M. T. van Genuchten

Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models

Variably saturated water flow in a dual-porosity medium may be described using two separate flow equations which are coupled by means of a sink source term Γw, to account for the transfer of water between the macropore (or fracture) and soil (or rock) matrix pore systems. In this study we propose a first-order rate expression for Γw, which assumes that water transfer is proportional to the difference in pressure head between the two pore systems. A general expression for the transfer coefficient αw was derived using Laplace transforms of the linearized horizontal flow equation. The value of αw could be related to the size and shape of the matrix blocks (or soil aggregates) and to the hydraulic conductivity Ka of the matrix at the fracture/matrix interface. The transfer term Γw, was evaluated by comparing simulation results with those obtained with equivalent one- and two-dimensional single-porosity flow models. Accurate results were obtained when Ka was evaluated using a simple arithmetic average of the interface conductivities associated with the fracture and matrix pressure heads. Results improved when an empirical scaling coefficient γw was included in αw. A single value of 0.4 for γw was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system.

A sequential uncertainty domain inverse procedure for estimating subsurface flow and transport parameters

A parameter estimation procedure, sequential uncertainty domain parameter fitting (SUFI), is presented and has the following characteristics. The procedure is sequential in nature, meaning that one more iteration can always be made before choosing the final estimates. The procedure has a Bayesian framework, indicating that the method operates within uncertainty domains (prior, posterior) associated with each parameter. The procedure is a fitting procedure, conditioning the unknown parameter estimates on an array of observed values. Finally, the procedure is iterative, requiring a stopping rule which is provided by a critical value of a goal function. Performance of the SUFI parameter estimation procedure is demonstrated using three examples of increasing complexity: (1) analysis of a solute breakthrough curve measured in the laboratory during steady state water flow, (2) estimation of the unsaturated soil hydraulic parameters from a transient drainage experiment carried out in a 6-m deep lysimeter, and (3) estimation of selected flow and transport parameters from a hypothetical ring infiltrometer experiment. The procedure was found to be general, stable, and always convergent.

New piecewise-continuous hydraulic functions for modeling preferential flow in an intermittent-flood-irrigated field

Modeling water flow in macroporous field soils near saturation has been a major challenge in vadose zone hydrology. Using in situ and laboratory measurements, we developed new piecewise-continuous soil water retention and hydraulic conductivity functions to describe preferential flow in tile drains under a flood-irrigated agricultural field in Las Nutrias, New Mexico. After incorporation into a two-dimensional numerical flow code, CHAIN_2D, the performance of the new piecewise-continuous hydraulic functions was compared with that of the unimodal van Genuchten-Mualem model and with measured tile-flow data at the field site during a number of irrigation events. Model parameters were collected/estimated by site characterization (e.g., soil texture, surface/ subsurface saturated/unsaturated soil hydraulic property measurements), as well as by local and regional-scale hydrologic monitoring (including the use of groundwater monitoring wells, piezometers, and different surface-irrigation and subsurface-drainage measurement systems). Comparison of numerical simulation results with the observed tile flow indicated that the new piecewise-continuous hydraulic functions generally predicted preferential flow in the tile drain reasonably well following all irrigation events at the field site. Also, the new bimodal soil water retention and hydraulic conductivity functions performed better than the unimodal van Genuchten-Mualem functions in terms of describing the observed flow regime at the field site.

Preferential transport of nitrate to a tile drain in an intermittent-flood-irrigated field: Model development and experimental evaluation

