Valentina Ciriello

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.

Evaluation of Reliability Indicators for WDNs with Demand-Driven and Pressure-Driven Models

Reliability of water distribution networks (WDNs) has received much attention in recent years due to progressive aging of infrastructures and climate change. Several reliability indicators, focusing on hydraulic aspects rather than water quality, have been proposed in literature. Reliability is generally assessed resorting to well established methods coupling hydraulic simulations and stochastic techniques that describe the WDNs hydraulic performance and component availability respectively. Two main algorithms are employed to simulate WDNs: the demand driven approach (DDA) that disregards the physical relationship between actual water demand and nodal pressure, and the pressure driven approach (PDA) that explicitly incorporates it. In this paper, we show how the choice of hydraulic solver may affect reliability indicators. We modify existing quantitative indicators at nodal and network level, and define novel indicators to consider water quality aspects. These indicators are evaluated for three example WDNs; discrepancies between results obtained with the two approaches depend on network size, feeding scheme and skeletonization. Results suggest to use with caution the DDA for reliability assessment at both local and global level.

Erratum to: Generalized Solution for 1-D Non-Newtonian Flow in a Porous Domain due to an Instantaneous Mass Injection

Non-Newtonian fluid flow through porous media is of considerable interest in several fields, ranging from environmental sciences to chemical and petroleum engineering. In this article, we consider an infinite porous domain of uniform permeability k and porosity ({phi}) , saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within the domain by an instantaneous mass injection in its origin. The pressure is taken initially to be constant in the porous domain. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; n, 1 shear-thickening behavior; for n = 1, the Newtonian case is recovered. The law of motion for the fluid is a modified Darcy’s law based on the effective viscosity μef, in turn a function of ({phi, H, n}) . Coupling the flow law with the mass balance equation yields the nonlinear partial differential equation governing the pressure field; an analytical solution is then derived as a function of a self-similar variable η = rtβ (the exponent β being a suitable function of n), combining spatial coordinate r and time t. We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem depending on a geometrical parameter d, valid for plane (d = 1), cylindrical (d = 2), and semi-spherical (d = 3) geometry. When a shear-thinning fluid is considered, the analytical solution exhibits traveling wave characteristics, in variance with Newtonian fluids; the front velocity is proportional to t(n-2)/2 in plane geometry, t(2n-3)/(3−n) in cylindrical geometry, and t(3n-4)/[2(2−n)] in semi-spherical geometry. To reflect the uncertainty inherent in the value of the problem parameters, we consider selected properties of fluid and matrix as independent random variables with an associated probability distribution. The influence of the uncertain parameters on the front position and the pressure field is investigated via a global sensitivity analysis evaluating the associated Sobol’ indices. The analysis reveals that compressibility coefficient and flow behavior index are the most influential variables affecting the front position; when the excess pressure is considered, compressibility and permeability coefficients contribute most to the total response variance. For both output variables the influence of the uncertainty in the porosity is decidedly lower.