Feike J. Leij

DATABASE-RELATED ACCURACY AND UNCERTAINTY OF PEDOTRANSFER FUNCTIONS

Pedotransfer functions (PTFs) are becoming a more common way to predict soil hydraulic properties from soil texture, bulk density, and organic matter content. Thus far, the calibration and validation of PTFs has been hampered by a lack of suitable databases. In this paper we employed three databases

Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review

The transport of linearly interacting solutes in porous media is investigated with the help of residence time distributions, transfer functions, methods of system dynamics, and time-moment analyses. The classical one-dimensional convection-dispersion equation is extended to two-region (mobile-immobile water) transport by including diffusional mass transfer limitations characteristic of aggregated soils. The two-region model is further revised by incorporating the effects of multiple retention sites (in parallel or in series), multiple porosity levels, and arbitrary but steady flow fields. It is shown that different physical situations can be represented by a relatively small number of transfer functions containing only two types of parameters: distribution coefficients to account for equilibrium properties and characteristic times reflecting kinetic processes. Relevant kinetic processes include convective transport, hydrodynamic dispersion, adsorption-desorption, and physical or chemical mass transfer limitations. In most situations, theoretical breakthrough curves are found to be relatively insensitive to the mathematical structure of the transfer function, irrespective of the physical interpretation of the distribution coefficients and the characteristic times in the model. This means that alternative physical and chemical interpretations of model parameters can lead to nearly identical breakthrough curves. Certain transfer time distributions can lead to quite unusual shapes in the breakthrough curves; these curves strongly depend on the characteristic times and a few operational variables. Results of this study show that the transfer time distribution is an extremely useful tool for explaining some unexpected experimental results in the solute transport literature.

Description of the unsaturated soil hydraulic database UNSODA version 2.0

Quantifying water flow and chemical transport in the vadose zone typically requires knowledge of the unsaturated soil hydraulic properties. The UNsaturated SOil hydraulic DAtabase (UNSODA) was developed to provide a source of unsaturated hydraulic data and some other soil properties for practitioners and researchers. The current database contains measured soil water retention, hydraulic conductivity and water diffusivity data as well as pedological information of some 790-soil samples from around the world. A first MS-DOS version of the database was released in 1996. It has been applied in numerous studies. In this paper, we describe the second version (UNSODA V2.0) for use with Microsoft Access-97®1. The format and structure of the new database have been modified to provide additional and more convenient options for data searches, to provide compatibility with other programs for easy loading and downloading of data, and to allow users to customise the contents and look of graphical output. This paper reviews the structure and contents of the database as well as the operations that can be performed on the different data types in UNSODA V2.0. The use and application of the new database are illustrated with two examples. The retrieval of data is briefly illustrated, followed by a more detailed example regarding the interpolation of soil particle-size distribution data obtained according to different national definitions of particle-size classes. The interpolation procedure, which is based on finding similar particle-size distribution curves from a large European data set, also performed well for soils that originate from other geographical areas.

A comprehensive set of analytical solutions for nonequilibrium solute transport with first‐order decay and zero‐order production

Solute transport in the subsurface is often considered to be a nonequilibrium process. Predictive models for nonequilibrium transport may be based either on chemical considerations by assuming the presence of a kinetic sorption process, or on physical considerations by assuming two-region (dual-porosity) type formulations which partition the liquid phase into mobile and immobile regions. For certain simplifying conditions, including steady state flow and linear sorption, the chemical and physical nonequilibrium transport models can be cast in the same dimensionless form. This paper presents a comprehensive set of analytical solutions for one-dimensional nonequilibrium solute transport through semi-infinite soil systems. The models involve the one-site, two-site, and two-region transport models, and include provisions for first-order decay and zero-order production. General solutions are derived for the volume-averaged (or resident) solute concentration using Laplace transforms assuming both first- and third-type inlet conditions, and arbitrary initial conditions, input solute concentrations, and solute production profiles. The solutions extend and generalize existing solutions for equilibrium and nonequilibrium solute transport. The general solutions are evaluated for some commonly used input and initial conditions, and zero-order production profiles. Expressions for the flux-averaged concentration are derived from the general and specific solutions assuming a third-type inlet condition. Typical examples of calculated concentration distributions resulting from several sets of initial and input conditions and zero-order production functions are also presented and briefly discussed.

Using neural networks to predict soil water retention and soil hydraulic conductivity

Direct measurement of hydraulic properties is time consuming, costly, and sometimes unreliable because of soil heterogeneity and experimental errors. Instead, hydraulic properties can be estimated from surrogate data such as soil texture and bulk density with pedotransfer functions (PTFs). This paper describes neural network PTFs to predict soil water retention, saturated and unsaturated hydraulic properties from limited or more extended sets of soil properties. Accuracy of prediction generally increased if more input data are used but there was always a considerable difference between predictions and measurements. The neural networks were combined with the bootstrap method to generate uncertainty estimates of the predicted hydraulic properties.

Analytical Solutions for Solute Transport in Three‐Dimensional Semi‐infinite Porous Media

This paper presents several analytical solutions for three-dimensional solute transport in semi-infinite porous media with unidirectional flow using first-type (or concentration) and third-type (or flux) boundary conditions at the inlet location of the medium. The solutions may be used for predicting solute concentrations in homogeneous media, verification of more comprehensive numerical models, and laboratory or field determination of solute transport parameters. The transport equation incorporates terms accounting for advection, dispersion, zero-order production, and first-order decay. General solutions were derived for an arbitrary initial distribution and solute input with the help of Laplace, Fourier, and Hankel transforms. Specific solutions are presented for rectangular and circular solute inflow regions, as well as for solutes initially present in the form of parallelepipedal or cylindrical regions of the medium. The solutions were mathematically verified against simplified analytical solutions. Examples of concentration profiles are presented for several solute transport parameters using both first- and third-type boundary conditions. A mass balance constraint is defined based on a prescribed solute influx; the third-type condition is shown to conserve mass whereas the first-type condition was found to always overestimate resident solute concentrations in the medium.

