Prediction of fracture and vug parameters in carbonate reservoirs using a combined T-GNO-PINN approach

Abstract

To address the challenges of fracture-vuggy parameter prediction in carbonate reservoirs, such as strong multi-scale heterogeneity and a lack of physical constraints, this study proposed a Transformer-Graph Neural Operator (GNO)-Physics-Informed Neural Network (PINN) joint prediction framework, which achieves a bidirectional coupling between multi-source data fusion and physical laws. First, a Transformer module with a multi-scale attention mechanism and spherical coordinate effectively captures cross-scale spatiotemporal features in three-dimensional geological space (reducing error by 12.3%). Second, a dynamic GNO based on physical similarity adaptively tracks the evolution of fracture-vuggy connectivity (achieving a topology update accuracy of 93.5%). Finally, a PINN module embedded in the seepage-mechanical coupling equations constrains the physical residual loss to the order of 0.42×10⁻3, reducing the conservation error from 3.17% to 0.48%. In an empirical study of Ordovician fracture-vuggy reservoirs in the Tarim Basin, this framework achieved a mean absolute error of 3.57% and an R2 of 0.90 for fracture-vuggy volume fraction (Vf). In high-pressure gradient regions (>5 MPa/m), the relative error was reduced by 18%, significantly outperforming traditional methods(reducing Kriging error by 40.7%) and single-module models (PINN error reduction of 15.3%). Experimental results showed that dynamic graph construction increased the spatial autocorrelation index (Moran’s I) to 0.71; the introduction of physical constraints reduced extreme error samples by 63%; and the multimodal collaborative training strategy resulted in a 19.7% improvement in overall performance. This research provides a new paradigm for high-precision and physically interpretable digital twin modeling of carbonate reservoirs.

Keywords

Carbonate reservoir / Fracture-vuggy parameter prediction / Transformer / Graph Neural Operator / Physical Information Neural Network / Multimodal fusion

Acknowledgments

None.

Funding

This research was financially supported by 2025 Doctoral Special Support Program Project of Chengdu Jincheng College (NO.2025JCKY(B)0018); the Key Research Base of Humanities and Social Sciences of the Education Department of Sichuan Province, Panzhihua University, Resource based City Development Research Center Project (NO.ZYZX-YB-2404); Mahasarakham University; and the Open Fund of Sichuan Oil and Gas Development Research Center (NO.2024SY017).

Conflict of interest

The authors declare that they have no competing interests.

Author contributions

Conceptualization: Tianwen Zhao, Guoqing Chen, Cong Pang, Yiru Du

Formal analysis: Tianwen Zhao, Guoqing Chen, Cong Pang

Funding acquisition: Tianwen Zhao, Guoqing Chen, Cong Pang

Investigation: Tianwen Zhao, Cong Pang, Yiru Du

Methodology: Tianwen Zhao, Guoqing Chen, Yiru Du

Visualization: Tianwen Zhao, Cong Pang, Yiru Du

Writing-original draft: Tianwen Zhao, Guoqing Chen, Yiru Du

Writing-review & editing: Tianwen Zhao, Guoqing Chen, Cong Pang, Yiru Du

Availability of data

Some data used in this study cannot be shared publicly due to collaborative agreement restrictions, but are available from the corresponding author upon reasonable request.

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