Machine Learning-Assisted Prediction of Oil Production and CO₂ Storage Effect in CO₂-Water-Alternating-Gas Injection (CO₂-WAG)

Abstract

In recent years, CO₂ flooding has emerged as an efficient method for improving oil recovery. It also has the advantage of storing CO₂ underground. As one of the promising types of CO₂ enhanced oil recovery (CO₂-EOR), CO₂ water-alternating-gas injection (CO₂-WAG) can suppress CO₂ fingering and early breakthrough problems that occur during oil recovery by CO₂ flooding. However, the evaluation of CO₂-WAG is strongly dependent on the injection parameters, which in turn renders numerical simulations computationally expensive. So, in this work, machine learning is used to help predict how well CO₂-WAG will work when different injection parameters are used. A total of 216 models were built by using CMG numerical simulation software to represent CO₂-WAG development scenarios of various injection parameters where 70% of them were used as training sets and 30% as testing sets. A random forest regression algorithm was used to predict CO₂-WAG performance in terms of oil production, CO₂ storage amount, and CO₂ storage efficiency. The CO₂-WAG period, CO₂ injection rate, and water–gas ratio were chosen as the three main characteristics of injection parameters. The prediction results showed that the predicted value of the test set was very close to the true value. The average absolute prediction deviations of cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency were 1.10%, 3.04%, and 2.24%, respectively. Furthermore, it only takes about 10 s to predict the results of all 216 scenarios by using machine learning methods, while the CMG simulation method spends about 108 min. It demonstrated that the proposed machine-learning method can rapidly predict CO₂-WAG performance with high accuracy and high computational efficiency under conditions of various injection parameters. This work gives more insights into the optimization of the injection parameters for CO₂-EOR.

1. Introduction

With the continuous improvement of oil and gas exploration and development, the proportion of heterogeneous and low-permeability reservoirs in exploration and development is gradually increasing. Using conventional water injection to develop low-permeability reservoirs results in a low recovery factor [1]. Compared to water, CO₂ is less viscous and can enter into small pores more easily, which can reduce the viscosity of crude oil, expand the volume of crude oil, improve the mobility ratio, and thus increase the oil recovery factor [2,3]. Therefore, CO₂-enhanced oil recovery (CO₂-EOR) has great potential for developing low-permeability reservoirs. In addition to this, CO₂-EOR can sequestrate CO₂ underground, which can help in achieving carbon neutrality [4]. However, in the CO₂ flooding method, during gas injection, the low viscosity of CO₂ may lead to a phenomenon referred to as viscous fingering. This results in an unfavorable mobility ratio, which seriously affects the improvement of swept volume [5]. Moreover, due to its low density, CO₂ can easily escape to the upper part of the reservoir, forming a fugitive flow channel [6]. This also constitutes a drawback for CO₂ flooding as it leads to a reduction of the swept volume.

In response to the problems of waterflooding and CO₂ flooding, researchers proposed CO₂-WAG methods [7]. This technology was first used by Mobil in 1957 in a sandstone reservoir in Alberta, Canada. It combines the characteristics of water flooding and CO₂ flooding, which increases the macroscopic sweep efficiency and thus improves the overall oil displacement efficiency. In addition, CO₂-WAG can mitigate the issue of rapid CO₂ flow and increase the gas phase’s flow resistance. It can also lower the resistance to the flow of the water phase and increase the mobility ratio. As a result of this, recovery efficiency can be greatly improved [7]. It has been reported that 80% of oilfield projects in the US using WAG technology have achieved good results [8]. Skauge et al. [9] studied 59 WAG fields and found that the average recovery of crude oil was improved by 10% for all WAG cases.

Recently, WAG has also been used in the Brazilian subsalt oilfield complex [10]. Subsalt oil and gas production was 2739 million barrels of oil equivalent per day (2.739 Mboe/day) by 2020, representing 70.3% of Brazil’s total oil equivalent. The Lula field, which conducted the WAG pilot test in April 2011, has a cumulative oil production of 2000 Mboe by 2020 and is the largest extracted/producing field in Brazil, with an average oil and gas production of 988,000 barrels/day and 43.2 Mm³/day, respectively [11].

