The accurate estimation of subsurface rock properties is crucial to petroleum exploration and reservoir management. And sonic logs play a key role by linking seismic and well data for integrated geoscience interpretations. They help in building good synthetic seismograms in well-seismic ties, in creating low frequency models in impedance inversions and in estimating pore pressures and geomechanical properties in wellbore stability studies. Yet, sonic logs are not regularly acquired in wells due to the high cost associated with acquiring them.
Several authors have used various methods to fill the gap of missing sonic logs. Conventional methods for predicting sonic logs have often relied on the empirical relationship between density and compressional velocity or between compression velocity and resistivity. Apart from this, shear logs are predicted from compressional sonic logs using Castagna’s equation, which is an empirical relation between compressional velocity and shear velocity in brine-saturated siliciclastic rocks, or the Greenberg-Castagna empirical method which attempts to predict shear velocity log from compressional velocity log for various pure and composite lithologies. However, the limitations of these methods in accurately capturing the complex subsurface formations led to the development of more sophisticated techniques. The advancement in machine learning techniques and high-resolution logging tools created an opportunity for the application of more comprehensive approaches.
Field Challenge
Bhagyam field is an onshore oilfield with moderate viscosity, situated in the Barmer Basin in the western region of Rajasthan, India. The principal producing layer, the Fatehgarh, consists of multistoried fluvial sandstones and is known for its excellent reservoir qualities, with multi-Darcy permeability. Discovered in 2004, the field has been in production since January 2012, and since then, more than 200 wells have been drilled. But sonic data have been acquired in only 13 wells due to the prohibitive costs of data acquisition and limited applications in borehole integrity studies previously. However, sonic logs are becoming crucial for various projects, including seismic-to-well ties, low frequency model in seismic inversion, and the estimation of pore pressure and rock strength properties. Consequently, it is necessary to predict these logs for the remaining wells.
ANNs
Recent advances in machine learning and artificial intelligence have led to the adoption of data-driven models. Among these, artificial neural networks have emerged as a powerful tool in predicting sonic logs.
ANNs are a class of machine-learning algorithms inspired by the structure and functioning of the human brain. They are powerful computational models capable of learning complex relationships and patterns within multidimensional data. ANNs consist of interconnected nodes, or “neurons,” organized in layers (figure 1). Each connection between neurons has an associated weight, which the network adjusts during the learning process.
ANNs have found success in a wide range of applications, including image and speech recognition, natural language processing, financial forecasting and, as in this study, geophysics, for tasks like sonic log prediction.
Methodology
In this study, we proposed a method that leverages ANNs and integrates GR, RHOB, LLD and CNL data, each offering unique insights into subsurface formations. GR measurements reveal mineral composition and radioactivity, RHOB provides crucial density data for lithological characterization, and LLD and CNL offer resistivity and porosity information for assessing fluid content and rock permeability. By combining these diverse attributes, we aimed to uncover nuanced subsurface relationships, refining predictions and enhancing the understanding of geological formations. This approach improves the precision of sonic log predictions and provides deeper insights into subsurface reservoirs.
Data Collection and Preprocessing
The dataset contains logs obtained from 13 wells in the Bhagyam field, Rajasthan, featuring both compressional and shear sonic data. Four primary logs – gamma ray (GR), density (Rhob), neutron porosity (CNL) and deep resistivity (LLD) – serve as input variables to predict sonic logs, specifically VP (compressional velocity) and VS (shear velocity). To ensure robust model performance, the dataset was divided into training and test sets. Data from nine wells formed the training set, while the remaining four wells were used to test the model’s predictions. The training wells were selected to capture maximum geological diversity and account for lateral geographical distribution. A comprehensive log data cleansing process was implemented to enhance data quality and accuracy.
Feature Selection and Engineering
This study utilized a meticulous process to select and engineer the input features, facilitating a two-step approach for sonic log prediction.
Step 1: Predicting compressional velocity (VP):
For VP prediction, the ANN architecture includes an input layer, two hidden layers, and an output layer. The input layer features four variables: density, deep resistivity, gamma ray and neutron porosity. These features contribute to the accurate estimation of VP (figure 2). The correlation matrix in figure 3 shows that neutron porosity has the highest negative correlation with VP at negative-71 percent, indicating an inverse relationship. VP has a positive correlation of 27 percent with GR, 33 percent with density and 11 percent with deep resistivity. The hidden layers use the Rectified Linear Unit (ReLU) activation function. ReLU is commonly used in neural networks due to its ease of training and performance benefits. The output layer predicts VP.
