Daniel B. Stephens

Hysteresis and state-dependent anisotropy in modeling unsaturated hillslope hydrologic processes

This paper describes a series of soil water tracer experiments and approaches taken to numerically model the flow and transport behavior observed in the field experiments. These experimental and numerical results strongly suggest that current widely held views and commonly applied modeling approaches are flawed in many cases for unsaturated flow, and provide strong supporting evidence for a variable, state-dependent anisotropy in the hydraulic conductivity of an unsaturated medium. This phenomenon has been previously postulated in a number of independent theoretical and experimental investigations. In general, the previous studies identify layered heterogeneity as a primary cause of the macroscopic anisotropy. In addition, we show how hysteresis in the soil moisture characteristics (θ-ψ relationship) can cause a lexturally homogeneous porous media profile to behave anisotropically under transient unsaturaied conditions. Recognizing that both of these factors (layered heterogeneity and capillary hysteresis) contribute the anisotropic behavior observed in the tracer experiments, we attempt to quantify the relative magnitude of their contributions in a numerical modeling investigation. For the numerical modeling study we use a finite element flow and transport code, and introduce a simple procedure for incorporating variable anisotropy into a predictive numerical model. To determine the relative magnitude of textural heterogeneity and capillary hysteresis as causes of the observed macroscopic anisotropy, we employ a diagnostic modeling approach. The results of the diagnostic modeling study indicate that textural heterogeneity is by far the most important contributor to the variable macroscopic anisotropy observed at the field site. The diagnostic simulations further show that the variable anisotropy approach is well suited to modeling field-scale problems. Subsequently, a sensitivity analysis was performed to determine how climate, geologic and topographic structure, and media lithology affect flow and transport behavior when soils were specified to have a variable macroscopic anisotropy. The results of this study clearly indicate that variable state-dependent anisotropy is a real and significant process at the field site and that modeling with consideration of variable anisotropy strongly affects model predictions.

An analytical solution for vertical transport of volatile chemicals in the vadose zone

An analytical solution is presented for one-dimensional vertical transport of volatile chemicals through the vadose zone to groundwater. The solution accounts for the important transport mechanisms of the steady advection of water and gas, diffusion and dispersion in water and gas, as well as adsorption, and first-order degradation. By assuming a linear, equilibrium partitioning between water, gas and the adsorbed chemical phases, the dependent variable in the mathematical model becomes the total resident concentration. The general solution was derived for cases having a constant initial total concentration over a discrete depth interval and a zero initial total concentration elsewhere. A zero concentration gradient is assumed at the groundwater table. Examples are given to demonstrate the application of the new solution for calculating the case of a non-uniform initial source concentration, and estimating the transport of chemicals to the groundwater and the atmosphere. The solution was also used to verify a numerical code called VLEACH. We discovered an error in VLEACH, and found that the new solution agreed very well with the numerical results by corrected VLEACH. A simplified solution to predict the migration of volatile organic chemical due to the gas density effect has shown that a high source concentration may lead to significant downward advective gas-phase transport in a soil with a high air-permeability.

Toward validating state-dependent macroscopic anisotropy in unsaturated media: Field experiments and modeling considerations

Abstract This paper describes a series of detailed soil-water tracer experiments conducted in a natural landscape and provides a discussion on approaches one might take to model the observed flow and transport. The field experiments provide supporting evidence for a variable, state-dependent anisotropy in the hydraulic conductivity of an unsaturated medium. This phenomenon has been postulated previously in a number of independent theoretical and experimental investigations. In general, these previous studies identify layered heterogeneity as a primary cause of the macroscopic state-dependent anisotropy. In addition, we develop a simple scenario to show how hysteresis-enhanced moisture content variations can cause a texturally homogeneous porous medium profile to behave anisotropically under transient unsaturated conditions. We recognize that both of these factors (layered heterogeneity and hysteresis-enhanced moisture content variations) contribute to the anisotropic behavior observed in the tracer experiments, but we do not quantify the relative magnitude of their contributions. However, we do introduce a simple procedure for incorporating variable anisotropy into a predictive numerical model.

Free surface and saturated-unsaturated analyses of borehole infiltration tests above the water table

Abstract Constant head borehole infiltration tests are widely used for the in situ evaluation of saturated hydraulic conductivities of unsaturated soils above the water table. The formulae employed in analysing the results of such tests disregard the fact that some of the infiltrating water may flow under unsaturated conditions. Instead, these formulae are based on various approximations of the classical free surface theory which treats the flow region as if it were fully saturated and enclosed within a distinct envelope, the so-called ‘free surface’. A finite element model capable of solving free surface problems is used to examine the mathematical accuracy of the borehole infiltration formulae. The results show that in the hypothetical case where unsaturated flow does not exist, the approximate formulae are reasonably accurate within·a practical range of borehole conditions. To see what happens under conditions closer to those actually encountered in the field, the effect of unsaturated flow on borehole infiltration is investigated by means of two different numerical models: a mixed explicit-implicit finite element model, and a mixed explicit-implicit integrated finite difference model. Both of these models give nearly identical results; however, the integrated finite difference model is considerably faster than the finite element model. The relatively low computational efficiency of the finite element scheme is attributed to the large number of operations required in order to re-evaluate the conductivity (stiffness) matrix at each iteration in this highly non-linear saturated-unsaturated flow problem. The saturated-unsaturated analysis demonstrates that the classical free surface approach provides a distorted picture of the flow pattern in the soil. Contrary to what one would expect on the basis of this theory, only a finite region of the soil in the immediate vicinity of the borehole is saturated, whereas a significant percentage of the flow takes place under unsaturated conditions. As a consequence of disregarding unsaturated flow, the available formulae may underestimate the saturated hydraulic conductivity of fine grained soils by a factor of two, three, or more. Our saturated-unsaturated analysis leads to an improved design of borehole infiltration tests and a more accurate method for interpreting the results of such tests. The analysis also shows how one can predict the steady state rate of infiltration from data collected during the early transient period of the test.