Currently, the optimization of WAG extraction schemes is the focus of many oil fields and related researchers [12,13,14,15,16,17,18,19,20]. Rodrigues et al. [21] used CMG reservoir numerical simulation software to optimize the application of WAG in a sub-salt offshore field in Brazil and proposed a design method for CO₂-WAG operations in carbonate reservoirs, focusing on the economics, the CO₂ cycle efficiency, and project risk. It is worth mentioning that the application of intelligent algorithms such as machine learning, which has developed rapidly in recent years, has been used in petroleum exploration and development [22,23], especially in optimization problems. For instance, Bilgesu et al. [24] proposed a method for bit optimization with the help of neural networks. Leite Cristofaro and Longhin et al. [25] optimized the mud loss problem in Brazilian deepwater subsalt fields with the help of KNN, MLP, and NB algorithms. Wang et al. [26] proposed a joint optimization method for well location and injection and extraction parameters using the random forest as well as a radial basis neural network. In general, memory-based learning algorithms perform better than any other family of algorithms. These methods assume that a given set of terms and class labels can be used as a mapping to identify unlabeled term classes [25].

Random forest is a decision tree-based machine learning algorithm proposed by Breiman and Cutler in 2001 [27]. The random forest regression model is built by combining the results obtained from several well-established decision tree models, and the final prediction result is obtained by averaging the prediction results of all decision tree models [28]. A large number of studies [29,30,31,32] have shown that random forest models have the advantages of strong generalization ability, insensitivity to input data deviations, and the ability to analyze the importance of input features. In this study, by combining the random regression forest algorithm with the numerical simulations, a method for rapidly forecasting the cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency of CO₂-WAG development schemes has been developed. This method can significantly increase the effectiveness of scheme optimization in oilfields.

2. Methods

2.1. CMG Base Model

The simulations are carried out by using a simulator known as the Computer Modeling Group Ltd. (CMG). The submodule GEM of the CMG simulator is a compositional simulator and it is widely employed for simulating the displacement behavior of CO₂-EOR in reservoir formations. Thus, this work employed the submodule GEM of CMG to conduct the simulation of CO₂-WAG.

2.1.1. Parameter Settings of the Base Model

A five-spot well pattern is established using CMG software, as shown in Figure 1. The model has a well in the middle where water and CO₂ can be injected alternatively. There are 23 grids both in the X and Y directions, with a grid size of 30 × 30 × 3 m in the X, Y, and Z directions, respectively. The model is divided into 8 layers in the Z direction, and thus the total number of grids is 23 × 23 × 8 = 4232.

The key reservoir parameters used in this work are selected based on the geological information of the Tuo 28 block in Shengli Oilfield [33,34], as shown in

Table 1. Key parameters of the model.

Serial No.	Input Parameters	Unit	Value
1	Average permeability in the X and Y directions	×10−3 μm3	50
2	Average permeability in the Z direction	×10−3 μm3	5
3	Oil layer thickness	m	27
4	Top depth	m	1800
5	Porosity	1	0.24
6	Initial oil saturation	1	0.7934
7	Crude oil viscosity	cp	15.4495
8	Crude oil density	kg/m3	760.9
9	Reservoir temperature	°C	85
10	Initial reservoir pressure	MPa	18

. The oil reservoir depth is 1800 m, and the reservoir pressure is 18 MPa due to the normal formation pressure coefficient of 1.0. The reservoir temperature is 85 °C. The porosity is 0.24, the initial oil saturation is 0.7934, the crude oil viscosity is 15.4495 cp, and the crude oil density is 760.9 kg/m³.

The permeability in the horizontal directions, for each layer from top to bottom, is 10 × 10⁻³ μm³, 20 × 10⁻³ μm³, 30 × 10⁻³ μm³, 40 × 10⁻³ μm³, 60 × 10⁻³ μm³, 70 × 10⁻³ μm³ and 90 × 10⁻³ μm³, as shown in

Table 2. Permeability in horizontal and vertical directions.

Layer	Permeability (×10−3 μm3)
	Horizontal Direction	Vertical Direction
1	10	1
2	20	2
3	30	3
4	40	4
5	60	6
6	70	7
7	80	8
8	90	9

, and the average permeability in horizontal directions is 50 × 10⁻³ μm³. The permeability in the vertical direction is 0.1 times the horizontal permeability (K_v/K_h = 0.1) and the average permeability in the vertical direction is 5 × 10⁻³ μm³, which is a typical non-homogeneous low permeability reservoir with a positive rhythm. The thickness of the whole reservoir is 27 m, with each layer measuring 3 m.

2.1.2. Injection and Production Settings

The model simulates a total of forty years, with depletion development occurring during the first eight years and CO₂-WAG production commencing in the ninth. Thus, the actual CO₂-WAG development length is 32 years. In this case, to compare the production effects of each CO₂-WAG scenario, it is necessary to carry out a period of depletion development first to exclude the natural energy disturbance. As shown in Figure 2, the pressure difference between the injection and production wells is less than 0.5 MPa after the first 8 years of depletion development. In addition, the production efficiency is low and no longer productive. Therefore, it is necessary to add energy, such as through CO₂-WAG development. In the base model, CO₂ injection starts in January of the ninth year and water injection starts in July, so the cycle is set to 12 months, including 6 months of gas injection and 6 months of water injection. The water–gas ratio is set to 1:1, which implies that the CO₂ injection rate is equal to the water injection rate under reservoir conditions. The water injection rate is set at 90 m³/day and the CO₂ injection rate is set at 20,000 m³/day. The bottom hole pressure of the four production wells is set to 7 MPa. As shown in Figure 3, the water cut in the produced fluid is more than 80% by the fortieth year of production. Thus, this work assumes that production is stopped after 40 years of production.

2.2. Machine Learning for CO₂-WAG Prediction

2.2.1. Principle of the Random Forest Regression Algorithm

Multiple regression decision trees constitute the random forest regression algorithm. Based on the idea of integrated learning, the mean value of each regression decision tree is taken as the prediction result [35].

$$\overline{f}(x)=\frac{1}{T}{\displaystyle \sum _{t=1}^T\left\{f\left(x,{\theta }_t\right)\right\}}$$

(1)

where: $\overline{f}(x)$ is the model prediction result, $f\left(x,{\theta }_t\right)$ is the output based on $x$ and ${\theta }_t$, $x$ is the independent variable, ${\theta }_t$ is the independent identically distributed random vector, and $T$ is the number of regression decision trees.

As a machine learning algorithm based on statistical theory, the random forest regression algorithm introduces the bagging method and the random subspace method [36] to avoid the problem of single decision tree models, which tend to be overfitted and not accurate.

(1) The bagging method [37], also known as bootstrap aggregating, is a bootstrap-based statistical method. Based on repeatable random sampling, multiple predictors are formed by the bootstrap repetitive sampling method. Assuming that there are N samples in the original sample, N samples are repeatedly sampled to form new training samples. When N approaches infinity, the probability of not being sampled again for each sample is 36.8%. Nearly 36.8% of the original samples will not appear in the training samples of the same tree, and the samples that are not drawn are called out-of-bag data (OOB) [27]. The generation of locally optimal solutions for regression decision trees can be avoided by the bagging method.

(2) Stochastic subspace method. Random features need to be selected when constructing the regression decision tree. Selecting random features means picking x feature attributes at random from the whole set of attributes. Node splitting selects the optimal features based on the principle of minimum mean squared deviation so that each tree is not pruned to achieve maximum growth. A random sampling of training samples and a random selection of feature attributes can make sure that the regression decision trees have as much variety as possible [38].

2.2.2. Randomized Regression Forest Algorithm Flow

The main flow of the randomized regression forest algorithm is presented in Figure 4 and described as follows:

(1) Sampling: K sets of datasets are sampled from the training dataset S by using the bagging method. Each set of datasets is divided into 2 types: sampled data and un-sampled data (out-of-bag data), and they are trained to produce a decision tree.

(2) Growing: Each decision tree is trained by training data. In each branching node, M features are randomly selected from M feature attributes, and the best features are chosen based on the Gini index for full branching growth until no more growth is possible without pruning.

