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Hierarchical discontinuous Galerkin method for reduced karst conduit-flow in carbonate porous media

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  • Mozolevski, Igor
  • Schuh, Luciane A.
  • Valmorbida, Edson L.
  • Murad, Marcio A.
  • Barroso, Josue

Abstract

We propose an innovative numerical model for single-phase flow in carbonate reservoirs containing karstified layers, characterized by partially enlarged fractures and high-permeability conduits formed through superimposed chemical dissolution along fracture intersections. The computational framework is based on a discontinuous Galerkin (dG) formulation applied to a modified system of mixed-dimensional flow equations, which explicitly incorporates permeability enhancement due to localized fracture enlargement near intersections. The methodology is designed with a hierarchical structure, allowing for a consistent and unified multiscale representation of the porous domain, encompassing 3D flow in the rock matrix, 2D flow within fractures, 1D flow along the partially dissolved conduits, and 0D interaction at fracture-conduit junctions. This formulation proves highly effective in capturing the complex, multidimensional flow dynamics induced by karstification, and in quantifying its influence on flow patterns and production curves. We also provide a rigorous mathematical analysis, establishing well-posedness and convergence in broken Sobolev spaces. A suite of computational experiments is presented to demonstrate the robustness, accuracy, and predictive capabilities of the model when applied to realistic karstified reservoir scenarios.

Suggested Citation

  • Mozolevski, Igor & Schuh, Luciane A. & Valmorbida, Edson L. & Murad, Marcio A. & Barroso, Josue, 2026. "Hierarchical discontinuous Galerkin method for reduced karst conduit-flow in carbonate porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 440-474.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:440-474
    DOI: 10.1016/j.matcom.2026.04.015
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    References listed on IDEAS

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    1. Mozolevski, Igor & Murad, Marcio A. & Schuh, Luciane A., 2021. "High order discontinuous Galerkin method for reduced flow models in fractured porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1317-1341.
    2. Rau, Greg H. & Knauss, Kevin G. & Langer, William H. & Caldeira, Ken, 2007. "Reducing energy-related CO2 emissions using accelerated weathering of limestone," Energy, Elsevier, vol. 32(8), pages 1471-1477.
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