A comprehensive field experiment was conducted near Las Nutrias, New Mexico, to study field-scale flow and transport in the vadose zone. The field data were analyzed in terms of a two-dimensional numerical model based on the Richards equation for variably saturated water flow, convection-dispersion equations with first-order chemical decay chains for solute transport, and bimodal piecewise-continuous unsaturated hydraulic functions to account for preferential flow of water and nitrate-nitrogen (NO3-N; loosely used as NO3 ) following flood irrigation events at the experimental site. The model was tested against measured NO3 flux concentrations in a subsurface tile drain, several monitoring wells and nested piezometers, and against resident NO3 concentrations in the soil profile (obtained at 52 spatial locations and four depths along a transect). NO3 transport at the field site could be described better with the bimodal hydraulic functions than using the conventional approach with unimodal van Genuchten-Mualem type hydraulic functions. Average resident nitrate concentrations measured across the soil profile were predicted reasonably well. However, NO3 flux concentrations in the subsurface tile drain and piezometers at the field site were occasionally underestimated or overestimated depending upon the irrigation sequence in three field benches, probably reflecting unrepresented three-dimensional regional flow/transport processes. Limiting the capture zone to a region closer to the tile drain did lead to a better match with observed sharp increases and decreases in predicted NO3 flux concentrations during the irrigation events. On the basis of this result we inferred that the preferential flow intercepted by the tile drain was generated in close proximity of the drain and essentially oriented vertically. In summary, our study suggests that irrigation scheduling in adjacent field plots, drainage design (e.g., spacing between tiles, drain depth, drain diameter) and effectiveness (e.g., drain blockage), preferential flow in (horizontal) surface-opened shallow cracks and (vertical) macropores, and transient regional groundwater flow can add significant uncertainty to the predictions of (local-scale) flow and transport to a tile drain.

Analytical modeling of nonaqueous phase liquid dissolution with Green's functions

Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Greens Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multi‐dimensional problems. The Greens functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semi‐infinite and infinite media. The GFM is applied to analytically model multi‐dimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first‐, second‐, or third‐type boundary or source input conditions. Away from the source, the first‐ and third‐type condition cannot be expected to represent the exact surface condition. The second‐type condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the third‐type condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.

An efficient Eulerian‐Lagrangian Method for solving solute transport problems in steady and transient flow fields

A computationally efficient, yet relatively simple Eulerian-Lagrangian method is proposed for solving the one-dimensional convection-dispersion solute transport equation assuming a steady or transient velocity field. The method uses a modified single-step reverse particle tracking (MSRPT) technique to handle steep concentration fronts. The scheme utilizes two weighting factors to control the movement of particles during a backward tracking step. One weighting factor greater than unity is used in the upstream region of the convection front, while another weighting factor less than unity is taken in the downstream region. The two factors were related empirically to the grid Peclet and Courant numbers. The MSRPT technique is carried out only within the concentration plume at each time step. For transient flow fields, the weighting factors were determined using an automatically adjustable procedure based on mass balance errors. The MSRPT method maintains the advantages of the traditional single-step reverse particle tracking (SRPT) procedure, i.e., producing efficient and oscillation-free calculations, but circumvents numerical dispersion introduced by SRPT. A large number of tests against analytical solutions for one-dimensional transport in uniform flow fields indicate that the proposed method can handle the entire range of Peclet numbers from zero to infinity. Numerical tests also show that the MSRPT method is a relatively accurate, efficient an d massconservative algorithm for solute transport in transient flow fields. The Courant number at present cannot exceed 1. The MSRPT approach was found especially useful for convection-dominated problems; in fact, an exact numerical solution may be obtained with MSRPT for pure convection. Convection-dispersion type equations are being widely used to model solute transport in soil and groundwater. Owing to the particular combination of hyperbolic and parabolic terms, serious difficulties are often encountered in obtaining accurate numerical solutions of these equations. A variety of numerical schemes have been developed to deal with these difficulties, including an extensive number of

Water and chloride transport in a fine-textured soil: field experiments and modeling.

Numerical models are being used increasingly to simulate water and solute movement in the subsurface for a variety of applications in research and soil/water management. Although a large number of models of varying degrees of complexity have been developed over the years, relatively few have been tested under field conditions. We tested the performance of the HYDRUS-1D computer model to simulate variably saturated water flow and chloride transport in a fine-textured Italian soil subject to a fluctuating saline groundwater table. The model was also used for estimating solute transport parameters using an inverse optimization scheme. Our results indicate that including the effects of immobile water produced better predictions of chloride transport compared with the traditional convection-dispersion transport approach. Including anion exclusion as well did not improve the model predictions appreciably. Occasional deviations between model prediction and field observation were attributed to unrepresented lateral groundwater flow processes and to preferential flow through macropores or other structural voids. The HYDRUS-1D model was found to be very useful for analyzing the relatively complex flow and solute transport processes at our field site and for estimating model parameters using inverse procedures.