Flow-induced channelization in a porous medium

Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement, and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed with bidisperse grains. When the local flow-induced stress exceeds a critical threshold, the smaller grains are dislodged and transported. This changes the porosity of the medium, thence, the local hydraulic conductivity, and leads to the development of erosional channels. Erosion is ultimately arrested due to the drop in the mean pressure gradient, while most of the flow occurs through the channels. We describe this using a minimal multiphase description of erosion where the volume fraction of the fluid, mobile, and immobile, grains change in space and time. Numerical solutions of the resulting initial boundary value problem yield results for the dynamics and morphology that are in qualitative agreement with our experiments. In addition to providing a basis for channelization in porous media, our study highlights how heterogeneity in porous media may arise from flow as a function of the erosion threshold. Copyright c © EPLA, 2012 The dynamics of fluid flow through porous continua is relevant over many orders of magnitude in length scale with applications that range from large-scale flow through fractured rock in aquifers and oil reservoirs to small-scale flows in natural and artificially engineered systems [1,2]. In all these cases, flows are characterized by large variations in hydraulic conductivity of the medium. This heterogeneity is usually ascribed to processes associated with the formation and consolidation of the porous medium via the agglomeration of grains (in geology) and cells (in biology). But heterogeneity and channelization may also arise due to selective erosion of material in non-cohesive porous media. Indeed, flow-induced erosion, on the surface of, and, in the bulk of porous media has been implicated in the formation of patterns on planetary [3,4], littoral [5], river-bank [6] and laboratory [7,8] scales that involve both unconsolidated and consolidated media [9–13]. Dissolution and liquefaction can also arise from reactive instabilities as seen in melt migration [14,15] and cave formation [16]. Here we explore the purely physical erosive instabilities occurring in the bulk of fluid saturated materials which (a)E-mail: [email protected] can lead to internal channelization via the dynamic coupling of flow and changes in hydraulic conductivity. We start by describing some experiments that demonstrate how erosion and channelization can occur in a saturated porous medium (see Movie1 1.mov in the supplementary information). The experiments were carried out in a fluid-saturated porous medium confined to a vertical quasi–two-dimensional chamber based on a Hele-Shaw cell filled with bidisperse mixture of glass beads as shown in fig. 1(A). The width between the walls of the apparatus is such that gravity is unimportant owing to the formation of arches between walls [17]. As our porous medium, we use a mixture of beads; 60% of the initial volume has large beads (diameter d1 = 4± 0.1mm) and 24% has small beads (d2 = 0.7± 0.1mm). The width of the chamber, chosen to be 1.2× d1, enables visualization of the porosity pattern, and allows the larger beads to be rearranged locally without being transported by the flow, while the smaller beads can be dislodged and transported through the matrix of large beads. Since only the smaller beads can be eroded, we scale the porosity by the maximum attainable absolute porosity, 0.4, so that the scaled porosity or liquid volume fraction φl ∈ [0, 1]. To observe