Fluctuation-dissipation theorems for multi-phase flow with memory in porous media

TL;DR

This paper develops a theoretical framework based on fluctuation-dissipation theorems with memory effects to describe and analyze the complex resonance phenomena in multiphase flow through porous media, supported by experimental data.

Contribution

It introduces a novel fluctuation-dissipation theory incorporating memory effects and multipeak Lorentzian functions for multiphase flow, enabling new insights into relaxation and resonance behaviors.

Findings

Multiple Lorentzian peaks observed in autocorrelation Fourier transforms.

Resonance frequencies similar to electric conductance phenomena.

New method for steady-state permeability measurement using fluctuation analysis.

Abstract

Recent works have reported on the collective behavior of multiphase systems under fractional flow. Such behavior has been linked to pressure and/or flux fluctuations under stationary flow conditions that occur over a broad range of resonance frequencies and associated relaxation times. However, there currently exists no theoretical development to deal with such phenomena. The aim of this paper is to develop a fundamental theory that can describe such behavior. Fluctuation-dissipation theorems for the case with memory are formulated, providing a new route to obtain frequency-dependent porous media permeability. We propose that multiphase flow systems can be explained by a multipeak Lorentzian memory function and provide supporting experimental data from the flow of decane and water in a porous medium made of glass beads. Our fluctuation dissipation theorems provide information on different types of relaxation phenomena and resonance frequencies that occur during fractional flow. We show, using experimental data, that Green-Kubo-like expressions can be formulated for two-phase fluid flow driven by a constant pressure drop. The resulting autocorrelation functions, or rather their Fourier transforms, exhibit multiple Lorentzian peak shapes. Resonances are similar to those of electric conductance. The analysis offers a new route to steady-state relative permeability measurements, including information on the relaxation times and resonance regimes that exist during fractional flow. Overall, the theory presented and supported by fractional flow experiments provides a rich set of possible directions for future developments that could fundamentally change the way multiphase flow systems are understood and studied.