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Artificial Neural Network-Based Caprock Structural Reliability Analysis for CO_{2} Injection Site—An Example from Northern North Sea

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## Abstract

**:**

_{2}sequestration projects, assessing caprock structural stability is crucial to assure the success and reliability of the CO

_{2}injection. However, since caprock experimental data are sparse, we applied a Monte Carlo (MC) algorithm to generate stochastic data from the given mean and standard deviation values. The generated data sets were introduced to a neural network (NN), including four hidden layers for classification purposes. The model was then used to evaluate organic-rich Draupne caprock shale failure in the Alpha structure, northern North Sea. The train and test were carried out with 75% and 25% of the input data, respectively. Following that, validation is accomplished with unseen data, yielding promising classification scores. The results show that introducing larger input data sizes to the established NN provides better convergence conditions and higher classification scores. Although the NN can predicts the failure states with a classification score of 97%, the structural reliability was significantly low compare to the failure results estimated using other method. Moreover, this indicated that during evaluating the field-scale caprock failure, more experimental data is needed for a reliable result. However, this study depicts the advantage of machine learning algorithms in geological CO

_{2}storage projects compared with similar finite elements methods in the aspect of short fitting time, high accuracy, and flexibility in processing different input data sizes with different scales.

## 1. Introduction

_{2}, CH

_{4}, etc.) have caused global temperature rises above pre-industrial levels, and emissions must be drastically reduced to avoid dire climate consequences such as sea-level rise, extreme weather events (e.g., floods, hurricanes), extreme cold and hot weathers, and so on [1,2]. Geological storage of anthropogenic CO

_{2}(GCS) into saline aquifers is one of the key options to reduce atmospheric CO

_{2}[3]. Numerous pilot projects worldwide have established this technique as a safe and reliable solution (e.g., Snøhvit, Norway [4], In Salah, Algeria [5], Sleipner, Norway [6], Ketzin, Germany [7], Otway, Australia [8], Quest, Canada [9]). However, GCS still needs advanced research to evaluate the injection-related risks for safe and permanent CO

_{2}storage. Injecting CO

_{2}into saline aquifers may increase the pore pressure resulting in geo-mechanical failure such as caprock shear and tensile failures, reactivation of existing faults, flexure of top-seal, etc. [10,11,12]. Caprock assessment is critical in finding a suitable storage location where supercritical CO

_{2}is prevented from vertically migrating out of traps. Due to exceptionally high capillary entry pressure, the fine-grained top seal acts as an impermeable layer. However, leakage occurs when the buoyancy pressure exceeds the capillary entry pressure, which is very unlikely for fine-grained caprock. However, mechanical failure of caprock becomes the primary failure mode in the case of reservoir pore pressure increase due to CO

_{2}injection [13]. Therefore, the caprock reliability assessment is necessary to prevent any CO

_{2}injection-related leakage risk. The Alpha prospect is a fault-bounded three-way structural closure located in the Smeaheia area, northern North Sea (Figure 1). The Alpha prospect was evaluated by Equinor and Gassonova as a potential CO

_{2}storage site [14]. The area is located east of the Troll east field and bounded by two major faults; Vette Fault (VF) in the west and Øygarden Fault Complex (ØFC) in the east. The studied site is positioned in the footwall of the VF with a three-way closure [15]. The main reservoir rocks comprise Upper Jurassic Sognefjord, Fensfjord, and Krossfjord formations, while the organic-rich Draupne and Heather shales act as the primary caprocks.

_{2}into abandoned oil fields disrupts the reservoir field pressure, which may result in leakage. Harmonic pulse testing (HPT) is a technique used in field testing to identify the pressure response of a leak from that of a non-leak. In a CO

_{2}capture and storage (CCS) project, CO

_{2}potentially may leak from numerous injection wells and depleted wells. Since human analysis of vast amounts of HPT data is challenging, ML approaches are viable alternatives. In this regard, Sinha et al. [23,24] predicted CO

_{2}leakage using a variety of NN approaches such as multilayer NN, convolutional neural network (CNN) and long-short term memory (LSTM). Sun et al. [25] used a NN technique to investigate the CO

_{2}trapping mechanisms in the Morrow B Sandstone in the Farnsworth Units. In light of the NN forecasts, they picked the reservoir model from an available historical data. The chosen model then was used to assess the effect of the structural-stratigraphic mineral trapping mechanisms on CO

