Numerical Simulations Of Unsaturated Flow Research Articles

Improved Lumped-Parameter and Numerical Modeling of Unsaturated Water Flow and Stable Water Isotopes.

Characterizing unsaturated water flow in the subsurface is a requirement for understanding effects of droughts on agricultural production or impacts of climate change on groundwater recharge. By employing an improved lumped-parameter model (LPM) approach that mimics variable flow we have interpreted stable water isotope data (δ18 O and δ2 H), taken over 3 years at a lysimeter site located in Germany. Lysimeter soil cores were characterized by sandy gravel (Ly1) and clayey sandy silt (Ly2), and both lysimeters were vegetated with maize. Results were compared with numerical simulation of unsaturated flow and stable water isotope transport using HYDRUS-1D. In addition, both approaches were extended by the consideration of preferential flow paths. Application of the extended LPM, and thus varying flow and transport parameters, substantially improved the description of stable water isotope observations in lysimeter seepage water. In general, findings obtained from the extended LPM were in good agreement to numerical modeling results. However, observations were more difficult to describe mathematically for Ly2, where the periodicity of seasonal stable water isotope fluctuation in seepage water was not fully met by numerical modeling. Furthermore, an extra isotopic upshift improved simulations for Ly2, probably controlled by stable water isotope exchange processes between mobile soil water and quasi-immobile water within stagnant zones. Finally, although LPM requires less input data compared with numerical models, both approaches achieve comparable decision-support integrity. The extended LPM approach can thus be a powerful tool for soil and groundwater management approaches.

An improved Picard iteration scheme for simulating unsaturated flow in porous media

The Richards equation is widely used in the simulation of unsaturated flow and related fields. In the numerical solution process, the finite volume method can be used to carry out numerical discretization, and the Picard method is used for iterative solution. However, in order to obtain a more reliable numerical solution, the space step size of the conventional uniform grid is often small. Especially under some unfavorable numerical conditions, such as infiltration into dry soil and layered soil with very different hydraulic conductivity, this will be very time-consuming and even slow to converge. Thus, combined with the non-uniform grid in the form of Chebyshev, an improved Picard method based on the non-uniform two-grid correction scheme (NTG-PI) is proposed to model 1D unsaturated flow in porous media. Through three examples of unsaturated flow under unfavorable conditions, the proposed scheme was verified. The results show that, compared with the conventional Picard method, NTG-PI can obtain higher numerical accuracy with a smaller number of nodes, and also has a faster convergence rate. This method can provide a certain reference for the numerical simulation of unsaturated flow.

Effective flow and transport properties of heterogeneous unsaturated soils

The heterogeneity of field scale soils poses a challenge to predictive large scale flow and transport modeling. The theory of effective macroscale parameters holds good and is applicable in dealing with such problems. But the validity of the analytic stochastic solutions obtained for randomly heterogeneous soils is debatable, as the test cases under which they are validated are of limited scope due to linearization and perturbation approximations. In this study, samples of heterogeneous soils are generated using sets of spatially correlated random field parameters that are either geometrically isotropic, or else, geometrically anisotropic with either horizontal or vertical stratification (perfect or imperfect). Several combinations of ratios of correlation length and capillary dispersion lengths are considered. Numerical simulations of unsaturated flow are performed on each randomly heterogeneous soil sample. The principal components K^ii(Ψ) of the macroscale effective unsaturated conductivity are then obtained as a function of the mean suction Ψ of the sample. They are compared to stochastic spectral perturbation theory, and to a probabilistic semi-empirical Power Average Model (PAM). They are also compared with arithmetic, geometric and harmonic mean conductivity-suction curves. The numerically upscaled principal conductivity curves match quite well the PAM, better than the classical means (Arithmetic, Geometric, Harmonic), and also somewhat better than the curves obtained from stochastic spectral perturbation theory. It is observed that the upscaled principal components Kii(ψ), obtained numerically and with the PAM along directions “i” orthogonal/parallel to perfect stratification coincide with the harmonic/arithmetic mean curves at low suctions (i.e., near saturation), but deviate from it and come closer to the geometric mean at higher suctions. The PAM appears suitable for generation of approximate upscaled conductivity curves, e.g., for obtaining the mesh-scale or block-scale conductivity curves in large scale simulation codes. Transient solute transport simulations are then performed on the detailed random velocity fields obtained from the steady state simulations of unsaturated flow in the randomly heterogeneous soil samples. Snapshots of solute concentration C(x,z,t) are taken at different times. The temporal evolution of spatial moments of concentration is analyzed in order to characterize the macroscale advection and dispersion of the unsaturated concentration plume, and in particular, its macro-dispersion coefficient (D) and dispersivity length scale (A). For the synthetic soil samples considered in this study, the macro-dispersive spreading of the solute is stronger for flow parallel to vertical stratification, compared to flow perpendicular to horizontal stratification, and also, compared to flow in statistically isotropic non-stratified soil.

