Relative permeability as a stationary process: Energy fluctuations in immiscible displacement
نویسندگان
چکیده
Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative relationship from conservation of energy, assuming that system be non-ergodic at large length scales and relying on averaging in both space time homogenize behavior. Explicit criteria are obtained define stationary conditions: (1) there can no net change for extensive measures state over interval; (2) energy inputs into zero, meaning rate work done must balance with heat removed; (3) performed due contribution internal fluctuations. Results then evaluated based direct numerical simulation. Dynamic connectivity observed during steady-state flow, which quantitatively assessed Euler characteristic. We show even low capillary number ([Formula: see text]), typical processes will explore multiple states. The residence each captured time-and-space average. distribution fluctuations shown multi-modal non-Gaussian when terms considered independently. However, demonstrate their sum zero. Given an appropriate choice thermodynamic driving force, conventional sufficient dissipation systems complex pore-scale dynamics routinely alter structure connected pathways.
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ژورنال
عنوان ژورنال: Physics of Fluids
سال: 2022
ISSN: ['1527-2435', '1089-7666', '1070-6631']
DOI: https://doi.org/10.1063/5.0107149