Model reduction of stochastic groundwater flow and transport processes

This work presents a comprehensive methodology for the reduction of analytical or numerical stochastic models characterized by uncertain input parameters or boundary conditions. The technique, based on the Polynomial Chaos Expansion (PCE) theory, represents a versatile solution to solve direct or inverse problems related to propagation of uncertainty. The potentiality of the methodology is assessed investigating different applicative contexts related to groundwater flow and transport scenarios, such as global sensitivity analysis, risk analysis and model calibration. This is achieved by implementing a numerical code, developed in the MATLAB environment, presented here in its main features and tested with literature examples. The procedure has been conceived under flexibility and efficiency criteria in order to ensure its adaptability to different fields of engineering; it has been applied to different case studies related to flow and transport in porous media. Each application is associated with innovative elements such as (i) new analytical formulations describing motion and displacement of non-Newtonian fluids in porous media, (ii) application of global sensitivity analysis to a high-complexity numerical model inspired by a real case of risk of radionuclide migration in the subsurface environment, and (iii) development of a novel sensitivity-based strategy for parameter calibration and experiment design in laboratory scale tracer transport

PROPAGATION OF GRAVITY CURRENTS OF NON-NEWTONIAN POWER-LAW FLUIDS IN POROUS MEDIA

A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by ; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, ; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters  and . Scalings for current length and thickness are derived in self similar form coupling the modified Darcy’s law accounting for the fluid rheology with the mass balance equation. The speed, thickness, and aspect ratio of the current are studied as a function of model parameters; several different critical values of  emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times

Porous gravity currents: A survey to determine the joint influence of fluid rheology and variations of medium properties

We develop a model to grasp the combined effect of rheology and spatial stratifications on two- dimensional non-Newtonian gravity-driven flow in porous media. We consider a power-law constitutive equation for the fluid, and a monomial variation of permeability and porosity along the vertical direction (transverse to the flow) or horizontal direction (parallel to the flow). Under these assumptions, similar- ity solutions are derived in semi-analytical form for thin gravity currents injected into a two-dimensional porous medium and having constant or time-varying volume. The extent and shape of the porous domain affected by the injection is significantly influenced by the interplay of model parameters. These describe the fluid (flow behaviour index n ), the spatial heterogeneity (coefficients β, γ, δ, ω for variations of per- meability and porosity in the horizontal or vertical direction), and the type of release (volume exponent α). Theoretical results are validated against two sets of experiments with α= 1 (constant inflow) con- ducted with a stratified porous medium (simulated by superimposing layers of glass beads of different diameter) and a Hele-Shaw analogue for power-law fluid flow, respectively. In the latter case, a recently established Hele-Shaw analogy is extended to the variation of properties parallel to the flow direction. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current front and the current profile

Multimodel framework for characterization of transport in porous media

We consider modeling approaches to characterize solute transport in porous media, integrating them into a unique theoretical and experimental framework for model evaluation and data interpretation. To date, development of (conservative and reactive chemical) transport models and formulation of model calibration methods grounded on sensitivity-based collection of measurements have been pursued in parallel. Key questions that remain include: For a given set of measurements, which conceptual picture of the transport processes, as embodied in a mathematical model or models, is most appropriate? What are the most valuable space-time locations for solute concentration measurements, depending on the model selected? How is model parameter uncertainty propagated to model output, and how does this propagation affect model calibration? We address these questions by merging parallel streams of research – model formulation, reduction, calibration, sensitivity analysis, and discrimination – offering our view on an emerging framework that guides (i) selection of an appropriate number and location of time-dependent concentration measurements given a transport model; and (ii) assessment (through discrimination criteria) of the relative benefit of applying any particular model from a set of several models. Our strategy is to employ metrics to quantify the relative contribution of each uncertain model parameter to the variability of the model output. We evaluate these metrics through construction of a surrogate (or "meta") transport model that has the additional benefit of enabling sensitivity analysis and model calibration at a highly reduced computational cost. We demonstrate the applicability of this framework, focusing on transport of reactive chemicals in laboratory-scale porous media

Inhibition of Ubc13-mediated ubiquitination by GPS2 regulates multiple stages of B cell development

Non-proteolytic ubiquitin signaling mediated by Lys63 ubiquitin chains plays a critical role in multiple pathways that are key to the development and activation of immune cells. Our previous work indicates that GPS2 (G-protein Pathway Suppressor 2) is a multifunctional protein regulating TNF signaling and lipid metabolism in the adipose tissue through modulation of Lys63 ubiquitination events. However, the full extent of GPS2-mediated regulation of ubiquitination and the underlying molecular mechanisms are unknown. Here, we report that GPS2 is required for restricting the activation of TLR and BCR signaling pathways and the AKT/FOXO1 pathway in immune cells based on direct inhibition of Ubc13 enzymatic activity. Relevance of this regulatory strategy is confirmed in vivo by B cell-targeted deletion of GPS2, resulting in developmental defects at multiple stages of B cell differentiation. Together, these findings reveal that GPS2 genomic and non-genomic functions are critical for the development and cellular homeostasis of B cells