Showing papers in "Water Resources Research in 1990"

A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation

Abstract: Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, characterized by large mass balance errors and erroneous estimates of infiltration depth. Conversely, numerical solutions based on the mixed form of Richards equation can be shown to possess the conservative property, so that mass is perfectly conserved. This leads to significant improvement in numerical solution performance, while requiring no additional computational effort. However, use of the mass-conservative method does not guarantee good solutions. Accurate solution of the unsaturated flow equation also requires use of a diagonal time (or mass) matrix. Only when diagonal time matrices are used can the solution be shown to obey a maximum principle, which guarantees smooth, nonoscillatory infiltration profiles. This highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow.

Evaluation of automated techniques for base flow and recession analyses

Abstract: This paper presents an evaluation of several automated techniques concerned with base flow separation and recession analyses. Two base flow techniques were considered, one based on a digital filter and the other on simple smoothing and separation rules. A comparison between two commonly used techniques of recession analyses, the correlation method and the matching strip method, was also undertaken. The relative performances of the techniques were evaluated using the results obtained from the daily streamflow records of 186 catchments in southeastern Australia. The work described in this paper was undertaken within the general framework of defining the low-flow characteristics of small rural catchments, the overall objective being the development of a regional model for use on ungauged catchments.

Calibration of time domain reflectometry for water content measurement using a composite dielectric approach

Abstract: Time domain reflectometry (TDR) has been developed to an operational level for the measurement of soil water content during the past decade. Because it is able to provide fast, precise and nondestructive in situ measurements, it has become an alternative to the neutron scattering method, in particular for monitoring water content under field conditions. One of the major disadvantages of the neutron scattering technique is that, due to the relatively high sensitivity of the signal to factors other than water content, site-specific calibration is usually required. In this paper a calibration curve for the TDR method is presented which is not restricted to specific soil conditions. The calibration is based on the dielectric mixing model of Dobson et al. (1985). Measurements of volumetric water content and dielectric number at eleven different field sites representing a wide range of soil types were used to determine the parameter of the model by weighted nonlinear regression. The uncertainty (root mean square error) of water content values calculated with the optimized calibration curve was estimated not to exceed 0.013 cm3/cm3. This value is comparable to the precision of the thermogravimetric method. From a sensitivity analysis it was determined that the temperature dependence of the TDR signal may have to be corrected to obtain optimum accuracy.

Universal scaling of hydraulic conductivities and dispersivities in geologic media

Abstract: An interpretation is offered for the observation that dispersivities increase with scale. Apparent longitudinal dispersivity data from a variety of hydrogeologic settings are assumed to represent a continuous hierarchy of log hydraulic conductivity fields with mutually uncorrelated increments, each field having its own exponential autocovariance, associated integral scale, and variance that increases as a power of scale. Such a hierarchy is shown theoretically to form a self-similar random field with homogeneous increments. Regardless of whether or not the underlying assumption is valid, one can justify interpreting the apparent dispersivities in a manner consistent with a recent quasi-linear theory of non-Fickian and Fickian dispersion in homogeneous media which supports the notion of a self-similar hierarchy a posteriori. The hierarchy is revealed to possess a semivariogram γ(s;) ≊ cs½, where c is a constant, and a fractal dimension D ≊ E + 0.75, where E is the topological dimension of interest. This can be viewed as a universal scaling rule about which large deviations occur due to local influences including the existence of discrete natural scales at which log hydraulic conductivity is statistically homogeneous. As such homogeneity is at best a local phenomenon occurring intermittently over narrow bands of the scale spectrum, one must question the utility of associating medium properties with representative elementary volumes and relying on Fickian models of dispersion over more than relatively narrow scale intervals. Porous and fractured media appear to follow the same idealized scaling rule for both flow and transport, raising a question about the validity of many distinctions commonly drawn between such media. Finally, the data suggest that conditioning transport models through calibration against hydraulic measurements has the effect of filtering out large-scale modes from the hierarchy.

A rationale for old water discharge through macropores in a steep, humid catchment.

