Space-time fractional diffusion: transient flow to a line source

Nonlocal diffusion to a line source well is addressed by space-time fractional diffusion to model transients governed by both long-range connectivity and distorted flow paths that result in interruptions in the geological medium as a consequence of intercalations, dead ends, etc. The former, superdiffusion, results in long-distance runs and the latter, subdiffusion, in pauses. Both phenomena are quantified through fractional constitutive laws, and two exponents α and β are used to model subdiffusion and superdiffusion, respectively. Consequently, we employ both time and space fractional derivatives. The spatiotemporal evolution of transients in 2D is evaluated numerically and insights on the structure of solutions described through asymptotic solutions are confirmed numerically. Pressure distributions may be classified through two situations (i) wherein 2α = β + 1 in which case solutions may be grouped on the basis of the classical Theis solution, and (ii) wherein 2α ≠ β + 1 in which case conventional expectations do not hold; regardless, at long enough times for the combined case, power-law responses are similar to those for pure subdiffusive flows. Pure superdiffusion on the other hand, although we consider a system that is infinite in its areal extent, interestingly, results in behaviors similar to steady-state flow. To our knowledge, documented behaviors are yet to be reported.

Analytical Modeling of Particle Tracking for Dynamic Pumping Conditions

Movement of fluid particles about historic subsurface releases and through well fields is often governed by dynamic subsurface water levels. Motivations for tracking the movement of fluid particles include tracking the fate of subsurface contaminants and resolving the fate of water stored in subsurface aquifers. Based on superposition of the Theis solution in both space and time, this research explores an analytical solution based on the Theis equation using dynamic pumping well data to resolve how fluid particles move around wells under dynamic pumping conditions. The results provide relatively uniform capture zones for a pumping well. Further, the results show that even under continuous pumping and injection conditions, groundwater will not flow far from the well. Accordingly, groundwater positions can be evaluated based on the research for dynamic pumping. Using the assumptions proposed by the Theis solution, the analytical solution developed in this study provides a simple method to evaluate particle movement in wells used to both store and recover water.

The Theis solution for subdiffusive flow in rocks

The central contribution of this work is the development of a “master” solution similar to the Theis solution to evaluate well responses under subdiffusive flow. Models based on subdiffusion employ fractional constitutive laws, a redefinition of Darcy’s law. Subdiffusive models discussed here are particularly useful to address situations where the internal architecture of the geological medium, such as fluvial and fractured systems, matters and where the existence of topological, geometrical and spatial influences result in distorted flow paths and a loss in connectivity. The developed solution provides the means for addressing these ends.

Stochastic analysis of the hydraulic conductivity estimated for a heterogeneous aquifer via numerical modelling

The paper aims to evaluate the impacts of the average hydraulic conductivity of the heterogeneous aquifer on the estimated hydraulic conductivity using the observations from pumping tests. The results of aquifer tests conducted at a karst aquifer are first introduced. A MODFLOW groundwater flow model was developed to perform numerical pumping tests, and the heterogeneous hydraulic conductivity (K) field was generated using the Monte Carlo method. The K was estimated by the Theis solution for an unconfined aquifer. The effective hydraulic conductivity (Ke) was calculated to represent the hydraulic conductivity of a heterogeneous aquifer. The results of numerical simulations demonstrate that Ke increase with the mean of hydraulic conductivity (EK), and decrease with the coefficient of variation of the hydraulic conductivity (Cv). The impact of spatial variability of K on the estimated Ke at two observation wells with smaller EK is less significant compared to the cases with larger EK.

Drawdown Cone Volume of Pumping Well in Non-Leaky Confined Aquifer

Drawdown cone volume of pumping well reflects the hydro geological conditions of aquifer, such as hydraulic parameters and elastic storage for confined aquifer. During later period of pumping test in non-leaky confined aquifer, the relationship between drawdown and distance appears as straight line in plots figure, and the relationship between drawdown and time appears as straight line in plots figure. Based on Theis solution, through analyzing of the slope of curves , and integrating, volume of drawdown cone of pumping well in non-leaky confined aquifer was derived in this paper.