Raymundo Gomezcásseres: ubicación contextual

• The study successfully synthesized NMR T2 distribution by processing easy-to- acquire well logs using deep neural networks. The neural networks utilize the hidden relationship between different well logs to synthesize NMR T2.

• Long short-term memory network and variational autoencoder based neural network synthesized the NMR T2 distribution at high accuracy and high smoothness. Quantification of the smoothness of the synthesized T2 distribution is needed to understand the realistic performance of the deep models.

• Deep learning models performed significantly better than shallow models. • Utilized a two-step training process to learn the inherent features of NMR T2 and

predict the entire NMR T2 distribution, comprising 64 T2 amplitudes measured at corresponding T2 times.

• A study of stability of the deep neural networks to the presence of noise indicates that addition of noise to training data makes the deep networks more stable to the presence of noise in test data.

3.10 Assumptions and Limitations of This Study

Each type of borehole-based subsurface measurements (referred here as well logs) are sensitive to specific formation properties. The compositions and contents of formation minerals and fluids have complex and hidden relationships with the various well logging

responses. Various well logs contain redundant information about formation properties. In well logging, engineers/geoscientists utilize dozens of well logs to better characterize the subsurface formation. Are all the well logs necessary? What are the minimum number of well logs needed to get all the information to represent a formation? The models applied in this study show that it is possible to generate NMR T2 distribution by processing other easy-to-acquire logs. Such a synthesis is essential for pore-scale characterization.

The idea is similar to the user portrait task in the computer science area. Big social network companies push content based on the users’ interests. Different users are presented with different content. Just like it is hard to describe the formation properties, it is hard to describe users’ habits. The users’ habit and interest can be inferred from all the activities associated. By processing the activity history, machine learning models can predict users’ characteristics. The characteristics are usually stable over time. The users can be divided into several categories and each user can be represented as an embedding vector in latent spaced. Every user is different, it is not possible to exactly measure every aspect of a user, but users’ behavior is statistically similar and stable over time. A vector is enough to represent a user in the social network industry. Maybe we don’t need all of the logs to represent a formation in the oil and gas industry.

In this work, I applied a similar idea. Formation measurements are statistically stable for different types of formations (e.g shale is usually associated with high GR, low porosity, etc.). Even for the shale formation in the same reservoir, the formation well logs are not the same. However, the same type of formations should have similar well log values. If we project all the formations into latent space, formations with similar

properties should be projected into similar places. The well logs derived from formations with similar properties should be similar. Machine learning models can learn the subtle differences of formation from existing well logs and utilize the hidden relationship that engineers cannot find. This work is based on the following assumptions:

• Information redundancy exists in well logs. It is not necessary to utilize dozens of well logs to describe a formation.

• NMR T2 logs can be generated from processing other formation logs by utilizing the information redundancy.

• The well logging responses for formations with similar properties are similar. • Machine learning models can learn the hidden relationships between different

well logs for generating other logs.

• Inverted well logs are more suitable for the NMR T2 synthesis task compared to raw logs.

3.11 Recommendations for Future Work

In this study, the models are trained and tested with a small dataset. Preprocessing and dimensionality reduction are performed to ensure the data quality, validation set, and training monitor is used for hyperparameter tuning and prevent overfitting. However, the following steps can be used to improve this work:

• Apply the model on a larger dataset.

• Perform cross well validation to generate a more robust conclusion about log synthesis.

• Log generation from embeddings. Just like a user in a social network can be presented as a vector, the formation can also be presented as a latent vector. Formation properties can be estimated from formation embeddings instead of well logs.

3.12 Conclusions

In this chapter, shallow and deep machine learning models are applied for the purpose of NMR T2 log synthesis from other logs. Two types of input logs are tested. The shallow and deep models are tuned by grid search on the validation dataset. For deep models, training monitors (early stopping callbacks) are applied to prevent overfitting. The models’ performance is evaluated on the testing dataset in terms of R2 _{values, mean}

square error (MSE), and smoothness. The following conclusions can be drawn from this study:

Deep learning models can be used to generate the NMR T2 distribution responses of the near-wellbore region by processing easy-to-acquire well logs under data constraints.

Bending energy from classical beam theory is used to evaluate the smoothness of NMR T2 generated. Smoothness is the inherent characteristic of NMR T2. Deep models show a good ability to generate NMR T2 with good smoothness. The simple ANN model does not generate NMR T2 with good smoothness.

Models with inverted formation composition logs as input perform better than models with raw logs as input. This is because raw logs contain a lot of highly correlated logs. Inverted formation composition logs are acquired by processing raw logs. Inverted logs do not exhibit high correlations between each other.

For the shallow models, K-neighbors regressor performs best. OLS, LASSO, and ElasticNet models have similar performance. NMR T2 generated by the ANN model is not as smooth as real NMR T2. The smoothness of real NMR T2 is around 1e-5 in terms of bending energy, whereas the NMR T2 generated by ANN is around 1e-3. SVR model has the worst performance in terms of both accuracy and smoothness.

For the deep models, all the four models generate NMR T2 as smooth as real NMR T2 (around 1e-5 in terms of bending energy). On average, the deep model performs better than shallow models on both inverted and raw logs. The R2 of best-performing shallow models is around 0.7. The best performing deep models achieve R2 of 0.75. LSTM and VAE models perform better than VAEc and GAN models. LSTM model takes a longer time (570s) to train, but it performs best among the four models (R2 of 0.75).

The performance of the models is greatly affected by the quality of the data. The models perform better on certain depth because there are not enough data samples that are similar for the models to learn from.

Deep learning models require more data to train, and more time for hyperparameter tuning. GAN does not perform as good as other models because it is hard to tune the generator and discriminator.

Shallow models use much less computational resources compared to the deep models. The NMR T2 generated by shallow models are not as good as deep models in terms of both accuracy and smoothness. Best-performing deep models can generate NMR T2 with R2 of 0.75 and smoothness of (1e-5), which outperforms all shallow models. But the k-neighbors model can generate NMR T2 data with R2 of 0.748 with inverted logs as input.

Chapter 4 Classification of Multipoint Compressional-Wave Travel