Abstract: Simultaneous observations of rapid preferential flow through macropores and isotopically “Old” water displacement remain unresolved in the Maimai (M8) catchment. Continuous, three-dimensional soil moisture energy conditions were monitored in two discrete catchment positions for a series of storm events in 1987. Tensiometric response was related to the soil water characteristic curve, hillslope throughflow, and total catchment runoff. For events yielding ≪2 mm hr−1 peak runoff, near-stream valley bottom groundwater systems discharged water volumes sufficient to account for storm period streamflow. This process was assisted by regular low ( 2 mm hr−1 peak storm flow, hillslope hollow drainage into steeply sloping first-order channels dominated old water production and most of the catchment storm flow. Highly transient macropore-driven processes of crack infiltration (bypass flow), slope water table development, and lateral pipe flow enabled large volumes of stored water to be delivered to the first-order channel bank at the appropriate time to satisfy catchment storm flow volumes and water isotopic and chemical composition.

Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model

Abstract: A large-scale investigation of fracture flow was recently conducted in a granite uranium mine at Fanay-Augeres, France. Its aim was to develop a methodology for the investigation of possible nuclear waste repository sites in crystalline environments, and thus to determine what measurements to make and what models to use in order to predict the flow and transport properties of the medium, i.e., their average behaviors and spatial variabilities at different scales. Four types of data were collected: (1) geometry of the fracture network; (2) local hydraulic properties measured by injection tests in boreholes; (3) global hydraulic behavior from flow rate and piezometric head distribution at a 106 m3 scale; and (4) tracer tests performed at a scale of up to 40 m. A stochastic fracture network model assuming negligible matrix permeability was developed and calibrated essentially on data 1 and 2 above; this was then used to predict data 3 and 4 in an attempt to validate both the parameters and the structure of the model. In this first part, only the flow problem (data 1) is discussed.

Dissolution of Trapped Nonaqueous Phase Liquids: Mass Transfer Characteristics

Abstract: Many groundwater contamination incidents begin with the release of an essentially immiscible fluid into the subsurface environment. Once in the subsurface, an immiscible fluid participates in a complex pattern of transport processes. For immiscible fluids that are commonly found in contaminated groundwater environments the interphase mass transfer between the nonaqueous phase liquids (NAPLs) phase and the aqueous phase is an important process. An experimental apparatus and procedure were used to isolate and measure mass transfer between toluene and water in glass bead media systems. The rate of interphase mass transfer was investigated in two-fluid systems as a function of aqueous phase velocity, aqueous- and nonaqueous-phase fluid saturations, and porous media characteristics. The rate of interphase mass transfer is found to be directly related to aqueous phase velocity and nonaqueous phase fluid saturation level, but no significant relation to mean particle size is found. Correlation expressions for the rate of interphase mass transfer are developed using relevant dimensionless parameters and are compared to literature values. Equilibrium between the two fluid phases investigated is shown to be achieved rapidly, over wide ranges of nonaqueous phase fluid saturations and aqueous phase velocities. The derived correlations provide a means for estimating the appropriateness ofmore » the local equilibrium assumption for a nonaqueous phase liquid-aqueous phase couple in multiphase groundwater systems.« less

A two‐phase decomposition method for optimal design of looped water distribution networks

Abstract: A two-phase decomposition method is proposed for the optimal design of new looped water distribution networks as well as for the parallel expansion of existing ones. The main feature of the method is that it generates a sequence of improving local optimal solutions. The first phase of the method takes a gradient approach with the flow distribution and pumping heads as decision variables and is an extension of the linear programming gradient method proposed by Alperovits and Shamir (1977) for nonlinear modeling. The technique is iterative and produces a local optimal solution. In the second phase the link head losses of this local optimal solution are fixed, and the resulting concave program is solved for the link flows and pumping heads; these then serve to restart the first phase to obtain an improved local optimal solution. The whole procedure continues until no further improvement can be achieved. Some applications and extensions of the method are also discussed.

