Luis Cueto-Felgueroso

Fluid mixing from viscous fingering.

Mixing efficiency at low Reynolds numbers can be enhanced by exploiting hydrodynamic instabilities that induce heterogeneity and disorder in the flow. The unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. Here we describe the dissipative structure of miscible viscous fingering, and propose a two-equation model for the scalar variance and its dissipation rate. Our analysis predicts the optimum range of viscosity contrasts that, for a given Péclet number, maximizes interfacial area and minimizes mixing time. In the spirit of turbulence modeling, the proposed two-equation model permits upscaling dissipation due to fingering at unresolved scales.

A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations

This paper presents a complete finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky type of equations. The spatial discretization is high-order accurate and suitable for general unstructured grids. The time integration is addressed by means of implicit an implicit-explicit fourth order Runge-Kutta schemes, with error control and adaptive time-stepping. The outcome is a practical, accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations. The use of adaptive time-stepping is of paramount importance in problems governed by the Cahn-Hilliard model; an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps. In addition to driving the simulations efficiently, the time-adaptive procedure provides a quantitative (not just qualitative) characterization of the rich temporal scales present in phase separation processes governed by the Cahn-Hilliard phase-field model.

Forecasting long-term gas production from shale.

Oil and natural gas from deep shale formations are transforming the United States economy and its energy outlook. Back in 2005, the US Energy Information Administration published projections of United States natural gas supply that stressed the need to develop an import infrastructure (1): by 2025, imports would account for almost one-third of United States consumption. When we compare those forecasts with the current ones to 2040 (Fig. 1) (2), it is inevitable to feel that a disruptive technology has emerged since. Natural gas consumption is expected to increase significantly over the next three decades, with strong demand growth from the electricity generation and industrial sectors. However, the United States will probably become a net exporter of gas before 2020, increasing domestic production by 44% over the projection period.

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

Infiltration of water in dry porous media is subject to a powerful gravity-driven instability. Although the phenomenon of unstable infiltration is well known, its description using continuum mathematical models has posed a significant challenge for several decades. The classical model of water flow in the unsaturated flow, the Richards equation, is unable to reproduce the instability. Here, we present a computational study of a model of unsaturated flow in porous media that extends the Richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively. The extended model is based on a phase-field formulation and is fourth-order in space. The new model poses a set of challenges for numerical discretizations, such as resolution of evolving interfaces, stiffness in space and time, treatment of singularly perturbed equations, and discretization of higher-order spatial partial-differential operators. We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient discretization of higher-order spatial operators in variational form. We illustrate the accuracy, efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media. We simulate, for the first time, unstable gravity-driven infiltration in three dimensions, and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium. Our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux.

A Metric of Influential Spreading during Contagion Dynamics through the Air Transportation Network

The spread of infectious diseases at the global scale is mediated by long-range human travel. Our ability to predict the impact of an outbreak on human health requires understanding the spatiotemporal signature of early-time spreading from a specific location. Here, we show that network topology, geography, traffic structure and individual mobility patterns are all essential for accurate predictions of disease spreading. Specifically, we study contagion dynamics through the air transportation network by means of a stochastic agent-tracking model that accounts for the spatial distribution of airports, detailed air traffic and the correlated nature of mobility patterns and waiting-time distributions of individual agents. From the simulation results and the empirical air-travel data, we formulate a metric of influential spreading––the geographic spreading centrality––which accounts for spatial organization and the hierarchical structure of the network traffic, and provides an accurate measure of the early-time spreading power of individual nodes.

Impact of viscous fingering and permeability heterogeneity on fluid mixing in porous media

Fluid mixing plays a fundamental role in many natural and engineered processes, including groundwater flows in porous media, enhanced oil recovery, and microfluidic lab-on-a-chip systems. Recent developments have explored the effect of viscosity contrast on mixing, suggesting that the unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. However, existing studies have not incorporated the effect of medium heterogeneity on the mixing rate. Here, we characterize the evolution of mixing between two fluids of different viscosity in heterogeneous porous media. We focus on a practical scenario of divergent-convergent flow in a quarter five spot geometry prototypical of well-driven groundwater flows. We study by means of numerical simulations the impact of permeability heterogeneity and viscosity contrast on the breakthrough curves and mixing efficiency, and we rationalize the nontrivial mixing behavior that emerges from the competition between the creation of fluid-fluid interfacial area and channeling.

Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media

Geological carbon dioxide (CO2) sequestration entails capturing and injecting CO2 into deep saline aquifers for long-term storage. The injected CO2 partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO2-rich brine, a process that greatly accelerates solubility trapping of the CO2. Here, we investigate the pattern-formation aspects of convective mixing during geological CO2 sequestration by means of high-resolution three-dimensional simulation. We find that the CO2 concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing.

Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme

Computational fluid dynamics (CFD) has become increasingly used in the industry for the simulation of flows. Nevertheless, the complex configurations of real engineering problems make the application of very accurate methods that only work on structured grids difficult. From this point of view, the development of higher-order methods for unstructured grids is desirable. The finite volume method can be used with unstructured grids, but unfortunately it is difficult to achieve an order of accuracy higher than two, and the common approach is a simple extension of the one-dimensional case. The increase of the order of accuracy in finite volume methods on general unstructured grids has been limited due to the difficulty in the evaluation of field derivatives. This problem is overcome with the application of the Moving Least Squares (MLS) technique on a finite volume framework. In this work we present the application of this method (FV-MLS) to the solution of aeroacoustic problems.

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.

Use of Pressure Management to Reduce the Probability of Pipe Breaks: A Bayesian Approach

AbstractAs pipe breaks in water distribution networks produce serious consequences, water authorities strive to minimize the frequency of their occurrence. Pressure management is an essential tool to reduce the frequency of breaks and it is closely linked to the proper analysis of a maximum pressure indicator. A methodology that compares the unconditional cumulative distribution function (CDF) and the parametric break-conditioned CDF of the maximum pressure indicator is proposed in this paper. The relationship between the CDFs compared is established by means of the Bayes’ theorem, which allows determining a probability ratio. The objective is to identify the range of operation of maximum pressure that is most likely to reduce pipe breaks. The methodology is applied to four sectors of the water distribution network in Madrid (Spain). In three of those sectors, the maximum pressure indicator is a good predictor of the probability of pipe breaks, confirming that the probability of breaks increases for high ...