_{2}sequestration. Furthermore, the NN-based model was capable of accurately predicting pressure, fluid saturation, and composition distributions. As a result, they concluded that mineral trapping contributes less to CO

_{2}sequestration than other trapping methods. Lima and Lin [26] predicted CO

_{2}and brine leaks in a GCS project using ml algorithms. They used seismic data and historical well pressure data from 500 simulations as inputs to the CNN model. Testing the model, 50 out 500 simulation data were used as the test data. They observed incorporating the pressure data gives a slight improvement in leakage prediction as well as increasing prediction accuracy. To predict CO

_{2}leakage, Zhong et al. [26] employed a combined version of CNN and LSTM model (ConvLSTM). They employed CNN and LSTM to handle spatial features (porosity and permeability) and temporal features (CO

_{2}injection rate per time), respectively. In other words, three 2D images were utilized as input to convLSTM, one of which included the injection rate and the other two were porosity and permeability distributions.

## 2. Theoretical Background

#### 2.1. Monte Carlo Simulations

_{0}) and friction angle (φ) and effective stresses (i.e., σ’

_{1}, and σ’

_{3}). In this approach, the given mean value, and standard deviation were substituted into Gaussian formalism at each MC step. In other words, replacing the mean value and variance in Equation (1) with relevant values (introduced in Table 1) allow having a Gaussian distribution from stochastic values for φ, S

_{0}, σ’

_{1}, and σ’

_{3}.

#### Model Definition

_{1}, σ

_{3}) and rock strength properties (i.e., S

_{0}, φ). These parameters act as load and resistance, which allow estimating failure probability with evaluating the safety margin. This context tests the Mohr-Coulomb failure criteria based on the factor of safety (FoS). Equation (2) is used to determine the factor of safety (FoS) by estimating the φ, S

_{0}, σ’

_{1}, and σ’

_{3}in combination with the MC algorithm.

_{0}is cohesion, φ is friction angle, σ’

_{1}is effective vertical stress, and σ’

_{3}is effective horizontal stress. The effective stresses are estimated from reservoir pore pressure (p

_{p}) following Equations (3) and (4).

_{p}in Equations (3) and (4) are pore pressure, which is considered 10.48 MPa [16]. For simplicity, the model has assumed an isotropic horizontal stress condition with a normal faulting regime. The deterministic FoS values are estimated using the stochastic data generated by MC algorithm. Afterward, the number of failures (FoS ≤ 0) and non-failure (FoS > 0) states are counted to estimate the failure percentages of caprock shales.

#### 2.2. Machine Learning

_{0}, σ’

_{1}, and σ’

_{3}) will be discovered with the ML algorithm. Afterward, with introducing the test dataset to the trained-ML algorithm, the corresponding g(x) will be predicted. Several ML algorithms have been developed, such as Bayesian network, neural network, decision tree, random forest, etc. In this simulation, the potential of the neural network (NN) has been investigated.

#### 2.2.1. Neural Network

_{1},…, x

_{n}as input from N neurons.

#### 2.2.2. Mathematical Description of NN

_{0}is the number of nodes in the first layer. For the l-th hidden layer, we have:

^{l}) are used for each layer. The closed form of forward propagation for a multilayer NN is written as:

_{l−1}× N

_{l}while $\stackrel{\u2322}{y}$ and $\stackrel{\u2322}{b}$ are output and bias vectors with a dimension of N

_{l}× 1, which are shown layer-wise. In Equation (9), the unknown parameters are biases and weights, which can be tuned to diminish the error of the NN model. The backpropagation algorithm [29] allows tuning of weights and biases by minimizing the cost function.

#### 2.3. K-Fold Cross-Validation

## 3. NN Model Implementation

_{0}, σ’

_{1}, and σ’

_{3}. The resulting MC data were then merged with pertinent g(x) values in a unique matrix to create input data sets with the size of 1000, 10,000, 50,000, and 100,000. The NN conjugated with a 10-fold cross-validation algorithm is developed to establish an ML model that can predict the proper g(x). Hereafter, the term “NN model” refers to a neural network combined with the 10-fold cross-validation algorithm. The NN with a simple architecture is designed via trial and error to minimize training time. Three layers of the NN model are proven to be sufficient to achieve a satisfactory outcome (14 nodes initial layer, 10 nodes second layer, and 1 node final layer) with a dropout rate of 20% to prevent overfitting. The last layer was activated using the sigmoid function, whereas the other layers utilized the rectified linear unit (ReLU) [30] activation function. In the NN model, each input data set contains four features (φ, S

