Developing machine learning models to predict CO2 trapping performance in deep saline aquifers

Deep saline formations are considered as potential sites for geological carbon storage (GCS). To better understand the CO 2 trapping mechanism in saline aquifers, it is necessary to develop robust tools to evaluate CO 2 trapping eciency. This paper introduces the application of Gaussian process regression (GPR), support vector machine (SVM), and random forest (RF) to predict CO 2 trapping eciency in saline formations. First, the uncertainty variables, including geologic parameters, petrophysical properties, and other physical characteristics data were utilized to create a training dataset. A total of 101 reservoir simulation samples were then performed, and the residual trapping, solubility trapping, and cumulative CO 2 injection were collected. The predicted results indicate that three machine learning (ML) models that evaluate performance from high to low: GPR, SVM, and RF can be selected to predict the CO 2 trapping eciency in deep saline formations. The GPR model has an excellent CO 2 trapping prediction eciency with the highest correlation factor (R 2 = 0.992) and lowest root mean square error (RMSE = 0.00491). The accuracy and stability of the GPR models were veried for an actual reservoir in offshore Vietnam. The predictive models obtained a good agreement between the simulated eld and the predicted trapping index. These ndings indicate that the GPR ML models can support the numerical simulation as a robust predictive tool for estimating the performance of CO 2 trapping in the subsurface.


Introduction
Geological carbon storage (GCS) is a potential method for tackling greenhouse gas emissions and mitigating climate change (Bachu, 2018(Bachu, , 2000Hitchon et al., 1999). CO 2 can be sequestered into many potential storage sites, such as deep saline aquifers, depleted oil and gas reservoirs, depleted unconventional formations, residual oil zones, and deep marine formations (Bachu, 2002 The International Energy Agency (IEA) stated that saline aquifers could store a maximum of 10,000 Canada. RF was also considered as a predictive model for evaluating CO 2 -EOR and storage performance in residual oil zones (ROZs) Pawar, 2018, 2019).
Furthermore, ML techniques have been widely applied to several subsurface problems, such as history matching (Hadi et  In CO 2 sequestration applications, the least square SVM can generate high-accuracy prediction models for CO 2 solubility in brine (Ahmadi and Ahmadi, 2016). These authors stated that the average absolute deviation between the predictive models and experimental data was less than 0.1%. Later, Yan et al. (2020) successfully constructed predictive models for estimating permeability changes during CO 2 sequestration in coal seams using SVM and intelligent optimization methods.
As presented in the literature review, ML techniques have not been considered for developing robust and fast predictive models to estimate the CO 2 trapping e ciency in deep saline formations. Thus, this study proposes supervised ML algorithms for predictive construction models to predict the effectiveness of CO 2 trapping feasibility by reducing the computational time of the reservoir simulator in deep saline formations.
This study aims to propose ML-based prediction models for CO 2 trapping e ciency. These models can be further adapted as a robust and fast tool to investigate the feasibility of CO 2 geosequestration in the initial phase of geological CO 2 storage projects.
Three popular ML techniques, GPR, SVM, and RF, were used to predict the effectiveness of CO 2 trapping e ciency. The best ML technique was then employed in a real reservoir offshore Vietnam to evaluate the accuracy and stability of the proposed predictive model. To the best of our knowledge, this study is the rst to adapt supervised ML techniques (GPR, SVM, RF) to develop predictive tools for CO 2 trapping in saline formation. Brie y, the main goals of our study were to: Develop predictive models based on ML techniques for the accurate prediction of CO 2 trapping e ciency in deep saline aquifers.
Build fast predictive tools to evaluate trapping performance in CO 2 geosequestration.
Evaluate the accuracy of the ML model using the real-eld case from a previous study.

Methodology
ML techniques are powerful tools for developing predictive models. ML applies pattern recognition to guide reservoir performance developed on a computer (Mohaghegh, 2011). Furthermore, the predictive models based on ML could generate a rapid and accurate forecast in place of the reservoir simulator. In this study, ML algorithms were adapted to develop predictive models to evaluate the trapping e ciency in deep saline aquifers. The work ow for creating the predictive models is shown in Fig. 1a.
