David B. McWhorter

Steady state mass transfer from single-component dense nonaqueous phase liquids in uniform flow fields

In recent years it has become increasingly clear that most remedial technologies fail to completely remove dense nonaqueous phase liquid (DNAPL) from subsurface source zones. Recognition of this limitation leads to the question of what benefit can be achieved through partial removal of DNAPL. To address this issue, a mathematical technique referred to as the multiple analytical source superposition technique (MASST) has been developed. MASST is based on a conceptualization of a DNAPL source zone as a grouping of discrete subzones containing DNAPL (e.g., fingers and/or pools) separated by portions of the aquifer that are entirely free of DNAPL. Using analytical techniques, spatial superposition of responses to multiple sources is used to estimate aqueous mass transfer rates from individual subzones. This procedure accounts for multiple DNAPL subzones with different volumes, geometries, and locations within an overall source zone that is otherwise free of the nonaqueous liquid. The mass transfer rate from a particular subzone is affected by mass transfer from all other subzones in the vicinity. Groundwater flow is assumed to be uniform, and transport processes are considered to be at a steady state. Comparison of MASST results with exact analytical solutions and laboratory data confirms the validity of MASST. Sensitivity analyses indicate that source-zone architecture is a primary factor governing bulk mass transfer and source longevity. Analysis of rate-limited mass transfer within DNAPL subzones and advective-dispersive transport about DNAPL subzones indicates that advective-dispersive transport is the primary factor controlling mass transfer rates. Finally, results indicate that removal of the vast majority of the DNAPL will likely be necessary to achieve significant near-term improvements in groundwater quality.

Unsteady radial flow of gas in the vadose zone

An exact, quasi-analytic solution for unsteady radial gas flow to injection or withdrawal wells is developed. Nonlinearities stemming from pressure-dependent density, viscosity, and gas permeability are accounted for in the general development. A new pseudo-pressure is defined and shown to be linearly related to ln(r2 t−1) for all t. Under the conditions of modest mass discharge and small pressure gradients expected to prevail in most hydrologic applications, the rigorous pseudo-pressure is closely approximated by a simple expression that is easily evaluated in terms of the actual gas pressure. The nonlinearity arising from the Klinkenberg effect is shown to be important only for circumstances that result in large pressure gradients such as will occur for large injection or withdrawal rates in media with low permeability. A procedure for determining the apparent gas permeability from test data is demonstrated using a set of simulated data generated from the quasi-analytic solution.

The use of macroscopic percolation theory to construct large‐scale capillary pressure curves

This paper introduces a macroscopic invasion percolation process suitable for simulating the displacement of one immiscible fluid by another through porous media under conditions of capillary-dominated flow. The theory is similar to classical percolation theory in that the structure of a real porous medium is represented as an ordered lattice, but differs in that each point of the lattice is assigned a local-scale porosity, permeability, and capillary pressure-saturation relationship, rather than microscale pore and pore throat dimensions. Unlike pore-scale percolation theory, each node of the lattice may be occupied by either one or two phases, thereby allowing bicontinua of fluids in two dimensions. To illustrate an application of the theory, both wetting and non wetting fluids are percolated through a heterogeneous porous medium while accounting for fluid trapping such that a hysteretic, large-scale capillary pressure-saturation curve is constructed. The simulations are carried out in spatially correlated, random permeability fields assuming that the local-scale capillary pressure-saturation relationships are perfectly correlated with permeability. The resulting large-scale capillary pressure curves are found to be influenced by the mean and variance of the assigned lognormal distribution of permeabilities. Very little sensitivity to the ratio of correlation lengths was observed. It is found that the threshold saturation giving rise to an initial percolating cluster of nonwetting fluid across the lattice corresponds to between 18.8% and 29.5% nonwetting saturation, depending on the statistics of the permeability field. Comparison of the percolation-derived capillary pressure curves to those based on a direct arithmetic average demonstrates that an arithmetic average is only valid through the range of fluid saturations where no trapping occurs.

Modeling salt transport in irrigated soils

Abstract This study evaluates the effects of the volume of leachate on the quality of the leachate. A numerical model of salt transport was used in the study. Field data were collected on 63 research plots located in the Grand Valley (Colorado, U.S.A.) and used to test and calibrate the model. The model was used in a series of hypothetical simulations designed to provide the required information. From the calibration of the moisture-flow model using infiltration data, soil water-content profiles, and soil water-storage change data, it was concluded that soil-water flow could be adequately modeled for the Grand Valley. The functional relations used for hydraulic conductivity and soil-water diffusivity and the method of averaging the values of the hydraulic parameters were developed during the course of the study. From comparisons of simulated and field data used in evaluating the chemistry model, it was concluded that total dissolved solids (TDS) concentrations were adequately modeled, but that individual ionic species concentrations were not. Comparison of calculated and measured data indicate that the CaSO 4 CaCO 3 Ca(HCO 3 ) 2 system is not properly modeled for the soil in the Grand Valley. Data for single growing season simulations using 7- and 14-day irrigation schedules and 2, 5, 20 and 40% leaching increments, coupled with data from a six-year simulation using a 14-day irrigation interval and 20% leaching increment, indicate that the salt concentration of the leachate at the bottom of the soil profile is independent of the volume of leachate.

Solute transport by a volatile solvent

Abstract In relatively dry porous media, water is transported as both liquid and vapor. Exact knowledge of this two-phase transport, and the phase transfer of water associated with it, is required for the prediction of solute transport. Combined liquid and vapor transport is examined starting from basic principles. An analytic solution is presented for the case of isothermal, transient, one-dimensional sorption of water with constant liquid content boundaries. A relation is also obtained for the evaporation and condensation within the flow field. A numerical solution for the solute transport is obtained which takes maximum advantage of the analytical flow solution. Using the properties of Lurgi retorted oil shale, several special cases are examined which show the relative importance of the separate phases in the total transport of water, the effects on the phase transfer, and the solute transport. It is expected that these methods and results can be applied to other problems in multiple phase transport, such as hazardous waste disposal and pesticide transport.