Table 1 Advantages and disadvantages of previous employed methods.

From: Enhanced machine learning—ensemble method for estimation of oil formation volume factor at reservoir conditions

Methods

Advantages

Disadvantages

Corrolations3,14,18,19,20

(1) Simplicity Correlations are often simple mathematical expressions that can be easily implemented and used without requiring complex calculations

(2) Quick calculations Correlations are typically computationally efficient, allowing for fast calculations and analysis

(3) Data availability Correlations are often developed based on large datasets and extensive experimental measurements, making them readily available for use

(1) Limited accuracy Correlations are empirical relationships derived from experimental data. As a result, they may not accurately capture the complex physics and fluid behavior of oil systems in all cases, leading to inaccuracies in predicting the Bo

(2) Applicability limitations Correlations are usually developed for specific ranges of temperature, pressure, and fluid composition. Extrapolating their use beyond these ranges may lead to unreliable results

(3) Lack of customization Correlations are general relationships that do not account for specific characteristics of a particular reservoir. They may not capture reservoir specific effects and variations, potentially leading to inaccuracies in Bo predictions

Equations of State21

(1) Thermodynamic consistency EOS provides a rigorous and thermodynamically consistent approach to model the behavior of fluids. They can handle a wide range of temperature, pressure, and fluid compositions, making them applicable to various reservoir conditions

(2) Accuracy EOS can offer higher accuracy compared to correlations when properly calibrated and parameterized. They consider the intermolecular interactions and phase behavior of the fluid, providing more detailed predictions

(3) Customization EOS can be customized and adjusted to match the specific characteristics of a particular reservoir. This allows for a more accurate representation of the fluid behavior and can improve Bo predictions

(1) Complexity EOS calculations are more complex and computationally demanding compared to correlations. They often require extensive fluid characterization and parameterization, which can be time-consuming and data-intensive

(2) Parameter uncertainty Accurate parameter estimation and calibration are crucial for EOS models. Obtaining reliable and accurate parameters may require additional experimental data, and uncertainties in the parameters can impact the accuracy of the Bo predictions

(3) Implementation challenges Proper implementation and usage of EOS models may require specialized software and expertise in fluid thermodynamics, which can pose challenges for some users

Nueral network4,21,22,23,24,27,29,30,32

(1) Nonlinearity Neural networks are capable of modeling nonlinear relationships in data, allowing them to capture complex patterns and make more accurate predictions

(2) Feature learning Neural networks can automatically learn relevant features from raw data, reducing the need for manual feature engineering

(3) Adaptability Neural networks can adapt and learn from new data, making them suitable for tasks where the underlying patterns or relationships change over time

(1) Training complexity Neural networks often require a large amount of training data and significant computational resources to train properly

(2) Black-box nature Neural networks are often considered black-box models, making it challenging to interpret and understand the inner workings of the model

(3) Overfitting Neural networks, especially with a large number of parameters, are prone to overfitting if not properly regularized or if the training data is limited or noisy

(4) Computational cost Training and running neural networks can be computationally expensive, especially for deep architectures with numerous layers

Traditional machine learning21,24,25,29,33,35

(1) Simplicity Traditional machine learning algorithms are often simpler to understand and interpret compared to complex models like neural networks

(2) Interpretability Traditional machine learning algorithms often provide transparent and interpretable models, allowing users to understand the factors driving the predictions

(3) Well-established theory Traditional machine learning algorithms are based on well-established statistical and mathematical principles, allowing for a better understanding of their behavior

(1) Limited capacity for complex patterns Traditional machine learning algorithms may struggle to capture highly complex patterns in data, particularly those involving nonlinearity or high-dimensional relationships

(2) Feature engineering Traditional machine learning algorithms often require manual feature engineering, where domain knowledge is needed to select relevant features and design appropriate representations

(3) Limited scalability Some traditional machine learning algorithms may have limitations in handling large datasets or datasets with high-dimensional features

(4) Sensitivity to input data Traditional machine learning algorithms may be sensitive to the quality and distribution of input data, which can affect their performance

Ensemble machine learning21,29

(1) Improved accuracy Ensemble methods combine multiple models, reducing bias and variance which leads to improved overall predictive accuracy

(2) Robustness Ensemble methods can be more robust to outliers and noise in the data, as the combined predictions can mitigate the impact of individual model errors

(3) Generalization Ensemble methods can capture a wider range of patterns and relationships in the data, enhancing their generalization capabilities

(4) Model diversity Ensemble methods incorporate diverse models, leveraging different perspectives and reducing the risk of model limitations

(1) Lack of transparency Ensemble models can be less transparent and harder to interpret compared to single models, making it challenging to understand the underlying decision-making process