Enhanced Prediction of Reservoir PVT Properties Using Stacking Ensemble Machine Learning Approach

Enhanced Prediction of Reservoir PVT Properties Using Stacking Ensemble Machine Learning Approach

Isemin A. Isemin (1) and Oluwatoyin O. Akinsete (2)

(1) Department of Petroleum Engineering, University of Uyo

(2) Department of Petroleum Engineering, University of Ibadan

Abstract – Pressure-Volume-Temperature (PVT) behaviour plays a significant role in determining reservoir fluid properties in petroleum reservoirs. Experimental data are difficult and expensive to obtain, while physics-based empirically derived equations vary from one region to another. This research proposes a Stacking Ensemble Learning (SEL) model to predict the Pressure-Volume-Temperature (PVT) properties of reservoir fluids, specifically Gas Solubility (Rs) and Bubble Point Pressure (Pb). The study compares this advanced ensemble method against Standalone Machine Learning (SAML) models (Artificial Neural Network, ANN; Support Vector Machine, SVM; and Decision Tree, DT) and traditional empirical correlations. The SEL algorithm was first designed; multiple algorithms were combined to create a stronger predictor. The base estimators used for initial predictions are the Decision Tree Regressor (DTR), the Extra Trees Regressor (ETR), and the Random Forest Regressor (RFR). The base estimators’ predictions were combined using a RidgeCV meta-model to produce the final output. Statistical results on prediction accuracy, model performance, and reliability demonstrate that the Stacking Ensemble technique achieves superior accuracy compared with SAML and widely used empirical correlations, offering a cost-effective alternative to difficult experimental procedures.

Keywords – PVT Properties, Ensemble Learning, Machine Learning, Gas Solubility, Bubble Point Pressure

1.0 INTRODUCTION

Research into PVT studies continues to garner increasing interest in the petroleum industry, as accurate determination and prediction of the fluid properties of oil and gas samples from a flowing well help to understand reservoir fluid behaviour. The determination and accurate description of crude oil properties have been useful in solving reservoir engineering problems, and this is heavily dependent on a good understanding of the crude’s physical properties. Areas where reservoir fluid properties play important roles in reservoir engineering include reserves estimation, well testing, material balance calculations, efficiency of enhanced oil recovery methods, and the prediction of reservoir performance. The importance of accurately estimating PVT properties cannot be overemphasised for engineering calculations and decision-making across the different stages of oil field life (Khabibullin et al., 2014; Dokla et al., 1990). Since comprehensive, consistent, or experimentally measured data are often unavailable, several region-specific, empirically derived PVT correlations have been developed. Research has shown that empirical correlations, aside from being an economical method for reservoir studies and decision-making, can, with varying simplified assumptions, predict fluid properties where experimental information is insufficient, similar to the laboratory PVT method.

Today, advances in technology and the data revolution have consolidated the use of intelligent techniques such as artificial intelligence and machine learning as a fast, accurate, and effective means of prediction. These technologies are now widely accepted in fields such as manufacturing, banking, and several other industries (Brownlee, J., 2019; Hastie et al., 2009; and James et al., 2013).

Ensemble learning methods work by combining functions learned by contributing members, and this approach is applicable to both classification and regression problems. Predictive modelling for classification refers to problems in which a class label is to be predicted; it combines the decision boundaries of the members. Predictive modelling for regression refers to problems involving numerical values to be predicted; i.e., it combines hyperplanes of members. The different types of ensemble machine learning techniques are Bagging, Boosting, and Stacking.

This work aims to develop a predictive model for PVT properties, namely gas solubility and bubble point pressure, using stacked ensemble machine learning. Stacking is an ensemble learning method that combines various estimators to reduce bias and is applicable to both classification and regression. The Stacking technique allows a model to learn how to combine multiple predictions given by weak learner models via meta-learning models and produces a final model with better predictions and high accuracy (Breiman Leo, 1996; Marios Michailidis 2017).