Evaluation of regional flood frequency analysis with a region of influence approach

Abstract: A novel approach to regional flood frequency analysis is presented and evaluated. The technique is referred to as the region of influence approach in that every site can have a potentially unique set of gauging stations for use in the estimation of at-site extremes. The rationale for the methodology is discussed, and several options for incorporating the approach into regional flood frequency analysis are developed and compared with traditional regional estimation procedures. Through a Monte Carlo experiment, the region of influence approach is demonstrated to provide improved at-site estimates of extreme flow quantlies in terms of network average root mean squared error and comparable results for bias. The method is further shown to have attractive features for estimating extremes for unusual sites in a network of gauging stations.

Tidal dynamics of the water table in beaches

Abstract: Tidal motions of the water table height inside a sloping beach are investigated via field measurements and theoretical considerations. Only the movements forced by the tide are considered, so a beach with negligible wave activity was chosen for the field measurements. The data show that even in the absence of precipitation the time averaged inland water table stands considerably above the mean sea level. Also the water table at a fixed point inside the beach is far from sinusoidal even though its variation is forced by an essentially sinusoidal tide. This latter effect is due to the boundary condition along the sloping beach face which acts as a highly nonlinear filter. The observed behavior of the water table is explained in terms of perturbation extensions to the classical “deep aquifer solution.” One extension deals with the nonlinearity in the interior, the other with the boundary condition at the sloping beach face.

Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media

Abstract: A three-dimensional solute transport model has been developed to study detailed contaminant movements through large heterogeneous flow systems in porous media. The model is based upon a random walk particle method (RWPM) which can readily treat multidimensional advection and dispersion processes in saturated or unsaturated media in a computationally efficient manner. The transport simulations are used to examine the large time and spatial effects of the variable flow field on developing solute plumes, and, in particular, to investigate the nature of the large-scale dispersive behavior. Numerical transport experiments were conducted using single realizations of random hydraulic conductivity fields with three different degrees of heterogeneity. Experiments with different source locations were used to investigate preasymptotic and nonergodic effects that would appear as differences in plume evolution among the experiments. Analyses of the simulations indicate the spatial moments of the particle distributions in statistically isotropic saturated media compare favorably with stochastic theory predictions in terms of longitudinal advection and mixing, but differ markedly from predictions of transverse mixing. The simulations also demonstrate that significant nonergodic effects occur, as reflected in strong differences in the second moment evolution curves among the individual experiments and as predicted from the ensemble stochastic theory.

Geochemical Modeling of the Madison Aquifer in Parts of Montana, Wyoming, and South Dakota

Abstract: Stable isotope data for dissolved carbonate, sulfate, and sulfide are combined with water compo­ sition data to construct geochemical reaction models along eight flow paths in the Madison aquifer in parts of Wyoming, Montana, and South Dakota. The sulfur isotope data are treated as an isotope dilution problem, whereas the carbon isotope data are treated as Rayleigh distillations. All reaction models reproduce the observed chemical and carbon and sulfur isotopic composition of the final waters and are partially validated by predicting the observed carbon and sulfur isotopic compositions of dolomite and anhydrite from the Madison Limestone. The geochemical reaction models indicate that the dominant groundwater reaction in the Madison aquifer is dedolomitization ~calcite precipita­ tion and dolomite dissolution driven by anhydrite dissolution). Sulfate reduction, [Ca + + Mg2+ ]INa+ cation exchange, and halite dissolution are locally important, particularly in central Montana. The groundwater system is treated as closed to C02 gas from external sources such as the soil zone or cross-formational leakage but open to C02 from oxidation of organic matter coupled with sulfate reduction and other redox processes occurring within the aquifer. The computed mineral mass transfers and modeled sulfur isotopic composition of Madison anhydrites are mapped throughout the study area. Carbon 14 groundwater ages, adjusted for the modeled carbon mass transfer, range from modem to about 23,000 years B.P. and indicate flow velocities of 7~7 ftlyr (2.1-26.5 rnlyr). Most horizontal hydraulic conductivities calculated from Darcy's Law using the average 14 C flow velocities are within a factor of 5 of those based on digital simulation. The calculated mineral mass transfer and adjusted 14 C groundwater ages permit determination of apparent rates of reaction in the aquifer. The apparent rate of organic matter oxidation is typically 0.12 JLIDOl/Uyr. Sulfate and, to a lesser extent, ferric iron are the predominant electron acceptors. The (kinetic) biochemical fractionation of 34 S between sulfate and hydrogen sulfide is approximately -44%o at 25•c, with a temperature variation of

