Explaining the Performance Hierarchy of Linear Regression, Support Vector Regression, and Random Forest on Physics-Generated PVT Data: A Real-Gas-Law and Gauss-Markov Perspective

Machine learning (ML) regression models are increasingly proposed as fast surrogates for deterministic Pressure-Volume-Temperature (PVT) simulation in reservoir and production engineering, yet the choice among competing algorithms is rarely justified on physical or statistical grounds. This study trains, evaluates, and compares three regression algorithms, Linear Regression (LR), Support Vector Regression (SVR), and Random Forest Regression (RF), on a PVT dataset generated from an industry-standard Integrated Production Modelling (IPM) software platform (PROSPER) using the Glaso correlation for a representative mature onshore Niger Delta oil well. Gas density was predicted from pressure and associated fluid properties across a depletion range of 1000 - 3500 psig. Following a structured preprocessing pipeline (exploratory data analysis, Isolation Forest anomaly removal, Min-Max normalization, K-means regime clustering, and time-series smoothing), the three algorithms were trained on an 80:20 split and evaluated using Root Mean Squared Error (RMSE) and the coefficient of determination (R²). Linear Regression achieved the highest accuracy (R² = 0.9954, RMSE = 0.2240 lb/ft³), followed by SVR (R² = 0.9408, RMSE = 0.8042 lb/ft³) and Random Forest (R² = 0.8389, RMSE = 1.4326 lb/ft³). Physically consistent extrapolation beyond the training range (correctly predicting monotonically increasing gas density at 4000 and 5000 psig) confirmed that the Linear Regression model had captured the governing thermodynamic relationship rather than an artefact of the training data. We show that this performance hierarchy is not an empirical coincidence but a direct, predictable consequence of two established results: the real gas law, which imposes a near-linear pressure-density relationship (Pearson r = 1.00) at approximately constant reservoir temperature, and the Gauss-Markov theorem, which guarantees that Ordinary Least Squares is the best linear unbiased estimator when the true relationship is linear. A bias-variance decomposition further explains why SVR’s kernel mismatch and Random Forest’s piecewise-constant approximation both add prediction variance without a compensating reduction in bias on this near-linear, physics-generated data. These findings provide petroleum engineers and applied ML practitioners with a principled, physics-grounded criterion for algorithm selection when training data are generated from simulator-based PVT correlations, rather than defaulting to the most