PREDICTIVE MODELING OF PRODUCTION ALLOCATION IN OIL WELLS USING APPI (+) FT-ICR MS AND MULTIVARIATE APPROACHES

Introduction

Understanding the individual contributions of geological compartments to total oil production is essential for accurate reservoir management, particularly in complex formations (England, 2007). In this study, we focus on a production allocation model for an oil well, where three crude oil samples were collected from different depths corresponding to the two geological formations. Prior studies (unpublished) indicated a lack of vertical fluid connectivity among these compartments, supporting the hypothesis that each one contributes independently to total production. This scenario creates a unique opportunity for compartment-specific modeling, which can guide targeted exploitation strategies.

To support this compartment-specific modeling, high-resolution mass spectrometry was employed to deeply characterize the molecular composition of the crude oil samples. The analytical platform selected was Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), coupled with atmospheric pressure photoionization in positive ion mode (APPI (+)), which enables unparalleled resolution and mass accuracy for detecting and identifying thousands of individual species in crude oil. This molecular-level information was then integrated with multivariate statistical approaches to develop predictive models capable of estimating the relative contribution of each geological compartment in ternary mixtures. The objective of this study was to build a robust and interpretable production allocation model for a specific oil well using ternary mixtures and high-resolution petroleomic data, offering valuable insights for reservoir characterization and production strategy.

 Experimental

Three crude oil samples were collected from a single well at increasing depths, representing two distinct geological formations. Based on prior studies indicating the absence of vertical fluid connectivity between these compartments, the samples were considered as independent sources for production allocation modeling. A total of 67 ternary mixtures were prepared by combining varying mass proportions of the three samples, maintaining a constant total of 100.0 mg of crude oil per mixture. The mixture design was developed to span a wide compositional space, enabling robust model calibration across diverse combinations.

Each mixture was analyzed using a SolariX 7T 2xR FT-ICR MS instrument (Bruker Daltonics, Bremen, Germany), equipped with an APPI source operated in positive ion mode. Mass spectra were acquired across an m/z range of 140 to 1200 and recalibrated using DataAnalysis® 5.0 SR1 (Bruker Daltonics). Molecular formulas were assigned using Composer® 1.5.3 (Sierra Analytics, USA) and the resulting composition tables, containing monoisotopic abundances and assigned molecular formulas, were imported into MATLAB R2024a (The MathWorks, Natick, USA) for multivariate analysis.

To develop a robust and interpretable production allocation model, a two-step chemometric strategy was employed, combining classification and regression techniques. The modeling was carried out using partial least squares (PLS) regression and PLS for discriminant analysis (PLS-DA), both enhanced by variable selection through the ordered predictors selection (OPS) algorithm and its discriminant adaptation (OPSDA) (Roque et al, 2019).

The modeling workflow began with a classification step designed to determine whether each of the three original crude oil sources was present in each mixture. This was addressed through three binary PLS-DA models, (one for each sample) predicting presence or absence based on molecular profiles. Following classification, the second step involved quantitative modeling of the relative contribution of each sample to the mixtures. Instead of using exact percentages, the response variables were discretized into concentration intervals of 10%, creating ten ordinal classes for each source. This approach, known as range-based or interval regression, was adopted to improve model robustness and minimize overfitting, particularly in regions where experimental uncertainty tends to be higher.

The independent variable matrix (X) was preprocessed by mean-centering or autoscaling, and row-wise normalization strategies were tested to optimize model performance. For each model, the number of latent variables was selected using cross-validation with random removal of three samples. The classification models were evaluated using balanced accuracy and precision, while the regression models were assessed using the root mean squared error (RMSE) and correlation coefficient (R) between predicted and reference values.

Results and Discussion

The classification models showed substantial variation in balanced accuracy and precision depending on the molecular variables used. For two of the oil sources (samples 2 and 3), perfect classification performance (balanced accuracy and precision = 1.000) was achieved when using the full variable set, as well as subsets based on HC⁺, N, NO⁺, and S (results not shown). These results indicate that the presence or absence of these two components in the mixtures was identified with high confidence, ensuring consistent and reliable predictions. In contrast, the third source (sample 1) displayed perfect classification performance in a subset based on N₂ radical species. Figure 1 illustrates the classification outputs from the best models. Red dots represent samples belonging to the target class and are positioned above the threshold (dotted line), while blue dots represent other samples. The consistent separation between classes across all three graphs confirms the reliability of the models. In particular, the classification of the second and third oil sources appears especially robust, with predictions clearly exceeding the threshold and minimal misclassification risk.

In quantitative models, the best performance was obtained using the full variable set. The regression models for the second and third oil sources achieved the best predictive accuracy, with Rc values above 0.95 and low RMSEC. The first source yielded a slightly lower Rc and higher RMSEC, suggesting greater variability in prediction. Figure 2 shows the comparison between predicted and reference concentration intervals (10% bins) for each oil source. The dashed diagonal line represents the ideal case where predictions match the reference values, and the red line shows the linear fit. For the majority of samples, predictions fall within the correct interval, confirming the practical accuracy of the models. Better alignment was observed for the second and third sources, while predictions for the first were more scattered, though still largely within the correct range.

The combined results suggest that an optimal allocation strategy would be to use the quantitative models for the two best-performing sources and estimate the third by difference. This approach minimizes the influence of the less reliable model while preserving the accuracy of the production breakdown. Validation with real production data would further enhance model applicability and refine this allocation methodology.

Conclusions

This study demonstrates the effectiveness of integrating high-resolution petroleomic data with chemometric modeling to predict the production allocation among geologically distinct compartments of a single oil well. By combining classification and interval-based regression strategies using PLS, PLS-DA, and OPS variable selection, it was possible to accurately identify the presence and estimate the relative contribution of each crude oil source in ternary mixtures. The use of FT-ICR MS with APPI (+) enabled detailed molecular characterization, which proved essential for building robust predictive models. The results indicate that two of the oil sources can be quantified with high reliability, allowing the third to be inferred by difference. This modeling framework offers a practical and reliable approach for compartment-specific production allocation and can be further refined through application to real production samples in future studies.

Acknowledgements

The authors thank Petrobras for financial support.

References

England, W.A. (2007). Reservoir geochemistry — A reservoir engineering perspective. J. Petrol. Sci. Eng., 58(3–4), 344–354.

Roque, J.V., Cardoso, W., Peternelli, L.A., & Teófilo, R.F. (2019). Comprehensive new approaches for variable selection using ordered predictors selection. Anal. Chim. Acta, 1075, 57–70.