A Borehole Field Method to determine unsaturated hydraulic conductivity

Unsaturated hydraulic conductivity is often the single most important soil property in vadose zone flow and transport. However, at depths below the root zone there is no field method available to determine it. The proposed method is directed toward developing a practical field tool to determine Unsaturated hydraulic conductivity in discrete intervals over any depth. The basic idea is to inject water at a point and monitor the steady state pressure distribution surrounding the source. We have developed an analytical solution to use either the observed steady state pressure heads at several points due to a single injection, or steady pressure heads at a single point due to multiple injections, to determine the unsaturated hydraulic conductivity. The approach is based on a linearization of the Unsaturated flow equation which uses the piecewise exponential model of unsaturated hydraulic conductivity. Examples of hydraulic conductivity calculations for three different soils give excellent results.

Steady Infiltration Into a Two‐Layered Soil from a Circular Source

Infiltration of water from a surface source is highly relevant to a wide range of problems in soil science, hydrology, and engineering. This article presents analytical solutions to steady infiltration in layered soils caused by a constant influent through a circular area (such as a pond or a ring infiltrometer) at the land surface. An exponential relationship between the unsaturated hydraulic conductivity and the pressure head, K = K0 exp (αψ), is assumed for both layers, and α is assumed to be the same for both layers. The solutions for two kinds of lower boundary conditions are discussed. The first condition assumes a semiinfinite system with very dry soil at an infinite depth; the second condition considers an impermeable boundary. Solutions are given for single layer and two-layer systems. As a special case of the two-layer solution, the single layer solution agrees very well with previous solutions when the boundary conditions are approximately the same. The effects of soil properties and layer thickness are also discussed.

Analysis of the Groundwater Monitoring Controversy at the Pavillion, Wyoming Natural Gas Field

The U.S. Environmental Protection Agency (EPA) was contacted by citizens of Pavillion, Wyoming 6 years ago regarding taste and odor in their water wells in an area where hydraulic fracturing operations were occurring. EPA conducted a field investigation, including drilling two deep monitor wells, and concluded in a draft report that constituents associated with hydraulic fracturing had impacted the drinking water aquifer. Following extensive media coverage, pressure from state and other federal agencies, and extensive technical criticism from industry, EPA stated the draft report would not undergo peer review, that it would not rely on the conclusions, and that it had relinquished its lead role in the investigation to the State of Wyoming for further investigation without resolving the source of the taste and odor problem. Review of the events leading up to EPAs decision suggests that much of the criticism could have been avoided through improved preproject planning with clear objectives. Such planning would have identified the high national significance and potential implications of the proposed work. Expanded stakeholder involvement and technical input could have eliminated some of the difficulties that plagued the investigation. However, collecting baseline groundwater quality data prior to initiating hydraulic fracturing likely would have been an effective way to evaluate potential impacts. The Pavillion groundwater investigation provides an excellent opportunity for improving field methods, report transparency, clarity of communication, and the peer review process in future investigations of the impacts of hydraulic fracturing on groundwater.

Numerical Simulations and Field Experiments of Unsaturated Flow and Transport: The Roles of Hysteresis and State-Dependent Anisotropy

This chapter describes a series of detailed soil-water tracer experiments conducted in a natural landscape. It also discusses three different approaches taken to numerically model the observed flow and transport. These field experiments provide the first conclusive evidence for the existence of a variable, state-dependent anisotropy in the hydraulic conductivity of an unsaturated, layered medium in a natural field setting. This concept has been previously postulated in a number of independent theoretical and experimental investigations. While previous studies have identified layered heterogeneity as the principal cause of state-dependent anisotropy, we develop a simple scenario to show how hysteresis in the soil-moisture characteristics (θ-ψ relationship) can contribute to the anisotropic behavior of a texturally homogeneous, porous media profile under transient, unsaturated conditions. Three approaches at modeling the observed flow and transport are implemented and compared. The results of the computer simulations indicate that even relatively uniform media (such as the sands from our field site) exhibit variable anisotropy, and that local (laboratory scale) hysteresis makes only minor contributions to macroscopic anisotropic flow behavior.