Hydrologic sensitivities of the Sacramento-San Joaquin River Basin, California, to global warming

Abstract: The hydrologic sensitivities of four medium-sized mountainous catchments in the Sacramento and San Joaquin River basins to long-term global warming were analyzed. The hydrologic response of these catchments, all of which are dominated by spring snowmelt runoff, were simulated by the coupling of the snowmelt and the soil moisture accounting models of the U.S. National Weather Service River Forecast System. In all four catchments the global warming pattern, which was indexed to CO{sub 2} doubling scenarios simulated by three (global) general circulation models, produced a major seasonal shift in the snow accumulation pattern. Under the alternative climate scenarios more winter precipitation fell as rain instead of snow, and winter runoff increased while spring snowmelt runoff decreased. In addition, large increases in the annual flood maxima were simulated, primarily due to an increase in rain-on-snow events, with the time of occurrence of many large floods shifting from spring to winter.

Fractal processes in soil water retention

Abstract: Numerous empirical models exist for soil water retention and unsaturated hydraulic conductivity data. It has generally been recognized that the empirical fitting coefficients in these models are somehow related to soil texture. However, the fact that they are empirical means that elaborate laboratory experiments must be performed for each soil to obtain values for the parameters. Moreover, empirical models do not shed insight into the fundamental physical principles that govern the processes of unsaturated flow and drainage. We propose a physical conceptual model for soil texture and pore structure that is based on the concept of fractal geometry. The motivation for a fractal model of soil texture is that some particle size distributions in granular soils have already been shown to display self-similar scaling that is typical of fractal objects. Hence it is reasonable to expect that pore size distributions may also display fractal scaling properties. The paradigm that we use for the soil pore size distribution is the Sierpinski carpet, which is a fractal that contains self similar “holes” (or pores) over a wide range of scales. We evaluate the water retention properties of regular and random Sierpinski carpets and relate these properties directly to the Brooks and Corey (or Campbell) empirical water retention model. We relate the water retention curves directly to the fractal dimension of the Sierpinski carpet and show that the fractal dimension strongly controls the water retention properties of the Sierpinski carpet “soil”. Higher fractal dimensions are shown to mimic clay-type soils, with very slow dewatering characteristics and relatively low fractal dimensions are shown to mimic a sandy soil with relatively rapid dewatering characteristics. Our fractal model of soil water retention removes the empirical fitting parameters from the soil water retention models and provides parameters (fractal dimension) which are intrinsic to the nature of the fractal porous structure. The relative permeability functions of Burdine and Mualem are also shown to be fractal directly from fractal water retention results.

Estimating groundwater exchange with lakes: 1. The stable isotope mass balance method

Abstract: Groundwater inflow and outflow contributions to the hydrologic budget of lakes can be determined using a stable isotope (18O/16O) mass balance method. The stable isotope method provides a way of integrating the spatial and temporal complexities of the flow field around a lake, thereby offering an appealing alternative to the traditional time and labor intensive methods using seepage meters and an extensive piezometer network. In this paper the method is applied to a lake in northern Wisconsin, demonstrating that it can be successfully applied to lakes in the upper midwest where thousands of similar lakes exist. Inflow and outflow rates calculated for the Wisconsin lake using the isotope mass balance method are 29 and 54 cm/yr, respectively, which compare well to estimates, derived independently using a three-dimensional groundwater flow and solute transport model, of 20 and 50 cm/yr. Such a favorable comparison lends confidence to the use of the stable isotope method to estimate groundwater exchange with lakes. In addition, utilization of stable isotopes in studies of groundwater-lake systems lends insight into mixing processes occurring in the unsaturated zone and in the aquifer surrounding the lake and verifies assumed flow paths based on head measurements in piezometers.

Simulation of lake evaporation with application to modeling lake level variations of Harney‐Malheur Lake, Oregon

Abstract: A physically based eddy diffusion model for simulating the seasonal variation in lake temperature and evaporation is presented and validated. Because no lake-specific fitting of the parameters of the model is necessary, the model can be used to simulate evaporation in studies of climate change and lake hydrology in a variety of settings. The eddy diffusion model is used to simulate evaporation for input to a simple lake level model that is applied to reconstruct recent fluctuations in the level of Harney-Malheur lake caused by climatic variations.

