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Continuous streamline trajectories on complex grids

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Abstract

Streamlines have been used for reservoir modeling and flow visualization in the petroleum industry and in computational fluid dynamics. When applied to the calculation of volumetric sweep and the identification of by-passed hydrocarbons for improved oil recovery, it is important that the velocity models that are used to trace trajectories across the cells of a grid are flux conservative. As such, the requirements on their tracing may be more stringent than in other disciplines. Flux conservation is also important at faults, at locally refined or coarsened embedded grid boundaries, and within unstructured grids, where the modeling of flow within a cell may not be consistent with the connection fluxes from adjacent cells. In such cases, additional degrees of freedom must be introduced to satisfy flux conservation. In this study, we introduce a flux conservative conforming cell face local boundary layer construction to resolve these inconsistencies. In contrast, solutions that rely upon spatial continuity of streamlines between elements are shown to not be flux conservative when these inconsistencies are present. The use of flux conservative conforming elements also allows the solution to be developed in local isoparametric coordinates, without explicit reference to cell or connection geometry. The solution has been implemented for both 3D corner point and for 2.5D PEBI grids. In all cases we utilize the lowest order Raviart–Thomas zeroth order velocity model, for which the trajectories and transit times may be obtained analytically. The results are demonstrated on a sequence of increasingly complex type, sector and full-field model applications.

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Acknowledgements

We would like to thank members of the Texas A&M University MCERI (Model Calibration and Efficient Reservoir Imaging) Joint Industry Project for their financial support. We also acknowledge the support of Schlumberger, Dynamic Graphics and the Computer Modelling Group for the use of their reservoir modeling software.

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Authors and Affiliations

  1. Texas A&M University-Kingsville, Kingsville, TX, USA

    Lihua Zuo

  2. SmartMind, Inc., Seoul, South Korea

    Jungtek Lim

  3. Texas A&M University, College Station, TX, USA

    Rongqiang Chen, Hongquan Chen & Michael J. King

  4. Computer Modelling Group, Calgary, Canada

    Abazar Shamekhi

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  1. Lihua Zuo
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  2. Jungtek Lim
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  6. Michael J. King
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Correspondence to Lihua Zuo.

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Zuo, L., Lim, J., Chen, R. et al. Continuous streamline trajectories on complex grids. Comput Geosci 25, 1539–1563 (2021). https://doi.org/10.1007/s10596-021-10056-z

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