1993 Conference Proceedings
Numerical analysis of a three-phase system with a fluctuating water table
M.D. White, R.J. Lenhard
Pacific Northwest National Laboratory, Richland, Washington
Proceedings of Thirteenth Annual American Geophysical Union Hydrology Days, Hydrology Days Publication, Atherton, California, pp. 219-236, 1993.
Abstract
Numerical simulations are presented of a one-dimensional, multiphase flow system that involves the redistribution of aqueous-phase liquids and nonaqueous-phase liquids (NAPLs) by a fluctuating water table. The numerical analyses were completed using an integrated-volume, finite-difference-based solution scheme of the governing multiphase conservation equations and constitutive theory. Conservation equations were solved for two components, water and oil, with the assumption of a passive gas-phase. Nonlinearities introduced into the governing conservation equations through the constitutive theory were handled with a multivariable Newton-Raphson iterative scheme. The functional relationships between the phase relative permeability, the phase saturation, and phase pressures in porous media were described with a general theoretical model that includes the effects of air and oil occlusion during imbibition. Parameters required for the theoretical model were defined for two-phase systems (e.g., air-water, air-oil, and oil-water). The theoretical model assumes that wettability decreases in the following order: water, oil, air. Results from the numerical simulations are compared against measurements taken from a previous multiphase flow experiment. The experiment involved subjecting an initially water-drained, three-phase system (i.e., air-oil-water) to a fluctuating water table. The experimental objective was to quantify the entrapment of air and NAPL by phases of greater wettability under dynamic conditions. Comparison of numerical and experimental results were made for two ratios of imbibition to drainage characteristic, curve-shape parameters, and two models for relative permeability in two-phase systems. The numerical methods used to solve the governing conservation and constitutive equations for multiphase hysteretic conditions are described.
Numerical modeling of hysteretic multiphase flow: 1. Model description and verification
M.D. White, R.J. Lenhard, K.R. Roberson
Pacific Northwest National Laboratory, Richland, Washington
EOS, 74(16), American Geophysical Union Spring Meeting, Baltimore, Maryland, 1993.
Abstract
In these companion papers, a description, verification solution, and validation exercise are presented for a numerical simulator with capabilities for nonisothermal subsurface transport. This paper focuses on the numerical theory and application of the solution scheme to two-phase displacement problems with exact integral solutions. The subject numerical simulator, referred to as STOMP, solves problems of subsurface transport over multiple phases, with an integrated-volume finite-difference-based solution scheme of the governing multiphase conservation equations and constitutive theory. The variable source code configuration of the simulator allows selective solution of the conservation equations for water, air, and volatile organic compound (VOC) mass, thermal energy, and species concentration under fifteen operational modes. Depending on the operational mode, transport of the conserved quantities occurs over the aqueous, nonaqueous liquid, gas, and/or solid phases. Nonlinearities introduced into the governing conservation equations through the constitutive theories are handled with a multivariable Newton-Raphson iteration scheme, with numerically computed Jacobian coefficients. Numerical recipes for computing these coefficients near saturation phase transitions are described. Transport capabilities of the numerical simulator for passive scalar species, including methods for addressing multiple-phase partitioning, hydraulic dispersion, and radioactive decay, are described. An isothermal verification exercise involving the horizontal, unsteady flow of two viscous, incompressible fluids is described and compared against exact integral solutions previously published. Verification exercises are reported for one-dimensional, unidirectional, and countercurrent displacement of wetting and nonwetting fluids.
This work was supported by the VOC-Arid Soils Integrated Demonstration Program, Office of Technology Development, U.S. Department of Energy (DOE). Pacific Northwest National Laboratory is operated for the DOE, by Battelle Memorial Institute, under Contract DE-AC06-76RLO 1830.
Numerical modeling of hysteretic multiphase flow: 2. A validation exercise
R.J. Lenhard, M.D. White, K.R. Roberson
Pacific Northwest National Laboratory, Richland, Washington
EOS, 74(16), American Geophysical Union Spring Meeting, Baltimore, Maryland, 1993.
Abstract
A modeling validation exercise was conducted to test the hysteretic permeability-saturation-pressure (k-S-P) relations that were embodied in the numerical simulator STOMP described in the previous paper. The constitutive k-S-P relations, which are published in the literature, will be only briefly outlined in the presentation. The relations account for the effects of nonaqueous-phase liquid (NAPL) entrapment by water and the effects of air entrapment by NAPL and water on S-P and k-S relations. The data used in the validation exercise were measured during a multiphase one-dimensional flow experiment where the elevation of the water table was fluctuated to produce wetting and drying fluid saturation paths. Water and NAPL contents were measured nondestructively at specified flow-cell locations via radiation attenuation. These measurements were compared to simulations of the experiment using STOMP. Close agreement was obtained between the experimental data and the numerical results, except for the highest and lowest measurement elevations. For the highest position, a slight modification to the relative permeability function provided better agreement with the experimental NAPL data. For the lowest position, the discrepancy between experimental data and numerical simulations is attributed to an absence of a nonwetting-fluid entry-pressure concept in the k-S-P model. Nonhysteretic simulations were also conducted, and the results differed from the experimental data more than did the hysteretic simulations. Additional comparisons among simulation results and experimental data are needed to validate multiphase flow models before they can be employed to accurately predict the subsurface fate of NAPLs.
This work was supported by the Subsurface Science Program, Office of Health and Environmental Research, U.S. Department of Energy (DOE). Pacific Northwest National Laboratory is operated for the DOE by Battelle Memorial Institute, under Contract DE-AC06-76RLO 1830.