Characteristics of displacement fluid fronts - from rapid interfacial jumps to steady capillary flows
Final Report Abstract
The predictions of drainage rates and the spatial and temporal distributions of fluid phases in porous media are of practical interest in many natural and engineering applications. In this project we developed a quantitative framework to predict drainage rates of liquid trapped behind a fast displacing front. For that purpose we simplified the representation of drainage processes in porous media by distinguishing two regions according to the dominant invasion mechanism: (i) a transient region along the displacement front where pores drain rapidly by piston-like invasion events and (ii) a region behind the front with water retained in crevices of the pore space with viscous corner flow. In a first study we expressed the amount of retained liquid as a function of drainage rate at the macroscale using the hydraulic functions of the porous media. To establish a better understanding of the processes at the pore scale, we imaged the liquid arrangement behind the front and could show that the fast draining pores become disconnected at a critical water content. This critical water content for the transition from fast drainage dominated by piston flow to steady water flow along corners is also important for the cessation of solute diffusion and attainment of field capacity and can be predicted using concepts of percolation theory. To predict drainage rates of processes controlled by corner flow we applied the foam drainage equation and established it as an alternative to Richards equation. The dynamics of the foam drainage equation evolve directly from capillary channel cross sectional geometries, linking the scales between pore scale mechanism and macroscopic flow without formulation of unsaturated hydraulic conductivity functions. To assign a representative channel network to a porous medium, we proposed a star shaped pore cross section that reproduces both macroscopic and pore scale properties. We applied the foam drainage formulation to simulate fluxes in homogeneous and heterogeneous media. Studies on transport of colloids and pathogens in crevices of the pore space with foam drainage equation will follow, where the FDE is in advantage compared to macroscopic approaches because it incorporates the corner flow and interfacial geometries that control the mobilization and velocity of such particles.
Publications
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(2012), Characteristics of acoustic emissions induced by fluid front displacement in porous media, Water Resources Research, 48, W11507
Moebius, F., D. Canone, and D. Or
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(2012), Interfacial jumps and pressure bursts during fluid displacement in interacting irregular capillaries, Journal of Colloid and Interface Science, 377, 406–415
Moebius, F., and D. Or
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(2013), The foam drainage equation for unsaturated flow in porous media, Water Resources Research, 49, 6258–6265
Or, D., and S. Assouline
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(2014), Inertial forces affect fluid front displacement dynamics in a pore-throat network model, Physical Review E 90, 023019
Moebius, F., and D. Or
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(2014), Pore scale dynamics underlying the motion of drainage fronts in porous media, Water Resources Research, 50
Moebius, F., and D. Or
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(2015), Natural length scales define the range of applicability of the Richards equation for capillary flows, Water Resources Research, 51, 7130–7144
Or, D., P. Lehmann, and S. Assouline
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(2015), The formation of viscous limited saturation zones behind rapid drainage fronts in porous media, Water Resources Research, 51(12), 9862–9890
Hoogland, F., P. Lehmann, and D. Or
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(2016), Drainage dynamics controlled by corner flow: Application of the foam drainage equation, Water Resources Research 52, 8402–8412
Hoogland, F., P. Lehmann, and D. Or
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(2016), Drainage mechanisms in porous media - from piston-like invasion to formation of corner flow networks, Water Resources Research 52, 8413–8436
Hoogland, F., P. Lehmann, and D. Or