Existing Empirical Correlations

Over the years, several PVT correlations have been developed and used to determine reservoir performance, estimate reserves, and make real-time decisions, among other applications. Standing (1947) correlation has been widely used in PVT analysis, where the pressure of any oil sample is a function of the GOR, oil gravity, gas gravity, and temperature. The correlation utilised 105 data points to develop empirical correlations for determining bubble point pressure, solution GOR, and oil formation volume factor. Lasater (1958) used 158 data points collected in Canada and the Western and Mid-Continental United States to develop an empirical correlation for predicting the bubble-point pressure of black oil. The bubble point pressures were experimentally measured. Vasquez and Beggs (1980) used 600 laboratory PVT data collected from different parts of the world. Glaso (1980) correlations were developed for North Sea Oils from 45 different samples within a 2248 °API range of oil mixtures. Petrosky and Farshad (1993) obtained fluid samples representative of offshore reservoirs in Texas and Louisiana and conducted 81 laboratory analyses to evaluate functional model forms. Al-Marhoun (1988) determined the bubble-point pressure and the oil formation volume factor at the bubble point as functions of temperature, average oil and gas relative densities, and gas solubility for Middle East crude oil. Petrosky and Farshad (1993) introduced fitting parameters in the Standing generalised functional form equation to develop the empirical correlation. De Ghetto et al. (1994) modified existing correlations to develop new ones for heavy oil and extra-heavy oil using PVT crude oil samples obtained from the Mediterranean Basin, Africa, and the Persian Gulf. Obomanu and Okpobiri (1987) developed empirical correlations for Niger Delta crude oil to determine Bo and solution GOR. Ikiensikiimama and Ogboja (2009) developed correlations for determining bubble-point pressure based on the functional form of the Lasater equation. Table 1.0 presents widely used correlations based on samples obtained across different regions. Yacob and Marco (2023) developed a unified PVT model for the Kuwait heavy Oil field.

Table 1.0 Correlation accuracies for Bubble Point Pressure and Gas Solubility

Source: Ikiensikimama and Ogboja, 2008

Application of Machine Learning in PVT Studies

Fatai et al. (2011) used SVM and ANN to predict oil and gas reservoir properties using two datasets from different geographical locations. Chukwuma (2018) compiled a dataset comprising 296 oil and 72 gas reservoirs to estimate PVT properties in the Niger Delta using machine learning models. Uzogor and Akinsete (2020) developed correlations to improve the prediction of PVT properties in the Niger Delta using advanced regression and intelligent techniques, including the KNN and Random Forest algorithms. Oladipo and Johnathan (2020) designed a novel algorithm that, when implemented, can predict PVT properties. Mohammad et al. (2021) developed compatible intelligent models that can estimate oil formation volume factor.

Amjed et al. (2020) used 250 datasets to predict PVT properties using artificial intelligence techniques. Isemin et al. (2022) used a Support Vector Machine (SVM) to predict gas-saturated and gas-undersaturated oil viscosities. While Kassem et al. (2022) used machine learning models to predict PVT properties. Isemin and Akinsete (2024) developed predictive models for PVT properties, namely Bubble Point Pressure and Gas-Oil Ratio, using a Bagging Ensemble.

2.0 METHODS

Data gathering and Processing

The data used in this work were obtained from nine reservoirs in the Niger Delta region of Nigeria and also from published journal articles, a total of 3424 data points. The specific range of data used is shown in Table 2.0 below. There were five input variables and predictors. To predict the target variable, bubble point pressure (pb), the input features are GOR, gas specific gravity, oil specific gravity, API, and temperature. To predict the target variable value GOR, the data input features are bubble point pressure, gas specific gravity, AP gravity, and temperature.

The data was cleaned, normalised, and pre-processed to get high-quality PVT data. The data was split into a training set, validation set, and testing set. Statistical evaluation metrics were used for the analysis of results, such as the correlation coefficient (R2), the root mean squared error (RMSE), the mean absolute error (MAE), and the average absolute percentage relative error (AAPRE), to analyse and compare results of the SEL, the SAML, and some selected existing empirical correlations. All models were built using Python Anaconda version 3.11.5, an interpreted, object-oriented, high-level programming language with dynamic semantics

Table 2.0 – Descriptive statistics of Data range

Model Training

1. Stacking Ensemble Technique

   As shown in Table 3.0, a Stacking ensemble algorithm was designed in this study to predict PVT properties of bubble point pressure and gas solubility, a concept designed by Wolpert David (1991).

