Forced air and water flow in porous media &#8211; Dynamics, Saturation degree, and phase distribution
Authors: Ben-Noah Ilan , P. Friedman Shmulik , Berkowitz Brian , J. Hidalgo Juan , Dentz Marco 
Published: March 2022

&lt;p&gt;Air saturation degree and flow pattern significantly affect physical, biological, and chemical processes in natural and industrial multiphase systems. However, despite long-standing and current research of multiphase flow, the predictive capabilities in conditions where unstable flow patterns prevail and their consequence on the phase distribution remain extremely limited.&lt;/p&gt;&lt;p&gt;We demonstrate the strong coupling between flow dynamics and phase saturation by analyzing experimental data of steady air injection into background (initially) saturated granular media. Next, we evaluate, using image analysis of recent multiphase experiments in microfluidic devices, the decoupled effect of the saturation degree on the micro-scale distribution of the phases.&lt;/p&gt;&lt;p&gt;We present a simple evaluation of the effects of the steady air flow velocity and of the media&amp;#8217;s grain diameter on the macroscale air saturation degree. Using only two variables, one for the matrix (grain diameter) and one for the flow (air velocity), for estimating the air (and water) saturation degree seems to be an oversimplification, especially if one considers the complexity of the two-phase flow problem and the differences between flow patterns and geometries. Nevertheless, the suggested power-law model explains about 90% of the value of the phase saturation across a wide range of saturation degrees and different flow patterns and geometries. Moreover, analysis of this data set reveals a positive effect of both flow velocity and grain diameter on the air saturation degree. Using dimensional analysis, we conclude that viscous and buoyancy forces increase air saturation while capillary forces decrease the saturation degree. Our findings also suggest a significant effect of inertial forces on air saturation in coarse granular media (glass beads). The effect of phase saturation on the flow pattern is significant as deduced from the two extremum conditions of continuum air flow in dry media and predominant unstable flow in initially water-saturated media. However, the effects of the air saturation and flow dynamics cannot be easily evaluated as these are strongly correlated. Recent experimental studies of nearly simultaneous steady air and water injection into microfluidic devices allow a morphological analysis of the phase distribution (e.g., water-filled pore size distribution, coordination number distribution), decoupled from the flow dynamics, i.e., for different saturation degrees of the same capillary number and vice-versa.&lt;/p&gt;&lt;p&gt;Quantifying the impact of macroscale phase saturation and flow dynamics on microscale phase distribution will enable a better prediction of the flow patterns (at the different scales), the local flow velocity distribution, and the effective hydraulic characteristics of the media. In this context, this work, for example, can refine Buckingham&amp;#8217;s &amp;#8220;law&amp;#8221; for different capillary equilibrium conditions.&lt;/p&gt;