Residual Saturation under Pressure-Controlled Drainage

Fernando Alonso-Marroquin; Hans J. Herrmann

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arXiv · 2608.04748

Residual Saturation under Pressure-Controlled Drainage

Fernando Alonso-Marroquin·Hans J. Herrmann

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Abstract

Here, pressure-controlled drainage is formulated as bond percolation with trapping on the pore-network graph, establishing a direct connection between percolation theory and pressure--saturation relations. In two dimensions, the deviation of the residual saturation from its non-vanishing thermodynamic limit obeys a finite-size scaling law with exponent $\delta \approx 0.25$, independent of microscopic details of the lattice. In three dimensions, finite-size corrections decay more rapidly ($\delta \approx 0.75$), while the asymptotic residual saturation remains finite and depends on coordination number. This extends the standard invasion-percolation picture beyond the breakthrough state, where the invading cluster is fractal and the invaded-phase saturation vanishes in the infinite-size limit.

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Fernando Alonso-Marroquin, Hans J. Herrmann. 2026-08-05. Residual Saturation under Pressure-Controlled Drainage. https://arxiv.org/abs/2608.04748

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