Exact integral solutions for two‐phase flow

Abstract: Exact integral solutions for the horizontal, unsteady flow of two viscous, incompressible fluids are derived. Both one-dimensional and radial displacements are calculated with full consideration of capillary drive and for arbitrary capillary-hydraulic properties. One-dimensional, unidirectional displacement of a nonwetting phase is shown to occur increasingly like a shock front as the pore-size distribution becomes wider. This is in contrast to the situation when an inviscid nonwetting phase is displaced. The penetration of a nonwetting phase into porous media otherwise saturated by a wetting phase occurs in narrow, elongate distributions. Such distributions result in rapid and extensive penetration by the nonwetting phase. The process is remarkably sensitive to the capillary-hydraulic properties that determine the value of knw/kw at large wetting phase saturations, a region in which laboratory measurements provide the least resolution. The penetration of a nonwetting phase can be expected to be dramatically affected by the presence of fissures, worm holes, or other macropores. Calculations for radial displacement of a nonwetting phase resident at a small initial saturation show the displacement to be inefficient. The fractional flow of the nonwetting phase falls rapidly and, for a specific example, becomes 1% by the time one pore volume of water has been injected.

Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion

Abstract: Transport of inert solutes in natural porous formations is dominated by convection and by the large-scale heterogeneity of permeability. A solute body inserted in the formation spreads because of the variation of velocity among and along the stream tubes which cross the plume. With neglect of the slow effect of pore-scale dispersion the solute particles preserve their initial concentration, but the body as a whole spreads in an irregular manner (Figures 1, 2, and ). The transport theory, based on representation of permeability and velocity as random space functions, can predict the expected value and variance of concentration, but under the above conditions, the coefficient of variation may be large. In contrast, the spatial moments of the solute body are less susceptible to uncertainty, depending on the transverse dimensions of the plume and on the travel time. The first and second spatial moments are regarded as random functions of time, and their expected value and variance are derived in terms of the velocity field. The moments are assumed to satisfy the ergodic hypothesis if their coefficients of variation are negligible. The conditions which ensure the fulfillment of this requirement are examined. The “effective dispersion coefficients” are defined with the aid of the spatial moments and are shown to depend generally on the initial size of the solute body and on travel time. The results are illustrated by an analytical solution of transport in a stratified formation with the average velocity parallel to the bedding.

Biofilm growth and the related changes in the physical properties of a porous medium: 1. Experimental investigation

Abstract: An experimental investigation was conducted to quantify the permeability reduction caused by enhanced biological growth in a porous medium. Studies were conducted using sand-packed column reactors for which variations in piezometric head, substrate concentration, and biomass measured as organic carbon were monitored in space and time. Methanol was used as a growth substrate. Permeability reductions by factors of order 10−3 were observed. The data show that a limit on permeability reduction exists, having a magnitude of 5 × 10−4 in the present study. The limit on permeability reduction and the existence of high densities of bacteria in substrate depleted zones are explained with an open pore model. Permeability reduction was observed to correlate well with biomass density for values less than about 0.4 mg/cm3, and exhibited independence at higher densities.

Deuterium variations in storm rainfall: Implications for stream hydrograph separation

Abstract: Isotopic variation in storm rainfall is an important consideration in hydrograph separation using the mass balance approach but is rarely considered when determining the accuracy of old water estimates. Study of a small watershed on the South Island of New Zealand in which new water is a major component of the storm hydrograph shows that, in addition to the within-storm isotopic variations themselves, rainfall weighting techniques may substantially influence estimates of old/new water as a function of both total runoff and total quick flow production. Two incremental approaches to rainfall weighting are presented. Results show that within-storm incremental weighting is better than the standard weighting technique, which imposes a total storm rainfall value exogenously on the mass balance equation.

