PREDICTION OF CO 2 GAS SATURATION DISTRIBUTION BASED ON DEEP LEARNING USING DEEP NEURAL NETWORK (DNN) ALGORITHM

. Multiphase flow analysis is essential for resolving subsurface flow issues in CO 2 capture and storage (CCS) systems. Predicting the distribution of CO 2 gas saturation is one example that is quite useful for evaluating multiphase flow. Multiphase flow simulation is typically performed using numerical simulations, such as the TOUGH2 simulator. Ordinary numerical simulations, on the other hand, have some limitations, such as high grid spatial resolution and significant processing costs. One option for estimating the distribution of CO 2 gas saturation is to employ deep learning with specific algorithms. A deep neural network (DNN) is a highly effective deep learning approach. A deep neural network is a network structure made up of three interconnected layers: input, hidden, and output. DNN learns from the input data about the previously constructed architecture. As input, DNN requires a significant amount of data train. The trained DNN model is then used to automatically estimate the distribution of CO 2 gas saturation. This algorithm is capable of dealing with complex data patterns, particularly gas saturation in multiphase flow issues. The reconstruction loss results revealed that the loss value lowers as the number of epochs grows. Furthermore, the model with 5 epochs and 0.001 regularization weight had the least error value 0.43. As a result, while this model is adequate for predicting the distribution of CO2 gas saturation, additional research is required to achieve more ideal outcomes.


INTRODUCTION
Multiphase flow in porous media is an important consideration in Carbon Capture and Storage (CCS) systems. This is because multiphase flows can be employed to solve transportation and subsurface flow problems (Pachauri et al, 2014). Variations in permeability and capillary pressure can be caused by subsurface geological heterogeneity (Pini et al, 2012).
Effective permeability is vital in multiphase systems for accurate modeling and predicting fluid flow by assessing the fluid's ability to flow (Yang et al, 2023). The presence of a low gas saturation value causes the low permeability value. Low saturation, on the other hand, can diminish the effect of gravitational forces on high permeability layers (Wen and Benson, 2019).
Numerical simulations are typically used to simulate multiphase flows (Pruess, 2005). The TOUGH2 simulator is the most often utilized numerical simulation. Ordinary numerical simulations, on the other hand, have various limitations, including high grid spatial resolution (Doughty, 2010;Wen and Benson, 2019) and significant processing costs (Khebzegga et al, 2020).
The application of the Deep Neural Network (DNN) algorithm is one way devised to overcome the shortcomings of numerical simulation. DNN is a type of artificial neural network with three layers: an input layer, a hidden layer, and an output layer (Addo et al, 2018). According to , one of the benefits of utilizing the DNN technique is that the results of the DNN model may produce CO2 migration forecasts with the same level of accuracy as traditional numerical simulations.
The loss reconstruction function must be used while creating the DNN model to indicate the extent to which the model can accurately rebuild data. The Mean Square Error (MSE) is a popular loss function. This function calculates the difference between the expected and actual values. The lower the values, the higher the model's ability to reconstruct the input data. Given a batch of train data, the parameters are updated to minimize the loss function, and the method is essentially similar to utilizing the objective function in the inverse problem. This function was http://dx.doi.org/10.12962/j25023659.v9i2.18089 choosen because increased CO2 gas saturation in multiphase flows is frequently associated with higher mobility, which necessitates high precision in plume prediction .
DNN modeling, on the other hand, employs a 3D temporal architecture that is intended to extract temporal information from the model to be forecasted. This architecture includes a temporal layer that can simulate the depth of the temporal convolution kernel, making it effective for acquiring temporal information in both the short and long term (Diba et al, 2017).
Thus, the objective of this research is to use th Deep Neural Network (DNN) algorithm approach to predict the distribution of CO2 gas saturation. So it is envisaged that our method would be able to meet the growing demand for analyzing CO2 storage.

METHODOLOGY
This research uses several software, such as Anaconda (with Python 3.6 environment), Jupyter Notebook, Microsoft Word, and Microsoft Excel. In addition, numerous libraries are used in this study to create the needed DNN architecture. The libraries utilized, as well as their applications, are listed in Table 3.1 below.

