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How to share underground reservoirs.

K J Schrenk1, N A M Araújo, H J Herrmann

  • 1Computational Physics for Engineering Materials, IfB , ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland. jschrenk@ethz.ch

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Simultaneously invading porous media with multiple fluids reveals fractal boundaries. These boundaries, crucial for resource sharing, form a complex network with a spanning thread and loop structures.

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Area of Science:

  • Geosciences
  • Physics of complex systems
  • Fluid dynamics in porous media

Background:

  • Resource extraction (oil, gas, water) from porous soils is often a shared endeavor.
  • Understanding the interfaces between different fluid phases is critical for equitable resource partitioning.
  • Previous models often simplify the complex geometry of these interfaces.

Purpose of the Study:

  • To characterize the fractal geometry of simultaneous fluid invasion boundaries in porous media.
  • To quantify the topological and dimensional properties of these complex interfaces.
  • To investigate the scaling laws and critical behavior associated with interface evolution.

Main Methods:

  • Simulated simultaneous invasion of porous media by multiple immiscible fluids.
  • Identification and characterization of the resulting boundary lines using fractal analysis.
  • Statistical analysis of loop size distribution and dimensional analysis of the boundary set.

Main Results:

  • The boundary between three fluid phases forms a fractal set, not simple surfaces.
  • This set comprises a single spanning thread (fractal dimension 1.55 ± 0.03) and a cloud of loops.
  • Loop size distribution follows a power law, and a tricritical point governs the set's evolution.

Conclusions:

  • Simultaneous fluid invasion creates complex, fractal interface structures in porous media.
  • These fractal dimensions and scaling laws provide a new framework for understanding resource partitioning.
  • The identified tricritical point offers insights into the dynamics of multiphase flow and interface formation.