Estimating interfacial areas for multi-fluid soil systems

Abstract Knowledge of the fluid-fluid and fluid-solid interfacial areas is important to better understand and quantify many flow and transport processes in porous media. This paper presents estimates for interfacial areas of porous media containing two or three fluids from measured capillary pressure (Pc)-saturation (S) relations. The thermodynamic treatment of two-fluid Pc−S relations presented by Morrow (1970) served as the basis for the predictions. In media containing two fluids (air-oil, air-water, oil-water), the solid-nonwetting interfacial area ( A sN ∗ ) equaled zero when the solid was completely wetted by the wetting fluid. The area under the Pc−S curve was directly proportional to the nonwetting-wetting interfacial area ( A NW ∗ ). If the solid surface was not completely wetted by one fluid, A NW ∗ and A sN ∗ were estimated by weighed partitioning of the area under the Pc−S curve. For porous media with fractional wettability, the procedure was applied separately to water- and oil-wet regions. The values of A NW ∗ and A sN ∗ were highest and lowest, respectively, in systems that were strongly wetted. In three-fluid media the wetting and spreading behavior of the liquids greatly affected the estimated interfacial areas. For a water-wet medium with a continuous intermediate oil phase, the interfacial areas were predicted from Pc−S data in a similar manner as for two-fluid media. The oil-water and oil-solid interfacial areas were estimated from the oil-water Pc−S curve, while the air-oil interfacial area was obtained from the air-oil Pc−S curve. For a fractional wettability or oil-wet medium there may be as many as six interfaces. These interfacial areas were estimated from three-fluid Pc−S relations based on previously developed methods for predicting three-fluid Pc−S relations from two-fluid data.

Modeling the dynamics of the soil pore-size distribution

Soil tillage often results in a structurally unstable soil layer with an elevated inter-aggregate porosity that is gradually decreased by the interplay of capillary and rheological processes. We have previously proposed to describe the evolution of the pore-size distribution (PSD) with the Fokker–Planck equation (FPE). The coefficients of this equation quantify the drift, dispersion, and degradation processes acting upon the PSD. An analytical solution for the PSD is presented for the case where drift and degradation coefficients depend on time, and the dispersion coefficient is proportional to the drift coefficient. These coefficients can be estimated from independent measurements of the PSD or (surrogate) water retention data or from mechanistic models. In this paper, we illustrate the application of the pore-size evolution model for: (i) a generic drift coefficient, (ii) static water retention data for soils under different tillage regimes, and (iii) dynamic hydraulic data for a soil subject to a sequence of wetting and drying cycles. These applications show the viability of our approach to model pore-size evolution. However, the development and application of the model is hampered by a lack of definitive data on soil structural and hydraulic dynamics.

Stochastic model for posttillage soil pore space evolution

Tillage operations disrupt surface layers of agricultural soils, creating a loosened structure with a substantial proportion of interaggregate porosity that enhances liquid and gaseous exchange properties favorable for plant growth. Unfortunately, such desirable soil tilth is structurally unstable and is susceptible to change by subsequent wetting and drying processes and other mechanical stresses that reduce total porosity and modify pore size distribution (PSD). Ability to model posttillage dynamics of soil pore space and concurrent changes in hydraulic properties is important for realistic predictions of transport processes through this surface layer. We propose a stochastic modeling framework that couples the probabilistic nature of pore space distributions with physically based soil deformation models using the Fokker-Planck equation (FPE) formalism. Three important features of soil pore space evolution are addressed: (1) reduction of the total porosity, (2) reduction of mean pore radius, and (3) changes in the variance of the PSD. The proposed framework may be used to provide input to hydrological models concerning temporal variations in near-surface soil hydraulic properties. In a preliminary investigation of this approach we link a previously proposed mechanistic model of soil aggregate coalescence to the stochastic FPE framework to determine the FPE coefficients. An illustrative example is presented which describes changes in interaggregate pore size due to wetting-drying cycles and the resulting effects on dynamics of the soil water characteristic curve and hydraulic conductivity functions.

Fractional wettability effects on two-and three-fluid capillary pressure-saturation relations

Studies of the relation between capillary pressure (Pc) and fluid saturation (S) for porous media containing oil-water or air-oil-water, often assume that the medium is strongly water-wet. Natural porous media, however, are composed of a variety of mineral constituents; such media are typically composed of water- and oil-wet fractions. This study reports on two- and three-fluid Pc-S data for media of different fractions of water- and oil-wet sands. The oil-water capillary pressure, defined as the oil minus the water pressure, was measured during drainage (primary and main curves) as well as imbibition (main curve only) of water. A decrease in oil-water pressure was observed as the oil-wet fraction increased in two-fluid media, q-he pressure became negative during imbibition of water for relatively oil-wet media. The Pc-S data could be adequately described by modifying the van Genuchten model for water retention. The observed differences between primary and main drainage curves were partly attributed to the effect of initial saturation. In three-fluid systems with fractional wettability, the observed dependency of capillary pressures on fluid saturations suggested that there was no continuous intermediate phase --even for a relatively low oil-wet fraction (25%). The oil-water and air-water capillary pressures decreased, at a particular water saturation, as the fraction of oil-wet sand increased. The water pressure is greater when water acts as the intermediate fluid than when it is the wetting fluid. The oil pressure, and hence the air-oil capillary pressure, was relatively insensitive to whether oil acted as wetting or intermediate fluid. There is a need to model three-fluid Pc-S curves that account for different wetting and intermediate fluids.