Preliminary Studies
This stage includes preliminary studies on CO2 capture and storage systems (CCS), multiphase flows, gas saturation, as well as Deep Neural Network (DNN) architectures and their constituent components. In addition, at this stage a preliminary study of the application of DNN was also carried out to predict the distribution of CO 2 gas saturation. This stage is useful as suporting data for data interpretation.

Developing DNN Architecture
This stage begins with importing the necessary libraries so that the script can run as needed. Then, define several values and layers that will be used, such as regularization weights, 3D convolution layers (convolution, reflection padding, batch normalization, and ReLU activation function), convolution residual layers (add layer), and nonlinear batch nordeconvolution layers (deconvolution, batch normalization, ReLU activation function).
After that, the process of developing the architecture is continued by compiling predetermined layers to form the VAE (Variational Autoencoder) model. Then the step of developing this architecture ends with making the output model.

Data Training Process
The training data process begins by importing the appropriate library and inputting the shape based on the architecture model that was created previously. Then proceed with loading the train data and test data, as well as shuffle the data. In this study, X and Y data are included in each train and test data set. The reservoir conditions (initial pressure, temperature, and formation thickness), geological model (permeability), and injection design (injection rate, injection duration, and perforation thickness) data sets comprise the train_x and test_x data sets. Meanwhile, the data train_y and test_y are separating processing data from the Eclipse (e300) software in the form of CO2 gas saturation data with 0 to 1 values. The data set is available at https://drive.google.com/drive/folders/1SVZFkax kAIjcGKew3rzGTmKW5tSBUGf7?usp=sharing.
After loading the data sets, the process is continued with the process of defining the loss function and determining the training specifications. The training process is continued by carrying out iterations for each epoch and batch, which ends with storing the model resulting the model resulting from the training data.

Data Prediction and Visualization Process
The initial stage in the data prediction and visualization process is to import the required library. Then the process is continued by loading test data to retrieve test data that will be predicted by the model.
After that, load the trained model as a result of the previous training process. The prediction process is carried out by taking test data and data from the trained model. Finally, a plot of the predicted results is performed to display the visualization of the model.

