
Table 14. Parameters Underlying the Recovery Prediction.
| no | length (m) | total fluid volume | cluster spacing | porosity (%) | permeability (mD) | saturation (%) | well spacing |
|---|---|---|---|---|---|---|---|
| 50 | 2011 | 36312.4 | 36.56364 | 8.84 | 1.44 | 58 | 300 |
| 51 | 1605 | 30433.6 | 31.47059 | 12.28 | 1.9 | 57.55 | 300 |
| 52 | 1678 | 29598.3 | 25.81538 | 10.13 | 1.799 | 54.74 | 300 |
| 53 | 1186 | 19,196 | 20.44828 | 9.435 | 1.252 | 54.632 | 300 |
| 54 | 1760 | 29919.4 | 42.92683 | 11.29 | 1.35 | 54.44 | 300 |
| 55 | 1421 | 22876.7 | 34.65854 | 9.815 | 1.543 | 50.22 | 400 |
| 56 | 1202 | 21158.1 | 30.05 | 9.581 | 1.113 | 47.504 | 400 |
| 57 | 1053.4 | 25812.3 | 28.47027 | 13.21 | 1.65 | 56 | 350 |
| 58 | 1495 | 25109.44 | 21.66667 | 10.147 | 2.83 | 54.86 | 300 |
| 59 | 1799 | 29896.5 | 32.125 | 10.6 | 0 | 50.6 | 300 |
| 60 | 2000 | 36736.8 | 33.89831 | 10.167 | 2.139 | 56.66 | 250 |
| 61 | 1802 | 29181.1 | 22.525 | 9.243 | 1 | 54.457 | 200 |
Table 13. Parameters Underlying the Recovery Prediction.
| no | length (m) | total fluid volume | cluster spacing | porosity (%) | permeability (mD) | saturation (%) | well spacing |
|---|---|---|---|---|---|---|---|
| 10 | 1209.0 | 27713.4 | 31.00 | 12.13 | 3.59 | 54.93 | 350 |
| 11 | 1194.0 | 21800.4 | 32.27 | 10.05 | 1.74 | 60.21 | 500 |
| 12 | 1202.0 | 24523.8 | 34.34 | 10.4 | 1.91 | 61.02 | 500 |
| 13 | 1148.0 | 20766.6 | 32.80 | 12.45 | 4.6 | 60.07 | 300 |
| 14 | 1202.0 | 20242.8 | 40.07 | 10.42 | 1.67 | 59.43 | 400 |
| 15 | 1472.0 | 25035.0 | 54.52 | 11.53 | 1.51 | 57.49 | 400 |
| 16 | 1201.0 | 23425.1 | 30.79 | 11.44 | 1.93 | 58 | 500 |
| 17 | 1403.0 | 21571.3 | 42.52 | 14.13 | 4.07 | 56.94 | 500 |
| 18 | 1701.0 | 25196.0 | 54.87 | 10.524 | 2.024 | 55.074 | 300 |
| 19 | 1047.0 | 17330.0 | 29.91 | 10.23 | 1.5 | 55.97 | 250 |
| 20 | 1035.6 | 18606.7 | 24.08 | 11.43 | 3.46 | 54.98 | 250 |
| 21 | 1168.0 | 22443.2 | 25.96 | 9.15 | 1.587 | 57.04 | 300 |
| 22 | 1159.0 | 17400.8 | 37.39 | 9.368 | 0.846 | 55.185 | 300 |
| 23 | 1200 | 20234.9 | 40.00 | 11.15 | 2.71 | 56.28 | 250 |
| 24 | 1535 | 24685.4 | 34.11 | 10.05 | 1.24 | 55.06 | 400 |
| 25 | 987 | 16395.6 | 23.50 | 12.22 | 4.19 | 59.07 | 400 |
| 26 | 1100 | 19674.2 | 28.95 | 11.371 | 3.81 | 56.3 | 500 |
| 27 | 1041 | 18884.1 | 25.39 | 11.16 | 1.81 | 58.31 | 500 |
| 28 | 1184 | 23828.8 | 42.29 | 10.38 | 2.17 | 58.28 | 300 |
| 29 | 1130 | 16499.6 | 36.45 | 11.371 | 3.81 | 56.3 | 200 |
| 30 | 1534 | 26291.2 | 52.90 | 11.84 | 2.12 | 58.28 | 200 |
| 31 | 1206 | 23575.3 | 57.43 | 9.859 | 1.955 | 53.962 | 300 |
| 32 | 1670 | 23390.1 | 40.73171 | 10.1 | 1.65 | 64.31 | 300 |
| 33 | 2022 | 29849.1 | 36.10714 | 10.4 | 3.67 | 58.7 | 300 |
| 34 | 2003 | 25611.8 | 46.5814 | 12.81 | 1.41 | 58.07 | 400 |
| 35 | 1803.47 | 24286.2 | 56.35844 | 11.79 | 1.44 | 55.65 | 400 |
| 36 | 1803.51 | 25688.4 | 46.24385 | 10.54 | 2.36 | 53.04 | 400 |
| 37 | 1574 | 25785.8 | 38.39024 | 10.08 | 1.85 | 54.81 | 400 |
| 38 | 1604 | 24578.2 | 38.19048 | 9.86 | 1.48 | 53.85 | 400 |
| 39 | 1965 | 38004.5 | 33.30508 | 12.91 | 1.88 | 56 | 300 |
| 40 | 1572 | 28072.7 | 25.77049 | 10.818 | 1.84 | 54.761 | 300 |
| 41 | 2000 | 33539.31 | 28.57143 | 11.25 | 1.955 | 55.54 | 300 |
| 42 | 1532 | 25964.7 | 25.53333 | 9.675 | 1.26 | 53.104 | 300 |
