Ensemble-Based Interpretation of Inter-Well Tracer Tests for Residual Oil Saturation Estimation Using ESMDA and Fourier Neural Operators

Abstract Partitioning Inter-well Tracer Test (PITT) is a valuable method for determining formation connectivity and remaining oil saturation (Sor ) due to its simplicity and large investigation volume. However, conventional interpretation methods often rely on simplistic assumptions (e.g., homogeneity), which can limit their application and compromise the reliability of the results. To overcome these limitations, our research introduces a novel interpretation workflow built upon the Ensemble Smoother with Multiple Data Assimilation (ESMDA) technique with numerical interpretation. Our approach leverages ESMDA to integrate diverse data types (pressure, production rates, and tracer data) into a unified analysis. This co-assimilation enables the simultaneous calibration of formation permeability and Sor, with each data source providing cross-constraints that enhance overall accuracy. A permeability-weighted Sor is introduced to better quantify recoverable oil. The method was validated first against a full-physics simulation by our in-house simulator UTCHEM and subsequently benchmarked using a deep learning proxy model (FNO) in place of the conventional simulator. The new workflow successfully captures the multi-peak response of the tracer profile caused by formation heterogeneity for both tracers by adjusting the spatial distributions of permeability and Sor with high confidence and minimal uncertainty. The FNO proxy model performed exceptionally well, matching the interpretation quality of the full-physics simulation while dramatically reducing computational time. A key advantage is ESMDA's ability to handle the inherent noise in the DL proxy's output, leading to reliable results. This research provides a significant advancement for PITT analysis by enabling simultaneously calibration of permeability and So, improving accuracy via data fusion, and offering a fast, transferable workflow for modern reservoir characterization and uncertainty analysis.