An experimental investigation of variable density flow and mixing in homogeneous and heterogeneous media

Abstract: This study is an experimental investigation of variable density groundwater flow in homogeneous, layered and lenticular porous media. At the scale of the experiments the flow of dissolved mass in water depends upon both forced and free convection. In addition, density differences as low as 0.0008 g/cm{sup 3} (1,000 mg/L NaCl) between a plume of dense water and ambient groundwater in a homogeneous medium produces gravitational instabilities at realistic groundwater velocities. These instabilities are manifest by lobe-shaped protuberances that formed first along the bottom edge of the plume and later within the plume. As the density difference increases to 0.0015 g/cm{sup 3} (2,000 mg/L NaCl), 0.037 g/cm{sup 3} (5,000 mg/L NaCl), or higher, this unstable mixing due to convective dispersion significantly alters the spreading process. In a layered medium, reductions in hydraulic conductivity of the order of half an order of magnitude or less can influence the flow of the dense plume. Dense water may accumulate along bedding interfaces, which when dipping can result in plume migration velocities larger than ambient groundwater velocities. In a lenticular medium the combination of convective dispersion and nonuniform flow due to heterogeneities result in relatively large dispersion. Scale considerations, further, indicate that convective dispersionmore » may provide an important component of mixing at the field scale.« less

The diversion capacity of capillary barriers

Abstract: An arrangement of unsaturated fine-grained soil overlying unsaturated coarse-grained soil along a sloping contact can, under appropriate circumstances, divert infiltrating water away from the coarser material. Such an arrangement is called a capillary barrier. The water diverted by a capillary barrier flows downdip above the contact. The volume of water moving laterally increases in the downdip direction as additional infiltration is diverted by the barrier. Sufficiently far downdip, the laterally moving water wets the contact to the point that an amount of water equal to the infiltration flows downward through the coarse soil. The lateral flow at such a point represents the diversion capacity of the capillary barrier because this flow will not increase farther downdip. If the width (measured in the direction of dip) of the system is large enough that total infiltration exceeds the diversion capacity, the downdip portion of the barrier will not be effective. The diversion capacity can be calculated exactly in the quasi-linear approximation where the relationship between relative permeability krel and pressure potential ψ takes the form krel = eαψ. This calculation shows that an upper bound on the width of capillary barriers is Ks tan o/qα, where Ks is the saturated hydraulic conductivity of the fine soil, o is the dip angle of the contact, and q is the infiltration rate.

Saltation of snow

Abstract: Saltation of snow, the transport of snow in periodic contact with and directly above the snow surface, is governed by the atmospheric shear forces applied to the erodible snow surface, the nonerodible surface, and the moving snow particles. Empirical data measured over a snow-covered plain suggest functions for parameters important to the apportionment of atmospheric shear forces; the aerodynamic roughness height during saltation, the mean horizontal velocity of saltating particles, and the efficiency of the saltation process. The resulting mass transport expression shows an approximately linear increase in snow saltation transport rate with friction velocity, in agreement with the measurements presented. The expression is sensitive to the cohesion of the snow surface, as indexed by the threshold wind speed, that wind speed at which transport ceases; for wind speeds well above the threshold condition, higher threshold wind speeds correspond to higher transport rates. An adaptation of the expression allows calculation of the mass concentration of saltating snow from measured data and the transport rate of saltating snow from the mean wind speed at 10 m height. Application of the transport rate expression using measured wind speeds, directions, and weather observations demonstrates that the directional component of annual saltating snow transport does not always correspond with wind direction frequency.

Sampling stochastic dynamic programming applied to reservoir operation

Abstract: Most models for reservoir operation optimization have employed either deterministic optimization or stochastic dynamic programming algorithms. This paper develops sampling stochastic dynamic programming (SSDP), a technique that captures the complex temporal and spatial structure of the streamflow process by using a large number of sample streamflow sequences. The best inflow forecast can be included as a hydrologic state variable to improve the reservoir operating policy. A case study using the hydroelectric system on the North Fork of the Feather River in California illustrates the SSDP approach and its performance.