Volume Change Consideration in Determining Unsaturated Soil Properties for Geotechnical Applications

AbstractA common underlying assumption in the development of soil-water characteristic curves (SWCCs) is that the soil is sufficiently stiff such that no changes occur in the volume of the soil associated with soil-suction change. A number of researchers recently recognized the importance of considering soil-volume changes in SWCCs; however, few researchers have evaluated the effect of volume change on the computed rate and degree of wetting/drying of unsaturated soils and the associated impact on computed soil-volume change response. This paper focuses on the impacts of considering soil-volume change in the determination of SWCCs for high-volume-change soils, with emphasis on the estimated unsaturated hydraulic conductivity function and response to wetting. Numerical simulations of unsaturated flow and suction-induced volume change were used to study the effect of consideration of volume change in the determination of SWCCs. Numerical analyses used laboratory-determined SWCCs with and without the inclusi...

Numerical simulation of water flow in a large waste rock pile, Haizhou coal mine, China

Waste rock is the large volume of broken rock and low grade ore materials tend to create potential problems, such as acid mine drainage (AMD), leaching of heavy metals, and slope stability problems. These problems are related to the flow of water through the waste rock. In this study, long term numerical simulations of unsaturated flow in a large waste rock pile are conducted to investigate the effect of internal variability in water flow and saturation. The approach first consists of a basic geotechnical properties investigation to define the main features of the pile. This is followed by numerical simulations of the unsaturated flow through the pile based on the results from the field and laboratory characterization. The simulation results showed that pile is unable to fully saturate and drain during the simulated period. It was also found that high evaporation and the high bottom flux rate and also coarse grain nature of waste rock materials results holding few amounts of water in the system.

Storage and mobilization of natural and septic nitrate in thick unsaturated zones, California

Summary Mobilization of natural and septic nitrate from the unsaturated zone as a result of managed aquifer recharge has degraded water quality from public-supply wells near Yucca Valley in the western Mojave Desert, California. The effect of nitrate storage and potential for denitrification in the unsaturated zone to mitigate increasing nitrate concentrations were investigated. Storage of water extractable nitrate in unsaturated alluvium up to 160 meters (m) thick, ranged from 420 to 6600 kilograms per hectare (kg/ha) as nitrogen (N) beneath undeveloped sites, from 6100 to 9200 kg/ha as N beneath unsewered sites. Nitrate reducing and denitrifying bacteria were less abundant under undeveloped sites and more abundant under unsewered sites; however, δ 15 N–NO 3 , and δ 18 O–NO 3 data show only about 5–10% denitrification of septic nitrate in most samples—although as much as 40% denitrification occurred in some parts the unsaturated zone and near the top of the water table. Storage of nitrate in thick unsaturated zones and dilution with low-nitrate groundwater are the primary attenuation mechanisms for nitrate from septic discharges in the study area. Numerical simulations of unsaturated flow, using the computer program TOUGH2, showed septic effluent movement through the unsaturated zone increased as the number and density of the septic tanks increased, and decreased with increased layering, and increased slope of layers, within the unsaturated zone. Managing housing density can delay arrival of septic discharges at the water table, especially in layered unsaturated alluvium, allowing time for development of strategies to address future water-quality issues.

Effect of Dense Material Layers on Unsaturated Water Flow Inside a Large Waste Rock Pile: A Numerical Investigation

The construction method used to build waste rock piles influences their internal structure. Commonly used methods typically lead to the creation of compacted material layers within otherwise loose, coarse-grained waste rock. These dense layers, which typically have a finer grain size, affect the movement and distribution of water inside the pile. Long-term numerical simulations of unsaturated flow in a large pile were conducted to investigate the effect of such layers. The simulations led to various observations that provide a better understanding of the hydrogeological behaviour of the modeled pile (based on an actual case). The results show how water distribution and seepage within the pile are influenced by the presence of these layers. Other factors, including the magnitude of precipitation (or recharge) and pile size, were also investigated. This article presents the main results of the simulations, with some comments on their practical implications for pile design.