_{0}, σ’

_{1}, and σ’

_{3}), as well as a target g(x) which may be either one (indicating non-Fail) or zero (showing Fail). Figure 5 illustrates the flowchart of NN establishment with train dataset and then validation with test dataset. The input data is split into train and test datasets before being fed to NN. The training dataset is necessary to fit the NN model, whereas the test dataset is utilized to evaluate the error of the model predictions. Here, the input dataset is divided into train and test datasets, with a percentage of 75% for training and 25% for testing.

_{0}, σ’

_{1}, and σ’

_{3}for different sample sizes. As seen, the PDF diagram behaves identically for various sample sizes, even though the depicted ranges vary by sample size. In other words, regardless of sample size, the mean value and standard deviation of each curve shown in Figure 6 are the same as those given in Table 1.

#### 3.1. Input Data Scaling

#### 3.2. NN Verification

#### 3.3. Metrics for Evaluating the NN Model

## 4. Alpha Site Case Study

_{2}storage located in Horda Platform, northern North Sea (Figure 1). It is critical to evaluate the structural reliability of the sealing effectiveness (i.e., caprock and fault) at the Alpha structure since it is a three-way closure against fault. In this study, the strength parameters are initially developed using MC algorithm as this approach was already employed by He et al. [32] to obtain the FOS variables. On the other hand, Wang and Goh [33] previously generated FOS parameters using random field finite (FE) element method. Here, MC generated strength parameters were then fed into NN model to assess the Draupne Formation shale caprock probabilistic failure potential. While He et al. [32] chose NN along with support vector regression, Wang and Goh [33] employed CNN approach in their study. However, the database used in this study is only limited to the Alpha prospect (well 32/4-1) without considering the spatial properties variation [15]. This includes additional constrained of the sampling method. Significantly good classification results in machine learning algorithms instill confidence in our capacity to evaluate field scale dependability using the NN model. However, in 1000 data samples, the small input data size has limited results and is not trustworthy. Therefore, the results of the 1000 data samples were excluded from Table 2. In other words, the reported results in Table 2 corresponds to the models with 10,000, 50,000, and 100,000 data samples. As seen in Table 2, as the sample size grew, the classification score climbed to 94%, 97%, and >97%, respectively. As mentioned before, this fact was already reported by He et al. [32]. It is worth mentioning that the test dataset used to validate the NN model represents 25% of total data samples, while the remaining data (i.e., 75%) is utilized for training the NN model. As shown in Table 2, the developed NN predicts that more than 50% of test data results will be in the failure state, which is significantly overestimation compare with the results estimated using other method [34]. As previously stated, the absence of experimental data may introduce substantial uncertainty into the presented findings. Moreover, subsurface structural reliability is a delicate procedure that is influenced by a variety of other parameters. Therefore, further comprehensive investigation is required to evaluate the critical top seal integrity for a safe and reliable subsurface CO

_{2}storage in the Alpha prospect.

## 5. Conclusions

- By increasing the size of the input data, the developed NN converges at shorter epochs.
- The classification score rises as the size of the input data increases and almost stabilizes after 50,000 data samples.
- The NN algorithms are feasible alternatives to time-consuming finite element techniques in terms of computing time. In other words, although the fitting time increases with increasing the input data size, it is still negligible when compared to conventional methods.
- Although the NN method tested in this study shows significantly high classification score, the Draupne caprock shale probabilistic failure significantly overestimated the failure potential. However, owing to a scarcity of experimental data and complex caprock behavior, additional field investigation and empirical evidence are required to predict the more definite failure state.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location map of the Horda Platform, the northern North Sea showing the major and minor faults with Troll fields as reference. The contour lines represent the Draupne Formation thickness adapted from [15]. The red polygon against the Vette fault is the Alpha prospect (

**left**). A generalized stratigraphic succession of the Horda Platform showing the Jurassic and Lower Cretaceous formations and the vertical distribution of the Upper Jurassic reservoir-caprock configuration is shown in well 32/4-1 (

**right**) (adapted from [16]).

**Figure 2.**The diagram illustrates the overall work flow of this study in chronological order. The Monte Carlo method generates data points of four distinct sizes for strength parameters of friction angle (φ), cohesion (S

_{0}) and effective stresses (i.e., σ’

_{1}, and σ’

_{3}). Then, each data point with a specific size is sent into NN for classification.