Step 2: Predicting Shear Velocity (VS):
In the second step, we expanded the ANN architecture to predict shear velocity (VS). Alongside the original four features (Rhob, LLD, GR and CNL), we included the previously predicted VP as an additional input, leveraging the strong 86-percent correlation between VS and VP (figure 3) to enhance accuracy. VS has higher correlations with neutron porosity (negative 80 percent) and resistivity (27 percent), and low correlations with GR (4 percent) and density (6 percent). The hidden layers use the ReLU activation function for effective information processing, while the output layer focuses on VS prediction. To optimize learning and convergence, we employ the Adam optimizer, which dynamically adjusts learning rates and updates the network weights and is more effective than classical stochastic gradient descent. This choice ensures efficient model training and improves predictive performance.
Training Process
The dataset was strategically partitioned into three sets for a comprehensive evaluation of the model’s performance. The training set, comprising 70 percent of the data, was used to expose the model to diverse input patterns, allowing it to learn complex relationships within the data. The validation set (15 percent of the data) helped identify overfitting and fine-tune hyperparameters during training. The test set (15 percent of the data) was reserved for the final evaluation to ensure an unbiased assessment of the model’s predictive capabilities.
Hyperparameters, such as the number of iterations (epochs), hidden layers and nodes, and the optimization function, control the complexity and learning process of the model. Optimizing these hyperparameters involved exploring various configurations for parameters like hidden neurons, batch size and epochs, significantly enhancing the model’s predictive accuracy.
Model Evaluation
After training the ANN, several key metrics were employed such as the mean absolute error (MAE), Pearson correlation coefficient and R-squared value (R2) to rigorously assess model performance. By meticulously analyzing these metrics, we gained valuable insights into the effectiveness of the ANN in accurately predicting compressional velocity (VP).
Results and Observations
In figure 4, we present our model’s predictions for compressional velocity (VP) and shear velocity (VS) for a representative well in the Bhagyam field. The left panel shows our ANN’s precise VP predictions, closely aligning with the ground truth, highlighting the model’s robustness. The right panel demonstrates similar accuracy in predicting VS, effectively capturing variations in shear velocity, crucial for subsurface characterization. These results validate the effectiveness of our ANN model. The model’s consistent performance across different wells underscores its robustness and ability to generalize across varying geological conditions. The mean absolute errors for VP and VS were around 81 meters per second and 55 meters per second respectively. The R2 score was around 0.85 and 0.89 for VP and VS respectively. The Pearson coefficient was approximately 0.92 for VP and 0.94 for VS.
Discussion
Our methodology described so far has provided several insights into the prediction of sonic log responses using ANN. This section delves into the significant findings, their implications, and possible directions for future research.
The adoption of a two-step approach, commencing with the prediction of compressional velocity (VP) and followed by shear velocity (VS), proved to be a judicious strategy. This approach leveraged the inherent correlation between VP and VS, resulting in precise predictions for both parameters. The observed accuracy in VP and VS predictions across multiple wells underscores the robustness of our ANN model.
The selection of input features, namely Rhob, LLD, GR and CNL, played a pivotal role in shaping the model’s predictive performance. The logarithmic transformation applied to LLD enhanced its contribution, resulting in more accurate predictions. This underlines the significance of feature engineering in optimizing the representation of critical parameters.
The evaluation metrics, including mean absolute error, Pearson correlation coefficient, and R-squared (R2) values, collectively affirm the proficiency of our model. The low MAE values signify close alignment between predicted and actual values, while the high correlation coefficient and R2 values validate the model’s ability to capture underlying relationships in the data.
The velocity prediction using our model was more robust and capable of handling different lithologies as compared to the conventional methods of estimation using Gardner’s or Faust’s equations. In figure 5, we can see the comparison between predicted VP from density using Gardner’s method (A), versus predicted VP from resistivity using Faust’s method (B) versus predicted VP using ANN (C). In the hydrocarbon bearing zone (Z1) (where resistivities are generally high), the VP predicted from resistivity (B) was erroneously large when estimated without compensating for the fluid. Also, in shale Zone Z2, the estimated velocities from density and resistivity were on the higher side due to complex lithologies of the formation. Our ANN model was able to capture both these complexities successfully without explicitly mentioning the hydrocarbon zone information.
While our study has yielded promising results, it is imperative to acknowledge certain limitations. The reliance on a specific dataset from the Bhagyam field necessitates cautious extrapolation to other geological settings. Additionally, the consideration of further features and the exploration of advanced modeling techniques offer avenues for future research.
Conclusion
In conclusion, our research highlights the effectiveness of artificial neural networks in predicting sonic log responses in the Bhagyam field. By combining feature engineering and model evaluation metrics, we achieved accurate estimates of velocities. These findings significantly improve the accuracy and reliability of subsurface characterization. The generated sonic logs are now used to build synthetic seismograms for well-seismic tie studies, serve as inputs for low-frequency models in impedance inversion, and estimate pore pressure and geomechanical properties for wellbore stability studies.