On the importance of hysteresis and heterogeneity in the numerical simulation of unsaturated flow

Soil hydraulic properties in field scale porous media are distributed with large spatial heterogeneity. Thus, detailed understanding of micro-physical properties leading to macro-scale heterogeneity is important for generalizing purposes in modeling. Hysteretic water retention properties greatly affect solute transport under unsaturated condition. In this study, laboratory infiltration experiments were carried out to investigate the importance of hysteresis in numerical modeling of water flow under heterogeneous distribution of hydraulic conductivity. Soil water content was observed by time domain reflectometry using small printed circuit board probes (PCBP). The PCBP observations were compared to results from numerical simulations involving saturated-unsaturated seepage analysis and two-phase flow with/without hysteresis effects. Observations were compared to both uniform and heterogeneous parameter modeling. Differences between unsaturated-saturated and two-phase flow were quite small in the numerical results for soil water content. The uniform parameter model, however, could not properly reproduce experimental water content change. The numerical results of water content change including hysteresis matched better observations for the unsaturated-saturated and two-phase flow cases. Results displayed that it is important to take heterogeneity and hysteresis into consideration in the numerical modeling in both two-phase and saturated-unsaturated flow analysis. (Less)

Numerical Evaluation of Uncertainty in Water Retention Parameters and Effect on Predictive Uncertainty

Uncertainty assessment of flow and contaminant transport in the vadose zone entails probability density functions (PDFs) of soil hydraulic parameters. An unconventional maximum likelihood (ML) approach was used in this study to estimate the PDFs of water retention parameters (e.g., van Genuchten α and m) for a situation common in field‐scale modeling where core samples are sparse and prior PDFs of the parameters are unknown. In this situation, the unconventional ML approach approximates the PDFs as multivariate Gaussian. This study developed a method of estimating the mean and covariance of the multivariate Gaussian PDF based on the results of least square methods that can be easily obtained in practice. The developed method was applied to and evaluated through numerical simulation of unsaturated flow and tracer transport at the proposed Yucca Mountain geologic repository. Another focus of this study was to investigate the effect of uncertainty in the water retention parameters on predictive uncertainty. By comparing the predictive uncertainty before and after incorporating random water retention parameters, it was found that the random water retention parameters had limited effects on the mean predictions of the state variables including percolation flux and tracer travel time from the potential repository to the water table. Incorporating the uncertainty in the water retention parameters, however, significantly increased the magnitude and spatial extent of predictive uncertainty of the state variables. In particular, incorporating the random water retention parameters significantly changed the 5th and 95th percentiles of the tracer travel time by tens of thousands of years.

Incorporating layer- and local-scale heterogeneities in numerical simulation of unsaturated flow and tracer transport

This study characterizes layer- and local-scale heterogeneities in hydraulic parameters (i.e., matrix permeability and porosity) and investigates the relative effect of layer- and local-scale heterogeneities on the uncertainty assessment of unsaturated flow and tracer transport in the unsaturated zone of Yucca Mountain, USA. The layer-scale heterogeneity is specific to hydrogeologic layers with layerwise properties, while the local-scale heterogeneity refers to the spatial variation of hydraulic properties within a layer. A Monte Carlo method is used to estimate mean, variance, and 5th, and 95th percentiles for the quantities of interest (e.g., matrix saturation and normalized cumulative mass arrival). Model simulations of unsaturated flow are evaluated by comparing the simulated and observed matrix saturations. Local-scale heterogeneity is examined by comparing the results of this study with those of the previous study that only considers layer-scale heterogeneity. We find that local-scale heterogeneity significantly increases predictive uncertainty in the percolation fluxes and tracer plumes, whereas the mean predictions are only slightly affected by the local-scale heterogeneity. The mean travel time of the conservative and reactive tracers to the water table in the early stage increases significantly due to the local-scale heterogeneity, while the influence of local-scale heterogeneity on travel time gradually decreases over time. Layer-scale heterogeneity is more important than local-scale heterogeneity for simulating overall tracer travel time, suggesting that it would be more cost-effective to reduce the layer-scale parameter uncertainty in order to reduce predictive uncertainty in tracer transport.

