Self organized spatio‐temporal structure within the fractured Vadose Zone: The influence of dynamic overloading at fracture intersections

Abstract

Under low flow conditions (where gravity and capillary forces dominate) within an unsaturated fracture network, fracture intersections act as capillary barriers to integrate flow from above and then release it as a pulse below. Water exiting a fracture intersection is often thought to enter the single connected fracture with the lowest invasion pressure. When the accumulated volume varies between intersections, the smaller volume intersections can be overloaded to cause all of the available fractures exiting an intersection to flow. We included the dynamic overloading process at fracture intersections within our previously discussed model where intersections were modeled as tipping buckets connected within a two‐dimensional diamond lattice. With dynamic overloading, the flow behavior transitioned smoothly from diverging to converging flow with increasing overload parameter, as a consequence of a heterogeneous field, and they impose a dynamic structure where additional pathways activate or deactivate in time.

Influence of fracture intersections under unsaturated, low‐flow conditions

“…Their results suggest that the presence of intersections that switch between outlets will work against large‐scale convergence of flow and contribute toward the formation of a self‐organized state characterized by fluid avalanches across a wide range of scales. The same authors also used numerical means to explore the potential effects of flow path splitting in response to convergence [ LaViolette and Glass , 2004]. Overloading of intersections along pathways was found to lead to splitting and the activation of new pathways.…”

Self-Organized Network of Chemical Reactions: A Model of Contaminated Converging and Diverging Flows in Fractured Media

“…Here, we studied a model of the degradation of contaminants continually introduced into a driven flow in fractured nonporous unsaturated media, combined with a dynamic population of microbial degradation sites. This model is the “tipping bucket model” (TBM), introduced in refs and . The TBM is a variant of the scale-free “sandpile” model of self-organized criticality .…”

“…Of the large effort and literature on this problem, the following recent work on models ,,, and experiments − dealing with fracture flows, and on models 2,3 and experiments ,− of microbial degradation in the subsurface, provides a context for this study. There is such a wide variety of biogeochemical scenarios in which biodegradation can occur that we ask, “To what extent can scale-free generalizations about such processes can be drawn?” With this question in mind, we present here a simple (possibly the simplest) model of the complicated (and possibly complex) biodegradation scenario in fractured media.…”

“…Description of the “Tipping Bucket” Model for the Fracture Flow. The “tipping bucket model” (TBM) is a cellular automaton similar to the generic directed “sandpile” model ,, but with the added complications of stochastic singly directed flow and dynamic overloading. , The TBM idealizes the fracture network as a regular, two-dimensional array of intersections arranged on a diamond lattice (Figure ). Here, we implemented periodic boundary conditions along the vertical edges of the network of 50 (horizontal) × 1000 (vertical) buckets.…”

“…In ref all of the thresholds were set equal to 10, but in ref the added realism of spatially (but not temporally) variable bucket thresholds within the network was found to be useful, so we employ the same distribution here. The θ j here were assigned to each bucket (to remain fixed thereafter), without spatial correlation, by randomly sampling from the Fréchet distribution f , that is, for θ ≥ 0, This unimodal distribution is a member of the “generalized extreme value” family of distributions and happens also to possess convenient scaling properties.…”