First step: CO 2 sequestration model construction. The 3D geological model was considered with a compositional modeling package (CMG-GEM) to simulate the CO 2 trapping mechanism. The speci c equations of the simulation package are expressed as follows (Nghiem et al., 2004): "Convection" represents the ow induced by the pressure difference; Darcy's Law explains this mechanism. The second factor is the rate of diffusion in the liquid state (Kim et al., 2017). The interaction between the reaction and injection results in precipitation and solubility between mineral components and the formation of brine (Kim et al., 2017), are key points in the CO 2 sequestration process (Nghiem et al., 2010 ). Therefore, the drainage and imbibition processes can be calculated during the simulation using Land's residual model (Land, 1968). Figure 1c depicts the relative permeability properties and the land trapping model used in this research.
To evaluate the e ciency of CO 2 trapping performance, three kinds of trapping indices need to be calculated (Nghiem et al., 2009a): In order to investigate the uncertainty of reservoir heterogeneities, 101 geological realizations were considered during the CO 2 injection process. The Petrel package was automatically transferred to the compositional simulation module (CMG-GEM) to conduct the CO 2 sequestration process. Then, the simulation result was evaluated by the optimizer (CMOST-AI) before creating the following geological models and uncertainty variables. The new porosity and permeability models were generated in each new simulation job (Vo Thanh et al., 2020b). Figure 2 represents the process for integrating the Petrel into CMOST to conduct simulations on different 101 geological realizations. Table 2 presents geological variables for creating realizations, consisting of azimuth, global seed number in the Petrel package. These variables would change the distribution of porosity and permeability for considering the geological uncertainty effect for machine learning models. Global seed number kv 20 10 50 Continuous CO 2 injection was applied for 10 years, followed by 490 years post-injection for this study.  Second step: De ne the uncertainty variables. There are many uncertainties in deep saline aquifers because less observation data are available from these reservoirs due to limiting nances in CO 2 storage projects. Therefore, these uncertainties can be used to develop ML models to predict the CO 2 trapping e ciency during saline formation. The uncertainty parameters are listed in Table 1. This module can perform sensitivity assessment, history matching, optimization, and uncertainty analysis for simulation projects (CMG, 2019). The key point of this step is to employ LHS because it is not dependent on the amount of training simulation jobs from the uncertainty parameters (Vo Thanh et al., 2020c).
Fourth step: Perform simulation jobs to gather inputs/outputs for the machine learning model. This procedure is vital for the development of ML models. The CMG-GEM module was used to perform 101 simulation experiments. For every simulation experiment, the uncertainty parameters and objective interests were gathered as the training dataset; residual trapping, solubility trapping, and cumulative CO 2 injection in a deep saline aquifer were the outcomes.
Furthermore, 4900 samples with elapsed time (10,20,30,.… 500 years) were prepared from 100 simulation experiments for training the ML models. In addition, 49 samples with the same elapsed time as the training stage from one simulation job was utilized to blind test ML models. These procedures are explained in detail in the nal section.
Fifth step: Generate predictive models using Machine Learning Techniques The predictive models can estimate the relationship between the input variables and output functions depending on the training reservoir results. In addition, the developed predictive models were built for each objective interest. To demonstrate the robustness of developed predictive models, three popular and powerful supervised ML algorithms (GP, SVM, and RF) were employed in this study. The detail of ML techniques was introduced in Supplement Material. All the ML techniques were conducted in a MATLAB 2020b environment running on an Intel ® Core ™ i7 -8550U CPU with 16 GB RAM.