Evaluation of volatilization by organic chemicals residing below the soil surface

Abstract: Although volatile organic compounds located in buried waste repositories or distributed through the unsaturated soil zone have the potential to migrate to the atmosphere by vapor diffusion, little attention has been paid in the past to estimating the importance of volatilization losses. In this paper a screening model is introduced which evaluates the relative volatilization losses of a number of organic compounds under standard soil conditions. The model is an analytic solution to the problem wherein the organic chemical is located at time zero at uniform concentration in a finite layer of soil covered by a layer of soil devoid of chemical. The compound is assumed to move by vapor or liquid diffusion and by mass flow under the influence of steady upward or zero water flow while undergoing first-order degradation and linear equilibrium adsorption. Loss to the atmosphere is governed by vapor diffusion through a stagnant air boundary layer. Calculations are performed on 35 organic compounds in two model soils with properties characteristic of sandy and clayey soil. The model identifies those compounds with high potential for loss during 1 year after incorporation under 100 cm of soil cover and also is used to calculate the minimum soil cover thickness required to reduce volatilization losses to insignificant levels during the lifetime of the compound in the soil. From the latter calculation it was determined that certain compounds may volatilize from deep subsurface locations or even groundwater unless the soil surface is sealed to prevent gas migration.

On Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Rock Fractures

Abstract: This paper presents a conceptual and numerical model of multiphase flow in fractures. The void space of real rough-walled rock fractures is conceptualized as a two-dimensional heterogeneous porous medium, characterized by aperture as a function of position in the fracture plane. Portions of a fracture are occupied by wetting and nonwetting phase, respectively, according to local capillary pressure and accessibility criteria. Phase occupancy and permeability are derived by assuming a parallel-plate approximation for suitably small subregions in the fracture plane. For log-normal aperture distributions, a simple approximation to fracture capillary pressure is obtained in closed form; it is found to resemble the typical shape of Leverett's j-function. Wetting and non-wetting phase relative permeabilities are calculated by numerically simulating single phase flows separately in the wetted and non-wetted pore spaces. Illustrative examples indicate that relative permeabilities depend sensitively on the nature and range of spatial correlation between apertures. It is also observed that interference between fluid phases flowing in a fracture tends to be strong, with the sum of wetting and nonwetting phase relative permeabilities being considerably less than 1 at intermediate saturations.

Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 2. The transport model

Abstract: As part of the development of a methodology for investigating flow and transport in fractured rocks, a large-scale experiment was recently performed at Fanay-Augeres, France. In a companion paper (Cacas et al., this issue) (paper 1) the results of the flow measurements were analyzed. In this paper, the results of the tracer experiments are interpreted. A particle following is coupled to the flow model, described in paper 1. Microscopic dispersion in the fractures and retardation effects due to unevenness of the flow paths are taken into account. The transport model is calibrated on in situ tracer tests, whereas the parameters of the hydraulic model were initially fitted on structural and hydraulic measurements (paper 1). The dispersive properties of the model are reasonably comparable to those of the real site. It tends to confirm the validity of the preliminary hydraulic calibration of the model and thus to validate further the approach used to simulate hydraulic and transport phenomena.

A Computer-Controlled 36-Channel Time Domain Reflectometry System for Monitoring Soil Water Contents

Abstract: Research on the spatial and temporal dynamics of soil water has long been impeded by the lack of an automated technique for the measurement of soil water content. A computer controlled time domain reflectometry (TDR) system is described which gives the possibility of making a large number of measurements at different sites at predetermined time intervals. The developed system operates on 12 V dc and has the capability to monitor water contents at 36 sites. The algorithm used for the automatic analysis of the measurements is also presented. It is based on the calculation of the travel time of the TDR signal between the beginning and the end of a three-wire probe.

Stochastic modeling of macrodispersion in heterogeneous porous media

Abstract: A method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media, is presented. Its main features are as follows: (1) The velocity field is assumed to be a space random function. Its moments are expressed through the physical parameters of the log transmissivity and head random fields by linearizing the flow equation. The random velocity, being a linear function of the head and log transmissivity, which are assumed to be jointly multivariate normal (MVN), is thus also MVN. Its pdf is completely defined by its first two moments. (2) The statistics of the dispersion process are obtained by the particle-tracking method through Monte Carlo simulations which are based on Gaussian conditioning. The method is applied to the Borden natural gradient tracer test (Freyberg, 1986), showing favorable results.