Publications

This report describes the use of PorSalsa, a parallel-processing, finite-element-based, unstructured-grid code for the simulation of subsurface nonisothermal two-phase, two component flow through heterogeneous porous materials. PorSalsa can also model the advective-dispersive transport of any number of species. General source term and transport coefficient implementation greatly expands possible applications. Spatially heterogeneous flow and transport data are accommodated via a flexible interface. Discretization methods include both Galerkin and control volume finite element methods, with various options for weighting of nonlinear coefficients. Time integration includes both first and second-order predictor/corrector methods with automatic time step selection. Parallel processing is accomplished by domain decomposition and message passing, using MPI, enabling seamless execution on single computers, networked clusters, and massively parallel computers.

Abstract not provided.

Many research activities in subsurface transport require the numerical simulation of multiphase flow in porous media. This capability is critical to research in environmental remediation (e.g. contaminations with dense, non-aqueous-phase liquids), nuclear waste management, reservoir engineering, and to the assessment of the future availability of groundwater in many parts of the world. This paper presents an unstructured grid numerical algorithm for subsurface transport in heterogeneous porous media implemented for use on massively parallel (MP) computers. The mathematical model considers nonisothermal two-phase (liquid/gas) flow, including capillary pressure effects, binary diffusion in the gas phase, conductive, latent, and sensible heat transport. The Galerkin finite element method is used for spatial discretization, and temporal integration is accomplished via a predictor/corrector scheme. Message-passing and domain decomposition techniques are used for implementing a scalable algorithm for distributed memory parallel computers. Illustrative applications are shown to demonstrate capabilities and performance, one of which is modeling hydrothermal transport at the Yucca Mountain site for a radioactive waste facility.

This document reports on the accomplishments of a laboratory-directed research and development (LDRD) project whose objective was to initiate a research program for developing a fundamental understanding of multiphase multicomponent subsurface transport in heterogeneous porous media and to develop parallel processing computational tools for numerical simulation of such problems. The main achievement of this project was the successful development of a general-purpose, unstructured grid, multiphase thermal simulator for subsurface transport in heterogeneous porous media implemented for use on massively parallel (MP) computers via message-passing and domain decomposition techniques. The numerical platform provides an excellent base for new and continuing project development in areas of current interest to SNL and the DOE complex including, subsurface nuclear waste disposal and cleanup, groundwater availability and contamination studies, fuel-spill transport for accident analysis, and DNAPL transport and remediation.

We present a numerical method for nonisothermal, multiphase subsurface transport in heterogeneous porous media. The mathematical model considers nonisothermal two-phase (liquid/gas) flow, including capillary pressure effects, binary diffusion in the gas phase, conductive, latent, and sensible heat transport. The Galerkin finite element method is used for spatial discretization, and temporal integration is accomplished via a predictor/corrector scheme. Message-passing and domain decomposition techniques are used for implementing a scalable algorithm for distributed memory parallel computers. An illustrative application is shown to demonstrate capabilities and performance.

A mathematical formulation is presented for describing the transport of air, water, NAPL, and energy through porous media. The development follows a continuum mechanics approach. The theory assumes the existence of various average macroscopic variables which describe the state of the system. Balance equations for mass and energy are formulated in terms of these macroscopic variables. The system is supplemented with constitutive equations relating fluxes to the state variables, and with transport property specifications. Specification of phase equilibrium criteria, various mixing rules and thermodynamic relations completes the system of equations. A numerical simulation scheme based on finite-differences is described.

A mathematical formulation is presented for describing the transport of air, water and energy through porous media. The development follows a continuum mechanics approach. The theory assumes the existence of various average macroscopic variables which describe the state of the system. Balance equations for mass and energy are formulated in terms of these macroscopic variables. The system is supplemented with constitutive equations relating fluxes to the state variables, and with transport property specifications. Specification of various mixing rules and thermodynamic relations completes the system of equations. A numerical simulation scheme, employing the method of lines, is described for one-dimensional flow. The numerical method is demonstrated on sample problems involving nonisothermal flow of air and water. The implementation is verified by comparison with existing numerical solutions.

In this report, we reconsider the various approximations made to the full equations of motion and energy transport for treating low-speed flows with significant temperature induced property variations. This entails assessment of the development of so-called anelastic for low-Mach number flows outside the range of validity of the Boussinesq equations. An integral part of this assessment is the development of a finite element-based numerical scheme for obtaining approximate numerical solutions to this class of problems. Several formulations were attempted and are compared.

A boundary integral equation method for steady unsaturated flow in nonhomogeneous porous media is presented. Steady unsaturated flow in porous media is described by the steady form of the so-called Richards equation, a highly nonlinear Fokker-Planck equation. By applying a Kirchhoff transformation and employing an exponential model for the relation between capillary pressure and hydraulic conductivity, the flow equation is rendered linear in each subdomain of a piece-wise homogeneous material. Unfortunately, the transformation results in nonlinear conditions along material interfaces, giving rise to a jump in the potential along these boundaries. An algorithm developed to solve the nonhomogeneous flow problem is described and verified by comparison to analytical and numerical solutions. The code is applied to examine the moisture distribution in a layered porous medium due to infiltration from a strip source, a model for infiltration from shallow ponds and washes in arid regions.

The governing equation for steady flow in a partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function that is exponential in the capillary-pressure head. The resulting linear field equation is well suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is compared to a more complex form often assumed for tuffs, and is found to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code an a finite-element code that solves the fully nonlinear problem is excellent, and is achieved at a substantial advantage in computer processing time. 26 refs., 23 figs., 8 tabs.

The distribution of moisture beneath a two-dimensional strip source is analyzed by applying the quasi-linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depth, D, below the surface, the depth varying from shallow to semi-infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of material sorptivity, {alpha}, the width of the strip source, 2L, and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when {alpha}L {much_lt} 1, for which absorption by capillary forces is dominant over gravity-induced flow. Conversely, the distribution becomes finger-like along the vertical when {alpha}L {much_gt} 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when {alpha}D is less than about 4; infiltration rates obtained when the water table depth is semi-infinite are of sufficient accuracy for greater values of {alpha}D. When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptivity and depth to the water table. 30 refs., 16 figs., 2 tabs.

The ignition of reactive powders by a semiconductor bridge (SCB) is analyzed by applying a multiphase flow model based upon the theory of mixtures. The hot plasma produced by the SCB permeates the cold granular explosive, deposits its latent heat upon fusing to the grains, therby heating the explosive granular surfaces to energy states required for self-sustained reaction. This mechanism is predicted to heat the granular explosive in a region local to the SCB to temperatures well above those required for thermal ignition. The analysis demonstates that this mechanism explains the prompt ignition of explosives using SCB's as opposed to the conductively controlled heating of conventional bridgewires. 16 refs., 14 figs., 1 tab.