Regarding the performance criteria for each ML model, Stazio et al.(2019) suggested that the root mean square error (RMSE) and coe cient of determination (R 2 ) were used as two statistical indicators to assess the developed predictive models from ML techniques. These statistical indicators were computed using the following equation: Final step: Validation of predictive models. The 100 simulation jobs were used for calibration (training) and 10 fold cross-validation (Geisser, 1993). One simulation job was used for blind testing to evaluate the stability of the predictive models. Subsequently, the selected predictive models were employed in the eld data from previous studies. This nal step would ensure the application of predictive models in the actual storage sites of the CO 2 trapping mechanism and other science disciplines. The MATLAB function of the developed training model for prediction in an existing reservoir is expressed as: Result = trainedModel.predictFcn(X) where X is the data matrix. The CO 2 trapping index will be calculated to develop ML models from simulation results using equations (11), (12), and (13). First, the ML models (GPR, SVM, and RF) used 100 simulation experiments for training and 10-fold cross-validation. A single simulation experiment was then used to blind test the best machine model to verify the over tting issue. Figure 5 depicts the performance of the ML models for predicting the solubility trapping index(STI), residual trapping index (RTI), and total e ciency index (TEI). Generally, a higher correlation factor (R 2 ) and lower RMSE correspond to a higher predictive model accuracy. All the computed statistical indicators of the three ML models are listed in Table 3. According to the table, the three predictive models can generate a reasonable prediction for STI, RTI, and TEI. However, the performance of GPR models is markedly higher than that of other models developed utilizing RF, especially those applied to estimate the STI and RTI. The SVM model version is slightly less than the predictive GPR model performance but much higher than that of the EBT models. GPR models provide higher predictive accuracy than the SVM and RF models. Thus, GPR models are selected for predicting CO 2 trapping index, including RTI, STI, and TEI. The tuning hyper-parameter of three machine learning approaches for developing the Although the GPR predictive models perform well in both indicators (RMSE and R 2 ), it is necessary to evaluate the selected GPR models using blind testing samples prior to the actual eld applications. A total of 49 simulation time-elapsed CO 2 trapping indices were used to verify the developed predictive models. These blind testing samples were not utilized in training ML models. The blind data samples had a structure of 49 rows and nine columns. Figure 6 highlights the blind testing results for RTI, STI, and TEI. The evaluated results t well with the correlation factors 0.9306, 0.9562, and 0.9552 for RTI, STI, and TEI, respectively. Moreover, the RMSE of these trapping indices also reached the low values in Figs. 6a, 6b, and 6c for RTI, STI, and TEI, respectively. The blind testing results indicate that the predictive models based on GPR ML are stable and reasonable for further applications. From these blind testing results, the machine-predicted models would produce highly-accurate predicted results depending on the characteristics of geological data and other parameters. In this study, the eld application of CO 2 sequestration is considered for validation from the development of predictive models. This validation will prove the practical applicability of the predictive models.

Application of the machine learning models by eld application
We deployed predictive models created using GPR techniques in an actual eld in the Cuu Long Basin, offshore Vietnam. The research area is located off southern Vietnam and consists of a uvial Oligocene sandstone reservoir (Vo Thanh et al., 2019). Figure 7 illustrates the location and lithology of the actual eld in offshore Vietnam.
The geological models were constructed based on geological and petrophysical data from Vo Thanh et al. (2020d). These models were used for simulating CO 2 trapping in this study. The eld simulation performance was used to validate the selected GPR ML models by comparing the reservoir simulator and predictive models' outputs. Figure 8 shows the petrophysical model of the dynamic simulation data. This model consisted of 87,000 grid cells in the X, Y, and Z directions. The geological model was historymatched for dynamic simulation using an integrated modeling framework in a recent study (Vo Thanh and Sugai, 2021). Figure 9 presents the results of the history-matching models. The history-matching of reservoirs proved that the eld simulated models could achieve good results for CO 2 trapping under actual conditions. The details of the simulation parameters are presented in Table 4. In this study, a total of one million tons of CO 2 was injected into the reservoir for 10 years, followed by a shut-in stage for 290 years of the monitoring period. The trapping index was then calculated to evaluate the effectiveness of the injected CO 2 . Figure 10 illustrates the CO 2 saturation in the uvial sandstone reservoir at the end of the simulation period.
As shown in this gure, CO 2 migrated into the sandstone reservoir through the sand channel distribution.
