Interfacial jumps and pressure bursts during fluid displacement in interacting irregular capillaries
Graphical abstract
Highlights
► We quantified pore scale pinning–jumping motions of displacement fluid fronts. ► Interfacial jumps are highly inertial exceeding 50 times mean front velocity. ► Waiting times between jumps influence displacement patterns and pressure fluctuations. ► A model of interacting pair of capillaries captures the observed complex dynamics.
Introduction
Fluid displacement processes in porous media are of interest for a wide range of applications from wetting and drying of soils, to building materials, food and paper products, and oil reservoir management. Detailed observations reveal that the macroscopically continuous and seemingly smooth motion of fluid displacement fronts results from numerous interfacial pore scale jumps. Such fast jumps have been known for more than 80 years as “Haines jumps” [1] or rheon [2] and are often dismissed as nothing more than curiosity. These jumps result from local (pore scale) competition between capillary, viscous and gravitational forces, affecting displacement regimes and shaping fluid front morphology (stable displacement, capillary and viscous fingering) [3]. Experimental studies and numerical simulations have established various scaling laws linking front morphology with dominating forces under a range of porous media, fluids and boundary conditions [3], [4], [5].
Most studies of dynamic capillary phenomena associated with pore scale fluid invasion have typically ignored inertia and focused primarily on balancing viscous, capillary and gravitational forces [6]. For certain conditions, additional insights were gained by consideration of inertial forces during capillary rise [7], [8] as elegantly demonstrated by Quere et al. [9], [10], [11] concerning the importance of inertial forces at the onset of interfacial displacement. Realistic account of pore shapes has been studied [12], [13] by linking geometrical parameters such as capillary shape with boundary conditions to deduce flow characteristics in a single irregular capillary. One of the early studies on pressure fluctuations during front displacement through glass beads was presented by Crawford et al. [14]. Nevertheless, with the notable exception of Måløy and coworkers [15], [16], [17], very few attempts have been made to develop a quantitative description of flow details and fluid interactions between neighboring pores along displacement fronts. Måløy and coworkers [15], [16], [17] have analyzed distributions of pressure bursts associated with interfacial pore scale jumps in a simple porous media (monolayer of glass beads). These studies provided new insights on key features characterizing distributions of jump volumes and waiting times deduced from invasion percolation arguments.
Considering the ubiquity of interfacial jumps and their rich dynamic interactions with associated pressure fluctuations and phase entrapment, the consequences of these pore scale processes on macroscopic fluid front behavior, on energy dissipation mechanisms and on phase entrapment remain largely unexplored [18], [19]. Quantification of these processes offers new insights on phase distributions resulting from passage of fluid fronts that greatly shape subsequent macroscopic transport properties such as gaseous diffusion and hydraulic conductivity of partially saturated porous media [18]. Resolving these processes may shed new light on other long-standing questions such as mechanisms associated with hysteresis [19], [20], [21] and the onset of apparent dynamic capillary pressure [22].
The goal of this study was to characterize pore scale dynamics associated with fluid front displacement focusing on interfacial jumps and interactions among hydraulically connected neighboring pores along the front. For the mechanistic modeling of these interactions, we considered the simplest case of a pair of interacting capillaries with irregular cross-section to facilitate systematic yet tractable treatment of interfacial motions and capillary pressure dynamics. In the next section, we present a theoretical framework using force and mass balance between two hydraulically connected irregular capillaries subjected to macroscopic (steady) fluid withdrawal at prescribed rates. The numerical results were supported by experimentally observed interfacial jumps and oscillations in regular sintered glass beads micro-model captured with a high-speed camera and with pressure sensors as described in Section 3. In Section 4, we compare experimental and modeling results, which support application of the model for systematic studies of effects of boundary conditions (flow rate), geometrical dimensions and liquid properties on dynamic behavior of menisci. We then show how physical properties influence displacement patterns and affect characteristics of interfacial oscillations. We summarize and draw conclusions on pore scale interfacial dynamics in the last section.
Section snippets
Theoretical framework
Natural porous media are comprised of complex pore spaces characterized by pore size distribution, porosity and connectivity that collectively determine capillary–saturation relations and permeability. Even for the geometrically simplest porous media (e.g., resulting from cubic packing of spheres), pores are invariably irregular and flow pathways are tortuous. The characteristics of displacement fluid fronts induced by macroscopic pressure gradients or by volume withdrawal at system boundaries
Experimental pore scale observation on interfacial jumps in micro-models
Detailed observations of fluid front displacement processes in sintered glass bead micro-model enabled extraction of some of the salient features taking place at the pore scale during motion of a displacement front. The experimental setup shown in Fig. 2 enabled concurrent imaging of menisci rapid jumps and pressure measurements in the liquid phase. The glass micro-model consisted of a monolayer of sintered glass beads (d = 4 mm) regularly arranged in a Hele-Shaw cell of height 140 mm and width 24
Pore scale interfacial dynamics in a glass micro-model
The highly resolved imaging of displacement front motions revealed pore scale pinning–jumping behavior along the displacement fluid front. The continuous (macroscopic) liquid withdrawal pulls the interfacial front slowly toward the first layer of pore throats where absolute value of capillary pressure increases as interfaces become pinned at pore throats (Fig. 3a and b). As the interfacial contact line becomes unstable (e.g., passes the pore throat), air rapidly invades through the largest
Conclusions
Pore scale interfacial dynamics associated with seemingly continuous motion of fluid fronts in porous media are inherently irregular exhibiting pinning–jumping behavior. Experimental observations provided insights on the characteristics of pore scale velocity jumps and subsequent interfacial oscillations (often indicative of inertial forces). Even during continuous fluid withdrawal from a porous sample, interfaces remain pinned for most of the time followed by abrupt and rapid motion. With
Acknowledgments
The authors gratefully acknowledge funding of project Multi-Scale Interfaces in Unsaturated Soil (MUSIS) by the German Research Foundation DFG (FOR 1083). We thank Daniel Breitenstein for generous assistance with respect to experimental setup, and Peter Lehmann for valuable discussion and his comments on previous versions of the manuscript.
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