| 43 | 1376 | 30456.6 | 20.53731 | 10.136 | 1.726 | 55.285 | 300 |
| 44 | 1652 | 30260.1 | 33.71429 | 13.31 | 1.88 | 57.51 | 300 |
| 45 | 1604 | 24688.6 | 35.64444 | 13.75 | 2.7 | 58 | 300 |
| 46 | 1608 | 36540.2 | 22.0274 | 11.98 | 2.07 | 63.5 | 300 |
| 47 | 1356.8 | 21540.9 | 26.09231 | 9.793 | 2.07 | 56.99 | 300 |
| 48 | 1704 | 33065.12 | 22.72 | 9.6 | 2.33 | 54.8 | 300 |
| 49 | 1669.9 | 26610.9 | 24.92388 | 10.729 | 2.2 | 55.813 | 300 |
4. Conclusions
First, the correlation coefficients between different influencing factors and recovery were quantitatively analyzed using gray correlation, Pearson, Spearman, Kendall, VS, univariate selection, and tree model. Second, based on the correlation coefficient analysis, the entropy weight method, CRITIC coefficient, and hierarchical analysis method were employed to determine the main controlling influencing factors of production capacity in tight reservoirs. Finally, the recovery prediction model was established using the comprehensive evaluation method. The following main conclusion can be obtained.
-
(1)
The correlation coefficient between porosity, permeability, oil saturation, cluster spacing, well spacing, total fluid volume, horizontal section length, and recovery is the largest and most significant influence on recovery. Thickness with sand strength has the lowest influence on recovery.
-
(2)
Porosity, permeability, oil saturation, cluster spacing, well distance, total fluid volume, and horizontal length contribute significantly to the recovery in the weighting analysis, and other factors have relatively small contributions.
-
(3)
The recovery obtained by the multiple linear regression model has a minor error with the actual recovery compared with the actual BP neural network, K nearest neighbor regression, and support vector machine, which indicates that this method can be used for the production capacity prediction of tight reservoirs.
In this paper, a new model for tight reservoir capacity prediction is proposed using the machine learning method, which considers the correlation coefficients and comprehensive weighs of the influencing factors, reduces the modeling error, and improves the accuracy of recovery prediction compared with the prediction model that have been proposed. However, the model fails to do further single-factor analysis due to the data set, so in the future, it is recommended to do single-factor analysis using machine learning methods to clarify the influence of each factor on the recovery, so as to achieve the capacity prediction and influence factor analysis by machine learning methods.
Acknowledgments
This study was supported by the Natural Fund for Promoting the Dynamic Mixing Mechanism of CO2 Drive in Low-Permeability Reservoirs Based on Ultrasonic Action (E040302).
Glossary
Abbreviations
- GRA
Gray relational analysis
- SCC
Spearman’s rank correlation coefficient
- FCB
feature selection based on tree models
- VS
variance selection
- UF
univariate feature selection test
- AHP
analytic hierarchy process
- CRITIC
criteria importance through intercriteria correlation
- EW
entropy weight
- b
horizontal length
- c
total of liquid volume
- a
cluster spacing
- e
well space
The authors declare no competing financial interest.
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