The effect of facies distribution on CO 2 plume migration was explored by Vo Thanh et al. (2018). The present study found that the CO 2 ow followed the direction of the sand channel in the subsurface. After the completion of the simulation of CO 2 trapping at the eld scale, the results of the trapping index of the simulated and GPR ML models would be compared for a better vision of our predictive models. The performance of the GPR models in the uvial sandstone reservoir of Nam Vang is depicted in Fig. 11. The uvial sandstone reservoir input parameters were considered to validate the GPR models using the R 2 and RMSE. Figure 11 shows the validation results of the GPR models in the uvial sandstone aquifer. A comparison of the predicted results and the simulation data for better evaluation was applied to the developed ML models. The GPR models achieved the prediction results with an R-squared value of 0.999 and an RMSE of 0.079 for STI. Regarding the RTI, the R-squared value was 0.9935, and the RMSE was 0.039. In TEI, the GPR models provided excellent performance matching between the target and actual values with an Rsquare of 0.992 and an RMSE of 0.084. The validation results showed that the GPR models were accurately predicted for 99.90%, 99.35%, and 99.2% of the STI, RTI, and TEI eld simulated effects. Table 5 shows the results of the GPR models for the predicted CO 2 trapping e ciency in uvial sandstone aquifers.
These results were compared to the trapping e ciency calculated using the eld simulation data. As shown in Fig. 11 and Table 5, these results suggest that predictive models based on the GPR ML technique can accurately predict CO 2 trapping e ciency in the eld scale of deep saline formations. Also, the predicted objective storage sites should have a similar geological setting to developing ML models.
To recap, the developed models will achieve different accuracy predicted results. In particular, the predicted samples are outside the range of creating models. The anticipated results may not be reliable for decision-making.

Comparison of proposed models and previous study
The eld-scale simulation and predicted results demonstrated the excellent performance of the GPR ML models. A comparative analysis was conducted to evaluate the predictive performance of the currently developed models. Kim et al. (2017) used an ANN to predict CO 2 trapping e ciency in saline aquifers.
Therefore, they completed a more comprehensive study to understand the developed models better.
The RMSE and R-squared indicators were used to evaluate the models by graphical analysis.

Discussions
Our ndings demonstrate the necessity of developing ML models to generate a robust predictive method for evaluating the CO 2 trapping performance in deep saline aquifers. We proved that the ML models could accurately predict CO 2 storage e ciency by comparing the simulation results for a uvial aquifer in the Cuu Long Basin, offshore Vietnam. The developed models obtained excellent predictive performance because the uncertainty variables were carefully selected for training and validating the ML models. Also, the blind testing performance is crucial for validating the accuracy and stability of ML models. Numerous studies have developed ML methods that ignore the blind testing process. Therefore, a blind testing process should be included to build predictive models based on ML.
Notably, each developed ML model was considered in a speci c range; the ML models are only used within the capacities of the uncertainty variables mentioned in this research. This study also emphasized saline aquifers for the application of the developed predictive models to saline formation. However, the work ow of this research can be easily adapted to other storage formations. The uncertainty parameters can be modi ed according to speci c storage formations.
Besides, the range of uncertainty variables used in developing predictive models should be carefully considered. The speci c training samples of ML models should be obtained from literature reviews or previous studies. ML predictive models cannot provide excellent performance if the models are employed on the samples inadequate for the proposed uncertainty bounds.
Our study found that GPR created excellent CO 2 trapping e ciency prediction compared with other ML methods such as SVM and RF. In terms of the correlation coe cient (R 2 ), the GPR models could predict the CO 2 trapping index in actual eld applications with higher R 2 values. We subjected GPR models to blind testing before employing them in the eld scale of saline aquifers. Previous studies have not focused on blind testing for the development of predictive models.
In conclusion, our work presents an innovative owchart for "construction," a robust and highly accurate ML predictive model. To validate the proposed method, it is suggested hitherto for other CO 2 geo-storage "formations" such as oil and gas reservoirs, ROZs, and fractured reservoirs. The limitations of ML models apply to other geological formations. However, the methodology of this study can be easily developed to address further engineering and science problems.

