A Dynamic Λ-Based Framework for Subsurface Fluid Systems: Nonlinear Pressure–Resistance Coupling, Numerical Simulation, and Offshore Implications

Version 1.1 (Revised preprint): This version includes structural corrections, improved clarity, refined discussion, and consistent referencing throughout the manuscript. Minor formatting issues have been resolved and the presentation of the Λ-based framework has been strengthened. Subsurface fluid systems are commonly interpreted using static accumulation models based on vertical migration and trapping. However, such approaches fail to capture the dynamic interplay between pressure evolution, geological heterogeneity, and localized migration pathways observed in natural systems. This work introduces a dynamic framework based on a dimensionless parameter Λ, defined as the ratio between fluid pressure and total geological resistance, including mechanical, external, and capillary components. A nonlinear numerical model is developed, coupling pressure diffusion with Λ-dependent permeability, enabling feedback between flow and resistance. Simulation results demonstrate that subsurface systems self-organize into predominantly stable regimes (Λ < 1) with localized instability zones (Λ ≥ 1), corresponding to emergent migration pathways such as chimneys. Under offshore conditions, elevated external pressure suppresses Λ globally while preserving localized high-Λ regions near fluid sources. Unlike classical diffusion models, which predict smooth and spatially uniform pressure distributions, the proposed framework captures nonlinear localization and provides a unified interpretation of pressure evolution, migration dynamics, and stability transitions. The Λ-parameter thus acts as a control variable governing the transition between confined and open-system behavior, with implications for reservoir formation, fluid escape, and subsurface flow prediction. This work introduces a novel Λ-based framework for subsurface fluid dynamics, integrating pressure, resistance, and nonlinear feedback mechanisms into a unified formulation.