RESULT AND DISCUSSION
The number of parameters obtained throughout the DNN model construction process can be utilized to analyze the model. The greater the number of parameters in a layer, the more complex the layer. When the model includes complicated layers, it can learn complex features from the data. Overfitting can also be caused by layers that are excessively complicated. Overfitting occurs when a model memorizes too much data and is unable to generalize to new data. The highest number of parameters that may be handled in this study is 40,399,489, with a total number of parameters that can be trained of 40,386,817. Because the model includes numerous layers, it is more prone to overfitting, according to the data.
Meanwhile, the ratio of train and test data used, and the number of epochs are among the hyperparameter values that may be studied using this DNN model. The ratio between train and test data used in this study is 70:30. This is due to the bulk of the train and test data being too enormous for the computer to load all of it.
The number of epochs used can also have an impact on the training process and outcomes. The more epochs employed, the more patterns in the training data set the model may learn through suitable repetition. As a result, in this study, epochs 3 and 5 were utilized, considering the amount of data, period of research, and computer performance.  The script used in this investigation to forecast the distribution of CO2 gas saturation is a version of the script developed by  and can be downloaded at the following link (https://github.com/gegewen/ccsnet_v1.0). The distribution visualization findings in Figure 4.1 reveal that high saturation is marked in yellow on the left.
The saturation distribution then expands to the right, with the lower saturation value moving to the right.
Likewise, the saturation distribution visualization findings in Figure 4.2 reveal that the saturation distribution expands to the right, with high saturation values on the left. Because the number of epochs employed differs just slightly, the predicted model results in Figures 4.1 and 4.2 appear identical at first glance. Similarly, because the variation in the number of epochs is not too great, the visualization results of the distribution in    (2021), there is a substantial difference. The manuscript's representation of the distribution prediction findings looks exactly like numerical simulation results; hence the error is small. In this investigation, however, the prediction outcomes were very different from the initial input. The variation in results is due to differences in numerous parameters used. Differences in the number of epochs, regularization weight values,  The value of the reconstruction loss should ideally decrease as the epoch rises. A decent reconstruction loss value is also close to zero (0). In general, a model with three epochs has a lower train loss and eval loss value as the epoch number grows. According to trend of the value of the train rebuilding loss, the loss's worth is diminishing. The trend in the value of the eval reconstruction loss is similar, with the loss value decreasing. Furthermore, Table 4.1 shows that the eval reconstruction loss value is less than the train reconstruction loss value. This means that the model performed better on the test data. In general, a model with 5 epochs has a lower train loss and eval loss value as the epoch number grows. According to the trend of the value of the train reconstruction loss, the loss's worth is diminishing. However, the value of the eval reconstruction loss declined until epoch 3 and then increased. This demonstrates that there are signs of overfitting in epochs 4 and 5. Nevertheless, a more thorough assessment of the models and data used is required to confirm that the data is actually overfitting.
The reconstruction loss value derived from the loss values computation throughout the training and testing procedure with a regularization weight of 0.001 is shown below. The loss values results are shown in Tables 4.3 and 4.4 below. In general, a model with three epochs has a lower train loss and eval loss value as the epoch number increases. According to the trend of the value of the train reconstruction loss, the loss's worth is diminishing. The trend in the value of the eval reconstruction loss is similar, with the loss value decreasing. Furthermore, Table 4.3 shows that the value of the eval reconstruction loss is greater than the value of the train reconstruction loss in the first epoch. This demonstrates overfitting in the first epoch. In general, a model with 5 epochs has a lower train loss and eval loss value as the epoch number grows. According to the trend of the value of the train reconstruction loss, the loss's worth is diminishing. The trend in the value of the eval reconstruction loss is similar, with the loss value decreasing. Furthermore, Table 4.4 shows that the value of the eval reconstruction loss is greater than the value of the train reconstruction loss in the first epoch. When the results in Table 4.4 are compared to the results in Table 4.2, there is no sign of overfitting in the 4 th and 5 th epochs.
The error value is another metric that may be used to determine the amount of accuracy of a http://dx.doi.org/10.12962/j25023659.v9i2.18089 model that has been created. In deep learning models, the Root Mean Square Error (RMSE) is a regularly used error value calculation. In simplicity, the RMSE value is calculated by taking the square root of the squared difference between the expected and actual values of the test data. The RMSE value is produced using these calculations, as demonstrated in Table 4.5 below: Depending on the RMSE calculation findings in Table 4.5 above, the model with a regularization weight of 0.00001, thus the model with epoch 3, has the minimum error value. This is consistent with the loss value results, which show that the model with epoch 5 has an indication of overfitting on the fourth and fifth repetitions. Consequently, the error value in the model with epoch 5 is larger than the error value in the model with epoch 3. Meanwhile, the model with a regularization weight of 0.001, thus the model with epoch 5 has the minimum error value. This is consistent with the loss value results, where the loss value trend in the model with epoch 5 is smaller than the loss value trend in the model with epoch 3. If the error value from all models is compared, the model with a regularization weight of 0.001 and epoch 5 has the lowest error value. When compared to the other three models, model 4 is the most similar to the numerical simulation findings.

CONCLUSIONS AND RECOMMENDATIONS
As a result of the research, it is possible to infer that the model is adequate for predicting the distribution of CO2 gas saturation. The resulting reconstruction loss value, which reduces as the number of epochs grows, demonstrates this. Furthermore, the obtained RMSE values ranged from 0.43 to 0.45. However, additional refinement of this model is required to achieve more ideal results.
Future work should consider using field data as input data to better represent the actual situation. The authors also expect future work to consider the use of more than 700 training data, 300 test data, and 5 epochs, as well as a regularization weight of 0.001.

ACKNOWLEDGMENTS
The author would like to thank the ITS for the internal institution funding to carry out this research, as well as all parties who cannot be mentioned one by one.