   The conceptual idea here is to first combine multiple algorithms to create a stronger predictor. The base estimators used for initial predictions are the Decision Tree Regressor (DTR), the Extra Trees Regressor (ETR), and the Random Forest Regressor (RFR). Next, use a RidgeCV meta-model to combine the base estimators’ predictions into the final output. To implement this method for the stacking algorithm, the data was split into train and test data. The training data was split into n-folds before fitting the individual models on the training set. Afterwards, prediction performance is evaluated on the test set. Furthermore, RidgeCV was used as a meta-model regressor to combine the base estimators via stacking; weights were assigned to the estimators before training RidgeCV on the cross-validated base-case predictions. Finally, the prediction is done for the stacking ensemble.

   Table 3.0 Design of Stacking Ensemble Learning Algorithm

   Stacking Algorithm

   • From the dataset, create multiple samples of n subsets

   • Input: training data = [(, )] =

   • Learn base models DTR, ETR, and RFR representing , ,

   • Output: estimators () for DTR, ETR, and RFR representing

     (), (), ()

   • Learn meta-regressor based on ()

     Predict stacked ensemble, = [(), (), ()]

     For optimal predictions, the two most important hyperparameter tuning parameters were the number of estimators (which specifies the number of models to be built) and the random state (set to 43 to control the random number seed and reproduce the same number at each call for each estimator). Figure 1.0 shows the result of stacking the base estimators using the RidgeCV meta-model. The tuning during the cross-validation search was necessary to identify the best strategy for improved prediction performance.

     Figure 1.0 – Stacking of base estimators

2. Standalone Artificial Neural Network (ANN) Modelling

   The type of artificial neural network was selected before randomly generating the architectures to define the layers, neurons, and activation functions. The model was compiled, then the optimiser, loss function, and metrics were set. The model was trained by adjusting weights (w) and biases (e) using backpropagation. Hyperparameter tuning was performed while also updating the network. The model was fine-tuned, and the evaluation mode was done. The Model was tested on unseen data to assess generalisation performance. Statistical analysis performed using metrics of RMSE and AAPRE. Figure 1.0 shows the ANN modelling framework.

3. Standalone Support Vector Machine (SVM)

   The RBF kernel was chosen due to the data’s complexity. Feature selection was performed for correlation analysis. The SVM model was initialised, and GridSearchCV was used to tune hyperparameters such as C, gamma, an kernel. This was followed by k-fold cross-validation (commonly k=5 or 10) on the training set. The SVM model was trained using the best parameters from the tuning process. The model was tested on unseen data, and predictions were made using the evaluation metrics.

4. Standalone Decision Tree

The decision tree was built by first initialising its parameters, such as max_depth and min_samples_split. The model was trained to fit the decision tree model, and afterwards, a decision tree regression was created on the training data. We conduct hyperparameter tuning using GridSearchCV to find optimal settings like max_depth, min_samples_split, and max_features. Evaluate the model performance using the test set and metrics like MAE, RMSE etc. Make predictions using the tuned and validated model to make predictions on new or test data

3.0 RESULT

Bubble Point Pressure

Shown in Table 4.0 is the statistical analysis of the stacking ensemble machine learning (SEL) and the standalone machine learning models of SVM, ANN, and DT, while Figure 2 depicts the performance evaluation of the SEML, SAML, and widely used empirical correlations for bubble point performance prediction. Stacking of estimators DTR, ETR, and RFR) with a final RidgeCV regressor and the tuning parameters influenced the model prediction performance of SEL with an R2 of 0.9263 when tested on an unseen data set. The next-best-performing model was the SVM, outperforming the best empirical correlation model by Petrosky and Farshad, with a value of 0.8810. Also, in terms of prediction accuracy and reliability, measured by RMSE and AAPRE. The SEL model performed better with an AAPRE of 0.1479, outperforming the best predicted correlation of 0.2166 from Petrosky and Farshad, while the best SAML was 0.2198 from the ANN model.

