Drainage in a model stratified porous medium

We show that when a non-wetting fluid drains a stratified porous medium at sufficiently small capillary numbers Ca, it flows only through the coarsest stratum of the medium; by contrast, above a threshold Ca, the non-wetting fluid is also forced laterally, into part of the adjacent, finer strata. The spatial extent of this partial invasion increases with Ca. We quantitatively understand this behavior by balancing the stratum-scale viscous pressure driving the flow with the capillary pressure required to invade individual pores. Because geological formations are frequently stratified, we anticipate that our results will be relevant to a number of important applications, including understanding oil migration, preventing groundwater contamination, and sub-surface CO2 storage. Copyright c © EPLA, 2013 Introduction. – Drainage, the displacement of a wetting fluid from a porous medium by an immiscible non-wetting fluid, arises in many technological problems, including oil migration and recovery [1,2], waste CO2 sequestration [3–6], and groundwater contamination [7–9]. The ability to accurately predict the flow behavior of the non-wetting fluid is critically important in all of these examples. To displace the wetting fluid from a pore, a threshold capillary pressure must build up in the nonwetting fluid at the pore entrance; this pressure is given by Pγ ∼ γ/at, where γ is the interfacial tension between the fluids and at is the radius of the pore entrance [10–12]. For a homogeneous porous medium, characterized by pores of a single average size, Pγ is typically much larger than the viscous pressure associated with flow into a pore. Consequently, the flow path taken during drainage depends primarily on the slight pore-scale variations of at [13–17]. However, many porous media are stratified, consisting of parallel strata characterized by different average pore sizes [18–20]. Such additional variation in the pore structure, on scales much larger than a single pore, may strongly modify the flow behavior [16,21–29]. Despite its enormous practical importance, a clear picture of how the subtle interplay between capillary and viscous forces determines the flow through a three-dimensional (3D) stratified porous medium remains elusive. This requires direct visualization of the multiphase flow, both at the scale of the individual pores and the overall strata. Unfortunately, the medium opacity typically precludes such visualization. As a result, knowledge of how exactly drainage proceeds within a stratified porous medium is missing. Here, we use confocal microscopy to investigate drainage within a 3D porous medium having parallel strata oriented along the flow direction; this allows us to directly visualize the multiphase flow at pore-scale resolution. We find that for sufficiently small capillary numbers, Ca, the nonwetting fluid flows only through the coarsest stratum of the medium. By contrast, above a threshold Ca, the non-wetting fluid is also forced laterally into part of the adjacent, finer strata. By balancing the viscous pressure driving the flow with the capillary pressure required to invade a pore, we show how both the threshold Ca and the spatial extent of the invasion depend on the pore sizes, cross-sectional areas, lengths, and relative positions of the strata. Our results thus help elucidate how the path taken by the non-wetting fluid is altered by stratification in a 3D porous medium. Experimental methodology. – We prepare rigid 3D porous media by lightly sintering densely-packed hydrophilic glass beads, with polydispersity ≈ 4%, in thin-walled rectangular quartz capillaries; these have cross-sectional areas A= 1, 3, or 4mm. The packings have porosity φ≈ 0.41, as measured with confocal microscopy [10]. To create stratified porous media, we arrange the beads into parallel strata characterized by different bead sizes and the same length L; the interface