Conclusions
This study used ML models to predict the CO 2 trapping index of deep saline aquifers. It found applicable ML models for predicting RTI, STI, and TEI in the Cuu Long Basin reservoir, offshore Vietnam. The highlights of this study are as follows.
Reservoir simulation of the CO 2 trapping mechanism in deep saline formation was performed to create a training database to develop predictive ML models. In this study, 101 simulation experiments were completed to gather objective interests, including residual trapping, solubility trapping, and cumulative CO 2 injection in the trapping reservoir model, for the training database.
Predictive results con rmed that GPR produced the best predictive performance compared to SVM and RF. Also, the predictive ML models developed by RF achieved the worst predictive accuracy. The GPR model was identi ed as a more suitable method for creating predictive models for CO 2 trapping e ciency in deep saline aquifers. This study used only 100 numerical simulation jobs with 49 elapsed times to develop highly accurate predictive models.
With regard to actual eld application, GPR ML models were adopted for a uvial sandstone reservoir in offshore Vietnam. The ndings of this study indicated that the GPR models could accurately predict CO 2 trapping in an actual eld. By comparing the trapping e ciency, the predictive performances obtained excellent tting with objective values and accuracy between the GPR models; a eld-scale simulation result was achieved with a high correlation factor (R 2 ) of more than 0.95, and a low RMSE of 0.016 for TEI. To the best of our knowledge, the CO 2 trapping e ciency has not yet been explored in deep saline aquifers using predictive models based on ML.
The developed GPR ML models can predict the CO 2 trapping index with high accuracy in deep saline aquifers. Our study recommends that the GPR models be reproduced and adapted in future carbon capture utilization and storage (CCUS) tasks, such as oil recovery prediction and storage performance in the CO 2 -EOR project. The proposed ML predictive work ow will also serve as a reference for future work, especially the machine techniques that could be coupled with a reservoir simulator to reduce computational time.
The proposed ML models can be coupled with a commercial reservoir simulator to improve their ability and accuracy for predicting CO 2 trapping at storage sites.
The proposed ML models demonstrated robustness compared to a previous study. This was inferred using R 2 and RMSE analysis. The ML models offered in this study have a larger R 2 and smaller RMSE in three prediction trapping e ciencies (RTI, STI, and TEI). Besides, this study demonstrated the power of the GPR models for predictive modeling. The GPR models had a better predictive performance than the ANN models.
Predictive models based on ML can be applied to tackle climate change by predicting CO 2 trapping e ciency deep underground.
However, there are some limitations in developing predictive models: The developed models could only be employed in deep saline aquifers and geological characteristics similar to the simulation model design expressed in this study.
The predictive ML models were applied within the bounds of the uncertainty factors identi ed in this study.
Declarations Figure 1 Flow chart of predictive models based machine learning work ow, geological model, and relative permeability curves. a. The work ow connected between the reservoir simulator and machine learning models b. The porosity model and permeability from PUNQS3 project was adapted for this work c. The relative permeability curves and Land trapping models used for CO2 trapping simulation.    Performance of predictive models obtained from GPR, SVM, and RF. a. Quality of predictive RTI using three machine learning models; b. quality of predictive STI from three machine learning models; c.
performance of predictive TEI from GPR, SVM, and RF.
Page 29/34 Figure 6 Blind testing results of GPR models for predicting CO2 trapping e ciency. a. Blind testing of RTI; b.
Excellent blind testing performance of STI; c. more signi cant 95% R2 for TEI  The porosity and permeability models of uvial channel saline aquifers to compare the prediction values and eld scale simulation. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 9
Page 32/34 History matching model of bottom hole pressure Figure 10 CO2 saturation performance at the end of the simulation period. The distribution of CO2 saturation in a uvial sandstone aquifer. a. 3D gas saturation model at the end of simulation period; b. the cross-section to represent the CO2 ow in uvial system; c. the injector is located in the uvial sandstone system. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 11
Validation results between GPR models and eld simulated CO2 trapping e ciency. a. Excellent agreement between GPR predicted and eld simulated RTI; b. remarkable correlation between predicted and eld simulated STI using GPR based machine learning predictive models; c. reasonable predicted TEI using GPR predictive models.