Also Consider the Recharge

Quantifying recharge is a common objective in many applications in ground water hydrology and is especially relevant to discussions about ground water sustainability. John Bredehoeft’s (2007) recent guest editorial, ‘‘It is the discharge,’’ is an important reminder for hydrogeologists to consider multiple techniques to determine basin recharge, including taking into account the basin discharge, when the system is in a condition of dynamic equilibrium. In a condition of dynamic equilibrium, basin recharge approximately equals basin discharge. Dr. Bredehoeft rightly notes that where ground water is visibly discharged—such as at springs, in base flow to streams, and via phreatophytes in a desert environment—it should be quantified. One reason he tells us ‘‘it is the discharge’’ is that pumping in desert ground water basins is more likely to reach a new dynamic equilibrium by capturing and diminishing ground water discharge than by capturing rejected recharge. He notes that ‘‘basin discharge is of much more pragmatic concern than recharge.’’ Thus, to understand basin dynamics and pumping impacts better, he encourages us to spend more effort on quantifying the discharge. Dr. Bredehoeft also states that ‘‘the recharge is the most difficult component of the ground water system to quantify.’’ Because of this, he feels that ‘‘recharge is better understood through the discharge’’ and that in lieu of research to understand recharge processes, ‘‘it is more fruitful to study the discharge.’’ It is these points on quantifying recharge through measurements of ground water discharge that I want to address in this commentary. In my experience, there are instances where measuring basin discharge to estimate recharge is not easy, reliable, appropriate, or feasible. In many cases, determining net infiltration below the root zone (i.e., deep percolation that later becomes recharge) and determining recharge from physical and chemical data collected in aquifers can be alternatives that are just as good, if not better, than using basin discharge as a surrogate. In some instances, basin discharge may be fairly easy to quantify, for example, by measuring spring flow or, where the stream is fed by ground water discharge, by measuring the gain in streamflow. However, estimation of these components of discharge may underestimate the total recharge in some basins because discharge by deep ground water flowing beneath near-surface discharge zones is neglected. If basin discharge is by evapotranspiration, quantifying discharge using site-specific data may be quite challenging. Although there are methods to estimate evapotranspiration from the literature and perhaps from available site information, measuring actual evapotranspiration may require constructing large-scale lysimeters from which measurements are collected for a year or more. Calculating actual evapotranspiration may require obtaining meteorological data and assessing seasonal variations of plant activity, as well as assessing vegetation density, root distributions, soil properties, and other parameters. Incidentally, these same lysimeter and meteorological measurements made in the recharge areas can be applied in soil-water balance calculations to quantify deep percolation that may become recharge. To support his theme of ‘‘it is the discharge,’’ Dr. Bredehoeft cites the widely used Maxey-Eakin method for estimating recharge. The Maxey-Eakin method is a convenient but poorly documented empirical relationship between mean precipitation in Nevada as of 1936 and basin discharge, e.g., by phreatophytes, with the latter used as a surrogate for recharge. The discharge from selected Nevada basins was based partly on evapotranspiration rates obtained from earlier publications on Owens Valley, California, and Escalante Valley, Utah. The Maxey-Eakin method has been updated recently by Nichols (2000) using more rigorous and site-specific analysis of evapotranspiration and basin underflow. Some ground water basins may have no surface expression of discharge at all, and in these cases, one may need to calculate discharge using Darcy’s law. To do this requires assessing subsurface geologic structure and stratigraphy, determining the width and saturated thickness of the aquifer, installing wells for establishing the hydraulic head gradient, and conducting aquifer tests. Although this standard hydrogeological information Daniel B. Stephens & Associates Inc., 6020 Academy Road NE, Suite 100, Albuquerque, NM 87109; (505) 822-9400; fax: (505) 821-2313; dan.stephens@dbstephens.com Copyright a 2008 The Author(s) Journal compilationa2008NationalGroundWater Association. doi: 10.1111/j.1745-6584.2008.00476.x

Groundwater flow and implications for groundwater contamination north of Prewitt, New Mexico, U.S.A.

Abstract In the southern San Juan Basin, New Mexico, strata of Permian and younger age dip gently toward the center of the basin. Most previous investigators believed that recharge to these strata occurred by precipitation on the outcrops and groundwater flowed downdip to the north and northeast. Recent water-level measurements in an undeveloped part of the basin near Prewitt, New Mexico, show that groundwater at shallow depths in alluvium and bedrock flows southward, opposite to the dip direction, and toward a major ephemeral drainage in a strike valley. North of this area, groundwater in deep bedrock aquifers does appear to flow northward. This information suggests that there are two groundwater circulation patterns; a shallow one controlled by topography and a deeper one controlled by geologic structure. Significant amounts of recharge to sandstone aquifers by infiltration through outcrops is unlikely due to the near-vertical exposures on cliffs, the gentle dip of the strata, and small annual precipitation. Numerical model results suggest that recharge to bedrock aquifers may be from downward leakage via aquitards over large areas and leakage from narrow alluvial aquifers in the subcrop area. The recharge mechanism is controlled by the hydraulic conductivity of the strata. As the flow path is controlled by hydraulic conductivity contrasts, geologic structure, and topography, contamination movement from surface impoundments is likely to be difficult to predict without a thorough hydrogeological site investigation.