Abstract

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in σY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999–3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019–3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139–193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit–Forchheimer assumption holds.

Abstract

Reactive impregnation concerns many science and engineering areas, such as corrosion in the steel-making industry and chemical engineering. Furthermore, reactive impregnation can become dangerous in some applications. Simulating non-reactive impregnation with classical methods is the first step before computing reactive impreg++nation. However, existing numerical methods present problems such as high computational cost and spurious oscillation. To avoid these computational difficulties, we propose the Self-organized Gradient Percolation model. It is a numerical model based on probabilistic approaches and, in particular, on percolation methods. This work aims to present a 2D model based on the 1D developed model. The first results are free from spurious oscillation and drastically reduced the computational cost compared with the classical methods.

Abstract

Abstract

This paper builds on the flexibility of the level-set representation to model in a unified manner the expansion of a hollow in the ground under different physical phenomena. In particular, the dissolving action of a flow of water in a saturated soil, and that of a jet of particles of water in a non-saturated one, are represented in a common framework. In that manner, the complex geometrical evolutions of the hollow can be followed without the need for remeshing and this approach allows for a smooth transition between saturated and non-saturated models of the soil. Implementation and numerical difficulties are discussed and two applications of industrial interest are considered. The first one describes the modeling of the piping phenomenon, and the second one the evolution of an excavation created by a leaking duct.

Abstract

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow.

Abstract

In the past few years, the development of inverse design and optimization methods has opened up new possibilities. The so-called Adjoint method is of great significance in that context, since it permits high fidelity to flow-physics at comparatively low computational costs. The present work is a sequel of a previous one presented in WCCM2018, called 'On the use of the Adjoint Method to evaluate sensitivities in adsorbed natural gas storage systems'. where one have developed and validated an Adjoint based approach to computing sensitivity derivatives for adsorbed natural gas (ANG) storage systems. The main goal of this work is to, by using the approach to compute sensitivities presented before, obtain and validate a basic structure of an optimization loop algorithm (OLA) for optimization of natural gas storage systems. Both flow and Adjoint solvers, which were previously developed, are assembled in FREEFEM++ platform. The OLA consists on solving sequential problems to achieve an optimal configuration of parameters that maximize/minimize an objective functional. It starts by solving the primal problem (flow solver), which consists in a physics flow solution, followed by the dual problem, based on the Adjoint Method. With both solutions, the OLA receives the sensitivity derivatives with respect to parameters and, if the configuration is not the optimal, a new values of parameters is obtained and the cycle restarts. To validate the OLA, we make use of the inverse design optimization, defining the objective functional as the mean square error, MSE, of the actual density of adsorption distribution q, with respect to an user--defined target distribution, qt. The strategy is generated a target distribution with a known filling flow curve and the OLA, starting the optimization cycles with other flow curve, minimizing the functional, finding the same curve as we use to generate qt. The results of the several tests showed that the OLA have the capacity to regenerate the original curves, proving the consistency of the source code. The next step for the future researchers is the application for the engineering purposes, by using operational requirements to optimize the process.