(3) Forming a forest: Repeat steps 1 and 2 to build multiple regression decision trees and maximize the growth of each tree to form a forest.

(4) Predicting: Using the chosen model, predictions are made about the new data set, and the final output is the average of all the predictions made by the decision trees.

This work first builds a series of numerical simulation models by adjusting the injection parameters and runs them to obtain simulation results for forming a test database. The train_test_split function from sklearn.model_selection is called to randomly divide the test database into two parts, one as a training set to train the regression prediction model and the other as a test set to compare with the results predicted by machine learning to verify the accuracy of the method. To make the results clearer and more intuitive, this work trains and predicts each of the three label variables separately with the random forest regression algorithm.

The CO₂-WAG period, fluid injection rate, and water–gas ratio are important parameters for CO₂-WAG optimization. Therefore, this work uses CO₂-WAG period, CO₂ injection rate and water–gas ratio as three features and cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency as labels for regression prediction to realize fast prediction of program effects with the help of a random forest regression algorithm in machine learning.

3. Results and Discussion

3.1. Base Case Analysis

The cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency of the base model as a function of time are shown in Figure 5 and Figure 6. The values of cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency are derived as the three labels for machine learning. The CO₂ storage amount is obtained by subtracting the cumulative CO₂ production from the cumulative CO₂ injection. The CO₂ storage efficiency is expressed as the ratio of the CO₂ storage amount to the CO₂ injection.

As shown in Figure 5, at first, the oil production rate goes up quickly because there is enough energy in the reservoir. As the reservoir energy gradually depletes, the oil production curve begins to level off gradually in the fifth year. Then, the reservoir energy is replenished by the nineth year after the CO₂-WAG started, and the oil production rate begins to increase rapidly. The oil production rate begins to decrease slowly from the twentieth year to the end of production.

At the beginning of the CO₂ injection, the CO₂ storage amount is almost equal to the CO₂ injection amount from the nineth year to the fifteenth year with little CO₂ produced (Figure 6a). CO₂ production begins in the fifteenth year and has a relatively stable rate. From the sixteenth year, the growth rate of CO₂ storage starts to be lower than that of CO₂ injection. With the increase in CO₂ production, the CO₂ storage amount nearly stopped increasing by the thirty-sixth year. Consequently, the CO₂ storage efficiency is almost equal to 1 at the beginning and then gradually decreases, as shown in Figure 6b.

As shown in Figure 7, the overall effects of oil production on both CO₂ flooding and CO₂-WAG are higher than those of water flooding. CO₂ flooding has higher oil production in the early stages of development before the thirty-sixth year because CO₂ is more mobile than water. CO₂ flooding produces oil at a higher rate than both water flooding and CO₂-WAG at this stage. Due to the heterogeneity of the reservoir, the CO₂ injected into the formation tends to form a dominant channel. So, the CO₂ flooding method starts to produce more oil in a slow way around the twenty-second year of its late stage of development. The CO₂-WAG method effectively combines the advantages of water flooding and CO₂ flooding and maintains a high oil production rate, especially after the thirty-sixth year, although the oil production rate is relatively lower than that of CO2 flooding before the thirty-sixth year. The overall oil production of CO₂-WAG is better than that of water flooding and CO₂ flooding.

For further analysis of the difference between the CO₂-WAG method and the CO₂ flooding method, this work compares the gas–oil ratio of the produced flow. As shown in Figure 8, the gas production rate starts to increase from the twelfth year (4 years after CO₂ injection) in the CO₂ flooding method and rises sharply from the nineteenth year onwards. This can be explained by the fact that the injected CO₂ forms a dominant channel, and thus the injected CO₂ returns to the surface directly from the dominant channel as an output gas.

In the CO₂-WAG method, the gas production rate is basically unchanged in the early stage of production and increases at a low rate in the late stage of production. Thus, the gas production volume is much smaller than that of CO₂ flooding. It can be speculated that the injected water in the CO₂-WAG method effectively hinders the breakthrough of CO₂ and the formation of a CO₂-dominant channel. Therefore, CO₂-WAG can effectively slow down the rate of CO₂ gas extraction compared to CO₂ flooding.

