Mario J. Martinez

The apparent conductivity for steady unsaturated flow in periodically fractured porous media

The influence of horizontal fractures on the steady seepage of moisture in variably saturated porous media is analyzed by analytical and numerical means. The fractures are assumed to contain many open (dry) regions, and to be distributed periodically in two dimensions. The dry regions of the fracture form a barrier to moisture flow through the geologic medium. An idealized two-dimensional model that maximizes the barrier effect of the fractures is analyzed. The results of the analysis quantify the effect of the dry regions of the fractures on global water flow through the fractured medium. An apparent conductivity is determined such that the fractured system can be replaced by a homogeneous medium for describing steady unsaturated flow. An asymptotic analysis yields an analytic expression for the apparent hydraulic conductivity through such a system in the limit of small sorptive number (fracture spacing divided by a characteristic capillary suction) for the intact matrix material. The apparent hydraulic conductivity for arbitrary spacing and sorptive number is determined by numerical means. The numerical model accounts for variable hydraulic conductivity as a function of the local pressure head, whereas the asymptotic solution represents the limit of constant conductivity. The numerical results confirm the analytical solution as a lower bound on the apparent hydraulic conductivity.

Computational thermal, chemical, fluid, and solid mechanics for geosystems management.

This document summarizes research performed under the SNL LDRD entitled - Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission. The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD. The main goal of this project was the development of a foundational capability for coupled thermal, hydrological, mechanical, chemical (THMC) simulation of heterogeneous geosystems utilizing massively parallel processing. To solve these complex issues, this project integrated research in numerical mathematics and algorithms for chemically reactive multiphase systems with computer science research in adaptive coupled solution control and framework architecture. This report summarizes and demonstrates the capabilities that were developed together with the supporting research underlying the models. Key accomplishments are: (1) General capability for modeling nonisothermal, multiphase, multicomponent flow in heterogeneous porous geologic materials; (2) General capability to model multiphase reactive transport of species in heterogeneous porous media; (3) Constitutive models for describing real, general geomaterials under multiphase conditions utilizing laboratory data; (4) General capability to couple nonisothermal reactive flow with geomechanics (THMC); (5) Phase behavior thermodynamics for the CO2-H2O-NaCl system. General implementation enables modeling of other fluid mixtures. Adaptive look-up tables enable thermodynamic capability to other simulators; (6) Capability for statistical modeling of heterogeneity in geologic materials; and (7) Simulator utilizes unstructured grids on parallel processing computers.

A three-dimensional boundary element method for steady unsaturated quasi-linear flow in porous media

A three-dimension boundary element method is developed to study unsaturated groundwater flows in heterogeneous porous media. The method is based on the Kirchhoff transformation of variables which transforms the nonlinear Richards equation into the Fokker-Planck equation. Several benchmark problems are considered involving cavity infiltration exclusion to demonstrate the reliability of the boundary element formulation. As an example application problem, the effective conductivity of a porous medium containing randomly positioned impermeable spherical inclusions is considered. 22 refs., 7 figs., 6 tabs.

Modeling in Nuclear Waste Isolation: Approximate Solutions for Flow in Unsaturated Porous Media

Mathematical modeling plays a key role in the design and licensing of repositories for radioactive waste. Because safe isolation of nuclear waste involves extremely long time scales, and there exists very little engineering experience upon which to draw, modeling takes on a particularly crucial role. An example of a model problem motivated by hydrological issues in high-level waste isolation is presented. A repository concept involving storage in rock above the water table requires models for the flow of groundwater in unsaturated, porous media. Such flow is governed by an extremely nonlinear diffusion equation, and poses some difficult numerical challenges. A special form of the hydraulic conductivity function however, results in a linear field equation for steady-state problems, for which a boundary integral method yields very fast solutions.

The influence of interfacial slip on two‐phase flow in rough pores

The migration and trapping of supercritical CO2 (scCO2) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability) dependent effective permeability to the invading fluid, a non-dimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO2 may be enhanced by approximately 30% during drainage, while the permeability to brine during re-imbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. A much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.

Numerical Modeling of an All Vanadium Redox Flow Battery

We develop a capability to simulate reduction-oxidation (redox) flow batteries in the Sierra Multi-Mechanics code base. Specifically, we focus on all-vanadium redox flow batteries; however, the capability is general in implementation and could be adopted to other chemistries. The electrochemical and porous flow models follow those developed in the recent publication by [28]. We review the model implemented in this work and its assumptions, and we show several verification cases including a binary electrolyte, and a battery half-cell. Then, we compare our model implementation with the experimental results shown in [28], with good agreement seen. Next, a sensitivity study is conducted for the major model parameters, which is beneficial in targeting specific features of the redox flow cell for improvement. Lastly, we simulate a three-dimensional version of the flow cell to determine the impact of plenum channels on the performance of the cell. Such channels are frequently seen in experimental designs where the current collector plates are borrowed from fuel cell designs. These designs use a serpentine channel etched into a solid collector plate.

Considerations for Developing Models of Multiphase Flow in Deformable Porous Media

This document summarizes research and planning for the development of a numerical simulation capability for nonisothermal multiphase, multicomponent transport in heterogeneous deformable porous materials. Particular attention is given to describing a mathematical formulation for flow in deformable media and for numerical techniques for dealing with phase transitions. A development plan is formulated to provide a computational capability motivated by current and future needs in geosystems management for energy security.

Generalized Fourier Analyses of Semi-Discretizations of the Advection-Diffusion Equation

This report presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speeds, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis (aka von Neumann analysis) provides an automatic process for separating the spectral behavior of the discrete advective operator into its symmetric dissipative and skew-symmetric advective components. Further it is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, streamline upwind control-volume, produce both an artificial diffusivity and an artificial phase speed in addition to the usual semi-discrete artifacts observed in the discrete phase speed, group speed and diffusivity. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behavior in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behavior. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework.