David E. Elrick

Prediction of fingering in porous media

Immiscible displacement, involving two fluids in a porous medium, can be unstable and fingered under certain conditions. In this paper, the original linear instability criterion of Chuoke et al. (1959) is generalized, considering wettability of two immiscible fluids to the porous medium. This is then used to predict 24 specific flow and porous medium conditions for the onset of wetting front instability in the subsurface. Wetting front instability is shown to be a function of the driving fluid wettability to the medium, differences in density and viscosity of the fluids, the magnitude of the interfacial tension, and the direction of flow with respect to gravity. Scenarios of water and nonaqueous-phase liquid infiltration into the vadose zone are examined to predict preferential flow and contamination of groundwater. The mechanisms of finger formation, propagation, and persistence in the vadose zone are reviewed, and the existing equations for calculating the size, the number and velocity of fingers are simplified for field applications. The analyses indicate that fingers initiate and propagate according to spatial and temporal distribution of the dynamic breakthrough (water- or air-entry) pressures in the porous medium. The predicted finger size and velocity are in close agreement with the experimental results.

Unsaturated Hydraulic Conductivity Measured by Time Domain Reflectometry Under a Rainfall Simulator

We used time domain reflectometry (TDR) probes installed vertically at the soil surface beneath a constant-rate rainfall simulator to measure cumulative water storage and the soils unsaturated hydraulic conductivity. The slope from linear regression of water storage on time before any applied water infiltrates to the bottom of the TDR probe gives an estimate of the local infiltration rate. Local infiltration rates measured by TDR in the field were plotted against the corresponding local steady state water contents to give an estimate of the soils unsaturated hydraulic conductivity over a range in water content of 20% using only two applied rainfall rates. The spatial variability in local infiltration rates may be the result of infrequent high-intensity pulses of rainfall leading to temporary ponding and redistribution of water at the soil surface. Nonlinear optimization was used to estimate the saturated hydraulic conductivity and inverse capillary length scale from TDR data.

AN ANALYSIS OF THE PERCOLATION TEST BASED ON THREE-DIMENSIONAL SATURATED-UNSATURATED FLOW FROM A CYLINDRICAL TEST HOLE

The percolation test is commonly used to determine site suitability and filter field design for on-site wastewater treatment facilities. As now practiced, however, the test is neither standardized nor scientifically sound. The test hole radius, the depth of water in the hole, and the measurement procedure vary widely within and between jurisdictions; and more importantly, the present interpretation of the percolation test does not take into account the capillarity component of flow in unsaturated soils. This paper presents a new analysis of the percolation test, based on three-dimensional, saturated-unsaturated flow theory. It accounts for capillarity, hole radius, and water depth, and it explains much of the anomalous behavior previously observed in percolation rates. The new analysis identifies the field-saturated hydraulic conductivity and the matric flux potential, rather than the percolation rate, as the main soil hydraulic properties relevant to determining site suitability and filter field design. Procedures are suggested for determining the field-saturated hydraulic conductivity and matric flux potential, and for dealing with spatial variability.

Comparison of steady flows from infiltration rings in “Green and Ampt” and “Gardner” soils

The field-saturated hydraulic conductivity Kfs can be obtained from measurements of the long-time steady flow rates from ring infiltrometers by assuming either that the soil is a “Green and Ampt” soil that has a relationship between hydraulic conductivity K and soil water pressure ψ, such that K = Kfs, 0 > ψ > ψf; K → 0, ψƒ < ψf, or that the soil is a “Gardner” soil with an exponential relationship K = Kfs exp(αψ), where α is a constant. It is shown that infiltration into a Green and Ampt soil from a surface source with zero head is the same as that for a Gardner soil with α → ∞ (gravity dominant) and with a surface source at a head |ψfs|. The shape factor G calculated for Gardner soils using a numerical solution of Richardss equation is used to calculate Kfs and α from ring infiltrometer tests based on Q = [aH/G + a/(αG) + πa2]Kfs, where Q is the steady state flow rate, H is the constant ponded head, and a is the ring radius. The equivalent G factor for Green and Ampt soils calculated using electric analogue solutions of Laplaces equation is shown to agree very well with the numerical solution. The slope of the linear relationship between the shape factor and the depth of insertion of the ring divided by the radius of the ring is shown to have a slope approximately equal to 1/π.

Infiltration under constant head and falling head conditions.

Prediction of the infiltration of water into field soils requires knowledge of the field-saturated hydraulic conductivity and a second parameter, such as the matric flux potential (corresponding to field saturation), or the Green and Ampt wetting-front pressure head, or the alpha parameter. Analytical solutions of 1-D infiltration under both constant and falling-head conditions are reviewed and several new solutions are developed based on the Green and Ampt assumptions. A laboratory experiment using the falling head technique is analyzed using several approximate analytical solutions.

Estimating the hydraulic conductivity of slowly permeable and swelling materials from single-ring experiments

The in situ determination of the field-saturated hydraulic conductivity of low-permeability porous materials is a major concern for both geotechnics and soil physics with regards to environmental protection or water resources management. Recent early-time single-ring infiltration experiments, involving sequential constant head and falling head conditions, allow its efficient estimation. Nevertheless, the theory on which the interpretation was based was still strictly valid to nondeformable soils and implicity relied on a particular form of the hydraulic conductivity-soil water pressure head relationship. This theory is now extended to deformable materials, without any restrictive hypothesis. A new concept, bulk sorptivity, which characterizes the solid phase movement, is introduced. Field experiments, conducted on two liners of swelling and slowly permeable materials, revealed that neglecting the soil deformation induces an underestimation of the actual coefficient of permeability of the soil.

Solute transport in sub-irrigated peat-based growing media

New legislation to reduce the amount of fertilizer leached into the environment by horticultural growers and the need to implement water-saving irrigation systems require an understanding of salt build-up and of nutrient cycles in order to develop efficient water-use strategies for growers. Solute transport in growing media is central to this process, but has received little attention thus far. The objectives of this study were to determine how solutes behave in sub-irrigated growing media and to assess a solute transport model for these media. A steady state evaporation (upward water flow) experiment was carried out with three different growing media in packed columns in the laboratory. Bromide, potassium and copper concentrations were determined using in-column pore water solution samplers and by sectioning the columns at the end of the experiment to obtain concentration profiles. The Hydrus-1D model was fitted to the solution sampler data assuming non-linear Freundlich adsorption, and then used to obta...

Observations of Infiltration Through Clogged Porous Concrete Block Pavers

James and Verspagen (1996), Thompson and James (1995), and Shahin 1994) have observed low runoff volumes from porous concrete paver laboratory test blocks used…

Correction to “Prediction of fingering in porous media”

[1] In the paper ‘‘Prediction of fingering in porous media’’ by Zhi Wang, Jan Feyen, and David E. Elrick (Water Resources Research 34(9), 2183–2190, 1998), the authors developed 24 specific criteria for predicting unstable flow in porous media, based on the Chuoke equation [Chuoke et al., 1959]. However, some of the results were inconsistent with predictions by others. For instance, de Rooij [2000] noted that the Wang criteria showed unstable flow for overly rapid upward flow in contrary to Philip’s [1975] theory that predicted an unconditionally stable flow. These discrepancies resulted from three mistakes in the theoretical development, namely, (1) an inconsistency in the transcription of the Chuoke equation (equation (1) in the original paper), (2) a discrepancy between the definition of s* compared to the Chuoke definition (leading to a wrong equation (3a)) and, (3) sign errors in the development of the criteria (Table 1). In the following, we give the correct development and revise the 24 stability criteria of Wang et al. [1998].

Constant Rate Rainfall Infiltration in a Field of Variable α

Spatial variability of hydraulic parameters is an important factor in prediction of water flow and solute transport in unsaturated soils. An analytical solution for one-dimensional constant rate rainfall infiltration in a homogeneous soil is incorporated into a model of a spatially variable field. The model is a composite of vertically homogeneous soil columns that differ in their hydraulic properties. In this study, horizontal variation in infiltration profiles is due to variation in the inverse macroscopic capillary length (α) of each column. The sill in travel time variance of wetting profiles with depth for the homogeneous column confirms the notion of a long-time traveling wave of fixed shape. Variation in α slightly enhances the spread of wetting profiles and delays formation of the traveling wave. Identification of the mean α value is more critical than inclusion of variability in α for wetting profile simulations under the examined conditions.