Currently, the treatment and separation of output gas to recover methane and reinjected carbon dioxide are priorities for many oilfields. Gas treatment stations in oilfields have a certain upper limit of gas that can be processed per day. In the CO₂ flooding method, the gas output rate may be too high, especially in the final stages of development. It may lead to a risk that a large amount of methane gas and carbon dioxide cannot be captured and recovered in time, causing a great loss of economic benefits and more emissions of greenhouse gases. In contrast, according to the preceding analysis, the CO₂-WAG method can solve the aforementioned issues by efficiently extracting crude oil and reducing the gas production rate, thereby allowing the gas treatment station sufficient time to capture and recover methane gas and reinject carbon dioxide.

3.2. Analysis of Influence Factors on CO₂-WAG

To analyze the principal influence factors of CO₂-WAG, this work designs a series of scenarios of the CO₂-WAG development method by modifying the CO₂-WAG period, fluid injection rate, and water–gas ratio based on the above base model. Among them, six schemes of the period adjustment are set as 4 months, 6 months, 12 months, 24 months, 48 months, and 96 months, respectively. Six schemes of the fluid injection rate adjustment are set as: (1) water injection rate of 65 m³/day and CO₂ injection rate of 12,000 m³/day; (2) water injection rate of 79 m³/day and CO₂ injection rate of 16,000 m³/day; (3) water injection rate of 90 m³/day and CO₂ injection rate of 20,000 m³/day; (4) water injection rate of 100 m³/day and CO₂ injection rate of 23,000 m³/day; (5) water injection rate of 110 m³/day and CO₂ injection rate of 27,000 m³/day; (6) water injection rate 120 m³/day and CO₂ injection rate of 31,000 m³/day. 6 schemes of the water–gas ratio adjustment are set as 0.33, 0.5, 1, 1.5, 2, and 3, respectively. Therefore, this work constructs a total of 6 × 6 × 6 = 216 scenarios. As the water injection rate varies simultaneously with the CO₂ injection rate, this work selects the CO₂ injection rate as one feature, and the period and water–gas ratio as the other two features.

The cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency of the 216 scenarios are simulated by CMG, and the results are detailed in Supporting Information. To elucidate more clearly the influence of CO₂-WAG parameters on production, the cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency of different cycle schemes (#85, #97, #103), different fluid injection rate schemes (#49, #121, #193), and different water–gas ratio schemes (#85, #87, #89) are compared by the single variable method, and the results are shown in Figure 9, Figure 10 and Figure 11.

As shown in Figure 9, the influence of the cycle on oil production is relatively small. When the CO₂-WAG cycle is relatively shorter, the cumulative oil production is higher. When the cycle is 8 years, the cumulative oil production starts to decline significantly, because in this case, the frequency of alternating water and carbon dioxide is low, similar to a small period of water flooding and gas flooding. The influence of the cycle on CO₂ storage is relatively large, both in terms of CO₂ storage amount and CO₂ storage efficiency. Throughout the production process, CO₂ storage amount and CO₂ storage efficiency fluctuate due to the alternate injection of water and CO₂. At the end of the process, the CO₂ storage amount and CO₂ storage efficiency decrease with the cycle.

As shown in Figure 10, the injection rate has a greater impact on oil production. As the injection rate increases, cumulative oil production also increases, but the CO₂ storage efficiency decreases. This is because more CO₂ will return to the surface from production wells as output gas when the CO₂ injection rate increases. Therefore, when optimizing the CO₂-WAG extraction scheme in the oilfield, the injection rate cannot be increased arbitrarily. The processing capacity of gas treatment stations in the oilfield needs to be considered. When CO₂ output is too fast, some CO₂ will not be recovered and treated in time. CO₂ will escape into the atmosphere, which may cause environmental issues and aggravate the greenhouse effect. It also causes waste of CO₂ gas resources and economic loss to the oilfield. At the same time, an over-high injection rate will instantly increase the bottom hole pressure of the injection well. When it exceeds the fracture pressure of the formation, it will crush the formation, causing damage to the formation on the one hand. On the other hand, it may cause CO₂ to escape and pollute other formations.

