172 research outputs found
A continuous time random walk model of transport in variably saturated heterogeneous porous media
We propose a unified physical framework for transport in variably saturated
porous media. This approach allows fluid flow and solute migration to be
treated as ensemble averages of fluid and solute particles, respectively. We
consider the cases of homogeneous and heterogeneous porous materials. Within a
fractal mobile-immobile (MIM) continuous time random walk framework, the
heterogeneity will be characterized by algebraically decaying particle
retention-times. We derive the corresponding (nonlinear) continuum limit
partial differential equations and we compare their solutions to Monte Carlo
simulation results. The proposed methodology is fairly general and can be used
to track fluid and solutes particles trajectories, for a variety of initial and
boundary conditions.Comment: 12 pages, 9 figure
Recommended from our members
Continuous time random walk analysis of solute transport in fractured porous media
The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable interconnected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the 'correct' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains
Pre-asymptotic corrections to fractional diffusion equations
The motion of contaminant particles through complex environments such as
fractured rocks or porous sediments is often characterized by anomalous
diffusion: the spread of the transported quantity is found to grow sublinearly
in time due to the presence of obstacles which hinder particle migration. The
asymptotic behavior of these systems is usually well described by fractional
diffusion, which provides an elegant and unified framework for modeling
anomalous transport. We show that pre-asymptotic corrections to fractional
diffusion might become relevant, depending on the microscopic dynamics of the
particles. To incorporate these effects, we derive a modified transport
equation and validate its effectiveness by a Monte Carlo simulation.Comment: 6 pages, 3 figure
A model of dispersive transport across sharp interfaces between porous materials
Recent laboratory experiments on solute migration in composite porous columns
have shown an asymmetry in the solute arrival time upon reversal of the flow
direction, which is not explained by current paradigms of transport. In this
work, we propose a definition for the solute flux across sharp interfaces and
explore the underlying microscopic particle dynamics by applying Monte Carlo
simulation. Our results are consistent with previous experimental findings and
explain the observed transport asymmetry. An interpretation of the proposed
physical mechanism in terms of a flux rectification is also provided. The
approach is quite general and can be extended to other situations involving
transport across sharp interfaces.Comment: 4 pages, 4 figure
Structural analysis of the double-walled copper-steel cryogenic chamber of the ASTAROTH experiment
This document describes the verification process of structural performance of the double- walled copper-steel cryogenic chamber of the ASTAROTH (All Sensitive crysTal ARray with lOw THreshold) experiment and the evaluation of the stresses generated near the thermal bridge connecting the inner and outer wall. The chamber consists of an external AISI 316L stainless steel dewar and an inner double-walled OF (Oxygen Free) copper dewar connected to an AISI 316L stainless steel flanged collar. The results showed that close to the thermal bridge (copper-steel junction) the stresses slightly exceed the YS of copper at the estimated operating temperature (localised strain-hardening condition). On the other hand, the safety coefficient respect to fracture is well above one for both materials. This condition, together with the fact that limited cooling cycles are expected during the operating life of the system, leads to the assumption that a progressive material hardening will occur in this area, thus locally raising the YS limit
- …