Numerical simulation of unsaturated flow along preferential pathways: implications for the use of mass balance calculations for isotope storm hydrograph separation

An objective common to many watershed studies is to separate storm hydrographs into two components: water that was present in the watershed prior to a storm event (soil moisture and groundwater) and water which fell on the watershed during the storm. To use this approach, a number of assumptions must be made including that the composition of water in the soil moisture and groundwater reservoirs are constant and known. The objective of this paper is to show that in settings where flow and transport are dominated by preferential pathways for flow, steady state mass balance calculations for quantitative hydrograph separation may be in error. We present field data from a site where flow and transport are dominated by preferential pathways (relict fractures in saprolite of sedimentary rocks) which indicate that the δ 18O content of the water in the unsaturated and shallow saturated zones is not constant over the course of a storm event. We use a numerical model to further explore the interactions between the fractures and surrounding matrix. Both the field data and modeling results indicate that the δ 18O of the previous storm event(s) has a strong influence on water in the fractures. On the time scale of a storm event, only the water in the matrix immediately surrounding the fracture mixes with water in the fracture, while the bulk of the matrix is isolated from fracture flow. The spatial and temporal heterogeneity of the δ 18O in the subsurface and the isolation of the most of the matrix water from flow in fractures make the measurement of a singular δ 18O value for subsurface reservoirs problematic and the assumption of a constant value doubtful. Since most near-surface geologic materials have preferential flow paths, we suggest that quantitative hydrograph separation using mass balance techniques is not possible in most situations. Future field and modeling investigations using the approach outlined here could be designed to explore the important temporal and spatial scales of variability in watersheds, and lead to a more quantitative approach to storm hydrograph separation.

Laboratory Evaluation of Sand Underdrains

Constant-head hydraulic conductivity tests are performed on layered heterogeneous porous media to evaluate the use of underdrains to calculate the hydraulic conductivity of an overlying, less permeable medium. The layered profiles consist of a barrier layer comprising sand mixed with 10% kaolin, overlying a foundation layer comprising sand mixed with only 5% kaolin. Underdrains are evaluated by replacing excavated portions of the foundation layer with only sand. The results indicate that preferential flow of water occurs around, rather than through, the sand underdrains resulting in an underestimate of the measured hydraulic conductivity of the barrier layer assuming 1D, saturated flow in accordance with standard practice. The observed preferential flow effect is consistent with previously published numerical simulations of unsaturated flow through similarly layered heterogeneous soil profiles that indicate lateral flow around underdrains due to the contrast in unsaturated properties of the soils. The results of this study have important ramifications with respect to the use of underdrains to measure in \Isitu\N hydraulic conductivity of compacted clay liners for waste containment.

Numerical simulation of unsaturated flow in woven fiber preforms during the resin transfer molding process

AbstractIn this paper, the unsaturated flow encountered in the woven or stitched fiber mats used in RTM is simulated using an adaptation of the Finite Element Method/Control Volume (FEM/CV) technique. The movement of resin through such fiber mats is modeled as flow through dual scale porous media and the mass balance in such media creates a sink term in the equation of continuity of the macroscopic flows. Combining this equation with Darcy's law leads to a non‐homogeneous non‐linear elliptic partial differential equation for pressure that is solved iteratively. First the simulation is used to study simple flows encountered during the characterization of preforms, such as the constant injection pressure 1‐D flow and the constant flow rate radial injection flow. Previously observed experimental results of relatively flatter pressure histories for the latter type of flows in wove fiber mats are replicated, both numerically and analytically, by the pressure equation with the sink term. A quantity called pore volume ratio is shown to play an important role in such flows. Finally, the unsaturated flow in a typical RTM mold, packed with woven fiber mats, is simulated numerically, and inlet pressures, fill times, and mat saturation are studied.

Uncertainty Analyses of Unsaturated Zone Travel Time at Yucca Mountain

AbstractUncertainty analysis methods can be applied to numerical models of ground‐water flow to estimate the relative importance of physical and hydrologie input variables with respect to ground‐water travel time. Monte Carlo numerical simulations of unsaturated flow in the Calico Hills nonwelded zeolitic (CHnz) layer at Yucca Mountain, Nevada, indicate that variability in recharge, and to a lesser extent in matrix porosity, explains most of the variability in predictions of water travel time through the unsaturated zone. Variations in saturated hydraulic conductivity and unsaturated curve‐fitting parameters were not statistically significant in explaining variability in water travel time through the unsaturated CHnz unit. The results of this study suggest that the large uncertainty associated with recharge rate estimates for the Yucca Mountain site is of concern because the performance of the potential repository would be more sensitive to uncertainty in recharge than to any other parameter evaluated. These results are not exhaustive because of the limited site characterization data available and because of the preliminary nature of this study, which is limited to a single stratigraphie unit, one dimension, and does not account for fracture flow or other potential fast pathways at Yucca Mountain.