The model in this study has a low reservoir pressure due to a period of depleted extraction in the early stage. In addition, the fluid injection rate is low, which means it cannot restore the reservoir pressure to the initial pressure. The simulated reservoir is a low-pressure reservoir. For this type of reservoir, as shown in Figure 11, the higher the water–gas ratio is, the better the oil production will be. In addition, when the injection rate and the reservoir pressure are high, a lower water–gas ratio has a higher oil recovery. A higher water–gas ratio results in less CO₂ being buried because the proportion of injected CO₂ is smaller, but the storage efficiency is higher. A lower water–gas ratio allows more CO₂ to be buried because the proportion of CO₂ in the injected fluid is larger. Moreover, more CO₂ will be produced from the production well, leading to lower storage efficiency.

3.3. Analysis of Machine Learning Results

To compare the CMG numerical simulation results with the machine learning regression prediction results, this work builds a database of 216 CMG numerical simulation models, of which 70% are used as the training set and 30% as the test set. The numerical simulation results of the test set are employed as the true values for verifying the accuracy of the machine learning prediction. The result plots for the three labels of cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency are shown in Figure 12. The predicted curve made by the random forest regression algorithm is very close to the true value curve in terms of cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency.

The relative deviation of cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency for each scheme are calculated and shown in Figure 13 for further discussion. The relative deviation of cumulative oil production between prediction and true values ranges from −4.76% to 2.51%, the maximum relative deviation is −4.76%, and the average absolute relative deviation is 1.10%. The maximum relative deviation of CO₂ storage amount between prediction and true values is −15.15%. Except for this, the relative deviation for all other scenarios ranges from −10.67% to 5.23%. The average absolute relative deviation for predicting CO₂ storage amount is 3.04%. For the prediction of CO₂ storage efficiency, except for three scenarios with large relative deviations of −13.35%, −11.93%, and 8.72%, respectively, the relative deviation for all other scenarios ranges from −6.31% to 4.55%. The average absolute relative deviation for predicting CO₂ storage efficiency is 2.24%.

According to the curve between the predicted value and the true value, and their relative deviation, the random forest regression algorithm can accurately predict the CO₂-WAG production. Therefore, the cumulative oil production, CO₂ storage amount, and CO₂ storage efficiency can be accurately estimated by this method for the cases of various periods, fluid injection rates, and water–gas ratios.

Moreover, compared to the simulation method, the machine learning-assisted prediction method can save the time of adjusting the CMG model and running data files. It takes about 30 s to run a case of the CMG model and 108 min for all of the 216 cases in this study. The machine learning method employed in this work only spends 10 s predicting all of the scenarios, which shows a big advantage in computational efficiency compared to the CMG simulation method. If the grid of the CMG model is refined, the timesaving advantage of the machine learning method will be much huger. Therefore, the machine learning-assisted method can greatly improve the prediction efficiency of CO₂-WAG and will be suitable for injection parameter optimization.

4. Conclusions

For the application of CO₂-WAG used in non-homogeneous, low-permeability reservoirs and the machine learning-assisted prediction method of CO₂-WAG, some conclusions can be drawn from this work as follows:

(1) Compared to water flooding and continuous CO₂ flooding, CO₂-WAG can effectively improve oil recovery. In addition, compared to CO₂ flooding, CO₂-WAG can reduce the CO₂ production rate, which is conducive to the storage of CO₂ for the reduction of greenhouse gas emissions.

(2) The CO₂-WAG cycle time has a slight influence on oil production. Both CO₂ storage amount and CO₂ storage efficiency decrease with the cycle. On the premise that the reservoir formation is not fractured, the oil production increases but CO₂ storage efficiency decreases with the fluid injection rate. For low-pressure reservoirs, the oil production increases with the water–gas ratio, but CO₂ storage efficiency decreases with the water–gas ratio.

(3) The random forest regression algorithm in machine learning has better fitting accuracy in predicting the results of CO₂-WAG development. Therefore, it can be used to predict the oil production and CO₂ storage results under different combinations of injection parameters.

(4) Compared to numerical simulations, using machine learning algorithms to predict results avoids the need to build models and run data files, which will save a lot of time for subsequent parameter optimization.