Abstract
We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In the theoretical framework presented, the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invading structure and its boundary, and the exponent describing the divergence of the correlation length in percolation. Furthermore, our theoretical description explains how the Haines jumps’ local activity and dissipation relate to dissipation on larger scales.
Highlights
Two-phase flow in porous media is crucial in a variety of sectors, ranging from fundamental research to applications in a wide array of industrial sectors such as fuel cell [1] and solar cell technology [2], fiber-reinforced composite materials [3], textile fabric characterization [4], prospection and exploration of oil and gas [5,6,7,8] etc
Let us first assume that the gravitational effect is large enough such that it is the characteristic length scale η that sets the width of the front η < w
We discussed the importance of capillary fluctuations in porous media, as well as the characteristic length scales set by the competition between capillary fluctuations and external fields, gravitational or viscous
Summary
Two-phase flow in porous media is crucial in a variety of sectors, ranging from fundamental research to applications in a wide array of industrial sectors such as fuel cell [1] and solar cell technology [2], fiber-reinforced composite materials [3], textile fabric characterization [4], prospection and exploration of oil and gas [5,6,7,8] etc. As a result, using the distribution function of the capillary pressure fluctuations and performing a bottom-up approach to integrate up the elastic energy released by the bursts, we can check the consistency of our theory as well as FIGURE 1 | Upper figure: A nonwetting fluid 1 invades another wetting fluid 2 in a porous model of width w, length L and coordinate system (x,y). We found as expected that the total elastic energy released by the bursts is equal to the work W 〈p〉ΔV, where 〈p〉 is the average pressure across the model and ΔV is the volume change of the invading fluid corresponding to the interface motion This result provides an important consistency check for the analysis. We further discovered an important analytical result: that the ratios Es/W and Φ/W are both independent of system size
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