**Figure 3.**The sketch illustrates the overall architecture of a classification NN including the forward and backward propagation algorithm.

**Figure 4.**The graph demonstrates the schematic of 5-fold cross-validation. As seen based on the given k (k = 5) value, the train and test datasets are divided into equal-sized folds. Averaging across several runs yields performance metrics such as accuracy and loss.

**Figure 5.**The flowchart illustrates establishing a NN using train data set and then validating the network with test data set.

**Figure 6.**The graphs depict the probability distribution function of ϕ, S

_{0}, σ’

_{1}, and σ’

_{3}for different sample sizes. The colors red, green, blue, and cyan indicate the distribution range for 1e+03, 1e+04, 5e+04, and 1e+05 samples generated using MC algorithm.

**Figure 7.**The Graphs depict the Gaussian distributions of ϕ, S

_{0}, σ’

_{1}, and σ’

_{3}after standardization. The colors red, green, blue, and cyan represent the 1e+03, 1e+04, 5e+04, and 1e+05 sample points. Standardizing involves scaling each input by subtracting the mean value (λ) and then dividing by the standard deviation (μ) to shift the distribution to have a mean of zero and a standard deviation of one.

**Figure 8.**The plots demonstrate the results of the NN verification with make-moons and make-circles data set, which is the scikit-learn standard data set.

**Figure 9.**The graphs demonstrate the trend of accuracy and loss function for the train and test datasets. The accuracy combined with the cross-entropy function can monitor the progress of NN convergence for classification. The blue and red circles depict the accuracy profile for train and test data sets, respectively, while the black and green circles depict the loss function profile for train and test data sets.

**Figure 10.**The plots demonstrate the results of the NN in the classification of the real train and test data sets. The mean values and standard deviations were plotted with filled circles and error bars, respectively.

**Figure 11.**Validation of the established NN model is performed with unseen data point of (

**a**) 250, (

**b**) 2500, (

**c**) 12,500, and (

**d**) 25,000.

**Table 1.**The used database, including mean value (λ) and standard deviation (μ) of strength parameters (φ and S

_{0}) and effective stresses (σ’

_{1}and σ’

_{3}) [16].

Parameters | Mean Value (λ) | Standard Deviation (μ) | Unit | Distribution | Sample Number |
---|---|---|---|---|---|

Φ | 19.50 | 3 | Degree | Normal | * Lab + Logs (429) |

S_{0} | 5.01 | 1 | MPa | Normal | ** XLOT (5) |

σ’_{1} | 22.25 | 0.55 | MPa | Normal | Lab + Logs (432) |

σ’_{3} | 16.85 | 0.7 | MPa | Normal | Lab (4) |

**Table 2.**Predictions made by the developed NN versus test data samples. It is worth mentioning that the test dataset used to validate the NN model represents 25% of total data samples.

Number of Total Test Data | Number of Correct Predictions | Non-Fail | Fail | Classification Score |
---|---|---|---|---|

2500 | 2374 | 43% | 57% | 94% |

12,500 | 12,131 | 42% | 58% | 97% |

25,000 | 24,311 | 42% | 58% | 97% |

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**MDPI and ACS Style**

Ahmadi Goltapeh, S.; Rahman, M.J.; Mondol, N.H.; Hellevang, H. Artificial Neural Network-Based Caprock Structural Reliability Analysis for CO_{2} Injection Site—An Example from Northern North Sea. *Energies* **2022**, *15*, 3365.
https://doi.org/10.3390/en15093365

**AMA Style**

Ahmadi Goltapeh S, Rahman MJ, Mondol NH, Hellevang H. Artificial Neural Network-Based Caprock Structural Reliability Analysis for CO_{2} Injection Site—An Example from Northern North Sea. *Energies*. 2022; 15(9):3365.
https://doi.org/10.3390/en15093365

**Chicago/Turabian Style**

Ahmadi Goltapeh, Sajjad, Md Jamilur Rahman, Nazmul Haque Mondol, and Helge Hellevang. 2022. "Artificial Neural Network-Based Caprock Structural Reliability Analysis for CO_{2} Injection Site—An Example from Northern North Sea" *Energies* 15, no. 9: 3365.
https://doi.org/10.3390/en15093365