Table 4.0 Performance evaluation for Bubble Point Pressure using SEL and SAML

R^2 MAE(*10^3) RMSE(*10^3) AAPRE

0.7229

0.8627004

0.6826621

0.2334

0.7715

0.9722217

0.7441109

0.2318

0.7105

0.9742081

0.7486277

0.2401

0.8005

0.9986333

0.7511311

0.2263

0.8810

1.060051

0.7706909

0.2166

0.7417

0.8891172

0.7558001

0.2286

0.8616

0.9224407

0.7720705

0.2216

0.8904

0.8613348

0.67371

0.2198

0.9011

0.8506271

0.63371

0.2216

0.8908

0.8756604

0.64038

0.2203

0.9263

0.3953771

0.6033621

0.1479

Figure 2.0 – Performance evaluation of SEL, SAML, and empirical correlations for bubble point pressure

Gas Solubility

It is important to note that in statistics, the higher the R2, the better the ensemble model will predict. The lower the MAE and RMSE values, the better the prediction accuracy. The AAPRE metric represents the average percentage difference between predicted and actual values and is used to assess model reliability. Table 5.0 presents the statistical analysis of SEL and SAML, while Figure 3.0 shows a representative performance evaluation of SEML, SAML, and widely used empirical correlations. The stacking ensemble performed better at predicting gas solubility, achieving higher R2, lower RMSE, and AAPRE of 0.9521, 279,1145, and 0.1782, respectively. Again, stacking estimators and tuning parameters improved prediction, accuracy, and reliability for the Stacking ensemble. The SVM outperforms other SAML models and existing correlation models.

Table 4.0 Performance evaluation for GOR prediction using SEL and SAML

R^2 MAE(*10^3) RMSE(*10^3) AAPRE

0.8122

0.7252

0.7015101

0.1887

0.7707

1.0850

0.7483228

0.2118

0.8604

0.9281

0.6616903

0.1866

0.8431

0.6444

0.6522884

0.1921

0.8661

1.2719

0.8028804

0.1832

0.8318

1.0803

0.6381119

0.1938

0.8706

0.7443

0.6725508

0.1966

0.8900

0.5225

0.59298

0.1821

0.9000

0.4980

0.59281

0.1746

0.8900

0.6191

0.60244

0.1822

0.9521

0.2791

0.4699525

0.1782

Figure 3.0 – Performance evaluation of SEL, SAML, and empirical correlations for gas oil ratio

Figure 4.0. – Prediction accuracy showing actual values vs predicted values of GOR with Stacking Ensemble technique

4.0 CONCLUSION

This study highlights the potential of Ensemble Learning in petroleum engineering. By stacking “weak” or diverse learners (such as Extra Trees, Decision Trees, and Random Forests) and optimising their combination with a meta-learner (RidgeCV), engineers can achieve higher accuracy in reservoir characterisation without relying on costly lab experiments or region-specific equations.

Bubble Point Pressure

APPENDIX A

=

( + 459.67)

• Standings Correlation

  = (, , , ))

• Vasquez and Beggs

• Modified Standings correlation

  = [ (/p>

  ) 10]

  = 31. 7648 [( )

  0.7857

  100.0009

  100.0148 ]

  • Glaso

= [(

)

0.816

0.172

• ]

  • Lasater

    0.989

  • Ikiensikiimama and Ogboja

    () ( + 10)

    0.989

    ×

    1 0.816

    =

    = (

    0.172 )

    • Obomanu and Okpobiri

      0.927

      2.15

      141.5

      1.27

      Gas Oil Ratio

  • Standing

    1

    100.0125

    =

    0.03008 ( 131.5)

    10.811(1.8 459.67)0.497

    = ((18.2 + 1.4) .

  • Vasquez and Beggs

    100.0091 )

    .

    Machine Learning Models

    • Artificial Neural Network

      = 2 (

      ( ))

      1

      3 + 459.7

      = [ ( + ) + ]

  • Glaso

APPENDIX B

Table A extract from dataset

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32. Competing Interests

33. The authors declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article